71

25th Working Meeting

of IFToMM Permanent Commission

for Standardization of Terminology on MMS

Saint-Petersburg Russia June 23 ndash 29 2014

HISTORY OF GEARING THEORY DEVELOPMENT

Andrey E Volkov Prof Dr Sci Moscow State University of Technology ldquoSTANKINrdquo

(Moscow Russia) volkov411gmailcom

Dmitry T Babichev Prof Dr Sci Tyumen State Oil and Gas University (Tyumen

Russia) babichevdtramblerru

ABSTRACT

The stages of gear meshing development are presented The leading role of Russian

scientists in evaluation of gearing theory as a Science is shown The main perspective

problems for further development are formulated The large volume of bibliographical

references is given

Key words gears gear meshing gearing theory synthesis and analysis of gearing

Science consists in grouping facts so

that general laws or conclusions may

be drawn from them

Charles Darwin

INTRODUCTION

Mechanics as a science has evolved in two periods

The first one is empirical pre-Newton period It is mainly characterized by solution of

various mechanical problems encountered in civil engineering military science etc This is

a stage of accumulation of facts their qualitative and quantitative description establishment

of separate laws

The second Period (Research or Newton Period) starts with emergence of mechanics as an

independent science Knowledge accumulated during the first period was summarized and

formalized by Newton as the system of axioms and owing to the works of JL dAlembert

JL Lagrange and other prominent scientists mechanics obtained a powerful tool to solve

72

practical problems This was the beginning of the rapid development of mechanics as the

result of which in particular many branches of mechanics had emerged which later

developed into independent branches of science Hydrodynamics aerodynamics structural

resistance and many others including the theory of machines and mechanisms which has

evolved through similar periods are among such sciences

Theory of mechanisms and machines also launched many of its sections such as robotics

machine dynamics the theory of gyroscopes and systems theory gear etc to develop as

separate sciences

The main purpose of this article is to trace the development of the theory of gearing and to

show the role of Russian scientists in the development of the theory of gearing

1 Empirical period of development of the theory of gearing

Elements of the theory of mechanisms and machines including gear units began to develop

inseparably with the mechanics starting with the construction of the pyramids in ancient

Egypt and may be even earlier To realize ambitious plans of construction unknown

engineers of the ancient world came up with and implemented a lot of mechanical designs

(wheel helical gear and others) Unfortunately many of them have not reached our time

Subsequently ancient enginemen created lifting mechanics and military engines turbines

and even the simplest machines It is sufficient to mention such names as Archimedes Mark

Vitruvius Heron of Alexandria

M Vitruvius a Roman architect and engineer (1st century BC) invented godometer [1 p

64] for measuring the covered distance and the clock which used spatial gear [1 p181]

In his treatise Fundamentals of Mechanics Vitruvius gave the first known definition of a

machine The machine is a combination of wooden parts joined together which possesses

tremendous force and capable of moving great weights [2 p 186] The first classification

of machines is contained therein Vitruvius classified the machines as under-bridge air and

lifting ones

Heron (1st century AD) in his book On machines [1 p61] described various automatic

devices invented by him including automatic puppet theater in which all the pieces were

driven automatically one after the other through a system of gears and laces The godometer

invented by Heron made use of gears with 8th and 30th teeth [1 p 63]

The period of empirical development of more complex machines continued through the

Middle Ages For example in the IX-X centuries in China a sand clock with engine was

used Its kinematic chain consisted of several gears with different numbers of teeth 16 33

36 etc [3 p 102]

The description of planetary (astronomical) clock of Italian watchmaker Giovanni Dondi

(1318-1387) [3 p149] has been preserved The clock frame was made of bronze and the

shafts wheels and dial were made of brass 100 of 297 pieces of Dondis clock were wheels

and gears which were manually blanked Teeth had triangular shape but for a variety of

73

astronomical gears blunt teeth (rounded with cut edges) were used To reproduce the

motion of the Moon the wheel should have 157 teeth which slicing was very difficult task

Blanking of 365 teeth on one wheel was another challenging task

Rapid development of machine engineering during the Renaissance gave rise to gearing

development Leonardo da Vinci considered toothed mechanisms of different types in his

printed works

Italian mathematician and engineer Gerolamo Cardano (1501-1576) became known for

designing various mechanisms including systems with large gear ratios that were used in

tower clocks [3 p169] It required knowledge of the most important kinematic relations

such as speed of the wheels and pinions with a certain amount of teeth and pinions

German mechanic of Czech origin Jacob Leipold (1674-1727) in his multivolume

encyclopedia of technical knowledge Theater of machines gathered data on almost all the

machines and tools known by the 20ies of the XVIII century Among other issues it

included description of the gear-tooth form elements of gear heads etc [4 p 129]

Russian mathematician and mechanic Pafnuty Lvovich Chebyshev (1821-1894) is

considered to be the founder of the Russian scientific school of the theory of mechanisms

He also made a substantial contribution into the theory of gearing which unfortunately was

underestimated by the domestic specialists In the tractate ldquoAbout gearsrdquo [5 p710] he on

the base of theory of functions deviating least of zero solved the problem of synthesis of

tooth profiles ldquodrawn around by circular arcs whereby irregularities of gear movement reach

the lowest limitrdquo Thus he proposed a mathematical model of tooth profile synthesis

according to the criterion of minimum of deviations of gear ratio from the constant value

over a period of one tooth pair meshing

Ibidem PL Chebyshev writes that ldquohellipin theory usually a given tooth form is assumed at

one gear wheel which is then used to find a tooth form on the other gear wheelrdquo and then

formulates the task ldquohellipit is necessary to have such technique of their drawing (ie synthesis

ndash authors) which would make it simple to obtain tooth forms on both gear wheels most

suitable for specific requirements of practical applicationrdquo Probably it was one of the first

statements of a problem in tooth flank optimization synthesis

German scientist Franz Reuleaux (1829-1905) in the monograph [6] developed and outlined

the main provisions of the structure and kinematics of mechanisms He defined kinematic

pair suggested teaching about the mechanisms and developed methods for the synthesis of

mechanisms

2 Gear drives and the gear machining origin

Mankind has been using gears for several thousand years in ancient Egypt they were used

in irrigation systems Initially the gears were made of wood with plug teeth made of

hardwood - they were used until the early twentieth century in particular in water mills

Since ancient times gears were made from copper alloys later ndash from iron and steel While

74

gears were usually cast they were sometimes forged and teeth on them were sawed or

ground

Since the mid-XIX century the creation of complex metal and gear-cutting machines has

begun This process ran parallel with the formation of the now world-renowned machine

tool companies [7]

Reishauer Corporation was founded in 1788 but the most important period that had

determined its further development was the mid-XIX century when the company was

headed by Jacob Friedrich Reishauer (1812-1862) He and his father in law (father of his

wife - approx Ed) IG Bodmer have developed a machine for the manufacture of threading

tools screw-cutting lathe Swiss engineer Johann Georg Bodmer (1786-1864) was a brilliant

inventor of the cutting tools so he could design and manufacture transmission spur gear

ratio to 145 as well as helical and bevel gears

The Gleason Works Company dates back to 1865 when a native of Ireland William Gleason

(1836-1922) organized a machine shop The first innovation of The Gleason Works

introduced in the industry was the invention of the planer to produce spur bevel gears in

1874

The British company David Brown was founded in 1860 by David Brown (1843-1903)

Business began with the production of molds for casting gear and later expanded by casting

gears themselves In 1898 the company started production of cutting gears and since 1915 -

involute worm gears

Swiss company Maag Gear AG a global leader in the production of gearboxes was founded

in 1913 by Swiss engineer and inventor Max Maag (1883-1960) In 1908 M Maag

developed unusual geometry of involute spur and helical gears This allows the designers to

avoid undercutting of teeth and increase the thickness of the teeth only by changing the

instrument relative to the wheel being processed

US firm Fellows Gear Shaper Company started production of spur wheels by chiselling

teeth in 1896 Method of teeth chiselling based on simulation of meshing of two gears as

they rotate around parallel axes was invented and commercialized by American inventor

Edwin R Fellows (1865-1945) Machine for grinding involute profile gear cutters used for

chiselling teeth of spur helical and special wheels was designed and manufactured in 1897

3 Origin and development of the theory of gearing

In the origin and development of the theory of gearing as a science certain periodicity can

be seen initially new particular tasks emerge in the society they are eventually solved

accumulated and systematized Then comes the moment when the quantity is transformed

into quality there is awareness of the accumulated knowledge theoretical propositions are

formulated and the foundations for the development of science and practice are laid for the

next cycle Based on theoretical foundations new designs and technologies are created and

the old ones are improved Then the cycle repeats at a new stage of development of the

75

industry emergence of new problems and their solution awareness formulation of new

theoretical propositions In our opinion the theory of gearing goes through three such

cycles two of them are completed while the third one is ongoing at the moment

The first cycle ndash creating the foundation for theory of gearing ndash began in antiquity gained

momentum in the XVIII century owing to works of Euler and L Camus and was enriched in

the XIX century by works of T Olivier R Willis and others Completion of the first cycle

by 1890 can be roughly related to the defense and publication of the masters thesis by HI

Hokhman (1851-1915) in 1886 in which the analytical solution of the main task of the

theory of gearing ndash finding the mating surface and determining its properties ndash is given

The second cycle ndash creating the classical theory of gearing ndash lasted for about 80 years and

was completed by early 70-ies of the XX century It can be assumed that the results of the

second cycle were finalized in 1968 by a monograph of FL Litvin [8] at Symposium on

gears in Leningrad in 1973 [9]

The third cycle ndash laying the groundwork for an updated theory of gearing and methods of

the gearing synthesis oriented at modern computer technologies Currently this cycle is not

completed yet although a lot of new challenges are accumulated and a number of topical

issues and unresolved problems are identified

Letrsquos consider the features of these three cycles of creation and development of the theory of

gearing

31 Laying the foundations of the theory of gearing

Theory of gearing like the majority of scientific disciplines is based on three points

An object of study and the basic concepts of the discipline

Methods and ways of working with the basic concepts

Basic laws of nature and of the given science which establish relationships between the

basic concepts These laws are often identified in the course of studies - in the form of

theorems mathematical formulas logical and computational models etc

The objects of study of the theory of gearing are

Higher kinematic pairs in the plane and space gear and cam mechanisms (working

engagement)

Cutting tools and processes in shaping gear treatment (technological engagement)

In the theory of gearing the basic concepts and ways of working with them are taken for

the most part from mathematics (line surface curvature etc) and mechanics (centroid

velocity acceleration force etc)

Basic laws and links between fundamental notions of the theory of gearing were identified

by mathematics and mechanics already in the XVIII-XIX centuries (L Euler L Camus F

Savary E Bobillier R Willis T Olivier HI Hokhman )

Member of the Russian Academy Leonhard Euler (1707-1783) discovered unique properties

76

of involute of circle and suggested using them in the gearing Note that currently more than

90 of all gears in the world are involute French astronomer Felix Savary (1797-1841) by

continuing the work of Euler revealed a relationship between the radii of curvature of the

tooth profiles in flat engagement with the radii of curvature of the centroid now known as

the Euler-Savary equation This unique equation is widely used nowadays On the basis of

the Euler-Savary equation French mathematician Etienne Bobillier (1798-1840) proposed a

geometrical construction for finding the centers of curvature profiles

The first scientists who were applied the scientific approach to study of gears were R Willis

and T Olivier English scientist R Willis was one of the first to apply a scientific approach

to the study of gearing He proved the fundamental theorem for plane gears ndash Willis [10]

theorem which in the modern interpretation reads as follows Common normal to the

profiles drawn at the point of tangency passes through the pole of engagement Willis

invented a special tool - odontograph - to define the geometry and type of drawing the teeth

and gears of different diameters and number of teeth

Scientific approach to gears formation goes back to the French mathematician and

mechanics Theodore Olivier (1793-1858) He formulated two ways of forming conjugated

gears which have not lost their generality and value up till now

The first Olivier method Generating surface Σ0 (eg rail or flat generating wheel) forms two

surfaces by rounding Σ1 on the gear and Σ2 on the wheel These surfaces are located at

different sides of the generating surface Σ0 (eg Σ1 is located at the top of Σ0 and Σ2 ndash at the

bottom of Σ0) Σ1 and Σ2 surface will be paired a linear contact (which occurs in cylindrical

and bevel gears) or touch points (eg helical gear) Most transmission with parallel and

intersecting axes ie cylindrical conical and helical-bevel ones are formed by this method

The first Olivier method was rarely used in gears with intersecting axes because it displays a

distinct tooth contact point which reduces the load capacity of the engagement

The second Olivier method Surface of one of the gears - for example Σ1 at the gear - is set

almost arbitrarily and the surface of the second gear - for example Σ2 at the wheel ndash is set

as an envelope to one-parameter family of surfaces Σ1 In general contact between Σ1 and

Σ2 will be linear Basically transmissions with intersecting axes including the worm gears

are formed according to this method

In the XIX century cycloidal engagement becomes widespread The work of the French

mathematician Charles Etienne Louis Camus (1699-1768) has become the basis for the

design of such gears Camusrsquo theorem states that paths of the same point of the auxiliary

centroid which is rolled along the centroids of meshing gears may be chosen as mating

teeth

Chaim Iegudovich Hokhmanrsquos [11] dissertation published in 1886 can be considered as the

work that summarizes the steps of creating the foundations for the theory of gearing He

developed a framework for the analytical theory of planar and spatial gearing Hokhman

created a new method for finding the envelope surfaces and lines of contact with those

surfaces which allowed to initially determine the line of contact of mutually enveloped

surfaces in any system of coordinates associated with any link of working or technological

77

engagement This simplifies finding the envelope surface as compared to classical methods

in mechanics and differential geometry

By the end of the XIX century the appearance of the fundamental principles of analytical

theory of gearing marked the end of the first cycle of development of the theory of gearing

These principles include

Basic concepts and methods of classical mechanics analytical and differential geometry

Two principles of formation of mating gears proposed by Olivier

Euler-Savary equation and Bobillierrsquos construction reflecting the relationship between the

centroid and the curvatures of mating profiles in plane gears

Hochman developed a method for finding the envelope profiles and surfaces as well as

points and lines of contact of mutually enveloped lines and surfaces in the plane and spatial

working and technological gears

32 Creation of the classical theory of gearing

The framework of analytical theory of gearing developed by the end of the XIX century has

become the basis for solving practical problems which were posed by the thriving industry

for the science

Late XIX amp early XX century had a rich history of inventions of new types of

transmissions machines tools and machine gears Conventionally these inventions can be

divided into two areas machinery and tools for forming gears based on engagement of the

mating surfaces and machines and tools for forming gears with non-conjugated surfaces of

teeth

The first approach is based on the Olivier principles

In the period from 1890 to 1920 the following technologies and machines for production of

gears based on the form-generating method were invented and implemented

- Machines for bevel gears including the ones circular teeth (JE Gleason)

- Machines for grinding involute profiles of gear cutters (E Fellows)

- Machines for cutting spur and helical gears with worm milling cutters (RH Pfauter)

- Technology for manufacturing globoid worm gear (SI Cohn and FW Lorenz)

- Involute worm gear based on the application of involute helical surface as the surface of

the worm mill thread (FD Bostock and P Brown)

These and many other inventions have set the task of generalization of the gear-forming

theory based on engagement of the mating surfaces Decisive role in complementing and

developing the Olivierrsquos principles belongs to Russian scientists AF Nikolaev (1901-

1957) YaS Davydov (1914-2003) and ML Erikhov (1937-2002) They used an auxiliary

(generating) surface to form the mating surfaces ML Novikov (1915-1957) proposed a

fundamentally different principle of forming the mating gears by moving (according to a

certain law) the contact point of two profiles along the line of engagement of the

78

synthesized transmission

All these principles are based on the theory of envelopes which was scientifically and

methodologically completed (at that period of time) in YaS Davydovrsquos VA Shishkovrsquos

and FL Litvinrsquos works Almost simultaneously and independently they proposed a method

for finding the kinematic envelope in which the meshing condition equation is used VN = 0

[8] At this time VA Shishkov [12] introduced a new concept - implementation speed Vn

equal to the scalar product Vn = V12n which became an effective tool in the study of gear

cutting tools working according to the form-generating method It became the basis of the

kinematic method for the synthesis and analysis of gearing in the second half of the XX

century

Ernest Wildhaber (1893-1979) a talented engineer and inventor of the company The

Gleason Works can be regarded as the founder of the second direction In 1927 he

proposed a method of forming hypoid gears and in 1930rsquos he patented Revacycle - the most

productive method (at that time) for spur bevel gears forming [13] Methods of forming

these transmissions are not based on Olivierrsquos principles E Wildhaber introduced gears

with non-conjugated tooth surfaces ndash transmissions with approximate meshing Basically

these gears cannot transmit rotation with constant gear ratio but the degree of deviation

from a constant gear ratio can be minimized by the targeted selection of values of gear

treatment process parameters Thus Wildhaber who abandoned the form-generating

method proved that there were possibilities of creating highly effective machining

processes for gears with non-conjugated tooth surfaces and thus initiated the theoretical

study of such transmissions

Active development of the theory of approximate meshing began after the 2nd World War

both in the US and the Soviet Union As the result the basic principle of the formation of

non-conjugate surfaces was formulated independently in the works of ML Baxter [14] and

FL Litvin [8] according to the principle the graph of deviation from the angular position

of the driven wheel from its position upon engagement of strictly conjugate surfaces is a

function similar to a parabola with the downward branches

At the same time it became clear that in order to meet challenges of synthesis and analysis

of gearing built on non-conjugated surfaces it is required to develop new mathematical

methods and models First mathematical models for studying gearing and computer

programs based on them appeared almost simultaneously in the US and the USSR

In the US TCA software package for the synthesis and analysis of hypoid gears [14] was

created under supervision of ML Baxter (1914-1994) chief engineer and researcher of The

Gleason Works

In the 1960rsquos methods for the synthesis of approximate gearing began to develop with the

advent of computers in the Soviet Union At first a software package for analysis and

synthesis of Revacycle spur bevel gear [9 p30-36] which included a numerical algorithm

for calculating the surface as an enveloping surface without using the theory of envelopes

[15] was developed at the Moscow Tooling and Machining Institute (STANKIN) under the

leadership of GI Sheveleva (1929-2005)

79

Similar software packages were developed in Saratov (Special Design Bureau of Gear ndash

Cutting Machines) under the leadership of MG Segal (1931-2000) and Leningrad (LITMO)

under supervision of FL Litvin The work on creation of universal programs for the

computer-based studies of spatial links was held in Tyumen [9 p36-43]

In the second half of the XX century the USSR became a recognized leader in terms of

volume and theoretical studies devoted to the study of the geometry of gears and gear

cutting tools After the end of World War II theoretical activities on creation of new methods

of analysis and synthesis of the working and technological gears was booming for 25-30

years Efforts of leading scientists (NI Kolchin FL Litvin VA Shishkov ML Novikov

LV Korostelyov GI Sheveleva II Dusev YaS Davydov ML Erikhov and others) have

led to creation of a new branch of science of the mechanisms - the gearing theory

The Soviet Union played the key role in creating the classical theory of gearing in early

1970rsquos The most important results obtained through efforts of domestic scientists which

formed the basis of the modern theory of gearing are listed below

1 Olivierrsquos principles for forming conjugate gearing are supplemented and developed AF

Nikolaev [16] ML Novikov [17] YaS Davydov [18] ML Erikhov [19]

2 New methods for analysis of the geometry of gears are developed and the existing ones

are improved differential (NI Kolchin the main publication of the year ndash 1957 [20])

screw (AF Nikolaev 1950 [16] KM Pismanik 1950 [21] NI Kolchin 1963 [22] VS

Lyukshin 1968 [23]) kinematic (YaS Davydov 1950 [24] VA Shishkov 1951 [12] NN

Krylov 1953 [25] FL Litvin 1960 [26] ML Erikhov 1972 [19]) matrix (FL Litvin

1968 [9]) power series (GI Sheveleva 1969 [27]) non-differential (GI Sheveleva 1969

[15]) tensor (II Dusev 1968 [28])

3 Methods of solving all major problems of synthesis and analysis of gears are established

Finding the envelope of a one-parameter and two-parameter family of surfaces (HI

Ketov NI Kolchin FL Litvin NN Krylov EG Ginsburg ML Erikhov) as well as

multi-parameter envelope family of surfaces and lines in spatial gearings (IL Brodsky DT

Babichev)

Finding an wrapping family of surfaces (GI Sheveleva)

Identifying the geometry generation features such as tooth undercutting interference and

others (MG Segal II Dusev GI Sheveleva VI Goldfarb BA Chyorny)

Synthesis of gearing geometry (local ndash FL Litvin ML Erikhov LV Korostelyov SA

Lagutin VN Rubtsov BP Timofeev and nonlocal ndash KI Gulyaev BA Chyorny MG

Segal)

Computation of curvatures in gearings (NI Kolchin FL Litvin VM Vasilyev II

Dusev EG Ginsburg LV Korostelyov ML Erikhov A M Pavlov MG Segal)

Computation of other geometric-kinematic characteristics of the teeth contact (AK

Georgiev VI Goldfarb SA Lagutin MF Lenski)

Solution of the inverse problem of the gearing theory tooth meshing analysis (KI

Gulyaev FL Litvin MG Segal BP Timofeev GI Sheveleva)

80

The impact of manufacturing errors and assembling on quality of engagement synthesis

of toothed meshing insensitive to errors (ML Erikhov NG Lindtrop LV Korostelyov

NN Krylov LY Liburkin GI Sheveleva)

Numerous studies of specific gears are conducted based on theoretical developments and

established procedures The most important practical problems solved during this period

are

1 Principally new types of gearing have been discovered helical gear in which arcs of

circles with radii small difference are selected as the profiles of cross-sections ndash Novikov-

Wildhaber gear [17] and gears with closed contact lines where the load between teeth is

transferred through the grease wedged in a closed cavity between active surfaces due to

closure of the contact line (LV Korostelyev SA Lagutin [29])

2 Geometric problems of synthesis of cylindrical involute gears were almost exhaustively

resolved and brought into engineering practice geometric calculation (VA Gavrylenko

1969 [30]) selection of the optimum addendum modification coefficients by using blocking

circuits (MB Groman 1957 [31]) according to the atlas compiled and published under the

direction of IA Bolotovsky 1967 [32]

3 New types of gearings have been studied and introduced In this regard various problems

related to analysis and synthesis of the following common types of gears have been solved

Bevel (NI Kolchin and VV Boldyrev 1937 YS Davydov 1950 VI Bezrukov 1963

VM Denisov 1963 GI Sheveleva 1966 HF Kabatov and GA Lopato 1966 MG

Segal 1971 KI Gulyaev 1974 VN Syzrantsev 1975)

Hypoid (GI Apukhtin 1952 FL Litvin 1962 KM Pismanik 1964 II Dusev and VM

Vasilyev 1968 MG Segal 1971)

Cylindrical gear drives with Novikovrsquos gear (ML Novikov 1956 RV Fedyakin and

VA Chesnokov 1958 VN Kudryavtsev 1959 EG Roslivker 1964 NI Kolchin 1968

VN Sevryuk 1972 and others)

Revacycle spur bevel gear (GI Sheveleva 1966)

New worm gear design toroid (YaI Dicker 1948) globoid (PS Zak 1962) worm gear

drives (FL Litvin 1962 IS Krivenko 1967 LV Korostelyev and SA Lagutin 1973

etc) spiroid (S Golubkov 1959 AK Georgiev and VI Goldfarb 1972 and others)

Less common known types of gears have also been studied and implemented

Hyperboloid (KM Pismanik 1950)

Helical-bevel (LY Liburkin 1968)

Wave (EG Ginsburg 1969)

Cylindrical with arched and spiral teeth (ML Erikhov and VN Syzrantsev 1975)

4 Techniques of analysis and synthesis of gears with non-circular wheels are developed [33]

and their production is organized

5 A lot of works are published including a number of classic books on theory of gearing

YaI Dieker (1935) NI Kolchin (1937-1952) FL Litvin (1952-1968) YaS Davydov

81

(1950) VA Gavrylenko (1949-1969) ML Novikov (1958) VA Zalgaller (1975) LD

Chasovnikov (1969) IA Bolotovsky et al (1962-1967) VN Kudryavtsev (1949-1971)

VN Kedrinsky (1960-1967) KM Pismanik (1964-1967) PS Zack (1962) NF Kabatov

and GA Lopato (1966) VA Shishkov (1951) and many others FL Litvinrsquos monograph

[8] stands out among these works it was published in 1968 and still remains a handbook for

professionals in the theory of gearing

The book by VA Zalgaller Envelope Theory [34] which is not very big in volume is

characterized by depth the mathematical rigor and completeness of the argumentation

Note that the appreciation level of the activities under the second cycle is confirmed by the

fact that in 1958 ML Novikov was awarded the Lenin Prize ndash the most prestigious USSR

award presented to individuals for accomplishments in the professional field

The following facts also confirm that the Soviet scientists made a decisive contribution to

the theory of gearing as a science and the fact that the Soviet Union had prepared a large

number of highly qualified specialists in the theory of gearing

FL Litvinrsquos monograph Theory of Gearing which was written in the late 60rsquos is still the

main handbook for gear specialists while Litvin is regarded as the creator of the modern

theory of gearing not only in CIS countries but also around the world

This monograph revised and expanded was reprinted abroad in English co-written with

FL Litvinrsquos new foreign students [35]

Number of qualified experts in the theory of gearing (by the way which were not widely

known in the Soviet Union and the CIS back then) have emigrated to the Western countries

and are writing and publishing quite significant books in English on the theory of gearing

and geometry of gears (SP Radzevich AL Kapelevich SV Lunin)

Summarizing the second cycle let us quote SA Lagutin who most accurately reflect the

essence of this bright period [36] it was a period of storm and pressure in the development

of the gearing theory in Russia when a whole galaxy of brilliant researchers were working

in this area headed by NI Kolchin and FL Litvin By collaborating and competing with

each other in a few years they have built amazingly beautiful building of the new science at

the junction of differential geometry and mechanics of machines

33 Laying the foundations of computer-oriented theory of gearing

The main purpose of such a theory is to become a basis for the methods of computer

analysis synthesis design and manufacturing gear parts for gear engagement

By the mid-70rsquos theory of gearing as a science has reached adulthood the main priority and

theoretical problems of analysis and synthesis of gearing have been resolved The number of

innovative theoretical work began to decline Studies are getting closer to the production

and the theory of gearing acts primarily as a tool for solving specific engineering problems

Since the mid 70-ies of XX century the theory of gearing as well as the machine tool

industry has evolved concurrently in two directions global and Russian

82

The global development of the theory of gearing has taken place against the backdrop of

revolution experienced by the machine tool industry since the 80rsquos

First machines with semi-rigid connections partially controlled by computer began to

appear in developed countries and then complete automatic machines (multi-axis CNC

machines) appeared

At that time for example machines for processing bevel gears with circular teeth Phoenix

(Gleason) and WNC30 (Klingelnberg) were developed The creation of such machines

occurred in parallel with the development of new mathematical models for shaping parts on

multi-axis machines and testing the parts operability before their casting in the metal At

that time software systems LTCA (Gleason) and Kimos (Klingelnberg) were developed

which made it possible to solve the problem of synthesis and analysis of bevel gears with

circular teeth [37]

All developed countries pursue the global direction in the development of the theory of

gearing in the same manner and using similar approaches The following was used by the

gear specialists to solve the problems of analysis and synthesis

Methods of classical theory of gearing (with computer design of the geometry of any kind

of gears)

Techniques of non-differential analysis of gear ndash forming processes using universal as

well as specially developed software packages

Methods of boundary and finite elements (at the analysis of the contact interaction of

acting surfaces of the teeth)

Finite element methods and integral equations (at the analysis of the stress-strain state of

the teeth)

Numerical optimization methods (at the synthesis of geometry of acting and fillet surfaces

of teeth)

An expanded list of quality indicators of gearings including new ones the design

thickness of the oil film criteria of hot and cold seizure criteria for assessing the conditions

for the formation of an oil wedge indicators of vibration activity of the gearing and others

Designing gear drives was regarded as a complex problem requiring an agreed solution of a

group of interrelated tasks

Selection of design scheme of a gear

Synthesis of permissible geometry

Geometry optimization

Structural arrangement and evaluation of quality indicators

Identification and addressing the weaknesses

Designing technical processes of manufacture selection or synthesis of tools subsequent

optimization etc

The developed theory of gearing is known as Theory of Real Gearing in Russia Ukraine

and Belarus while abroad it is called ldquoIntegrated Gear Designrdquo (IGD) or Integrated Design

83

of Gears

Russian direction in the development of the theory of gearing has several specific features

attributable to the following objective circumstances

Firstly first clear signs of stagnation appeared in the USSR industry in the late 70rsquos

Secondly the number of graduate students reduced as the universities basically solved the

problem of teachers which they faced in the early 60rsquos due to a drastic increase in the

number of students being trained in engineering specialties And finally Russia lost the top

three main theorists in the field of the theory of gearing FL Litvin was forced to emigrate

to the USA LV Korostelyov died in a car crash YaS Davydov departed from active

research and subsequently left for the USA

And nevertheless in 15-20 years preceding the collapse of the USSR in 1991 the theory

and geometry of gearing in the Soviet Union was continuing to develop At that time new

centers specializing in different aspects of the theory of gearing were established Let us list

the most interesting in our opinion research topics at the end of the last century

- Issues of strength and solution of the tooth contact problem (EL Airapetov VN

Syzrantsev GI Sheveleva)

- Research on gear bending bending stresses calculation (GI Sheveleva VI Medvedev)

- Non-differential methods for the determination of the contact surfaces characteristics (VI

Goldfarb GI Sheveleva AE Volkov)

- Issues of design synthesis analysis and manufacturing spiroid gear drives (AK Georgiev

VI Goldfarb)

- Issues of design synthesis analysis and manufacturing worm gear drives (SA Lagutin

AI Sandler)

- Research of hypoid bevel gear drives with circular teeth (MG Segal GI Sheveleva VN

Syzrantsev)

- Research of gear drives with intermediate bodies (AE Belyaev)

- Research of helical-bevel gear drives (BA Lopatin)

- Development of methods for the synthesis of gear drives (MG Segal SA Lagutin GI

Sheveleva VI Medvedev VN Syzrantsev)

- Forming a theoretical framework for the development of universal programs for the

analysis of spatial working and technological meshings and the creation of corresponding

programs (DT Babichev)

As a result of these studies software systems were developed in the Soviet Union which

were aimed at solving the problems of synthesis and analysis primarily for bevel gears with

circular teeth The best known ones include PC Volga5 made under the direction of MG

Segal [38] and PC Expert created under the direction of GI Sheveleva [39]

The fact that MG Segal was the main developer of the PC Kimos (firm Klingelnberg) in

the 90rsquos confirms the high level of those developments

It should also be noted that a work on the selection of optimal schemes for multi-axis CNC

84

machines for processing gear was carried out in 1990 in Saratov (MG Segal LI Shejko

[40]) These developments have also been used by Klingelnberg

The researches (above all theoretical ones) continued after the collapse of the USSR in

Russia Ukraine and Belarus

At that time the development of the theory of gearing was distinguished by a high level of

theoretical studies based on the introduction of new geometric geometric-kinematic and

other concepts and development (on their basis) of new mathematical models methods and

algorithms for analysis and synthesis of the working and technological gear engagements

These works were performed mostly at their own initiative by highly qualified specialists-

theorists in the field of theory and geometry of working and technological gear meshing

Usually they were elderly university professors who were practically deprived of relations

with the machine-building industry after its stagnation during the collapse of the USSR

It should be noted that it is very difficult to distinguish the most important areas of research

in the modern theory of gearing As the poet said Great things are better seen from a

distance Therefore we will list the most interesting in our view theoretical works on the

development of the theory of gearing with greater focus on the Russian line of research

However we practically do not consider the works on gear geometry ndash they are too

numerous A fairly complete picture of the theoretical works of this period can be obtained

from the proceedings of symposia and conferences held in Kurgan (KMI) Izhevsk

(IzhSTU) and Sevastopol (KhPI Kharkov) The main directions in the development of the

theory of gearing and the most important theoretical results after 1970s include the

following

1 Introduction and use of new concepts such as

Meshing Space (SA Lagutin [41])

Wrapping surface (GI Sheveleva [39])

Fan wedge and normal beam accelerating of implantation (DT Babichev [42])

2 Development of methods for analyzing processes of generation

A new method of finding a singularity in the flat gearing (SA Lagutin) based on the

situation [43] return point at the gear profile occurs at the point in the line of engagement

in which the normal to this line intersects the axis of rotation of the pinion The method was

extended to the spatial gearing (AE Volkov [44])

3 Development of methods of synthesis

Based on the new concept of space of engagement and its properties This approach was

used during the synthesis of both spatial transmission (SA Lagutin [45]) and the cylindrical

(DT Babichev [46])

By using as objective function new criteria of load capacity - permissible contact

pressure(VI Medvedev [47]) the specific work of working surfaces of teeth (DT Babichev

[48]) and others

For bevel gears with small cross-axis angle (SA Lagutin [49] VI Medvedev [50])

Synthesis of gears considering technological limitations of the given production processes

85

(VI Medvedev [51] VN Syzrantsev [52])

By using and developing a method of synthesis of gears in generalizing parameters

originally proposed by EB Vulgakov for involute gears The method was modified by VL

Dorofeev - for involute and ON Tsukanov and BA Lopatin ndash for non-involute gears

(including cylinder-conical ones) [53]

By using variational methods of synthesis when the equation of an optimal surface of the

tooth and its coefficients are determined This approach was first applied apparently by

Alan Lebec [54] in the United States it was used in Ukraine [55] and being developed in

Russia where equal strength gears have been synthesized by using the method (by Hertz

contact strength) [46 56] and the method of synthesis of bevel gear with circular teeth

according to the criteria of minimal contact pressure and bending stresses while maintaining

the overall dimensions of the gear has been developed which is important for aviation

where the weight of the structure is crucial [57]

Increasing the bending strength of circular tooth bevel gears by optimizing the shape of

the tool [58]

Increasing the load-bearing capacity of high-speed heavy-duty cylindrical involute gears

Note that EB Vulgakov VL Dorofeev and AL Kapelevich have made a significant

contribution to the development of synthesis aviation gear in recent decades [59]

4 Development of methods of analysis of loaded gears considering multipairness of

contact

For bevel gears with circular teeth [60]

For spiroid gears [61]

5 Significant progress has been made in the methods of analysis synthesis design and

manufacture of worm gear transmissions

The main input in this field of gearing has been made by two groups of researchers under

the leadership of VI Goldfarb and SA Lagutin The techniques of minimizing meshing

errors and worm hob errors that appear when regrinding and relieving works are fulfilled

have been developed by SA Lagutin and AI Sandler The techniques of synthesis and

production of gears with localized contact were drilled worm gears (SA Lagutin AI

Sandler [62]) and spiroid ones (VI Goldfarb ES Trubachyov [63])

The drives with the increased load capacity were designed based on a study of meshing

space of non-orthogonal gears spiroid (ES Trubachyov [63]) and worm ones (VYu

Puzanov) Designing of spiroid transmissions is carried out using CAD ldquoSPDIAL+rdquo

developed by a group headed by VI Goldfarb Configurator of gearbox systems for

optimization structural synthesis of their structures is being created (OV Malina etal)

Unified worm hob cutters cutting gears for the drives with localized contact were designed

It became possible to cut the gear wheels in engagement with multiple-thread worm by a

single-pass mill (VI Goldfarb and his disciples)

In the Institute of Mechanics IzhSTU a group led by VI Goldfarb essentially laid the

foundation for a new Russian machine building sub-industry ndash construction of gearboxes for

86

isolation and control valves for pipelines

- Theoretical studies of spiroid and worm gears are at a high scientific level

- A modern design process is applied synthesis of perfect engagement synthesis of

localized contact simulation of the stress strain state analysis of real engagement under

load forecasting the state of transmission

- Three generations of dimension-type series of quarter-turn and multi-turn spiroid gear

drives are developed their production with modern quality control and acceptance tests is

organized

6 Application of unconventional gears and gearing helical-bevel gears (BA Lopatin [65])

transmissions with intermediate rolling bodies (AE Belyaev [66]) hydraulic and

pneumatic machines with non-circular gears (An-I-Kahn [67]) precessing transmissions

(IA Bostan [68] EI Tesker [69] VN Syzrantsev BA Lopatin) and other

7 Development of kinematic analysis methods of working and technological meshings Note

that modern designing is the computer designing This factor imposes high requirements to

the theory of gearing as the main mathematical basis for such designing We have to admit

that the classical theory of gearing does not fully comply with these demanding

requirements Thus according to Prof MG Segal who was working with Klingelnberg in

the last years of his life the head of the company prohibited to use differential methods ndash

the basis of the classical theory of gearing ndash in the programs being created The reason for

the ban was inadequacy of the results of computer simulation as compared to real processes

of formation Theoretical research aimed at creating computational models that are

adequate to the real processes of formation and contact of moving bodies were developed by

AE Volkov and VI Medvedev (Moscow) and DT Babichev (Tyumen)

To eliminate the phenomenon DT Babichev elaborated a unified kinematic method for

analysis of the processes of formation [70] based on the ldquotriadrdquo ruptures + envelopes + new

concepts of curvilinear coordinates As the result the cause of inadequacy between the

classical methods of the theory of gearing and real-life processes of formation was

established and rectified The developed kinematic method

Allows to find all the surfaces formed on the item at gear machining formed by smooth

surfaces and inflections of bodies including at advanceretraction of machine tool and in

secondary cutting areas

Has the reliability of non-differential methods but is superior to them in speed of

operation by two orders of magnitude which is confirmed by its partial use in CAD

ldquoSPDIAL +rdquo

Also allows to define the curvatures in gearing

8 Development of the system for assigning real ITS (Initial Tool Surfaces) and construction

of mathematical models for them [71] Real ITS is the set of all forming tools (pieces of

surfaces cutting and boundary edges and corners) for which uniform curvilinear coordinates

are introduced

9 By using the concept of ldquothe acceleration of installationrdquo new techniques for solving

87

multitude of tasks are created calculating the radii of curvature in the gearing identifying

cutting areas and thickness of the layers being cut by tool cutting edges and others (DT

Babichev [48])

For example based on the concept of the acceleration of installation a new basic formula

for calculating the reduced curvature in any normal sections at the contact point of two

moving bodies in contact along the line is created

1Rnp=-

where ɷrol is angular velocity of rolling bodies in the plane of the section in which the

curvature is calculated aB is the acceleration of installation The fundamental nature of the

obtained formula is that

1) in its generality it is commensurate with the kinematic formulas of Rodrigues and Freinet

known in differential geometry but it is intended for a different class of surfaces produced

in the process of formation by the rounding methods

2) curvature in any normal section of all surfaces formed by the rounding methods is

determined by only two scalar parameters and one of them (acceleration of installation)

does not depend on the direction of the section

It was also established that the sign of the acceleration of installation allow to make an

unambiguous judgement on the nature of the contact of bodies For example if aВgt 0 then

the envelope is formed inside the body of the generating element Acceleration of

installation allows to determine (ldquoincidentallyrdquo) the value of the radii of curvature and

faceting value across the whole surface formed by rounding at band- and flake-type

roughness

Thus over the past decade a substantial volume of theoretical knowledge to complete the

third cycle (creation of a computer-oriented theory of gearing) was accumulated

A lot of new notions are introduced and used in theory of gearing

Based on these new notions methods for analysis and synthesis of gear drives and cutter

tool meshings oriented at computer technologies have been developed and continue to be

improved

Intensive investigations to improve methods of optimization synthesis of gearing and to

develop methodologies of computer design and construction of gear boxes are performed

4 Problems and expected directions of the theory of gearing

Let us list the main problems in the gearing theory which in our opinion are the most

important

Problem 1 Creation of the theory of optimization synthesis of structures and parameters of

higher pairs of kinematic elements transmitting the motion and load at the preset and

optimal correlation of normal and friction forces At the present time theory of higher pairs

is being developed only as a pure geometrical science

88

Problem 2 Elaboration of methods of tooth optimal geometry synthesis oriented at the

modern processing technologies instead of traditional ones In this case a designer will have

to solve the variation problem with limitations providing for maximum possible load

capacity of gear drive in accordance with preselected criteria of performance efficiency

Problem 3 Development of methods for analysis of the process of the tooth preset surfaces

changeover taking into account the values of load tooth displacement manufacturing errors

of drive elements errors of relative position of engaging links dynamics of changeover

process

Problem 4 Creation of a unique interrelated complex of application software packages to

enable the designers and manufactures of gear drives to carry out optimization designing

engineering design preparation for production of various drives by meshing

Possible directions of development of the theory of gearing naturally follow from the afore-

described problems

CONCLUSIONS

In the second half of the XIX century the number and complexity of technical inventions of

various machines and mechanisms using the gear drives reached a critical mass and by

around 1890 the scientists had created the scientific basis of the theory of gearing And the

modern theory of gearing was formed by the beginning of the 1970rsquos

The third cycle of the gearing theory development which is oriented at computer technology

is underway

In our opinion the prospects for the development of theory of gearing as a part of the

theory of mechanisms and machines are higher as compared for example with the

linkages Firstly gears are more commonly used in cars than linkages Secondly the

theory of gearing is not only the theory of higher kinematic pairs - it is also the basis for the

theory of gear machining design

It is necessary to note that the current version of the paper is based on the paper published in

the first edition of the given Proceedings [72] but is as close as possible to the paper [73] by

the same authors This version of the article has been prepared by VE Starzhinsky

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1934 ndash 215 с (Diels GA Antique appliances - Moscow-Leningrad ONTI - Gos tehn-

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2 Витрувий Десять книг об архитектуре ndash Москва laquoАрхитектура-Сraquo 2006 ndash 328 с

(Vitruvius Ten Books on Architecture ndash Moscov Architecture-C 2006 ndash 328 p)

3 Пипуныров ВН История часов с древнейших времен до наших дней - Москва

89

Наука 1982 ndash 496 c (Pipunyrov VN The clock story from ancient times to the present

day ndash Moscow Nauka 1982 ndash 496 p)

4 Академик ИИ Артоболевский Сборник Сост АМ Лепихов ndash М Знание 1983

ndash 176 c (Collection Comp AM Lepihov ndash Moscow Znanie 1983 ndash 176 p)

5 Чебышёв ПЛ Избранные труды ndash М Изд-во АН СССР 1955 ndash 926 с (Chebyshjov

PL Selected Works ndash Moscow AN SSSR 1955 ndash 926 p)

6 Рёло Ф Теоретическая кинематика 1875 (Relo F Theoretical Kinematics 1875)

7 Портретная галерея выдающихся инженеров и ученых в области зубчатых передач

ndash Сборник докладов научно-технической конференции с международным участием

Теория и практика зубчатых передач и редукторостроения Ижевск 2008 ndash C 378-

395 (Portrait Gallery of Disting wished Engineers and Scientist in Gearing ndash Proceedings

of Scientific-Engineering Conference with International Participation Theory and Practice

of Gearing and Reducer Building Izhevsk 2008 ndash P 378-395)

8 Литвин ФЛ Теория зубчатых зацеплений ndash М Наука 1968 ndash 584 с (Litvin FL

Theory of gearing ndash Moscow Nauka 1968 ndash 584 p)

9 Механика машин вып 45 ndash Москва Наука 1974 (Mechanics of machines No 45 ndash

Moscow Nauka 1974)

10 Willis R Principles of Mechanism ndash Cambridge London 1841

11 Гохман ХИ Теория зацеплений обобщенная и развитая путем анализа Дисс

магистра механики Одесса ndash 1886 ndash 232 с (Hokhman HI Link Theory generalized and

developed by analyzing Diss mastermechanic Odessa 1886 ndash 232 p)

12 Шишков ВА Образование поверхностей резанием по методу обкатки ndash Москва

Машгиз 1951 ndash 150 с (Shishkov VA Formation of surface machining by burnishing

method ndash Moscow Mashgiz 1951 ndash 150 p)

13 Вильдгабер Э Основы зацепления конических и гипоидных передач ndash Машгиз

1948 ndash 236 с (Vildgaber Je Principles of engagement bevel and hypoid gears ndash Moscow

Mashgiz 1948 ndash 236 p)

14 Baxter ML Basic Geometry and Tooth Contact of Hypoid Gears ldquoIndustrial

Mathematicsrdquo ndash 1961 ndash No 11 ndash P 19-42

15 Шевелева ГИ Алгоритм численного расчета обрабатываемой поверхности Станки

и инструмент ndash 1969 ndash 8 ndash C17-20 (Sheveleva GI Algorithm for the numerical

calculation of the treated surface Machines and Tooling ndash 1969 ndash No 8 ndash P 17-20)

16 Николаев АФ Диаграмма винта и ее применение к определению сопряженных

линейчатых поверхностей с линейным касанием Труды семинара по ТММ вып 37

1950 ndash С52ndash106 (Nikolaev AF Diagram of the screw and its application to the

determination of conjugate ruled surfaces with a linear contact Proceedings of the

Seminar on TMM ndash 1950 ndash No 37 ndash P52-106)

17 Новиков МЛ Зубчатые передачи с новым зацеплением ndash М Изд ВВИА им

Жуковского 1958 ndash 186 с (Novikov ML Gears with a new engagement ndash Moscow

Publisher VVIA by named Zhukovsky 1958 ndash 186 p)

18 Давыдов ЯС Об одном обобщении метода Оливье для образования сопряженных

90

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1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

73

astronomical gears blunt teeth (rounded with cut edges) were used To reproduce the

motion of the Moon the wheel should have 157 teeth which slicing was very difficult task

Blanking of 365 teeth on one wheel was another challenging task

Rapid development of machine engineering during the Renaissance gave rise to gearing

development Leonardo da Vinci considered toothed mechanisms of different types in his

printed works

Italian mathematician and engineer Gerolamo Cardano (1501-1576) became known for

designing various mechanisms including systems with large gear ratios that were used in

tower clocks [3 p169] It required knowledge of the most important kinematic relations

such as speed of the wheels and pinions with a certain amount of teeth and pinions

German mechanic of Czech origin Jacob Leipold (1674-1727) in his multivolume

encyclopedia of technical knowledge Theater of machines gathered data on almost all the

machines and tools known by the 20ies of the XVIII century Among other issues it

included description of the gear-tooth form elements of gear heads etc [4 p 129]

Russian mathematician and mechanic Pafnuty Lvovich Chebyshev (1821-1894) is

considered to be the founder of the Russian scientific school of the theory of mechanisms

He also made a substantial contribution into the theory of gearing which unfortunately was

underestimated by the domestic specialists In the tractate ldquoAbout gearsrdquo [5 p710] he on

the base of theory of functions deviating least of zero solved the problem of synthesis of

tooth profiles ldquodrawn around by circular arcs whereby irregularities of gear movement reach

the lowest limitrdquo Thus he proposed a mathematical model of tooth profile synthesis

according to the criterion of minimum of deviations of gear ratio from the constant value

over a period of one tooth pair meshing

Ibidem PL Chebyshev writes that ldquohellipin theory usually a given tooth form is assumed at

one gear wheel which is then used to find a tooth form on the other gear wheelrdquo and then

formulates the task ldquohellipit is necessary to have such technique of their drawing (ie synthesis

ndash authors) which would make it simple to obtain tooth forms on both gear wheels most

suitable for specific requirements of practical applicationrdquo Probably it was one of the first

statements of a problem in tooth flank optimization synthesis

German scientist Franz Reuleaux (1829-1905) in the monograph [6] developed and outlined

the main provisions of the structure and kinematics of mechanisms He defined kinematic

pair suggested teaching about the mechanisms and developed methods for the synthesis of

mechanisms

2 Gear drives and the gear machining origin

Mankind has been using gears for several thousand years in ancient Egypt they were used

in irrigation systems Initially the gears were made of wood with plug teeth made of

hardwood - they were used until the early twentieth century in particular in water mills

Since ancient times gears were made from copper alloys later ndash from iron and steel While

74

gears were usually cast they were sometimes forged and teeth on them were sawed or

ground

Since the mid-XIX century the creation of complex metal and gear-cutting machines has

begun This process ran parallel with the formation of the now world-renowned machine

tool companies [7]

Reishauer Corporation was founded in 1788 but the most important period that had

determined its further development was the mid-XIX century when the company was

headed by Jacob Friedrich Reishauer (1812-1862) He and his father in law (father of his

wife - approx Ed) IG Bodmer have developed a machine for the manufacture of threading

tools screw-cutting lathe Swiss engineer Johann Georg Bodmer (1786-1864) was a brilliant

inventor of the cutting tools so he could design and manufacture transmission spur gear

ratio to 145 as well as helical and bevel gears

The Gleason Works Company dates back to 1865 when a native of Ireland William Gleason

(1836-1922) organized a machine shop The first innovation of The Gleason Works

introduced in the industry was the invention of the planer to produce spur bevel gears in

1874

The British company David Brown was founded in 1860 by David Brown (1843-1903)

Business began with the production of molds for casting gear and later expanded by casting

gears themselves In 1898 the company started production of cutting gears and since 1915 -

involute worm gears

Swiss company Maag Gear AG a global leader in the production of gearboxes was founded

in 1913 by Swiss engineer and inventor Max Maag (1883-1960) In 1908 M Maag

developed unusual geometry of involute spur and helical gears This allows the designers to

avoid undercutting of teeth and increase the thickness of the teeth only by changing the

instrument relative to the wheel being processed

US firm Fellows Gear Shaper Company started production of spur wheels by chiselling

teeth in 1896 Method of teeth chiselling based on simulation of meshing of two gears as

they rotate around parallel axes was invented and commercialized by American inventor

Edwin R Fellows (1865-1945) Machine for grinding involute profile gear cutters used for

chiselling teeth of spur helical and special wheels was designed and manufactured in 1897

3 Origin and development of the theory of gearing

In the origin and development of the theory of gearing as a science certain periodicity can

be seen initially new particular tasks emerge in the society they are eventually solved

accumulated and systematized Then comes the moment when the quantity is transformed

into quality there is awareness of the accumulated knowledge theoretical propositions are

formulated and the foundations for the development of science and practice are laid for the

next cycle Based on theoretical foundations new designs and technologies are created and

the old ones are improved Then the cycle repeats at a new stage of development of the

75

industry emergence of new problems and their solution awareness formulation of new

theoretical propositions In our opinion the theory of gearing goes through three such

cycles two of them are completed while the third one is ongoing at the moment

The first cycle ndash creating the foundation for theory of gearing ndash began in antiquity gained

momentum in the XVIII century owing to works of Euler and L Camus and was enriched in

the XIX century by works of T Olivier R Willis and others Completion of the first cycle

by 1890 can be roughly related to the defense and publication of the masters thesis by HI

Hokhman (1851-1915) in 1886 in which the analytical solution of the main task of the

theory of gearing ndash finding the mating surface and determining its properties ndash is given

The second cycle ndash creating the classical theory of gearing ndash lasted for about 80 years and

was completed by early 70-ies of the XX century It can be assumed that the results of the

second cycle were finalized in 1968 by a monograph of FL Litvin [8] at Symposium on

gears in Leningrad in 1973 [9]

The third cycle ndash laying the groundwork for an updated theory of gearing and methods of

the gearing synthesis oriented at modern computer technologies Currently this cycle is not

completed yet although a lot of new challenges are accumulated and a number of topical

issues and unresolved problems are identified

Letrsquos consider the features of these three cycles of creation and development of the theory of

gearing

31 Laying the foundations of the theory of gearing

Theory of gearing like the majority of scientific disciplines is based on three points

An object of study and the basic concepts of the discipline

Methods and ways of working with the basic concepts

Basic laws of nature and of the given science which establish relationships between the

basic concepts These laws are often identified in the course of studies - in the form of

theorems mathematical formulas logical and computational models etc

The objects of study of the theory of gearing are

Higher kinematic pairs in the plane and space gear and cam mechanisms (working

engagement)

Cutting tools and processes in shaping gear treatment (technological engagement)

In the theory of gearing the basic concepts and ways of working with them are taken for

the most part from mathematics (line surface curvature etc) and mechanics (centroid

velocity acceleration force etc)

Basic laws and links between fundamental notions of the theory of gearing were identified

by mathematics and mechanics already in the XVIII-XIX centuries (L Euler L Camus F

Savary E Bobillier R Willis T Olivier HI Hokhman )

Member of the Russian Academy Leonhard Euler (1707-1783) discovered unique properties

76

of involute of circle and suggested using them in the gearing Note that currently more than

90 of all gears in the world are involute French astronomer Felix Savary (1797-1841) by

continuing the work of Euler revealed a relationship between the radii of curvature of the

tooth profiles in flat engagement with the radii of curvature of the centroid now known as

the Euler-Savary equation This unique equation is widely used nowadays On the basis of

the Euler-Savary equation French mathematician Etienne Bobillier (1798-1840) proposed a

geometrical construction for finding the centers of curvature profiles

The first scientists who were applied the scientific approach to study of gears were R Willis

and T Olivier English scientist R Willis was one of the first to apply a scientific approach

to the study of gearing He proved the fundamental theorem for plane gears ndash Willis [10]

theorem which in the modern interpretation reads as follows Common normal to the

profiles drawn at the point of tangency passes through the pole of engagement Willis

invented a special tool - odontograph - to define the geometry and type of drawing the teeth

and gears of different diameters and number of teeth

Scientific approach to gears formation goes back to the French mathematician and

mechanics Theodore Olivier (1793-1858) He formulated two ways of forming conjugated

gears which have not lost their generality and value up till now

The first Olivier method Generating surface Σ0 (eg rail or flat generating wheel) forms two

surfaces by rounding Σ1 on the gear and Σ2 on the wheel These surfaces are located at

different sides of the generating surface Σ0 (eg Σ1 is located at the top of Σ0 and Σ2 ndash at the

bottom of Σ0) Σ1 and Σ2 surface will be paired a linear contact (which occurs in cylindrical

and bevel gears) or touch points (eg helical gear) Most transmission with parallel and

intersecting axes ie cylindrical conical and helical-bevel ones are formed by this method

The first Olivier method was rarely used in gears with intersecting axes because it displays a

distinct tooth contact point which reduces the load capacity of the engagement

The second Olivier method Surface of one of the gears - for example Σ1 at the gear - is set

almost arbitrarily and the surface of the second gear - for example Σ2 at the wheel ndash is set

as an envelope to one-parameter family of surfaces Σ1 In general contact between Σ1 and

Σ2 will be linear Basically transmissions with intersecting axes including the worm gears

are formed according to this method

In the XIX century cycloidal engagement becomes widespread The work of the French

mathematician Charles Etienne Louis Camus (1699-1768) has become the basis for the

design of such gears Camusrsquo theorem states that paths of the same point of the auxiliary

centroid which is rolled along the centroids of meshing gears may be chosen as mating

teeth

Chaim Iegudovich Hokhmanrsquos [11] dissertation published in 1886 can be considered as the

work that summarizes the steps of creating the foundations for the theory of gearing He

developed a framework for the analytical theory of planar and spatial gearing Hokhman

created a new method for finding the envelope surfaces and lines of contact with those

surfaces which allowed to initially determine the line of contact of mutually enveloped

surfaces in any system of coordinates associated with any link of working or technological

77

engagement This simplifies finding the envelope surface as compared to classical methods

in mechanics and differential geometry

By the end of the XIX century the appearance of the fundamental principles of analytical

theory of gearing marked the end of the first cycle of development of the theory of gearing

These principles include

Basic concepts and methods of classical mechanics analytical and differential geometry

Two principles of formation of mating gears proposed by Olivier

Euler-Savary equation and Bobillierrsquos construction reflecting the relationship between the

centroid and the curvatures of mating profiles in plane gears

Hochman developed a method for finding the envelope profiles and surfaces as well as

points and lines of contact of mutually enveloped lines and surfaces in the plane and spatial

working and technological gears

32 Creation of the classical theory of gearing

The framework of analytical theory of gearing developed by the end of the XIX century has

become the basis for solving practical problems which were posed by the thriving industry

for the science

Late XIX amp early XX century had a rich history of inventions of new types of

transmissions machines tools and machine gears Conventionally these inventions can be

divided into two areas machinery and tools for forming gears based on engagement of the

mating surfaces and machines and tools for forming gears with non-conjugated surfaces of

teeth

The first approach is based on the Olivier principles

In the period from 1890 to 1920 the following technologies and machines for production of

gears based on the form-generating method were invented and implemented

- Machines for bevel gears including the ones circular teeth (JE Gleason)

- Machines for grinding involute profiles of gear cutters (E Fellows)

- Machines for cutting spur and helical gears with worm milling cutters (RH Pfauter)

- Technology for manufacturing globoid worm gear (SI Cohn and FW Lorenz)

- Involute worm gear based on the application of involute helical surface as the surface of

the worm mill thread (FD Bostock and P Brown)

These and many other inventions have set the task of generalization of the gear-forming

theory based on engagement of the mating surfaces Decisive role in complementing and

developing the Olivierrsquos principles belongs to Russian scientists AF Nikolaev (1901-

1957) YaS Davydov (1914-2003) and ML Erikhov (1937-2002) They used an auxiliary

(generating) surface to form the mating surfaces ML Novikov (1915-1957) proposed a

fundamentally different principle of forming the mating gears by moving (according to a

certain law) the contact point of two profiles along the line of engagement of the

78

synthesized transmission

All these principles are based on the theory of envelopes which was scientifically and

methodologically completed (at that period of time) in YaS Davydovrsquos VA Shishkovrsquos

and FL Litvinrsquos works Almost simultaneously and independently they proposed a method

for finding the kinematic envelope in which the meshing condition equation is used VN = 0

[8] At this time VA Shishkov [12] introduced a new concept - implementation speed Vn

equal to the scalar product Vn = V12n which became an effective tool in the study of gear

cutting tools working according to the form-generating method It became the basis of the

kinematic method for the synthesis and analysis of gearing in the second half of the XX

century

Ernest Wildhaber (1893-1979) a talented engineer and inventor of the company The

Gleason Works can be regarded as the founder of the second direction In 1927 he

proposed a method of forming hypoid gears and in 1930rsquos he patented Revacycle - the most

productive method (at that time) for spur bevel gears forming [13] Methods of forming

these transmissions are not based on Olivierrsquos principles E Wildhaber introduced gears

with non-conjugated tooth surfaces ndash transmissions with approximate meshing Basically

these gears cannot transmit rotation with constant gear ratio but the degree of deviation

from a constant gear ratio can be minimized by the targeted selection of values of gear

treatment process parameters Thus Wildhaber who abandoned the form-generating

method proved that there were possibilities of creating highly effective machining

processes for gears with non-conjugated tooth surfaces and thus initiated the theoretical

study of such transmissions

Active development of the theory of approximate meshing began after the 2nd World War

both in the US and the Soviet Union As the result the basic principle of the formation of

non-conjugate surfaces was formulated independently in the works of ML Baxter [14] and

FL Litvin [8] according to the principle the graph of deviation from the angular position

of the driven wheel from its position upon engagement of strictly conjugate surfaces is a

function similar to a parabola with the downward branches

At the same time it became clear that in order to meet challenges of synthesis and analysis

of gearing built on non-conjugated surfaces it is required to develop new mathematical

methods and models First mathematical models for studying gearing and computer

programs based on them appeared almost simultaneously in the US and the USSR

In the US TCA software package for the synthesis and analysis of hypoid gears [14] was

created under supervision of ML Baxter (1914-1994) chief engineer and researcher of The

Gleason Works

In the 1960rsquos methods for the synthesis of approximate gearing began to develop with the

advent of computers in the Soviet Union At first a software package for analysis and

synthesis of Revacycle spur bevel gear [9 p30-36] which included a numerical algorithm

for calculating the surface as an enveloping surface without using the theory of envelopes

[15] was developed at the Moscow Tooling and Machining Institute (STANKIN) under the

leadership of GI Sheveleva (1929-2005)

79

Similar software packages were developed in Saratov (Special Design Bureau of Gear ndash

Cutting Machines) under the leadership of MG Segal (1931-2000) and Leningrad (LITMO)

under supervision of FL Litvin The work on creation of universal programs for the

computer-based studies of spatial links was held in Tyumen [9 p36-43]

In the second half of the XX century the USSR became a recognized leader in terms of

volume and theoretical studies devoted to the study of the geometry of gears and gear

cutting tools After the end of World War II theoretical activities on creation of new methods

of analysis and synthesis of the working and technological gears was booming for 25-30

years Efforts of leading scientists (NI Kolchin FL Litvin VA Shishkov ML Novikov

LV Korostelyov GI Sheveleva II Dusev YaS Davydov ML Erikhov and others) have

led to creation of a new branch of science of the mechanisms - the gearing theory

The Soviet Union played the key role in creating the classical theory of gearing in early

1970rsquos The most important results obtained through efforts of domestic scientists which

formed the basis of the modern theory of gearing are listed below

1 Olivierrsquos principles for forming conjugate gearing are supplemented and developed AF

Nikolaev [16] ML Novikov [17] YaS Davydov [18] ML Erikhov [19]

2 New methods for analysis of the geometry of gears are developed and the existing ones

are improved differential (NI Kolchin the main publication of the year ndash 1957 [20])

screw (AF Nikolaev 1950 [16] KM Pismanik 1950 [21] NI Kolchin 1963 [22] VS

Lyukshin 1968 [23]) kinematic (YaS Davydov 1950 [24] VA Shishkov 1951 [12] NN

Krylov 1953 [25] FL Litvin 1960 [26] ML Erikhov 1972 [19]) matrix (FL Litvin

1968 [9]) power series (GI Sheveleva 1969 [27]) non-differential (GI Sheveleva 1969

[15]) tensor (II Dusev 1968 [28])

3 Methods of solving all major problems of synthesis and analysis of gears are established

Finding the envelope of a one-parameter and two-parameter family of surfaces (HI

Ketov NI Kolchin FL Litvin NN Krylov EG Ginsburg ML Erikhov) as well as

multi-parameter envelope family of surfaces and lines in spatial gearings (IL Brodsky DT

Babichev)

Finding an wrapping family of surfaces (GI Sheveleva)

Identifying the geometry generation features such as tooth undercutting interference and

others (MG Segal II Dusev GI Sheveleva VI Goldfarb BA Chyorny)

Synthesis of gearing geometry (local ndash FL Litvin ML Erikhov LV Korostelyov SA

Lagutin VN Rubtsov BP Timofeev and nonlocal ndash KI Gulyaev BA Chyorny MG

Segal)

Computation of curvatures in gearings (NI Kolchin FL Litvin VM Vasilyev II

Dusev EG Ginsburg LV Korostelyov ML Erikhov A M Pavlov MG Segal)

Computation of other geometric-kinematic characteristics of the teeth contact (AK

Georgiev VI Goldfarb SA Lagutin MF Lenski)

Solution of the inverse problem of the gearing theory tooth meshing analysis (KI

Gulyaev FL Litvin MG Segal BP Timofeev GI Sheveleva)

80

The impact of manufacturing errors and assembling on quality of engagement synthesis

of toothed meshing insensitive to errors (ML Erikhov NG Lindtrop LV Korostelyov

NN Krylov LY Liburkin GI Sheveleva)

Numerous studies of specific gears are conducted based on theoretical developments and

established procedures The most important practical problems solved during this period

are

1 Principally new types of gearing have been discovered helical gear in which arcs of

circles with radii small difference are selected as the profiles of cross-sections ndash Novikov-

Wildhaber gear [17] and gears with closed contact lines where the load between teeth is

transferred through the grease wedged in a closed cavity between active surfaces due to

closure of the contact line (LV Korostelyev SA Lagutin [29])

2 Geometric problems of synthesis of cylindrical involute gears were almost exhaustively

resolved and brought into engineering practice geometric calculation (VA Gavrylenko

1969 [30]) selection of the optimum addendum modification coefficients by using blocking

circuits (MB Groman 1957 [31]) according to the atlas compiled and published under the

direction of IA Bolotovsky 1967 [32]

3 New types of gearings have been studied and introduced In this regard various problems

related to analysis and synthesis of the following common types of gears have been solved

Bevel (NI Kolchin and VV Boldyrev 1937 YS Davydov 1950 VI Bezrukov 1963

VM Denisov 1963 GI Sheveleva 1966 HF Kabatov and GA Lopato 1966 MG

Segal 1971 KI Gulyaev 1974 VN Syzrantsev 1975)

Hypoid (GI Apukhtin 1952 FL Litvin 1962 KM Pismanik 1964 II Dusev and VM

Vasilyev 1968 MG Segal 1971)

Cylindrical gear drives with Novikovrsquos gear (ML Novikov 1956 RV Fedyakin and

VA Chesnokov 1958 VN Kudryavtsev 1959 EG Roslivker 1964 NI Kolchin 1968

VN Sevryuk 1972 and others)

Revacycle spur bevel gear (GI Sheveleva 1966)

New worm gear design toroid (YaI Dicker 1948) globoid (PS Zak 1962) worm gear

drives (FL Litvin 1962 IS Krivenko 1967 LV Korostelyev and SA Lagutin 1973

etc) spiroid (S Golubkov 1959 AK Georgiev and VI Goldfarb 1972 and others)

Less common known types of gears have also been studied and implemented

Hyperboloid (KM Pismanik 1950)

Helical-bevel (LY Liburkin 1968)

Wave (EG Ginsburg 1969)

Cylindrical with arched and spiral teeth (ML Erikhov and VN Syzrantsev 1975)

4 Techniques of analysis and synthesis of gears with non-circular wheels are developed [33]

and their production is organized

5 A lot of works are published including a number of classic books on theory of gearing

YaI Dieker (1935) NI Kolchin (1937-1952) FL Litvin (1952-1968) YaS Davydov

81

(1950) VA Gavrylenko (1949-1969) ML Novikov (1958) VA Zalgaller (1975) LD

Chasovnikov (1969) IA Bolotovsky et al (1962-1967) VN Kudryavtsev (1949-1971)

VN Kedrinsky (1960-1967) KM Pismanik (1964-1967) PS Zack (1962) NF Kabatov

and GA Lopato (1966) VA Shishkov (1951) and many others FL Litvinrsquos monograph

[8] stands out among these works it was published in 1968 and still remains a handbook for

professionals in the theory of gearing

The book by VA Zalgaller Envelope Theory [34] which is not very big in volume is

characterized by depth the mathematical rigor and completeness of the argumentation

Note that the appreciation level of the activities under the second cycle is confirmed by the

fact that in 1958 ML Novikov was awarded the Lenin Prize ndash the most prestigious USSR

award presented to individuals for accomplishments in the professional field

The following facts also confirm that the Soviet scientists made a decisive contribution to

the theory of gearing as a science and the fact that the Soviet Union had prepared a large

number of highly qualified specialists in the theory of gearing

FL Litvinrsquos monograph Theory of Gearing which was written in the late 60rsquos is still the

main handbook for gear specialists while Litvin is regarded as the creator of the modern

theory of gearing not only in CIS countries but also around the world

This monograph revised and expanded was reprinted abroad in English co-written with

FL Litvinrsquos new foreign students [35]

Number of qualified experts in the theory of gearing (by the way which were not widely

known in the Soviet Union and the CIS back then) have emigrated to the Western countries

and are writing and publishing quite significant books in English on the theory of gearing

and geometry of gears (SP Radzevich AL Kapelevich SV Lunin)

Summarizing the second cycle let us quote SA Lagutin who most accurately reflect the

essence of this bright period [36] it was a period of storm and pressure in the development

of the gearing theory in Russia when a whole galaxy of brilliant researchers were working

in this area headed by NI Kolchin and FL Litvin By collaborating and competing with

each other in a few years they have built amazingly beautiful building of the new science at

the junction of differential geometry and mechanics of machines

33 Laying the foundations of computer-oriented theory of gearing

The main purpose of such a theory is to become a basis for the methods of computer

analysis synthesis design and manufacturing gear parts for gear engagement

By the mid-70rsquos theory of gearing as a science has reached adulthood the main priority and

theoretical problems of analysis and synthesis of gearing have been resolved The number of

innovative theoretical work began to decline Studies are getting closer to the production

and the theory of gearing acts primarily as a tool for solving specific engineering problems

Since the mid 70-ies of XX century the theory of gearing as well as the machine tool

industry has evolved concurrently in two directions global and Russian

82

The global development of the theory of gearing has taken place against the backdrop of

revolution experienced by the machine tool industry since the 80rsquos

First machines with semi-rigid connections partially controlled by computer began to

appear in developed countries and then complete automatic machines (multi-axis CNC

machines) appeared

At that time for example machines for processing bevel gears with circular teeth Phoenix

(Gleason) and WNC30 (Klingelnberg) were developed The creation of such machines

occurred in parallel with the development of new mathematical models for shaping parts on

multi-axis machines and testing the parts operability before their casting in the metal At

that time software systems LTCA (Gleason) and Kimos (Klingelnberg) were developed

which made it possible to solve the problem of synthesis and analysis of bevel gears with

circular teeth [37]

All developed countries pursue the global direction in the development of the theory of

gearing in the same manner and using similar approaches The following was used by the

gear specialists to solve the problems of analysis and synthesis

Methods of classical theory of gearing (with computer design of the geometry of any kind

of gears)

Techniques of non-differential analysis of gear ndash forming processes using universal as

well as specially developed software packages

Methods of boundary and finite elements (at the analysis of the contact interaction of

acting surfaces of the teeth)

Finite element methods and integral equations (at the analysis of the stress-strain state of

the teeth)

Numerical optimization methods (at the synthesis of geometry of acting and fillet surfaces

of teeth)

An expanded list of quality indicators of gearings including new ones the design

thickness of the oil film criteria of hot and cold seizure criteria for assessing the conditions

for the formation of an oil wedge indicators of vibration activity of the gearing and others

Designing gear drives was regarded as a complex problem requiring an agreed solution of a

group of interrelated tasks

Selection of design scheme of a gear

Synthesis of permissible geometry

Geometry optimization

Structural arrangement and evaluation of quality indicators

Identification and addressing the weaknesses

Designing technical processes of manufacture selection or synthesis of tools subsequent

optimization etc

The developed theory of gearing is known as Theory of Real Gearing in Russia Ukraine

and Belarus while abroad it is called ldquoIntegrated Gear Designrdquo (IGD) or Integrated Design

83

of Gears

Russian direction in the development of the theory of gearing has several specific features

attributable to the following objective circumstances

Firstly first clear signs of stagnation appeared in the USSR industry in the late 70rsquos

Secondly the number of graduate students reduced as the universities basically solved the

problem of teachers which they faced in the early 60rsquos due to a drastic increase in the

number of students being trained in engineering specialties And finally Russia lost the top

three main theorists in the field of the theory of gearing FL Litvin was forced to emigrate

to the USA LV Korostelyov died in a car crash YaS Davydov departed from active

research and subsequently left for the USA

And nevertheless in 15-20 years preceding the collapse of the USSR in 1991 the theory

and geometry of gearing in the Soviet Union was continuing to develop At that time new

centers specializing in different aspects of the theory of gearing were established Let us list

the most interesting in our opinion research topics at the end of the last century

- Issues of strength and solution of the tooth contact problem (EL Airapetov VN

Syzrantsev GI Sheveleva)

- Research on gear bending bending stresses calculation (GI Sheveleva VI Medvedev)

- Non-differential methods for the determination of the contact surfaces characteristics (VI

Goldfarb GI Sheveleva AE Volkov)

- Issues of design synthesis analysis and manufacturing spiroid gear drives (AK Georgiev

VI Goldfarb)

- Issues of design synthesis analysis and manufacturing worm gear drives (SA Lagutin

AI Sandler)

- Research of hypoid bevel gear drives with circular teeth (MG Segal GI Sheveleva VN

Syzrantsev)

- Research of gear drives with intermediate bodies (AE Belyaev)

- Research of helical-bevel gear drives (BA Lopatin)

- Development of methods for the synthesis of gear drives (MG Segal SA Lagutin GI

Sheveleva VI Medvedev VN Syzrantsev)

- Forming a theoretical framework for the development of universal programs for the

analysis of spatial working and technological meshings and the creation of corresponding

programs (DT Babichev)

As a result of these studies software systems were developed in the Soviet Union which

were aimed at solving the problems of synthesis and analysis primarily for bevel gears with

circular teeth The best known ones include PC Volga5 made under the direction of MG

Segal [38] and PC Expert created under the direction of GI Sheveleva [39]

The fact that MG Segal was the main developer of the PC Kimos (firm Klingelnberg) in

the 90rsquos confirms the high level of those developments

It should also be noted that a work on the selection of optimal schemes for multi-axis CNC

84

machines for processing gear was carried out in 1990 in Saratov (MG Segal LI Shejko

[40]) These developments have also been used by Klingelnberg

The researches (above all theoretical ones) continued after the collapse of the USSR in

Russia Ukraine and Belarus

At that time the development of the theory of gearing was distinguished by a high level of

theoretical studies based on the introduction of new geometric geometric-kinematic and

other concepts and development (on their basis) of new mathematical models methods and

algorithms for analysis and synthesis of the working and technological gear engagements

These works were performed mostly at their own initiative by highly qualified specialists-

theorists in the field of theory and geometry of working and technological gear meshing

Usually they were elderly university professors who were practically deprived of relations

with the machine-building industry after its stagnation during the collapse of the USSR

It should be noted that it is very difficult to distinguish the most important areas of research

in the modern theory of gearing As the poet said Great things are better seen from a

distance Therefore we will list the most interesting in our view theoretical works on the

development of the theory of gearing with greater focus on the Russian line of research

However we practically do not consider the works on gear geometry ndash they are too

numerous A fairly complete picture of the theoretical works of this period can be obtained

from the proceedings of symposia and conferences held in Kurgan (KMI) Izhevsk

(IzhSTU) and Sevastopol (KhPI Kharkov) The main directions in the development of the

theory of gearing and the most important theoretical results after 1970s include the

following

1 Introduction and use of new concepts such as

Meshing Space (SA Lagutin [41])

Wrapping surface (GI Sheveleva [39])

Fan wedge and normal beam accelerating of implantation (DT Babichev [42])

2 Development of methods for analyzing processes of generation

A new method of finding a singularity in the flat gearing (SA Lagutin) based on the

situation [43] return point at the gear profile occurs at the point in the line of engagement

in which the normal to this line intersects the axis of rotation of the pinion The method was

extended to the spatial gearing (AE Volkov [44])

3 Development of methods of synthesis

Based on the new concept of space of engagement and its properties This approach was

used during the synthesis of both spatial transmission (SA Lagutin [45]) and the cylindrical

(DT Babichev [46])

By using as objective function new criteria of load capacity - permissible contact

pressure(VI Medvedev [47]) the specific work of working surfaces of teeth (DT Babichev

[48]) and others

For bevel gears with small cross-axis angle (SA Lagutin [49] VI Medvedev [50])

Synthesis of gears considering technological limitations of the given production processes

85

(VI Medvedev [51] VN Syzrantsev [52])

By using and developing a method of synthesis of gears in generalizing parameters

originally proposed by EB Vulgakov for involute gears The method was modified by VL

Dorofeev - for involute and ON Tsukanov and BA Lopatin ndash for non-involute gears

(including cylinder-conical ones) [53]

By using variational methods of synthesis when the equation of an optimal surface of the

tooth and its coefficients are determined This approach was first applied apparently by

Alan Lebec [54] in the United States it was used in Ukraine [55] and being developed in

Russia where equal strength gears have been synthesized by using the method (by Hertz

contact strength) [46 56] and the method of synthesis of bevel gear with circular teeth

according to the criteria of minimal contact pressure and bending stresses while maintaining

the overall dimensions of the gear has been developed which is important for aviation

where the weight of the structure is crucial [57]

Increasing the bending strength of circular tooth bevel gears by optimizing the shape of

the tool [58]

Increasing the load-bearing capacity of high-speed heavy-duty cylindrical involute gears

Note that EB Vulgakov VL Dorofeev and AL Kapelevich have made a significant

contribution to the development of synthesis aviation gear in recent decades [59]

4 Development of methods of analysis of loaded gears considering multipairness of

contact

For bevel gears with circular teeth [60]

For spiroid gears [61]

5 Significant progress has been made in the methods of analysis synthesis design and

manufacture of worm gear transmissions

The main input in this field of gearing has been made by two groups of researchers under

the leadership of VI Goldfarb and SA Lagutin The techniques of minimizing meshing

errors and worm hob errors that appear when regrinding and relieving works are fulfilled

have been developed by SA Lagutin and AI Sandler The techniques of synthesis and

production of gears with localized contact were drilled worm gears (SA Lagutin AI

Sandler [62]) and spiroid ones (VI Goldfarb ES Trubachyov [63])

The drives with the increased load capacity were designed based on a study of meshing

space of non-orthogonal gears spiroid (ES Trubachyov [63]) and worm ones (VYu

Puzanov) Designing of spiroid transmissions is carried out using CAD ldquoSPDIAL+rdquo

developed by a group headed by VI Goldfarb Configurator of gearbox systems for

optimization structural synthesis of their structures is being created (OV Malina etal)

Unified worm hob cutters cutting gears for the drives with localized contact were designed

It became possible to cut the gear wheels in engagement with multiple-thread worm by a

single-pass mill (VI Goldfarb and his disciples)

In the Institute of Mechanics IzhSTU a group led by VI Goldfarb essentially laid the

foundation for a new Russian machine building sub-industry ndash construction of gearboxes for

86

isolation and control valves for pipelines

- Theoretical studies of spiroid and worm gears are at a high scientific level

- A modern design process is applied synthesis of perfect engagement synthesis of

localized contact simulation of the stress strain state analysis of real engagement under

load forecasting the state of transmission

- Three generations of dimension-type series of quarter-turn and multi-turn spiroid gear

drives are developed their production with modern quality control and acceptance tests is

organized

6 Application of unconventional gears and gearing helical-bevel gears (BA Lopatin [65])

transmissions with intermediate rolling bodies (AE Belyaev [66]) hydraulic and

pneumatic machines with non-circular gears (An-I-Kahn [67]) precessing transmissions

(IA Bostan [68] EI Tesker [69] VN Syzrantsev BA Lopatin) and other

7 Development of kinematic analysis methods of working and technological meshings Note

that modern designing is the computer designing This factor imposes high requirements to

the theory of gearing as the main mathematical basis for such designing We have to admit

that the classical theory of gearing does not fully comply with these demanding

requirements Thus according to Prof MG Segal who was working with Klingelnberg in

the last years of his life the head of the company prohibited to use differential methods ndash

the basis of the classical theory of gearing ndash in the programs being created The reason for

the ban was inadequacy of the results of computer simulation as compared to real processes

of formation Theoretical research aimed at creating computational models that are

adequate to the real processes of formation and contact of moving bodies were developed by

AE Volkov and VI Medvedev (Moscow) and DT Babichev (Tyumen)

To eliminate the phenomenon DT Babichev elaborated a unified kinematic method for

analysis of the processes of formation [70] based on the ldquotriadrdquo ruptures + envelopes + new

concepts of curvilinear coordinates As the result the cause of inadequacy between the

classical methods of the theory of gearing and real-life processes of formation was

established and rectified The developed kinematic method

Allows to find all the surfaces formed on the item at gear machining formed by smooth

surfaces and inflections of bodies including at advanceretraction of machine tool and in

secondary cutting areas

Has the reliability of non-differential methods but is superior to them in speed of

operation by two orders of magnitude which is confirmed by its partial use in CAD

ldquoSPDIAL +rdquo

Also allows to define the curvatures in gearing

8 Development of the system for assigning real ITS (Initial Tool Surfaces) and construction

of mathematical models for them [71] Real ITS is the set of all forming tools (pieces of

surfaces cutting and boundary edges and corners) for which uniform curvilinear coordinates

are introduced

9 By using the concept of ldquothe acceleration of installationrdquo new techniques for solving

87

multitude of tasks are created calculating the radii of curvature in the gearing identifying

cutting areas and thickness of the layers being cut by tool cutting edges and others (DT

Babichev [48])

For example based on the concept of the acceleration of installation a new basic formula

for calculating the reduced curvature in any normal sections at the contact point of two

moving bodies in contact along the line is created

1Rnp=-

where ɷrol is angular velocity of rolling bodies in the plane of the section in which the

curvature is calculated aB is the acceleration of installation The fundamental nature of the

obtained formula is that

1) in its generality it is commensurate with the kinematic formulas of Rodrigues and Freinet

known in differential geometry but it is intended for a different class of surfaces produced

in the process of formation by the rounding methods

2) curvature in any normal section of all surfaces formed by the rounding methods is

determined by only two scalar parameters and one of them (acceleration of installation)

does not depend on the direction of the section

It was also established that the sign of the acceleration of installation allow to make an

unambiguous judgement on the nature of the contact of bodies For example if aВgt 0 then

the envelope is formed inside the body of the generating element Acceleration of

installation allows to determine (ldquoincidentallyrdquo) the value of the radii of curvature and

faceting value across the whole surface formed by rounding at band- and flake-type

roughness

Thus over the past decade a substantial volume of theoretical knowledge to complete the

third cycle (creation of a computer-oriented theory of gearing) was accumulated

A lot of new notions are introduced and used in theory of gearing

Based on these new notions methods for analysis and synthesis of gear drives and cutter

tool meshings oriented at computer technologies have been developed and continue to be

improved

Intensive investigations to improve methods of optimization synthesis of gearing and to

develop methodologies of computer design and construction of gear boxes are performed

4 Problems and expected directions of the theory of gearing

Let us list the main problems in the gearing theory which in our opinion are the most

important

Problem 1 Creation of the theory of optimization synthesis of structures and parameters of

higher pairs of kinematic elements transmitting the motion and load at the preset and

optimal correlation of normal and friction forces At the present time theory of higher pairs

is being developed only as a pure geometrical science

88

Problem 2 Elaboration of methods of tooth optimal geometry synthesis oriented at the

modern processing technologies instead of traditional ones In this case a designer will have

to solve the variation problem with limitations providing for maximum possible load

capacity of gear drive in accordance with preselected criteria of performance efficiency

Problem 3 Development of methods for analysis of the process of the tooth preset surfaces

changeover taking into account the values of load tooth displacement manufacturing errors

of drive elements errors of relative position of engaging links dynamics of changeover

process

Problem 4 Creation of a unique interrelated complex of application software packages to

enable the designers and manufactures of gear drives to carry out optimization designing

engineering design preparation for production of various drives by meshing

Possible directions of development of the theory of gearing naturally follow from the afore-

described problems

CONCLUSIONS

In the second half of the XIX century the number and complexity of technical inventions of

various machines and mechanisms using the gear drives reached a critical mass and by

around 1890 the scientists had created the scientific basis of the theory of gearing And the

modern theory of gearing was formed by the beginning of the 1970rsquos

The third cycle of the gearing theory development which is oriented at computer technology

is underway

In our opinion the prospects for the development of theory of gearing as a part of the

theory of mechanisms and machines are higher as compared for example with the

linkages Firstly gears are more commonly used in cars than linkages Secondly the

theory of gearing is not only the theory of higher kinematic pairs - it is also the basis for the

theory of gear machining design

It is necessary to note that the current version of the paper is based on the paper published in

the first edition of the given Proceedings [72] but is as close as possible to the paper [73] by

the same authors This version of the article has been prepared by VE Starzhinsky

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1 Дильс ГА Античная техника Москва-Ленинград ОНТИ - Гос техн-теор изд-во ndash

1934 ndash 215 с (Diels GA Antique appliances - Moscow-Leningrad ONTI - Gos tehn-

teor Publ 1934 ndash 215 p)

2 Витрувий Десять книг об архитектуре ndash Москва laquoАрхитектура-Сraquo 2006 ndash 328 с

(Vitruvius Ten Books on Architecture ndash Moscov Architecture-C 2006 ndash 328 p)

3 Пипуныров ВН История часов с древнейших времен до наших дней - Москва

89

Наука 1982 ndash 496 c (Pipunyrov VN The clock story from ancient times to the present

day ndash Moscow Nauka 1982 ndash 496 p)

4 Академик ИИ Артоболевский Сборник Сост АМ Лепихов ndash М Знание 1983

ndash 176 c (Collection Comp AM Lepihov ndash Moscow Znanie 1983 ndash 176 p)

5 Чебышёв ПЛ Избранные труды ndash М Изд-во АН СССР 1955 ndash 926 с (Chebyshjov

PL Selected Works ndash Moscow AN SSSR 1955 ndash 926 p)

6 Рёло Ф Теоретическая кинематика 1875 (Relo F Theoretical Kinematics 1875)

7 Портретная галерея выдающихся инженеров и ученых в области зубчатых передач

ndash Сборник докладов научно-технической конференции с международным участием

Теория и практика зубчатых передач и редукторостроения Ижевск 2008 ndash C 378-

395 (Portrait Gallery of Disting wished Engineers and Scientist in Gearing ndash Proceedings

of Scientific-Engineering Conference with International Participation Theory and Practice

of Gearing and Reducer Building Izhevsk 2008 ndash P 378-395)

8 Литвин ФЛ Теория зубчатых зацеплений ndash М Наука 1968 ndash 584 с (Litvin FL

Theory of gearing ndash Moscow Nauka 1968 ndash 584 p)

9 Механика машин вып 45 ndash Москва Наука 1974 (Mechanics of machines No 45 ndash

Moscow Nauka 1974)

10 Willis R Principles of Mechanism ndash Cambridge London 1841

11 Гохман ХИ Теория зацеплений обобщенная и развитая путем анализа Дисс

магистра механики Одесса ndash 1886 ndash 232 с (Hokhman HI Link Theory generalized and

developed by analyzing Diss mastermechanic Odessa 1886 ndash 232 p)

12 Шишков ВА Образование поверхностей резанием по методу обкатки ndash Москва

Машгиз 1951 ndash 150 с (Shishkov VA Formation of surface machining by burnishing

method ndash Moscow Mashgiz 1951 ndash 150 p)

13 Вильдгабер Э Основы зацепления конических и гипоидных передач ndash Машгиз

1948 ndash 236 с (Vildgaber Je Principles of engagement bevel and hypoid gears ndash Moscow

Mashgiz 1948 ndash 236 p)

14 Baxter ML Basic Geometry and Tooth Contact of Hypoid Gears ldquoIndustrial

Mathematicsrdquo ndash 1961 ndash No 11 ndash P 19-42

15 Шевелева ГИ Алгоритм численного расчета обрабатываемой поверхности Станки

и инструмент ndash 1969 ndash 8 ndash C17-20 (Sheveleva GI Algorithm for the numerical

calculation of the treated surface Machines and Tooling ndash 1969 ndash No 8 ndash P 17-20)

16 Николаев АФ Диаграмма винта и ее применение к определению сопряженных

линейчатых поверхностей с линейным касанием Труды семинара по ТММ вып 37

1950 ndash С52ndash106 (Nikolaev AF Diagram of the screw and its application to the

determination of conjugate ruled surfaces with a linear contact Proceedings of the

Seminar on TMM ndash 1950 ndash No 37 ndash P52-106)

17 Новиков МЛ Зубчатые передачи с новым зацеплением ndash М Изд ВВИА им

Жуковского 1958 ndash 186 с (Novikov ML Gears with a new engagement ndash Moscow

Publisher VVIA by named Zhukovsky 1958 ndash 186 p)

18 Давыдов ЯС Об одном обобщении метода Оливье для образования сопряженных

90

поверхностей в зубчатых передачах Сб laquoТеорияпередачвмашинахraquo М Машгиз

1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

74

gears were usually cast they were sometimes forged and teeth on them were sawed or

ground

Since the mid-XIX century the creation of complex metal and gear-cutting machines has

begun This process ran parallel with the formation of the now world-renowned machine

tool companies [7]

Reishauer Corporation was founded in 1788 but the most important period that had

determined its further development was the mid-XIX century when the company was

headed by Jacob Friedrich Reishauer (1812-1862) He and his father in law (father of his

wife - approx Ed) IG Bodmer have developed a machine for the manufacture of threading

tools screw-cutting lathe Swiss engineer Johann Georg Bodmer (1786-1864) was a brilliant

inventor of the cutting tools so he could design and manufacture transmission spur gear

ratio to 145 as well as helical and bevel gears

The Gleason Works Company dates back to 1865 when a native of Ireland William Gleason

(1836-1922) organized a machine shop The first innovation of The Gleason Works

introduced in the industry was the invention of the planer to produce spur bevel gears in

1874

The British company David Brown was founded in 1860 by David Brown (1843-1903)

Business began with the production of molds for casting gear and later expanded by casting

gears themselves In 1898 the company started production of cutting gears and since 1915 -

involute worm gears

Swiss company Maag Gear AG a global leader in the production of gearboxes was founded

in 1913 by Swiss engineer and inventor Max Maag (1883-1960) In 1908 M Maag

developed unusual geometry of involute spur and helical gears This allows the designers to

avoid undercutting of teeth and increase the thickness of the teeth only by changing the

instrument relative to the wheel being processed

US firm Fellows Gear Shaper Company started production of spur wheels by chiselling

teeth in 1896 Method of teeth chiselling based on simulation of meshing of two gears as

they rotate around parallel axes was invented and commercialized by American inventor

Edwin R Fellows (1865-1945) Machine for grinding involute profile gear cutters used for

chiselling teeth of spur helical and special wheels was designed and manufactured in 1897

3 Origin and development of the theory of gearing

In the origin and development of the theory of gearing as a science certain periodicity can

be seen initially new particular tasks emerge in the society they are eventually solved

accumulated and systematized Then comes the moment when the quantity is transformed

into quality there is awareness of the accumulated knowledge theoretical propositions are

formulated and the foundations for the development of science and practice are laid for the

next cycle Based on theoretical foundations new designs and technologies are created and

the old ones are improved Then the cycle repeats at a new stage of development of the

75

industry emergence of new problems and their solution awareness formulation of new

theoretical propositions In our opinion the theory of gearing goes through three such

cycles two of them are completed while the third one is ongoing at the moment

The first cycle ndash creating the foundation for theory of gearing ndash began in antiquity gained

momentum in the XVIII century owing to works of Euler and L Camus and was enriched in

the XIX century by works of T Olivier R Willis and others Completion of the first cycle

by 1890 can be roughly related to the defense and publication of the masters thesis by HI

Hokhman (1851-1915) in 1886 in which the analytical solution of the main task of the

theory of gearing ndash finding the mating surface and determining its properties ndash is given

The second cycle ndash creating the classical theory of gearing ndash lasted for about 80 years and

was completed by early 70-ies of the XX century It can be assumed that the results of the

second cycle were finalized in 1968 by a monograph of FL Litvin [8] at Symposium on

gears in Leningrad in 1973 [9]

The third cycle ndash laying the groundwork for an updated theory of gearing and methods of

the gearing synthesis oriented at modern computer technologies Currently this cycle is not

completed yet although a lot of new challenges are accumulated and a number of topical

issues and unresolved problems are identified

Letrsquos consider the features of these three cycles of creation and development of the theory of

gearing

31 Laying the foundations of the theory of gearing

Theory of gearing like the majority of scientific disciplines is based on three points

An object of study and the basic concepts of the discipline

Methods and ways of working with the basic concepts

Basic laws of nature and of the given science which establish relationships between the

basic concepts These laws are often identified in the course of studies - in the form of

theorems mathematical formulas logical and computational models etc

The objects of study of the theory of gearing are

Higher kinematic pairs in the plane and space gear and cam mechanisms (working

engagement)

Cutting tools and processes in shaping gear treatment (technological engagement)

In the theory of gearing the basic concepts and ways of working with them are taken for

the most part from mathematics (line surface curvature etc) and mechanics (centroid

velocity acceleration force etc)

Basic laws and links between fundamental notions of the theory of gearing were identified

by mathematics and mechanics already in the XVIII-XIX centuries (L Euler L Camus F

Savary E Bobillier R Willis T Olivier HI Hokhman )

Member of the Russian Academy Leonhard Euler (1707-1783) discovered unique properties

76

of involute of circle and suggested using them in the gearing Note that currently more than

90 of all gears in the world are involute French astronomer Felix Savary (1797-1841) by

continuing the work of Euler revealed a relationship between the radii of curvature of the

tooth profiles in flat engagement with the radii of curvature of the centroid now known as

the Euler-Savary equation This unique equation is widely used nowadays On the basis of

the Euler-Savary equation French mathematician Etienne Bobillier (1798-1840) proposed a

geometrical construction for finding the centers of curvature profiles

The first scientists who were applied the scientific approach to study of gears were R Willis

and T Olivier English scientist R Willis was one of the first to apply a scientific approach

to the study of gearing He proved the fundamental theorem for plane gears ndash Willis [10]

theorem which in the modern interpretation reads as follows Common normal to the

profiles drawn at the point of tangency passes through the pole of engagement Willis

invented a special tool - odontograph - to define the geometry and type of drawing the teeth

and gears of different diameters and number of teeth

Scientific approach to gears formation goes back to the French mathematician and

mechanics Theodore Olivier (1793-1858) He formulated two ways of forming conjugated

gears which have not lost their generality and value up till now

The first Olivier method Generating surface Σ0 (eg rail or flat generating wheel) forms two

surfaces by rounding Σ1 on the gear and Σ2 on the wheel These surfaces are located at

different sides of the generating surface Σ0 (eg Σ1 is located at the top of Σ0 and Σ2 ndash at the

bottom of Σ0) Σ1 and Σ2 surface will be paired a linear contact (which occurs in cylindrical

and bevel gears) or touch points (eg helical gear) Most transmission with parallel and

intersecting axes ie cylindrical conical and helical-bevel ones are formed by this method

The first Olivier method was rarely used in gears with intersecting axes because it displays a

distinct tooth contact point which reduces the load capacity of the engagement

The second Olivier method Surface of one of the gears - for example Σ1 at the gear - is set

almost arbitrarily and the surface of the second gear - for example Σ2 at the wheel ndash is set

as an envelope to one-parameter family of surfaces Σ1 In general contact between Σ1 and

Σ2 will be linear Basically transmissions with intersecting axes including the worm gears

are formed according to this method

In the XIX century cycloidal engagement becomes widespread The work of the French

mathematician Charles Etienne Louis Camus (1699-1768) has become the basis for the

design of such gears Camusrsquo theorem states that paths of the same point of the auxiliary

centroid which is rolled along the centroids of meshing gears may be chosen as mating

teeth

Chaim Iegudovich Hokhmanrsquos [11] dissertation published in 1886 can be considered as the

work that summarizes the steps of creating the foundations for the theory of gearing He

developed a framework for the analytical theory of planar and spatial gearing Hokhman

created a new method for finding the envelope surfaces and lines of contact with those

surfaces which allowed to initially determine the line of contact of mutually enveloped

surfaces in any system of coordinates associated with any link of working or technological

77

engagement This simplifies finding the envelope surface as compared to classical methods

in mechanics and differential geometry

By the end of the XIX century the appearance of the fundamental principles of analytical

theory of gearing marked the end of the first cycle of development of the theory of gearing

These principles include

Basic concepts and methods of classical mechanics analytical and differential geometry

Two principles of formation of mating gears proposed by Olivier

Euler-Savary equation and Bobillierrsquos construction reflecting the relationship between the

centroid and the curvatures of mating profiles in plane gears

Hochman developed a method for finding the envelope profiles and surfaces as well as

points and lines of contact of mutually enveloped lines and surfaces in the plane and spatial

working and technological gears

32 Creation of the classical theory of gearing

The framework of analytical theory of gearing developed by the end of the XIX century has

become the basis for solving practical problems which were posed by the thriving industry

for the science

Late XIX amp early XX century had a rich history of inventions of new types of

transmissions machines tools and machine gears Conventionally these inventions can be

divided into two areas machinery and tools for forming gears based on engagement of the

mating surfaces and machines and tools for forming gears with non-conjugated surfaces of

teeth

The first approach is based on the Olivier principles

In the period from 1890 to 1920 the following technologies and machines for production of

gears based on the form-generating method were invented and implemented

- Machines for bevel gears including the ones circular teeth (JE Gleason)

- Machines for grinding involute profiles of gear cutters (E Fellows)

- Machines for cutting spur and helical gears with worm milling cutters (RH Pfauter)

- Technology for manufacturing globoid worm gear (SI Cohn and FW Lorenz)

- Involute worm gear based on the application of involute helical surface as the surface of

the worm mill thread (FD Bostock and P Brown)

These and many other inventions have set the task of generalization of the gear-forming

theory based on engagement of the mating surfaces Decisive role in complementing and

developing the Olivierrsquos principles belongs to Russian scientists AF Nikolaev (1901-

1957) YaS Davydov (1914-2003) and ML Erikhov (1937-2002) They used an auxiliary

(generating) surface to form the mating surfaces ML Novikov (1915-1957) proposed a

fundamentally different principle of forming the mating gears by moving (according to a

certain law) the contact point of two profiles along the line of engagement of the

78

synthesized transmission

All these principles are based on the theory of envelopes which was scientifically and

methodologically completed (at that period of time) in YaS Davydovrsquos VA Shishkovrsquos

and FL Litvinrsquos works Almost simultaneously and independently they proposed a method

for finding the kinematic envelope in which the meshing condition equation is used VN = 0

[8] At this time VA Shishkov [12] introduced a new concept - implementation speed Vn

equal to the scalar product Vn = V12n which became an effective tool in the study of gear

cutting tools working according to the form-generating method It became the basis of the

kinematic method for the synthesis and analysis of gearing in the second half of the XX

century

Ernest Wildhaber (1893-1979) a talented engineer and inventor of the company The

Gleason Works can be regarded as the founder of the second direction In 1927 he

proposed a method of forming hypoid gears and in 1930rsquos he patented Revacycle - the most

productive method (at that time) for spur bevel gears forming [13] Methods of forming

these transmissions are not based on Olivierrsquos principles E Wildhaber introduced gears

with non-conjugated tooth surfaces ndash transmissions with approximate meshing Basically

these gears cannot transmit rotation with constant gear ratio but the degree of deviation

from a constant gear ratio can be minimized by the targeted selection of values of gear

treatment process parameters Thus Wildhaber who abandoned the form-generating

method proved that there were possibilities of creating highly effective machining

processes for gears with non-conjugated tooth surfaces and thus initiated the theoretical

study of such transmissions

Active development of the theory of approximate meshing began after the 2nd World War

both in the US and the Soviet Union As the result the basic principle of the formation of

non-conjugate surfaces was formulated independently in the works of ML Baxter [14] and

FL Litvin [8] according to the principle the graph of deviation from the angular position

of the driven wheel from its position upon engagement of strictly conjugate surfaces is a

function similar to a parabola with the downward branches

At the same time it became clear that in order to meet challenges of synthesis and analysis

of gearing built on non-conjugated surfaces it is required to develop new mathematical

methods and models First mathematical models for studying gearing and computer

programs based on them appeared almost simultaneously in the US and the USSR

In the US TCA software package for the synthesis and analysis of hypoid gears [14] was

created under supervision of ML Baxter (1914-1994) chief engineer and researcher of The

Gleason Works

In the 1960rsquos methods for the synthesis of approximate gearing began to develop with the

advent of computers in the Soviet Union At first a software package for analysis and

synthesis of Revacycle spur bevel gear [9 p30-36] which included a numerical algorithm

for calculating the surface as an enveloping surface without using the theory of envelopes

[15] was developed at the Moscow Tooling and Machining Institute (STANKIN) under the

leadership of GI Sheveleva (1929-2005)

79

Similar software packages were developed in Saratov (Special Design Bureau of Gear ndash

Cutting Machines) under the leadership of MG Segal (1931-2000) and Leningrad (LITMO)

under supervision of FL Litvin The work on creation of universal programs for the

computer-based studies of spatial links was held in Tyumen [9 p36-43]

In the second half of the XX century the USSR became a recognized leader in terms of

volume and theoretical studies devoted to the study of the geometry of gears and gear

cutting tools After the end of World War II theoretical activities on creation of new methods

of analysis and synthesis of the working and technological gears was booming for 25-30

years Efforts of leading scientists (NI Kolchin FL Litvin VA Shishkov ML Novikov

LV Korostelyov GI Sheveleva II Dusev YaS Davydov ML Erikhov and others) have

led to creation of a new branch of science of the mechanisms - the gearing theory

The Soviet Union played the key role in creating the classical theory of gearing in early

1970rsquos The most important results obtained through efforts of domestic scientists which

formed the basis of the modern theory of gearing are listed below

1 Olivierrsquos principles for forming conjugate gearing are supplemented and developed AF

Nikolaev [16] ML Novikov [17] YaS Davydov [18] ML Erikhov [19]

2 New methods for analysis of the geometry of gears are developed and the existing ones

are improved differential (NI Kolchin the main publication of the year ndash 1957 [20])

screw (AF Nikolaev 1950 [16] KM Pismanik 1950 [21] NI Kolchin 1963 [22] VS

Lyukshin 1968 [23]) kinematic (YaS Davydov 1950 [24] VA Shishkov 1951 [12] NN

Krylov 1953 [25] FL Litvin 1960 [26] ML Erikhov 1972 [19]) matrix (FL Litvin

1968 [9]) power series (GI Sheveleva 1969 [27]) non-differential (GI Sheveleva 1969

[15]) tensor (II Dusev 1968 [28])

3 Methods of solving all major problems of synthesis and analysis of gears are established

Finding the envelope of a one-parameter and two-parameter family of surfaces (HI

Ketov NI Kolchin FL Litvin NN Krylov EG Ginsburg ML Erikhov) as well as

multi-parameter envelope family of surfaces and lines in spatial gearings (IL Brodsky DT

Babichev)

Finding an wrapping family of surfaces (GI Sheveleva)

Identifying the geometry generation features such as tooth undercutting interference and

others (MG Segal II Dusev GI Sheveleva VI Goldfarb BA Chyorny)

Synthesis of gearing geometry (local ndash FL Litvin ML Erikhov LV Korostelyov SA

Lagutin VN Rubtsov BP Timofeev and nonlocal ndash KI Gulyaev BA Chyorny MG

Segal)

Computation of curvatures in gearings (NI Kolchin FL Litvin VM Vasilyev II

Dusev EG Ginsburg LV Korostelyov ML Erikhov A M Pavlov MG Segal)

Computation of other geometric-kinematic characteristics of the teeth contact (AK

Georgiev VI Goldfarb SA Lagutin MF Lenski)

Solution of the inverse problem of the gearing theory tooth meshing analysis (KI

Gulyaev FL Litvin MG Segal BP Timofeev GI Sheveleva)

80

The impact of manufacturing errors and assembling on quality of engagement synthesis

of toothed meshing insensitive to errors (ML Erikhov NG Lindtrop LV Korostelyov

NN Krylov LY Liburkin GI Sheveleva)

Numerous studies of specific gears are conducted based on theoretical developments and

established procedures The most important practical problems solved during this period

are

1 Principally new types of gearing have been discovered helical gear in which arcs of

circles with radii small difference are selected as the profiles of cross-sections ndash Novikov-

Wildhaber gear [17] and gears with closed contact lines where the load between teeth is

transferred through the grease wedged in a closed cavity between active surfaces due to

closure of the contact line (LV Korostelyev SA Lagutin [29])

2 Geometric problems of synthesis of cylindrical involute gears were almost exhaustively

resolved and brought into engineering practice geometric calculation (VA Gavrylenko

1969 [30]) selection of the optimum addendum modification coefficients by using blocking

circuits (MB Groman 1957 [31]) according to the atlas compiled and published under the

direction of IA Bolotovsky 1967 [32]

3 New types of gearings have been studied and introduced In this regard various problems

related to analysis and synthesis of the following common types of gears have been solved

Bevel (NI Kolchin and VV Boldyrev 1937 YS Davydov 1950 VI Bezrukov 1963

VM Denisov 1963 GI Sheveleva 1966 HF Kabatov and GA Lopato 1966 MG

Segal 1971 KI Gulyaev 1974 VN Syzrantsev 1975)

Hypoid (GI Apukhtin 1952 FL Litvin 1962 KM Pismanik 1964 II Dusev and VM

Vasilyev 1968 MG Segal 1971)

Cylindrical gear drives with Novikovrsquos gear (ML Novikov 1956 RV Fedyakin and

VA Chesnokov 1958 VN Kudryavtsev 1959 EG Roslivker 1964 NI Kolchin 1968

VN Sevryuk 1972 and others)

Revacycle spur bevel gear (GI Sheveleva 1966)

New worm gear design toroid (YaI Dicker 1948) globoid (PS Zak 1962) worm gear

drives (FL Litvin 1962 IS Krivenko 1967 LV Korostelyev and SA Lagutin 1973

etc) spiroid (S Golubkov 1959 AK Georgiev and VI Goldfarb 1972 and others)

Less common known types of gears have also been studied and implemented

Hyperboloid (KM Pismanik 1950)

Helical-bevel (LY Liburkin 1968)

Wave (EG Ginsburg 1969)

Cylindrical with arched and spiral teeth (ML Erikhov and VN Syzrantsev 1975)

4 Techniques of analysis and synthesis of gears with non-circular wheels are developed [33]

and their production is organized

5 A lot of works are published including a number of classic books on theory of gearing

YaI Dieker (1935) NI Kolchin (1937-1952) FL Litvin (1952-1968) YaS Davydov

81

(1950) VA Gavrylenko (1949-1969) ML Novikov (1958) VA Zalgaller (1975) LD

Chasovnikov (1969) IA Bolotovsky et al (1962-1967) VN Kudryavtsev (1949-1971)

VN Kedrinsky (1960-1967) KM Pismanik (1964-1967) PS Zack (1962) NF Kabatov

and GA Lopato (1966) VA Shishkov (1951) and many others FL Litvinrsquos monograph

[8] stands out among these works it was published in 1968 and still remains a handbook for

professionals in the theory of gearing

The book by VA Zalgaller Envelope Theory [34] which is not very big in volume is

characterized by depth the mathematical rigor and completeness of the argumentation

Note that the appreciation level of the activities under the second cycle is confirmed by the

fact that in 1958 ML Novikov was awarded the Lenin Prize ndash the most prestigious USSR

award presented to individuals for accomplishments in the professional field

The following facts also confirm that the Soviet scientists made a decisive contribution to

the theory of gearing as a science and the fact that the Soviet Union had prepared a large

number of highly qualified specialists in the theory of gearing

FL Litvinrsquos monograph Theory of Gearing which was written in the late 60rsquos is still the

main handbook for gear specialists while Litvin is regarded as the creator of the modern

theory of gearing not only in CIS countries but also around the world

This monograph revised and expanded was reprinted abroad in English co-written with

FL Litvinrsquos new foreign students [35]

Number of qualified experts in the theory of gearing (by the way which were not widely

known in the Soviet Union and the CIS back then) have emigrated to the Western countries

and are writing and publishing quite significant books in English on the theory of gearing

and geometry of gears (SP Radzevich AL Kapelevich SV Lunin)

Summarizing the second cycle let us quote SA Lagutin who most accurately reflect the

essence of this bright period [36] it was a period of storm and pressure in the development

of the gearing theory in Russia when a whole galaxy of brilliant researchers were working

in this area headed by NI Kolchin and FL Litvin By collaborating and competing with

each other in a few years they have built amazingly beautiful building of the new science at

the junction of differential geometry and mechanics of machines

33 Laying the foundations of computer-oriented theory of gearing

The main purpose of such a theory is to become a basis for the methods of computer

analysis synthesis design and manufacturing gear parts for gear engagement

By the mid-70rsquos theory of gearing as a science has reached adulthood the main priority and

theoretical problems of analysis and synthesis of gearing have been resolved The number of

innovative theoretical work began to decline Studies are getting closer to the production

and the theory of gearing acts primarily as a tool for solving specific engineering problems

Since the mid 70-ies of XX century the theory of gearing as well as the machine tool

industry has evolved concurrently in two directions global and Russian

82

The global development of the theory of gearing has taken place against the backdrop of

revolution experienced by the machine tool industry since the 80rsquos

First machines with semi-rigid connections partially controlled by computer began to

appear in developed countries and then complete automatic machines (multi-axis CNC

machines) appeared

At that time for example machines for processing bevel gears with circular teeth Phoenix

(Gleason) and WNC30 (Klingelnberg) were developed The creation of such machines

occurred in parallel with the development of new mathematical models for shaping parts on

multi-axis machines and testing the parts operability before their casting in the metal At

that time software systems LTCA (Gleason) and Kimos (Klingelnberg) were developed

which made it possible to solve the problem of synthesis and analysis of bevel gears with

circular teeth [37]

All developed countries pursue the global direction in the development of the theory of

gearing in the same manner and using similar approaches The following was used by the

gear specialists to solve the problems of analysis and synthesis

Methods of classical theory of gearing (with computer design of the geometry of any kind

of gears)

Techniques of non-differential analysis of gear ndash forming processes using universal as

well as specially developed software packages

Methods of boundary and finite elements (at the analysis of the contact interaction of

acting surfaces of the teeth)

Finite element methods and integral equations (at the analysis of the stress-strain state of

the teeth)

Numerical optimization methods (at the synthesis of geometry of acting and fillet surfaces

of teeth)

An expanded list of quality indicators of gearings including new ones the design

thickness of the oil film criteria of hot and cold seizure criteria for assessing the conditions

for the formation of an oil wedge indicators of vibration activity of the gearing and others

Designing gear drives was regarded as a complex problem requiring an agreed solution of a

group of interrelated tasks

Selection of design scheme of a gear

Synthesis of permissible geometry

Geometry optimization

Structural arrangement and evaluation of quality indicators

Identification and addressing the weaknesses

Designing technical processes of manufacture selection or synthesis of tools subsequent

optimization etc

The developed theory of gearing is known as Theory of Real Gearing in Russia Ukraine

and Belarus while abroad it is called ldquoIntegrated Gear Designrdquo (IGD) or Integrated Design

83

of Gears

Russian direction in the development of the theory of gearing has several specific features

attributable to the following objective circumstances

Firstly first clear signs of stagnation appeared in the USSR industry in the late 70rsquos

Secondly the number of graduate students reduced as the universities basically solved the

problem of teachers which they faced in the early 60rsquos due to a drastic increase in the

number of students being trained in engineering specialties And finally Russia lost the top

three main theorists in the field of the theory of gearing FL Litvin was forced to emigrate

to the USA LV Korostelyov died in a car crash YaS Davydov departed from active

research and subsequently left for the USA

And nevertheless in 15-20 years preceding the collapse of the USSR in 1991 the theory

and geometry of gearing in the Soviet Union was continuing to develop At that time new

centers specializing in different aspects of the theory of gearing were established Let us list

the most interesting in our opinion research topics at the end of the last century

- Issues of strength and solution of the tooth contact problem (EL Airapetov VN

Syzrantsev GI Sheveleva)

- Research on gear bending bending stresses calculation (GI Sheveleva VI Medvedev)

- Non-differential methods for the determination of the contact surfaces characteristics (VI

Goldfarb GI Sheveleva AE Volkov)

- Issues of design synthesis analysis and manufacturing spiroid gear drives (AK Georgiev

VI Goldfarb)

- Issues of design synthesis analysis and manufacturing worm gear drives (SA Lagutin

AI Sandler)

- Research of hypoid bevel gear drives with circular teeth (MG Segal GI Sheveleva VN

Syzrantsev)

- Research of gear drives with intermediate bodies (AE Belyaev)

- Research of helical-bevel gear drives (BA Lopatin)

- Development of methods for the synthesis of gear drives (MG Segal SA Lagutin GI

Sheveleva VI Medvedev VN Syzrantsev)

- Forming a theoretical framework for the development of universal programs for the

analysis of spatial working and technological meshings and the creation of corresponding

programs (DT Babichev)

As a result of these studies software systems were developed in the Soviet Union which

were aimed at solving the problems of synthesis and analysis primarily for bevel gears with

circular teeth The best known ones include PC Volga5 made under the direction of MG

Segal [38] and PC Expert created under the direction of GI Sheveleva [39]

The fact that MG Segal was the main developer of the PC Kimos (firm Klingelnberg) in

the 90rsquos confirms the high level of those developments

It should also be noted that a work on the selection of optimal schemes for multi-axis CNC

84

machines for processing gear was carried out in 1990 in Saratov (MG Segal LI Shejko

[40]) These developments have also been used by Klingelnberg

The researches (above all theoretical ones) continued after the collapse of the USSR in

Russia Ukraine and Belarus

At that time the development of the theory of gearing was distinguished by a high level of

theoretical studies based on the introduction of new geometric geometric-kinematic and

other concepts and development (on their basis) of new mathematical models methods and

algorithms for analysis and synthesis of the working and technological gear engagements

These works were performed mostly at their own initiative by highly qualified specialists-

theorists in the field of theory and geometry of working and technological gear meshing

Usually they were elderly university professors who were practically deprived of relations

with the machine-building industry after its stagnation during the collapse of the USSR

It should be noted that it is very difficult to distinguish the most important areas of research

in the modern theory of gearing As the poet said Great things are better seen from a

distance Therefore we will list the most interesting in our view theoretical works on the

development of the theory of gearing with greater focus on the Russian line of research

However we practically do not consider the works on gear geometry ndash they are too

numerous A fairly complete picture of the theoretical works of this period can be obtained

from the proceedings of symposia and conferences held in Kurgan (KMI) Izhevsk

(IzhSTU) and Sevastopol (KhPI Kharkov) The main directions in the development of the

theory of gearing and the most important theoretical results after 1970s include the

following

1 Introduction and use of new concepts such as

Meshing Space (SA Lagutin [41])

Wrapping surface (GI Sheveleva [39])

Fan wedge and normal beam accelerating of implantation (DT Babichev [42])

2 Development of methods for analyzing processes of generation

A new method of finding a singularity in the flat gearing (SA Lagutin) based on the

situation [43] return point at the gear profile occurs at the point in the line of engagement

in which the normal to this line intersects the axis of rotation of the pinion The method was

extended to the spatial gearing (AE Volkov [44])

3 Development of methods of synthesis

Based on the new concept of space of engagement and its properties This approach was

used during the synthesis of both spatial transmission (SA Lagutin [45]) and the cylindrical

(DT Babichev [46])

By using as objective function new criteria of load capacity - permissible contact

pressure(VI Medvedev [47]) the specific work of working surfaces of teeth (DT Babichev

[48]) and others

For bevel gears with small cross-axis angle (SA Lagutin [49] VI Medvedev [50])

Synthesis of gears considering technological limitations of the given production processes

85

(VI Medvedev [51] VN Syzrantsev [52])

By using and developing a method of synthesis of gears in generalizing parameters

originally proposed by EB Vulgakov for involute gears The method was modified by VL

Dorofeev - for involute and ON Tsukanov and BA Lopatin ndash for non-involute gears

(including cylinder-conical ones) [53]

By using variational methods of synthesis when the equation of an optimal surface of the

tooth and its coefficients are determined This approach was first applied apparently by

Alan Lebec [54] in the United States it was used in Ukraine [55] and being developed in

Russia where equal strength gears have been synthesized by using the method (by Hertz

contact strength) [46 56] and the method of synthesis of bevel gear with circular teeth

according to the criteria of minimal contact pressure and bending stresses while maintaining

the overall dimensions of the gear has been developed which is important for aviation

where the weight of the structure is crucial [57]

Increasing the bending strength of circular tooth bevel gears by optimizing the shape of

the tool [58]

Increasing the load-bearing capacity of high-speed heavy-duty cylindrical involute gears

Note that EB Vulgakov VL Dorofeev and AL Kapelevich have made a significant

contribution to the development of synthesis aviation gear in recent decades [59]

4 Development of methods of analysis of loaded gears considering multipairness of

contact

For bevel gears with circular teeth [60]

For spiroid gears [61]

5 Significant progress has been made in the methods of analysis synthesis design and

manufacture of worm gear transmissions

The main input in this field of gearing has been made by two groups of researchers under

the leadership of VI Goldfarb and SA Lagutin The techniques of minimizing meshing

errors and worm hob errors that appear when regrinding and relieving works are fulfilled

have been developed by SA Lagutin and AI Sandler The techniques of synthesis and

production of gears with localized contact were drilled worm gears (SA Lagutin AI

Sandler [62]) and spiroid ones (VI Goldfarb ES Trubachyov [63])

The drives with the increased load capacity were designed based on a study of meshing

space of non-orthogonal gears spiroid (ES Trubachyov [63]) and worm ones (VYu

Puzanov) Designing of spiroid transmissions is carried out using CAD ldquoSPDIAL+rdquo

developed by a group headed by VI Goldfarb Configurator of gearbox systems for

optimization structural synthesis of their structures is being created (OV Malina etal)

Unified worm hob cutters cutting gears for the drives with localized contact were designed

It became possible to cut the gear wheels in engagement with multiple-thread worm by a

single-pass mill (VI Goldfarb and his disciples)

In the Institute of Mechanics IzhSTU a group led by VI Goldfarb essentially laid the

foundation for a new Russian machine building sub-industry ndash construction of gearboxes for

86

isolation and control valves for pipelines

- Theoretical studies of spiroid and worm gears are at a high scientific level

- A modern design process is applied synthesis of perfect engagement synthesis of

localized contact simulation of the stress strain state analysis of real engagement under

load forecasting the state of transmission

- Three generations of dimension-type series of quarter-turn and multi-turn spiroid gear

drives are developed their production with modern quality control and acceptance tests is

organized

6 Application of unconventional gears and gearing helical-bevel gears (BA Lopatin [65])

transmissions with intermediate rolling bodies (AE Belyaev [66]) hydraulic and

pneumatic machines with non-circular gears (An-I-Kahn [67]) precessing transmissions

(IA Bostan [68] EI Tesker [69] VN Syzrantsev BA Lopatin) and other

7 Development of kinematic analysis methods of working and technological meshings Note

that modern designing is the computer designing This factor imposes high requirements to

the theory of gearing as the main mathematical basis for such designing We have to admit

that the classical theory of gearing does not fully comply with these demanding

requirements Thus according to Prof MG Segal who was working with Klingelnberg in

the last years of his life the head of the company prohibited to use differential methods ndash

the basis of the classical theory of gearing ndash in the programs being created The reason for

the ban was inadequacy of the results of computer simulation as compared to real processes

of formation Theoretical research aimed at creating computational models that are

adequate to the real processes of formation and contact of moving bodies were developed by

AE Volkov and VI Medvedev (Moscow) and DT Babichev (Tyumen)

To eliminate the phenomenon DT Babichev elaborated a unified kinematic method for

analysis of the processes of formation [70] based on the ldquotriadrdquo ruptures + envelopes + new

concepts of curvilinear coordinates As the result the cause of inadequacy between the

classical methods of the theory of gearing and real-life processes of formation was

established and rectified The developed kinematic method

Allows to find all the surfaces formed on the item at gear machining formed by smooth

surfaces and inflections of bodies including at advanceretraction of machine tool and in

secondary cutting areas

Has the reliability of non-differential methods but is superior to them in speed of

operation by two orders of magnitude which is confirmed by its partial use in CAD

ldquoSPDIAL +rdquo

Also allows to define the curvatures in gearing

8 Development of the system for assigning real ITS (Initial Tool Surfaces) and construction

of mathematical models for them [71] Real ITS is the set of all forming tools (pieces of

surfaces cutting and boundary edges and corners) for which uniform curvilinear coordinates

are introduced

9 By using the concept of ldquothe acceleration of installationrdquo new techniques for solving

87

multitude of tasks are created calculating the radii of curvature in the gearing identifying

cutting areas and thickness of the layers being cut by tool cutting edges and others (DT

Babichev [48])

For example based on the concept of the acceleration of installation a new basic formula

for calculating the reduced curvature in any normal sections at the contact point of two

moving bodies in contact along the line is created

1Rnp=-

where ɷrol is angular velocity of rolling bodies in the plane of the section in which the

curvature is calculated aB is the acceleration of installation The fundamental nature of the

obtained formula is that

1) in its generality it is commensurate with the kinematic formulas of Rodrigues and Freinet

known in differential geometry but it is intended for a different class of surfaces produced

in the process of formation by the rounding methods

2) curvature in any normal section of all surfaces formed by the rounding methods is

determined by only two scalar parameters and one of them (acceleration of installation)

does not depend on the direction of the section

It was also established that the sign of the acceleration of installation allow to make an

unambiguous judgement on the nature of the contact of bodies For example if aВgt 0 then

the envelope is formed inside the body of the generating element Acceleration of

installation allows to determine (ldquoincidentallyrdquo) the value of the radii of curvature and

faceting value across the whole surface formed by rounding at band- and flake-type

roughness

Thus over the past decade a substantial volume of theoretical knowledge to complete the

third cycle (creation of a computer-oriented theory of gearing) was accumulated

A lot of new notions are introduced and used in theory of gearing

Based on these new notions methods for analysis and synthesis of gear drives and cutter

tool meshings oriented at computer technologies have been developed and continue to be

improved

Intensive investigations to improve methods of optimization synthesis of gearing and to

develop methodologies of computer design and construction of gear boxes are performed

4 Problems and expected directions of the theory of gearing

Let us list the main problems in the gearing theory which in our opinion are the most

important

Problem 1 Creation of the theory of optimization synthesis of structures and parameters of

higher pairs of kinematic elements transmitting the motion and load at the preset and

optimal correlation of normal and friction forces At the present time theory of higher pairs

is being developed only as a pure geometrical science

88

Problem 2 Elaboration of methods of tooth optimal geometry synthesis oriented at the

modern processing technologies instead of traditional ones In this case a designer will have

to solve the variation problem with limitations providing for maximum possible load

capacity of gear drive in accordance with preselected criteria of performance efficiency

Problem 3 Development of methods for analysis of the process of the tooth preset surfaces

changeover taking into account the values of load tooth displacement manufacturing errors

of drive elements errors of relative position of engaging links dynamics of changeover

process

Problem 4 Creation of a unique interrelated complex of application software packages to

enable the designers and manufactures of gear drives to carry out optimization designing

engineering design preparation for production of various drives by meshing

Possible directions of development of the theory of gearing naturally follow from the afore-

described problems

CONCLUSIONS

In the second half of the XIX century the number and complexity of technical inventions of

various machines and mechanisms using the gear drives reached a critical mass and by

around 1890 the scientists had created the scientific basis of the theory of gearing And the

modern theory of gearing was formed by the beginning of the 1970rsquos

The third cycle of the gearing theory development which is oriented at computer technology

is underway

In our opinion the prospects for the development of theory of gearing as a part of the

theory of mechanisms and machines are higher as compared for example with the

linkages Firstly gears are more commonly used in cars than linkages Secondly the

theory of gearing is not only the theory of higher kinematic pairs - it is also the basis for the

theory of gear machining design

It is necessary to note that the current version of the paper is based on the paper published in

the first edition of the given Proceedings [72] but is as close as possible to the paper [73] by

the same authors This version of the article has been prepared by VE Starzhinsky

REFERENCES

1 Дильс ГА Античная техника Москва-Ленинград ОНТИ - Гос техн-теор изд-во ndash

1934 ndash 215 с (Diels GA Antique appliances - Moscow-Leningrad ONTI - Gos tehn-

teor Publ 1934 ndash 215 p)

2 Витрувий Десять книг об архитектуре ndash Москва laquoАрхитектура-Сraquo 2006 ndash 328 с

(Vitruvius Ten Books on Architecture ndash Moscov Architecture-C 2006 ndash 328 p)

3 Пипуныров ВН История часов с древнейших времен до наших дней - Москва

89

Наука 1982 ndash 496 c (Pipunyrov VN The clock story from ancient times to the present

day ndash Moscow Nauka 1982 ndash 496 p)

4 Академик ИИ Артоболевский Сборник Сост АМ Лепихов ndash М Знание 1983

ndash 176 c (Collection Comp AM Lepihov ndash Moscow Znanie 1983 ndash 176 p)

5 Чебышёв ПЛ Избранные труды ndash М Изд-во АН СССР 1955 ndash 926 с (Chebyshjov

PL Selected Works ndash Moscow AN SSSR 1955 ndash 926 p)

6 Рёло Ф Теоретическая кинематика 1875 (Relo F Theoretical Kinematics 1875)

7 Портретная галерея выдающихся инженеров и ученых в области зубчатых передач

ndash Сборник докладов научно-технической конференции с международным участием

Теория и практика зубчатых передач и редукторостроения Ижевск 2008 ndash C 378-

395 (Portrait Gallery of Disting wished Engineers and Scientist in Gearing ndash Proceedings

of Scientific-Engineering Conference with International Participation Theory and Practice

of Gearing and Reducer Building Izhevsk 2008 ndash P 378-395)

8 Литвин ФЛ Теория зубчатых зацеплений ndash М Наука 1968 ndash 584 с (Litvin FL

Theory of gearing ndash Moscow Nauka 1968 ndash 584 p)

9 Механика машин вып 45 ndash Москва Наука 1974 (Mechanics of machines No 45 ndash

Moscow Nauka 1974)

10 Willis R Principles of Mechanism ndash Cambridge London 1841

11 Гохман ХИ Теория зацеплений обобщенная и развитая путем анализа Дисс

магистра механики Одесса ndash 1886 ndash 232 с (Hokhman HI Link Theory generalized and

developed by analyzing Diss mastermechanic Odessa 1886 ndash 232 p)

12 Шишков ВА Образование поверхностей резанием по методу обкатки ndash Москва

Машгиз 1951 ndash 150 с (Shishkov VA Formation of surface machining by burnishing

method ndash Moscow Mashgiz 1951 ndash 150 p)

13 Вильдгабер Э Основы зацепления конических и гипоидных передач ndash Машгиз

1948 ndash 236 с (Vildgaber Je Principles of engagement bevel and hypoid gears ndash Moscow

Mashgiz 1948 ndash 236 p)

14 Baxter ML Basic Geometry and Tooth Contact of Hypoid Gears ldquoIndustrial

Mathematicsrdquo ndash 1961 ndash No 11 ndash P 19-42

15 Шевелева ГИ Алгоритм численного расчета обрабатываемой поверхности Станки

и инструмент ndash 1969 ndash 8 ndash C17-20 (Sheveleva GI Algorithm for the numerical

calculation of the treated surface Machines and Tooling ndash 1969 ndash No 8 ndash P 17-20)

16 Николаев АФ Диаграмма винта и ее применение к определению сопряженных

линейчатых поверхностей с линейным касанием Труды семинара по ТММ вып 37

1950 ndash С52ndash106 (Nikolaev AF Diagram of the screw and its application to the

determination of conjugate ruled surfaces with a linear contact Proceedings of the

Seminar on TMM ndash 1950 ndash No 37 ndash P52-106)

17 Новиков МЛ Зубчатые передачи с новым зацеплением ndash М Изд ВВИА им

Жуковского 1958 ndash 186 с (Novikov ML Gears with a new engagement ndash Moscow

Publisher VVIA by named Zhukovsky 1958 ndash 186 p)

18 Давыдов ЯС Об одном обобщении метода Оливье для образования сопряженных

90

поверхностей в зубчатых передачах Сб laquoТеорияпередачвмашинахraquo М Машгиз

1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

75

industry emergence of new problems and their solution awareness formulation of new

theoretical propositions In our opinion the theory of gearing goes through three such

cycles two of them are completed while the third one is ongoing at the moment

The first cycle ndash creating the foundation for theory of gearing ndash began in antiquity gained

momentum in the XVIII century owing to works of Euler and L Camus and was enriched in

the XIX century by works of T Olivier R Willis and others Completion of the first cycle

by 1890 can be roughly related to the defense and publication of the masters thesis by HI

Hokhman (1851-1915) in 1886 in which the analytical solution of the main task of the

theory of gearing ndash finding the mating surface and determining its properties ndash is given

The second cycle ndash creating the classical theory of gearing ndash lasted for about 80 years and

was completed by early 70-ies of the XX century It can be assumed that the results of the

second cycle were finalized in 1968 by a monograph of FL Litvin [8] at Symposium on

gears in Leningrad in 1973 [9]

The third cycle ndash laying the groundwork for an updated theory of gearing and methods of

the gearing synthesis oriented at modern computer technologies Currently this cycle is not

completed yet although a lot of new challenges are accumulated and a number of topical

issues and unresolved problems are identified

Letrsquos consider the features of these three cycles of creation and development of the theory of

gearing

31 Laying the foundations of the theory of gearing

Theory of gearing like the majority of scientific disciplines is based on three points

An object of study and the basic concepts of the discipline

Methods and ways of working with the basic concepts

Basic laws of nature and of the given science which establish relationships between the

basic concepts These laws are often identified in the course of studies - in the form of

theorems mathematical formulas logical and computational models etc

The objects of study of the theory of gearing are

Higher kinematic pairs in the plane and space gear and cam mechanisms (working

engagement)

Cutting tools and processes in shaping gear treatment (technological engagement)

In the theory of gearing the basic concepts and ways of working with them are taken for

the most part from mathematics (line surface curvature etc) and mechanics (centroid

velocity acceleration force etc)

Basic laws and links between fundamental notions of the theory of gearing were identified

by mathematics and mechanics already in the XVIII-XIX centuries (L Euler L Camus F

Savary E Bobillier R Willis T Olivier HI Hokhman )

Member of the Russian Academy Leonhard Euler (1707-1783) discovered unique properties

76

of involute of circle and suggested using them in the gearing Note that currently more than

90 of all gears in the world are involute French astronomer Felix Savary (1797-1841) by

continuing the work of Euler revealed a relationship between the radii of curvature of the

tooth profiles in flat engagement with the radii of curvature of the centroid now known as

the Euler-Savary equation This unique equation is widely used nowadays On the basis of

the Euler-Savary equation French mathematician Etienne Bobillier (1798-1840) proposed a

geometrical construction for finding the centers of curvature profiles

The first scientists who were applied the scientific approach to study of gears were R Willis

and T Olivier English scientist R Willis was one of the first to apply a scientific approach

to the study of gearing He proved the fundamental theorem for plane gears ndash Willis [10]

theorem which in the modern interpretation reads as follows Common normal to the

profiles drawn at the point of tangency passes through the pole of engagement Willis

invented a special tool - odontograph - to define the geometry and type of drawing the teeth

and gears of different diameters and number of teeth

Scientific approach to gears formation goes back to the French mathematician and

mechanics Theodore Olivier (1793-1858) He formulated two ways of forming conjugated

gears which have not lost their generality and value up till now

The first Olivier method Generating surface Σ0 (eg rail or flat generating wheel) forms two

surfaces by rounding Σ1 on the gear and Σ2 on the wheel These surfaces are located at

different sides of the generating surface Σ0 (eg Σ1 is located at the top of Σ0 and Σ2 ndash at the

bottom of Σ0) Σ1 and Σ2 surface will be paired a linear contact (which occurs in cylindrical

and bevel gears) or touch points (eg helical gear) Most transmission with parallel and

intersecting axes ie cylindrical conical and helical-bevel ones are formed by this method

The first Olivier method was rarely used in gears with intersecting axes because it displays a

distinct tooth contact point which reduces the load capacity of the engagement

The second Olivier method Surface of one of the gears - for example Σ1 at the gear - is set

almost arbitrarily and the surface of the second gear - for example Σ2 at the wheel ndash is set

as an envelope to one-parameter family of surfaces Σ1 In general contact between Σ1 and

Σ2 will be linear Basically transmissions with intersecting axes including the worm gears

are formed according to this method

In the XIX century cycloidal engagement becomes widespread The work of the French

mathematician Charles Etienne Louis Camus (1699-1768) has become the basis for the

design of such gears Camusrsquo theorem states that paths of the same point of the auxiliary

centroid which is rolled along the centroids of meshing gears may be chosen as mating

teeth

Chaim Iegudovich Hokhmanrsquos [11] dissertation published in 1886 can be considered as the

work that summarizes the steps of creating the foundations for the theory of gearing He

developed a framework for the analytical theory of planar and spatial gearing Hokhman

created a new method for finding the envelope surfaces and lines of contact with those

surfaces which allowed to initially determine the line of contact of mutually enveloped

surfaces in any system of coordinates associated with any link of working or technological

77

engagement This simplifies finding the envelope surface as compared to classical methods

in mechanics and differential geometry

By the end of the XIX century the appearance of the fundamental principles of analytical

theory of gearing marked the end of the first cycle of development of the theory of gearing

These principles include

Basic concepts and methods of classical mechanics analytical and differential geometry

Two principles of formation of mating gears proposed by Olivier

Euler-Savary equation and Bobillierrsquos construction reflecting the relationship between the

centroid and the curvatures of mating profiles in plane gears

Hochman developed a method for finding the envelope profiles and surfaces as well as

points and lines of contact of mutually enveloped lines and surfaces in the plane and spatial

working and technological gears

32 Creation of the classical theory of gearing

The framework of analytical theory of gearing developed by the end of the XIX century has

become the basis for solving practical problems which were posed by the thriving industry

for the science

Late XIX amp early XX century had a rich history of inventions of new types of

transmissions machines tools and machine gears Conventionally these inventions can be

divided into two areas machinery and tools for forming gears based on engagement of the

mating surfaces and machines and tools for forming gears with non-conjugated surfaces of

teeth

The first approach is based on the Olivier principles

In the period from 1890 to 1920 the following technologies and machines for production of

gears based on the form-generating method were invented and implemented

- Machines for bevel gears including the ones circular teeth (JE Gleason)

- Machines for grinding involute profiles of gear cutters (E Fellows)

- Machines for cutting spur and helical gears with worm milling cutters (RH Pfauter)

- Technology for manufacturing globoid worm gear (SI Cohn and FW Lorenz)

- Involute worm gear based on the application of involute helical surface as the surface of

the worm mill thread (FD Bostock and P Brown)

These and many other inventions have set the task of generalization of the gear-forming

theory based on engagement of the mating surfaces Decisive role in complementing and

developing the Olivierrsquos principles belongs to Russian scientists AF Nikolaev (1901-

1957) YaS Davydov (1914-2003) and ML Erikhov (1937-2002) They used an auxiliary

(generating) surface to form the mating surfaces ML Novikov (1915-1957) proposed a

fundamentally different principle of forming the mating gears by moving (according to a

certain law) the contact point of two profiles along the line of engagement of the

78

synthesized transmission

All these principles are based on the theory of envelopes which was scientifically and

methodologically completed (at that period of time) in YaS Davydovrsquos VA Shishkovrsquos

and FL Litvinrsquos works Almost simultaneously and independently they proposed a method

for finding the kinematic envelope in which the meshing condition equation is used VN = 0

[8] At this time VA Shishkov [12] introduced a new concept - implementation speed Vn

equal to the scalar product Vn = V12n which became an effective tool in the study of gear

cutting tools working according to the form-generating method It became the basis of the

kinematic method for the synthesis and analysis of gearing in the second half of the XX

century

Ernest Wildhaber (1893-1979) a talented engineer and inventor of the company The

Gleason Works can be regarded as the founder of the second direction In 1927 he

proposed a method of forming hypoid gears and in 1930rsquos he patented Revacycle - the most

productive method (at that time) for spur bevel gears forming [13] Methods of forming

these transmissions are not based on Olivierrsquos principles E Wildhaber introduced gears

with non-conjugated tooth surfaces ndash transmissions with approximate meshing Basically

these gears cannot transmit rotation with constant gear ratio but the degree of deviation

from a constant gear ratio can be minimized by the targeted selection of values of gear

treatment process parameters Thus Wildhaber who abandoned the form-generating

method proved that there were possibilities of creating highly effective machining

processes for gears with non-conjugated tooth surfaces and thus initiated the theoretical

study of such transmissions

Active development of the theory of approximate meshing began after the 2nd World War

both in the US and the Soviet Union As the result the basic principle of the formation of

non-conjugate surfaces was formulated independently in the works of ML Baxter [14] and

FL Litvin [8] according to the principle the graph of deviation from the angular position

of the driven wheel from its position upon engagement of strictly conjugate surfaces is a

function similar to a parabola with the downward branches

At the same time it became clear that in order to meet challenges of synthesis and analysis

of gearing built on non-conjugated surfaces it is required to develop new mathematical

methods and models First mathematical models for studying gearing and computer

programs based on them appeared almost simultaneously in the US and the USSR

In the US TCA software package for the synthesis and analysis of hypoid gears [14] was

created under supervision of ML Baxter (1914-1994) chief engineer and researcher of The

Gleason Works

In the 1960rsquos methods for the synthesis of approximate gearing began to develop with the

advent of computers in the Soviet Union At first a software package for analysis and

synthesis of Revacycle spur bevel gear [9 p30-36] which included a numerical algorithm

for calculating the surface as an enveloping surface without using the theory of envelopes

[15] was developed at the Moscow Tooling and Machining Institute (STANKIN) under the

leadership of GI Sheveleva (1929-2005)

79

Similar software packages were developed in Saratov (Special Design Bureau of Gear ndash

Cutting Machines) under the leadership of MG Segal (1931-2000) and Leningrad (LITMO)

under supervision of FL Litvin The work on creation of universal programs for the

computer-based studies of spatial links was held in Tyumen [9 p36-43]

In the second half of the XX century the USSR became a recognized leader in terms of

volume and theoretical studies devoted to the study of the geometry of gears and gear

cutting tools After the end of World War II theoretical activities on creation of new methods

of analysis and synthesis of the working and technological gears was booming for 25-30

years Efforts of leading scientists (NI Kolchin FL Litvin VA Shishkov ML Novikov

LV Korostelyov GI Sheveleva II Dusev YaS Davydov ML Erikhov and others) have

led to creation of a new branch of science of the mechanisms - the gearing theory

The Soviet Union played the key role in creating the classical theory of gearing in early

1970rsquos The most important results obtained through efforts of domestic scientists which

formed the basis of the modern theory of gearing are listed below

1 Olivierrsquos principles for forming conjugate gearing are supplemented and developed AF

Nikolaev [16] ML Novikov [17] YaS Davydov [18] ML Erikhov [19]

2 New methods for analysis of the geometry of gears are developed and the existing ones

are improved differential (NI Kolchin the main publication of the year ndash 1957 [20])

screw (AF Nikolaev 1950 [16] KM Pismanik 1950 [21] NI Kolchin 1963 [22] VS

Lyukshin 1968 [23]) kinematic (YaS Davydov 1950 [24] VA Shishkov 1951 [12] NN

Krylov 1953 [25] FL Litvin 1960 [26] ML Erikhov 1972 [19]) matrix (FL Litvin

1968 [9]) power series (GI Sheveleva 1969 [27]) non-differential (GI Sheveleva 1969

[15]) tensor (II Dusev 1968 [28])

3 Methods of solving all major problems of synthesis and analysis of gears are established

Finding the envelope of a one-parameter and two-parameter family of surfaces (HI

Ketov NI Kolchin FL Litvin NN Krylov EG Ginsburg ML Erikhov) as well as

multi-parameter envelope family of surfaces and lines in spatial gearings (IL Brodsky DT

Babichev)

Finding an wrapping family of surfaces (GI Sheveleva)

Identifying the geometry generation features such as tooth undercutting interference and

others (MG Segal II Dusev GI Sheveleva VI Goldfarb BA Chyorny)

Synthesis of gearing geometry (local ndash FL Litvin ML Erikhov LV Korostelyov SA

Lagutin VN Rubtsov BP Timofeev and nonlocal ndash KI Gulyaev BA Chyorny MG

Segal)

Computation of curvatures in gearings (NI Kolchin FL Litvin VM Vasilyev II

Dusev EG Ginsburg LV Korostelyov ML Erikhov A M Pavlov MG Segal)

Computation of other geometric-kinematic characteristics of the teeth contact (AK

Georgiev VI Goldfarb SA Lagutin MF Lenski)

Solution of the inverse problem of the gearing theory tooth meshing analysis (KI

Gulyaev FL Litvin MG Segal BP Timofeev GI Sheveleva)

80

The impact of manufacturing errors and assembling on quality of engagement synthesis

of toothed meshing insensitive to errors (ML Erikhov NG Lindtrop LV Korostelyov

NN Krylov LY Liburkin GI Sheveleva)

Numerous studies of specific gears are conducted based on theoretical developments and

established procedures The most important practical problems solved during this period

are

1 Principally new types of gearing have been discovered helical gear in which arcs of

circles with radii small difference are selected as the profiles of cross-sections ndash Novikov-

Wildhaber gear [17] and gears with closed contact lines where the load between teeth is

transferred through the grease wedged in a closed cavity between active surfaces due to

closure of the contact line (LV Korostelyev SA Lagutin [29])

2 Geometric problems of synthesis of cylindrical involute gears were almost exhaustively

resolved and brought into engineering practice geometric calculation (VA Gavrylenko

1969 [30]) selection of the optimum addendum modification coefficients by using blocking

circuits (MB Groman 1957 [31]) according to the atlas compiled and published under the

direction of IA Bolotovsky 1967 [32]

3 New types of gearings have been studied and introduced In this regard various problems

related to analysis and synthesis of the following common types of gears have been solved

Bevel (NI Kolchin and VV Boldyrev 1937 YS Davydov 1950 VI Bezrukov 1963

VM Denisov 1963 GI Sheveleva 1966 HF Kabatov and GA Lopato 1966 MG

Segal 1971 KI Gulyaev 1974 VN Syzrantsev 1975)

Hypoid (GI Apukhtin 1952 FL Litvin 1962 KM Pismanik 1964 II Dusev and VM

Vasilyev 1968 MG Segal 1971)

Cylindrical gear drives with Novikovrsquos gear (ML Novikov 1956 RV Fedyakin and

VA Chesnokov 1958 VN Kudryavtsev 1959 EG Roslivker 1964 NI Kolchin 1968

VN Sevryuk 1972 and others)

Revacycle spur bevel gear (GI Sheveleva 1966)

New worm gear design toroid (YaI Dicker 1948) globoid (PS Zak 1962) worm gear

drives (FL Litvin 1962 IS Krivenko 1967 LV Korostelyev and SA Lagutin 1973

etc) spiroid (S Golubkov 1959 AK Georgiev and VI Goldfarb 1972 and others)

Less common known types of gears have also been studied and implemented

Hyperboloid (KM Pismanik 1950)

Helical-bevel (LY Liburkin 1968)

Wave (EG Ginsburg 1969)

Cylindrical with arched and spiral teeth (ML Erikhov and VN Syzrantsev 1975)

4 Techniques of analysis and synthesis of gears with non-circular wheels are developed [33]

and their production is organized

5 A lot of works are published including a number of classic books on theory of gearing

YaI Dieker (1935) NI Kolchin (1937-1952) FL Litvin (1952-1968) YaS Davydov

81

(1950) VA Gavrylenko (1949-1969) ML Novikov (1958) VA Zalgaller (1975) LD

Chasovnikov (1969) IA Bolotovsky et al (1962-1967) VN Kudryavtsev (1949-1971)

VN Kedrinsky (1960-1967) KM Pismanik (1964-1967) PS Zack (1962) NF Kabatov

and GA Lopato (1966) VA Shishkov (1951) and many others FL Litvinrsquos monograph

[8] stands out among these works it was published in 1968 and still remains a handbook for

professionals in the theory of gearing

The book by VA Zalgaller Envelope Theory [34] which is not very big in volume is

characterized by depth the mathematical rigor and completeness of the argumentation

Note that the appreciation level of the activities under the second cycle is confirmed by the

fact that in 1958 ML Novikov was awarded the Lenin Prize ndash the most prestigious USSR

award presented to individuals for accomplishments in the professional field

The following facts also confirm that the Soviet scientists made a decisive contribution to

the theory of gearing as a science and the fact that the Soviet Union had prepared a large

number of highly qualified specialists in the theory of gearing

FL Litvinrsquos monograph Theory of Gearing which was written in the late 60rsquos is still the

main handbook for gear specialists while Litvin is regarded as the creator of the modern

theory of gearing not only in CIS countries but also around the world

This monograph revised and expanded was reprinted abroad in English co-written with

FL Litvinrsquos new foreign students [35]

Number of qualified experts in the theory of gearing (by the way which were not widely

known in the Soviet Union and the CIS back then) have emigrated to the Western countries

and are writing and publishing quite significant books in English on the theory of gearing

and geometry of gears (SP Radzevich AL Kapelevich SV Lunin)

Summarizing the second cycle let us quote SA Lagutin who most accurately reflect the

essence of this bright period [36] it was a period of storm and pressure in the development

of the gearing theory in Russia when a whole galaxy of brilliant researchers were working

in this area headed by NI Kolchin and FL Litvin By collaborating and competing with

each other in a few years they have built amazingly beautiful building of the new science at

the junction of differential geometry and mechanics of machines

33 Laying the foundations of computer-oriented theory of gearing

The main purpose of such a theory is to become a basis for the methods of computer

analysis synthesis design and manufacturing gear parts for gear engagement

By the mid-70rsquos theory of gearing as a science has reached adulthood the main priority and

theoretical problems of analysis and synthesis of gearing have been resolved The number of

innovative theoretical work began to decline Studies are getting closer to the production

and the theory of gearing acts primarily as a tool for solving specific engineering problems

Since the mid 70-ies of XX century the theory of gearing as well as the machine tool

industry has evolved concurrently in two directions global and Russian

82

The global development of the theory of gearing has taken place against the backdrop of

revolution experienced by the machine tool industry since the 80rsquos

First machines with semi-rigid connections partially controlled by computer began to

appear in developed countries and then complete automatic machines (multi-axis CNC

machines) appeared

At that time for example machines for processing bevel gears with circular teeth Phoenix

(Gleason) and WNC30 (Klingelnberg) were developed The creation of such machines

occurred in parallel with the development of new mathematical models for shaping parts on

multi-axis machines and testing the parts operability before their casting in the metal At

that time software systems LTCA (Gleason) and Kimos (Klingelnberg) were developed

which made it possible to solve the problem of synthesis and analysis of bevel gears with

circular teeth [37]

All developed countries pursue the global direction in the development of the theory of

gearing in the same manner and using similar approaches The following was used by the

gear specialists to solve the problems of analysis and synthesis

Methods of classical theory of gearing (with computer design of the geometry of any kind

of gears)

Techniques of non-differential analysis of gear ndash forming processes using universal as

well as specially developed software packages

Methods of boundary and finite elements (at the analysis of the contact interaction of

acting surfaces of the teeth)

Finite element methods and integral equations (at the analysis of the stress-strain state of

the teeth)

Numerical optimization methods (at the synthesis of geometry of acting and fillet surfaces

of teeth)

An expanded list of quality indicators of gearings including new ones the design

thickness of the oil film criteria of hot and cold seizure criteria for assessing the conditions

for the formation of an oil wedge indicators of vibration activity of the gearing and others

Designing gear drives was regarded as a complex problem requiring an agreed solution of a

group of interrelated tasks

Selection of design scheme of a gear

Synthesis of permissible geometry

Geometry optimization

Structural arrangement and evaluation of quality indicators

Identification and addressing the weaknesses

Designing technical processes of manufacture selection or synthesis of tools subsequent

optimization etc

The developed theory of gearing is known as Theory of Real Gearing in Russia Ukraine

and Belarus while abroad it is called ldquoIntegrated Gear Designrdquo (IGD) or Integrated Design

83

of Gears

Russian direction in the development of the theory of gearing has several specific features

attributable to the following objective circumstances

Firstly first clear signs of stagnation appeared in the USSR industry in the late 70rsquos

Secondly the number of graduate students reduced as the universities basically solved the

problem of teachers which they faced in the early 60rsquos due to a drastic increase in the

number of students being trained in engineering specialties And finally Russia lost the top

three main theorists in the field of the theory of gearing FL Litvin was forced to emigrate

to the USA LV Korostelyov died in a car crash YaS Davydov departed from active

research and subsequently left for the USA

And nevertheless in 15-20 years preceding the collapse of the USSR in 1991 the theory

and geometry of gearing in the Soviet Union was continuing to develop At that time new

centers specializing in different aspects of the theory of gearing were established Let us list

the most interesting in our opinion research topics at the end of the last century

- Issues of strength and solution of the tooth contact problem (EL Airapetov VN

Syzrantsev GI Sheveleva)

- Research on gear bending bending stresses calculation (GI Sheveleva VI Medvedev)

- Non-differential methods for the determination of the contact surfaces characteristics (VI

Goldfarb GI Sheveleva AE Volkov)

- Issues of design synthesis analysis and manufacturing spiroid gear drives (AK Georgiev

VI Goldfarb)

- Issues of design synthesis analysis and manufacturing worm gear drives (SA Lagutin

AI Sandler)

- Research of hypoid bevel gear drives with circular teeth (MG Segal GI Sheveleva VN

Syzrantsev)

- Research of gear drives with intermediate bodies (AE Belyaev)

- Research of helical-bevel gear drives (BA Lopatin)

- Development of methods for the synthesis of gear drives (MG Segal SA Lagutin GI

Sheveleva VI Medvedev VN Syzrantsev)

- Forming a theoretical framework for the development of universal programs for the

analysis of spatial working and technological meshings and the creation of corresponding

programs (DT Babichev)

As a result of these studies software systems were developed in the Soviet Union which

were aimed at solving the problems of synthesis and analysis primarily for bevel gears with

circular teeth The best known ones include PC Volga5 made under the direction of MG

Segal [38] and PC Expert created under the direction of GI Sheveleva [39]

The fact that MG Segal was the main developer of the PC Kimos (firm Klingelnberg) in

the 90rsquos confirms the high level of those developments

It should also be noted that a work on the selection of optimal schemes for multi-axis CNC

84

machines for processing gear was carried out in 1990 in Saratov (MG Segal LI Shejko

[40]) These developments have also been used by Klingelnberg

The researches (above all theoretical ones) continued after the collapse of the USSR in

Russia Ukraine and Belarus

At that time the development of the theory of gearing was distinguished by a high level of

theoretical studies based on the introduction of new geometric geometric-kinematic and

other concepts and development (on their basis) of new mathematical models methods and

algorithms for analysis and synthesis of the working and technological gear engagements

These works were performed mostly at their own initiative by highly qualified specialists-

theorists in the field of theory and geometry of working and technological gear meshing

Usually they were elderly university professors who were practically deprived of relations

with the machine-building industry after its stagnation during the collapse of the USSR

It should be noted that it is very difficult to distinguish the most important areas of research

in the modern theory of gearing As the poet said Great things are better seen from a

distance Therefore we will list the most interesting in our view theoretical works on the

development of the theory of gearing with greater focus on the Russian line of research

However we practically do not consider the works on gear geometry ndash they are too

numerous A fairly complete picture of the theoretical works of this period can be obtained

from the proceedings of symposia and conferences held in Kurgan (KMI) Izhevsk

(IzhSTU) and Sevastopol (KhPI Kharkov) The main directions in the development of the

theory of gearing and the most important theoretical results after 1970s include the

following

1 Introduction and use of new concepts such as

Meshing Space (SA Lagutin [41])

Wrapping surface (GI Sheveleva [39])

Fan wedge and normal beam accelerating of implantation (DT Babichev [42])

2 Development of methods for analyzing processes of generation

A new method of finding a singularity in the flat gearing (SA Lagutin) based on the

situation [43] return point at the gear profile occurs at the point in the line of engagement

in which the normal to this line intersects the axis of rotation of the pinion The method was

extended to the spatial gearing (AE Volkov [44])

3 Development of methods of synthesis

Based on the new concept of space of engagement and its properties This approach was

used during the synthesis of both spatial transmission (SA Lagutin [45]) and the cylindrical

(DT Babichev [46])

By using as objective function new criteria of load capacity - permissible contact

pressure(VI Medvedev [47]) the specific work of working surfaces of teeth (DT Babichev

[48]) and others

For bevel gears with small cross-axis angle (SA Lagutin [49] VI Medvedev [50])

Synthesis of gears considering technological limitations of the given production processes

85

(VI Medvedev [51] VN Syzrantsev [52])

By using and developing a method of synthesis of gears in generalizing parameters

originally proposed by EB Vulgakov for involute gears The method was modified by VL

Dorofeev - for involute and ON Tsukanov and BA Lopatin ndash for non-involute gears

(including cylinder-conical ones) [53]

By using variational methods of synthesis when the equation of an optimal surface of the

tooth and its coefficients are determined This approach was first applied apparently by

Alan Lebec [54] in the United States it was used in Ukraine [55] and being developed in

Russia where equal strength gears have been synthesized by using the method (by Hertz

contact strength) [46 56] and the method of synthesis of bevel gear with circular teeth

according to the criteria of minimal contact pressure and bending stresses while maintaining

the overall dimensions of the gear has been developed which is important for aviation

where the weight of the structure is crucial [57]

Increasing the bending strength of circular tooth bevel gears by optimizing the shape of

the tool [58]

Increasing the load-bearing capacity of high-speed heavy-duty cylindrical involute gears

Note that EB Vulgakov VL Dorofeev and AL Kapelevich have made a significant

contribution to the development of synthesis aviation gear in recent decades [59]

4 Development of methods of analysis of loaded gears considering multipairness of

contact

For bevel gears with circular teeth [60]

For spiroid gears [61]

5 Significant progress has been made in the methods of analysis synthesis design and

manufacture of worm gear transmissions

The main input in this field of gearing has been made by two groups of researchers under

the leadership of VI Goldfarb and SA Lagutin The techniques of minimizing meshing

errors and worm hob errors that appear when regrinding and relieving works are fulfilled

have been developed by SA Lagutin and AI Sandler The techniques of synthesis and

production of gears with localized contact were drilled worm gears (SA Lagutin AI

Sandler [62]) and spiroid ones (VI Goldfarb ES Trubachyov [63])

The drives with the increased load capacity were designed based on a study of meshing

space of non-orthogonal gears spiroid (ES Trubachyov [63]) and worm ones (VYu

Puzanov) Designing of spiroid transmissions is carried out using CAD ldquoSPDIAL+rdquo

developed by a group headed by VI Goldfarb Configurator of gearbox systems for

optimization structural synthesis of their structures is being created (OV Malina etal)

Unified worm hob cutters cutting gears for the drives with localized contact were designed

It became possible to cut the gear wheels in engagement with multiple-thread worm by a

single-pass mill (VI Goldfarb and his disciples)

In the Institute of Mechanics IzhSTU a group led by VI Goldfarb essentially laid the

foundation for a new Russian machine building sub-industry ndash construction of gearboxes for

86

isolation and control valves for pipelines

- Theoretical studies of spiroid and worm gears are at a high scientific level

- A modern design process is applied synthesis of perfect engagement synthesis of

localized contact simulation of the stress strain state analysis of real engagement under

load forecasting the state of transmission

- Three generations of dimension-type series of quarter-turn and multi-turn spiroid gear

drives are developed their production with modern quality control and acceptance tests is

organized

6 Application of unconventional gears and gearing helical-bevel gears (BA Lopatin [65])

transmissions with intermediate rolling bodies (AE Belyaev [66]) hydraulic and

pneumatic machines with non-circular gears (An-I-Kahn [67]) precessing transmissions

(IA Bostan [68] EI Tesker [69] VN Syzrantsev BA Lopatin) and other

7 Development of kinematic analysis methods of working and technological meshings Note

that modern designing is the computer designing This factor imposes high requirements to

the theory of gearing as the main mathematical basis for such designing We have to admit

that the classical theory of gearing does not fully comply with these demanding

requirements Thus according to Prof MG Segal who was working with Klingelnberg in

the last years of his life the head of the company prohibited to use differential methods ndash

the basis of the classical theory of gearing ndash in the programs being created The reason for

the ban was inadequacy of the results of computer simulation as compared to real processes

of formation Theoretical research aimed at creating computational models that are

adequate to the real processes of formation and contact of moving bodies were developed by

AE Volkov and VI Medvedev (Moscow) and DT Babichev (Tyumen)

To eliminate the phenomenon DT Babichev elaborated a unified kinematic method for

analysis of the processes of formation [70] based on the ldquotriadrdquo ruptures + envelopes + new

concepts of curvilinear coordinates As the result the cause of inadequacy between the

classical methods of the theory of gearing and real-life processes of formation was

established and rectified The developed kinematic method

Allows to find all the surfaces formed on the item at gear machining formed by smooth

surfaces and inflections of bodies including at advanceretraction of machine tool and in

secondary cutting areas

Has the reliability of non-differential methods but is superior to them in speed of

operation by two orders of magnitude which is confirmed by its partial use in CAD

ldquoSPDIAL +rdquo

Also allows to define the curvatures in gearing

8 Development of the system for assigning real ITS (Initial Tool Surfaces) and construction

of mathematical models for them [71] Real ITS is the set of all forming tools (pieces of

surfaces cutting and boundary edges and corners) for which uniform curvilinear coordinates

are introduced

9 By using the concept of ldquothe acceleration of installationrdquo new techniques for solving

87

multitude of tasks are created calculating the radii of curvature in the gearing identifying

cutting areas and thickness of the layers being cut by tool cutting edges and others (DT

Babichev [48])

For example based on the concept of the acceleration of installation a new basic formula

for calculating the reduced curvature in any normal sections at the contact point of two

moving bodies in contact along the line is created

1Rnp=-

where ɷrol is angular velocity of rolling bodies in the plane of the section in which the

curvature is calculated aB is the acceleration of installation The fundamental nature of the

obtained formula is that

1) in its generality it is commensurate with the kinematic formulas of Rodrigues and Freinet

known in differential geometry but it is intended for a different class of surfaces produced

in the process of formation by the rounding methods

2) curvature in any normal section of all surfaces formed by the rounding methods is

determined by only two scalar parameters and one of them (acceleration of installation)

does not depend on the direction of the section

It was also established that the sign of the acceleration of installation allow to make an

unambiguous judgement on the nature of the contact of bodies For example if aВgt 0 then

the envelope is formed inside the body of the generating element Acceleration of

installation allows to determine (ldquoincidentallyrdquo) the value of the radii of curvature and

faceting value across the whole surface formed by rounding at band- and flake-type

roughness

Thus over the past decade a substantial volume of theoretical knowledge to complete the

third cycle (creation of a computer-oriented theory of gearing) was accumulated

A lot of new notions are introduced and used in theory of gearing

Based on these new notions methods for analysis and synthesis of gear drives and cutter

tool meshings oriented at computer technologies have been developed and continue to be

improved

Intensive investigations to improve methods of optimization synthesis of gearing and to

develop methodologies of computer design and construction of gear boxes are performed

4 Problems and expected directions of the theory of gearing

Let us list the main problems in the gearing theory which in our opinion are the most

important

Problem 1 Creation of the theory of optimization synthesis of structures and parameters of

higher pairs of kinematic elements transmitting the motion and load at the preset and

optimal correlation of normal and friction forces At the present time theory of higher pairs

is being developed only as a pure geometrical science

88

Problem 2 Elaboration of methods of tooth optimal geometry synthesis oriented at the

modern processing technologies instead of traditional ones In this case a designer will have

to solve the variation problem with limitations providing for maximum possible load

capacity of gear drive in accordance with preselected criteria of performance efficiency

Problem 3 Development of methods for analysis of the process of the tooth preset surfaces

changeover taking into account the values of load tooth displacement manufacturing errors

of drive elements errors of relative position of engaging links dynamics of changeover

process

Problem 4 Creation of a unique interrelated complex of application software packages to

enable the designers and manufactures of gear drives to carry out optimization designing

engineering design preparation for production of various drives by meshing

Possible directions of development of the theory of gearing naturally follow from the afore-

described problems

CONCLUSIONS

In the second half of the XIX century the number and complexity of technical inventions of

various machines and mechanisms using the gear drives reached a critical mass and by

around 1890 the scientists had created the scientific basis of the theory of gearing And the

modern theory of gearing was formed by the beginning of the 1970rsquos

The third cycle of the gearing theory development which is oriented at computer technology

is underway

In our opinion the prospects for the development of theory of gearing as a part of the

theory of mechanisms and machines are higher as compared for example with the

linkages Firstly gears are more commonly used in cars than linkages Secondly the

theory of gearing is not only the theory of higher kinematic pairs - it is also the basis for the

theory of gear machining design

It is necessary to note that the current version of the paper is based on the paper published in

the first edition of the given Proceedings [72] but is as close as possible to the paper [73] by

the same authors This version of the article has been prepared by VE Starzhinsky

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2 Витрувий Десять книг об архитектуре ndash Москва laquoАрхитектура-Сraquo 2006 ndash 328 с

(Vitruvius Ten Books on Architecture ndash Moscov Architecture-C 2006 ndash 328 p)

3 Пипуныров ВН История часов с древнейших времен до наших дней - Москва

89

Наука 1982 ndash 496 c (Pipunyrov VN The clock story from ancient times to the present

day ndash Moscow Nauka 1982 ndash 496 p)

4 Академик ИИ Артоболевский Сборник Сост АМ Лепихов ndash М Знание 1983

ndash 176 c (Collection Comp AM Lepihov ndash Moscow Znanie 1983 ndash 176 p)

5 Чебышёв ПЛ Избранные труды ndash М Изд-во АН СССР 1955 ndash 926 с (Chebyshjov

PL Selected Works ndash Moscow AN SSSR 1955 ndash 926 p)

6 Рёло Ф Теоретическая кинематика 1875 (Relo F Theoretical Kinematics 1875)

7 Портретная галерея выдающихся инженеров и ученых в области зубчатых передач

ndash Сборник докладов научно-технической конференции с международным участием

Теория и практика зубчатых передач и редукторостроения Ижевск 2008 ndash C 378-

395 (Portrait Gallery of Disting wished Engineers and Scientist in Gearing ndash Proceedings

of Scientific-Engineering Conference with International Participation Theory and Practice

of Gearing and Reducer Building Izhevsk 2008 ndash P 378-395)

8 Литвин ФЛ Теория зубчатых зацеплений ndash М Наука 1968 ndash 584 с (Litvin FL

Theory of gearing ndash Moscow Nauka 1968 ndash 584 p)

9 Механика машин вып 45 ndash Москва Наука 1974 (Mechanics of machines No 45 ndash

Moscow Nauka 1974)

10 Willis R Principles of Mechanism ndash Cambridge London 1841

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магистра механики Одесса ndash 1886 ndash 232 с (Hokhman HI Link Theory generalized and

developed by analyzing Diss mastermechanic Odessa 1886 ndash 232 p)

12 Шишков ВА Образование поверхностей резанием по методу обкатки ndash Москва

Машгиз 1951 ndash 150 с (Shishkov VA Formation of surface machining by burnishing

method ndash Moscow Mashgiz 1951 ndash 150 p)

13 Вильдгабер Э Основы зацепления конических и гипоидных передач ndash Машгиз

1948 ndash 236 с (Vildgaber Je Principles of engagement bevel and hypoid gears ndash Moscow

Mashgiz 1948 ndash 236 p)

14 Baxter ML Basic Geometry and Tooth Contact of Hypoid Gears ldquoIndustrial

Mathematicsrdquo ndash 1961 ndash No 11 ndash P 19-42

15 Шевелева ГИ Алгоритм численного расчета обрабатываемой поверхности Станки

и инструмент ndash 1969 ndash 8 ndash C17-20 (Sheveleva GI Algorithm for the numerical

calculation of the treated surface Machines and Tooling ndash 1969 ndash No 8 ndash P 17-20)

16 Николаев АФ Диаграмма винта и ее применение к определению сопряженных

линейчатых поверхностей с линейным касанием Труды семинара по ТММ вып 37

1950 ndash С52ndash106 (Nikolaev AF Diagram of the screw and its application to the

determination of conjugate ruled surfaces with a linear contact Proceedings of the

Seminar on TMM ndash 1950 ndash No 37 ndash P52-106)

17 Новиков МЛ Зубчатые передачи с новым зацеплением ndash М Изд ВВИА им

Жуковского 1958 ndash 186 с (Novikov ML Gears with a new engagement ndash Moscow

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18 Давыдов ЯС Об одном обобщении метода Оливье для образования сопряженных

90

поверхностей в зубчатых передачах Сб laquoТеорияпередачвмашинахraquo М Машгиз

1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

76

of involute of circle and suggested using them in the gearing Note that currently more than

90 of all gears in the world are involute French astronomer Felix Savary (1797-1841) by

continuing the work of Euler revealed a relationship between the radii of curvature of the

tooth profiles in flat engagement with the radii of curvature of the centroid now known as

the Euler-Savary equation This unique equation is widely used nowadays On the basis of

the Euler-Savary equation French mathematician Etienne Bobillier (1798-1840) proposed a

geometrical construction for finding the centers of curvature profiles

The first scientists who were applied the scientific approach to study of gears were R Willis

and T Olivier English scientist R Willis was one of the first to apply a scientific approach

to the study of gearing He proved the fundamental theorem for plane gears ndash Willis [10]

theorem which in the modern interpretation reads as follows Common normal to the

profiles drawn at the point of tangency passes through the pole of engagement Willis

invented a special tool - odontograph - to define the geometry and type of drawing the teeth

and gears of different diameters and number of teeth

Scientific approach to gears formation goes back to the French mathematician and

mechanics Theodore Olivier (1793-1858) He formulated two ways of forming conjugated

gears which have not lost their generality and value up till now

The first Olivier method Generating surface Σ0 (eg rail or flat generating wheel) forms two

surfaces by rounding Σ1 on the gear and Σ2 on the wheel These surfaces are located at

different sides of the generating surface Σ0 (eg Σ1 is located at the top of Σ0 and Σ2 ndash at the

bottom of Σ0) Σ1 and Σ2 surface will be paired a linear contact (which occurs in cylindrical

and bevel gears) or touch points (eg helical gear) Most transmission with parallel and

intersecting axes ie cylindrical conical and helical-bevel ones are formed by this method

The first Olivier method was rarely used in gears with intersecting axes because it displays a

distinct tooth contact point which reduces the load capacity of the engagement

The second Olivier method Surface of one of the gears - for example Σ1 at the gear - is set

almost arbitrarily and the surface of the second gear - for example Σ2 at the wheel ndash is set

as an envelope to one-parameter family of surfaces Σ1 In general contact between Σ1 and

Σ2 will be linear Basically transmissions with intersecting axes including the worm gears

are formed according to this method

In the XIX century cycloidal engagement becomes widespread The work of the French

mathematician Charles Etienne Louis Camus (1699-1768) has become the basis for the

design of such gears Camusrsquo theorem states that paths of the same point of the auxiliary

centroid which is rolled along the centroids of meshing gears may be chosen as mating

teeth

Chaim Iegudovich Hokhmanrsquos [11] dissertation published in 1886 can be considered as the

work that summarizes the steps of creating the foundations for the theory of gearing He

developed a framework for the analytical theory of planar and spatial gearing Hokhman

created a new method for finding the envelope surfaces and lines of contact with those

surfaces which allowed to initially determine the line of contact of mutually enveloped

surfaces in any system of coordinates associated with any link of working or technological

77

engagement This simplifies finding the envelope surface as compared to classical methods

in mechanics and differential geometry

By the end of the XIX century the appearance of the fundamental principles of analytical

theory of gearing marked the end of the first cycle of development of the theory of gearing

These principles include

Basic concepts and methods of classical mechanics analytical and differential geometry

Two principles of formation of mating gears proposed by Olivier

Euler-Savary equation and Bobillierrsquos construction reflecting the relationship between the

centroid and the curvatures of mating profiles in plane gears

Hochman developed a method for finding the envelope profiles and surfaces as well as

points and lines of contact of mutually enveloped lines and surfaces in the plane and spatial

working and technological gears

32 Creation of the classical theory of gearing

The framework of analytical theory of gearing developed by the end of the XIX century has

become the basis for solving practical problems which were posed by the thriving industry

for the science

Late XIX amp early XX century had a rich history of inventions of new types of

transmissions machines tools and machine gears Conventionally these inventions can be

divided into two areas machinery and tools for forming gears based on engagement of the

mating surfaces and machines and tools for forming gears with non-conjugated surfaces of

teeth

The first approach is based on the Olivier principles

In the period from 1890 to 1920 the following technologies and machines for production of

gears based on the form-generating method were invented and implemented

- Machines for bevel gears including the ones circular teeth (JE Gleason)

- Machines for grinding involute profiles of gear cutters (E Fellows)

- Machines for cutting spur and helical gears with worm milling cutters (RH Pfauter)

- Technology for manufacturing globoid worm gear (SI Cohn and FW Lorenz)

- Involute worm gear based on the application of involute helical surface as the surface of

the worm mill thread (FD Bostock and P Brown)

These and many other inventions have set the task of generalization of the gear-forming

theory based on engagement of the mating surfaces Decisive role in complementing and

developing the Olivierrsquos principles belongs to Russian scientists AF Nikolaev (1901-

1957) YaS Davydov (1914-2003) and ML Erikhov (1937-2002) They used an auxiliary

(generating) surface to form the mating surfaces ML Novikov (1915-1957) proposed a

fundamentally different principle of forming the mating gears by moving (according to a

certain law) the contact point of two profiles along the line of engagement of the

78

synthesized transmission

All these principles are based on the theory of envelopes which was scientifically and

methodologically completed (at that period of time) in YaS Davydovrsquos VA Shishkovrsquos

and FL Litvinrsquos works Almost simultaneously and independently they proposed a method

for finding the kinematic envelope in which the meshing condition equation is used VN = 0

[8] At this time VA Shishkov [12] introduced a new concept - implementation speed Vn

equal to the scalar product Vn = V12n which became an effective tool in the study of gear

cutting tools working according to the form-generating method It became the basis of the

kinematic method for the synthesis and analysis of gearing in the second half of the XX

century

Ernest Wildhaber (1893-1979) a talented engineer and inventor of the company The

Gleason Works can be regarded as the founder of the second direction In 1927 he

proposed a method of forming hypoid gears and in 1930rsquos he patented Revacycle - the most

productive method (at that time) for spur bevel gears forming [13] Methods of forming

these transmissions are not based on Olivierrsquos principles E Wildhaber introduced gears

with non-conjugated tooth surfaces ndash transmissions with approximate meshing Basically

these gears cannot transmit rotation with constant gear ratio but the degree of deviation

from a constant gear ratio can be minimized by the targeted selection of values of gear

treatment process parameters Thus Wildhaber who abandoned the form-generating

method proved that there were possibilities of creating highly effective machining

processes for gears with non-conjugated tooth surfaces and thus initiated the theoretical

study of such transmissions

Active development of the theory of approximate meshing began after the 2nd World War

both in the US and the Soviet Union As the result the basic principle of the formation of

non-conjugate surfaces was formulated independently in the works of ML Baxter [14] and

FL Litvin [8] according to the principle the graph of deviation from the angular position

of the driven wheel from its position upon engagement of strictly conjugate surfaces is a

function similar to a parabola with the downward branches

At the same time it became clear that in order to meet challenges of synthesis and analysis

of gearing built on non-conjugated surfaces it is required to develop new mathematical

methods and models First mathematical models for studying gearing and computer

programs based on them appeared almost simultaneously in the US and the USSR

In the US TCA software package for the synthesis and analysis of hypoid gears [14] was

created under supervision of ML Baxter (1914-1994) chief engineer and researcher of The

Gleason Works

In the 1960rsquos methods for the synthesis of approximate gearing began to develop with the

advent of computers in the Soviet Union At first a software package for analysis and

synthesis of Revacycle spur bevel gear [9 p30-36] which included a numerical algorithm

for calculating the surface as an enveloping surface without using the theory of envelopes

[15] was developed at the Moscow Tooling and Machining Institute (STANKIN) under the

leadership of GI Sheveleva (1929-2005)

79

Similar software packages were developed in Saratov (Special Design Bureau of Gear ndash

Cutting Machines) under the leadership of MG Segal (1931-2000) and Leningrad (LITMO)

under supervision of FL Litvin The work on creation of universal programs for the

computer-based studies of spatial links was held in Tyumen [9 p36-43]

In the second half of the XX century the USSR became a recognized leader in terms of

volume and theoretical studies devoted to the study of the geometry of gears and gear

cutting tools After the end of World War II theoretical activities on creation of new methods

of analysis and synthesis of the working and technological gears was booming for 25-30

years Efforts of leading scientists (NI Kolchin FL Litvin VA Shishkov ML Novikov

LV Korostelyov GI Sheveleva II Dusev YaS Davydov ML Erikhov and others) have

led to creation of a new branch of science of the mechanisms - the gearing theory

The Soviet Union played the key role in creating the classical theory of gearing in early

1970rsquos The most important results obtained through efforts of domestic scientists which

formed the basis of the modern theory of gearing are listed below

1 Olivierrsquos principles for forming conjugate gearing are supplemented and developed AF

Nikolaev [16] ML Novikov [17] YaS Davydov [18] ML Erikhov [19]

2 New methods for analysis of the geometry of gears are developed and the existing ones

are improved differential (NI Kolchin the main publication of the year ndash 1957 [20])

screw (AF Nikolaev 1950 [16] KM Pismanik 1950 [21] NI Kolchin 1963 [22] VS

Lyukshin 1968 [23]) kinematic (YaS Davydov 1950 [24] VA Shishkov 1951 [12] NN

Krylov 1953 [25] FL Litvin 1960 [26] ML Erikhov 1972 [19]) matrix (FL Litvin

1968 [9]) power series (GI Sheveleva 1969 [27]) non-differential (GI Sheveleva 1969

[15]) tensor (II Dusev 1968 [28])

3 Methods of solving all major problems of synthesis and analysis of gears are established

Finding the envelope of a one-parameter and two-parameter family of surfaces (HI

Ketov NI Kolchin FL Litvin NN Krylov EG Ginsburg ML Erikhov) as well as

multi-parameter envelope family of surfaces and lines in spatial gearings (IL Brodsky DT

Babichev)

Finding an wrapping family of surfaces (GI Sheveleva)

Identifying the geometry generation features such as tooth undercutting interference and

others (MG Segal II Dusev GI Sheveleva VI Goldfarb BA Chyorny)

Synthesis of gearing geometry (local ndash FL Litvin ML Erikhov LV Korostelyov SA

Lagutin VN Rubtsov BP Timofeev and nonlocal ndash KI Gulyaev BA Chyorny MG

Segal)

Computation of curvatures in gearings (NI Kolchin FL Litvin VM Vasilyev II

Dusev EG Ginsburg LV Korostelyov ML Erikhov A M Pavlov MG Segal)

Computation of other geometric-kinematic characteristics of the teeth contact (AK

Georgiev VI Goldfarb SA Lagutin MF Lenski)

Solution of the inverse problem of the gearing theory tooth meshing analysis (KI

Gulyaev FL Litvin MG Segal BP Timofeev GI Sheveleva)

80

The impact of manufacturing errors and assembling on quality of engagement synthesis

of toothed meshing insensitive to errors (ML Erikhov NG Lindtrop LV Korostelyov

NN Krylov LY Liburkin GI Sheveleva)

Numerous studies of specific gears are conducted based on theoretical developments and

established procedures The most important practical problems solved during this period

are

1 Principally new types of gearing have been discovered helical gear in which arcs of

circles with radii small difference are selected as the profiles of cross-sections ndash Novikov-

Wildhaber gear [17] and gears with closed contact lines where the load between teeth is

transferred through the grease wedged in a closed cavity between active surfaces due to

closure of the contact line (LV Korostelyev SA Lagutin [29])

2 Geometric problems of synthesis of cylindrical involute gears were almost exhaustively

resolved and brought into engineering practice geometric calculation (VA Gavrylenko

1969 [30]) selection of the optimum addendum modification coefficients by using blocking

circuits (MB Groman 1957 [31]) according to the atlas compiled and published under the

direction of IA Bolotovsky 1967 [32]

3 New types of gearings have been studied and introduced In this regard various problems

related to analysis and synthesis of the following common types of gears have been solved

Bevel (NI Kolchin and VV Boldyrev 1937 YS Davydov 1950 VI Bezrukov 1963

VM Denisov 1963 GI Sheveleva 1966 HF Kabatov and GA Lopato 1966 MG

Segal 1971 KI Gulyaev 1974 VN Syzrantsev 1975)

Hypoid (GI Apukhtin 1952 FL Litvin 1962 KM Pismanik 1964 II Dusev and VM

Vasilyev 1968 MG Segal 1971)

Cylindrical gear drives with Novikovrsquos gear (ML Novikov 1956 RV Fedyakin and

VA Chesnokov 1958 VN Kudryavtsev 1959 EG Roslivker 1964 NI Kolchin 1968

VN Sevryuk 1972 and others)

Revacycle spur bevel gear (GI Sheveleva 1966)

New worm gear design toroid (YaI Dicker 1948) globoid (PS Zak 1962) worm gear

drives (FL Litvin 1962 IS Krivenko 1967 LV Korostelyev and SA Lagutin 1973

etc) spiroid (S Golubkov 1959 AK Georgiev and VI Goldfarb 1972 and others)

Less common known types of gears have also been studied and implemented

Hyperboloid (KM Pismanik 1950)

Helical-bevel (LY Liburkin 1968)

Wave (EG Ginsburg 1969)

Cylindrical with arched and spiral teeth (ML Erikhov and VN Syzrantsev 1975)

4 Techniques of analysis and synthesis of gears with non-circular wheels are developed [33]

and their production is organized

5 A lot of works are published including a number of classic books on theory of gearing

YaI Dieker (1935) NI Kolchin (1937-1952) FL Litvin (1952-1968) YaS Davydov

81

(1950) VA Gavrylenko (1949-1969) ML Novikov (1958) VA Zalgaller (1975) LD

Chasovnikov (1969) IA Bolotovsky et al (1962-1967) VN Kudryavtsev (1949-1971)

VN Kedrinsky (1960-1967) KM Pismanik (1964-1967) PS Zack (1962) NF Kabatov

and GA Lopato (1966) VA Shishkov (1951) and many others FL Litvinrsquos monograph

[8] stands out among these works it was published in 1968 and still remains a handbook for

professionals in the theory of gearing

The book by VA Zalgaller Envelope Theory [34] which is not very big in volume is

characterized by depth the mathematical rigor and completeness of the argumentation

Note that the appreciation level of the activities under the second cycle is confirmed by the

fact that in 1958 ML Novikov was awarded the Lenin Prize ndash the most prestigious USSR

award presented to individuals for accomplishments in the professional field

The following facts also confirm that the Soviet scientists made a decisive contribution to

the theory of gearing as a science and the fact that the Soviet Union had prepared a large

number of highly qualified specialists in the theory of gearing

FL Litvinrsquos monograph Theory of Gearing which was written in the late 60rsquos is still the

main handbook for gear specialists while Litvin is regarded as the creator of the modern

theory of gearing not only in CIS countries but also around the world

This monograph revised and expanded was reprinted abroad in English co-written with

FL Litvinrsquos new foreign students [35]

Number of qualified experts in the theory of gearing (by the way which were not widely

known in the Soviet Union and the CIS back then) have emigrated to the Western countries

and are writing and publishing quite significant books in English on the theory of gearing

and geometry of gears (SP Radzevich AL Kapelevich SV Lunin)

Summarizing the second cycle let us quote SA Lagutin who most accurately reflect the

essence of this bright period [36] it was a period of storm and pressure in the development

of the gearing theory in Russia when a whole galaxy of brilliant researchers were working

in this area headed by NI Kolchin and FL Litvin By collaborating and competing with

each other in a few years they have built amazingly beautiful building of the new science at

the junction of differential geometry and mechanics of machines

33 Laying the foundations of computer-oriented theory of gearing

The main purpose of such a theory is to become a basis for the methods of computer

analysis synthesis design and manufacturing gear parts for gear engagement

By the mid-70rsquos theory of gearing as a science has reached adulthood the main priority and

theoretical problems of analysis and synthesis of gearing have been resolved The number of

innovative theoretical work began to decline Studies are getting closer to the production

and the theory of gearing acts primarily as a tool for solving specific engineering problems

Since the mid 70-ies of XX century the theory of gearing as well as the machine tool

industry has evolved concurrently in two directions global and Russian

82

The global development of the theory of gearing has taken place against the backdrop of

revolution experienced by the machine tool industry since the 80rsquos

First machines with semi-rigid connections partially controlled by computer began to

appear in developed countries and then complete automatic machines (multi-axis CNC

machines) appeared

At that time for example machines for processing bevel gears with circular teeth Phoenix

(Gleason) and WNC30 (Klingelnberg) were developed The creation of such machines

occurred in parallel with the development of new mathematical models for shaping parts on

multi-axis machines and testing the parts operability before their casting in the metal At

that time software systems LTCA (Gleason) and Kimos (Klingelnberg) were developed

which made it possible to solve the problem of synthesis and analysis of bevel gears with

circular teeth [37]

All developed countries pursue the global direction in the development of the theory of

gearing in the same manner and using similar approaches The following was used by the

gear specialists to solve the problems of analysis and synthesis

Methods of classical theory of gearing (with computer design of the geometry of any kind

of gears)

Techniques of non-differential analysis of gear ndash forming processes using universal as

well as specially developed software packages

Methods of boundary and finite elements (at the analysis of the contact interaction of

acting surfaces of the teeth)

Finite element methods and integral equations (at the analysis of the stress-strain state of

the teeth)

Numerical optimization methods (at the synthesis of geometry of acting and fillet surfaces

of teeth)

An expanded list of quality indicators of gearings including new ones the design

thickness of the oil film criteria of hot and cold seizure criteria for assessing the conditions

for the formation of an oil wedge indicators of vibration activity of the gearing and others

Designing gear drives was regarded as a complex problem requiring an agreed solution of a

group of interrelated tasks

Selection of design scheme of a gear

Synthesis of permissible geometry

Geometry optimization

Structural arrangement and evaluation of quality indicators

Identification and addressing the weaknesses

Designing technical processes of manufacture selection or synthesis of tools subsequent

optimization etc

The developed theory of gearing is known as Theory of Real Gearing in Russia Ukraine

and Belarus while abroad it is called ldquoIntegrated Gear Designrdquo (IGD) or Integrated Design

83

of Gears

Russian direction in the development of the theory of gearing has several specific features

attributable to the following objective circumstances

Firstly first clear signs of stagnation appeared in the USSR industry in the late 70rsquos

Secondly the number of graduate students reduced as the universities basically solved the

problem of teachers which they faced in the early 60rsquos due to a drastic increase in the

number of students being trained in engineering specialties And finally Russia lost the top

three main theorists in the field of the theory of gearing FL Litvin was forced to emigrate

to the USA LV Korostelyov died in a car crash YaS Davydov departed from active

research and subsequently left for the USA

And nevertheless in 15-20 years preceding the collapse of the USSR in 1991 the theory

and geometry of gearing in the Soviet Union was continuing to develop At that time new

centers specializing in different aspects of the theory of gearing were established Let us list

the most interesting in our opinion research topics at the end of the last century

- Issues of strength and solution of the tooth contact problem (EL Airapetov VN

Syzrantsev GI Sheveleva)

- Research on gear bending bending stresses calculation (GI Sheveleva VI Medvedev)

- Non-differential methods for the determination of the contact surfaces characteristics (VI

Goldfarb GI Sheveleva AE Volkov)

- Issues of design synthesis analysis and manufacturing spiroid gear drives (AK Georgiev

VI Goldfarb)

- Issues of design synthesis analysis and manufacturing worm gear drives (SA Lagutin

AI Sandler)

- Research of hypoid bevel gear drives with circular teeth (MG Segal GI Sheveleva VN

Syzrantsev)

- Research of gear drives with intermediate bodies (AE Belyaev)

- Research of helical-bevel gear drives (BA Lopatin)

- Development of methods for the synthesis of gear drives (MG Segal SA Lagutin GI

Sheveleva VI Medvedev VN Syzrantsev)

- Forming a theoretical framework for the development of universal programs for the

analysis of spatial working and technological meshings and the creation of corresponding

programs (DT Babichev)

As a result of these studies software systems were developed in the Soviet Union which

were aimed at solving the problems of synthesis and analysis primarily for bevel gears with

circular teeth The best known ones include PC Volga5 made under the direction of MG

Segal [38] and PC Expert created under the direction of GI Sheveleva [39]

The fact that MG Segal was the main developer of the PC Kimos (firm Klingelnberg) in

the 90rsquos confirms the high level of those developments

It should also be noted that a work on the selection of optimal schemes for multi-axis CNC

84

machines for processing gear was carried out in 1990 in Saratov (MG Segal LI Shejko

[40]) These developments have also been used by Klingelnberg

The researches (above all theoretical ones) continued after the collapse of the USSR in

Russia Ukraine and Belarus

At that time the development of the theory of gearing was distinguished by a high level of

theoretical studies based on the introduction of new geometric geometric-kinematic and

other concepts and development (on their basis) of new mathematical models methods and

algorithms for analysis and synthesis of the working and technological gear engagements

These works were performed mostly at their own initiative by highly qualified specialists-

theorists in the field of theory and geometry of working and technological gear meshing

Usually they were elderly university professors who were practically deprived of relations

with the machine-building industry after its stagnation during the collapse of the USSR

It should be noted that it is very difficult to distinguish the most important areas of research

in the modern theory of gearing As the poet said Great things are better seen from a

distance Therefore we will list the most interesting in our view theoretical works on the

development of the theory of gearing with greater focus on the Russian line of research

However we practically do not consider the works on gear geometry ndash they are too

numerous A fairly complete picture of the theoretical works of this period can be obtained

from the proceedings of symposia and conferences held in Kurgan (KMI) Izhevsk

(IzhSTU) and Sevastopol (KhPI Kharkov) The main directions in the development of the

theory of gearing and the most important theoretical results after 1970s include the

following

1 Introduction and use of new concepts such as

Meshing Space (SA Lagutin [41])

Wrapping surface (GI Sheveleva [39])

Fan wedge and normal beam accelerating of implantation (DT Babichev [42])

2 Development of methods for analyzing processes of generation

A new method of finding a singularity in the flat gearing (SA Lagutin) based on the

situation [43] return point at the gear profile occurs at the point in the line of engagement

in which the normal to this line intersects the axis of rotation of the pinion The method was

extended to the spatial gearing (AE Volkov [44])

3 Development of methods of synthesis

Based on the new concept of space of engagement and its properties This approach was

used during the synthesis of both spatial transmission (SA Lagutin [45]) and the cylindrical

(DT Babichev [46])

By using as objective function new criteria of load capacity - permissible contact

pressure(VI Medvedev [47]) the specific work of working surfaces of teeth (DT Babichev

[48]) and others

For bevel gears with small cross-axis angle (SA Lagutin [49] VI Medvedev [50])

Synthesis of gears considering technological limitations of the given production processes

85

(VI Medvedev [51] VN Syzrantsev [52])

By using and developing a method of synthesis of gears in generalizing parameters

originally proposed by EB Vulgakov for involute gears The method was modified by VL

Dorofeev - for involute and ON Tsukanov and BA Lopatin ndash for non-involute gears

(including cylinder-conical ones) [53]

By using variational methods of synthesis when the equation of an optimal surface of the

tooth and its coefficients are determined This approach was first applied apparently by

Alan Lebec [54] in the United States it was used in Ukraine [55] and being developed in

Russia where equal strength gears have been synthesized by using the method (by Hertz

contact strength) [46 56] and the method of synthesis of bevel gear with circular teeth

according to the criteria of minimal contact pressure and bending stresses while maintaining

the overall dimensions of the gear has been developed which is important for aviation

where the weight of the structure is crucial [57]

Increasing the bending strength of circular tooth bevel gears by optimizing the shape of

the tool [58]

Increasing the load-bearing capacity of high-speed heavy-duty cylindrical involute gears

Note that EB Vulgakov VL Dorofeev and AL Kapelevich have made a significant

contribution to the development of synthesis aviation gear in recent decades [59]

4 Development of methods of analysis of loaded gears considering multipairness of

contact

For bevel gears with circular teeth [60]

For spiroid gears [61]

5 Significant progress has been made in the methods of analysis synthesis design and

manufacture of worm gear transmissions

The main input in this field of gearing has been made by two groups of researchers under

the leadership of VI Goldfarb and SA Lagutin The techniques of minimizing meshing

errors and worm hob errors that appear when regrinding and relieving works are fulfilled

have been developed by SA Lagutin and AI Sandler The techniques of synthesis and

production of gears with localized contact were drilled worm gears (SA Lagutin AI

Sandler [62]) and spiroid ones (VI Goldfarb ES Trubachyov [63])

The drives with the increased load capacity were designed based on a study of meshing

space of non-orthogonal gears spiroid (ES Trubachyov [63]) and worm ones (VYu

Puzanov) Designing of spiroid transmissions is carried out using CAD ldquoSPDIAL+rdquo

developed by a group headed by VI Goldfarb Configurator of gearbox systems for

optimization structural synthesis of their structures is being created (OV Malina etal)

Unified worm hob cutters cutting gears for the drives with localized contact were designed

It became possible to cut the gear wheels in engagement with multiple-thread worm by a

single-pass mill (VI Goldfarb and his disciples)

In the Institute of Mechanics IzhSTU a group led by VI Goldfarb essentially laid the

foundation for a new Russian machine building sub-industry ndash construction of gearboxes for

86

isolation and control valves for pipelines

- Theoretical studies of spiroid and worm gears are at a high scientific level

- A modern design process is applied synthesis of perfect engagement synthesis of

localized contact simulation of the stress strain state analysis of real engagement under

load forecasting the state of transmission

- Three generations of dimension-type series of quarter-turn and multi-turn spiroid gear

drives are developed their production with modern quality control and acceptance tests is

organized

6 Application of unconventional gears and gearing helical-bevel gears (BA Lopatin [65])

transmissions with intermediate rolling bodies (AE Belyaev [66]) hydraulic and

pneumatic machines with non-circular gears (An-I-Kahn [67]) precessing transmissions

(IA Bostan [68] EI Tesker [69] VN Syzrantsev BA Lopatin) and other

7 Development of kinematic analysis methods of working and technological meshings Note

that modern designing is the computer designing This factor imposes high requirements to

the theory of gearing as the main mathematical basis for such designing We have to admit

that the classical theory of gearing does not fully comply with these demanding

requirements Thus according to Prof MG Segal who was working with Klingelnberg in

the last years of his life the head of the company prohibited to use differential methods ndash

the basis of the classical theory of gearing ndash in the programs being created The reason for

the ban was inadequacy of the results of computer simulation as compared to real processes

of formation Theoretical research aimed at creating computational models that are

adequate to the real processes of formation and contact of moving bodies were developed by

AE Volkov and VI Medvedev (Moscow) and DT Babichev (Tyumen)

To eliminate the phenomenon DT Babichev elaborated a unified kinematic method for

analysis of the processes of formation [70] based on the ldquotriadrdquo ruptures + envelopes + new

concepts of curvilinear coordinates As the result the cause of inadequacy between the

classical methods of the theory of gearing and real-life processes of formation was

established and rectified The developed kinematic method

Allows to find all the surfaces formed on the item at gear machining formed by smooth

surfaces and inflections of bodies including at advanceretraction of machine tool and in

secondary cutting areas

Has the reliability of non-differential methods but is superior to them in speed of

operation by two orders of magnitude which is confirmed by its partial use in CAD

ldquoSPDIAL +rdquo

Also allows to define the curvatures in gearing

8 Development of the system for assigning real ITS (Initial Tool Surfaces) and construction

of mathematical models for them [71] Real ITS is the set of all forming tools (pieces of

surfaces cutting and boundary edges and corners) for which uniform curvilinear coordinates

are introduced

9 By using the concept of ldquothe acceleration of installationrdquo new techniques for solving

87

multitude of tasks are created calculating the radii of curvature in the gearing identifying

cutting areas and thickness of the layers being cut by tool cutting edges and others (DT

Babichev [48])

For example based on the concept of the acceleration of installation a new basic formula

for calculating the reduced curvature in any normal sections at the contact point of two

moving bodies in contact along the line is created

1Rnp=-

where ɷrol is angular velocity of rolling bodies in the plane of the section in which the

curvature is calculated aB is the acceleration of installation The fundamental nature of the

obtained formula is that

1) in its generality it is commensurate with the kinematic formulas of Rodrigues and Freinet

known in differential geometry but it is intended for a different class of surfaces produced

in the process of formation by the rounding methods

2) curvature in any normal section of all surfaces formed by the rounding methods is

determined by only two scalar parameters and one of them (acceleration of installation)

does not depend on the direction of the section

It was also established that the sign of the acceleration of installation allow to make an

unambiguous judgement on the nature of the contact of bodies For example if aВgt 0 then

the envelope is formed inside the body of the generating element Acceleration of

installation allows to determine (ldquoincidentallyrdquo) the value of the radii of curvature and

faceting value across the whole surface formed by rounding at band- and flake-type

roughness

Thus over the past decade a substantial volume of theoretical knowledge to complete the

third cycle (creation of a computer-oriented theory of gearing) was accumulated

A lot of new notions are introduced and used in theory of gearing

Based on these new notions methods for analysis and synthesis of gear drives and cutter

tool meshings oriented at computer technologies have been developed and continue to be

improved

Intensive investigations to improve methods of optimization synthesis of gearing and to

develop methodologies of computer design and construction of gear boxes are performed

4 Problems and expected directions of the theory of gearing

Let us list the main problems in the gearing theory which in our opinion are the most

important

Problem 1 Creation of the theory of optimization synthesis of structures and parameters of

higher pairs of kinematic elements transmitting the motion and load at the preset and

optimal correlation of normal and friction forces At the present time theory of higher pairs

is being developed only as a pure geometrical science

88

Problem 2 Elaboration of methods of tooth optimal geometry synthesis oriented at the

modern processing technologies instead of traditional ones In this case a designer will have

to solve the variation problem with limitations providing for maximum possible load

capacity of gear drive in accordance with preselected criteria of performance efficiency

Problem 3 Development of methods for analysis of the process of the tooth preset surfaces

changeover taking into account the values of load tooth displacement manufacturing errors

of drive elements errors of relative position of engaging links dynamics of changeover

process

Problem 4 Creation of a unique interrelated complex of application software packages to

enable the designers and manufactures of gear drives to carry out optimization designing

engineering design preparation for production of various drives by meshing

Possible directions of development of the theory of gearing naturally follow from the afore-

described problems

CONCLUSIONS

In the second half of the XIX century the number and complexity of technical inventions of

various machines and mechanisms using the gear drives reached a critical mass and by

around 1890 the scientists had created the scientific basis of the theory of gearing And the

modern theory of gearing was formed by the beginning of the 1970rsquos

The third cycle of the gearing theory development which is oriented at computer technology

is underway

In our opinion the prospects for the development of theory of gearing as a part of the

theory of mechanisms and machines are higher as compared for example with the

linkages Firstly gears are more commonly used in cars than linkages Secondly the

theory of gearing is not only the theory of higher kinematic pairs - it is also the basis for the

theory of gear machining design

It is necessary to note that the current version of the paper is based on the paper published in

the first edition of the given Proceedings [72] but is as close as possible to the paper [73] by

the same authors This version of the article has been prepared by VE Starzhinsky

REFERENCES

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1934 ndash 215 с (Diels GA Antique appliances - Moscow-Leningrad ONTI - Gos tehn-

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2 Витрувий Десять книг об архитектуре ndash Москва laquoАрхитектура-Сraquo 2006 ndash 328 с

(Vitruvius Ten Books on Architecture ndash Moscov Architecture-C 2006 ndash 328 p)

3 Пипуныров ВН История часов с древнейших времен до наших дней - Москва

89

Наука 1982 ndash 496 c (Pipunyrov VN The clock story from ancient times to the present

day ndash Moscow Nauka 1982 ndash 496 p)

4 Академик ИИ Артоболевский Сборник Сост АМ Лепихов ndash М Знание 1983

ndash 176 c (Collection Comp AM Lepihov ndash Moscow Znanie 1983 ndash 176 p)

5 Чебышёв ПЛ Избранные труды ndash М Изд-во АН СССР 1955 ndash 926 с (Chebyshjov

PL Selected Works ndash Moscow AN SSSR 1955 ndash 926 p)

6 Рёло Ф Теоретическая кинематика 1875 (Relo F Theoretical Kinematics 1875)

7 Портретная галерея выдающихся инженеров и ученых в области зубчатых передач

ndash Сборник докладов научно-технической конференции с международным участием

Теория и практика зубчатых передач и редукторостроения Ижевск 2008 ndash C 378-

395 (Portrait Gallery of Disting wished Engineers and Scientist in Gearing ndash Proceedings

of Scientific-Engineering Conference with International Participation Theory and Practice

of Gearing and Reducer Building Izhevsk 2008 ndash P 378-395)

8 Литвин ФЛ Теория зубчатых зацеплений ndash М Наука 1968 ndash 584 с (Litvin FL

Theory of gearing ndash Moscow Nauka 1968 ndash 584 p)

9 Механика машин вып 45 ndash Москва Наука 1974 (Mechanics of machines No 45 ndash

Moscow Nauka 1974)

10 Willis R Principles of Mechanism ndash Cambridge London 1841

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магистра механики Одесса ndash 1886 ndash 232 с (Hokhman HI Link Theory generalized and

developed by analyzing Diss mastermechanic Odessa 1886 ndash 232 p)

12 Шишков ВА Образование поверхностей резанием по методу обкатки ndash Москва

Машгиз 1951 ndash 150 с (Shishkov VA Formation of surface machining by burnishing

method ndash Moscow Mashgiz 1951 ndash 150 p)

13 Вильдгабер Э Основы зацепления конических и гипоидных передач ndash Машгиз

1948 ndash 236 с (Vildgaber Je Principles of engagement bevel and hypoid gears ndash Moscow

Mashgiz 1948 ndash 236 p)

14 Baxter ML Basic Geometry and Tooth Contact of Hypoid Gears ldquoIndustrial

Mathematicsrdquo ndash 1961 ndash No 11 ndash P 19-42

15 Шевелева ГИ Алгоритм численного расчета обрабатываемой поверхности Станки

и инструмент ndash 1969 ndash 8 ndash C17-20 (Sheveleva GI Algorithm for the numerical

calculation of the treated surface Machines and Tooling ndash 1969 ndash No 8 ndash P 17-20)

16 Николаев АФ Диаграмма винта и ее применение к определению сопряженных

линейчатых поверхностей с линейным касанием Труды семинара по ТММ вып 37

1950 ndash С52ndash106 (Nikolaev AF Diagram of the screw and its application to the

determination of conjugate ruled surfaces with a linear contact Proceedings of the

Seminar on TMM ndash 1950 ndash No 37 ndash P52-106)

17 Новиков МЛ Зубчатые передачи с новым зацеплением ndash М Изд ВВИА им

Жуковского 1958 ndash 186 с (Novikov ML Gears with a new engagement ndash Moscow

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18 Давыдов ЯС Об одном обобщении метода Оливье для образования сопряженных

90

поверхностей в зубчатых передачах Сб laquoТеорияпередачвмашинахraquo М Машгиз

1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

77

engagement This simplifies finding the envelope surface as compared to classical methods

in mechanics and differential geometry

By the end of the XIX century the appearance of the fundamental principles of analytical

theory of gearing marked the end of the first cycle of development of the theory of gearing

These principles include

Basic concepts and methods of classical mechanics analytical and differential geometry

Two principles of formation of mating gears proposed by Olivier

Euler-Savary equation and Bobillierrsquos construction reflecting the relationship between the

centroid and the curvatures of mating profiles in plane gears

Hochman developed a method for finding the envelope profiles and surfaces as well as

points and lines of contact of mutually enveloped lines and surfaces in the plane and spatial

working and technological gears

32 Creation of the classical theory of gearing

The framework of analytical theory of gearing developed by the end of the XIX century has

become the basis for solving practical problems which were posed by the thriving industry

for the science

Late XIX amp early XX century had a rich history of inventions of new types of

transmissions machines tools and machine gears Conventionally these inventions can be

divided into two areas machinery and tools for forming gears based on engagement of the

mating surfaces and machines and tools for forming gears with non-conjugated surfaces of

teeth

The first approach is based on the Olivier principles

In the period from 1890 to 1920 the following technologies and machines for production of

gears based on the form-generating method were invented and implemented

- Machines for bevel gears including the ones circular teeth (JE Gleason)

- Machines for grinding involute profiles of gear cutters (E Fellows)

- Machines for cutting spur and helical gears with worm milling cutters (RH Pfauter)

- Technology for manufacturing globoid worm gear (SI Cohn and FW Lorenz)

- Involute worm gear based on the application of involute helical surface as the surface of

the worm mill thread (FD Bostock and P Brown)

These and many other inventions have set the task of generalization of the gear-forming

theory based on engagement of the mating surfaces Decisive role in complementing and

developing the Olivierrsquos principles belongs to Russian scientists AF Nikolaev (1901-

1957) YaS Davydov (1914-2003) and ML Erikhov (1937-2002) They used an auxiliary

(generating) surface to form the mating surfaces ML Novikov (1915-1957) proposed a

fundamentally different principle of forming the mating gears by moving (according to a

certain law) the contact point of two profiles along the line of engagement of the

78

synthesized transmission

All these principles are based on the theory of envelopes which was scientifically and

methodologically completed (at that period of time) in YaS Davydovrsquos VA Shishkovrsquos

and FL Litvinrsquos works Almost simultaneously and independently they proposed a method

for finding the kinematic envelope in which the meshing condition equation is used VN = 0

[8] At this time VA Shishkov [12] introduced a new concept - implementation speed Vn

equal to the scalar product Vn = V12n which became an effective tool in the study of gear

cutting tools working according to the form-generating method It became the basis of the

kinematic method for the synthesis and analysis of gearing in the second half of the XX

century

Ernest Wildhaber (1893-1979) a talented engineer and inventor of the company The

Gleason Works can be regarded as the founder of the second direction In 1927 he

proposed a method of forming hypoid gears and in 1930rsquos he patented Revacycle - the most

productive method (at that time) for spur bevel gears forming [13] Methods of forming

these transmissions are not based on Olivierrsquos principles E Wildhaber introduced gears

with non-conjugated tooth surfaces ndash transmissions with approximate meshing Basically

these gears cannot transmit rotation with constant gear ratio but the degree of deviation

from a constant gear ratio can be minimized by the targeted selection of values of gear

treatment process parameters Thus Wildhaber who abandoned the form-generating

method proved that there were possibilities of creating highly effective machining

processes for gears with non-conjugated tooth surfaces and thus initiated the theoretical

study of such transmissions

Active development of the theory of approximate meshing began after the 2nd World War

both in the US and the Soviet Union As the result the basic principle of the formation of

non-conjugate surfaces was formulated independently in the works of ML Baxter [14] and

FL Litvin [8] according to the principle the graph of deviation from the angular position

of the driven wheel from its position upon engagement of strictly conjugate surfaces is a

function similar to a parabola with the downward branches

At the same time it became clear that in order to meet challenges of synthesis and analysis

of gearing built on non-conjugated surfaces it is required to develop new mathematical

methods and models First mathematical models for studying gearing and computer

programs based on them appeared almost simultaneously in the US and the USSR

In the US TCA software package for the synthesis and analysis of hypoid gears [14] was

created under supervision of ML Baxter (1914-1994) chief engineer and researcher of The

Gleason Works

In the 1960rsquos methods for the synthesis of approximate gearing began to develop with the

advent of computers in the Soviet Union At first a software package for analysis and

synthesis of Revacycle spur bevel gear [9 p30-36] which included a numerical algorithm

for calculating the surface as an enveloping surface without using the theory of envelopes

[15] was developed at the Moscow Tooling and Machining Institute (STANKIN) under the

leadership of GI Sheveleva (1929-2005)

79

Similar software packages were developed in Saratov (Special Design Bureau of Gear ndash

Cutting Machines) under the leadership of MG Segal (1931-2000) and Leningrad (LITMO)

under supervision of FL Litvin The work on creation of universal programs for the

computer-based studies of spatial links was held in Tyumen [9 p36-43]

In the second half of the XX century the USSR became a recognized leader in terms of

volume and theoretical studies devoted to the study of the geometry of gears and gear

cutting tools After the end of World War II theoretical activities on creation of new methods

of analysis and synthesis of the working and technological gears was booming for 25-30

years Efforts of leading scientists (NI Kolchin FL Litvin VA Shishkov ML Novikov

LV Korostelyov GI Sheveleva II Dusev YaS Davydov ML Erikhov and others) have

led to creation of a new branch of science of the mechanisms - the gearing theory

The Soviet Union played the key role in creating the classical theory of gearing in early

1970rsquos The most important results obtained through efforts of domestic scientists which

formed the basis of the modern theory of gearing are listed below

1 Olivierrsquos principles for forming conjugate gearing are supplemented and developed AF

Nikolaev [16] ML Novikov [17] YaS Davydov [18] ML Erikhov [19]

2 New methods for analysis of the geometry of gears are developed and the existing ones

are improved differential (NI Kolchin the main publication of the year ndash 1957 [20])

screw (AF Nikolaev 1950 [16] KM Pismanik 1950 [21] NI Kolchin 1963 [22] VS

Lyukshin 1968 [23]) kinematic (YaS Davydov 1950 [24] VA Shishkov 1951 [12] NN

Krylov 1953 [25] FL Litvin 1960 [26] ML Erikhov 1972 [19]) matrix (FL Litvin

1968 [9]) power series (GI Sheveleva 1969 [27]) non-differential (GI Sheveleva 1969

[15]) tensor (II Dusev 1968 [28])

3 Methods of solving all major problems of synthesis and analysis of gears are established

Finding the envelope of a one-parameter and two-parameter family of surfaces (HI

Ketov NI Kolchin FL Litvin NN Krylov EG Ginsburg ML Erikhov) as well as

multi-parameter envelope family of surfaces and lines in spatial gearings (IL Brodsky DT

Babichev)

Finding an wrapping family of surfaces (GI Sheveleva)

Identifying the geometry generation features such as tooth undercutting interference and

others (MG Segal II Dusev GI Sheveleva VI Goldfarb BA Chyorny)

Synthesis of gearing geometry (local ndash FL Litvin ML Erikhov LV Korostelyov SA

Lagutin VN Rubtsov BP Timofeev and nonlocal ndash KI Gulyaev BA Chyorny MG

Segal)

Computation of curvatures in gearings (NI Kolchin FL Litvin VM Vasilyev II

Dusev EG Ginsburg LV Korostelyov ML Erikhov A M Pavlov MG Segal)

Computation of other geometric-kinematic characteristics of the teeth contact (AK

Georgiev VI Goldfarb SA Lagutin MF Lenski)

Solution of the inverse problem of the gearing theory tooth meshing analysis (KI

Gulyaev FL Litvin MG Segal BP Timofeev GI Sheveleva)

80

The impact of manufacturing errors and assembling on quality of engagement synthesis

of toothed meshing insensitive to errors (ML Erikhov NG Lindtrop LV Korostelyov

NN Krylov LY Liburkin GI Sheveleva)

Numerous studies of specific gears are conducted based on theoretical developments and

established procedures The most important practical problems solved during this period

are

1 Principally new types of gearing have been discovered helical gear in which arcs of

circles with radii small difference are selected as the profiles of cross-sections ndash Novikov-

Wildhaber gear [17] and gears with closed contact lines where the load between teeth is

transferred through the grease wedged in a closed cavity between active surfaces due to

closure of the contact line (LV Korostelyev SA Lagutin [29])

2 Geometric problems of synthesis of cylindrical involute gears were almost exhaustively

resolved and brought into engineering practice geometric calculation (VA Gavrylenko

1969 [30]) selection of the optimum addendum modification coefficients by using blocking

circuits (MB Groman 1957 [31]) according to the atlas compiled and published under the

direction of IA Bolotovsky 1967 [32]

3 New types of gearings have been studied and introduced In this regard various problems

related to analysis and synthesis of the following common types of gears have been solved

Bevel (NI Kolchin and VV Boldyrev 1937 YS Davydov 1950 VI Bezrukov 1963

VM Denisov 1963 GI Sheveleva 1966 HF Kabatov and GA Lopato 1966 MG

Segal 1971 KI Gulyaev 1974 VN Syzrantsev 1975)

Hypoid (GI Apukhtin 1952 FL Litvin 1962 KM Pismanik 1964 II Dusev and VM

Vasilyev 1968 MG Segal 1971)

Cylindrical gear drives with Novikovrsquos gear (ML Novikov 1956 RV Fedyakin and

VA Chesnokov 1958 VN Kudryavtsev 1959 EG Roslivker 1964 NI Kolchin 1968

VN Sevryuk 1972 and others)

Revacycle spur bevel gear (GI Sheveleva 1966)

New worm gear design toroid (YaI Dicker 1948) globoid (PS Zak 1962) worm gear

drives (FL Litvin 1962 IS Krivenko 1967 LV Korostelyev and SA Lagutin 1973

etc) spiroid (S Golubkov 1959 AK Georgiev and VI Goldfarb 1972 and others)

Less common known types of gears have also been studied and implemented

Hyperboloid (KM Pismanik 1950)

Helical-bevel (LY Liburkin 1968)

Wave (EG Ginsburg 1969)

Cylindrical with arched and spiral teeth (ML Erikhov and VN Syzrantsev 1975)

4 Techniques of analysis and synthesis of gears with non-circular wheels are developed [33]

and their production is organized

5 A lot of works are published including a number of classic books on theory of gearing

YaI Dieker (1935) NI Kolchin (1937-1952) FL Litvin (1952-1968) YaS Davydov

81

(1950) VA Gavrylenko (1949-1969) ML Novikov (1958) VA Zalgaller (1975) LD

Chasovnikov (1969) IA Bolotovsky et al (1962-1967) VN Kudryavtsev (1949-1971)

VN Kedrinsky (1960-1967) KM Pismanik (1964-1967) PS Zack (1962) NF Kabatov

and GA Lopato (1966) VA Shishkov (1951) and many others FL Litvinrsquos monograph

[8] stands out among these works it was published in 1968 and still remains a handbook for

professionals in the theory of gearing

The book by VA Zalgaller Envelope Theory [34] which is not very big in volume is

characterized by depth the mathematical rigor and completeness of the argumentation

Note that the appreciation level of the activities under the second cycle is confirmed by the

fact that in 1958 ML Novikov was awarded the Lenin Prize ndash the most prestigious USSR

award presented to individuals for accomplishments in the professional field

The following facts also confirm that the Soviet scientists made a decisive contribution to

the theory of gearing as a science and the fact that the Soviet Union had prepared a large

number of highly qualified specialists in the theory of gearing

FL Litvinrsquos monograph Theory of Gearing which was written in the late 60rsquos is still the

main handbook for gear specialists while Litvin is regarded as the creator of the modern

theory of gearing not only in CIS countries but also around the world

This monograph revised and expanded was reprinted abroad in English co-written with

FL Litvinrsquos new foreign students [35]

Number of qualified experts in the theory of gearing (by the way which were not widely

known in the Soviet Union and the CIS back then) have emigrated to the Western countries

and are writing and publishing quite significant books in English on the theory of gearing

and geometry of gears (SP Radzevich AL Kapelevich SV Lunin)

Summarizing the second cycle let us quote SA Lagutin who most accurately reflect the

essence of this bright period [36] it was a period of storm and pressure in the development

of the gearing theory in Russia when a whole galaxy of brilliant researchers were working

in this area headed by NI Kolchin and FL Litvin By collaborating and competing with

each other in a few years they have built amazingly beautiful building of the new science at

the junction of differential geometry and mechanics of machines

33 Laying the foundations of computer-oriented theory of gearing

The main purpose of such a theory is to become a basis for the methods of computer

analysis synthesis design and manufacturing gear parts for gear engagement

By the mid-70rsquos theory of gearing as a science has reached adulthood the main priority and

theoretical problems of analysis and synthesis of gearing have been resolved The number of

innovative theoretical work began to decline Studies are getting closer to the production

and the theory of gearing acts primarily as a tool for solving specific engineering problems

Since the mid 70-ies of XX century the theory of gearing as well as the machine tool

industry has evolved concurrently in two directions global and Russian

82

The global development of the theory of gearing has taken place against the backdrop of

revolution experienced by the machine tool industry since the 80rsquos

First machines with semi-rigid connections partially controlled by computer began to

appear in developed countries and then complete automatic machines (multi-axis CNC

machines) appeared

At that time for example machines for processing bevel gears with circular teeth Phoenix

(Gleason) and WNC30 (Klingelnberg) were developed The creation of such machines

occurred in parallel with the development of new mathematical models for shaping parts on

multi-axis machines and testing the parts operability before their casting in the metal At

that time software systems LTCA (Gleason) and Kimos (Klingelnberg) were developed

which made it possible to solve the problem of synthesis and analysis of bevel gears with

circular teeth [37]

All developed countries pursue the global direction in the development of the theory of

gearing in the same manner and using similar approaches The following was used by the

gear specialists to solve the problems of analysis and synthesis

Methods of classical theory of gearing (with computer design of the geometry of any kind

of gears)

Techniques of non-differential analysis of gear ndash forming processes using universal as

well as specially developed software packages

Methods of boundary and finite elements (at the analysis of the contact interaction of

acting surfaces of the teeth)

Finite element methods and integral equations (at the analysis of the stress-strain state of

the teeth)

Numerical optimization methods (at the synthesis of geometry of acting and fillet surfaces

of teeth)

An expanded list of quality indicators of gearings including new ones the design

thickness of the oil film criteria of hot and cold seizure criteria for assessing the conditions

for the formation of an oil wedge indicators of vibration activity of the gearing and others

Designing gear drives was regarded as a complex problem requiring an agreed solution of a

group of interrelated tasks

Selection of design scheme of a gear

Synthesis of permissible geometry

Geometry optimization

Structural arrangement and evaluation of quality indicators

Identification and addressing the weaknesses

Designing technical processes of manufacture selection or synthesis of tools subsequent

optimization etc

The developed theory of gearing is known as Theory of Real Gearing in Russia Ukraine

and Belarus while abroad it is called ldquoIntegrated Gear Designrdquo (IGD) or Integrated Design

83

of Gears

Russian direction in the development of the theory of gearing has several specific features

attributable to the following objective circumstances

Firstly first clear signs of stagnation appeared in the USSR industry in the late 70rsquos

Secondly the number of graduate students reduced as the universities basically solved the

problem of teachers which they faced in the early 60rsquos due to a drastic increase in the

number of students being trained in engineering specialties And finally Russia lost the top

three main theorists in the field of the theory of gearing FL Litvin was forced to emigrate

to the USA LV Korostelyov died in a car crash YaS Davydov departed from active

research and subsequently left for the USA

And nevertheless in 15-20 years preceding the collapse of the USSR in 1991 the theory

and geometry of gearing in the Soviet Union was continuing to develop At that time new

centers specializing in different aspects of the theory of gearing were established Let us list

the most interesting in our opinion research topics at the end of the last century

- Issues of strength and solution of the tooth contact problem (EL Airapetov VN

Syzrantsev GI Sheveleva)

- Research on gear bending bending stresses calculation (GI Sheveleva VI Medvedev)

- Non-differential methods for the determination of the contact surfaces characteristics (VI

Goldfarb GI Sheveleva AE Volkov)

- Issues of design synthesis analysis and manufacturing spiroid gear drives (AK Georgiev

VI Goldfarb)

- Issues of design synthesis analysis and manufacturing worm gear drives (SA Lagutin

AI Sandler)

- Research of hypoid bevel gear drives with circular teeth (MG Segal GI Sheveleva VN

Syzrantsev)

- Research of gear drives with intermediate bodies (AE Belyaev)

- Research of helical-bevel gear drives (BA Lopatin)

- Development of methods for the synthesis of gear drives (MG Segal SA Lagutin GI

Sheveleva VI Medvedev VN Syzrantsev)

- Forming a theoretical framework for the development of universal programs for the

analysis of spatial working and technological meshings and the creation of corresponding

programs (DT Babichev)

As a result of these studies software systems were developed in the Soviet Union which

were aimed at solving the problems of synthesis and analysis primarily for bevel gears with

circular teeth The best known ones include PC Volga5 made under the direction of MG

Segal [38] and PC Expert created under the direction of GI Sheveleva [39]

The fact that MG Segal was the main developer of the PC Kimos (firm Klingelnberg) in

the 90rsquos confirms the high level of those developments

It should also be noted that a work on the selection of optimal schemes for multi-axis CNC

84

machines for processing gear was carried out in 1990 in Saratov (MG Segal LI Shejko

[40]) These developments have also been used by Klingelnberg

The researches (above all theoretical ones) continued after the collapse of the USSR in

Russia Ukraine and Belarus

At that time the development of the theory of gearing was distinguished by a high level of

theoretical studies based on the introduction of new geometric geometric-kinematic and

other concepts and development (on their basis) of new mathematical models methods and

algorithms for analysis and synthesis of the working and technological gear engagements

These works were performed mostly at their own initiative by highly qualified specialists-

theorists in the field of theory and geometry of working and technological gear meshing

Usually they were elderly university professors who were practically deprived of relations

with the machine-building industry after its stagnation during the collapse of the USSR

It should be noted that it is very difficult to distinguish the most important areas of research

in the modern theory of gearing As the poet said Great things are better seen from a

distance Therefore we will list the most interesting in our view theoretical works on the

development of the theory of gearing with greater focus on the Russian line of research

However we practically do not consider the works on gear geometry ndash they are too

numerous A fairly complete picture of the theoretical works of this period can be obtained

from the proceedings of symposia and conferences held in Kurgan (KMI) Izhevsk

(IzhSTU) and Sevastopol (KhPI Kharkov) The main directions in the development of the

theory of gearing and the most important theoretical results after 1970s include the

following

1 Introduction and use of new concepts such as

Meshing Space (SA Lagutin [41])

Wrapping surface (GI Sheveleva [39])

Fan wedge and normal beam accelerating of implantation (DT Babichev [42])

2 Development of methods for analyzing processes of generation

A new method of finding a singularity in the flat gearing (SA Lagutin) based on the

situation [43] return point at the gear profile occurs at the point in the line of engagement

in which the normal to this line intersects the axis of rotation of the pinion The method was

extended to the spatial gearing (AE Volkov [44])

3 Development of methods of synthesis

Based on the new concept of space of engagement and its properties This approach was

used during the synthesis of both spatial transmission (SA Lagutin [45]) and the cylindrical

(DT Babichev [46])

By using as objective function new criteria of load capacity - permissible contact

pressure(VI Medvedev [47]) the specific work of working surfaces of teeth (DT Babichev

[48]) and others

For bevel gears with small cross-axis angle (SA Lagutin [49] VI Medvedev [50])

Synthesis of gears considering technological limitations of the given production processes

85

(VI Medvedev [51] VN Syzrantsev [52])

By using and developing a method of synthesis of gears in generalizing parameters

originally proposed by EB Vulgakov for involute gears The method was modified by VL

Dorofeev - for involute and ON Tsukanov and BA Lopatin ndash for non-involute gears

(including cylinder-conical ones) [53]

By using variational methods of synthesis when the equation of an optimal surface of the

tooth and its coefficients are determined This approach was first applied apparently by

Alan Lebec [54] in the United States it was used in Ukraine [55] and being developed in

Russia where equal strength gears have been synthesized by using the method (by Hertz

contact strength) [46 56] and the method of synthesis of bevel gear with circular teeth

according to the criteria of minimal contact pressure and bending stresses while maintaining

the overall dimensions of the gear has been developed which is important for aviation

where the weight of the structure is crucial [57]

Increasing the bending strength of circular tooth bevel gears by optimizing the shape of

the tool [58]

Increasing the load-bearing capacity of high-speed heavy-duty cylindrical involute gears

Note that EB Vulgakov VL Dorofeev and AL Kapelevich have made a significant

contribution to the development of synthesis aviation gear in recent decades [59]

4 Development of methods of analysis of loaded gears considering multipairness of

contact

For bevel gears with circular teeth [60]

For spiroid gears [61]

5 Significant progress has been made in the methods of analysis synthesis design and

manufacture of worm gear transmissions

The main input in this field of gearing has been made by two groups of researchers under

the leadership of VI Goldfarb and SA Lagutin The techniques of minimizing meshing

errors and worm hob errors that appear when regrinding and relieving works are fulfilled

have been developed by SA Lagutin and AI Sandler The techniques of synthesis and

production of gears with localized contact were drilled worm gears (SA Lagutin AI

Sandler [62]) and spiroid ones (VI Goldfarb ES Trubachyov [63])

The drives with the increased load capacity were designed based on a study of meshing

space of non-orthogonal gears spiroid (ES Trubachyov [63]) and worm ones (VYu

Puzanov) Designing of spiroid transmissions is carried out using CAD ldquoSPDIAL+rdquo

developed by a group headed by VI Goldfarb Configurator of gearbox systems for

optimization structural synthesis of their structures is being created (OV Malina etal)

Unified worm hob cutters cutting gears for the drives with localized contact were designed

It became possible to cut the gear wheels in engagement with multiple-thread worm by a

single-pass mill (VI Goldfarb and his disciples)

In the Institute of Mechanics IzhSTU a group led by VI Goldfarb essentially laid the

foundation for a new Russian machine building sub-industry ndash construction of gearboxes for

86

isolation and control valves for pipelines

- Theoretical studies of spiroid and worm gears are at a high scientific level

- A modern design process is applied synthesis of perfect engagement synthesis of

localized contact simulation of the stress strain state analysis of real engagement under

load forecasting the state of transmission

- Three generations of dimension-type series of quarter-turn and multi-turn spiroid gear

drives are developed their production with modern quality control and acceptance tests is

organized

6 Application of unconventional gears and gearing helical-bevel gears (BA Lopatin [65])

transmissions with intermediate rolling bodies (AE Belyaev [66]) hydraulic and

pneumatic machines with non-circular gears (An-I-Kahn [67]) precessing transmissions

(IA Bostan [68] EI Tesker [69] VN Syzrantsev BA Lopatin) and other

7 Development of kinematic analysis methods of working and technological meshings Note

that modern designing is the computer designing This factor imposes high requirements to

the theory of gearing as the main mathematical basis for such designing We have to admit

that the classical theory of gearing does not fully comply with these demanding

requirements Thus according to Prof MG Segal who was working with Klingelnberg in

the last years of his life the head of the company prohibited to use differential methods ndash

the basis of the classical theory of gearing ndash in the programs being created The reason for

the ban was inadequacy of the results of computer simulation as compared to real processes

of formation Theoretical research aimed at creating computational models that are

adequate to the real processes of formation and contact of moving bodies were developed by

AE Volkov and VI Medvedev (Moscow) and DT Babichev (Tyumen)

To eliminate the phenomenon DT Babichev elaborated a unified kinematic method for

analysis of the processes of formation [70] based on the ldquotriadrdquo ruptures + envelopes + new

concepts of curvilinear coordinates As the result the cause of inadequacy between the

classical methods of the theory of gearing and real-life processes of formation was

established and rectified The developed kinematic method

Allows to find all the surfaces formed on the item at gear machining formed by smooth

surfaces and inflections of bodies including at advanceretraction of machine tool and in

secondary cutting areas

Has the reliability of non-differential methods but is superior to them in speed of

operation by two orders of magnitude which is confirmed by its partial use in CAD

ldquoSPDIAL +rdquo

Also allows to define the curvatures in gearing

8 Development of the system for assigning real ITS (Initial Tool Surfaces) and construction

of mathematical models for them [71] Real ITS is the set of all forming tools (pieces of

surfaces cutting and boundary edges and corners) for which uniform curvilinear coordinates

are introduced

9 By using the concept of ldquothe acceleration of installationrdquo new techniques for solving

87

multitude of tasks are created calculating the radii of curvature in the gearing identifying

cutting areas and thickness of the layers being cut by tool cutting edges and others (DT

Babichev [48])

For example based on the concept of the acceleration of installation a new basic formula

for calculating the reduced curvature in any normal sections at the contact point of two

moving bodies in contact along the line is created

1Rnp=-

where ɷrol is angular velocity of rolling bodies in the plane of the section in which the

curvature is calculated aB is the acceleration of installation The fundamental nature of the

obtained formula is that

1) in its generality it is commensurate with the kinematic formulas of Rodrigues and Freinet

known in differential geometry but it is intended for a different class of surfaces produced

in the process of formation by the rounding methods

2) curvature in any normal section of all surfaces formed by the rounding methods is

determined by only two scalar parameters and one of them (acceleration of installation)

does not depend on the direction of the section

It was also established that the sign of the acceleration of installation allow to make an

unambiguous judgement on the nature of the contact of bodies For example if aВgt 0 then

the envelope is formed inside the body of the generating element Acceleration of

installation allows to determine (ldquoincidentallyrdquo) the value of the radii of curvature and

faceting value across the whole surface formed by rounding at band- and flake-type

roughness

Thus over the past decade a substantial volume of theoretical knowledge to complete the

third cycle (creation of a computer-oriented theory of gearing) was accumulated

A lot of new notions are introduced and used in theory of gearing

Based on these new notions methods for analysis and synthesis of gear drives and cutter

tool meshings oriented at computer technologies have been developed and continue to be

improved

Intensive investigations to improve methods of optimization synthesis of gearing and to

develop methodologies of computer design and construction of gear boxes are performed

4 Problems and expected directions of the theory of gearing

Let us list the main problems in the gearing theory which in our opinion are the most

important

Problem 1 Creation of the theory of optimization synthesis of structures and parameters of

higher pairs of kinematic elements transmitting the motion and load at the preset and

optimal correlation of normal and friction forces At the present time theory of higher pairs

is being developed only as a pure geometrical science

88

Problem 2 Elaboration of methods of tooth optimal geometry synthesis oriented at the

modern processing technologies instead of traditional ones In this case a designer will have

to solve the variation problem with limitations providing for maximum possible load

capacity of gear drive in accordance with preselected criteria of performance efficiency

Problem 3 Development of methods for analysis of the process of the tooth preset surfaces

changeover taking into account the values of load tooth displacement manufacturing errors

of drive elements errors of relative position of engaging links dynamics of changeover

process

Problem 4 Creation of a unique interrelated complex of application software packages to

enable the designers and manufactures of gear drives to carry out optimization designing

engineering design preparation for production of various drives by meshing

Possible directions of development of the theory of gearing naturally follow from the afore-

described problems

CONCLUSIONS

In the second half of the XIX century the number and complexity of technical inventions of

various machines and mechanisms using the gear drives reached a critical mass and by

around 1890 the scientists had created the scientific basis of the theory of gearing And the

modern theory of gearing was formed by the beginning of the 1970rsquos

The third cycle of the gearing theory development which is oriented at computer technology

is underway

In our opinion the prospects for the development of theory of gearing as a part of the

theory of mechanisms and machines are higher as compared for example with the

linkages Firstly gears are more commonly used in cars than linkages Secondly the

theory of gearing is not only the theory of higher kinematic pairs - it is also the basis for the

theory of gear machining design

It is necessary to note that the current version of the paper is based on the paper published in

the first edition of the given Proceedings [72] but is as close as possible to the paper [73] by

the same authors This version of the article has been prepared by VE Starzhinsky

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2 Витрувий Десять книг об архитектуре ndash Москва laquoАрхитектура-Сraquo 2006 ndash 328 с

(Vitruvius Ten Books on Architecture ndash Moscov Architecture-C 2006 ndash 328 p)

3 Пипуныров ВН История часов с древнейших времен до наших дней - Москва

89

Наука 1982 ndash 496 c (Pipunyrov VN The clock story from ancient times to the present

day ndash Moscow Nauka 1982 ndash 496 p)

4 Академик ИИ Артоболевский Сборник Сост АМ Лепихов ndash М Знание 1983

ndash 176 c (Collection Comp AM Lepihov ndash Moscow Znanie 1983 ndash 176 p)

5 Чебышёв ПЛ Избранные труды ndash М Изд-во АН СССР 1955 ndash 926 с (Chebyshjov

PL Selected Works ndash Moscow AN SSSR 1955 ndash 926 p)

6 Рёло Ф Теоретическая кинематика 1875 (Relo F Theoretical Kinematics 1875)

7 Портретная галерея выдающихся инженеров и ученых в области зубчатых передач

ndash Сборник докладов научно-технической конференции с международным участием

Теория и практика зубчатых передач и редукторостроения Ижевск 2008 ndash C 378-

395 (Portrait Gallery of Disting wished Engineers and Scientist in Gearing ndash Proceedings

of Scientific-Engineering Conference with International Participation Theory and Practice

of Gearing and Reducer Building Izhevsk 2008 ndash P 378-395)

8 Литвин ФЛ Теория зубчатых зацеплений ndash М Наука 1968 ndash 584 с (Litvin FL

Theory of gearing ndash Moscow Nauka 1968 ndash 584 p)

9 Механика машин вып 45 ndash Москва Наука 1974 (Mechanics of machines No 45 ndash

Moscow Nauka 1974)

10 Willis R Principles of Mechanism ndash Cambridge London 1841

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магистра механики Одесса ndash 1886 ndash 232 с (Hokhman HI Link Theory generalized and

developed by analyzing Diss mastermechanic Odessa 1886 ndash 232 p)

12 Шишков ВА Образование поверхностей резанием по методу обкатки ndash Москва

Машгиз 1951 ndash 150 с (Shishkov VA Formation of surface machining by burnishing

method ndash Moscow Mashgiz 1951 ndash 150 p)

13 Вильдгабер Э Основы зацепления конических и гипоидных передач ndash Машгиз

1948 ndash 236 с (Vildgaber Je Principles of engagement bevel and hypoid gears ndash Moscow

Mashgiz 1948 ndash 236 p)

14 Baxter ML Basic Geometry and Tooth Contact of Hypoid Gears ldquoIndustrial

Mathematicsrdquo ndash 1961 ndash No 11 ndash P 19-42

15 Шевелева ГИ Алгоритм численного расчета обрабатываемой поверхности Станки

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calculation of the treated surface Machines and Tooling ndash 1969 ndash No 8 ndash P 17-20)

16 Николаев АФ Диаграмма винта и ее применение к определению сопряженных

линейчатых поверхностей с линейным касанием Труды семинара по ТММ вып 37

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Seminar on TMM ndash 1950 ndash No 37 ndash P52-106)

17 Новиков МЛ Зубчатые передачи с новым зацеплением ndash М Изд ВВИА им

Жуковского 1958 ndash 186 с (Novikov ML Gears with a new engagement ndash Moscow

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90

поверхностей в зубчатых передачах Сб laquoТеорияпередачвмашинахraquo М Машгиз

1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

78

synthesized transmission

All these principles are based on the theory of envelopes which was scientifically and

methodologically completed (at that period of time) in YaS Davydovrsquos VA Shishkovrsquos

and FL Litvinrsquos works Almost simultaneously and independently they proposed a method

for finding the kinematic envelope in which the meshing condition equation is used VN = 0

[8] At this time VA Shishkov [12] introduced a new concept - implementation speed Vn

equal to the scalar product Vn = V12n which became an effective tool in the study of gear

cutting tools working according to the form-generating method It became the basis of the

kinematic method for the synthesis and analysis of gearing in the second half of the XX

century

Ernest Wildhaber (1893-1979) a talented engineer and inventor of the company The

Gleason Works can be regarded as the founder of the second direction In 1927 he

proposed a method of forming hypoid gears and in 1930rsquos he patented Revacycle - the most

productive method (at that time) for spur bevel gears forming [13] Methods of forming

these transmissions are not based on Olivierrsquos principles E Wildhaber introduced gears

with non-conjugated tooth surfaces ndash transmissions with approximate meshing Basically

these gears cannot transmit rotation with constant gear ratio but the degree of deviation

from a constant gear ratio can be minimized by the targeted selection of values of gear

treatment process parameters Thus Wildhaber who abandoned the form-generating

method proved that there were possibilities of creating highly effective machining

processes for gears with non-conjugated tooth surfaces and thus initiated the theoretical

study of such transmissions

Active development of the theory of approximate meshing began after the 2nd World War

both in the US and the Soviet Union As the result the basic principle of the formation of

non-conjugate surfaces was formulated independently in the works of ML Baxter [14] and

FL Litvin [8] according to the principle the graph of deviation from the angular position

of the driven wheel from its position upon engagement of strictly conjugate surfaces is a

function similar to a parabola with the downward branches

At the same time it became clear that in order to meet challenges of synthesis and analysis

of gearing built on non-conjugated surfaces it is required to develop new mathematical

methods and models First mathematical models for studying gearing and computer

programs based on them appeared almost simultaneously in the US and the USSR

In the US TCA software package for the synthesis and analysis of hypoid gears [14] was

created under supervision of ML Baxter (1914-1994) chief engineer and researcher of The

Gleason Works

In the 1960rsquos methods for the synthesis of approximate gearing began to develop with the

advent of computers in the Soviet Union At first a software package for analysis and

synthesis of Revacycle spur bevel gear [9 p30-36] which included a numerical algorithm

for calculating the surface as an enveloping surface without using the theory of envelopes

[15] was developed at the Moscow Tooling and Machining Institute (STANKIN) under the

leadership of GI Sheveleva (1929-2005)

79

Similar software packages were developed in Saratov (Special Design Bureau of Gear ndash

Cutting Machines) under the leadership of MG Segal (1931-2000) and Leningrad (LITMO)

under supervision of FL Litvin The work on creation of universal programs for the

computer-based studies of spatial links was held in Tyumen [9 p36-43]

In the second half of the XX century the USSR became a recognized leader in terms of

volume and theoretical studies devoted to the study of the geometry of gears and gear

cutting tools After the end of World War II theoretical activities on creation of new methods

of analysis and synthesis of the working and technological gears was booming for 25-30

years Efforts of leading scientists (NI Kolchin FL Litvin VA Shishkov ML Novikov

LV Korostelyov GI Sheveleva II Dusev YaS Davydov ML Erikhov and others) have

led to creation of a new branch of science of the mechanisms - the gearing theory

The Soviet Union played the key role in creating the classical theory of gearing in early

1970rsquos The most important results obtained through efforts of domestic scientists which

formed the basis of the modern theory of gearing are listed below

1 Olivierrsquos principles for forming conjugate gearing are supplemented and developed AF

Nikolaev [16] ML Novikov [17] YaS Davydov [18] ML Erikhov [19]

2 New methods for analysis of the geometry of gears are developed and the existing ones

are improved differential (NI Kolchin the main publication of the year ndash 1957 [20])

screw (AF Nikolaev 1950 [16] KM Pismanik 1950 [21] NI Kolchin 1963 [22] VS

Lyukshin 1968 [23]) kinematic (YaS Davydov 1950 [24] VA Shishkov 1951 [12] NN

Krylov 1953 [25] FL Litvin 1960 [26] ML Erikhov 1972 [19]) matrix (FL Litvin

1968 [9]) power series (GI Sheveleva 1969 [27]) non-differential (GI Sheveleva 1969

[15]) tensor (II Dusev 1968 [28])

3 Methods of solving all major problems of synthesis and analysis of gears are established

Finding the envelope of a one-parameter and two-parameter family of surfaces (HI

Ketov NI Kolchin FL Litvin NN Krylov EG Ginsburg ML Erikhov) as well as

multi-parameter envelope family of surfaces and lines in spatial gearings (IL Brodsky DT

Babichev)

Finding an wrapping family of surfaces (GI Sheveleva)

Identifying the geometry generation features such as tooth undercutting interference and

others (MG Segal II Dusev GI Sheveleva VI Goldfarb BA Chyorny)

Synthesis of gearing geometry (local ndash FL Litvin ML Erikhov LV Korostelyov SA

Lagutin VN Rubtsov BP Timofeev and nonlocal ndash KI Gulyaev BA Chyorny MG

Segal)

Computation of curvatures in gearings (NI Kolchin FL Litvin VM Vasilyev II

Dusev EG Ginsburg LV Korostelyov ML Erikhov A M Pavlov MG Segal)

Computation of other geometric-kinematic characteristics of the teeth contact (AK

Georgiev VI Goldfarb SA Lagutin MF Lenski)

Solution of the inverse problem of the gearing theory tooth meshing analysis (KI

Gulyaev FL Litvin MG Segal BP Timofeev GI Sheveleva)

80

The impact of manufacturing errors and assembling on quality of engagement synthesis

of toothed meshing insensitive to errors (ML Erikhov NG Lindtrop LV Korostelyov

NN Krylov LY Liburkin GI Sheveleva)

Numerous studies of specific gears are conducted based on theoretical developments and

established procedures The most important practical problems solved during this period

are

1 Principally new types of gearing have been discovered helical gear in which arcs of

circles with radii small difference are selected as the profiles of cross-sections ndash Novikov-

Wildhaber gear [17] and gears with closed contact lines where the load between teeth is

transferred through the grease wedged in a closed cavity between active surfaces due to

closure of the contact line (LV Korostelyev SA Lagutin [29])

2 Geometric problems of synthesis of cylindrical involute gears were almost exhaustively

resolved and brought into engineering practice geometric calculation (VA Gavrylenko

1969 [30]) selection of the optimum addendum modification coefficients by using blocking

circuits (MB Groman 1957 [31]) according to the atlas compiled and published under the

direction of IA Bolotovsky 1967 [32]

3 New types of gearings have been studied and introduced In this regard various problems

related to analysis and synthesis of the following common types of gears have been solved

Bevel (NI Kolchin and VV Boldyrev 1937 YS Davydov 1950 VI Bezrukov 1963

VM Denisov 1963 GI Sheveleva 1966 HF Kabatov and GA Lopato 1966 MG

Segal 1971 KI Gulyaev 1974 VN Syzrantsev 1975)

Hypoid (GI Apukhtin 1952 FL Litvin 1962 KM Pismanik 1964 II Dusev and VM

Vasilyev 1968 MG Segal 1971)

Cylindrical gear drives with Novikovrsquos gear (ML Novikov 1956 RV Fedyakin and

VA Chesnokov 1958 VN Kudryavtsev 1959 EG Roslivker 1964 NI Kolchin 1968

VN Sevryuk 1972 and others)

Revacycle spur bevel gear (GI Sheveleva 1966)

New worm gear design toroid (YaI Dicker 1948) globoid (PS Zak 1962) worm gear

drives (FL Litvin 1962 IS Krivenko 1967 LV Korostelyev and SA Lagutin 1973

etc) spiroid (S Golubkov 1959 AK Georgiev and VI Goldfarb 1972 and others)

Less common known types of gears have also been studied and implemented

Hyperboloid (KM Pismanik 1950)

Helical-bevel (LY Liburkin 1968)

Wave (EG Ginsburg 1969)

Cylindrical with arched and spiral teeth (ML Erikhov and VN Syzrantsev 1975)

4 Techniques of analysis and synthesis of gears with non-circular wheels are developed [33]

and their production is organized

5 A lot of works are published including a number of classic books on theory of gearing

YaI Dieker (1935) NI Kolchin (1937-1952) FL Litvin (1952-1968) YaS Davydov

81

(1950) VA Gavrylenko (1949-1969) ML Novikov (1958) VA Zalgaller (1975) LD

Chasovnikov (1969) IA Bolotovsky et al (1962-1967) VN Kudryavtsev (1949-1971)

VN Kedrinsky (1960-1967) KM Pismanik (1964-1967) PS Zack (1962) NF Kabatov

and GA Lopato (1966) VA Shishkov (1951) and many others FL Litvinrsquos monograph

[8] stands out among these works it was published in 1968 and still remains a handbook for

professionals in the theory of gearing

The book by VA Zalgaller Envelope Theory [34] which is not very big in volume is

characterized by depth the mathematical rigor and completeness of the argumentation

Note that the appreciation level of the activities under the second cycle is confirmed by the

fact that in 1958 ML Novikov was awarded the Lenin Prize ndash the most prestigious USSR

award presented to individuals for accomplishments in the professional field

The following facts also confirm that the Soviet scientists made a decisive contribution to

the theory of gearing as a science and the fact that the Soviet Union had prepared a large

number of highly qualified specialists in the theory of gearing

FL Litvinrsquos monograph Theory of Gearing which was written in the late 60rsquos is still the

main handbook for gear specialists while Litvin is regarded as the creator of the modern

theory of gearing not only in CIS countries but also around the world

This monograph revised and expanded was reprinted abroad in English co-written with

FL Litvinrsquos new foreign students [35]

Number of qualified experts in the theory of gearing (by the way which were not widely

known in the Soviet Union and the CIS back then) have emigrated to the Western countries

and are writing and publishing quite significant books in English on the theory of gearing

and geometry of gears (SP Radzevich AL Kapelevich SV Lunin)

Summarizing the second cycle let us quote SA Lagutin who most accurately reflect the

essence of this bright period [36] it was a period of storm and pressure in the development

of the gearing theory in Russia when a whole galaxy of brilliant researchers were working

in this area headed by NI Kolchin and FL Litvin By collaborating and competing with

each other in a few years they have built amazingly beautiful building of the new science at

the junction of differential geometry and mechanics of machines

33 Laying the foundations of computer-oriented theory of gearing

The main purpose of such a theory is to become a basis for the methods of computer

analysis synthesis design and manufacturing gear parts for gear engagement

By the mid-70rsquos theory of gearing as a science has reached adulthood the main priority and

theoretical problems of analysis and synthesis of gearing have been resolved The number of

innovative theoretical work began to decline Studies are getting closer to the production

and the theory of gearing acts primarily as a tool for solving specific engineering problems

Since the mid 70-ies of XX century the theory of gearing as well as the machine tool

industry has evolved concurrently in two directions global and Russian

82

The global development of the theory of gearing has taken place against the backdrop of

revolution experienced by the machine tool industry since the 80rsquos

First machines with semi-rigid connections partially controlled by computer began to

appear in developed countries and then complete automatic machines (multi-axis CNC

machines) appeared

At that time for example machines for processing bevel gears with circular teeth Phoenix

(Gleason) and WNC30 (Klingelnberg) were developed The creation of such machines

occurred in parallel with the development of new mathematical models for shaping parts on

multi-axis machines and testing the parts operability before their casting in the metal At

that time software systems LTCA (Gleason) and Kimos (Klingelnberg) were developed

which made it possible to solve the problem of synthesis and analysis of bevel gears with

circular teeth [37]

All developed countries pursue the global direction in the development of the theory of

gearing in the same manner and using similar approaches The following was used by the

gear specialists to solve the problems of analysis and synthesis

Methods of classical theory of gearing (with computer design of the geometry of any kind

of gears)

Techniques of non-differential analysis of gear ndash forming processes using universal as

well as specially developed software packages

Methods of boundary and finite elements (at the analysis of the contact interaction of

acting surfaces of the teeth)

Finite element methods and integral equations (at the analysis of the stress-strain state of

the teeth)

Numerical optimization methods (at the synthesis of geometry of acting and fillet surfaces

of teeth)

An expanded list of quality indicators of gearings including new ones the design

thickness of the oil film criteria of hot and cold seizure criteria for assessing the conditions

for the formation of an oil wedge indicators of vibration activity of the gearing and others

Designing gear drives was regarded as a complex problem requiring an agreed solution of a

group of interrelated tasks

Selection of design scheme of a gear

Synthesis of permissible geometry

Geometry optimization

Structural arrangement and evaluation of quality indicators

Identification and addressing the weaknesses

Designing technical processes of manufacture selection or synthesis of tools subsequent

optimization etc

The developed theory of gearing is known as Theory of Real Gearing in Russia Ukraine

and Belarus while abroad it is called ldquoIntegrated Gear Designrdquo (IGD) or Integrated Design

83

of Gears

Russian direction in the development of the theory of gearing has several specific features

attributable to the following objective circumstances

Firstly first clear signs of stagnation appeared in the USSR industry in the late 70rsquos

Secondly the number of graduate students reduced as the universities basically solved the

problem of teachers which they faced in the early 60rsquos due to a drastic increase in the

number of students being trained in engineering specialties And finally Russia lost the top

three main theorists in the field of the theory of gearing FL Litvin was forced to emigrate

to the USA LV Korostelyov died in a car crash YaS Davydov departed from active

research and subsequently left for the USA

And nevertheless in 15-20 years preceding the collapse of the USSR in 1991 the theory

and geometry of gearing in the Soviet Union was continuing to develop At that time new

centers specializing in different aspects of the theory of gearing were established Let us list

the most interesting in our opinion research topics at the end of the last century

- Issues of strength and solution of the tooth contact problem (EL Airapetov VN

Syzrantsev GI Sheveleva)

- Research on gear bending bending stresses calculation (GI Sheveleva VI Medvedev)

- Non-differential methods for the determination of the contact surfaces characteristics (VI

Goldfarb GI Sheveleva AE Volkov)

- Issues of design synthesis analysis and manufacturing spiroid gear drives (AK Georgiev

VI Goldfarb)

- Issues of design synthesis analysis and manufacturing worm gear drives (SA Lagutin

AI Sandler)

- Research of hypoid bevel gear drives with circular teeth (MG Segal GI Sheveleva VN

Syzrantsev)

- Research of gear drives with intermediate bodies (AE Belyaev)

- Research of helical-bevel gear drives (BA Lopatin)

- Development of methods for the synthesis of gear drives (MG Segal SA Lagutin GI

Sheveleva VI Medvedev VN Syzrantsev)

- Forming a theoretical framework for the development of universal programs for the

analysis of spatial working and technological meshings and the creation of corresponding

programs (DT Babichev)

As a result of these studies software systems were developed in the Soviet Union which

were aimed at solving the problems of synthesis and analysis primarily for bevel gears with

circular teeth The best known ones include PC Volga5 made under the direction of MG

Segal [38] and PC Expert created under the direction of GI Sheveleva [39]

The fact that MG Segal was the main developer of the PC Kimos (firm Klingelnberg) in

the 90rsquos confirms the high level of those developments

It should also be noted that a work on the selection of optimal schemes for multi-axis CNC

84

machines for processing gear was carried out in 1990 in Saratov (MG Segal LI Shejko

[40]) These developments have also been used by Klingelnberg

The researches (above all theoretical ones) continued after the collapse of the USSR in

Russia Ukraine and Belarus

At that time the development of the theory of gearing was distinguished by a high level of

theoretical studies based on the introduction of new geometric geometric-kinematic and

other concepts and development (on their basis) of new mathematical models methods and

algorithms for analysis and synthesis of the working and technological gear engagements

These works were performed mostly at their own initiative by highly qualified specialists-

theorists in the field of theory and geometry of working and technological gear meshing

Usually they were elderly university professors who were practically deprived of relations

with the machine-building industry after its stagnation during the collapse of the USSR

It should be noted that it is very difficult to distinguish the most important areas of research

in the modern theory of gearing As the poet said Great things are better seen from a

distance Therefore we will list the most interesting in our view theoretical works on the

development of the theory of gearing with greater focus on the Russian line of research

However we practically do not consider the works on gear geometry ndash they are too

numerous A fairly complete picture of the theoretical works of this period can be obtained

from the proceedings of symposia and conferences held in Kurgan (KMI) Izhevsk

(IzhSTU) and Sevastopol (KhPI Kharkov) The main directions in the development of the

theory of gearing and the most important theoretical results after 1970s include the

following

1 Introduction and use of new concepts such as

Meshing Space (SA Lagutin [41])

Wrapping surface (GI Sheveleva [39])

Fan wedge and normal beam accelerating of implantation (DT Babichev [42])

2 Development of methods for analyzing processes of generation

A new method of finding a singularity in the flat gearing (SA Lagutin) based on the

situation [43] return point at the gear profile occurs at the point in the line of engagement

in which the normal to this line intersects the axis of rotation of the pinion The method was

extended to the spatial gearing (AE Volkov [44])

3 Development of methods of synthesis

Based on the new concept of space of engagement and its properties This approach was

used during the synthesis of both spatial transmission (SA Lagutin [45]) and the cylindrical

(DT Babichev [46])

By using as objective function new criteria of load capacity - permissible contact

pressure(VI Medvedev [47]) the specific work of working surfaces of teeth (DT Babichev

[48]) and others

For bevel gears with small cross-axis angle (SA Lagutin [49] VI Medvedev [50])

Synthesis of gears considering technological limitations of the given production processes

85

(VI Medvedev [51] VN Syzrantsev [52])

By using and developing a method of synthesis of gears in generalizing parameters

originally proposed by EB Vulgakov for involute gears The method was modified by VL

Dorofeev - for involute and ON Tsukanov and BA Lopatin ndash for non-involute gears

(including cylinder-conical ones) [53]

By using variational methods of synthesis when the equation of an optimal surface of the

tooth and its coefficients are determined This approach was first applied apparently by

Alan Lebec [54] in the United States it was used in Ukraine [55] and being developed in

Russia where equal strength gears have been synthesized by using the method (by Hertz

contact strength) [46 56] and the method of synthesis of bevel gear with circular teeth

according to the criteria of minimal contact pressure and bending stresses while maintaining

the overall dimensions of the gear has been developed which is important for aviation

where the weight of the structure is crucial [57]

Increasing the bending strength of circular tooth bevel gears by optimizing the shape of

the tool [58]

Increasing the load-bearing capacity of high-speed heavy-duty cylindrical involute gears

Note that EB Vulgakov VL Dorofeev and AL Kapelevich have made a significant

contribution to the development of synthesis aviation gear in recent decades [59]

4 Development of methods of analysis of loaded gears considering multipairness of

contact

For bevel gears with circular teeth [60]

For spiroid gears [61]

5 Significant progress has been made in the methods of analysis synthesis design and

manufacture of worm gear transmissions

The main input in this field of gearing has been made by two groups of researchers under

the leadership of VI Goldfarb and SA Lagutin The techniques of minimizing meshing

errors and worm hob errors that appear when regrinding and relieving works are fulfilled

have been developed by SA Lagutin and AI Sandler The techniques of synthesis and

production of gears with localized contact were drilled worm gears (SA Lagutin AI

Sandler [62]) and spiroid ones (VI Goldfarb ES Trubachyov [63])

The drives with the increased load capacity were designed based on a study of meshing

space of non-orthogonal gears spiroid (ES Trubachyov [63]) and worm ones (VYu

Puzanov) Designing of spiroid transmissions is carried out using CAD ldquoSPDIAL+rdquo

developed by a group headed by VI Goldfarb Configurator of gearbox systems for

optimization structural synthesis of their structures is being created (OV Malina etal)

Unified worm hob cutters cutting gears for the drives with localized contact were designed

It became possible to cut the gear wheels in engagement with multiple-thread worm by a

single-pass mill (VI Goldfarb and his disciples)

In the Institute of Mechanics IzhSTU a group led by VI Goldfarb essentially laid the

foundation for a new Russian machine building sub-industry ndash construction of gearboxes for

86

isolation and control valves for pipelines

- Theoretical studies of spiroid and worm gears are at a high scientific level

- A modern design process is applied synthesis of perfect engagement synthesis of

localized contact simulation of the stress strain state analysis of real engagement under

load forecasting the state of transmission

- Three generations of dimension-type series of quarter-turn and multi-turn spiroid gear

drives are developed their production with modern quality control and acceptance tests is

organized

6 Application of unconventional gears and gearing helical-bevel gears (BA Lopatin [65])

transmissions with intermediate rolling bodies (AE Belyaev [66]) hydraulic and

pneumatic machines with non-circular gears (An-I-Kahn [67]) precessing transmissions

(IA Bostan [68] EI Tesker [69] VN Syzrantsev BA Lopatin) and other

7 Development of kinematic analysis methods of working and technological meshings Note

that modern designing is the computer designing This factor imposes high requirements to

the theory of gearing as the main mathematical basis for such designing We have to admit

that the classical theory of gearing does not fully comply with these demanding

requirements Thus according to Prof MG Segal who was working with Klingelnberg in

the last years of his life the head of the company prohibited to use differential methods ndash

the basis of the classical theory of gearing ndash in the programs being created The reason for

the ban was inadequacy of the results of computer simulation as compared to real processes

of formation Theoretical research aimed at creating computational models that are

adequate to the real processes of formation and contact of moving bodies were developed by

AE Volkov and VI Medvedev (Moscow) and DT Babichev (Tyumen)

To eliminate the phenomenon DT Babichev elaborated a unified kinematic method for

analysis of the processes of formation [70] based on the ldquotriadrdquo ruptures + envelopes + new

concepts of curvilinear coordinates As the result the cause of inadequacy between the

classical methods of the theory of gearing and real-life processes of formation was

established and rectified The developed kinematic method

Allows to find all the surfaces formed on the item at gear machining formed by smooth

surfaces and inflections of bodies including at advanceretraction of machine tool and in

secondary cutting areas

Has the reliability of non-differential methods but is superior to them in speed of

operation by two orders of magnitude which is confirmed by its partial use in CAD

ldquoSPDIAL +rdquo

Also allows to define the curvatures in gearing

8 Development of the system for assigning real ITS (Initial Tool Surfaces) and construction

of mathematical models for them [71] Real ITS is the set of all forming tools (pieces of

surfaces cutting and boundary edges and corners) for which uniform curvilinear coordinates

are introduced

9 By using the concept of ldquothe acceleration of installationrdquo new techniques for solving

87

multitude of tasks are created calculating the radii of curvature in the gearing identifying

cutting areas and thickness of the layers being cut by tool cutting edges and others (DT

Babichev [48])

For example based on the concept of the acceleration of installation a new basic formula

for calculating the reduced curvature in any normal sections at the contact point of two

moving bodies in contact along the line is created

1Rnp=-

where ɷrol is angular velocity of rolling bodies in the plane of the section in which the

curvature is calculated aB is the acceleration of installation The fundamental nature of the

obtained formula is that

1) in its generality it is commensurate with the kinematic formulas of Rodrigues and Freinet

known in differential geometry but it is intended for a different class of surfaces produced

in the process of formation by the rounding methods

2) curvature in any normal section of all surfaces formed by the rounding methods is

determined by only two scalar parameters and one of them (acceleration of installation)

does not depend on the direction of the section

It was also established that the sign of the acceleration of installation allow to make an

unambiguous judgement on the nature of the contact of bodies For example if aВgt 0 then

the envelope is formed inside the body of the generating element Acceleration of

installation allows to determine (ldquoincidentallyrdquo) the value of the radii of curvature and

faceting value across the whole surface formed by rounding at band- and flake-type

roughness

Thus over the past decade a substantial volume of theoretical knowledge to complete the

third cycle (creation of a computer-oriented theory of gearing) was accumulated

A lot of new notions are introduced and used in theory of gearing

Based on these new notions methods for analysis and synthesis of gear drives and cutter

tool meshings oriented at computer technologies have been developed and continue to be

improved

Intensive investigations to improve methods of optimization synthesis of gearing and to

develop methodologies of computer design and construction of gear boxes are performed

4 Problems and expected directions of the theory of gearing

Let us list the main problems in the gearing theory which in our opinion are the most

important

Problem 1 Creation of the theory of optimization synthesis of structures and parameters of

higher pairs of kinematic elements transmitting the motion and load at the preset and

optimal correlation of normal and friction forces At the present time theory of higher pairs

is being developed only as a pure geometrical science

88

Problem 2 Elaboration of methods of tooth optimal geometry synthesis oriented at the

modern processing technologies instead of traditional ones In this case a designer will have

to solve the variation problem with limitations providing for maximum possible load

capacity of gear drive in accordance with preselected criteria of performance efficiency

Problem 3 Development of methods for analysis of the process of the tooth preset surfaces

changeover taking into account the values of load tooth displacement manufacturing errors

of drive elements errors of relative position of engaging links dynamics of changeover

process

Problem 4 Creation of a unique interrelated complex of application software packages to

enable the designers and manufactures of gear drives to carry out optimization designing

engineering design preparation for production of various drives by meshing

Possible directions of development of the theory of gearing naturally follow from the afore-

described problems

CONCLUSIONS

In the second half of the XIX century the number and complexity of technical inventions of

various machines and mechanisms using the gear drives reached a critical mass and by

around 1890 the scientists had created the scientific basis of the theory of gearing And the

modern theory of gearing was formed by the beginning of the 1970rsquos

The third cycle of the gearing theory development which is oriented at computer technology

is underway

In our opinion the prospects for the development of theory of gearing as a part of the

theory of mechanisms and machines are higher as compared for example with the

linkages Firstly gears are more commonly used in cars than linkages Secondly the

theory of gearing is not only the theory of higher kinematic pairs - it is also the basis for the

theory of gear machining design

It is necessary to note that the current version of the paper is based on the paper published in

the first edition of the given Proceedings [72] but is as close as possible to the paper [73] by

the same authors This version of the article has been prepared by VE Starzhinsky

REFERENCES

1 Дильс ГА Античная техника Москва-Ленинград ОНТИ - Гос техн-теор изд-во ndash

1934 ndash 215 с (Diels GA Antique appliances - Moscow-Leningrad ONTI - Gos tehn-

teor Publ 1934 ndash 215 p)

2 Витрувий Десять книг об архитектуре ndash Москва laquoАрхитектура-Сraquo 2006 ndash 328 с

(Vitruvius Ten Books on Architecture ndash Moscov Architecture-C 2006 ndash 328 p)

3 Пипуныров ВН История часов с древнейших времен до наших дней - Москва

89

Наука 1982 ndash 496 c (Pipunyrov VN The clock story from ancient times to the present

day ndash Moscow Nauka 1982 ndash 496 p)

4 Академик ИИ Артоболевский Сборник Сост АМ Лепихов ndash М Знание 1983

ndash 176 c (Collection Comp AM Lepihov ndash Moscow Znanie 1983 ndash 176 p)

5 Чебышёв ПЛ Избранные труды ndash М Изд-во АН СССР 1955 ndash 926 с (Chebyshjov

PL Selected Works ndash Moscow AN SSSR 1955 ndash 926 p)

6 Рёло Ф Теоретическая кинематика 1875 (Relo F Theoretical Kinematics 1875)

7 Портретная галерея выдающихся инженеров и ученых в области зубчатых передач

ndash Сборник докладов научно-технической конференции с международным участием

Теория и практика зубчатых передач и редукторостроения Ижевск 2008 ndash C 378-

395 (Portrait Gallery of Disting wished Engineers and Scientist in Gearing ndash Proceedings

of Scientific-Engineering Conference with International Participation Theory and Practice

of Gearing and Reducer Building Izhevsk 2008 ndash P 378-395)

8 Литвин ФЛ Теория зубчатых зацеплений ndash М Наука 1968 ndash 584 с (Litvin FL

Theory of gearing ndash Moscow Nauka 1968 ndash 584 p)

9 Механика машин вып 45 ndash Москва Наука 1974 (Mechanics of machines No 45 ndash

Moscow Nauka 1974)

10 Willis R Principles of Mechanism ndash Cambridge London 1841

11 Гохман ХИ Теория зацеплений обобщенная и развитая путем анализа Дисс

магистра механики Одесса ndash 1886 ndash 232 с (Hokhman HI Link Theory generalized and

developed by analyzing Diss mastermechanic Odessa 1886 ndash 232 p)

12 Шишков ВА Образование поверхностей резанием по методу обкатки ndash Москва

Машгиз 1951 ndash 150 с (Shishkov VA Formation of surface machining by burnishing

method ndash Moscow Mashgiz 1951 ndash 150 p)

13 Вильдгабер Э Основы зацепления конических и гипоидных передач ndash Машгиз

1948 ndash 236 с (Vildgaber Je Principles of engagement bevel and hypoid gears ndash Moscow

Mashgiz 1948 ndash 236 p)

14 Baxter ML Basic Geometry and Tooth Contact of Hypoid Gears ldquoIndustrial

Mathematicsrdquo ndash 1961 ndash No 11 ndash P 19-42

15 Шевелева ГИ Алгоритм численного расчета обрабатываемой поверхности Станки

и инструмент ndash 1969 ndash 8 ndash C17-20 (Sheveleva GI Algorithm for the numerical

calculation of the treated surface Machines and Tooling ndash 1969 ndash No 8 ndash P 17-20)

16 Николаев АФ Диаграмма винта и ее применение к определению сопряженных

линейчатых поверхностей с линейным касанием Труды семинара по ТММ вып 37

1950 ndash С52ndash106 (Nikolaev AF Diagram of the screw and its application to the

determination of conjugate ruled surfaces with a linear contact Proceedings of the

Seminar on TMM ndash 1950 ndash No 37 ndash P52-106)

17 Новиков МЛ Зубчатые передачи с новым зацеплением ndash М Изд ВВИА им

Жуковского 1958 ndash 186 с (Novikov ML Gears with a new engagement ndash Moscow

Publisher VVIA by named Zhukovsky 1958 ndash 186 p)

18 Давыдов ЯС Об одном обобщении метода Оливье для образования сопряженных

90

поверхностей в зубчатых передачах Сб laquoТеорияпередачвмашинахraquo М Машгиз

1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

79

Similar software packages were developed in Saratov (Special Design Bureau of Gear ndash

Cutting Machines) under the leadership of MG Segal (1931-2000) and Leningrad (LITMO)

under supervision of FL Litvin The work on creation of universal programs for the

computer-based studies of spatial links was held in Tyumen [9 p36-43]

In the second half of the XX century the USSR became a recognized leader in terms of

volume and theoretical studies devoted to the study of the geometry of gears and gear

cutting tools After the end of World War II theoretical activities on creation of new methods

of analysis and synthesis of the working and technological gears was booming for 25-30

years Efforts of leading scientists (NI Kolchin FL Litvin VA Shishkov ML Novikov

LV Korostelyov GI Sheveleva II Dusev YaS Davydov ML Erikhov and others) have

led to creation of a new branch of science of the mechanisms - the gearing theory

The Soviet Union played the key role in creating the classical theory of gearing in early

1970rsquos The most important results obtained through efforts of domestic scientists which

formed the basis of the modern theory of gearing are listed below

1 Olivierrsquos principles for forming conjugate gearing are supplemented and developed AF

Nikolaev [16] ML Novikov [17] YaS Davydov [18] ML Erikhov [19]

2 New methods for analysis of the geometry of gears are developed and the existing ones

are improved differential (NI Kolchin the main publication of the year ndash 1957 [20])

screw (AF Nikolaev 1950 [16] KM Pismanik 1950 [21] NI Kolchin 1963 [22] VS

Lyukshin 1968 [23]) kinematic (YaS Davydov 1950 [24] VA Shishkov 1951 [12] NN

Krylov 1953 [25] FL Litvin 1960 [26] ML Erikhov 1972 [19]) matrix (FL Litvin

1968 [9]) power series (GI Sheveleva 1969 [27]) non-differential (GI Sheveleva 1969

[15]) tensor (II Dusev 1968 [28])

3 Methods of solving all major problems of synthesis and analysis of gears are established

Finding the envelope of a one-parameter and two-parameter family of surfaces (HI

Ketov NI Kolchin FL Litvin NN Krylov EG Ginsburg ML Erikhov) as well as

multi-parameter envelope family of surfaces and lines in spatial gearings (IL Brodsky DT

Babichev)

Finding an wrapping family of surfaces (GI Sheveleva)

Identifying the geometry generation features such as tooth undercutting interference and

others (MG Segal II Dusev GI Sheveleva VI Goldfarb BA Chyorny)

Synthesis of gearing geometry (local ndash FL Litvin ML Erikhov LV Korostelyov SA

Lagutin VN Rubtsov BP Timofeev and nonlocal ndash KI Gulyaev BA Chyorny MG

Segal)

Computation of curvatures in gearings (NI Kolchin FL Litvin VM Vasilyev II

Dusev EG Ginsburg LV Korostelyov ML Erikhov A M Pavlov MG Segal)

Computation of other geometric-kinematic characteristics of the teeth contact (AK

Georgiev VI Goldfarb SA Lagutin MF Lenski)

Solution of the inverse problem of the gearing theory tooth meshing analysis (KI

Gulyaev FL Litvin MG Segal BP Timofeev GI Sheveleva)

80

The impact of manufacturing errors and assembling on quality of engagement synthesis

of toothed meshing insensitive to errors (ML Erikhov NG Lindtrop LV Korostelyov

NN Krylov LY Liburkin GI Sheveleva)

Numerous studies of specific gears are conducted based on theoretical developments and

established procedures The most important practical problems solved during this period

are

1 Principally new types of gearing have been discovered helical gear in which arcs of

circles with radii small difference are selected as the profiles of cross-sections ndash Novikov-

Wildhaber gear [17] and gears with closed contact lines where the load between teeth is

transferred through the grease wedged in a closed cavity between active surfaces due to

closure of the contact line (LV Korostelyev SA Lagutin [29])

2 Geometric problems of synthesis of cylindrical involute gears were almost exhaustively

resolved and brought into engineering practice geometric calculation (VA Gavrylenko

1969 [30]) selection of the optimum addendum modification coefficients by using blocking

circuits (MB Groman 1957 [31]) according to the atlas compiled and published under the

direction of IA Bolotovsky 1967 [32]

3 New types of gearings have been studied and introduced In this regard various problems

related to analysis and synthesis of the following common types of gears have been solved

Bevel (NI Kolchin and VV Boldyrev 1937 YS Davydov 1950 VI Bezrukov 1963

VM Denisov 1963 GI Sheveleva 1966 HF Kabatov and GA Lopato 1966 MG

Segal 1971 KI Gulyaev 1974 VN Syzrantsev 1975)

Hypoid (GI Apukhtin 1952 FL Litvin 1962 KM Pismanik 1964 II Dusev and VM

Vasilyev 1968 MG Segal 1971)

Cylindrical gear drives with Novikovrsquos gear (ML Novikov 1956 RV Fedyakin and

VA Chesnokov 1958 VN Kudryavtsev 1959 EG Roslivker 1964 NI Kolchin 1968

VN Sevryuk 1972 and others)

Revacycle spur bevel gear (GI Sheveleva 1966)

New worm gear design toroid (YaI Dicker 1948) globoid (PS Zak 1962) worm gear

drives (FL Litvin 1962 IS Krivenko 1967 LV Korostelyev and SA Lagutin 1973

etc) spiroid (S Golubkov 1959 AK Georgiev and VI Goldfarb 1972 and others)

Less common known types of gears have also been studied and implemented

Hyperboloid (KM Pismanik 1950)

Helical-bevel (LY Liburkin 1968)

Wave (EG Ginsburg 1969)

Cylindrical with arched and spiral teeth (ML Erikhov and VN Syzrantsev 1975)

4 Techniques of analysis and synthesis of gears with non-circular wheels are developed [33]

and their production is organized

5 A lot of works are published including a number of classic books on theory of gearing

YaI Dieker (1935) NI Kolchin (1937-1952) FL Litvin (1952-1968) YaS Davydov

81

(1950) VA Gavrylenko (1949-1969) ML Novikov (1958) VA Zalgaller (1975) LD

Chasovnikov (1969) IA Bolotovsky et al (1962-1967) VN Kudryavtsev (1949-1971)

VN Kedrinsky (1960-1967) KM Pismanik (1964-1967) PS Zack (1962) NF Kabatov

and GA Lopato (1966) VA Shishkov (1951) and many others FL Litvinrsquos monograph

[8] stands out among these works it was published in 1968 and still remains a handbook for

professionals in the theory of gearing

The book by VA Zalgaller Envelope Theory [34] which is not very big in volume is

characterized by depth the mathematical rigor and completeness of the argumentation

Note that the appreciation level of the activities under the second cycle is confirmed by the

fact that in 1958 ML Novikov was awarded the Lenin Prize ndash the most prestigious USSR

award presented to individuals for accomplishments in the professional field

The following facts also confirm that the Soviet scientists made a decisive contribution to

the theory of gearing as a science and the fact that the Soviet Union had prepared a large

number of highly qualified specialists in the theory of gearing

FL Litvinrsquos monograph Theory of Gearing which was written in the late 60rsquos is still the

main handbook for gear specialists while Litvin is regarded as the creator of the modern

theory of gearing not only in CIS countries but also around the world

This monograph revised and expanded was reprinted abroad in English co-written with

FL Litvinrsquos new foreign students [35]

Number of qualified experts in the theory of gearing (by the way which were not widely

known in the Soviet Union and the CIS back then) have emigrated to the Western countries

and are writing and publishing quite significant books in English on the theory of gearing

and geometry of gears (SP Radzevich AL Kapelevich SV Lunin)

Summarizing the second cycle let us quote SA Lagutin who most accurately reflect the

essence of this bright period [36] it was a period of storm and pressure in the development

of the gearing theory in Russia when a whole galaxy of brilliant researchers were working

in this area headed by NI Kolchin and FL Litvin By collaborating and competing with

each other in a few years they have built amazingly beautiful building of the new science at

the junction of differential geometry and mechanics of machines

33 Laying the foundations of computer-oriented theory of gearing

The main purpose of such a theory is to become a basis for the methods of computer

analysis synthesis design and manufacturing gear parts for gear engagement

By the mid-70rsquos theory of gearing as a science has reached adulthood the main priority and

theoretical problems of analysis and synthesis of gearing have been resolved The number of

innovative theoretical work began to decline Studies are getting closer to the production

and the theory of gearing acts primarily as a tool for solving specific engineering problems

Since the mid 70-ies of XX century the theory of gearing as well as the machine tool

industry has evolved concurrently in two directions global and Russian

82

The global development of the theory of gearing has taken place against the backdrop of

revolution experienced by the machine tool industry since the 80rsquos

First machines with semi-rigid connections partially controlled by computer began to

appear in developed countries and then complete automatic machines (multi-axis CNC

machines) appeared

At that time for example machines for processing bevel gears with circular teeth Phoenix

(Gleason) and WNC30 (Klingelnberg) were developed The creation of such machines

occurred in parallel with the development of new mathematical models for shaping parts on

multi-axis machines and testing the parts operability before their casting in the metal At

that time software systems LTCA (Gleason) and Kimos (Klingelnberg) were developed

which made it possible to solve the problem of synthesis and analysis of bevel gears with

circular teeth [37]

All developed countries pursue the global direction in the development of the theory of

gearing in the same manner and using similar approaches The following was used by the

gear specialists to solve the problems of analysis and synthesis

Methods of classical theory of gearing (with computer design of the geometry of any kind

of gears)

Techniques of non-differential analysis of gear ndash forming processes using universal as

well as specially developed software packages

Methods of boundary and finite elements (at the analysis of the contact interaction of

acting surfaces of the teeth)

Finite element methods and integral equations (at the analysis of the stress-strain state of

the teeth)

Numerical optimization methods (at the synthesis of geometry of acting and fillet surfaces

of teeth)

An expanded list of quality indicators of gearings including new ones the design

thickness of the oil film criteria of hot and cold seizure criteria for assessing the conditions

for the formation of an oil wedge indicators of vibration activity of the gearing and others

Designing gear drives was regarded as a complex problem requiring an agreed solution of a

group of interrelated tasks

Selection of design scheme of a gear

Synthesis of permissible geometry

Geometry optimization

Structural arrangement and evaluation of quality indicators

Identification and addressing the weaknesses

Designing technical processes of manufacture selection or synthesis of tools subsequent

optimization etc

The developed theory of gearing is known as Theory of Real Gearing in Russia Ukraine

and Belarus while abroad it is called ldquoIntegrated Gear Designrdquo (IGD) or Integrated Design

83

of Gears

Russian direction in the development of the theory of gearing has several specific features

attributable to the following objective circumstances

Firstly first clear signs of stagnation appeared in the USSR industry in the late 70rsquos

Secondly the number of graduate students reduced as the universities basically solved the

problem of teachers which they faced in the early 60rsquos due to a drastic increase in the

number of students being trained in engineering specialties And finally Russia lost the top

three main theorists in the field of the theory of gearing FL Litvin was forced to emigrate

to the USA LV Korostelyov died in a car crash YaS Davydov departed from active

research and subsequently left for the USA

And nevertheless in 15-20 years preceding the collapse of the USSR in 1991 the theory

and geometry of gearing in the Soviet Union was continuing to develop At that time new

centers specializing in different aspects of the theory of gearing were established Let us list

the most interesting in our opinion research topics at the end of the last century

- Issues of strength and solution of the tooth contact problem (EL Airapetov VN

Syzrantsev GI Sheveleva)

- Research on gear bending bending stresses calculation (GI Sheveleva VI Medvedev)

- Non-differential methods for the determination of the contact surfaces characteristics (VI

Goldfarb GI Sheveleva AE Volkov)

- Issues of design synthesis analysis and manufacturing spiroid gear drives (AK Georgiev

VI Goldfarb)

- Issues of design synthesis analysis and manufacturing worm gear drives (SA Lagutin

AI Sandler)

- Research of hypoid bevel gear drives with circular teeth (MG Segal GI Sheveleva VN

Syzrantsev)

- Research of gear drives with intermediate bodies (AE Belyaev)

- Research of helical-bevel gear drives (BA Lopatin)

- Development of methods for the synthesis of gear drives (MG Segal SA Lagutin GI

Sheveleva VI Medvedev VN Syzrantsev)

- Forming a theoretical framework for the development of universal programs for the

analysis of spatial working and technological meshings and the creation of corresponding

programs (DT Babichev)

As a result of these studies software systems were developed in the Soviet Union which

were aimed at solving the problems of synthesis and analysis primarily for bevel gears with

circular teeth The best known ones include PC Volga5 made under the direction of MG

Segal [38] and PC Expert created under the direction of GI Sheveleva [39]

The fact that MG Segal was the main developer of the PC Kimos (firm Klingelnberg) in

the 90rsquos confirms the high level of those developments

It should also be noted that a work on the selection of optimal schemes for multi-axis CNC

84

machines for processing gear was carried out in 1990 in Saratov (MG Segal LI Shejko

[40]) These developments have also been used by Klingelnberg

The researches (above all theoretical ones) continued after the collapse of the USSR in

Russia Ukraine and Belarus

At that time the development of the theory of gearing was distinguished by a high level of

theoretical studies based on the introduction of new geometric geometric-kinematic and

other concepts and development (on their basis) of new mathematical models methods and

algorithms for analysis and synthesis of the working and technological gear engagements

These works were performed mostly at their own initiative by highly qualified specialists-

theorists in the field of theory and geometry of working and technological gear meshing

Usually they were elderly university professors who were practically deprived of relations

with the machine-building industry after its stagnation during the collapse of the USSR

It should be noted that it is very difficult to distinguish the most important areas of research

in the modern theory of gearing As the poet said Great things are better seen from a

distance Therefore we will list the most interesting in our view theoretical works on the

development of the theory of gearing with greater focus on the Russian line of research

However we practically do not consider the works on gear geometry ndash they are too

numerous A fairly complete picture of the theoretical works of this period can be obtained

from the proceedings of symposia and conferences held in Kurgan (KMI) Izhevsk

(IzhSTU) and Sevastopol (KhPI Kharkov) The main directions in the development of the

theory of gearing and the most important theoretical results after 1970s include the

following

1 Introduction and use of new concepts such as

Meshing Space (SA Lagutin [41])

Wrapping surface (GI Sheveleva [39])

Fan wedge and normal beam accelerating of implantation (DT Babichev [42])

2 Development of methods for analyzing processes of generation

A new method of finding a singularity in the flat gearing (SA Lagutin) based on the

situation [43] return point at the gear profile occurs at the point in the line of engagement

in which the normal to this line intersects the axis of rotation of the pinion The method was

extended to the spatial gearing (AE Volkov [44])

3 Development of methods of synthesis

Based on the new concept of space of engagement and its properties This approach was

used during the synthesis of both spatial transmission (SA Lagutin [45]) and the cylindrical

(DT Babichev [46])

By using as objective function new criteria of load capacity - permissible contact

pressure(VI Medvedev [47]) the specific work of working surfaces of teeth (DT Babichev

[48]) and others

For bevel gears with small cross-axis angle (SA Lagutin [49] VI Medvedev [50])

Synthesis of gears considering technological limitations of the given production processes

85

(VI Medvedev [51] VN Syzrantsev [52])

By using and developing a method of synthesis of gears in generalizing parameters

originally proposed by EB Vulgakov for involute gears The method was modified by VL

Dorofeev - for involute and ON Tsukanov and BA Lopatin ndash for non-involute gears

(including cylinder-conical ones) [53]

By using variational methods of synthesis when the equation of an optimal surface of the

tooth and its coefficients are determined This approach was first applied apparently by

Alan Lebec [54] in the United States it was used in Ukraine [55] and being developed in

Russia where equal strength gears have been synthesized by using the method (by Hertz

contact strength) [46 56] and the method of synthesis of bevel gear with circular teeth

according to the criteria of minimal contact pressure and bending stresses while maintaining

the overall dimensions of the gear has been developed which is important for aviation

where the weight of the structure is crucial [57]

Increasing the bending strength of circular tooth bevel gears by optimizing the shape of

the tool [58]

Increasing the load-bearing capacity of high-speed heavy-duty cylindrical involute gears

Note that EB Vulgakov VL Dorofeev and AL Kapelevich have made a significant

contribution to the development of synthesis aviation gear in recent decades [59]

4 Development of methods of analysis of loaded gears considering multipairness of

contact

For bevel gears with circular teeth [60]

For spiroid gears [61]

5 Significant progress has been made in the methods of analysis synthesis design and

manufacture of worm gear transmissions

The main input in this field of gearing has been made by two groups of researchers under

the leadership of VI Goldfarb and SA Lagutin The techniques of minimizing meshing

errors and worm hob errors that appear when regrinding and relieving works are fulfilled

have been developed by SA Lagutin and AI Sandler The techniques of synthesis and

production of gears with localized contact were drilled worm gears (SA Lagutin AI

Sandler [62]) and spiroid ones (VI Goldfarb ES Trubachyov [63])

The drives with the increased load capacity were designed based on a study of meshing

space of non-orthogonal gears spiroid (ES Trubachyov [63]) and worm ones (VYu

Puzanov) Designing of spiroid transmissions is carried out using CAD ldquoSPDIAL+rdquo

developed by a group headed by VI Goldfarb Configurator of gearbox systems for

optimization structural synthesis of their structures is being created (OV Malina etal)

Unified worm hob cutters cutting gears for the drives with localized contact were designed

It became possible to cut the gear wheels in engagement with multiple-thread worm by a

single-pass mill (VI Goldfarb and his disciples)

In the Institute of Mechanics IzhSTU a group led by VI Goldfarb essentially laid the

foundation for a new Russian machine building sub-industry ndash construction of gearboxes for

86

isolation and control valves for pipelines

- Theoretical studies of spiroid and worm gears are at a high scientific level

- A modern design process is applied synthesis of perfect engagement synthesis of

localized contact simulation of the stress strain state analysis of real engagement under

load forecasting the state of transmission

- Three generations of dimension-type series of quarter-turn and multi-turn spiroid gear

drives are developed their production with modern quality control and acceptance tests is

organized

6 Application of unconventional gears and gearing helical-bevel gears (BA Lopatin [65])

transmissions with intermediate rolling bodies (AE Belyaev [66]) hydraulic and

pneumatic machines with non-circular gears (An-I-Kahn [67]) precessing transmissions

(IA Bostan [68] EI Tesker [69] VN Syzrantsev BA Lopatin) and other

7 Development of kinematic analysis methods of working and technological meshings Note

that modern designing is the computer designing This factor imposes high requirements to

the theory of gearing as the main mathematical basis for such designing We have to admit

that the classical theory of gearing does not fully comply with these demanding

requirements Thus according to Prof MG Segal who was working with Klingelnberg in

the last years of his life the head of the company prohibited to use differential methods ndash

the basis of the classical theory of gearing ndash in the programs being created The reason for

the ban was inadequacy of the results of computer simulation as compared to real processes

of formation Theoretical research aimed at creating computational models that are

adequate to the real processes of formation and contact of moving bodies were developed by

AE Volkov and VI Medvedev (Moscow) and DT Babichev (Tyumen)

To eliminate the phenomenon DT Babichev elaborated a unified kinematic method for

analysis of the processes of formation [70] based on the ldquotriadrdquo ruptures + envelopes + new

concepts of curvilinear coordinates As the result the cause of inadequacy between the

classical methods of the theory of gearing and real-life processes of formation was

established and rectified The developed kinematic method

Allows to find all the surfaces formed on the item at gear machining formed by smooth

surfaces and inflections of bodies including at advanceretraction of machine tool and in

secondary cutting areas

Has the reliability of non-differential methods but is superior to them in speed of

operation by two orders of magnitude which is confirmed by its partial use in CAD

ldquoSPDIAL +rdquo

Also allows to define the curvatures in gearing

8 Development of the system for assigning real ITS (Initial Tool Surfaces) and construction

of mathematical models for them [71] Real ITS is the set of all forming tools (pieces of

surfaces cutting and boundary edges and corners) for which uniform curvilinear coordinates

are introduced

9 By using the concept of ldquothe acceleration of installationrdquo new techniques for solving

87

multitude of tasks are created calculating the radii of curvature in the gearing identifying

cutting areas and thickness of the layers being cut by tool cutting edges and others (DT

Babichev [48])

For example based on the concept of the acceleration of installation a new basic formula

for calculating the reduced curvature in any normal sections at the contact point of two

moving bodies in contact along the line is created

1Rnp=-

where ɷrol is angular velocity of rolling bodies in the plane of the section in which the

curvature is calculated aB is the acceleration of installation The fundamental nature of the

obtained formula is that

1) in its generality it is commensurate with the kinematic formulas of Rodrigues and Freinet

known in differential geometry but it is intended for a different class of surfaces produced

in the process of formation by the rounding methods

2) curvature in any normal section of all surfaces formed by the rounding methods is

determined by only two scalar parameters and one of them (acceleration of installation)

does not depend on the direction of the section

It was also established that the sign of the acceleration of installation allow to make an

unambiguous judgement on the nature of the contact of bodies For example if aВgt 0 then

the envelope is formed inside the body of the generating element Acceleration of

installation allows to determine (ldquoincidentallyrdquo) the value of the radii of curvature and

faceting value across the whole surface formed by rounding at band- and flake-type

roughness

Thus over the past decade a substantial volume of theoretical knowledge to complete the

third cycle (creation of a computer-oriented theory of gearing) was accumulated

A lot of new notions are introduced and used in theory of gearing

Based on these new notions methods for analysis and synthesis of gear drives and cutter

tool meshings oriented at computer technologies have been developed and continue to be

improved

Intensive investigations to improve methods of optimization synthesis of gearing and to

develop methodologies of computer design and construction of gear boxes are performed

4 Problems and expected directions of the theory of gearing

Let us list the main problems in the gearing theory which in our opinion are the most

important

Problem 1 Creation of the theory of optimization synthesis of structures and parameters of

higher pairs of kinematic elements transmitting the motion and load at the preset and

optimal correlation of normal and friction forces At the present time theory of higher pairs

is being developed only as a pure geometrical science

88

Problem 2 Elaboration of methods of tooth optimal geometry synthesis oriented at the

modern processing technologies instead of traditional ones In this case a designer will have

to solve the variation problem with limitations providing for maximum possible load

capacity of gear drive in accordance with preselected criteria of performance efficiency

Problem 3 Development of methods for analysis of the process of the tooth preset surfaces

changeover taking into account the values of load tooth displacement manufacturing errors

of drive elements errors of relative position of engaging links dynamics of changeover

process

Problem 4 Creation of a unique interrelated complex of application software packages to

enable the designers and manufactures of gear drives to carry out optimization designing

engineering design preparation for production of various drives by meshing

Possible directions of development of the theory of gearing naturally follow from the afore-

described problems

CONCLUSIONS

In the second half of the XIX century the number and complexity of technical inventions of

various machines and mechanisms using the gear drives reached a critical mass and by

around 1890 the scientists had created the scientific basis of the theory of gearing And the

modern theory of gearing was formed by the beginning of the 1970rsquos

The third cycle of the gearing theory development which is oriented at computer technology

is underway

In our opinion the prospects for the development of theory of gearing as a part of the

theory of mechanisms and machines are higher as compared for example with the

linkages Firstly gears are more commonly used in cars than linkages Secondly the

theory of gearing is not only the theory of higher kinematic pairs - it is also the basis for the

theory of gear machining design

It is necessary to note that the current version of the paper is based on the paper published in

the first edition of the given Proceedings [72] but is as close as possible to the paper [73] by

the same authors This version of the article has been prepared by VE Starzhinsky

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1 Дильс ГА Античная техника Москва-Ленинград ОНТИ - Гос техн-теор изд-во ndash

1934 ndash 215 с (Diels GA Antique appliances - Moscow-Leningrad ONTI - Gos tehn-

teor Publ 1934 ndash 215 p)

2 Витрувий Десять книг об архитектуре ndash Москва laquoАрхитектура-Сraquo 2006 ndash 328 с

(Vitruvius Ten Books on Architecture ndash Moscov Architecture-C 2006 ndash 328 p)

3 Пипуныров ВН История часов с древнейших времен до наших дней - Москва

89

Наука 1982 ndash 496 c (Pipunyrov VN The clock story from ancient times to the present

day ndash Moscow Nauka 1982 ndash 496 p)

4 Академик ИИ Артоболевский Сборник Сост АМ Лепихов ndash М Знание 1983

ndash 176 c (Collection Comp AM Lepihov ndash Moscow Znanie 1983 ndash 176 p)

5 Чебышёв ПЛ Избранные труды ndash М Изд-во АН СССР 1955 ndash 926 с (Chebyshjov

PL Selected Works ndash Moscow AN SSSR 1955 ndash 926 p)

6 Рёло Ф Теоретическая кинематика 1875 (Relo F Theoretical Kinematics 1875)

7 Портретная галерея выдающихся инженеров и ученых в области зубчатых передач

ndash Сборник докладов научно-технической конференции с международным участием

Теория и практика зубчатых передач и редукторостроения Ижевск 2008 ndash C 378-

395 (Portrait Gallery of Disting wished Engineers and Scientist in Gearing ndash Proceedings

of Scientific-Engineering Conference with International Participation Theory and Practice

of Gearing and Reducer Building Izhevsk 2008 ndash P 378-395)

8 Литвин ФЛ Теория зубчатых зацеплений ndash М Наука 1968 ndash 584 с (Litvin FL

Theory of gearing ndash Moscow Nauka 1968 ndash 584 p)

9 Механика машин вып 45 ndash Москва Наука 1974 (Mechanics of machines No 45 ndash

Moscow Nauka 1974)

10 Willis R Principles of Mechanism ndash Cambridge London 1841

11 Гохман ХИ Теория зацеплений обобщенная и развитая путем анализа Дисс

магистра механики Одесса ndash 1886 ndash 232 с (Hokhman HI Link Theory generalized and

developed by analyzing Diss mastermechanic Odessa 1886 ndash 232 p)

12 Шишков ВА Образование поверхностей резанием по методу обкатки ndash Москва

Машгиз 1951 ndash 150 с (Shishkov VA Formation of surface machining by burnishing

method ndash Moscow Mashgiz 1951 ndash 150 p)

13 Вильдгабер Э Основы зацепления конических и гипоидных передач ndash Машгиз

1948 ndash 236 с (Vildgaber Je Principles of engagement bevel and hypoid gears ndash Moscow

Mashgiz 1948 ndash 236 p)

14 Baxter ML Basic Geometry and Tooth Contact of Hypoid Gears ldquoIndustrial

Mathematicsrdquo ndash 1961 ndash No 11 ndash P 19-42

15 Шевелева ГИ Алгоритм численного расчета обрабатываемой поверхности Станки

и инструмент ndash 1969 ndash 8 ndash C17-20 (Sheveleva GI Algorithm for the numerical

calculation of the treated surface Machines and Tooling ndash 1969 ndash No 8 ndash P 17-20)

16 Николаев АФ Диаграмма винта и ее применение к определению сопряженных

линейчатых поверхностей с линейным касанием Труды семинара по ТММ вып 37

1950 ndash С52ndash106 (Nikolaev AF Diagram of the screw and its application to the

determination of conjugate ruled surfaces with a linear contact Proceedings of the

Seminar on TMM ndash 1950 ndash No 37 ndash P52-106)

17 Новиков МЛ Зубчатые передачи с новым зацеплением ndash М Изд ВВИА им

Жуковского 1958 ndash 186 с (Novikov ML Gears with a new engagement ndash Moscow

Publisher VVIA by named Zhukovsky 1958 ndash 186 p)

18 Давыдов ЯС Об одном обобщении метода Оливье для образования сопряженных

90

поверхностей в зубчатых передачах Сб laquoТеорияпередачвмашинахraquo М Машгиз

1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

80

The impact of manufacturing errors and assembling on quality of engagement synthesis

of toothed meshing insensitive to errors (ML Erikhov NG Lindtrop LV Korostelyov

NN Krylov LY Liburkin GI Sheveleva)

Numerous studies of specific gears are conducted based on theoretical developments and

established procedures The most important practical problems solved during this period

are

1 Principally new types of gearing have been discovered helical gear in which arcs of

circles with radii small difference are selected as the profiles of cross-sections ndash Novikov-

Wildhaber gear [17] and gears with closed contact lines where the load between teeth is

transferred through the grease wedged in a closed cavity between active surfaces due to

closure of the contact line (LV Korostelyev SA Lagutin [29])

2 Geometric problems of synthesis of cylindrical involute gears were almost exhaustively

resolved and brought into engineering practice geometric calculation (VA Gavrylenko

1969 [30]) selection of the optimum addendum modification coefficients by using blocking

circuits (MB Groman 1957 [31]) according to the atlas compiled and published under the

direction of IA Bolotovsky 1967 [32]

3 New types of gearings have been studied and introduced In this regard various problems

related to analysis and synthesis of the following common types of gears have been solved

Bevel (NI Kolchin and VV Boldyrev 1937 YS Davydov 1950 VI Bezrukov 1963

VM Denisov 1963 GI Sheveleva 1966 HF Kabatov and GA Lopato 1966 MG

Segal 1971 KI Gulyaev 1974 VN Syzrantsev 1975)

Hypoid (GI Apukhtin 1952 FL Litvin 1962 KM Pismanik 1964 II Dusev and VM

Vasilyev 1968 MG Segal 1971)

Cylindrical gear drives with Novikovrsquos gear (ML Novikov 1956 RV Fedyakin and

VA Chesnokov 1958 VN Kudryavtsev 1959 EG Roslivker 1964 NI Kolchin 1968

VN Sevryuk 1972 and others)

Revacycle spur bevel gear (GI Sheveleva 1966)

New worm gear design toroid (YaI Dicker 1948) globoid (PS Zak 1962) worm gear

drives (FL Litvin 1962 IS Krivenko 1967 LV Korostelyev and SA Lagutin 1973

etc) spiroid (S Golubkov 1959 AK Georgiev and VI Goldfarb 1972 and others)

Less common known types of gears have also been studied and implemented

Hyperboloid (KM Pismanik 1950)

Helical-bevel (LY Liburkin 1968)

Wave (EG Ginsburg 1969)

Cylindrical with arched and spiral teeth (ML Erikhov and VN Syzrantsev 1975)

4 Techniques of analysis and synthesis of gears with non-circular wheels are developed [33]

and their production is organized

5 A lot of works are published including a number of classic books on theory of gearing

YaI Dieker (1935) NI Kolchin (1937-1952) FL Litvin (1952-1968) YaS Davydov

81

(1950) VA Gavrylenko (1949-1969) ML Novikov (1958) VA Zalgaller (1975) LD

Chasovnikov (1969) IA Bolotovsky et al (1962-1967) VN Kudryavtsev (1949-1971)

VN Kedrinsky (1960-1967) KM Pismanik (1964-1967) PS Zack (1962) NF Kabatov

and GA Lopato (1966) VA Shishkov (1951) and many others FL Litvinrsquos monograph

[8] stands out among these works it was published in 1968 and still remains a handbook for

professionals in the theory of gearing

The book by VA Zalgaller Envelope Theory [34] which is not very big in volume is

characterized by depth the mathematical rigor and completeness of the argumentation

Note that the appreciation level of the activities under the second cycle is confirmed by the

fact that in 1958 ML Novikov was awarded the Lenin Prize ndash the most prestigious USSR

award presented to individuals for accomplishments in the professional field

The following facts also confirm that the Soviet scientists made a decisive contribution to

the theory of gearing as a science and the fact that the Soviet Union had prepared a large

number of highly qualified specialists in the theory of gearing

FL Litvinrsquos monograph Theory of Gearing which was written in the late 60rsquos is still the

main handbook for gear specialists while Litvin is regarded as the creator of the modern

theory of gearing not only in CIS countries but also around the world

This monograph revised and expanded was reprinted abroad in English co-written with

FL Litvinrsquos new foreign students [35]

Number of qualified experts in the theory of gearing (by the way which were not widely

known in the Soviet Union and the CIS back then) have emigrated to the Western countries

and are writing and publishing quite significant books in English on the theory of gearing

and geometry of gears (SP Radzevich AL Kapelevich SV Lunin)

Summarizing the second cycle let us quote SA Lagutin who most accurately reflect the

essence of this bright period [36] it was a period of storm and pressure in the development

of the gearing theory in Russia when a whole galaxy of brilliant researchers were working

in this area headed by NI Kolchin and FL Litvin By collaborating and competing with

each other in a few years they have built amazingly beautiful building of the new science at

the junction of differential geometry and mechanics of machines

33 Laying the foundations of computer-oriented theory of gearing

The main purpose of such a theory is to become a basis for the methods of computer

analysis synthesis design and manufacturing gear parts for gear engagement

By the mid-70rsquos theory of gearing as a science has reached adulthood the main priority and

theoretical problems of analysis and synthesis of gearing have been resolved The number of

innovative theoretical work began to decline Studies are getting closer to the production

and the theory of gearing acts primarily as a tool for solving specific engineering problems

Since the mid 70-ies of XX century the theory of gearing as well as the machine tool

industry has evolved concurrently in two directions global and Russian

82

The global development of the theory of gearing has taken place against the backdrop of

revolution experienced by the machine tool industry since the 80rsquos

First machines with semi-rigid connections partially controlled by computer began to

appear in developed countries and then complete automatic machines (multi-axis CNC

machines) appeared

At that time for example machines for processing bevel gears with circular teeth Phoenix

(Gleason) and WNC30 (Klingelnberg) were developed The creation of such machines

occurred in parallel with the development of new mathematical models for shaping parts on

multi-axis machines and testing the parts operability before their casting in the metal At

that time software systems LTCA (Gleason) and Kimos (Klingelnberg) were developed

which made it possible to solve the problem of synthesis and analysis of bevel gears with

circular teeth [37]

All developed countries pursue the global direction in the development of the theory of

gearing in the same manner and using similar approaches The following was used by the

gear specialists to solve the problems of analysis and synthesis

Methods of classical theory of gearing (with computer design of the geometry of any kind

of gears)

Techniques of non-differential analysis of gear ndash forming processes using universal as

well as specially developed software packages

Methods of boundary and finite elements (at the analysis of the contact interaction of

acting surfaces of the teeth)

Finite element methods and integral equations (at the analysis of the stress-strain state of

the teeth)

Numerical optimization methods (at the synthesis of geometry of acting and fillet surfaces

of teeth)

An expanded list of quality indicators of gearings including new ones the design

thickness of the oil film criteria of hot and cold seizure criteria for assessing the conditions

for the formation of an oil wedge indicators of vibration activity of the gearing and others

Designing gear drives was regarded as a complex problem requiring an agreed solution of a

group of interrelated tasks

Selection of design scheme of a gear

Synthesis of permissible geometry

Geometry optimization

Structural arrangement and evaluation of quality indicators

Identification and addressing the weaknesses

Designing technical processes of manufacture selection or synthesis of tools subsequent

optimization etc

The developed theory of gearing is known as Theory of Real Gearing in Russia Ukraine

and Belarus while abroad it is called ldquoIntegrated Gear Designrdquo (IGD) or Integrated Design

83

of Gears

Russian direction in the development of the theory of gearing has several specific features

attributable to the following objective circumstances

Firstly first clear signs of stagnation appeared in the USSR industry in the late 70rsquos

Secondly the number of graduate students reduced as the universities basically solved the

problem of teachers which they faced in the early 60rsquos due to a drastic increase in the

number of students being trained in engineering specialties And finally Russia lost the top

three main theorists in the field of the theory of gearing FL Litvin was forced to emigrate

to the USA LV Korostelyov died in a car crash YaS Davydov departed from active

research and subsequently left for the USA

And nevertheless in 15-20 years preceding the collapse of the USSR in 1991 the theory

and geometry of gearing in the Soviet Union was continuing to develop At that time new

centers specializing in different aspects of the theory of gearing were established Let us list

the most interesting in our opinion research topics at the end of the last century

- Issues of strength and solution of the tooth contact problem (EL Airapetov VN

Syzrantsev GI Sheveleva)

- Research on gear bending bending stresses calculation (GI Sheveleva VI Medvedev)

- Non-differential methods for the determination of the contact surfaces characteristics (VI

Goldfarb GI Sheveleva AE Volkov)

- Issues of design synthesis analysis and manufacturing spiroid gear drives (AK Georgiev

VI Goldfarb)

- Issues of design synthesis analysis and manufacturing worm gear drives (SA Lagutin

AI Sandler)

- Research of hypoid bevel gear drives with circular teeth (MG Segal GI Sheveleva VN

Syzrantsev)

- Research of gear drives with intermediate bodies (AE Belyaev)

- Research of helical-bevel gear drives (BA Lopatin)

- Development of methods for the synthesis of gear drives (MG Segal SA Lagutin GI

Sheveleva VI Medvedev VN Syzrantsev)

- Forming a theoretical framework for the development of universal programs for the

analysis of spatial working and technological meshings and the creation of corresponding

programs (DT Babichev)

As a result of these studies software systems were developed in the Soviet Union which

were aimed at solving the problems of synthesis and analysis primarily for bevel gears with

circular teeth The best known ones include PC Volga5 made under the direction of MG

Segal [38] and PC Expert created under the direction of GI Sheveleva [39]

The fact that MG Segal was the main developer of the PC Kimos (firm Klingelnberg) in

the 90rsquos confirms the high level of those developments

It should also be noted that a work on the selection of optimal schemes for multi-axis CNC

84

machines for processing gear was carried out in 1990 in Saratov (MG Segal LI Shejko

[40]) These developments have also been used by Klingelnberg

The researches (above all theoretical ones) continued after the collapse of the USSR in

Russia Ukraine and Belarus

At that time the development of the theory of gearing was distinguished by a high level of

theoretical studies based on the introduction of new geometric geometric-kinematic and

other concepts and development (on their basis) of new mathematical models methods and

algorithms for analysis and synthesis of the working and technological gear engagements

These works were performed mostly at their own initiative by highly qualified specialists-

theorists in the field of theory and geometry of working and technological gear meshing

Usually they were elderly university professors who were practically deprived of relations

with the machine-building industry after its stagnation during the collapse of the USSR

It should be noted that it is very difficult to distinguish the most important areas of research

in the modern theory of gearing As the poet said Great things are better seen from a

distance Therefore we will list the most interesting in our view theoretical works on the

development of the theory of gearing with greater focus on the Russian line of research

However we practically do not consider the works on gear geometry ndash they are too

numerous A fairly complete picture of the theoretical works of this period can be obtained

from the proceedings of symposia and conferences held in Kurgan (KMI) Izhevsk

(IzhSTU) and Sevastopol (KhPI Kharkov) The main directions in the development of the

theory of gearing and the most important theoretical results after 1970s include the

following

1 Introduction and use of new concepts such as

Meshing Space (SA Lagutin [41])

Wrapping surface (GI Sheveleva [39])

Fan wedge and normal beam accelerating of implantation (DT Babichev [42])

2 Development of methods for analyzing processes of generation

A new method of finding a singularity in the flat gearing (SA Lagutin) based on the

situation [43] return point at the gear profile occurs at the point in the line of engagement

in which the normal to this line intersects the axis of rotation of the pinion The method was

extended to the spatial gearing (AE Volkov [44])

3 Development of methods of synthesis

Based on the new concept of space of engagement and its properties This approach was

used during the synthesis of both spatial transmission (SA Lagutin [45]) and the cylindrical

(DT Babichev [46])

By using as objective function new criteria of load capacity - permissible contact

pressure(VI Medvedev [47]) the specific work of working surfaces of teeth (DT Babichev

[48]) and others

For bevel gears with small cross-axis angle (SA Lagutin [49] VI Medvedev [50])

Synthesis of gears considering technological limitations of the given production processes

85

(VI Medvedev [51] VN Syzrantsev [52])

By using and developing a method of synthesis of gears in generalizing parameters

originally proposed by EB Vulgakov for involute gears The method was modified by VL

Dorofeev - for involute and ON Tsukanov and BA Lopatin ndash for non-involute gears

(including cylinder-conical ones) [53]

By using variational methods of synthesis when the equation of an optimal surface of the

tooth and its coefficients are determined This approach was first applied apparently by

Alan Lebec [54] in the United States it was used in Ukraine [55] and being developed in

Russia where equal strength gears have been synthesized by using the method (by Hertz

contact strength) [46 56] and the method of synthesis of bevel gear with circular teeth

according to the criteria of minimal contact pressure and bending stresses while maintaining

the overall dimensions of the gear has been developed which is important for aviation

where the weight of the structure is crucial [57]

Increasing the bending strength of circular tooth bevel gears by optimizing the shape of

the tool [58]

Increasing the load-bearing capacity of high-speed heavy-duty cylindrical involute gears

Note that EB Vulgakov VL Dorofeev and AL Kapelevich have made a significant

contribution to the development of synthesis aviation gear in recent decades [59]

4 Development of methods of analysis of loaded gears considering multipairness of

contact

For bevel gears with circular teeth [60]

For spiroid gears [61]

5 Significant progress has been made in the methods of analysis synthesis design and

manufacture of worm gear transmissions

The main input in this field of gearing has been made by two groups of researchers under

the leadership of VI Goldfarb and SA Lagutin The techniques of minimizing meshing

errors and worm hob errors that appear when regrinding and relieving works are fulfilled

have been developed by SA Lagutin and AI Sandler The techniques of synthesis and

production of gears with localized contact were drilled worm gears (SA Lagutin AI

Sandler [62]) and spiroid ones (VI Goldfarb ES Trubachyov [63])

The drives with the increased load capacity were designed based on a study of meshing

space of non-orthogonal gears spiroid (ES Trubachyov [63]) and worm ones (VYu

Puzanov) Designing of spiroid transmissions is carried out using CAD ldquoSPDIAL+rdquo

developed by a group headed by VI Goldfarb Configurator of gearbox systems for

optimization structural synthesis of their structures is being created (OV Malina etal)

Unified worm hob cutters cutting gears for the drives with localized contact were designed

It became possible to cut the gear wheels in engagement with multiple-thread worm by a

single-pass mill (VI Goldfarb and his disciples)

In the Institute of Mechanics IzhSTU a group led by VI Goldfarb essentially laid the

foundation for a new Russian machine building sub-industry ndash construction of gearboxes for

86

isolation and control valves for pipelines

- Theoretical studies of spiroid and worm gears are at a high scientific level

- A modern design process is applied synthesis of perfect engagement synthesis of

localized contact simulation of the stress strain state analysis of real engagement under

load forecasting the state of transmission

- Three generations of dimension-type series of quarter-turn and multi-turn spiroid gear

drives are developed their production with modern quality control and acceptance tests is

organized

6 Application of unconventional gears and gearing helical-bevel gears (BA Lopatin [65])

transmissions with intermediate rolling bodies (AE Belyaev [66]) hydraulic and

pneumatic machines with non-circular gears (An-I-Kahn [67]) precessing transmissions

(IA Bostan [68] EI Tesker [69] VN Syzrantsev BA Lopatin) and other

7 Development of kinematic analysis methods of working and technological meshings Note

that modern designing is the computer designing This factor imposes high requirements to

the theory of gearing as the main mathematical basis for such designing We have to admit

that the classical theory of gearing does not fully comply with these demanding

requirements Thus according to Prof MG Segal who was working with Klingelnberg in

the last years of his life the head of the company prohibited to use differential methods ndash

the basis of the classical theory of gearing ndash in the programs being created The reason for

the ban was inadequacy of the results of computer simulation as compared to real processes

of formation Theoretical research aimed at creating computational models that are

adequate to the real processes of formation and contact of moving bodies were developed by

AE Volkov and VI Medvedev (Moscow) and DT Babichev (Tyumen)

To eliminate the phenomenon DT Babichev elaborated a unified kinematic method for

analysis of the processes of formation [70] based on the ldquotriadrdquo ruptures + envelopes + new

concepts of curvilinear coordinates As the result the cause of inadequacy between the

classical methods of the theory of gearing and real-life processes of formation was

established and rectified The developed kinematic method

Allows to find all the surfaces formed on the item at gear machining formed by smooth

surfaces and inflections of bodies including at advanceretraction of machine tool and in

secondary cutting areas

Has the reliability of non-differential methods but is superior to them in speed of

operation by two orders of magnitude which is confirmed by its partial use in CAD

ldquoSPDIAL +rdquo

Also allows to define the curvatures in gearing

8 Development of the system for assigning real ITS (Initial Tool Surfaces) and construction

of mathematical models for them [71] Real ITS is the set of all forming tools (pieces of

surfaces cutting and boundary edges and corners) for which uniform curvilinear coordinates

are introduced

9 By using the concept of ldquothe acceleration of installationrdquo new techniques for solving

87

multitude of tasks are created calculating the radii of curvature in the gearing identifying

cutting areas and thickness of the layers being cut by tool cutting edges and others (DT

Babichev [48])

For example based on the concept of the acceleration of installation a new basic formula

for calculating the reduced curvature in any normal sections at the contact point of two

moving bodies in contact along the line is created

1Rnp=-

where ɷrol is angular velocity of rolling bodies in the plane of the section in which the

curvature is calculated aB is the acceleration of installation The fundamental nature of the

obtained formula is that

1) in its generality it is commensurate with the kinematic formulas of Rodrigues and Freinet

known in differential geometry but it is intended for a different class of surfaces produced

in the process of formation by the rounding methods

2) curvature in any normal section of all surfaces formed by the rounding methods is

determined by only two scalar parameters and one of them (acceleration of installation)

does not depend on the direction of the section

It was also established that the sign of the acceleration of installation allow to make an

unambiguous judgement on the nature of the contact of bodies For example if aВgt 0 then

the envelope is formed inside the body of the generating element Acceleration of

installation allows to determine (ldquoincidentallyrdquo) the value of the radii of curvature and

faceting value across the whole surface formed by rounding at band- and flake-type

roughness

Thus over the past decade a substantial volume of theoretical knowledge to complete the

third cycle (creation of a computer-oriented theory of gearing) was accumulated

A lot of new notions are introduced and used in theory of gearing

Based on these new notions methods for analysis and synthesis of gear drives and cutter

tool meshings oriented at computer technologies have been developed and continue to be

improved

Intensive investigations to improve methods of optimization synthesis of gearing and to

develop methodologies of computer design and construction of gear boxes are performed

4 Problems and expected directions of the theory of gearing

Let us list the main problems in the gearing theory which in our opinion are the most

important

Problem 1 Creation of the theory of optimization synthesis of structures and parameters of

higher pairs of kinematic elements transmitting the motion and load at the preset and

optimal correlation of normal and friction forces At the present time theory of higher pairs

is being developed only as a pure geometrical science

88

Problem 2 Elaboration of methods of tooth optimal geometry synthesis oriented at the

modern processing technologies instead of traditional ones In this case a designer will have

to solve the variation problem with limitations providing for maximum possible load

capacity of gear drive in accordance with preselected criteria of performance efficiency

Problem 3 Development of methods for analysis of the process of the tooth preset surfaces

changeover taking into account the values of load tooth displacement manufacturing errors

of drive elements errors of relative position of engaging links dynamics of changeover

process

Problem 4 Creation of a unique interrelated complex of application software packages to

enable the designers and manufactures of gear drives to carry out optimization designing

engineering design preparation for production of various drives by meshing

Possible directions of development of the theory of gearing naturally follow from the afore-

described problems

CONCLUSIONS

In the second half of the XIX century the number and complexity of technical inventions of

various machines and mechanisms using the gear drives reached a critical mass and by

around 1890 the scientists had created the scientific basis of the theory of gearing And the

modern theory of gearing was formed by the beginning of the 1970rsquos

The third cycle of the gearing theory development which is oriented at computer technology

is underway

In our opinion the prospects for the development of theory of gearing as a part of the

theory of mechanisms and machines are higher as compared for example with the

linkages Firstly gears are more commonly used in cars than linkages Secondly the

theory of gearing is not only the theory of higher kinematic pairs - it is also the basis for the

theory of gear machining design

It is necessary to note that the current version of the paper is based on the paper published in

the first edition of the given Proceedings [72] but is as close as possible to the paper [73] by

the same authors This version of the article has been prepared by VE Starzhinsky

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1934 ndash 215 с (Diels GA Antique appliances - Moscow-Leningrad ONTI - Gos tehn-

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2 Витрувий Десять книг об архитектуре ndash Москва laquoАрхитектура-Сraquo 2006 ndash 328 с

(Vitruvius Ten Books on Architecture ndash Moscov Architecture-C 2006 ndash 328 p)

3 Пипуныров ВН История часов с древнейших времен до наших дней - Москва

89

Наука 1982 ndash 496 c (Pipunyrov VN The clock story from ancient times to the present

day ndash Moscow Nauka 1982 ndash 496 p)

4 Академик ИИ Артоболевский Сборник Сост АМ Лепихов ndash М Знание 1983

ndash 176 c (Collection Comp AM Lepihov ndash Moscow Znanie 1983 ndash 176 p)

5 Чебышёв ПЛ Избранные труды ndash М Изд-во АН СССР 1955 ndash 926 с (Chebyshjov

PL Selected Works ndash Moscow AN SSSR 1955 ndash 926 p)

6 Рёло Ф Теоретическая кинематика 1875 (Relo F Theoretical Kinematics 1875)

7 Портретная галерея выдающихся инженеров и ученых в области зубчатых передач

ndash Сборник докладов научно-технической конференции с международным участием

Теория и практика зубчатых передач и редукторостроения Ижевск 2008 ndash C 378-

395 (Portrait Gallery of Disting wished Engineers and Scientist in Gearing ndash Proceedings

of Scientific-Engineering Conference with International Participation Theory and Practice

of Gearing and Reducer Building Izhevsk 2008 ndash P 378-395)

8 Литвин ФЛ Теория зубчатых зацеплений ndash М Наука 1968 ndash 584 с (Litvin FL

Theory of gearing ndash Moscow Nauka 1968 ndash 584 p)

9 Механика машин вып 45 ndash Москва Наука 1974 (Mechanics of machines No 45 ndash

Moscow Nauka 1974)

10 Willis R Principles of Mechanism ndash Cambridge London 1841

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магистра механики Одесса ndash 1886 ndash 232 с (Hokhman HI Link Theory generalized and

developed by analyzing Diss mastermechanic Odessa 1886 ndash 232 p)

12 Шишков ВА Образование поверхностей резанием по методу обкатки ndash Москва

Машгиз 1951 ndash 150 с (Shishkov VA Formation of surface machining by burnishing

method ndash Moscow Mashgiz 1951 ndash 150 p)

13 Вильдгабер Э Основы зацепления конических и гипоидных передач ndash Машгиз

1948 ndash 236 с (Vildgaber Je Principles of engagement bevel and hypoid gears ndash Moscow

Mashgiz 1948 ndash 236 p)

14 Baxter ML Basic Geometry and Tooth Contact of Hypoid Gears ldquoIndustrial

Mathematicsrdquo ndash 1961 ndash No 11 ndash P 19-42

15 Шевелева ГИ Алгоритм численного расчета обрабатываемой поверхности Станки

и инструмент ndash 1969 ndash 8 ndash C17-20 (Sheveleva GI Algorithm for the numerical

calculation of the treated surface Machines and Tooling ndash 1969 ndash No 8 ndash P 17-20)

16 Николаев АФ Диаграмма винта и ее применение к определению сопряженных

линейчатых поверхностей с линейным касанием Труды семинара по ТММ вып 37

1950 ndash С52ndash106 (Nikolaev AF Diagram of the screw and its application to the

determination of conjugate ruled surfaces with a linear contact Proceedings of the

Seminar on TMM ndash 1950 ndash No 37 ndash P52-106)

17 Новиков МЛ Зубчатые передачи с новым зацеплением ndash М Изд ВВИА им

Жуковского 1958 ndash 186 с (Novikov ML Gears with a new engagement ndash Moscow

Publisher VVIA by named Zhukovsky 1958 ndash 186 p)

18 Давыдов ЯС Об одном обобщении метода Оливье для образования сопряженных

90

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1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

81

(1950) VA Gavrylenko (1949-1969) ML Novikov (1958) VA Zalgaller (1975) LD

Chasovnikov (1969) IA Bolotovsky et al (1962-1967) VN Kudryavtsev (1949-1971)

VN Kedrinsky (1960-1967) KM Pismanik (1964-1967) PS Zack (1962) NF Kabatov

and GA Lopato (1966) VA Shishkov (1951) and many others FL Litvinrsquos monograph

[8] stands out among these works it was published in 1968 and still remains a handbook for

professionals in the theory of gearing

The book by VA Zalgaller Envelope Theory [34] which is not very big in volume is

characterized by depth the mathematical rigor and completeness of the argumentation

Note that the appreciation level of the activities under the second cycle is confirmed by the

fact that in 1958 ML Novikov was awarded the Lenin Prize ndash the most prestigious USSR

award presented to individuals for accomplishments in the professional field

The following facts also confirm that the Soviet scientists made a decisive contribution to

the theory of gearing as a science and the fact that the Soviet Union had prepared a large

number of highly qualified specialists in the theory of gearing

FL Litvinrsquos monograph Theory of Gearing which was written in the late 60rsquos is still the

main handbook for gear specialists while Litvin is regarded as the creator of the modern

theory of gearing not only in CIS countries but also around the world

This monograph revised and expanded was reprinted abroad in English co-written with

FL Litvinrsquos new foreign students [35]

Number of qualified experts in the theory of gearing (by the way which were not widely

known in the Soviet Union and the CIS back then) have emigrated to the Western countries

and are writing and publishing quite significant books in English on the theory of gearing

and geometry of gears (SP Radzevich AL Kapelevich SV Lunin)

Summarizing the second cycle let us quote SA Lagutin who most accurately reflect the

essence of this bright period [36] it was a period of storm and pressure in the development

of the gearing theory in Russia when a whole galaxy of brilliant researchers were working

in this area headed by NI Kolchin and FL Litvin By collaborating and competing with

each other in a few years they have built amazingly beautiful building of the new science at

the junction of differential geometry and mechanics of machines

33 Laying the foundations of computer-oriented theory of gearing

The main purpose of such a theory is to become a basis for the methods of computer

analysis synthesis design and manufacturing gear parts for gear engagement

By the mid-70rsquos theory of gearing as a science has reached adulthood the main priority and

theoretical problems of analysis and synthesis of gearing have been resolved The number of

innovative theoretical work began to decline Studies are getting closer to the production

and the theory of gearing acts primarily as a tool for solving specific engineering problems

Since the mid 70-ies of XX century the theory of gearing as well as the machine tool

industry has evolved concurrently in two directions global and Russian

82

The global development of the theory of gearing has taken place against the backdrop of

revolution experienced by the machine tool industry since the 80rsquos

First machines with semi-rigid connections partially controlled by computer began to

appear in developed countries and then complete automatic machines (multi-axis CNC

machines) appeared

At that time for example machines for processing bevel gears with circular teeth Phoenix

(Gleason) and WNC30 (Klingelnberg) were developed The creation of such machines

occurred in parallel with the development of new mathematical models for shaping parts on

multi-axis machines and testing the parts operability before their casting in the metal At

that time software systems LTCA (Gleason) and Kimos (Klingelnberg) were developed

which made it possible to solve the problem of synthesis and analysis of bevel gears with

circular teeth [37]

All developed countries pursue the global direction in the development of the theory of

gearing in the same manner and using similar approaches The following was used by the

gear specialists to solve the problems of analysis and synthesis

Methods of classical theory of gearing (with computer design of the geometry of any kind

of gears)

Techniques of non-differential analysis of gear ndash forming processes using universal as

well as specially developed software packages

Methods of boundary and finite elements (at the analysis of the contact interaction of

acting surfaces of the teeth)

Finite element methods and integral equations (at the analysis of the stress-strain state of

the teeth)

Numerical optimization methods (at the synthesis of geometry of acting and fillet surfaces

of teeth)

An expanded list of quality indicators of gearings including new ones the design

thickness of the oil film criteria of hot and cold seizure criteria for assessing the conditions

for the formation of an oil wedge indicators of vibration activity of the gearing and others

Designing gear drives was regarded as a complex problem requiring an agreed solution of a

group of interrelated tasks

Selection of design scheme of a gear

Synthesis of permissible geometry

Geometry optimization

Structural arrangement and evaluation of quality indicators

Identification and addressing the weaknesses

Designing technical processes of manufacture selection or synthesis of tools subsequent

optimization etc

The developed theory of gearing is known as Theory of Real Gearing in Russia Ukraine

and Belarus while abroad it is called ldquoIntegrated Gear Designrdquo (IGD) or Integrated Design

83

of Gears

Russian direction in the development of the theory of gearing has several specific features

attributable to the following objective circumstances

Firstly first clear signs of stagnation appeared in the USSR industry in the late 70rsquos

Secondly the number of graduate students reduced as the universities basically solved the

problem of teachers which they faced in the early 60rsquos due to a drastic increase in the

number of students being trained in engineering specialties And finally Russia lost the top

three main theorists in the field of the theory of gearing FL Litvin was forced to emigrate

to the USA LV Korostelyov died in a car crash YaS Davydov departed from active

research and subsequently left for the USA

And nevertheless in 15-20 years preceding the collapse of the USSR in 1991 the theory

and geometry of gearing in the Soviet Union was continuing to develop At that time new

centers specializing in different aspects of the theory of gearing were established Let us list

the most interesting in our opinion research topics at the end of the last century

- Issues of strength and solution of the tooth contact problem (EL Airapetov VN

Syzrantsev GI Sheveleva)

- Research on gear bending bending stresses calculation (GI Sheveleva VI Medvedev)

- Non-differential methods for the determination of the contact surfaces characteristics (VI

Goldfarb GI Sheveleva AE Volkov)

- Issues of design synthesis analysis and manufacturing spiroid gear drives (AK Georgiev

VI Goldfarb)

- Issues of design synthesis analysis and manufacturing worm gear drives (SA Lagutin

AI Sandler)

- Research of hypoid bevel gear drives with circular teeth (MG Segal GI Sheveleva VN

Syzrantsev)

- Research of gear drives with intermediate bodies (AE Belyaev)

- Research of helical-bevel gear drives (BA Lopatin)

- Development of methods for the synthesis of gear drives (MG Segal SA Lagutin GI

Sheveleva VI Medvedev VN Syzrantsev)

- Forming a theoretical framework for the development of universal programs for the

analysis of spatial working and technological meshings and the creation of corresponding

programs (DT Babichev)

As a result of these studies software systems were developed in the Soviet Union which

were aimed at solving the problems of synthesis and analysis primarily for bevel gears with

circular teeth The best known ones include PC Volga5 made under the direction of MG

Segal [38] and PC Expert created under the direction of GI Sheveleva [39]

The fact that MG Segal was the main developer of the PC Kimos (firm Klingelnberg) in

the 90rsquos confirms the high level of those developments

It should also be noted that a work on the selection of optimal schemes for multi-axis CNC

84

machines for processing gear was carried out in 1990 in Saratov (MG Segal LI Shejko

[40]) These developments have also been used by Klingelnberg

The researches (above all theoretical ones) continued after the collapse of the USSR in

Russia Ukraine and Belarus

At that time the development of the theory of gearing was distinguished by a high level of

theoretical studies based on the introduction of new geometric geometric-kinematic and

other concepts and development (on their basis) of new mathematical models methods and

algorithms for analysis and synthesis of the working and technological gear engagements

These works were performed mostly at their own initiative by highly qualified specialists-

theorists in the field of theory and geometry of working and technological gear meshing

Usually they were elderly university professors who were practically deprived of relations

with the machine-building industry after its stagnation during the collapse of the USSR

It should be noted that it is very difficult to distinguish the most important areas of research

in the modern theory of gearing As the poet said Great things are better seen from a

distance Therefore we will list the most interesting in our view theoretical works on the

development of the theory of gearing with greater focus on the Russian line of research

However we practically do not consider the works on gear geometry ndash they are too

numerous A fairly complete picture of the theoretical works of this period can be obtained

from the proceedings of symposia and conferences held in Kurgan (KMI) Izhevsk

(IzhSTU) and Sevastopol (KhPI Kharkov) The main directions in the development of the

theory of gearing and the most important theoretical results after 1970s include the

following

1 Introduction and use of new concepts such as

Meshing Space (SA Lagutin [41])

Wrapping surface (GI Sheveleva [39])

Fan wedge and normal beam accelerating of implantation (DT Babichev [42])

2 Development of methods for analyzing processes of generation

A new method of finding a singularity in the flat gearing (SA Lagutin) based on the

situation [43] return point at the gear profile occurs at the point in the line of engagement

in which the normal to this line intersects the axis of rotation of the pinion The method was

extended to the spatial gearing (AE Volkov [44])

3 Development of methods of synthesis

Based on the new concept of space of engagement and its properties This approach was

used during the synthesis of both spatial transmission (SA Lagutin [45]) and the cylindrical

(DT Babichev [46])

By using as objective function new criteria of load capacity - permissible contact

pressure(VI Medvedev [47]) the specific work of working surfaces of teeth (DT Babichev

[48]) and others

For bevel gears with small cross-axis angle (SA Lagutin [49] VI Medvedev [50])

Synthesis of gears considering technological limitations of the given production processes

85

(VI Medvedev [51] VN Syzrantsev [52])

By using and developing a method of synthesis of gears in generalizing parameters

originally proposed by EB Vulgakov for involute gears The method was modified by VL

Dorofeev - for involute and ON Tsukanov and BA Lopatin ndash for non-involute gears

(including cylinder-conical ones) [53]

By using variational methods of synthesis when the equation of an optimal surface of the

tooth and its coefficients are determined This approach was first applied apparently by

Alan Lebec [54] in the United States it was used in Ukraine [55] and being developed in

Russia where equal strength gears have been synthesized by using the method (by Hertz

contact strength) [46 56] and the method of synthesis of bevel gear with circular teeth

according to the criteria of minimal contact pressure and bending stresses while maintaining

the overall dimensions of the gear has been developed which is important for aviation

where the weight of the structure is crucial [57]

Increasing the bending strength of circular tooth bevel gears by optimizing the shape of

the tool [58]

Increasing the load-bearing capacity of high-speed heavy-duty cylindrical involute gears

Note that EB Vulgakov VL Dorofeev and AL Kapelevich have made a significant

contribution to the development of synthesis aviation gear in recent decades [59]

4 Development of methods of analysis of loaded gears considering multipairness of

contact

For bevel gears with circular teeth [60]

For spiroid gears [61]

5 Significant progress has been made in the methods of analysis synthesis design and

manufacture of worm gear transmissions

The main input in this field of gearing has been made by two groups of researchers under

the leadership of VI Goldfarb and SA Lagutin The techniques of minimizing meshing

errors and worm hob errors that appear when regrinding and relieving works are fulfilled

have been developed by SA Lagutin and AI Sandler The techniques of synthesis and

production of gears with localized contact were drilled worm gears (SA Lagutin AI

Sandler [62]) and spiroid ones (VI Goldfarb ES Trubachyov [63])

The drives with the increased load capacity were designed based on a study of meshing

space of non-orthogonal gears spiroid (ES Trubachyov [63]) and worm ones (VYu

Puzanov) Designing of spiroid transmissions is carried out using CAD ldquoSPDIAL+rdquo

developed by a group headed by VI Goldfarb Configurator of gearbox systems for

optimization structural synthesis of their structures is being created (OV Malina etal)

Unified worm hob cutters cutting gears for the drives with localized contact were designed

It became possible to cut the gear wheels in engagement with multiple-thread worm by a

single-pass mill (VI Goldfarb and his disciples)

In the Institute of Mechanics IzhSTU a group led by VI Goldfarb essentially laid the

foundation for a new Russian machine building sub-industry ndash construction of gearboxes for

86

isolation and control valves for pipelines

- Theoretical studies of spiroid and worm gears are at a high scientific level

- A modern design process is applied synthesis of perfect engagement synthesis of

localized contact simulation of the stress strain state analysis of real engagement under

load forecasting the state of transmission

- Three generations of dimension-type series of quarter-turn and multi-turn spiroid gear

drives are developed their production with modern quality control and acceptance tests is

organized

6 Application of unconventional gears and gearing helical-bevel gears (BA Lopatin [65])

transmissions with intermediate rolling bodies (AE Belyaev [66]) hydraulic and

pneumatic machines with non-circular gears (An-I-Kahn [67]) precessing transmissions

(IA Bostan [68] EI Tesker [69] VN Syzrantsev BA Lopatin) and other

7 Development of kinematic analysis methods of working and technological meshings Note

that modern designing is the computer designing This factor imposes high requirements to

the theory of gearing as the main mathematical basis for such designing We have to admit

that the classical theory of gearing does not fully comply with these demanding

requirements Thus according to Prof MG Segal who was working with Klingelnberg in

the last years of his life the head of the company prohibited to use differential methods ndash

the basis of the classical theory of gearing ndash in the programs being created The reason for

the ban was inadequacy of the results of computer simulation as compared to real processes

of formation Theoretical research aimed at creating computational models that are

adequate to the real processes of formation and contact of moving bodies were developed by

AE Volkov and VI Medvedev (Moscow) and DT Babichev (Tyumen)

To eliminate the phenomenon DT Babichev elaborated a unified kinematic method for

analysis of the processes of formation [70] based on the ldquotriadrdquo ruptures + envelopes + new

concepts of curvilinear coordinates As the result the cause of inadequacy between the

classical methods of the theory of gearing and real-life processes of formation was

established and rectified The developed kinematic method

Allows to find all the surfaces formed on the item at gear machining formed by smooth

surfaces and inflections of bodies including at advanceretraction of machine tool and in

secondary cutting areas

Has the reliability of non-differential methods but is superior to them in speed of

operation by two orders of magnitude which is confirmed by its partial use in CAD

ldquoSPDIAL +rdquo

Also allows to define the curvatures in gearing

8 Development of the system for assigning real ITS (Initial Tool Surfaces) and construction

of mathematical models for them [71] Real ITS is the set of all forming tools (pieces of

surfaces cutting and boundary edges and corners) for which uniform curvilinear coordinates

are introduced

9 By using the concept of ldquothe acceleration of installationrdquo new techniques for solving

87

multitude of tasks are created calculating the radii of curvature in the gearing identifying

cutting areas and thickness of the layers being cut by tool cutting edges and others (DT

Babichev [48])

For example based on the concept of the acceleration of installation a new basic formula

for calculating the reduced curvature in any normal sections at the contact point of two

moving bodies in contact along the line is created

1Rnp=-

where ɷrol is angular velocity of rolling bodies in the plane of the section in which the

curvature is calculated aB is the acceleration of installation The fundamental nature of the

obtained formula is that

1) in its generality it is commensurate with the kinematic formulas of Rodrigues and Freinet

known in differential geometry but it is intended for a different class of surfaces produced

in the process of formation by the rounding methods

2) curvature in any normal section of all surfaces formed by the rounding methods is

determined by only two scalar parameters and one of them (acceleration of installation)

does not depend on the direction of the section

It was also established that the sign of the acceleration of installation allow to make an

unambiguous judgement on the nature of the contact of bodies For example if aВgt 0 then

the envelope is formed inside the body of the generating element Acceleration of

installation allows to determine (ldquoincidentallyrdquo) the value of the radii of curvature and

faceting value across the whole surface formed by rounding at band- and flake-type

roughness

Thus over the past decade a substantial volume of theoretical knowledge to complete the

third cycle (creation of a computer-oriented theory of gearing) was accumulated

A lot of new notions are introduced and used in theory of gearing

Based on these new notions methods for analysis and synthesis of gear drives and cutter

tool meshings oriented at computer technologies have been developed and continue to be

improved

Intensive investigations to improve methods of optimization synthesis of gearing and to

develop methodologies of computer design and construction of gear boxes are performed

4 Problems and expected directions of the theory of gearing

Let us list the main problems in the gearing theory which in our opinion are the most

important

Problem 1 Creation of the theory of optimization synthesis of structures and parameters of

higher pairs of kinematic elements transmitting the motion and load at the preset and

optimal correlation of normal and friction forces At the present time theory of higher pairs

is being developed only as a pure geometrical science

88

Problem 2 Elaboration of methods of tooth optimal geometry synthesis oriented at the

modern processing technologies instead of traditional ones In this case a designer will have

to solve the variation problem with limitations providing for maximum possible load

capacity of gear drive in accordance with preselected criteria of performance efficiency

Problem 3 Development of methods for analysis of the process of the tooth preset surfaces

changeover taking into account the values of load tooth displacement manufacturing errors

of drive elements errors of relative position of engaging links dynamics of changeover

process

Problem 4 Creation of a unique interrelated complex of application software packages to

enable the designers and manufactures of gear drives to carry out optimization designing

engineering design preparation for production of various drives by meshing

Possible directions of development of the theory of gearing naturally follow from the afore-

described problems

CONCLUSIONS

In the second half of the XIX century the number and complexity of technical inventions of

various machines and mechanisms using the gear drives reached a critical mass and by

around 1890 the scientists had created the scientific basis of the theory of gearing And the

modern theory of gearing was formed by the beginning of the 1970rsquos

The third cycle of the gearing theory development which is oriented at computer technology

is underway

In our opinion the prospects for the development of theory of gearing as a part of the

theory of mechanisms and machines are higher as compared for example with the

linkages Firstly gears are more commonly used in cars than linkages Secondly the

theory of gearing is not only the theory of higher kinematic pairs - it is also the basis for the

theory of gear machining design

It is necessary to note that the current version of the paper is based on the paper published in

the first edition of the given Proceedings [72] but is as close as possible to the paper [73] by

the same authors This version of the article has been prepared by VE Starzhinsky

REFERENCES

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1934 ndash 215 с (Diels GA Antique appliances - Moscow-Leningrad ONTI - Gos tehn-

teor Publ 1934 ndash 215 p)

2 Витрувий Десять книг об архитектуре ndash Москва laquoАрхитектура-Сraquo 2006 ndash 328 с

(Vitruvius Ten Books on Architecture ndash Moscov Architecture-C 2006 ndash 328 p)

3 Пипуныров ВН История часов с древнейших времен до наших дней - Москва

89

Наука 1982 ndash 496 c (Pipunyrov VN The clock story from ancient times to the present

day ndash Moscow Nauka 1982 ndash 496 p)

4 Академик ИИ Артоболевский Сборник Сост АМ Лепихов ndash М Знание 1983

ndash 176 c (Collection Comp AM Lepihov ndash Moscow Znanie 1983 ndash 176 p)

5 Чебышёв ПЛ Избранные труды ndash М Изд-во АН СССР 1955 ndash 926 с (Chebyshjov

PL Selected Works ndash Moscow AN SSSR 1955 ndash 926 p)

6 Рёло Ф Теоретическая кинематика 1875 (Relo F Theoretical Kinematics 1875)

7 Портретная галерея выдающихся инженеров и ученых в области зубчатых передач

ndash Сборник докладов научно-технической конференции с международным участием

Теория и практика зубчатых передач и редукторостроения Ижевск 2008 ndash C 378-

395 (Portrait Gallery of Disting wished Engineers and Scientist in Gearing ndash Proceedings

of Scientific-Engineering Conference with International Participation Theory and Practice

of Gearing and Reducer Building Izhevsk 2008 ndash P 378-395)

8 Литвин ФЛ Теория зубчатых зацеплений ndash М Наука 1968 ndash 584 с (Litvin FL

Theory of gearing ndash Moscow Nauka 1968 ndash 584 p)

9 Механика машин вып 45 ndash Москва Наука 1974 (Mechanics of machines No 45 ndash

Moscow Nauka 1974)

10 Willis R Principles of Mechanism ndash Cambridge London 1841

11 Гохман ХИ Теория зацеплений обобщенная и развитая путем анализа Дисс

магистра механики Одесса ndash 1886 ndash 232 с (Hokhman HI Link Theory generalized and

developed by analyzing Diss mastermechanic Odessa 1886 ndash 232 p)

12 Шишков ВА Образование поверхностей резанием по методу обкатки ndash Москва

Машгиз 1951 ndash 150 с (Shishkov VA Formation of surface machining by burnishing

method ndash Moscow Mashgiz 1951 ndash 150 p)

13 Вильдгабер Э Основы зацепления конических и гипоидных передач ndash Машгиз

1948 ndash 236 с (Vildgaber Je Principles of engagement bevel and hypoid gears ndash Moscow

Mashgiz 1948 ndash 236 p)

14 Baxter ML Basic Geometry and Tooth Contact of Hypoid Gears ldquoIndustrial

Mathematicsrdquo ndash 1961 ndash No 11 ndash P 19-42

15 Шевелева ГИ Алгоритм численного расчета обрабатываемой поверхности Станки

и инструмент ndash 1969 ndash 8 ndash C17-20 (Sheveleva GI Algorithm for the numerical

calculation of the treated surface Machines and Tooling ndash 1969 ndash No 8 ndash P 17-20)

16 Николаев АФ Диаграмма винта и ее применение к определению сопряженных

линейчатых поверхностей с линейным касанием Труды семинара по ТММ вып 37

1950 ndash С52ndash106 (Nikolaev AF Diagram of the screw and its application to the

determination of conjugate ruled surfaces with a linear contact Proceedings of the

Seminar on TMM ndash 1950 ndash No 37 ndash P52-106)

17 Новиков МЛ Зубчатые передачи с новым зацеплением ndash М Изд ВВИА им

Жуковского 1958 ndash 186 с (Novikov ML Gears with a new engagement ndash Moscow

Publisher VVIA by named Zhukovsky 1958 ndash 186 p)

18 Давыдов ЯС Об одном обобщении метода Оливье для образования сопряженных

90

поверхностей в зубчатых передачах Сб laquoТеорияпередачвмашинахraquo М Машгиз

1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

82

The global development of the theory of gearing has taken place against the backdrop of

revolution experienced by the machine tool industry since the 80rsquos

First machines with semi-rigid connections partially controlled by computer began to

appear in developed countries and then complete automatic machines (multi-axis CNC

machines) appeared

At that time for example machines for processing bevel gears with circular teeth Phoenix

(Gleason) and WNC30 (Klingelnberg) were developed The creation of such machines

occurred in parallel with the development of new mathematical models for shaping parts on

multi-axis machines and testing the parts operability before their casting in the metal At

that time software systems LTCA (Gleason) and Kimos (Klingelnberg) were developed

which made it possible to solve the problem of synthesis and analysis of bevel gears with

circular teeth [37]

All developed countries pursue the global direction in the development of the theory of

gearing in the same manner and using similar approaches The following was used by the

gear specialists to solve the problems of analysis and synthesis

Methods of classical theory of gearing (with computer design of the geometry of any kind

of gears)

Techniques of non-differential analysis of gear ndash forming processes using universal as

well as specially developed software packages

Methods of boundary and finite elements (at the analysis of the contact interaction of

acting surfaces of the teeth)

Finite element methods and integral equations (at the analysis of the stress-strain state of

the teeth)

Numerical optimization methods (at the synthesis of geometry of acting and fillet surfaces

of teeth)

An expanded list of quality indicators of gearings including new ones the design

thickness of the oil film criteria of hot and cold seizure criteria for assessing the conditions

for the formation of an oil wedge indicators of vibration activity of the gearing and others

Designing gear drives was regarded as a complex problem requiring an agreed solution of a

group of interrelated tasks

Selection of design scheme of a gear

Synthesis of permissible geometry

Geometry optimization

Structural arrangement and evaluation of quality indicators

Identification and addressing the weaknesses

Designing technical processes of manufacture selection or synthesis of tools subsequent

optimization etc

The developed theory of gearing is known as Theory of Real Gearing in Russia Ukraine

and Belarus while abroad it is called ldquoIntegrated Gear Designrdquo (IGD) or Integrated Design

83

of Gears

Russian direction in the development of the theory of gearing has several specific features

attributable to the following objective circumstances

Firstly first clear signs of stagnation appeared in the USSR industry in the late 70rsquos

Secondly the number of graduate students reduced as the universities basically solved the

problem of teachers which they faced in the early 60rsquos due to a drastic increase in the

number of students being trained in engineering specialties And finally Russia lost the top

three main theorists in the field of the theory of gearing FL Litvin was forced to emigrate

to the USA LV Korostelyov died in a car crash YaS Davydov departed from active

research and subsequently left for the USA

And nevertheless in 15-20 years preceding the collapse of the USSR in 1991 the theory

and geometry of gearing in the Soviet Union was continuing to develop At that time new

centers specializing in different aspects of the theory of gearing were established Let us list

the most interesting in our opinion research topics at the end of the last century

- Issues of strength and solution of the tooth contact problem (EL Airapetov VN

Syzrantsev GI Sheveleva)

- Research on gear bending bending stresses calculation (GI Sheveleva VI Medvedev)

- Non-differential methods for the determination of the contact surfaces characteristics (VI

Goldfarb GI Sheveleva AE Volkov)

- Issues of design synthesis analysis and manufacturing spiroid gear drives (AK Georgiev

VI Goldfarb)

- Issues of design synthesis analysis and manufacturing worm gear drives (SA Lagutin

AI Sandler)

- Research of hypoid bevel gear drives with circular teeth (MG Segal GI Sheveleva VN

Syzrantsev)

- Research of gear drives with intermediate bodies (AE Belyaev)

- Research of helical-bevel gear drives (BA Lopatin)

- Development of methods for the synthesis of gear drives (MG Segal SA Lagutin GI

Sheveleva VI Medvedev VN Syzrantsev)

- Forming a theoretical framework for the development of universal programs for the

analysis of spatial working and technological meshings and the creation of corresponding

programs (DT Babichev)

As a result of these studies software systems were developed in the Soviet Union which

were aimed at solving the problems of synthesis and analysis primarily for bevel gears with

circular teeth The best known ones include PC Volga5 made under the direction of MG

Segal [38] and PC Expert created under the direction of GI Sheveleva [39]

The fact that MG Segal was the main developer of the PC Kimos (firm Klingelnberg) in

the 90rsquos confirms the high level of those developments

It should also be noted that a work on the selection of optimal schemes for multi-axis CNC

84

machines for processing gear was carried out in 1990 in Saratov (MG Segal LI Shejko

[40]) These developments have also been used by Klingelnberg

The researches (above all theoretical ones) continued after the collapse of the USSR in

Russia Ukraine and Belarus

At that time the development of the theory of gearing was distinguished by a high level of

theoretical studies based on the introduction of new geometric geometric-kinematic and

other concepts and development (on their basis) of new mathematical models methods and

algorithms for analysis and synthesis of the working and technological gear engagements

These works were performed mostly at their own initiative by highly qualified specialists-

theorists in the field of theory and geometry of working and technological gear meshing

Usually they were elderly university professors who were practically deprived of relations

with the machine-building industry after its stagnation during the collapse of the USSR

It should be noted that it is very difficult to distinguish the most important areas of research

in the modern theory of gearing As the poet said Great things are better seen from a

distance Therefore we will list the most interesting in our view theoretical works on the

development of the theory of gearing with greater focus on the Russian line of research

However we practically do not consider the works on gear geometry ndash they are too

numerous A fairly complete picture of the theoretical works of this period can be obtained

from the proceedings of symposia and conferences held in Kurgan (KMI) Izhevsk

(IzhSTU) and Sevastopol (KhPI Kharkov) The main directions in the development of the

theory of gearing and the most important theoretical results after 1970s include the

following

1 Introduction and use of new concepts such as

Meshing Space (SA Lagutin [41])

Wrapping surface (GI Sheveleva [39])

Fan wedge and normal beam accelerating of implantation (DT Babichev [42])

2 Development of methods for analyzing processes of generation

A new method of finding a singularity in the flat gearing (SA Lagutin) based on the

situation [43] return point at the gear profile occurs at the point in the line of engagement

in which the normal to this line intersects the axis of rotation of the pinion The method was

extended to the spatial gearing (AE Volkov [44])

3 Development of methods of synthesis

Based on the new concept of space of engagement and its properties This approach was

used during the synthesis of both spatial transmission (SA Lagutin [45]) and the cylindrical

(DT Babichev [46])

By using as objective function new criteria of load capacity - permissible contact

pressure(VI Medvedev [47]) the specific work of working surfaces of teeth (DT Babichev

[48]) and others

For bevel gears with small cross-axis angle (SA Lagutin [49] VI Medvedev [50])

Synthesis of gears considering technological limitations of the given production processes

85

(VI Medvedev [51] VN Syzrantsev [52])

By using and developing a method of synthesis of gears in generalizing parameters

originally proposed by EB Vulgakov for involute gears The method was modified by VL

Dorofeev - for involute and ON Tsukanov and BA Lopatin ndash for non-involute gears

(including cylinder-conical ones) [53]

By using variational methods of synthesis when the equation of an optimal surface of the

tooth and its coefficients are determined This approach was first applied apparently by

Alan Lebec [54] in the United States it was used in Ukraine [55] and being developed in

Russia where equal strength gears have been synthesized by using the method (by Hertz

contact strength) [46 56] and the method of synthesis of bevel gear with circular teeth

according to the criteria of minimal contact pressure and bending stresses while maintaining

the overall dimensions of the gear has been developed which is important for aviation

where the weight of the structure is crucial [57]

Increasing the bending strength of circular tooth bevel gears by optimizing the shape of

the tool [58]

Increasing the load-bearing capacity of high-speed heavy-duty cylindrical involute gears

Note that EB Vulgakov VL Dorofeev and AL Kapelevich have made a significant

contribution to the development of synthesis aviation gear in recent decades [59]

4 Development of methods of analysis of loaded gears considering multipairness of

contact

For bevel gears with circular teeth [60]

For spiroid gears [61]

5 Significant progress has been made in the methods of analysis synthesis design and

manufacture of worm gear transmissions

The main input in this field of gearing has been made by two groups of researchers under

the leadership of VI Goldfarb and SA Lagutin The techniques of minimizing meshing

errors and worm hob errors that appear when regrinding and relieving works are fulfilled

have been developed by SA Lagutin and AI Sandler The techniques of synthesis and

production of gears with localized contact were drilled worm gears (SA Lagutin AI

Sandler [62]) and spiroid ones (VI Goldfarb ES Trubachyov [63])

The drives with the increased load capacity were designed based on a study of meshing

space of non-orthogonal gears spiroid (ES Trubachyov [63]) and worm ones (VYu

Puzanov) Designing of spiroid transmissions is carried out using CAD ldquoSPDIAL+rdquo

developed by a group headed by VI Goldfarb Configurator of gearbox systems for

optimization structural synthesis of their structures is being created (OV Malina etal)

Unified worm hob cutters cutting gears for the drives with localized contact were designed

It became possible to cut the gear wheels in engagement with multiple-thread worm by a

single-pass mill (VI Goldfarb and his disciples)

In the Institute of Mechanics IzhSTU a group led by VI Goldfarb essentially laid the

foundation for a new Russian machine building sub-industry ndash construction of gearboxes for

86

isolation and control valves for pipelines

- Theoretical studies of spiroid and worm gears are at a high scientific level

- A modern design process is applied synthesis of perfect engagement synthesis of

localized contact simulation of the stress strain state analysis of real engagement under

load forecasting the state of transmission

- Three generations of dimension-type series of quarter-turn and multi-turn spiroid gear

drives are developed their production with modern quality control and acceptance tests is

organized

6 Application of unconventional gears and gearing helical-bevel gears (BA Lopatin [65])

transmissions with intermediate rolling bodies (AE Belyaev [66]) hydraulic and

pneumatic machines with non-circular gears (An-I-Kahn [67]) precessing transmissions

(IA Bostan [68] EI Tesker [69] VN Syzrantsev BA Lopatin) and other

7 Development of kinematic analysis methods of working and technological meshings Note

that modern designing is the computer designing This factor imposes high requirements to

the theory of gearing as the main mathematical basis for such designing We have to admit

that the classical theory of gearing does not fully comply with these demanding

requirements Thus according to Prof MG Segal who was working with Klingelnberg in

the last years of his life the head of the company prohibited to use differential methods ndash

the basis of the classical theory of gearing ndash in the programs being created The reason for

the ban was inadequacy of the results of computer simulation as compared to real processes

of formation Theoretical research aimed at creating computational models that are

adequate to the real processes of formation and contact of moving bodies were developed by

AE Volkov and VI Medvedev (Moscow) and DT Babichev (Tyumen)

To eliminate the phenomenon DT Babichev elaborated a unified kinematic method for

analysis of the processes of formation [70] based on the ldquotriadrdquo ruptures + envelopes + new

concepts of curvilinear coordinates As the result the cause of inadequacy between the

classical methods of the theory of gearing and real-life processes of formation was

established and rectified The developed kinematic method

Allows to find all the surfaces formed on the item at gear machining formed by smooth

surfaces and inflections of bodies including at advanceretraction of machine tool and in

secondary cutting areas

Has the reliability of non-differential methods but is superior to them in speed of

operation by two orders of magnitude which is confirmed by its partial use in CAD

ldquoSPDIAL +rdquo

Also allows to define the curvatures in gearing

8 Development of the system for assigning real ITS (Initial Tool Surfaces) and construction

of mathematical models for them [71] Real ITS is the set of all forming tools (pieces of

surfaces cutting and boundary edges and corners) for which uniform curvilinear coordinates

are introduced

9 By using the concept of ldquothe acceleration of installationrdquo new techniques for solving

87

multitude of tasks are created calculating the radii of curvature in the gearing identifying

cutting areas and thickness of the layers being cut by tool cutting edges and others (DT

Babichev [48])

For example based on the concept of the acceleration of installation a new basic formula

for calculating the reduced curvature in any normal sections at the contact point of two

moving bodies in contact along the line is created

1Rnp=-

where ɷrol is angular velocity of rolling bodies in the plane of the section in which the

curvature is calculated aB is the acceleration of installation The fundamental nature of the

obtained formula is that

1) in its generality it is commensurate with the kinematic formulas of Rodrigues and Freinet

known in differential geometry but it is intended for a different class of surfaces produced

in the process of formation by the rounding methods

2) curvature in any normal section of all surfaces formed by the rounding methods is

determined by only two scalar parameters and one of them (acceleration of installation)

does not depend on the direction of the section

It was also established that the sign of the acceleration of installation allow to make an

unambiguous judgement on the nature of the contact of bodies For example if aВgt 0 then

the envelope is formed inside the body of the generating element Acceleration of

installation allows to determine (ldquoincidentallyrdquo) the value of the radii of curvature and

faceting value across the whole surface formed by rounding at band- and flake-type

roughness

Thus over the past decade a substantial volume of theoretical knowledge to complete the

third cycle (creation of a computer-oriented theory of gearing) was accumulated

A lot of new notions are introduced and used in theory of gearing

Based on these new notions methods for analysis and synthesis of gear drives and cutter

tool meshings oriented at computer technologies have been developed and continue to be

improved

Intensive investigations to improve methods of optimization synthesis of gearing and to

develop methodologies of computer design and construction of gear boxes are performed

4 Problems and expected directions of the theory of gearing

Let us list the main problems in the gearing theory which in our opinion are the most

important

Problem 1 Creation of the theory of optimization synthesis of structures and parameters of

higher pairs of kinematic elements transmitting the motion and load at the preset and

optimal correlation of normal and friction forces At the present time theory of higher pairs

is being developed only as a pure geometrical science

88

Problem 2 Elaboration of methods of tooth optimal geometry synthesis oriented at the

modern processing technologies instead of traditional ones In this case a designer will have

to solve the variation problem with limitations providing for maximum possible load

capacity of gear drive in accordance with preselected criteria of performance efficiency

Problem 3 Development of methods for analysis of the process of the tooth preset surfaces

changeover taking into account the values of load tooth displacement manufacturing errors

of drive elements errors of relative position of engaging links dynamics of changeover

process

Problem 4 Creation of a unique interrelated complex of application software packages to

enable the designers and manufactures of gear drives to carry out optimization designing

engineering design preparation for production of various drives by meshing

Possible directions of development of the theory of gearing naturally follow from the afore-

described problems

CONCLUSIONS

In the second half of the XIX century the number and complexity of technical inventions of

various machines and mechanisms using the gear drives reached a critical mass and by

around 1890 the scientists had created the scientific basis of the theory of gearing And the

modern theory of gearing was formed by the beginning of the 1970rsquos

The third cycle of the gearing theory development which is oriented at computer technology

is underway

In our opinion the prospects for the development of theory of gearing as a part of the

theory of mechanisms and machines are higher as compared for example with the

linkages Firstly gears are more commonly used in cars than linkages Secondly the

theory of gearing is not only the theory of higher kinematic pairs - it is also the basis for the

theory of gear machining design

It is necessary to note that the current version of the paper is based on the paper published in

the first edition of the given Proceedings [72] but is as close as possible to the paper [73] by

the same authors This version of the article has been prepared by VE Starzhinsky

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2 Витрувий Десять книг об архитектуре ndash Москва laquoАрхитектура-Сraquo 2006 ndash 328 с

(Vitruvius Ten Books on Architecture ndash Moscov Architecture-C 2006 ndash 328 p)

3 Пипуныров ВН История часов с древнейших времен до наших дней - Москва

89

Наука 1982 ndash 496 c (Pipunyrov VN The clock story from ancient times to the present

day ndash Moscow Nauka 1982 ndash 496 p)

4 Академик ИИ Артоболевский Сборник Сост АМ Лепихов ndash М Знание 1983

ndash 176 c (Collection Comp AM Lepihov ndash Moscow Znanie 1983 ndash 176 p)

5 Чебышёв ПЛ Избранные труды ndash М Изд-во АН СССР 1955 ndash 926 с (Chebyshjov

PL Selected Works ndash Moscow AN SSSR 1955 ndash 926 p)

6 Рёло Ф Теоретическая кинематика 1875 (Relo F Theoretical Kinematics 1875)

7 Портретная галерея выдающихся инженеров и ученых в области зубчатых передач

ndash Сборник докладов научно-технической конференции с международным участием

Теория и практика зубчатых передач и редукторостроения Ижевск 2008 ndash C 378-

395 (Portrait Gallery of Disting wished Engineers and Scientist in Gearing ndash Proceedings

of Scientific-Engineering Conference with International Participation Theory and Practice

of Gearing and Reducer Building Izhevsk 2008 ndash P 378-395)

8 Литвин ФЛ Теория зубчатых зацеплений ndash М Наука 1968 ndash 584 с (Litvin FL

Theory of gearing ndash Moscow Nauka 1968 ndash 584 p)

9 Механика машин вып 45 ndash Москва Наука 1974 (Mechanics of machines No 45 ndash

Moscow Nauka 1974)

10 Willis R Principles of Mechanism ndash Cambridge London 1841

11 Гохман ХИ Теория зацеплений обобщенная и развитая путем анализа Дисс

магистра механики Одесса ndash 1886 ndash 232 с (Hokhman HI Link Theory generalized and

developed by analyzing Diss mastermechanic Odessa 1886 ndash 232 p)

12 Шишков ВА Образование поверхностей резанием по методу обкатки ndash Москва

Машгиз 1951 ndash 150 с (Shishkov VA Formation of surface machining by burnishing

method ndash Moscow Mashgiz 1951 ndash 150 p)

13 Вильдгабер Э Основы зацепления конических и гипоидных передач ndash Машгиз

1948 ndash 236 с (Vildgaber Je Principles of engagement bevel and hypoid gears ndash Moscow

Mashgiz 1948 ndash 236 p)

14 Baxter ML Basic Geometry and Tooth Contact of Hypoid Gears ldquoIndustrial

Mathematicsrdquo ndash 1961 ndash No 11 ndash P 19-42

15 Шевелева ГИ Алгоритм численного расчета обрабатываемой поверхности Станки

и инструмент ndash 1969 ndash 8 ndash C17-20 (Sheveleva GI Algorithm for the numerical

calculation of the treated surface Machines and Tooling ndash 1969 ndash No 8 ndash P 17-20)

16 Николаев АФ Диаграмма винта и ее применение к определению сопряженных

линейчатых поверхностей с линейным касанием Труды семинара по ТММ вып 37

1950 ndash С52ndash106 (Nikolaev AF Diagram of the screw and its application to the

determination of conjugate ruled surfaces with a linear contact Proceedings of the

Seminar on TMM ndash 1950 ndash No 37 ndash P52-106)

17 Новиков МЛ Зубчатые передачи с новым зацеплением ndash М Изд ВВИА им

Жуковского 1958 ndash 186 с (Novikov ML Gears with a new engagement ndash Moscow

Publisher VVIA by named Zhukovsky 1958 ndash 186 p)

18 Давыдов ЯС Об одном обобщении метода Оливье для образования сопряженных

90

поверхностей в зубчатых передачах Сб laquoТеорияпередачвмашинахraquo М Машгиз

1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

83

of Gears

Russian direction in the development of the theory of gearing has several specific features

attributable to the following objective circumstances

Firstly first clear signs of stagnation appeared in the USSR industry in the late 70rsquos

Secondly the number of graduate students reduced as the universities basically solved the

problem of teachers which they faced in the early 60rsquos due to a drastic increase in the

number of students being trained in engineering specialties And finally Russia lost the top

three main theorists in the field of the theory of gearing FL Litvin was forced to emigrate

to the USA LV Korostelyov died in a car crash YaS Davydov departed from active

research and subsequently left for the USA

And nevertheless in 15-20 years preceding the collapse of the USSR in 1991 the theory

and geometry of gearing in the Soviet Union was continuing to develop At that time new

centers specializing in different aspects of the theory of gearing were established Let us list

the most interesting in our opinion research topics at the end of the last century

- Issues of strength and solution of the tooth contact problem (EL Airapetov VN

Syzrantsev GI Sheveleva)

- Research on gear bending bending stresses calculation (GI Sheveleva VI Medvedev)

- Non-differential methods for the determination of the contact surfaces characteristics (VI

Goldfarb GI Sheveleva AE Volkov)

- Issues of design synthesis analysis and manufacturing spiroid gear drives (AK Georgiev

VI Goldfarb)

- Issues of design synthesis analysis and manufacturing worm gear drives (SA Lagutin

AI Sandler)

- Research of hypoid bevel gear drives with circular teeth (MG Segal GI Sheveleva VN

Syzrantsev)

- Research of gear drives with intermediate bodies (AE Belyaev)

- Research of helical-bevel gear drives (BA Lopatin)

- Development of methods for the synthesis of gear drives (MG Segal SA Lagutin GI

Sheveleva VI Medvedev VN Syzrantsev)

- Forming a theoretical framework for the development of universal programs for the

analysis of spatial working and technological meshings and the creation of corresponding

programs (DT Babichev)

As a result of these studies software systems were developed in the Soviet Union which

were aimed at solving the problems of synthesis and analysis primarily for bevel gears with

circular teeth The best known ones include PC Volga5 made under the direction of MG

Segal [38] and PC Expert created under the direction of GI Sheveleva [39]

The fact that MG Segal was the main developer of the PC Kimos (firm Klingelnberg) in

the 90rsquos confirms the high level of those developments

It should also be noted that a work on the selection of optimal schemes for multi-axis CNC

84

machines for processing gear was carried out in 1990 in Saratov (MG Segal LI Shejko

[40]) These developments have also been used by Klingelnberg

The researches (above all theoretical ones) continued after the collapse of the USSR in

Russia Ukraine and Belarus

At that time the development of the theory of gearing was distinguished by a high level of

theoretical studies based on the introduction of new geometric geometric-kinematic and

other concepts and development (on their basis) of new mathematical models methods and

algorithms for analysis and synthesis of the working and technological gear engagements

These works were performed mostly at their own initiative by highly qualified specialists-

theorists in the field of theory and geometry of working and technological gear meshing

Usually they were elderly university professors who were practically deprived of relations

with the machine-building industry after its stagnation during the collapse of the USSR

It should be noted that it is very difficult to distinguish the most important areas of research

in the modern theory of gearing As the poet said Great things are better seen from a

distance Therefore we will list the most interesting in our view theoretical works on the

development of the theory of gearing with greater focus on the Russian line of research

However we practically do not consider the works on gear geometry ndash they are too

numerous A fairly complete picture of the theoretical works of this period can be obtained

from the proceedings of symposia and conferences held in Kurgan (KMI) Izhevsk

(IzhSTU) and Sevastopol (KhPI Kharkov) The main directions in the development of the

theory of gearing and the most important theoretical results after 1970s include the

following

1 Introduction and use of new concepts such as

Meshing Space (SA Lagutin [41])

Wrapping surface (GI Sheveleva [39])

Fan wedge and normal beam accelerating of implantation (DT Babichev [42])

2 Development of methods for analyzing processes of generation

A new method of finding a singularity in the flat gearing (SA Lagutin) based on the

situation [43] return point at the gear profile occurs at the point in the line of engagement

in which the normal to this line intersects the axis of rotation of the pinion The method was

extended to the spatial gearing (AE Volkov [44])

3 Development of methods of synthesis

Based on the new concept of space of engagement and its properties This approach was

used during the synthesis of both spatial transmission (SA Lagutin [45]) and the cylindrical

(DT Babichev [46])

By using as objective function new criteria of load capacity - permissible contact

pressure(VI Medvedev [47]) the specific work of working surfaces of teeth (DT Babichev

[48]) and others

For bevel gears with small cross-axis angle (SA Lagutin [49] VI Medvedev [50])

Synthesis of gears considering technological limitations of the given production processes

85

(VI Medvedev [51] VN Syzrantsev [52])

By using and developing a method of synthesis of gears in generalizing parameters

originally proposed by EB Vulgakov for involute gears The method was modified by VL

Dorofeev - for involute and ON Tsukanov and BA Lopatin ndash for non-involute gears

(including cylinder-conical ones) [53]

By using variational methods of synthesis when the equation of an optimal surface of the

tooth and its coefficients are determined This approach was first applied apparently by

Alan Lebec [54] in the United States it was used in Ukraine [55] and being developed in

Russia where equal strength gears have been synthesized by using the method (by Hertz

contact strength) [46 56] and the method of synthesis of bevel gear with circular teeth

according to the criteria of minimal contact pressure and bending stresses while maintaining

the overall dimensions of the gear has been developed which is important for aviation

where the weight of the structure is crucial [57]

Increasing the bending strength of circular tooth bevel gears by optimizing the shape of

the tool [58]

Increasing the load-bearing capacity of high-speed heavy-duty cylindrical involute gears

Note that EB Vulgakov VL Dorofeev and AL Kapelevich have made a significant

contribution to the development of synthesis aviation gear in recent decades [59]

4 Development of methods of analysis of loaded gears considering multipairness of

contact

For bevel gears with circular teeth [60]

For spiroid gears [61]

5 Significant progress has been made in the methods of analysis synthesis design and

manufacture of worm gear transmissions

The main input in this field of gearing has been made by two groups of researchers under

the leadership of VI Goldfarb and SA Lagutin The techniques of minimizing meshing

errors and worm hob errors that appear when regrinding and relieving works are fulfilled

have been developed by SA Lagutin and AI Sandler The techniques of synthesis and

production of gears with localized contact were drilled worm gears (SA Lagutin AI

Sandler [62]) and spiroid ones (VI Goldfarb ES Trubachyov [63])

The drives with the increased load capacity were designed based on a study of meshing

space of non-orthogonal gears spiroid (ES Trubachyov [63]) and worm ones (VYu

Puzanov) Designing of spiroid transmissions is carried out using CAD ldquoSPDIAL+rdquo

developed by a group headed by VI Goldfarb Configurator of gearbox systems for

optimization structural synthesis of their structures is being created (OV Malina etal)

Unified worm hob cutters cutting gears for the drives with localized contact were designed

It became possible to cut the gear wheels in engagement with multiple-thread worm by a

single-pass mill (VI Goldfarb and his disciples)

In the Institute of Mechanics IzhSTU a group led by VI Goldfarb essentially laid the

foundation for a new Russian machine building sub-industry ndash construction of gearboxes for

86

isolation and control valves for pipelines

- Theoretical studies of spiroid and worm gears are at a high scientific level

- A modern design process is applied synthesis of perfect engagement synthesis of

localized contact simulation of the stress strain state analysis of real engagement under

load forecasting the state of transmission

- Three generations of dimension-type series of quarter-turn and multi-turn spiroid gear

drives are developed their production with modern quality control and acceptance tests is

organized

6 Application of unconventional gears and gearing helical-bevel gears (BA Lopatin [65])

transmissions with intermediate rolling bodies (AE Belyaev [66]) hydraulic and

pneumatic machines with non-circular gears (An-I-Kahn [67]) precessing transmissions

(IA Bostan [68] EI Tesker [69] VN Syzrantsev BA Lopatin) and other

7 Development of kinematic analysis methods of working and technological meshings Note

that modern designing is the computer designing This factor imposes high requirements to

the theory of gearing as the main mathematical basis for such designing We have to admit

that the classical theory of gearing does not fully comply with these demanding

requirements Thus according to Prof MG Segal who was working with Klingelnberg in

the last years of his life the head of the company prohibited to use differential methods ndash

the basis of the classical theory of gearing ndash in the programs being created The reason for

the ban was inadequacy of the results of computer simulation as compared to real processes

of formation Theoretical research aimed at creating computational models that are

adequate to the real processes of formation and contact of moving bodies were developed by

AE Volkov and VI Medvedev (Moscow) and DT Babichev (Tyumen)

To eliminate the phenomenon DT Babichev elaborated a unified kinematic method for

analysis of the processes of formation [70] based on the ldquotriadrdquo ruptures + envelopes + new

concepts of curvilinear coordinates As the result the cause of inadequacy between the

classical methods of the theory of gearing and real-life processes of formation was

established and rectified The developed kinematic method

Allows to find all the surfaces formed on the item at gear machining formed by smooth

surfaces and inflections of bodies including at advanceretraction of machine tool and in

secondary cutting areas

Has the reliability of non-differential methods but is superior to them in speed of

operation by two orders of magnitude which is confirmed by its partial use in CAD

ldquoSPDIAL +rdquo

Also allows to define the curvatures in gearing

8 Development of the system for assigning real ITS (Initial Tool Surfaces) and construction

of mathematical models for them [71] Real ITS is the set of all forming tools (pieces of

surfaces cutting and boundary edges and corners) for which uniform curvilinear coordinates

are introduced

9 By using the concept of ldquothe acceleration of installationrdquo new techniques for solving

87

multitude of tasks are created calculating the radii of curvature in the gearing identifying

cutting areas and thickness of the layers being cut by tool cutting edges and others (DT

Babichev [48])

For example based on the concept of the acceleration of installation a new basic formula

for calculating the reduced curvature in any normal sections at the contact point of two

moving bodies in contact along the line is created

1Rnp=-

where ɷrol is angular velocity of rolling bodies in the plane of the section in which the

curvature is calculated aB is the acceleration of installation The fundamental nature of the

obtained formula is that

1) in its generality it is commensurate with the kinematic formulas of Rodrigues and Freinet

known in differential geometry but it is intended for a different class of surfaces produced

in the process of formation by the rounding methods

2) curvature in any normal section of all surfaces formed by the rounding methods is

determined by only two scalar parameters and one of them (acceleration of installation)

does not depend on the direction of the section

It was also established that the sign of the acceleration of installation allow to make an

unambiguous judgement on the nature of the contact of bodies For example if aВgt 0 then

the envelope is formed inside the body of the generating element Acceleration of

installation allows to determine (ldquoincidentallyrdquo) the value of the radii of curvature and

faceting value across the whole surface formed by rounding at band- and flake-type

roughness

Thus over the past decade a substantial volume of theoretical knowledge to complete the

third cycle (creation of a computer-oriented theory of gearing) was accumulated

A lot of new notions are introduced and used in theory of gearing

Based on these new notions methods for analysis and synthesis of gear drives and cutter

tool meshings oriented at computer technologies have been developed and continue to be

improved

Intensive investigations to improve methods of optimization synthesis of gearing and to

develop methodologies of computer design and construction of gear boxes are performed

4 Problems and expected directions of the theory of gearing

Let us list the main problems in the gearing theory which in our opinion are the most

important

Problem 1 Creation of the theory of optimization synthesis of structures and parameters of

higher pairs of kinematic elements transmitting the motion and load at the preset and

optimal correlation of normal and friction forces At the present time theory of higher pairs

is being developed only as a pure geometrical science

88

Problem 2 Elaboration of methods of tooth optimal geometry synthesis oriented at the

modern processing technologies instead of traditional ones In this case a designer will have

to solve the variation problem with limitations providing for maximum possible load

capacity of gear drive in accordance with preselected criteria of performance efficiency

Problem 3 Development of methods for analysis of the process of the tooth preset surfaces

changeover taking into account the values of load tooth displacement manufacturing errors

of drive elements errors of relative position of engaging links dynamics of changeover

process

Problem 4 Creation of a unique interrelated complex of application software packages to

enable the designers and manufactures of gear drives to carry out optimization designing

engineering design preparation for production of various drives by meshing

Possible directions of development of the theory of gearing naturally follow from the afore-

described problems

CONCLUSIONS

In the second half of the XIX century the number and complexity of technical inventions of

various machines and mechanisms using the gear drives reached a critical mass and by

around 1890 the scientists had created the scientific basis of the theory of gearing And the

modern theory of gearing was formed by the beginning of the 1970rsquos

The third cycle of the gearing theory development which is oriented at computer technology

is underway

In our opinion the prospects for the development of theory of gearing as a part of the

theory of mechanisms and machines are higher as compared for example with the

linkages Firstly gears are more commonly used in cars than linkages Secondly the

theory of gearing is not only the theory of higher kinematic pairs - it is also the basis for the

theory of gear machining design

It is necessary to note that the current version of the paper is based on the paper published in

the first edition of the given Proceedings [72] but is as close as possible to the paper [73] by

the same authors This version of the article has been prepared by VE Starzhinsky

REFERENCES

1 Дильс ГА Античная техника Москва-Ленинград ОНТИ - Гос техн-теор изд-во ndash

1934 ndash 215 с (Diels GA Antique appliances - Moscow-Leningrad ONTI - Gos tehn-

teor Publ 1934 ndash 215 p)

2 Витрувий Десять книг об архитектуре ndash Москва laquoАрхитектура-Сraquo 2006 ndash 328 с

(Vitruvius Ten Books on Architecture ndash Moscov Architecture-C 2006 ndash 328 p)

3 Пипуныров ВН История часов с древнейших времен до наших дней - Москва

89

Наука 1982 ndash 496 c (Pipunyrov VN The clock story from ancient times to the present

day ndash Moscow Nauka 1982 ndash 496 p)

4 Академик ИИ Артоболевский Сборник Сост АМ Лепихов ndash М Знание 1983

ndash 176 c (Collection Comp AM Lepihov ndash Moscow Znanie 1983 ndash 176 p)

5 Чебышёв ПЛ Избранные труды ndash М Изд-во АН СССР 1955 ndash 926 с (Chebyshjov

PL Selected Works ndash Moscow AN SSSR 1955 ndash 926 p)

6 Рёло Ф Теоретическая кинематика 1875 (Relo F Theoretical Kinematics 1875)

7 Портретная галерея выдающихся инженеров и ученых в области зубчатых передач

ndash Сборник докладов научно-технической конференции с международным участием

Теория и практика зубчатых передач и редукторостроения Ижевск 2008 ndash C 378-

395 (Portrait Gallery of Disting wished Engineers and Scientist in Gearing ndash Proceedings

of Scientific-Engineering Conference with International Participation Theory and Practice

of Gearing and Reducer Building Izhevsk 2008 ndash P 378-395)

8 Литвин ФЛ Теория зубчатых зацеплений ndash М Наука 1968 ndash 584 с (Litvin FL

Theory of gearing ndash Moscow Nauka 1968 ndash 584 p)

9 Механика машин вып 45 ndash Москва Наука 1974 (Mechanics of machines No 45 ndash

Moscow Nauka 1974)

10 Willis R Principles of Mechanism ndash Cambridge London 1841

11 Гохман ХИ Теория зацеплений обобщенная и развитая путем анализа Дисс

магистра механики Одесса ndash 1886 ndash 232 с (Hokhman HI Link Theory generalized and

developed by analyzing Diss mastermechanic Odessa 1886 ndash 232 p)

12 Шишков ВА Образование поверхностей резанием по методу обкатки ndash Москва

Машгиз 1951 ndash 150 с (Shishkov VA Formation of surface machining by burnishing

method ndash Moscow Mashgiz 1951 ndash 150 p)

13 Вильдгабер Э Основы зацепления конических и гипоидных передач ndash Машгиз

1948 ndash 236 с (Vildgaber Je Principles of engagement bevel and hypoid gears ndash Moscow

Mashgiz 1948 ndash 236 p)

14 Baxter ML Basic Geometry and Tooth Contact of Hypoid Gears ldquoIndustrial

Mathematicsrdquo ndash 1961 ndash No 11 ndash P 19-42

15 Шевелева ГИ Алгоритм численного расчета обрабатываемой поверхности Станки

и инструмент ndash 1969 ndash 8 ndash C17-20 (Sheveleva GI Algorithm for the numerical

calculation of the treated surface Machines and Tooling ndash 1969 ndash No 8 ndash P 17-20)

16 Николаев АФ Диаграмма винта и ее применение к определению сопряженных

линейчатых поверхностей с линейным касанием Труды семинара по ТММ вып 37

1950 ndash С52ndash106 (Nikolaev AF Diagram of the screw and its application to the

determination of conjugate ruled surfaces with a linear contact Proceedings of the

Seminar on TMM ndash 1950 ndash No 37 ndash P52-106)

17 Новиков МЛ Зубчатые передачи с новым зацеплением ndash М Изд ВВИА им

Жуковского 1958 ndash 186 с (Novikov ML Gears with a new engagement ndash Moscow

Publisher VVIA by named Zhukovsky 1958 ndash 186 p)

18 Давыдов ЯС Об одном обобщении метода Оливье для образования сопряженных

90

поверхностей в зубчатых передачах Сб laquoТеорияпередачвмашинахraquo М Машгиз

1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

84

machines for processing gear was carried out in 1990 in Saratov (MG Segal LI Shejko

[40]) These developments have also been used by Klingelnberg

The researches (above all theoretical ones) continued after the collapse of the USSR in

Russia Ukraine and Belarus

At that time the development of the theory of gearing was distinguished by a high level of

theoretical studies based on the introduction of new geometric geometric-kinematic and

other concepts and development (on their basis) of new mathematical models methods and

algorithms for analysis and synthesis of the working and technological gear engagements

These works were performed mostly at their own initiative by highly qualified specialists-

theorists in the field of theory and geometry of working and technological gear meshing

Usually they were elderly university professors who were practically deprived of relations

with the machine-building industry after its stagnation during the collapse of the USSR

It should be noted that it is very difficult to distinguish the most important areas of research

in the modern theory of gearing As the poet said Great things are better seen from a

distance Therefore we will list the most interesting in our view theoretical works on the

development of the theory of gearing with greater focus on the Russian line of research

However we practically do not consider the works on gear geometry ndash they are too

numerous A fairly complete picture of the theoretical works of this period can be obtained

from the proceedings of symposia and conferences held in Kurgan (KMI) Izhevsk

(IzhSTU) and Sevastopol (KhPI Kharkov) The main directions in the development of the

theory of gearing and the most important theoretical results after 1970s include the

following

1 Introduction and use of new concepts such as

Meshing Space (SA Lagutin [41])

Wrapping surface (GI Sheveleva [39])

Fan wedge and normal beam accelerating of implantation (DT Babichev [42])

2 Development of methods for analyzing processes of generation

A new method of finding a singularity in the flat gearing (SA Lagutin) based on the

situation [43] return point at the gear profile occurs at the point in the line of engagement

in which the normal to this line intersects the axis of rotation of the pinion The method was

extended to the spatial gearing (AE Volkov [44])

3 Development of methods of synthesis

Based on the new concept of space of engagement and its properties This approach was

used during the synthesis of both spatial transmission (SA Lagutin [45]) and the cylindrical

(DT Babichev [46])

By using as objective function new criteria of load capacity - permissible contact

pressure(VI Medvedev [47]) the specific work of working surfaces of teeth (DT Babichev

[48]) and others

For bevel gears with small cross-axis angle (SA Lagutin [49] VI Medvedev [50])

Synthesis of gears considering technological limitations of the given production processes

85

(VI Medvedev [51] VN Syzrantsev [52])

By using and developing a method of synthesis of gears in generalizing parameters

originally proposed by EB Vulgakov for involute gears The method was modified by VL

Dorofeev - for involute and ON Tsukanov and BA Lopatin ndash for non-involute gears

(including cylinder-conical ones) [53]

By using variational methods of synthesis when the equation of an optimal surface of the

tooth and its coefficients are determined This approach was first applied apparently by

Alan Lebec [54] in the United States it was used in Ukraine [55] and being developed in

Russia where equal strength gears have been synthesized by using the method (by Hertz

contact strength) [46 56] and the method of synthesis of bevel gear with circular teeth

according to the criteria of minimal contact pressure and bending stresses while maintaining

the overall dimensions of the gear has been developed which is important for aviation

where the weight of the structure is crucial [57]

Increasing the bending strength of circular tooth bevel gears by optimizing the shape of

the tool [58]

Increasing the load-bearing capacity of high-speed heavy-duty cylindrical involute gears

Note that EB Vulgakov VL Dorofeev and AL Kapelevich have made a significant

contribution to the development of synthesis aviation gear in recent decades [59]

4 Development of methods of analysis of loaded gears considering multipairness of

contact

For bevel gears with circular teeth [60]

For spiroid gears [61]

5 Significant progress has been made in the methods of analysis synthesis design and

manufacture of worm gear transmissions

The main input in this field of gearing has been made by two groups of researchers under

the leadership of VI Goldfarb and SA Lagutin The techniques of minimizing meshing

errors and worm hob errors that appear when regrinding and relieving works are fulfilled

have been developed by SA Lagutin and AI Sandler The techniques of synthesis and

production of gears with localized contact were drilled worm gears (SA Lagutin AI

Sandler [62]) and spiroid ones (VI Goldfarb ES Trubachyov [63])

The drives with the increased load capacity were designed based on a study of meshing

space of non-orthogonal gears spiroid (ES Trubachyov [63]) and worm ones (VYu

Puzanov) Designing of spiroid transmissions is carried out using CAD ldquoSPDIAL+rdquo

developed by a group headed by VI Goldfarb Configurator of gearbox systems for

optimization structural synthesis of their structures is being created (OV Malina etal)

Unified worm hob cutters cutting gears for the drives with localized contact were designed

It became possible to cut the gear wheels in engagement with multiple-thread worm by a

single-pass mill (VI Goldfarb and his disciples)

In the Institute of Mechanics IzhSTU a group led by VI Goldfarb essentially laid the

foundation for a new Russian machine building sub-industry ndash construction of gearboxes for

86

isolation and control valves for pipelines

- Theoretical studies of spiroid and worm gears are at a high scientific level

- A modern design process is applied synthesis of perfect engagement synthesis of

localized contact simulation of the stress strain state analysis of real engagement under

load forecasting the state of transmission

- Three generations of dimension-type series of quarter-turn and multi-turn spiroid gear

drives are developed their production with modern quality control and acceptance tests is

organized

6 Application of unconventional gears and gearing helical-bevel gears (BA Lopatin [65])

transmissions with intermediate rolling bodies (AE Belyaev [66]) hydraulic and

pneumatic machines with non-circular gears (An-I-Kahn [67]) precessing transmissions

(IA Bostan [68] EI Tesker [69] VN Syzrantsev BA Lopatin) and other

7 Development of kinematic analysis methods of working and technological meshings Note

that modern designing is the computer designing This factor imposes high requirements to

the theory of gearing as the main mathematical basis for such designing We have to admit

that the classical theory of gearing does not fully comply with these demanding

requirements Thus according to Prof MG Segal who was working with Klingelnberg in

the last years of his life the head of the company prohibited to use differential methods ndash

the basis of the classical theory of gearing ndash in the programs being created The reason for

the ban was inadequacy of the results of computer simulation as compared to real processes

of formation Theoretical research aimed at creating computational models that are

adequate to the real processes of formation and contact of moving bodies were developed by

AE Volkov and VI Medvedev (Moscow) and DT Babichev (Tyumen)

To eliminate the phenomenon DT Babichev elaborated a unified kinematic method for

analysis of the processes of formation [70] based on the ldquotriadrdquo ruptures + envelopes + new

concepts of curvilinear coordinates As the result the cause of inadequacy between the

classical methods of the theory of gearing and real-life processes of formation was

established and rectified The developed kinematic method

Allows to find all the surfaces formed on the item at gear machining formed by smooth

surfaces and inflections of bodies including at advanceretraction of machine tool and in

secondary cutting areas

Has the reliability of non-differential methods but is superior to them in speed of

operation by two orders of magnitude which is confirmed by its partial use in CAD

ldquoSPDIAL +rdquo

Also allows to define the curvatures in gearing

8 Development of the system for assigning real ITS (Initial Tool Surfaces) and construction

of mathematical models for them [71] Real ITS is the set of all forming tools (pieces of

surfaces cutting and boundary edges and corners) for which uniform curvilinear coordinates

are introduced

9 By using the concept of ldquothe acceleration of installationrdquo new techniques for solving

87

multitude of tasks are created calculating the radii of curvature in the gearing identifying

cutting areas and thickness of the layers being cut by tool cutting edges and others (DT

Babichev [48])

For example based on the concept of the acceleration of installation a new basic formula

for calculating the reduced curvature in any normal sections at the contact point of two

moving bodies in contact along the line is created

1Rnp=-

where ɷrol is angular velocity of rolling bodies in the plane of the section in which the

curvature is calculated aB is the acceleration of installation The fundamental nature of the

obtained formula is that

1) in its generality it is commensurate with the kinematic formulas of Rodrigues and Freinet

known in differential geometry but it is intended for a different class of surfaces produced

in the process of formation by the rounding methods

2) curvature in any normal section of all surfaces formed by the rounding methods is

determined by only two scalar parameters and one of them (acceleration of installation)

does not depend on the direction of the section

It was also established that the sign of the acceleration of installation allow to make an

unambiguous judgement on the nature of the contact of bodies For example if aВgt 0 then

the envelope is formed inside the body of the generating element Acceleration of

installation allows to determine (ldquoincidentallyrdquo) the value of the radii of curvature and

faceting value across the whole surface formed by rounding at band- and flake-type

roughness

Thus over the past decade a substantial volume of theoretical knowledge to complete the

third cycle (creation of a computer-oriented theory of gearing) was accumulated

A lot of new notions are introduced and used in theory of gearing

Based on these new notions methods for analysis and synthesis of gear drives and cutter

tool meshings oriented at computer technologies have been developed and continue to be

improved

Intensive investigations to improve methods of optimization synthesis of gearing and to

develop methodologies of computer design and construction of gear boxes are performed

4 Problems and expected directions of the theory of gearing

Let us list the main problems in the gearing theory which in our opinion are the most

important

Problem 1 Creation of the theory of optimization synthesis of structures and parameters of

higher pairs of kinematic elements transmitting the motion and load at the preset and

optimal correlation of normal and friction forces At the present time theory of higher pairs

is being developed only as a pure geometrical science

88

Problem 2 Elaboration of methods of tooth optimal geometry synthesis oriented at the

modern processing technologies instead of traditional ones In this case a designer will have

to solve the variation problem with limitations providing for maximum possible load

capacity of gear drive in accordance with preselected criteria of performance efficiency

Problem 3 Development of methods for analysis of the process of the tooth preset surfaces

changeover taking into account the values of load tooth displacement manufacturing errors

of drive elements errors of relative position of engaging links dynamics of changeover

process

Problem 4 Creation of a unique interrelated complex of application software packages to

enable the designers and manufactures of gear drives to carry out optimization designing

engineering design preparation for production of various drives by meshing

Possible directions of development of the theory of gearing naturally follow from the afore-

described problems

CONCLUSIONS

In the second half of the XIX century the number and complexity of technical inventions of

various machines and mechanisms using the gear drives reached a critical mass and by

around 1890 the scientists had created the scientific basis of the theory of gearing And the

modern theory of gearing was formed by the beginning of the 1970rsquos

The third cycle of the gearing theory development which is oriented at computer technology

is underway

In our opinion the prospects for the development of theory of gearing as a part of the

theory of mechanisms and machines are higher as compared for example with the

linkages Firstly gears are more commonly used in cars than linkages Secondly the

theory of gearing is not only the theory of higher kinematic pairs - it is also the basis for the

theory of gear machining design

It is necessary to note that the current version of the paper is based on the paper published in

the first edition of the given Proceedings [72] but is as close as possible to the paper [73] by

the same authors This version of the article has been prepared by VE Starzhinsky

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1934 ndash 215 с (Diels GA Antique appliances - Moscow-Leningrad ONTI - Gos tehn-

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2 Витрувий Десять книг об архитектуре ndash Москва laquoАрхитектура-Сraquo 2006 ndash 328 с

(Vitruvius Ten Books on Architecture ndash Moscov Architecture-C 2006 ndash 328 p)

3 Пипуныров ВН История часов с древнейших времен до наших дней - Москва

89

Наука 1982 ndash 496 c (Pipunyrov VN The clock story from ancient times to the present

day ndash Moscow Nauka 1982 ndash 496 p)

4 Академик ИИ Артоболевский Сборник Сост АМ Лепихов ndash М Знание 1983

ndash 176 c (Collection Comp AM Lepihov ndash Moscow Znanie 1983 ndash 176 p)

5 Чебышёв ПЛ Избранные труды ndash М Изд-во АН СССР 1955 ndash 926 с (Chebyshjov

PL Selected Works ndash Moscow AN SSSR 1955 ndash 926 p)

6 Рёло Ф Теоретическая кинематика 1875 (Relo F Theoretical Kinematics 1875)

7 Портретная галерея выдающихся инженеров и ученых в области зубчатых передач

ndash Сборник докладов научно-технической конференции с международным участием

Теория и практика зубчатых передач и редукторостроения Ижевск 2008 ndash C 378-

395 (Portrait Gallery of Disting wished Engineers and Scientist in Gearing ndash Proceedings

of Scientific-Engineering Conference with International Participation Theory and Practice

of Gearing and Reducer Building Izhevsk 2008 ndash P 378-395)

8 Литвин ФЛ Теория зубчатых зацеплений ndash М Наука 1968 ndash 584 с (Litvin FL

Theory of gearing ndash Moscow Nauka 1968 ndash 584 p)

9 Механика машин вып 45 ndash Москва Наука 1974 (Mechanics of machines No 45 ndash

Moscow Nauka 1974)

10 Willis R Principles of Mechanism ndash Cambridge London 1841

11 Гохман ХИ Теория зацеплений обобщенная и развитая путем анализа Дисс

магистра механики Одесса ndash 1886 ndash 232 с (Hokhman HI Link Theory generalized and

developed by analyzing Diss mastermechanic Odessa 1886 ndash 232 p)

12 Шишков ВА Образование поверхностей резанием по методу обкатки ndash Москва

Машгиз 1951 ndash 150 с (Shishkov VA Formation of surface machining by burnishing

method ndash Moscow Mashgiz 1951 ndash 150 p)

13 Вильдгабер Э Основы зацепления конических и гипоидных передач ndash Машгиз

1948 ndash 236 с (Vildgaber Je Principles of engagement bevel and hypoid gears ndash Moscow

Mashgiz 1948 ndash 236 p)

14 Baxter ML Basic Geometry and Tooth Contact of Hypoid Gears ldquoIndustrial

Mathematicsrdquo ndash 1961 ndash No 11 ndash P 19-42

15 Шевелева ГИ Алгоритм численного расчета обрабатываемой поверхности Станки

и инструмент ndash 1969 ndash 8 ndash C17-20 (Sheveleva GI Algorithm for the numerical

calculation of the treated surface Machines and Tooling ndash 1969 ndash No 8 ndash P 17-20)

16 Николаев АФ Диаграмма винта и ее применение к определению сопряженных

линейчатых поверхностей с линейным касанием Труды семинара по ТММ вып 37

1950 ndash С52ndash106 (Nikolaev AF Diagram of the screw and its application to the

determination of conjugate ruled surfaces with a linear contact Proceedings of the

Seminar on TMM ndash 1950 ndash No 37 ndash P52-106)

17 Новиков МЛ Зубчатые передачи с новым зацеплением ndash М Изд ВВИА им

Жуковского 1958 ndash 186 с (Novikov ML Gears with a new engagement ndash Moscow

Publisher VVIA by named Zhukovsky 1958 ndash 186 p)

18 Давыдов ЯС Об одном обобщении метода Оливье для образования сопряженных

90

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1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

85

(VI Medvedev [51] VN Syzrantsev [52])

By using and developing a method of synthesis of gears in generalizing parameters

originally proposed by EB Vulgakov for involute gears The method was modified by VL

Dorofeev - for involute and ON Tsukanov and BA Lopatin ndash for non-involute gears

(including cylinder-conical ones) [53]

By using variational methods of synthesis when the equation of an optimal surface of the

tooth and its coefficients are determined This approach was first applied apparently by

Alan Lebec [54] in the United States it was used in Ukraine [55] and being developed in

Russia where equal strength gears have been synthesized by using the method (by Hertz

contact strength) [46 56] and the method of synthesis of bevel gear with circular teeth

according to the criteria of minimal contact pressure and bending stresses while maintaining

the overall dimensions of the gear has been developed which is important for aviation

where the weight of the structure is crucial [57]

Increasing the bending strength of circular tooth bevel gears by optimizing the shape of

the tool [58]

Increasing the load-bearing capacity of high-speed heavy-duty cylindrical involute gears

Note that EB Vulgakov VL Dorofeev and AL Kapelevich have made a significant

contribution to the development of synthesis aviation gear in recent decades [59]

4 Development of methods of analysis of loaded gears considering multipairness of

contact

For bevel gears with circular teeth [60]

For spiroid gears [61]

5 Significant progress has been made in the methods of analysis synthesis design and

manufacture of worm gear transmissions

The main input in this field of gearing has been made by two groups of researchers under

the leadership of VI Goldfarb and SA Lagutin The techniques of minimizing meshing

errors and worm hob errors that appear when regrinding and relieving works are fulfilled

have been developed by SA Lagutin and AI Sandler The techniques of synthesis and

production of gears with localized contact were drilled worm gears (SA Lagutin AI

Sandler [62]) and spiroid ones (VI Goldfarb ES Trubachyov [63])

The drives with the increased load capacity were designed based on a study of meshing

space of non-orthogonal gears spiroid (ES Trubachyov [63]) and worm ones (VYu

Puzanov) Designing of spiroid transmissions is carried out using CAD ldquoSPDIAL+rdquo

developed by a group headed by VI Goldfarb Configurator of gearbox systems for

optimization structural synthesis of their structures is being created (OV Malina etal)

Unified worm hob cutters cutting gears for the drives with localized contact were designed

It became possible to cut the gear wheels in engagement with multiple-thread worm by a

single-pass mill (VI Goldfarb and his disciples)

In the Institute of Mechanics IzhSTU a group led by VI Goldfarb essentially laid the

foundation for a new Russian machine building sub-industry ndash construction of gearboxes for

86

isolation and control valves for pipelines

- Theoretical studies of spiroid and worm gears are at a high scientific level

- A modern design process is applied synthesis of perfect engagement synthesis of

localized contact simulation of the stress strain state analysis of real engagement under

load forecasting the state of transmission

- Three generations of dimension-type series of quarter-turn and multi-turn spiroid gear

drives are developed their production with modern quality control and acceptance tests is

organized

6 Application of unconventional gears and gearing helical-bevel gears (BA Lopatin [65])

transmissions with intermediate rolling bodies (AE Belyaev [66]) hydraulic and

pneumatic machines with non-circular gears (An-I-Kahn [67]) precessing transmissions

(IA Bostan [68] EI Tesker [69] VN Syzrantsev BA Lopatin) and other

7 Development of kinematic analysis methods of working and technological meshings Note

that modern designing is the computer designing This factor imposes high requirements to

the theory of gearing as the main mathematical basis for such designing We have to admit

that the classical theory of gearing does not fully comply with these demanding

requirements Thus according to Prof MG Segal who was working with Klingelnberg in

the last years of his life the head of the company prohibited to use differential methods ndash

the basis of the classical theory of gearing ndash in the programs being created The reason for

the ban was inadequacy of the results of computer simulation as compared to real processes

of formation Theoretical research aimed at creating computational models that are

adequate to the real processes of formation and contact of moving bodies were developed by

AE Volkov and VI Medvedev (Moscow) and DT Babichev (Tyumen)

To eliminate the phenomenon DT Babichev elaborated a unified kinematic method for

analysis of the processes of formation [70] based on the ldquotriadrdquo ruptures + envelopes + new

concepts of curvilinear coordinates As the result the cause of inadequacy between the

classical methods of the theory of gearing and real-life processes of formation was

established and rectified The developed kinematic method

Allows to find all the surfaces formed on the item at gear machining formed by smooth

surfaces and inflections of bodies including at advanceretraction of machine tool and in

secondary cutting areas

Has the reliability of non-differential methods but is superior to them in speed of

operation by two orders of magnitude which is confirmed by its partial use in CAD

ldquoSPDIAL +rdquo

Also allows to define the curvatures in gearing

8 Development of the system for assigning real ITS (Initial Tool Surfaces) and construction

of mathematical models for them [71] Real ITS is the set of all forming tools (pieces of

surfaces cutting and boundary edges and corners) for which uniform curvilinear coordinates

are introduced

9 By using the concept of ldquothe acceleration of installationrdquo new techniques for solving

87

multitude of tasks are created calculating the radii of curvature in the gearing identifying

cutting areas and thickness of the layers being cut by tool cutting edges and others (DT

Babichev [48])

For example based on the concept of the acceleration of installation a new basic formula

for calculating the reduced curvature in any normal sections at the contact point of two

moving bodies in contact along the line is created

1Rnp=-

where ɷrol is angular velocity of rolling bodies in the plane of the section in which the

curvature is calculated aB is the acceleration of installation The fundamental nature of the

obtained formula is that

1) in its generality it is commensurate with the kinematic formulas of Rodrigues and Freinet

known in differential geometry but it is intended for a different class of surfaces produced

in the process of formation by the rounding methods

2) curvature in any normal section of all surfaces formed by the rounding methods is

determined by only two scalar parameters and one of them (acceleration of installation)

does not depend on the direction of the section

It was also established that the sign of the acceleration of installation allow to make an

unambiguous judgement on the nature of the contact of bodies For example if aВgt 0 then

the envelope is formed inside the body of the generating element Acceleration of

installation allows to determine (ldquoincidentallyrdquo) the value of the radii of curvature and

faceting value across the whole surface formed by rounding at band- and flake-type

roughness

Thus over the past decade a substantial volume of theoretical knowledge to complete the

third cycle (creation of a computer-oriented theory of gearing) was accumulated

A lot of new notions are introduced and used in theory of gearing

Based on these new notions methods for analysis and synthesis of gear drives and cutter

tool meshings oriented at computer technologies have been developed and continue to be

improved

Intensive investigations to improve methods of optimization synthesis of gearing and to

develop methodologies of computer design and construction of gear boxes are performed

4 Problems and expected directions of the theory of gearing

Let us list the main problems in the gearing theory which in our opinion are the most

important

Problem 1 Creation of the theory of optimization synthesis of structures and parameters of

higher pairs of kinematic elements transmitting the motion and load at the preset and

optimal correlation of normal and friction forces At the present time theory of higher pairs

is being developed only as a pure geometrical science

88

Problem 2 Elaboration of methods of tooth optimal geometry synthesis oriented at the

modern processing technologies instead of traditional ones In this case a designer will have

to solve the variation problem with limitations providing for maximum possible load

capacity of gear drive in accordance with preselected criteria of performance efficiency

Problem 3 Development of methods for analysis of the process of the tooth preset surfaces

changeover taking into account the values of load tooth displacement manufacturing errors

of drive elements errors of relative position of engaging links dynamics of changeover

process

Problem 4 Creation of a unique interrelated complex of application software packages to

enable the designers and manufactures of gear drives to carry out optimization designing

engineering design preparation for production of various drives by meshing

Possible directions of development of the theory of gearing naturally follow from the afore-

described problems

CONCLUSIONS

In the second half of the XIX century the number and complexity of technical inventions of

various machines and mechanisms using the gear drives reached a critical mass and by

around 1890 the scientists had created the scientific basis of the theory of gearing And the

modern theory of gearing was formed by the beginning of the 1970rsquos

The third cycle of the gearing theory development which is oriented at computer technology

is underway

In our opinion the prospects for the development of theory of gearing as a part of the

theory of mechanisms and machines are higher as compared for example with the

linkages Firstly gears are more commonly used in cars than linkages Secondly the

theory of gearing is not only the theory of higher kinematic pairs - it is also the basis for the

theory of gear machining design

It is necessary to note that the current version of the paper is based on the paper published in

the first edition of the given Proceedings [72] but is as close as possible to the paper [73] by

the same authors This version of the article has been prepared by VE Starzhinsky

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1934 ndash 215 с (Diels GA Antique appliances - Moscow-Leningrad ONTI - Gos tehn-

teor Publ 1934 ndash 215 p)

2 Витрувий Десять книг об архитектуре ndash Москва laquoАрхитектура-Сraquo 2006 ndash 328 с

(Vitruvius Ten Books on Architecture ndash Moscov Architecture-C 2006 ndash 328 p)

3 Пипуныров ВН История часов с древнейших времен до наших дней - Москва

89

Наука 1982 ndash 496 c (Pipunyrov VN The clock story from ancient times to the present

day ndash Moscow Nauka 1982 ndash 496 p)

4 Академик ИИ Артоболевский Сборник Сост АМ Лепихов ndash М Знание 1983

ndash 176 c (Collection Comp AM Lepihov ndash Moscow Znanie 1983 ndash 176 p)

5 Чебышёв ПЛ Избранные труды ndash М Изд-во АН СССР 1955 ndash 926 с (Chebyshjov

PL Selected Works ndash Moscow AN SSSR 1955 ndash 926 p)

6 Рёло Ф Теоретическая кинематика 1875 (Relo F Theoretical Kinematics 1875)

7 Портретная галерея выдающихся инженеров и ученых в области зубчатых передач

ndash Сборник докладов научно-технической конференции с международным участием

Теория и практика зубчатых передач и редукторостроения Ижевск 2008 ndash C 378-

395 (Portrait Gallery of Disting wished Engineers and Scientist in Gearing ndash Proceedings

of Scientific-Engineering Conference with International Participation Theory and Practice

of Gearing and Reducer Building Izhevsk 2008 ndash P 378-395)

8 Литвин ФЛ Теория зубчатых зацеплений ndash М Наука 1968 ndash 584 с (Litvin FL

Theory of gearing ndash Moscow Nauka 1968 ndash 584 p)

9 Механика машин вып 45 ndash Москва Наука 1974 (Mechanics of machines No 45 ndash

Moscow Nauka 1974)

10 Willis R Principles of Mechanism ndash Cambridge London 1841

11 Гохман ХИ Теория зацеплений обобщенная и развитая путем анализа Дисс

магистра механики Одесса ndash 1886 ndash 232 с (Hokhman HI Link Theory generalized and

developed by analyzing Diss mastermechanic Odessa 1886 ndash 232 p)

12 Шишков ВА Образование поверхностей резанием по методу обкатки ndash Москва

Машгиз 1951 ndash 150 с (Shishkov VA Formation of surface machining by burnishing

method ndash Moscow Mashgiz 1951 ndash 150 p)

13 Вильдгабер Э Основы зацепления конических и гипоидных передач ndash Машгиз

1948 ndash 236 с (Vildgaber Je Principles of engagement bevel and hypoid gears ndash Moscow

Mashgiz 1948 ndash 236 p)

14 Baxter ML Basic Geometry and Tooth Contact of Hypoid Gears ldquoIndustrial

Mathematicsrdquo ndash 1961 ndash No 11 ndash P 19-42

15 Шевелева ГИ Алгоритм численного расчета обрабатываемой поверхности Станки

и инструмент ndash 1969 ndash 8 ndash C17-20 (Sheveleva GI Algorithm for the numerical

calculation of the treated surface Machines and Tooling ndash 1969 ndash No 8 ndash P 17-20)

16 Николаев АФ Диаграмма винта и ее применение к определению сопряженных

линейчатых поверхностей с линейным касанием Труды семинара по ТММ вып 37

1950 ndash С52ndash106 (Nikolaev AF Diagram of the screw and its application to the

determination of conjugate ruled surfaces with a linear contact Proceedings of the

Seminar on TMM ndash 1950 ndash No 37 ndash P52-106)

17 Новиков МЛ Зубчатые передачи с новым зацеплением ndash М Изд ВВИА им

Жуковского 1958 ndash 186 с (Novikov ML Gears with a new engagement ndash Moscow

Publisher VVIA by named Zhukovsky 1958 ndash 186 p)

18 Давыдов ЯС Об одном обобщении метода Оливье для образования сопряженных

90

поверхностей в зубчатых передачах Сб laquoТеорияпередачвмашинахraquo М Машгиз

1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

86

isolation and control valves for pipelines

- Theoretical studies of spiroid and worm gears are at a high scientific level

- A modern design process is applied synthesis of perfect engagement synthesis of

localized contact simulation of the stress strain state analysis of real engagement under

load forecasting the state of transmission

- Three generations of dimension-type series of quarter-turn and multi-turn spiroid gear

drives are developed their production with modern quality control and acceptance tests is

organized

6 Application of unconventional gears and gearing helical-bevel gears (BA Lopatin [65])

transmissions with intermediate rolling bodies (AE Belyaev [66]) hydraulic and

pneumatic machines with non-circular gears (An-I-Kahn [67]) precessing transmissions

(IA Bostan [68] EI Tesker [69] VN Syzrantsev BA Lopatin) and other

7 Development of kinematic analysis methods of working and technological meshings Note

that modern designing is the computer designing This factor imposes high requirements to

the theory of gearing as the main mathematical basis for such designing We have to admit

that the classical theory of gearing does not fully comply with these demanding

requirements Thus according to Prof MG Segal who was working with Klingelnberg in

the last years of his life the head of the company prohibited to use differential methods ndash

the basis of the classical theory of gearing ndash in the programs being created The reason for

the ban was inadequacy of the results of computer simulation as compared to real processes

of formation Theoretical research aimed at creating computational models that are

adequate to the real processes of formation and contact of moving bodies were developed by

AE Volkov and VI Medvedev (Moscow) and DT Babichev (Tyumen)

To eliminate the phenomenon DT Babichev elaborated a unified kinematic method for

analysis of the processes of formation [70] based on the ldquotriadrdquo ruptures + envelopes + new

concepts of curvilinear coordinates As the result the cause of inadequacy between the

classical methods of the theory of gearing and real-life processes of formation was

established and rectified The developed kinematic method

Allows to find all the surfaces formed on the item at gear machining formed by smooth

surfaces and inflections of bodies including at advanceretraction of machine tool and in

secondary cutting areas

Has the reliability of non-differential methods but is superior to them in speed of

operation by two orders of magnitude which is confirmed by its partial use in CAD

ldquoSPDIAL +rdquo

Also allows to define the curvatures in gearing

8 Development of the system for assigning real ITS (Initial Tool Surfaces) and construction

of mathematical models for them [71] Real ITS is the set of all forming tools (pieces of

surfaces cutting and boundary edges and corners) for which uniform curvilinear coordinates

are introduced

9 By using the concept of ldquothe acceleration of installationrdquo new techniques for solving

87

multitude of tasks are created calculating the radii of curvature in the gearing identifying

cutting areas and thickness of the layers being cut by tool cutting edges and others (DT

Babichev [48])

For example based on the concept of the acceleration of installation a new basic formula

for calculating the reduced curvature in any normal sections at the contact point of two

moving bodies in contact along the line is created

1Rnp=-

where ɷrol is angular velocity of rolling bodies in the plane of the section in which the

curvature is calculated aB is the acceleration of installation The fundamental nature of the

obtained formula is that

1) in its generality it is commensurate with the kinematic formulas of Rodrigues and Freinet

known in differential geometry but it is intended for a different class of surfaces produced

in the process of formation by the rounding methods

2) curvature in any normal section of all surfaces formed by the rounding methods is

determined by only two scalar parameters and one of them (acceleration of installation)

does not depend on the direction of the section

It was also established that the sign of the acceleration of installation allow to make an

unambiguous judgement on the nature of the contact of bodies For example if aВgt 0 then

the envelope is formed inside the body of the generating element Acceleration of

installation allows to determine (ldquoincidentallyrdquo) the value of the radii of curvature and

faceting value across the whole surface formed by rounding at band- and flake-type

roughness

Thus over the past decade a substantial volume of theoretical knowledge to complete the

third cycle (creation of a computer-oriented theory of gearing) was accumulated

A lot of new notions are introduced and used in theory of gearing

Based on these new notions methods for analysis and synthesis of gear drives and cutter

tool meshings oriented at computer technologies have been developed and continue to be

improved

Intensive investigations to improve methods of optimization synthesis of gearing and to

develop methodologies of computer design and construction of gear boxes are performed

4 Problems and expected directions of the theory of gearing

Let us list the main problems in the gearing theory which in our opinion are the most

important

Problem 1 Creation of the theory of optimization synthesis of structures and parameters of

higher pairs of kinematic elements transmitting the motion and load at the preset and

optimal correlation of normal and friction forces At the present time theory of higher pairs

is being developed only as a pure geometrical science

88

Problem 2 Elaboration of methods of tooth optimal geometry synthesis oriented at the

modern processing technologies instead of traditional ones In this case a designer will have

to solve the variation problem with limitations providing for maximum possible load

capacity of gear drive in accordance with preselected criteria of performance efficiency

Problem 3 Development of methods for analysis of the process of the tooth preset surfaces

changeover taking into account the values of load tooth displacement manufacturing errors

of drive elements errors of relative position of engaging links dynamics of changeover

process

Problem 4 Creation of a unique interrelated complex of application software packages to

enable the designers and manufactures of gear drives to carry out optimization designing

engineering design preparation for production of various drives by meshing

Possible directions of development of the theory of gearing naturally follow from the afore-

described problems

CONCLUSIONS

In the second half of the XIX century the number and complexity of technical inventions of

various machines and mechanisms using the gear drives reached a critical mass and by

around 1890 the scientists had created the scientific basis of the theory of gearing And the

modern theory of gearing was formed by the beginning of the 1970rsquos

The third cycle of the gearing theory development which is oriented at computer technology

is underway

In our opinion the prospects for the development of theory of gearing as a part of the

theory of mechanisms and machines are higher as compared for example with the

linkages Firstly gears are more commonly used in cars than linkages Secondly the

theory of gearing is not only the theory of higher kinematic pairs - it is also the basis for the

theory of gear machining design

It is necessary to note that the current version of the paper is based on the paper published in

the first edition of the given Proceedings [72] but is as close as possible to the paper [73] by

the same authors This version of the article has been prepared by VE Starzhinsky

REFERENCES

1 Дильс ГА Античная техника Москва-Ленинград ОНТИ - Гос техн-теор изд-во ndash

1934 ndash 215 с (Diels GA Antique appliances - Moscow-Leningrad ONTI - Gos tehn-

teor Publ 1934 ndash 215 p)

2 Витрувий Десять книг об архитектуре ndash Москва laquoАрхитектура-Сraquo 2006 ndash 328 с

(Vitruvius Ten Books on Architecture ndash Moscov Architecture-C 2006 ndash 328 p)

3 Пипуныров ВН История часов с древнейших времен до наших дней - Москва

89

Наука 1982 ndash 496 c (Pipunyrov VN The clock story from ancient times to the present

day ndash Moscow Nauka 1982 ndash 496 p)

4 Академик ИИ Артоболевский Сборник Сост АМ Лепихов ndash М Знание 1983

ndash 176 c (Collection Comp AM Lepihov ndash Moscow Znanie 1983 ndash 176 p)

5 Чебышёв ПЛ Избранные труды ndash М Изд-во АН СССР 1955 ndash 926 с (Chebyshjov

PL Selected Works ndash Moscow AN SSSR 1955 ndash 926 p)

6 Рёло Ф Теоретическая кинематика 1875 (Relo F Theoretical Kinematics 1875)

7 Портретная галерея выдающихся инженеров и ученых в области зубчатых передач

ndash Сборник докладов научно-технической конференции с международным участием

Теория и практика зубчатых передач и редукторостроения Ижевск 2008 ndash C 378-

395 (Portrait Gallery of Disting wished Engineers and Scientist in Gearing ndash Proceedings

of Scientific-Engineering Conference with International Participation Theory and Practice

of Gearing and Reducer Building Izhevsk 2008 ndash P 378-395)

8 Литвин ФЛ Теория зубчатых зацеплений ndash М Наука 1968 ndash 584 с (Litvin FL

Theory of gearing ndash Moscow Nauka 1968 ndash 584 p)

9 Механика машин вып 45 ndash Москва Наука 1974 (Mechanics of machines No 45 ndash

Moscow Nauka 1974)

10 Willis R Principles of Mechanism ndash Cambridge London 1841

11 Гохман ХИ Теория зацеплений обобщенная и развитая путем анализа Дисс

магистра механики Одесса ndash 1886 ndash 232 с (Hokhman HI Link Theory generalized and

developed by analyzing Diss mastermechanic Odessa 1886 ndash 232 p)

12 Шишков ВА Образование поверхностей резанием по методу обкатки ndash Москва

Машгиз 1951 ndash 150 с (Shishkov VA Formation of surface machining by burnishing

method ndash Moscow Mashgiz 1951 ndash 150 p)

13 Вильдгабер Э Основы зацепления конических и гипоидных передач ndash Машгиз

1948 ndash 236 с (Vildgaber Je Principles of engagement bevel and hypoid gears ndash Moscow

Mashgiz 1948 ndash 236 p)

14 Baxter ML Basic Geometry and Tooth Contact of Hypoid Gears ldquoIndustrial

Mathematicsrdquo ndash 1961 ndash No 11 ndash P 19-42

15 Шевелева ГИ Алгоритм численного расчета обрабатываемой поверхности Станки

и инструмент ndash 1969 ndash 8 ndash C17-20 (Sheveleva GI Algorithm for the numerical

calculation of the treated surface Machines and Tooling ndash 1969 ndash No 8 ndash P 17-20)

16 Николаев АФ Диаграмма винта и ее применение к определению сопряженных

линейчатых поверхностей с линейным касанием Труды семинара по ТММ вып 37

1950 ndash С52ndash106 (Nikolaev AF Diagram of the screw and its application to the

determination of conjugate ruled surfaces with a linear contact Proceedings of the

Seminar on TMM ndash 1950 ndash No 37 ndash P52-106)

17 Новиков МЛ Зубчатые передачи с новым зацеплением ndash М Изд ВВИА им

Жуковского 1958 ndash 186 с (Novikov ML Gears with a new engagement ndash Moscow

Publisher VVIA by named Zhukovsky 1958 ndash 186 p)

18 Давыдов ЯС Об одном обобщении метода Оливье для образования сопряженных

90

поверхностей в зубчатых передачах Сб laquoТеорияпередачвмашинахraquo М Машгиз

1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

87

multitude of tasks are created calculating the radii of curvature in the gearing identifying

cutting areas and thickness of the layers being cut by tool cutting edges and others (DT

Babichev [48])

For example based on the concept of the acceleration of installation a new basic formula

for calculating the reduced curvature in any normal sections at the contact point of two

moving bodies in contact along the line is created

1Rnp=-

where ɷrol is angular velocity of rolling bodies in the plane of the section in which the

curvature is calculated aB is the acceleration of installation The fundamental nature of the

obtained formula is that

1) in its generality it is commensurate with the kinematic formulas of Rodrigues and Freinet

known in differential geometry but it is intended for a different class of surfaces produced

in the process of formation by the rounding methods

2) curvature in any normal section of all surfaces formed by the rounding methods is

determined by only two scalar parameters and one of them (acceleration of installation)

does not depend on the direction of the section

It was also established that the sign of the acceleration of installation allow to make an

unambiguous judgement on the nature of the contact of bodies For example if aВgt 0 then

the envelope is formed inside the body of the generating element Acceleration of

installation allows to determine (ldquoincidentallyrdquo) the value of the radii of curvature and

faceting value across the whole surface formed by rounding at band- and flake-type

roughness

Thus over the past decade a substantial volume of theoretical knowledge to complete the

third cycle (creation of a computer-oriented theory of gearing) was accumulated

A lot of new notions are introduced and used in theory of gearing

Based on these new notions methods for analysis and synthesis of gear drives and cutter

tool meshings oriented at computer technologies have been developed and continue to be

improved

Intensive investigations to improve methods of optimization synthesis of gearing and to

develop methodologies of computer design and construction of gear boxes are performed

4 Problems and expected directions of the theory of gearing

Let us list the main problems in the gearing theory which in our opinion are the most

important

Problem 1 Creation of the theory of optimization synthesis of structures and parameters of

higher pairs of kinematic elements transmitting the motion and load at the preset and

optimal correlation of normal and friction forces At the present time theory of higher pairs

is being developed only as a pure geometrical science

88

Problem 2 Elaboration of methods of tooth optimal geometry synthesis oriented at the

modern processing technologies instead of traditional ones In this case a designer will have

to solve the variation problem with limitations providing for maximum possible load

capacity of gear drive in accordance with preselected criteria of performance efficiency

Problem 3 Development of methods for analysis of the process of the tooth preset surfaces

changeover taking into account the values of load tooth displacement manufacturing errors

of drive elements errors of relative position of engaging links dynamics of changeover

process

Problem 4 Creation of a unique interrelated complex of application software packages to

enable the designers and manufactures of gear drives to carry out optimization designing

engineering design preparation for production of various drives by meshing

Possible directions of development of the theory of gearing naturally follow from the afore-

described problems

CONCLUSIONS

In the second half of the XIX century the number and complexity of technical inventions of

various machines and mechanisms using the gear drives reached a critical mass and by

around 1890 the scientists had created the scientific basis of the theory of gearing And the

modern theory of gearing was formed by the beginning of the 1970rsquos

The third cycle of the gearing theory development which is oriented at computer technology

is underway

In our opinion the prospects for the development of theory of gearing as a part of the

theory of mechanisms and machines are higher as compared for example with the

linkages Firstly gears are more commonly used in cars than linkages Secondly the

theory of gearing is not only the theory of higher kinematic pairs - it is also the basis for the

theory of gear machining design

It is necessary to note that the current version of the paper is based on the paper published in

the first edition of the given Proceedings [72] but is as close as possible to the paper [73] by

the same authors This version of the article has been prepared by VE Starzhinsky

REFERENCES

1 Дильс ГА Античная техника Москва-Ленинград ОНТИ - Гос техн-теор изд-во ndash

1934 ndash 215 с (Diels GA Antique appliances - Moscow-Leningrad ONTI - Gos tehn-

teor Publ 1934 ndash 215 p)

2 Витрувий Десять книг об архитектуре ndash Москва laquoАрхитектура-Сraquo 2006 ndash 328 с

(Vitruvius Ten Books on Architecture ndash Moscov Architecture-C 2006 ndash 328 p)

3 Пипуныров ВН История часов с древнейших времен до наших дней - Москва

89

Наука 1982 ndash 496 c (Pipunyrov VN The clock story from ancient times to the present

day ndash Moscow Nauka 1982 ndash 496 p)

4 Академик ИИ Артоболевский Сборник Сост АМ Лепихов ndash М Знание 1983

ndash 176 c (Collection Comp AM Lepihov ndash Moscow Znanie 1983 ndash 176 p)

5 Чебышёв ПЛ Избранные труды ndash М Изд-во АН СССР 1955 ndash 926 с (Chebyshjov

PL Selected Works ndash Moscow AN SSSR 1955 ndash 926 p)

6 Рёло Ф Теоретическая кинематика 1875 (Relo F Theoretical Kinematics 1875)

7 Портретная галерея выдающихся инженеров и ученых в области зубчатых передач

ndash Сборник докладов научно-технической конференции с международным участием

Теория и практика зубчатых передач и редукторостроения Ижевск 2008 ndash C 378-

395 (Portrait Gallery of Disting wished Engineers and Scientist in Gearing ndash Proceedings

of Scientific-Engineering Conference with International Participation Theory and Practice

of Gearing and Reducer Building Izhevsk 2008 ndash P 378-395)

8 Литвин ФЛ Теория зубчатых зацеплений ndash М Наука 1968 ndash 584 с (Litvin FL

Theory of gearing ndash Moscow Nauka 1968 ndash 584 p)

9 Механика машин вып 45 ndash Москва Наука 1974 (Mechanics of machines No 45 ndash

Moscow Nauka 1974)

10 Willis R Principles of Mechanism ndash Cambridge London 1841

11 Гохман ХИ Теория зацеплений обобщенная и развитая путем анализа Дисс

магистра механики Одесса ndash 1886 ndash 232 с (Hokhman HI Link Theory generalized and

developed by analyzing Diss mastermechanic Odessa 1886 ndash 232 p)

12 Шишков ВА Образование поверхностей резанием по методу обкатки ndash Москва

Машгиз 1951 ndash 150 с (Shishkov VA Formation of surface machining by burnishing

method ndash Moscow Mashgiz 1951 ndash 150 p)

13 Вильдгабер Э Основы зацепления конических и гипоидных передач ndash Машгиз

1948 ndash 236 с (Vildgaber Je Principles of engagement bevel and hypoid gears ndash Moscow

Mashgiz 1948 ndash 236 p)

14 Baxter ML Basic Geometry and Tooth Contact of Hypoid Gears ldquoIndustrial

Mathematicsrdquo ndash 1961 ndash No 11 ndash P 19-42

15 Шевелева ГИ Алгоритм численного расчета обрабатываемой поверхности Станки

и инструмент ndash 1969 ndash 8 ndash C17-20 (Sheveleva GI Algorithm for the numerical

calculation of the treated surface Machines and Tooling ndash 1969 ndash No 8 ndash P 17-20)

16 Николаев АФ Диаграмма винта и ее применение к определению сопряженных

линейчатых поверхностей с линейным касанием Труды семинара по ТММ вып 37

1950 ndash С52ndash106 (Nikolaev AF Diagram of the screw and its application to the

determination of conjugate ruled surfaces with a linear contact Proceedings of the

Seminar on TMM ndash 1950 ndash No 37 ndash P52-106)

17 Новиков МЛ Зубчатые передачи с новым зацеплением ndash М Изд ВВИА им

Жуковского 1958 ndash 186 с (Novikov ML Gears with a new engagement ndash Moscow

Publisher VVIA by named Zhukovsky 1958 ndash 186 p)

18 Давыдов ЯС Об одном обобщении метода Оливье для образования сопряженных

90

поверхностей в зубчатых передачах Сб laquoТеорияпередачвмашинахraquo М Машгиз

1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

88

Problem 2 Elaboration of methods of tooth optimal geometry synthesis oriented at the

modern processing technologies instead of traditional ones In this case a designer will have

to solve the variation problem with limitations providing for maximum possible load

capacity of gear drive in accordance with preselected criteria of performance efficiency

Problem 3 Development of methods for analysis of the process of the tooth preset surfaces

changeover taking into account the values of load tooth displacement manufacturing errors

of drive elements errors of relative position of engaging links dynamics of changeover

process

Problem 4 Creation of a unique interrelated complex of application software packages to

enable the designers and manufactures of gear drives to carry out optimization designing

engineering design preparation for production of various drives by meshing

Possible directions of development of the theory of gearing naturally follow from the afore-

described problems

CONCLUSIONS

In the second half of the XIX century the number and complexity of technical inventions of

various machines and mechanisms using the gear drives reached a critical mass and by

around 1890 the scientists had created the scientific basis of the theory of gearing And the

modern theory of gearing was formed by the beginning of the 1970rsquos

The third cycle of the gearing theory development which is oriented at computer technology

is underway

In our opinion the prospects for the development of theory of gearing as a part of the

theory of mechanisms and machines are higher as compared for example with the

linkages Firstly gears are more commonly used in cars than linkages Secondly the

theory of gearing is not only the theory of higher kinematic pairs - it is also the basis for the

theory of gear machining design

It is necessary to note that the current version of the paper is based on the paper published in

the first edition of the given Proceedings [72] but is as close as possible to the paper [73] by

the same authors This version of the article has been prepared by VE Starzhinsky

REFERENCES

1 Дильс ГА Античная техника Москва-Ленинград ОНТИ - Гос техн-теор изд-во ndash

1934 ndash 215 с (Diels GA Antique appliances - Moscow-Leningrad ONTI - Gos tehn-

teor Publ 1934 ndash 215 p)

2 Витрувий Десять книг об архитектуре ndash Москва laquoАрхитектура-Сraquo 2006 ndash 328 с

(Vitruvius Ten Books on Architecture ndash Moscov Architecture-C 2006 ndash 328 p)

3 Пипуныров ВН История часов с древнейших времен до наших дней - Москва

89

Наука 1982 ndash 496 c (Pipunyrov VN The clock story from ancient times to the present

day ndash Moscow Nauka 1982 ndash 496 p)

4 Академик ИИ Артоболевский Сборник Сост АМ Лепихов ndash М Знание 1983

ndash 176 c (Collection Comp AM Lepihov ndash Moscow Znanie 1983 ndash 176 p)

5 Чебышёв ПЛ Избранные труды ndash М Изд-во АН СССР 1955 ndash 926 с (Chebyshjov

PL Selected Works ndash Moscow AN SSSR 1955 ndash 926 p)

6 Рёло Ф Теоретическая кинематика 1875 (Relo F Theoretical Kinematics 1875)

7 Портретная галерея выдающихся инженеров и ученых в области зубчатых передач

ndash Сборник докладов научно-технической конференции с международным участием

Теория и практика зубчатых передач и редукторостроения Ижевск 2008 ndash C 378-

395 (Portrait Gallery of Disting wished Engineers and Scientist in Gearing ndash Proceedings

of Scientific-Engineering Conference with International Participation Theory and Practice

of Gearing and Reducer Building Izhevsk 2008 ndash P 378-395)

8 Литвин ФЛ Теория зубчатых зацеплений ndash М Наука 1968 ndash 584 с (Litvin FL

Theory of gearing ndash Moscow Nauka 1968 ndash 584 p)

9 Механика машин вып 45 ndash Москва Наука 1974 (Mechanics of machines No 45 ndash

Moscow Nauka 1974)

10 Willis R Principles of Mechanism ndash Cambridge London 1841

11 Гохман ХИ Теория зацеплений обобщенная и развитая путем анализа Дисс

магистра механики Одесса ndash 1886 ndash 232 с (Hokhman HI Link Theory generalized and

developed by analyzing Diss mastermechanic Odessa 1886 ndash 232 p)

12 Шишков ВА Образование поверхностей резанием по методу обкатки ndash Москва

Машгиз 1951 ndash 150 с (Shishkov VA Formation of surface machining by burnishing

method ndash Moscow Mashgiz 1951 ndash 150 p)

13 Вильдгабер Э Основы зацепления конических и гипоидных передач ndash Машгиз

1948 ndash 236 с (Vildgaber Je Principles of engagement bevel and hypoid gears ndash Moscow

Mashgiz 1948 ndash 236 p)

14 Baxter ML Basic Geometry and Tooth Contact of Hypoid Gears ldquoIndustrial

Mathematicsrdquo ndash 1961 ndash No 11 ndash P 19-42

15 Шевелева ГИ Алгоритм численного расчета обрабатываемой поверхности Станки

и инструмент ndash 1969 ndash 8 ndash C17-20 (Sheveleva GI Algorithm for the numerical

calculation of the treated surface Machines and Tooling ndash 1969 ndash No 8 ndash P 17-20)

16 Николаев АФ Диаграмма винта и ее применение к определению сопряженных

линейчатых поверхностей с линейным касанием Труды семинара по ТММ вып 37

1950 ndash С52ndash106 (Nikolaev AF Diagram of the screw and its application to the

determination of conjugate ruled surfaces with a linear contact Proceedings of the

Seminar on TMM ndash 1950 ndash No 37 ndash P52-106)

17 Новиков МЛ Зубчатые передачи с новым зацеплением ndash М Изд ВВИА им

Жуковского 1958 ndash 186 с (Novikov ML Gears with a new engagement ndash Moscow

Publisher VVIA by named Zhukovsky 1958 ndash 186 p)

18 Давыдов ЯС Об одном обобщении метода Оливье для образования сопряженных

90

поверхностей в зубчатых передачах Сб laquoТеорияпередачвмашинахraquo М Машгиз

1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

89

Наука 1982 ndash 496 c (Pipunyrov VN The clock story from ancient times to the present

day ndash Moscow Nauka 1982 ndash 496 p)

4 Академик ИИ Артоболевский Сборник Сост АМ Лепихов ndash М Знание 1983

ndash 176 c (Collection Comp AM Lepihov ndash Moscow Znanie 1983 ndash 176 p)

5 Чебышёв ПЛ Избранные труды ndash М Изд-во АН СССР 1955 ndash 926 с (Chebyshjov

PL Selected Works ndash Moscow AN SSSR 1955 ndash 926 p)

6 Рёло Ф Теоретическая кинематика 1875 (Relo F Theoretical Kinematics 1875)

7 Портретная галерея выдающихся инженеров и ученых в области зубчатых передач

ndash Сборник докладов научно-технической конференции с международным участием

Теория и практика зубчатых передач и редукторостроения Ижевск 2008 ndash C 378-

395 (Portrait Gallery of Disting wished Engineers and Scientist in Gearing ndash Proceedings

of Scientific-Engineering Conference with International Participation Theory and Practice

of Gearing and Reducer Building Izhevsk 2008 ndash P 378-395)

8 Литвин ФЛ Теория зубчатых зацеплений ndash М Наука 1968 ndash 584 с (Litvin FL

Theory of gearing ndash Moscow Nauka 1968 ndash 584 p)

9 Механика машин вып 45 ndash Москва Наука 1974 (Mechanics of machines No 45 ndash

Moscow Nauka 1974)

10 Willis R Principles of Mechanism ndash Cambridge London 1841

11 Гохман ХИ Теория зацеплений обобщенная и развитая путем анализа Дисс

магистра механики Одесса ndash 1886 ndash 232 с (Hokhman HI Link Theory generalized and

developed by analyzing Diss mastermechanic Odessa 1886 ndash 232 p)

12 Шишков ВА Образование поверхностей резанием по методу обкатки ndash Москва

Машгиз 1951 ndash 150 с (Shishkov VA Formation of surface machining by burnishing

method ndash Moscow Mashgiz 1951 ndash 150 p)

13 Вильдгабер Э Основы зацепления конических и гипоидных передач ndash Машгиз

1948 ndash 236 с (Vildgaber Je Principles of engagement bevel and hypoid gears ndash Moscow

Mashgiz 1948 ndash 236 p)

14 Baxter ML Basic Geometry and Tooth Contact of Hypoid Gears ldquoIndustrial

Mathematicsrdquo ndash 1961 ndash No 11 ndash P 19-42

15 Шевелева ГИ Алгоритм численного расчета обрабатываемой поверхности Станки

и инструмент ndash 1969 ndash 8 ndash C17-20 (Sheveleva GI Algorithm for the numerical

calculation of the treated surface Machines and Tooling ndash 1969 ndash No 8 ndash P 17-20)

16 Николаев АФ Диаграмма винта и ее применение к определению сопряженных

линейчатых поверхностей с линейным касанием Труды семинара по ТММ вып 37

1950 ndash С52ndash106 (Nikolaev AF Diagram of the screw and its application to the

determination of conjugate ruled surfaces with a linear contact Proceedings of the

Seminar on TMM ndash 1950 ndash No 37 ndash P52-106)

17 Новиков МЛ Зубчатые передачи с новым зацеплением ndash М Изд ВВИА им

Жуковского 1958 ndash 186 с (Novikov ML Gears with a new engagement ndash Moscow

Publisher VVIA by named Zhukovsky 1958 ndash 186 p)

18 Давыдов ЯС Об одном обобщении метода Оливье для образования сопряженных

90

поверхностей в зубчатых передачах Сб laquoТеорияпередачвмашинахraquo М Машгиз

1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

90

поверхностей в зубчатых передачах Сб laquoТеорияпередачвмашинахraquo М Машгиз

1963 ndash С 19-25 (Davydov YaS On a generalization of Olivier method for the formation

surfaces in gears Proceedings of the Theory of gears in machines ndash Moscow Mashgiz

1963 ndash P 19-25)

19 Ерихов МЛ Метод последовательного огибания Механика машин 1972 вып

31ndash32 ndash С 12ndash20 (Erikhov ML Method of successive diffraction Mechanics of

machines ndash 1972 ndash Nos 31ndash32 ndash P 12-20 )

20 Колчин НИ Аналитические основы дифференциального метода исследования

зубчатых зацеплений Труды семинара по ТММ АН СССР вып 64 1957 (Kolchin NI

Analytical basics of differential method of gearing research Proc of Workshop on TMM

USSR Academy of Sciences Issue 64 1957)

21 Писманик КМ Об оси зацепления червячных передач Труды семинара по ТММ

1950 вып 39 (Pismanik KM About of axis of worm gear drives Proc Of Workshop on

TMM USSR Academy of Sciences Issue 39 1950)

22 Колчин НИ Метод винтового комплекса в теории пространственных зацеплений

Сб laquoТеория передач в машинахraquo ndash М Машгиз 1963 ndash С 7-18 (Kolchin NI Method

of Screw Complex in the Theory of Spatial Gearing Collection ldquoTheory of Transfers in

Machinesrdquo Moscow Mashgiz 1963 ndash P 7-18)

23 Люкшин ВС Теория винтовых поверхностей в проектировании режущих

инструментов ndash М Машиностроение 1968 ndash 371 с (Lyukshin VS Theory of screw

surfaces in the machining tool design ndash Moscow Mashinostroenie 1968 ndash 371 p)

24 Давыдов ЯС Неэвольвентное зацепление ndash М Машгиз 1950 ndash 189 с (Davydov

YaS Noninvolute gearing ndash Moscow Mashgiz 1950 ndash 189 p)

25 Крылов НН Глобоидальное зацепление при произвольном угле скрещивания осей

Труды семинара по ТММ вып 50 АН СССР 1953 (Krylov NN Globoidal meching

at unspecified angle of axes intersection Proc Of Workshop on ТММ Issue 50 USSR

Academy of Sciences 1953)

26 Литвин ФЛ Теория зубчатых зацеплений ndash М Физматгиз 1960 ndash 444 с (Litvin

FL Theory of Gearing ndash Moscow Fizmatgiz 1960 ndash 444 p)

27 Шевелева ГИ Метод степенных рядов в теории зубчатых зацеплений с точечным

контактом Машиноведение 4 1969 ndash С58-65 (Sheveleva GI Method of formal power

series in the theory of gearing with the point contact Mashinovedenie No 4 1969 ndash P58-65)

28 Дусев ИИ Васильев ВМ Аналитическая теория пространственных зацеплений и

ее применение к исследованию гипоидных передач ndash Новочеркасск Изд НПИ 1968

ndash 148 с (Dusev II Vasilrsquoev VM Analytical theory of spatial gearing and its application to

the hypoid gear drive research Novocherkassk Publisher NPI 1968 ndash 148 p)

29 Коростелев ЛВ Лагутин СА Синтез зубчатых передач с замкнутой линией

контакта Машиноведение ndash 1969 ndash 6 ndash С 44-50 (Korostelev LV Lagutin SA

Synthesis of gears with a closed line of contact Mashinovedenie ndash 1969 ndash No 6 ndash P 44-50)

30 Гавриленко ВА Основы теории эвольвентной зубчатой передачи ndash М

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

91

Машиностроение 1969 ndash 431 с (Gavrilenko VA Basics of the theory of involute

gearing ndash Moscow Mashinostroenie 1969 ndash 431 p)

31 Громан МБ Графики для подбора коррекции прямозубых зубчатых передач и

указания по их применению Вестник машиностроения 7 1957 ndash с 32ndash38

(Groman MB Diagrams for selection of spur gear correction and instructions for their

application Bulletin of Mechanical Engineering Russian Jornal ldquoVestnik

Mashinostroeniyardquo No 7 1957 ndash p 32ndash38)

32 Болотовская ТП Болотовский ИА Бочаров ГС Ефименко АБ и др

Справочник по корригированию зубчатых колес ч2 М Машиностроение 1967 ndash

576 с (Bolotovskaya TP Bolotovskay IA Boxharov GS [et al] Guide on correction of

gears Part 2 Moscow Mashinostroenie 1976 ndash 567 p)

33 Литвин ФЛ Некруглые зубчатые колеса ndash М-Л Машгиз 1956 ndash 312 с (Litvin

FL Non-circular gears ndash Moscow-Leningrad Mashgiz 1956 ndash 312 p)

34 Залгаллер ВА Теория огибающих ndash М Наука 1975 ndash 104 с (Zalgaller VA

Theory of envelopes ndash Moscow Nauka 1975 ndash 104 p)

35 Litvin FL Fuentes A Gear Geometry and Applied Theory ndash Cambridge Univer press

2004 ndash 800 p

36 Лагутин СА Профессор ЛВ Коростелев Передачи и трансмиссии ndash 1997 ndash

2 ndash C34-37 (Lagutin SA Professor LV Korostelev Gears and Transmissions ndash 1997 ndash

No 2 ndash P 34-37)

37 Stadtfeld HJ Handbook of Bevel and Hypoid Gears Calculation - Manufacturing -

Optimization ndash 1st Edition Rochester Institute of Technology NY 1993 ndash 251 p

38 Сегаль МГ Ковалев ВГ Ромалис ММ Анализ качества зацепления и расчет

наладочных параметров для профилирования прямых зубьев конических колес

Известия ВУЗов Машиностроение 10 1990 (Segal MG Kovalev VG Romalis

MM Analysis of meshing quality and calculation of development setting for profiling of

straight tooth of bevel gears Izvestiya VUZov Mashinostroenie No 10 1999)

39 Шевелева ГИ Теория формообразования и контакта движущихся тел ndash М

Мосстанкин 1999 ndash 494 с (Sheveleva GI The theory of generation and contact of

moving bodies ndash Moscow Mosstankin 1999 ndash 494 p)

40 Сегаль МГ Шейко ЛИ Классификация компоновок многокоординатных станков

для обработки конических колес с криволинейными зубьями Станки и инструмент ndash

1998 ndash 7 ndash С8-11 (Segal MG Shejko LI Classification layouts multiaxis machine

tools for bevel gears with curved teeth Stanki i instrument ndash 1998 ndash No 7 ndash P 8-11

41 Лагутин СА Пространство зацепления и его элементы Машиноведение ndash 1987

ndash 4 ndash С 69-75 (Lagutin SA The meshing space and its elements] Machine Science

ndash 1987 ndash No 4 ndash P 69 -75)

42 Бабичев ДТ О базовых геометрических примитивах теории зубчатых зацеплений

Теория и практика зубчатых передач Труды межд конф Ижевск 1996 ndash С 469ndash

474 (Babichev DT On the basic geometric primitives of the theory of gearing

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

92

Proceedings of the International Conference Theory and practice of gearing Izhevsk

Russia 1996 ndash P 469-474)

43 Litvin FL De Donno M Lian Q and Lagutin SA Alternative Approach for

Determination of Singularities and Envelopes to a Family of Parametric Surfaces Comput

Methods Appl Mech Engrg ndash 1998 ndash No 167 ndash P 153-165

44 Волков АЭ Методика выявления подрезания круговых зубьев конических и

гипоидных колес Проблемы машиностроения и надежности машин 4 2000 ndash

С66-74 (Volkov AE Technique of emergence of circular teeth undercutting of bevel and

hypoid gears Problems of mechanical engineering and reliability of machines No 4 2000

ndash P 66-74)

45 Lagutin SA Synthesis of Spatial Gearings by Aid of Meshing Space Proc of International

Conference laquoPower Transmissions-03raquo Vol1 Varna Bulgaria 2003 pp 343-346

46 Бабичев ДТ Сторчак МГ Бабичев ДА Геометрический синтез и компьютерное

исследование равнопрочных цилиндрических прямозубых передач Теория и

практика зубчатых передач Сб трудов Международ симпоз Ижевск Изд-во

ИжГТУ 2013 ndash С 309-315 (Babichev DT Starchak MG Babichev DA Geometrical

synthesis and computer research of equal in strength spur gears Proceedings of

International Symposium ldquoTheory and Practice of Gearingrdquo Izhevsk Publiser IzGTU

2013 ndash P 309-315)

47 Медведев ВИ Шевелева ГИ Синтез конической передачи с круговыми зубьями

по допустимым контактным давлениям Материалы всероссийской научно-

практической конференции laquoРедукторостроение России состояние проблемы

перспективыraquo Санкт-Петербург ndash 2002 ndash С59-61 (Medvedev VI Sheveleva GI

Synthesis of spiral bevel gear on permissible contact pressure Proceedings of the All-

Russian scientific and practical conference Reduktorostroenie Russia status problems and

prospects Saint-Petersburg Russia 2002 ndash P 59-61)

48 Бабичев ДТ Развитие теории зацеплений и формообразования поверхностей на

основе новых геометро-кинематических представлений дисс hellip докт техн наук ndash

Тюмень 2005 ndash 421с (Авторефndash Тюмень ТюмГНГУ 2005 ndash 47 с) Babichev DT The

development of the theory of links and forming surfaces on the basis of new geometric-

kinematic representations Diss hellip Doctor technical Sciences ndash Tjumen 2005 ndash 421 p

(Avtoref ndash Tjumen TjumGNGU 2005 ndash 47 p)

49 Akimov VV Lagutin SA Volkov AE New Approach to the Local Synthesis of Spiral

Bevel Gears Proceedings of the 10th Int ASME Power Transmission And Gearing

Conference September 4-7 2007 Las Vegas Nevada USA p13-17

50 Волков АЭ Медведев ВИ Жучков ИВ Семячкова ЕГ Технологический синтез

конических передач с круговыми зубьями с малым межосевым углом Вестник МГТУ

Станкин 1 (18) том 1 2012 ndash С 98-102 (Volkov AE Medvedev VI Zhuchkov IV

Semyachkova EG Technological synthesis of bevel gear drives with circuit teeth with small

crossed axis angle Bulletin MSTU ldquoStankinrdquo No 1(18) Vol 1 2012 ndash P 98-102)

51 Волков АЭ Медведев ВИ Жучков ИВ Расчет наладок для обработки круговых

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

93

зубьев конических передач при наличии технологических ограничений с

использованием модифицированного движения обката Вестник МГТУ laquoСтанкинraquo

2 2010 ndash С20-28 (Volkov AE Medvedev VI Zhuchkov IV Calculation of

debuggingrsquos for tooling of circular teeth of bevel gears in the presence of technological

boundary conditions with using of modified movement of running in mesh Bulletin MSTU

ldquoStankinrdquo No 2 2010 ndash P 20-28)

52 Сызранцев ВН Ратманов ЭВ Котликова ВЯ Оценка возможности изготовления

конических и гипоидных пар в условиях жестких технологических ограничений

Техника машиностроения 2 2001 ndash С52-56 (Syzrantsev VN Ratmanov EV Kotlikova

VYa Evaluation of possibility of manufacturing bevel and hypoid gear pairs of rigid

technological boundary conditions Engineering of Machine Building No 2 2001 ndash С52-56)

53 Лопатин БА Цуканов ОН Способы формирования рабочих поверхностей зубчатых

передач с малым межосевым углом Передачи и трансмиссии 2 1997 ndash С 38-49

(Lopatin BA Tsukanov ON Techniques of Formation of Active Tooth Surfaces of Drives

with Small Crossed Axis Angle Gearing and Transmissions No 2 1997 ndash P 38-39)

54 Lebek AO Radzimovsky EI The synthesis of profile shapes and spur gears of high

load capacity Trans ASME ndash 1970 ndash Vol B 92 No 3 ndash P 543-551

55 Шишов ВП Носко ПЛ Филь ПВ Теоретические основы синтеза передач

зацеплением ndash Луганск СНУ им Даля 2006 ndash 408 с (Shishov VP Nosko PL Fil PV

Theoretical bases of synthesis transmission gearing ndash Lugansk SNU im Dalja 2006 ndash 408 p)

56 Babichev D and Storchak M Synthesis of cylindrical gears with optimum rolling

fatigue strength Production Engineering Research and Development v 9 N 1 ndash Springer

2015 p 87-97

57 Медведев ВИ Матвеенков ДС О построении оптимальных поверхностей

круговых зубьев конических пар Вестник МГТУ laquoСтанкинraquo ndash 2009 ndash 1 ndash С 59-

64 (Medvedev VI Matveenkov DS Construction of Optimal Circular-Tooth Surfaces of

bevel gears Vestnik MGTU laquoStankinraquo ndash 2009 ndash No 1 ndash P 59-64)

58 Медведев ВИ Расчет изгибных напряжений в круговых зубьях конических колес

Проблемы машиностроения и надежности машин ndash 2003 ndash 4 ndash С 32-40

(Medvedev VI Calculation of bending stresses in circular teeth of bevel gears Problems

of mechanical engineering and machine reliability ndash 2003 ndash No 4 ndash P 32-40)

59 Вулгаков ЭБ Теория эвольвентных зубчатых передач ndash М Машиностроение 1995

ndash 320 с (Vulgakov EB The theory of involute gears ndash M Mashinostroenie 1995 ndash 320 p)

60 Medvedev VI Volkov AE Volosova MA Zubelevich OE Mathematical model and

algorithm for contact stress analysis of gears with multi-pair contact Mechanism and

Machine Theory 86 (2015) 156-171

61 Goldfarb VI Trubachov ES Kuznetsov AS Load Distribution in Statically Loaded

Spiroid Gear Proceedings on the 2nd International Conference ldquoPower transmissions 2006rdquo

Novi Sad Serbia amp Montenegro 2006 pp 369-376

62 Сандлер АИ Лагутин СА Верховский АВ Производство червячных передач

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

94

под общ ред СА Лагутина ndash М Машиностроение 2008 ndash 272 с (Sandler AI

Lagutin SA Verkhovsky AV Production of Worm Gear Drives Edited by SA Lagutin

Moscow Mashinostroenie 2008 ndash 272 p)

63 Гольдфарб ВИ Трубачев ЕС Об осях зацепления в спироидной передаче

Пространство зацеплений Сборник докладов научного семинара Учебно-научного

центра зубчатых передач и редукторостроения Ижевск ndash Электросталь 2001 ndash С 71-

76 (Goldfarb VI Trubachyev ES About Axes of Meshing in Spiroid Gear Drive Meshing

Space Proceedings of Scientific Seminar Izhevsk ndash Elektrostal 2001 ndash P 71-76)

64 Трубачев ЕС Метод расчета параметров станочного зацепления с геликоидальной

производящей поверхностью Современные информационные технологии

Проблемы исследования проектирования и производства зубчатых передач Сборник

докладов международного научного семинара Ижевск 2001 ndash С 163-169 (Trubachyev

ES Method of Calculation of Cutter Tool Meshing with Cross-Axis Helical Generating

Surface Modern Information Technologies Proceedings of International Scientific

Seminar Izhevsk 2001 ndash P 163-169)

65 Лопатин БА Разработка теоретических основ проектирования изготовления и

испытания цилиндро-конических зубчатых передач с малыми межосевыми углами

Автореф дис докт техннаук ndash Челябинск 1999 ndash 46 с (Lopatin BA Development

of Theoretical Basics of Design Manufacturing and Testing Bevel-Cylindrical Gear Drives

with Small Cross-Axes Angles Thesis hellip of DrSci(Eng) Chelyabinsk 1999 ndash 46 p)

66 Беляев АЕ Механические передачи с шариковыми промежуточными телами ndash

Томск Изд ЦНТИ 1992 ndash 231 с (Belyaev AE Mechanical Drives with Ball

Intermediate Bodies Tomsk Publicsher TsNTI 1992 ndash 231 p)

67 Ан И-Кан Беляев АЕ Синтез планетарных передач применительно к роторным

гидромашинам Новоуральск НПИ МИФИ 2001 ndash 90 с (An I-Kahn Belgaev AE

Synthesis of Planetary Gear Drives Relating to Rotor Hydraulic Machines Novouralsk NPI

MIFI 2001 ndash 90 p)

68 Бостан ИА Прецессионные передачи с многопарным зацеплением Под ред СА

Шувалова Кишинев Штпинца 1991 ndash 342 с (Bostan IA Precessional Gear Frives

with Multipair Meshing Edited by SA Shuvalov Kishinew Shtipnitsa 1991 ndash 342 p)

69 Кислов СЮ Тескер ЕИ Тимофеев БП Прецессирующие конические передачи

внутреннего зацепления Теория и практика зубчатых передач Труды

международной конференции Ижевск 1996 ndash С387-392 (Kislov SYu Tesker EI

Timofeev BF Precessing Bevel Gear Drives of Internal Meshing Proceeding of

International Conference ldquoTheory and Practice of Gearingrdquo Izhevsk 1996 ndash P 387-392)

70 Бабичев ДТ Основы альтернативной теории формообразования базирующейся на

новых геометрических понятиях Международная конференция Техника проводов 03

докл I-58 ndash Болгария София 2003 ndash С270-275 (Babichev DT Foundations of Alternative

Theory of Forming Based on New Geometrical Notions Proceedings of International Conference

ldquoTechniques of Power Transmissions-03rdquo Paper 1-58 Bulgarua Sofia 2003 ndash P 270-275)

71 Бабичев ДТ О применении многопараметрических огибаний при компьютерном

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

95

моделировании процессов формообразования в рабочих и технологических

зацеплениях Теория и практика зубчатых передач Ижевск 2004 ndash С 302-315

(Babichev DT About Application of Parametric at Computer Simulation of Forming

Processes in Working and Technological Gearingrsquos Proc of International Conference

ldquoTheory and Practice of Gearingrdquo Izhevsk 2004 ndash P 302-315)

72 Terminology for the Mechanism and Machine Science Proceedings of the Scientific

Seminar 25th Working Meeting of IFToMM Permanent Commission for Standardization of

Terminology on MMS (Saint-Petersburg Russia June 23-29 2014) Saint-Petersburgndash

Gomel SPbITMO University 2014 ndash 138 p

73 Бабичев ДТ Волков АЭ История развития теории зубчатых передач Вестник

научно-технического развития 2015 5 (93) ndash С 25-42 (httpwwwvntrru) (Babichev

DT Volkov AE History of the Development of the Gears Theory Bulletin of Scientific

and Engineering Evaluation 2015 No 5(93) ndash Pp 25-42 (httpwwwvntrru)

Comments of Editors

The paper written by the authors Prof Andre E Volkov and Prof Dmitry T Babichev is one

of the raw analytical studies at the moment allowing us to estimate the role of scientists of

CIS countries in the development of theory of machines and mechanisms (TMM) and

theory of toothed engagements

Taking into account the refinement aspect one can say that Tula State University which was

performing under leadership of Profs P G Sidorov [1] and VYa Raspopov [2] together

with ldquoProgressrdquo plant (Michurinsk) under the corresponding grant of Ministry of Education

and Science of Russian Federation became the second center in the industry with respect to

manufacturing of gearboxes for pipeline valves The organizers of the International

Conference which was devoted to the problems of gearboxes for pipeline valves make an

attempt to find the common idea in the work mentioned above

In the field of gearbox manufacturing on the whole as well as in particular directions it is

necessary to develop and extend the ideas of Prof Snesarev GA [3] such attempts were

carried out by Prof VI Goldfarb [4] Prof EV Shalobaev [5] and in reports of leaders of

some specialized plants in Russia which organized the First Russian conference on this

subject in 2002 [6] that continues to be relevant till now

It is important to analyze the studies of plastic gears which became widespread not only in

device manufacturing [7-10] but in the machine building too [11]

One must consider the so-called ldquodevicerdquo gears and gearboxes as well as

microelectromechanical systems (MEMS) which are the issues of micromechatronics The

particularities of using such gears in mechatronics including micromechatronics are

discussed in the works [10 12]

New technologies for production and provision for gears quality [11] are needed too

We must add here the review on a theory of gear engagement by using the data related to the

precision of gears as well as normalization of gear parameters (the studies of Prof BA

96

Taits [13 14] Prof MP Kozlov [15] Dr VA Kutsokon [16] Prof BP Timofeev [17-19]

Prof EV Shalobaev [17 19-21] Prof PK Popov [22] Prof LO Shtripling [22] Prof IP

Nezhurin [23] Prof EI Tesker [24 25] etc) After Russia has become a member of WТО

it is necessary to harmonize the normative documentation according to international and

national standards of other countries [26]

To complete the picture in conclusion let us present the main publications on gearing edited

over the recent years

We already referred to the papers from the Proceedings of the International Symposium

[27] It should be added that in its plenary sectional and poster sessions more than 80

reports have been presented by the scientists from 12 countries (Belarus Bulgaria China

Germany Italy Japan Poland Russia Serbia Spain Ukraine USA) Part of selected papers

has been published in the special edition [28] dedicated to the 100th anniversary of Prof

Faydor L Litvin the famous scientist founder of the modern theory of gearing

Expansive informative material has been presented at the 2015 IFToMM Workshop on

History of Mechanism and Machine Science (May 26-28 2015 St-Petersburg Russia)

Contributors from the Russia Italy China Japan Belarus Taiwan and other countries

participated in more than 60 proceedings on different aspects of MMS Workshop has been

organized under auspices of the IFToMM by Department of Robotics and Complex

Automation (Moscow Bauman State Technical University Prof Olga V Egorova) and

Department of Theory of Mechanisms and Machines (Peter the Great St-Petersburg

Polytechnic University Prof Alexander N Evgrafov) Inter alia papers regarding the

different sphere of gearing and gear drives history [29 30] terminology [311] multistage

and multipath mechanisms [32] gear drive quality [33] design automation [34] improving

serviceability [35] standardization [36] vibrating monitoring [37] and muscle type

actuators [38] can be found on httphmms2015ru site

It should be noted that the paper [39] concerning the history of Russian Gearing School

development has been published (together with other papers on the MMS History) in

Special Issue of the Journal ldquoFrontiers of Mechanical Engineeringrdquo

Besides it is necessary to consider the latest publications on design of gear drives in the

ldquoSystem of Generalized Parametersrdquo Generalization of information for involute gears has

been fulfilled by Dr AL Kapelevich (the high-flyer pupil and follower of Prof Edgar B

Vulgakov founder of this conception) under trademark brand ldquoDirect Gear Designrdquo [40]

Analogous direction for gears with asymmetric teeth called ldquoDirect Synthesisrdquo was

developed by Prof VL Dorofeev with coauthors (see for example [40-43]) Their

investigations show that optimal correlation between the profile angle αnd forming the tooth

drive flank (according to VL Dorofeev ldquobasic anglerdquo) and the profile angle αnc forming the

tooth coast flank (ldquodirecting anglerdquo) should be those αnd = 33o αnc = 20o Alongside with the

indicated topics it is necessary to mention another sphere of interest of the abovementioned

authors Software Complex ldquoAEROFLANKrdquo providing design aircraft gear drives with

reduced level of wear and vibration design gears with optimal geometry stress stiffness

and vibration for aircraft theoretical and experimental investigations of gears with presence

97

of profile errors and runout etc The basics of non-involute gearing in ldquoGeneralized

Parameters Systemrdquo have been developed by ON Tsukanov mathematical methodological

and software support is presented in the monograph [44]

In the given context it is appropriate to mention the books dedicated to designing and

production of different types of gear drives and results of their investigations The problems

of development of spiroid gearboxes and the main design procedure when developing their

layout have been given in monograph [45] Theory and practice of production of worm gear

drives are considered in [46] The basic types and tendencies in development of worm gear

drives in the modern mechanisms and machines are considered

Recently the new direction regarding to processional gearboxes has been developed in

Belarus (Belorussko-Rossiiskii University Mogilev Belarus) Results of theoretical and

experimental investigations of epicyclical precessional pairs and structures of different

drives elaborated on the base of this sort gear pairs have been referred in [47] Technological

processes of manufacturing different structures of machining attachment for generation of

gear tooth working surfaces of mentioned drives were described in [48]

Results of investigations of dynamical processes in gear drives developing the methods of

their vibration diagnostics and unique technic of accelerated tests were carried out in [49]

Ibidem on-board systems of vibration monitoring of technical state of transmissions of

mobile motor-cars were described

In conclusion it makes sense to give information about Interstate Standard GOST 13755-

2015 [50] elaborated by the Russian Federal State Unitary Enterprise ldquoCentral Institute for

Aviation Motor Development named after P I Baranovrdquo (development engineer Prof VL

Dorofeev) instead of GOST 13755-81 Parameters of the Standard basic rack tooth profile

(A) and other ones (B C D) with different bottom clearance whole tooth depth and radius

of curvature of a basic rack tooth profile fillet as well as modified basic rack tooth profiles

with different profile modification parameters (I Г L K C D) were established

REFERENCES

1 Сидоров ПГ Пашин АА Плясов АВ Многопоточные зубчатые трансмиссии

Теория и методология проектирования ndash М Машиностроение 2011 ndash 340 с (Sidorov

PG Pashin AA Plyasov AV Multipath Gear Transmissions Theory and Metodology of

Design ndash Moscow Mashinostroenie 2011 ndash 340 p)

2 Грязев МВ Дмитриев АД Иванов ЮВ и др Многооборотный электропривод

трубопроводной арматуры Под редакцией ВЯ Распопов ndash Тула Изд-во ТулГУ 2011

ndash 322 с (Gryazev MV Dmitriev AV Ivanov YuV et al Multipath Electrodrive of

Pipeline Accessories Editor V Ya Raspopov ndash Tula Publishing House of Tula State

Technical University 2011 ndash 322 p)

3 Снесарев ГА Генеральные задачи редукторостроения Передачи и трансмиссии ndash

1991 1 ndash с 5-7 (Snesarev GA General Task of Development of Gear Boxes

Manufacturing Gearing and Transmissions ndash 1991 ndash No 1 ndash P 5-7)

4 Гольдфарб ВИ Российская программа laquoПрогрессивные зубчатые передачиraquo

98

Зубчатые передачи и трансмиссии1998 - 2 ndash с30-41 (Goldfarb VI Russian Program

ldquoProgressive Gear Boxes ldquo Gearing and Transmissions 1998 ndash No 2 ndash P 30-41)

5 Шалобаев ЕВ Модернизированные редукторы отечественного производства

Фундаментальные и прикладные проблемы техники и технологии 2010 - 6-2 ndash

с105-111 (Shalobaev EV Modernized Gear Boxes of Native Production Fundamental

and Application problems of Engineering and Technologies2010 ndash No 62 ndash P 105-115)

6 Молчанов СМ Парубец ВИ Пшизов ШП О состоянии и задачах

редукторостроения России Материалы Всероссийской конференции

Редукторостроение России Состояние Проблемы Перспективы Под редакцией ЕВ

Шалобаева ndash СПб ЦЦП laquoСветочraquo2003 ndash с27-29 (Molchanov SM Parubets VI

Pshizov ShP About the State and Tasks of Gear Boxes Manufacturing of Russia

Proceeding at All-Russian Conference Gear Boxes Manufacturing of Russia State

Problems and Perspectives Editor EV Shalobaev ndash Saint Petersburg Publishing House

ldquoSvetochrdquo 2003 ndash P 27-29)

7 Пластмассовые зубчатые колеса в механизмах приборов Под ред ВЕ

Старжинского и ЕВ Шалобаева ndash Санкт-Петербург ndash Гомель ИММС НАНБ1998 ndash

528с (Plastic Gears in Instrument Drives Edited by VE Starzhinsky and EV Shalobaev ndash

Saint Petersburg ndash Gomel MPRI NAS of Belarus 1998 ndash 528 p)

8 Старжинский ВЕ Осипенко СА Передачи с зубчатыми колесами из термопластов

Проектирование и технология производства Передачи и трансмиссии 2001 ndash 1 ndash

C 57-70 (Starzhinsky VE Ossipenko SA Drives with Gears from Thermoplastic Design

and Technology Review Gearing and Transmissions ndash 2001 ndash No 1 ndash P 57-70)

9 Шалобаев ЕВ Старжинский ВЕ Шилько СВ и др Обеспечение качественных

показателей зубчатых колес венцы которых выполнены из пластмасс и композитов

Известия Тульского государственного университета 2012 - 12ч1 ndash с142-149

(Shalobaev EV Starzhinsky VE Shilko SV Providing Quality Parameters of Gears with

Polymer Composite Toothed Ring Bulletin of Tula State Technical University ndash 2012 ndash

No 23 ndash P 142-149)

10 Старжинский ВЕ Шалобаев ЕВ Шилько СВ Элементы приводов приборов

Под ред ЮМ Плескачевского Минск Белорусская навука2012 ndash 769с (Starzhinsky

VE Shalobaev EV Shilko SV et al Elements of Instrument Drives Editor YuM

Pleskachevsky ndash Minsk Publishing House ldquoBelaruskaya Navukardquo 2012 ndash 769 p)

11 Технология производства и методы обеспечения качества зубчатых колес и передач

Под ред ВЕ Старжинского и ММ Кане Санкт-Петербург Профессия2007 ndash 832с

(Technology and Methods of Providing Quality of Gears and Gear Drives Edited by VE

Starzhinsky and MM Kane Second Issue corrected and extended ndash Saint Petersburg

Publishing House ldquoProfessijardquo 2007 ndash 832 p)

12 Олексюк В Роль зубчатых передач в мехатронных устройствах Передачи и

трансмиссии2001 - 1 ndash с44-57 (Oleksuk V Role of Gear Drives in Mechatronic

Device Gearing and Transmissions ndash 2001 ndash No 1 ndash P 44-57)

13 Производство зубчатых передач Справочник Под ред БА Тайца М

99

Машиностроение1972 ndash 368с (Production of Gears Reference Book Editor BA Taits

ndash Moscow Mashinostroenie 1972 ndash 368 p)

14 Тайц БА Точность и контроль зубчатых передач Москва Машиностроение 1972 ndash

368с (Taits BA Accuracy and Control of Gears ndash Moscow Mashinostroenie 1972 ndash 368 p)

15 Козлов МП Зубчатые передачи точного приборостроения2-е изд ndash М

Машиностроение 1969 ndash 400с (Kozlov MP Gear Drives of Precision Instrument

Making ndash Moscow Oborongiz 1958 ndash 393 p)

16 Куцоконь ВА Точность кинематических цепей приборов ndash Л-М

Машиностроение1980 ndash 220с (Kutsоkon VA Accuracy of Gear Drives and Kinematic

Chains of Devices ndash Leningrad Mashinostroenie 1980 ndash 220 p)

17 Тимофеев БП Шалобаев ЕВ Состояние и перспективы нормирования зубчатых

колес и передач Вестник машиностроения1990 - 12 ndash с33-39 (Timofeev BP

Shalobaev EV State and Perspectives of Development of Accuracy Normalization of Gears

and Gear Drives Vestnik Mashinostroenia 1990 ndash No 12 ndash P 33-39)

18 Тимофеев БП Точность зубчатых передач и кинематических цепей В кн Механика

машин М Высшая школа 1989 ndash с204-224 (Timofeev BP Accuracy of Gear Drives and

Kinematic Chains Mechanics of Machines ndash Moscow Vysshaya Shkola 1989 ndash P 204-224)

19 Тимофеев БП Шалобаев ЕВ Расчет точности зубчатых передач и

кинематических цепей1998 ndash с296-346 (Timofeev BP Shalobaev EV Calculation of

Gear Drives and Kinematic Chains Plastic Gears and Mechanisms of Devices ndash Saint

PetersburgndashGomel MRPI NAS of Belarus 1998 ndash P 296-346)

20 Шалобаев ЕВ Конструкторско-технологическое обеспечение качества приборных

зубчатых передач В кн Технология производства и методы обеспечения качества

зубчатых колес и передач (Shalobaev EV Design Technology Providing Accuracy of

Instrument Drives Technology and Methods of Providing Quality of Gears and Gear

Drives Edited by VE Starzhinsky and MMKane ndash Saint Petersburg Publishing House

Professiya 2007 ndash P 527-535)

21 Шалобаев ЕВ Методика определения степени точности зубчатых колес в

передаче по нормам кинематической точности с учетом погрешностей изготовления и

монтажа В кн Технология производства и методы обеспечения качества зубчатых

колес и передач ndash с794-801 (Shalobaev EV Technique of definition of Accuracy Grade

of Gears in the Gear Drives in according the Norms of Kinematic Accuracy Taken into

Account Errors of Manufacturing and Assembling of Parts ndash P 794-801)

22 Попов ПК Штриплинг ЛО Предпосылки пересмотра нормативной

документации по расчету точности зубчатых передач Вестник

машиностроения1998 - 6 ndash с59-62 (PK Popov LO Shtripling Background of

Revision of Normative Documents on Calculation of Gear Drive Accuracy Vestnik

Mashinostroenia1998 ndash No 6 ndash P 59-62)

23 Нежурин ИП Точность зубчатых передач В кн Производство зубчатых колес

газотурбинных двигателей под ред ЮС Елисеева М Высшая школа 2001 ndash с44-

87 (Nezhurin IP Accuracy of Gear Drives Tolerances Production of Gear Drives of Gas-

Turbine Engines Editor YuS Eliseev ndash Moscow Vysshaya Shkola 2001 ndash P 44-87)

100

24 Tesker E Tesker S Modern methods of calculation and increasing the load- carrying

capacity of surface-hardened gears of transmissions and drives Theory and Practice of

Gearing and Transmissions In Honor of Professor Faydor L Litvin Editors Veniamin

Goldfarb Natalya Barmina Mechanism and Machine Science Vol 34 Series editor Marco

Ceccarelli Springer ndash 2016 ndash Pp 233-261

25 Тескер ЕИ Современные методы расчета и повышения несущей способности

поверхностно-упрочненных зубчатых передач трансмиссий и приводов Москва

Машиностроение 2011 ndash 433 с (Tesker EI Modern Methods of Design and Increasing

Load-Carrying Capasity of Case-Hardened Gear Drives and Transmissions Moscow

Mashinostroenie 2011 ndash 433 p)

26 Шалобаев ЕВ Проблема гармонизации отечественных стандартов с системой

международных и национальных стандартов Сборник докладов научно-технической

конференции laquoТеория и практика зубчатых передачraquo Ижевск2004 ndash с44-48 (Shalobaev

EV Problems of Harmonization of Native Standards with the System of International and

National Standards Proceedings of the International Conference with International

Participation ldquoTheory and Practice of Gear Drivesrdquo Izhevsk ndash 2004 ndash P44-48)

27 Теория и практика зубчатых передач Сборник трудов Международного

симпозиума (21-23 января 2014 г Россия Ижевск) Ижевск Изд-во ИжГТУ 2013 ndash

580 с (Theory and Practice of Gearing Proceedings of the International Symposium

January 21-23 2014 Russia Izhevsk Publisher IzSTU 2013 ndash 580 p)

28 Theory and Practice of Gearing and Transmissions In Honor of Professor Faydor L

Litvin Editors Veniamin Goldfarb Natalya Barmina Mechanism and Machine Science

Vol 34 Series editor Marco Ceccarelli Springer ndash 2016 ndash 450 p

(wwwspringercomseries8779)

29 Babichev D Lagutin S Barmina N Review of the Russian school in the theory and

geometry of gearing Part 1 Origins of the theory of gearing and its Golden period of 1935-

1975 Proceedings of 2015 IFToMM Workshop on History of Mechanism and Machine

Science May 26-28 2015 St-Petersburg Russia httphmms2015ru

30 Algin VB History and State of Art of Belarussian Scientific School in the Field of

Computation and Designing Mobile Machine Transmission Proceedings of 2015 IFToMM

Workshop on History of Mechanism and Machine Science May 26-28 2015 St-Petersburg

Russia httphmms2015ru

31 Starzhinsky VE Antonyuk VE Kane MM Shilko SV Contribution of Belarussian

Scientists in the Problem of Gearing Terminology Identification Proceedings of 2015

IFToMM Workshop on History of Mechanism and Machine Science May 26-28 2015 St-

Petersburg Russia httphmms2015ru

32 Starzhinsky VE Basiniuk UL Mardasevich AI Lobkova MP Optimization

Computation of Multistage and Multi-Path Instrument Toothed Mechanisms Proceedings of

2015 IFToMM Workshop on History of Mechanism and Machine Science May 26-28

2015 St-Petersburg Russia httphmms2015ru

33 Kane MM Starzhinsky VE Quality Rise of High-Loaded Cylindrical Gear Drives in

98

Зубчатые передачи и трансмиссии1998 - 2 ndash с30-41 (Goldfarb VI Russian Program

ldquoProgressive Gear Boxes ldquo Gearing and Transmissions 1998 ndash No 2 ndash P 30-41)

5 Шалобаев ЕВ Модернизированные редукторы отечественного производства

Фундаментальные и прикладные проблемы техники и технологии 2010 - 6-2 ndash

с105-111 (Shalobaev EV Modernized Gear Boxes of Native Production Fundamental

and Application problems of Engineering and Technologies2010 ndash No 62 ndash P 105-115)

6 Молчанов СМ Парубец ВИ Пшизов ШП О состоянии и задачах

редукторостроения России Материалы Всероссийской конференции

Редукторостроение России Состояние Проблемы Перспективы Под редакцией ЕВ

Шалобаева ndash СПб ЦЦП laquoСветочraquo2003 ndash с27-29 (Molchanov SM Parubets VI

Pshizov ShP About the State and Tasks of Gear Boxes Manufacturing of Russia

Proceeding at All-Russian Conference Gear Boxes Manufacturing of Russia State

Problems and Perspectives Editor EV Shalobaev ndash Saint Petersburg Publishing House

ldquoSvetochrdquo 2003 ndash P 27-29)

7 Пластмассовые зубчатые колеса в механизмах приборов Под ред ВЕ

Старжинского и ЕВ Шалобаева ndash Санкт-Петербург ndash Гомель ИММС НАНБ1998 ndash

528с (Plastic Gears in Instrument Drives Edited by VE Starzhinsky and EV Shalobaev ndash

Saint Petersburg ndash Gomel MPRI NAS of Belarus 1998 ndash 528 p)

8 Старжинский ВЕ Осипенко СА Передачи с зубчатыми колесами из термопластов

Проектирование и технология производства Передачи и трансмиссии 2001 ndash 1 ndash

C 57-70 (Starzhinsky VE Ossipenko SA Drives with Gears from Thermoplastic Design

and Technology Review Gearing and Transmissions ndash 2001 ndash No 1 ndash P 57-70)

9 Шалобаев ЕВ Старжинский ВЕ Шилько СВ и др Обеспечение качественных

показателей зубчатых колес венцы которых выполнены из пластмасс и композитов

Известия Тульского государственного университета 2012 - 12ч1 ndash с142-149

(Shalobaev EV Starzhinsky VE Shilko SV Providing Quality Parameters of Gears with

Polymer Composite Toothed Ring Bulletin of Tula State Technical University ndash 2012 ndash

No 23 ndash P 142-149)

10 Старжинский ВЕ Шалобаев ЕВ Шилько СВ Элементы приводов приборов

Под ред ЮМ Плескачевского Минск Белорусская навука2012 ndash 769с (Starzhinsky

VE Shalobaev EV Shilko SV et al Elements of Instrument Drives Editor YuM

Pleskachevsky ndash Minsk Publishing House ldquoBelaruskaya Navukardquo 2012 ndash 769 p)

11 Технология производства и методы обеспечения качества зубчатых колес и передач

Под ред ВЕ Старжинского и ММ Кане Санкт-Петербург Профессия2007 ndash 832с

(Technology and Methods of Providing Quality of Gears and Gear Drives Edited by VE

Starzhinsky and MM Kane Second Issue corrected and extended ndash Saint Petersburg

Publishing House ldquoProfessijardquo 2007 ndash 832 p)

12 Олексюк В Роль зубчатых передач в мехатронных устройствах Передачи и

трансмиссии2001 - 1 ndash с44-57 (Oleksuk V Role of Gear Drives in Mechatronic

Device Gearing and Transmissions ndash 2001 ndash No 1 ndash P 44-57)

13 Производство зубчатых передач Справочник Под ред БА Тайца М

99

Машиностроение1972 ndash 368с (Production of Gears Reference Book Editor BA Taits

ndash Moscow Mashinostroenie 1972 ndash 368 p)

14 Тайц БА Точность и контроль зубчатых передач Москва Машиностроение 1972 ndash

368с (Taits BA Accuracy and Control of Gears ndash Moscow Mashinostroenie 1972 ndash 368 p)

15 Козлов МП Зубчатые передачи точного приборостроения2-е изд ndash М

Машиностроение 1969 ndash 400с (Kozlov MP Gear Drives of Precision Instrument

Making ndash Moscow Oborongiz 1958 ndash 393 p)

16 Куцоконь ВА Точность кинематических цепей приборов ndash Л-М

Машиностроение1980 ndash 220с (Kutsоkon VA Accuracy of Gear Drives and Kinematic

Chains of Devices ndash Leningrad Mashinostroenie 1980 ndash 220 p)

17 Тимофеев БП Шалобаев ЕВ Состояние и перспективы нормирования зубчатых

колес и передач Вестник машиностроения1990 - 12 ndash с33-39 (Timofeev BP

Shalobaev EV State and Perspectives of Development of Accuracy Normalization of Gears

and Gear Drives Vestnik Mashinostroenia 1990 ndash No 12 ndash P 33-39)

18 Тимофеев БП Точность зубчатых передач и кинематических цепей В кн Механика

машин М Высшая школа 1989 ndash с204-224 (Timofeev BP Accuracy of Gear Drives and

Kinematic Chains Mechanics of Machines ndash Moscow Vysshaya Shkola 1989 ndash P 204-224)

19 Тимофеев БП Шалобаев ЕВ Расчет точности зубчатых передач и

кинематических цепей1998 ndash с296-346 (Timofeev BP Shalobaev EV Calculation of

Gear Drives and Kinematic Chains Plastic Gears and Mechanisms of Devices ndash Saint

PetersburgndashGomel MRPI NAS of Belarus 1998 ndash P 296-346)

20 Шалобаев ЕВ Конструкторско-технологическое обеспечение качества приборных

зубчатых передач В кн Технология производства и методы обеспечения качества

зубчатых колес и передач (Shalobaev EV Design Technology Providing Accuracy of

Instrument Drives Technology and Methods of Providing Quality of Gears and Gear

Drives Edited by VE Starzhinsky and MMKane ndash Saint Petersburg Publishing House

Professiya 2007 ndash P 527-535)

21 Шалобаев ЕВ Методика определения степени точности зубчатых колес в

передаче по нормам кинематической точности с учетом погрешностей изготовления и

монтажа В кн Технология производства и методы обеспечения качества зубчатых

колес и передач ndash с794-801 (Shalobaev EV Technique of definition of Accuracy Grade

of Gears in the Gear Drives in according the Norms of Kinematic Accuracy Taken into

Account Errors of Manufacturing and Assembling of Parts ndash P 794-801)

22 Попов ПК Штриплинг ЛО Предпосылки пересмотра нормативной

документации по расчету точности зубчатых передач Вестник

машиностроения1998 - 6 ndash с59-62 (PK Popov LO Shtripling Background of

Revision of Normative Documents on Calculation of Gear Drive Accuracy Vestnik

Mashinostroenia1998 ndash No 6 ndash P 59-62)

23 Нежурин ИП Точность зубчатых передач В кн Производство зубчатых колес

газотурбинных двигателей под ред ЮС Елисеева М Высшая школа 2001 ndash с44-

87 (Nezhurin IP Accuracy of Gear Drives Tolerances Production of Gear Drives of Gas-

Turbine Engines Editor YuS Eliseev ndash Moscow Vysshaya Shkola 2001 ndash P 44-87)

100

24 Tesker E Tesker S Modern methods of calculation and increasing the load- carrying

capacity of surface-hardened gears of transmissions and drives Theory and Practice of

Gearing and Transmissions In Honor of Professor Faydor L Litvin Editors Veniamin

Goldfarb Natalya Barmina Mechanism and Machine Science Vol 34 Series editor Marco

Ceccarelli Springer ndash 2016 ndash Pp 233-261

25 Тескер ЕИ Современные методы расчета и повышения несущей способности

поверхностно-упрочненных зубчатых передач трансмиссий и приводов Москва

Машиностроение 2011 ndash 433 с (Tesker EI Modern Methods of Design and Increasing

Load-Carrying Capasity of Case-Hardened Gear Drives and Transmissions Moscow

Mashinostroenie 2011 ndash 433 p)

26 Шалобаев ЕВ Проблема гармонизации отечественных стандартов с системой

международных и национальных стандартов Сборник докладов научно-технической

конференции laquoТеория и практика зубчатых передачraquo Ижевск2004 ndash с44-48 (Shalobaev

EV Problems of Harmonization of Native Standards with the System of International and

National Standards Proceedings of the International Conference with International

Participation ldquoTheory and Practice of Gear Drivesrdquo Izhevsk ndash 2004 ndash P44-48)

27 Теория и практика зубчатых передач Сборник трудов Международного

симпозиума (21-23 января 2014 г Россия Ижевск) Ижевск Изд-во ИжГТУ 2013 ndash

580 с (Theory and Practice of Gearing Proceedings of the International Symposium

January 21-23 2014 Russia Izhevsk Publisher IzSTU 2013 ndash 580 p)

28 Theory and Practice of Gearing and Transmissions In Honor of Professor Faydor L

Litvin Editors Veniamin Goldfarb Natalya Barmina Mechanism and Machine Science

Vol 34 Series editor Marco Ceccarelli Springer ndash 2016 ndash 450 p

(wwwspringercomseries8779)

29 Babichev D Lagutin S Barmina N Review of the Russian school in the theory and

geometry of gearing Part 1 Origins of the theory of gearing and its Golden period of 1935-

1975 Proceedings of 2015 IFToMM Workshop on History of Mechanism and Machine

Science May 26-28 2015 St-Petersburg Russia httphmms2015ru

30 Algin VB History and State of Art of Belarussian Scientific School in the Field of

Computation and Designing Mobile Machine Transmission Proceedings of 2015 IFToMM

Workshop on History of Mechanism and Machine Science May 26-28 2015 St-Petersburg

Russia httphmms2015ru

31 Starzhinsky VE Antonyuk VE Kane MM Shilko SV Contribution of Belarussian

Scientists in the Problem of Gearing Terminology Identification Proceedings of 2015

IFToMM Workshop on History of Mechanism and Machine Science May 26-28 2015 St-

Petersburg Russia httphmms2015ru

32 Starzhinsky VE Basiniuk UL Mardasevich AI Lobkova MP Optimization

Computation of Multistage and Multi-Path Instrument Toothed Mechanisms Proceedings of

2015 IFToMM Workshop on History of Mechanism and Machine Science May 26-28

2015 St-Petersburg Russia httphmms2015ru

33 Kane MM Starzhinsky VE Quality Rise of High-Loaded Cylindrical Gear Drives in

99

Машиностроение1972 ndash 368с (Production of Gears Reference Book Editor BA Taits

ndash Moscow Mashinostroenie 1972 ndash 368 p)

14 Тайц БА Точность и контроль зубчатых передач Москва Машиностроение 1972 ndash

368с (Taits BA Accuracy and Control of Gears ndash Moscow Mashinostroenie 1972 ndash 368 p)

15 Козлов МП Зубчатые передачи точного приборостроения2-е изд ndash М

Машиностроение 1969 ndash 400с (Kozlov MP Gear Drives of Precision Instrument

Making ndash Moscow Oborongiz 1958 ndash 393 p)

16 Куцоконь ВА Точность кинематических цепей приборов ndash Л-М

Машиностроение1980 ndash 220с (Kutsоkon VA Accuracy of Gear Drives and Kinematic

Chains of Devices ndash Leningrad Mashinostroenie 1980 ndash 220 p)

17 Тимофеев БП Шалобаев ЕВ Состояние и перспективы нормирования зубчатых

колес и передач Вестник машиностроения1990 - 12 ndash с33-39 (Timofeev BP

Shalobaev EV State and Perspectives of Development of Accuracy Normalization of Gears

and Gear Drives Vestnik Mashinostroenia 1990 ndash No 12 ndash P 33-39)

18 Тимофеев БП Точность зубчатых передач и кинематических цепей В кн Механика

машин М Высшая школа 1989 ndash с204-224 (Timofeev BP Accuracy of Gear Drives and

Kinematic Chains Mechanics of Machines ndash Moscow Vysshaya Shkola 1989 ndash P 204-224)

19 Тимофеев БП Шалобаев ЕВ Расчет точности зубчатых передач и

кинематических цепей1998 ndash с296-346 (Timofeev BP Shalobaev EV Calculation of

Gear Drives and Kinematic Chains Plastic Gears and Mechanisms of Devices ndash Saint

PetersburgndashGomel MRPI NAS of Belarus 1998 ndash P 296-346)

20 Шалобаев ЕВ Конструкторско-технологическое обеспечение качества приборных

зубчатых передач В кн Технология производства и методы обеспечения качества

зубчатых колес и передач (Shalobaev EV Design Technology Providing Accuracy of

Instrument Drives Technology and Methods of Providing Quality of Gears and Gear

Drives Edited by VE Starzhinsky and MMKane ndash Saint Petersburg Publishing House

Professiya 2007 ndash P 527-535)

21 Шалобаев ЕВ Методика определения степени точности зубчатых колес в

передаче по нормам кинематической точности с учетом погрешностей изготовления и

монтажа В кн Технология производства и методы обеспечения качества зубчатых

колес и передач ndash с794-801 (Shalobaev EV Technique of definition of Accuracy Grade

of Gears in the Gear Drives in according the Norms of Kinematic Accuracy Taken into

Account Errors of Manufacturing and Assembling of Parts ndash P 794-801)

22 Попов ПК Штриплинг ЛО Предпосылки пересмотра нормативной

документации по расчету точности зубчатых передач Вестник

машиностроения1998 - 6 ndash с59-62 (PK Popov LO Shtripling Background of

Revision of Normative Documents on Calculation of Gear Drive Accuracy Vestnik

Mashinostroenia1998 ndash No 6 ndash P 59-62)

23 Нежурин ИП Точность зубчатых передач В кн Производство зубчатых колес

газотурбинных двигателей под ред ЮС Елисеева М Высшая школа 2001 ndash с44-

87 (Nezhurin IP Accuracy of Gear Drives Tolerances Production of Gear Drives of Gas-

Turbine Engines Editor YuS Eliseev ndash Moscow Vysshaya Shkola 2001 ndash P 44-87)

100

24 Tesker E Tesker S Modern methods of calculation and increasing the load- carrying

capacity of surface-hardened gears of transmissions and drives Theory and Practice of

Gearing and Transmissions In Honor of Professor Faydor L Litvin Editors Veniamin

Goldfarb Natalya Barmina Mechanism and Machine Science Vol 34 Series editor Marco

Ceccarelli Springer ndash 2016 ndash Pp 233-261

25 Тескер ЕИ Современные методы расчета и повышения несущей способности

поверхностно-упрочненных зубчатых передач трансмиссий и приводов Москва

Машиностроение 2011 ndash 433 с (Tesker EI Modern Methods of Design and Increasing

Load-Carrying Capasity of Case-Hardened Gear Drives and Transmissions Moscow

Mashinostroenie 2011 ndash 433 p)

26 Шалобаев ЕВ Проблема гармонизации отечественных стандартов с системой

международных и национальных стандартов Сборник докладов научно-технической

конференции laquoТеория и практика зубчатых передачraquo Ижевск2004 ndash с44-48 (Shalobaev

EV Problems of Harmonization of Native Standards with the System of International and

National Standards Proceedings of the International Conference with International

Participation ldquoTheory and Practice of Gear Drivesrdquo Izhevsk ndash 2004 ndash P44-48)

27 Теория и практика зубчатых передач Сборник трудов Международного

симпозиума (21-23 января 2014 г Россия Ижевск) Ижевск Изд-во ИжГТУ 2013 ndash

580 с (Theory and Practice of Gearing Proceedings of the International Symposium

January 21-23 2014 Russia Izhevsk Publisher IzSTU 2013 ndash 580 p)

28 Theory and Practice of Gearing and Transmissions In Honor of Professor Faydor L

Litvin Editors Veniamin Goldfarb Natalya Barmina Mechanism and Machine Science

Vol 34 Series editor Marco Ceccarelli Springer ndash 2016 ndash 450 p

(wwwspringercomseries8779)

29 Babichev D Lagutin S Barmina N Review of the Russian school in the theory and

geometry of gearing Part 1 Origins of the theory of gearing and its Golden period of 1935-

1975 Proceedings of 2015 IFToMM Workshop on History of Mechanism and Machine

Science May 26-28 2015 St-Petersburg Russia httphmms2015ru

30 Algin VB History and State of Art of Belarussian Scientific School in the Field of

Computation and Designing Mobile Machine Transmission Proceedings of 2015 IFToMM

Workshop on History of Mechanism and Machine Science May 26-28 2015 St-Petersburg

Russia httphmms2015ru

31 Starzhinsky VE Antonyuk VE Kane MM Shilko SV Contribution of Belarussian

Scientists in the Problem of Gearing Terminology Identification Proceedings of 2015

IFToMM Workshop on History of Mechanism and Machine Science May 26-28 2015 St-

Petersburg Russia httphmms2015ru

32 Starzhinsky VE Basiniuk UL Mardasevich AI Lobkova MP Optimization

Computation of Multistage and Multi-Path Instrument Toothed Mechanisms Proceedings of

2015 IFToMM Workshop on History of Mechanism and Machine Science May 26-28

2015 St-Petersburg Russia httphmms2015ru

33 Kane MM Starzhinsky VE Quality Rise of High-Loaded Cylindrical Gear Drives in

100

24 Tesker E Tesker S Modern methods of calculation and increasing the load- carrying

capacity of surface-hardened gears of transmissions and drives Theory and Practice of

Gearing and Transmissions In Honor of Professor Faydor L Litvin Editors Veniamin

Goldfarb Natalya Barmina Mechanism and Machine Science Vol 34 Series editor Marco

Ceccarelli Springer ndash 2016 ndash Pp 233-261

25 Тескер ЕИ Современные методы расчета и повышения несущей способности

поверхностно-упрочненных зубчатых передач трансмиссий и приводов Москва

Машиностроение 2011 ndash 433 с (Tesker EI Modern Methods of Design and Increasing

Load-Carrying Capasity of Case-Hardened Gear Drives and Transmissions Moscow

Mashinostroenie 2011 ndash 433 p)

26 Шалобаев ЕВ Проблема гармонизации отечественных стандартов с системой

международных и национальных стандартов Сборник докладов научно-технической

конференции laquoТеория и практика зубчатых передачraquo Ижевск2004 ndash с44-48 (Shalobaev

EV Problems of Harmonization of Native Standards with the System of International and

National Standards Proceedings of the International Conference with International

Participation ldquoTheory and Practice of Gear Drivesrdquo Izhevsk ndash 2004 ndash P44-48)

27 Теория и практика зубчатых передач Сборник трудов Международного

симпозиума (21-23 января 2014 г Россия Ижевск) Ижевск Изд-во ИжГТУ 2013 ndash

580 с (Theory and Practice of Gearing Proceedings of the International Symposium

January 21-23 2014 Russia Izhevsk Publisher IzSTU 2013 ndash 580 p)

28 Theory and Practice of Gearing and Transmissions In Honor of Professor Faydor L

Litvin Editors Veniamin Goldfarb Natalya Barmina Mechanism and Machine Science

Vol 34 Series editor Marco Ceccarelli Springer ndash 2016 ndash 450 p

(wwwspringercomseries8779)

29 Babichev D Lagutin S Barmina N Review of the Russian school in the theory and

geometry of gearing Part 1 Origins of the theory of gearing and its Golden period of 1935-

1975 Proceedings of 2015 IFToMM Workshop on History of Mechanism and Machine

Science May 26-28 2015 St-Petersburg Russia httphmms2015ru

30 Algin VB History and State of Art of Belarussian Scientific School in the Field of

Computation and Designing Mobile Machine Transmission Proceedings of 2015 IFToMM

Workshop on History of Mechanism and Machine Science May 26-28 2015 St-Petersburg

Russia httphmms2015ru

31 Starzhinsky VE Antonyuk VE Kane MM Shilko SV Contribution of Belarussian

Scientists in the Problem of Gearing Terminology Identification Proceedings of 2015

IFToMM Workshop on History of Mechanism and Machine Science May 26-28 2015 St-

Petersburg Russia httphmms2015ru

32 Starzhinsky VE Basiniuk UL Mardasevich AI Lobkova MP Optimization

Computation of Multistage and Multi-Path Instrument Toothed Mechanisms Proceedings of

2015 IFToMM Workshop on History of Mechanism and Machine Science May 26-28

2015 St-Petersburg Russia httphmms2015ru

33 Kane MM Starzhinsky VE Quality Rise of High-Loaded Cylindrical Gear Drives in

101

Design and Manufacture Proceedings of 2015 IFToMM Workshop on History of

Mechanism and Machine Science May 26-28 2015 St-Petersburg Russia

httphmms2015ru

34 Supin VV Starzhinsky VE Antonyuk VE Design automation of Gear Drive and Gear

Forming Tool Proceedings of 2015 IFToMM Workshop on History of Mechanism and

Machine Science May 26-28 2015 St-Petersburg Russia httphmms2015ru

35 Antonyuk VE Goman AM Ishin NN Starzhinsky VE Supin VV Methods of Increasing

Gear Drive Serviceability Proceedings of 2015 IFToMM Workshop on History of Mechanism

and Machine Science May 26-28 2015 St-Petersburg Russia httphmms2015ru

36 Antonyuk VE Starzhinsky VE Kane MM Sosnovskiy LA Komissarov VV Actual

Problems of Standardization in the Field of Gear Drives Proceedings of 2015 IFToMM

Workshop on History of Mechanism and Machine Science May 26-28 2015 St-Petersburg

Russia httphmms2015ru

37 Shilrsquoko SV Starzhinsky VE Basinyuk VL Chernous DA Mesomechanical

modeling of muscle type actuator elements for controlled electric drive Proceedings of

2015 IFToMM Workshop on History of Mechanism and Machine Science May 26-28

2015 St-Petersburg Russia httphmms2015ru

38 Ishin NN Goman AM Skorokhodov AS Vibrating monitoring technical condition of

the transmission systems of mobile machines Proceedings of 2015 IFToMM Workshop on

History of Mechanism and Machine Science May 26-28 2015 St-Petersburg Russia

httphmms2015ru

39 Babichev D Lagutin S Barmina N Russian school of the theory and geometry of

gearing Its origin and golden period (1935--1975) [J] Frontiers of Mechanical Engineering

Guest Editor Marco Ceccarelli 2016 Vol 11 No1 ndash Pp 44-59

httplinkspringercomarticle101007s11465-015-0360-z

httpjournalhepcomcnfmeEN101007s11465-015-0360-z

40 Kapelevich AA Direct Gear Design CRC Press 2013 ndash 300 p

(httpwwwtaylorandfranciscom httpwwwcrcpresscom)

41 Arnaudov KB Golovanov VV Dorofeev VL Dorofeev DV Selection of optimal

geometry and stress calculation on wheel teeth with asymmetrical tooth profile International

Conference on Gears Europe invites the world (October 7-9 2013) Garching near Munich

Germany Technical University of Munich VDI ndash Berichte 21992 2013 ndash Pp1341-1353

42 Дорофеев ВЛ Дорофеев ДВ Голованов ВВ Гукасян СГ Метод полного

прямого синтеза авиационных зубчатых передач Научно-технический конгресс по

двигателестроению (НТКД-2014) Сборник тезисов (15-17 апреля 2014 г Москва

Россия) Москва Изд-во АССАД 2014 С104-108 (Dorofeev VL Dorofeev DV

Golovanov VV [et al] Method of the Full Direct Synthesis of Aircraft Gear Drives

Proceedings of Scientific and Technical Congress on Engine-Building NTKD-2014 (april

15-17 2014 Moscow Russia) Moscow Publisher ASSAD 2014 ndash Pp 108-110)

43 Novikov A Golovanov V Dorofeev V Terminology and Disign of Asymmetrical Gears

102

for Aircraft Theory and Practice of Gearing and Transmissions In Honor of Professor

Faydor L Litvin Editors V Goldfarb N Barmina Spriger 2016 ndash Pp 381-392

44 Цуканов ОН Основы синтеза неэвольвентных зубчатых зацеплений в

обобщающих параметрах Челябинск Издательский центр ЮУрГУ 2011 ndash 140 с

(Tsukanov ON Basics of Noninvolute Gearing Synthesis in Generalized Parameters

Chelyabinsk Publishing Center of South Ural State University 2011 ndash 140 p)

45 Гольдфарб ВИ Главатских ДВ Трубачев ЕС и др Спироидные редукторы

трубопроводной арматуры Под ред ВИ Гольдфарба Москва Вече 2011 ndash 222 с

(Goldfarb VI Glavatskich DV Trubachyov ES [et al] Spiroid Gearboxes for Pipeline

Valves Edited by VI Goldfarb Moskow Publisher ldquoVecherdquo 2011 ndash 222 p)

46 Сандлер АИ Лагутин СА Гудов ЕА Теория и практика производства

червячных передач общего вида Издательство laquoИнфо-Инженерияraquo 2016 ndash 346 c

(Sandler AI Lagutin SA Gudov EA Theory and Practice of Manufacturing Worm Gear

Drives of General Arrangement Publisher Infa-Engineering 2016 ndash 346 p)

47 Громыко ПН Макаревич ДМ Доконов ЛГ и др Прецессионные редуцирующие

механизмы различного назначения Могилев Белорусско-Российский университет

2013 ndash 273 с (Gromyko PN Makaryevich DM Dokonov LG [et al] Precessional

Reducing Mechanisms of Different Dedication Mogilev Publisher ldquoByelorussko-Rossiiskii

Universityrdquo 2013 ndash 273 p)

48 Громыко ПН Лустенков МЕ Хатетовский СН и др Технологические аспекты

создания рабочих поверхностей передач новых типов Могилев ГУВПО laquoБелорусско-

Российский университет 2012 ndash 209 с (Gromyko PN Lustenkov ME Khatetovsky

SN [et al] Technological Aspects of Generating Tooth Flanks for Drives of the New Types

Mogilev Publisher ldquoByelorussko-Rossiiskii Universityrdquo 2012 ndash 209 p)

49 Ишин НН Динамика и вибромониторинг зубчатых передач Минск Беларуская

навука 2013 ndash 432 с (Ishin NN Dynamics and Vibration Monitoring of Gear Drives

Minsk Publisher ldquoBelaruskaya Navukardquo 2013 ndash 432 p)

50 ГОСТ 13755-2015 Передачи зубчатые цилиндрические эвольвентные Исходные

контуры (ISO 531998 Cylindrical gears for general and heavy engineering ndash Standard

basic rack tooth profile MOD)

103

25th Working Meeting

of IFToMM Permanent Commission

for Standardization of Terminology on MMS

Saint-Petersburg Russia June 23 ndash 29 2014

IFToMM Permanent Commission (A)

for Standardization of Terminology on MMS

(2012-2014)

Chairmen Prof Torsten Brix (Germany)

Members

Prof Dr Păun Antonescu (Romania)

Dr Ovidiu Antonescu (Romania)

Prof Dr Istvaacuten Biacuteroacute (Hungary)

Prof Dr Burkhard Corves (Germany)

Dr Ulf Doumlring (observer) (Germany)

Prof Raffaele Di Gregorio (Italy)

Prof Dr Antoni Gronowicz (Poland)

Prof Dr Mikio Horie (Japan)

Dr Eng Theodor G Ionescu (Romania)

Prof Dr Mark M Kane (Belarus)

Prof Dr Antonius J Klein Breteler (The Netherlands)

Prof Dr Zhaohui Lan (China)

Prof Tatu Leinonen (Finland)

Dr-Ing Nenad T Pavlovic (Serbia)

Gordon R Pennock (USA)

Prof Dr Didier Remond (France)

Prof Dr Yuri L Sarkissyan (Armenia)

Prof Dr Stefan Segla (Czech Republic)

Prof Eugeni Shalobaev (Russia)

Prof Dr Victor E Starzhinsky (Belarus)

Prof Dr Rymantas T Tolocka (Lithuania)

Prof Dr-Ing Shyi-Jeng Tsai (China)

Prof Dr Hab Eng Jozef Wojnarowski (Poland)

Prof Dr Yue-Qing Yu (China)

104

Members who attended the meeting

Prof Dr Istvaacuten Biacuteroacute (Hungary)

Prof Eugeni Shalobaev (Russia)

Prof Dr Victor E Starzhinsky (Belarus)

Invited guests who attended the meeting

Dr Serge V Shilko (MPRI NASB Belarus)

Dr Yevsej I Gutman (MTS System Corporation Minneapolis USA)

Dr RR Magdiev (ITMO University Russia)

Dr NN Dmitriev (Saint-Petersburg State University Russia)

Dr II Komarov (ITMO University Russia)

Dipl Eng OD Kozyreva (ITMO University Russia)

Dipl Eng RA Yurieva (ITMO University Russia)

DG Surikov (ITMO University Russia)

105

25th Working Meeting

of IFToMM Permanent Commission

for Standardization of Terminology on MMS

Saint-Petersburg Russia June 23 ndash 29 2014

П О В Е С Т К А Д Н Я З А С Е Д А Н И Я

A G E N D A

1 Открытие заседания (23 июня 0900) и согласование повестки дня

Opening of the meeting (June 23 0900 am) and agreement of the agenda

2 Уведомление об участии и принесение извинений за неучастие

Apologize for absence and acknowledgements

3 Проблемы членства

Membership issues

4 Протокол 24го рабочего заседания (24-30 июня 2012 ТУ Ильменау германия) Обсуждение и

утверждение

Minutes of the 24th Working Meeting (June 24-30 2012 TU Ilmenau Germany) Discussion and approval

5 Доклады председателей комиссии

Годовой доклад ndash июль 2012 ndash июнь 2013

Годовой доклад ndash июль 2013 ndash июнь 2014

Reports of the chairmenrsquos

Annual report July 2012 ndash June 2013

Annual report July 2013 ndash June 2014

6 Доклады подкомиссий

Reports of the subcommissions

7 Терминология IFToMM Обсуждение глав 15 и 16

IFToMM terminology Discussion of Chapters 15 and 16

8 Информация о контактах с Постоянными комиссиями и техническими комитетами IFToMM

другими родственными организациями

Information about the contacts with IFToMM PCs TCs and with other affiliates

9 Другие вопросы (при необходимости)

Other issues and problems (as needed)

10 Научный семинар по терминологии

Symposium on terminology scientific papers and lecture

11 Закрытие заседания

Closure of the meeting

106

Dr S Shilrsquokorsquos Presentation

103

25th Working Meeting

of IFToMM Permanent Commission

for Standardization of Terminology on MMS

Saint-Petersburg Russia June 23 ndash 29 2014

IFToMM Permanent Commission (A)

for Standardization of Terminology on MMS

(2012-2014)

Chairmen Prof Torsten Brix (Germany)

Members

Prof Dr Păun Antonescu (Romania)

Dr Ovidiu Antonescu (Romania)

Prof Dr Istvaacuten Biacuteroacute (Hungary)

Prof Dr Burkhard Corves (Germany)

Dr Ulf Doumlring (observer) (Germany)

Prof Raffaele Di Gregorio (Italy)

Prof Dr Antoni Gronowicz (Poland)

Prof Dr Mikio Horie (Japan)

Dr Eng Theodor G Ionescu (Romania)

Prof Dr Mark M Kane (Belarus)

Prof Dr Antonius J Klein Breteler (The Netherlands)

Prof Dr Zhaohui Lan (China)

Prof Tatu Leinonen (Finland)

Dr-Ing Nenad T Pavlovic (Serbia)

Gordon R Pennock (USA)

Prof Dr Didier Remond (France)

Prof Dr Yuri L Sarkissyan (Armenia)

Prof Dr Stefan Segla (Czech Republic)

Prof Eugeni Shalobaev (Russia)

Prof Dr Victor E Starzhinsky (Belarus)

Prof Dr Rymantas T Tolocka (Lithuania)

Prof Dr-Ing Shyi-Jeng Tsai (China)

Prof Dr Hab Eng Jozef Wojnarowski (Poland)

Prof Dr Yue-Qing Yu (China)

104

Members who attended the meeting

Prof Dr Istvaacuten Biacuteroacute (Hungary)

Prof Eugeni Shalobaev (Russia)

Prof Dr Victor E Starzhinsky (Belarus)

Invited guests who attended the meeting

Dr Serge V Shilko (MPRI NASB Belarus)

Dr Yevsej I Gutman (MTS System Corporation Minneapolis USA)

Dr RR Magdiev (ITMO University Russia)

Dr NN Dmitriev (Saint-Petersburg State University Russia)

Dr II Komarov (ITMO University Russia)

Dipl Eng OD Kozyreva (ITMO University Russia)

Dipl Eng RA Yurieva (ITMO University Russia)

DG Surikov (ITMO University Russia)

105

25th Working Meeting

of IFToMM Permanent Commission

for Standardization of Terminology on MMS

Saint-Petersburg Russia June 23 ndash 29 2014

П О В Е С Т К А Д Н Я З А С Е Д А Н И Я

A G E N D A

1 Открытие заседания (23 июня 0900) и согласование повестки дня

Opening of the meeting (June 23 0900 am) and agreement of the agenda

2 Уведомление об участии и принесение извинений за неучастие

Apologize for absence and acknowledgements

3 Проблемы членства

Membership issues

4 Протокол 24го рабочего заседания (24-30 июня 2012 ТУ Ильменау германия) Обсуждение и

утверждение

Minutes of the 24th Working Meeting (June 24-30 2012 TU Ilmenau Germany) Discussion and approval

5 Доклады председателей комиссии

Годовой доклад ndash июль 2012 ndash июнь 2013

Годовой доклад ndash июль 2013 ndash июнь 2014

Reports of the chairmenrsquos

Annual report July 2012 ndash June 2013

Annual report July 2013 ndash June 2014

6 Доклады подкомиссий

Reports of the subcommissions

7 Терминология IFToMM Обсуждение глав 15 и 16

IFToMM terminology Discussion of Chapters 15 and 16

8 Информация о контактах с Постоянными комиссиями и техническими комитетами IFToMM

другими родственными организациями

Information about the contacts with IFToMM PCs TCs and with other affiliates

9 Другие вопросы (при необходимости)

Other issues and problems (as needed)

10 Научный семинар по терминологии

Symposium on terminology scientific papers and lecture

11 Закрытие заседания

Closure of the meeting

106

Dr S Shilrsquokorsquos Presentation

104

Members who attended the meeting

Prof Dr Istvaacuten Biacuteroacute (Hungary)

Prof Eugeni Shalobaev (Russia)

Prof Dr Victor E Starzhinsky (Belarus)

Invited guests who attended the meeting

Dr Serge V Shilko (MPRI NASB Belarus)

Dr Yevsej I Gutman (MTS System Corporation Minneapolis USA)

Dr RR Magdiev (ITMO University Russia)

Dr NN Dmitriev (Saint-Petersburg State University Russia)

Dr II Komarov (ITMO University Russia)

Dipl Eng OD Kozyreva (ITMO University Russia)

Dipl Eng RA Yurieva (ITMO University Russia)

DG Surikov (ITMO University Russia)

105

25th Working Meeting

of IFToMM Permanent Commission

for Standardization of Terminology on MMS

Saint-Petersburg Russia June 23 ndash 29 2014

П О В Е С Т К А Д Н Я З А С Е Д А Н И Я

A G E N D A

1 Открытие заседания (23 июня 0900) и согласование повестки дня

Opening of the meeting (June 23 0900 am) and agreement of the agenda

2 Уведомление об участии и принесение извинений за неучастие

Apologize for absence and acknowledgements

3 Проблемы членства

Membership issues

4 Протокол 24го рабочего заседания (24-30 июня 2012 ТУ Ильменау германия) Обсуждение и

утверждение

Minutes of the 24th Working Meeting (June 24-30 2012 TU Ilmenau Germany) Discussion and approval

5 Доклады председателей комиссии

Годовой доклад ndash июль 2012 ndash июнь 2013

Годовой доклад ndash июль 2013 ndash июнь 2014

Reports of the chairmenrsquos

Annual report July 2012 ndash June 2013

Annual report July 2013 ndash June 2014

6 Доклады подкомиссий

Reports of the subcommissions

7 Терминология IFToMM Обсуждение глав 15 и 16

IFToMM terminology Discussion of Chapters 15 and 16

8 Информация о контактах с Постоянными комиссиями и техническими комитетами IFToMM

другими родственными организациями

Information about the contacts with IFToMM PCs TCs and with other affiliates

9 Другие вопросы (при необходимости)

Other issues and problems (as needed)

10 Научный семинар по терминологии

Symposium on terminology scientific papers and lecture

11 Закрытие заседания

Closure of the meeting

106

Dr S Shilrsquokorsquos Presentation

105

25th Working Meeting

of IFToMM Permanent Commission

for Standardization of Terminology on MMS

Saint-Petersburg Russia June 23 ndash 29 2014

П О В Е С Т К А Д Н Я З А С Е Д А Н И Я

A G E N D A

1 Открытие заседания (23 июня 0900) и согласование повестки дня

Opening of the meeting (June 23 0900 am) and agreement of the agenda

2 Уведомление об участии и принесение извинений за неучастие

Apologize for absence and acknowledgements

3 Проблемы членства

Membership issues

4 Протокол 24го рабочего заседания (24-30 июня 2012 ТУ Ильменау германия) Обсуждение и

утверждение

Minutes of the 24th Working Meeting (June 24-30 2012 TU Ilmenau Germany) Discussion and approval

5 Доклады председателей комиссии

Годовой доклад ndash июль 2012 ndash июнь 2013

Годовой доклад ndash июль 2013 ndash июнь 2014

Reports of the chairmenrsquos

Annual report July 2012 ndash June 2013

Annual report July 2013 ndash June 2014

6 Доклады подкомиссий

Reports of the subcommissions

7 Терминология IFToMM Обсуждение глав 15 и 16

IFToMM terminology Discussion of Chapters 15 and 16

8 Информация о контактах с Постоянными комиссиями и техническими комитетами IFToMM

другими родственными организациями

Information about the contacts with IFToMM PCs TCs and with other affiliates

9 Другие вопросы (при необходимости)

Other issues and problems (as needed)

10 Научный семинар по терминологии

Symposium on terminology scientific papers and lecture

11 Закрытие заседания

Closure of the meeting

106

Dr S Shilrsquokorsquos Presentation

106

Dr S Shilrsquokorsquos Presentation