Doctoral Thesis in Machine Design A Comparative ...

Doctoral Thesis in Machine Design

A Comparative Investigation of Gear Performance Between Wrought and Sintered Powder Metallurgical SteelUtilizing In-situ Surface Pro le Measurements toInvestigate the Initiation and Evolution of Micropitting and Pitting Damage

EDWIN BERGSTEDT

Stockholm Sweden 2021wwwkthse

ISBN 978-91-7873-821-2TRITA-ITM-AVL 202113

KTH ROYAL INSTITUTE OF TECHNOLOGY

EDWIN BERGSTEDT

A Comparative Investigation of G

ear Performance Betw

een Wrought and Sintered Pow

der Metallurgical Steel

KTH

2021

A Comparative Investigation of Gear Performance Between Wrought and Sintered Powder Metallurgical SteelUtilizing In-situ Surface Profile Measurements to Investigate the Initiation and Evolution of Micropitting and Pitting Damage

EDWIN BERGSTEDT

Doctoral Thesis in Machine DesignKTH Royal Institute of TechnologyStockholm Sweden 2021

Academic Dissertation which with due permission of the KTH Royal Institute of Technology is submitted for public defence for the Degree of Doctor of Engineering on Friday June 4th online via Zoom 2021 at 1000 AM

copy Edwin Bergstedt ISBN 978-91-7873-821-2TRITA-ITM-AVL 202113 Printed by Universitetsservice US-AB Sweden 2021

Abstract

Vehicle electrification is a strong trend that introduces new challenges such asincreased input speed of the transmission and increased power density Alsothe noise emittance of the gearbox is of increasing importance as the sound ofthe gearbox is no longer masked by the internal combustion engine Pressedand sintered powder metallurgical steel could be an interesting alternative towrought steel the internal porosity has a dampening effect on the noise andgears can be made in a fast and efficient process However current manufactur-ing of powder metallurgical steel has significant performance limitations TheNanotechnology Enhanced Sintered Steel Processing project aims to reduce thegap in performance between conventional steel and powder metallurgical steelOne of the potential benefits is that with the inclusion of nano-powder thedensity can be increased To validate the new material its performance needsto be compared to the performance of current generation powder metallurgicalmaterials and also to wrought steel It is therefor crucial to be able to test andevaluate different materials and gears This thesis has developed methods fortesting comparing and evaluating the performance of gears Powder metal-lurgical steel has been tested and compared to wrought steel the efficiency aswell as pitting life have been investigated in an FZG test rig Also the effectsof different surface finishing operations have been evaluated The gear flankswere measured in-situ in the gearbox using a stylus instrument an optimisationroutine was created to fit the measurements to the theoretical involute profileThis enabled an in-depth analysis of surface wear and presented an opportunityto investigate micropitting initiation It was found that the damage mecha-nisms of wrought steel and powder metallurgical steel are similar and relatedto the surface finishing method However the powder metallurgical steel wasalso susceptible to sub-surface cracks Superfinished gears can be negativelyinfluenced by the lack of tip relief as cracks initiate in the surface layer of theroot rapidly destroying the tooth

KeywordsGear testing Micropitting Pitting Efficiency Surface transformation

SammanfattningDen pagaende elektrifieringen staller nya krav pa transmissioner och kugghjulFor att minska forluster bor elmotorn anvandas vid hoga varvtal dessutomar ljudnivan allt mer viktig da forbranningsmotorns ljud inte langre doljer detvinande ljudet fran transmissionen Pressade och sintrade komponenter avpulvermetall ar ett intressant alternativ till konventionellt stal da processen arsnabb och effektiv dessutom dampar porerna inne i materialet ljud da ljudvagorinte kan propagera lika fritt genom gas som genom solidt stal Dagens pulver-metallurgiskamaterial har dock vissa begransningar sa som lagre styrka SSFprojektet Nanotechnology Enhanced Sintered Steel Processing jobbar mot attforbattra dagens pulvermetall material Genom att blanda in nano-partiklar sakan densiteten okas och darmed forbattras materialets egenskaper

For att kunna utvardera nya kugghjul och materialkombinationer sa behoverprestandan kartlaggas for dagens material Det ar darmed viktigt att hitta enmetod for att kunna testa och gora relevanta jamforelser

Denna avhandling presenterar metoder for att testa samt utvardera pre-standan for olika material och darmed generera underlag for att kunna jamforade olika materialen Genom att genomfora effektivitets samt pittingprov i enFZG testrig har prestandan for dagens pulvermetallmaterial kunnat jamforasmot konventionellt stal utover materialskillnader har ett antal olika slutbear-betningsmetorder har ocksa utvarderats Kuggflankerna har matts pa plats ivaxelladan fortlopande under testningen med ett slapnalsinstrument en metodfor att optimera positionen av de matta profilerna mot den teoretiska kuggpro-filen har ocksa utvecklats Genom denna metod ar det mojligt att direkt jamforaolika matningar for att se hur slitage paverkar profilen Darmed kan man stud-era hur mikropitting initieras och aven forsta hur skademekanismerna paverkasav material och slutbearbetningsmetod Vid samma slutbearbetningsmetod sauppvisade pulvermetallmaterialen liknande ytinitierade skademekanismer somkonventionellt stal En skillnad ar att pulvermetallmaterialet aven uppvisadeskador som initierats inuti materialet Kugghjul med superfinerad yta uppvisadetidigt omfattande skador i pittingtesten Detta ar kopplat till avsaknaden avtoppavlattning (en parameter som modifierar kuggprofilens utseende) pa kugg-profilen kraftiga slag ger sprickbildning i roten och nar tillracklig mangd sprickoransamlats sa borjar kuggflanken flagna darefter propagerar skadan snabbt mottoppen av tanden

NyckelordKugghjulstestning Micropitting Pitting Effektivitetsmatning Yttransformationer

PrefaceThe work conducted that is the foundation to this thesis was carried out at KTHRoyal Institute of Technology in Stockholm at the Department of MachineDesign between January 2017 and December of 2020

I am grateful for the opportunity given to me to pursue a doctoracutes de-gree without the funding from Swedish Foundation for Strategic Research thisproject would not have been possible I would also like to thank the personsthat have supported and guided me through out the endeavour leading to mydisputation especially my main supervisor Ulf Olofsson and my co-supervisorsPer Lindholm Ellen Bergseth and Asa Kassman Rudolphi I am also gratefulfor the support from Hoganas AB and Michael Andersson

I would like to give special appreciation to my co-author Jiachun Lin ofBeijing University of Technology during your time as a guest researcher inSweden we had a really good collaboration And I am glad that we couldmaintain our collaboration even though you went home to China

There are also persons working at the Department of Machine Design thatare deeply appreciated Peter Carlsson and Thomas Ostberg was always therefor me to make my life easier

Many thanks are also directed to Minghui Tu and Yezhe Lyu and my otherco-workers at Machine Design you made the experience really memorable andfun

Finally I would like to thank my family and friends With a special thankyou to my beloved wife Linn Bergstedt for her love and support Before startingto work towards a PhD we had no children now we have two wonderful kidsNils and Signe who fill our lives with joy every day

As I look back to the code I first wrote when I started my PhD I often findmyself reflecting on this quote

When I wrote this code Only God and I knew what i did Now only God does- Unknown

Tullinge March 2021Edwin Bergstedt

J

iii

List of appended papers

Paper ABergstedt E Holmberg A Lindholm P and Olofsson U rdquoInfluence of the Din3962 Quality Class on the Efficiency in Honed Powder Metal and Wrought SteelGearsrdquo Tribology Transactions Accepted 13th of July 2020

Paper BLin J Bergstedt E Lindholm P and Olofsson U rdquoIn Situ Measurement ofGear Tooth Profile During FZG Gear Micropitting Testrdquo IOP Publishing Sur-face Topology Metrology and Properties Accepted 11th of February 2019

Paper CBergstedt E Lin J and Olofsson U rdquoInfluence of Gear Surface Roughness onthe Pitting and Micropitting Liferdquo Proceedings of the Institution of MechanicalEngineers Part C Journal of Mechanical Engineering Science Accepted 9thof May 2020

Paper DLin J Teng C Bergstedt E Li H Shi Z and Olofsson U rdquoA Quantitative Dis-tributed Wear Measurement Method for Spur Gears During FZG MicropittingTestrdquo Tribology International Accepted 26th of December 2020

Paper EBergstedt E Lin J Andersson M Bergseth E and Olofsson U rdquoGear Micro-pitting Initiation of Ground and Superfinished Gears Wrought versus Pressedand Sintered Steelrdquo Tribology International Accepted 19th of April 2021

iv

Division of work between authors

Paper ACRediT authorship contribution statementEdwin Bergstedt Data curation Investigation Formal analysis Visualisa-tion Writing - original draft Anders Holmberg Resources Writing - reviewamp editing Per Lindholm Supervision Writing - review amp editing Ulf Olof-sson Conceptualisation Supervision Project administration Funding acquisi-tion Writing - review amp editing

Paper BCRediT authorship contribution statementJiachun Lin Conceptualisation Methodology Visualisation Writing - originaldraft Funding acquisition Edwin Bergstedt Data curation Writing - reviewamp editing Investigation Per Lindholm Supervision Writing - review amp edit-ing Ulf Olofsson Supervision Project administration Funding acquisitionWriting - review amp editing

Paper CCRediT authorship contribution statementEdwin Bergstedt Conceptualization Data curation Investigation Formalanalysis Visualisation Writing - original draft Jiachun Lin Conceptualisa-tion Methodology Visualisation Writing - original draft Funding acquisitionUlf Olofsson Supervision Project administration Funding acquisition Writ-ing - review amp editing

Paper DCRediT authorship contribution statementJiachun Lin Conceptualisation Methodology Visualisation Writing - originaldraft Funding acquisition Chen Teng Methodology Software Writing -review amp editing Edwin Bergstedt Data curation Writing - review amp editingInvestigation Hanxiao Li Formal analysis Visualisation Writing - review ampediting Zhaoyao Shi Funding acquisition Writing - review amp editing UlfOlofsson Supervision Project administration Funding acquisition Writing -review amp editing

v

Paper ECRediT authorship contribution statementEdwin Bergstedt Conceptualisation Data curation Investigation Formalanalysis Visualisation Writing - original draft Jiachun Lin MethodologySoftware Funding acquisition Writing - review amp editing Michael AnderssonResources Writing - review amp editing Ellen Bergseth Supervision Writing- review amp editing Ulf Olofsson Conceptualisation Supervision Projectadministration Funding acquisition Writing - review amp editing

vi

Contents

1 Introduction 111 Swedish Foundation for Strategic Research - SSF 212 Sustainability 313 Thesis outline 314 Thesis objective 415 Research questions 4

2 Gear manufacturing and surface failures 521 Gear manufacturing 5

211 Wrought steel gears 5212 Pressed and sintered powder metal steel gears 8

22 Gear surface finishing 9221 Grinding 9222 Honing 9223 Lapping 9224 Shaving 10225 Roll finishing 10226 Superfinishing 10227 Shot peening 10

23 Gear terminology 1124 Gear profile evaluation methods 1125 Gearbox efficiency 1226 Gear surface failures 13

261 Micropitting 13262 Pitting 14

3 Gear performance evaluation methodology 1531 Test equipment 15

311 FZG Test rig 15312 In-situ tooth profile measurements 16

32 Gear specimen 18

vii

CONTENTS

321 Materials and surface finish 1833 Test procedures 19

331 Efficiency test 19332 Pitting test 19

34 Calculations 21341 Gear efficiency calculation 21342 Profile measurement optimisation and fitting 23343 Film thickness calculation 30

4 Summary of appended papers 31

5 Discussion 3551 Research questions 3552 Other aspects of the thesis results 39

6 Conclusions 41

7 Future Work 43

viii

Nomenclature

Abbreviations

EV Electric Vehicle

FZG Forschungsstelle fur Zahnrader und Getreibebau

GR Ground (Surface)

HIP Hot Isostatic Pressing

HO Honed (Surface)

ICE Internal Combustion Engine

LS Load Stage

PAO Polyalphaolefin (Lubricant)

PM Powder Metal (Pressed and Sintered)

SF Superfinished (Surface)

SSF Swedish Foundation for Strategic Research

W Wrought (Steel)

Efficiency Parameters

ηGearminusMesh Gear mesh efficiency [-]

ηT otal Total efficiency [-]

ω12 In-going angular speed of the pinion gear [ms]

n Rotations per minute [rpm]

T1 The applied load in the inner power loop [Nm]

TBearings Torque loss of the bearings [Nm]

ix

NOMENCLATURE

TGearminusMesh Torque loss of the gear mesh [Nm]

TLoadminusDependent Load dependent torque loss [Nm]

TLoadminusIndependent Load independent torque loss [Nm]

TST A12 KTH model load-dependent torque loss [Nm]

TT otal Total loss torque [Nm]

u Gear ratio [-]

Film thickness Parameters

ρnYThe normal radius of relative curvature at point Y

GM The material parameter

hY The local lubricant film thickness

KA The application factor

KV The dynamic factor

pHYA The local nominal Hertzian contact stresscalculated with a 3D loaddistribution program

Ra The effective arithmetic mean roughness value

SGFY The local sliding parameter

UY The local velocity parameter

WY The local load parameter

Gear Parameters

α Pressure angle [deg]

β Helix angle [deg]

a Centre distance [mm]

b Face width [mm]

da12 Tip diameter [mm]

dw12 Working pitch diameter [mm]

m Module [-]

x

NOMENCLATURE

x12 Profile shift factor [-]

z12 Number of teeth [-]

Measurement Parameters

λS Cut off length [mm]

σ20III

Cost function performance index

N The normal to point P

P Any point on the involute profile

P0 Start of the involute profile on the base circle

rB Base circle [mm]

rm The measured tooth profile coordinate vector

rϑ Positional vector that describes the location P using an angle ϑ [mm]

ϑa The roll angle where the tip break starts [deg]

ϑF The roll angle at the start of the involute [deg]

a Fitting parameters

ag Form fitting parameter

ap Position fitting parameter

ar Rotational fitting parameter

B The point where the normal N intersects the base circle

dmin The minimum distance between the measured profile and the optimisedtheoretical profile

I The identity matrix

PTP The weighting matrix

R Rotational matrix

Wi Cumulative wear the difference compared to the initial profile

wi Stage wear the difference compared to the previous profile

XY Z Local coordinate system

xi

NOMENCLATURE

xyz Global machine coordinate system

rprime The optimal position of the theoretical involute after fitting to themeasured profile rm

X prime The optimal minimum position points

Subscripts

1 Pinion

2 Gear

xii

Chapter 1

Introduction

The invention of gears has enabled much of the technology we know today Thefirst gear-like mechanism consisted of a crude system of interlinking woodenpins In its time it was truly revolutionary suddenly there was a way to transferpower and change the direction of power Also by changing the gear ratiothe speed of the input and output shafts can be adjusted to better suit theapplication Gears provide a means to harness the energy from for examplea water wheel The energy can be transferred and manipulated enabling theuse of heavy equipment eg to mill or to hammer wrought steel Moderngear applications are faced with a completely different set of challenges Fiercecompetition and demand for cost savings spurs the interest in alternative gearmanufacturing methods Also the power density of the entire drive train isincreasing

To reach the stipulated environmental goal and minimise the effect of globalwarming [1] a severe reduction in the volume of emitted greenhouse gases isneeded Therefore the efficiency and gear mesh losses are increasingly impor-tant as tougher emission legislations are passed The modern gear has to beproduced cheaply be sufficiently strong and durable for its application Fur-thermore the losses and sound emitted should be kept to a minimum Aninteresting alternative to the traditionally machined gears are gears made frompressed and sintered powder metal (PM) This PM material can be shaped intonear-net shape with significantly less waste material [2] [3] and with signifi-cantly shorter cycle time compared to traditional gear generating methods [4]Another potential benefit of the PM material is that it can dampen vibrationand reduce the emitted noise [5] this is due to the internal porosity preventingthe sound waves to propagate freely The current generation of sintered PMmaterials can reach a density of roughly 73 gcm3 after compaction and sin-tering The maximum density that is achievable is dependent on many factorssuch as the size and shape distribution of the metal powder and the proper-ties of the additives The main issue is the exponential increase in compaction

1

CHAPTER 1 INTRODUCTION

pressure needed to compress the powder particles before sintering [6] Thedensity also effects mechanical properties such as the Youngrsquos modulus tensilestrength and hardness [7] [8]

Today sintered PM gears are mainly used in low loaded applications as thegears are weaker than the wrought steel counterpart If the strength of the PMgears can be increased the PM gears would be an interesting option to consideras there are several benefits in choosing a PM material for gears The man-ufacturing process is fast and efficient with hardly any wasted metal powderAnother benefit of using PM technology in manufacturing gears is the possi-bility for creating complex shaped gears as the limitations of the conventionalgear generation methods do not apply [9] Applications could be optimised rootgeometry for decreasing the local load concentrations and also creating gearswith complex shapes eg holes for weight material reduction However themaking of complex-shaped gears requires a specialised tool which is more ex-pensive than for the standard gear This can be compensated by a large volumeand the materials saved per gear manufactured

11 Swedish Foundation for Strategic Research -SSF

The Swedish Foundation for Strategic Research (SSF) is a foundation thatgrants funding to research projects in science engineering and medicine Thegoal is to ensure that Sweden can maintain its strong position in research andinnovation and remain competitive in the future

This PhD thesis is part of the rdquoNanotechnology Enhanced Sintered SteelProcessingrdquo project funded by SSF Grant No GMT14-0045 The projectis a collaboration between Chalmers University of Technology Lund Univer-sity KTH Royal Institute of Technology and Uppsala University Hoganas isinvolved as a industrial partner and supports the project with resources andtechnical knowledge Chalmers University is responsible for manufacturing thenano powder creating material samples and evaluating the materials on a labscale level KTH and Uppsala are responsible for evaluating the materialsacute per-formance tribologically as well as conducting metallographic analyses LundUniversity is responsible for analysing the projectacutes potential from a cost andsustainability perspective in comparison to traditional gear manufacturing

The rdquoNanotechnology Enhanced Sintered Steel Processingrdquo project is de-voted to exploring the possibilities with mixing in ultra-fine nano-sized powderparticles into the regular powder mix used for sinter steel There are severalpotential benefits with a nano enhanced material The density can be increased

2

12 SUSTAINABILITY

as the nano powder can fill voids between normal powder particles Even a smallincrease in density could potentially be of great importance as closed porosityis then achieved ie the pathways in between pores are closed With closedporosity the material can be run through a hot isostatic pressing (HIP) processwithout the need to first be capsuled in a sealed enclosure [10] thus a fullydense material can be made at relatively low cost Another potential benefit ofthe nano-enhanced material is that the small particles will have a lower meltingpoint thus initiate the necking process in between the regular particles andincreasing the initial diffusion rates

12 SustainabilityThe research conducted in the scope of this thesis could potentially increasethe sustainability By finding better materials and surface treatment methodsthe gear mesh efficiency can be increased thus lowering energy consumptionBoth conventional internal combustion engines (ICE) and electric vehicles (EV)benefit from increased efficiency ie lower fuel consumption for the ICE andsmaller battery pack size and thus less weight for the EV Another challenge forthe electrification is that in order to increase efficiency of the electric motorsthe operating speed needs to be several times higher than the normal operat-ing speed of an ICE engine [11] [12] This poses new challenges as higherspeed results in far more contacts thus increasing the surface fatigue damageManufacturing gears from metal powder also has potential to increase sustain-ability as the process has fewer processing steps and can utilise the materialmore efficiently ie less waste material The PM process also has another in-teresting property a gear made with a complex shape and with holes to reduceweight [9] is more sustainable as less powder is used The main disadvantageto the PM technology is that it requires high volume to compensate for theinitially higher tool cost [13] also the strength of the material is lower than forwrought steel However the strength and performance can be compensated forand the surface can be densified to obtain a hybrid material with a porous coreand a dense surface layer

13 Thesis outlineThis Chapter aims to give an introduction to the subjects discussed in thisthesis and the research questions that are to be answered An overview of theresearch project of which this doctoral thesis is a part is also presented Thesustainability impact of the work in this thesis can also be seen in this chapterChapter 2 provides a brief overview of gears such as the gear manufacturingprocess both for wrought steel as well as gears made from pressed and sintered

3


materials Also some gear surface finishing techniques a basic introduction togear micro geometry and gear flank damage are presented Chapter 3 containsthe methods used in conducting the research such as the test procedurestest equipment and calculation methods Chapter 4 summarises the appendedpapers and in Chapter 5 the research questions are discussed and answeredChapter 6 summarises the most important findings for the readeracutes convenience

14 Thesis objectiveThis thesis seeks to increasing knowledge on how to evaluate the performanceof both conventional gears as well as sintered and pressed powder metallurgicalgears Research and development of methods for comparing and assessingprofile changes during gear testing can contribute to a deeper understandingof how different surface finishing operations affect the pitting life and gearefficiency

15 Research questionsThis thesis seeks to explore the subject of gears The objective is to achievea deeper understanding and further knowledge in testing and evaluating gearperformance In order to achieve this the a number of research questions wereformulated and presented below The research questions are discussed furtherin Section 51

bull Can the gear mesh efficiency be directly related to the DIN 3962 gearquality class index

bull Does the gear mesh efficiency differ significantly between honed PM steelgears and honed gears made from wrought steel

bull Can micropitting initiation mechanisms be evaluated using surface profilemeasurements during an FZG pitting test

bull How can the gear surface finishing method affect the surface damagemechanism for wrought steel gears

bull How do the principal surface damage mechanisms compare between wroughtsteel and PM steel gears

4

Chapter 2

Gear manufacturing and surface failures

21 Gear manufacturingThis section is meant to give the reader a basic introduction to gears in terms ofmanufacturing surface finishing processes gear measurement and gear surfacefailure

211 Wrought steel gearsIn order to make a gear from a piece of wrought steel first the teeth are cutfrom the gear blank This leaves a rough surface The next step is to use afinishing process and apply a heat treatment to harden the gear the order ofthese steps can be chosen to best suite the products needs In the finishingprocess the gear profile is finalised to achieve the desired geometrical shapesurface texture and surface roughness

There are several methods for making gears these methods can be di-vided into two sub categories generating methods and forming methods Themain distinction is that the tool used for gear generating can produce gearswith various number of teeth while forming method incorporates tools that arespecifically made for one specific gear ie a set number of teeth module andpressure angle

Generating methods

In gear manufacturing with a pinion type cutter the cutter is made to the imageof a the mating gear that one wants to generate The gear blank and tool isthen locked in rotation as a pair of mating gears would The tool is positionedabove the work piece and at a distance so that the tool barely touches the gearblank The tool is then moved down over the gear flank cutting the surfacethe tool is backed away from the cut and moved back up to make a new cut

5

CHAPTER 2 GEAR MANUFACTURING AND SURFACE FAILURES

The Maag generating method shown in Figure 21 uses a rack cutter thiscan be thought of as involute gear of infinite size

Figure 21 Illustration of gear generation using the Maag method with a rackcutter the cutting rack is positioned above the gear blank and moved down ina cutting stroke The tool is then moved away from the gear blank and up tothe initial position the gear is rotated a bit for the next cut to be performed

The Fellows method uses a cutting tool that is round or in contrary to theMaag method has a finite radius In Figure 22 one example of the Fellowsgenerating method can be seen One benefit compared to the Maag method isthat the Fellows method is also suitable for cutting internal gears

Another common generating method is hobbing as can be seen in Figure 23The hob tool is at first glance a bit awkward in shape almost like a rollingpin for making flat bread with small knobs all over Upon further inspectionone can see that there are some important differences The gear hob is notstraight as the rolling pin it is in fact a single tooth worm gear that has beencut perpendicular to the rolling direction at several positions this create thecutting edges of the gear hob The result can be seen as a collection of rackcutters mounted on a cylinder but with the helical shape of the worm gearBy rotating the hob in sync with the gear blank and moving the hob over thewidth of the gear the teeth are generated

Forming methods

Gear forming is different from gear generating for gear forming the gear blank isfixed in position and the material in-between two adjacent teeth are milled away

6

21 GEAR MANUFACTURING

Figure 22 Illustration of gear forming using the Fellows generating methodwith a pinion type cutter the tool and gear blank is rotated together thepinion cutter is positioned above the gear blank and moves down in a cuttingstroke then returns to the initial position and rotated a bit for the next cut

Figure 23 Illustration of gear forming using a hob cutter the hob and gearblank rotates in sync and the hob is moved down to perform the cut

7


in a milling machine The gear blank is rotated by a distance corresponding toone tooth for the next cut the process repeats until the gear is completed Itis important to notice that only spur gears can be made using this method

212 Pressed and sintered powder metal steel gearsManufacturing components by pressing and sintering powder metal is a conve-nient and fast mean of production The process of pressing the metal powdercan be seen in Figure 24 [10] The powder metal gears are made by filling agear shaped cavity with a metal powder mixed with additives [14] Then byusing a set of punches the powder is compacted under high load to a semi-solidcomponent a green body where the individual powder particles have bondedmechanically but are not fused together

The whole filling and compaction process is quick and only takes a few sec-onds per gear Afterwards the green body gears are sintered that is subjectingthe gears to specially designed heat cycles The heat fuses the individual pow-der particles together resulting in a solid material although with reminiscentporosity The process shrinks the gear as the density increases Even toughthe compaction process seems simple at first glance it is still possible to createcomplex shaped gears such as helical gears

Die fill stage Compaction Part ejection

Die

PowderGreen body part

Upper punch

Lower punch

Figure 24 Die pressing of metallic powders

8

22 GEAR SURFACE FINISHING

22 Gear surface finishingThe use of finishing operations are crucial to obtain the correct geometricalproperty and surface finish on the gears After the machining operations thesurface finish and micro geometry is usually not adequate for the needed appli-cation Furthermore if the gear have been subjected to a hardening processthe gears will distort to some degree by the heat The surface finishing op-erations remove the outermost surface layer and ensures the correct shape ofthe gear profile There are several available methods for gear surface finishingeg grinding honing lapping shaving and roll finishing Superfinishing is anadditional process that can further enhance the surface finish

221 GrindingThere are two main methods of gear grinding form grinding and generationgrinding The former uses a grinding disc wheel that is dressed to the shapeof the involute profile and runs in the space in-between two teeth The latteris either a single straight edge grinding wheel or multiple grinding wheels theflanks mimic a toothed rack and the it rolls over the reference circle of thegear The grinding disc spins and is moved over the surface to grind the teethto the involute profile shape The benefit of grinding is that it can satisfyhigh tolerance requirements it is also possible to grind hardened gear surfacesThe downside is that the process generates heat and that the process is timeconsuming

222 HoningHoning of gears is a hard grinding process where a honing tool is moved over thegear flank [15] The honing stone is resin matrix containing abrasive particlesthe tool is moulded to a external gear and dressed using a diamond wheel forthe specified gear parameters The gear is rotated against the honing toolresulting in a surface texture that are almost parallel to the tooth at the tipand root and perpendicular to the tooth at the pitch

223 LappingLapping is a mechanical polishing process where a paste containing abrasiveparticles are used in between a set of mating gears [16] The gears are revolvedand quickly reciprocated along the gear face at a controlled pressure Thusconforming the surfaces to one another One way is to use a master lappinggear this ensures that the production gear can conform with high accuracy tothe form of the master gear

9


224 ShavingGear shaving can only be used on non hardened gear surfaces the accuracy isthus limited as distortions can occur during the heat treatment cycle [17] Theshaving process uses a tool shaped like a gear with serrations forming numerousof cutting edges [16] The tool and gear is positioned with crossed axes a motorrotates the tool driving the gear which can rotate freely The centre distanceis reduced in small increments until the final form is achieved The processremoves waviness and cutter marks from previous machining One benefit ofshaving is that the process generates low heat in comparison to grinding

225 Roll finishingGear rolling does not remove any material it is purely a yield process where thesurface is conformed to the shape of the counter surface The gear is mountedand meshed against a tool by applying pressure and rotating the gear the metalflows smoothing the surface also good dimensional control is possible As nomaterial is removed with the roll finishing process the excess material will flowand form lips at the tip and sides of the gear The rolling process is speciallybeneficial for PM components as the rolling compresses the surface and closespores reducing the chances of sub-surface fatigue damage

226 SuperfinishingSuperfinishing is an additional treatment that can be performed to enhance thesurface further It is a type of polishing that can be mechanical chemical or acombination of both The theory is the same regardless the polishing processremoves the surface peaks leaving a mirror-like surface finish The mechanicalprocess uses a extremely fine grit abrasive the abrasive is either moved over thesurface while rotating or oscillating creating a cross pattern on the surface [18]The chemical process etches the surface the peaks will etch more than the basematerial as the surface area in contrast to the volume is high One importantdownside to the superfinishing process is that it is a slow and costly processoften only suitable for high performance applications ie helicopter gears etc

227 Shot peeningShot peening is a method of enhancing the surface properties of a material andcan be used on gears Shoot peening strikes the surface with a high numberof small circular objects eg glass metal or ceramic The velocity is highenough to cause plastic deformation in the surface layer which introduces acompressive residual stress The treatment makes the gears less susceptible forsurface damage such as cracks

10

23 GEAR TERMINOLOGY

23 Gear terminologyIn Figure 25 some of the most important gear terminology can be seen Thereare several important regions of the gear tooth represented by circles originatingfrom the centre of the gear At the root circle the tooth begins and the basecircle is the start of the involute profile The pitch circle is the point where thepinion and wheel in theory have a pure rolling contact Finally the addendumcircle denounces the end of the involute profile at the tip of the gear toothThe addendum and dedendum regions is the name of the involute profile aboveand below the pitch circle respectively

Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle

Figure 25 Illustration of a gear with important gear terminology marked

24 Gear profile evaluation methodsThe gear surface profile is usually measured in a gear coordinate measurementmachine as can be seen in Figure 26 The gear is mounted and positioned inthe device and indexed according to the gear teeth A ball probe then measuresthe position of the surface the gear surface profile is usually measured in a gridshaped pattern the number of points to probe can be selected however a largenumber of probing points will take a significant amount of time to measure

11


The coordinate measuring machine is suitable for measuring the form of thegear tooth however it is not suitable for measuring the surface roughness Itis important to note that the coordinate measuring machine is also used formeasuring distance between teeth inner diameter of the gear as well as othergear parameters

Figure 26 Gear profile measurement using a ball probe

25 Gearbox efficiencyGearbox efficiency is a measure of how much losses a set of gears have in agearbox There are several factors contributing to the total losses and theycan be divided in to load dependent and load independent losses [19] Load-independent losses are losses related to the rotation of the gears such as oilchurning losses and losses from the bearing seals Load-dependent losses arelosses that are influenced of the applied load such as bearing losses and gearmesh losses The gear mesh efficiency is important as a slight increase inefficiency could have a large impact of the total energy consumption of themotor

12

26 GEAR SURFACE FAILURES

26 Gear surface failuresAs the gears rotate the teeth are constantly subjected to both rolling and slidingalong the involute profile At the pitch the contact is mostly rolling and at thetip and in the root the sliding speed is high Pitting damage is a contact fatiguedamage that can occur due to the rolling and sliding on the gear surface Pittingdamage can be divided into two categories based on the appearance of thedamage micropitting or macropitting There are also other types of damagethat can occur on gears such as scuffing where the surfaces bond due to egfailure of the lubricant

261 MicropittingMicropitting or gray staining is usually found in high loaded and hardenedgears the damage is caused by the interaction between surface asperities Theappearance of a micropitted surface is dull as the surface is filled with micro-cracks dispersing and scattering the light hence the name gray staining [20]By observing micropitted surfaces in a scanning electron microscope it wasconcluded that the damage mechanism is the same as for pitting the scale isonly smaller [21] As the micro-cracks grow in number and size the surface isundermined with cavities with a size roughly equal to the asperities Mallipeddiet al [22] found one type of micropitting initiation They found plasticallydeformed regions below asperities down to a depth of 15microm when studyingmicropitting in an FZG test rig The plastic deformation forced dislocations tomove in slip bands inside the grains of the material The pileup of dislocationsin grain boundaries enabled cracks to nucleate thus initiating the micropittingdamage

Both the gear micro geometry and surface finish are important to mitigatemicropitting a superfinished surface protects against micropitting and also theuse of tip relief on the gear profile can prevent micropitting from occuring [23]

13


262 PittingMacropitting or pitting is damage that occur on or below the pitch in a lu-bricated contact the repeated contacts and high contact pressure affects boththe surface and a region below the surface [21] The contact initiates cracksthat propagate until small pieces of the surface is separated the shape of thedamage can either be pin-holes or spalls Pin-holes are small circular holes inthe surface where the material have been lost while spalls are a v-shaped dam-age that initiate in a point on the surface [24] the cracks then propagate at anangle in a v-shape and also down into the material the damage grows belowthe surface until the critical crack length is achieved and a piece of the surfaceis removed The resulting damage is shaped like a clam-shell which is also acommon name for the damage

14

Chapter 3

Gear performance evaluationmethodology

31 Test equipment

311 FZG Test rig

The FZG back-to-back test rig was designed by the Gear Research Centre(Forschungsstelle fur Zahnrader und Getreibebau) at the Technical Universityof Munich The FZG test rig uses a circulating power loop that is loaded me-chanically using lever arms and weights This makes the test rig efficient asthe electric motor only needs to supply energy to account for the losses in thepower loop The FZG test rig can be used in different configurations in thiswork two main setups were used a setup to measure efficiency and one forconducting pitting tests For conducting efficiency measurements the test rigis configured according to Figure 31

The second configuration can be seen in Figure 32 The FZG test rigconsists of two gearboxes (1) and (3) containing one pinion and one gearwhich are connected with two shafts forming a circulating power loop Oneof the shafts is fitted with a load clutch (2) used for applying a pre-load intothe power loop Finally an electric motor (5) drives the power loop Thedifference between the efficiency and pitting setups is at positions (3) and (4)In the efficiency test gearbox (1) and slave gearbox (3) are identical but forthe pitting test the gears in the slave gearbox (3) are replaced with anothergearbox with wider helical gears This is done to promote pitting only in thetest gearbox (1) At position (4) there is a torque sensor for the efficiency testand for the pitting test setup a speed reducer is fitted The speed reducer canrun either a 11 or 251 gear ratio

15

CHAPTER 3 GEAR PERFORMANCE EVALUATION METHODOLOGY

Figure 31 Schematic of the FZG back-to-back test rig in the efficiencymeasurement configuration (1) Test gearbox (2) Load clutch (3) Slavegearbox (4) Torque sensor (5) Motor Source The figure was created byEdwin86bergstedt and is not altered The figure is licensed under the Creative CommonsAttribution-Share Alike 40 International licencehttpscreativecommonsorglicensesby-sa40deeden

1 2 3 54

Figure 32 Schematic of the FZG back-to-back test rig in the pitting testconfiguration (1) Test gearbox (2) Load clutch (3) Slave gearbox (4)Reduction gearbox (5) Motor Source The figure was created by Edwin86bergstedtand is not altered The figure is licensed under the Creative Commons Attribution-ShareAlike 40 International licencehttpscreativecommonsorglicensesby-sa40deeden

312 In-situ tooth profile measurementsA methodology for measuring gears in-situ in the gearbox was developed atKTH by Sosa et al [25] A Taylor Hobson Intra 50 stylus instrument wasmounted on a bracket attached to the test gearbox with bolts and guide pinsFigure 33 shows the measurement device mounted on the gearbox and alsothe probe position in the root of the gear The in-situ measurement methodhas a couple of advantages compared to traditional methods of evaluating wearin gears ie weighing or measuring them in a coordinate gear measuring ma-chine The gears can be measured without disassembling the test rig This isconvenient for the operator and it also reduces the risk of influencing the testresults With the bracket mounted on the gearbox a high positional accuracycan be obtained which enables repeatable measurements that can accurately

16

31 TEST EQUIPMENT

track profile changes during the course of a pitting test Three factors mainlyaffect the quality of the measurement The gearsacute angular measurement posi-tion the position along the width of the tooth and the calibrated start positionof the stylus instrument The gearsacute angular position is aligned using a spiritlevel placed on top of the gear The accuracy of the spirit level was stated as 15min of arc The position along the tooth width is controlled by a micrometerscrew gauge with an accuracy of plusmn5 microm The starting position of the mea-surement can change slightly due to limitations of the measurement device theshift is usually below 20 measurement points or plusmn10 microm

In order to minimise errors due to local variations three teeth evenly spacedaround the gear (teeth number 1 9 and 17) were measured At each toothsix parallel traces were measured starting in the centre of the tooth width andspaced 01mm apart Profile measurements were conducted initially before thepitting test commenced after running-in and after the finish of each consec-utive test In total 18 measurements were recorded for each load tested andas the tests were repeated two times a total of 36 measurements are availableper tested load stage

Figure 33 The Taylor Hobson stylus instrument mounted on the test gearboxthe position of the probe in the root of the gear is also visible in the figure

17


32 Gear specimenThe gears used in Papers A to E are standard FZG C-Pt spur gears without anyprofile modifications ie tip root relief or crowning Same gear type is usedfor both the efficiency test procedure (Section 331) and for the pitting test(Section 332) The data of the gears can be seen in Table 31

Table 31 Gear parameters for the tested C-Pt gears

Symbol Unit C-PtCentre distance a mm 915Number of teeth Pinion z1 - 16

Gear z2 - 24Module m mm 45Pressure angle α deg 20Helix angle β deg 0Face width b mm 14Profile shift factor Pinion x1 - 01817

Gear x2 - 01715Working pitch diameter Pinion dw1 mm 732

Gear dw2 mm 1098Tip diameter Pinion da1 mm 825

Gear da2 mm 1184Material - 16MnCr5Heat treatment - Case carburizedSurface roughness Ra microm 05 plusmn 01

321 Materials and surface finishIn Papers A to E several materials and surface finishing operations are utilisedTwo material types wrought steel and pressed and sintered powder metallurgicalsteel were tested The wrought steel is a common commercial gear steel16MnCr5 The two PM steels used Distaloytrade AQ and Astaloytrade Mo weresupplied by Hoganas The chemical composition of the materials tested ispresented in Table 32

Three surface finishing methods were tested experimentally honing grind-ing and superfinishing The superfinishing process was performed as an addi-tional step on the ground surface

18

33 TEST PROCEDURES

Table 32 The chemical composition of the wrought steel and powder metalmaterials

Chemical composition (weight )Fe Mn Cr Ni Mo C S P Si

16MnCr5 9695-9878 1-13 11 - - 014-019 le 0035 le 0025 04Distaloytrade AQ 988 05 - 05 - 02 - - -Astaloytrade Mo 983 - - - 15 02 - - -

33 Test procedures331 Efficiency testThe efficiency measurement test procedure was developed at KTH and haseffectively been used in a wide range of research projects see eg [19] [26]ndash[31] The efficiency tests required a new set of gears for each test In orderto change the test gears in both the test and slave gearbox the test rig wasdismounted The top and side panels of the gearbox were removed Both themotor and torque sensor were moved to change gears in the slave gearbox Thereassembly was performed following a strict procedure as Andersson et al [29]concluded that a rebuild of the test rig can influence the efficiency results

The gearboxes were filled with 15 L of a Polyalphaolefin (PAO) lubricantup to the centre of the shaft The specified nominal viscosity of the PAOlubricant was 641 mm2s (cSt) at 40degC and 118 mm2s (cSt) at 100degC

The efficiency test starts with a running-in of the gears for four hours usingload stage (LS) 5 corresponding to a pitch line torque of 941 Nm and with apitch line velocity of 05 ms The efficiency test starts by running a baselinetest without any load applied this is to isolate the load independent losses Theloss torque is measured at five-minute intervals in order to reach a steady statefor the losses A series of eight speeds were tested 05 1 2 32 83 10 15and 20 ms The test series is then repeated at three additional load stages 45 and 7 in order to calculate the load-dependent losses The pitch line torquefor the load stages is shown in Table 33 Each efficiency test was repeatedthree times using new gears in both gearboxes During the tests the speed oiltemperature and loss torque were recorded at a sample rate of 1 Hz The oiltemperature in the gearboxes was kept at a constant 90degC (-1 to +4degC)

332 Pitting testIn Papers B to E pitting tests were performed in the FZG test rig The pittingtest procedure used was based upon the DGMK [32] short pitting test pro-cedure The DGMK test consists of a run-in for 13times 105 contacts at LS 3corresponding to a pitch line torque of 353 Nm followed by the pitting test

19


which was run at intervals of 21times 106 contacts The speed of the pinion was2250 RPM and the oil temperature was kept constant at 90degC There were afew alterations made to the procedure to account for more load stages thusenabling the gathering of surface profile data in a wider range The DGMKmethod uses a run-in period one run at LS 7 (1834 Nm) and then the testcontinues at LS 10 (3727 Nm) until a certain profile deviation is reachedIn the altered procedure all load stages from LS 3 to LSmax were tested insequence where LSmax is set to LS 9 and LS 10 for the pressed and sinteredPM material and wrought steel respectively When the test reaches the max-imum load level LSmax the test continues at this level until either a pittingdamage greater than 5 mm2 is observed or run-out is reached at 40times 107

contacts The load stages and corresponding pitch line torque are presentedin Table 33 The oil temperature had to be lowered from 90degC to 80degC asthe cooling system of the FZG test rig used had difficulties with maintaininga constant temperature at 90degC A flowchart overview of the pitting test andmeasuring procedure can be found in Figure 34

Table 33 FZG Load stage and corresponding pitch line torque in Nm

LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start

Running-in13middot105 contacts

LS=3

Test21middot10⁶ contacts

LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile

Run-Out40middot106 contacts

at LSmax

No

Yes

Figure 34 A flowchart of the pitting test and surface measurementprocedure LSmax is 9 and 10 for the PM and the wrought steel respectivelySource The figure was created by Edwin86bergstedt and is unaltered except the text fontThe figure is licensed under the Creative Commons Attribution-Share Alike 40 Internationallicence httpscreativecommonsorglicensesby-sa40deeden

34 Calculations

341 Gear efficiency calculation

The losses for the FZG test rig operating in efficiency mode (Figure 31) canbe assumed to be equal to the torque supplied by the electric motor to keepthe test rig at a constant velocity The pre-loaded inner loop maintains thepower within the loop and the electric motor therefore needs to supply enoughtorque to overcome the total losses TT otal The total losses can be dividedinto load-dependent TLoadminusDependent and load-independent TLoadminusDependent

21


losses

TT otal = TLoadminusDependent + TLoadminusIndependent (31)Load-dependent losses are all losses related to the applied load ie gear

mesh losses and losses in the bearings is given by

TLoadminusDependent = TBearings + TGearminusMesh (32)The load-independent losses are losses that are not affected by the applied

load oil churning losses[33] and losses from the bearing seals is given by

TLoadminusIndependent = TOilminusChurning + TBearingminusSeal (33)To calculate the gear mesh loss torque Equation 32 is substituted into

Equation 31 giving the following expression

TGearminusMesh = TT otal minus TLoadminusIndependent minus TBearings (34)The load independent losses can be obtained by performing tests at each

speed without any load applied in the power loop The gearbox efficiency forone gearbox can be calculated using the following expression

ηT otal = 1minus 12 middot

TT otal

uT1(35)

Where u is the gear ratio and T1 is the nominal torque transferred by thepinion T1 is equal to the load applied to the inner power loop and was assumedto remain constant throughout the experiment Given the assumption that thegearboxes contribute equally to the losses the efficiency for one gearbox canbe obtained by multiplying the ratio by 1

2 There are several models available for calculating the bearing losses One

commonly used method for NJ 406 cylindrical roller bearings used in the FZGtest rig was developed by SKF Industries inc Researchers at KTH have de-veloped another empirical bearing model named STA [34] The STA bearingmodel is shown below

TST A12 = An+ B

n+ C (36)

Where the parameters A B and C (Appendix A) were determined empiri-cally and depend on the load temperature lubricant and bearing type

The loss torque of the bearings can be calculated using Equation 37 whereω12 is the in-going angular speed of the pinion and gear shafts

TBearings = 4(TST A1 middot ω1 + TST A2 middot ω2

ω2

)(37)

22

34 CALCULATIONS

The gear mesh loss can be obtained by using the bearing losses the mea-sured total loss and the measured load-independent loss into the following ex-pression

ηGearminusMesh = 1minus 12 middot

TGearminusMesh

uT1(38)

Finally the gear mesh efficiency can be calculated using Equation 38

342 Profile measurement optimisation and fittingThe measured gear involute profiles will not be able to fit on top of each otherin the as-measured state As the positioning of the gear is done by a spirit levelthe accuracy is not sufficient to ensure the exact same measurement angle anexample of the magnitude of the problem can be seen in Figure 35 Alsothe starting position of the stylus instrument will vary by some tens of pointscorresponding to roughly plusmn 10microm

Figure 35 A sample of measurements illustrating the effect of the angularposition error on the shape and position of the measurements [35]

In order to directly compare the measured profiles the profiles need to betransformed to a common reference The theoretical involute profile is suitablein this regard The theoretical profile was generated using the gear parameters

23


listed in Table 31 An involute profile is the path the end of a straight linefollows when the line is rolled over a circle To generate the involute profile firsta coordinate system O (x y) is created with origin in the centre of the gearFigure 36 shows the generation of an involute profile where the start of theinvolute profile P0 is on the vertical axis and lies on the base circle rb At anypoint P on the involute profile the normal N is tangent to the base circle rB

in point B The involute radius of curvature in point P is given by the distancePB which is also equal to the length of the arc segment between

_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ

Figure 36 Generation of an involute curve [35]

The position of any point P along the involute profile can thus be describedusing a position vector rϑ The function for calculating the position vectorrϑ [36] is given by

r (ϑ) = x (θ) i+ y (ϑ) j = rb [(sinϑminus ϑcosϑ) i+ (cosϑ+ ϑsinϑ) j] (39)

Where i and j are the unit vectors of the x and y axes and the parameter ϑvaries in the interval [ϑF ϑa]

The tooth profile was measured using a stylus instrument initially and aftereach performed test the measured tooth profile rm contains the coordinates

24

34 CALCULATIONS

for each measured point n as can be seen in Equation 310

rmi= xmi

ymin

i=1 (310)

As each measured profile n is located in its own local coordinate systemXY Zn the theoretical involute profile is generated in a global machine coor-dinate system xyz

X (XY Z)T x (x y z)T

The coordinate systems can be related to one another using Equation 311where R is a rotational matrix and X0 is the origin of the model coordinateframe xyz referenced to the machine coordinate frame XY Z

x = R (X minusX0) (311)

The end goal is to find the solution X prime that has the smallest geometricdistance to each point of the measured profile X The geometric distance isa suitable measurement for the error as it is invariant to coordinate transfor-mation ie rotation and translation In order to find the best solution forthe problem described the Orthogonal Distance Fitting (ODF) model can beused Several fitting parameters a need to be optimised ag form parametersar rotation parameters and ap position parameters As the form of the theo-retical involute is fixed the complexity of the problem can be reduced by usingtemplate matching Template matching is a special case of ODF where theshape and size of the object is known the form parameter ag can therefore beignored To solve the ODF two cost functions are used as performance indicesσ2

0 and the goal is to minimise both of them Where Equation 312 is thesquare sum and Equation 313 is the distance between the measured pointsand the corresponding points on the modelled involute profile

σ20I

= X minusX primeTPTP X minusX prime (312)

σ20II

= (X minusX prime)TPTP (X minusX prime) (313)

Here PTP is the weighting matrix for most ODF applications the weightingmatrix can be replaced by the identity matrix I [37] a ntimes n zero matrix withones in the diagonal

PTP = I =

1 0 00 1 00 0 1

By using the variable-separation method [37] the optimisation problem can

25


be solved using a nested iteration scheme Equation 314 The model parame-ters a and the minimum distance points X prime are solved

mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)

The inner loop of the optimisation is performed every iteration cycle andcalculates the minimum distance points for the current set of parameters Theouter loop updates the parameter set The optimisation is terminated when nomore improvement to the performance indices σ2

0IIIcan be achieved Equa-

tions 312 and 313 The optimisation problem can then be solved using anumerical solving method of choice such as the Newton method the Gauss-Newton method or the Gradient Descent method

By substituting the notations from our measurements into the general Equa-tions 312 and 313 we obtain two performance indices that should be min-imised

σ20I

= rm minus rprimeTPTP rm minus rprime

σ20II

= (rm minus rprime)TPTP (rm minus rprime)

Where rrsquo can be obtained from rearranging Equation 311

rrsquo = rRminus1 + r0

The minimum distance dmin between the measured profile and the optimisedtheoretical profile can thus be calculated

dmin = rm minus racute (315)As the profiles are worn and damaged the deviation from the theoretical

profile is large and the fitting is troublesome To mitigate this the measuredprofiles were filtered using a spline high-pass filter [38] with a cut-off lengthof λc = 008mm The mean deviation to the profile measured before run-ning in was calculated as well as the standard deviation Line segments thatdeviated more than one standard deviation from the initial measurement wereomitted while aligning the profiles The profiles were finally aligned using across correlation algorithm on the undamaged parts of the profiles

After the fitting and alignment procedure is complete the measured profileshow a nearly perfect match as can be seen in Figure 37

In order to evaluate the form changes one option is to look at the cumulativewear Equation 316 the difference between each measured profile comparedto the initial measurement The cumulative wear gives a representation of thefull extent of the damage over time the damage progression can therefore befollowed An example is presented in Figure 38

Wi = dTiminus dT1 i isin 2 middot middot middot n (316)

26

34 CALCULATIONS

Figure 37 The aligned and fitted profiles [35]

Another method is to evaluate the stage wear Equation 317 which is thedifference in regard to the previous measurement Stage wear is useful as itgives a clear indication when the surface damage first appears and at whichlocation An example is presented in Figure 39

wi = dTi minus dTiminus1 i isin 2 middot middot middot n (317)

27


Figure 38 The cumulative wear each profile is shifted down 5 microm from theprevious to increase readability [35]

28

34 CALCULATIONS

Figure 39 The stage wear each profile is shifted down 5 microm from theprevious to increase readability [35]

29


343 Film thickness calculationOne method of calculating the specific lubricant film thickness λGFY is pre-sented in ISO 6336-22 Method A Equation 318 This relationship was firstpresented in the Dowson Higginson formula

λGFY = hY

Ra(318)

The calculations in the ISO standard are based on the relation between thelocal lubricant film thickness (hY ) and the average surface roughness (Ra)given in Equations 319 and 320

hY = 1600 middot ρnY middot G06M middot U07

Y middot Wminus013Y middot S022

GFY (319)

Ra = Ra1 +Ra2

2 (320)

One important difference from the original Dowson Higginson formula isthat the radius of the involute (ρnY ) as well as the local sliding (SGFY ) istaken into consideration when calculating hY

In addition to the radius of the involute and local sliding parameter Equa-tion 319 consists of the material parameter GM the local velocity parameterUY and local load parameter WY In order to calculate the local load pa-rameter the local Herzian contact stress needs to be obtained According toMethod A of ISO 6336-22 the local Herzian contact stress (pdynYA) shouldbe obtained from performing a 3D mesh contact and load distribution analysisprocedure If the local nominal Hertzian contact stress (pHYA) is known thelocal Hertzian contact stress can be calculated using Equation 321

pdynYA = pHYA middotradicKA middot KV (321)

Where KA is the application factor and KV is the dynamic factor accordingto ISO 6336-1

30

Chapter 4

Summary of appended papers

Paper A

Influence of the Din 3962 Quality Class on the Efficiency in Honed PowderMetal and Wrought Steel GearsThis paper seeks to investigate the relation between the DIN 3962 quality classindex and the gear mesh efficiency Two materials a standard wrought gearsteel and a powder metal steel were tested All of the gears were first groundand later honed as a finishing operation The tested gears were measured andawarded a DIN 3962 quality class according to the measurement results Gearswith quality 6 to ge 9 were selected and tested in an FZG back-to-back testrig for gear mesh efficiency where ge 9 denotes the extreme case scenario withthe gears of the lowest quality available The results showed no significantseparation in efficiency between the honed wrought steel and the powder metalmaterial There was also no clear correlation between the DIN 3962 qualityclass and the measured efficiency It was found that whith the wrought steeldespite the range of the quality class tested the reproducibility was within therange of the assembly error for the FZG test rig

Paper B

In Situ Measurement of Gear Tooth Profile During FZG Gear Micropitting TestThis paper presents a novel way of fitting involute profile measurements to atheoretical involute profile Previous methods of fitting the measured profileto the nominal shape of the involute profile were limited as they could not beapplied to gear flanks subjected to modifications ie inclusion of a tip reliefThe most common method of measuring gears is by using a gear measuringmachine or coordinate measuring device A drawback with these devices is thatin order to measure the gear it needs to be placed in a fixture There are sev-eral benefits to using a profilometer to measure the gears most gear measuring

31

CHAPTER 4 SUMMARY OF APPENDED PAPERS

machines do not provide the raw data of the measurement only the calculatedgear parameters From the profilometer the full range of data is acquired andthus it is possible to compare surface roughness between tests A profilometerwas attached to the gearbox in an FZG back-to-back test rig enabling in-situmeasurements of the gearsacute involute profile without needing to disassemblethe test rig A pitting test was performed using FZG C-Pt gears and an ex-tended test procedure based on the short micropitting test procedure proposedby DGMK where the main difference was the incorporation of more load stepsand a slightly lower oil temperature in the test gearbox 80degC as supposed to90degC The gears were measured in-situ initially and after each performed testThe resulting profile measurements were used to validate the new proposedmodel The mounting bracket for the profilometer on the gearbox enables twodegrees of freedom the gear is free to rotate on its axle and the position in thetooth width direction can be adjusted using a micrometer screw gauge Thegear rotation is positioned using a spirit level placed on top of the gear Toevaluate the measured profiles the measurements need to be rotated aroundthe centre of the gear so that the measurements match the specified directionof tolerance for profile deviations defined by the ISO standard As the startingposition on the involute profile is unknown a cross correlation analysis can beused for determining the optimal shift needed to match the measured profilewith the nominal theoretical profile The optimisation routine presented strivesto find the profileacutes optimal rotation angle and shift As the optimisation rou-tine needs to be able to fit profiles with severe pitting damage the least squarefitting criterion was not suitable The fitting criterion was instead chosen as thestandard deviation of the difference between the measured and theoretical pro-files The paper concluded that the method proposed was capable of accuratelyfitting measured gear involute profiles to their theoretical counterpart The op-timisation also handles the inclusions of profile modifications and deviations inthe measured profile from pitting damage

Paper C

Influence of Gear Surface Roughness on the Pitting and Micropitting LifeIn paper C the optimisation routine presented in paper B is used for analysingthe profile change during a pitting test Pitting tests were performed in anFZG test rig using standard FZG C-Pt gears The test method was an adaptionof the short micropitting test proposed by DGMK The gears were run-in atload stage 3 and then tested for 21 million cycles at each consecutive loadstage from 3 to 10 corresponding to a pitch line torque of between 353 and3727 Nm The tests were run at the final load stage until pitting occurredSurface profile measurements were performed in-situ using a Taylor HobsonForm Talysurf Intra 50 stylus instrument the measurements were performed

32

initially and after each test Three teeth evenly spaced around the gear wereselected and six profiles were measured on each in the centre of the tooth widthand with 01 mm in-between The wrought steel gears used in the pitting testhad a ground surface and one pair was also superfinished to reduce the surfaceroughness Two test series were performed for each surface finishing methodThe results showed that the ground gears survived for 10 and 11 runs at thehighest load before pitting damage of ge 5 mm2 was observed on any gear flankBoth tests using gears with superfinished surface showed pitting after the firstrun at the highest load stage The findings were regarded as remarkable asthe commonly accepted belief is that a reduced surface roughness increases thepitting resistance By utilizing the surface profile measurements it was possibleto note a few key differences between the ground and superfinished gears Theground gears exhibited profile changes in the root after load stage 8 while thesuperfinished gears did not show any signs of damage until after load stage10 where pitting had already occurred The profile measurements were usedto calculate the specific film thickness From the results it was seen that forthe ground gear the specific film thickness approaches 1 between load stage7 and 8 which is where the transition from full film to mixed lubrication isexpected For the superfinished gears the specific film thickness approaches 1at load stage 10 which can explain why no damage was visible before this loadstage A theory for the rapid failure of the superfinished gear surface is thatthe wear seen in the root of the ground gears removes surface cracks formingin the surface layer due to the lack of tip relief in the gear geometry As thesuperfinished gears had a roughness that prevented the wear from removing thecracks the damage could grow and eventually cause the gear flank to collapserapidly

Paper D

A Quantitative Distributed Wear Measurement Method for Spur Gears DuringFZG Micropitting TestA method of quantitatively assessing the form change during a pitting test ispresented The article is based upon the method presented in paper B animproved method for fitting the measured profiles to the theoretical involuteprofile was developed Measurements were taken in-situ of the gear flank duringFZG pitting test the profiles were thereafter fitted via an optimisation routinein order to be able to directly compare them It was found that both cumulativetooth wear as well as stage wear (the profile change in regard to the previoustest) could be monitored with high accuracy It was furthermore possible todetect minute profile changes before any visible pitting damage was observedon the gear flank The fitted measured profiles can be used to obtain local wearcoefficients that can be used in wear simulations

33


Paper E

Gear Micropitting Initiation of Ground and Superfinished Gears Wrought ver-sus Pressed and Sintered SteelIn this paper the gears made of two types of materials were compared in pittingtests Wrought steel and sintered powder metallurgical steel with both groundand superfinished surfaces were tested in a back-to-back FZG test rig Thetests started using low pitch line torque and after each successful run the loadwas increased until the maximum load was reached 302 Nm and 3727 Nmfor the sintered powder metallurgical material and wrought steel respectivelyThe surface profile of the gear wheel was measured in-situ in the gearbox usinga Tylor Hobson stylus instrument The surface was measured initially as wellas after each performed test Six traces parallel to the involute profile weremeasured with 01 mm space in between in the centre of the width of the gearThese measurements were performed on three teeth evenly spaced around thegear Results from the pitting test showed that the wrought steel gears withground surface survived for ten times at the maximum load all other configura-tions exhibited pitting damage after the first run at the highest load The shortpitting life of the superfinished wrought steel gears was found to be linked to theabsence of tip relief which introduced rapid and violent kinematics in the rootof the teeth thus causing cracks in the surface layer and a rapid deterioration ofthe gear flank For both materials with ground surface the wear pattern alongthe tooth flank was found to be similar Micropitting was discerned in the rootand near the pitch while for the gears with superfinished surface the damageappeared on all positions along the flank One difference between the wroughtsteel and the sintered powder metallurgical steel gears was the initiation of thedamage The wrought steel gears only showed signs of surface-initiated dam-age while the powder metallurgical material showed a combination of surfaceand sub-surface damage The performance of powder metal gears could beimproved by performing a densification process on the surface such as rollingwhich can help to inhibit the sub-surface damage mechanisms In order to testgears with low surface roughness the addition of a tip andor root modificationis needed in order prevent the premature failure mode discovered in this paper

34

Chapter 5

Discussion

51 Research questionsIn this section the research questions formulated in section 15 are answeredand discussed

Can the gear mesh efficiency be directly related to the DIN3962 gear quality class indexGear manufacturing is complex and there are numerous variables to take intoconsideration All of these parameters have their own range of acceptable toler-ances Depending on the application the demands on the gears are different Ahelicopter transmission failure will have large consequences thus requirementsfor gear quality are high Gear quality class standards such as DIN 3962 [39]are a convenient and fast way of determining if a gear is made to specificationwith minimal errors or if the errors are high nb the DIN 3962 standard hasbeen replaced by ISO 6336 standard although the classification system is thesame in both standards The lower the number the more accurate the gear is

There are ever increasing demands to reduce emissions By minimising lossesin the gear mesh the total efficiency of the system increases Paper A seeks toanswer if the gear classification system can also be used to estimate the gearmesh losses The losses in the gear mesh are dependant on numerous factorsthe surface parameters such as roughness [33] waviness and topology and thegeometrical errors of the involute profile Also the type of lubricant and theadditives in the lubricant as well as the lubrication film thickness will influencethe efficiency Different materials have different losses as the materials affinityto bond to itself differs The tests performed in Paper A showed no significantimpact on the gear mesh efficiency between high quality gears and gears withlow quality The gear quality class is determined by the single worst parameter

35

CHAPTER 5 DISCUSSION

in a long list of parameters One or several of these parameters could have alarge impact on the gear mesh efficiency however the overall gear quality classis not suitable to obtain an estimate of the gear mesh losses

Does the gear mesh efficiency differ significantly betweenhoned PM steel gears and honed gears made from wroughtsteel

From the measurements conducted in Paper A it is clear that there is no sig-nificant difference in the gear mesh efficiency between honed wrought steel andhoned PM steel gears Although the signal to noise ration of the PM is higherindicating a larger scatter in the measurements there is little to no differencein the mean efficiency The difference is within the test rigs reassembly errorinvestigated by Andersson et al [29] There are larger differences when com-paring surface treatment methods such as ground superfinished and honedsurfaces It should also be noted that different surfaces perform optimally atdifferent speeds The superfinished gears have low losses at high speed buthave higher losses at low speeds [19] making the decision process even morecomplicated as the surface finish method should ideally be selected dependingon the operating conditions

Can micropitting initiation mechanisms be evaluated usingsurface profile measurements during an FZG pitting test

In order to evaluate the initiation of micropitting one needs to be able toaccurately monitor the gear flank Also the method of monitoring the surfaceneeds to be sensitive enough to be able to differentiate profile changes on a submicron level Gears are usually measured in coordinate measuring machinesusing a sparse grid and a ball probe This method does not have enoughresolution to detect the initiation of micropitting Without an optimisationroutine the surface profile measurements measured with a stylus instrumentwould not be suitable to monitor micropitting initiation as the measurementerrors and misalignment distort the result However with a refined optimisationroutine (presented in Papers B and D) it is possible to take advantage of thehigh resolution of the stylus instrument and precisely track surface changes overthe course of a pitting test Figure 38 shows clearly that the surface startsto change long before any damage is visible to the naked eye The damageprogresses until a large pitting damage suddenly appears

36

51 RESEARCH QUESTIONS

How can the gear surface finishing method affect the surfacedamage mechanism for wrought steel gears

There is a general consensus that the pitting life of a gear can be prolonged byreducing the surface roughness eg using a superfinishing process [40]ndash[42]Jao et al [43] found that for tests performed in the FZG test rig using gearswith rougher surfaces increased the pitting life This finding was also confirmedin a test series performed in Paper C where the ground gears outlived thesmoother superfinished gears by a factor of ten

The outcome of the test was unexpected as no signs of damage were visibleon the gears with superfinished surface until there was suddenly severe damageon several teeth Upon further inspection it was concluded that no indication ofwear could be discerned on any of the profile measurements before the failureappeared For the ground gears the profile measurements showed signs of wearmicropitting damage in the root at LS 9 This damage progressed graduallyfor each consecutive test until a large pitting damage occurred at the pitchWinkelmann et al [42] performed a study using a similar gear test methodologythe main difference was the lubricant and lubricant temperature and that thesuperfinished gears were processed to an even smoother surface finish Theyfound that the superfinished gears outperformed the ground gears and theywere able to run the superfinished gears to run-out

In Paper C the specific film thickness was calculated for both the groundand the superfinished gears using the measured surface profiles as input tocalculate the local contact pressure distribution For the ground gears the filmthickness is above one at LS 7 and at one at LS9 while for the superfinishedgears the transition is pushed upwards to LS 10 In theory a specific filmthickness of greater than one ensures that the surfaces are completely separatedby the lubrication film [44] It is clearly visible on the profile measurements thatprofile changes start at the load where the specific film thickness can no longerseparate the surfaces

Any surface defects such as cracks initiating in the root of the gear cantherefore be worn away An equilibrium between the surface profile wear andcrack initiation is thus achieved [45] [46] For the gear with the superfinishedsurface no such equilibrium is achieved the surface is smooth enough to preventwear from removing surface cracks However in this case the surface was notsmooth enough to prevent the formation of said cracks Thus enabling crackgrowth in the surface layer where the tip of the gear repeatably impacts in theroot Paper E shows cross sections from the root the figure clearly shows thatfor the superfinished surface the whole surface layer is filled with micro cracks

As the pitting test progresses the crack density in the root increases atsome point the cracks change direction and start to propagate towards the tipof the gear The process is rapid and peels off the entire width of the tooth

37


surface from the root and towards the tip the tooth flank of several of thepinion teeth was completely gone The phenomena observed during testing aremost likely due to the test method In FZG pitting tests the gear geometrieshave neither tip nor root relief For the standard ground wrought steel gearsthis poses no issue as the gear geometry will wear and reduce the initial stressFor other materials surface finishing methods the absence of a tip relief cangreatly impact the test results negatively

How do the principal surface damage mechanisms comparebetween wrought steel and PM steel gearsThe damage on the PM material differs depending on the surface finishingmethod On the ground gears micropitting is detected at LS 8 while for thesuperfinished PM the damage starts at LS 9 The trend is similar to the wroughtsteel counterpart however the load where the damage is observed is lowerUtilizing the large quantity of measurement data recorded enables an in-depthanalysis of the surface changes during the pitting tests Paper E presentsfigures where the the surface roughness can be viewed in regard to either theposition along the tooth flank or in regard to the tested load stage The damagepattern along the tooth profile is similar when comparing the materials with thesame surface finish There are however differences between the ground andsuperfinished gears The ground gears exhibit damage where the tip interactsin the root this region is followed by a region in the dedendum where almostno change is measured The pitting damage appears near the pitch wear canalso be seen on the tip The superfinished gears do not share the same damagepattern the damage appears all along the gear tooth flank with no unscathedregions

For the PM materials the surface finishing processes are more difficult todistinguish between one contributing factor is that the tested maximum loadchosen was too high A consequence of this is that all except one test failed atthe first run of the maximum load The one test that survived was run a secondtime resulting in a catastrophic root breakage failure Another contributingfactor is that the superfinishing process only reduced the surface roughnesslevel marginally With the limitations discussed it is difficult to conclude if thedifferences in appearance are solely due to differences in the surface finishingoperations or if the difference is due to the natural and expected scatter inpitting life

One key difference between the wrought steel and the PM steel is thatthe wrought steel only showed signs of surface-initiated damage while for thePM material there was a combination between surface and sub-surface initiateddamage Within the PM material there were cracks visible propagating betweenpores it is obvious that the porosity close to the surface reduces the strength

38

52 OTHER ASPECTS OF THE THESIS RESULTS

of the PM material considerably However it is worth noting that the pores arenatural to the PM material and the properties of the material are both reliableand predictable The strength of the PM material is usually adequate even forhighly loaded components In order for a PM material to be a valid alternativeto wrought steel in all applications the negative influence of the surface layerporosity needs to be mitigated This can be achieved in several ways either byusing an HIP process effectively closing all the porosity or by increasing thedensity in the surface layer ie performing a surface rolling process [9] It isalso important to notice that the limited life of the PM material could be anartefact of the testing methodology The lack of a tiproot relief will createviolent impacts at high sliding speed that affects both the surface as well asthe material beneath the surface negatively

52 Other aspects of the thesis resultsThe increasing demand for electrification of personal vehicles poses new designchallenges for gearbox manufacturers An electric motor can be designed todrive a vehicle using a single fixed gear ratio However Ahssan et al [47]who studied different configurations of e-powertrains found that the increasedcost of adding more gears is recovered by the increase in efficiency Thusa smaller battery pack is required and the electric power consumption costdecreases throughout the lifetime [47] There is a trend in the industry toincrease the operational speed of the electric motor in order to increase thepower density thus enabling more compact drivetrains [48] EV drivetrainscould therefore operate at speeds in excess of 15K RPM [12] [48] significantlyhigher than the normal operating speed of the ICE There is research beingconducted on even higher operational speeds 50K [11] and 100K [49] RPM Asthe electric power source is silent compared to an internal combustion engineother sources of noise such as wind road and transmission noise are perceivedas more dominant [50] Running the gearbox at high speed increases the numberof contacts which increases damage from surface fatigue mechanisms suchas micropitting and pitting Gearbox efficiency is important as it is one ofthe dominant causes of friction losses in EVs [51] The increasing number ofcontacts in high-speed gearboxes and the cost of battery packs further increasethe importance of designing for high gear mesh efficiency Surface fatiguedamage and gearbox efficiency is therefore an important consideration in EVtransmission design

In order to reduce environmental noise pollution EV manufacturers needto consider gear transmission design influence on noise The sound originatingfrom the electric powertrain can be divided into electromagnetic noise inverterswitching noise and gear whine Fang et al [52] found that the gear whine hadthe greatest contribution to the perceived sound quality while Akerblom [53]

39


stated that the gear noise should be 10 dB lower than other sources of noise inorder not to be intrusive Gear whine is also dominant in the cabin [50]

40

Chapter 6

Conclusions

The following conclusions can be made from the research questions presentedin Section 15

bull The DIN quality class is not suitable to estimate the efficiency of gears

bull The efficiency of honed PM and wrought steel gears are not statisticallydifferent as the magnitude of the difference is comparable to the naturalscatter of reassembling the test rig although the PM material had anoverall larger scatter in the measured efficiency

bull It is possible to use the methodology presented to evaluate and monitorthe initiation of micropitting damage this can be done as the accuracyof the profile measurements and the sensitivity of the stylus instrumentis high

bull The superfinished wrought steel gears failed prematurely in the pittingtest This was attributed to the lack of a tip relief that caused the build-up of cracks in the sub-surface of the root leading to a total collapse ofthe gear tooth flank On the ground gear this phenomenon is avoided aswear removes the cracks and thus prolongs the gear life

bull Powder metal gears and wrought steel gears exhibit comparable surfacedamage behaviour although the PM material begins to wear at a slightlylower load

bull The wrought steel gears only showed evidence of surface fatigue damagewhile the PM material had a combination of surface and sub-surfaceinitiated fatigue damage

41

Chapter 7

Future Work

During the time frame of doing the research for and writing this thesis it wasfound that the wear and damage of the PM material gears initiated at a lowerload level than for the wrought steel gears The difference could potentially becaused by the difference in density Holmberg et al [54] found that the rollingcontact fatigue could be increased by a factor four when going from a densityof 68 to 715 gcm3 By further increasing the density it might be possibleto further reduce the performance gap to wrought steel Therefore it wouldbe interesting to perform tests with PM materials with higher density than thecurrent maximum of 73 gcm3 Inclusion of a nano powder in the powdermixture is one solution to potentially achieve an increase in density

Several interesting areas would benefit from further research in order toincrease the fundamental understanding of pitting micropitting damage aswell as PM materials

bull How does the inclusion of a tiproot relief affect the pitting life results

bull Can a nano particle enhanced PM material achieve closed porosity andis this a viable option in creating high performance PM components

bull Could the efficiency and pitting life of gears be improved by the use ofcoatings eg DLC coatings

bull Could PM gears be used in EV transmissions as a mean of reducing thegearbox noises

bull How much can the pitting life performance be improved by densifying thesurface of PM gears

43

AppendixAppendix AThe constants used in Equation 36 are presented in Table 71

Table 71 Constants for A B and C in dip lubrication

61 Nm 94 Nm 183 NmA 219times 10minus5 267times 10minus5 278times 10minus5

B 126 341 651C minus580times 10minus3 minus100times 10minus2 minus540times 10minus3

Bibliography

[1] United Nations ldquoSummary of the Paris Agreementrdquo United NationsFramework Convention on Climate Change pp 27ndash52 2015 [Online]Available httpbigpictureunfcccintcontent-the-paris-agreemen

[2] W Schatt and K-P Wieters Powder metallurgy processing and materi-als W Schatt Ed European powder metallurgy association 1997 isbn1899072055

[3] European Powder Metallurgy Association - Economic Advantages [On-line] Available https www epma com powder - metallurgy -economic-advantages

[4] B Kianian ldquoComparing acquisition and operation life cycle costs of pow-der metallurgy and conventional wrought steel gear manufacturing tech-niquesrdquo Procedia CIRP vol 81 pp 1101ndash1106 2019 issn 22128271doi 101016jprocir201903260 [Online] Available httpsdoiorg101016jprocir201903260

[5] G Kotthoff ldquoNVH Potential of PM Gears for Electrified DrivetrainsrdquoGear Technology no October p 4 2018 [Online] Available httpswwwgeartechnologycomarticles0918NVH_Potential_of_PM_Gears_for_Electrified_Drivetrains

[6] T Background ldquoCompressibility and Compactibility of Metal Powders[1]rdquoPowder Metallurgy pp 171ndash178 2018 doi 1031399asmhbv07a0006032

[7] H Danninger and C Gierl-Mayer ldquoAdvances in Powder Metallurgyrdquo inProperties Processing and Applications ser Woodhead Publishing Seriesin Metals and Surface Engineering I Chang and Y Zhao Eds Cam-bridge UK Woodhead Publishing 2013 ch 7 isbn 978-0-85709-420-9doi httpsdoiorg10153397808570989002149 [Online]Available httpwwwsciencedirectcomsciencearticlepiiB9780857094209500076

45

BIBLIOGRAPHY

[8] A Buch and S Goldschmidt ldquoInfluence of porosity on elastic moduliof sintered materialsrdquo Materials Science and Engineering vol 5 no 2pp 111ndash118 1970 issn 0025-5416 doi https doi org 10 1016 0025 - 5416(70 ) 90040 - 6 [Online] Available http www sciencedirectcomsciencearticlepii0025541670900406

[9] A Flodin ldquoPowder metal gear technology A review of the state of theartrdquo American Gear Manufacturers Association Fall Technical Meeting2015 AGMA FTM 2015 no March pp 67ndash77 2015

[10] A Khodaee ldquoInnovative Manufacturing Method for Gears for HeavyVehicle Applicationrdquo PhD dissertation KTH Production Engineering2021 p 93 isbn 978-91-7873-794-9

[11] M Mileti P Strobl H Pflaum and K Stahl ldquoDesign of a Hyper-High-Speed Powertrain for EV to Achieve Maximum Rangesrdquo Berlin SpringerBerlin Heidelberg 2020 pp 265ndash273 isbn 9783662588666 doi 101007978-3-662-58866-6 [Online] Available httpdxdoiorg101007978-3-662-58866-6_21

[12] D Fodorean L Idoumghar M Brevilliers P Minciunescu and C IrimialdquoHybrid Differential Evolution Algorithm Employed for the Optimum De-sign of a High-Speed PMSM Used for EV Propulsionrdquo IEEE Transactionson Industrial Electronics vol 64 no 12 pp 9824ndash9833 2017 issn02780046 doi 101109TIE20172701788

[13] B Kianian and C Andersson ldquoAnalysis of Manufacturing Costs for Pow-der Metallurgy (PM) Gear Manufacturing Processes A Case Study of aHelical Drive Gearrdquo in EcoDesign and Sustainability I ser SustainableProduction Life Cycle Engineering and Management Singapore SpringerSingapore 2020 pp 471ndash487

[14] A Simchi and A Nojoomi ldquoWarm compaction of metallic powdersrdquoAdvances in Powder Metallurgy Properties Processing and Applicationspp 86ndash108 2013 doi 1015339780857098900186

[15] E Fritz Klocke and A Kuchie ldquoHoningrdquo in Manufacturing Processes2 Grinding Honing Lapping Berlin Heidelberg Springer Berlin Heidel-berg 2009 pp 1ndash36 isbn 978-3-540-92259-9 doi 101007978-3-540-92259-9_7 [Online] Available httpsdoiorg101007978-3-540-92259-9_7

[16] H J Watson ldquoShaving and Lappingrdquo Modern Gear Production pp 240ndash255 1970 doi 101016b978-0-08-015835-850017-1

[17] D T Jelaska Gears and Gear Drives Hoboken Hoboken Wiley 2012isbn 9781119941309 doi 1010029781118392393

[18] R Schmitt CIRP Encyclopedia of Production Engineering 2014 isbn9783642206177 doi 101007978-3-642-20617-7

46

BIBLIOGRAPHY

[19] M Andersson M Sosa and U Olofsson ldquoThe effect of running-in onthe efficiency of superfinished gearsrdquo Tribology International vol 93pp 71ndash77 2016 issn 0301-679X doi httpdxdoiorg101016jtriboint201508010 [Online] Available httpwwwsciencedirectcomsciencearticlepiiS0301679X15003527

[20] S Li and A Kahraman ldquoA micro-pitting model for spur gear contactsrdquoInternational Journal of Fatigue vol 59 pp 224ndash233 2014 issn 01421123doi 101016jijfatigue201308015 [Online] Available httpdxdoiorg101016jijfatigue201308015

[21] V Vullo Gears Volume 2 Analysis of Load Carrying Capacity and StrengthDesign 1st ed 20 ser Springer Series in Solid and Structural Mechanics11 2020 isbn 3-030-38632-5

[22] D Mallipeddi M Norell V M Naidu X Zhang M Naslund and LNyborg ldquoMicropitting and microstructural evolution during gear testing-from initial cycles to failurerdquo Tribology International vol 156 no July2020 2021 issn 0301679X doi 101016jtriboint2020106820

[23] I S Al-Tubi H Long J Zhang and B Shaw ldquoExperimental and ana-lytical study of gear micropitting initiation and propagation under varyingloading conditionsrdquo Wear vol 328-329 pp 8ndash16 2015 issn 00431648doi 101016jwear201412050 [Online] Available httpdxdoiorg101016jwear201412050

[24] D Hannes and B Alfredsson ldquoModelling of surface initiated rollingcontact fatigue damagerdquo Procedia Engineering vol 66 no Decemberpp 766ndash774 2013 issn 18777058 doi 101016jproeng201312130

[25] M Sosa S Bjorklund U Sellgren and U Olofsson ldquoIn situ surface char-acterization of running-in of involute gearsrdquo Wear vol 340-341 pp 41ndash46 2014 issn 00431648 doi 101016jwear201503008

[26] E Bergstedt A Holmberg P Lindholm and U Olofsson ldquoInfluenceof the DIN 3962 Quality Class on the Efficiency in Honed Powder Metaland Wrought Steel Gearsrdquo Tribology Transactions vol 0 no 0 pp 1ndash9Aug 2020 issn 1040-2004 doi 1010801040200420201790707[Online] Available httpsdoiorg101080104020042020179070720httpswwwtandfonlinecomdoifull1010801040200420201790707

[27] X LI and U Olofsson ldquoFZG gear efficiency and pin-on-disc frictionalstudy of sintered and wrought steel gear materialsrdquo Tribology lettersvol 60 no 9 2015 issn 1023-8883 doi 101007s11249- 015-0582-6

47

BIBLIOGRAPHY

[28] X Li M Sosa M Andersson and U Olofsson ldquoA study of the efficiencyof spur gears made of powder metallurgy materials - ground versus super-finished surfacesrdquo Tribology International vol 95 no 1 pp 211ndash2202016 issn 0301-679X doi 101016jtriboint201511021

[29] M Andersson M Sosa S Sjoberg and U Olofsson ldquoEffect of AssemblyErrors in Back-to-Back Gear Efficiency Testingrdquo International Gear Con-ference 2014 pp 784ndash793 Dec 2014 doi 1015339781782421955784

[30] S Sjoberg M Sosa M Andersson and U Olofsson ldquoAnalysis of ef-ficiency of spur ground gears and the influence of running-inrdquo Tribol-ogy International vol 93 pp 172ndash181 2016 issn 0301-679X doi101016jtriboint201508045

[31] M Andersson M Sosa and U Olofsson ldquoEfficiency and temperature ofspur gears using spray lubrication compared to dip lubricationrdquo JournalOf Engineering Tribology 2017 [Online] Available httpwwwdiva-portalorg20httpurnkbseresolveurn=urnnbnsekthdiva-202984

[32] D W Gesellschaft ldquoShort Test Procedure for the investigation of themicropitting load capacityof gear lubricantsrdquo DGMK Information sheetvol 2002 no August 2002

[33] S Seetharaman A Kahraman M D Moorhead and T T Petry-JohnsonldquoOil Churning Power Losses of a Gear Pair Experiments and Model Val-idationrdquo Journal of Tribology vol 131 no 2 p 022 202 2009 issn07424787 doi 10111513085942 [Online] Available httptribology asmedigitalcollection asme org article aspx articleid=1468269

[34] M Tu M Sosa M Andersson and U Olofsson ldquoModelling power lossesof cylindrical roller bearings in an FZG gear test rigrdquo Bearing WorldJournal vol 2 pp 51ndash59 2017

[35] J Lin C Teng E Bergstedt H Li Z Shi and U Olofsson ldquoA quantita-tively distributed wear-measurement method for spur gears during micro-pitting and pitting testsrdquo Tribology International vol 157 no November2020 p 106 839 2020 issn 0301679X doi 101016jtriboint2020106839 [Online] Available httpsdoiorg101016jtriboint2020106839

[36] V Vullo Gears Volume 1 Geometric and Kinematic Design ChamCham Springer International Publishing vol 10 doi 101007978-3-030-36502-8

[37] S J Ahn Least Squares Orthogonal Distance Fitting of Curves andSurfaces in Space 2004 vol 3151 isbn 3540239669

48

BIBLIOGRAPHY

[38] M Krystek ldquoForm filtering by splinesrdquo Measurement Journal of theInternational Measurement Confederation vol 18 no 1 pp 9ndash15 1996issn 02632241 doi 1010160263-2241(96)00039-5

[39] DIN 3962-11978-08 Tolerances for Cylindrical Gear Teeth Tolerances forDeviations of Individual Parameters BEUTH 1978 [Online] Availablehttpswwwbeuthdeenstandarddin-3962-1722996

[40] H Ronkainen O Elomaa S Varjus L Kilpi T Jaatinen and J Kosk-inen ldquoThe influence of carbon based coatings and surface finish onthe tribological performance in high-load contactsrdquo Tribology Interna-tional vol 96 pp 402ndash409 2016 issn 0301679X doi 101016jtriboint201504019 [Online] Available httpdxdoiorg101016jtriboint201504019

[41] T L Krantz ldquoThe Influence of Roughness on Gear Surface Fatigue TheNASA STI Program Office in Profilerdquo no October 2005 2005

[42] L Winkelmann E-S O and B M ldquoThe effect of superfinishing ongear micropittingrdquo Gear Technololgoy vol 2 no April pp 60ndash65 2009

[43] T Jao ldquoInfluence of Surface Roughness on Gear Pitting Behaviorrdquovol 129 no May 2009 pp 595ndash602 2007 issn 07436858 doi 10111512736451

[44] B I H P H Dawson ldquoEffect of Metallic Contact on the Pitting ofLubricated Rolling Surfacesrdquo vol 180 no I pp 95ndash100 1962

[45] G E Morales-Espejel and V Brizmer ldquoMicropitting modelling in rollingndashslidingcontacts Application to rolling bearingsrdquo Tribology Transactions vol 54no 4 pp 625ndash643 2011 issn 1547397X doi 101080104020042011587633

[46] H Fan L M Keer W Cheng and H S Cheng ldquoCompetition BetweenFatigue Crack Propagation and Wearrdquo Journal of Tribology vol 115no 1 pp 141ndash147 1993 issn 07424787 doi 10111512920967

[47] M R Ahssan M M Ektesabi and S A Gorji ldquoElectric Vehicle withMulti-Speed Transmission A Review on Performances and Complexi-tiesrdquo SAE International Journal of Alternative Powertrains vol 7 no 2pp 169ndash182 2018 issn 21674205 doi 10427108-07-02-0011

[48] I Lopez E Ibarra A Matallana J Andreu and I Kortabarria ldquoNextgeneration electric drives for HEVEV propulsion systems Technologytrends and challengesrdquo Renewable and Sustainable Energy Reviews vol 114no April 2018 p 109 336 2019 issn 18790690 doi 101016jrser2019109336 [Online] Available httpsdoiorg101016jrser2019109336

49

BIBLIOGRAPHY

[49] A Damiano A Floris G Fois I Marongiu M Porru and A SerpildquoDesign of a High-Speed Ferrite-Based Brushless DC Machine for Elec-tric Vehiclesrdquo IEEE Transactions on Industry Applications vol 53 no 5pp 4279ndash4287 2017 issn 00939994 doi 10 1109 TIA 2017 2699164

[50] Y Cao D Wang T Zhao X Liu C Li and H Hou ldquoElectric VehicleInterior Noise Contribution Analysisrdquo SAE Technical Papers 2016 issn01487191 doi 1042712016-01-1296

[51] L I Farfan-Cabrera ldquoTribology of electric vehicles A review of criticalcomponents current state and future improvement trendsrdquo TribologyInternational vol 138 no April pp 473ndash486 2019 issn 0301679Xdoi 101016jtriboint201906029 [Online] Available httpsdoiorg101016jtriboint201906029

[52] Y Fang and T Zhang ldquoSound quality investigation and improvement ofan electric powertrain for electric vehiclesrdquo IEEE Transactions on Indus-trial Electronics vol 65 no 2 pp 1149ndash1157 2017 issn 02780046doi 101109TIE20172736481

[53] M Akerblom ldquoGearbox noise Correlation with transmission error andinfluence of bearing preloadrdquo PhD dissertation KTH Machine Design(Dept) 2008 pp viii 20

[54] A Holmberg M Andersson and A K Rudolphi ldquoRolling fatigue life ofPM steel with different porosity and surface finishrdquo Wear vol 426-427pp 454ndash461 2019 issn 00431648 doi 101016jwear201901006

50

A Comparative Investigation of Gear Performance Between Wrought and Sintered Powder Metallurgical SteelUtilizing In-situ Surface Profile Measurements to Investigate the Initiation and Evolution of Micropitting and Pitting Damage

EDWIN BERGSTEDT

Doctoral Thesis in Machine DesignKTH Royal Institute of TechnologyStockholm Sweden 2021

Academic Dissertation which with due permission of the KTH Royal Institute of Technology is submitted for public defence for the Degree of Doctor of Engineering on Friday June 4th online via Zoom 2021 at 1000 AM


Abstract
















J

iii







iv






v


vi

Contents









32 Gear specimen 18

vii

CONTENTS






6 Conclusions 41

7 Future Work 43

viii

Nomenclature

Abbreviations

EV Electric Vehicle


GR Ground (Surface)


HO Honed (Surface)


LS Load Stage





W Wrought (Steel)








ix

NOMENCLATURE






u Gear ratio [-]












Gear Parameters




b Face width [mm]



m Module [-]

x

NOMENCLATURE





σ20III





rB Base circle [mm]













R Rotational matrix




xi

NOMENCLATURE




Subscripts

1 Pinion

2 Gear

xii

Chapter 1

Introduction



1








2

12 SUSTAINABILITY




3










4

Chapter 2





Generating methods


5






Forming methods


6




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50


Abstract
















J

iii







iv






v


vi

Contents









32 Gear specimen 18

vii

CONTENTS






6 Conclusions 41

7 Future Work 43

viii

Nomenclature

Abbreviations

EV Electric Vehicle


GR Ground (Surface)


HO Honed (Surface)


LS Load Stage





W Wrought (Steel)








ix

NOMENCLATURE






u Gear ratio [-]












Gear Parameters




b Face width [mm]



m Module [-]

x

NOMENCLATURE





σ20III





rB Base circle [mm]













R Rotational matrix




xi

NOMENCLATURE




Subscripts

1 Pinion

2 Gear

xii

Chapter 1

Introduction



1








2

12 SUSTAINABILITY




3










4

Chapter 2





Generating methods


5






Forming methods


6




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50














J

iii







iv






v


vi

Contents









32 Gear specimen 18

vii

CONTENTS






6 Conclusions 41

7 Future Work 43

viii

Nomenclature

Abbreviations

EV Electric Vehicle


GR Ground (Surface)


HO Honed (Surface)


LS Load Stage





W Wrought (Steel)








ix

NOMENCLATURE






u Gear ratio [-]












Gear Parameters




b Face width [mm]



m Module [-]

x

NOMENCLATURE





σ20III





rB Base circle [mm]













R Rotational matrix




xi

NOMENCLATURE




Subscripts

1 Pinion

2 Gear

xii

Chapter 1

Introduction



1








2

12 SUSTAINABILITY




3










4

Chapter 2





Generating methods


5






Forming methods


6




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50







iv






v


vi

Contents









32 Gear specimen 18

vii

CONTENTS






6 Conclusions 41

7 Future Work 43

viii

Nomenclature

Abbreviations

EV Electric Vehicle


GR Ground (Surface)


HO Honed (Surface)


LS Load Stage





W Wrought (Steel)








ix

NOMENCLATURE






u Gear ratio [-]












Gear Parameters




b Face width [mm]



m Module [-]

x

NOMENCLATURE





σ20III





rB Base circle [mm]













R Rotational matrix




xi

NOMENCLATURE




Subscripts

1 Pinion

2 Gear

xii

Chapter 1

Introduction



1








2

12 SUSTAINABILITY




3










4

Chapter 2





Generating methods


5






Forming methods


6




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50






v


vi

Contents









32 Gear specimen 18

vii

CONTENTS






6 Conclusions 41

7 Future Work 43

viii

Nomenclature

Abbreviations

EV Electric Vehicle


GR Ground (Surface)


HO Honed (Surface)


LS Load Stage





W Wrought (Steel)








ix

NOMENCLATURE






u Gear ratio [-]












Gear Parameters




b Face width [mm]



m Module [-]

x

NOMENCLATURE





σ20III





rB Base circle [mm]













R Rotational matrix




xi

NOMENCLATURE




Subscripts

1 Pinion

2 Gear

xii

Chapter 1

Introduction



1








2

12 SUSTAINABILITY




3










4

Chapter 2





Generating methods


5






Forming methods


6




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50


vi

Contents









32 Gear specimen 18

vii

CONTENTS






6 Conclusions 41

7 Future Work 43

viii

Nomenclature

Abbreviations

EV Electric Vehicle


GR Ground (Surface)


HO Honed (Surface)


LS Load Stage





W Wrought (Steel)








ix

NOMENCLATURE






u Gear ratio [-]












Gear Parameters




b Face width [mm]



m Module [-]

x

NOMENCLATURE





σ20III





rB Base circle [mm]













R Rotational matrix




xi

NOMENCLATURE




Subscripts

1 Pinion

2 Gear

xii

Chapter 1

Introduction



1








2

12 SUSTAINABILITY




3










4

Chapter 2





Generating methods


5






Forming methods


6




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50

Contents









32 Gear specimen 18

vii

CONTENTS






6 Conclusions 41

7 Future Work 43

viii

Nomenclature

Abbreviations

EV Electric Vehicle


GR Ground (Surface)


HO Honed (Surface)


LS Load Stage





W Wrought (Steel)








ix

NOMENCLATURE






u Gear ratio [-]












Gear Parameters




b Face width [mm]



m Module [-]

x

NOMENCLATURE





σ20III





rB Base circle [mm]













R Rotational matrix




xi

NOMENCLATURE




Subscripts

1 Pinion

2 Gear

xii

Chapter 1

Introduction



1








2

12 SUSTAINABILITY




3










4

Chapter 2





Generating methods


5






Forming methods


6




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50

CONTENTS






6 Conclusions 41

7 Future Work 43

viii

Nomenclature

Abbreviations

EV Electric Vehicle


GR Ground (Surface)


HO Honed (Surface)


LS Load Stage





W Wrought (Steel)








ix

NOMENCLATURE






u Gear ratio [-]












Gear Parameters




b Face width [mm]



m Module [-]

x

NOMENCLATURE





σ20III





rB Base circle [mm]













R Rotational matrix




xi

NOMENCLATURE




Subscripts

1 Pinion

2 Gear

xii

Chapter 1

Introduction



1








2

12 SUSTAINABILITY




3










4

Chapter 2





Generating methods


5






Forming methods


6




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50

Nomenclature

Abbreviations

EV Electric Vehicle


GR Ground (Surface)


HO Honed (Surface)


LS Load Stage





W Wrought (Steel)








ix

NOMENCLATURE






u Gear ratio [-]












Gear Parameters




b Face width [mm]



m Module [-]

x

NOMENCLATURE





σ20III





rB Base circle [mm]













R Rotational matrix




xi

NOMENCLATURE




Subscripts

1 Pinion

2 Gear

xii

Chapter 1

Introduction



1








2

12 SUSTAINABILITY




3










4

Chapter 2





Generating methods


5






Forming methods


6




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50

NOMENCLATURE






u Gear ratio [-]












Gear Parameters




b Face width [mm]



m Module [-]

x

NOMENCLATURE





σ20III





rB Base circle [mm]













R Rotational matrix




xi

NOMENCLATURE




Subscripts

1 Pinion

2 Gear

xii

Chapter 1

Introduction



1








2

12 SUSTAINABILITY




3










4

Chapter 2





Generating methods


5






Forming methods


6




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50

NOMENCLATURE





σ20III





rB Base circle [mm]













R Rotational matrix




xi

NOMENCLATURE




Subscripts

1 Pinion

2 Gear

xii

Chapter 1

Introduction



1








2

12 SUSTAINABILITY




3










4

Chapter 2





Generating methods


5






Forming methods


6




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50

NOMENCLATURE




Subscripts

1 Pinion

2 Gear

xii

Chapter 1

Introduction



1








2

12 SUSTAINABILITY




3










4

Chapter 2





Generating methods


5






Forming methods


6




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50

Chapter 1

Introduction



1








2

12 SUSTAINABILITY




3










4

Chapter 2





Generating methods


5






Forming methods


6




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50








2

12 SUSTAINABILITY




3










4

Chapter 2





Generating methods


5






Forming methods


6




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50

12 SUSTAINABILITY




3










4

Chapter 2





Generating methods


5






Forming methods


6




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50










4

Chapter 2





Generating methods


5






Forming methods


6




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50

Chapter 2





Generating methods


5






Forming methods


6




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50






Forming methods


6




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50




7






Die


Upper punch

Lower punch


8






9






10

23 GEAR TERMINOLOGY


Root Circle

Pitch Circle

Base Circle

Addendum

Dedendum

Addendum Circle



11





12





13



14

Chapter 3


31 Test equipment

311 FZG Test rig



15



1 2 3 54



16

31 TEST EQUIPMENT




17











18

33 TEST PROCEDURES








19





LS 3 4 5 6 7 8 9 10Torque [Nm] 353 608 941 1353 1834 2393 3020 3727

20

34 CALCULATIONS

Start


LS=3


LS

Measure profile

Pitting

Abort test

LS = LSmax

LS = LS + 1

Yes

Yes

No

No

Measure profile

Measure profile


at LSmax

No

Yes


34 Calculations



21


losses










TT otal

uT1(35)




TST A12 = An+ B

n+ C (36)




ω2

)(37)

22

34 CALCULATIONS



TGearminusMesh

uT1(38)





23




_

P0B

N

O

P0

y

x

Base Circle

T

BGenerating line

Gear tooth profile

P

r

rb

ϑ






24

34 CALCULATIONS


rmi= xmi

ymin

i=1 (310)




x = R (X minusX0) (311)



σ20I


σ20II



PTP = I =

1 0 00 1 00 0 1


25



mina=apar

minXprime

im

i=1

σ20(X primei (a)m

i=1)

(314)





σ20I


σ20II










26

34 CALCULATIONS




27



28

34 CALCULATIONS


29



λGFY = hY

Ra(318)




GFY (319)

Ra = Ra1 +Ra2

2 (320)





30

Chapter 4


Paper A


Paper B


31



Paper C


32


Paper D


33


Paper E


34

Chapter 5

Discussion




35







36








37






38





39



40

Chapter 6

Conclusions








41

Chapter 7

Future Work








43





Bibliography








45

BIBLIOGRAPHY












46

BIBLIOGRAPHY










47

BIBLIOGRAPHY











48

BIBLIOGRAPHY












49

BIBLIOGRAPHY







50

Doctoral Thesis in Machine Design A Comparative ...

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Transcript of Doctoral Thesis in Machine Design A Comparative ...