TOMSK POLYTECHNIC UNIVERSITY

Yu. B. Chervach, I.S. Okhotin

ENGINEERING METROLOGY IN MECHANICAL ENGINEERING

Tomsk Polytechnic University Publishing House 2013

UDC 621.81 (075.8) BBC 00000

C00 Chervach Yu.B., Okhotin I.S.

C00 Engineering Metrology in Mechanical Engineering: study aid / Yu.B. Chervach, I.S. Okhotin; Tomsk Polytechnic University. – Tomsk: TPU Publishing House, 2013, 100 p.

The book presents the basic concepts of engineering measurements in mechanical

engineering, relevant examples of size distribution calculation in inspection are consid-ered.

The book is recommended for English-speaking students following the Bachelor Degree Program in Mechanical Engineering at Tomsk Polytechnic University.

UDC 621.81 (075.8) BBC 00000

Linguistic Advisor Manager of the

Department for Academic Affairs of the Institute of Cybernetics, TPU E.A. Panasenko

Reviewers

Doctor of Science (Technical) Associate professor of the

Department of Automated Mechanical Manufacturing Engineering, TPU V.F. Skvortsov

Deputy Director for Manufacturing of “Center for Precision Machining”, Limited Liability Company

V.M. Gusev

© STE HPT TPU, 2013 © Chervach Yu.B., Okhotin I.S., 2013 © Design. Tomsk Polytechnic University

Publishing House, 2013

3

Preface Present-day mechanical engineering can be characterized as inter-

changeable high-performance and precise manufacturing. Interchangeable manufacturing implies that mating parts are often made not only by different people, but also on different machines, in different shops, and sometimes even in different cities and countries and at different times.

Such interchangeable production is provided by the relevant documenta-tion, machine tools, fixtures, cutting tools and the availability of appropriate measuring tools that ensure required accuracy and performance of measure-ments performed in different workplaces, by different operators.

The main type of measurements in mechanical engineering is the meas-urement of linear and angular dimensions.

90-95% of all measurements in mechanical engineering are measure-ment of linear dimensions. In the electric machine engineering this type of measurement is about 80%.

The proposed book is intended to facilitate study of the course “Engi-neering measurements in mechanical engineering” by the students that follow the Bachelor Degree Program 150700 "Mechanical Engineering".

Issues of the engineering measurements are considered in many publica-tions, but generalized textbook or study aid on this subject is unheard.

The given book presents fundamentals of the mechanical engineering measurements.

The first section of the book provides an overview of the engineering measurements and information on the legal basis of metrology.

The second section of the book gives the classification of the types and methods of measurements in mechanical engineering.

The third section introduces basic, additional and derived units of the In-ternational System of Units of physical quantities.

The fourth section provides a classification of measurands and values of measurands of the objects being measured.

The fifth section outlines the standard conditions for linear and angular measurements in accordance with GOST 8.050-73.

The sixth section is devoted to the means of measurement: measurement standards, measures, reference instruments, gauge blocks, angle blocks and detailed metrological characteristics and forms of application of the means. In addition, the section describes the procedure of dissemination of standards (transferring of units of physical quantities from the standards to the measur-ing means of lower ranks), classifies measuring instruments and devices, and indicates metrological parameters and characteristics of the measuring in-struments.

4

In the seventh section the types of measurement errors and analysis of the causes for the errors are examined.

The eighth section provides methods for ensuring the traceability and accuracy of measurements, the structure of verifications, inspections and ex-aminations of measuring means and structure of the mandatory state testing of measuring instrumentation.

The ninth section is devoted to the structure of the product quality con-trol.

The tenth section examines implementation of measurement and inspec-tion, the selection of the universal means of measurement and inspection, and accuracy of the means. Procedure and examples of the measurement results analysis are also given.

The book is recommended for students that study course “Engineering measurements in mechanical engineering” within the Mechanical Engineer-ing Program. The material of the book can be useful in preparing graduation thesis.

5

CONTENTS

Preface .......................................................................................................... 3 CONTENTS ................................................................................................. 5 1. General Concepts. Legal Basis of Metrology.......................................... 7 2. Types and Methods of Measurements .................................................... 9 3. International System of Units ................................................................ 14

3.1. SI base units ..................................................................................... 14 3.2. SI derived units ................................................................................ 15

4. Objects of Measurement ........................................................................ 17 4.1. Measurands ...................................................................................... 17 4.2. Dimension of a measurand .............................................................. 18

5. Standard Conditions for Linear and Angular Measurements ............ 20 6. Means of Measurement ......................................................................... 22

6.1 Measurement Standards .................................................................. 22 6.2 Measures and Reference Measuring Instruments .......................... 25 6.3 Gauge Blocks..................................................................................... 27 6.4 Angle Gauge Blocks .......................................................................... 40 6.5 Transfer of Physical Quantity .......................................................... 47 6.6 Measuring Instruments and Devices ............................................... 49 6.7 Metrological Parameters and Characteristics of Measuring Instruments ............................................................................................. 50

7. Measurement Errors and Causes of the Errors ................................... 53 8. Measurement Traceability Assurance .................................................. 56

8.1 Verification, Inspection and Expertise of Measuring Instruments 58 8.2 State Testing of Measuring Instruments ......................................... 59

9. Product Quality Control ........................................................................ 61 9.1 Types of Inspection ........................................................................... 61

10. Measurement and Inspection of the Product Parameters ................. 64 10.1 Measurement and Inspection ......................................................... 64 10.2 Selection of Means of Measurement and Inspection ..................... 65 10.3 Accuracy of Means of Measurement and Inspection .................... 66 10.4 Measurement Results Analysis ...................................................... 70 10.5 Examples of Measurement Results Analysis ................................. 77

6

10.6 Example of Creating Frequency Polygon and Histogram in Excel 2007 ......................................................................................................... 84 10.7 Example of Creating Histogram, Polygon and Curve of Normal Distribution in Statistica 7.0 .................................................................. 87

Conclusion .................................................................................................. 92 Index ........................................................................................................... 93 References .................................................................................................. 97

7

1. General Concepts. Legal Basis of Metrology Metrology is the science of measurements, methods and means to ensure

traceability and achieve required accuracy. Thus, metrology includes three interrelated problems: implementation of

measurement processes, measurement traceability assurance, methods and means of measurement.

The main tasks of metrology according to RMG 29-99 are: establishment of physical units; establishment of state standards and reference measuring instruments; development of the theory, methods and means of measurement and

inspection; measurement traceability assurance; development of methods for assessing errors and condition of the

means of measurement and inspection; development of methods of transferring units from standards or refer-

ence measurement means to the working measurements means. The legal framework of metrology includes the following general doc-

uments: RF Law “On ensuring the traceability of measurements”; RMG 29-99 “State system for ensuring the traceability of measure-

ments. Metrology. Key Terms and Definitions”; MI 2247-93 GSI “Metrology. Key Terms and Definitions”; GOST 8.417-2002 “GSI. Physical units”; PR 50.2.006-94 “GSI. Verification of measurement tools. Organiza-

tion and procedure of verification”; PR 50.2.009-94 “GSI. Procedure of testing and approval of the

measuring instruments type”; PR 50.2.014-94 “GSI. Accreditation of metrological services of legal

entities for the right for verification of measuring means”; MI 2277-94 “GSI. System of certification of measurements means.

The fundamentals and procedures of the certification”; PR 50.2.002-94 “GSI. Procedure of the state metrological supervision of

release, condition and use of measuring instruments; supervision of certified methods of measurement, measurement standards and compliance with met-rological rules and norms”.

The law “On ensuring the traceability of measurements” regulates the relations in the field of ensuring the traceability of measurements in the Rus-

8

sian Federation in accordance with the Constitution of the Russian Federa-tion. The law establishes the following: the basic concepts, such as: organiza-tion of governmental control of measurement traceability; regulations on measurements traceability, units and national standards of units; the means and methods of measurement. The law establishes the National service of le-gal metrology and other services aimed at ensuring traceability of measure-ments, metrology services of public authorities and legal entities, as well as the types and area of distribution of governmental metrological control and supervision. The law reflects the establishment of market relations in the Russian Federation, defining the basis of metrological services of the public authorities and legal entities. The activity of the metrological departments of the enterprises is beyond the legal metrology and is regulated by the econom-ic methods.

The activities that are not directly controlled by the government are sub-jected to the Russian Calibration System, which is aimed at ensuring the traceability of measurements too. The Calibration System is a system of agents and calibration activities aimed at ensuring the traceability of meas-urements in areas that are not subjected to the governmental metrological control and supervision, which act on the basis of the established require-ments for the organization and implementation of the process of calibration. The law provides for cooperation between the international and national sys-tems of measurement. This allows for the mutual recognition of the results of tests, calibration and certification, and to use international experience and trends of modern metrology. There are other laws, regulations and standardi-zation documents relating to the legal basis of metrology.

9

2. Types and Methods of Measurements Measurement is the process of empirical finding the physical quantity

value by measuring means. The result of the measuring process is the value of a physical quantity:

Q qU , where q – the numerical value of a physical quantity in the adopted unified units; U – the unit of a physical quantity. The value of the physical quantity Q, found in the measurement is called actual value.

Principle of measurement is a physical phenomenon or a combination of physical phenomena underlying the measurement. For example, measure-ment of the mass of a body by weighing it with gravity proportional to the mass, or temperature measurement using the thermoelectric effect.

Measurement method is a set of principles and means of measuring. Means of measurement are the means with specified metrological

characteristics used to perform measurements. There are various types of measurements. Classification of the meas-

urements is made on the basis of the measurand dependence on the time, type of measurement equation, conditions that determine accuracy of the meas-urement results and ways of expressing these results.

Depending on the nature of the measurand dependence on the time, all measurements are divided into static and dynamic measurements.

Static measurement is the measurement when the measurand remains constant over time. Examples of static measurements are the measurements of product dimensions, static pressure, temperature and other quantities.

Dynamic measurement is a measurement, during which the measurand varies with time, for example, measurement of pressure and temperature of gas being compressed in the engine cylinder.

Depending on the way of obtaining measurement result, which is deter-mined by the type of measurement equation, measurements are classified as direct, indirect, transposition and joint measurements.

Direct measurement is the measurement in which the value of the physical quantity is obtained directly from experimental data without any calculations. Direct measurements can be expressed by the following equa-tion: Q x , where Q – the desired value of the quantity to be measured, and x – the value obtained directly from the experimental data. Examples of such measure-

10

ments are measurement of the length by a ruler or tape-measure, measure-ment of the diameter by a vernier caliper or micrometer, measurement of the angle by a protractor, measurement of the temperature by a thermometer, etc.

Indirect measurement is the measurement in which the value of the quantity is determined on the basis of the known relationship between the de-sired value and quantities, the values of which are obtained through direct measurements. Thus, the quantity value is calculated according to the follow-ing equation: 1 2( , ,..., )nQ F x x x , where Q – the required value of the quantity; F – known functional depend-ence; 1 2, ,..., nx x x - the values obtained by direct measurements.

Examples of indirect measurements: calculation of the body volume from direct measurements of its geometrical dimensions, finding the specific electrical resistance of the conductor by measuring its resistance, length and cross-section area, measurement of the screw pitch diameter by three-wire method, etc. Indirect measurements are common in the cases when the de-sired value is impossible or too difficult to measure by the direct measure-ment. There are cases when the value can only be measured indirectly, e.g., sizes of the intra-atomic or astronomical order.

Transposition measurements are the measurements in which the val-ues of the measurands are determined from results of repeated measurements of one or more quantities of the same kind with different combinations of the measures or the quantities. Value of the desired quantity is determined by solving the set of equations formulated by the results of several direct meas-urements.

An example of the transposition measurements is finding of the mass of weights from a set, i.e. calibration by the known mass of one of the weight and by the results of direct measurements and comparison of masses of dif-ferent combinations of weights. Consider an example of transposition meas-urements which is the calibration of weights, consisting of weights of 1, 2, 2*, 5, 10 and 20 kg. Several weights (except 2*) represent standard measures of mass. An asterisk indicates a weight that has a value other than the exact value of 2 kg. The calibration is to determine the mass of each weight with the help of the standard measure, such as weight with mass of 1 kg. The measurements are performed by changing the combination of weights. We form the equations, where the numbers denote the mass of the weights, e.g., a 1ref denotes the mass of the standard weight of 1 kg weight, then: aref 11 ; bref 211 ; c 2*2 ; 1 2 2* 5 d and so on.

Additional weights, which must be added to the mass of the weight indi-cated on the right side of the equation, or subtracted from it to balance the

11

scales, are indicated as a , b , c , d . Solving this system of equations, we can determine the mass of each weight.

Joint measurement is the measurement, performed simultaneously for two or more unlike values for finding the functional dependence between them. Examples of joint measurements are finding of the length of a rod, de-pending on its temperature or finding of the electrical resistance of a conduc-tor depending on pressure and temperature.

On the basis of accuracy the measurements are divided into three clas-ses.

1. Measurements of the maximum possible accuracy are the measure-ments that can be achieved with the state-of-the-art engineering. This class includes all the high-precision measurements and, in the first place, the refer-ence measurements associated with the highest possible accuracy reproduc-tion of the physical quantities. This also includes measurement of physical constants, especially universal, such as measurement of the absolute value of the acceleration of free fall.

2. Testing-calibrating measurements are the measurements, which error has a defined probability not to exceed a predetermined value. This class in-cludes measurements performed by laboratories of state supervision on tech-nical regulations, measuring equipment condition and plant measurement la-boratories. These measurements ensure that with a certain probability the measurement error is not exceeding a certain specified value.

3. Engineering measurements are the measurements in which the error of the result is determined by the characteristics of the measuring instru-ments. Examples of engineering measurements are measurements performed in manufacturing processes in industry, in service sector etc.

On the basis of measurement result expression, the measurements are divided into absolute and comparison measurements.

Absolute measurements are the measurements based on direct meas-urements of one or more base quantities or on the use of values of the physi-cal constants. Examples of absolute measurements include measurements of length in meters, electric current in amperes and acceleration of free fall in m/s2.

Comparison measurements are the measurements in which the un-known quantity is compared with a known value of the same quantity, which plays the role of a unit or reference quantity. Examples of comparison meas-urements are: measurement of the shell diameter by measuring number of revolutions of the measuring wheel, measurement of the air relative humidity defined as the ratio of the amount of water vapor in 1 m3 of air to the amount of water vapour in 1 m3 of air at a given temperature.

12

Depending on the method of determining values of the quantities to be measured two basic methods of measurement are distinguished: method of direct evaluation and method of comparison with the measure.

The method of direct evaluation is a method of measurement in which the value of the quantity is determined directly from the reading device of the measuring instrument of direct action. Examples of such measurements are as follows: length measurement with a ruler, micrometer or protractor, pressure measurement with a manometer and so on.

The method of comparison with a standard measure is a method of measurement, in which the quantities to be measured are compared with the value reproduced by the standard measure. For example, to measure diameter of the limit gauge the optimeter is set to zero with the help of the stack of gauge blocks, and the measurement result is indicated by the deflection of the pointer optimeter from zero. Thus, the quantity to be measured is compared with the size of the gauge block stack. There are several types of the compar-ison method:

a) method of opposition, in which the quantity to be measured and the standard measure simultaneously act on the comparator, allowing to establish relationship between these variables, e.g., measurement of the resistance with a bridge circuit when the indicating device is in the diagonal of the bridge circuit;

b) differential method, in which the quantity to be measured is compared with a known quantity reproduced by a reference measure. This method, for example, is used for determining the deviation of the part diameter by an op-timeter after setting it to zero with the help of a stack of gauge blocks;

c) method of null measurement is also a method of comparison with a standard measure in which the resulting effect of the values on the instrument is brought to zero. This method of measurement is used to determine electri-cal resistance with the balanced bridge circuit;

g) with the coincidence method the difference between the quantity to be measured and a quantity reproduced by a reference measure, is determined by identifying coincidence of the scale marks or periodic signals. For example, measurements with a vernier caliper are based on observation of the match-ing marks of the main and vernier scales.

Depending on the method of obtaining measurement data the measure-ments are divided into contact and non-contact.

Depending on the type of the measuring means, there are instrumental, expert, heuristic and organoleptic methods of measurement.

The instrumental method is based on the use of special means of meas-urement, including automated and automatic.

The expert method is based on the judgments of the group of experts.

13

Heuristic methods are based on intuition. Organoleptic methods are based on the use of the human senses. Assessment of the state of an object can also be performed with ele-

ment-by-element and complex measurements. Element-by-element method is characterized by measurements of each parameter of the product separately. For example, eccentricity, ellipticity, faceting of a cylindrical shaft. The complex method is characterized by measuring the total quality parameter, which is influenced by its individual components. For example, the meas-urement of radial run-out of a shaft, which is affected by eccentricity, ellipti-city and other parameters; inspection of the profile position by the limiting contours etc.

14

3. International System of Units Coordinated International System of Units was approved in 1960 by XI

CGPM (General Conference on Weights and Measures). The international system is SI system (the initial letters of French name Systeme International). The system provides the list of 7 base units: metre, kilogram, second, ampere, kelvin, candela, mole and 2 supplementary units: radian, steradian, including prefixes for forming multiple and sub-multiple units (Table 1).

3.1. SI base units

Metre is equal to the length of the path travelled by light in vacuum dur-

ing a time interval of 1/299792458 of a second. Table 1

SI base and supplementary units

SI base units

Quantity Unit Symbol Name Russian international

Length L metre м m Mass M kilogram кг kg Time T second с s

Electric current I ampere А A Thermodynamic temper-

ature kelvin К K

Luminous intensity candela кд cd Amount of substance mole моль mol

SI supplementary units

Quantity Unit Symbol Name Russian international

Plane angle radian рад rad Solid angle steradian ср sr

15

Kilogram is equal to the mass of the International Prototype of the Kilo-gram.

Second is defined as the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

Ampere is constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular, and placed one metre apart in vacuum, would produce between these conductors a force equal to

7102 newton per metre of length. Kelvin is defined as the fraction 1⁄273.16 of the thermodynamic tempera-

ture of the triple point of water. Mole is the amount of substance that contains as many elementary entities

as there are atoms in 12 grams of pure carbon 12. Candela is equal to the luminous intensity, in a given direction, of a source

that emits monochromatic radiation of frequency 1210540 hertz and that has a radiant intensity in that direction of 1⁄683 watt per steradian.

3.2. SI derived units

The SI derived units are formed with the help of simplest equations be-

tween quantities with numeric coefficient, equivalent to 1. For example, in order to define dimension of linear speed we use the expression for uniform linear speed. If the length of the distance travelled is tvl (m) and the trav-el time t (s), then speed is measured in metres per second (m/s). Therefore, SI speed unit is a metre per second – that is speed of uniformly moving point that travels the distance of 1 m over the time of 1 s. Other units have the same methods of formation including coefficient not equal to 1 (Table 2).

16

Table 2 Units derived from SI base units

Name Unit Expression in terms of SI base units

Quantity Name Symbol Other units Base and sup-

plementary units

Frequency hertz Hz – s-1 Force newton N – mkgs-2

Pressure pascal Pa N/m2 m-1kgs-2 Energy, work joule J Nm m-1kgs-2

Power watt W J/s m-2kgs-3 Electric charge coulomb C As sА

Electric potential volt V V/А m2kgs-3А-1

Electrical capaci-tance farad F C/V m-2kg-1s4А2

Electrical resistance ohm Ω V/А m2kgs-3А-2 Electrical conduct-

ance siemens S А/V m-2kg-1s3А2

Magnetic flux weber Wb Vs m2kgs-2А-1 Magnetic flux densi-

ty tesla T Wb/m2 kgs-2А-1

Inductance henry H Wb/А m2kgs-2А-2 Luminous flux lumen lm cdsr Luminous flux lux lx m2cdsr Radioactivity becquerel Bq s-1 s-1

Absorbed dose gray Gy J/kg m2s-2

17

4. Objects of Measurement

Objects of measurement may be represented by any parameters of phys-ical entities and processes describing their properties.

4.1. Measurands

Measurement of geometric quantities: length; diameters; angles; form

and location deviation; surface finish; clearance. Measurement of mechanical and kinematic quantities: mass; force;

stress and strain; hardness; torque; linear and rotational speed; kinematic pa-rameters of gears and gear drives.

Measurement of parameters of liquids and gases: flow, level, volume; static and dynamic pressure; parameters of boundary layer.

Physical-chemical measurements: viscosity; density; concentration of components in solid, liquid and gaseous materials; humidity; electrochemical measurements.

Thermo-physical and thermodynamic measurements: temperature; pressure, thermal quantities; cycle parameters; energy conversion efficiency.

Time and frequency measurement: time and periods of time; measure-ment of frequency of periodic processes.

Measurement of electrical and magnetic quantities: voltage, electric current, resistance, capacitance, inductance; magnetic field parameters; mag-netic properties of materials.

Radioelectronic measurements: signal intensity; signal form and spec-trum; properties of substances and materials by radio-engineering methods.

Acoustic quantities measurement: in air, gas and water media; in solid medium; audiometry and noise-level measurement.

Optical and optical-physical measurement: measurement of optical properties of materials; pulse parameters of incoherent optical radiation; spectral and frequency characteristics; laser polarization; parameters of opti-cal elements, optical characteristics of materials; photomaterial characteris-tics.

Measurement of ionization radiation and nuclear constants: dosimet-ric characteristics of ionizing radiation; spectral characteristics of ionizing radiation; radionuclide activity; radiometric characteristics of ionizing radia-tion.

18

4.2. Dimension of a measurand

The purpose of measurement is to receive information on the value of

physical quantity. Physical quantity is defined as a property which, in a qualitative sense,

is universal for many objects, but in a quantitative sense is individual for each object. Leonhard Euler defined quantity in the following way: “quantity is anything that can be reduced or increased, or it is anything you can add or take away from”.

Dimension is a quantitative characteristic of the measurand. In practice, it becomes necessary to take measurements of quantities

which characterize properties of phenomena and processes. Some properties reveal to be qualitative, other – quantitative. Representation of properties as a set of elements or numbers or symbols is a measurement scale of the given properties.

A measurement scale is an ordered set of values that the quantity may take serving as a basis for its measurement. Let’s explain the notion by the example of temperature scales. The Celsius scale takes ice-point temperature as a starting point and a steam point as the fundamental interval (reference point). One hundredth part of this interval is a temperature unit (Celsius de-gree).

There are several types of scales: nominal, ordinal, difference (inter-val), ratio, absolute etc.

Nominal scales are characterized only by relation of equivalence (rela-tion of equality). Nominal scale is qualitative; it doesn’t contain any quantita-tive information and doesn’t have zero and units of measurement. The ele-ments of these scales are characterized only by relation of equivalence (equality) and similarity of specific qualitative demonstration of properties. As an example we can call colorimetric atlas (colour scale). The measure-ment process consists of visual comparison of a coloured item with test col-ours (samples of atlas).

Ordinal scales characterize the dimension of measurand in numbers. These scales describe properties for which not only relations of equivalence but also rank relations in ascending or descending order are meaningful. The typical examples of such scales are scales of hardness, earthquake intensity scales, wind strength scales, nuclear event scales, etc. Highly specialized or-dinal scales are widely used in methods of testing various products.

It is impossible in these scales to implement units of measurement since they are not only basically nonlinear but also the type of their nonlinear na-

19

ture can be different and unknown on different parts of the scale. The hard-ness measurements, for example, are expressed in Vickers hardness numbers, Rockwell hardness numbers, Brinell numbers, Shore numbers and not in units of measurement. Ordinal scales allow monotonic transformation, they can have or not a zero value.

Interval scales (difference) differ from ordinal scales in that they pro-vide both relation of equivalence and order and summation of interval values (differences) between different quantitative demonstrations of properties. The typical example is a time scale.

The time intervals (for example, working periods and study periods) can be added and subtracted but it is senseless to summarize the dates of some events.

Another example, a length (distance) scale of space intervals is applied by fixing of zero mark of the scale at one point and making the reading at the second point. This type of scales includes the centigrade Celsius scale, Fahr-enheit temperature scale, Reaumur temperature scale.

Interval scales have standard (agreed) units of measurement and zeros, based on reference elements or data.

These scales allow linear transformations; procedures for finding of mathematical expectation, standard deviation, skewness and displaced mo-ments are applicable for them.

Ratio scales have natural zero, and the unit of measurement is deter-mined by agreement. For example, mass scales starting with zero can be graded differently in accordance with required weight accuracy. Just compare chemical balance and household scales. These scales apply relations of equivalency and order – operations of subtraction and multiplication (ratio scales of the 1st type – proportional scales) and in many cases the sum opera-tions (ratio scales of the 2nd type – additive scales).

The masses of different objects can be summarized but it is no use in summarizing temperatures of different bodies, though we can estimate the difference and relation of their thermodynamic temperatures. The examples of ratio scales include mass scales (2nd type), thermodynamic temperature scale (1st type).

The ratio scales are widely used in physics and engineering allowing all arithmetic and statistic operations.

Absolute scales possess all the characteristics of ratio scales but they additionally have natural unambiguous determination of unit of measure-ment. Such scales are used to measure relative quantities (relations of similar quantities: magnitude ratio, attenuation ratio, efficiency coefficient, reflection and absorption coefficients, amplitude modulation index and so on).

20

5. Standard Conditions for Linear and Angular Measurements Standard conditions of linear measurements within 1-500 mm and angu-

lar measurements with the smaller side of an angle up to 500 mm are defined in the standard GOST 8.050-73. Standard conditions must be provided to practically eliminate additional errors of measurements. The standard defines the following values of basic parameters that influence measurement accura-cy:

Parameter Value

Environmental temperature, ºC Atmosphere pressure, kPa (mmHg) Relative humidity, % Acceleration of free fall, m/s2

20 101.3 (760)

58 9.8

Allowable deviations from standard values are: for atmosphere pressure

±4 kPa (±30 mmHg), for relative humidity +22…-18%. Temperature deviations have the highest influence on measurement ac-

curacy. In accordance with tolerances and range of measured dimensions there are fixed limits of allowable variations of temperature of a measured part and workplace area (Table 3.)

Table 3

Limits of allowable variations of temperature, ºC, of the measured object and work place,

from standard value during the measurement

Dimension rang-es, mm

Tolerance grade 01 0 From 1 to 5 From 6 to 8 From 9 to 10

Over 1 to 18 0.8 1.0 1.5 3.0 4.0 Over 18 to 50 0.3 0.5 1.0 2.0 3.0 Over 50 to 500 0.2 0.3 0.5 1.0 2.0

In angle measurements the limits of allowable variations of temperature

of the measuring object and workplace area from standard value are 3.5 ºC. The waiting period of the part to be measured and measuring instrument

in the workplace area before starting the measurements must be not less than stated in the Table 4. The standard GOST 8.050-73 specifies the standard di-

21

rection of measurement line. For measurements of external linear dimensions up to 160 mm the direction of measurement line is vertical; for dimensions more than 160 mm and for dimensions of holes, width and depth of slots the direction of measurement line is horizontal. Position of the flat surface for angular measurements is horizontal.

Table 4

The waiting period of the part to be measured and measuring instrument in

the workplace area, h

Mass of the measured object,

kg

Tolerance grade 01 and 0 From 1 to 5 From 6 to 8 From 9 to10

To 10 6 4 3 2 Over 10 to 50 14 8 6 4 Over 50 to 200 24 14 10 7

Over 200 to 500 36 20 16 12

The allowable variations from standard direction of measurement line must be not more than 1º for the IT 01 and IT 0; 2º for the IT 1-5; 5º for the IT 6-10.

To reduce the error of measurement it is necessary to align the standard direction of measurement line with the corresponding direction of the refer-ence gages and reference parts.

Standard conditions in workplace area must be provided during the whole process of measurement.

22

6. Means of Measurement Measurements are performed with the use of technical means. Technical

means required for measurements are: material measure – measuring instruments intended for reproduc-

ing the physical quantity with a given value. The measures of the highest order of accuracy are called measurement standards or eta-lons;

measurement standards are measuring instruments or systems that ensure reproduction, storage and transfer of legal units of physical quantities to the measuring instruments of the lower levels;

reference measuring instruments are material measures, measur-ing instruments or transducers approved as a reference for the verifi-cation of the other means of measurement;

working measuring instruments are the instruments designated for measurements not connected with transfer of the quantities.

6.1 Measurement Standards

The means of measurement of the highest accuracy – the standards

are divided into several grades. The standard reproducing unit with the highest accuracy in the country

is called the state primary standard. The standard of the unit of a physical quantity is reproduced with almost the highest possible accuracy using spe-cial tools.

In 1983, at the XVII General Conference on Weights and Measures the metre was approved as a standard unit of length – the length of the path trav-eled by light in vacuum during a time interval of 1/299792458 of a second. Previously, the standard of the meter was equal to 1650763.73 wavelengths of light in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the isotope krypton-86.

The second was adopted as a standard unit of time, equal to the duration of 9192631770 periods of the radiation corresponding to the transition be-tween the two hyperfine levels of the ground state of the cesium 133 atom.

23

The standard of the mass unit (1 kg) is a cylinder made from an alloy of platinum (90%) and iridium (10%) with diameter and height being approxi-mately the same (about 30 mm).

The mole was recognised as a unit of amount of substance. The mole is the amount of substance of a system which contains as many elementary enti-ties as there are atoms in 12.000 grams of carbon-12.

As a standard unit of luminous intensity the candela was adopted, which is the luminous intensity, in a given direction, of a source that emits mono-chromatic radiation of frequency 540x1012 Hz and radiant intensity in that di-rection of 1/683 watt per steradian.

As a standard unit of current the ampere was adopted, which is the con-stant electric current which, flowing in two parallel straight conductors of in-finite length, of negligible circular cross-sectional area, located one metre apart in vacuum, produces between these conductors an interaction force equal to 2x10-7 newtons per metre of length.

The standard unit of thermodynamic temperature is Kelvin, constituting the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

If the direct transfer of the unit value from the existing etalons with the required accuracy is not technically feasible in view of the special conditions, then the special standards are produced for the unit reproduction. Such condi-tions may include: high or low pressure, high humidity, measurements at ex-treme boundaries of the range of values of the measured quantity.

In metrological practice secondary standards, working standards and reference standards are widely used. These standards are produced and ap-proved for organization of verification procedures, as well as to ensure safety and minimize wear of the state primary standard.

The following categories of standards are also used: transfer standard is the secondary standard used to compare stand-

ards, which for some reason cannot be checked against each other; duplicate standard is the secondary standard used to test the integri-

ty of the state standard or to replace it in case of damage or loss; reference standard is the secondary standard to transfer unit value

to the working standards. It may not always be an exact physical copy of the state standard;

working standard is the secondary standard that is used to store the unit and transfer it to the reference measuring instruments or to the most accurate working measuring instruments.

24

The working standards can be implemented as a single standard (or sin-gle material measure), as a collective standard, as a complex of measuring instruments and as a group standard.

An example of a single standard is the standard of mass in the form of platinum-iridium weight. An example of a collective standard is the reference standard of volt, consisting of 20 normal cells. An example of a measuring instruments complex is the standard unit of the molar fraction of the concen-tration of components in gas mixtures. In this case the different components, different concentration ranges and different diluent gases create a large num-ber of measurement tasks with the general formulation. Therefore, in this case a standard consists of several tens of measuring instruments. An exam-ple of a group standard is a set of instruments for measuring density of liq-uids in different parts of the density range.

Such a wide range of varieties of standards is not specified in the inter-national metrological documents. International standards stored at the Inter-national Bureau of Weights and Measures reproduce a limited number of physical units. Typically, this is either the basic units of the SI system or units which can be reproduced at accuracy equal to or exceeding the accuracy of the standard of basic unit. An example of such a standard is the standard of volt based on the Josephson effect, which consists in the flow of direct cur-rent across the junction formed by two superconductors separated by a thin dielectric layer (stationary effect), or in the flow of alternating current across the junction of two superconductors, to which direct voltage is applied (non-stationary effect).

The number of international standards is small in comparison with Rus-sian standards due to the fact that the concept of standards and reference measuring instrument does not have a clear distinction in many countries. There is a vast concept – a standard, which can be applied to the secondary standard (reference measuring instrument) or an etalon (original reference measuring instrument).

25

6.2 Measures and Reference Measuring Instruments

The measures and the reference measuring instruments are examples of

the reference measuring means. They are intended for verification and gradu-ation of other measuring instruments. These means have a reading error that 2-3 times smaller than that of the instruments being verified, these means are issued a certificate for the right to carry out verification.

The measure could be implemented in the form of a body, substance or device for reproducing, storing and transferring unit of physical quantity from one measuring instrument to another. The measure reproduces quantity, which value is associated with the accepted unit of a certain well-known equation.

Measures and reference measuring instruments, serving for reproduction and storage of units with the highest accuracy possible at the present state-of- -the-art, belong to the standards. In contrast to the standard, the measure re-produces not only a unit, but its sub-multiples and multiple values. For ex-ample, one metre rod or a set of gauge blocks of various sizes can be used as a measure of length.

Measures of mass are not only the reference kilogram weights and their copies, but also weights of different masses.

Measures are essential means of measurement, because they are used as means of transferring units of physical quantities from one instrument to an-other.

In many countries, including Russia, special storages of measures are constructed, which functions include comparison of state measures with in-ternational. The first storage in Russia was established in 1842 as the Depot of Standard measures, and in 1893 the Central Office of Weights and Measures under the direction of D.I. Mendeleev was established.

Measures as means of measurements are available in various grades of accuracy, which are regulated by the relevant state standards and verification procedures. The so-called certified reference materials belong to a particular class of measures.

A certified reference material is a measure in the form of substance with which a size of the unit of physical quantity is reproduced as property or as a composition of matter, from which the certified reference material is made. Examples of such measures are substances that under certain conditions re-produce a unit or its sub-multiple or multiple value. Examples include con-stant temperature corresponding to the transition from one state of matter into another 1063 °C – the melting point of gold, 960.8 °C – the melting point of

26

silver, 444.6 ° C – the melting point of sulphur, 100 °C – boiling point of wa-ter, 182.97 ° C – the boiling point of oxygen etc.

Another example of the certified reference material, which uses the properties of matter, is folic acid. The combustion of a certain mass of folic acid in a closed volume generates a fixed quantity of heat. According to the results of preliminary tests the certificate is issued on the certified reference material, and the material is registered in the State Register of certified refer-ence materials. Certified reference material, as well as other measures are pe-riodically compared and stored in the metrological organizations.

In the Russian Federation, the State Register of certified reference mate-rials is kept in a special institute in Yekaterinburg. A special place in the sys-tem of measures is occupied by the certified reference materials of composi-tion – reference gas mixtures. These reference materials have features that distinguish them from reference materials made in the form of liquids or sol-ids. The main difference is that the reference gas mixture is consumed in the process of measurement, which may lead to changes in gas composition. It is also impossible to store the reference gas mixture that is being analysed. Therefore, a batch of vessels with mixtures is prepared for analysis.

The measures are divided into single-valued and multi-valued. Single-value measures are measures that reproduce constant value of

the physical quantity. It can be a unit or a multiple or a sub-multiple value (weights, gauge blocks, receiving flasks, standard cells of electromotive force, electrical resistance coils etc.). For convenience of use the sets of measures (weights, gauge blocks and other measures) are manufactured. A set of measures combined in one mechanical unit with a device is called a measure box (resistance box, capacitance box, and so on).

Multi-valued measures reproduce not one, but several sub-multiple or multiple values of units. Such measures are, for example, a millimeter ruler and other graduated measures, graduated variable capacitors, variometer and so on. To reproduce a length the line gauge blocks and end gauge blocks are widely used in the industry. The line gauge blocks are made in the form of samples, rulers, tape measures and scales with the indicating elements.

27

6.3 Gauge Blocks

The plane-parallel end measures of length or gauge blocks come in sets

of parallelepipeds (plates and blocks), which are made of steel for lengths up to 1000 mm or carbide for lengths up to 100 mm with two mutually parallel planar measuring surfaces (GOST 9038-90). They are designed for the direct measurement of the linear dimensions, as well as for transferring unit of length from the primary standard to gauge blocks of lower accuracy.

Gauge blocks are used for verification, calibration and adjustment of the measuring instruments, measuring devices, machine tools etc. With the wringability (i.e., adhering), due to the action of intermolecular forces of at-traction, gauge blocks can be assembled into stacks of the required size, which do not fall apart while handling. The gauge block sets are made from various numbers of gauge blocks (from 2 to 112 blocks).

The gauge blocks are available in the following accuracy grades: 00, 01, 0, 1, 2, 3 – for steel blocks; 00, 0, 1, 2 and 3 – for carbide blocks. Each set of gauge blocks is supplied with a certificate according to GOST 2.601-95 and an instruction manual. By stacking four or five gauge blocks, from a set with block sizes from 0.001 mm to 100 mm, it is possible to build up stacks of de-sired size.

GOST 9038-90 applies to the plane-parallel end measures of length (hereinafter – gauge blocks) made of steel with lengths up to 1000 mm and to carbide gauge blocks with lengths up to 100 mm, having a rectangular paral-lelepiped shape with two opposing measuring surfaces ground flat and mutu-ally parallel.

The gauge blocks are designed to be used as: working measures to ad-just and set up indicating instruments for direct measurement of linear di-mensions of industrial products; reference measures to transfer the size of a unit of length from the primary standard to the gauge blocks of the lower ac-curacy and for verification and calibration of measuring instruments.

Nominal length of a gauge block must meet the requirements specified in the Table 5.

Gauge blocks are manufactured of the following accuracy grades: 0, 1, 2, 3 – for steel blocks, 0, 1, 2 and 3 – for carbide blocks. Steel and carbide gauge blocks of accuracy grades 00 and 01 are supplied upon request.

The gauge block used as a reference should be verified as reference, of the 1, 2, 3, and 4th class according to the MI 1604. The reference gauge blocks should have a distinctive mark stamped during manufacture. Accuracy grade of a gauge blocks set is determined by the lowest accuracy grade of the

28

individual gauge block of the set. Gauge block of 1.005 mm available in sets 1, 2, 3, 12, and 15 of the third accuracy grade, should have accuracy grade not lower than 2nd.

Table 5

Nominal length of gauge blocks

Size increment Gauge block nominal lengths

- 1.0005

0.001 From 0.99 to 1.01 From 1.99 to 2.01

From 9.99 to 10.01 0.005 From 0.40 to 0.41

0.05

From 0.1 to 0.7 From 0.9 to 1.5

From 2 to 3 From 9.9 to 10.1

0.1 From 0.1 to 3 0.5 From 0.5 to 25 1 From 1 to 25

10 From 10 to 100 25 From 25 to 200 50 From 50 to 300 100 From 100 to 1000

Cross section dimensions of gauge blocks (a, b) must meet the require-

ments specified in the Table 6.

Table 6 Cross section dimensions of gauge blocks

Gauge block nominal

lengths Cross section dimensions аb

a b From 0.1 to 0.20 15-0.45 5-0.3 Over 0.20 to 0.29

30-0.45

03.03.09

Over 0.29 to 0.6

20-0.3

30-0.3 Over 0.6 to 10.1 Over 10 to 1000 35-0.3

29

Examples of gauge block designation according to the GOST 9038-90:

set 2: steel gauge blocks of the 1st accuracy grade

– gauge blocks 1-H2 GOST 9038-90;

set 3: carbide gauge blocks of the 2nd accuracy grade

– gauge blocks 2-H3-T GOST 9038-90;

steel gauge block of 1.49 mm of the 3rd accuracy grade

– gauge block 3-1,49 GOST 9038-90;

set of the reference gauge blocks of the 1st class

– reference gauge blocks 1-KO GOST 9038-90;

set 3: reference gauge blocks of the 2nd class

– reference gauge blocks 2HO3 GOST 9038-90

Technical requirements: gauge blocks have to be manufactured in ac-

cordance with the requirements of the standard and working drawings. Permissible length deviations and deviations from flatness of the meas-

uring surfaces of the gauge blocks at 20 °C must not exceed values, given in the Table 7.

Table 7

Gauge blocks deviations

Nominal length of a gauge block, mm

Permissible deviations from nominal length, ± μm, related to the accuracy grade

from flatness and parallelism, μm, related to the accuracy grade

00 01 0 1 2 3 00 01 0 1 2 3 To 0.29 - - - 0.20 0.40 0.80 - - - 0.16 0.30 0.30

Over 0.29 to 0.9 - - 0.12 0.20 0.40 0.80 - - 0.10 0.16 0.30 0.30

Over 0.9 to 10 0.06 0.20 0.12 0.20 0.40 0.80 0.05 0.05 0.10 0.16 0.30 0.30 Over 10 to 25 0.07 0.30 0.14 0.30 0.60 1.20 0.05 0.05 0.10 0.16 0.30 0.30 Over 25 to 50 0.10 0.40 0.20 0.40 0.80 1.60 0.06 0.06 0.10 0.18 0.30 0.30 Over 50 to 75 0.12 0.50 0.25 0.50 1.00 2.00 0.06 0.06 0.12 0.18 0.35 0.40

Over 75 to 100 0.14 0.60 0.30 0.60 1.20 2.50 0.07 0.07 0.12 0.20 0.35 0.40 Over 100 to

150 0.20 0.80 0.40 0.80 1.60 3.00 0.08 0.08 0.14 0.20 0.40 0.40

Over 150 to 0.25 1.00 0.50 1.00 2.00 4.00 0.09 0.09 0.16 0.25 0.40 0.40

30

Nominal length of a gauge block, mm

Permissible deviations from nominal length, ± μm, related to the accuracy grade

from flatness and parallelism, μm, related to the accuracy grade

00 01 0 1 2 3 00 01 0 1 2 3 200 250 0.30 1.20 0.60 1.20 2.40 5.00 0.10 0.10 0.16 0.25 0.45 0.50 300 0.35 1.40 0.70 1.40 2.80 6.00 0.10 0.10 0.18 0.25 0.50 0.50 400 0.45 1.80 0.90 1.80 3.60 7.00 0.12 0.12 0.20 0.30 0.50 0.50 500 0.50 2.00 1.00 2.00 4.00 8.00 0.14 0.14 0.25 0.35 0.60 0.60 600 0.60 2.50 1.30 2.50 5.00 10.0 0.16 0.16 0.25 0.40 0.70 0.70 700 0.70 3.00 1.50 3.00 6.00 11.0 0.18 0.18 0.30 0.45 0.70 0.80 800 0.80 3.20 1.60 3.20 6.50 13.0 0.20 0.20 0.30 0.50 0.80 0.80 900 0.90 3.60 1.80 3.60 7.00 14.0 0.20 0.20 0.35 0.50 0.90 0.90

1000 1.00 4.00 2.00 4.00 8.00 16.0 0.25 0.25 0.40 0.60 1.00 1.00 These requirements are not applied to the zone adjacent to the edges of

the measuring surfaces; the zone is 0.5 mm wide for gauge blocks of nominal length up to 0.29 mm and 0.8 mm wide for gauge blocks of nominal length of more than 0.29 mm.

Deviations from flatness of the measuring surfaces of gauge blocks with the nominal length from 0.9 to 3 mm in free state (not wrung) should not ex-ceed 2 μm.

Wringability of the gauge block measuring surfaces must meet the re-quirements specified in the Table 8.

Flatness tolerance of the optical flats is equal to 0.03 μm for accuracy grades 00, 01 and 0, and is equal to 0.1 μm for accuracy grades 1, 2 and 3.

Gauge blocks surface roughness parameter Rz<0.063 μm is in accord-ance with GOST 2789.

The edges of the measuring surfaces of gauge blocks should be rounded to a radius less than 0.3 mm or have a chamfer of less than 0.3 mm.

The measuring surfaces of gauge blocks, including zone of the chamfers transition to the measuring surface, should be free of defects that adversely affect the use of gauge blocks.

Scratches on the measuring surfaces of gauge blocks are allowed as long as they do not affect wringability, deviation of length from the nominal value and deviation from flatness and parallelism.

31

Table 8

Wringability requirements

Accuracy grade

Wringability of gauge blocks to the lower (supporting) optical flats of 60 mm in diameter ac-

cording to TU 33.2123

Wringability of gauge blocks to each other

Steel gauge blocks with lengths from

0.6 to 100 mm

Carbide gauge blocks with lengths

from 0.99 to 100 mm

00 01 Without fringes and shades

viewed with white light Sliding pres-sure from 29.4

to 78.5 N

-

0

Sliding pressure from 29.4 to 98.1 N 1, 2 and 3

Without fringes. Shades in the form of bright spots, viewed

with white light

The measuring surfaces of carbide gauge blocks, at a distance of 1 mm

from the center of the measuring surface and at the corner points at a distance of 1-2 mm from the non-working surfaces, are not allowed to have dents larger than 120 μm in width for the 00 and 0 accuracy grades, and larger than 200 μm in width for the 1, 2 and 3 accuracy grades. The porosity should not be higher than 0.4% according to GOST 9391.

Coefficient of thermal expansion of the steel gauge blocks per 1 m and 1 °C must be within 10.5-12.5 μm in the temperature range from 10 to 30 °C.

Table 9

Coefficients of thermal expansion for the carbide gauge blocks

Nominal length of a

gauge block, mm Coefficient of thermal expansion, μm,

per 1 m and 1 °С Accuracy grade

From 2 to 5 3.5 – 12.5 1; 2 and 3 Over 5 to 10 8 – 12.5 1 Over 5 to 10 3.5 – 12.5 2 and 3

Over 10 to 25 8 – 12.5 1; 2 and 3 Over 25 to 100 10.5 – 12.5 1; 2 and 3

32

Carbide gauge blocks should have a coefficient of thermal expansion and allowable elongation at a temperature range from 10 to 30 °C in accord-ance with the Tables 9 and 10. The carbide gauge blocks should be manufac-tured as entirely solid carbide gauge block or as steel block with carbide-tipped measuring surfaces.

Table 10

Permissible change of the gauge block length

Accuracy grade Permissible change of the gauge block length (l, mm) in the course of year, μm

00 and 01 0.02 + 0.0002l 0 0.02 + 0.0005l

1; 2 and 3 0.05 + 0.001l Manufacturer of the carbide gauge blocks must indicate a coefficient of

thermal expansion corresponding to the grade of the carbide used. Hardness of the measuring surfaces of steel gauge blocks should be at least 800 HV ac-cording to GOST 2999.

The change in length of the gauge blocks in the course of year, due to instability of the material, must not exceed the values given in the Table 10. The requirements for the stability of the gauge blocks over time should be ensured by the manufacturer, provided that the gauge blocks are not subject-ed to sudden temperature shocks, vibrations and impacts, as well as the ef-fects of magnetic fields, excluding magnetic field of the earth.

The perpendicularity tolerance of the non-working surfaces with respect to the measuring surfaces must meet values specified in the Table 11.

Table 11

Perpendicularity tolerance of the non-working surfaces of gauge blocks

Nominal length of a gauge block, mm

Perpendicularity tolerance of non-working surfaces with respect to the measuring surfaces over the whole

length of the gauge block, μm From 10.5 to 25 70 Over 25 to 60 90 Over 60 to 150 110

Over 150 to 400 140 Over 400 to 1000 180

33

Non-working surfaces of gauge blocks of nominal length over 100 mm

should have marks engraved at a distance of l211.0 from the block sides. To clamp gauge blocks together with the ties, according to GOST 4119,

the gauge blocks of the sets 8 and 9, as well as gauge blocks longer than 100 mm of the sets 22-24 should have two holes; wear blocks of 50 mm nominal length and gauge blocks of 51.4 and 71.5 mm nominal length of the sets 22-24 – should have one hole.

The holes should be located at a distance of 25 mm from the measuring surfaces, and for gauge blocks of 51.4 and 71.5 mm length – at the distance from one of the measuring surfaces.

Explanation of terms used in this section is given in the Tables 12 and 15.

Each set of gauge blocks and kits of the set should be packed in a case with an enclosed certificate in accordance with GOST 2.601, and for the ref-erence gauge blocks a calibration certificate according to the MI 1604 should be enclosed as well.

The nominal length of a block should be stamped on it. For the gauge blocks of length equal to and smaller than 5.5 mm, the nominal length mark-ing should be shifted from the middle of the measuring surface, so that its central zone of 9 mm long remains free of markings.

For the gauge blocks of length greater than 5.5 mm, the nominal length marking and trademark of the manufacturer should be applied to the non-working surface. Additional distinctive sign, in addition to the markings men-tioned above, should be applied to the wear blocks and reference gauge blocks. It is allowed to label gauge blocks of the 00, 01 and 0 accuracy grades with the set number or other additional information.

Marking on the case of the gauge block set should include: trademark of the manufacturer (on the outer surface of the cover); serial number of the set or kit; accuracy grade (for working gauge blocks), class (for reference

gauge blocks), the words “reference gauge blocks” (on the outer sur-face of the case cover of a set or kit of reference gauge blocks);

reference to GOST 9038-90; letter "T" (for carbide gauge blocks) on the inner surface of the case. Each pocket should be supplied with an indication of the nominal length

of the gauge block placed in. Gauge blocks sets and gauge block of length from 500 to 1000 mm, de-

livered individually, must be packed in cases made of materials specified in GOST 13762.

34

Each gauge block in a set must be placed in the appropriate pocket and shouldn’t fall out when the closed case is turned upside-down.

Acceptance of gauge blocks To verify compliance of the gauge block with the requirements of

GOST 9038-90, the following activities are carried out: state tests, metrologi-cal certification (for reference gauge blocks), acceptance inspection, periodic testing and testing for compliance of coefficient of thermal expansion and stability of the gauge blocks length over time.

State tests are conducted in accordance with GOST 8.383 and 8.001, metrological certification – according to GOST 8.326.

During the acceptance inspection, each gauge block is checked for com-pliance with the requirements of wringability to optical flats. The sliding pressure is checked selectively.

Periodic tests are conducted at least once every three years for compli-ance with all requirements of GOST 9038-90. Periodic testing should be per-formed on typical representatives:

any set of steel gauge blocks with lengths to 100 mm of any accuracy grade and/or class;

any set of steel gauge blocks with lengths from 100 mm of any accu-racy grade and/or class;

any set of carbide gauge blocks of any accuracy grade and/or class. At least 10% of the gauge blocks, but not less than four, are selected

from each set. From the set composed of carbide and steel gauge blocks, 10% of car-

bide and 10% of steel blocks, but at least in fours of carbide and steel blocks, are selected.

The results of periodic testing are considered satisfactory if all tested pa-rameters of the gauge blocks meet all requirements.

The testing in accordance with MI 1604 is held at least once every three years, on at least four blocks of each representative group. In case tests are performed together with periodic tests, the gauge blocks selected for periodic testing are used.

It is allowed to carry out testing on at least four separately manufactured carbide and steel blocks.

The results of testing are considered satisfactory if all tested parameters of the gauge blocks meet all requirements.

35

Inspection and testing of gauge blocks Verification of gauge blocks is performed in accordance with MI 2079,

MI 2186, GOST 8.367 and MI 1604. The effect of climatic factors of environment on transportation is tested

in climatic chambers. Tests are carried out in the following conditions: at a temperature of plus (50 ± 3) °C, at a temperature of minus (50 ± 3) °C and relative humidity of (95 ± 3) % at a temperature of (35 ± 3) °C. Exposure time in the given conditions in a climate chamber is equal to 2 hours.

Upon completion of tests, all tested gauge blocks must comply with the requirements of the standards mentioned above.

For testing effect of transport shaking a shock table, which creates shak-ing with acceleration of 30 m/s2 and frequency of 80-120 beats per minute, is used.

Boxes packed with gauge blocks are attached to the table and undergo a total of 15,000 strokes. After the test, the metrological characteristics of the gauge blocks should not exceed values, specified in GOST 9038-90.

Description of terms used in the section and gauge block sets is given in the Tables 12, 13 and 14.

Table 12

Terms concerned with the gauge blocks

Term Explanation

Length of a gauge block (at any point)

Length of a perpendicular from a given point of a measuring surface to the opposite measuring surface. Note. As an opposite measuring surface, in absolute inter-ferometric method of measurement of the block length, a flat surface of the auxiliary plate made of the same material and same surface finish as the gauge block, to which it is wrung, is used.

Deviation of the gauge block nominal length

The highest difference in absolute value between the length of the gauge block at any point and nominal length of the gauge block.

Deviation from flat-ness and parallelism

The difference between the maximum and minimum lengths of the gauge block.

36

Term Explanation

Wringability of a gauge block

Property of the measuring surfaces of a gauge block that provides a firm bond between gauge blocks or between a gauge block and a flat metal or optical flat when a block is applied or slid across a block or a plate. Wringability is characterized by sliding pressure.

Wear block The block included at the ends of the gauge blocks stack to protect the gauge blocks from wear.

A set of special gauge blocks

A set of gauge blocks designed for verification of certain products and measuring devices (wires, micrometers, verni-er calipers, optikators).

Table 13

Sets of gauge blocks

Set num-ber

Quan-tity of blocks in a set

Size incre-ment, mm

Nominal lengths, mm

Block quan-tity

Wear blocks Accuracy grade

Nominal length,

mm

Quanti-ty of

blocks

Steel blocks

Carbide blocks

1 83

- 1.005 1

- - 0; 1; 2 and 3

1; 2 and 3

0.01 From 1 to 1.5 51 0.1 From 1.6 to 2 5 0.5 0.5 1

From 2.5 to 10 16 10 From 20 to 100 9

2 38

- 1.005 1

- - 1; 2 and 3

1; 2 and 3

0.01 From 1 to 1.1 11 0.1 From 1.2 to 2 9 1 From 3 to 10 8

10 From 20 to 100 9

3 112

- 1.005 1

- - 0; 1; 2 and 3

1; 2 and 3

0.01 From 1 to 1.5 51 0.1 From 1.6 to 2 5

0.5 0.5 1 From 2.5 to 25 46

10 From 30 to 100 8 4 11 0.001 From 2 to 2.01 11 - - 0;1; 2 - 5 11 0.001 From 1.99 to 2 11 - - 0; 1; 2 -

37

Set num-ber

Quan-tity of blocks in a set

Size incre-ment, mm

Nominal lengths, mm

Block quan-tity

Wear blocks Accuracy grade

Nominal length,

mm

Quanti-ty of

blocks

Steel blocks

Carbide blocks

6 11 0.001 From 1 to 1.01 11 - - 0; 1; 2 0 and 1 7 11 0.001 From 0.99 to 1 11 - - 0; 1; 2 0 and 1

8 10 25 50 100

From 125 to 200 From 250 to 300 From 400 to 500

4 2 2

50 2 0; 1

2 and 3

9 12 100 From 100 to 1000 10 50 2 0; 1; 2

and 3 -

10 20 0.01 From 0.1 to 0.29 20 - - 1; 2 and 3 -

11 43 0.01 0.1

From 0.3 to 0.7 Over 0.8 to 0.9

41 2 - - 0; 1; 2

and 3 -

12 74

- 0.01 0.1 -

0.5

1.005 From 0.9 to 1.5 From 1.6 to 2

0.5 From 2.5 to 5

1 61 5 1 6

1; 2; 3

13 11 - 10

5 From 10 to 100

1 10 - - 1; 2; 3 -

14 38 0.5 10

From 10.5 to 25 From 30 to 100

30 8 - - 0; 1;

2; 3 -

15 29

0.001 0.01 0.1 1

1.005 From 1 to 1.1 From 1.2 to 2 From 3 to 10

1 11 9 8

1; 2 and 3

16 19 0.001 From 0.991 to 1.009 19 - - 0; 1

and 2 0 and 1

17 19 0.001 From 1.991 to 2.009 19 - - 0; 1

and 2 -

18 2 - - - 1 2 - 1; 2 and 3

19 2 - - - 2 2 - 1; 2 and 3

Note: The carbide gauge blocks of sets 1, 2 and 3 with length over 5

mm may be replaced by steel gauge blocks.

38

Table 14

Set of special gauge blocks

Nominal lengths, mm

Accuracy grade of a set Class of

a set Steel blocks

Carbide blocks

Set 20 (23 blocks) 0.12; 0.14; 0.17; 0.2; 0.23; 0.26; 0.29; 0.34; 0.4; 0.43; 0.46; 0.57; 0.7; 0.9; 1.0; 1.16; 1.3; 1.44; 1.6; 1.7; 1.9;

2; 3.5

1 and 2 - 1, 2, 3, 4

Set 21 (20 blocks) 5.12; 10.24; 15.36; 21.5; 25; 30.12; 35.24; 40.36;

46.5; 50; 55.12; 60.24; 65.36; 71.5; 75; 80.12; 85.24; 90.36; 96.5; 100

1 and 2 1 and 2 1, 2, 3, 4

Set 22 (7 blocks) 21.2; 51.4; 71.5; 101.6; 126.8; 150; 175 3 3 -

Set 23 (13 blocks) 1.00; 1.00; 1.05; 1.10; 2.00; 2.00; 21.2; 51.4; 71.5;

101.6; 126.8; 150; 175 2 and 3 -

Set 24 (25 blocks) 1.00; 1.00; 1.04; 1.05; 1.06; 1.10; 1.11; 1.12; 1.13; 1.17; 1.18; 1.19; 2.00; 2.00; 21.2; 51.4; 71.5; 101.6;

126.8; 150; 175; 250; 400; 600; 1000

- 2 and 3 -

Set 25 (15 blocks) 0.990; 0.992; 0.994; 0.995; 0.996; 0.998; 1.000; 1.002; 1.005; 1.010; 1.015; 1.020; 1.030; 1.040;

1.050

- - 2

Set 26 (8 blocks) 0.990; 0.995; 1.000; 1.005; 1.010; 1.020; 1.030;

1.050 - - 2

Set 27 (9 blocks) 1.00; 1.02; 1.04; 1.05; 1.06; 1.08; 1.10; 1.15; 1.20 - - 3

Set 28 (28 blocks) 1.00; 1.02; 1.04; 1.06; 1.08; 1.10; 1.12; 1.14; 1.16; 1.18; 1.20; 1.24; 1.28; 1.30; 1.32; 1.36; 1.40; 1.50;

1.60; 1.70; 1.80; 1.90; 2.0; 2.2; 2.4; 2.6; 2.8; 3.0

- - 3

39

Nominal lengths, mm

Accuracy grade of a set Class of

a set Steel blocks

Carbide blocks

Set 29 (8 blocks) 0.990; 0.995; 1.000; 1.005; 1.010; 1.020; 1.030;

1.040 - - 3

Set 30 (7 blocks) 5.12; 10.24; 15.36; 19.50; 20; 21.50; 25 - - 4

Set 31 (9 blocks) 1; 1.01; 1.02; 1.03; 1.04; 1.05; 1.06; 1.08; 1.10 - - 3

Set 32 (7 blocks) 0.995; 1; 1.005; 1.010; 1.020; 1.030; 1.040 - - 3

Set 33 (7 blocks) 1; 1.06; 1.10; 1.12; 1.18; 1.20; 1.30 - - 3

Set 34 (9 blocks) 1.001; 1.002; 1.003; 1.005; 1.006; 1.007; 1.008;

1.009 - - 1

Set 35 (9 blocks) 1.01; 1.02; 1.03; 1.04; 1.05; 1.06; 1.07; 1.08; 1.09 - - 1

Set 36 (13 blocks) 1; 1.001; 1.002; 1.003; 1.004; 1.005; 1.006; 1.010;

1.020; 1.030; 1.040; 1.050; 1.060 - - 2

Set 37 (8 blocks) 1 – 2 pcs; 10 – 2 pcs; 50 – 2 pcs; 100 – 2 pcs - - 1

Note: The carbide gauge blocks of sets 23 and 24 with length over 5

mm may be replaced by steel gauge blocks.

40

6.4 Angle Gauge Blocks

Angle gauge blocks (GOST 2875-88) are intended for inspection of the

inner and outer angles of tools, templates, parts and verification of devices, etc. The angle gauge blocks of five types are available: 1 and 2 – with one working angle either with a truncated top or sharp top; 3 – with four working angles; 4 – regular polyhedrons; 5 – with three working angles. Angle gauge blocks of types 1, 2 and 3 are manufactured of three accuracy grades (0, 1 and 2), multi-faceted blocks of type 4 are made of four accuracy grades (00, 0, 1 and 2), angle blocks of type 5 – are available of grade 1. A wide range of nominal angles is possible by wringing angle gauge blocks together.

GOST 2875-88 applies to angle blocks accessories and angle gauge blocks of plane angle (hereinafter – the angle gauge blocks) having shape of a right prism with a number of side faces, some of them or all of them are measuring surfaces, pairs of which form the working angles.

Angle gauge blocks are intended to be used as: working measures for adjusting and setting-up angle measuring in-

struments and direct measurement of angles of industrial products; reference measures for transferring size of the unit of plane angle

from the primary standard to working angle measuring instruments. Terms and their explanations used in GOST 2875-88, as well as descrip-

tion of angle gauge block sets are given in the Tables 15 and 16.

Table 15

Terms and their explanations used in GOST 2875-88

Term Explanation Right prism Prismatic block of a plane angle, the base of which is a

regular convex polygon, the nominal values of the interi-or angles at the vertices of the polygon are equal and less than 180, the nominal values of the lengths of its sides are equal.

Working angle of a block

Angle in the plane of measurement made by two measur-ing surfaces or two normals to the measuring surfaces.

Plane of measurement The imaginary plane which is placed in the body at pos-sibly equal distances from the base and top surfaces and oriented so that the measuring surfaces, chosen to fix it,

41

Term Explanation were equally inclined thereto. It is allowed to place the plane of measurement parallel to the base surface of the block or the block mount.

Wringability of an angle gauge block

Property of the angle gauge block measuring surfaces, which provides a strong bond with an optical flat or be-tween two blocks when lapped measuring faces are put or slid together.

Basic parameters and dimensions of angle gauge blocks Angle gauge blocks are produced in sets or as individual blocks of the

following types: 1 – with one working angle and truncated top; 2 – with one working angle and sharp top; 3 – with four working angles; 4 – a multi-faceted right (n-sided) prism.

Table 16

Angle gauge block sets

Set num-ber

(quan-tity of blocks in the set)

Block type

Increcre-ment

Nominal values of working an-gles

Quan-tity of blocks

Accu-racy

grades

Mass of a set, kg, less than

1 (93)

2 1 From 10 to 79 70

1, 2 15

10' From 1510' to 1550' 5 1' From 1501' to 1509' 9

3 -

80 – 81 – 100 – 99 82 – 83 – 98 – 97 84 – 85 – 96 – 95 86 – 87 – 94 – 93 88 – 89 – 92 – 91 90 – 90 – 90 – 90

6

42

Set num-ber

(quan-tity of blocks in the set)

Block type

Increcre-ment

Nominal values of working an-gles

Quan-tity of blocks

Accu-racy

grades

Mass of a set, kg, less than

8910' - 8920' - 9050' - 9040' 8930' - 8940' - 9030' - 9020' 8950' - 8959' - 9010' - 9001'

3

2 (33)

2

10 From 30 to 70 5

1, 2 5

1 From 10 to 20 11 - 45 1

10' From 1510' to 1550' 5 1' From 1501' to 1509' 9

3 - 80 – 81 – 100 – 99 90 – 90 – 90 – 90 2

3 (8)

2 - 10, 15, 20, 30, 45, 55,60 7 1, 2 2 3 - 90 – 90 – 90 – 90 1

4 (8)

2 - 1510', 3020', 4500', 4530', 5000', 6040', 7550' 7 1 2

3 - 90 – 90 – 90 – 90 1 5

(24) 1 1 From 1 to 9 9 1 4 2' From 1' to 29' 15 Examples of designation of:

a set 2 composed of angle gauge blocks, accuracy grade 1

– angle gauge block H2-1 GOST 2875–88;

an angle gauge block of type 4, 24-sided prism, accuracy grade 0

– angle gauge block 4-24-0 GOST 2875–88;

an angle gauge block of type 3 with working angles 80-81-100-99, accuracy grade 2

– angle gauge block 3-80, 81, 100, 99°–2 GOST 2875–88.

Basic dimensions and accuracy grades of angle blocks must be con-

sistent with those indicated in the Table 17.

43

Table 17

Angle gauge blocks

Block type Drawing Accuracy grade

1

B

5

1; 2

2

70 M1

M2

N

B

5

1; 2

3

M2

M1

M3

M4

a3a1

a4a2

B

5

30

1; 2

4

M4

M6

M1

M2

M3

B

20min

0; 1; 2

Note. Designations used in the drawings are as follows: M – measuring

surface; N – non-measuring surface; B – base surface; T – top (engraved) surface; α – working angle.

Nominal values of working angles of angle blocks of types 1, 2 and 3

must correspond to the angles indicated in the Table 18.

44

Table 18

Working angles

Block type Measurement range Increment

1 От 1' до 29' From 1 to 9

2' 1

2

From 10 to 79 From 15 to 16

From 15 to 1510' From 15 to 1501'

From 1510' to 7550'

1 10'

1'

15" 1010'

3

80 – 81 – 100 – 99; 82 – 83 – 98 – 97; 84 – 85 – 96 – 95; 86 – 87 – 94 – 93; 88 – 89 – 92 – 91; 90 – 90 – 90 – 90;

1

8910' – 8920' – 9050' – 9040' 8930' – 8940' – 9030' – 9020' 8950' – 8959' – 9010' – 9001'

90 – 90 – 90 – 90;

10'

8959'30" – 8959'45" – 9000'30" – 9000'15 90 – 90 – 90 – 90; 15"

Blocks of the types 1, 2 and 3 should have holes for clamping them to-

gether into stacks with the holders from accessory sets. Blocks of the type 4 must be manufactured with 6, 8, 10, 12, 18, 20, 24

and 36 measuring surfaces (side faces). Angle gauge blocks with the number of measuring surfaces 6 8, 10 and

12 should have a central hole with a diameter d = 20H7; angle gauge blocks with the number of measuring surfaces 18, 20, 24 and 36 should have a cen-tral hole with a d = 32H7.

Width of the measuring surfaces (length of a polygon) must be not less than 15 mm. The difference between the maximum and minimum width of a measurement surface should not exceed 0.8 mm.

The distance from the measuring surface to the wall of the central hole should be at least 15 mm.

45

Specification requirements for angle gauge blocks Permissible deviations of gauge blocks from the nominal values, toler-

ances of perpendicularity of the measuring surfaces to the base surface of the block or the block mount, as well as tolerances of the measuring faces flat-ness should not exceed values given in the Table 19.

Deviations of working angles from the nominal value are determined between the adjacent faces.

Hardness of the measuring surfaces of steel blocks must be not less than 61 HRC.

Surface roughness parameters of the gauge block surfaces are set in technical specifications for specific types of gauge blocks.

Failure-free performance of gauge blocks of types 1, 2 and 3 shall be not less than 220 wringings.

Mean life of the gauge blocks of types 1, 2 and 3 must be at least 2 years, gauge blocks of the type 4 – no less than 10 years.

The established full service life of the gauge blocks of types 1, 2 and 3 must be at least 1 year, gauge blocks of the type 4 – at least 5 years.

Failure criteria and limit state of a block are set in the technical specifi-cations for specific types of gauge blocks.

Gauge blocks of types 1, 2 and 3, and a special ruler should be made of steel ШХ-15 GOST 801-78 or other steel grades compliant with the basic characteristics of the mentioned grade.

Gauge blocks of the type 4 must be made of optical grade glass-ceramic С0115M. It is allowed to use optical glass К8 or ЛК7 GOST 3514-76 or steel ШХ-15 GOST 801-78.

Table 19

Tolerances and deviations of the angular gauge blocks

Block type

Permissible deviations from nominal values

Tolerance Perpendicularity of the

measuring surfaces with respect to the base surface of the block or

the block mount

Flatness of the meas-uring surfaces, μm

Accuracy grades 0 1 2 0 1 2 0 1 2

1 2 3 4

- - -

±5"

±10" ±10" ±10" ±8"

±30" ±30" ±30" ±15"

- - -

±5"

±60" ±60" ±60" ±20"

±100" ±100" ±100" ±30"

- - -

0.05

0.15 0.15 0.15 0.07

0.30 0.30 0.30 0.10

46

Note. Flatness requirements are not applied to the area of the measuring

surfaces adjacent to the non-measuring surfaces; the area is 3 mm wide from the short edges and 1 mm wide from the long edges for gauge blocks of types 1, 2 and 3. Flatness tolerance for these areas for the mentioned gauge blocks types is 0.6 μm. Flatness tolerances for the edge areas of the measuring sur-faces and their dimensions for gauge blocks of the type 4 should be set in en-gineering documentation.

Sets of gauge blocks of types 1, 2 and 3 (see the Table 16) include a

special ruler, clamping accessories and screwdriver. All sets (individual blocks) or a multi-faceted prism in a mount are

packed in a case or packing box. The set includes a certificate in accordance with GOST 2.001-93 and a manual.

Gauge blocks are marked according to GOST 13762-86. Nominal val-ues of working angles should be marked on the upper surface of each block of type 1, 2 and 3.

The upper surface of each block of the type 1 should be labeled with plus sign (+) and minus sign (–), indicating the direction of the imaginary in-tersection of measuring surfaces (dihedral angle vertex). The minus sign (-) must be marked on the side of the angle vertex.

The upper surface of the blocks of the type 4 must be marked with: the serial number according to the numbering system of the manufacturer; accu-racy grade; order number of faces (1, 2, 3, .. n) or nominal value of the angles in degrees (0, ..., N) from the first face in the direction opposite to the clockwise direction.

The table on the case of the gauge blocks should include: designation for the gauge blocks of types 1, 2, 3 or 4; the order number according to the numbering system of the manufacturer; year of production or reference des-ignation of the year.

For the blocks of types 1, 2 and 3 each pocket in a case should be sup-plied with an indication of the nominal value of the gauge block placed in.

47

Acceptance and Test To verify compliance with the requirements of the standard, the state

check testing, acceptance testing, periodic testing and reliability testing are carried out.

The state check tests are carried out in accordance with GOST 8.001-80 and GOST 8.383-80.

During the acceptance tests, each gauge block must be tested for com-pliance with GOST 2875-88.

Gauge blocks should be subjected to periodic tests at least once every three years for compliance with all requirements of GOST 2875-88.

Gauge blocks of the types 1, 2 and 3 are selected in fives from the sets 1 and 2 for tests.

If the tests reveal that the gauge blocks comply with all requirements of the standard, periodic testing results are considered satisfactory.

Reliability testing is carried out at least once every three years for com-pliance with the requirements of the standard. It is allowed to combine relia-bility tests with periodic tests.

The effect of climatic factors of environment on transportation is tested in climatic chambers. Tests are carried out in the following conditions: first at a temperature of minus (50 ± 3) °C, then at a temperature of plus (50 ± 3) °C and finally at a relative humidity of (95 ± 3) % at a temperature of (35 ± 3) °C. Exposure time in each of the given conditions in a climate chamber is at least 2 hours. Upon completion of the tests, gauge blocks deviations must not exceed values given in the Table 18.

6.5 Transfer of Physical Quantity

The procedure of transfer of units of physical quantity from the standard

or base reference measuring instruments to the standards of lower accuracy, including working standards, is provided in accordance with the verification chain. The verification chain of length transfer involves parallel intercompar-ison and verification. The transfer of unit is done from working standard to reference standard, then to standards of lower accuracy, then to working measuring instruments (optimeters, measuring machines, automatic checking machines, etc.). The structure of the verification chain consists of several lev-els, corresponding to stages of transfer of units.

There are various types of verification of measuring instruments.

48

1. The usage of a reference standard being calibrated according to the standards. This type of verification may be conducted by any service agency, including industrial standardization service.

2. Intercomparison of the instrument readings and readings of the ref-erence instrument or reference device. Reference instrumentation has higher accuracy grade and respectively quite high cost, for these rea-sons, as a rule, verification is carried out in special organizations – centres of standardization and metrology.

3. Elemental-equivalent method is the most time-consuming type of verification. The method consists in the fact that if the instrument has, for example, a sensor, an amplifier, an analog-digital converter and some other auxiliary devices, then the working performance and measurement errors are determined for all the elements of the in-strument, without verification of the instrument as a whole. In this case, depending on the type of auxiliary devices, these may be tested as the instruments that measure physical quantities different from those for measurement of which the instrument is intended. For ex-ample, profilograph-profilometer may consist of a diamond stylus, an electrical measuring converter, an amplifier, an integrating block and a high voltage direct-writing instrument or output to computer. It is possible to verify the mechanical, electrical and electronic parts of the instrument individually and to arrive at conclusions about work-ing performance and accuracy grade of the instrument as a surface layer quality measuring instrument.

In some cases, when a new type of the measuring instrument is verified, the mentioned type of verification turns out to be more suitable and even in some cases the only one possible. Verification of some types of measuring instruments can be conducted without using reference instruments or stand-ards. The measuring instrument readings may be checked by the tables of physical constants and standard reference data. Among these constants, for example, there are electromagnetic constant, Avogadro constant – the num-ber of particles in one mole of a substance, Newtonian gravitational constant and so on. Readings of these measuring instruments are checked with physi-cal constants or standard reference data.

49

6.6 Measuring Instruments and Devices

The measurements of physical quantities in production are carried out

with the help of working measuring instrumentation – measuring instruments or measuring units.

The measuring instrument is a measuring device aimed at obtaining measuring data in such a form which is comprehensible to an observer. The measurement instrument represents a device calibrated as a rule in units of the measurand.

The measuring instruments include: a measuring transducer (sensor), da-ta digitizer or analog transducer, signal amplifier, readout device.

In addition, the modern measuring instruments can be equipped with various electronic devices. For example, they may include digital readout de-vices, recorders or magnetic storage, special devices for jointing instrument and computer. If the measuring instrument has digital outputs, such as USB, the user has some extra options, for example, statistical processing of data under dynamic conditions of measurement, measurement of parameters of rapidly changing processes.

Depending on the software used for measuring procedure, different pos-sibilities are available, such as: computer can manage the measurement pro-cess, carry out an analysis of current measurement information, etc.

The measuring transducer is a device designed to issue signal of meas-urement information in an easy-to-use form for its transfer, conversion, pro-cessing and storage. The transducer includes a sensor (primary transducer), an intermediate transducer, a transmitting transducer and a multiplier:

the sensor comes first in the measurement chain and directly acquires measurement information. The sensor has a sensitive element (con-tact or non-contact) which is influenced by the measurand;

the intermediate transducer is placed second in the measurement chain;

the transmitting transducer is intended for remote signal transmis-sion;

the multiplier is designed to increase the quantity in several times. The transducers differ in construction and operating principles. They are

available of the following types: mechanical, optical, capacitance, inductive, laser and etc.

The amplifiers are realized as cathode amplifiers, frequency converters and matching devices with computer output.

50

The measuring device is a complex including several devices and auxil-iary components. The differences between instruments and devices are very subtle. For example, if the temperature is measured with the help of thermo-couple and voltmeter, one can call it either a thermoelectric device or an elec-tric thermometer.

Another example is a universal measuring microscope (MMM) which is used to measure geometrical parameters of parts, but essentially is a measur-ing device with a variety of auxiliary devices and appliances.

Besides measuring devices and auxiliary devices the measuring systems may include measures or reference sets. For example, there are sets of re-placeable scales, interchangeable lenses with different focal distance, weight sets, resistance multipliers and inductance boxes, normal galvanic cells, etc.

At the present time geographically spread means of measurement may be connected by communication channels, forming a network. All in total represent information and measurement system. Information in such a system is provided in the most comprehensible form and can be transmitted via the network. The measuring system allows carrying out electronic information processing, analyzing and using it for automatic control of production pro-cesses.

6.7 Metrological Parameters and Characteristics of Measuring In-struments

Metrological parameters and characteristics of measuring instruments

and devices include scale range, measurement range, scale interval, scale spacing, sensitivity and variation, etc.

The indication range is a range of scale values limited by initial and fi-nite values of the scale. The maximum and minimum values of a measurand marked at the scale are called initial and finite values of the instrument scale. For example, for optimeters of IKV-3 type the scale range corresponds to ±0.1 mm; for length gauges of IZV type the scale range corresponds to 0…100 mm.

The measurement range is a range of measurand values, within which the measuring instruments errors are standard. For the optimeters of IKV-3 type the measurement range is equal to 0…200 mm, and for the length gauge – to 0…250 mm.

The scale interval is a difference in values of the quantity corresponding to the two adjacent marks on the scale. For example, for optimeters and length gauges it equals to 0.001 mm, and for a micrometer – 0.01 mm.

51

The scale spacing is a distance between centres of two adjacent marks of the scale measured along the imaginary line passing through the centres of the marks of the scale. It is clear that the bigger the scale spacing is, the high-er the magnification is and the easier the way of comprehension of measure-ment information by an observer is.

The measuring instrument sensitivity is a relation of the measuring in-strument output signal variation to the caused variation of the measurand. For example, if the measurand variation equals to 0.01 mm , when measuring a shaft diameter with nominal dimension x=100 mm, caused travel of a pointer of the given device over 100 mm, then it means that absolute sensitivity is 10/0.01 = 1,000, and relative sensitivity equals to 10∙(0.01/100) = 10,000. For the indicating measuring instrument the absolute sensitivity is numerically equal to the transmission ratio and with change of scale interval the instru-ment sensitivity remains invariant. But sensitivity may differ with respect to the section of the scale. The concept of sensitivity can be determined by transfer function as the function of a relationship between input and output signals of a transducer. Depending on the type of the function, the sensitivity may be a constant quantity or a quantity dependent on this function. If a func-tion is linear, then the scale of an instrument is linear and vice versa. The scale linearity depends not only on the transducer characteristics but also on the type of physical quantity unit.

Together with sensitivity there is a concept of threshold of sensitivity, which is the minimum value of measurand variation which may be shown by the device. The lower the threshold of sensitivity is, the greater the sensitivity is. Furthermore it is dependable on definite conditions of observation, such as possibility to differentiate small deviations, stability of indications, static fric-tion magnitude and others.

Reading variation is defined as a difference in device indications ob-tained for a point of the measurement range, when the point is slowly ap-proached from the left and from the right. The reading variation represents algebraic difference of the maximum and minimum values of the multiple measurements of the same quantity in fixed conditions. Variation character-izes instability of indications of a measuring instrument.

A calibration characteristic is a relationship between input and output values of a measuring instrument represented by a formula, table or diagram. In most cases instruments are calibrated in such a way that the scale interval exceeds the maximum calibration error but this principle is not always appli-cable. Thus, although there is a certain relation between accuracy and sensi-tivity, we should not confuse these concepts. The device calibration charac-teristics can be used for refinement of measurement results.

52

The important characteristic of contact measuring instruments is meas-uring pressure, which is applied on a measurement line and creates defor-mation at the contact of a measuring point with a part surface.

The measuring instruments can be analog and digital. In analog instru-ments the indications are determined by the scale and are continuous function of measurand variation. In digital devices the discrete signals of measuring information are produced and the result is represented in a digital form.

53

7. Measurement Errors and Causes of the Errors The quality of measurement is characterized by accuracy, certainty, cor-

rectness, repeatability and reproducibility of measurement. The measuring device accuracy is a metrological characteristic determined by measurement error within the limits of which we can use the given measuring instrument.

In metrology a concept of “accuracy grade” of a device or material measure is used. The accuracy grade of means of measurement (GOST 8.401-80) is a general characteristic which is determined by the limits of in-trinsic or complementary errors including some other properties influencing accuracy which values are specified by the standards issued on different types of measuring instruments.

The accuracy grade describes properties of measuring instruments but not accuracy of the measurement itself, as to determine measurement errors it is necessary to take into account errors of the method of measurement, cali-bration errors, etc.

Depending on accuracy all devices are divided into grades: the first, the second, etc. The permissible errors for different types of instruments are specified in national standards. Accuracy is a measurement quality that repre-sents closeness of measurement results to the true value of a measurand. Quantitative assessment of accuracy is a reciprocal absolute value of a rela-tive error. For example, if the measurement error is equal to 10-6, then the ac-curacy equals to10+6.

The measurement accuracy depends on measurement errors: absolute error of measurement is a difference between measured val-

ue of a quantity and its true value expressed in units of a measurand; relative error of measurement is a relation of absolute error of meas-

urement to the true value of a measurand; systematic error of measurement is an error component being con-

stant or varying in accordance with a definite law within repeated measurements of the same quantity. Systematic error can be elimi-nated with the help of corrections;

random error of measurement is an error component varying within measurements of the same quantity repeated in a random manner;

gross error of measurement is defined as an error, which value is es-sentially greater than the expected one.

54

According to the sequence of errors origin there are several types of er-rors:

instrument error is a measurement error component depending on er-rors of the given measuring instruments. These errors are determined by the quality of measuring instruments;

error of the method of measurement is a measurement error compo-nent caused by imperfection of a measurement method;

calibration error is a measurement error component caused by imper-fection of the calibration process;

reading error is a measurement error component caused by inaccurate reading of a measuring instrument. The error is caused by visible var-iation of the relative positions of scale marks as a result of move-ments of the line of sight; this error is called a parallax error;

verification error is a measurement error component which is a result of imperfection of verification of means of measurement. The errors due to measuring pressure take place when a contact measuring in-strument is used. In estimating of measuring pressure effect on meas-urement error it is vital to define elastic deformation of a positioning part of the instrument and deformation in a contact area of a measur-ing point with a part;

influence quantity is a physical quantity that is not being measured by a given instrument, but which influences the value of the measur-and, for example, temperature and ambient pressure, relative humidi-ty and other parameters different from standard values.

The error of a measuring instrument that occurs when the instrument is

used in standard conditions, when the influence quantities are within the lim-its of reference range, is called intrinsic error.

If the value of the influence quantity is out of the standard range, the complementary error arises.

Standard conditions for the measuring instruments application are the conditions in which influence quantities have normal values or are within the limits of a standard (working) range. The standard conditions for implementation of linear and angular measurements and verification are specified in GOST 8.050-73 and GOST 8.395-80 respectively.

Standard temperature of measurements is equal to 20°C (293 K), here-with the working range of temperatures is equal to 20±1 °C.

Thermal errors are caused by thermal deformations. The reason for the deformations is a difference of temperatures of an object being measured and a measuring instrument. There are two basic reasons that cause errors by

55

thermal deformations: deviation of air temperature from 20 °C and short-term variation of air temperature during the measurement.

Personal errors are the errors depending on an operator. Four types of personal errors are possible:

1. reading error; 2. presence error (influence of operator’s thermal radiation on ambient

temperature and thus on a measuring instrument); 3. implementation error (brought in by an operator during the device

setting up); 4. professional errors (are connected with operator’s qualification and

his/her attitude to the procedure of measurement). Observation result is the value of a quantity obtained under individual

observation. Result of a measurement is the value of a quantity obtained during

measurement after observation results analysis. Stability of a measuring instrument is a qualitative characteristic of a

measuring instrument, reflecting invariability of its metrological properties. Uncertainties of a measuring instrument or variations in its indications

serve as a quantitative evaluation of stability. The reliability of measurements characterizes the degree of confidence in measurement results. The reliability of error evaluation is determined by the laws of probability theory and math-ematical statistics. It allows choosing means and methods of measurement for each individual case providing results, which errors do not exceed the nomi-nal values with the necessary certainty.

Correctness of measurement is the quality of measurement that reflects closeness of the systematic errors to zero in the measurement results.

Repeatability is the quality of measurement that reflects closeness of measuring results to each other, taken on the same parameter, by the same instrument, the same method of measurement, in the same conditions and with the same care.

Reproducibility is the quality of measurement that reflects closeness of measuring results to each other, made in different conditions (in different time, places, by different methods and means).

56

8. Measurement Traceability Assurance Measurement traceability assurance is activity of metrological or other

services of the country aimed at establishment of necessary standards, refer-ence and working measuring instruments, correct selection and application of the instruments; development and application of metrological standards and regulations; implementation of other metrological activities required for pro-vision of required quality of measurements at the workplace, in enterprises and organizations, in industry and in the national economy.

Measurement assurance is aimed at provision of traceability and accura-cy of measurements in order to achieve desired characteristics of the equip-ment functioning in accordance with specifications. Measurement assurance represents a set of scientific, technical and organizational activities carried out by corresponding organizations and specialists. Measurement assurance includes: theory and techniques of measurement, inspection and assurance of accuracy and traceability; technical and organizational issues of traceability of measurements, including technical documents such as national standards, procedural guidelines, technical specification and conditions that specify pro-cedure and rules of processes implementation.

The practice of measurement assurance organizations covers a large range of issues. Application of statutorily prescribed system of physical quantities is monitored by the organizations. Traceability and accuracy of measurements is assured by dissemination of physical quantities from nation-al standards to reference measuring instruments and then to working measur-ing instruments. Functioning of national and departmental verification schemes is also monitored. New methods of measurements providing pin-point accuracy are constantly developed. Thereupon standards and reference measuring instruments are established.

The condition of means of measurement in departments and ministries is monitored. Measurement assurance of measuring instruments solves quite specific issues on the different stages of the instruments service life:

specification of requirements to volume, quality and nomenclature of measurements and control means, the parameters and characteristics of metrological systems and measuring instruments are studied;

analysis and selection of means of measurement and inspection among the series-produced ones. If there are no appropriate means of measurement, then specifications for production of the new ones are developed;

57

implementation of the verification of means of measurement; analysis of the manufacturing processes in terms of selection of

measuring instruments, sequence of the inspection operations and metrological characteristics of corresponding measuring instruments;

production support of batch measuring instruments and inspection means with the purpose of timely re-equipment of enterprises;

metrological testing of drawings and engineering documentation to-gether with updating of methods of measurement and inspection.

Responsibility for correctness, timeliness and integrity of measurement

assurance of technical equipment is laid on the users. Metrological services of organizations and enterprises are in charge of solution of issues on meas-urement assurance.

Technical foundations for measurement traceability assurance are the following:

a system (set) of national standards of units and scales of physical quantities known as a national standard base;

a system of dissemination of units and scales of physical quantities from standards to all measuring instruments with the help of stand-ards and other means of verification;

a system of development, manufacture startup and production of working measuring instruments which ensure activities connected with research, development, identification of product characteristics, manufacturing processes and other objects with required accuracy;

a state system of testing of measuring instruments (approval of meas-uring instruments type) designed for batch production or mass pro-duction and import;

a system of state and departmental metrological certification, verifi-cation and calibration of measuring instruments;

a system of certified reference materials of composition and proper-ties of materials;

a system of standard reference data on physical constants and proper-ties of materials.

58

8.1 Verification, Inspection and Expertise of Measuring Instruments

One of the most important forms of state supervision of measuring

equipment is state (or departmental) verification of measuring instruments, which ensures metrological accuracy.

The measuring instruments undergo initial, periodic, additional or in-spectional verifications:

initial verification is carried out along with the output of measuring instruments after the manufacture or repair;

periodic inspection is carried out when measuring instruments are in operation or storage, at appropriate intervals determined in such a way so that to provide metrological accuracy of measuring instru-ments for the periods between verifications;

additional verification is carried out when it is necessary to prove ac-curacy of a measuring instrument in the process of correction of veri-fication intervals, in cases of damage of verification mark or seal or loss of documents, including some other cases, while the timing of the inspection is determined independently from the timing of period-ic inspections;

inspectional verification is carried out to identify metrological accu-racy of the currently used measuring instruments; during metrologi-cal inspection in organizations, at enterprises and supply bases.

The following measuring instruments are subjected to compulsory state

verification: measuring instruments used by national service of legal metrology

and reference measuring instruments serving as initial ones in metro-logical organizations of ministries and departments;

measuring instruments used for estimation of the material values, in mutual settlements and trade;

measuring instruments related to health care of population and safety regulations;

measuring instruments used for state testing of new measuring in-struments, as well as instruments, the readings of which are used in registration of official international and national sport records;

measuring instruments used for merchandise accounting: weight measuring devices, flow meters, electricity meters, gas meters, oil meters, water meters etc.;

59

devices used in population health care: sound level meter, dosimeters, roentgen meters, tonometers, medical thermometers, etc.;

measuring instruments that ensure safety of works: radiometers, mi-crowave field-intensity meters, gas-analyzers, etc.

Other measuring instruments are subjected to compulsory departmental

verification. Timing of the inspection (verification intervals) are assigned and corrected by metrological departments of enterprises, organizations and other establishments exploiting measuring instruments in such a manner to provide their metrological accuracy for the periods between verifications.

Initial verification interval is determined in state testing of the measur-ing instrument. Verification of measuring instruments should be carried out in accordance with current national standards that cover measurement chains, methods and means of verification.

The successful results of verification are certified by giving a verifica-tion mark to the measuring instrument and issuing a verification certificate. Metrological inspection includes verification of measuring instruments con-ditions and implementation of a verification procedure. The results of metro-logical inspection are filed under the act containing particular verification re-sults including also proposals on withdrawal of measuring instruments acknowledged as nonserviceable, and proposals on corrective measures with time indication.

8.2 State Testing of Measuring Instruments

The measuring instruments designed for batch production and import

from abroad are put to compulsory state testing by agencies of National ser-vice of legal metrology. State testing involves examination of engineering documentation of measuring instruments and experimental investigation of the instruments in order to determine the conformance to the specified stand-ards and manufacturing requirements. State-of-the-art of the measuring equipment is also evaluated for reasonability of manufacture or purchase of new equipment.

State testing can be of two types: state acceptance testing of the proto-types of measuring instruments of new types that designed for a batch pro-duction or import into the Russian Federation, and state check testing of the pilot samples from the preproduction batch and batch-produced measuring instruments.

60

State acceptance tests are carried out by corresponding national services of legal metrology or special national commissions consisting of representa-tives of institutes of metrology, organizations-developers, manufacturers and customers. In the process of state acceptance testing of pilot samples of the measuring instruments the service checks conformity of measuring instru-ments with the state-of-the-art, requirements of the performance specifica-tion, specification project and national standards.

Normalized metrological characteristics and possibility of their inspec-tion during manufacturing, after repairing and in operation, the possibility of verification and maintainability of the measuring instruments being tested are also subjected to inspection. On the basis of study and analysis of the engi-neering documentation and instruments being tested the state acceptance commission makes recommendations on expediency (or non-expediency) of production of the measuring instruments of the given type.

The governmental agency on standardization and metrology studies the materials of the state testing and concludes on approval of output of a meas-uring instrument. After that this type of a measuring instrument is registered in the national registry of measuring instruments.

State check testing is carried out by territorial organizations of the gov-ernmental agency on standardization and metrology.

The purpose of state check testing is verification of conformity of the manufactured measuring instruments and measuring instruments imported from abroad with the standard requirements and standard specifications. Check testing of batch-produced measuring instruments is carried out in cer-tain cases. Tests of this type are required during the manufacture of new measuring instruments of a preproduction batch, in case there is a quality de-terioration of the measuring instruments produced by a manufacturer.

Check testing is carried out if there are some changes in the structure or technology of measuring instruments production, which influence standard-ized metrological characteristics. The testing also takes place in order to con-trol quality of the manufactured measuring instruments within the terms which are assigned by the governmental agency.

61

9. Product Quality Control Product quality is a set of product properties that determines product

ability to meet some definite requirements in accordance with the product application.

Quality control is acquisition and processing of information on an ob-ject with the purpose of finding object parameters within the specified limits. The process of control involves identifying if the actual values of physical quantities correspond to the specified limit values. The purpose of control is to answer the question whether the inspected physical quantity is within the tolerance zone or not.

Control of parameters and characteristics of an object related to deter-mination of actual values of physical quantities is called inspection by meas-urement.

When there is no need to determine numerical values of a physical quantity, but it is required to determine the fact that the parameter is within the tolerance zone or out of it, a qualitative estimation of object parameters, i.e. quality inspection is made. Quality inspection unlike inspection by meas-urement is simply called inspection.

9.1 Types of Inspection

Classification of types of quality inspection is based on various criteria:

time and position of measurement in the manufacturing route, control action of the inspection, object of inspection, etc. Let’s consider the most common types of inspection.

Inspection can be of destructive or nondestructive type. In destructive testing to perform checking operations it is required to

destruct an object making it unsuitable for further use. The example of de-structive testing, when the checking of compliance of a controlled parameter with the specified limit deviations is accompanied by the object destruction, is the product strength testing.

In nondestructive testing the compliance of a controlled value with the specified limit deviations is determined on the results of acquired information on the object of inspection. Interaction of measuring instrument elements with the object of inspection doesn’t cause destruction of the object and doesn’t change its properties. The examples of nondestructive testing can be:

62

inspection of the part dimensions, form deviation and location deviation, pressure, temperature, etc.

The results of inspection can be used to work on the manufacturing pro-cess. Depending on nature of this action the inspection is divided into in-process (or active) control and passive control.

In-process control is carried out in the technological process of product shaping, for example during the part machining. The active results of in-process control give information on necessity of change of the machining pa-rameters or correction of manufacturing equipment parameters, for example the necessity of change of position between cutting tool and part. In-process control can be manual when the machine is operated by a man during manu-facturing process or automatic when operation is carried out with the help of commands from the control unit. Application of in-process control helps to increase labour productivity, improve quality of manufacture, introduce sim-ultaneous handling of component parts of equipment, achieve high accuracy of products, and employ semiskilled operators to such kind of work. The cre-ation of in-process control devices that operate according to reference models without any adjustment is rather future-oriented. These can be both tangible objects (for example, reference parts) and corresponding software.

Unlike the in-process control the passive control is carried out after the completion of either a single manufacturing operation or entire technological cycle of the object manufacturing (batch of parts or product). At the stages of product life cycle, including production process, the given type of control has different purposes and time needed for implementation.

There are incoming quality control, operational inspection, acceptance inspection and also continuous, periodic and casual inspection.

Raw materials, initial materials, semi-finished products, component parts, engineering documentation and etc. are put to incoming quality con-trol. The control is carried out in accordance with several parameters, includ-ing visual inspection control and instrumental verification of product geome-try, compliance with shipping documents, defects evidence etc. The devel-opment of product quality in the process of manufacturing at the enterprise starts with income quality control.

Operational or interoperational inspection is carried out at different stages of manufacturing process of batch production. Its purpose and proce-dure is specified in manufacturing documentation – by route or operation sheets.

Acceptance inspection consists of inspection of finished products and critical components. Relative position of the product elements, quality of joints (tightening force and torque of the threaded joints, quality of adjust-ment of joint surfaces etc.), correctness of positioning and presence of parts

63

in assemblies, the mass of components and product in whole, balance of ro-tating parts, etc. are subjected to this kind of control.

Continuous and periodic inspection means either continuous checking of the controlled parameters compliance with the standards of accuracy or correspondingly the periodic inspection in definite time intervals.

The casual inspection may take place at any arbitrary time. The inspection is carried out in end-to-end manner; objects of govern-

mental, regional and international significance are subjected to state control and supervision. For example, it refers to the objects subjected to the re-quirements of technical regulations, state supervision on measuring equip-ment, supervision of application of statutorily prescribed system of units of physical quantities.

Another stage is inspection checkup which can be departmental, inter-departmental, non-departmental.

Further, there are manufacturing inspection, inspection implemented by the quality control department (QCD) of the enterprise, shop inspection by a shop foreman and individual inspection at the workplace.

Depending on the site of inspection implementation, there can be non-stationary and stationary inspection.

Most of the inspection types are carried out directly at the workplaces: at the machine tool, at production areas, in the workshops etc. Such kind of inspection is called non-stationary. But in some cases it is impossible to carry out non-stationary type of inspection, since it requires use of special means of inspection such as separate test areas, inspection stands, laboratories and sometimes detached structures as, for example, for radiation control. This type of inspection is called stationary.

The objects of the inspection are: manufactured products; engineering, trade and accompanying documentation; parameters of manufacturing pro-cess; fixtures and tools; reclamation documentation; rules of observance of operational conditions; technical discipline and qualification of employees.

According to production output there are two types of inspection: single and multiple inspections.

In accordance with sampling procedure there can be 100% inspection and inspection sampling. 100% inspection of all the manufactured products without any exception takes place in job production and small-batch produc-tion.

In case of large-batch production or mass production the statistical qual-ity inspection is carried out.

64

10. Measurement and Inspection of the Product Parameters

10.1 Measurement and Inspection

The main requirement for carrying out inspection during the manufac-

turing process is to ensure accuracy. The measurement accuracy depends on a number of factors, the main are: the maximum errors of the means of meas-urement and inspection, metrological principles of the instruments design, accuracy of the implemented measurement methods, influence of the external factors.

The development and adoption of procedures of measurement and in-spection is of great importance. The measurement procedure is a series of methods, tools, procedures, conditions of preparation and implementation of measurements, as well as rules for the processing of the experimental data to perform specific measurements.

Measurements should be carried out in accordance with the appropriate-ly certified procedures. The development of the measurement procedures should include:

analysis of technical requirements for the accuracy of the object be-ing measured;

identification of the required conditions of measurement; selection of measuring instruments; designing of the supplementary metrological equipment; testing of the means of measurement and inspection; planning of the processes of measurement and inspection; development and selection of an algorithm for analysis of the results

of observation; designing of the execution and presentation of the results of meas-

urement. Technical documents that regulate measurement procedures are: GOSTs and procedural guidelines on procedures of measurement.

Standards are issued in case the means of measurements are regis-tered in National registry of measuring instruments;

industrial procedures of measurement that are used within the branch of industry;

65

standards of enterprises on procedures of measurement that are used in the enterprise. The procedures of measurement include: the stand-ards of the measurement accuracy; functional features of the meas-ured value; the need for measurement automation; the use of software for data processing, etc.

Measurement procedures before the implementation should be certified

or standardized. Certification of measurement procedures is performed by the state and

departmental metrological services. Here, the state metrological services cer-tify procedures of the extra accurate and vital measurements.

The standardization of procedures is used for the measurements that are widely used in enterprises. Measurement procedures are reviewed periodical-ly for the purpose of their improvement.

10.2 Selection of Means of Measurement and Inspection

Selection of means of measurement and inspection provides the solution

of the issues related to the selection of organizational and technical forms of inspection, expediency of inspection of the specified parameters and perfor-mance of these means.

The same metrological task can be solved with the help of various measuring instruments that have different costs and different metrological characteristics. The set of metrological, operational and economic character-istics should be considered in interconnection.

The metrological parameters, which should be primarily taken into ac-count are:

maximum error; scale interval; measurement force; measurement limits. Operational and economic characteristics include: cost and reliability of

measuring instruments, operating period until repair, time spent on setup and the measurement process, weight, dimensions, etc.

In most cases, the higher the required accuracy of measurement tools is, the heavier and more expensive the instrument is, the higher the requirements for the operating conditions are.

66

10.3 Accuracy of Means of Measurement and Inspection

Accuracy of means of measurement and inspection influences applica-

tion of the standard tolerance T of the part dimension, which is reduced in a way (Fig. 1a). Let the measuring tool be perfect, i.e. without errors, then it can be set to the limits E1 and E2, and the tolerance T would remain un-changed.

Fig. 1 Variants of the acceptance borders relative to the tolerance zone

In fact, there is always a metrological error of measurement METR ,

thus to avoid acceptance of defective parts and admission of the parts, by mistake, as non-defective, value of the tolerance T must be reduced to the value of the manufacturing tolerance METRr TT 4 (Fig. 1, b). The vari-ant, corresponding to the situation when an instrument is set to the limits of error METR , which are the limits of the tolerance zone 1E and 2E , reduces the manufacturing tolerance and, therefore, increases the cost of manufacture. Reduction of manufacturing costs can be achieved either by reducing a met-rological error METR , or by changing the setup, i.e. establishing acceptance

67

limits outside of the tolerance zone (Fig. 1d). Thus, the tolerance will extend to the guaranteed value GT . The actual combination of measurement error and deviation of the measured parameter is a random event.

Assuming that both components are subjected to the normal distribution, the following can be written 2

METRrTT . Analysis of these dependen-cies shows that if 1.0/ TMETR , then almost all the tolerance is used to compensate for manufacturing errors, since 995.09.0/ TTr in this case. Assuming that 4.0/ TTr , then T)917.06.0( can be used to compensate for manufacturing errors. According to GOST 8.051-81, the maximum per-missible error of measurement, for a range of 5001 mm, can range from 20% (for lower accuracy grades) to 35% of the standard tolerance value.

Standardized measurement errors include both random and systematic errors of the measuring instruments, including errors of gauge blocks, locat-ing elements, etc. They are the maximum permissible total errors.

In practice, it is economically reasonable to take value of the random er-ror of approximately 0.1 of the standard tolerance value. Consequently, the accuracy of measuring instruments must be an order of magnitude higher than the accuracy of the parameter being inspected. The increase in accuracy of product manufacturing, in order to ensure the required level of quality, leads to the need to create measuring instruments with much greater accuracy of measurement, i.e. the principle of advanced raise of accuracy of measuring instruments compared to the accuracy of the manufacturing tools must act.

Another variant of positioning measurement error zone is symmetrical location with respect to the limits of size (Fig. 1, c). However, in case of such location, there is a risk, though not large, that defective parts can be mistak-enly accepted and good parts will be rejected. If it is necessary to reduce the risk of accepting defective parts the acceptance limits are shifted inside the tolerance zone on the value of c (Fig. 1, d).

Value of the acceptance limits offset can be taken equal to 2/METRc , if the accuracy of the manufacturing process is known, then c is to be calcu-lated. The permissible error of measurement depends on the part tolerance and, thus is taken into account when selecting measuring instrument. Permis-sible errors of measurement for IT2 - IT17 grades and range of sizes from 1 to 500 mm are given in GOST 8.051-81.

The relative error of measurement is expressed by the following equa-tion:

TA METRMETR /)( , where METR is the standard deviation of the error of measurement.

68

The influence of the measurement errors in acceptance inspection upon linear dimensions can be estimated with the help of parameters m, n and c (Fig. 2), where: m – portion of the measured parts with dimensions exceeding the limits of size, but taken among the good parts (wrongly accepted); n – portion of the parts with dimensions not exceeding limits of size, but rejected (wrongly rejected); c – the probabilistic maximum value of the wrongly ac-cepted parts sizes overrun.

Fig. 2 shows the distribution curves of the part dimensions ( manufy ), and measurement errors ( metry ), with the center of distribution of the measure-ment errors coinciding with the tolerance limits.

Fig. 2 Distribution curves of the inspected parameters with measurement errors

taken into account

69

The superposition of curves of manufy and metry distorts the distribution curve y ( METR , MANUF ), as a result, the probability areas of m and n appear, which cause the size to exceed the tolerance limit on the value of c. The greater the ratio TMETR / is, which means more accurate manufacturing pro-cess, the smaller the number of incorrectly accepted parts compared to incor-rectly rejected parts is, since 1.11.0/ nm . The maximum value of the c is in the range (1.5-1.73) METR .

The parameters m, n, and c may be defined according to the Table 20, it is recommended to take )(METRA =0.16 for the grades IT2-IT7;

)(METRA =0.12 for the grades IT8, IT9; )(METRA =0.1 for the grade IT10 and lower. The smaller values of m, n and c in the Table 20 correspond to the normal distribution of measurement error, the greater values correspond to the law of equal probability.

With the unknown law of measurement error distribution the values of m, n and c can be defined as the average of the range values given in the Ta-ble 20. Limit values of m, n and c/T include only the influence of the random component of the error of measurement. Values of m, n and c are also given in the literature as nomograms.

GOST 8.051-81 provides two methods of establishing acceptance bor-

ders. The first method implies that the acceptance borders coincide with the limits of size, in the second method the acceptance borders are shifted inward with respect to the limits of size.

Table 20

Values of the relative error of measurement for different distribution laws

)(METRA , % m , % n , % /c T 1.60 0.37...0.39 0.70...0.75 0.01 3.0 0.87...0.90 1.20...1.30 0.03 5.0 1.60...1.70 2.00...2.25 0.06 8.0 2.60...2.80 3.40...3.70 0.10 10.0 3.10...3.50 4.50...4.75 0.14 12.0 3.75...4.11 5.40...5.80 0.17 16.0 5.00...5.40 7.80...8.25 0.25

Let’s consider examples of the measuring tools accuracy selection.

70

Example 1. Determine the accuracy of the measuring instruments

required for the procedure of acceptance of manufactured shafts with 100h6(-0.022), and determine values of the statistical parameters m, n, and c. Acceptance limits are set matching the limits of size.

The permissible error of measurement, according to GOST 8.051-81, is 6METR microns for %16)( METRA (accuracy grade IT6). According to

the Table 20 the number of defective parts being accepted is m=5.2%, the number of incorrectly rejected parts is n=8%, and c=5.5%. The general dispersion of the error of measurement of the accepted defective parts is in the range from 5.27 to 5.5 microns (see Fig. 1, c), i.e. up to 5.2% of defective parts with permissible deviations of +0.0055 mm and -0.0275 mm can be found among the accepted ones.

Example 2. The decrease in accuracy due to errors of measurement is

unacceptable, therefore acceptance borders are shifted inside the tolerance zone on the value c (see Fig. 1, d).

Depending on whether the manufacturing process accuracy is known or unknown, there may be two ways of manufacturing tolerance defining. In the first case it is needed to define limits of size when the accuracy of the manu-facturing process is unknown. In accordance with GOST 8.051-81 the limits of size are shifted by half of a permissible error of measurement. For the ex-ample considered, it would be 003.0

019.0100 . In the second case it is needed to

define limits of size when the accuracy of the manufacturing process is known. In this case the limits of size are reduced by the value of c parameter.

Suppose that for the example mentioned above the 4/ MANUFT (there is 4.5% rejection rate on the both limits of size after the manufacture):

%16)( METRA , c/T=0.1, c=22 microns. Accuracy requirements for the size of the shaft, with respect to these data, will be the following: 002.0

020.0100 .

10.4 Measurement Results Analysis

Processing of measurement results, using statistical methods, is applied

in practice towards the following tasks: determination of the measuring instrument error; identification of whether the manufacturing process parameters meet

the specified accuracy of the product; calculation of the manufacturing tolerance;

71

determination of accuracy characteristics of the preproduction batch-es and sample batches of parts, to control and manage quality of the products;

setting of the quality scattering parameters of similar products; etc. Measurement results are obtained by appropriate processing of observa-

tions, readings obtained by means of measurements. The following concepts are implemented here: result of observation – the value of the instrument readings, obtained

by an individual measurement; result of measurement – the value, obtained after processing the re-

sults of observations. During the manufacture of the batch of parts, scattering of their geomet-

rical and physical-mechanical parameters inevitably occurs. Therefore, re-sults of measurement of the parameters of each individual part are random variables. The same thing happens with repeated measurements of one part with a given means of measurement.

In manufacture and measurements there are systematic and random er-rors.

Systematic errors are errors constant in magnitude and sign, or changing in a predetermined law, depending on the effects of certain predictable rea-sons.

Systematic errors occur, for example, because of inaccurate machine tool setup, measuring instrument errors, deviations of temperature from the standard operating temperature (including the subjective actions of the opera-tor), deformations, etc.

Systematic errors of measurement can be partially or completely elimi-nated, for example, with the help of a correction table to the incorrectly grad-uated scale of the device or by determining the arithmetic mean values of several readings in opposite positions, for example, when measuring the thread pitch and half angle of the thread profile or by correcting wrong ac-tions of an operator (the effect of breath or touch on the temperature, the ex-ceeding of the measurement force).

Random errors are variable in magnitude and sign errors, which occur in the manufacture or measurement, and take a particular numerical value de-pending on the number of randomly acting reasons.

A characteristic feature of the random error is a variation of their values in repeated experiments.

72

The random errors are caused by many randomly varying factors, such as: inaccuracies of the measuring instrument components, machining allow-ance, mechanical properties of the material, cutting force, measuring force, varying accuracy of installation of parts on the measuring position and other factors, and in general, none of these factors prevails.

Manufacturing errors and measurement errors are random variables. Ex-amples of random variables are: dimensions of parts during manufacture, clearances in sliding joints, results of repeated measurements of the same quantity, etc.

Random errors are difficult to eliminate, that’s why they are taken into account when assigning a tolerance for a dimensional or any other parameter.

The numeric value of a random variable being a result of a measurement is considered as a random event. The same thing happens during product test-ing, for example, when it is needed to establish product quality indicators.

The ratio of n events of a random value A to the N produced tests, in which the event might occur, is called relative frequency of W(A)=n/N.

With a sufficiently large number of trials N, the ratio value for most of the random events is found to be stable. The value of W(A) for the event A will fluctuate around some constant number equal to one. This number, al-ways less than one, is called the probability P(A) of the event A, i.e., P(A) is a measure of the objective possibility of occurrence of the event A.

The probability of a certain event is equal to one, probability of an im-possible event – to zero.

The relative frequency can be taken as the approximate value of the probability P(A) of the event A at a sufficient number of tests:

NnAWAP /)()( . (1) Relative frequency W(A) is different from the probability P(A) that it is

a random variable, which in various series of similar tests may take, depend-ing on the random factors, different values, whereas the probability P(A) is a constant, for a given event, number, which on average determines the relative frequency of the event occurrence in the experiments.

With the increasing N the relative frequency approaches the probability. The relationship between the numerical values of the random variable

and the probability of their occurrence is established by the law of probability distribution of random variables. Probability distribution of a discrete random variable can be represented as a table or diagram, showing how likely a ran-dom variable x takes a particular numerical value xi.

Probability distribution of the continuous random variable, which can take any value within a given interval, can not be represented as a table.

The distribution is represented as a differential function of distribution or probability density function px(x). This function is the limit of the ratio of

73

the probability of the fact that the random variable x takes the value that lies in the interval from x to xx to the value of the interval x , when x tends to zero.

The nature of the scattering of the essentialy large set of values of a ran-dom variable usually corresponds to a theoretical distribution law.

The scattering of the random variable values, the change of which de-pends on a number of factors, when no one factor has predominant influence, follows the normal distribution law (Gaussian), shown in Fig. 3.

3 3

y

x

a

Fig. 3 Curve of the normal distribution

To this law with some approximation may be subjected: variance of er-

rors of the multiple measurements; variance of manufacturing errors; errors of measurement of linear and angular dimensions; masses of parts; values of hardness and of other mechanical and physical quantities.

Normal distribution law has the following properties: the probability of positive errors is equal to the probability of nega-

tive errors; small in magnitude errors have a greater probability of occurrence

than the errors of larger magnitude; the algebraic sum of the deviations from the mean value is equal to

zero. The dependence of the probability density is defined by the equation:

74

2

2

2)(

21

ax

x ey , (2)

where a and σ are the parameters of the distribution; x is the argument of the probability density function, i.e. a random variable that varies in the range

x ; e is the base of natural logarithms. The normal distribution curve is symmetrical about the ordinate axis.

The value of a is equal to the mathematical expectation M(x) of the random variable x, which is determined by the equations:

for discrete values

k

iii xpxxM

1)()( , (3)

where ix is the possible value of a discrete random variable; )( ixp is the probability of the value ix of a discrete random variable;

for continuous variables

dxxxpxM )()( , (4)

where p(x) is the probability density of a continuous random variable x. The value of M(x) represents the position of the center of variance of

random variables, the place where, for example, the sizes of the most parts of the batch are grouped around.

In the absence of systematic errors in the results of repeated measure-ments of the same quantity in the same conditions, the expectation can be re-garded as the closest approximation to the true value of the measurand.

In analysis of the nature of the variance of the machined parts dimen-sions, the expectation can be regarded as the dimension, for which the ma-chine tool has been set up.

The magnitude of the random variable variance from the expected value is defined by the parameter σ, which is called standard deviation of a random variable and is determined by the equation:

for discrete value

k

iii xpxMxx

1

2 )()()( , (5)

for continuous variable

dxxpxMxx )()()( 2 . (6)

Scattering of the random variables is also characterized by variance 2)()( xxD .

75

Formula (2) represents an equation of the curve for the case when the origin is located at an arbitrary position on the x-axis. If the center of vari-ance coincides with the origin of x-axis, the equation of the normal distribu-tion curve will take the form:

2

2

2

21)(

x

exy . (7)

At the same time, there are other distribution laws that describe the ran-dom variables, which have the nature of a somewhat different nature.

In this case it is necessary to mention Maxwell law, to which the essen-tially positive quantities are subjected; such quantities are: the scattering of eccentricity values, axial and radial run-out, concentricity deviation, imbal-ance and other quantities that cannot be negative.

To evaluate the reliability of products Weibull law, which gives an idea of the probability of failures, is used.

Simpson law (or the triangular distribution law) and the law of equal probability also have become widespread.

However, for the analysis of observations the normal distribution law – Gaussian law is used.

The probability for the value to fall into a given interval can be defined as follows. The branches of the theoretical normal distribution curve (Fig. 3) go into infinity, asymptotically approaching the x-axis. The area enclosed by the curve and the abscissa is equal to the probability that the random variable, for example, error of size, belongs to range . The area under the distribu-tion curve is equal to 1 or, what is the same, 100%, and is determined by the integral:

12

1 2

2

2

dxex

. (8)

The origin is located at the point coincident with the center of variance.

Since the integrand is even and the curve is symmetrical with respect to the maximum ordinate, we can write:

5.02

1 2

2

2

dxex

. (9)

To express the random variable x as a fraction of its σ let’s assume that

zx / hence zx , dzdx . In this case, the abscissa in Fig. 3 is ex-

76

pressed in fractions of σ. If 0 and z are taken as limits of integration, then the integral in equation (8) is a function of z, i.e.:

z

n

z

dzezz

20 2

1)( . (10)

The function )(0 z is called a normalized error function (Laplace func-

tion): 0)0(0 ; )()( 00 zz ; 5.0)(0 ; 5.0)(0 . It is followed from equation (9) and Fig. 4 that the area enclosed by a

segment –z1+z1 of the x-axis, the probability density curve and the two ordi-nates corresponding to the boundaries of the segment is the probability that a random variable z1 falls into the given interval.

Values for functions )(0 z are given in the handbooks. Using data giv-en in these handbooks it is possible to determine the probability that a ran-dom variable x, expressed in terms of σ, will be within a particular interval

1z . For example, we find that for z1=3, which corresponds to the random variable x=3σ, error function is equal to 49865.0)3(0 or

9973.0)3(2)3()3( 000 . Since the area enclosed by the Gauss curve and abscissa axis is equal

to 1, then the area, which lies outside the values x=3σ, is equal to 1-0.9973=0.0027 and is located symmetrically in 0.00135 or 0.135% on the right and on the left relative to the y-axis (Fig. 4).

y

x-3 -2 -1 0 1 2 3

0,135 % 0,135 %0 1(- )z 0 1(+ )z

Fig. 4 Normal distribution curve and representation of integrands

77

Therefore, with a probability close to unity, one can assert that the ran-dom variable x will not exceed the limits of 3σ. Therefore, with the distribu-tion of the random variable according to the Gaussian law, the range of dis-persion is equal to 6limV or the range 3 is considered as a sensibly limiting range of dispersion of a random variable and is taken as the stand-ard of accuracy – tolerance. Here the probability of a random variable to ex-ceed the limits of 3σ is equal to 0.0027 or 0.27%.

In production environment, due to the limited number of measurements, analysis involves not the mathematical expectation and variance but their ap-proximate statistical estimates – the empirical average x and the empirical variance s2 respectively, which characterise the average result of the meas-urements and the degree of results variance. These estimates are determined by the equations:

k

i

ii

k

kk

Nnx

nnnnxnxnxx

121

2211

...... ; (11)

k

i

i

Nnxxs

1

2)( . (12)

In these equations xi is the value, corresponding to the middle of the i-th

interval, and k is the number of intervals. The smaller the value of s is, the higher the accuracy of the manufacturing process or the measurement is, i.e. the smaller the magnitude of random errors is. Hence, the parameter s is used as a measure of the manufacturing process accuracy or, in repeated measure-ments of the same value, as a measure of the measurement method accuracy.

10.5 Examples of Measurement Results Analysis

If a set of random variables follows the law of normal distribution or the

law close to the normal distribution, then it is possible to establish, using cor-responding criteria that the considered empirical distribution in the best way conforms to that law.

In the process of inspection of dimensions of a batch of parts or multiple measurement of any parameter of the same part, one can find out that the ob-servation results represent a set of values of discrete random variable, i.e. set of actual dimension values or values of size errors.

Let’s study the examples of observation results analysis.

78

The method of statistical analysis of observation results is considered on the example of measurement of discrete sizes of the shafts with 12h10(–0.07) machined on a lathe. The size of a sample out of the statistical population (batch size) is equal to N = 200. Measurements are carried out by instruments like length gage or optimeter with the scale interval 0.001 mm.

Analyzing the observation results, we conclude that among these values there are such values which are significantly different from most of the re-sults, so we can call them gross errors. Such observations can be caused by inspector’s inattention, by extraneous parts in the sample and some other causes that break normal conditions of experimental results generation. We should keep in mind that these observations differ visually significantly from the average for the given sample. In the case of gross errors, their causes should be analyzed and eliminated.

The result that is the gross error is excluded from the population and the remained results are processed again and new values of x and s are calculat-ed; then the furthest analysis is carried out and, if necessary, other gross er-rors are also excluded by means of Kolmogorov criterion, Irwin’s criterion or others. In preliminary calculations the errors, i.e. deviations from x , exceed-ing absolute value 3 are excluded.

The observation results after the preliminary analysis are arranged in or-der of magnitude forming the variational series. We shall find maximum and minimum values of dmax and dmin and find the range of the series.

In our example the minimum value of the observed dimension equals to 11.915 mm, the maximum value – to 12.005 mm and then the range R, equal to the difference of the found limit values, is equal to:

R=dmax – dmin=12.005 – 11.915=0.09 mm. Then we shall divide the variational series into k intervals. The number

of k intervals, to some extent, depends on the sample size N and can be taken by the following recommendations: 5 7k with 40N ; 7 9k with 40 100N ; 9 12k with 100 500N , moreover with the small num-ber of intervals it is better to take k as an odd number. So we can see that the values are considerably overlapped and selection of the interval number is not determinant, thus the recommendations are only suggestive, not literal.

Taking k = 9, the interval value is equal to R/k= 0.09/9 = 0.01 mm and a half interval totals to 0.5 R/k= 0.005 mm. We shall find the values of the class marks and form interval series, for that we shall add 0.5R/k to dmin, then to the found value we shall add 0.5 R/k again and so on, as a result we shall ob-tain kRd /5.0max , i.e. 12.000 mm.

Then we shall find a number of observations falling in each interval, for example, 20 results have fallen in the interval 11.935…11.945; 12 results

79

have fallen in the interval 11.975…11.985 and so on. We should keep in mind that the values that coincide with the interval boundary are included in-to the left interval.

The number of observations fallen in the given interval is called fre-quency.

The order of results analysis and the example of analysis presentation is given in the Table 21. The values x and s are determined by equations (11) and (12):

960.11200/)2000.12...6930.112920.11( x mm; 015.001.0)04.0(...03.0)03.0(01.0)04.0( 222 S mm.

Table 21

The example of measurement results analysis

Intervals of actual dimensions di, mm

Average xi of an interval,

mm

Number ni of parts in an

interval

Deviation from av-erage xxv ii ,

mm

Relative frequency

Nni /

from 11.915 to 11.925 11.920 2 –0.04 0.01

over 11.925 to 11.935 11.930 6 –0.03 0.03

over 11.935 to 11.945 11.940 20 –0.02 0.10

over 11.945 to 11.955 11.950 48 –0.01 0.24

over 11.955 to 11.965 11.960 56 0.00 0.28

over 11.965 to 11.975 11.970 34 +0.01 0.17

over 11.975 to 11.985 11.980 20 +0.02 0.10

over 11.985 to 11.995 11.990 12 +0.03 0.06

over 11.995 to 12.005 12.000 2 +0.04 0.01

96.11x -- 200N

i

iv 010.010.0

i

i

Nn 1

The dispersion pattern of values of the random variable, which in the

considered example is actual dimension of the shaft, is graphically represent-

80

ed by the histogram consisting of rectangles, which height equals to frequen-cy and width – to the range of the interval.

The dispersion is also determined by the empirical curve of distribution, which is called distribution polygon (Fig. 5). Graphical representation of re-sults in manual analysis is easier to perform with the help of squared paper. X-direction means intervals of the actual dimensions of the shaft, Y-direction is the height of rectangles equal to frequency.

Distances along X-axis and Y-axis are recommended to plot in relation equal to 0.8 – 1.0. In Fig. 5 you can see polygon and histogram of distribu-tion of shaft dimensions and location of tolerance zone that reflects require-ments to accuracy according to the drawing; as we can see the empirical re-sults do not meet the requirements of engineering documentation and this is as it should be.

Histogram

Polygon

ni

50

40

30

20

10

0 -11.92 11.94 11.96 11.98 12.00 xi, mm

Tolerance zone 70 µmdmin=11.93 dmax=12.00

ec=-0.035 0ei=-0.07

Tolerance zonemidpoint 11.965

Empirical center ofvariance 11.96

Histogram

Polygon

ni

50

40

30

20

10

0 -11.92 11.94 11.96 11.98 12.00 xi, mm

dmin=11.93 dmax=12.00

ec=-0.035 0ei=-0.07

Empirical center ofvariance 11.96

Fig. 5 Histogram and frequency polygon of a random value

81

For example, noncoincidence of tolerance zone midpoint with empirical

centre of variance is equal to 0.005 mm and the range exceeds tolerance by the value equal to 0.09 – 0.07 = 0.02 mm. In order to make conclusion on batch acceptance, it is necessary to analyze the obtained results according to the following features:

compliance of empirical distribution with the normal distribution law;

estimation of confidence probability of empirical parameters; manufacturing tolerancing. The results analysis of random variable measurement becomes possible

if we know which theoretical law of random value distribution the empirical distribution corresponds to.

On the basis of empirical curve shape and values of empirical parame-ters, the correspondence of the curve to one of theoretical laws is suggested.

We shouldn’t forget about the importance of graphical representation of the empirical curve, which is influenced, among other things, by selection of intervals number and ratio of values along X- and Y-axes.

Correspondence of empirical distribution to the supposed theoretical distribution is determined on the basis of criteria 2 , for example, of the Kolmogorov criterion, according to GOST 11.006-74.

Comparison of characteristics of empirical and theoretical distributions is carried out in the following manner. Values of parameters of empirical and assumed theoretical distributions are considered. The parameters x and s, de-termined by sampled data, give only approximate response of accuracy of en-tire population of the objects.

Mathematical expectation M(x) and standard deviation serve as a characteristic of random variable values dispersion in entire assembly.

The difference between probabilistic characteristics M(x) and σ and em-pirical values x and s lies in that the first are considered as unknown con-stants characterizing distribution of the statistical population, and the second are random variables, defined from the sample, and give only approximate estimate of M(x) and σ.

The difference between M(x) and x and between σ and s reduces with the increase of sample size and number of observations.

Analysis of the observation results of the sample allows to define the limits, within which the values of the statistical population parameters will lie.

82

The degree of that confidence that is so called confidence interval is se-lected in accordance with standard specifications to the product performance characteristics.

Limits of the confidence interval determine confidence probability, which characterizes reliability of the results.

In case of normal distribution, such confidence interval for mathemati-cal expectation M(x), for example, is the interval with the limits of M(x) equal to x 3 where x is a standard deviation for distribution of values x .

Since

1

Nsi

x ,

the limits of confidence interval will be

isN

x1

3

.

From the table of values )(0 z we shall find that within the limits

31z , there is 99.73% of all values of random variable x, expressed by z, as 9973.049865.02)3(0 . Thus, with reliability 0.9973 we can predicate that the M(x) value is within the interval xx 3 .

As x and s are random variables, the confidence intervals, as it follows from the calculation given above, depend on a factor multiplying x3 , which we shall denote for general case by z.

It is evident that the reliability of that the value of M(x) will be within limits of xzx is more than 0.9973 if z>3 and is less than 0.9973 with z<3.

It is common when reliability is equal to one of the following quantities: 0.90, 0.95, 0.99, 0.999, which is equivalent of z equal to 1.645, 1.96, 2.576, 3.291.

Let’s study the example, assume that the distribution described above is the sample with N = 200 and is normal distribution, then:

001.0

199015.0

1

Nsi

x mm.

The confidence interval for M(x) is determined by the equation:

xx zxxMzx )( .

83

So with reliability 0.9 or 90% we may expect:

001.0645.196.11)(001.0645.196.11 xM

or 962.11)(958.11 xM .

For the samples of small sizes the multiplier x should be replaced by a

multiplier t which is determined in the Table 22 according to Student’s dis-tribution.

Table 22

The value of Student’s coefficient with different confidence probability P

Num

ber o

f ob

serv

atio

ns The value of Student’s coefficient

with different confidence probabil-ity P

Num

ber o

f ob

serv

atio

ns

The value of Student’s coeffi-cient

with different confidence prob-ability P

0.05 0.90 0.95 0.98 0.99 0.05 0.90 0.95 0.98 0.99

2 3 4 5 6 7 8 9

1.0 0.82 0.77 0.74 0.73 0.72 0.71 0.71

6.31 2.92 2.35 2.13 2.01 1.94 1.90 1.86

12.71 4.30 3.18 2.78 2.57 2.45 2.36 2.31

31.82 6.96 4.54 3.75 3.65 3.14 2.97 2.90

63.66 9.92 5.84 4.60 4.03 3.71 3.50 3.36

10 15 20 30 60

120 ∞

0.70 0.69 0.69 0.68 0.68 0,68 0,67

1.84 1.76 1.73 1.70 1.67 1.66 1.65

2.26 2.14 2.09 2.04 2.00 1.98 1.96

2.76 2.60 2.53 2.46 2.39 2.36 2.33

3.25 2.98 2.86 2.76 2.66 2.62 2.58

The value t depends on the sample size, i.e. on N - 1; using these table

we may find that with N = 20 and reliability 0.9 the coefficient t is equal to 1.73; with the same value N and reliability 0.95, 0.99 and 0.999 the t equals correspondingly to 2.09, 2.86 and 3.88.

The selection of reliability is defined by the object of manufacture, for example: for general-purpose products the reliability can be equal to 0.9; for critical parts – 0.95; for aeronautical equipment – 0.99; and finally 0.999 for

84

critical equipment which malfunction can pose a hazard to human health and life.

Thus, if the values 96.11x and 015.0s were obtained from the sample of 20 pieces, but not 200 pieces (as it has been shown in the previous exam-ple), so with reliability 0.9 the limits of confidence interval would be the fol-lowing:

001.0199015.0

1

Nsi

x mm.

001.073.196.11)(001.073.196.11 xM

or

965.11)(955.11 xM . For the reliability equal to 0.999, the confidence interval is significantly

larger: 001.088.396.11)(001.088.396.11 xM

or

972.11)(948.11 xM . With the sample size decreasing and the required reliability increasing,

the width of the confidence interval will increase, i.e. the limits of possible values M(x) will expand.

Similarly to this, the confidence intervals for the value x can be found.

10.6 Example of Creating Frequency Polygon and Histogram in Excel 2007

Open “Microsoft Excel 2007” and into the Table (Fig. 6) enter data of

the example given in Section 10.5 (Table 21): average value ix of the interval and number in of parts in interval, having doubled the column with the val-ues in .

85

Fig. 6 Initial data

Perform the following actions: 1. At the toolbar push the button “Insert” (Fig. 7). First choose the

type “Histogram”. Then push the button “OK”.

Fig. 7 Choosing “Histogram” type of graphic representation

2. Secondly it is necessary to specify the source of the diagram data.

To do this, click the right mouse button in the opened white panel and choose “Select data”. In the bar “Range of data for the dia-gram” push the button with red arrow and having pressed the left mouse button select two columns with values in , then push the but-ton with red arrow again returning to the panel of diagram master.

86

3. Then in the same panel “Select data” go to tab “Bar/Column”. In the bar “Labels on horizontal axis” click on “Edit” and also push the button with red arrow and select column with values xi, then push the button with red arrow again returning to the panel of dia-gram master. Click “OK”.

4. At the constructed diagram click the right mouse button on any column of the histogram and select “Format data series”, go to the tab “Parameters of series” and set the width of side clearance equal to zero, press “OK”. So we have constructed the distribution histo-gram for the given values (Fig. 8).

0

5

10

15

20

25

30

35

2,2190 2,2202 2,2214 2,2226 2,2238 2,2250

Ряд1

Ряд2

Fig. 8 Completed histogram

5. The next step is the construction of distribution polygon. On the con-

structed distribution histogram we do the following actions: click by left mouse button on any column of the histogram and at the toolbar select “Insert”, then “Diagram” and select one of the suggested dia-grams. As a result we have got histogram and distribution polygon (Fig. 9).

87

0

5

10

15

20

25

30

35

2,2190 2,2202 2,2214 2,2226 2,2238 2,2250

Ряд1

Ряд2

Fig. 9 Histogram and distribution polygon

10.7 Example of Creating Histogram, Polygon and Curve of Normal Distribution in Statistica 7.0

The system Statistica is a package for complete statistical analysis

which involves broad graphic possibilities. The package Statistica includes a great number of different categories and diagram types.

In order to construct histogram and polygon with curve of normal distri-bution it is necessary to have only initial data for the histogram. These data should be entered into the table of Statistica 7.0 (Fig. 10). Fig. 10 represents only small part of data.

88

Fig. 10 Initial data

Then, in horizontal menu, select “Graphs” and “Histograms” (Fig. 11).

Fig. 11 2D histograms

89

With the next step it is necessary to set the number of histogram col-umns (“Categories”). In our case we set 6 columns and push the button “OK”. Now we can see the window of data selection for the histogram (Fig. 12). Select a column with data and press “OK” again.

Fig. 12 Data selection window

So we have the constructed histogram and theoretical curve of normal

distribution (Fig. 13).

Fig. 13 Histogram and distribution curve

90

For the construction of distribution polygon it is necessary to push the

right mouse button on the constructed histogram and in the dropdown menu select “Fitting”. Then it is needed to push “Add new fit” (Fig. 14) and select the type “Lowess” (Fig. 15).

Fig. 14 “Fitting” window

Fig. 15 Fit type selection

So we have got the histogram, polygon and theoretical curve of normal distribution for the entered data (Fig. 16).

91

Fig. 16 histogram, polygon and theoretical curve of normal distribution

Thus, the package Statistica 7.0 substantially helps to simplify analysis and processing of data and provides simple tools of diagram construction.

The outlined method allows to estimate any manufacturing process, nu-merically assess accuracy of the process, determine values of the parameters that exceed acceptance limits.

92

Conclusion

A limited volume of the book is not allowed to consider a number of

practical issues of engineering measurements in mechanical engineering. The degree of importance varies and the questions are commonly examined in the literature.

The issue of the maximum achievable accuracy of measurements, which depends on the accumulated knowledge in the basic sciences, is expected to be considered in a separate book.

Verification of measuring instruments, as well as metrological certifica-tion, calibration and graduation is received relatively little attention. Further information on these questions can be found in the recommendations MI 1967-89.

Of great importance for the practical activities are the development of techniques of measurement of the required quantity, the choice of the method and means of measurement, planning of the inspection process, etc. Further information on these questions can be found in handbooks on engineering measurements in the relevant areas of industrial production.

93

Index

A

abscissa axis, 74 absolute error of measurement, 53 absolute measurements, 11 absolute scale, 19 acceptance border, 69 acceptance inspection, 34 accuracy grade, 25 actual dimension, 77 analog, 48 analysis of measurements results, 70 area under the curve, 76 automatic control, 62 B base unit, 14 batch of parts, 62 batch production, 59 C calibration, 8 calibration characteristic, 51 calibration error, 54 casual inspection, 63 center of variance, 74 certain event, 72 certified reference material, 26 clearance, 72 collective standard, 24 comparison measurements, 11 complementary error, 54

complex of measuring instruments, 24 component parts, 62 confidence interval, 82 confidence probability, 82 contact method of measurement, 12 continuous inspection, 62 continuous quantity, 74 correction table, 71 correctness of measurement,53 cutting force, 72 D defective part (faulty part), 66 derived unit, 14 destructive testing, 61 deviation, 12 dimension, 9 direct measurement, 9 discrete quantity, 74 duplicate standard, 23 E elemental-equivalent method of veri-fication, 48 empirical average, 77 empirical variance, 77 engineering documentation, 46 Engineering measurements, 11 error function, 76 error of method of measurement, 54 essentially positive quantity, 73 event (random event), 67 extraneous part, 78

94

F frequency, 15 frequency polygon, 80 gauge block, 12 gauge block holder, 44 G Gaussian law, 73 gross error, 53 group standard, 24 guaranteed tolerance, 67 H handbook, 76 histogram, 80 I imbalance, 75 implementation error, 55 incoming quality control, 62 indication range / scale range, 50 indirect measurement, 10 influence quantity, 54 initial material, 62 in-process control, 62 inspection / review, 7 instrument error, 54 instrument error, 70 integrand, 76 interchangeable, 50 intermediate transducer, 49 inter-operational inspection, 62 interval, 19 interval scale, 19 interval series, 78 intrinsic error, 54

Irwin's criterion, 78 J job production, 63 joint measurement, 11 K Kolmogorov criterion, 78 L length measuring gauge, 78 limit of integration, 76 M machining allowance, 72 maintainability, repairability, 60 manual inspection, 62 manufacturing documentation, 62 manufacturing process, manufactur-ing route, 62 manufacturing tolerance, 66 mass production, 63 material measure, 22 mathematical expectation, 19 Maxwell law, 75 mean life, 45 means of measurement, measuring instrument, 7 measurand, 9 measure box, 26 measurement, 9 measurement datum, 49 measurement error, 11 measurement force, 65 measurement method, 9 measurement position, 72 measurement range, 50

95

measurement result, 10 measurement standard, standard, eta-lon, 22 measurement traceability (uniformity of measurement), 7 measuring instrument, 7 measuring instrument sensitivity, 51 measuring transducer, 49 method of comparison with a stand-ard measure, 12 method of direct evaluation, 12 multiplier, 49 multi-value measure, 26 N nominal scale, 18 non-contact method of measurement, 12 nondestructive testing, 61 normal distribution, 67 normal distribution law, 73 O observation result, 55 operation sheet, 62 operational inspection, 62 optimeter, 12 ordinate, 73 ordinate axis, 80 P passive control, 62 periodic inspection, 34 personal error, 55 physical quantity, 9 presence error, 55 principle of measurement, 64 probability, 55

probability density, 73 product quality, 61 production process, 62 professional error, 55 Q quality control, 61 quality control department, 63 R random error, 53 random variable, 71 range, 20 range of dispersion, 77 ratio scale, 19 raw material, 62 reading error, 25 reading variation, 51 reference measuring instruments, 25 reference standard, 23 reject, 67 relative error of measurement, 53 relative frequency, 72 relative frequency, 72 reliability, 47 repeatability, 53 reproducibility, 53 route sheet, 62 S sample, 71 sample size, 81 scale, 18 scale interval, 50 scale spacing, 50 sensor, 48 service life, 45

96

Simpson distribution (Triangular dis-tribution), 75 single-value measure, 26 squared paper, 80 stability of a measuring instrument, 55 standard conditions, 20 standard deviation, 19 standard of accuracy, 77 standard tolerance, 66 state testing, 34 statistical analysis, 78 statistical estimate, 77 statistical population, 78 Student's coefficient, 83 Student's distribution, 83 surface layer quality, 48 systematic error, 53 T testing-calibrating measurements, 11 thread pitch threshold of sensitivity, 51 tie, 33 tolerance, 20 tolerance zone, 66

transfer standard, 23 transmitting transducer, 49 transposition measurement, 9 true value, 53 U unit, 8 unit of physical quantity, 14 V variance, 73 variational series, 78 verification, 7 verification error, 54 W wear block, 33 Weibull law, 75 working measuring instruments, 22 working standard, 23 workshop, 63 wringability, 27

97

References 1. ГОСТ 8.207-76 ГСИ. Прямые измерения с многократными наблю-

дениями. Методы обработки результатов наблюдений. Основные положения

2. Допуски и посадки. Справочник. В 2-х частях / Под ред. Палея М.А. – М.: Машиностроение. 2002. 1032 c.

3. Марков Н.Н., Ганевский Г.М. Конструкция, расчет и эксплуатация контрольно-измерительных инструментов и приборов. – М.: Ма-шиностроение, 1993. 416 с.

4. Пронкин Н. С. Основы метрологии: Практикум по метрологии и измерениям. — М.: Логос, 2007.

5. РМГ 29-99. МЕТРОЛОГИЯ: Основные термины и определения (State system for ensuring the uniformity of measurements. Metrology. Basic terms and definitions).

6. Технический контроль в машиностроении: Справочник инструмен-тальщика / Под общ. ред. В.Н. Чупырина, А.Д. Никифорова. – М.: Машиностроения, 1987. 512 с.

7. Тартаковский Д.Ф., Ястребов А.С. Метрология, стандартизация и технические средства измерений. – М.: Высшая школа. 2001. 205 с.

8. Якушев А.И., Воронцов Л.Н., Федотов Н.М. Взаимозаменяемость, стандартизация и технические измерения. – М.: Машиностроение, 1986. 352 с.

9. Alper, T. M. (1985). A note on real measurement structures of scale type (m, m + 1). Journal of Mathematical Psychology, 29, 73–81.

10. Anand K. Bewoor, Vinay A. Kulkarni. Metrology & Measurement, Tata McGraw-Hill,2009.

11. ANSI Y14.5M – 1982, Dimensioning and Tolerancing. 12. ASME Y14.5M-1994, Dimensioning and Tolerancing. 13. Bell, S. Measurement Good Practice Guide No. 11. A Beginner's Guide

to Uncertainty of Measurement. Tech. rep., National Physical Laborato-ry, 1999.

14. Bryan R. Fischer. Mechanical Tolerance Stackup and Analysis, Marcel Dekker Inc.

15. Douglas Hubbard: "How to Measure Anything", Wiley (2007), p. 21. 16. Drake P. Dimensioning and tolerancing handbook. McGraw-Hill, New

York, 1999. 17. Encyclopedia of production and manufacturing management / Editor

Paul M. Swamidass. Kluwer Academic Publishers, 2000.

98

18. Foster L.W. Geometrics III: The application of geometric and toleranc-ing technique. Addison-Wesley, 1994.

19. Geometric Dimensioning and Tolerancing for Mechanical Design. Gene Cogorno. Publisher: McGraw-Hill Professional. 2011

20. Galyer J.F.W., Shotbolt C.R. “Metrology for Engineers”, Cassell, 1969. 21. Greve J.W., Wilson F.W. “Handbook of Industrial Metrology”, Prentice

Hall, 1967. 22. Handbook of Dimensional Measurement (4th edition). Mark Curtis.

Publisher: Industrial Press, Inc. 2010 23. H. Dagnall M.A. Exploring Surface Texture. Rank Taylor Hobson, 1980 24. H. Dagnall M.A. Let’s Talk Roundness. Rank Taylor Hobson, 1976 25. Ibrahim Z. Mastering CAD/CAM. McGraw-Hill, New York, 2005. 26. ISO 1101:2004, Geometrical Product Specifications (GPS) – Geomet-

rical tolerancing – Tolerances of form, orientation, location and run-out. 27. ISO 8015:1985, Technical drawings – Fundamental tolerancing princi-

ples 28. Jain R. K. Engineering Metrology. Khanna Publishers, New Delhi. 29. Joint Committee for Guides in Metrology (JCGM), International Vo-

cabulary of Metrology, Basic and General Concepts and Associated Terms (VIM), III ed., Pavillon de Breteuil: JCGM 200:2012.

30. Kent J. Gregory, Giovani Bibbo, and John E. Pattison (2005), A Stand-ard Approach to Measurement Uncertainties for Scientists and Engi-neers in Medicine, Australasian Physical and Engineering Sciences in Medicine 28(2):131-139.

31. Kruliowski A. Geometric dimensioning: a self-study course. SME Pub-lications, Effective training Inc., 1992.

32. Literature of the “Engineering metrology” laboratory and AMME de-partment.

33. Majcen N., Taylor P. (Editors), Practical examples on traceability, measurement uncertainty and validation in chemistry, Vol 1

34. Manual of Engineering Drawing to British and International Standards. Second edition. Colin H. Simmons, Dennis E. Maguire, Printed by Else-vier Newnes, 2004.

35. Manufacturing Engineering and Technology. Fifth edition. Serope Kal-pakjian, Steven R. Schmid, 2006

36. Meadows D.J. Geometric dimensioning and tolerancing: application and techniques for use in design, manufacturing and inspection. Marcel Dekker, New York, 1995.

37. Metrology for Non-metrologists. Rocio M. Marban, Julio A. Pellecer C., 2002.

99

38. Metrology in industry: the key for quality / edited by French College of Metrology, Printed by Antony Rowe Ltd, 2006.

39. Pedhazur, Elazar J.; Schmelkin, Liora Pedhazur (1991). Measurement, Design, and Analysis: An Integrated Approach (1st ed.). Hillsdale, NJ: Lawrence Erlbaum Associates. pp. 15–29

40. Phillip Ostwald,Jairo Muñoz, Manufacturing Processes and Systems (9th Edition) John Wiley & Sons, 1997

41. Scarr A.J.T. “Metrology and Precision Engineering”, McGraw-Hill, 1967.

42. Velleman, Paul F.; Wilkinson,Leland (1993). "Nominal, Ordinal, Inter-val, and Ratio Typologies Are Misleading". The American Statistician (American Statistical Association).

43. Wilson B.A. Dimensioning and tolerancing handbook. Genium, New York, 1995.

44. Electronic Design Library: Fits and Tolerances // http://www.ecs.umass.edu/mie/labs/mda/dlib/fit_tol/fitandtol.html

45. Federal Agency on Technical Regulation and Metrology // http://protect.gost.ru

46. Institute for Geometrical Product Specifications // www.ifGPS.com 47. International Organization for Standardization //

www.iso.org/iso/home.html

100

Educational Edition

Национальный исследовательский Томский политехнический университет

ЧЕРВАЧ Юрий Борисович ОХОТИН Иван Сергеевич

ТЕХНИЧЕСИЕ ИЗМЕРЕНИЯ В МАШИНОСТРОЕНИИ

Учебное пособие

Издательство Томского политехнического университета, 2013 На английском языке

Published in author’s version

Translator A.B. Kim

Linguistic Advisor Senior lecturer E.A. Panasenko

Printed in the TPU Publishing House in full accordance with the quality of the given make up page

Signed for the press 00.00.2009. Format 60х84/16. Paper “Snegurochka”. Print XEROX. Arbitrary printer’s sheet 000. Publisher's signature 000.

Order XXX. Size of print run XXX.

Tomsk Polytechnic University Quality management system

of Tomsk Polytechnic University was certified by NATIONAL QUALITY ASSURANCE on BS EN ISO 9001:2008

. 30, Lenina Ave, Tomsk, 634050, Russia Tel/fax: +7 (3822) 56-35-35, www.tpu.ru