investigation of roundness tester’s · pdf file2-6 the relationship between measurement...

INVESTIGATION OF ROUNDNESS TESTER’S ACCURACY

AND COMPENSATION ALGORITHM

MISS NITIMA NULONG

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF MASTER OF SCIENCE

IN PRODUCTION ENGINEERING

SIRINDHORN INTERNATIONAL THAI-GERMAN GRADUATE SCHOOL OF ENGINEERING

(TGGS)

GRADUATE COLLEGE

KING MONGKUT'S INSTITUTE OF TECHNOLOGY NORTH BANGKOK

ACADEMIC YEAR 2007

COPYRIGHT OF KING MONGKUT'S INSTITUTE OF TECHNOLOGY NORTH BANGKOK

ACKNOWLEDGEMENTS

This thesis was supported by Mahr GmbH and Sirindhorn International Thai-

German Graduate School of Engineering, King Mongkut’s institute of Technology

North Bangkok. I would like to thank Dr.Robert Buchmann, Associate Professor

Banleng Sornil and Professor Dr.-Ing. Rolf H. Jansen for their responsibility in the

co-operation program. I would like to thank Mr.Ralf Terbruggen, my internship

Industry Mentor, for giving me the opportunity to pursue my thesis at Mahr Company

and for supporting my work. I would like to thank Associate Professor Dr.Jaramporn

Hassamontr for his have supported and advised since the beginning of my thesis. I am

grateful to Mr.Markus Diedrich and Mr.Burkhard Soehne, my thesis Industry Mentor,

for their supporting and for invaluable suggestions and discussions. I would like to

thank Dr.Wilde Michael and Mr.Dirk Meier for many valuable suggestion and

discussion. I would like to thank Mr.Mike Schmidt, Mr.Markus Sladkowski, and my

colleagues at MMQ400 development section for their supporting during my practice

and task. I am very thankful to Mr.Hoffmann Malte and Mr.Sellmann Manuel for

their encouragement and valuable advice. A special thank you goes to Mrs.Sabine

Schluer and Mrs.Arch Kristiane for many valuable suggestions supported and

facilitated all detail with social and culture. I would like to thank my master

classmates, Mr.Prasert Prachprayoon and Mr.Nopparat Seemuang, for their

encouragement and kindness in representative myself during I stayed in Germany. I

am very thankful to Dr.Poramate Manoonpong and Mr.Sunpeth Cumnuantip for being

such faithful proofreaders. I would like to thank my friends at Goettingen for their

friendship. Moreover, I would like to thank my parents and my family for being my

power and for taking care of me all times. Finally, I am very much grateful to all the

people who have contributed the many useful materials to complete my thesis and

who also offered many useful ideas and suggestion.

Nitima Nulong

v

TABLE OF CONTENTS

Page

Abstract (in English) ii

Abstract (in Thai) iv

Acknowledgements v

List of Tables viii

List of Figures ix

List of Abbreviations and Symbols xiii

Chapter 1 Introduction 1

Chapter 2 Literature review 5

2.1 Uncertainty of measurement 5

2.2 Dimensioning and Tolerancing 11

2.3 Form Measuring Machine 14

2.4 Capability study 21

2.5 International standards related to form measurement

and uncertainty measurement 25

Chapter 3 Measurement Process 27

3.1 Measurement machine (MMQ400) and software 27

3.2 Reference measurement machine (MFU100) 29

3.3 Temperature measurement device 30

3.4 Workpiece and clampling device 32

3.5 Measurement program 33

Chapter 4 Measurement results and discussions 39

4.1 The effect of air-conditioning room 41

4.2 The effect of machine compensation in temperature-controlled room 45

4.3 The effect of machine compensation in normal room temperature 50

4.4 The effect of machine handling (center re-positioning) in

temperature-controlled room 52

4.5 The effect of machine handling (center re-positioning) in

normal room temperature 57

4.6 The effect of probe zeroize strategies 60

4.7 Summary 63

vi

TABLE OF CONTENTS (CONTINUED)

Page

Chapter 5 Measurement system analysis 65

5.1 The percentage of the average increment 65

5.2 The uncertainty of measurement 68

5.3 Capability index 77

Chapter 6 Conclusions 85

References 89

Appendix A 91

Definition of Terms 92

Appendix B 107

Screening Experimental 108

Biography 127

vii

LIST OF TABLES

Table Page

2-1 Form and Location Tolerance 12

2-2 The causes for form deviations according to the VDI 2601 13

2-3 Comparison of the feature-based metrology and the profile metrology 16

2-4 Relationship between the machine uncertainty component and

specific measured features 18

3-1 The technical data of probe type according to the Testo information 30

3-2 Comparison of sensors 31

3-3 The conditions of the measurement program 33

4-1 The temperature information when are measured at the different

controlled air conditioning room 40

5-1 The average of mean value 66

5-2 The percentage of the average increment 66

5-3 The relative between the machine component errors and the measured

features 73

5-4 The summary table of the significant approval of bias, the capability

index calculations and the permissible range of the measured value 80

A-1 Symbol and definition of feature tolerance 103

A-2 The evaluation methods 104

viii

LIST OF FIGURES

Figure Page

2-1 The procedure of the measuring 6

2-2 Cause and effect diagram of production metrology 7

2-3 Types of measurement errors 8

2-4 Accuracy definition 9

2-5 The different between accuracy and precision 10

2-6 The relationship between measurement uncertainty and workpiece

tolerance 11

2-7 Polar and Linear filter 15

2-8 Geometrical characteristics of surface measurement 16

2-9 The characteristic of measuring machine 20

2-10 The concept of capability index 23

2-11 The comparison between the combined standard uncertainty (Upm)

and the capability indices type-1 study (Cg, Cgk) 24

3-1 MMQ400 the precision measuring machine 27

3-2 The structure level of MarWin software module 29

3-3 The cylindrical standard workpiece information 32

3-4 The specification information of the cylindrical standard workpiece 35

4-1 Roundness and cylindricity deviations when the machine’s

compensation is activated off 42

4-2 Roundness deviation including flick and runout deviations with the

z axis as datum when the machine’s compensation is activated off 43

4-3 Straightness deviations when the machine’s compensation is off 44

4-4 Parallelism and conicity deviations when the machine’s compensation

is activated off 44

4-5 Compensation’s algorithm 45

4-6 Machine structures of form measuring machine 46

4-7 The measurement results determined from polar profiles between the

machine’s compensation is activated off (Left) and on (Right) when

measured in the room with air condition 47

ix

LIST OF FIGURES (CONTINUED)

Figure Page

4-8 The measurement results determined from linear profiles between

the machine’s compensation is activated off (Left) and on (Right)

when measured in the room with air condition 49

4-9 The measurement results determined from polar profiles between


when measured in the room without air condition 50



when measured in the room without air condition 51

4-11 Alignment concept 52


with (Left) and without (Right) workpiece’s handling when measured

in the room with air condition 54

4-13 Radial runout deviation with z axis as datum (Left) and Permissible

eccentricity value (Right) when measured in the room with

air conditioning under condition on-compensation and with handling 55



in the room with air condition 56

4-15 Measurement strategies of Straightness and Parallelism 57



in the room without air condition 58



in the room without air condition 59


the probe zeroize every measured profiles (Left) and the probe zeroize

only one time at pre-position height (Right) 61

x


Figure Page


the probe zeroize every measured profiles (Left) and the probe

zeroize only one time at pre-position height (Right) 62

B-1 Input, Output and Measurement conditions of screening experimental 109

B-2 The center point of three circle substitute elements in x and y axis

of the machine coordinate system 110

B-3 The center point of three circle substitute elements in z axis of the

machine coordinate system 110

B-4 The roundness deviation (Left) The roundness deviation of each circle

substitute element when the evaluation criterion is MZC. (Right)

The roundness deviation of the second circle substitute element (C2)

when the evaluation criteria are MZC and LSC 111

B-5 The radial runout deviation. (Left) the four radial runout deviation

with the difference reference datum when the evaluation criteria is

MZC.(Right) the comparison between the roundness and the radial

runout deviation of the same profile (C2) when the evaluation criteria

are MZC 112

B-6 The cylindricity deviation when evaluation criteria are MZC.

(Left) The probe zeroizes every circle. (Right) The probe zeroize

only one time at pre-position height 114

B-7 The roundness deviation when evaluation criteria are MZC.



B-8 The radial runout deviation when evaluation criteria are MZC.



B-9 The center point of three circle substitute elements in x and y axis

of machine coordinate system. (Left) The probe zeroizes every circle.

(Right) The probe zeroize only one time at pre-position height 116

xi


Figure Page

B-10 The center point of three circle substitute elements in z axis

of machine coordinate system. (Left) The probe zeroizes every circle.

(Right) The probe zeroize only one time at pre-position height 118

B-11 The screening experimental measurement result; Element information

results in x, y and z-coordinate of the position vector 119

B-12 The screening experimental measurement results; form and

location tolerance 120

B-13 The protocol of the screening experimental with the zeroing probes

every circle 121

B-14 The protocol of the screening experimental with the zeroing probe


B-15 The example of the cylindricity profile in the protocol 123

xii

LIST OF ABBREVIATIONS AND SYMBOLS

ISO International Organisation of Standardisation

GUM Guide to the Expression of Uncertainty in Measurement

VIM International Vocabulary of Basic and General Terms in Metrology

Cg capability index

Cgk capability index

upr undulations per revolution

MZC Minimum Zone Circles

LSS Least Square Straight line

pt100 Resistance sensor

NTC Thermistors

xiii

CHAPTER 1

INTRODUCTION

In recent years, the trend of technology and products is moving towards smaller

sizes and higher quality. The dimensional unit of production part changes from

“decimal of millimeter” to “decimal of micrometer or nanometer.” According to the

unique understanding for workpiece acceptance criteria in controlling and monitoring

process, workpiece shape and its characteristic are defined by dimensioning and

tolerancing. The inspection gages and measuring machines are very important to

control quality and process. The measuring machine accuracy must be significantly

higher than that of the production machine and must be also higher than the

workpiece specification tolerance. Therefore, the high accuracy of the measuring

machine is important not only in producing and controlling but also in limiting

unnecessary measuring equipment investments.

The accuracy of the measuring machine expressed as measured value with

respect to the estimated true value, can be characterized by the uncertainty of

measurement. The uncertainty of measurement and the measurement errors are

related. When the errors are clearly identified, the uncertainty of measurement can be

estimated. By correcting or controlling errors, the measurement uncertainty is

improved. And vice verse, the accuracy of measuring process is improved by reducing

and controlling the uncertainty of measurement.

The error compensation is applied to the measuring machine in order to get

more accurate measurement results. Thereby complete and sufficient compensation on

the formtester is important. The measuring machine can correct some sources of

errors at machine design and production stage. As a result of correcting known

systematic errors, the measurement result is excluded from residual errors. These

errors could be the deformation of machine structures due to temperature and their

weight, the parallelism between the line of scale (machine) and the line of

measurement (workpiece), etc. However, some sources of errors can not be fixed such

as the error caused by random distribution error, scale error (resolution), deformation

of workpiece and probe deformation due to contact. Therefore, every measurement

2

result has uncertainty due to these errors. The complete measurement result is

presented by the estimated true value and its measurement uncertainty.

The combined uncertainty is calculated according to the ISO Guide to the

Expression of Uncertainty in Measurement (GUM) [1]. This study uses a form

measuring machine, MMQ400, to measure a cylindrical standard workpiece.

MMQ400 is a precision measuring equipment, a new machine within the series of

MarForm Desktop Formtester of the Mahr Company. This cylinder workpiece has the

same characteristics as a universal cylinder used for calibrating the signal

transmission and testing the straightness and parallelism of the axes. A temperature

device, TESTCO950 with a resistance temperature sensor probe pt100, is used to

collect temperature data during the measurement. The measurement procedure is

created following the Bosch book10 standard on Capability of Measurement and Test

Processes [2].

For the purpose of this study, the measurement process has three main setting

conditions: the error compensation algorithm, the workpiece handling and the

temperature. First, the error compensation is referred to the correction of the errors in

the z and c axes. The compensation algorithm in the machine can be either activated

or de-activated. Secondly, the handling condition is defined as resetting the workpiece

position by rotary table. During the measurement, the workpiece should be removed

and put back in between subsequent measurements. In the handling condition, the

measurement program automatically resetting workpiece position by moving the

rotary table away from the measurement position. This motion gives the effect as

automatically taking the workpiece off and applying new clamping before starting

each measurement in order to test the alignment of centering and tilting table. This

condition seems to be the normal situation of measurement without operator’s effects.

In without handling condition, the measurement is repeated fifty times after the first

alignment under the permissible eccentricity value 2.0 µm. The without handling

condition is created in order to observe drifts in machine’s column during the

measurement. This condition can be used as a reference condition for comparing its

measurement result with other conditions. The third setting condition is temperature.

The measurement is made in two rooms which are different in the presence of air

conditioning in order to observe the effect of temperature. Temperature is one

influencing factor on form measurement result. The temperature has an effect on the

3

material expansion. Therefore the effects of temperature on form measuring machine

are interesting. The room is controlled to 20±1°C by air conditioning unit.

The workpiece of this study is made of steel with a height of 100 mm and a

diameter of 20 mm. This cylinder workpiece have two flat areas at a specific height of

the workpiece. This flat area is called flick area. The testing of the capability of the

cylinder standard workpiece is performed by the software measurement program of

the regularly calibrated form measuring machine. The cylindrical standard workpiece

is used for calibrating the sensitivity of the signal transmission chain by two flicks

sections of the standard and for testing the straightness and parallelism of the linear

measuring axes of the machine. The measured profiles are evaluated by seven form

and location tolerances: the roundness, the roundness including flick, the straightness,

the parallelism, the conicity, the radial runout and the cylindricity deviations.

Additionally, the radial runout with the machine datum deviation is added in the

measurement program in order to observe the changes of the measuring machine axis.

Furthermore the cylindricity deviation that is evaluated from the circular profiles at

three different heights is added into the measurement program as it can be directly

calculated from roundness measurement. This study is performed under the

assumption that dimensional error is randomly distributed.

In order to represent performance of the measuring machine, capability index is

calculated according to the Bosch book10 standard on Capability of Measurement and

Test Processes [2]. The capability indices are calculated from the percentages of

process variance and measurement system variation. Finally, the measurement results

and their uncertainty are explained together with their capability index. The capability

indices and measurement results can be used to estimate the combined uncertainty.

On the other hand, the standard deviation of repeated measurement results relative to

the capability index and the uncertainty of measurement are used to calculate the

minimum tolerance. The minimum tolerance of each measuring feature is used as the

permissible tolerance value of this measuring machine.

Chapter 2 describes related theory and literature review. The measurement

process consists of measuring machine, reference measuring machine, temperature

measuring device, workpiece and measurement program described in chapter 3.

Chapter 4 shows measurement results measured under three conditions in two

difference rooms of air conditioning unit. The measurement results are discussed in

4

term of their accuracy and causes of errors. The measurement results of each

condition are compared together in order to observe the effect of the compensation,

the handling and temperature. Furthermore, this chapter describes the correlation

between form and location tolerances that are used to prove the correction of the

measurement results due to their correlated definitions. Additionally, different results

after program modification due to software compensation (the calibration) and the

probe zeroize method are explained and discussed in this chapter also.

Chapter 5 explains the uncertainty calculation relative to the measurement

results. Each influencing factor is set as individual uncertainty components: the

repeated measurement, the calibration, the measurement method, the temperature and

the workpiece. On the other hand, the capability indexes are explained relative to their

measurement result. The capability indexes of the reference condition are described to

perform the characteristic of the measuring machine in this study. The differences of

the capability indexes resulting from different conditions are described in order to see

whether capability index result agree with their measurement result. Additionally, the

percentage of the average increment of each measured features are calculated in this

chapter. Finally, chapter 6 obtains the conclusions related to the capability index and

the uncertainty relative to the measurement results.

CHAPTER 2

LITERATURE REVIEW

2.1 Uncertainty of Measurement

The definition of uncertainty of measurement according to the International

Vocabulary of Basic and General Terms in Metrology (VIM) 3.9 [3] is “parameter,

associated with the result of a measurement, that characterizes the dispersion of the

values that could reasonably be attributed to the measurand”. This is a formal

definition also used in the ISO Guide to the Expression of Uncertainty in

Measurement (GUM). The concept of uncertainty of measurement according to the

GUM focuses on the measurement result and its evaluated uncertainty.

According to the VIM 3.1 [3], result of a measurement is “value attributed to a

measurand, obtained by measurement”. Additionally from the notes of the

VIM 3.1 [3], “a complete statement of the result of a measurement includes

information about the uncertainty of measurement”. Even though the value obtained

from the measurement is indicated in terms of single value without measurement

uncertainty, the true result is the combined value between an estimate of true value

and the uncertainty of measurement. According to VIM 1.19 [3], true value is “a

value that would be obtained by a perfect measurement”. In general, the perfect

measurement is an ideal situation. Then the true value is the ideal value or the ideal

concept value. This definition agrees with the error propagation law that the true value

will never be known.

The GUM defines the uncertainty of the result of measurement as a standard

deviation and divides the uncertainties into two types; type-A and type-B standard

uncertainties. A type-A standard uncertainty evaluates input quantity from repeated

observations by calculating standard deviations of the mean value. On the other hand,

a type-B standard uncertainty evaluates input quantity from a single observation or

judgment based on experience by calculating the estimated value lies within the

boundaries with percentage of a confidence level. The individual uncertainties that are

independent from one another are combined together he combined standard

uncertainty is determined through the addition of the squares of the uncertainty

6

components. Finally, the result is multiplied by an appropriate coverage factor to yield

an expanded uncertainty.

Determining the thickness of a given sheet of material 20 deg C

Value of the measurand due to incomplete

Value of the measurand (non-realisable true value)

Unadjusted arithmetic mean of the observed values

Measurement the thickness the sheet at 25 deg C with a micrometer and measuring the applied pressure

Defining the measurand (specifying the quantity to be measured, depending on the required measurement uncertainty)

Measuring the realized

Complete measurement result

Measurement result (best estimate)

Correcting all know systematic influences

Determining the measurement

Unadjusted observed values

Correcting the influences of temperature and pressure

Taking into account the uncertainly of the micrometer and the correction

Residual error

FIGURE 2-1 The procedure of the measuring

Figure 2-1 shows an example of the procedure for determining the measurement

uncertainty modified from Tilo Pfeifer [4]. First, the measurand is described in terms

of specific quantity with the measurement uncertainty. Next, the measurand is

measured in accordance with the definition of the measurand. In this stage, the

measurand is corrected on the basis of information regarding recognized influences

such as probe diameter, the parallelism between the line of measurement and the line

of scale, etc. The arithmetic mean of the measurement results is the unadjusted

observed value. After all known systematic influences are corrected, the measurement

result is estimated along with residual error. The complete measurement result is

7

reported as combined value between the best estimated measurement result and its

measurement uncertainty.

2.1.1 Measurement Uncertainty and Measurement Error

The definition of error (of measurement) is the result of measured value minus

true value of the measurand according to the VIM 3.10 [3]. The measurement errors

occur in measurement process due to several influences and the nature of the

measurement process. Every measurement result is related to the measurement error

in the same way as the measurement uncertainty. The measurement uncertainty is

determined by considering several measurement error components.

FIGURE 2-2 Cause and effect diagram of production metrology

The errors are identified or classified according to their causes as shown in

figure 2-2. The causes of measurement errors are presented by a cause and effect

diagram modified from Tilo Pfeifer [4]. In the general, the main factors influencing

the measurement of production process are human, material, method, environment,

machine and measurement. This cause and effect diagram presents the cause of

measurement error in the measurement process within production metrology.

Therefore, the measurement itself is excluded from influence factors in figure 2-2.

8

Figure 2-3 modified from Tilo Pfeifer [4] shows the classification of errors

according to their type. The sources of errors are divided into two groups; a

systematic and coincidental measurement errors. The systematic errors always occur

in the measurement because the measurement is not perfect as having many sources

of error. According to the VIM 3.14 [3], “the systematic error is result from an infinite

number of measurements of the same measurand carried out under repeatability

conditions minus a true value of the measurand”. With regard to characteristic of the

measuring instrument, the systematic error is a bias of the measuring instrument. “The

bias of a measuring instrument is normally estimated by averaging the error of

indication over an appropriate number of repeated measurements” according to the

VIM 5.25 [3].

Some sources of the systematic errors are known and corrected into the

measurement result. Some sources of errors are known but can not be corrected.

These errors, called residual errors, are included in the uncertainty of measurement.

Similar to residual errors, unknown systematic errors are calculated and included in

the uncertainty of measurement also. Because of these reasons, the systematic errors

and their causes can not be completely known. On the other hand, the coincidental

measurement error is the result from random nature of the measurement.

FIGURE 2-3 Types of measurement errors

9

Even though these errors can not be eliminated, they can be reduced by the

controlling and monitoring the measurement process. For example, the influence of

the coincidental errors can be reduced by measurement repetitions.

In consequence, the measurement result is the corrected value as some known

sources of error are corrected into the measurement result. The measurement

uncertainty is calculated from the residual errors, the unknown systematic errors and

the coincidental measurement errors.

2.1.2 Measurement Uncertainty and Accuracy of Measurement

Standard deviation of the measurement value is used to express measurement

uncertainty according to the GUM. In statistics, standard deviation represents the

dispersion of measurement results relative to its mean value. The closeness of the

agreement between the mean of measurement results and a true value of the

measurand is defined as an accuracy of measurement according to the VIM 3.5.

FIGURE 2-4 Accuracy definition

Additionally the accuracy of the measurement has the same meaning as the error

of the measurement. Both words express the difference between the result of a

measurement and the true value. The definition of the accuracy of measurement is

shown in figure 2-4.

In contrast, the accuracy is not the same as precision. According to the notes of

the VIM 3.5, “the term precision should not be used for accuracy”. However, both

words are frequently used in explaining the characteristics of the measuring machine.

Consequently the understanding of these two words is important.

10

FIGURE 2-5 The different between accuracy and precision

The difference between these two words can be explained by an example of

shooting scores in figure 2-5. The score comes from sufficient number of shooting.

While the patterns of shooting result of gun A and gun B are similar, the shooting

score of gun A is less than that of B. However, the three patterns, B, C and D, get the

same score even though the different pattern of shooting results. The shooting result

of gun B spread around the target. The shooting result of gun C spread only one side

of the target, while the shooting result of gun D is spread around the target as the gun

B but the area of the shooting result of gun D is closer to the middle point than that of

the gun B. Then gun C and D are more precise than gun B.

Additionally the accuracy of measurement is more important than the precision

in controlling process and measurement system. Even the patterns of shooting are the

same as the previous example; the shooting scores of three patterns, A, B and C are

changing immediately when the position of target is changed or the shooting area is

decreased. However, the pattern D gets the same score even though the position of

target is changed or the shooting area is decreased. Changing target position by

moving target point to the right side of picture approximately the distance between

two circles is the same as moving the arithmetic mean of the measurement results by

the influencing effects. The shooting area is the same as specific tolerance of

measurement. The shooting area is decreased from circles rounds to two circles of

target as the specification area is narrowed by measurement uncertainty or customer’s

specification. In accordance with these examples, the closeness of measurement

results to the actual value is more important than the dispersion of measurement

results.

11

2.1.3 Measurement Uncertainty and Tolerance

FIGURE 2-6 The relationship between measurement uncertainty

and workpiece tolerance [4]

Figure 2-6 shows the relationship between measurement uncertainty and

workpiece specification. The specification area called tolerance width is narrow by

the uncertainty of measurement. The conformance zone is also reduced by the

uncertainty of measurement. In order to get the small value of the measurement

uncertainty, the measurement process including the measuring machine, the

measurement method, the measurement environmental, and etc must be controlled.

The expanded uncertainty is considered when the tolerance is specified in the

drawing because of the relationship between the measurement uncertainty and the

workpiece tolerance. For example, the tolerance zone is not smaller value than the

uncertainty of measuring machine determining from calibration certificate. The

measurement uncertainties should not be greater than a fifth or a tenth of the

tolerance.

2.2 Dimensioning and Tolerancing

All geometrical and dimensional specification of workpiece is clearly defined

by Geometrical Dimensioning and Tolerancing (GD&T). The geometry expresses

form and location of workpiece. The geometrical elements such as planes, spheres and

cylinders are used to describe shape of workpiece. Some elements can be directly

measured from workpiece for example diameter, straightness, flatness, etc. Some can

not be directly measured from such as center of circle, symmetry, etc. A deviation of

dimensions, form and position of geometrical feature are represented tolerancing.

12

The geometric characteristics of workpiece can be divided into five groups that

are shown in table 2-1. On the one hand, form tolerance is the largest possible

deviation of a form element from its geometrical ideal form. The form element can be

point, line, plane, circle or cylinder. The form tolerance is divided into two groups;

form and profile tolerance.

On the other hand, location tolerance is the permitted deviation of ideal

elements with respect to reference element (datum). This tolerance is divided into

tolerance of orientation, location and runout. The definitions of form and location

tolerance are additionally described in Appendix A.

The difference between a produced workpiece and a desired geometry

workpiece come from many sources. The VDI 2601 is cited in Pfeifer [4] that

“machine, workpiece and environment are the causes for form deviation”. The causes

for form deviations according to the VDI 2601 are shown in table 2-2.

TABLE 2-1 Form and Location Tolerance

Form Tolerance Location Tolerance

1. Form tolerance expresses how far an

actual surface or feature is permitted to

vary from the desired form implied by

the drawing. This tolerance consist of

features;

- straightness

- flatness

- roundness / circularity

- cylindricity / cylinder form

2. Profile tolerance expresses how far an


vary from the desired form on the

drawing and/or vary relative to a datum

or data. This tolerance consist of

features;

3. Orientation tolerance expresses how

far an actual surface or feature is

permitted to vary relative to a datum or

data. This tolerance consist of features;

- parallelism

- perpendicularity

- angularity

4. Runout tolerance expresses how far an


vary from the desired form implied by the

drawing during full (360°) rotation of the

part on a datum axis. This tolerance

consist of features;

- runout

- total runout

13

TABLE 2-1 (CONTINUED)

Form Tolerance Location Tolerance

- line profile

- surface profile

5. Location tolerance expresses how far

an actual size feature is permitted to vary

from the perfect location implied by the

drawing as related to a datum or data, or

other feature. This tolerance consist of

features;

- position

- concentricity, coaxiality

- symmetry

TABLE 2-2 The causes for form deviations according to the VDI 2601[4]

Every workpiece, no matter how precisely it has been manufactured, displays

deviations from the geometrically ideal form.

Machine-

dependent cause

Workpiece-

Dependent cause

Environmentally-

dependent cause

- Static and dynamic

deviation of form due to

guile rails and bearing of

mobile machine

components.

- Positioning deviations of

these mobile

components.

- Elastic deformations of

the machine, the guide

rails or the tool

- Tool wear

- Bearing play

- Vibration between tool

and the machine

- Material inhomogeneities

- Deformation of the

workpiece during

processing

- Differing local

temperature distribution

during the production

process

- Subsequent shrinkage

after processing

- Releasing of inner stress

after processing

- Deformation due to

hardening

- Local temperature

fluctuations

- Temporal temperature

fluctuations

- Vibrations transferred to

the machine from the

surrounding via the

foundation

14

2.3 Form Measuring Machine

The Military Standard, Gage Inspection, MIL-STD-120 classifies gages and

equipments involved in metrology into eight groups [5];

2.3.1 Length Standards: Standards of length and angle from which all

measurements of gages are desired.

2.3.2 Master Gages: Master gages are used for checking and setting inspection

of manufacturer’s gages.

2.3.3 Inspection Gages: Inspection gages are used to inspect products for

acceptance. These gages are made in accordance with established design

requirements. Tolerances of inspection gages are prescribed by specified drawing

limits.

2.3.4 Manufacturer’s Gages: Manufacturers’ gages are used for inspection of

parts during production.

2.3.5 Noprecision Measuring Equipment: Simple tools are used to measure by

means of line graduation.

2.3.6 Precision Measuring Equipment: Tools are used to measure in thousandths

of an inch or finer.

2.3.7 Comparators: Comparators are precision measuring equipment used for

comparative measurements between the work and a contact standard such as gage or

gage blocks.

2.3.8 Optical Comparators and Gages: Optical comparators and gages are those

which apply optical methods of magnification exclusively.

The word gage and gauge are frequently used interchangeably in writing

however they refer to different thing in terms of metrology. These words are defined

in the 1983 interim standard for coordinate measuring machines.

Gage: A mechanical artifact of high precision used either for checking a part

of for checking the accuracy of a machine

Gauge: A measuring device with a proportional range and some form of

indicator, either analog or digital.

The function of form testing technology is “the metrological acquisition of form

deviations on a workpiece and making a predication about the quality of

manufactured components by comparing the determined from parameters with the

tolerated dimensions” [4].

15

The form measuring machine measures workpiece either by moving machine

axes while workpiece is fixed position or by turning workpiece when machine axes

are fixed. The measuring points on workpiece are collected and saved in term of

measured profile. The recorded data are corrected by errors such as stylus tip radius,

contacting force, alignment between line of measurement and line of machine scale,

etc. The filter is used to create the measured profile within the specification range of

measurement. The substitute elements such as point, line, plane, circle, cylinder taper

sphere and parabola are calculated from measured profiles. The form deviation is

calculated by placing the substitute element into a smallest tolerance zone by an

evaluation method. The tolerance zone expresses as the distance between two form

elements that the substitute element lies within. The evaluation method is described in

Appendix A.

The low-pass filter is used to reduce the signal fluctuation and cut-off the

measured profile waves to range of form deviations. The height of wave is reduced to

a pre-specified percentage of the original wave’s height when passing through the

filter. The filter can be explained by their characteristic or type. The filter is divided

into two types; polar and linear filtering as shown in figure 2-7.

FIGURE 2-7 Polar and Linear filter

With polar profile, the unit of polar filter is the number of undulations per

revolution (upr). The value of profile filter means the number of peak or valley on one

polar measured profile.

16

On the other hand, the unit of linear filter is millimeter (mm). The linear filter

cutoff wavelength number means the length of one wavelength or the distance from

peak to next peak or from valley to next one.

Geometrical characteristics of surface measurement can be divided into two

structural deviations; microstructure and macrostructure as shown in figure 2-8. Form

and location tolerance are macrostructure.

The data processing flow of form measuring machine is different from

Coordinate Measuring Machine (CMM). The data processing flow of CMM called

Feature-based metrology, disagree with the data processing method in profile

metrology and length metrology [6]. The Profile metrology is data processing method

of form measuring machine. The difference between the data processing of CMM and

form measuring machine are shown in table 2-3.

FIGURE 2-8 Geometrical characteristics of surface measurement [4]

TABLE 2-3 Comparison of the feature-based metrology and the profile metrology [6]

Feature-based metrology Profile metrology

Number of measured

points

Small

(10–20 in 3D)

Many

(1000–10,000 in 3D)

Uncertainty of measured

points

Large Small

17


Feature-based metrology Profile metrology

Density of measured

points

Low

(discrete sampling)

High

(continuous sampling)

Data processing Extrapolate,

least squares method

Filtering

Objects of measurement Parameters of feature Profile

Model of feature Yes No

As a result in table 2-3, the uncertainty of measured points of form measuring

machine based on profile metrology is small. However previous study is mostly focus

on the effects of the CMM [7], the measurement uncertainty in Coordinate

Measurement [8], the uncertainty analysis in geometric best fit [9] or the uncertainty

analysis of vectorial tolerance [10]. In this study, the study related CMM are reviewed

in order to get ideas.

Regarding to the previous studies, the sources of uncertainty or the source of

errors are one part of discussion. The uncertainty of measurement comes from many

sources and relates with the accuracy of machine. Therefore the accuracy expressed as

the dispersion of measurement results is improved by reducing the measurement

uncertainty. The uncertainties are classified into many schemes.

Qing Lin, et al. [7] divides the source of error into four types; measurement

machine component and probe, data acquisition or sampling strategy, data processing

and measurement environment. Wilhelm [8] classifies coordinate measurement

systems uncertainties into five main categories: hardware, workpiece, sampling

strategy, fitting and evaluation algorithms, and extrinsic factors. Each category

consists of many error components. For example, the hardware uncertainty occurs in

the stage of designing machine such as machine scales, machine geometry, probing

system, etc. The workpiece uncertainty category relates to the error from the

properties of the workpiece and the measurement interaction with the workpiece: part

form deviation, clamping effects, contact mechanics, surface finish and elastic

deformation.

However, Wilhelm [8] cited Trapet, et al. [11] that the uncertainties are

classified to similar errors and divided them into two categories. One is generally

18

accessed by measurements, and the others are normally estimated. The first category

of uncertainty include systematic errors of the probing process, random probing

errors, probe changing and probe articulation uncertainties, and systematic and

stochastic errors of the CMM geometry. The other category includes the uncertainties

in assessments of systematic errors, long-term changes of the individual systematic

errors, temperature influences on these errors, model imperfections, and drift effects.

Additionally, Wilhelm [8] cited to Salsbury [12] that a categorization scheme divides

the uncertainty into four categories including; machine components, probe

components, part components, and repeatability components. Salsbury presented the

relationship between the uncertainty components and the geometric dimensioning and

tolerancing by table. An example of such relationship is shown in table 2-4. This table

explains whether a specific error affects the measured features.

TABLE 2-4 Relationship between the machine uncertainty component and specific

measured features [8]

Characteristic Machine

Feature of size Yes

Length (not feature of size) Yes

Angle, cone Possible, more likely for larger surfaces

Angle, between features Yes

Flatness Unlikely, except very large surfaces

Straightness Unlikely, except very large surfaces

Circularity (roundness) Unlikely, except very large surfaces

Cylindricity Unlikely, except very large surfaces

Perpendicularity (squareness) Yes

Angularity Yes

Parallelism Yes

Profile of a surface (no datums) Possible, more likely for larger surfaces

Profile of a line (no datums) Possible, more likely for larger surfaces

Profile of a surface (with datums) Yes

Profile of a line (with datums) Yes

Circular runout Yes

19


Characteristic Machine

Total runout Yes

Position (features of size) Yes

Position (not feature of size) Yes

In conclusion, Salsbury [8] said that “Consequently, the ability to determine all

of the uncertainty sources and to include them in an uncertainty evaluation for the

measurement at hand is more important than the categorization scheme of error

components that lead to uncertainties”.

The measuring machine is one factor for complete measurement results. It has

influences to the production and control processes. The characteristics of measuring

machine must be known such as accuracy, repeatability, stability, linearity, etc. figure

2-9 shows some characteristics of measuring machine.

20

FIGURE 2-9 The characteristic of measuring machine [13]

These definitions refer to Ford guideline for measurement system and

equipment capability [13].

Accuracy is the systematic difference between the observed average of

measurements and the true average of the same characteristic on the same component.

The accuracy of the measurement system is affected by its calibration.

Stability is the difference in the average of at least two sets of measurements

obtained with the same equipment on the same components taken at different times.

21

Linearity is the difference in the accuracy over the whole range of the

equipment.

Repeatability is the variation in the measurements obtained with the same

equipment, when used several times by one operator whilst measuring the same

identical characteristic on the same component.

Reproducibility is the variation in the average of measurement made by

different users or in different locations using the same gauge whilst measuring the

identical characteristic on the same component.

Due to the Ford guideline for measurement system and equipment capability,

the five types of variation are combined to influence the overall performance of a

measurement system. On the other hand, the definition of the measurement system

according to the VIM 4.5 is “a complete set of measuring instruments and other

equipment assembled to carry out specified measurements” [3].

2.4 Capability study

The capability study is one method in production metrology used for quality

control and preventative processes of quality assurance. The objectives of capability

study are to express the quality characteristic of the measurement system, to calculate

the variations in the measurement system and to get the information data for choosing

or adjusting the optimal system and processes for the various measurements and

testing tasks.

The capability is used in the monitoring process and equipment. According to

the definition by Tilo Pfeifer [4], the capability testing is divided into three different

investigations: process capability, machine capability and test equipment capability.

The test equipment capability is calculated by statistic evaluation of measurement of

reference part. This value describes the performance of chosen test equipment to

judge a process in accordance with the appropriate parameters. The test equipment

has to be monitored regularly to ensure its capability in order to control the quality of

the production process and product as the reference. The process and the machine

capabilities are calculated by the statistic evaluation of measurement results. The

process capability describes the performance of process relative to process conditions.

The machine capability describes the performance of machine under ideal conditions.

22

According to the Bosch book10 standard about Capability of Measurement and

Test Processes, the procedure for Testing Capability consists of five procedures

including:

Procedure 1: Variation and average position of measured values (Bias and

Repeatability).

Procedure 2: Variation of measured values by influence of handling by several

operators.

Procedure 3: Variation of measured values by influence of the measuring

objects.

Procedure 4: Linearity.

Procedure 5: Inspection and test equipment for qualitative characteristics.

The purpose of these procedures is testing of the capability and monitoring of

the stability of measurement processes to ensure that measuring device is capable of

measurement with a sufficiently small variation of measured value. The Procedure 1

is to investigate the capability testing in order to perform the repeatability and

accuracy of the measuring machine according to objectives of this study.

The Procedure 1 requires twenty-five or fifty times of measurement with a

standard workpiece or a production part which is done by one operator. The

measurement system must be calibrated before starting the measurement. In

accordance with the note in Procedure 1, the systematic deviation (bias) must always

be corrected by modification (e.g. adjustment) of the measurement system or it can be

compensated by correction of every result of the measurement. In addition, the

standard workpiece or the production part must be removed or replaced for each

measurement due to the procedure of Ford guideline for measurement system and

equipment capability [13]. The equations 2-1 and 2-2 are used to calculate the

capability indices (Cg, Cgk). The minimum requirements on capability indices of

Bosch standard are 1.33 while the uncertainty of calibration must be significantly

small when this value is less than 10% of tolerance. The capability indices can be

calculated as follows.

g

g s6T2.0C = Eq. 2-1

23

( )

∑

∑

=

=

=

−−

=

=

n

1ii

2n

1igi

Xn1X

XX1n

1

Tolerance T Where

gs

g

mg

gk s3

XXT1.0C

−−= Eq. 2-2

(master) workpiecestandard of valueTrueX

value)(absolute X and Xbetween differenceXX Where

m

mgmg

=

=−

2.0

)s6(CT gg

min = Eq. 2-3

10[2])Book Bosch with

accoedingindex capability theoft requiremen minimum (the 1.33C Where g =

FIGURE 2-10 The concept of capability index

24

Figure 2-10 shows the capability indices calculate the specified tolerance in the

comparison with the dispersion of the measurement value.

Measurement Uncertainty combined standard uncertainty

Measurement System Capability Type-1 Study Cg, Cgk

Documentation Part No., Description,Characteristic, Tolerance, Gage Gage No., Resolution, Actual Dimension, etc

Ustandard = (Ustandard/2) with P = 95% Ures = (1/2) · 0.6 · Resolution

Ustandard ≤ 5% of T Resolution ≤ 5% of T

Measure the standard Xmn times

Usys = 0.6 · mg XX ⋅

Uw = n

sg

Upm = 2x

2w

2sys

2res

2dardtans UUUUU ++++

Ux = other interference factors

Average gX

Bias mg XX ⋅

Standard Deviation Sg

Cg = gS4T2.0

⋅⋅

Cgk = g

g

S2

XmXT1.0 −−⋅

Type-2 Study

3 · (Upm/T) · ≤ 0.1 or 0.2

Extended Measurement Uncertainty

CgCgk ≥ 1.33 Improve

gauge

FIGURE 2-11 The comparison between the combined standard uncertainty (Upm)

and the capability indices type-1 study (Cg, Cgk)

In figure 2-11, the procedure of the measurement uncertainty calculation and the

procedure of the capability indices calculation can be combined into one diagram.

This figure shows the comparison between the machine uncertainty and the test

25

equipment capability procedure. The measurement uncertainty of the machine is

determined by the VDA5 whereas the capability indices are determined by the

automobile industrial standard.

Even though the reference standard for calculating the measurement uncertainty

and the capability indices in this figure is not the same as that used in this study, this

figure is a good explanation that the result from the capability study can be used to

estimate the combined uncertainty of measurement.

The average, the bias and the standard deviation of measurement result are used

in the calculation of the measurement uncertainty and the capability indices. This

corresponds with the introduction in the Bosch standard [2] that “the measurement

uncertainty must be specified when the measuring equipment is calibrated and

monitored”.

2.5 International standards related to form measurement and uncertainty

measurement

Most dimensioning standards used in industries refer to the American Society of

Mechanical Engineers (ASME) or the International Organization for Standardization

(ISO) standards. Due to dimensioning and Tolerancing document, the ASME and the

ISO standard are different. The ASME standard explains all dimensioning and

Tolerancing topic into a single standard. The approach to dimensioning based on the

functioning of product that is supported with illustrated examples of tolerancing

applications. The ASME standards on dimensioning are ASME Y14.5 Dimensioning

and Tolerancing, ASME Y14.5.1M Mathematical Definition of Dimensioning and

Tolerancing Principles, ASME Y14.8 Castings and Forgings and ASME Y14.32.1

Chassis Dimensioning Practices. On the other hand, the ISO standard covers multiple

standards that are explained in the theoretical subsets of dimensioning and tolerancing

topics for example:

ISO1101 Technical drawing- Geometrical Tolerancing-Tolerances of form,

orientation, location and runout – Generalities, definitions, symbols, indications on

drawings,

ISO2692 Technical drawing- Geometrical Tolerancing-Maximum material

principle,

ISO5458 Technical drawing- Geometrical Tolerancing-Positional Tolerancing

26

ISO8015 Technical drawing- Fundamental Tolerancing principle,

ISO10209-1 Technical product documentation vocabulary-Part 1: - Terms

relating to technical drawing – General and types of drawings, Etc.

However, the ASME and ISO standards organizations are continually making

revisions that bring the two standards closer together. Paul J. Drake [14] said that

“currently the ASME and ISO dimensioning standards are 60 to 70% common”.

Consequently, the trend of developing standard is toward a unique standard. The

national standards and the primary standards are combined and compared for making

the international standard references. Most the national laboratories have accepted the

GUM for analysis measurement uncertainty. The seven international standards and

metrology organizations, including International Bureau of Weights and Measures

(BIPM), International Electrotechnical Commission (IEC), International Federation of

Clinical Chemistry (IFCC), International Union of Pure and Applied Chemistry

(IUPAC), International Union of Pure and Applied Physics (IUPAP), International

Organization of Legal Metrology (OIML) and International Organization for

Standardization (ISO) take part in developing the GUM. The purposes of this standard

are to promote information about the uncertainty and to provide a basic for the

international comparison of measurement results.

CHAPTER 3

MEASUREMENT PROCESS

3.1 Measuring Machine (MMQ400) and Software

A measuring machine consists of the machine, a probe system and software.

First of all, MMQ400 is a precision measuring equipment, a new series of MarForm

Desktop Formtester of the Mahr Company. According to the company definition,

MMQ400 is a high-precision shop floor equipment for fast setting of the

manufacturing process for large measuring volume and large weight capacity of the

rotary table. MMQ400 machine consists of 3 main modules, a centering and tilting

table, vertical and horizontal axes. The combination of modules is made in order to

build up the machine for the customer satisfaction according to their budget and

requirements.

The measuring machine in this study is MMQ400_CNC of which its centering

and tilting table is computer numerically controlled as shown in figure 3-1. The linear

scale on the vertical axis (the z axis) has a measuring length of 350 mm while that on

a horizontal axis (the x axis) has a measuring length of 180 mm. The probe unit is

digital rotary encoder (T7W probe).

FIGURE 3-1 MMQ400 the precision measuring machine [15]

28

Mechanical elements of the measuring machine affect its accuracy. In the

designing stage, the sources of error in each component are analyzed in order to meet

the measuring machine requirements; high dimensional stability, high stiffness, light

weight, high damping capacity, low coefficient of thermal expansion and high thermal

conductivity. Due to the effect of temperature to the structure of the measuring

machine component, homogenous materials are used to minimize such effects. The

base unit and the vertical measuring axis are made from highly stable steel body. In

addition, the MMQ400 has a high damping capacity and large loading capability of

the centering and tilting table due to mechanical bearing. Even though the air bearing

has advantages with less fiction, no stick-slip effect and self-cleaning characteristics,

it is sensitive to the external surrounding effect. While this mechanical bearing has

similar quality as good air bearing. It is produced by Mahr with special production

techniques and materials.

Secondly, the T7W CNC probe system is augmented by motor-driven rotational

axis. It is possible to probe the workpiece 360° and can contact workpiece into two

directions; positive and negative probe angularity. The T7W probe can measure

internal or external surface as well as end face or top surface of the workpiece.

Because the probe arm is fixed with the probe system by magnetic mounting, it

ensures the flexibility of using multi-probe and the safety of the probe collision. The

technical data of T7W are;

Total measurement range of 2,000 µm (0.079")

Zero probe with a working range of ± 500 μm (± 0.0197")

Measuring force adjustable from 0.01 to 0.2 N

Contacting angle in 1° steps (Probe resolution)

Thirdly, MMQ400 operates with the software module that is designed and

developed by the Mahr Company. This software module supports a variety of

applications. It can generate the required information to carry out measurement data

in different programming methods. This software can operate the measuring machine

with the manual programming, learning programming or teach-in procedure and the

offline programming procedure. The structure level of MarWin software module used

to operate Mahr Form testers is shown in figure 3-2.

The measurement programs of this study are run in MarEdit module that is part

of the Professional Form software package and is an optional module in Advanced

29

Form software package. MarEdit is operated by "MarScript", a measuring language

based on C and Pascal programming languages. These include comments, definitions,

control structures (e.g. loops), statements and preprocessor statements. MarEdit is

suitable for specific tasks. It is able to program automatically motion cycles and

functional commands. It can be used to operate without a measuring device also.

FIGURE 3-2 The structure level of MarWin software module [15]

3.2 Reference measurement machine (MFU100)

MFU100 is one of Mahr Formtester series. The company definition of MFU100

is the reference form measuring machine for the inspection laboratory and the

production environment. In accordance with the measurement rule, the reference

machine should be more accurate than the measuring machine by at least 10 times. In

comparing the technical data of both machines, the resolution in X, Y, Z and C-axis of

MFU100 are 0.001 µm, 0.005 µm, 0.001 µm and 0.0001° while the resolution in X, Z

and C-axis of MMQ400 are 5.0 µm, 5.0 µm and 0.05°.

In addition, MFU100 has an attached sensor inside the machine to monitor the

temperature during measurement. The measurement results are corrected for the

temperature effect directly. The temperature compensation can be performed either

directly when the profile is being recorded or after the measurement. MMQ400 can

not compensate the temperature influence by the software technique as MFU100.

Thus it should be operated in the temperature controlled room in order to reduce the

temperature effect. This is also one of the reasons that the MFU100 is more accurate

than MMQ400.

30

Because of the above reasons, MFU100 can be used to obtain the reference

value of the workpiece in this study. The technical data of this measuring machine is

shown in Appendix B.

3.3 Temperature measurement device

Testo950, temperature measuring instrument of Testo AG, is a highly accurate

measuring instrument. Many kinds of probes can be used with this measuring

instrument for the variety applications such as a thermocouple sensor, a resistance

sensor (pt100) and a thermistor (NTC). “The probe type is determined by the

measuring task. The suitable temperature sensor is selected according to the following

criteria: measuring range, accuracy, design, response time and resistance [16].”

The probe type pt100, the precision air probe, is used to collect temperature data

in this study. Pt100 is the abbreviation for the resistance temperature sensor. This

probe is made from Platinum. It has a specified resistance of 100.00 ohms at 0°C. The

selected probe type is applicable to the 0-50°C measurement range.

TABLE 3-1 The technical data of probe type according to the Testo information [16] Technical data

Probe type Pt100 NTC Type K (NiCr-Ni)

Meas. range -200 to +800°C -40 to +150°C -200 to +1370°C

Accuracy

±1 digit

±0.1°C (-49.9 to +99.9°C)

±0.4°C (-99.9 to -50°C)

±0.4°C (+100 to +199.9°C)

±1°C (-200 to -100°C)

±1°C (+200 to +800°C)

±0.2°C (-10 to +50°C)

±0.4°C (-40 to -10.1°C)

±0.4°C (+50.1 to +150°C)

±0.4°C (-100 to +200°C)

±1°C (-200 to -100.1°C)

±1°C (+200.1 to +1370°C)

Resolution 0.01°C (-99.9 to +300°C)

0.1°C (-200 to -100°C)

0.1°C (+300 to +800°C)

0.1°C (-40 to +150°C)

0.1°C (-200 to +1370°C)

In the experiment, the testco950 put on the machine base in order to measure the

temperature at every 5 second. With this period of collecting temperature data, it can

be automatic recorded data for the experimental up to 22 hrs. The amount of recorded

data depends on the memory size of the measuring temperature device. The accuracy

of temperature measurement result is ±0.1°C when is measured at –49.4 to 99.9°C.

31

The resolution of this temperature measurement device is 0.01°C when is measured at

–99.9 to 300°C. Table 3-1 shows the technical data of the probe type from Testo

information. The probe pt100 is more accurate than others.

In normal cases, thermocouple has a shorter long-term stability characteristic

and is less accurate than the resistance thermometer. The advantages and disadvantage

of three probe type are shown in table 3-2. The pt100 probe is accurate, relatively

inexpensive and easy to use according to the opinion of the expert [17].

TABLE 3-2 Comparison of sensors [17] THERMOCOUPLE PT100 THERMISTOR

OPERATING RANGE Very wide:

Type T can go down

below -200°C. Type W5

can approach 1800°C

Wide:

-200°C to 600°C

Narrow.

Typically -40°C to

300°C

PRICE Generally inexpensive

although type R & S use

expensive platinum wire.

Fairly inexpensive Low accuracy types

very inexpensive -

high accuracy types

more expensive than

Pt100

ACCURACY Moderate Excellent Poor to excellent

LINEARITY Poor Good Terrible

PHYSICAL

STRENGTH

Excellent Poor to very good -

Depends on probe

construction

Poor to very good -

Depends on probe

construction

CHANGE IN

CHARACTERISTIC

WITH

TEMPERATURE

Small Reasonable Very large

LONG TERM

STABILITY

Reasonable Excellent Poor to excellent

PREFERRED

APPLICATIONS

Industrial processes

where temperature range

or physical requirements

preclude other devices.

All industrial

processes within

operating range

where accuracy and

repeatability are

required.

Preset temperature

applications.

Control where narrow

hysteresis is required.

32

3.4 Workpiece and clampling device

A cylindrical standard workpiece of this study is made of steel with a height of

100 mm and a diameter of 20 mm. This cylinder workpiece have two flat areas called

flick areas, at specific heights of the workpiece. The workpiece is called a universal

cylinder square or a high-precision cylinder square. It is used to calibrate the signal

transmission chain at two flick sections and to test the straightness and parallelism of

the axes as shown in figure 3-3.

In this study, the reference values of the workpiece are obtained from MFU100

along with calculated measurement uncertainty and the capability indices.

In addition, the workpiece has the same characteristics as that used in

interlaboratory comparison of parallelism measurements. The purpose of the

intercomparison of the parallelism measurements [18] are to make information of

straightness and parallelism measurement, to improve parallelism measurement

capabilities, to study the problem of the measuring machine and to test the uncertainty

evaluation. This workpiece characteristic is observed from the calibration results

which may reveal for any instability of form.

FIGURE 3-3 The cylindrical standard workpiece information [15]

On the other hand, the clamping device or fixturing is one of the influencing

factors on the form measurement. It is a possible source of error due to deformation

and workpiece alignment. Workpiece deforms due to applied probe force and

fixturing method. Its bending leads to imperfect parallelism between the line of

workpiece and the line of measurement. Moreover, fixturing directly affects

workpiece alignment.

33

3.5 Measurement Program

3.5.1 Measurement conditions

In this study, there are three main parameters to be studied. There are error

compensation algorithm, the workpiece handling and the temperature.

First, the compensation algorithm in the machine can be either activated or de-

activated. Secondly, the rotary table may reset its position every time the

measurement takes place. Due to capability testing procedure, the workpiece must be

removed and put back in before every measurement. By moving the rotary table away

from the alignment position, the first step of measurement program is aligning the

workpiece. This simulation of workpiece handling gives the effect as automatically

taking the workpiece off and applying new clampling before starting each

measurement. Thirdly, the measurements may take place in temperature-controlled

environment or not.

According to the parameter combination, the measurement test has three main

conditions in the two different rooms as shown in table 3-3.

TABLE 3-3 The conditions of the measurement program

Conditions A room with

air conditioning

A room without

air conditioning

The measuring machine’s

compensation is off

1. the without handling


The measuring machine’s

compensation is on


3. the with handling

2 the without handling

3 the with handling

The abbreviation codes for the three measurement conditions are:

“Condition 1” refers to the measurement program continually repeating

measurements without workpiece handling after the first position alignment and

machine’s compensation is off.

“Condition 2” refers to the measurement program continually repeating

measurements without workpiece handling after the first alignment positioning and

machine’s compensation is on.

34

“Condition 3” refers to the measurement program having the workpiece

handling simulation by the resetting position of the rotational table before making

measurements and machine’s compensation is on.

The measurement program having the workpiece handling simulation by the

moving position of the rotational table before measurements and machine’s

compensation is off is not considered here. In normal case, the compensation in the

measuring machine is activated on only. The compensation is de-activated in order to

compare the correction of the measurement result between on and off compensation

and to prove the effect of the compensation algorithm.

Condition 2 is the primary condition to compare with other conditions.

Condition 2 is compared with Condition 1 in order to observe the effect of machine’s

compensation. The difference between measurement results between Condition 1 and

Condition 2 reveals the effectiveness of the compensation. On the other hand,

Condition 2 is compared with Condition 3 to observe the effect of workpiece handling

and the drifts in measuring machine‘s column during the measurement.

Finally, the measurement results of each condition when measured in the

temperature controlled and the temperature uncontrolled rooms are used to observe

the effect of temperature.

3.5.2 The measurement program steps

The measurement program created by MarWin software program is modified

from the cylindrical standard workpiece’s capability testing. The capability testing of

the cylinder standard workpiece is performed by the software program in the regularly

calibrated formtester. In this study, some commands are added in the measurement

program to collect additional data to meet the purposes.

The steps of measurement program consist of

3.5.2.1 Probe qualification

The probe information must be verified. In this study, probe diameter is 1.0 mm.

Its arm length is 60.0 mm. The probe angle is 12.0° following the settings in the

standard measurement program.

3.5.2.2 Setting the workpiece coordinate

The workpiece coordinate is set at the upper edge of the lowest workpiece

height in order to identify the measurement height following the specification

drawing. figure 3-4 modified from Mahr [15] show the measurement positions.

35

FIGURE 3-4 The specification information of the cylindrical standard workpiece

The measured positions and the determined features in this study are shown in

figure 3-4. The abbreviation code for the measurement results consists of two parts-

the feature name and the number of cutoff wavelength. The first group focuses on

measurement at certain positions:

“R10” refers to roundness deviation at 10 mm height in workpiece coordinates,

“G0” refers to straightness deviation at 0°,

“P0_180” ” refers to parallelism deviation at 0° and 180°,

“K0_180” ” refers to conicity deviation at 0° and 180°,

“RUNOUT” refers to radial runout deviation with z axis of the machine as

datum,

36

“CYL” refers to cylindricity deviation,

“RUNOUT1” refers to radial runout deviation with workpiece related datum.

3.5.2.3 Aligning workpiece

The workpiece is aligned by the scanning two polar coordinates in order to

make the line of measurement (the workpiece) parallel with the line of scale (the

machine). The setting of the permissible eccentricity value is 2.0 µm. From the

workpiece drawing, the first circle of alignment is at 5 mm above workpiece reference

coordinate. The second circle is at 95 mm above workpiece reference coordinate. The

distance between two aligned circles is considered evaluation length.

3.5.2.4 Setting the actual workpiece coordinate

The workpiece is moved to the suitable position that the line of the

measurement (the workpiece) and the line of scale (the machine) are parallel.

Depending on the actual position from aligning workpiece, it is necessary to set the

new workpiece coordinate system.

3.5.2.5 Measuring

The measuring machine scans three circles at 15.0, 50.0 and 85.0 mm of the

workpiece coordinate and two circles at 10.0 and 20.0 mm where the flicks are

located. Consequently, the measuring machine sequentially scans four lines at 0°,

180°, 90° and 270° of the rotary table. The measuring speed and acceleration of the

polar measurement are 30.0 °/sec and 50.0 °/sec2. The measuring speed and

acceleration of the linear measurement are 5.0 mm/s and 25.0 mm/sec2. The polar

measuring interval is 0.1° while the linear measuring interval is 0.1 mm. All the

measured profiles are saved for the purpose of re-calculation with other criteria.

The measurement program, under no-handling condition, repeat the

measurement until the number of measurements is fifty. The workpiece is aligned

once time at the beginning of the entire measurement process. In contrast, workpiece

is aligned before starting each repeated measurement under the handling condition.

3.5.2.6 Evaluating the measured profile

The measured profile is cut into specific wavelength by filtering process. With

polar measurements, the measured profile is cut off by low-pass filters of 15, 50, 150

and 500 undulations per revolution (upr). According the filtering principle, the lowest

polar cutoff wavelength number has the strongest filtering effect. However the higher

upr means not only less filtering effect but also allows more of the surrounding

37

disturbances. In this study, the measurement is performed in two different air

conditioning controlled rooms in order to observe the temperature effects.

Measurements in a room without air conditioning have more environmental

disturbances than those in a room with air conditioning. Consequently, the cutoff

wavelength number 150 upr is chosen for creating the circular profile.

The linear profile is determined by low-pass filter of 0.25 mm and 0.80 mm of

wavelengths. High linear cutoff wavelength number has strong filtering effect. The

filter 0.25 mm of wavelength is selected as a reference. The filter information is

described in section 2.3.

3.5.2.7 Determining Form and Location Tolerance

The evaluation method for the polar measurement is the Minimum Zone Circles

(MZC) while the evaluation method for the linear measurement is the Least Square

Straight line (LSS). The evaluation method details are described in Appendix A.

The measurement program of cylindrical standard workpiece (the high-precision

cylinder square) makes five polar measurements and four linear measurements and

combines with four polar filters and two linear filters. According to these steps, the

measured profiles are used to determine eight features:

a) Roundness at three different heights,

b) Roundness with flick at two different heights where the flick

are on workpiece,

c) Straightness at four angularity of the workpiece,

d) Parallelism by evaluating the same profile as straightness and

the opposite line as datum,

e) Conicity by evaluating the same profile as straightness and

the opposite line as datum,

f) Radial runout with machine datum by evaluating the middle

circular profile,

g) Radial runout with workpiece datum by creating workpiece

datum from three circles and evaluating the middle circular profile,

h) Cylindricity by evaluating three circles.

Roundness and straightness measurements provide information on form

tolerance of polar and linear profile. Parallelism and conicity are evaluated from the

same profile as straightness with the opposite line as datum. Radial runout with z axis

38

as datum is determined in this measurement program in order to investigate the

temperature effect on the machine column. The selected datum depends on the

measurement objective. The datum line is crated by evaluating with machine

information (machine datum) or determining line from centre of each polar profiles-

substitute circle elements (workpiece datum). The c-axis or the z-axis of the

formtester should be selected to be the reference element. Both machine-axes give the

same radial run out measurement results. The more detail about the comparison

between the radial run out with the machine datum when using the c-axis or the z-axis

of the formtester are described in Appendix B. As a result of the same profile,

roundness, radial runout with the machine datum and radial runout with workpiece

related datum are discussed together in order to verify the results. Cylindricity is

evaluated from the three profiles of roundness.

All evaluated values are saved in the form of electronic data for calculating the

measurement uncertainty and capability indices. The protocol of the measurement

result is saved for checking the complement of the measured profile. The example of

the measurement protocol is shown in Appendix B.

3.5.2.8 Calculating the Capability index

The capability testing of the cylinder standard workpiece can be done by

software measurement program. The workpiece is also used for calibrating the

sensitivity of the signal transmission chain by two flicks sections of the standard and

for testing the straightness and parallelism of the linear measuring axes of the

machine. The measurement program calculates the capability indices according to

Bosch Book 10 described in section 2.4.

The capability index is determined by the other measurement program along

with manual calculation. All measurement results of each feature are plotted in

graphs.

CHAPTER 4

MEASUREMENT RESULTS AND DISCUSSIONS

Eight measurements are selected in order to observe their deviations using

specific cutoff wavelength number. These results are R10_150, R50_150, CYL_150,

RUNOUT_150, G0_025, G180_025, P0_180_025 and K0_180_025.

“R10_150” represents roundness deviation measured at 10 mm height in

workpiece coordinates including the small flick, filtered by cutoff wavelength number

150 upr,

“R50_150” represents roundness deviation measured at 50 mm height in

workpiece coordinates, filtered by cutoff wavelength number 150 upr,

“CYL_150” represents cylindricity deviation determined by three polar

measurements at 15, 50 and 85 mm heights in workpiece coordinates, filtered by

cutoff wavelength number 150 upr,

“RUNOUT_150” represents radial runout deviation with z axis of the machine

as datum measured at 50 mm height in workpiece coordinates, filtered by cutoff

wavelength number 150 upr,

“G0_025” represents straightness deviation measured at 0 degree in workpiece

coordinates, filtered by cutoff wavelength number 0.25 mm,

“G180_025” represents straightness deviation measured at 180 degrees in

workpiece coordinates, filtered by cutoff wavelength number 0.25 mm,

“P0_180_025” represents maximum parallelism deviation for the generating

lines on the opposite side of the cylinder measured at 0 and 180 degrees in workpiece

coordinates, filtered by cutoff wavelength number 0.25 mm,

“K0_180_025” represents maximum conicity deviation for the generating lines

on the opposite side of the cylinder measured at 0 and 180 degree in workpiece

coordinates, filtered by cutoff wavelength number 0.25 mm.

The measurement at 10 mm height in workpiece coordinate is selected to

represent roundness deviation including the flick. Roundness deviations determined

from polar profile at 50 mm of the workpiece coordinate are selected to represent

roundness deviation. Cylindricity determined from three polar profiles are selected

40

also. Cylindricity feature is added to the measurement program as it is widely used in

various industries. Cylindricity tolerance is often used to measure bores, shafts and

pins. The three polar profiles are used to determine cylindricity deviation. Radial

runout deviation (RUNOUT_150) is determined from the same measured profile as

roundness deviation at 50 mm of the workpiece coordinate. Radial runout deviation

with the machine’s axes as datum (RUNOUT_150) is added to the measurement

program in order to study the effect of temperature on machine column.

Among others, the measurement program scans four vertical lines at 0, 90, 180

and 270 degrees in workpiece coordinates. The linear measured profile at 0° and 180°

in workpiece coordinates are selected not only to investigate straightness deviation

(G0_025 and G180_025) but also to check parallelism and conicity deviations.

Therefore, the parallelism and conicity at 0° and 180° in workpiece coordinates

(P0_180_025 and K0_180_025) are also included in this study.

Each measurement condition is performed in two separate rooms. Temperature

during the measurement is collected by the temperature measuring device: testco950.

The characteristic and technical data of the temperature measuring device is described

in section 3.3. The temperature information of each condition is shown in table 4-1.

TABLE 4-1 The temperature information when are measured at the different

controlled air conditioning room.

with air conditioning

without air conditioning





Range (°C) 1 1.81 0.68 2.23 0.45 5.61Maximum (°C) 20.49 27.67 20.52 30.6 20.81 33.8Minimum (°C) 19.49 25.86 19.84 28.37 20.36 28.19

Condition 2 Condition 3 Condition Temperature

Condition 1

The first room is controlled at 20±1°C by an air conditioning unit. 20±1°C is the

standard controlled temperature of precision measurement. The other room has no air

conditioning. Temperatures of the room without air conditioning under three

conditions are different depending on different date of measurement. Temperature

under Condition 1 has the lowest range among other results measured in the room

without air conditioning. Temperature of the room without air conditioning under

Condition 1 is 26±2°C. Temperatures of the room without air conditioning are

30±2°C under Condition 2 and 31±3°C under Condition 3. The ranges of temperature

41

measured in the room without air conditioning are bigger than those measured in the

room with air conditioning.

Mean value of repeated measurements is used to compare with the reference

value of the workpiece. The reference value is obtained from more accurate

measuring machine (MFU100). The mean value, standard deviation and range are the

main quantitative values for discussion and comparison of results under different

conditions. More details on the setting conditions are described in section 3.5.

4.1 The effect of air-conditioning room

The influence of temperature is more significant with length measurement as the

result of the expansion of workpiece and machine components. To diminish the

measurement uncertainty, it is necessary to decrease the sensitivity of measuring

device with respect to the environment or to carry out the measurements where

temperature can be controlled. This formtester, MMQ400, does not have an attached

sensor inside the machine to detect temperature during measurement. Then MMQ400

can not compensate the measurement results from temperature effect.

In this section, the measurement results between with and without air

conditioning is compared when the compensation is activated off. The difference

between two represent calibration room and production. The left-hand side in

figure 4-1 shows the measurement results from the room with air conditioning, while

the right-hand side shows the measurement results from the room without air

conditioning. Due to the comparison of the measurement results, the diagrams are

plotted between the number of measurement (time) and the deviations of each feature

in micrometer unit (µm).

Temperature has little effect on measurement features determined from only

polar profile. However, some features such as cylindricity and radial runout

deviations are not only determined from polar profile but also related to the

parallelism between the z and c axes. These features depend significantly on

temperature.

Three polar profiles at the specific heights are used to determine roundness and

cylindricity deviations. In figure 4-1, roundness deviations when measured in the

room with and without air conditioning are slightly different. Then roundness

42

deviations has little effect from temperature because this feature is only determined

from it polar profile.

FIGURE 4-1 Roundness and cylindricity deviations when the machine’s

compensation is activated off

43

While Cylindricity deviations measured in the room without air conditioning

fluctuate in wide range than others. Cylindricity deviations are determined from three

polar profiles at different height in z axis. Then this feature is affected by radial

direction in x-axis from each circles and axial direction in z-axis at different height of

measurements. Cylindricity is affected by temperature when the compensation is

activated off.

FIGURE 4-2 Roundness deviation including flick and runout deviations with the z

axis as datum when the machine’s compensation is activated off

Figure 4-2 shows roundness deviation including flick similar to roundness

deviations as shown in figure 4-1. The dispersions of this feature when measured in

the room with air conditioning are similar to the measurement results when measured

in the room without air conditioning.

In this study, radial runout deviation is determined from the same polar

measured profile as roundness deviation. The selected datum is the z axis of

measuring machine in order to observe the deformation of machine axes in relation to

time and temperature. Similar to cylindricity deviation, radial runout deviations with z

axis of the machine as datum has larger effect on measurement results in two different

air conditioning controlled room when the compensation is activated off.

44

FIGURE 4-3 Straightness deviations when the machine’s compensation is off

Figure 4-3 shows straightness deviations when measured in the room with and

without air conditioning. However straightness deviation is determined from it profile

only as roundness deviaition, straightness represent to temperature effects. These

features are not only determined from its profile but also related to the deformation of

machine column. Straightness deviation is determined from the linear profile that

measured at the side of the cylindrical standard workpiece. The formtester is turned

the workpiece into the specific angular position by rotary table. The probe is moved

along the workpiece in the z direction.

FIGURE 4-4 Parallelism and conicity deviations when the machine’s

compensation is activated off

Subsequently, parallelism and conicity deviations are determined from the same

linear measurement profiles as straightness deviations. Under evaluation method, linear

profile is determined itself in relation to the other lines that used to be reference

45

(datum). Parallelism and conicity deviation represent to form and direction of linear

measured profile. These features are related to the parallelism between the z and c axes.

In figure 4-4, the range of parallelism and conicity deviations when measured in

the room without air conditioning are larger than the measurement results when

measured in the room with air conditioning. The mean values when measured in the

room without air conditioning are higher than the measurement results when

measured in the room with air conditioning. The arithmetic mean value of

measurement results are affected from temperature changed from 20±1°C to 26±2°°C.

4.2 The effect of machine compensation in temperature-controlled room

Even machine components are made from highly stable steel body in order to

reduce errors such as deformation of machine column due to temperature, their

weight, their surface quality, etc. However, a small tilt due to a parallel offset of the

measuring distance and the reference distance already causes measurement errors

which are no negligible. Thereby, the mechanical accuracy of measuring machine

relates with the straightness of the guide rails and the perpendicularity of the guides to

one another. The errors involving the z and c axes of the machine are compensated in

order to accomplish the accuracy of measurement.

FIGURE 4-5 Compensation’s algorithm

46

The measurement errors in measuring machine occur from many causes such as

statistic behavior, dynamic behavior, internal evaluation of device and its structure.

Some sources of errors can not be fixed such as the error caused by the random

distribution error, the scale error (resolution) and the deformation of workpiece from

the probe contacting. Some sources of errors can be fixed or corrected upon the

machine designing and producing stage. These errors could be e.g. the deformation of

machine structures due to the temperature and their weight, the parallel between the

line of scale (machine) and the line of measurement (workpiece), etc. Thereby, error

compensation is applied in measuring machines in order to get accurate measurement

result as shown in figure 4-5.

FIGURE 4-6 Machine structures of form measuring machine

Structure of the measuring machine consists of three main modules as shown in

figure 4-6. First module is the machine column. The vertical axis of machine is

defined as axis z. The machine can be moved along this axis to make measurement

along workpiece or vertical measurement. The horizontal axis is the second module.

The probe unit is built in this axis. The probe can be moved in the x direction by the

operation of this module. The x axis must be perpendicular with the z axis. The third

module is rotary table. A line axis is on the center of rotary table and parallel with the

z axis of machine called c axis. This module is used for rotating and aligning

47

workpiece. Workpiece is clamped on and turned around by the rotary table. After

completely alignment, workpiece is set into the suitable measurement position which

is the line of measurement parallel with the line of scale.

FIGURE 4-7 The measurement results determined from polar profiles between the

machine’s compensation is activated off (Left) and on (Right)

when measured in the room with air condition

48

In this section, the measurement results when the machine’s compensation is

activated on and off are compared together. The left-hand side shows the

measurement results when the compensation is activated off. The right-hand side

shows the measurement results when the compensation is activated on. Both are

measured in the room with air conditioning.

When the machine’s compensation is activated on and off, roundness deviations

are similar as shown in figure 4-7. Then, roundness deviation has little effect on

compensation. Moreover mean value of these features when the machine is activated

on compensation are close to its reference value more than when the machine is

activated off compensation. Then results when the compensation is activated on are

more accurate than the results when the compensation is activated off.

Cylindricity and radial runout deviations when the machine’s compensation is

activated on are similar to the measurement results when the machine’s compensation

is activated off.

However, it can be noticed that cylindricity values are high value. The

fluctuation of cylindricity is in the big range when compare with the dispersion of

roundness. Cylindricity deviation is calculated relative to not only radial direction in

x-axis from each circles but also axial direction in z-axis at different height of

measurements. The mean value of cylindricity deviation under both condition are

between 0.7-1.0 µm. The technical official of roundness deviation is

0.02 µm+0.0005 µm. per mm of measurement height when using measurement

criteria LSC and filter 15 upr. These results have other influencing factors or some

errors occurred in that time of measurement. The details about how to get the precise

cylindricity deviation value are explained in section 4.6.

In figure 4-7, radial run out deviations with the z axis as datum have the off set

value at the beginning. It causes by the quality of alignment. The alignment is

complete when the parallelism between the c and z axes not exceeds the permissible

eccentricity value. When the machine’s compensation is off, the first radial runout

deviation is higher value than the result when the machine’s compensation id on.

Therefore, compensation has effect on features determined from polar profile

and related to the parallelism between the z and c axes such as cylindricity and radial

deviations.

49

FIGURE 4-8 The measurement results determined from linear profiles between


when measured in the room with air condition

Figure 4-8 shows the measurement results in with air conditioning unit and the

measurement program continually repeating measurements without workpiece

handling after the first position alignment. Straightness deviations when the

machine’s compensation is on and off are slightly different. Then the compensation

has little effect on straightness deviation because straightness deviations are only

determined from its profile.

Subsequently, parallelism and conicity deviations are determined from the same

linear measurement profiles as straightness deviations. Under evaluation method,

linear profile is determined itself in relation to the other lines that used to be reference

(datum). Due to the relation of the parallelism between z and c axes, these features are

affected by the compensation and the temperature.

50

4.3 The effect of machine compensation in normal room temperature

The measurement results are compared between machine’s compensation is

activated on and off when measured in the room without air conditioning.

FIGURE 4-9 The measurement results determined from polar profiles between


when measured in the room without air condition

51

The machine compensation has little effect on roundness when measured in the

room without air conditioning. As shown in figure 4-9, roundness deviations when the

machine’s compensation is activated on are similar to the measurement results when

the machine’s compensation is activated off.

In the room without air conditioning, cylindricity and radial runout deviations

are different when the machine’s compensation is activated between on and off. The

measurement temperature depends on date of measurement. Room’s temperature

when the machine is activated off is 26±2°C while room’s temperature when the

machine is activated on is 30±2°C. The difference of temperature affects to arithmetic

mean value of measurement results. Cylindricity and radial runout with z axis of the

machine as datum are not only affected by compensation but also temperature.



when measured in the room without air condition

52

The compensation has effect on features determined from linear profiles

especially parallelism and conicity deviations. In figure 4-10, straightness deviations

are quite similar when the compensation is activated between on and off. However,

straightness deviations when the machine’s compensation is off are more accurate

than the results when the machine’s compensation is on. The difference of arithmetic

mean value of these results depends on temperature and its changing. This graph

represent to the effect of temperature and compensation.

By conclusion of the measurement in the room without air conditioning unit,

features evaluated from linear profile such as straightness, parallelism and conicity

have compensation effect due to the relation of parallelism between the z and c axes

and represent to temperature effect also.

4.4 The effect of machine handling (center re-positioning) in temperature-

controlled room

In accordance with description of type-1 study (Cg study) [13], the standard or

master must be removed and replaced for each measurement and should not be

subject to changes over time. “Handling” refers to the workpiece handle before

starting the new measurement by moving position of rotation table. This condition is

created in order to observe drifts in measuring machine’s column during the

measurement. The handling condition is in relevant to the rotational c axis table and

the centering and tilting table.

FIGURE 4-11 Alignment concept

53

Under handling condition, the step of measurement program are searching a

new workpiece coordinate and new aligning workpiece before starting a new time of

measurement. When aligning workpiece, two circles are scanned in addition in

measurement program for using in the state of aligning while the rotary table moves

to new position after each time of measurement. These is different from without

handling condition that the measurement program are repeated without aligning

workpiece if the residual eccentricity value is not exceed the permissible eccentricity

value. Figure 4-11 shows the relation of workpiece axis and machine axis after

alignment workpiece.

In this section, the machine’s compensation is only activated on when measured

in the room controlled by air conditioning. The left-hand side shows the measurement

results when the measurement program continually repeating measurement without

the workpiece handling from the first alignment positioning. On the other hand, it

shows the measurement program having the workpiece handling simulation by the

moving position of the rotation table before each number of the measurement.

As shown in figure 4-12, roundness deviations are slightly different when

measured under with and without handling. The difference of mean value when the

workpiece with and without handling is small as the handling has no larger effect to

roundness deviation of MMQ400. On the other hand, cylindricity and radial runout

deviations with z axis of the machine as datum are affected by the handling. The

graphs of radial runout deviation when measured under with handling condition are

different from another.

Under without handling condition, radial runout deviations with machine axis as

datum are increased relation to time or number of measurement. The increasing

values represent to the deformation of machine column.

On the other hand, radial run out deviations are scatter in two areas; one range is

1.0-1.5 µm another is 3.5-4.0 µm. It cause by the parallelism between the z and c

axes. The measurement starts to measure after workpiece is completely alignment.

When the permissible eccentricity value is 2 µm, the residual eccentricity value is

possible close to 0 or 2 µm. Therefore radial runout deviations are affected from the

handling as similar to the aligning workpiece.

54


with (Left) and without (Right) workpiece’s handling when

measured in the room with air condition

55

FIGURE 4-13 Radial runout deviation with z axis as datum (Left) and Permissible

eccentricity value (Right) when measured in the room with

air conditioning under condition on-compensation and with handling

Figure 4-13 shows the comparison between radial runout deviation and their

residual eccentricity value. The graph of radial runout deviation are similar to the

graph of residual eccentricity value however radial runout deviations is bigger than

residual eccentricity value in the way of offset value. Every residual eccentricity value

is less than 2.0 µm.

Additionally, the selected datum for determining radial run out depends on the

measurement objectives. The datum line can be crated by evaluating with machine

information (machine datum) or determining line from centre of each polar profiles-

substitute circle elements (workpiece datum). The c axis or z axis of the formtester

should be selected to be the reference element. Both machine axes give the same

tolerance value of radial runout. More details about radial runout deviation with

different datum axis are described in Appendix B.

Figure 4-14 shows straightness deviations at 0° and 180° when the workpiece

aligned only one time at the beginning of measurement similar to the results when the

workpiece aligned before every time of measurement. Then straightness deviation has

little effected on the handling.

In contrast with parallelism and conicity are evaluated from linear profiles and

determined in relative to the parallelism between the z and c axes. The measurement

results under conditions between with and without handling are different. These

features have effect on handling.

56

Parallelism and conicity deviations at 0° and 180° under with handling

condition are more accurate than when measured under without handling. The trend

line of parallelism deviations under without handling condition is increased due to the

deformation of machine column. On the other hand, parallelism and conicity

deviations are fluctuated in the range as straight line. The parallelism between the z

and c axes is adjusted by new workpiece’s alignment.



measured in the room with air condition

Additionally, the trend of conicity measurement is possible to increase in the

same way with parallelism deviation measurement results or decrease in the other

direction.

57

FIGURE 4-15 Measurement strategies of Straightness and Parallelism

The strategy of the evaluation of parallelism and conicity is quite different that

are shown in figure 4-15. The principle to determine parallelism is calculated the

minimum parallel distance of two lines. Both lines must be parallel with datum line

that evaluated by LSLI method (Gaussian method) and the whole linear profiles are

cover in parallelism tolerance zone. Then the profile peak is affected in parallelism

deviation. For determine conicity, the tolerance zone are the minimum parallel

distance of two lines. Both lines must be parallel with datum line that evaluated by

LSLI method (Gaussian method) and substitute line element that crated from the

beginning to the end of profile. Then it is possible that the whole linear profiles are

not covered in conicity tolerance zone and conicity tolerance should be equal or less

than parallelism tolerance. Beside that conicity shows the direction of the workpiece

tapering by the sign of deviation value. The results of conicity deviation express form

and direction of measured profile as same as parallelism deviation. But conicity

present the sign plus (+) or minus (-) in deviation results to express more detail of

direction between workpiece axis and machine axis.

4.5 The effect of machine handling (center re-positioning) in normal room

temperature

The measurement temperature depends on date of measurement. Room’s

temperature under without handling condition is 30±2°C while room’s temperature

under with handling is 31±3°C.

As similar to the results in controlled room by air conditioning, roundness

deviations are little affected from the handling. Figure 4-16 shows roundness

deviations under without handling is slightly different from the measurement results

under with handling. The difference of mean value when the workpiece with and

58

without handling is small as workpiece handling has no effect to roundness deviation

of MMQ400. Roundness deviation is only determined from its polar profile.



measured in the room without air condition

59

Cylindricity and radial runout deviations are determined not only its profile but

also the relation to the parallelism between c and z axis. However, it can be noticed

that cylindricity values are high value. As previous section, the fluctuation of

cylindricity is in the big range when compare with the dispersion of roundness. The

details about how to get the precise cylindricity deviation value are explained in

section 4.6.

Under without handling condition, radial runout deviations are increased due to

time. These results are continually values and represent to the deformation of machine

axes. The first value of radial runout deviation is high value at the beginning. The

increasing of radial runout depends on temperature and its changing. The fluctuation

of radial runout deviations under with handling is different from under without

handling condition.



measured in the room without air condition

60

On the hand, the step of measurement program are searching a new workpiece

coordinate and new aligning workpiece before starting a new time of measurement.

Then the parallelism between the z and c axes is new set after each time of alignment.

Radial runout deviations fluctuate as straightness line under with handling condition.

Therefore, cylindricity and radial runout with z axis of the machine as datum are not

only affected by compensation but also temperature.

Figure 4-17 shows form deviations evaluated from linear profiles when

measured in the room without air conditioning under conditions between without and

with handling. Straightness, parallelism and conicity when measured under with and

without handling condition are different.

Under with handling condition, straightness deviations are high values at the

beginning and have peak values during the measurement. These peak points cause by

the surrounding disturbances due to the protocol observation. The peak values of

straightness deviation have effect on parallelism and conicity deviations. Then it can

make conclusion that these features determined from linear profiles have effect of not

only handling but also temperature and environmental disturbance.

4.6 The effect of probe zeroize strategies

From the previous results, cylindricity values are high value. In the reason of

getting precise measurement results by reduction movement of machine axis, the

probe is set to zero before the starting position a bit and did not take off from the

workpiece during make three circles for evaluation cylindricity. The probe force error

and machine position error are neglected of the measurement result. In screening

experimental, the probe zeroize only one time is the probe is not take off from the

workpiece during the measurement. Probe force is adequate to keep the probe in

contact with the workpiece throughout the measurement. So that the expected results

of measurement after changing the method of measurement from zeroize the probe in

every profile to zeroize the probe only one time is improvement by reducing the

source of errors.

61



zeroize only one time at pre-position height (Right)

62

In figured 4-18, cylindricity deviation when evaluated from polar profiles

getting from one time zeroize the probe is stable than results from zeroize the probe

every circles. The fluctuation of cylindricity deviations when evaluated from polar

profiles getting from one time zeroize the probe is in the narrow range than results

from zeroize the probe every circles. The range of cylindricity is better by the

reduction movement of machine as similar as reducing the probe force error and

machine position error.

When look at other features that evaluated from the same polar profile such as

roundness and radial run out, the first results are high value seemed that the

measurement is added off-set value at the beginning. That means, these measurement

present not only the effect probe zeroize strategies but also the error between the z

and c axes.



zeroize only one time at pre-position height (Right)

63

As see also in figure 4-19, the range of straightness parallelism and conicity

deviations when zeroize the probe only one time are smaller than the results when

zeroize the probe every circles. Thereby, straightness parallelism and conicity

deviations are improved by changing the probe zeroize strategies.

Consequently, the zeroize probe is one significant factor to get the precise

measurement result. In comparison the zeroize method between zeroize the probe

only one time and zeroize the probe every circle, the spread of each feature is better

by changing the probe zeroize strategies. All feature are improved from changing the

probe zeroize method. The standard deviation of each feature when zeroize the probe

only one time is smaller than when zeroize the probe every circles. However, the

probe zeroize strategies have larger effect on the features related to the parallelism

between the z and c axes.

4.7 Summary

Conclusions drawn from measurement result analysis can be summarized as

follows:

4.7.1 Temperature has effect on the measurement results due to material

expansion property especially features evaluated from linear profiles such as

straightness, parallelism and conicity or features measured relative to the machine

column such as radial runout with z axis as datum.

4.7.2 The temperature affect can be reduced by measuring in the air-

conditioning controlled room. The formtester can be used in shop floor when

measuring features are determined form polar profile itself and not related to the

parallelism between the z and c axes such as roundness.

4.7.3 Features determined relative to the machine column is affected by

compensation and handling. They are determined not only from linear profile such as

parallelism and conicity but also from polar profile such as radial runout with z axis

as datum and cylindricity. Then compensation and handling has little effect on

roundness because it is only determined from polar profile.

4.7.4 As a result of this study, the measuring machine must be adjusted so that

the z axis is parallel to the c axis as the parallelism between the measured line and the

scale machine line. Even the small tilt between the two axes will cause measurement

errors.

64

4.7.5 The probe zeroize measurement method has influence on all measurement

features. Every time the probe touches the workpiece in order to make measurement,

errors take place. Therefore, errors can be reduced by minimizing the number of

movement points.

CHAPTER 5

MEASUREMENT SYSTEM ANALYSIS

The measurement results explained in chapter 4 are informed to calculate of a

capability index and its uncertainty. Mean value of each condition are compared

together to calculate a percentage of average increment in section 5.1. Section 5.2

describes about the uncertainty calculation. When calibrating and monitoring

measuring equipment, the measurement uncertainty must be specified in order to

characterize a range of measurement result relation to an estimated true value. Each

influence factors are determined to be individual uncertainty components. The

capability testing of the cylindrical standard workpiece has five individual uncertainty

components: repeated measurement, machine, measurement method, temperature and

workpiece.

In section 5.3, the capability indexes are explained relation to their measurement

results. The capability indexes of a reference condition are described to perform the

measuring machine’s characteristic. The difference in capability indexes results for

different conditions are described in order to perform the agreement of the capability

index result and their measurement result.

5.1 The percentage of the average increment

Each feature are calculated the average of mean value as shown in table 5-1.

The percentage of the average increment shown in table 5-2 can be calculated as follow.

| meani - meanref | x 100 Eq. 5-1

| meanref |

when

meani = mean value on the reference condition

meanref = mean value on the comparative condition

66

TABLE 5-1 The average of mean value

unit : micrometer

TABLE 5-2 The percentage of the average increment

Conclusions drawn from table 5-1 and table 5-2 can be summarized as follows.

5.1.1 Each feature is different affected from each setting influencing factors

depending on the relation of the parallelism between the z and c axes.

5.1.2 The compensation of the errors involving the z and c axes of the machine

is important to obtain the accurate measurement results. The measured features

affected from the compensation are parallelism, conicity, radial run out deviation with

the z axis as the reference datum and cylindricity deviations. These features are

related to the parallelism between the z and c axes of the machine. When the machine

is activated off compensation, the mean values of these feature is increased from the

67

reference mean value of the activated on compensation. The percentages of the

average increment are in between 12% to 70% depending on the relation of

measurement feature to the machine’s errors involving the z and c axes of the.

However, the compensation has little effect on roundness, roundness including

flick and straightness deviations. These features are only determined from its

measured profile.

5.1.3 The handling is more significant effect on three measurement results:

parallelism, conicity and radial run out with the z axis of the machine as datum. These

features are measured and calculated relation to the parallelism between the z and c

axes. The absolute percentages of the average increment are 34%, 64% and 272%

5.1.4 Temperature is primary effect on the four features: straightness,

parallelism, conicity and radial run out with the z axis of machine as datum.

Straightness, parallelism and conicity are sensitive to temperature due to their type of

measured profiles. The formtester scans linear profiles along the workpiece’s height

relation to the machine axis column. Due to the expansion property, the materials are

deformed as shown in these measurement results. On the other hand, run out deviation

with the z axis of machine as datum is determined from polar profile but related to the

the parallelism between the z and c axes.

When the temperature changes from 20±1°C to 28±2°C, the percentages of the

average increment are between 53% to 510% depend on the relation of the measured

feature to the errors involving the z and c axes of the machine.

5.1.5 In order to obtain the precision measurement result, the reduction errors by

reducing the movement of the machine is introduced. The probe contacting strategy is

changed from the probe set zero at every circle (PZE) to the probe set zero only one

time at the pre-position height (PZO).

When the measurement program changes the contacting method of probe from

PZE to PZO, every feature affect from the probe contacting strategy. The contacting

strategy of the probe combined to the other influencing factor make the percentage of

the average increment up to 1,000%.

5.1.6 Features determined from only one polar measured profile are smaller

sensitive to three setting conditions; the compensation, the handling and the

temperature. The percentages of the average increment are in between 0% to 5%.

These features are roundness and roundness including flick. The percentages of the

68

average increment of these features are less than 10% which is the repeatability of this

machine. Therefore, the compensation, the handling and the temperature has little

effect on roundness and roundness including flick.

5.1.7 Cylindricity and radial run out deviation with the z axis as datum are not

only determined from polar profiles but also evaluated relative to the parallelism

between the z and c axes. Therefore, radial run out deviation with the z axis of

machine as datum is more sensitive to the temperature than other setting conditions.

The second effect is the handling.

5.1.8 Features determined from linear profiles are more sensitive to the

temperature more than the compensation and the handling. As a result of this study,

straightness, parallelism and conicity deviations have higher effect on the temperature

condition than the compensation and the handling.

5.2 The uncertainty of measurement

According to the VIM 3.9 [3], uncertainty of measurement is “a parameter,

associated with the result of a measurement that characterizes the dispersion of the

values that could reasonably be attributed to the measurand”. Therefore, the

measurement results are used to analyze and evaluate the measurement uncertainty.

The range of a measurement result can be expressed in term of the measurement result

of a measurand with its uncertainty by a mathematical equation:

y - U ≤ Y ≤ y + U Eq. 5-2

when Y = the result of the measurement

y = the estimated measurement value

U = an expanded uncertainty

(the measurement uncertainty for a particular level of confidence)

The measurand is determined by the set of input qualities. The function relative

of the measurand with the input quantities is:

Y = f(X1, X2, X3, X4,..Xn) Eq. 5-3

when Y = the measurand (the quantity of interest)

X = the input quality

69

The measurement result dependence on the influence factors of measuring

uncertainty is described by the mathematic function model:

y = f(x1, x2, x3, x4,... xn ) Eq. 5-4

when y = the measurement result (the estimated value)

x = the influence factor in the measurement uncertainty evaluation

The measurement results has five main influencing factors; Man, Machine,

Method, Material and environment. The uncertainty of measurement result has effect

to these factors also. Corresponding to these reasons, the uncertainty components are

classified following these factors dependence on measurement conditions. In this

study, the relative between measurement results to influence factors is described by

the mathematic function:

y = f(x1, x2, x3, x4, x5) Eq. 5-5

when x1 is random (the effect from the repeated measurement)

x2 is machine (the effect from the machine)

x3 is method (the effect from the handling and the zeroing)

x4 is environment (the effect from the temperature)

x5 is material (the effect from the workpiece)

The effect from human is neglected for the reason that the measurements are

operated by only one person. The measurement is automatically repeated by setting

command in measurement program. The influence of operator is tested following the

capability testing procedure 2 and 3 of Bosch book 10 standards. This capability

testing is the procedure 1-the bias and repeatability.

Additionally, the uncertainties are divided into two types; type A and type B

standard uncertainties according to the GUM. The type-A standard uncertainty

evaluates the input quantities from repeated observations by calculating standard

uncertainty of the mean value. Whiles the type-B standard uncertainty evaluates input

quantities from a single observation or personal judgement based on experience. The

type-B standard uncertainty is calculated by calculating the estimated value that lies

within the boundaries with percentage of a confidence level. According to their

definition, the determining the uncertainty through repeated measurement is defined

70

as the type-A standard uncertainty. The effect of the repeated measurement, the

calibration, the temperature and the workpiece are classified into the type-A standard

uncertainty. The type-B standard uncertainty consists of the effect of the measurement

method that is combined from the effect of the handling and the zeroing.

5.2.1 The effect of the repeated measurement

The deformation of overall measuring machine is presented by their variation of

measurement result. To present the repeatability, the measurement result is calculated

in the assumption that the measurement result is a random variable for the same

conditions of the measurement. The standard deviation of repeated measurement is

calculated following the equation 5-6.

u1 = Sg Eq. 5-6

√n

when sg = the standard deviation of the observed values

n = the number of the observed values.

5.2.2 The effect of the machine

Every measuring machine has individual property and has many errors inside.

This measuring machine has three main parts; the machine structure, the probe system

and the software. The sources of error that relate to the mechanical structure are

identified and corrected since the machine design stage. For example, some of the

measuring machine elements, the base unit and the column, made from a highly stable

steel body in order to avoid the effect of the temperature with the structural. Even

though some errors can be identified and corrected, some can not and is calculated to be

the uncertainty of measurement. For example, the line of measurement (the workpiece)

must be in the same line of the scale (the machine) following the abbe’s rule. However

the guide and the measurement system can not align in the same line because of the

machine structure. Therefore, the calibration is performed in order to ensure the

straightness of the guide rails and the perpendicularity of the guides to one another.

The probe system is calibrated their sensitivity in order to inform their diameter,

length and direction of the probe arm. The probe signal and the probe force are also in

relative to the correction of the measurement result. However, the measurement result

is not affected with only the influence of the probe system. Therefore, the probe

71

system is not separated to be one factor in uncertainty calculation of this study. In

order to operate the measuring machine by the software, it is one main important part

of the machine. The software is tested their correction as the machine structure.

Corresponding to the combination of these three main parts, the variation of the

repeated measurement results are represented to the characteristic of the machine. The

standard uncertainty affected from the measuring machine is calculated by the

equation 5-7. This uncertainty component is calculated under the assumption that the

distribution of measurement result is normal distribution.

u2 = Sg Eq. 5-7

when sg = the standard deviation of the observed values

5.2.3 The effect of the handling and the zeroing

The measurement method is one influencing factor of the complete

measurement result following the cause and effect diagram of the production

metrology [4]. The repeatability of the measurement process is calculated the repeated

measurement result for the same conditions of the measurement. Therefore, the

differences of the measurement method represent to the effect of them to the

measurement result.

In accordance with the measurement conditions, the handling condition is set in

order to prove the centering and tilting table properties and the machine column

changing. The radial run out deviation with the z axis of the machine as datum is

added in the measurement program in order to observe the drift of the machine

column during the repeated measurement. As can be seen from the radial run out

deviation with the z axis of the machine as datum for the reference condition, the

machine column deforms in relative to the time. Additionally, the straightness, the

parallelism and the conicity deviations also show the effect of the handling.

On the other hand, the differences of the measurement method between zeroing

probes every profiles and the zeroing probe only one time at pre-position represent to

the zeroing effect to the measurement result. At the beginning, the different of the

probe zeroize method is the solution of the improvement the precise cylindricity

measurement result value. As can be seen from the measurement a result, every

72

measurement feature is affected by the probe zeroize method changing. The zeroing

effect to the form measurement result is described in section 4.6.

Due to their effect to the measurement result, the handling and the zeroing are

combined to be the one influence factor of the uncertainty calculation. The

measurement result values are assumed that the distribution of measurement result is

rectangular with 100% confidence level of the value when the uncertainty from the

method influencing factor is estimated.

With the uncertainty calculation from the handling effect, the boundary area of

the handling effect is 1.0 µm following the centering and tilting table machine

technical data. The measurement result effect from the parallel between the c and z

axes as a result of the handling effect. The parallel of the c and z axes depends on the

property of the centering and tilting table and the complete workpiece alignment.

According to the above reasons, the dispersion of the repeated measurement result

that effects from the handling effect is on the range of the centering and tilting table.

The tilting quality of the centering and tilting table is 10.0 µm per 1.0 m that equal to

1.0 µm per 100 mm.

With the uncertainty calculation from the zeroing effect, the boundary of

zeroing probe is set following the quality of the probe zeroize. The range of the probe

zeroize method is ±0.1 µm as a result of the positioning errors in the direction of x

and y axis when the machine searches the same position. Therefore, the boundary of

the zeroing effect is 0.2 µm. The more detail about the quality of the probe zeroize is

described in Appendix B. Equation 5-8 is used to calculate the standard uncertainty

affected from the handling and the zeroing according to these assumptions.

u3 = √ u231 + u2

32 Eq. 5-8

when u31 = the uncertainty component of the handling effect = 0.2 µm

√ 6

u32 = the uncertainty component of the zeroing effect = 1.0 µm

√ 6

73

TABLE 5-3 The relative between the machine component errors and the measured

features

Additionally, the relative between the machine component errors and the

easu

ir axes movements and

and the axis movement of machine of each feature.

The measured feature

roun

dnes

s

roun

dnes

s with

flic

k

radi

al ru

nout

with

m

achi

ne d

atum

radi

al ru

nout

with

w

orkp

iece

dat

um

cylin

dric

ity

stra

ight

ness

0°

stra

ight

ness

180

°

para

llelis

m

coni

city

measurement directionmeasurement in x-axis of machine x x x x x x x x xmeasurement in y-axis of machine measurement in z-axis of machine x x x x xmeasurement in c-axis of machine x x x x x x x xcalculation in relate with the reference x x x x

Source of errorsposition error in x-axis of x-axis x x x x x x x x xposition error in y-axis of x-axis x x x x x x x x xposition error in z-axis of x-axis x x x x x x x x xposition error in x-axis of y-axisposition error in y-axis of y-axisposition error in z-axis of y-axisposition error in x-axis of z-axis x x x x xposition error in y-axis of z-axis x x x x xposition error in z-axis of z-axis x x x x xangularity error in x-axis of x-axis x x x x xangularity error in y-axis of x-axis x x x x xangularity error in z-axis of x-axis x x x x xangularity error in x-axis of y-axisangularity error in y-axis of y-axisangularity error in z-axis of y-axisangularity error in x-axis of z-axis x x x x xangularity error in y-axis of z-axis x x x x xangularity error in z-axis of z-axis x x x x xperpendicularity between x-axis and y-axis x x x x xperpendicularity between y-axis and z-axis x x x x xperpendicularity between x-axis and z-axis x x x x x x x x x

m red features is shown in table 5-3. This table is used to analyze the dependence

of the related features and the handling and the zeroing effect.

The measured features are plotted in the relation with the

their evaluation method which is calculated with the reference datum. On the other

hand, the measuring machine has errors occurring at least 21 components of errors

when the machine is assumed to be a rigid body. These errors are the three positioning

errors and the three rotating errors for each axis adding with three squareness errors

between axes. These errors are plotted in relation of the form and tolerance principle

74

According to this table, the measured features, which are related to the

measurement in the c axis of the machine and are calculated with respect to the

perpendicular of the x and z axes. The probe zeroize expresses the

omb

ditioning is set to be the

ea he temperature effect. As can be expected, the

ation expresses the

5-9

w w M·ΔtM) Eq. 5-10

when L = the leng

α = Linear extension coefficient

reference datum, are calculated the uncertainty component of the handling effect.

Therefore, the four features are calculated with respect to the handling effect. These

four features are the radial run out deviation with the workpiece related datum, the

radial run out deviation with the z axis of the machine as datum, the parallelism and

the conicity.

On the other hand, the uncertainty component of the zeroing effect is calculated

following the

c ined errors of the x and z axes. These errors represent to the positioning, the

angularity and the perpendicular errors of the x and z axes.

5.2.4 The effect of the temperature

The measurement in the different rooms of air con

m surement conditions in order to study t

temperature effects to the measurement result due to the material expansion property.

The range of all repeated measurement results in the room with air conditioning is bigger

than the measurement results in the room without air conditioning.

The temperature standard uncertainty is calculated by the workpiece

deformation due to the temperature. The basic expansion equ

differential length caused by the temperature in term of the relation between the

length of measurement, the material linear extension coefficient and the differential

temperature. The variations of the measurement result are divided into the variation of

the workpiece and the variation of the measuring machine as the result of the different

material expansion property. The length variation of the workpiece and the length

variation of the measuring machine component are considered in a measurement

system due to the different material of them.

ΔL = L·α·Δt Eq.

ΔL = L·(α ·Δt - α

th of measurement

t = temperature

75

A er artial differentiatft p ion, the equation consists of four terms. Each term is

ece and the measuring machine have the same

mpe

sumption uΔtM = 0

effect of the temperature according to the

rgin of the temperature

thermal expansion of the cylindrical standard steel

u4 = L·√(uαw·Δtw)² + (uΔtw·αw)² + (uαM·ΔtM)² + (uΔtM·αM)² Eq. 5-11

when uα = Uncertainty of the linear extension coefficient

5.2.5 The effect of the workpiece

c of the workpiece direct effect to the

asu

owever, the quality of workpiece characteristic by itself depends on the

equally meaning as each sources of error. The standard uncertainty from temperature

effect is calculated by the equation 5-11 under the two assumptions.

The first assumption Δtw = ΔtM

The cylindrical standard workpi

te rature because the workpiece and the measuring machine put in the same air

conditioning room.

The second as

The measuring machine has no

technical data of this machine.

when uΔtw = ΔK / sqr(3)

ΔK = The error ma

αw = 12x10-6/K.

(the coefficient of

workpiece).

uΔt = Uncertainty of the temperature measurement

The property and characteristi

me rement result. According to the expansion material property, the workpiece

characteristic is changed in relative to the temperature. The variation of the workpiece

characteristic from the effect of the temperature is classified and calculated in section

5.2.4.

H

production and the controlling process. The reference value as the result of the

estimated true value of the workpiece characteristic is one parameter in the capability

study. The estimated true values of the workpiece characteristic obtain from the mean

repeated measurement value of the reference measuring machine (MFU100). As the

variation of the measurement result from the mean value is the measurement

76

accuracy, the variation of the repeated measurement of MFU100 from the mean is the

accuracy of the measurement result.

Therefore, the quality of the workpiece characteristic is represented by the

variation of the repeated measurement that is use to calculate the reference value of

the workpiece. As similar to the variation of the measurement result is represented to

the quality of the measurement process or the measurement machine.

The affected from the fixture and the fixing workpiece are neglected in this

study because the measurement results are not affected with only the fixture

influence. The effect of the workpiece and the clampling device are combined

together and are presented by the workpiece uncertainty component.

This uncertainty component is calculated under the assumption that the standard

deviation of the measurement result by the reference measuring machine is the

dispersion area of the workpiece characteristic. In addition, the measurement result

values of MFU100 are assumed that the measurement result distribution is uniform

with 100% confidence level of the value. Equation 5-12 is used to calculate the

workpiece uncertainty according to these assumptions.

U5 = Sg(reference value) Eq. 5-12

√3

when sg = the standard deviation of the repeated measurement by the

reference measuring machine.

5.2.6 The combined standard uncertainty

An estimated combined standard uncertainty is calculated by combining the

individual standard uncertainties together.

uc = √ u12 + u2

2 + u32 + u4

2 + u52 Eq. 5-13

5.2.7 The measurement result relative to the measurement uncertainty.

5.2.7.1 The method uncertainty is highest significant effect to the

combined uncertainty. The method uncertainty values are bigger than the other

individual uncertainty components. The method uncertainty is calculated by the

combined the effect of the workpiece handling with the probe zeroing method. These

effects are related to the parallelism between the z and c axes.

77

5.2.7.2 The variation of the workpiece causes by their property and their

characteristic. The variation due to their characteristic quality is identify and

calculated in the workpiece uncertainty component. Whiles the deformation of the

workpiece due to the temperature is identified and calculated to be the temperature

uncertainty components.

5.2.7.3 The machine uncertainty is expressed by the standard deviation

of the measuring machine. The workpiece uncertainty is expressed by the standard

deviation of the reference measuring machine. The workpiece uncertainty values are

smaller than the machine uncertainty values for all features when the measuring

machine is on activated compensation. These results prove the correction of the

calculation of the machine uncertainty and the workpiece uncertainty due to the

measurement principle and the objective of the workpiece calibration.

5.2.7.4 The workpiece uncertainty is least significant effect to the

combined uncertainty. The workpiece uncertainty values are smaller than the other

individual uncertainty components. As a result of using the standard workpiece to

perform the capability index, the variation of the standard workpiece is small.

5.2.7.5 When the measuring machine is activated on compensation, the

temperature uncertainty values are smaller than the repeated uncertainty values and

the machine uncertainty value for all features. These agree with the measurement

result in the room with air conditioning conclusion that the temperature is less

significant effect to the measurement result than other factors. The other factors are

the handling, the compensation and the parallelism between the z and c axes.

5.2.7.6 The correct and complete identification of the component of

uncertainty is more important than the classification of the type of uncertainty (type A

or B). Every individual uncertainty components are combined together as a result of

the combined standard uncertainty.

5.3 Capability index

The testing of the capability and the monitoring of the stability of measurement

processes are important in order to estimate the quality of the measurement process

and to modify the measurement results or the courses of error. According to the Bosch

book10 Capability of Measurement and Test Processes, the five procedures are

specified for investigating testing equipment. The purpose of these procedures is to

78

ensure that a measuring device is capable of measuring a quality characteristic at the

place of use with a sufficiently small variation of measured value.

In this study, the capability testing of a cylindrical standard workpiece is

performed on a formtester in order to test a machine axes property and to calculate the

sensitivity of the signal transmission chain. The results of this testing are used to

estimate the quality of the measuring machine and to modify the measurement

process. The changing characteristics of the measuring machine are evaluated and

guaranteed by the capability testing as a result of the calibration and the monitoring

process. Corresponding to the capability testing procedure 1, the capability of the

measurement process expresses the variation and the position of the measured value

in the tolerance zone of a characteristic. This measurement procedure, Bias and

Repeatability, is the precondition for implement of procedure 2 to 5.

The formtester is activated only on compensation status in the general case. The

measurement which the measuring machine is activated off compensation is set in

order to observe the different measurement results between the on and off

compensation. Therefore, the calculation of handling conditions are discussed and

analyzed in this section.

The variation of the measured values is small when using the standard

workpiece. However, the variation of the measured values is significant when using

the calibrated production workpiece. In this study, the workpiece is the cylindrical

standard workpiece. Even though the variation of the measured value of the standard

workpiece is small, the systematic deviation (bias) is proved in order to inform about

the measurement system.

The systematic deviation or bias of the measurement result is the difference

value between the mean of the repeated measurement result and the estimated true

value. The systematic deviation (bias) is proved by the relation to the standard

deviation of the measured value.

For n = 25 bias is significant if │ x – xm│ > 0.413·s

For n = 50 bias is significant if │ x – xm│ > 0.284·s

when x = the mean of the repeated measurement result.

xm = the estimated true value (the reference value)

s = the standard deviation of the repeated measurement result.

79

Due to its definition, the systematic deviation represents to the closeness

between the mean of the repeated measurement result ( x ) and the reference value

(xm) as the accuracy of the measurement. The bias is significant when the difference

between the mean of the repeated measurement result ( x ) and the reference value

(xm) is greater than the acceptance criteria. In other words, the repeated measurement

results are not more accurate due to the high value of the bias.

By the capability criteria approval, both conditions show that almost the

systematic deviations of the measured features have significant. Only R15_50 for the

ON compensation WITH handling condition is not significant bias. As a result of the

bias, the roundness at the lowest height is more accurate than other features. The

roundness deviation has effect of the measurement height due to the centering and

tilting property and the deformation of machine column.

For the reference condition, the bias is not significant at R15_50, R50_15,

R50_50, R50_150 and R85_500. Similar with the measurement result for Condition 3,

only the roundness deviations have no significant bias. The bias of the other measured

features is significant.

The numbers of insignificant bias for the both conditions are different due to the

different measurement steps. The results of Condition 3 are represented to the result

related to the deformation of the machine axes. On the other hand, the workpiece is a

new alignment before starting each time of measurement according to the handling

condition. By the alignment, the workpiece is moved to the new position. As a result

of the workpiece alignment, the numbers of insignificant measured feature for the

Condition 3 is more than for Condition 2 as the reference condition. As a result of the

influencing factor, the workpiece alignment effects to the accuracy of the

measurement result.

However, it can be noticed that the systematic deviation expresses only the

different value between the mean of the repeated measurement result ( x ) and the

reference value (xm) with respect to its standard deviation. When the workpiece

characteristic is small value as the roundness deviation of the cylinder standard

workpiece, the other influencing effect can not be identified by the acceptance of the

systematic deviation value. For example, the systematic deviation of R15_15 is not

80

significant whiles their measured profiles are affected by the environmental

disturbances from the first to the seventeenth of the number of measurement.

Next, the data of the repeated measurement is use to calculate the capability

index. The capability Indexes Cg and Cgk calculated from the equation 5-14 and 5-15.

The capability index calculations are summarized in table 5-4 together with the

significant approval of systematic deviation and the permissible range of the

measured value.

g

g s6T2.0C = Eq. 5-14

( )

∑

∑

=

=

=

−−

=

=

n

1ii

2n

1igig

Xn1X

XX1n

1s

Tolerance T Where

g

mg

gk s3

XXT1.0C

−−= Eq. 5-15

(master) workpiecestandard of valueTrueX

value)(absolute X and Xbetween differenceXX Where

m

mgmg

=

=−

TABLE 5-4 The summary table of the significant approval of bias, the capability

index calculations and the permissible range of the measured value

Measurement condition

Acceptance criteria

Condition 2

on activated compensation

without the handling

Condition 3


with the handling

The approval of the

significant of the systematic

deviation following the

capability criteria.

(│ x – xm│ > 0.284·s )

The systematic deviation is

not significant in only 5

measured features;

R15_15, R50_15, R50_50,

R50_150 and R85_500.

The systematic deviation is

not significant in R15_50

only.

81



Acceptance criteria

Condition 2



Condition 3


with the handling

The comparison the

calculated capability index

with the minimum

requirement of the

capability ( Cg ≥ 1.33 )

The 12 acceptance features

are;

- 2 roundness deviations;

R50_15 and R85_15.

- 8 roundness with flick

deviations (all)

- 2 straightness deviations;

G0_080 and G180_080.


are;


R15_15, R15_50,

R50_15, R50_50, R85_15

and R85_50.


deviations (all)

- 2 straightness deviations;

G90_080 and G180_080.

The comparison the

calculated capability index

with respect to the

systematic deviation

with the minimum

requirement of the

capability ( Cgk ≥ 1.33 )


are;


deviations at 10 mm of the

workpiece coordinate (all)


deviations at 20 mm of the

workpiece coordinate;

R20_15 and R20_500.


are;


R15_15 and R15_50


deviations at 10 mm of

the workpiece coordinate

(all)


deviations at 20 mm of

the workpiece coordinate;

R20_15 and R20_500.

82



Acceptance criteria

Condition 2



Condition 3


with the handling

The comparison between

their mean with their

combined uncertainty

(L_tol < mean±U < U_tol )

when

L_tol = Lower tolerance

U_tol = Upper tolerance

U = the combined uncertainty

The 33 measured features

are accepted according to

this criteria excluding

R10_15,

R20_15, and

P0_180_080.

The 34 measured features

are accepted according to

this criteria excluding

R10_15 and R20_15.

Remarkable from the

measurement result

- The polar measured

profile at 15 mm of the

workpiece coordinate

(R15) has environmental

disturbances at the

beginning of the repeated

measurement.

- The linear measured

profiles at C=90° and

C=180° have a

environmental disturbance.

Conclusions drawn from the analysis of the measurement result and capability

index can be summarized as follows:

5.3.1 The measuring machine must be adjusted the properties of the z and c axes

as the parallel offset of the measured line and the scale machine line in order to obtain

the accurate measurement result.. With the parallel offset of the measuring distance

and the reference distance, the small tilt already causes the measurement errors. The

acceptance measured results by the criteria of the capability testing and the

measurement uncertainty calculation show the problem of the measurement machine

in relative with the parallel of the z and the c axes.

83

5.3.2 The systematic deviation (bias) can be proved by the relation with the

standard deviation of the measurement value following the Bosch Book 10 standard.

The significant of the systematic deviation (bias) represent to the dispersion of the

measurement result with respect to the reference value as the accuracy of the

measurement. However it can not used to verify the source of errors. For example, the

measurement result R15_15 for the reference condition is not significant following

the systematic deviation criteria. However, the repeated measurement result of this

feature has the peaks at the beginning.

5.3.3 The tolerance factor and the sigma factor are significant factors in the

capability calculation as the correlative between the process and the measuring

machine. These factors effect to the tolerance zone. The suitable of these factors is

more important due to analyze the cause and effect of the measurement result by the

capability index results. The capability index can present the major unacceptable

results when using the suitable the correlative factors.

5.3.4 The problem of the measuring machine can be represented by the

comparison of the permissible range for the measured result with its tolerance. The

permissible range for the measured values is expressed by its estimated measurement

value (mean) and its combined uncertainty. The acceptance measured feature

following these criteria agrees with the measurement results.

The correction of the permissible range for the measured values depends on the

correction of the calculated measurement uncertainty. The measurement uncertainty is

importance influencing effect to the measurement result. Every measurement result

respects to the measurement uncertainty as same as the errors.

5.3.5 The number of the acceptance measured features due to Cg calculation is

more than due to Cgk calculation. The capability index (Cg) is calculated by the

relative of the process and the measuring machine. The capability index (Cgk) is

calculated by the relative of the process and the measuring machine and it systematic

deviation. The different of the acceptance measured feature between Cg and Cgk can

be used to observe the effect of the reference value as a result of the significant of the

systematic deviation.

5.3.6 The most of the acceptance measured feature is determined from the polar

measurement. A few of the straightness deviation is acceptable by Cg according to the

effect on linear measurement. These measurement results represent to the major

84

problem of the measuring machine in the stage of the study relating to it z axis. The

out off tolerance of the measured features can be represented to the cause and effect

of the measurement result. The parallelism deviation (P0_180) is out off its tolerance

as a result of the incomplete parallel between the z and c axes.

5.3.7 The unacceptance measured feature by the capability testing is not

presented only the problem of the machine characteristic but also the unsuitable of the

calculation factors and the effect of the other influencing. The influencing factors that

relates to the capability calculation are the setting tolerance of each measured feature

and the capability index factors. The other influencing factors to the measurement

system are the environmental disturbances, the measurement method, the workpiece,

etc.

Corresponding to these results, the major problems can be represented by

unacceptance features of the capability testing as the measurement result discussion

and the result of measurement uncertainty.

CHAPTER 6

CONCLUSIONS

The purpose of this thesis is to study the effects of compensation on a form

measuring machine. The mechanical accuracy of the measuring machine relates with

the straightness of the guide rails and the perpendicularity of the guides to one

another. The errors involving the z and c axes of the machine are compensated in

order to accomplish the accuracy of the measurement.

Capability testing of the cylindrical standard workpiece is used for ensuring the

performance of the formtester in a normal case and testing the functionality of the

machine compensation in this study. The capability testing is compiled with the

Bosch book 10 standard about Capability of Measurement and Test processes [2].

Three parameters are investigated: the error compensation, the workpiece handling

and the temperature. Measurements are made in two rooms differentiated by the

presence of air conditioning.

In the general state, the measuring machine is necessary to activate on

compensation. By compensation, the errors in the z and c axes are corrected into

every measurement results. When the machine is activated off compensation, the

mean values are increased from their reference mean value between 0% and 70%

depending on the relation of the measured features to the deformation of the machine

column. Therefore, the complete and sufficient of the machine’s compensation has a

direct effect on accurate measurement. However, the compensation is not the highest

effect for the accuracy of measurement results in this study.

Temperature is the primary effect to features determined from both the linear

profile such as straightness, parallelism and conicity and the polar profile such as

radial runout with the machine axis as datum. These features relate to the errors

involving the z and c axes of the machine. When the temperature changes from

20±1°C to 30±2°C, the percentages of the average increment of these four features are

in between 53% to 510%. Due to the temperature effect, the measurement in the room

with the air conditioning is recommended especially to measure features relative to

the parallelism between the z and c axes.

86

The handling condition is designed to observe the drift of the machine column

during the measurement. Increasing of radial runout deviation with the z axis of

machine as datum can represent the deformation of the machine column. On the other

hand, the handling is related to the property of centering and tilting table as an effect

of workpiece alignment. The efficiency of workpiece alignment affects the accuracy

measurement results as an effect from the parallelism between the z and c axes.

Only one feature is smaller sensitive to three setting conditions: the

compensation, the handling and the temperature. The percentages of the average

increment of roundness deviations are in between 0% to 5% and less than 10% which

is the repeatability of this machine. Roundness deviations are determined from only

the polar profile. Consequently, this formtester can be used on the shop floor when

measuring features are determined from the polar profile itself and not related to the

parallelism between the z and c axes, such as roundness.

The changing contacting strategy of the probe from the probe set zero at every

measured profile to the probe set zero only one time at pre-position height is

introduced in order to obtain a precise value of form measurement results. The probe

zeroize method is has influence on all features. Every time the probe touches the

workpiece in order to make a measurement, errors take place. Therefore, errors can be

reduced by minimizing the number of movement points. The mean values of the

measured features are decreased between 3% and 80% from the reference mean value

depending on the number of probe contacting. However, the probe zeroize strategies

have a larger effect on the features related to the parallel between the z and c axes.

As a result of this study, the accuracy of the measurement results is affected

from not only the three setting parameters, but also the contacting strategy of the

probe. The sensitivity of the measured feature with respect to each condition depends

on the relation of the measured features to the machine axis involving its

measurement.

Additionally, the setting tolerance and the capability index factors are

significant in order to analyze the capability index result and investigate the high

priority of problems related to the measurement process. With an insufficient setting

tolerance and unsuitable capability index factors, the high priority of the problem is

not executed, because the measurement process has many influence factors.

Accordingly, it is necessary to study and determined the uncertainty of the

87

measurement during the capability testing in order to not only perform and guarantee

the reliability of the measurement result, but also to inform of significant errors of the

measuring machine.

The data and the result of the capability testing can be used not only to perform

the main effects for improving the accurate measurement, but also to calculate the

measurement uncertainty for ensuring the reliability of the measurement result. The

ISO-Guide for the Expression of Uncertainty in Measurement [1] is used to be a

guideline for the estimation of the measurement uncertainty. The error sources of the

uncertainty measurement are classified into main five influence factors: random,

machine, method, environment and material. These individual uncertainty

components are combined together to be the combined uncertainty in order to identify

a permissible range of the measurement result. By the interpretation of each

calculated uncertainty component with respect to the measurement results, the

calculated uncertainties agree with the measurement results discussion. Therefore, the

measurement results, the results of the capability testing and the measurement

uncertainty are discussed together to perform the characteristics of the machine.

In conclusion, the error compensation algorithm is important and useful. The

machine compensation is a significant effect to the measurement results. However,

the compensation is not the only technique and method that is affected to the correct

and accurate measurement results. In terms of the precision measurement, the high

precision measuring machine is not only obtains precise measurement results, but also

effects the sensitivity of the parameters related in the measurement. In order to get the

complete and correct measurement results, the measurement process must be

controlled or the influencing factors must be reduced. The understanding in the

performance of the measuring machine, the machine characteristics, the measurement

uncertainty, the measurement process and their errors to control and reduce the

uncertainty and errors in the measurement is more important when using the high

precision measuring machine.

REFERENCES

1. International Organization of Standardization. Guide to the Expression of

Uncertainty in Measurement. 1st ed. Geneva : International Organization

of Standardization, 1993.

2. Robert Bosch GmbH. Quality Management in the Bosch Group. Technical

Statistics. No.10. 1st ed. [n.p.], 2003.

3. International Organization of Standardization. International Vocabulary of

Basic and General Terms in Metrology. 2nd ed. Geneva : International

Organization of Standardization, 1993.

4. Tilo Pfeifer. Production Metrology. Műnchen : Oldenbourg, 2002.

5. Department of Defense. Military Standard Gage Inspection MIL-STD-120.

Washington DC : United states government printing office, 1963.

6. Takamasu, K. Furutani, R. and Ozono, S. “Basic concept of feature-based

metrology.” Measurement. 26(3), (1999) : 151-156.

7. Liu, Q. Zhang, C. and Wang, H. P. Ben. “On the effects of CMM measurement

error on form tolerance estimation.” Measurement. 30(1), (1999) : 33-47.

8. R.G. Wilhelm, R. Hocken and H. Schwenke. “Task Specific Uncertainty in

Coordinate Measurement.” CIRP Annals - Manufacturing Technology.

50(2), (2001) : 553-563.

9. Yau, Hong-Tzong. “Uncertainty analysis in geometric best fit.” International

Journal of Machine Tools & Manufacture. 38(10), (1988) : 1323-1342.

10. Yau, Hong-Tzong. “Evaluation and uncertainty analysis of vectorial tolerances.”

Precision Engineering. 20(2), (1997) : 123-l37.

11. Trapet, E. and Waldele, F. “The Virtual CMM Concept, In Advanced

Mathematical Tools in Metrology II.” World Scientific. 40 (1996) : 238-247.

12. Salsbury, J.G. “A Simplified Methodology for the Uncertainty Analysis of CMM

Measurements.” Society of Manufacturing Engineers. (1995). cited in

R.G. Wilhelm, R. Hocken, H. Schwenke. “Task Specific Uncertainty in

Coordinate Measurement.” CIRP Annals - Manufacturing Technology.

50(2), (2001) : 553-563.

90

13. Dietrich, Schulze. Guidelines for the evaluation of Measurement Systems and

Processes, Acceptance of Production Facilities. Munich : Hanser

Publishers, 1998.

14. Paul J. Drake, Jr. Dimensioning and Tolerancing Handbook. New York :

McGraw-Hill, 1999.

15. Mahr GmbH. Mahr Information; Presentation and Catalog. GÖttingen : Mahr

GmbH, 2004.

16. Testo Inc. Temperature Measurement Engineering. [online] 2006. [cited 12

November 2006]. Available from : URL : http://www.testo.com

17. Philpott, Fred. The Pt100 Sensor. [online] 2006. [cited 12 November 2006].

Available from : URL : http://www.iqinstruments.com/temperatue/pt100

18. Thalmann, R. “Intercomparison of parallelism measurements.” Measurement.

17(1), (1996) : 17-27.

19. Mahr Academy. Level 3 Training Length metrology Part 1. GÖttingen : Mahr

GmbH, 2004.

APPENDIX A

DEFINITION OF TERMS

92

A.1 Measurement Definition and Terms

All definition and Terms refer to the International Vocabulary of Basic and

General Terms in Metrology (VIM) [3]. The Terms present following the sequent of

Alphabet letter. Each term express with a reference index. The reference index is

“VIM (x.y)” where: x is the number of chapter in VIM and y is the number of

definition and terms in each chapter.

The chapter of all definition and Terms in Metrology are classified into six

chapters;

A.1.1 QUANTITIES AND UNITS

A.1.2 MEASUREMENTS

A.1.3 MEASUREMENT RESULTS

A.1.4 MEASURING INSTRUMENTS

Many different terms are employed to describe the artefacts which are used in

measurement. This Vocabulary defines only a selection of preferred terms; the

following list is more complete and is arranged in an approximate order of increasing

complexity. These terms are not mutually exclusive.

A.1.4.1 element

A.1.4.2 component

A.1.4.3 part

A.1.4.4 measuring transducer

A.1.4.5 measuring device

A.1.4.6 reference material

A.1.4.7 material measure

A.1.4.8 measuring instrument

A.1.4.9 apparatus

A.1.4.10 equipment

A.1.4.11 measuring chain

A.1.4.12 measuring system

A.1.4.13 measuring installation

A.1.5 CHARACTERISTICS OF MEASURING INSTRUMENTS

Some of the terms used to describe the characteristics of a measuring instrument

are equally applicable to a measuring device, a measuring transducer or a measuring

93

system and by analogy may also be applied to a material measure or a reference

material.

The input signal to a measuring system may be called the stimulus; the output

signal may be called the response.

In this chapter, the term "measurand" means the quantity that is applied to a

measuring instrument.

A.1.6 MEASUREMENT STANDARDS, ETALONS

In science and technology, the English word "standard" is used with two

different meanings: as a widely adopted written technical standard, specification,

technical recommendation or similar document (in French "norme") and also as a

measurement standard (in French "étalon"). This Vocabulary is concerned solely with

the second meaning and the qualifier measurement" is generally omitted for brevity.

accuracy of a measuring instrument (VIM 5.18)

ability of a measuring instrument to give responses close to a true value

NOTE "Accuracy" is a qualitative concept.

accuracy of measurement (VIM 3.5)

closeness of the agreement between the result of a measurement and a true value

of the measurand

NOTES

1. "Accuracy" is a qualitative concept.

2. The term precision should not be used for "accuracy".

bias (of a measuring instrument) (VIM 5.25)

systematic error of the indication of a measuring instrument

NOTE The bias of a measuring instrument is normally estimated by averaging

the error of indication over an appropriate number of repeated measurements.

calibration (VIM 6.11)

set of operations that establish, under specified conditions, the relationship

between values of quantities indicated by a measuring instrument or measuring

system, or values represented by a material measure or a reference material, and the

corresponding values realized by standards

94

NOTES

1. The result of a calibration permits either the assignment of values of

measurands to the indications or the determination of corrections with respect to

indications.

2. A calibration may also determine other metrological properties such as the

effect of influence quantities.

3. The result of a calibration may be recorded in a document, sometimes called

a calibration certificate or a calibration report.

corrected result (VIM 3.4)

result of a measurement after correction for systematic error

correction (VIM 3.15)

value added algebraically to the uncorrected result of a measurement to

compensate for systematic error

NOTES

1. The correction is equal to the negative of the estimated systematic error.

2. Since the systematic error cannot be known perfectly, the compensation

cannot be complete.

correction factor (VIM 3.16)

numerical factor by which the uncorrected result of a measurement is multiplied

to compensate for systematic error

NOTE Since the systematic error cannot be known perfectly, the compensation

cannot be complete.

datum error (of a measuring instrument) (VIM 5.22)

error of a measuring instrument at a specified indication or a specified value of

the measurand, chosen for checking the instrument

deviation (VIM 3.11)

value minus its reference value

drift (VIM 5.16)

characteristic slow change of a metrological of a measuring instrument

error (of measurement) (VIM 3.10)

result of a measurement minus a true value of the measurand

95

NOTES

1. Since a true value cannot be determined, in practice a conventional true

value is used (see 1. 1 9 and 1.20).

2. When it is necessary to distinguish "error" from "relative error", the former

is sometimes called absolute error of measurement. This should not be confused with

absolute value of error, which is the modulus of the error.

experimental standard deviation (VIM 3.8)

for a series of n measurements of the same measurand, the quantity s

characterizing the dispersion of the results and given by the formula:

s = [∑ (xi-x) 2/ (n-1)] 1/2

xi being the result of the i-th measurement and x being the arithmetic mean of

the n results considered

NOTES

1. Considering the series of n values as a sample of a distribution, x is an

unbiased estimate of the mean m, and s2 is an unbiased estimate of the variance s, of

that distribution.

2. The expression s/√n is an estimate of the standard deviation of the

distribution of x and is called the experimental standard deviation of the mean.

3. Experimental standard deviation of the mean is sometimes incorrectly called

standard error of the mean.

fiducial error (of a measuring instrument) (VIM 5.28)

error of a measuring instrument divided by a value specified for the instrument

NOTE The specified value is generally called the fiducial value, and may be, for

example, the span or the upper limit of the nominal range of the measuring

instrument.

influence quantity (VIM 2.7)

quantity that is not the measurand but that affects the result of the measurement

EXAMPLES

a) temperature of a micrometer used to measure length;

b) frequency in the measurement of the amplitude of an alternating electric

potential difference;

c) bilirubin concentration in the measurement of haemoglobin concentration in

a sample of human blood plasma.

96

international (measurement) standard (VIM 6.2)

standard recognized by an international agreement to serve internationally as the

basis for assigning values to other standards of the quantity concerned

intrinsic error (of a measuring instrument) (VIM 5.24)

error of a measuring instrument, determined under reference conditions

limiting conditions (VIM 5.6)

extreme conditions that a measuring instrument is required to withstand without

damage, and without degradation of specified metrological characteristics when it is

subsequently operated under its rated operating conditions

NOTES

1. The limiting conditions for storage, transport and operation may be different.

2. The limiting conditions may include limiting values of the measurand and of

the influence quantities.

maximum permissible errors (of a measuring instrument) (VIM 5.21)

limits of permissible error (of a measuring instrument)

extreme values of an error permitted by specifications, regulations, etc. for a

given measuring instrument

measurand (VIM 2.6)

particular quantity subject to measurement

EXAMPLE vapour pressure of a given sample of water at 20 °C.

NOTE The specification of a measurand may require statements about

quantities such as time, temperature and pressure.

measuring instrument (VIM 4.1)

device intended to be used to make measurements, alone or in conjunction with

supplementary device(s)

measuring system (VIM 4.5)

complete set of measuring instruments and other equipment assembled to carry

out specified measurements

EXAMPLES

apparatus for measuring the conductivity of semiconductor materials;

apparatus for the calibration of clinical thermometers.

97

NOTES

1. The system may include material measures and chemical reagents.

2. A measuring system that is permanently installed is called a measuring

installation.

measurement procedure (VIM 2.5)

set of operations, described specifically, used in the performance of particular

measurements according to a given method

NOTE A measurement procedure is usually recorded in a document that is

sometimes itself called a "measurement procedure" (or a measurement method) and is

usually in sufficient detail to enable an operator to carry out a measurement without

additional information.

method of measurement (VIM 2.4)

logical sequence of operations, described generically, used in the performance

of measurements

NOTE Methods of measurement may be qualified in various ways such as:

substitution method, differential method, null method.

metrology (VIM 2.2)

science of measurement

NOTE Metrology includes all aspects both theoretical and practical with

reference to measurements, whatever their uncertainty, and in whatever fields of

science or technology they occur.

national (measurement) standard (VIM 6.3)

standard recognized by a national decision to serve, in a country, as the basis for

assigning values to other standards of the quantity concerned

nominal value (VIM 5.3)

rounded or approximate value of a characteristic of a measuring instrument that

provides a guide to its use

EXAMPLES

a) 1 00 W as the value marked on a standard resistor;

b) 1 L as the value marked on a single-mark volumetric flask;

c) 0.1 mol/L as the amount-of-substance concentration of a solution of

hydrogen chloride, HCl;

d) 25 °C as the set point of a thermostatically controlled bath.

98

random error (VIM 3.13)

result of a measurement minus the mean that would result from an infinite

number of measurements of the same measurand carried out under repeatability

conditions

NOTES

1. Random error is equal to error minus systematic error.

2. Because only a finite number of measurements can be made, it is possible to

determine only an estimate of random error.

reference conditions (VIM 5.7)

conditions of use prescribed for testing the performance of a measuring

instrument or for intercomparison of results of measurements

NOTE The reference conditions generally include reference values or reference

ranges for the influence quantities affecting the measuring instrument.

relative error (VIM 3.12)

error of measurement divided by a true value of the measurand

NOTE Since a true value cannot be determined, in practice a conventional true

value is used (see 1.19 and 1.20).

resolution (of a displaying device) (VIM 5.12)

smallest difference between indications of a displaying device that can be

meaningfully distinguished

NOTES

1. For a digital displaying device, this is the change in the indication when the

least significant digit changes by one step.

2. This concept applies also to a recording device.

repeatability (of a measuring instrument) (VIM 5.27)

ability of a measuring instrument to provide closely similar indications for

repeated applications of the same measurand under the same conditions of

measurement

NOTES

1. These conditions include: reduction to a minimum of the variations due to

the observer, the same measurement procedure, the same observer, the same

measuring equipment, used under the same conditions, the same location and

repetition over a short period of time.

99

2. Repeatability may be expressed quantitatively in terms of the dispersion

characteristics of the indications.

repeatability (of results of measurements) (VIM 3.6)

closeness of the agreement between the results of successive measurements of

the same measurand carried out under the same conditions of measurement

NOTES

1. These conditions are called repeatability conditions.

2. Repeatability conditions include: the same measurement procedure, the

same observer, the same measuring instrument, used under the same conditions, the

same location, repetition over a short period of time.

3. Repeatability may be expressed quantitatively in terms of the dispersion

characteristics of the results.

reproducibility (of results of measurements) (VIM 3.7)

closeness of the agreement between the results of measurements of the same

measurand carried out under changed conditions of measurement

NOTES

1. A valid statement of reproducibility requires specification of the conditions

changed.

2. The changed conditions may include: principle of measurement, method of

measurement, observer, measuring instrument, reference standard, location,

conditions of use and time.

3. Reproducibility may be expressed quantitatively in terms of the dispersion

characteristics of the results.

4. Results are here usually understood to be corrected results.

response time (VIM 5.17)

time interval between the instant when a stimulus is subjected to a specified

abrupt change and the instant when the response reaches and remains within specified

limits around its final steady value

result of a measurement (VIM 3.1)

value attributed to a measurand, obtained by measurement

100

NOTES

1. When a result is given, it should be made clear whether it refers to: the

indication, the uncorrected result, the corrected result and whether several values are

averaged.

2. A complete statement of the result of a measurement includes information

about the uncertainty of measurement.

span (VIM 5.2)

modulus of the difference between the two limits of a nominal range

EXAMPLE for a nominal range of -10 V to +10 V, the span is 20 V.

NOTE In some fields of knowledge, the difference between the greatest and

smallest values is called range.

stability (VIM 5.14)

ability of a measuring instrument to maintain constant its metrological

characteristics with time

NOTES

1. Where stability with respect to a quantity other than time is considered, this

should be stated explicitly.

2. Stability may be quantified in several ways, for example: in terms of the

time over which a metrological characteristic changes by a stated amount, or - in

terms of the change in a characteristic over a stated time.

systematic error (VIM 3.14)

mean that would result from an infinite number of measurements of the same

measurand carried out under repeatability conditions minus a true value of the

measurand

NOTES

1. Systematic error is equal to error minus random error.

2. Like true value, systematic error and its causes cannot be completely known.

3. For a measuring instrument, see "bias" (5.25).

traceability (VIM 6.10)

property of the result of a measurement or the value of a standard whereby it

can be related to stated references, usually national or international standards, through

an unbroken chain of comparisons all having stated uncertainties

101

NOTES

1. The concept is often expressed by the adjective traceable.

2. The unbroken chain of comparisons is called a traceability chain.

transparency (VIM 5.15)

ability of a measuring instrument not to alter the measurand

EXAMPLES

a) a mass balance is transparent;

b) a resistance thermometer that heats the medium whose temperature it is

intended to measure is not transparent.

true value (of a quantity) (VIM 1.19)

value consistent with the definition of a given particular quantity

NOTES

1. This is a value that would be obtained by a perfect measurement.

2. True values are by nature indeterminate.

3. The indefinite article "a", rather than the definite article "the", is used in

conjunction with "true value" because there may be many values consistent with the

definition of a given particular quantity.

uncertainty of measurement (VIM 3.9)

parameter, associated with the result of a measurement, that characterizes the

dispersion of the values that could reasonably be attributed to the measurand

NOTES

1. The parameter may be, for example, a standard deviation (or a given

multiple of it), or the half-width of an interval having a stated level of confidence.

2. Uncertainty of measurement comprises, in general, many components. Some

of these components may be evaluated from the statistical distribution of the results of

series of measurements and can be characterized by experimental standard deviations.

The other components, which can also be characterized by standard deviations, are

evaluated from assumed probability distributions based on experience or other

information.

3. It is understood that the result of the measurement is the best estimate of the

value of the measurand, and that all components of uncertainty, including those

arising from systematic effects, such as components associated with corrections and

reference standards, contribute to the dispersion.

102

This definition is that of the "Guide to the expression of uncertainty in

measurement" in which its rationale is detailed (see, in particular, 2.2.4 and

annex D [10]).

uncorrected result (VIM 3.3)

result of a measurement before correction for systematic error

value (of a quantity) (VIM 1.18)

magnitude of a particular quantity generally expressed as a unit of measurement

multiplied by a number

EXAMPLES

a) length of a rod: 5.34 m or 534 cm;

b) mass of a body: 0.152kg or 152g;

c) amount of substance of a sample of water (H2O): 0.012 mol or 12 mmol.

NOTES

1. The value of a quantity may be positive, negative or zero.

2. The value of a quantity may be expressed in more than one way.

3. The values of quantities of dimension one are generally expressed as pure

numbers.

4. A quantity that cannot be expressed as a unit of measurement multiplied by

a number may be expressed by reference to a conventional reference scale or to a

measurement procedure or to both.

zero error (of a measuring instrument) (VIM 5.23)

datum error for zero value of the measurand

A.2 Feature Tolerance

The definitions of feature tolerance that are frequent used and used in this study

are described following with Mahr information [15]. This information refers to

ISO1101.

103

TABLE A-1 Symbol and definition of feature tolerance

Feature tolerance Symbol Definition

Straightness

The tolerance zone is limited in the

measuring plane by two parallel straight

lines a distance t apart.

Roundness /

Circularity


measuring plane perpendicular to the axis

by two concentric circles a distance t

apart.

Cylindricity /

Cylinder form

The tolerance zone is limited by two

coaxial cylinders a distance t apart.

Parallelism


measuring plane by two straight lines a

distance t apart and parallel to the datum.

Radial run out


measuring plane perpendicular to the axis

by two concentric circles a distance t

apart, the common centre of which lies on

the datum axis.

104

TABLE A-1 (CONTINUED)

Feature tolerance Symbol Definition

Conicity

Not yet described by

standards.


measuring plane by two straight lines a

distance t apart and parallel to the datum.

Not the measured profile, but that section

of the reference straight line calculated

according to LSS which is restricted to the

measuring length shall be contained

within the tolerance zone.

A.3 The Evaluation Methods

The definitions of The Evaluation Methods described following with Mahr

information [15]. This information refers to ISO2766.

TABLE A-2 The evaluation methods

Regression circle (Gaussian straight circle)

Circle laid into the measured circular profile such that the

sum of the squares of all profile deviations is a minimum.

(LSC =Least Square Circle)

Circular zone with minimum radial separation

Concentric circles enclosing the circular profile and having

the least radial separation.

(MZC =Minimum Zone Circles)

Minimum circumscribed circle

Smallest possible circle which can be fitted around the

circular profile.

(MCC =Minimum Circumscribed Circle)

105

TABLE A-2 (CONTINUED)

Maximum inscribed circle

Largest possible circle which can be fitted within the

circular profile.

(MIC =Maximum Inscribed Circle)

Regression straight line (Gaussian straight line)

Mean line laid through the measured profile such that the

sum of the squares of all profile deviations is a minimum.

(LSS =Least Square Straight line)

Enveloping parallel lines

Parallel, straight lines enclosing the profile and having the

least separation.

(MZS=Minimum Zone Straight lines)

Regression parabola

Mean parabola (2nd order) laid through the profile such

that the sum of the squares of all profile deviations is a

minimum.

(LSP =Least Square Parabola)

Edge identifikation

The position of a profile interruption (edge) is determines.

The profile is evaluated up to the edge according to LSS.

(EID =Edge IDentification)

APPENDIX B

SCREENING EXPERIMENTAL

108

B.1 Introduction

A screening experimental measures a cylindrical standard workpiece that is used

as the workpiece in this study. This screening experimental is used for checking the

assumption and the evaluation parameters in relative to the experimental. It is

performed in a temperature uncontrolled room with air conditioning unit. In normal

case, form measurement directly affect from temperature and its changing. The

objectives of this screening experimental are:

To present a positioning error in the direction of x, y and z axis when machine

searches the same position.

To compare roundness deviation when using the different evaluation criteria:

MZC and LSC.

To compare radial runout deviation when using z axis and c axis as reference

datum.

To compare radial runout deviation with workpiece related datum when using

the different number of circles or data points to calculate workpiece datum.

To prove the assumption that radial runout deviation with workpiece related

datum is limitation of roundness deviation when using the same profile to determine

both features.

To compare cylindricity deviation when using different methods of scanning

polar profiles: between zeroing the probe only one time for three circles and zeroing

the probes every circle.

B.2 Experimental Procedure

First, the workpiece is aligned by scanning two circles at 15 and 85 mm height

of the workpiece coordinate under the permissible eccentricity value is less than

2.0 µm. Next, the measurement program scans three circles (C1, C2 and C3) at three

different heights of workpiece coordinate to collect data for determining tolerance

feature. The heights of scanning circle are 15, 50, 85 mm of workpiece coordinate.

These specific heights of measurement are the same as the setting parameters in the

study experimental. However two heights of scanning circle, 15 and 85 mm, are the

same as two heights used to workpiece’s alignment. In normal case, alignment area

must cover measurement area. The measuring heights are not the same height as

aligning height in order to obtain accurate result. Due to these setting measurement

109

heights, the aligned distance covers three different heights also. Roundness deviations

are used to observe probe’s positioning error on the aligned heights.

FIGURE B-1 Input, Output and Measurement conditions of screening experimental

The three circular profiles are used to calculate the center points of each

substitute element. These profiles are also used to determine three features:

roundness, radial runout and cylindricity deviation. The input, output and

measurement conditions of the screening experimental are shown in figure B-1 where

[X], [Y] and [Z] refer to x, y and z-coordinate of the position vector, “rdh” refers to

roundness deviation, “runout” refers to radial runout and “cyl” refers to cylindricity

deviation.

B.3 Measurement Results

B.3.1 The center point of circle substitute element

Position vector specifies the position of the transferred substitute element.

While point in coordinate system are expressed by its x, y and z coordinate values,

position vector of circular substitute element is represented by its center point.

Figure B-2 shows the x and y coordinate value of the center point of circle substitute

elements in micrometer while figure B-3 shows the z coordinate value of the center

point of circle substitute element in millimeter. Both figures present the positioning

error in the direction of x, y and z axis when the machine is searched the same

position.

110

ELEMENT INFO - POSITION VECTOR

-0.500-0.400-0.300-0.200-0.1000.0000.1000.2000.300

0.4000.500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

No. of measurement

(µm)

[x1] [x2] [x3]


-0.500-0.400

-0.300-0.200-0.100

0.0000.100

0.2000.300

0.4000.500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

No. of measurement

(µm)

[y1] [y2] [y3]

FIGURE B-2 The center point of three circle substitute elements in x and y axis of

the machine coordinate system

In figure B-2, the graph of x coordinate value of each circle substitute element

increase. As the graph of the center point of each circle substitute element in y

direction increase also. The range of x and y-coordinate value of each circle substitute

element are 0.20-0.35 µm while the range of z coordinate value is bigger than that.

However it can be noticed that the graphs of the center of each circle substitute

element in z coordinate have a few peak values. Figure B-3 shows the peak points of

each circle substitute element occurring in the different number of measurement. The

ranges of z coordinate value are in between 7.0-16.0 µm. These peak points cause by

the property of the mechanical bearing. However the ranges of z coordinate values are

bigger than the range of x and y coordinates value.


99.990

99.995

100.000

100.005

100.010

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49No. of measurement

(mm) [z1] ELEMENT INFO - POSITION VECTOR

135.000

135.005

135.010

135.015

135.020

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

No. of measurement

(mm) [z2]


169.990

169.995

170.000

170.005

170.010

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

No. of measurement

(mm) [z3]

FIGURE B-3 The center point of three circle substitute elements in z axis of

the machine coordinate system

111

Normally, the protocol is used to observe disturbances or affects from

measuring environment such as dust or vibration. Due to the peak value in z direction,

these protocols can not do that. Because these circular profiles are the plane in x and

y-direction, the peak points in z-direction do not represent by the protocols.

Corresponding to this reason, the profile results of the roundness and the radial runout

deviation are normal and do not have the peak or valley in the protocol of the number

of measurement having the peak point.

B.3.2 Roundness deviation

roundnees

0.000

0.100

0.200

0.300

0.400

0.500

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

No. of measurement

devi

atio

n (µ

m)

rdh_1

rdh_2

rdh_3

roundness (same profile_different measurement criteria)

0.000

0.100

0.200

0.300

0.400

0.500

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49No. of measurement

devi

atio

n (µ

m)

rdh_1

rdh_11

FIGURE B-4 Roundness deviation

(Left) Roundness deviations when evaluation criteria are MZC

(Right) Roundness deviation of the second circle substitute element

(C2) when evaluation criteria are MZC and LSC

Three circular profiles are determined roundness deviations with MZC

evaluation criteria. Roundness deviations of each circle substitute element when using

MZC evaluation criteria are shown in the left-hand side of figure B-4. Roundness

deviations of three circles with the MZC evaluation criteria are nearly similarity in the

range 0.040-0.090 µm. However it can be noticed that the range and the mean value

of the third circular profile are bigger than others. These results agree with the

formtester principle, the measurement height affect to roundness deviation.

Roundness deviation is increased when the measurement height increases due to the

deformation of machine column. Then technical data of measuring machine represent

roundness deviation in µm+µm per mm of measurement height in the general.

Furthermore, the first circular profile (C1) is determined roundness with LSC

evaluation criteria for comparing roundness deviation when using the different

evaluation criteria between MZC and LSC. Figure B-4 in the right-hand side of shows

112

roundness measurement result of the same profile is difference when using the

different evaluation criteria. Roundness deviations with LSC evaluation criterion are

bigger than roundness deviations with MZC evaluation criterion in every

measurement. The range of roundness deviations with LSC evaluation criterion is also

bigger than the range of roundness deviations with MZC evaluation criterion. The

range of roundness deviations of the first circular profile when evaluating with MZC

and LSC criteria are 0.050535 µm and 0.065824 µm. Due to the changing in every

measurement, evaluation criteria effect to the measurement result. Therefore, the

comparison or the analysis of form measurement results must be done with similar

evaluation criteria.

However it can be noticed that roundness deviation evaluated with MZC

evaluation criteria is not bigger than roundness deviation evaluated with MZC

evaluation criteria in every time of measurement.

B.3.3 radial runout deviation

The second circular profile (C2) is determined radial runout deviation with the

four difference reference datum in order to observe the effect of difference reference

datum to radial runout deviation.

radial run out

0.000

0.100

0.200

0.300

0.400

0.500

0.600


devi

atio

n (µ

m)

runout_1 runout_2 runout_3 runout_4

roundness and radial run out (same profile)

0.000

0.100

0.200

0.300

0.400

0.500

0.600

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

No. of measurement

devi

atio

n (µ

m)

rdh_2 runout_2 runout_3 runout_4

FIGURE B-5 Radial runout deviation

(Left) four radial runout deviations with the difference reference

datum when evaluation criteria are MZC

(Right) the comparison between roundness and radial runout

deviation determined from the same profile (C2) when evaluation

criteria are MZC

The first comparison is radial runout with the different machine datum between

z and c axes (runout_1and runout_2). The z axis of the measuring machine is machine

113

column while the c axis refers to the line axis that is on the center point of the

rotational table and parallel with the z axis of measuring machine. Even through the z

and c axes are not the same axis according to the machine definition, radial runout

deviation with both machine as datum are also the same value. Because the

determining of the recorded profile deviation uses the probe ball to be the reference

coordinate system, both of the machine datum lines refer from the center of the c-

rotary table. The z axis are calculated from the center of the c-rotary table adding up

the radial of the workpiece and the radial of the probe tip while the c axis refers to the

line axis that is on the center point of the rotary table and parallel with the z axis of

the measuring machine. Figure B-5(Left) shows radial runout deviations with z axis

of the machine as datum are the same value as radial runout deviations with c axis of

the machine as datum.

Additionally, radial runout deviation with the machine as datum changes from

0.200 to 0.600 µm during one hour and thirty minute of the measurement program. It

is interesting what is the main influencing factor that affected with this measurement

result but the measurement result and the recorded data of this screening experimental

is less for making conclusion. Normally, radial runout deviation with the machine as

datum is affected from many sources of error for example the bending in machine

column form temperature, the parallel between machine column axis and the rotary

axis, the complement of aligning workpiece that made the workpiece axis parallel

with machine axis, etc.

The second comparison is radial runout with different workpiece related datum

between datum_A (runout_3) and datum_B (runout_4). The workpiece datum_A is

crated from three circles that measured at 15, 50 and 85 mm refer from the height of

workpiece while the workpiece datum_B is crated from two circles that measured at

15 and 85 mm. Figure B-5 in the left-hand side shows both radial runout deviations

with workpiece related datum are slightly the same. Because the workpiece datum is

the substitute line element that is calculated from the center of each circle substitute

element, the workpiece datum that evaluated from the different number of circles or

the different data points is not the same thing or the same datum.

In assumption that radial runout deviation with workpiece related datum is

limitation of roundness deviation when using the same profile in order to determining

both features. Figure B-5 in the right-hand side shows roundness deviation is smaller

114

value than radial runout deviation with four difference reference datum. Due to the

principle of evaluation criteria, roundness deviation is calculated the distance between

inside and outside circle that cover circular profile while radial runout deviations are

evaluated circular profile with respect to datum line reference. However, only radial

runout deviation with workpiece related datum can be limitation of roundness

deviation because workpiece datum is determined from the centre of each circle

substitute element. Radial runout with workpiece related datum illustrates the result of

its polar profile relative to itself while radial runout with machine as datum illustrates

the result of its polar profile relative to machine axis.

B.3.4 Cylindricity deviation

Cylindricity deviation is evaluated from three polar measurements that are also

determined roundness deviation. In the left-hand side of figure B-6, cylindricity

values fluctuate in big range. These cylindricity measurement results are measured by

the probe zeroizes every circle measurement method. However cylindricity values are

not excess 2.0 µm that is the permissible eccentricity of this screening experimental.

cylindricity

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1.600

1.800

2.000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

No. of measurement

devi

atio

n (µ

m)

[cylindricity] cylindricity

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1.600

1.800

2.000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

No. of measurement

devi

atio

n (µ

m)

[cylindricity]

FIGURE B-6 Cylindricity deviation when evaluation criteria are MZC

(Left) The probe zeroizes every circle

(Right) The probe zeroize only one time at pre-position height

As compare the left-hand side to the right-hand side of this figure, cylindricity

measurement results are measured from different the probe zeroize method. The

measurement method changes form the probe zeroizes every circle to the probe

zeroizes only one time at pre-position height. The reduction movement of machine

axis is one method to reduce the errors in order to get precise measurement results.

The fluctuation is decreased by changing the probe zeroize method. The changing

115

probe zeroizes method from the probe zeroizes every circle to the zeroing probe only

one time in scanning can improve cylindricity deviation.

Furthermore, it can be seen that cylindricity deviations at the beginning is

stable. Cylindricity deviations increased after the measurement number fourteen cause

by surrounding disturbances. The highest peak point is at the twenty-three of number

of measurement. These observations can explain by comparison figure B-6 to and

figure B-7.

roundnees

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

No. of measurement

devi

atio

n (µ

m)

rdh_1 rdh_2 rdh_3

roundnees

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

No. of measurement

devi

atio

n (µ

m)

rdh_1 rdh_2 rdh_3

FIGURE B-7 Roundness deviation when evaluation criteria are MZC



Figure B-7 shows roundness deviations when measured profiles by different

probe zeroize method. The left-hand side of the figure show results when the probe

zeroizes every circle. The right-hand side of the figure show results when the probe

zeroizes only one time at the pre-position height. These three roundness deviations are

determined from the same polar profiles used to determine cylindricity deviation. The

first polar profile is changed from the measurement number forty-one while the

second and the third polar profile are changed from the measurement number fourteen

as same as cylindricity. As these results, the increasing of cylindricity deviation after

the number fourteen causes by surrounding disturbances. These roundness results

agree with their protocols that show peaks and valleys in circular profiles. Protocol is

used to observe disturbances or surrounding affected such as dust or vibration.

Additionally, radial runout deviations evaluated from same polar profile as

roundness and cylindricity deviations is shown in figure B-8. The right-hand side of

this figure shows radial runout deviations when the probe zeroizes only one time at

pre-position height. Radial runout deviation with workpiece related as datum agrees

116

with roundness and cylindricity. The results of roundness and radial runout deviation

with workpiece related as datum are also increasing as cylindricity deviation. The

increasing of repeated measurement causes by surrounding disturbance.

runout

0.000

0.100

0.200

0.300

0.400

0.500

0.600


devi

atio

n (µ

m)


runout

0.000

1.000

2.000

3.000

4.000

5.000

6.000

7.000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

No. of measurement

devi

atio

n (µ

m)


FIGURE B-8 Radial runout deviation when evaluation criteria are MZC



However it can be noticed that radial runout deviation with machine axis as

datum is big value until the beginning of measurement. The mean value of this feature

has the off-set value at the beginning. Radial runout deviations with machine axis as

datum represent to other influencing factor to polar measurement results.


-0.500-0.400-0.300-0.200-0.1000.000

0.1000.2000.300

0.4000.500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

No. of measurement

(µm)

[x1] [x2] [x3]


-0.500

-0.400

-0.300-0.200

-0.1000.000

0.1000.2000.3000.400

0.500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

No. of measurement

(µm)

[y1] [y2] [y3]


0.0000.2000.4000.6000.8001.0001.2001.4001.6001.8002.0002.2002.4002.6002.800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

No. of measurement

(µm)

[x1] [x2] [x3]


0.0000.2000.4000.6000.8001.0001.2001.4001.6001.8002.0002.2002.4002.6002.800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

No. of measurement

(µm)

[y1] [y2] [y3]

FIGURE B-9 The center point of three circle substitute elements in x and y axis of

machine coordinate system. (Left) The probe zeroizes every circle


117

On the other hand, the x, y and z-coordinate value of the center point of each

circle substitute element are presented in order to prove the other influencing factors.

In figure B-9, the left-hand side of figure shows measurement results when the probe

zeroizes every circle. The right-hand side of this figure shows results when the probe

zeroizes only one time at the pre-position height. Under the different zeroing methods

of probe, the trend lines of repeated measurement of each circular profile are similar.

The positioning value in x and y direction increases in relative to measurement’s time.

However the x and y absolute value of circle center point when the probe zeroizes

only one time are higher than when the probe zeroizes every circle. These cause by

complement of workpiece alignment. Due to the setting permissible eccentricity

value, the acceptance workpiece aligning position does not exceed 2 µm. The

workpiece axis and the machine axis are parallel in between 0-2 µm. As figure B-9,

the first value of every circle substitute element is under 2 µm.

These results agree with radial runout deviations with the machine axis as datum

is big value at the beginning of repeated measurement. The mean value of this feature

has off-set value at the beginning.

In contrast, the z value of center point when the zeroing probe only one time at

pre-position height is shown in figure B-10. When the probe zeroizes every circle, the

z value of circle center point of each circle should be changing in the same range.

Some peak points occurred during measurement because of random error from

mechanical bearing property.

When the probe zeroize only one time at pre-position, the range of z value of the

first circle is smaller range than other circles. The range of z position vector of C2 and

C3 is together similar but different from the first circle. As see also in the right-hand

side of figure B-10, the positioning error in z direction of circle 1(C1) is

approximately 3.0 µm while the positioning errors in z direction of others (C2 and

C3) are approximately 8.0 µm. The range of z coordinate value of C2 and C3 height

when the zeroing probe only one time at pre-position are bigger than the range of z-

coordinate value of C1. However the range of z-coordinate value of C1, C2 and C3

when the probe zeroize only one time at pre-position height are smaller than when the

probe zeroize every circle. The position vector result agree with cylindricity results

improved by changing the zeroize method.

118


99.990

99.995

100.000

100.005

100.010

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

No. of measurement

(mm) [z1]


135.000

135.005

135.010

135.015

135.020


(mm) [z2]


169.990

169.995

170.000

170.005

170.010


(mm) [z3]


99.990

99.995

100.000

100.005

100.010

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

No. of measurement

(mm) [z1]


135.000

135.005

135.010

135.015

135.020

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

No. of measurement

(mm) [z2]


169.990

169.995

170.000

170.005

170.010

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

No. of measurement

(mm) [z3]

FIGURE B-10 The center point of three circle substitute elements in z axis of

machine coordinate system. (Left) The probe zeroizes every circle


The examples of the measurement result of this screening experimental are

shown in figure B-11 and figure B-12. While the protocol of the measurement number

24 when the probe set zero at every circles and when the probe set zero only one time

are shown in figure B-13 and figure B-14.

119

FIGURE B-11 The screening experimental measurement result; element information

results in x, y and z-coordinate of the position vector

120

FIGURE B-12 The screening experimental measurement results; form and location

tolerance

121

FIGURE B-13 The protocol of the screening experimental with the zeroing probes

every circle

122

FIGURE B-14 The protocol of the screening experimental with the zeroing probe

only one time at pre-position height

123

FIGURE B-15 The example of cylindricity profile in the protocol

Figure B-15 shows the example of cylindricity profile in protocol when using

“AUTO” scale to perform the profile measurement result. In normal case, cylindricity

profile in protocol should be form of cone that expresses the effect of bending in

machine column and probe force due to time.

In the screening experimental with the probe zeroizes every circle, almost

cylindricity profile result present in figure B-15(b) and figure B-15(d). Figure B-15(b)

has 15 records and figure B-15(d) has 17 records. Whiles the other forms are

presented in a few record numbers. The 5 records, 31, 34, 36, 40 and 44, are presented

in figure B-15(a). The 3 records, 29, 42 and 46, are presented in figure B-15(c). The 5

records, 3, 4, 6, 20 and 25, are presented in figure B-15(e). The 3 record, 26, 41 and

48, are presented in figure B-15(f). And 2 records, 1 and 39, are presented in figure B-

15(g). These are different from the profile of cylindricity when the probe zeroize

every cycle. On the other hand, all cylindricity recorded profile presents in the form of

figure B-15(h) when the probe zeroize only one time at pre-position height.

According to these results, cylindricity values are improved by reducing

movement of machine with the zeroing probes only one time. The protocol of

124

cylindricity profile can used to prove the effect on the machine column bending and

the probe force. However, the presented profile is adjusted by changing horizontal

scale. Only cylindricity recorded profile can not prove the causes that cylindricity

deviation is out of tolerance by only itself.

For example, figure B-13 shows protocol of screening experimental with the

probe zeroizes every circle. The three roundness deviations are 0.132, 0.138 and

0.196 µm while cylindricity deviation is 1.603 µm. If cylindricity relates with only

one circular profile, cylindricity protocol should be in cone form as figure B-15(a).

But cylindricity protocol express in form that having big diameter in the middle of the

cylindrical workpiece figure B-15(d). That means having other affected to cylindricity

determination. The second circular profile that is used to determine roundness and

radial runout deviation with workpiece related datum are similar. Both recorded

profiles have no high peak or valley. However protocols of radial runout deviation

with machine axis as datum are different from roundness and radial runout deviations

with workpiece related datum. It explains that the bigger diameter in the middle of the

cylindrical workpiece affect in relative to machine axes.

In figure B-14, protocol of screening experimental with the zeroing probe only

one time at pre-position height show three roundness deviation are 0.107, 0.487 and

0.487 µm. The second circular profile has a peak approximately 0.45 µm while the

third circular profile has a valley approximately 0.40 µm. The peak and the valley are

presented in cylindricity protocol. The protocols of radial runout deviation with

machine axis as datum and radial runout deviation with workpiece related as datum

have peak points as same as roundness. Cylindricity deviation is 0.868 µm and

cylindricity protocol express in form of cone. Cylindricity deviation measured by

zeroing the probe only one time is less value than by zeroing the probe every circle

even though the second and the third profiles of cylindricity have disturbances. It is

interesting what is the main influencing factor that affected with cylindricity

measurement result but the measurement result and the recorded data of this screening

experimental is less for making conclusion.

However the increasing of cylindricity value does not relates to only the

increasing of roundness. Because cylindricity deviation is evaluated from three circles

that measured at different heights. The x and y positioning error come form each

circle profile and the z positioning error comes from different height of polar

125

measurement. In addition, the cylinder substitute element is crated in three-dimension

element. Then the positioning in x, y and z direction are related with this feature. The

alternatively to the cylindricity form tolerance, the straightness, the circularity and the

parallelism can be tolerated [4]. That agrees with the explanation in Mahr manual

[19].

The cylindricity tolerance also indirectly limits the roundness and straightness

deviations, the parallelism deviations of the opposite generating lines as well as the

straightness deviations of the symmetry axis of the tolerance workpiece element.

However, it may be useful to perform additional roundness and straightness

measurement on the test surface in order to find the possible reason, why cylindricity

is out of tolerance.

B.4 Conclusions

B.4.1 Each of measurement point has at least the positioning errors. The value of

positioning errors in the x and y axes are closely. The values of positioning errors in

the z axis are bigger than others due to the effect of property of mechanical bearing

located in rotational table.

B.4.2 Due to evaluation criteria effect, the comparison or the analysis of form

measurement results must ensure that the deviation is determined by the same

evaluation criteria.

B.4.3 Radial runout deviation with the c axis as datum is the same value as radial

runout deviation with the z axis as datum. Both machine axes have no difference in

radial runout deviations because the software evaluates the position from probe ball.

As probe ball is used for the reference coordinate system in determining recorded

profile. The software compiles the c axis and the z axis of the measuring machine as

the same line.

B.4.4 The workpiece datum is the substitute line element that is calculated from

the centers of each circle substitute element. The workpiece lines datum that are

evaluated from the different number of circles or the different data points are not the

same datum. Radial runout deviation with workpiece related datum does not obtain

the same values when they are determined by different workpiece datum.

B.4.5 Radial runout deviation with workpiece related as datum is the limitation

of roundness deviation, because roundness deviation represents only deviation of its

126

polar profile. While radial runout deviation with workpiece related datum represents

deviation of its polar profile in relative to line reference calculated from measurement

on workpiece.

B.4.6 In order to get precise measurement results, cylindricity deviation are

improved by changing the probe zeroizes method. The probe zeroize method are

changed from zeroing the probe every circles to zeroing the probe only one time at

pre-position height in order to reduce the number of probe position. Due to reducing

positioning movement of machine, the sources of errors are reduced also because each

point of probe position has at least the positioning errors.

B.4.7 In this screening experiment, cylindricity deviation is determined from

three polar profiles. As cylindricity deviation is evaluated in form of three-

dimensioning, the sources of error in x, y, z and c direction of workpiece are added in

the cylindricity tolerance. The correct cylindricity deviation can be represented to the

complete measuring machine. However, many influencing factors are significant in

cylindricity evaluation. Additionally, only cylindricity deviation and its recorded

profile can not prove the causes of error that cylindricity deviation is out of tolerance.

Corresponding to these reasons, the other tolerances are also shown when determining

cylindricity deviation.

127

BIOGRAPHY

Name : Miss Nitima Nulong

Thesis Title : Investigation of Roundness Tester’s Accuracy and Compensation

Algorithm

Major Field : Production Engineering

Biography

I was born on September 13, 1977. I graduated Bachelor degree of Engineering

major Industrial Engineering in 1999 at Prince of Songkla university.

My contact address is 133/21 moo 3 Jangwattana Rd., Pak-kard, Nontaburee,

11120 Thailand. My e-mail address is [email protected]

investigation of roundness tester’s · pdf file2-6 the relationship between measurement...

Documents