Final Report - BIPM

Slovenský metrologický ústav Slovak Institute of Metrology Slowakisches Institut für Metrologie

EUROMET Supplementary Comparison #570

Comparison of squareness measurements Final Report

File: Project_SQUARE_Final-an.doc / Issue 28. 02. 2005

Jiri Mokros, SMU, Bratislava, February 2005


Content 1 Introduction............................................................................. 1 2 Organisation ............................................................................ 1 3 Participants.............................................................................. 2 4 Time schedule.......................................................................... 3 5 Description of the Standards...................................................... 3 6 Measurement instructions.......................................................... 3 6.1 Definitions ............................................................................. 3 7 Measurement (calibration) results .............................................. 5 7.1 Supplementary data ................................................................ 6 8 Measurement uncertainty .......................................................... 6 9 Measuring devices and procedures.............................................. 7 9.1 SMU ...................................................................................... 7 9.2 METAS ................................................................................... 7 9.3 PTB ....................................................................................... 8 9.4 GUM .................................................................................... 10 9.5 MIRS (SMIS) ........................................................................ 11 9.6 MIKES ................................................................................. 12 9.7 IPQ ..................................................................................... 13 9.8 BNM-LNE.............................................................................. 13 9.9 SP ....................................................................................... 14 9.10 OMH .................................................................................... 15 9.11 CMI .................................................................................... 16 9.12 NMI VSL............................................................................... 16 10 Results.................................................................................. 17 10.1 Granite square...................................................................... 18 10.1.1 Straightness............................................................................................... 18 10.1.2 Squareness ................................................................................................ 28 10.2 Cylinder Square .................................................................... 31 10.2.1 Straightness............................................................................................... 31 10.2.2 Squareness ................................................................................................ 45 11 Conclusion ............................................................................. 50


Final Report of EUROMET Comparison of squareness measurements No: 570 1

1

Introduction

The comparison of squareness measurement was aimed to compare and verify the declared calibration measurement capabilities of participating laboratories and to investigate the effect of systematic influences in the measurement process and their elimination. As regards the technical parameters, the standards which were circulated represent the standards currently used in the metrological praxis. It makes possible to compare the standard devices in the real conditions. The standards had to be calibrated by the measurement process currently used in the participant’s laboratory (i.e. in the horizontal or vertical position of the square). This comparison could help us to gain an important information revealing imperfections of measurement process related to measurement systems of individual participating NMIs. Such an information could be in turn used for the upgrade of measurement system or measurement procedure. For the sensing of real profile must be performed prior to the determination of the angle deviation between two arms of square, ISO 1101 was not applied. The straightness deviation and angles have been calculated separately. 2

Organisation

This comparison will be submitted as the EUROMET supplementary comparison in the framework of the Mutual Recognition Arrangement (MRA) of the Metre Convention and shall support confidence in calibration and measurement certificates issued by the participating national metrology institutes (NMI). The comparison was organised according to the rules set up by the BIPM1.

1

T.J. Quinn, Guidelines for CIPM key comparisons (Appendix F to the MRA, 1. March 1999, BIPM, Paris)


2

Participants NMI

Slovak Institute of Metrology Swiss Federal Office of Metrology and Accreditation

Address Karloveská 63, SMU SK-842 55 Bratislava Slovakia Lindenweg 50, METAS CH-3003 Bern-Wabern Switzerland

Physikalisch-Technische Bundesanstalt

PTB

Czech metrological institute

CMI

Central Office of Measures

GUM

National Office of Measures

OMH

Instituto Português da Qualidade IPQ University of Maribor, Faculty of Mechanical Engineering, Laboratory for Production Measurement

MIRS (SMIS)

MIKES Konepajametrologia

MIKES

BNM - Laboratoire National d'Essais

BNMLNE

NMi VSL B.V. Swedish National Testing and Research Institute

SP

Bundesallee 100, D-38116 Braunschweig Germany V Botanice 4, Praha 5, CZ15072 Czech republic ul. Elektoralna 2, 00-950 Warszawa, P-10, Poland Nemetvolgyi út 37-39, H-1124 Budapest Hungary Rua António Gião, 2, 2829-513 CAPARICA Portugal Smetanova 17, 2000 Maribor Slovenia Metallimiehenkuja 6 FIN-02150 ESPOO Finland 1, rue G. Boissier 75724 PARIS Cedx 15 France P.O. Box 654, 2600 AR, Delft, The Netherlands Department of Metrology, Brinellgatan 4, SE-501 15 BORÅS, Sweden

Name

E-mail

Telephone

FAX

Jirko Mokroš

[email protected]

+421 2 60294 253

+421 2 65429 592

Ruedi Thalmann

[email protected]

+41 31 323 33 85

+41 31 323 32 10

Reinhard Probst

[email protected]

+49 531 592 5220

+49 531 592 5205

Otto Jusko

[email protected]

+49 531 592 5310

+49 531 592 5305

Vít Zelený

[email protected]

+420 257 288 387

+420 257 328 077

Barbara Smereczynska

[email protected]

+48 22 620 54 38

+48 22 620 8378

Edit Banreti

[email protected]

+36 1 4585 800 +36 1 4585 944

+36 1 214 3157

Maria Fernanda Saraiva

[email protected]

+351 21 2948160

+351 21 2948188

Bojan Ačko

[email protected]

+386 2 220 7581

+386 2 220 7990

Heikki Lehto

[email protected]

+358 9 4565350

+358 9 460627

Georges Vailleau

[email protected]

+33 1 40 43 37 00

+33 1 40 43 37 37

Rob Bergmans

[email protected]

+31 15 269 15 00

-31 15 261 29 71

Stefan Källberg

[email protected]

+46 33 16 56 26

+46 33 10 69 73


3

Time schedule

The time schedule was currently modified few times, reflecting the requirements of some participants. In the interim the standards were delivered back to the SMU in June 2001, in order they be equipped with a new ATA-carnet. The real time schedule is shown in the following table. Laboratory SMU METAS, part 1 PTB GUM MIRS (SMIS) MIKES SMU (no measurement) IPQ METAS, part 2 BNM-LNE SP OMH CMI NMi VSL SMU

Country SK CH DE PL SI FI SK PT CH FR SE HU CZ NL SK

Date September – October 2000 October – December 2000 December 2000 – February 2001 January – March 2001 April 2001 May – June 2001 June 2001 July – August 2001 August 2001 September – October 2001 October – November 2001 November – December 2001 December 2001 – February 2002 February – May 2002 June – November 2002

One abnormality has happened during the circulation – in the period between the measurements in CMI and in NMi VSL, the local damage (approximately 1,5 x 1 mm) to one edge of the granite square has been observed. Nevertheless, this damage seemed to have no effect to the measured parameters. 5

Description of the Standards

Two standards were calibrated: - granite squareness standard of rectangular shape (500x300x70) mm with four marked functional surfaces, weight 26 kg, - cylindrical squareness standard of steel with 102 mm diameter and 401,5 mm height with marked positions for the profile lines, weight 25 kg.

6

Measurement instructions

6.1 Definitions Zero point of the coordinate system – the intersection of the functional planes and the measurement plane (see Fig. 1).

Final Report of EUROMET Comparison of squareness measurements No: 570

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Local deviation from straightness – the distance between the measured point and the LS regression-line fitted through the measured profile in the measured plane; the positive value corresponded to the orientation outside from the material of square (see Fig. 1). Angle between fitting lines (in the case of granite standard) – interior angle gLS between the LS regression-lines fitted through the measured profiles AB and AC (see Fig. 1). The fitting line of the profile AC could be replaced by the envelope regression line (interior angle gB) – see Fig. 1. Angle between fitting line (in the case of the cylindrical standard) – the angles are understood as the interior angles between the corresponding LS regression-lines fitted through the measured profiles at 0°, 90°, 180°, 270° and the envelope plane of the basis (see Fig. 2).

Fig. 1 Specification of the granite square


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Fig. 2 Specification of the cylindrical square The measured profiles (in the case of the granite standard) are defined in the longitudinal axis in the middle of each functional plane. The measured profiles (in the case of cylindrical squareness standard) – the generatrix profiles at 0°, 90°, 180°, 270° (marked on the "TOP" plane) around the circumference of a cylinder. The starting point of measurement – 5 mm from the zero point (defined above). In the case of cylindrical squareness standard, four zero points are given by the inter-section of four generatrix profiles with BASIS plane. The density of measuring points of the profile shall be 0,5 mm (in extra cases should be allowed the integer multiple of 0,5 mm, max. 2 mm). Angles of the squares were measured using the technique currently applied by the participant. This method was described in details by each participant in the annex A2 "Measurement Report". The squares were measured in the position currently used in the laboratory – horizontally or vertically. 7

Measurement (calibration) results

Due to the properties of measurement devices, two following kinds of definition of the square angle are being applied: „envelope – LS regression“ and „LS regression – LS regression“. Of totally 12 NMIs involved, 4 NMIs are using the first definition


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(envelope – LS regression) and 9 NMIs are using the second one (LS regression – LS regression), while one NMI carried out the measurements applying both definitions. As for the final evaluation, it is necessary to choose a single definition from those two mentioned above (with the transformation between "envelope - LS regression"). The practical determination of the LS regression line is a simple mathematical operation, which doesn‘t differ from the theoretical definition. The practical determination of the envelope line is significantly more complicated, since it is determined by the contact points of the functional plane and the basis of the measurement device. It is difficult to describe this contact exactly, because of the flatness deviations of the basis and elastic deformations of the parts adjacent to the contact points. The following parameters had to be calibrated: - granite squareness standard of rectangular shape: interior angle gB between two lines AB and AC (envelope - LS regression) fitted through the measured profiles, and / or - granite squareness standard of rectangular shape: interior angle gLS between two LS regression-lines AB and AC fitted through the measured profiles, - cylindrical squareness standard: interior angles g0, g90, g180, g270 between the LS regression-line fitted through the measurement profiles at 0°, 90°, 180°, 270° and the envelope plane of the basis (resting on a surface plate), - local LS straightness deviation for all measured profiles (2 and 4) of both standards (results had to be reported in electronic format only).

7.1 Supplementary data - radius of the probe tip, - ambient temperature and its time drift during the measurement period, - description of the standard device on which the calibration has been performed, - description of the measurement methods and the data evaluation, - the method of calculation of the combined standard uncertainty uC (k = 1) related to the angle between fitting lines and uncertainty of local deviation from straightness, - measurement uncertainty budget.

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Measurement uncertainty

The combined standard uncertainty uC (k = 1) of all measurement results had to be estimated according to the ISO Guide for the Expression of Uncertainty in Measurement.


7

The participants were asked to report their measurement uncertainty budget in the annex A2 "Measurement Report". 9

Measuring devices and procedures

The measuring devices used by the participants are shortly described below. The required form of data reporting was designed in order to reveal possible error sources of individual NMIs. Despite of this procedure is more demanding for the evaluation than simple reporting of squareness and straightness deviation according to ISO 1101, the content of information provided by the participant was noticeably larger. That is why all participants had to report the measurement data corresponding to local straightness deviation and angles between LS lines. 9.1 SMU Description of measuring device The measuring device NME 90° (with 1300 mm straightness column, resting on a surface plate and air bearing carriage) compares form and angle position of vertical arm of measured rectangular standard with form and position of measuring column. Air bearing carriage bears two inductive sensors, which read a profile line of the measured square. The square standard under test is placed on a granite base plate so its horizontal arm is connected with this plate (envelope plane). The angle of square is defined by the fitting line (evaluated from individual measured points on vertical arm) and by the horizontal plane, given by the granite base plate of device. Such a determination of square was chosen by the device producers, because this way is usually used in industry. Procedure of measurement For the measurement of angle standard the well-known method of error separation technique (reversal technique) by means of “self-calibration” is used. This method allows the evaluation of the profile of square vertical arm without beforehand information about the profile of the measuring column. Process of the measurement consists of two steps – measurement of the square standard in 0° position and in 180° position. Procedure of result calculation: Measurement profiles are transferred to an Excel worksheet. The slope of the profiles is calculated by linear regression, resulting in the angle of the squareness standard. Deviation of each measured point from the LS regression line is the local straightness deviation.

9.2 METAS Description of measuring device


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Horizontal Measurements: Numerically controlled 800 mm straightness measuring device (STRAIGHTLine®) with air bearing carriage, combined with numerically controlled air bearing rotary table with Heidenhain RON 905 encoder. Vertical Measurements: Numerically controlled 1000 mm straightness column (SQUAREMaster®) with air bearing carriage, resting on a surface plate. Procedure of measurement Horizontal Measurements: Straightness measurement instrument is calibrated with reversal technique using a 1000 mm ceramic straight edge, resulting in error correction file. The granite squareness standard is resting horizontally on the rotary table at the 0° position, while probing line AB with the straightness measuring instrument. Subsequent rotation of granite square by 90°, then probing line AC. Vertical Measurements: The squareness standard (granite square or cylinder) is resting vertically on a surface plate. The device under test is rotated around its vertical axis to apply reversal error separation. Procedure of result calculation: Measurement profiles are transferred to an Excel worksheet. The slope of the profiles is calculated by linear regression, resulting in the angle of the squareness standard.

9.3 PTB For granite square Air bearing linear guideway, PTB construction, photoelectric linear encoder HEIDENHAIN LIDA 185, resolution 0,05 µm, measurement range L=1000 mm, indexing table ULTRADEX for 90° turn, reference: 90° angle block STARRETT, twoaxis electronic autocollimator Möller-Wedel ELCOMAT 2000, resolution 0,01", inductive displacement transducer Mahr Millitron 1204 with probe 1303, resolution 0,01µm, measurement range ±3µm. Description of measuring device Measurement of straightness deviation on line A – B from B to A, 90° turn of the object by use of indexing table, Measurement of 90° deviation by use of angle block and autocollimator, Measurement of straightness deviation on Line A – C from A to C Procedure of measurement controlled by computer Procedure of result calculation: Calculation of the straightness deviation from the regression fitting lines, Calculation of the 90° angle deviation from the slope difference of the regression fitting lines,


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Correction of the straightness deviation of the guideway by reversal technique and of the angle deviation of the 90° angle block from calibration. Software used: Microsoft EXEL 97


10

For cylinder square Description of measuring device The measuring device used for calibration of cylindrical square standard was developed by PTB, based on the form tester MFU 8 (Mahr). With this instrument the measurands diameter, roundness, straightness, parallelism and squareness of cylindrical and spherical objects can be calibrated in one single set-up. Procedure of measurement The straightness deviations of the z-guide amount to 0,15 µm over 400 mm. The angle between C-axis and z-guide can be adjusted within about ± 2 µm/ 400 mm (1´´). A complete reversal technique has been used to correct both, the straightness deviations and the orientation of the z-axis.

9.4 GUM Description of measuring device Coordinate measuring machine SIP CMM5. Procedure of measurement Granite square. The angle "A" between corresponding LS fitting lines was measured in four positions in XY measuring plane of the machine in order to eliminate squareness and straightness deviation of the machine axes. In every position the angle "A" was measured five times. The LS fitting lines were measured in two ways. Firstly by probing points using special program for line measurement. Secondly by probing points using scanning mode. The density of measuring points on each line was about 0,5 mm in both used methods of measurement. These two methods of measurement were used in order to compare obtained results. The cylindrical square was measured in vertical position in ZX measuring plane of the machine. It was placed on the granite surface plate which was set on measuring table of the machine. This surface plate established a measuring basis. The corresponding LS fitting lines were measured using two methods of measurement (in the same way as during measurement of granite square). Firstly by probing points using special program for line measurement. Secondly by probing points using scanning mode. The density of measuring points on each line was about 0,5 mm in both used methods of measurement. The angles between the respective LS fitting lines (0°, 90°, 180°, 270°) and envelope plane of the basis were measured five times. The reference system was established according to the axis of the cylindrical square. These two methods of measurement were used for comparison of the results. Procedure of result calculation: Granite square: In each measuring position the value of the angle "A" was calculated as a mean value obtained from five measurements. The calculations were carried out for the two methods of measurement. The angle "A" between the respective LS fitting lines


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was calculated as a mean value obtained from four positions of the granite square on the measuring table of the machine. Calculations for the two methods of measurement were done separately. As regards the local straightness deviation the corresponding LS fitting lines were estimated from all measured points probed only in scanning mode because the software of the machine does not show the values of points using special program for line measurement. Then the distances between the respective points and corresponding points lying on these lines were calculated. As a result the worst deviations were chosen from all measured lines for each respective LS fitting line. Cylindrical square: The angles between the respective LS fitting lines (0°, 90°, 180°, 270°) and the basis were calculated as a mean value obtained from all measurements made for the each line. The calculations were carried out for the two methods of measurement separately. As regards the local straightness deviation of the respective LS fitting line the calculations were carried out in the same way as in case of granite square. As a result the worst deviations from the respective LS fitting lines were chosen from all measured lines.

9.5 MIRS (SMIS) Description of measuring device: Coordinate measuring machine CMM Zeiss UMC 850. Procedure of measurement: - Square: The granite square was measured in horizontal position (plane XY of CMM). It was put on the CMM table. Line AC was positioned in Y axis direction and served as a basis element for the coordinate system transformation (from CMM to the square). The square was positioned very precisely along Y axis (physically).The angle was measured in positions A (probing direction for line AB: +Y) and B (probing direction for line AB: -Y). The line AC was in both cases probed in –X direction. When the square was turned from position A to B, the line AC remained in the same position. The result was calculated as a mean value of both measured angles. The whole measurement was repeated 4 times and the mean value was calculated. Straightness was measured separately. Lines AC and AB were probed in two opposite directions (+ X and – X). The beginning and ending points were set as required by the instructions. Density of points was 2 mm because the results were transferred manually to PC and the number was anyway quite high. The result was calculated as a mean value of point coordinates in position A (probing direction +X) and in position B (probing direction -X). - Cylinder: The cylinder was measured on the CMM in vertical position. It vas put on a very precise Heidenhain granite plate (in fact this is a stand used for measurements with


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incremental precise probes). This plane served as an envelope plane of the cylinder basis. The envelope plane served as a basis element for the coordinate system transformation (from CMM to the cylinder). The position of the cylinder regarding measurement lines was first positioned as position A. All lines were measured in this position and angles were calculated (g0°A, g90°A, g180°A, g270°A). After that the cylinder was turned into position B. The lines were measured again and the angles (g0°B, g90°B, g180°B, g270°B) were calculated. The result was calculated as a mean value of both measured angles (A and B). Straightness of lines was measured separately. The cylinder was put in horizontal position along Y axis and each line was measured in two positions(position A – probing direction –X, position B – probing direction +X). The beginning and ending points were set as required by the instructions. Density of points was 2 mm from the same reason as by the square. The result was calculated as a mean value of point coordinates in position A and in position B.

9.6 MIKES Description of measuring device: The straightness was measured by using the vertical movement of Talyrond 262 cylindricity measuring machine made by Rank Taylor Hobson Ltd. The vertical movement “L” is 510 mm and the horizontal movement is 200 mm. The straightness deviation of the vertical movement is 630 nm and the repeatability of the movement is 65 nm. The machine is mostly used for roundness and cylindricity measurements. The squareness was measured with squareness measuring machine made by Mikes. Main parts of the machine are: the surface plate 1600 x 800 mm (made by Mikes), the granite square 1000 x 600 x 100 mm (made by Planolith), the unit for movements “L” 1000 mm and “y” 250 mm (made by IF Werner GmbH) and several inductive sensors (made by Tesa Sa). The flatness of the surface plate is 2 µm (limited area), The flatness of the granite square is on 1000x100 mm surface 3,7 µm and on 600x100 surface 2,4 µm, but the straightness on the used area is (of surface 1000x100 mm) is 0,5 µm. The deviation of the angle between surface plate and granite square is 1,5” (on the used area). The machine is used for calibration of squares. Procedure of measurement: The straightness was measured by comparison using the straightness of the Talyrond 262 vertical movement as reference. The “squareness” was measured by repeating the measurements when the standard has been turned 180° with the squareness measuring machine. Procedure of result calculation:


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The mean of three straightness results has first be corrected with the actual values of the vertical movement and then fixed to the 0,5 mm division. From this values the LS-regression line has been calculated and used as reference to the given values. The squareness has been calculated using a mean of five measurements for each measured surface (granite square lines A-B and C-D and from the cylindrical standard the lines 0°, 90°, 180° and 270°). From the lines only the direction of the LS-regression line is used. The results of this calculations has been corrected with the difference of “diameter”. 9.7 IPQ The description of measurement system is not described here, because this NMI asked to be excluded from the project.

9.8 BNM-LNE Description of measuring device: 3D Measuring machine SIP CMM5, equipped with measuring probe head. The machine is traceable through laser interferometer for X and Y axis. Perpendicularity of X axis versus Y axis is checked with a ball plate and results are taken into account in the software. Procedure of measurement (for granite square): The probed points are situated on a line which is situated in the middle of each face. The square have been measured in 4 positions. Procedure of measurement (for cylindrical square): 391 points on each generatrix line and 24 on the face. The cylinder have been measured in 2 positions, first with the axis in X machine direction and second with the axis in Y machine direction. Procedure of result calculation: For granit square The result is the mean value of the four measurements. Angle are given by the angle between the LS lines For cylindrical square Angle are the mean value of the 2 measurements Straightness No error separation technique have been employed


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9.9 SP Description of measuring device: Straightness measurements: A form-measuring instrument, type Tr 260, manufactured by Rank Taylor-Hobson. The pillar is 500 mm (max L) and on high resolution the pick-up’s measuring range is ±200 µm with resolution 12 nm. Straight angle measurements: Comparison against a reference angle standard using a height-measuring instrument in combination with a dial-gauge. In this case the height-measuring instrument is used only as a vertical column holding the dialgauge, which measures the deviations in interest. Procedure of measurement (for granite square): Cylindrical straightness measurements: An error separation technique is used with Tr 260; each line along the cylinder’s surface is measured twice with the cylinder rotated 180 degrees between each measurement. By combining the two measurements, the straightness deviation of the instrument is removed. Straightness measurements on granite square: Using Tr260, the measured profiles are corrected by subtracting the instruments form error (obtained from calibration with a 500 mm cylinder standard and error separation). Deviation from straight angle: Comparison with reference angle standard in two heights, 10 mm and 390 mm. Several measurements have been made, with the object and reference placed in different positions on the plane table. A typical measurement series consists of three repeated measurements on the reference square, three measurements on the object and finally back to the reference again. In order to reduce effects from local surface variations, a mean value of the dialgauge’s readings over a 1 mm distance was used. Procedure of result calculation: Cylindrical straightness measurements: The instrument’s straightness error is removed by, for each line (0°, 90° etc.), taking the sum of two unfiltered straightness curves measured in different directions (rotated 180° in between) and then divide this sum by 2. Since the measuring points are separated by only approximately 0,15 mm, the reported straightness profiles have been obtained taking the values nearest every whole 0,5 mm. Finally the profiles have been aligned using a least square fit. Straightness measurements on granite square: The measured profiles have been corrected by subtracting the instrument’s deviation from straightness in the appropriate measurement range (5 mm to 295 mm or 5 mm to 495 mm). The measuring points are separated by only approximately 0,10 mm – 0,20 mm so the reported straightness profiles have been obtained taking the values nearest every whole 0,5 mm point. Finally the profiles have been aligned using a least square fit. Deviation from straight angle: The following method has been used for both the cylinder and the granite square. The calibration certificate for the reference square (400x300x55 mm) expresses the deviation from straight angle as the angle between “envelope – LS regression”. When the reference square is standing on a plane, this angle correspond to certain


15

deviations (expressed in µm) from a perfect straight angle, depending on the height above the table and the straightness profile of the reference square. Since the measurements are performed by comparing measured deviations (using a “heightmeasuring instrument” in combination with a dial-gauge) at 10 mm and 390 mm, basically only these two height are of interest. Below, 10 mm and 390 mm are referring to the measured deviations in these heights: X (µm) = Object (390 mm – 10 mm) – Reference (390 mm – 10 mm) X is then translated to the object’s “envelope - LS regression”-angle by taking into account the local straightness profiles of both the object and the reference.

9.10 OMH Description of measuring device: Three coordinate measuring machine SIP CMM5 Procedure of measurement: No special corrections for the machine parameters were applied (as it is measured for normal customers). Granite: The planes involving AC and AB were probed. The intersection line of the 2 planes was used for spatial alignment, the normal vector of the plane AB for the planar alignment and the intersection between the mentioned line and the upper surface for 0 setting. The granite was measured in the position as indicated on Fig. 1 of the written procedure (AC in x direction, AB in y). There was not enough time to measure the standards in reversed positions but the straightness error of the machine is within the value of max.0,4 mm measured by laserinterferometer and the perpendicular error of the x-y axis is less than 0,3” according to previous measurements. These values are taken into account in the uncertainty determination. The measurement was repeated 5 times. The mean value of 5 is given as the result. Cylinder: The plane was probed and its normal vector was defined as the element for spatial alignment (x axis) and for x=0. The cylinder was taken from 6 points and used for 0 setting on y and z. The cylinder gauge was measured first in the position where 90-0-270 could be probed and after with rotating the cylinder by 180° in the position where 270-180-90 could be measured. With this method a rough estimation could be taken (for 90 and 180) if the deviation comes from the straightness of the machine or of the cylinder. The measurements were repeated 5 times.


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Procedure of result calculation: The final results were calculated as the mean of 5 measurements. To determine the repeatibility of the measuring process, the standard deviation was calculated and used. No special correction was taken like in the normal procedure for customers. The regression line and the individual straightness deviation were calculated by the Concerto software.

9.11 CMI Description of measuring device: Three coordinate measuring machine SIP CMM5 Procedure of measurement: Granit square: 5 times 2 measurements 180° rotated to eliminate systematic errors Steel cylinder: 3 times 4 measurements 90° rotated to eliminate systematic errors Procedure of result calculation: Straightness: pointwise average from all pair Angle: average from all pair

9.12 NMI VSL Description of measuring device: Coordinate Measuring Machine Zeiss UC550, Measuring volume 1200x550x450 mm Procedure of measurement: Generally speaking, our CMC calibration (quality system) does not include the option of a local straightness analysis for customers’ calibrations. Instead of the measured profile or its residuals to the LS-line, our software returns one value for the global straightness only. Therefore, the profile/residuals presented with our work were sampled independently from the normal calibration procedure in order to still allow comparison. Granite square: The two relevant sides of the granite square are probed with the ordinary ball probe of the CMM. The calibration is performed 12 times applying the reversal method, eliminating the systematic deviation of the CMM. The


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measurement and its results are completely done with the software of the CMM. First the basis line (short arm) is probed and a LS-line fitted to it. Then the long arm is probed relative to the LS-line of the short arm. The software then automatically returns the global straightness of the long arm and the angle between the LS-lines through the long arm and the basis line. In addition and for verification purposes only, the electronic level is applied to determine the straightness of the long arm. Cylindrical square: An electronic level with a pitch of 20mm is attached to the CMM as a probe. It is applied to measure the straightness of the cylinder. At each measurement point, the slope of the level is recorded. The distance between the measurement points equals the pitch of the level, 20 mm. The profile is then sequentially reconstructed by multiplying the slope with the pitch and adding it to the previous profile height. The angle of squareness is determined by the angle between the LS-line through the straightness profile and the LS-plane through the basis plane of the cylinder, see 3.1.2 for details. The basis plane of the cylinder is measured with an ordinary CMM ball probe and the CMM software fits an LS-plane to the basis plane. Relative to this LS-plane, the first and the last point of the profile are probed with the stylus. Applying the reversal method and changing the position and orientation of the square a total of 8 times, each profile is measured 4 times. The systematic deviation of the CMM is thus eliminated. Procedure of result calculation: Granit square: The basis line (short arm) is probed at 15 points with 5 mm spacing. The CMM software then fits a LS-line through these points and adjusts its coordinate system so that this line becomes the new x-axis. Then the long arm is probed at 24 points with 5 mm spacing, relative to the new coordinate system. The software of the CMM determines then the global straightness of the sides as well as the angle through the least-squares lines through the two profiles, see also “5. Comments”. This measurement is repeated 12 times at different positions and orientations of the square, using the reversal method. Cylindrical square: Applying the reversal method and changing the position and orientation of the square a total of 8 times, each profile line is measured 4 times.

10 Results In the following analyses the individual NMIs were given in the order corresponding to the real time schedule. IPG asked to exclude their results from the measurement analysis. After the first evaluation at the pilot laboratory, unexpectedly large deviations corresponding to the angles and the shape of profile lines were found. Because of this, all participants were asked to check the provided data. After collecting the corrected data, they were analysed again.


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10.1 Granite square 10.1.1 Straightness Some NMIs provided data with random disturbances, as e.g. bounce of measuring tip, dirt etc. These were for calculation of reference profile eliminated if the local deviation exceeded twice the value corresponding to the dispersion of remaining points around the LS regression line. As the consequence of the surface structure of the granite square, the P-V value of short-period waviness is approximately 12 µm. For this reason, this component was eliminated from the measured profiles by the filtration using the drifting arithmetic mean with length of 5 mm. These modified data were used just for the calculation of the most conceivable middle profile (reference profile). Since not all NMIs measured with step 0,5 mm, the linear interpolation of the measured points with increment of 0,5 mm has been carried out (with the exception of the NMi VSL). At the PTB, the local straightness was defined by the following way: the zero point of the coordinate system was located to the centre of profile line and in the case of profile AB the orientation of the L coordinate was opposite to other participants (direction BA). Exact position of the zero point with respect to its definition according to chapter 6 was not given. Since the length measured at PTB was smaller than its original length, the coordinator after agreement PTB transformed the first measured point to the intersection of the profile with the bevel edge. By means of graphical comparison of the shape of profile lines there was found, that the „L“ coordinate stated at MIKES was in fact shorter by approximately 15 mm. For this reason, the multiplication coefficient k = 1,040107 was applied to all points of the profile AC. In the case of profile line AB, the „L“ coordinate was correct. The weighted mean profile (reference profile) was calculated, applying the weighting coefficients

(

w = u cNMI

)

-2

(1)

The profile of NMi VSL was not contributing to the weighted mean, since it did not correspond to the conditions according to Chapter 6 (distances between adjacent measured points were 20 mm) and the profile AC was not measured at all (the profile of NMi VSL for the granite square was supplied as a bonus for verification only). Uncertainties of reference profiles: mean of uC = 0,03 µm (581 values)

max. of uC = 0,09 µm

From the individual NMi profiles, without filtration, modified by interpolation only - step 0,5 mm (only in PTB by means of transformation and in MIKES by correction of length gauge), there were calculated the AB and AC profiles deviations from the reference profile Since the profile lines provided by GUM seem to be too far from the weighted mean and their shape is very different from the mean profile, there is possible to handle with them as they are out of tolerance (application of the Grubbs test for local straightness is due to the input data too complicated). Similarly, the profiles measured at NMi VSL


19

were not included in the calculation of weighted mean, from the reason mentioned above. For this reason was the weighted mean determined again, but after the exclusion of the mentioned NMIs. The profiles measured by the individual NMIs, reference (weighted mean) profile and deviations from the reference profile are shown in the following graphs. The scale if it possible is uniformed. Profiles, measured by the individual NMIs:


20


21


22


23

Final Report of EUROMET Comparison of squareness measurements No: 570 Reference profile:

Deviations from the reference profile for profile AB:

24


25


Analogically, for the profile AC:

26


27


28

Comments to the graphs: The scale was chosen uniform. In order to consider the stability of devices, evaluated were all (incl. repeated) measurements of NMIs. In the case of METAS (the measurements of cylinder square were not completed due to the problems with measuring device, in the second stage the repeating of measurements of both standards) the differences fit into uC. In the case of SMU, the differences were caused by the replacement of axial inductive probe by the lever type probe in 2002. Kinematics properties of axial probe combined with elasticity of their holders caused the additive deviations of indicated profile. The measurements (SMU 1 and METAS 1 from year 2000) were not included to calculation of the reference profile.

10.1.2 Squareness Measuring facilities of individual NMIs are based on two used definitions of regression profile lines („envelope – LS regression“ and „LS regression – LS regression“). For the sake of uniformity, the angle between envelope line and LS regression line of line AC was determined. The value of this angle has been estimated from the resulting reference profile-graphs of AC profile: gLS - gB = -0,07”. The measurements (SMU 1 and METAS 1 from year 2000) were not included to calculation of the reference profile. Applying this correction, all results were transformed to the system „LS regression – LS regression“ and the mean value of angle was calculated, using the weighting coefficient „w“ the weighted mean value of


29

angle and deviations of gLS from it. Since the values of gLS were differing significantly, the test of statistic consistence of data by means of Birge ratio (see Annex A) was carried out. The calculated value RB = 1,39 is nearly equal to the critical value (for coverage factor of k = 2) RBcrit = 1,34. Therefore the Grubbs test has been applied (see Annex A) both to the values gLS and to the differences from the weighted mean. On the basis of such analysis there is obvious, that values of three NMI MIKES are possible to be considered as outliers. After the exclusion of results of these NMI, the weighted mean was calculated again. The change of weighted mean (0,03”) was after exclusion of these NMIs negligible. Results of this analysis are contained in the following table:


30

Angle between: LS regression-fitting line and basis (gB) or LS regression-fitting line (gLS) (”): gLS - gB = -0,07 after normalisation:

from NMI: gBasis SMU 2000 -1,60 METAS horiz. Dec. 2000 PTB GUM MIRS MIKES -0,35 METAS horiz. Aug. 2001 METAS vert. 89° 59’ 58.73” Aug. 2001 BNM-LNE SP -1,48 OMH CMI NMi VSL SMU 2002 -1,40 mean weighted mean I weighted mean II

gLS 89° 59’ 58.44” -1,55 89,99956° 89° 59´ 58,4” 89° 59’ 58.66”

89° 59’ 58.52’’

difference g - (weighted mean)

Meas. Device

Grubbs test for:

0,20 0.12

straight. uc Angle (µm) -1,60 -1,53 0,20 0,10 Square-device -1,56 0,12 0,08 Rotary Table

Square-device linear guideway

-0,12 -0,15

-0,08 -0,11

-0,509 -0,592

-0,323 -0,406

0,07 0,24 0,45 0,3 0.12

-1,55 -1,58 -1,60 -0,35 -0,28 -1,34

linear guideway CMM CMM Talyrond 262 linear guideway

-0,14 -0,18 -0,19 1,13 0,07

-0,10 -0,14 -0,15 1,17 0,11

-0,565 -0,656 -0,699 2,853 0,000

-0,380 -0,471 -0,514 3,039 0,186

0.13

-1,27 -1,20 0,13

0,12 Square-device

Square-device

0,21

0,25

0,377

0,562

-1,48 -1,48 -1,41 -0,90 -1,48 -1,52 -1,40 -1,33

0,60 0,25 0,50 0,28 0,13 0,10

CMM RTH Tr260 CMM CMM Bridge 20mm Square-device Birge ratio RB =

-0,07 0,00 0,51 -0,07 -0,11 0,08 1,39 1,34

-0,03 0,04 0,55 -0,03 -0,07 0,11 1,38

-0,376 -0,188 1,185 -0,366 -0,484 0,020

-0,191 -0,003 1,370 -0,180 -0,299 0,205

Gp 5% Gp 1%

2,507 2,755

Angle uc

0,4 0,31 89,99975° 0,5 89,99959° 0.00017° 89° 59’ 58.48” 0,67 0,20

gB (")

(excl. SMU 2000, METAS 2000) (excl. SMU 2000, METAS 2000) (excl. SMU 2000, METAS 2000, MIKES) uint uxt

gLS (")

-1,31 -1,41 -1,44 0,04 0,06

uc (")

0,07 0,24 0,45 0,30 0,12

0,40 0,31 0,50 0,61 0,67 0,20

0,08 0,34 0,30 0,31 0,08

90° Angle block CMM CMM Square-device Rotary Table

CMM Ref. Square CMM CMM CMM Square-device

Straightness

RB (crit.) =

diff I gLS

diff II gLS

gLS

diff I


31

Angle deviations of individual NMIs from the weighted mean are shown in the following graph:

Comments to the graph: Angle deviations of first 5 NMIs compared to the values of remaining participants indicate the suspect of change of measurand itself, i.e. the change of angle of measured artefact (casual change of profile as the consequence of the contact with the base plate of measuring facilities). Nevertheless, after the analysis of profile lines of both arms at the beginning and at the end of comparison no significant change could be revealed, which could support this hypothesis. Analysing the data of individual NMIs, for MIRS there must be taken into account that angles and local straightness deviation are independent (they were measured separately).

10.2 Cylinder Square 10.2.1 Straightness Similarly as in the case of granite square, some NMIs provided data incl. the random disturbations, as e.g. bounces of measuring tip, dirt etc. These were excluded from the calculation of reference profile if the local deviation exceeded twice the value corresponding to the dispersion of remaining points around the LS regression line. As the consequence of the artefact surface finishing, the P-V value of short-period waviness of generatrixes of the cylinder is approximately 1,5 µm. For this reason, the short-periodicity component was eliminated by means of drifting arithmetic mean with


32

length of 5 mm. These modified data were used just for the calculation of the most conceivable middle profile (reference profile). Since not all NMIs measured with step 0,5 mm, the linear interpolation of the measured points with increment of 0,5 mm has been carried out (with the exception of the NMi VSL). From the comparison of graphs there was found, that „L“ coordinate MIKES was shorter by approximately 15 mm. For this reason, the coefficient k = 1,040107 has been applied for all the measuring points. Similarly as in the case of granite square, applying the weighting „w“ coefficient the weighted mean profiles corresponding to 0°, 90°, 180° and 270° were calculated. Due to the two-fold measurement at the SMU (SMU 1, SMU 2) and large shape difference of measured results obtained (GUM, MIRS, CMI), four data sets (SMU 1, GUM, MIRS, CMI) were excluded from the reference profile calculation. After the calculation of the weighted mean, the results of GUM, MIRS and CMI are deemed to be outlying. Likewise as in the case of granite square, the application of Grubbs test is too complicated due to the input data. Moreover, from the course of lines is obvious, that at GUM the sign for the line 180° has been changed, at CMI the sign of „L“ coordinate was changed for all lines. Since all three mentioned NMIs checked their values after the information of the pilot and they confirmed data provided before, the evaluation was done without change of originally sent data set. The profiles, measured by the individual NMIs, reference (weighted mean) profile and deviations from the reference profile, are shown in the following graphs. The scale if it possible is uniformed. Uncertainties of reference profiles: mean of uC = 0,02 µm (792 values)

max. of uC = 0,10 µm

Final Report of EUROMET Comparison of squareness measurements No: 570 Profile, measured by the individual NMIs. Profile 0°:

33


Profile 90°:

34


35

Final Report of EUROMET Comparison of squareness measurements No: 570 Profile 180°:

36


Profile 270°:

37


38

Final Report of EUROMET Comparison of squareness measurements No: 570 Reference profile:

Deviations from the reference profile for profile 0°:

39


40

Final Report of EUROMET Comparison of squareness measurements No: 570 Deviations from the reference profile for profile 90°:

41


Deviations from the reference profile for profile 180°:

42


43

Final Report of EUROMET Comparison of squareness measurements No: 570 Deviations from the reference profile for profile 270°:

44


45

10.2.2 Squareness Correspondingly as for the granite square, the mean value of angles of LS regression lines with envelope basis plane was calculated, using the “w” coefficient and the deviations of g from it. Since the values of g were too differing each other, the test of statistic consistence of data by means of Birge ratio (see Annex A) was carried out. The calculated value RB = (4,30; 1,10; 4,26; 1,10) is greater than critical value (for coverage factor of k = 2) RBcrit = 1,38. Therefore the Grubbs test was applied (see Annex A) both for the values of g and for the differences from the weighted mean. From the comparison of results of both tests there is obvious, that values of angles provided by GUM and MIRS can be considered as outlying. After the exclusion of results of SMU 2000 (SMU 1), GUM and MIRS, the weighted mean value was calculated repeatedly. Results of this analysis are given in the following table:


46

Angle between: LS regression-fitting line and basis from NMI: NMI SMU 2000 PTB GUM MIRS MIKES METAS vert. BNM-LNE SP OMH CMI NMi VSL SMU 2002

g0°

after normalisations: g90°

g180°

g270°

Angle uc

2,08 -0,1 -2,81 -0,35 0,2 2,8 -0,2 -3,2 -0,1 0,5 90,00095o 90,0004° 89,99950o 90,00025o 0,56 89° 59´ 56,4” 90° 0´ 0” 90° 0´ 2,9" 89° 59´ 59,3” 0,45 2,4 0,5 -2,2 -0,4 0,29 90° 0’ 2.55” 90° 0’ 0” 89° 59’ 57.02” 89° 59’ 59.62” 0,22 90° 00' 02,0" 90° 00' 00,4" 89° 59' 57,4" 89° 59' 59,4" 1 2,44 -0,09 -3,31 -1,13 0,39 89,99989° 90,00001° 89,99969° 90,00004° 0,8 90,00057° 90,00015° 89,99957° 89,99999° 0,00014° 90° 00’ 02.46” 89° 59’ 59.99” 89° 59’ 57.35” 90° 00’ 00.07” 0,75 2,35 -0,13 -3,25 -0,60 0,2 mean weighted mean I (excl. SMU2000) weighted mean II (excl. SMU2000, GUM, MIRS) uint uext

g0° 2,08 2,8 3,42 -3,6 2,4 2,55 2 2,44 -0,396 2,052 2,46 2,35 1,87 2,06 2,368 0.41

Meas. Device uc (")

g90°

g180°

g270°

-0,1 -0,2 1,44 0 0,5 0 0,4 -0,09 0,036 0,54 -0,01 -0,13

-2,81 -3,2 -1,8 2,9 -2,2 -2,98 -2,6 -3,31 -1,116 -1,548 -2,65 -3,25

-0,35 0,2 -0,1 0,5 0,9 0,56 -0,7 0,45 -0,4 0,29 -0,38 0,22 -0,6 1 -1,13 0,39 0,144 0,8 -0,036 0,504 0,07 0,75 -0,60 0,20

0,22 -2,23 0,06 -2,56 0,051 -2,863 0,10 0.11 0.41

-0,29 -0,41 -0,467 0.11

straight uc (µm) 0,1 0,05 0,48 0,3 0,12 0,1 0,6 0,13 0,6 0,29 0,07 0,1

Angle

Straightness

Square-device MFU 8 - PTB CMM CMM Square-device Square-device CMM Ref. Square CMM CMM CMM Square-device

Square-device MFU 8 - PTB CMM CMM Talyrond 262 Square-device CMM RTH Tr260 CMM CMM Bridge 20mm & level Square-device


difference: g - weighted mean I NMI SMU 2000 PTB GUM MIRS MIKES METAS vert. BNM-LNE SP OMH CMI NMi VSL SMU 2002 Birge ratio RB = RB (crit.) =

dif g0° dif g90° dif g180° dif g270° 0,021 0,741 1,356 -5,659 0,341 0,491 -0,059 0,376 -2,455 -0,012 0,401 0,287 4,30

-0,201 -0,301 1,385 -0,101 0,399 -0,101 0,299 -0,145 -0,065 0,485 -0,111 -0,229

-0,324 -0,714 0,760 5,386 0,286 -0,494 -0,114 -0,750 1,370 1,012 -0,164 -0,766

1,10 4,26 1,38

47

Grubbs test for gLS 0

for gLS 90

for gLS 180

for gLS 270

0,079 c -0,750 -0,371 -0,131 0,329 0,501 -0,966 -0,599 0,355 1,311 0,827 2,563 0,220 2,298 -0,271 -2,865 -0,535 2,968 -0,811 0,029 0,291 0,541 -0,014 -0,228 0,049 0,370 -0,535 -0,470 -0,189 -0,171 0,080 0,325 -0,248 -0,616 -0,719 0,312 -0,729 -0,663 -1,646 0,573 -1,180 -0,458 0,620 0,829 0,375 0,108 0,627 0,367 0,479 0,499 0,322 -0,557 -0,277 0,685 -0,166 0,262 -0,811 -0,630 -0,607 s = 1,901 0,465 1,710 0,515 1,10 Gp 5% 2,412 Gp 1% 2,636

for diff for diff for diff for diff 0° 90° 180° 270° 0,011 -0,421 -0,189 0,155 0,390 -0,631 -0,418 0,642 0,713 2,906 0,445 2,556 -2,978 -0,211 3,153 -0,527 0,179 0,838 0,168 0,057 0,258 -0,211 -0,289 0,096 -0,031 0,628 -0,066 -0,332 0,198 -0,304 -0,439 -1,401 -1,292 -0,135 0,802 1,118 -0,006 1,018 0,593 0,732 0,211 -0,232 -0,096 0,973 0,151 -0,480 -0,449 -0,323 1,90 0,477 1,709 0,513

difference II: g - weighted mean II diff g0° -0,288 0,432 1,052 -5,968 0,032 0,182 -0,368 0,072 -2,764 -0,316 0,092 -0,022

diff g90° -0,151 -0,251 1,389 -0,051 0,449 -0,051 0,349 -0,141 -0,015 0,489 -0,061 -0,180

diff g180° 0,053 -0,337 1,063 5,763 0,663 -0,117 0,263 -0,447 1,747 1,315 0,213 -0,390

diff g270° 0,117 0,367 1,367 -0,233 0,067 0,087 -0,133 -0,663 0,611 0,431 0,537 -0,128


48

Angle deviations of individual NMIs from the weighted mean are in the following graph s, the scale is uniform:


49


50

Comment to graphs: Both NMIs are using CMM. It would be interesting to analyse the measurement procedure with respect of the equal error compensation of CMM for the X and Y axes. Analysing the results of individual NMIs, it should be kept in mind, that at MIRS the angles and straightness deviation were measured separately. The graphs indicate an underestimation of uncertainties by some NMIs, which caused a deviation of the reference value.

11 Conclusion In order to compare the individual deviations mutually (25 profiles for the granit square and 44 profiles for the cylinder) the graphical illustration of “standard deviations“ and both extreme values (max. and min.) of deviations was created. Granit square, table of angels and profiles: NMI

SMU 2000 METAS horizontal 1 PTB GUM MIRS MIKES METAS horizontal 2 METAS vertical BNM-LNE SP OMH CMI Nmi VSL SMU 2002

diff. gLS

-0,08 -0,11 -0,10 -0,14 -0,15 1,17 0,11 0,25 -0,03 0,04 0,55 -0,03 -0,07 0,11 Gp 5%=

Grubbs test diff. gLS

-0,33 -0,41 -0,39 -0,48 -0,52 3,09 0,19 0,57 -0,19 0,00 1,39 -0,18 -0,30 0,21 2,51

sd AB

0,18 0,09 0,13 0,44 0,21 0,24 0,07 0,15 0,20 0,20 0,25 0,24

Min AB

-0,48 -0,29 -0,52 -1,62 -1,35 -0,89 -0,32 -0,62 -0,69 -0,80 -0,79 -0,80

Max AB

sd AC

Min AC

Max AC

0,48 0,35 0,54 1,11 0,73 1,00 0,27 0,53 0,74 0,68 0,70 0,83

0,07 0,06 0,10 0,47 0,23 0,22 0,05

-0,21 -0,28 -0,32 -1,25 -0,58 -0,80 -0,23

0,27 0,22 0,41 1,01 0,86 0,53 0,19

0,16 0,18 0,18 0,18

-0,54 -0,55 -0,50 -0,84

0,49 0,58 0,50 0,60

0,11 -0,42 0,33 0,06 -0,21 0,21

Final Report of EUROMET Comparison of squareness measurements No: 570 Granit square, graphs of profiles:

51


52

Granit square, graphs of angels:

Cylinder square, table of profiles: NMI SMU 2000 PTB GUM SMIS MIKES METAS vertical BNM-LNE SP OMH CMI SMU 2002

sd 0° 0,09 0,05 0,39 0,86 0,05 0,02 0,10 0,04 0,17 0,33 0,05

Min Max 0° 0° -0,13 0,48 -0,17 0,15 -1,80 0,71 -2,51 1,65 -0,17 0,12 -0,12 0,05 -0,31 0,34 -0,14 0,09 -0,51 0,40 -0,88 0,94 -0,08 0,16

sd Min Max sd 90° 90° 90° 180° 0,10 -0,15 0,50 0,16 0,02 -0,18 0,06 0,03 0,40 -1,66 0,91 1,15 0,35 -1,00 0,80 0,70 0,05 -0,17 0,10 0,06 0,02 -0,09 0,15 0,02 0,10 -0,40 0,26 0,11 0,04 -0,11 0,09 0,03 0,09 -0,28 0,30 0,17 0,30 -0,87 0,96 0,34 0,04 -0,08 0,15 0,06

Min Max sd Min Max 180° 180° 270° 270° 270° -0,24 0,70 0,15 -0,23 0,55 -0,23 0,07 0,02 -0,18 0,06 -1,77 2,66 0,80 -1,33 2,27 -1,41 1,53 0,79 -1,67 1,56 -0,17 0,16 0,04 -0,20 0,11 -0,13 0,06 0,02 -0,07 0,05 -0,45 0,38 0,13 -0,43 0,33 -0,10 0,07 0,04 -0,13 0,11 -0,43 0,54 0,11 -0,41 0,27 -1,12 0,91 0,21 -0,61 0,61 -0,10 0,20 0,04 -0,08 0,21

Final Report of EUROMET Comparison of squareness measurements No: 570 Cylinder square, graphs of profiles:

53


54


55

Cylinder square, table of angles: NMI

SMU 2000 PTB GUM MIRS MIKES METAS vertical BNM-LNE SP OMH CMI NMi VSL SMU 2002

diff II diff II g0° g90°

Grubbs Grubbs diff II diff II Grubbs Grubbs test test test test g180° g270° diff. 0° diff. 90° diff. 180° diff. 270°

-0,29 0,43 1,05 -5,97 0,03 0,18 -0,37 0,07 -2,76 -0,32 0,09 -0,02

0,05 -0,34 1,06 5,76 0,66 -0,12 0,26 -0,45 1,75 1,32 0,21 -0,39

-0,15 -0,25 1,39 -0,05 0,45 -0,05 0,35 -0,14 -0,02 0,49 -0,06 -0,18

Cylinder square, graphs of angles:

0,12 0,37 1,37 -0,23 0,07 0,09 -0,13 -0,66 0,61 0,43 0,54 -0,13

0,01 0,39 0,71 -2,98 0,18 0,26 -0,03 0,20 -1,29 -0,01 0,21 0,15

-0,42 -0,19 -0,63 -0,42 2,91 0,45 -0,21 3,15 0,84 0,17 -0,21 -0,29 0,63 -0,07 -0,30 -0,44 -0,14 0,80 1,02 0,59 -0,23 -0,10 -0,48 -0,45 Gp 5% = 2,41

0,15 0,64 2,56 -0,53 0,06 0,10 -0,33 -1,40 1,12 0,73 0,97 -0,32


56


57

This regional supplementary comparison was the first comparison in this field. It has provided the independent information about metrological properties of measuring equipment and method comparing to participated NMIs. Comparison results of squareness were in the good conformity with probable values of standards for most of participated laboratories. Some NMIs probably did not include all the possible error sources into the calculation and therefore their uncertainties were too small in relation to the deviations from the reference. Shape of profile lines provided by some NMIs was significantly different from the weighted mean. The reason could be in the insufficient compensation of the errors of guiding probing part in the measuring procedure. This comparison provided the information about state of metrological services provision in the field of big squares measurement. For the sake of effective exploatation of the energy demanded by this comparison, it has to be followed by the analysis of influencing factors in each participating NMI and revision of this category in Appendix C MRA. Coordinator is thankful to all participants for the good cooperation.


58

ANNEX A A.1 Consistency of results and outliers Some reported measurement result seemed to be inconsistent with other results, and could change the reference values. A.1 Arithmetic mean The arithmetic mean reference value xref was calculated by the average of all measurement values xi :

xref =

1 n å xi n i =1

(1)

The arithmetic mean does not take into account the uncertainty of the individual results contributing to the reference value. For a relatively small number of participants, results with large deviations, but still not to be considered as outliers, can strongly influence the mean. The standard uncertainty u(xref) of the arithmetic mean can either be determined by application of the error propagation law, i.e. by taking into account the uncertainties u(xi) of the individual results [Eq. (2)], or by the spread of the results, i.e. by the standard deviation divided by the square root of the number n of results contributing to the mean [Eq. (A3)]. u ( x ref ) =

u 1 n 2 å u ( xi ) = rms n i =1 n

(2)

or u ( xref ) =

n 1 å ( xi - x ref ) 2 n(n - 1) i =1

(3)

A.2 Statistical consistency The statistical consistency of a comparison can be investigated by the so-called Birge ratio2 RB , which compares the observed spread of the results with the spread expected from the individual reported uncertainties.

2

Statistical Analysis of Interlaboratory Comparisons, EUROMET workshop held at NPL on 11.-12. November 1999, http://www.npl.co.uk/ssfm/download/documents/sss_m_00_173.pdf


59

The application of least squares algorithms and the c2-test leads to the Birge ratio u ext u in

RB =

(4)

where uin, the internal standard deviation, is given by the reported uncertainties æn ö u in = ç å u - 2 ( xi ) ÷ è i =1 ø

-1 / 2

(5)

and the external standard deviation uext is the standard deviation of the spread of the results xi, weighted by the associated uncertainties u(xi): u ext

æ å u - 2 ( xi )( xi - x w ) 2 = çç -2 è (n - 1)å u ( xi )

1/ 2

ö ÷ ÷ ø

(6)

x w is the weighted mean given by n

xw =

å u - 2 ( xi ) × xi i =1

n

(7)

-2

å u ( xi ) i =1

The Birge ratio has an expectation value of RB = 1. For a coverage factor of k = 2, the data in a comparison are consistent provided that RBcrit = 1 + 8 /(n - 1)

(8) who n = number of participating laboratories

crit

A value RB > RB may be interpreted such that the laboratories have underestimated their uncertainties. A.3 Weighted mean The weighted mean reference value xref was calculated by the mean of all measurement values xi weighted by the inverse square of the standard uncertainties u(xi) associated with the measurements. n

xref =

å u -2 ( xi ) × xi

i =1

n

-2

(9)

å u ( xi )

i =1

The weighted mean approach requires the individual uncertainties from the laboratories can be estimated according to a common approach (which should be the case, since all participants were requested to estimate the uncertainties according to the ISO Guide). If this is not the case, a single "wrong" value with a strongly underestimated (too small) uncertainty could strongly influence or even fully determine the weighted mean. On the other hand, a high quality measurement with


60

overestimated uncertainty would contribute to the reference value only to a small extent. The standard uncertainty u(xref) of the reference value is calculated either by appropriately combining the individual uncertainties [Eq. (10)], or by the spread of the results [Eq. (11)], which is identical to the internal and external standard deviation given in Eq. (5, 6) æn ö u ( x ref ) = ç å u -2 ( xi ) ÷ è i =1 ø

-1/ 2

(10)

or

å u - 2 ( xi )( xi - x ref ) 2 u ( x ref ) = (n - 1)å u -2 ( xi )

(11)

It has to be noted that Eqs. (3) and (11) do not result from the law of error propagation and are certainly not in accordance to the GUM. In statistically consistent cases, these standard deviations should be approximately equal to the standard uncertainties evaluated according to Eqs. (2) and (10), respectively, resulting in a Birge ratio of approximately 1 (see section A.1 Statistical consistency). A.4 Grubbs' test The Grubbs’ test according to the ISO 5725-2: 20003 was applied for one outlying observation. The test applied on the smallest and largest value of the set of data, xi for i = 1,2, …p. The Grubbs’ statistic is calculated as

Gp =

x=

(x

p

-x s

1 p å xi p i =1

)

or

Gp =

and

s=

(x - x ) 1

s

where

1 p å ( x i - x )2 p - 1 i =1

(12)

(13)

If the test statistic is less than or equal to 5% of critical value and less than or equal to its 1% of critical value, the item tested is called a straggler. If the test is greater than its 1 % of critical value, the item is called a statistical outlier.

3

ISO 5725-2 : Accuracy (trueness and precision) of measurement methods and results – part 2 : Basic method for the determination of repeatability and reproductibility of a standard measurement method.

Final Report of EUROMET Comparison of squareness measurements No: 570 Outliers do not participate in the calculation of the means.

61

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