Centro Nacional de Metrología. CIPM Key Comparison CCL KC-6

Transcription

1 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 1/162 Centro Nacional de Metrología CIPM Key Comparison CCL KC-6 Calibration of Coordinate Measuring Machine (CMM) Two-dimensional (2-D) Artifacts (Ball Plates & Bore Plates) Final Report

2 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 2/162 1 Introduction Organization Participants Initial Schedule Problems during circulation Final Timetable and Circulation Scheme Description of the Standards Artifacts Measurement instructions Traceability Measurands Measurement instructions Measurement methods and instruments used by the participants Stability and condition of the artifacts Claimed Uncertainties Measurement Results Steel Ball Plate ZERODUR Bore Plate Measurement Results in Cylindrical Coordinates Ball Plate ZERODUR Bore Plate Key Comparison Reference Value (KCRV) Determination Outlier elimination process Uncertainty of the KCRV KCRV determination for the Steel Ball Plate KCRV determination for the ZERODUR Bore Plate Participants results with respect to KCRV Steel Ball Plate Results ZERODUR Bore Plate Average Normalized Errors for the Steel Ball Plate Average Normalized Errors for the ZERODUR Bore Plate Birge Ratio Calculation Birge Ratio for the Measuring Elements of the Steel Ball Plate Birge Ratio for the Measuring Elements of the ZERODUR Bore Plate Conclusions... 87

3 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 3/ On the results of the comparison Suggestions for future comparisons of this kind Acknowledgements References Appendix Equivalences of participant laboratories results (i) with respect to reference values (R) Pairwise equivalences between results of participant laboratories i and j

4 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 4/162 1 Introduction The metrological equivalence of national measurement standards and calibration certificates issued by National Metrology Institutes (NMIs) is established by a set of key comparisons chosen and organized by the Consultative committees of the CIPM or by the regional organizations in collaboration with the consultative committees. At its meeting in 1997, the Consultative Committee for Length (CCL) identified several key comparisons in the field of dimensional metrology. In particular, it decided that comparisons on CMM 1-D and CMM 2-D artifacts should be carried out. The Centro Nacional de Metrología (CENAM), was designated as pilot laboratory for the CMM 2-D artifact comparison. It was proposed to start it once the 1-D would be finished. However, at the 1998 meeting, the Chairman of the Working Group in Dimensional Metrology (WGDM), Dr. Jim Pekelsky, urged to start it as soon as possible. This report of the comparison was circulated among the participants as Draft B v 0.5 and after review and approval by all of them became the final report. It comprises all information about the comparison measurement results (Draft A). In addition, the choice of a Key Comparison Reference Value (KCRV), its estimated uncertainty, the performance of each participant with respect to this value and the Birge ratio of the different measurands of each artifact is presented. 2 Organization Following the Guidelines to CIPM key comparisons [1] the choice of artifacts and a preliminary list of participants was made, as well as circulation scheme. Then a technical protocol was written [2] by Edgar Arizmendi and Miguel Viliesid from the pilot NMI, CENAM, and sent to the participants.

5 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 5/ Participants No. COUNTRY REGION CONTACT PERSON / ADDRESS 1 AUSTRALIA APMP Nicholas BROWN National Metrology Institute of Australia (NMIA 1 ) Division of Telecommunications and Industrial Physics National Measurement Laboratory (Room B24E) Bradfield Rd. West Lindfield NSW 2070 Tel , Fax nick.brown@tip.csiro.au 2 CANADA SIM Kostadin DOYTCHINOV Institute for National Measurement Standards National Research Council Canada (INMS-NRC) Montreal Rd. M-36 Ottawa, K1A 0R6 Tel , Fax kostadin.doytchinov@nrc.ca 3 CHINA APMP Shen SHAOXI National Institute of Metrology (NIM) No. 18 Bei San Huan Dong Lu Beijing. shenshx@nim.ac.cn 4 CZECH REPUBLIC EUROMET Vit ZELENY Czech Metrology Institute (CMI) V botanice Praha 5 tel. (+420 2) , fax. (+420 2) vzeleny@cmi.cz 5 FRANCE EUROMET Georges-Pierre VAILLEAU Bureau National de Metrologie-Laboratorie National de'essais (BNM-LNE) Division 32 Metrologie dimensionelle 1, rue G Boissier Paris Cedex 15 FRANCE tel , fax Georges.Vailleau@lne.fr 6 GERMANY EUROMET Heinrich SCHWENKE 5.32 Laboratorium für Koordinatenmessgeraete / CMM-Section Physikalisch-Technische Bundesanstalt (PTB) Bundesallee Braunschweig Fon ++49/531/ , Fax ++49/531/ Heinrich.Schwenke@ptb.de 7 JAPAN APMP Tomizo KUROSAWA National Metrology Institute of Japan (NMIJ 2 ) 1-1-4, Umezono, Tsukuba, Ibaraki Japan Phone: , Fax: kurosawa@nrlm.go.jp 1 Formerly, CSIRO. 2 Formerly, National Research Laboratory of Metrology, NRLM.

6 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 6/162 8 NETHERLANDS EUROMET Robbert BERGMANS Netherlands Meetinstituut VSL B.V. (NMi VSL) Department of Mechanics Shoemakerstraat 97 P.O. Box AR Delft Tel.: , Fax: rbergmans@nmi.nl 9 RUSSIA COOMET Valery LYSSENKO Head of Department of geometrical measurement VNIIMS 46, Ozernaya Moskow , Russia Phone , Fax Office.VNIIMS@g23.relcom.ru. 10 SOUTH AFRICA 3 SADCMET John. R. HANNAFORD National Metrology Laboratory CSIR Building 5 Meiring Naude Rd. Brummeria Pretoria 0001 Tel , Fax jrhannaf@csir.co.za 11 UNITED KINGDOM EUROMET Andrew LEWIS Centre for Basic, Thermal and Length Metrology National Physical Laboratory (NPL) Teddington,Middlesex, TW11 0LW Tel: , Fax: Andrew.Lewis@npl.co.uk 12 UNITED STATES SIM Jack STONE National Institute of Standards and Technology (NIST) Precision Engineering Division Metrology Bldg. (220), R. A107 MET B113 Gaithersburg, MD Tel jack.stone@nist.gov 13 MEXICO (PILOT) SIM Miguel VILIESID or Edgar ARIZMENDI Centro Nacional de Metrología (CENAM) Jefe de División Metrología Dimensional Apartado Postal1 100 Centro Querétaro, Qro Mexico Tel ext.: 3277 or 3282 Fax mviliesi@cenam.mx earizmen@cenam.mx Table 1.- List of participants of comparison CCL-K6. 3 This laboratory withdrew form the comparison after receiving the artifacts for measurement and did not report any results.

7 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 7/ Initial Schedule An initial time schedule was drawn as shown in Table 2. The circulation of artifacts should have taken place within a 24 month period starting on January 2001 with the participation of 13 NMIs from the five Regional Metrology Organizations (RMO). Region NMI Country Period Pilot Laboratory SIM CENAM Mexico NIST USA to EUROMET BNM-LNE France to PTB Germany to CMI Czech to Republic 4 COOMET VNIIMS Russia to EUROMET NPL United Kingdom to Pilot Laboratory CENAM Mexico to APMP NIM China to NRLM Japan to CSIRO Australia to SADCMET CSIR South Africa to Euromet NMi Netherlands to SIM Pilot Laboratory NRC Canada to CENAM Mexico to Table 2.- Initial timetable for the comparison. 2.3 Problems during circulation Several problems arose during the circulation of the artifacts: A few countries were skipped at their initial allocated period and had to be scheduled a new time period after due to custom clearance problems or heavy working load agenda at that NMI at the initial allocated period. Official holidays coincided with some participants designated measurement period. 4 This country was allocated a longer period of time for holiday reasons.

8 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 8/162 Breakdown of the pilot s CMM. The machine was out of service for more than two years. Unscheduled control measurements made by a designated co-pilot laboratory performed in place of those the pilot laboratory was unable to carry out because their CMM was out of service. Re-measurement by one laboratory after detecting problems with their reported measurements. Customs clearance and shipping delays. Last minute withdrawal of one NMI. Re-commissioning of pilot laboratory closure measurements. Other delays of some participants. 2.4 Final Timetable and Circulation Scheme The final circulation scheme and timetable is shown in table 3. Mexico Japan USA Australia France South Africa Germany Netherlands Czech Rep China UK Russia USA Canada China USA Mexico Table 3.- Final circulation scheme and timetable.

9 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 9/162 3 Description of the Standards 3.1 Artifacts The measurement artifacts are the following: Ball Plate Make: KOBA Serial Number: , Material: Steel frame with ceramic balls. Thermal expansion coefficient of steel, α = K -1 at 20 C. Dimensions (mm): S3 85 Sphere φ S1 S2 Fixture points Figure 1.- Ball plate description

10 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 10/162 Bore Plate Serial Number: NONE Material: ZERODUR Thermal expansion coefficient of ZERODUR: 0 at 20 C. Dimensions (mm): Aluminum frame Zerodur plate S S1 S Figure 2.- Bore plate description.

11 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 11/162 4 Measurement instructions 4.1 Traceability Length measurements should have been independently traceable to the latest realization of the mètre as set out in the current Mise en Pratique. This means that the length unit should have been transferred to the ball and bore plates with the CMM by one of the following methods: laser interferometer, gauge blocks, ball beams, ball bar or step gauges. Whatever the instrument or standard used, traceability to the definition of the length unit should have been achieved through calibrations performed in house. Temperature measurements should be made using the International Temperature Scale of 1990 (ITS-90). 4.2 Measurands Ball Plate. - The object reference plane was defined by the center of balls number 1, 5 and 21. The origin of object coordinate system was the center of ball number 1. The X-axis of the object reference system was defined by the line that passes through the center of ball number 1 and the center of ball number 5. The direction from the origin to ball number 5 defines the positive X-axis direction. The Y-axis is defined was the orthogonal line that passes through the center of ball number 1. The positive direction was from ball number 1 to ball number 21. The measurands of the ball plate are the coordinates of each ball center with respect to the origin of object coordinate system (Fig.3) with the plate lying horizontally and fixed as described in section Yobj Ball 21 (x,y,0) Xobj Ball 1 (0,0,0) Ball 5 (x,0,0) Figure 3.- Ball plate coordinate system.

12 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 12/162 Bore Plate.- A plane for the bore plate should have been determined by measuring three or more points wide spread over one of the plate's faces (for example, three points located at the vicinity of three bores in the corners). This plane should have been translated into the plate's symmetry plane in the z direction, half the plate's nominal thickness (thickness should not be measured). This plane is the object reference plane. The origin of object coordinate system lies on the object reference plane and was the center point of the bore at the corner where the yellow sticker appears. The X-axis of the object reference system was defined by the line that passes through the origin and the center of the last bore in the X direction, as shown by the yellow sticker. The direction from the origin to the last bore in the row defined the positive X-axis direction. The Y-axis was defined as the orthogonal line that passes through the origin of the object coordinate reference system and the positive direction was the one shown by the yellow sticker (figure 4). The measurands of the bore plate were the center coordinates of each bore with respect to the object coordinate system with the plate lying horizontally and fixed as described in section The thermal expansion coefficient used should have been the quoted values for each plate. Laboratories should report the temperatures at which the length measurements were made. Laboratories should only measure the artifacts at a temperature of (20 ± 0,3) C. Yobj Bore (x,y) Xobj Bore (0,0) Bore (x,0) Figure 4.- Bore plate coordinate system.

13 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 13/ Measurement instructions Each laboratory was free to use its own measuring method. However, measurements were to be reported in the object reference coordinate system described in 4.2. Appendix A5 in the protocol described a measurement method that could be used. Before measurement, the artifacts should have been inspected for damage. Special attention was to be paid to the measurement surfaces and form elements (balls or bores). Any scratches rust spots or other damages should have been documented. Appendix A1 contained a form that should have been filled and sent upon reception quoting the state of the artifacts as received Before measurement, the plates and supports were to be cleaned. The form elements should have been cleaned with special care individually as well as the measuring surfaces in the vicinity of all probing points Included with the ball plate, there were three fixtures to mount it in horizontal position: one conical, one with a V-grove and a flat one. Three hemispherical supports were screwed to the ball plate (points S1, S2 and S3 of Fig. 1). The three supports should have been fixed to the CMM table as to support each of the hemispheres in the following order. Firstly, the cone base should be attached to the support point S1. Secondly, the V-grove base should be attached to point S2, with the grove aligned towards the cone. Finally, the plane base should be attached to point S Included with the bore plate, there were three identical fixtures to mount it in horizontal position. The three fixtures should have been screwed to the edges of the bore plate in the points S1, S2 and S3 shown Fig. 2. It was intended that the plate lay horizontal over the CMM table The measurement results should have been corrected to the reference temperature of 20 C using the values of the thermal expansion coefficient provided by the pilot laboratory No other measurements were to be attempted by the participants and the artifacts should not be used for any purpose other than described in this document. The artifacts could not be given to any party other than the participants in the comparison If for any reason a laboratory was not able to make all the measurements of one or both artifacts, it is still encouraged to report the rest of the results. Foreseeing this possibility, the laboratory could have chosen to make only the determination of the position of peripheral form elements, for example. 5 Measurement methods and instruments used by the participants Out of the twelve final participants, eight applied the recommended reversal method described in Appendix 5 of the protocol. These were: NMIA, INMS-NRC, NIM, CMI, BNM-LNE, PTB, VNIIMS and CENAM. The other five used their own custom methods. All custom methods incorporated the use of a laser interferometer or that of interferometric scales.

14 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 14/162 NMIJ-AIST combined the reversal method of Appendix 5 with interferometric measurements of the central ball rows crossing the ball plate at the center and then applied a correction to the previous measurements. They did something similar with the bore plate but used a couple of bore lines crossing on X and Y directions. NMi also used a laser interferometer to measure each row of balls in the X direction, then rotated the plate and measured each row in Y direction, then measured all the 45 º diagonals in one direction and finally all the other rows in the other diagonal direction. NPL made the dimensional measurements conventionally with the CMM probe and CMM scales. However, they made additional measurements with an interferometric set-up to correct for CMM scale errors. The measurements were made on the comparison artifact by measuring the two ball or bore central lines on X and Y directions. The method is similar to that applied by NMIJ, with the additional feature that the target probe is not only tracked by a displacement interferometer, but also by a column reference interferometer; and that both positions bare double beam and therefore it corrects for tilt in the two directions. Finally, NIST used a CMM fully equipped with interferometric scales replacing the original ones, and they did not apply the reversal method but rather measured twice in 90º different orientations and the data is combined to separate CMM from artifact errors. The measurements are repeated four times and linear drift is also corrected. Table 4 summarizes the methods applied. 6 Stability and condition of the artifacts There were no major reports of damage of the artifacts. However, the following remarks were made. PTB reported two minor damages in bores 12 (coordinates (3,2)) and 48 ((5,8)) of the ZERODUR bore plate not influencing measurements. CMI reported light scratches on the conical edges of the same bores 12 and 48; NPL reported damage to the casing of the ball plate with no consequences to the artifact; and CSIRO reported minor scratches and marks in both artifacts and specifically on bores 26, 34 and 48 of the bore plate. INMS-NRC commented they detected unusually large error in bore 12. However they did not attribute it to any damage but rather suspected that the bore plate could rock inside its aluminum frame when moving in the X-direction at certain acceleration in CMMs with moving tables. No comments were reported on the steel ball plate. The pilot laboratory, CENAM and the copilot laboratory, NIST, performed control measurements during the exercise. Considering the modulus r of the x and y coordinates reported for the center of all balls with respect to the center of ball 1, figure 5 shows the deviation from the nominal r distance to each ball center. The graph shows the deviations from nominal position for each measuring element with ball 20 having the largest of about 0.15 µm. Among the whole set of measurements, for all measuring elements and for the five participations of both laboratories, the mean of the variations between any

15 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 15/162 combination of two stets of measurements in time was µm; and the largest value was µm occurring at ball 22 between CENAM set of measurements number 1 ( ) and NIST set of measurements number 3 ( ). If the simple mean of these five sets of measurements is taken as reference value, all results appear to be consistent in terms of the average normalized error for the 24 measuring elements in the artifact (all average E n values between 0.36 and 0.87), as well as in terms of the declared uncertainties by each laboratory averaged over all 24 measuring elements (in average the reference value crosses well within the standard uncertainty bar of the laboratory). Figure 5 shows no visible trend in any of the balls, nor the deviations change significantly through the control measurements and therefore we conclude the artifact behaved reasonably well during the comparison exercise and no drift may be inferred out of the measurements performed by the pilot laboratories. Similarly, figures 6, 7 and 8 show the same kind of plots for the ZERODUR bore plate. As there are 61 bores in this case, the graph had to be split into three. While in the steel ball plate all deviations from nominal are positive, here most of them are negative and the largest one is of around 0.15 µm also (bore 58). Among the whole set of measurements, for all measuring elements and for the five participations of both laboratories, the mean of the variations between any combination of two stets of measurements in time was µm; and the largest value being µm occurring at ball 53 between CENAM set of measurements number 1 ( ) and NIST set of measurements number 1 ( ). If the simple mean of these five sets of measurements is taken as reference value, all results appear to be consistent in terms of the average normalized error for the 60 measuring elements in the artifact (all average E n values between 0.39 and 0.61), as well as in terms of the declared uncertainties by each laboratory averaged over all 60 measuring elements (in average the reference value crosses the standard uncertainty bar of the laboratory). Figures 6 through 8 show no visible trend in any of the balls, nor the deviations change significantly through the control measurements and therefore we conclude the artifact behaved reasonably well during the comparison exercise and no drift may be inferred out of the measurements performed by the pilot laboratories. Figure 9 show the control measurement results made by the pilot laboratories for the central ball 13 and for the corner balls 5, 21 and 25 of the steel ball plate along with the claimed uncertainties for the modulus r of the x and y coordinates reported with their uncertainties at k = 1. A visual inspection shows that correspondence is good for the central ball 13 and for the ball 5 that lays over the X-axis (y = 0). Ball 25 shows very good correspondence between the NIST measurements and good between the CENAM ones, however, the correspondence between laboratories is not as good. In any case, this is certainly due to laboratory equipment and conditions and not due to artifact changes. Ball 21 shows less good agreement but it does not seem significant to invalidate any results as discussed above. Figure 10 shows similar plots for the measurements made by the pilot laboratories of the central bore 35 and of the corner bores 9, 53 and 61 of the ZERODUR bore plate. Exception made of bore 53; the other three bores are in very good agreement between the five measurements. Bore 53 presents very good correspondence between the NIST measurements and good correspondence between the CENAM ones. There is poor correspondence between the results

16 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 16/162 obtained between the two laboratories. However, this must be attributed to changes in the laboratories conditions and equipment and not to the artifacts. Again, this does not seem to invalidate the results as discussed above. 7 Claimed Uncertainties Uncertainties were quoted in different ways. Most laboratories quoted two equations, one for the steel ball plate and one for the ZERODUR bore plate. However, some quoted only one equation for both and one laboratory preferred to state a linear equation instead of the suggested equation of the form u ( l) = a + bl. Another laboratory stated values in X and Y for each of the coordinates of each geometrical feature of the plates without stating an equation. A quadratic curve was adjusted by the pilot to these points just to be able to compare it to the rest of the participants. For the Steel Plate, claimed standard uncertainty equations had a relatively wide spread with an mean value of 6 µm and a standard deviation of this mean of 0,023 µm at L = 0 mm; and a mean of µm and standard deviation of µm at L = 1000 mm. For the ZERODUR bore plate some participants estimated a smaller uncertainty and the correspondent respective values for the mean and the standard deviation were µm and µm at L = 0 mm; and µm and µm at L = 1000 mm. Table 5 shows the quoted standard uncertainty equations for each participant along with the values that these equations take at L = 0 mm and L = 1000 mm. For the laboratories that quoted different equations for each plate, both equations appear. Figure 11 shows the plot of the steel ball plate standard uncertainty equations and figure 12 plots those of the ZERODUR bore plate. 8 Measurement Results 8.1 Steel Ball Plate Table 6 shows the measurement results of the comparison as stated by the participants. It was not required to state the Z coordinates but most laboratories reported them and they are also shown along with the X and Y coordinates. However, they are not used in any calculations. The table is split in four parts, a, b, c and d. 8.2 ZERODUR Bore Plate Table 7 shows the measurement results of the comparison as stated by the participants. The table is split in three parts, a, b, c and d.

17 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 17/162 COUNTRY LABORATORY MEASUREMENT INSTRUMENT TRACEABILITY MEASUREMENT METHOD Temperature span during measurements (ºC) AUSTRALIA NMIA (CSIRO) LEITZ PMM866 Cal. laser interf. + cal. length bar + cal. sphere Appendix 5 of protocol Ball p.: 19.6 to 20.2 Bore p.: 20.0 to 20.3 CANADA INMS-NRC MITUTOYO LEGEX #707 Calibrated gauge blocks Appendix 5 of protocol Ball p.: to Bore p.: to CHINA NIM LEITZ (B&Sh) PMM12106MG with laser interferometer Laser interf. calibrated against MeP laser Appendix 5 of protocol 19.7 to 20.3 CZECH REPUBLIC CMI SIP CMM 5 Calibrated gauge blocks Appendix 5 of protocol 19.9 to 20.1 FRANCE BNM-LNE SIP CMM 5/SIP Laser interf. calibrated Appendix 5 of protocol Not quoted Concerto GERMANY PTB CMM LEITZ PMM laser interferometer JAPAN NMIJ-AIST (NRLM) LEITZ (B&Sh) PMM866P + laser interferometer NETHERLANDS NMi ZEISS UC550 + laser interferometer in X and Y/ UMESS-Basic against MeP laser Laser interf. calibrated against MeP laser Laser interf. calibrated against MeP laser? Laser interf. calibrated against MeP laser Appendix 5 of protocol Ball p.:20.05 TO Bore p.: not quoted Appendix 5 + own method with interferometer Own method with interferometer Ball p.: to Bore p.: to Ball p.: to Bore p.: to RUSSIA VNIIMS ZEISS UPCM 850 Calibrated gauge blocks Appendix 5 of protocol Not quoted UNITED NPL KINGDOM LEITZ PMM12106 custom high accuracy/ QUINDOS UNITED STATES NIST MOORE M48 with interferometric scales MEXICO (PILOT) CENAM SIP CMM5L/ CONCERTO Gauge blocks + step gauge + cal. laser interferometer + cal. shpere Laser interf. calibrated against MeP laser Combination of modified App. 5 + own method with interferometer Own modified app. 5 method Ball p.: to Bore p.: 19.1 to to 20.2 Calibrated step gauge Appendix 5 of protocol to Table 4.- Participant countries, name of institute, method to obtain traceability, calibration method and reported temperature variation during measurements.

18 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 18/ Ball Desviation from nomina Figure 5.- Ball plate measurements reported as deviations from nominal modulus r (µm) performed by pilot laboratory, CENAM, and co-pilot NIST at different dates.

19 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 19/ Bore Deviation from nomina Figure 6.- Bore plate measurements reported as deviations from nominal modulus r (µm) of the first 20 bores performed by pilot, CENAM, and co-pilot NIST at different dates.

20 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 20/ Bore Deviation from nomina Figure 7.- Bore plate measurements reported as deviations from nominal modulus r (µm) of bores 21 to 40 performed by pilot, CENAM, and co-pilot NIST at different dates.

21 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 21/ Bore Deviation from nomina Figure 8.- Bore plate measurements reported as deviations from nominal modulus r (µm) of the last 21 bores performed by pilot, CENAM, and co-pilot NIST at different dates.

22 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 22/162 BALL 21 BALL NIST1 NIST2 NIST3 CENAM1 CENAM NIST1 NIST2 NIST3 CENAM1 CENAM2 BALL 13 BALL NIST1 NIST2 NIST3 CENAM1 CENAM2 - NIST1 NIST2 NIST3 CENAM1 CENAM2 - - Figure 9.- Center ball 13 and corner balls 5, 21 and 25 deviations from nominal modulus r (µm) performed by pilot, CENAM, and co-pilot NIST at different control dates along with claimed standard uncertainties.

23 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 23/162 Ball 53 Ball NIST1 NIST2 NIST3 CENAM1 CENAM2 - - NIST1 NIST2 NIST3 CENAM1 CENAM Ball 35 Ball NIST1 NIST2 NIST3 CENAM1 CENAM NIST1 NIST2 NIST3 CENAM1 CENAM2 Figure 10.- Center bore 35 and corner bores 9, 53 and 61 deviations from nominal modulus r (µm) performed by pilot, CENAM, and co-pilot NIST at different control dates along with claimed standard uncertainties.

24 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 24/162 Country Claimed Combined Standard Uncertainty as quoted u c (µm) L = 0 u c (µm) L = 1 m Australia Canada China Czech Rep. Ball P.: uc ( l ) = 2 2 ( (1.12 * L /1000) L in mm Bore P.: uc ( l ) = 2 2 ( (0.91* L /1000) L in mm Ball P.: u 2 c= L 2 µm, L in mm Bore P.: u 2 c= L 2 µm, L in mm Ball P.: Bore P.: u c ( l) = (0.14) µ m + ( ) L u c ( l) = (0.14) µ m + ( ) L Ball P.: uc ( l ) = 0, ,40 2 l 2 Bore P.: uc ( l ) = 0, ,36 2 l France Ball P.: u c (L) = (470 nm) 2 + (1,43 L) 2 + 0,3 µm. L Bore P.: u c (L) = (470 nm) 2 + (0,85 L) 2 + 0,3 µm. L Germany Ball P.: ( l) (0.2 m + ( L) ) u c = µ Bore P.: ( l) (0.2 m + ( L) ) u c = µ Japan Netherlands United Kingdom Ball P.: u= sqrt(126^ /L) ^2 [nm] Bore P.: u= sqrt(119^ /L) ^2 [nm] Did not state equations. Equations adjusted by pilot: ( (047* L) Ball P.: uc ( l ) = 2 2 ( (047* L) Bore P.: uc l 2 2 Ball P.: uc l + (0.44 l) 2 µm Bore P.: uc l + (0.33 l) 2 µm Russia 6 2 Uc( l) = 0, , l mkm USA 1 For both: uc ( l) = ± * L USA 2 and 3 Mexico 1 and 2 For both uc ( l) = ± * L u 2 c = 0,27µ m + 0, 43L Ball P.: ( ) ( ) 2 u 2 c = 0,27µ m + 0, 33L Bore P.: ( ) ( ) Table 5.- Claimed uncertainty equations of participants. All uncertainties are combined standard uncertainties.

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26 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 26/162 Figure 11.- Claimed Standard Uncertainty Curves of participants for the Steel Ball Plate. X-axis in millimeters and Y-axis in micrometers. Figure 12.- Claimed standard uncertainty curves of participants for the ZERODUR Bore Plate. X-axis in millimeters and Y-axis in micrometers.

27 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 27/162 NMI NMIA (CSIRO) INMS-NRC NIM CMI Bola X Y Z X Y Z X Y Z X Y Z Table 6 a.- Coordinates of the center of the balls for the 25 balls of the steel ball plate. All values in millimeters.

28 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 28/162 NMI BNM-LNE PTB NMIJ (NRLM) NMi Bola X Y Z X Y Z X Y Z X Y Z / / / / / / / / / / / / / / / / / / / / / / / / / Table 6 b.- Coordinates of the center of the balls for the 25 balls of the steel ball plate. All values in millimeters.

29 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 29/162 NMI VNIIMS 5 NPL NIST 1 CENAM 1 Bola X Y Z X Y Z X Y Z X Y Z Table 6 c.- Coordinates of the center of the balls for the 25 balls of the steel ball plate. All values in millimeters. 5 This laboratory did not report the final result but sent the whole set of measurements in every position. The pilot laboratory calculated the best estimate as the arithmetic mean of the set of measurements.

30 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 30/162 NMI NIST 2 6 NIST 3 6 CENAM 2 6 Bola X Y Z X Y Z Table 6 d.- Coordinates of the center of the balls for the 25 balls of the steel ball plate. All values in millimeters. 6 These values were control values performed by the pilot and co-pilot laboratories.

31 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 31/162 NMI NMIA (CSIRO) INMS-NRC NIM CMI Bore x y x y x y x y Table 7 a.- Coordinates of center of bores for bores of the ZERODUR bore plate. All values in mm.

32 CIPM CCL Key comparison: Calibration of CMM 2-D Artifacts 32/162 NMI BNM-LNE PTB NMIJ (NRLM) NMi Bore x y x y x y x y Table 7 b.- Coordinates of center of bores for bores of the ZERODUR bore plate. All values in mm.