AGMA 99FTM3-1999 Measurement Uncertainty for Pitch and Runout Artifacts《齿距和圆跳动标准器的测量不确定度》.pdf

1、I Measurement Uncertainty for Pitch and Runout Artifacts by: B. Cox, Lockheed Martin Energy Systems, Inc. TECHNICAL PAPER COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Servicesa Measurement Uncertainty for Pitch and Runout Artifacts Bruce Cox, Lockheed Marti

2、n Energy Systems, Inc. The statements and opinions contained herein,re those of the author and should not be construed as an official action or opinion of the American Gear Manufacturers Association. Abstract Primary-level calibration of pitch and runout artifacts require quantifying the measurement

3、 uncertainty on the artifact being calibrated by a method that does not rely on a transfer comparison. The measurement decomposition method, developed jointly by National Institute of Standardsand Technology (NIST) and Oak Ridge Metrology Center (ORMC) personnel, is used to determine the uncertainty

4、 of each component of the measurement task. Once quantified, these components are added in quadrature according to NISTTechnicalNote 1297,1994 Edition). Verification of this method was accomplished by inter-comparison between ORMC and NIST using high precision coordinate measurement machines and rot

5、ary tables. The results were also compared with data obtained using the circle closure principie. Copyright O 1999 American Gear Manufacturers Association 1500 King Street, Suite 201 Alexandria. Virginia, 22314 October. 1999 ISBN: I-55589-741-X COPYRIGHT American Gear Manufacturers Association, Inc.

6、Licensed by Information Handling ServicesIndex and Runout Artifact Measurement Decomposition In the case of an index and runout artifact, the uncertainty determination consists of checking pitch error using a rotary table and a 1440 Divider by the closure method; checking radial runout of the rotary

7、 table; and checking repeatability using an index artifact. The pitch test which involved repeated measurements on three balls mounted so that a line through the first and second ball centers and a line through the first and third ball centers formed a 15“ angle. In the pitch test, the balls were mo

8、unted on a1440 divider, which was also mounted on the rotary table, see Figure 1. When the divider was rotated 15“, the rotary table was rotated 15“ in the opposite direction. The angle positions were analyzed by using the circle closure method, where all angles must add to 360“. The angle results a

9、re summarized in Table 1. Figure 1 Checking rotary table error using 3 balls and 1440 divider by circle closure 2 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services1 Table 1. Pitch test with 3 balls using closure (arcseconds) I I -0.50400 -0.43200 -0.396

10、00 -0.43200 -0.50400 -0.43200 -0.46800 -0.54000 -0.39601 -0.25200 -0.25200 -0.21 600 -0.18000 -0.28800 -0.2 1600 -0.2 160C -0.32400 -0.2520( -0.10800 -0.07200 -0.07200 -0.03600 -0.10800 -0.10800 -0.07200 -0.10800 -0.18001 I -0.4680a -0.54000( -0.1440a -0.0360 , I l 0.0000ol 0.00000l The results of 1

11、3 runs of the pitch test, in arcseconds, were a maximum deviation of 0.432 a minimum deviation of -0.972. Using a rectangular distribution the standard deviation is calculated below (in arcseconds): 0.432 - (-0.972) = 0.405 - 2J3 “P - Next, a test was conducted, which involved a known ball mounted i

12、n the center of the rotary table at two heights to determine the radial runout of the table. A ball was mounted on the centerline of the rotary table and the radial runout was measured at two heights above the table, 9 7/8“ and 2 1/2“, see Figure 2. The results are shown below in Table 2: 3 COPYRIGH

13、T American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesFigure 2 Radial runout test Table 2. Radial Runout Test (mm) Number Radial Runout High Radial Runout Low 9 718“ 2 Y2“ 1 0.00028 0.000 18 2 3 4 1 0.0003 1 0.00014 O. 0003 2 0.000 16 0. 00028 0.000 18 I - 51 0.0003

14、1 0.000171 7 8 I 61 0.0003 11 o. 00022 I 0.0003 1 0.00015 0.0003 1 0.00019 Il 12 I 101 O. 00034 0.0001 0.00032 0.0002 1 0.0003 1 0.000 15 The maximum deviation of the radial runout test at two heights was 0.000340 mm. Taking the arctan of the maximum deviation times sin 20“ divided by the base radiu

15、s of 57.15 mm (simulating a 4.5“ base circle diameter) and multiplying by 3600 to convert to arcseconds gives a total range of 10.420 arcseconds (see Figure 3). 4 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesA=arctan( Y/57.15)*3600 Figure 3 Calculat

16、ion of angle error due to radial runout The corresponding uncertainty is (in arcseconds): = 0.242 0.420 + 0.420 u, = The index artifact from R. E. Smith, Inc. was used to measure repeatability, see Figure 4. The NIST part program was used with two modifications. Instead of one point being taken at t

17、he pitch diameter, five points were taken at the same location and the average of all points was used. The coordinate system was re-established on the first tooth at every 45“ around the rotary table. One run constitutes eight measurements of each tooth (at every 45“ position). The average of all ei

18、ght measurements on each tooth is the value for each run. The results below in Tables 3 and 4 show the runs, the average of all runs, and the standard deviation of all runs: Figure 4 R. E. Smith index artifact 5 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling

19、ServicesO Table 3. Index Repeatability Runs (Right Flank) Smith gear new 1 pt method i DATE: 12/15/98 12/18/98 12/22/98 12/22/98 12/23/98 12/28/98 12/29/98AVG STD DEV TOOTH # Microns Microns Microns Microns Microns Microns Microns Microns Micron F 1 2 3 4 0.000 0.000 0.000 0.000 0.000 0.000 0.006 0.

20、000 0.000 1.573 1.579 1.863 1.762 1.569 1.595 1.498 1.634. 0.129 -0.059 -0.093 0.048 0.068 -0.083 -0.167 -0.1 14 -0.057 0.086 0.985 1.042 1.255 1.24C 1,010 1.051 1.022 1.086 0.112 10 11 12 13 6 -0.456 -0.311 0.024 -0.111 -0.135 -0.242 -0.321 -0.222 0.160 -0.124 0.065 0.400 0.188 0.189 0.13C 0.059 0.

21、130 0.160 0.805 0.994 1.340 1.113 1.133 1.039 1.028 1.063 0.162 0.333 0.520 0.745 0.508 0.666 0.596 0.593 0.566 0.131 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services Table 4. Index Repeatability Runs (Left Hank) The maximum standard deviation for all

22、runs was O. 180 microns. The maximum standard deviation in microns was converted to arcseconds by dividing by the deviation by the 1000* cosine (20“). then taking the arctanent of this product divided by the pitch radius of 78 mm and multiplying by 3600. see Figure 5. . 7 COPYRIGHT American Gear Man

23、ufacturers Association, Inc.Licensed by Information Handling ServicesFigure 5 Calculation of qngle error due to repeatability The corresponding uncertainty is (in arcseconds): urp = 0.508 Index Measurement Uncertainty The index measurement uncertainty standard deviation estimate (ui) is thus (in arc

24、seconds): ui = dw = 40.405 +0.2422 +OSOS =0.734 Multiplication of ui by a factor (k) of 2 gives a total 95% confidence level uncertainty for index measurements Ui = 1.6 arcseconds The uncertainty in deviation normal to the surface is expressed as: Ui = R*tan(A/3600)*cos(PA) Where: R - is the measure

25、ment radius A - is the uncertainty in arcseconds PA - is the pressure angle at the measurement radius of the index artifact For example, the Bob Smith artifact uncertainty normal to the surface is: Ui = 78*tan (1.6/3600)*cos(20“) Ui = 0.57 micrometers 8 COPYRIGHT American Gear Manufacturers Associat

26、ion, Inc.Licensed by Information Handling ServicesPnter-comparison Measurements Inter-comparison measurements were made between CMMs at NIST and ORMC; and between a CMM at Gleason using the R. E. Smith artifact, see Figures 6-14. The inspection program between NIST and ORMC is nearly identical, whil

27、e the inspection analysis application software on the Gleason CMM is completely different. The ORMC and Gleason runout data is from a physical ball check using a 7/16“ diameter ball for the ORMC measurements and an 8 mm diameter ball for the Gleason measurements. R. E. Smith also input some of the i

28、ndex data from ORMC into his gear checking software to calculate runout. The R. E. Smith artifact has two alignment bands, one concentric to the gear teeth and one misaligned in order to show a large runout. All index inter-comparison measurements were within 3 microns and all runout inter- comparis

29、on measurements were within 10 microns. There seems to be some irregularities in the runout data from ORMC. ex of Srnith Artifact (NIST, ORMC, & Smith) 2.5 2.0 1.5 1 .o 0.5 0.0 -0.5 -1 .o I -g. Nist Data Left Flank (Concentric Band 1- I- I -1.5 I -I -2.01 I, I, I I I I I, I #4ll,ll,ll 1 2 3 4 5 6 7

30、8 9101112131415161718192021222324 Tooth Numbe Data Figure 6 Index Inter-Comparison Data Between NIST, ORMC, and Smith (Gleason) For Concentric Band on Left Flank of R. E. Smith Aritfact 9 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesIndex of Smith A

31、rtifact (NIST,ORMC,&Smith) & Nist Data 2.0 O O a L 0.0 .2 I 0- ci .I -1 .o -2.0 -3.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Tooth Number Figure 7 Index Inter-Comparison Data Between NIST, ORMC, and Smith (Gleason) For Concentric Band on Right Flank of R. E. Smith Aritfact Ind

32、ex of Smith Artifact (NIST, ORMC, & Smith) 80.0 -E- ORMC Data -A- Smith (Gleason) Data 60.0 40.0 20.0 0.0 -20.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Tooth Number Figure 8 Index Inter-Comparison Data Between NIST, ORMC, and Smith (Gleason) For Non- Concentric Band on Left Fl

33、ank of R. E. Smith Aritfact 10 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesIndex of Smith Artifact (NIST, ORMC,&Smith) Right Flank (Non-concentric Band) 80.0 1 7 I & NIST Data 40.0 20.0 0.0 -20.0 -40.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1

34、9 20 21 22 23 24 Tooth Number Figure 9 Index Inter-Comparison Data Between NIST, ORMC, and Smith (Gleason) For Non- Concentric Band on Right Flank of R. E. Smith Aritfact Index of Smith Artifact (NIST, ORMC, & Smith) Left Flank (Non-concentirc Band) Ecc. Rem., - -E- ORMC Data 0.6 1 2 3 4 5 6 7 8 9 1

35、0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Tooth Number Figure 10 Index Inter-Comparison Data Between NIST, ORMC, and Smith (Gleason) For Non- Concentric Band on Left Flank of R. E. Smith Aritfact with the Eccentricity Removed 11 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by In

36、formation Handling ServicesIndex of Smith Artifact (NIST, ORIMC,&Smith) Right Flank (Mon-concentric Band) Ecc. Rem. -0.8 - 1 .o 0.8 - + NIST Data -LI- ORMC Data i i 0.4 0.2 0.0 -0.2 -0.4 -0.6 &Smith (Gleason) Data Tooth Number Figure 11 Index Inter-Comparison Data Between NIST, ORMC, and Smith (Glea

37、son) For Non- Concentric Band on Right Flank of R. E. Smith Aritfact with the Eccentricity Removed Runout of Smith Artifact (ORMC &Smith) Concentric Band -+- ORMC by (Veridex) + ORMC Data 8- - - I1 l- I -A- Smith (Gieason) Data i 6- 5- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 T

38、ooth Number Figure 12 Runout Inter-Comparison Data Between ORMC, ORMC Calculated From Index, and Smith (Gleason) For Concentric Band of R. E. Smith Aritfact 12 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesRunout of Smith Artifact (QWMC &Smith) Non-c

39、oncentric Band -E-ORMC Data 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 I Tooth Number Figure 13 Runout Inter-Comparison Data Between QRMC, QRMC Calculated From Index, and Smith (Gleason) For Non-Concentric Band of R. E. Smith Aritfact Runout of mith Artifact (QRMC &Srnith) Non-co

40、ncentric Band ECC. Rem. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Tooth Number Figure 14 Runout Inter-Comparison Data Between QPWIC, ORMC Calculated From Index, and Smith (Gleason) For Non-Concentric Band of R. E. Smith Aritfact with the Eccentricity Removed 13 COPYRIGHT America

41、n Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesConclusions O The established measurement uncertainty for index is _+ 1.6 arcseconds or 2 0.6 micrometers for a 78 mm radius artifact. Runout can either be calculated from index data or measured with a ball in contact wit

42、h both flanks of the index and runout artifact. Inter-comparisons between NIST and ORMC are within the above stated uncertainty, but inter-comparison measurements with a Zeiss CMM at Gleason is slightly outside the stated uncertainty. There also seems to be some measurement irregularities when measu

43、ring runout at ORMC. This is probably due to dirt or lint on the artifact. The R. E. Smith artifact is well designed to measure both index and runout with the concentric and non-concentric bands. Acknowledgemens We thank R. E. Smith for providing the index and runout artifact for our inter-compariso

44、n and for providing runout calculations from our ORMC index data. We also wish to thank Mark May at The Gleason Works for providing inter-comparison measurements on the R. E. Smith artifact. References 1. Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, NIST Tech

45、nical Note 1287, National Institute of Standards and Technology, O Gaithersburg, MD., 1994. 14 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesPUBUSHED BY AMERICAN GEAR MANUFACTURERS ASSOCIATION 1500 KING STREET, ALEXANDRIA, VIRGINIA 22314 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services