1、5. 1 98FTM6 Calibration of Master Gears on Coordinate Measurement Machines by: B.L. Cox, B. Rasnick, B. Adkins, Lockheed Martin Energy Systems, Inc., and E. Walker, NC A however, there are at least five approaches used in industry. The Global approach uses ANSI/ASME B89.1 .12M-19902 or similar perfo
2、rmance tests to form a basis for uncertainty estimates. The Virtual Coordinate Measuring Machine (CMM) method requires a detailed model of all the machine and probing errors. Once this model is created the predicted machine errors can be combined appropriately with the artifact geometry to predict t
3、he measurement errors for specific measurement tasks. The Comparator method involves measuring O a master artifact and a test artifact one after the other in the same position on the measuring machine. A calibrated artifact nearly identical to the workpiece is required but very low uncertainties can
4、 be achieved. The Surrogate artifact method approximates a measurement task on a spatial arrangement of reference (simple geometry, low uncertainty) artifacts. The Decomposition method breaks down the measurement task into its basic components. The method uses reference artifacts to characterize mea
5、surement errors and their effect on the final measurement task. This paper describes the general concept of measurement decomposition for a master gear. A more detailed discussion of each uncertainty method is provided in Y-12 Technical Report Y/AMT-3283. Master Gear Measurement Decomposition In the
6、 case of a master gear, the uncertainty determination consists of measuring an involute profile artifact, a tooth alignment artifact, and an index artifact in the same orientation as a gear. The uncertainty of each artifact has been previously determined measurement decomposition and repeatability m
7、easurements are made in the new orientation to determine the uncertainty of each feature ( involute profile, tooth alignment, and index). For the involute profile artifact and the tooth alignment artifact, the reference surfaces are a plane and one shaft center, when orientated on the rotary table.
8、The artifacts are shown in figures 1-3. -1 - Figure 1. involute profile artifact positioned for master gear uncertainty test Figure 2. Tooth alignment artifact positioned for master gear uncertainty test -2- Figure 3. Index artifact positioned for master gear uncertainty test A spur master gear will
9、 also be used for internal process control purposes and inter-comparison measurements are being conducted with NET. The measurement decompositions for the involute profile artifact and the tooth alignment artifact are discussed in AGMA 97FTM1 4. Inter-comparison results are presented below. In order
10、 to verify the uncertainty estimate, three independent measurements were made for inter-comparison. A surrogate artifact was available from a previous experiment. This artifact is a spatial arrangement of three precision spheres that closely simulates the basic elements of a gear profile artifact (f
11、igure 4). Previous measurements provided an informal 2-sigma estimated uncertainty of however, scanning with the CMM is possible. ACMM program was developed, in conjunction with the FORTRAN program, to accept the parameters and the inspection points then generates all inspection points and clearance
12、 points for all other teeth to be inspected. These programs reduced the programming time to less than one hour, but limits the inspection to a certain type CMM and probe configuration. A sample of the data input for the FORTRAN program is shown below: 1. 2. 3. 4. 5. 6. 7. Type of gear (spur or helic
13、al) External or internal Units (inches or millimeters) Lead Helix angle Base circle diameter Normal module 8. Number of teeth 9. Pitch diameter 10. Face width 11. Outer diameter 12. Bore diameter, length, etc. 13. Number of levels to check on bore 14. Number of points per level on bore 15. Number of
14、 teeth to check 16. Number of involute profiles per tooth 17. Number of points per involute profile 18. Number of lead profiles per tooth 19. Number of points per lead trace A long term solution was also started, with the help of Dr. Earnest Walker and his summer intern students at the North Carolin
15、aA for more complex artifacts. Ultimately, it is the users responsibility to translate the traceability and uncertainty to the product gears. This can be accomplished by directly comparing the calibrated artifact with the unknown artifact or product gear. Several examples of this process are given b
16、elow: . Note: It is noted, that for process control, it may be necessary to operate inspection instrument in the same environment as manufacturing equipment. When the temperature varies significantly from 20“ C, the inspection instrument must be calibrated at the operating temperature and the calibr
17、ated artifact and product gear should be sufficiently normalized at this temperature. It may be difficultto predict the effect of temperature on inspection equipment due to geometry and coefficient of thermal expansion (CTE) of different materials, so for certification purposes it is required to cor
18、rect both the instrument and artifact back to 20“ C. A. Example - Uncertainty of a gear measuring instrument using the direct comparison method and a calibrated involute master Note: Assume that once the uncertainty of the instrument is determined, only one measurement is taken on the product gear o
19、r gear artifact. If more than one measurement is taken, then the value can be averaged and the U95 uncertaintycan be divided by the square root of the number of measurements taken. 1, Make at least 1 O measurement runs on the gear measuring instrument using the calibrated master as the known artifac
20、t. Ten is not a magic number, more would be better for estimating standard deviations but 10 is a minimum. These runs should be made very carefully in an effort to obtain the best possible results. - 13- From the (n) runs in step Al, determine the average (icm) and standard deviation (Jcm). If the g
21、ear measuring instrument is not operated at 20“ C, you must either correct the calibrated value (v) to the operating temperature or correct the measured value (x) back to 20“ C. See section Appendix B for correcting for temperature effects on gear artifacts. From the values in step A2, determine the
22、 lack of agreement (Sd(cm) between the calibrated value and the measured value. This lack of agreement is due to the variability in the mean of the measurements and the variability of the calibrated value as shown in figures Al and A2. The variability in the mean cannot be less than the variability
23、in the calibrated value because each measurement of the artifact is limited by the uncertainty of the calibrated value. A “student Y“ test could be used, but it has the complication of which “k“ value to use when determining the variability of the artifact. Sd(cm = JoZm - + -where S: Sv is the stand
24、ard ncm nv deviation of the calibrated value usually , ncm is the number of expressed as - “95jcd I 2 measurements in step 2, and n, is the number of times the calibrated artifact has been calibrated. Over a sufficiently long period of calibrations, the uncertainty of the calibrated artifact could b
25、e reduced to the mean of the calibrated artifact measurements plus the non-statistical component uncertainties. To determine the bias, subtract the calibrated value from the average from step A2. If the absolute value of the bias is larger than the absolute value of 2Sd(cm), then a significant bias
26、(more than the 95% confidence level) from the calibrated values exists. Either the gear measuring instrument should be re-calibrated or the values should be corrected for the bias. Variabi in calib value ( - u, = 2 JSV + 02 f la 4 4 I * Bias f lo .I - Lack of agreement = Root sum square of variabili
27、ty in mean + variability in calibrated value (Sd) Repeatability (0) Figure AI. Graphical description of Uss Uncertainty for corrected bias Variability in Cali brated value (S,) U, = (BIAS( -t- 2 JSf + o2 + S; Figure A2. Graphical description of Ug5 uncertainty for uncorrected bias 5. If the bias is
28、corrected or does not exist, then the 6. If the bias is not corrected, then the most Ug5 uncertainty is two times the root sum conservative calculation of the Ug5 uncertainty squares of the calibrated standard deviation is to add the absolute value of the bias to the plus the standard deviation of t
29、he values in (corrected) uncertainty in step 5 step 2. including the lack of agreement determined in U,(corrected) = 24s: + o$, step 3. U95cm(uncorrected) = (bias,/ + 2 - 14- 7. The uncertainty either from step A5 or A6, depending on the bias, is the uncertainty applied to product gears or to gear a
30、rtifacts. Sample comparison of slope of an involute artifact Calibrated value = -0.05 pm Sv = 0.45 pm Operating temperature = 22.2222“ C Run Slope (um) Cor. Slope (pm) U95(cal) = 0.9 pm 1 -1.3 2 -1.2 3 -1.1 4 -1 .o 5 -1.5 6 -1 .o 7 -1.6 8 -1.2 9 -1.3 10 -1.5 Avg. (Gem)= -1.474 pm (km = 0.211 pm bias
31、(,) = -1.474 - (- -1.5 -1.4 -1.3 -1.2 -1.7 -1.2 -1.8 -1.4 -1.5 -1.7 ) = -1.42,. pm Sd(cm) = J-3 0.455pm , 2sd(cm) = 0.910 pm 1-1.4241 10.9101 therefore the bias is significant “95uTv = I - 1.4241 + 2 0.45 + 0.21 1 + 0.4552 = 2.77 pm B. Example - Calibrate a working master from a calibrated grand mas
32、ter. NOTE: Assume that more than one measurement is taken so that the value can be averaged and the U95 uncertainty can be divided by the square root of the number of measurements taken. 1. Make at least 1 O measurement runs on the gear measuring instrument using the calibrated master as the known a
33、rtifact and the working master as an unknown. Ten is not a magic number, more would be better for estimating standard deviations but 10 is a minimum. These runs should be made very carefully in an effort to obtain the best possible results. 2. 3. 4. 5. 6. 7. From the (n) runs in step 81, determine t
34、he average (Ywm) and standard deviation (uwm) of the differences in the two masters. If the gear measuring instrument is not operated at 20“ C, you must either correct the calibrated value (v) to the operating temperature or correct the measured value (x) back to 20“ C. See section Appendix B for co
35、rrecting for temperature effects on gear artifacts. Since the uncertainty of the working master will always be based on several careful measurements, the standard deviation in step 82 can be divided by the square root of the number of measurements. From the values in steps 82 and 83, determine the l
36、ack of agreement (Sd(cm) between the calibrated value and the measured value. standard deviation of the calibrated master “95 = 2 J-a If the bias is not corrected, then the most conservative calculation of the Ug5 uncertainty is to add the absolute value of the bias to the U95(wm) (corrected) uncert
37、ainty in step B6 - 15- . including the lack of agreement determined in step 4. 8. The uncertainty either from step B6 or 87, . depending on the bias, is the uncertainty applied to working master. Sample comparison of working and calibrated involute artifacts (slope) Ug5(crn) = 2.77 urn (from A.7) Sv
38、(crn) = 7 2.77 - 1.39 pm Operating temperature = 20“ C Run 1 2 3 4 5 6 7 8 9 10 Slope Difference (pm) -0.5 -0.4 -0.3 -0.2 -0.7 -0.2 -0.8 -0.4 -0.5 -0.7 Avg. (zwm) = -0.47 um (Twm = 0.211 um = 0.21 1 = 0.067 pm (wma & 10 bias(,) = -0.47 um Sd(wm) 2sd(wrn) =2.78 um = Jw + 1.3g2 = 1.39 pm (-0.471 12.78
39、1 therefore the bias is not significant U95(wm) = 2 1 .3g2 i 0.0672 = 2.78 um C. Example - Calibrate a product involute master from a working involute master. NOTE: Assume that the calibration of the product artifacts will be based on the results of a single run rather than the average of more than
40、one run. 1. Obtain measurements from at least ten runs of a product involute master against a working master. These runs can be already available from previous efforts or can be made for this 2. 3. 4. 5. 6. study. The intent is that they represent routine operating conditions for measurements in an
41、effort to estimate the repeatability of the measurement process when no special care is taken in contrast to theexample B above. From the (n) runs in step C1, determine the average (Xpm) and standard deviation (Tpm) of the differences in the two masters. If the gear measuring instrument is not opera
42、ted at 20“ C, you must either correct the calibrated value (v) to the operating temperature or correct the measured value (x) back to 20“ C. See section Appendix B for correcting for temperature effects on gear artifacts. From the values in step C2, determine the lack of agreement (Sd(pm) between th
43、e working master and the product master. where Sv(wm) is the standard deviation of the working master usually expressed as. U95iWrnI 2 The bias is the average of the differences between the two masters. If the absolute value of the bias is larger than the absolute value of 2sd(cm), then a significan
44、t bias (more than the 95% confidence level) from the calibrated values exists. Either the gear measuring instrument should be re-calibrated or the values should be corrected for the bias. If the bias is corrected or does not exist, then the Ug5 uncertainty is two times the root sum squares of the ca
45、librated standard deviation (Sv(wm) from step 6.8) plus the standard deviation of the values in step C2. . If the bias is not corrected, then the most conservative calculation of the U95 uncertainty is to add the absolute value of the bias to the U95(pm) (corrected) uncertainty in step C5 including
46、the lack of agreement determined in - 16- 7. The uncertainty either from step C5 or C6, depending on the bias, is the uncertainty applied to product master. Sample comparison of product and working involute artifacts (slope) UgS(wm) = 2.78 um (from 8.8) s(,) = y = i .39 pm Operating temperature = 20
47、“ C Run Slope Difference (um) 1 -0.25 2 -0.2 3 -0.15 4 -0.1 5 -0.45 6 -0.1 7 -0.4 8 -0.2 9 -0.25 10 -0.45 Avg. (Xpm)= -0.255 um = -0.255 pm = ,/- = 1.39 um UPm = 0.134 um Sd(Pm) 2Sd(pm) = 2.78 pm 1-0.2551 12.781 therefore the bias is not significant = 2 ji .392 + 0.1342 = 2.79 pm “95(pm) - 17- . :.Y
48、:,. .,. - I. . . Appendix B Effect of. Temperature on Gear Artifacts The effect of temperature on involute profile, tooth alignment, pitch, and runout are described. For involute, profile, the effect of temperature is essentially due to the change in base circle diameter and the corresponding roll l
49、ength Base radius = 57.15 mm Amount of roll angel = 20“ Temperature difference = 2.5“ C difference. To calculate the deviation. determine the roll length of the starting artifact and subtract this value from the roll length of the expanded/contracted base radius . due to temperature. CTE = 0,00001 15 ppm R = (57.15 mm)(20+j = 19.949113 mm 180 Roll lengthl = Rb2 = Rb1 f (Rbl)(AC)(CTE) = 57.15 + (57.15)(2.5)(0.0000115) = 57.151643 mm Roll length2 Deviation = Rb2c = (57.151643 mm)(20“)(&) = 19.949687 mm = Roll length2 - Roll lengthl = 19.949687 - 19.19491 1
