A three-point method has been used to separate the roundness profile of a workpiece and radial motions of a turntable. First, weighted addition is used to extract the roundness profile, and then, inverse filtering is used to recover the original roundness profile. The three-point method works well in the low spatial frequency domain. However, in the high spatial frequency domain, the setting angle error of the sensor causes a large deflection of the transfer function. Therefore, a combination method of the three-point method for roundness profile measurement and an integration method for the straightness profile measurement is proposed. The three-point method for roundness profile measurement is used to estimate low spatial frequency domain and the integration method for straightness profile measurement is used to estimate the high spatial frequency domain. Experimental results showed that the standard deviation of the combination method was smaller than that of the three-point method for most positions.

1. [1] T. Nakata and A. Yamamoto, “Methods of Measuring True Roundness of Cylindrical Work,” J. of The Japan Society of Mechanical Engineers, Vol.53, No.376, pp. 159-163, 1950 (in Japanese). https://doi.org/10.1299/jsmemag.53.376_159
2. [2] Y. Aoki and S. Ozono, “On a New Method of Roundness Measurement Based on the Three-point Method,” J. of The Japan Society for Precision Engineering, Vol.32, No.12, pp. 831-836, 1966 (in Japanese).
3. [3] S. Ozono, “On a New Methodof Roundness Measurement based on the three points method,” Proc. of 1st Int. Conf. on Production Engineering, Tokyo, 1974.
4. [4] K. Mitsui, “A Study on Accuracy Diagnosis : Development of a New Measuring Method for Spindle Rotation Accuracy by Three Points Method,” J. of The Japan Society of Mechanical Engineers, Vol.48, No.425, pp. 115-123, 1982 (in Japanese). https://doi.org/10.1299/kikaic.48.115
5. [5] D. J. Whitehouse, “Some theoretical aspects of error separation techniques in surface metrology,” J. of Physics E, Scientific Instruments, Vol.9, No.7, pp. 531-536, 1976. https://doi.org/10.1088/0022-3735/9/7/007
6. [6] D. G. Chetwynd and G. J. Siddall, “Improving the accuracy of roundness measurement,” J. of Physics E, Scientific Instruments, Vol.9, No.7, pp. 537-544, 1976. https://doi.org/10.1088/0022-3735/9/7/008
7. [7] C. J. Evans et al., “Self-Calibration: Reversal, Redundancy, Error Separation, and ‘Absolute testing’,” Annuals of CIRP, Vol.45, Issue 2, pp. 617-634, 1996. https://doi.org/10.1016/S0007-8506(07)60515-0
8. [8] S. Sonozaki and H. Fujiwara, “Simultaneous Measurement of Cylindrical Parts Profile and Rotating Accuracy Using Multi-Three-Points-Method,” J. of The Japan Society for Precision Engineering, Vol.54, No.11, pp. 2095-2100, 1988 (in Japanese). https://doi.org/10.2493/jjspe.54.2095
9. [9] M. Fukuda, “Coupled Three Point Method for Runout Error Measurement,” Proc. of JSPE (Autumn), pp. 11-12, 2012 (in Japanese). https://doi.org/10.11522/pscjspe.2012A.0.11.0
10. [10] W. Gao, S. Kiyono, and T. Nomura, “A new multiprobe method of roundness measurements,” Prec. Eng., Vol.19, Issue 1, pp. 37-45, 1996. https://doi.org/10.1016/0141-6359(96)00006-2
11. [11] E. R. Marsha, D. A. Arnesonb, and D. L. Martin, “A comparison of reversal and multiprobe error separation,” Prec. Eng., Vol.34, Issue 1, pp. 85-91, 2010. https://doi.org/10.1016/j.precisioneng.2009.03.001
12. [12] E. Okuyama and H. Moritoki, “A Study on the Roundness Measurement and the Radjal Motion Measurement based on the 3-point Method,” J. of The Japan Society for Precision Engineering, Vol.65, No.9, pp. 1312-1316, 1999 (in Japanese).
13. [13] K. Goho, K. Katsurada, and K. Mitsui, “New analysis algorithm for 3-point method,” Proc. of JSPE (Autumn), p. 458, 1999 (in Japanese).
14. [14] E. Okuyama, “Inverse matrix method for the roundness measurement and the radial motion measurement based on the 3-point method,” J. JSPE, Vol.67, No.3, p. 649, 2001 (in Japanese).
15. [15] E. Okuyama, K. Goho and K. Mitsui, “New analytical method for V-block three-point method,” Precision Engineering, Vol.27, No.3, pp. 234-244, 2003. https://doi.org/10.1016/S0141-6359(03)00002-3
16. [16] H. Tanaka and H. Sato, “Basic Characteristics of Straightness Measurement Method by Two Sequential Points,” J. of the Japan Society of Mechanical Engineers, Vol.48, No.436, pp. 1930-1937, 1982 (in Japanese).
17. [17] S. Kiyobo, E. Okuyama, and M. Sumita, “Study on measurement of surface undulation (2nd report), Feature measurement and digital filter,” J. of JSPE, Vol.54, No.3, pp. 513-518, 1988 (in Japanese).
18. [18] E. Okuyama and H. Ishikawa, “Generalized Two-point Method Using Inverse Filtering for Surface Profile Measurement,” Int. J. Automation Technol., Vol.8, No.1, pp. 43-48, 2014. https://doi.org/10.20965/ijat.2014.p0043
19. [19] M. Sawabe, “Bebefit drived from history of length measuring technology,” Bulletin of the Society of Historical Metrology, Japan, Vol.22, No.1, pp. 9-16, 2000 (in Japanese).
20. [20] S. Kiyono, “Ultra-precision Measurement,” 2007 (in Japanese).
21. [21] E. Okuyama et al., “Surface Profile Measurement Based on the Concept of Multi-Step Division of Length,” Int. J. Automation Technol., Vol.11, No.5, pp. 716-720, 2017. https://doi.org/10.20965/ijat.2017.p0716