Abstract

The rotary axis is the basis for rotational motion. Its motion errors have critical effects on the accuracy of the related equipment, such as a five-axis computer numerical control machine tool. There are several difficult problems in the implementation of high-precision and fast measurement of the multi-degree-of-freedom motion errors of a rotary axis. In this paper, a novel method for the simultaneous measurement of five-degree-of-freedom motion errors of a rotary axis is proposed, which uses a single-mode fiber-coupled laser with a full-circle measuring range. It has the advantages of high efficiency, low cost, and it requires no decoupling calculation. An experimental system was built and a series of experiments were performed. The standard deviation of stability for 60 min of the five-degree-of-freedom measurement is 0.05 arcsec, 0.06 arcsec, 0.04 μm, 0.03 μm, and 0.19 arcsec, respectively. The repeatability deviation of measuring an indexing table is ± 3.4 arcsec, ± 4.6 arcsec, ± 2.6 μm, ± 2.4 μm, and ± 3.2 arcsec. The maximum deviation of comparison is 3.9 arcsec and 3.2 arcsec. These results demonstrate the effectiveness of the proposed method; thus, a new approach of simultaneous measurement of the multi-degree-of-freedom motion errors of a rotary axis is provided.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  3. S. Zhu, G. Ding, S. Qin, J. Lei, L. Zhuang, and K. Yan, “Integrated geometric error modeling, identification and compensation of CNC machine tools,” Int. J. Mach. Tools Manuf. 52(1), 24–29 (2012).
    [Crossref]
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    [Crossref]
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  15. C. J. Chen, P. D. Lin, and W. Y. Jywe, “An optoelectronic measurement system for measuring 6-degree-of-freedom motion error of rotary parts,” Opt. Express 15(22), 14601–14617 (2007).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  24. Y. S. Zhai, Z. F. Zhang, Y. L. Su, X. J. Wang, and Q. B. Feng, “A high-precision roll angle measurement method,” Optik (Stuttg.) 126(24), 4837–4840 (2015).
    [Crossref]
  25. X. F. Zhang, X. Yu, C. Z. Jiang, and B. G. Wang, “The experimental study on PSD,” Chinese J. Sci. Instrum. 24(4), 250–252 (2003).

2017 (2)

D. Kono, Y. Moriya, and A. Matsubara, “Influence of rotary axis on tool-workpiece loop compliance for five-axis machine tools,” Precis. Eng. 49, 278–286 (2017).
[Crossref]

U. Mutilba, E. Gomez-Acedo, G. Kortaberria, A. Olarra, and J. A. Yagüe-Fabra, “Traceability of on-machine tool measurement: a review,” Sensors (Basel) 17(7), 1605 (2017).
[Crossref] [PubMed]

2016 (1)

2015 (3)

M. Holler and J. Raabe, “Error motion compensating tracking interferometer for the position measurement of objects with rotational degree of freedom,” Opt. Eng. 54(5), 054101 (2015).
[Crossref]

Z. Y. He, J. Z. Fu, L. C. Zhang, and X. H. Yao, “A new error measurement method to identify all six error parameters of a rotational axis of a machine tool,” Int. J. Mach. Tools Manuf. 88, 1–8 (2015).
[Crossref]

Y. S. Zhai, Z. F. Zhang, Y. L. Su, X. J. Wang, and Q. B. Feng, “A high-precision roll angle measurement method,” Optik (Stuttg.) 126(24), 4837–4840 (2015).
[Crossref]

2014 (3)

H. Murakami, A. Katsuki, and T. Sajimab, “Department simple and simultaneous measurement of five-degrees-of- freedom error motions of high-speed micro-spindle: Error analysis,” Precis. Eng. 38(2), 249–256 (2014).
[Crossref]

H. Murakami, N. Kawagoishi, E. Kondo, and A. Kodama, “Optical technique to measure five-degree-of-freedom error motions for a high-speed micro-spindle,” Int. J. Precis. Eng. Manuf. 11(6), 845–850 (2014).
[Crossref]

Z. Yang, J. Hong, J. H. Zhang, and M. Y. Wang, “Research on the rotational accuracy measurement of an aerostatic spindle in a rolling bearing performance analysis instrument,” Int. J. Precis. Eng. Manuf. 15(7), 1293–1302 (2014).
[Crossref]

2013 (1)

2012 (1)

S. Zhu, G. Ding, S. Qin, J. Lei, L. Zhuang, and K. Yan, “Integrated geometric error modeling, identification and compensation of CNC machine tools,” Int. J. Mach. Tools Manuf. 52(1), 24–29 (2012).
[Crossref]

2011 (1)

H. Cefu, S. Ibaraki, and A. Matsubara, “Influence of position-dependent geometric errors of rotary axes on a machining test of cone frustum by five-axis machine tools,” Precis. Eng. 35(1), 1–11 (2011).
[Crossref]

2010 (1)

S. R. Park, T. K. Hoang, and S. H. Yang, “A new optical measurement system for determining the geometrical errors of rotary axis of a 5-axis miniaturized machine tool,” J. Mech. Sci. Technol. 24(1), 175–179 (2010).
[Crossref]

2009 (1)

S. T. Lin and W. J. Syu, “Heterodyne angular interferometer using a square prism,” Opt. Lasers Eng. 47(1), 80–83 (2009).
[Crossref]

2007 (4)

W. Y. Jywel, C. J. Chen, W. H. Hsieh, P. D. Lin, H. H. Jwo, and T. Y. Yang, “A novel simple and low cost 4 degree of freedom angular indexing calibrating technique for a precision rotary table,” Int. J. Mach. Tools Manuf. 47(12–13), 1978–1987 (2007).

C. J. Chen, P. D. Lin, and W. Y. Jywe, “An optoelectronic measurement system for measuring 6-degree-of-freedom motion error of rotary parts,” Opt. Express 15(22), 14601–14617 (2007).
[Crossref] [PubMed]

C. J. Chen and P. D. Lin, “High-accuracy small-angle measurement of the positioning error of a rotary table by using multiple-reflection optoelectronic methodology,” Opt. Eng. 46(11), 113604 (2007).
[Crossref]

C. F. Kuang, E. Hong, Q. B. Feng, B. Zhang, and Z. Zhang, “A novel method to enhance the sensitivity for two-degrees-of-freedom straightness measurement,” Meas. Sci. Technol. 18(12), 3795–3800 (2007).
[Crossref]

2004 (1)

Q. B. Feng, B. Zhang, and C. F. Kuang, “A straightness measurement system using a single-mode fiber-coupled laser module,” Opt. Laser Technol. 36(4), 279–283 (2004).
[Crossref]

2003 (1)

X. F. Zhang, X. Yu, C. Z. Jiang, and B. G. Wang, “The experimental study on PSD,” Chinese J. Sci. Instrum. 24(4), 250–252 (2003).

Bin, Z.

Cefu, H.

H. Cefu, S. Ibaraki, and A. Matsubara, “Influence of position-dependent geometric errors of rotary axes on a machining test of cone frustum by five-axis machine tools,” Precis. Eng. 35(1), 1–11 (2011).
[Crossref]

Chen, C. J.

W. Y. Jywel, C. J. Chen, W. H. Hsieh, P. D. Lin, H. H. Jwo, and T. Y. Yang, “A novel simple and low cost 4 degree of freedom angular indexing calibrating technique for a precision rotary table,” Int. J. Mach. Tools Manuf. 47(12–13), 1978–1987 (2007).

C. J. Chen and P. D. Lin, “High-accuracy small-angle measurement of the positioning error of a rotary table by using multiple-reflection optoelectronic methodology,” Opt. Eng. 46(11), 113604 (2007).
[Crossref]

C. J. Chen, P. D. Lin, and W. Y. Jywe, “An optoelectronic measurement system for measuring 6-degree-of-freedom motion error of rotary parts,” Opt. Express 15(22), 14601–14617 (2007).
[Crossref] [PubMed]

Chen, L. Y.

Cuifang, K.

Cunxing, C.

Ding, G.

S. Zhu, G. Ding, S. Qin, J. Lei, L. Zhuang, and K. Yan, “Integrated geometric error modeling, identification and compensation of CNC machine tools,” Int. J. Mach. Tools Manuf. 52(1), 24–29 (2012).
[Crossref]

Feng, Q. B.

Y. S. Zhai, Z. F. Zhang, Y. L. Su, X. J. Wang, and Q. B. Feng, “A high-precision roll angle measurement method,” Optik (Stuttg.) 126(24), 4837–4840 (2015).
[Crossref]

C. F. Kuang, E. Hong, Q. B. Feng, B. Zhang, and Z. Zhang, “A novel method to enhance the sensitivity for two-degrees-of-freedom straightness measurement,” Meas. Sci. Technol. 18(12), 3795–3800 (2007).
[Crossref]

Q. B. Feng, B. Zhang, and C. F. Kuang, “A straightness measurement system using a single-mode fiber-coupled laser module,” Opt. Laser Technol. 36(4), 279–283 (2004).
[Crossref]

Fenglin, Y.

Fu, J. Z.

Z. Y. He, J. Z. Fu, L. C. Zhang, and X. H. Yao, “A new error measurement method to identify all six error parameters of a rotational axis of a machine tool,” Int. J. Mach. Tools Manuf. 88, 1–8 (2015).
[Crossref]

Gomez-Acedo, E.

U. Mutilba, E. Gomez-Acedo, G. Kortaberria, A. Olarra, and J. A. Yagüe-Fabra, “Traceability of on-machine tool measurement: a review,” Sensors (Basel) 17(7), 1605 (2017).
[Crossref] [PubMed]

He, Z. Y.

Z. Y. He, J. Z. Fu, L. C. Zhang, and X. H. Yao, “A new error measurement method to identify all six error parameters of a rotational axis of a machine tool,” Int. J. Mach. Tools Manuf. 88, 1–8 (2015).
[Crossref]

Hoang, T. K.

S. R. Park, T. K. Hoang, and S. H. Yang, “A new optical measurement system for determining the geometrical errors of rotary axis of a 5-axis miniaturized machine tool,” J. Mech. Sci. Technol. 24(1), 175–179 (2010).
[Crossref]

Holler, M.

M. Holler and J. Raabe, “Error motion compensating tracking interferometer for the position measurement of objects with rotational degree of freedom,” Opt. Eng. 54(5), 054101 (2015).
[Crossref]

Hong, E.

C. F. Kuang, E. Hong, Q. B. Feng, B. Zhang, and Z. Zhang, “A novel method to enhance the sensitivity for two-degrees-of-freedom straightness measurement,” Meas. Sci. Technol. 18(12), 3795–3800 (2007).
[Crossref]

Hong, J.

Z. Yang, J. Hong, J. H. Zhang, and M. Y. Wang, “Research on the rotational accuracy measurement of an aerostatic spindle in a rolling bearing performance analysis instrument,” Int. J. Precis. Eng. Manuf. 15(7), 1293–1302 (2014).
[Crossref]

Hsieh, H. L.

Hsieh, W. H.

W. Y. Jywel, C. J. Chen, W. H. Hsieh, P. D. Lin, H. H. Jwo, and T. Y. Yang, “A novel simple and low cost 4 degree of freedom angular indexing calibrating technique for a precision rotary table,” Int. J. Mach. Tools Manuf. 47(12–13), 1978–1987 (2007).

Ibaraki, S.

H. Cefu, S. Ibaraki, and A. Matsubara, “Influence of position-dependent geometric errors of rotary axes on a machining test of cone frustum by five-axis machine tools,” Precis. Eng. 35(1), 1–11 (2011).
[Crossref]

Jiang, C. Z.

X. F. Zhang, X. Yu, C. Z. Jiang, and B. G. Wang, “The experimental study on PSD,” Chinese J. Sci. Instrum. 24(4), 250–252 (2003).

Jwo, H. H.

W. Y. Jywel, C. J. Chen, W. H. Hsieh, P. D. Lin, H. H. Jwo, and T. Y. Yang, “A novel simple and low cost 4 degree of freedom angular indexing calibrating technique for a precision rotary table,” Int. J. Mach. Tools Manuf. 47(12–13), 1978–1987 (2007).

Jywe, W. Y.

Jywel, W. Y.

W. Y. Jywel, C. J. Chen, W. H. Hsieh, P. D. Lin, H. H. Jwo, and T. Y. Yang, “A novel simple and low cost 4 degree of freedom angular indexing calibrating technique for a precision rotary table,” Int. J. Mach. Tools Manuf. 47(12–13), 1978–1987 (2007).

Katsuki, A.

H. Murakami, A. Katsuki, and T. Sajimab, “Department simple and simultaneous measurement of five-degrees-of- freedom error motions of high-speed micro-spindle: Error analysis,” Precis. Eng. 38(2), 249–256 (2014).
[Crossref]

Kawagoishi, N.

H. Murakami, N. Kawagoishi, E. Kondo, and A. Kodama, “Optical technique to measure five-degree-of-freedom error motions for a high-speed micro-spindle,” Int. J. Precis. Eng. Manuf. 11(6), 845–850 (2014).
[Crossref]

Kodama, A.

H. Murakami, N. Kawagoishi, E. Kondo, and A. Kodama, “Optical technique to measure five-degree-of-freedom error motions for a high-speed micro-spindle,” Int. J. Precis. Eng. Manuf. 11(6), 845–850 (2014).
[Crossref]

Kondo, E.

H. Murakami, N. Kawagoishi, E. Kondo, and A. Kodama, “Optical technique to measure five-degree-of-freedom error motions for a high-speed micro-spindle,” Int. J. Precis. Eng. Manuf. 11(6), 845–850 (2014).
[Crossref]

Kono, D.

D. Kono, Y. Moriya, and A. Matsubara, “Influence of rotary axis on tool-workpiece loop compliance for five-axis machine tools,” Precis. Eng. 49, 278–286 (2017).
[Crossref]

Kortaberria, G.

U. Mutilba, E. Gomez-Acedo, G. Kortaberria, A. Olarra, and J. A. Yagüe-Fabra, “Traceability of on-machine tool measurement: a review,” Sensors (Basel) 17(7), 1605 (2017).
[Crossref] [PubMed]

Kuang, C. F.

C. F. Kuang, E. Hong, Q. B. Feng, B. Zhang, and Z. Zhang, “A novel method to enhance the sensitivity for two-degrees-of-freedom straightness measurement,” Meas. Sci. Technol. 18(12), 3795–3800 (2007).
[Crossref]

Q. B. Feng, B. Zhang, and C. F. Kuang, “A straightness measurement system using a single-mode fiber-coupled laser module,” Opt. Laser Technol. 36(4), 279–283 (2004).
[Crossref]

Lee, J. Y.

Lei, J.

S. Zhu, G. Ding, S. Qin, J. Lei, L. Zhuang, and K. Yan, “Integrated geometric error modeling, identification and compensation of CNC machine tools,” Int. J. Mach. Tools Manuf. 52(1), 24–29 (2012).
[Crossref]

Lin, P. D.

W. Y. Jywel, C. J. Chen, W. H. Hsieh, P. D. Lin, H. H. Jwo, and T. Y. Yang, “A novel simple and low cost 4 degree of freedom angular indexing calibrating technique for a precision rotary table,” Int. J. Mach. Tools Manuf. 47(12–13), 1978–1987 (2007).

C. J. Chen and P. D. Lin, “High-accuracy small-angle measurement of the positioning error of a rotary table by using multiple-reflection optoelectronic methodology,” Opt. Eng. 46(11), 113604 (2007).
[Crossref]

C. J. Chen, P. D. Lin, and W. Y. Jywe, “An optoelectronic measurement system for measuring 6-degree-of-freedom motion error of rotary parts,” Opt. Express 15(22), 14601–14617 (2007).
[Crossref] [PubMed]

Lin, S. T.

S. T. Lin and W. J. Syu, “Heterodyne angular interferometer using a square prism,” Opt. Lasers Eng. 47(1), 80–83 (2009).
[Crossref]

Matsubara, A.

D. Kono, Y. Moriya, and A. Matsubara, “Influence of rotary axis on tool-workpiece loop compliance for five-axis machine tools,” Precis. Eng. 49, 278–286 (2017).
[Crossref]

H. Cefu, S. Ibaraki, and A. Matsubara, “Influence of position-dependent geometric errors of rotary axes on a machining test of cone frustum by five-axis machine tools,” Precis. Eng. 35(1), 1–11 (2011).
[Crossref]

Moriya, Y.

D. Kono, Y. Moriya, and A. Matsubara, “Influence of rotary axis on tool-workpiece loop compliance for five-axis machine tools,” Precis. Eng. 49, 278–286 (2017).
[Crossref]

Murakami, H.

H. Murakami, A. Katsuki, and T. Sajimab, “Department simple and simultaneous measurement of five-degrees-of- freedom error motions of high-speed micro-spindle: Error analysis,” Precis. Eng. 38(2), 249–256 (2014).
[Crossref]

H. Murakami, N. Kawagoishi, E. Kondo, and A. Kodama, “Optical technique to measure five-degree-of-freedom error motions for a high-speed micro-spindle,” Int. J. Precis. Eng. Manuf. 11(6), 845–850 (2014).
[Crossref]

Mutilba, U.

U. Mutilba, E. Gomez-Acedo, G. Kortaberria, A. Olarra, and J. A. Yagüe-Fabra, “Traceability of on-machine tool measurement: a review,” Sensors (Basel) 17(7), 1605 (2017).
[Crossref] [PubMed]

Olarra, A.

U. Mutilba, E. Gomez-Acedo, G. Kortaberria, A. Olarra, and J. A. Yagüe-Fabra, “Traceability of on-machine tool measurement: a review,” Sensors (Basel) 17(7), 1605 (2017).
[Crossref] [PubMed]

Park, S. R.

S. R. Park, T. K. Hoang, and S. H. Yang, “A new optical measurement system for determining the geometrical errors of rotary axis of a 5-axis miniaturized machine tool,” J. Mech. Sci. Technol. 24(1), 175–179 (2010).
[Crossref]

Qibo, F.

Qin, S.

S. Zhu, G. Ding, S. Qin, J. Lei, L. Zhuang, and K. Yan, “Integrated geometric error modeling, identification and compensation of CNC machine tools,” Int. J. Mach. Tools Manuf. 52(1), 24–29 (2012).
[Crossref]

Raabe, J.

M. Holler and J. Raabe, “Error motion compensating tracking interferometer for the position measurement of objects with rotational degree of freedom,” Opt. Eng. 54(5), 054101 (2015).
[Crossref]

Sajimab, T.

H. Murakami, A. Katsuki, and T. Sajimab, “Department simple and simultaneous measurement of five-degrees-of- freedom error motions of high-speed micro-spindle: Error analysis,” Precis. Eng. 38(2), 249–256 (2014).
[Crossref]

Su, Y. L.

Y. S. Zhai, Z. F. Zhang, Y. L. Su, X. J. Wang, and Q. B. Feng, “A high-precision roll angle measurement method,” Optik (Stuttg.) 126(24), 4837–4840 (2015).
[Crossref]

Syu, W. J.

S. T. Lin and W. J. Syu, “Heterodyne angular interferometer using a square prism,” Opt. Lasers Eng. 47(1), 80–83 (2009).
[Crossref]

Wang, B. G.

X. F. Zhang, X. Yu, C. Z. Jiang, and B. G. Wang, “The experimental study on PSD,” Chinese J. Sci. Instrum. 24(4), 250–252 (2003).

Wang, M. Y.

Z. Yang, J. Hong, J. H. Zhang, and M. Y. Wang, “Research on the rotational accuracy measurement of an aerostatic spindle in a rolling bearing performance analysis instrument,” Int. J. Precis. Eng. Manuf. 15(7), 1293–1302 (2014).
[Crossref]

Wang, X. J.

Y. S. Zhai, Z. F. Zhang, Y. L. Su, X. J. Wang, and Q. B. Feng, “A high-precision roll angle measurement method,” Optik (Stuttg.) 126(24), 4837–4840 (2015).
[Crossref]

Yagüe-Fabra, J. A.

U. Mutilba, E. Gomez-Acedo, G. Kortaberria, A. Olarra, and J. A. Yagüe-Fabra, “Traceability of on-machine tool measurement: a review,” Sensors (Basel) 17(7), 1605 (2017).
[Crossref] [PubMed]

Yan, K.

S. Zhu, G. Ding, S. Qin, J. Lei, L. Zhuang, and K. Yan, “Integrated geometric error modeling, identification and compensation of CNC machine tools,” Int. J. Mach. Tools Manuf. 52(1), 24–29 (2012).
[Crossref]

Yang, S. H.

S. R. Park, T. K. Hoang, and S. H. Yang, “A new optical measurement system for determining the geometrical errors of rotary axis of a 5-axis miniaturized machine tool,” J. Mech. Sci. Technol. 24(1), 175–179 (2010).
[Crossref]

Yang, T. Y.

W. Y. Jywel, C. J. Chen, W. H. Hsieh, P. D. Lin, H. H. Jwo, and T. Y. Yang, “A novel simple and low cost 4 degree of freedom angular indexing calibrating technique for a precision rotary table,” Int. J. Mach. Tools Manuf. 47(12–13), 1978–1987 (2007).

Yang, Y.

Yang, Z.

Z. Yang, J. Hong, J. H. Zhang, and M. Y. Wang, “Research on the rotational accuracy measurement of an aerostatic spindle in a rolling bearing performance analysis instrument,” Int. J. Precis. Eng. Manuf. 15(7), 1293–1302 (2014).
[Crossref]

Yao, X. H.

Z. Y. He, J. Z. Fu, L. C. Zhang, and X. H. Yao, “A new error measurement method to identify all six error parameters of a rotational axis of a machine tool,” Int. J. Mach. Tools Manuf. 88, 1–8 (2015).
[Crossref]

Yu, X.

X. F. Zhang, X. Yu, C. Z. Jiang, and B. G. Wang, “The experimental study on PSD,” Chinese J. Sci. Instrum. 24(4), 250–252 (2003).

Yusheng, Z.

Zhai, Y. S.

Y. S. Zhai, Z. F. Zhang, Y. L. Su, X. J. Wang, and Q. B. Feng, “A high-precision roll angle measurement method,” Optik (Stuttg.) 126(24), 4837–4840 (2015).
[Crossref]

Zhang, B.

C. F. Kuang, E. Hong, Q. B. Feng, B. Zhang, and Z. Zhang, “A novel method to enhance the sensitivity for two-degrees-of-freedom straightness measurement,” Meas. Sci. Technol. 18(12), 3795–3800 (2007).
[Crossref]

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C. F. Kuang, E. Hong, Q. B. Feng, B. Zhang, and Z. Zhang, “A novel method to enhance the sensitivity for two-degrees-of-freedom straightness measurement,” Meas. Sci. Technol. 18(12), 3795–3800 (2007).
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Y. S. Zhai, Z. F. Zhang, Y. L. Su, X. J. Wang, and Q. B. Feng, “A high-precision roll angle measurement method,” Optik (Stuttg.) 126(24), 4837–4840 (2015).
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S. Zhu, G. Ding, S. Qin, J. Lei, L. Zhuang, and K. Yan, “Integrated geometric error modeling, identification and compensation of CNC machine tools,” Int. J. Mach. Tools Manuf. 52(1), 24–29 (2012).
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S. Zhu, G. Ding, S. Qin, J. Lei, L. Zhuang, and K. Yan, “Integrated geometric error modeling, identification and compensation of CNC machine tools,” Int. J. Mach. Tools Manuf. 52(1), 24–29 (2012).
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Chinese J. Sci. Instrum. (1)

X. F. Zhang, X. Yu, C. Z. Jiang, and B. G. Wang, “The experimental study on PSD,” Chinese J. Sci. Instrum. 24(4), 250–252 (2003).

Int. J. Mach. Tools Manuf. (3)

S. Zhu, G. Ding, S. Qin, J. Lei, L. Zhuang, and K. Yan, “Integrated geometric error modeling, identification and compensation of CNC machine tools,” Int. J. Mach. Tools Manuf. 52(1), 24–29 (2012).
[Crossref]

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[Crossref]

W. Y. Jywel, C. J. Chen, W. H. Hsieh, P. D. Lin, H. H. Jwo, and T. Y. Yang, “A novel simple and low cost 4 degree of freedom angular indexing calibrating technique for a precision rotary table,” Int. J. Mach. Tools Manuf. 47(12–13), 1978–1987 (2007).

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H. Murakami, N. Kawagoishi, E. Kondo, and A. Kodama, “Optical technique to measure five-degree-of-freedom error motions for a high-speed micro-spindle,” Int. J. Precis. Eng. Manuf. 11(6), 845–850 (2014).
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S. R. Park, T. K. Hoang, and S. H. Yang, “A new optical measurement system for determining the geometrical errors of rotary axis of a 5-axis miniaturized machine tool,” J. Mech. Sci. Technol. 24(1), 175–179 (2010).
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C. F. Kuang, E. Hong, Q. B. Feng, B. Zhang, and Z. Zhang, “A novel method to enhance the sensitivity for two-degrees-of-freedom straightness measurement,” Meas. Sci. Technol. 18(12), 3795–3800 (2007).
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S. T. Lin and W. J. Syu, “Heterodyne angular interferometer using a square prism,” Opt. Lasers Eng. 47(1), 80–83 (2009).
[Crossref]

Optik (Stuttg.) (1)

Y. S. Zhai, Z. F. Zhang, Y. L. Su, X. J. Wang, and Q. B. Feng, “A high-precision roll angle measurement method,” Optik (Stuttg.) 126(24), 4837–4840 (2015).
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Figures (7)

Fig. 1
Fig. 1 Six DOF geometric motion errors of a rotary axis.
Fig. 2
Fig. 2 Schematic of the proposed method.
Fig. 3
Fig. 3 Schematic of the measurement and common-path compensation of the angular drift.
Fig. 4
Fig. 4 Experimental system.
Fig. 5
Fig. 5 Calibration results of the QDs for measuring displacement errors (left) and of the PSDs for measuring angular errors (right).
Fig. 6
Fig. 6 Results of the stability experiments (60 min).
Fig. 7
Fig. 7 Results of the repeatability and comparison experiments.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

ε z ( θ ) = Δ Y PSD 1 2 f 1 ,
ε y ( θ ) = Δ Z PSD 1 2 f 1 ,
ε z ( θ ) = Δ Y PSD 1 2 f 1 + θ ref θ ,
δ y ( θ ) = Δ Y QD 1 2 = Δ Y QD2 2 .
δ z ( θ ) = Δ Z QD1 2 = Δ Z QD2 2 ,
ε x ( θ ) = Δ Z QD 1 Δ Z QD 2 2 h ,
Δ β = Δ Y PSD2 f 2 , Δ γ = Δ Z PSD2 f 2 ,
ε z ( θ ) = Δ Y PSD 1 2 f 1 ± Δ β ε y ( θ ) = Δ Z PSD 1 2 f 1 ± Δ γ .
δ y ( θ ) = Δ Y QD1 2 ± l Δ β = Δ Y QD2 2 ± l Δ β δ z ( θ ) = Δ Z QD1 2 ± l Δ γ = Δ Z QD2 2 ± l Δ γ .

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