A compensation method for angular indexing error was introduced based on sparse decomposition to correct the angular indexing error caused by the eccentric and tilt of circular gratings installment in a precision turntable. First
the effect of circular grating installed eccentric and tilt on the angular indexing error was analyzed. Next
according to the characteristics of different orders of error in measuring error of circular grating angle
a compensation model of angular indexing error was built based on the sparse decomposition theory and the harmonic analysis to compensate the angular indexing error of the turntable. Finally
a test platform was established
and the effectiveness of the proposed method was verified to compensate the angular indexing error of a precision turntable. The experimental results show that the proposed method can increase 2 orders of magnitude of the angular indexing accuracy. The maximum value of angular indexing error can be reduced to 0.64" from 90.85" through proposed error compensation method. After error compensation with the method
the accuracy of angle positioning can be remarkably improved
meeting the high-accuracy testing requirements of angular displacement of a precision turntable.
JIANG D M, WEI L, YAO T J, et al.. Error analysis and compensation for high accuracy turntable[J]. Navigation and Control, 2015, 14(3):108-111+107. (in Chinese)
GUO J B, CAO H Y, WANG K X, et al.. Study on verification and compensation of indexing errors for turntable[J]. China Mechanical Engineering, 2014, 25(7):894-899. (in Chinese)
ZHAO R J, MA W L. Improving the accuracy of new-type encoders using error harmonic compensation[J]. Electronic Instrumentation Customer, 2009, 16(3):69-71. (in Chinese)
AI CH G, CHU M, SUN H X. Eccentric testing of benchmark circular grating and compensation of angular error[J]. Opt. Precision Eng., 2012, 20(11):2479-2484.(in Chinese)
MI X T, GAO SH Y. Effect of eccentric of circular gratings on angular position accuracy of simulator[J]. Journal of Changchun University of Science and Technology(Natural Science Edition), 2014, 37(3):9-12. (in Chinese)
GUO J B, CAO H Y, WANG K X, et al.. Check of indexing error for turntable and establishment of its compensation model[J]. Journal of Tianjin University(Science and Technology), 2014, 47(6):524-529. (in Chinese)
SHE W J, GAO L M, YANG Y Q, et al.. Calibration and compensation of angular error in laser tracker[J]. Chinese Journal of Scientific Instrument, 2015, 36(SI):52-56.(in Chinese)
FENG CH P, ZHU L Q, PAN ZH K, et al.. New self-calibration method of circular grating eccentric parameters[J]. Chinese Journal of Scientific Instrument, 2016, 37(11):2459-2464. (in Chinese)
LAO D B, ZHOU W H, LI W H, et al.. Cylindrical grating angle measurement technology based on genetic algorithm[J]. Infrared and Laser Engineering, 2015, 44(7):2182-2188. (in Chinese)
KAUL S K, TICKOO A K, KOUL R, et al.. Improving the accuracy of low-cost resolver-based encoders using harmonic analysis[J]. Nuclear Instruments & Methods in Physics Research, 2008, 586(2):345-355.
GAO X, WAN Q H, WANG SH J, et al.. Development of signal compensation technology for photoelectric rotary encoder[J]. Optoelectronic Technology, 2013, 33(2):131-136. (in Chinese)
SU Y Q, ZHANG J X, CHEN B G, et al.. Harmonic analysis application in accuracy improvement of precise turntable[J]. Infrared and Laser Engineering, 2014, 43(1):274-278. (in Chinese)
ZHANG G, ZHANG X F, WANG Y F, et al.. Study on error compensation of angular position measurement[J]. Journal of Test and Measurement Technology, 2016, 30(4):353-357. (in Chinese)
DONOHO D L, ELAD M, TEMLYAKOV V N. Stable recovery of sparse overcomplete representations in the presence of noise[J]. IEEE Transactions on Information Theory, 2006, 52(1):6-18.