Angle-error Separation and Self-calibration at Arbitrary Angular Positions for Circular Grating Encoders

doi:10.3901/JME.260103

Abstract

Abstract: The overall accuracy of circular-grating angle encoders is known to determine the performance of high-end equipment and precision metrology. To address the sparse sampling and incomplete full-circle characterization inherent to discrete calibration with an autocollimator and polygon prism, a self-calibration framework without external references is proposed. An angle-error detection model based on Fourier time-shift characteristics is formulated; an analytical transfer relation between multi-sensor angle measurements and the error spectrum is derived; and three data-fusion weighting strategies—minimum-variance, arithmetic-mean, and magnitude-based—are designed so that continuous full-circle error extraction and compensation can be achieved. Simulations (including Monte Carlo analyses of installation phase and noise) and experiments are performed with respect to sensor layout, fusion weights, sensor consistency, and sampling density. An angular-metrology platform is constructed using a Renishaw REXM20USA255 disk with T2001-30A reading heads and a Ti2000A12E interpolator, and independent comparisons are conducted with a photoelectric autocollimator and polygon prism. It is demonstrated that minimum-variance weighting yields the best detection performance; after self-calibration, an absolute full-circle error of ±0.8″ is achieved with a single sensor. By increasing sampling density, residual harmonic errors are markedly reduced (PV decreases from 0.29″ to 0.10″). Considering observability and noise robustness, a three-reading heads layout is recommended. The effectiveness of the self-calibration approach is thereby validated, and a deployable solution is provided for scenarios in which external high-precision instruments cannot be used.

Key words: angle measurement error, error self-calibration, Fourier time shift, data fusion, reading head layout, circular grating encoder

CLC Number:

TG806

JIN Yusheng, DING Jianjun, LI Changsheng, LIU Yangpeng, LIU Xindong. Angle-error Separation and Self-calibration at Arbitrary Angular Positions for Circular Grating Encoders[J]. Journal of Mechanical Engineering, 2026, 62(4): 25-36.

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