Metrological assessment and direction-aware compensation of an industrial rotary encoder calibration system

Abstract This work presents a comprehensive metrological assessment of an industrial rotary encoder calibration system based on polygon-autocollimator cross-calibration. The system was evaluated using clockwise (CW), counterclockwise (CCW), and bi-directional measurement protocols to characterize direction-dependent behavior. Evaluation according to ISO-230-2 revealed systematic positioning E , repeatability R and reversal B errors leading to the total positioning error A up to 6.57″–7.37″. Environmental conditions were monitored during calibration, confirming sufficient thermal stability. High-precision encoder sub-divisional errors were quantified using signal quality analysis, and Fourier harmonic decomposition was applied to the calibrated deviation curves to identify dominant mechanical error sources. A three-factor analysis of variance (ANOVA) was performed to statistically separate the effects of angular position, rotation direction, and measurement series, demonstrating that both direction and position–direction interaction are highly significant contributors to measurement variability. Based on these findings, an enhanced Type A uncertainty evaluation incorporating ANOVA variance components was applied, preventing underestimation of uncertainty compared to conventional pooled repeatability approaches. A complete GUM-compliant uncertainty budget was established, including Type A and Type B contributions, with the expanded uncertainty reaching up to 0.98″ for bi-directional operating mode. Motivated by the statistical evidence of direction dependence, direction-aware error compensation strategy was developed and validated, including a unified bi-directional model explicitly incorporating rotation direction. The proposed compensation approach achieved substantial reduction of systematic positioning errors ( E ≈ 0 ) and improved angular accuracy by 75%–78% . The presented methodology provides a practical and statistically rigorous framework for industrial rotary encoder calibration and performance optimization.