Theoretical and Experimental Decomposition of Mechanical Error Propagation in Optical Rotary Encoders

This paper presents a combined theoretical and experimental methodology for analysing and validating mechanical error propagation in optical rotary encoders. A vector-based mathematical model is experimentally verified using a three-stage methodology comprising measurement of shaft centre motion, grating disc motion and encoder angular error. Independent measurements of the individual mechanical error sources are combined to predict the encoder angular error and compared with traceable angular comparator measurements. The proposed methodology achieved correlation coefficients up to 0.984 for two different grating disc mounting conditions, demonstrating good agreement between the predicted and measured angular error profiles. The results confirm that encoder angular error is governed by the combined contribution of multiple mechanical error sources and demonstrate that, once the dominant eccentricity component is minimised, optimisation of the circumferential optical readhead position provides an effective means of reducing the residual angular error. The proposed methodology provides a practical framework for analysing, predicting and optimising mechanical error sources during the design, assembly and calibration of high-accuracy optical rotary encoders.