Dynamic model of NC rotary table in angle measurements with time series

Abstract

In this study, a dynamic model of absolute time grating, a novel kind of displacement sensor, is established in order to apply the absolute time grating sensor, instead of the optical grating sensor, as an angle encoder to the full closed-loop numerical control (NC) rotary table. Time series analysis is employed in the dynamic model, and given the series of past measured angles, therefore, the dynamic model can be used to forecast the next future measured angle. As a result, the original absolute signal sampled in equal time intervals of an absolute time grating sensor can be transformed into continuous incremental pulses for a full closed-loop NC rotary table. When the current angle is deduced, the latest measured angle of the time series is interpolated as standard quantity to compensate for the last forecast error. In this way, the forecast error can be corrected between neighboring sampling periods, and cumulative errors can be eliminated. The forecasting accuracy of incremental pulses for the time grating sensor can reach ±3″ which validates the dynamic model in improving the performance of the time grating displacement sensor in dynamic measurement.