Application of time series analysis in thermal error modeling of motorized spindle

Aiming at the problem that the radial thermal angle error was ignored in three-point based measurement and modeling of spindle thermal error, five-point method was used to measure the error and an Autoregressive Moving Average (ARIMA) model was proposed for thermal elongation and declination angles based on time series analysis. The augmented dickey-fuller test algorithm was applied to determine the stability of thermal error sequence, and the model pattern was identified by autocorrelation/partial autocorrelation function. By combining Yule-Walker equations with information criteria, the model's order and parameters were solved effectively, which improved the prediction accuracy and generalization ability of the models. Moreover, a method to test the goodness of prediction of the time series model was presented. Spindle thermal error modeling contained axial elongation and radial thermal angle error was more suitable for actual conditions, and it could describe thermal error space pose more accurately. The proposed method was validated through performing a case of motorized spindle.