时序分析在电主轴热误差建模中的应用

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

针对电主轴热误差基于三点法测量和建模中忽略径向热倾角误差的问题,采用五点法对主轴热误差进行测量,建立基于时序分析的热误差自回归滑动平均混合模型ARIMA。通过引用单位根检验算法实现对热误差序列的平稳性判定,运用自相关/偏自相关函数完成模型的高效识别;利用信息准则解决热误差模型的定阶问题,结合Yule-Walker方程实现自回归参数以及滑动平均参数的求解,从而提高了模型的预测精度及泛化能力,设定了模型的预测优度评价标准。电主轴热误差模型蕴含轴向伸长及径向热倾角,更符合实际,模型可更准确地描述主轴热误差空间位姿状态。通过电主轴热误差建模的应用实例,验证了所提测量及建模方法的有效性。

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 Mov- ing Average （ARIMA） model was proposed for thermal elongation and declination angles based on time series analy- sis. 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 e- quations 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.