Exogenous input autoregressive model based on mixed variables for offline prediction thermal errors of CNC Swiss lathes

Accurate prediction models of thermal errors are very useful for improving the machining accuracy of machine tools; it is also the core of thermal error compensation technology. Often, it is preferable to predict thermal deformation using a dynamic model, as opposed to computational inaccuracy and non-robustness existing in the static model. Autoregressive models are one of the most commonly used dynamic models. However, the autoregressive model needs to measure the thermal error online, which can be intrusive to the production process and reduce production efficiency. This paper presents a new exogenous input autoregressive modeling approach based on mixed variables (MV-ARX) in CNC Swiss lathes. In addition, offline prediction is achieved by replacing online measurements with estimates of thermal errors. The effects of factors on thermal error, such as ambient temperature and spindle speed, are analyzed through thermal characteristic experiments. The K-means clustering method was used to select the thermal critical point, and the exogenous input autoregressive prediction model was optimized by combining the selected temperature variables with the spindle speed to improve the accuracy and robustness of offline prediction. Compared with the model based on temperature-variable autoregression (TV-ARX) and multivariate linear regression (MLR), the proposed model shows better prediction performance. The offline prediction of thermal errors also showed good performance under non-training conditions, with an offline prediction accuracy of up to 83.52%. The modeling method proposed in this work may pave the way for improving the prediction of other errors with similar nonlinear hysteresis dynamical systems.