Uncertainty quantification for spindle axial thermal error of CNC machine tools considering hysteresis effect

Abstract

Most of the existing research on thermal error regression modeling of CNC machine tools establishes deterministic models, presents point predictions for thermal errors and focuses on the scenario where there is no hysteresis effect between input and output. There is little research on quantifying the uncertainties of spindle axial thermal error when there exist significant hysteresis effects between the temperature points and spindle axial thermal error. In this regard, this paper presents a novel uncertainty modeling method for spindle axial thermal error. Firstly, to screen out key temperature points, the whole temperature points are sorted according to the minimal redundancy maximal relevance (mRMR) criterion, and the candidate input feature sets are generated. Then, the gated recurrent unit (GRU) model is introduced to handle the hysteresis effects. Finally, the deterministic GRU model is transformed into the prediction interval-based GRU (PI-GRU) model, which can produce prediction intervals (PIs) of the spindle axial thermal error. The correctness and effectiveness of this method are verified by the spindle axial thermal error experiments. In contrast with the Gaussian process regression (GPR) method, the proposed method deals with the hysteresis effects more appropriately and performs better in uncertainty prediction accuracy.