Thermal error modeling of motorized spindle considering temperature hysteresis: A GRU-Transformer prediction model

Abstract

The “zero-transmission” structure of the motorized spindle significantly improves precision and efficiency, but the heat generated by the internal motor and bearings also leads to more thermal errors. To eliminate the impact of these errors on machining, it is necessary to establish a thermal error model. However, the hysteresis of temperature can affect the accuracy of the thermal error model. In this study, the thermal characteristics of the motorized spindle were first analyzed, and a thermal characteristics experimental platform for the spindle was built. Next, a Support Vector Machine based spindle state classification was established to classify whether the spindle is rotating. The Temporal Convolutional Network model was then used to predict the spindle temperature. Subsequently, the Gated Recurrent Unit and Transformer models were combined to construct a thermal error prediction model. While ensuring the extraction of features related to temperature and thermal error, the periodicity of the time series was preserved. This improved the prediction accuracy of temperature and thermal errors under different operating conditions, ensuring the robustness of the model. Finally, experimental validation was conducted on the SVM state classification, TCN temperature prediction model, and GRU-Transformer thermal error model. The results showed that the accuracy of the SVM state classifier exceeded 93 %, the $R^2$ value of the SVM-TCN temperature prediction model was greater than 0.94, and the $R^2$ value of the GRU-Transformer thermal error model was greater than 0.92. Furthermore, the overall performance of these models was superior to that of existing models.