Thermal Error Prediction of Ball Screws in Full Time Series Using Working Condition Data Based on Mechanism and Data Hybrid-Driven Model

The ball screw, serving as a vital component in the feed drive systems of machine tools, is susceptible to thermal errors that significantly impact its accuracy. Nevertheless, current thermal error modeling methods for ball screws face significant challenges in achieving full time series prediction. Furthermore, these methods also impose stringent requirements for a complex temperature data collection process, which is further constrained by the compact structure of machine tools. Additionally, valuable working condition data that is readily available remains underutilized in thermal error prediction. This paper proposes a novel hybrid-driven model that combines mechanism and data driven approaches to achieve full time series thermal error prediction of ball screws. The proposed model utilizes the operating rotational speed as a key input parameter, eliminating the need for temperature collection during both the modeling stage and the compensation process. The temperature model as a mechanism-driven model based on heat transfer theory was proposed to calculate the temperature of the thermal sensitive points by utilizing operating rotational speed, and the accuracy of the model was validated through thermal characteristics experiments of ball screws under four different working conditions. The data-driven models based on different traditional neural networks are established to predict thermal errors according to the time series temperature data obtained from the temperature model, and the hyperparameters of different neural networks were optimized by Beetle Antennae Search (BAS). Comparative analysis among different neural network-based hybrid-driven models reveals that the BAS-CNN model consistently exhibits lower absolute errors, predominantly below 10μm, as well as lower root mean squared error (RMSE) and mean absolute error (MAE) values in each working condition. The BAS-CNN model, within the hybrid-driven model framework, proves to be better suited for full-time series prediction of thermal errors in ball screws. It serves as a foundation for thermal error compensation by utilizing working condition data.