Prediction of the Temperature Rise and Thermal Error of Feed Systems Under Repeatable Operating Conditions Using a Superposition Method

In precision machining, the feed system is a critical subsystem. However, it can generate considerable frictional heat during operation, causing the temperature of the ball screw feed system to rise and resulting in thermal expansion of the ball screw. This thermal expansion reduces the machining accuracy of the final parts. To detect and compensate for the temperature and thermal error of the ball screw feed system in real time, rapidly assessing its temperature field is essential. Traditional methods such as the finite element method (FEM) provide high computational accuracy and have been extensively studied. However, their long computation process limits their application in real-time thermal error prediction. To address this, a feed drive superposition method (FDSM) is proposed herein to rapidly compute the temperature and thermal error of the ball screw feed system using the superposition principle. The FEM model divides the screw into 108 elements, each 10 mm long. The resulting temperature rise data for each element under each boundary condition are stored to form a screw temperature rise database. In practice, the actual machining conditions determine the boundary condition values. The corresponding temperature rise data are retrieved and superimposed to compute the complete screw temperature rise and thermal error. Crucially, the FDSM reduces the computation time from hours to less than 2 s—achieving an acceleration of over 3600-fold—while maintaining high accuracy. Across all three cases, the RMSE between the FDSM and FEM results is consistently below 1.2 μm, while comparison with experimental data yields an RMSE of 6.0 μm, demonstrating both its reliability and suitability for real-time thermal error compensation in ball screw feed systems.