Transient thermal error modeling of a ball screw feed system

The thermal behaviors of the ball screw feed system significantly affect the machining accuracy of the machine tool, which is widely valued by users and manufacturers. In the current ball screws thermal error models, the moving heat source at nuts is simplified to a fixed heat source to simplify the calculation, which can decrease the model's prediction accuracy. A novel thermal error modeling method for the ball screw feed system is proposed by this paper based on the FEM. In the proposed method, the moving heat source at the nut is loaded into the model by changing the grid distribution at different time steps. Meanwhile, a series of thermal experiments are carried out to collect the thermodynamic data with the machine tool's feed drive system operating at a different speed. And then the multi-objective optimization method is introduced to obtain the heat generated by the nuts and the convection coefficient between the air and the screw. The experimental results show that the thermal error of the ball screw feed system is different when the feed system runs in different intervals, even if the temperature rise at measuring points is the same. In the final, experiments under different conditions are carried out, and the proposed model is accurate enough to predict the thermal error of the ball screw feed system.