Prediction of the Thermal Elongation of the Ball Screw Mechanism under Various Rotational Speeds

In numerical control machines, the thermal elongation of the ball screw influences the position accuracy. Different rotational speeds lead to different temperature changes at different positions in a ball screw system. In this paper, a new method is proposed to calculate the temperature rise of different positions when the ball screw is in the thermal equilibrium state. The thermal transmission of ball screws is analyzed, and the heat generation and transfer coefficient are calculated based on the laws of thermodynamics. The function between the temperature rise and position is built by solving the thermal equilibrium differential equations. The thermal elongation is obtained after the temperature rise is calculated. In order to prove the validity of this model, a series of detection tests are conducted to obtain the temperature rise of a ball screw and the thermal elongation under different rotational speeds. The experimental results show that the realistic temperature rise and the thermal elongation agree well with the theoretical values.