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.

在数控机床中，滚珠丝杠的热伸长会影响位置精度。在滚珠丝杠系统的不同位置，不同的转速会导致不同的温度变化。本文提出了一种新的计算滚珠丝杠处于热平衡状态下不同位置的温升的方法。分析了滚珠丝杠的热传递，并根据热力学定律计算了热量的产生和传递系数。温升与位置之间的函数是通过求解热平衡微分方程建立的。在计算出温度升高之后获得热伸长率。为了证明该模型的有效性，进行了一系列检测测试，以获取滚珠丝杠的温度升高和不同转速下的热伸长率。实验结果表明，实际温升和热伸长率与理论值吻合良好。