Among the errors in precision machining, thermal error has been recognized as the most significant error. The heat of the nut in the feed drive system plays an important role in the thermal error generated by the feed drive system. To better estimate and further understand the increase in temperature and thermal deformation of the ball screw during operation, a new correlation equation for the frictional torque of the nut is proposed and determined in this study for the calculation of the frictional torque of the nut and the heat generated by the nut at different feed velocities and nut temperatures. In this study, a set of devices for measuring the frictional torque of the nut under different feed velocities and different nut temperatures is designed and established. Various experimental conditions are designed to measure the frictional torque of the nut at different feed velocities and different nut temperatures to establish a correlation equation for the frictional torque of the nut. In addition, for further confirmation, the method for measuring the frictional torque of the nut used in this study is compared with the method using a handheld digital force gauge. The correlation equation for the frictional torque of the nut established in this study is based on the LuGre model and the formula of the frictional torque due to the viscosity of the lubricant of the bearing at different temperatures. The results show that the root-mean-square error between the frictional torque of the nut calculated by the correlation equation and that measured experimentally is 0.0301 N-m, indicating that the correlation equation for the frictional torque of the nut proposed in this study is accurate and feasible.

在精密加工中的误差中，热误差被认为是最大的误差。进给驱动系统中螺母的热量在进给驱动系统产生的热误差中起重要作用。为了更好地估算和进一步了解滚珠丝杠在运行过程中温度和热变形的增加，提出了一个新的螺母摩擦转矩相关方程，并在本研究中确定了该方程，用于计算螺母和螺母的摩擦转矩。螺母在不同的进给速度和螺母温度下产生的热量。在这项研究中，设计并建立了一套用于在不同进给速度和不同螺母温度下测量螺母摩擦扭矩的装置。设计了各种实验条件，以测量在不同进给速度和不同螺母温度下螺母的摩擦扭矩，从而建立了螺母摩擦扭矩的相关方程。此外，为进一步确认，将本研究中使用的螺母摩擦扭矩的测量方法与使用手持式数字测力计的方法进行了比较。这项研究中建立的螺母摩擦扭矩的相关方程基于LuGre模型和由于轴承润滑剂在不同温度下的粘度而引起的摩擦扭矩的公式。结果表明，由相关方程计算出的螺母的摩擦扭矩与实验测得的扭矩之间的均方根误差为0.0301 Nm，