数控机床进给系统热误差自适应解析模型

Adaptive Analytical Model of Thermal Error Prediction for the Ball Screw Feed Drive Systems in CNC Machine Tools

提出了基于丝杠热源表面检测温度的滚珠丝杠热误差预测解析模型.首先,基于变量分离法推导出丝杠轴一维热传导方程的解析解.然后,将两个轴承视为固定热源,将螺母简化为连续分布的多个可移动热源,给出了各热源激励起丝杠温度分布的解析表达式,进而依据叠加原理得出了多热源作用下丝杠轴温度的预测方程.依据各热源表面测点和中心温度的有限元计算结果,确定了其温度差随进给速度和时间变化函数曲线的拟合参数,进而提出了丝杠热误差预测的解析模型.最后通过试验验证了预测模型的有效性.

This paper presents an analytical model of thermal error prediction for the ball screw based on temperatures measured on the surfaces of the heat sources. First, the analytical solution of one dimensional heat conduct equation for the screw shaft is derived based on the variable separation method. Consequently, the two bearings are considered to be fixed heat sources,and the nut is divided into a few of moving heat sources distributed continually. The temperature distribution formula on the screw shaft excited by each heat source is given, and the temperature distribution equation is acquired based on the superposition principle of heat sources. The curve fitting parameters of relation functions of temperature difference between the heat source center and the measured surface point are obtained using FEM calculation data. Then an analytical model is proposed to predict the thermal error distribution of the ball screw shaft on line. Finally,the effectiveness is verified by the experiments.