Abstract: 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.

Key words: thermal error, temperature, ball screw feed drive system, CNC machine tool, one dimensional heat conduct equation, variable separation method