Friction is one of the important factors resulting in the contour error of feed servo systems for high-speed, high precision CNC machine tools. A mathematics model of a high speed high precision feed servo table with PID controlling has been established with consideration of friction effects. The friction can be calculated according to the sliding speed and the oil film between the two contact surfaces by using a two-component mixed friction model. The protrusion error occurring at the quadrant boundary in the circular motion is profoundly studied by means of numerical simulation and experiments under different work conditions, and the conclusion that the quadrant protrusion error lags with the rising of the feed rate is obtained. Comparisons between the simulation results and the experiment results demonstrate that with the mathematics model, the dynamics of high speed high precision servo feed systems under PID controlling can be accurately simulated, and the friction error and its characteristics in the course of the feeding can be precisely predicted.

本文提出了计算表面电机气隙磁通量密度分布的分析方法。首先，建立了表面电机磁场的分析模型，给出了磁标量位的拉普拉斯方程以及一系列边界条件。然后用分离变量法获得了永磁体在气隙中产生的磁场强度和磁通量密度的分析表达式。最后将分析结果与实验结果进行对比，证明了分析方法的正确性。为进行表面电机对比研究、优化设计和机械动力学建模提供了基础。

errors, a model is developed to analyze load distribution of ball screw with errors in various load conditions are theoretically investigated. Negative errors makes the load on ball or guiding grooves in corresponding position smaller, even there is no contact in the position when the negative errors reaches certain value. Positive error makes the load bigger. If error heights are assumed to be normally distribution random, the load distribution without error is average value of that in random-error contact. It is valuable for equilibrating load distribution to correct nut groove. The simulation results show that model proposed in this paper is significant to study characteristics of ball screw with regard of errors.