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.

A method of optimal design for minimization of magnetic density ripple in Surface Motor without Finite Element Analysis (FEA) data is described. By using motor geometric parameters obtained by this optimal design method, magnetic density ripple minimized and force maximized motor is developed and tested by experiment.

表面电机是应用于微米/纳米制造和超精密加工中的定位装置。应用有限元方法，提出了表面电机的磁场分析方法。首先应用ANSYS的电磁部分建立了表面电机的二维有限元模型。然后根据磁场和电流的基本关系，应用面电流模拟方法，建立了永磁体的数学模型，并计算了它的相对磁导率。在此基础上，结合表面电机基本结构，定义所用材料的基本属性，采用ANSYS的平面单元PLANE13和远场单元INFIN110对模型进行网格划分，并在气隙处对网格进行加密。网格的边界条件满足狄利克莱（Dirichlet）边界条件。根据表面电机的通电方式给与永磁体位置相对应的绕组加电流密度J，电流方向与Z轴平行。最后，通过ANSYS的后处理器，获得了表面电机的气隙磁场通量线和磁感应强度分布图。对某些点的磁感应强度值与用传统的解析方法所得到的结果进行比较，其结果基本吻合。为进行表面电 机的动力学分析与设计制造提供了依据。本文提出的数值解法，也同样适用于永磁直线电机。