中文摘要：

分子电流理论是一种计算永磁轴承力学特性的经典理论,利用此理论分析计算永磁轴承承载力时一般采用蒙特卡罗法或椭圆积分法等求解四重积分,蒙特卡罗法数值稳定性差,椭圆积分法求解析解过程中,有时会出现奇异值。为了简化计算,提出了永磁轴承承载力方程的积分定义求解方法,该方法将被积函数的积分域分割成有限个微域,对于每个微域,以被积函数的微域中心值与微域体积的乘积作为被积函数的积分值,将所有微域的积分和值近似作为函数积分值;基于双丝杠导轨副与3维力传感器,研制了永磁轴承力学性能的测试装置,完成永磁轴承承载力的试验验证;较为系统地对比分析了积分定义法与蒙特卡罗法、有限元法数值解的计算结果。研究结果表明：积分定义法计算过程简单,易于编写计算程序,相对误差较小。

英文摘要：

The equivalent surface current is a typical method for calculating the mechanical property of permanent magnet bearing. However, Monte Carlo method or elliptic integral method are usually used to solve a quadruple integral for the equivalent surface current. However, the numerical stability is poor for the Monte Carlo method, and singular values sometimes appear for the elliptic integral method. In order to simplify the calculation, the integral definition method is proposed to solve the equations of the load capacity for the permanent magnet bearing, in details, the integral domain of integrand is divided into a infinite number of small domains, the integral value of each small domain is approximatively equal to the production of the center value of integrand and the volume of small domain, the integral value of integrand is approximatively equal to the sum of total integral value of small domains. The testing device is developed by using double layers ball screw drive systems and a 3-DOF force sensor to test the mechanical property for the permanent magnet bearing, and the results show the theoretical value of the integral definition method agrees well with the tested one. A comparative study confirms that the integral definition method is superior to the Monte Carlo method and finite element method in either the simplification of calculation process and program development or the calculation error.