中文摘要：

轴向刚度分析是永磁轴承设计过程中的重要环节，现有的几类模型计算结果与实测结果存在一定的误差。使用基于分子电流法分析计算轴向永磁轴承的轴向刚度时，由于分子电流法在计算轴向力时需要求解四重积分，计算周期长，甚至不能获得解析解，因此采用蒙特卡罗算法来近似计算轴承的轴向力，使求解过程简单化。通过与有限元法数值解进行比较表明，分子电流法建模可较准确地分析轴向永磁轴承轴向刚度，运用蒙特卡罗算法求解方程，突破了分子电流法难以工程应用的技术难题。

英文摘要：

Computation of axial stiffness of permanent magnet bearings is very important in the design process of permanent magnet bearings. There exists a certain error in the calculation results of several kinds of existing models in comparison to the measured result. The equivalent surface currents method is employed to analyze the stiffness of axial permanent magnet beating, but the solution cannot be obtained easily for a quadruplicate integral. Monte Carlo method is used to solve the equation to simplify the calculation of the stiffness of axial permanent magnet bearing. Thus the equivalent surface currents method can be easily used in engineering. The stiffness of the permanent magnet bearing with the equivalent surface currents method is verified by comparing the simulating result obtained by using the finite element method. The conclusion is that the equivalent surface currents method can be used to calculate the axial stiffness of permanent magnet bearings, and the application of the equivalent surface currents to engineering is not difficult by using the Monte Carlo method.