Abstract: 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.

Key words: equivalent surface currents, integral definition method, load capacity, permanent magnet bearings