Calculation and Verification of Magnetic Force in a Radial Permanent Magnetic Bearing based on Quasi-Monte Carlo Method

Permanent magnetic bearings (PMB) are used nowadays in many applications ranging from turbomachinery to energy storage flywheels due to their simple construction, no contact, and no wear. The calculation of the magnetic force is of great significance in the optimal design progress. However, the current magnetic force expression obtained by the equivalent magnetic charge model is a multidimensional integral with a complex integrand. In order to simplify the calculation under the premise of ensuring accuracy, the equal distribution sequence Quasi-Monte Carlo method (QMC) is used to calculate the magnetic force between two ring magnets in this paper. Based on Monte Carlo method (MC), it is proposed to solve the multidimensional integral by using a sequence of low-discrepancy irrational numbers that are more uniform than the randomly generated point distribution to avoid aliasing of projections and have a faster rate of convergence. The integral is programmed in MATLAB using MC and QMC and verified using the finite element method (FEM), then the results are compared with the data in published literature. The results show that QMC has higher accuracy and better repeatability than MC, and the calculation efficiency is higher. The results of the proposed method are in good agreement with FEM and published literature, and the required time is shorter than FEM, which is a more suitable method for magnetic force calculation in some cases.