Experimental Verification of Force and Stiffness Between Two Ring Magnets Calculated by Monte Carlo Integration Technique

Abstract

This paper presents the calculation and experimental verification of force and stiffness between two concentric ring-shaped rare earth magnets. This kind of magnet configuration is invariably used in magnetic bearing, micromass measurement system, turbomachineries and space applications. Estimation of magnetic force and stiffness is always important in any application of permanent magnet as it influences the stability and performance of the system. Some analytical methods are available which involve direct solution of elliptic integral, which made the calculation tedious, complex, time- and space consuming. In this work, a simple approach based on Monte Carlo integration technique is proposed to calculate the force and stiffness. Monte Carlo integration technique is preferred to calculate the multidimensional elliptic integrals due to simplicity of the method, less computational time and memory requirement. The result is compared with existing finite element method and verified with experimental result. The verification process indicates that there is a small deviation in result of the proposed method from experimentally obtained result, but taking into account simplicity, space and time requirement, this approach may be considered to be a useful alternative method to calculate force and stiffness of a magnetic system. The proposed method is one of the best examples of utilizing an old computational concept in modern complicated problem solution.