A Computational Approach for the Analysis and Synthesis of the Interactive Force Between Two General Permanent Magnets by Using Monte Carlo Integration

This article presents a numerical approach for computing and synthesizing the force between two permanent magnets (PMs) under general conditions. Initially, a general formula for determining the interactive force between two arbitrary PMs is derived, resulting in a unified 6-D integral for any magnet pairs. Following this, a computational algorithm utilizing Monte Carlo (M-C) integration for solving the integral is developed. The significance of the presented method is twofold. First, the derived formula and algorithm are unified, enabling the computation of forces between two magnets under general conditions, allowing for arbitrary shapes, magnetizations, and relative locations of the magnets. Second, the approach is applicable to the design synthesis problems, where the geometries of the magnets are to be designed to achieve the prescribed interactive force. Numerical examples are provided to demonstrate the generality and feasibility of the method for magnet-force analysis and synthesis. In addition, the accuracy and efficiency of the proposed approach are discussed and compared with the finite-element-analysis (FEA) simulation in the case studies.