Magnetic Modeling of Magnetic Levitation Systems Based on a Fast Finite Difference Method

An accurate magnetic force model is crucial for the high-precision control of magnetic levitation systems. Soft magnetic materials, renowned for their excellent magnetic properties, are commonly employed in these systems. However, traditional computational methods either failing to yield accurate magnetic force models estimates in the presence of soft magnetic cores or demanding excessive computational resources, resulting in significant increased processing times. This paper proposes an accurate, efficient, and robust fast finite difference method. The method leverages the finite difference method to solve Maxwell’s equations and derive the spatial distribution of the magnetic field. The computations are performed on a non-uniform grid using an iterative multigrid solver, which enhances both algorithmic efficiency and numerical stability. Following this, the Maxwell stress tensor is applied to compute the spatial distribution of the Lorentz forces. To validate the method, we computed magnetic force models across various magnetic levitation systems and compared its performance with the finite element method software COMSOL and the boundary element method software Radia. Comparative results confirm that the proposed approach is an accurate, versatile, and highly efficient solution.