An Improved Surface Charge Model for the Static Force Calculation among the Permanent Magnets in Magnetic Bearings or Magnetic Springs

This article presents an improved surface charge model for the static force calculation among the permanent magnets (PMs). Generally, there is an error source of the classical surface magnetic charge model due to the assumption of the unit relative permeability. This error source can be ignored for the ferromagnetic actuators but will bring a significant deviation to the ironless devices, such as the magnetic bearings or magnetic springs. To calculate the static force among the PMs more accurately, the estimation for the actual working point of each PM is required. The magnetic field iteration method is used in this article, in which the inner magnetic field intensity of one PM is decided by itself and the external magnetic field sources. By dividing one cuboid magnet into amounts of small cubes, the integral operation can be simplified into the numerical superposition when calculating the average working point. The influences of the number of nodes and iteration times on the model accuracy are analyzed. Finally, two magnetic springs are manufactured and well tested. The static force calculation is based on the expressions of Yonnet and the improved surface charge model. Compared with the classical model, the model error of the improved model can be reduced and the static force values are closer to the 3-D finite-element method (FEM) and experiment results. Furthermore, the improved model has remarkable advantage over the 3-D FEM in aspect of computation time, which is suitable for the design and analysis of the magnetic bearing or magnetic springs.