Repulsive Magnetic Levitation Force Calculation for a High Precision 6-DoF Magnetic Levitation Positioning System

The analytical calculation of magnetic forces is currently an interesting alternative to the time-consuming 3-D finite-element method due to their high accuracy and low computational cost. In this paper, a new semi-analytical solution for determining the levitation force of the repulsive magnetic guidance that has a significant role for controlling and developing high precision magnetic levitation positioning system is presented. An important result is that this new expression, compared with other known equations in the literature, considers the position dependence of the magnetic levitation force over the whole travel range. In order to derive this force, the magnetic field of the permanent magnet is first calculated by introducing and solving the magnetic scalar potential. Taking Lorentz force law into consideration, the proposed equation is finally derived. This semi-analytical equation is suitable for designing and optimizing the magnetic guidance. Furthermore, it can also be used for developing other ironless actuators. The calculated levitation force from the derived equation and the verification by measurements are likewise presented in this paper.