Fully Analytical Calculation Method for Suspension Force Between Permanent Magnet and Coil in Magnetic Levitation Positioning Systems

In six-degree-of-freedom (6-DoF) magnetic levitation positioning systems, accurate calculation of the suspension force between permanent magnets and coils is critical for system design and control. A fully analytical calculation method is proposed for the repulsive suspension force between square coils and cubic permanent magnets. This method derives a closed-form analytical expression for the x-component magnetic flux density B _x generated by the permanent magnet in space using the magnetic charge model and Maxwell’s equations, and further obtains an analytical integral formula for the z-component suspension force F _z through the Lorentz force equation. Compared with traditional three-dimensional finite element method (3D-FEM), the fully analytical method can compute the force field distribution quickly and accurately without numerical integration. By introducing an integration range correction coefficient and dynamically adjusting the integration boundaries of the four coil sides, the accuracy of force calculation under displacement variations is effectively improved. Experimental verification results show that the error between analytical calculation results and measured values is less than 5%, meeting the design requirements of high-precision magnetic levitation positioning systems.