Analysis of the magnetic levitation characteristics of the vertical Halbach array in a permanent magnet rotor

Compensating for the gravity of mechanical components using electromagnetic force is a key and challenging task in creating a microgravity environment on the ground. Studying the variation of electromagnetic force, particularly its nonlinear nature, with the change in air gap is essential for the precise control of synthetic gravity. In this paper, we explore the variation of electromagnetic force as a vertical toroidal Halbach permanent magnet rotor (THPMR) approaches a conductive plate. Theoretical and experimental studies are performed to establish a levitation model of the THPMR. We focus on the magnetic field distribution of the rotor and the value of the repulsive force. Virtual magnetic charge theory analyses are presented to completely describe the magnetic potential distribution function in the whole space. The method to solve the main problem includes the magnetic potential constraint equations established by Maxwell’s equations, the magnetic field characteristics on two-dimensional surfaces in the toroidal magnet expansion, and the second-order partial differential equations established by the second-order vector magnetic potential, all of which account for the nonlinear behaviour. To validate our theoretical model, experiments are meticulously conducted with conductive plates of various specifications under different air gap conditions. The results corroborate the theoretical predictions, demonstrating the model’s accuracy and the consistency between theoretical and experimental outcomes. An electromagnetic force reaching 35 N is achieved. Additionally, recommendations are provided for gravity compensation schemes based on this nonlinear approach.