Analytical Solution of Transient Forces in a Null-Flux Superconducting Electrodynamic Suspension Train Based on Harmonic Approximation

Electrodynamic suspension (EDS) technology has broad application prospects in high-speed rail transit systems. Accurate and efficient electromagnetic force calculations are essential for system design and optimization. This paper derives analytical expressions for transient forces in a null-flux superconducting EDS train based on the harmonic approximation of mutual inductance. Neumann's formula, combined with a cross-sectional discretization technique, is employed to accurately compute the dynamic mutual inductance between the onboard superconducting magnets and the ground suspension coils. Induced current in the coils is derived from dynamic circuit theory, and the transient forces on the magnets are obtained via the virtual displacement method. An equivalent impedance is introduced to account for electromagnetic coupling among the suspension coils. This model is validated against experimental data, with relative errors of less than 3%. A comparative analysis with both finite element and widely used analytical models demonstrates that our model yields force calculation error below 2.4%, while reducing computation time by 43% compared to the most popular analytical model. The influence of mutual inductance harmonics on transient forces is analyzed. The results indicate that over 98% of the average suspension force is determined by the fundamental mutual inductance, while the force harmonics are even multiples of the magnet-to-coil length ratio, originating from the 3rd, 5th, and 11th harmonics of the mutual inductance. This study establishes a theoretical foundation and offers methodological guidance for optimizing the electromagnetic performance of EDS trains.