A Precise Semianalytical Model for Efficiently Calculating the Magnetic-Track Coupled Forces in a Superconducting Electrodynamic Suspension Train

In superconducting electrodynamic suspension (EDS) trains, the magnetic-track coupled forces arise from the electromagnetic interaction between the onboard magnets and track coils, enabling the train’s suspension, guidance, and propulsion. These forces can be determined based on the mutual inductance between the magnets and track coils. This paper presents a novel segregated integration approach for accurately and efficiently calculating mutual inductance. Building on this approach, we develop a semianalytical model capable of simulating an infinitely long track to compute the magnetic-track coupled forces in an EDS train with high accuracy and efficiency. To validate the model, we conducted force measurements on a superconducting EDS prototype and compared the results with our semianalytical model, which demonstrated a relative error of less than 3%. Additionally, we performed a systematic evaluation of the semianalytical model by comparing it with a finite element model and a widely adopted analytical model based on Neumann’s formula to thoroughly assess its accuracy and applicability. The results show that, compared to the finite element model, our model enhances computational speed by two orders of magnitude while maintaining an accuracy on the order of 10^-3. Furthermore, it surpasses the analytical model in both accuracy and efficiency. Using this developed model, we investigated the forces in an EDS train with a stepped onboard magnet. The results show that employing stepped magnets can suppress the first harmonic of the suspension force by 65% without compromising the train’s suspension and propulsion capabilities.