Dynamic analysis of a 7 degrees of freedom non-linear electrodynamic suspension system for a hyperloop pod

Hyperloop is a concept that efficiently enables high-speed travel. When travelling in a railway system, main forces that slow down are wheel friction and aerodynamic drag. A Hyperloop system aims to eliminate both opposing forces by travelling in vacuum tubes, which will eliminate the aerodynamic drag, and by making the pod levitate, which will eliminate the wheel friction. During levitation, the stability of the system is crucial. A 7 DOF model is proposed to evaluate the dynamic behaviour of different degrees of freedom of the pod, which are relevant to passenger safety and comfort. The objective of this study is to model the behaviour of the lift forces produced by the permanent magnet levitation system as a spring force, which is non-linear in nature, study the variation of non-linear frequencies with different amplitudes, analyse the type of non-linearity (hardening or softening), study the response of the pod when it is excited by various possibilities such as irregularities in the conductive track while travelling at different speeds, and study the response of the pod under acceleration and braking events due to the inertial forces plus the magnetic drag forces. A mathematical model for the system was derived, and the response was obtained by solving the governing equations using the Newmark β method for the linear model and a successive iterative scheme for solving the non-linear model. Finally, the linear and non-linear results were compared.