System analysis and active vibration control of a simplified electromagnetic track brake model

Abstract

Magnetic track brakes are prone to self-excited vibrations at low velocities, which can harm the mechanical structure and need to be mitigated. To avoid severe vibrations, active control strategies utilising the available electromagnetic system are investigated in this study. As the electromagnetic-mechanical coupling is a cause for self-excited vibrations itself, energy-based analyses are conducted on a simplified model to examine the underlying excitation mechanisms first. They are then assessed to identify effective countermeasures. An analytical equation for the effective energy input into the oscillating system is obtained, highlighting that the negative gradient of the sliding friction coefficient and the involved dynamics of the coupled electromagnetic system are reasons for the loss of stability. It is shown that the dominating phenomenon can change with the vehicle velocity and that each cause can initiate self-excited vibrations without the other being present. Conducted bifurcation analyses confirm analytical findings and reveal a significant reduction in the magnetic attraction force by increasing oscillating amplitudes, leading to decreased braking performance during oscillations. Building on the acquired findings, an active vibration control strategy is presented to force the phase shift between the electromagnetic and mechanical states to a particular value, minimising the effective energy input. Results from the nonlinear stability analysis of the closed-loop system show that the implemented state feedback can suppress the excitation mechanism associated with the electromagnetic coupling, further actively dissipate energy, and prevent vibrations over the whole velocity range.