Analysis reveals that bifurcation control enhances stability domain for hybrid electromagnetic suspension, suggesting improved control parameters may prevent self-excited vibrations.
The self-excited vibration of the static suspension of the hybrid maglev train and the vehicle resonance caused by aerodynamic loads will affect the safety and comfort of vehicle operation. This study investigates the improvement of nonlinear vibration characteristics by analyzing the stable domain of control parameters and bifurcation control. A dual-loop control model for a two-degree-of-freedom hybrid electromagnetic suspension system is derived using the Lagrange equation. The stability domain of the proportional differential control parameters is determined via the Hurwitz algebraic criterion for Hopf bifurcation, revealing that control parameters selected at different positions within the domain influence the system’s vibration characteristics. Additionally, the control parameter conditions for the Hopf bifurcation are given. It is demonstrated that the upper boundary of the stability domain is effectively expanded by increasing the thickness of permanent magnets, thereby enhancing the flexibility in selecting stable control parameters. Although aerodynamic loading broadens the extent of the stability domain, it concurrently induces a downward translation of the entire region and lowers the threshold for self-excited vibrations. The system exhibits good vibration characteristics when control parameters are positioned within the stability domain and distant from its boundaries. Specifically, self-excited vibrations can be suppressed by increasing velocity and current control parameters, while displacement control parameters should avoid approaching the margins of the stability domain. Under aerodynamic forces, the amplitude of unsteady aerodynamic excitation is observed to influence the resonant response amplitude of the suspension system significantly. Velocity and current control parameters are found to strongly reduce the resonance at the natural frequency of the suspension frame. This research provides a theoretical foundation for optimizing control parameters and suppressing nonlinear vibrations in hybrid maglev systems. It holds practical engineering significance for enhancing maglev trains’ operational stability and ride comfort.
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Wang et al. (2025) studied this question.
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