Three DOF internal resonance for electromechanical integrated toroidal drive

In this paper, based on the electromechanical coupled nonlinear dynamic equations of the drive system, the analytical solutions of the free vibration under 3-DOF internal resonance are proposed. The analytical solutions of the forced responses under 3-DOF internal resonance are proposed as well when the exciting frequency is far from or near three different natural frequencies. Using these equations, the free vibration and the forced responses of the drive system under 3-DOF internal resonance are investigated. The results show that under internal resonance conditions, the system responses are different when the exciting frequency is near the three different natural frequencies. Some of them correspond to the unstable vibration state. Some correspond to the synthetic responses of the resonance responses and the internal resonance. The amplitudes of the forced responses with internal resonance are relatively large. In order to avoid unfavorable noise and large dynamic load, the internal resonance should be removed in design of the drive system.

► The analytical solutions of the free vibration under 3 DOF internal resonance are proposed.
► The analytical solutions of the forced responses under 3 DOF internal resonance are proposed.
► The free vibration and the forced responses of the drive system under 3 DOF internal resonance are investigated.
► Under 3 DOF internal resonance, the system responses are complicated and the amplitudes of the forced responses are large.