Nonlinear Analysis of Magnetic Gear Dynamics Using Superposition and Conservation of Energy

This paper presents an analytical approach to the nonlinear dynamics of magnetic gears. Without compromising the system's nonlinearity, a magnetic gear's motion can be separated into rigid body motion and motion about a fixed center. Then, neglecting losses, the behavior of the torque angle can be evaluated using the conservation of energy principle. This approach shows excellent agreement with a Simulink model and a transient finite element analysis (FEA) model of a magnetic gear with sinusoidal torque angle curves. However, there are some discrepancies in the predicted velocities and oscillation frequencies compared to results produced by FEA models of designs with significant torque ripples, but the proposed approach still agrees with each of the FEA models about whether the gear will slip for over 98.5% of the cases. Also, cases with viscous friction are considered, but this has a limited effect on the system's dynamic behavior immediately after a change in the applied torques. With viscous friction, the proposed approach still agrees with each of the FEA models about whether the gear will slip for at least 93.5% of the cases. This analysis also demonstrates the significant impact of the effective inertia ratio on the system's dynamic performance.