Considering the nonlinear magnetic coupling stiffness among components of the magnetic gear with intersecting axes and a straight SP (MGIASS), the nonlinear dynamic model and differential equations of the MGIASS system are established. Then, the expression of the forced response is obtained when the excited frequency is close to the torsional mode frequency of the input rotor. The forced responses analysis of the example system shows that: the response frequencies include the excited frequency and the double frequency. Multiple proximity between the natural frequencies directly affects the stability and resonance amplitude.

The dynamic performance optimization of magnetic gear devices is essential to their industrialization. In this study, upon considering the magnetic field coupling characteristics of different components of a field modulated magnetic gear with intersecting axes (FMMGIA), we first obtained the magnetic coupling stiffnesses of these components via the finite element method. On this basis, we further established a dynamic model as well as the corresponding differential equations for the magnetic gear. Thereafter, we analyzed the modal characteristics and the influences of the primary design parameters on the modal frequency of the FMMGIA system. The results indicated that the magnetic coupling stiffnesses among the FMMGIA components were significantly lower than the meshing stiffnesses of the mechanical gears. In addition, the magnetic gear system consisted of three orders of torsional modals as well as three orders of horizontal vibration modals, among which the torsional modal frequencies of both the input and output rotors were substantially lower than others. Finally, parameters such as the minimum axial length and the permanent magnet remanence demonstrated considerable have impacts on the modal frequencies of the FMMGIA system.

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