Formulation of a non-dimensional criterion for stable dynamical response in coaxial magnetic gears

Coaxial magnetic gears have been investigated thoroughly in recent years. However, magnetic gears are prone to slippage that could be caused by overloading or acceleration of the drive. In the present work, the dynamical system of equations in coaxial magnetic gears was investigated in order to calculate the maximum operational characteristic of the drive. A non-dimensional condition was derived analytically that can determine the dynamical behaviour and whether the system will converge or diverge without the requirement of a numerical solution of the dynamical equation of the drive. A case study was performed where different values of acceleration and applied torque were considered. The convergence of the system was initially examined with the developed non-dimensional condition and then the equation was solved numerically in order to verify the prediction. The developed condition correctly predicted the behaviour of the drive in all cases. Finally, with the developed model the operational characteristics of a coaxial magnetic gear that yield a required transmission error can be calculated analytically. Therefore, with the developed model the maximum operational characteristics in coaxial magnetic gears can be determined analytically with a non-dimensional criterion without implementing iterative methods that would significantly increase the computational cost.