A reduction ratio for minimizing dissipated energy in a mechatronic system with a gear train

In order to minimize the energy dissipated in a mechanical servo system, the present paper proposes a design method for a reduction ratio in a gear train with frictions of all types. The Coulomb friction in the servo system is represented by the efficiency of the gear train. Even if the system is nonlinear due to the Coulomb friction, an optimal velocity function can be obtained analytically by introducing a zero crossing time. This is the time at which the input torque of the gear changes from the positive direction to the negative one. This velocity function depends on the system parameters and thus the moment of inertia and the viscous friction of the gear train are expressed in terms of the reduction gear ratio. The energy dissipated due to the optimal velocity function is partially differentiated with respect to the zero crossing time and the gear ratio. The resulting optimal gear ratio is compared to that obtained from the conventional inertia matching method. The results of simulations indicate that the optimal gear ratio can greatly reduce the amount of the dissipated energy.