Abstract
In order to help reduce the amount of energy dissipated in machines, electric motors are used as power engines because of the high efficiency and the easy regeneration capability. The power of the motors is transmitted to the mechanical load via a gear. The present paper discusses the optimal gear ratio that minimizes the energy dissipated in a mechatronic system. The dissipated energy is composed of Joule loss in the motor and friction losses in the mechanical system including the gear. The minimum dissipated energy under an optimal velocity function can be formulated analytically as a function of the gear ratio, when a viscous friction force is neglected. However, in the presence of the viscous friction force, the minimum dissipated energy can not be formulated analytically because the optimal velocity function is very complicated. In order to simplify the determination of the optimal gear ratio, the viscous friction is assumed to be constant. From this assumption, the optimal gear ratio can be easily obtained by solving a algebraic equation with respect to one variable. It is seen by simulations that the proposed optimal gear ratio is well approximated to a strictly optimal gear ratio, and can make the great effect of energy-saving compared to the ratio obtained by the conventional inertia matching method.
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