Abstract
This paper discusses an optimal velocity function and an optimal reduction gear ratio which minimize the dissipated energy in a mechanical servo system. Coulomb friction of gears is represented by the efficiency and proposed to be proportional to the absolute value of the output torque of a motor with Coulomb friction. The optimal current and velocity functions can be obtained from an optimal control theory by introducing a zero cross time t_c, when the output torque of a motor is changed from positive to negative. As the dissipated energy can be expressed by a function of t_c, an optimal cross time t_c* minimizing the energy can be represented by a simple function of efficiency of the gears. An optimal number of stages of gear trains is determined from the minimized energy which is a function of the reduction ratio. The theory minimizing the energy is verified by experiments using planetary gear trains driven with a DC motor.
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