Optimal design of lead for minimizing energy dissipated in a mechatronic system with a ball screw-nut

It is important to minimize the dissipated energy even in a mechatronic system that repeats start and stop motions frequently. A forklift and an injection molder are a typical mechatronic system that repeat reciprocating motions. The reciprocal motions are realized by a ball screw-nut, which converts rotation into translation motion. The present paper proposes a simple method for determining an optimal lead of the ball screw-nut which minimizes the dissipated energy of the mechatronic system. The forward and backward efficiencies of the ball screw-nut are different and are functions of the lead. The dissipated energy depends on these efficiencies and the viscous friction of the system. By simplifying the viscous friction, the energy can be formulated as a function of the efficiencies. The optimal lead can be easily obtained by solving a quartic equation, which is reduced from the formulated energy function. It is verified that the proposed optimal lead is approximated well to the strictly optimal lead that is calculated numerically. The dissipated energy by the proposed optimal lead can be significantly decreased compared to a conventional inertia matching method.