An optimal lead of a ball screw-nut for minimizing energy dissipated in a linear actuator

In order to help reduce global warming, it is important to minimize the dissipated energy even in a mechanical servo system. The present paper proposes a simple method for determining an optimal lead of a ball screw-nut used in the servo system. The rolling friction is represented by the efficiency of the ball screw-nut system. Even if the system is nonlinear due to rolling friction, an optimal velocity function can be obtained analytically by introducing a zero crossing time. This is the time at which the input torque to the ball screw-nut changes from positive to negative. The optimal velocity function is determined from the optimal zero crossing time which depends a forward and a backward efficiencies of the ball screw-nut system. The energy dissipated by the optimal velocity function can be obtained analytically by neglecting the viscous friction. The optimal lead of the ball screw-nut, which minimizes this analytical dissipated energy, is obtained by solving an algebraic equation. The results of simulations indicate that the optimal lead can greatly reduce the amount of dissipated energy.