Minimization of energy dissipated in a ball screw-nut with all kinds of friction

It is important to reduce the energy dissipated even in a mechatronic system. The present paper proposes an optimal velocity function in a position control and an optimal lead of a ball screw-nut in a linear actuator. The linear actuator system is composed of a motor, a ball screw-nut and a load. The system has three kinds of friction, rolling friction in the ball screw-nut, Coulomb friction between the nut and the guides and viscous friction due to lubricating oil. The rolling friction forces are different for the driving sides, a screw and a nut. The frictions are represented by the forward and backward efficiencies of the ball screw-nut, and assumed to be proportional to the absolute value of the input torque. Even if the system is nonlinear due to the rolling friction, an analytical optimal function can be solved by introducing a zero crossing time, when the input torque of the ball screw-nut changes from the positive to the negative directions. The experiment shows that the minimum dissipated energy caused by analytical optimal function is valid. The influence of the lead upon the minimum energy is examined by simulations. The results of the simulations and the experiments indicate that the dissipated energy can be greatly reduced by applying the optimal velocity function and selecting the optimal lead when the inertia of the load is large.