Optimal Design of Mechanical Transmissions for High Performance Servo-Drive Systems

Abstract

Optimizing the design of the mechanical transmission elements in a servo-drive system has a profound effect on its dynamic performance; the acceleration capability. Servo-drive systems can be classified, according to the type of its inertial load, into rotary and translatory systems. Accordingly, the components of the transmission system mainly include a gear set and/or a ball-screw. In this paper the effect of the mechanical transmission characteristics (moments of inertia, gear set reduction ratio and ball-screw pitch) on the acceleration capability of the servo-drive system is investigated. Three gear schemes are presented in order to describe the variation of the gear set moment of inertia as function of its reduction ratio. In the first gear scheme, the driving pinion dimensions and moment of inertia remain constant, while the driven gear wheel pitch circle diameter increases as the gear set reduction ratio increases. The second gear scheme assumes a fixed center distance between the pinion and gear wheel for any gear set reduction ratio. Finally, the third gear scheme expresses the mass moment of inertia of the pinion and the gear wheel as a function of the gear set reduction ratio and the mass moment of inertia of the pinion at unity gear ratio. A generalized relation, applicable to any gear scheme, between the pinion moment of inertia at unity reduction ratio and the applied torque is presented. The effect of the choice of the gear scheme on the acceleration capability of the rotary and translatory servo-drive systems is investigated and compared. The paper provides the servo-system designer with means for integrating the “variable” reduction gear characteristics into the mechanical model in an adaptive manner.