Revisiting the inertia matching condition for energy efficiency

The issue of designing servo-actuated systems for enhancing their energy efficiency is dealt with in this paper. Starting from a detailed representation of the energy dissipation in a motor-reducer set, the overall energy cost associated with the execution of a motion task is expressed, in a closed form, as a function of the main design parameters. The analysis is based on the use of scaling rules, which allow to condense the main physical parameters of the motors and of the gearboxes by means of a reduced set of parameters. The resulting framework is implemented into an automatic procedure which selects all feasible designs and evaluates their associated energy costs. Two design test cases are taken into consideration, and the results are used to discuss the traditional sizing method based on the inertia matching rule, showing that it is often unsuited to capturing an energy-optimal design.