Tradeoff analysis in minimum volume design of multi-stage spur gear reduction units

The problem of minimum volume preliminary design of simple and multiple-stage spur gear reduction units has been a subject of considerable interest, since many high-performance power transmission applications (e.g., automotive and aerospace) require low weight. One of the principal steps in traditional design procedures relates to the determination of an “optimal” value of diametral pitch at which tooth bending fatigue failure and surface fatigue failure are equally likely. The purpose of this paper is to present a generalized optimal design formulation with multiple objectives which is, in principle, applicable to a gear train of arbitrary complexity. The methodology is applied to the design of two-stage and three-stage spur gear reduction units, subject to identical loading conditions and design criteria. The approach serves to extend traditional design procedures by demonstrating the tradeoff between surface fatigue life and minimum volume using a basic multiobjective optimization procedure. This information allows the designer to judge overall trends and, for example, to assess the penalty in surface fatigue lifetime which would occur for a given weight reduction.