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

The problem of minimum volume preliminary design of simple and multiple-sta ge spur gear reduction units has been a subject of considerable interest, s ince many high-performance power transmission applications (e.g.,automotive and aerospace) require low weight. One of the principal steps in tradition al 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 gener alized optimal design formulation with multiple objectives which is, in pri nciple, 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 app roach serves to extend traditional design procedures by demonstrating the t radeoff between surface fatigue life and minimum volume using a basic multi objective optimization procedure. This information allows the designer to j udge overall trends and, for example, to assess the penalty in surface fati gue lifetime which would occur for a given weight reduction. (C) 1999 Elsev ier Science Ltd. All rights reserved.