Optimization and unification of two - stage helical gear reducer

Gears were used in ancient times although in a primitive form. A turning point in the rapid development of gears was in the late nineteenth and early twentieth century. In this time the invention of high-performance tools, highresistant materials and the creation of sufficient, accurate methods of heat and chemical treatment took place. Further improvement by optimizing the transmission structure, and the unification of its components is of great practical and economic importance. These problems are presented in this contribution. In particular, this paper deals with the problem of optimization and unification of two stage helical gear reducer with axial and opposite input and output shafts. The basic goal of this study is to unify the case because the case is one of the most expensive transmission elements. In connection with that, it is possible to put into the same case different sets of wheels to obtain predetermined different total gear ratios. An optimization procedure is very useful for a choice of the set of gear wheels. The total mass of gear wheels is assumed as an objective function. Equality and inequality restriction conditions are determined with respect to the standard recommendations and the literature. The center distance between the shafts is obtained through the optimization procedure imposed on the stage of the reducer which is subjected to the maximum load. The center distance after rounding is used next as a parameter in all variants of the reducer. The general formulation of the problem is presented for the considered engineering example. The numerical calculations are carried out for the specific data.