Application of mathematical optimization in designing spiral bevel and hypoid gear blanks

The best geometry of a gear set usually is found by varying the parameters of most influence within reasonable bounds. The quantity to be minimized, the so-called objective function, often is taken to be the root bending stress of the pinion. The parameters varied are the number of teeth of the pinion and of the gear, and spiral angle, sum of pressure angles, and others. Finding the best layout by varying many quantities independently is cumbersome, and takes a lot of time. In this paper, it is shown how to design spiral bevel and hypoid gear blanks by applying mathematical optimization. Here a simplified model of the original engineering problem is used. Even with this restriction, the practical value of the pertinent optimization program is considerable.