David F. Goldsing Manufacturing Variance to Design Gears With Minimum Transmission Error

Abstract

This paper deals with the design of spur gears that have minimum transmission error and are insensitive to manufacturing variance. We address two stages of design: (1) generation of candidate designs (selection of number of teeth, pressure angle, etc.), and (2) tooth profile modification. The first stage involves a search of discrete combinations of design variables, while the second stage utilizes numerical optimization techniques. The key research issue is finding a candidate design and its profile modification that not only has low transmission error, but is insensitive to variations in the design values caused by the manufacturing process. To achieve this goal, the procedure applies Taguchi’s concept of parameter design. In this paper, we consider a design problem with a set specification: fixed center distance, speed ratio, and transmission torque. We seek to find a limited number of candidate designs by applying conventional design generation techniques and some design heuristics. For each candidate design, the procedure determines the optimum profile modification (linear tip relief) by linking the Load Distribution Program (LDP) for gears with an optimization program package (OPTPAK). From the resulting peak optimum, we further seek the statistical optimum using an algorithm developed in this paper. The statistical optimum shows a nominal increase in the transmission error, but is quite insensitive to typical process error associated with gear manufacturing. The developed algorithm readily applies to other gear designs as well as other types of machine elements. In particular, we foresee our procedure to be particularly effective for helical gears. We hope to further our method by developing a means to add statistical heuristics to the discrete design generation stage.