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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.

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This paper describes a procedure that incorporates manufacturing and operational variances to achieve designs with robust and optimal performance. The procedure optimizes the expected value of a performance characteristic subject to a set of constraints. It uses concepts from statistical design of experiments to approximate the expected value of a performance characteristic. The procedure incorporates uncertainties in design variables and variations in constraints due to uncertainty in design variables. This paper discusses the following three methods to incorporate variations in constraints: 1) A method using heuristics that evaluates constraints at the worst combinations of design variables, 2) A method with built-in constraint variation that models constraints using first order Taylor expansion, and 3) A method based on differentiating KKT optimality conditions. The design of spur and helical gears with minimum transmission error serves as the target application. The key gear design research issue is to determine the optimal combination of geometric design variables like number of teeth, pressure angle that minimizes transmission error subject to constraints like minimum number of teeth to avoid undercut and maximum bending stress.