A robust optimization procedure with variations on design variables and constraints

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 the 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 the 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 and pressure angle that minimizes transmission error subject to constraints like minimum number of teeth to avoid undercut and maximum bending stress.