Design for robustness using manufacturing variation patterns and quadrature factorial models

This dissertation proposes a design procedure that incorporates manufacturing errors and operational variations in the optimization process to seek the feasible robust optimum. Our study focuses on variation characteristics including interaction effects, variation nonlinearity, and correlation to improve the estimation of design robustness. Robust product designs perform the intended function and satisfy design constraints in spite of these variations. This research proposes a new objective function consisting of the Expected Performance (EP) and the weighted Quality Index (QI). This definition assures design optimality and robustness. Our study also adopts statistical design of experiments that greatly reduces the number of experiments. The estimation scheme introduces the Quadrature Factorial Design which provides superior accuracy even if the variation nonlinearity is significant. Another challenge in this work is dealing with variation correlation and constraint uncertainties. Manufacturing errors often affect design variables with characteristic patterns. This research proposes the Manufacturing Variation Patterns (MVP) for design variables to estimate the performance variation and determine the constraint activities. Our study matches the variation patterns with typical manufacturing processes including heat treatment and injection molding, and addresses their effects to design feasibility. We redefine the constraint activity based on the MVP and present the procedure to seek feasible optimum. Theoretical development leads to our applications in helical gears with minimized transmission error and heat treated shafts with optimum dimensional stability. The gear example extends our previous study in tooth profile modification and considers quadratic effects, interaction effects, and variation correlation in the estimations of performance mean and deviation. The robust optimums outperform the results of previous studies and show significant reduction in the performance variations due to manufacturing errors, shaft misalignment, and load variations. The heat treatment example focuses on geometric design of transmission shaft to minimize the diametral distortion. This study establishes the regression models from field data and modifies non-critical dimensions to improve the dimensional stability of critical section. The application of the concept of MVP leads to the constrained robust shaft design.