Application of Polynomial Chaos Expansion to Tolerance Analysis and Synthesis in Compliant Assemblies Subject to Loading

Abstract

Statistical tolerance analysis and synthesis in assemblies subject to loading are of significant importance to optimized manufacturing. Modeling the effects of loads on mechanical assemblies in tolerance analysis typically requires the use of numerical CAE simulations. The associated uncertainty quantification (UQ) methods used for estimating yield in tolerance analysis must subsequently accommodate implicit response functions, and techniques such as Monte Carlo (MC) sampling are typically applied due to their robustness; however, these methods are computationally expensive. A variety of UQ methods have been proposed with potentially higher efficiency than MC methods. These offer the potential to make tolerance analysis and synthesis of assemblies under loading practically feasible. This work reports on the practical application of polynomial chaos expansion (PCE) for UQ in tolerance analysis. A process integration and design optimization (PIDO) tool based, computer aided tolerancing (CAT) platform is developed for multiobjective, tolerance synthesis in assemblies subject to loading. The process integration, design of experiments (DOE), and statistical data analysis capabilities of PIDO tools are combined with highly efficient UQ methods for optimization of tolerances to maximize assembly yield while minimizing cost. A practical case study is presented which demonstrates that the application of PCE based UQ to tolerance analysis can significantly reduce computation time while accurately estimating yield of compliant assemblies subject to loading.