Research Papers: Design for Manufacture and the Life Cycle

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

[+] Author and Article Information
Maciej Mazur

RMIT Centre for Additive Manufacturing,
School of Aerospace, Mechanical, and
Manufacturing Engineering,
RMIT University,
P.O. Box 71, Melbourne,
Bundoora VIC 3083, Australia
e-mail: maciej.mazur@rmit.edu.au

Martin Leary

RMIT Centre for Additive Manufacturing,
School of Aerospace, Mechanical, and
Manufacturing Engineering,
RMIT University,
P.O. Box 71, Melbourne,
Bundoora VIC 3083, Australia
e-mail: martin.leary@rmit.edu.au

Aleksandar Subic

School of Aerospace, Mechanical, and
Manufacturing Engineering,
RMIT University,
P.O. Box 71, Melbourne,
Bundoora VIC 3083, Australia
e-mail: aleksandar.subic@rmit.edu.au

1Corresponding author.

Contributed by the Design for Manufacturing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received May 25, 2014; final manuscript received November 30, 2014; published online January 9, 2015. Assoc. Editor: Rikard Söderberg.

J. Mech. Des 137(3), 031701 (Mar 01, 2015) (16 pages) Paper No: MD-14-1300; doi: 10.1115/1.4029283 History: Received May 25, 2014; Revised November 30, 2014; Online January 09, 2015

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 multi-objective, 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.

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Fig. 2

PIDO based tolerance platform. Extension of a tolerance analysis platform presented in Ref. [83]

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Fig. 1

Multidimensional full product and SG Gauss–Hermite quadrature with level 2 for two dimensions and O = 2l+1-1 growth rule

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Fig. 3

Cost-tolerance curves for rail bend angles (lower horizontal axis) and bend radii (upper horizontal axis) for varying levels of variation control difficulty. The process curves are plotted only within the feasible limits of the associated process.

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Fig. 5

Case study PIDO based tolerance synthesis workflow

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Fig. 6

Objectives space of tolerance synthesis for case study




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