Research Papers

Reliability-Based Optimal Design and Tolerancing for Multibody Systems Using Explicit Design Space Decomposition

[+] Author and Article Information
Henry Arenbeck

 RWTH-Aachen University, Institute of Automatic Control, 52074 Aachen, Germanyh.arenbeck@irt.rwth-aachen.de

Samy Missoum

Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721smissoum@email.arizona.edu

Anirban Basudhar

Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721anirban@email.arizona.edu

Parviz Nikravesh

Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721pen@email.arizona.edu

Assuming statistical independence of all geometric measures.

As an alternative to calculating the cutting measures analytically, they can be calculated numerically during simulation. To accomplish that, a rigid joint can be introduced for each body and, at each time step, shifted over the whole body length. The cutting measures can then be found as the joint-related reaction forces and moments, emerging at each considered joint position.

J. Mech. Des 132(2), 021010 (Feb 09, 2010) (11 pages) doi:10.1115/1.4000760 History: Received January 30, 2009; Revised November 16, 2009; Published February 09, 2010; Online February 09, 2010

This paper introduces a new approach for the optimal geometric design and tolerancing of multibody systems. The approach optimizes both the nominal system dimensions and the associated tolerances by solving a reliability-based design optimization (RDBO) problem under the assumption of truncated normal distributions of the geometric properties. The solution is obtained by first constructing the explicit boundaries of the failure regions (limit state function) using a support vector machine, combined with adaptive sampling and uniform design of experiments. The use of explicit boundaries enables the treatment of systems with discontinuous or binary behaviors. The explicit boundaries also allow for an efficient calculation of the probability of failure using importance sampling. The probability of failure is subsequently approximated over the whole design space (the nominal system dimensions and the associated tolerances), thus making the solution of the RBDO problem straightforward. The proposed approach is applied to the optimization of a web cutter mechanism.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Overall scheme of geometric design methodology

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Figure 2

Basic scheme of geometric configuration classification by means of multibody simulation

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Figure 3

Example of three “behaviors.” Definition of explicit boundaries in the parameter space (x1,x2) corresponding to the behaviors.

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Figure 4

Adaptive sampling method to construct an SVM limit state function

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Figure 5

Explicit failure region boundary constructed with an SVM (left), and MCS (right). Example with two random variables x1 and x2 with means μ1 and μ2.

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Figure 6

Sketch of a simplified web cutter mechanism

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Figure 7

Multibody model of a web cutter mechanism

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Figure 8

Assumed real world marginal PDF of a geometric measure xi

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Figure 9

Configuration space, spanned by uncertain geometric measures x1, x2, and x3. Domains associated to each failure event (Subfigs. 1–12) and overall safe domain.

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Figure 10

SVM-based approximation of the limit state (meshed surface), samples used for training of the SVM-function (large dots), and samples of the reference data set, which were falsely reclassified based on the SVM-function (small dots)

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Figure 11

Optimal nominal measures (dot at intersection of lines) and associated optimal tolerances (represented by rectangles) of the web cutter mechanism. Outer surface: SVM-based approximation of the limit state. Inner surface: isosurface of the joint probability density function of a geometric system outcome, which corresponds to a constant function value of 7.01×10−4.



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