Research Papers

Stability Based Robust Eigenvalue Design for Tolerance

[+] Author and Article Information
XinJiang Lu

Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong, SAR China50008245@student.cityu.edu.hk

Han-Xiong Li

Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong, SAR China; School of Mechanical and Electrical Engineering, Central South University, Hunan 410083, Chinamehxli@cityu.edu.hk

J. Mech. Des 131(8), 081007 (Jul 20, 2009) (7 pages) doi:10.1115/1.3179237 History: Received November 14, 2008; Revised May 06, 2009; Published July 20, 2009

A novel integrated approach is developed to design systems for stability and robustness. First, design parameters with large variation bounds are chosen to maintain system stability. Then, a robust eigenvalue design problem is considered to make the dynamic response less sensitive to parameter variations. A new complex sensitivity matrix is derived from the system dynamics with the eigenvalue variation approximated into a first-order model by means of the eigenvector orthogonal theory. Through a proper transformation, the complex eigenvalue sensitivity of the Jacobian matrix can still be processed by the traditional robust design approach. By minimizing the eigenvalue sensitivity, design parameters can be obtained for stability as well as robustness. Furthermore, the tolerance space of the selected parameters can be maximized to improve robust performance. A Laval rotor example is used to demonstrate the effectiveness of the proposed robust design method.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Constraint of the eigenvalue by both stability and robustness

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Figure 2

The variation bounds

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Figure 3

A two-dimensional eigenvalue sensitivity ellipsoid

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Figure 5

Physical model of a rotor system

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Figure 6

Nominal stability parameter space Sn

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Figure 7

Stability parameter space Ss

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Figure 8

(a) Mean of the error e(mi,mb,j) and (b) variance of the error e(mi,mb,j)

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Figure 4

Tolerance synthesis



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