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Research Papers

Balancing of Flexible Rotors Using Convex Optimization Techniques: Optimum Min-Max LMI Influence Coefficient Balancing

[+] Author and Article Information
Costin D. Untaroiu1

Mechanical and Aerospace Engineering Department, University of Virginia, 1011 Linden Ave., Charlottesville, VA, 22902cdu4q@virginia.edu

Paul E. Allaire

Mechanical and Aerospace Engineering Department, University of Virginia, 122 Engineer’s Way, Charlottesville, VA, 22904pea@virginia.edu

William C. Foiles

 BP—Exploration & Production Technology Group, 501 Westlake Park Blvd., Houston, TX 77079Bill.Foiles@bp.com

1

Corresponding author.

J. Vib. Acoust 130(2), 021006 (Feb 04, 2008) (5 pages) doi:10.1115/1.2730535 History: Received March 13, 2006; Revised October 19, 2006; Published February 04, 2008

In some industrial applications, influence coefficient balancing methods fail to find the optimum vibration reduction due to the limitations of the least-squares optimization methods. Previous min-max balancing methods have not included practical constraints often encountered in industrial balancing. In this paper, the influence coefficient balancing equations, with suitable constraints on the level of the residual vibrations and the magnitude of correction weights, are cast in linear matrix inequality (LMI) forms and solved with the numerical algorithms developed in convex optimization theory. The effectiveness and flexibility of the proposed method have been illustrated by solving two numerical balancing examples with complicated requirements. It is believed that the new methods developed in this work will help in reducing the time and cost of the original equipment manufacturer or field balancing procedures by finding an optimum solution of difficult balancing problems. The resulting method is called the optimum min-max LMI balancing method.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 3

Initial vibration and residual vibrations (in μm<degree)—Example 2

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Figure 1

Schematic of the turbine-generator system used in the Example 2

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Figure 2

Initial vibration and residual vibrations—Example 1

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