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Shock and Vibration
Volume 16 (2009), Issue 1, Pages 1-12

Constrained Balancing of Two Industrial Rotor Systems: Least Squares and Min-Max Approaches

Bin Huang,1 Daiki Fujimura,2 Paul Allaire,3 Zongli Lin,1 and Guoxin Li3

1Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22904-4743, USA
2Commissioning & Testing Section, Power Plant Construction Department, Takasago Machinery Works, Mitsubishi Heavy Industries Ltd., 2-1-1 Shinhama Arai-cho Takasago Hyogo, 676-8686, Japan
3Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22904-4746, USA

Received 5 April 2007; Revised 5 April 2007

Copyright © 2009 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Rotor vibrations caused by rotor mass unbalance distributions are a major source of maintenance problems in high-speed rotating machinery. Minimizing this vibration by balancing under practical constraints is quite important to industry. This paper considers balancing of two large industrial rotor systems by constrained least squares and min-max balancing methods. In current industrial practice, the weighted least squares method has been utilized to minimize rotor vibrations for many years. One of its disadvantages is that it cannot guarantee that the maximum value of vibration is below a specified value. To achieve better balancing performance, the min-max balancing method utilizing the Second Order Cone Programming (SOCP) with the maximum correction weight constraint, the maximum residual response constraint as well as the weight splitting constraint has been utilized for effective balancing. The min-max balancing method can guarantee a maximum residual vibration value below an optimum value and is shown by simulation to significantly outperform the weighted least squares method.