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and
Machine Theory
Mechanism and Machine Theory 43 (2008) 891–908
ate/mechmt
Optimal balancing of flexible rotors by minimizing the
condition number of influence coefficients
Yuan Kang a,b,*, Tsu-Wei Lin a, Yaw-Jen Chang a, Yeon-Pun Chang a,b,
Chun-Chieh Wang a
a Department of Mechanical Engineering, Chung Yuan Christian University, 200, Chung Pei Road, Chung Li 32023, Taiwan, ROC
b R&D Center for Membrane Technology, Chung Yuan Christian University, Taiwan, ROC
Received 17 May 2006; received in revised form 10 June 2007; accepted 23 June 2007
Available online 7 August 2007
Abstract
The Hermitian matrix of influence coefficients is one indicator of a balancing experiment’s overall effectiveness. The
condition number of this matrix is determined by the sensor locations and balancing planes selected for the balancing pro-
cedure. In this research, we use finite element analysis to simulate the balancing of flexible rotor-bearing systems under
various arrangements of sensors and planes. The condition number turns out to be inversely related to the accuracy of
the balancing and directly related to the sum of correction masses; in other words, the accuracy and efficiency of rotor
balancing can be improved by selecting sensor locations and balancing planes which reduce the condition number. This
result is validated by experimental measurements of a physical rotor system.
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: Flexible rotor; Rotor balancing; Accuracy improvement; Influence coefficient method; Condition number; Sensor location;
Balancing location
1. Introduction
The influence coefficient method is a standard and widely used approach for field balancing in industrial
applications. This balancing operation is easy to carry out on puter, and requires very little knowledge
of the rotating system. However, certain errors are introduced by uracy of the sensors and nonlinearity of
the rotor-bearing system.
The first