Optimal balancing of flexible rotors by minimizing the condition number of influence coefficients

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 procedure. 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.