Development and modification of a unified balancing method for unsymmetrical rotor-bearing systems

On the basis of theoretical developments, this study proposes procedures for a modified unified balancing method for unsymmetrical rotor-bearing systems. A formulation of modal influence coefficient matrices is derived from the motion equations for unsymmetrical rotors, using a complex co-ordinate representation and the finite element method. Due to unequal properties in two principal directions, two sets of modal influence coefficients are presented. This formulation indicates that two trial masses in different directions are required in the two trial operations for each balancing plane. Also, the modal influence coefficients are found to be correlated with forward precession and unbalanced forces when asymmetry of bearings is considered. Therefore, forward precessions instead of measured displacements are required to calculate the unbalance distribution. Several examples are presented to verify the validity of the present work.