Application of the Principle of Reciprocity to Flexible Rotor Balancing

The least desirable feature of most flexible rotor balancing procedures is the considerable number of trial mass runs required. This is of particular importance in the balancing of machines which require a substantial stabilization time during start-up. Using an adaptation of the principle of reciprocity, it is possible to significantly reduce the required number of trial mass runs for certain rotors when using either influence coefficient balancing or the Unified Balancing Approach. This may be applied to the more empirical forms of modal balancing, as well. When applied to flexible rotor balancing, the principle of reciprocity states that, given two rotor axial locations, A and B, at which both balancing planes and vibration sensors are located, the influence coefficient relating the vibration level at A to the unbalance at B is identical to that relating the vibration level at B to the unbalance at A. This is true even in the presence of damping. This chapter begins with a theoretical discussion of the principle of reciprocity and its application to flexible rotor balancing. The particular means by which reciprocity can be applied to improve the influence coefficient and Unified Balancing Approach procedures are then described in detail. Results of a numerical study to verify this application of reciprocity and to investigate any possible limitations are also discussed, along with the results of a similar experimental study using two substantially different tests rotors.