Steady Synchronous Response and Balancing of Rotor Systems with Residual Shaft Bow

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A procedure is presented for balancing a multi-degree-offreedom flexible rotor system including the effects of residual bow. The procedure is a generalization of methods presented by J. C. Nicholas, E. J. Gunter, and P. E. Allaire (1976a, 1976b) for a Laval-Jeffcott type rotor. These methods include: 1) treatment of the residual bow and unbalance as an equivalent unbalance force at the balance speed, 2) subtraction of the runout (residual bow response at near-zero speed) from the measured response at the balance speed, and 3) reducing the shaft response at the balance speed using data from a different measurement speed. The theoretical process is developed and an example, using simulated experimental data, is presented to illustrate the application of the three different strategies of balancing. The application of the balancing procedure requires the knowledge of a validated linear mathematical model for the rotor system. The mathematical model for the system must either be developed from theory, with appropriate experimental validation, or established directly from experimental data. Thus, application of the method is limited to those systems where mathematical models can be readily obtained.