Modal Balancing Using Parametric Combination Resonance

Abstract

In traditional modal balancing, a representative response of each mode to be balanced must be present in the measurement data. This is usually achieved by measuring the rotor response close to each critical speed corresponding to the modes of interest. The main disadvantage of this procedure is the time consumed during run-up/run-down cycles: at least one for each test mass configuration for determining the influence coefficients. Besides, several critical speeds are passed, which may cause high levels of vibration or even several run-ups if the resulting unbalance is critical. This paper proposes a balancing method for which the system needs to rotate up to the first critical speed only. It is known that parametric combination resonance has the ability to transfer kinetic energy between the mode shapes of a flexible structure (modal interaction). Therefore, controllable bearings such as active magnetic bearings are used to introduce a parametric excitation at different parametric combination resonances, inducing a modal energy transfer from the first critical speed to higher modes. This energy transfer has a similar effect to that obtained if the rotor is operated near higher critical speeds. This allows for estimating influence coefficients and corresponding correction masses using a procedure similar to the traditional modal balancing. The proposed method avoids the need for spinning the rotor above its first critical speed; thus, saving time and allowing for high-speed rotor balancing at low speed. The theory of the proposed balancing method using parametric excitation is presented along with simulations to illustrate its potential.