Rotor Balancing Method using LMI Optimization

This paper deals with a rotor balancing method based on influence coefficient method and LMI (Linear Matrix Inequality) optimization technique. The three rotor balancing objectives; (a) minimization of maximum residual vibration, (b) minimization of the least mean square of residual vibration and (c) minimization of the least mean square of correction masses, are considered. Since the conventional influence coefficient method cannot properly treat the objectives (a) and (c), these objectives (a) and (c) have been considered by heuristic trial & error method. In this paper, first, the LMI formulation of the rotor balancing objectives (a)-(c) are derived applying two basic LMI lemmas. Based on these LMI formulation of the objectives, a LMI optimization framework for rotor balancing is then constructed. The proposed method enables us to efficiently achieve the objectives (a)-(c) with the relative weight vector c using LMI optimization technique. Moreover, a reduction algorithm for the number of the correction planes, which is useful in the actual field balancing, is also considered. Finally, the effectiveness of the proposed rotor balancing method is evaluated by numerical simulations and experiments with a model rotor system.