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On the balancing of flexible rotating machines by using an inverse problem approach

The aim of this work is to propose a methodology for the experimental determination of the matrix relating unbalance forces to measured displacements for a rotating machine. The goal is to obtain an alternative solution to special situations found in the industrial context, especially for highly flexible rotors that may lead to a nonlinear behavior of the system. The trial-weights-based techniques, such as the influence coefficients method or the modal method, cannot be applied in such configurations. The proposed balancing method is based on the use of an identified model for the system. A pseudo-random optimization technique using genetic algorithms was applied for the identification process. The basic idea is to obtain the flexible rotor unbalance response, which is then mimicked by using a finite element method model in which the unbalance masses and their corresponding angular positions are the design variables from the optimization viewpoint. This way, an inverse problem is solved and the corrective masses are obtained. The model characteristics of the system are adjusted experimentally. Experimental investigations were carried out and the results show the efficiency of the method developed; the limitations and improvements are finally discussed.