Finite Element Model Reduction for Rotating Systems

Complex rotors are usually modeled by means of Finite Element Method (FEM) to cope with nonelementary shape of the shaft and of the rotating appendices connected to it (…gure 1). To account for the the complex geometry, the discretization at the base of the FEM model is usually characterized by a high number of nodes and, correspondingly of degrees of freedom. The FE model is then characterized by a high number of densely populated modes. Such an high order model takes the geometrical complexity of the structure into account but may fail to bring into evidence the more relevant modes both in terms of energy content and observability and controllability by available sensors and actuators. Nevertheless, FE high order models may indicate substantial criticities in the design of complex rotors due to unwanted parasitic resonances in the working frequency range of the machine. In any case, modern rotor engineering strongly relies on FE numerical models before undertaking any actual construction. In particular for what the active magnetic bearings (AMB) are concerned, a model is necessary to design the control law to stabilize the system represented by the rotor and the active magnetic suspensions. In such a context, only a few modes are really relevant to the system stability but they must be identi…ed within their densely populated frequency range. In other words, resonant modes due to appendices supported by the rotor must be separated from those due to the rotor itself once they are checked to be of minor importance (energetically speaking).