Approximate Explicit Calculation of First Vibration Frequencies of an Unsymmetrical High Speed Rotor

In order to easily predict and optimize the dynamic behavior of a high speed switched reluctance motor, a full analytic model, that gives directly and quickly the three first eigenfrequencies of the rotor, is proposed. The rotor is modelled as a 3 DOF Timoshenko’s beam model. The stiffness matrix is calculated with the Castigliano’s second theorem in structural analysis, which allows to obtain explicitly the eigenfrequencies expression and prevents to use classical finite element analysis. The influence of design and material modifications is studied and the dynamic behavior quickly predicted. The calculation time needed for testing a geometry is strongly smaller than with a finite element analysis.