Analysis of Nonlinear Dynamic Behavior of a Rotating Electrical Machine Rotor-Bearing System Using Optimal Auxiliary Functions Method

Rotating electrical machines are widely used in engineering and industry applications due to their reliability. The machines under study are subjected to a parametric excitation caused by an inertial thrust and a forcing excitation caused by an unbalanced force of the rotor while the entire system is being supported by nonlinear bearings with nonlinear stiffness characteristics and damping properties. The nonlinear suspension makes the analytical study very difficult, leading to strong nonlinear differential equations, which are hard to be solved through classical methods. Supplementary problems could arise in case of some horizontal rotating machines, when the gravity effect is not negligible for certain stiffness conditions. Also, the misalignment could occur in the electrical machine after some amount of running. In our paper, a new analytical approach, namely the Optimal Auxiliary Functions Method (OAFM) is employed to solve the problem of an electrical machine supported by nonlinear bearings characterized by nonlinear stiffness of Duffing type and the entire system is subjected to a parametric excitation due to the axial thrust and a forcing excitation caused by an unbalanced force of the rotor. This study contains an effective and easy to use procedure which is independent of the presence of small or large parameters in the nonlinear equations. The approximate analytical solution is in very good agreement with the numerical simulation results, which prove the reliability of this procedure.