Stability of steady-state solutions of Jeffcott rotor with varying rotational speed
Abstract The behavior of flexible rotating systems with varying rotational speeds is essential in engineering applications. Analysis methods that consider linear dynamic models and many existing nonlinear analysis approaches assume constant rotational speed. These approaches are unsuited to study the dynamic interaction between driving torque and whirling motion in this class of applications. In this paper, an analysis of the stability and control of a Jeffcott rotor under varying operational conditions is presented. A nonlinear dynamic model of the system is formulated to enable a detailed stability and parametric analysis. A proportional-integral (PI) torque command is employed to achieve a steady-state rotational speed. Assuming constant lateral control effort, system equilibrium points and their stability characteristics as functions of the system’s parameters are analyzed. A control law that minimizes the lateral effort is derived. A feedback proportional lateral control strategy is introduced to enhance the system’s region of stability, particularly in the supercritical speed range. Finally, a simulation study is conducted to validate the analytical findings. Simulation results demonstrate the effectiveness of the proposed approach for defining stable operating conditions and improving system performance.