On the oscillatory behaviours and rub-impact forces of a horizontally supported asymmetric rotor system under position-velocity feedback controller

Abstract This work is meant to investigate and control the nonlinear dynamical behaviours of a nonlinear asymmetric rotating shaft system. The studied system is modeled as a nonlinear dynamical system having both quadratic and cubic nonlinearities and excited at the primary resonance. A linear proportional-derivative controller is introduced to eliminate the nonlinear behaviours and to suppress the lateral vibrations of the rotating shaft. The influences of different control parameters on the oscillatory behaviours of the considered system are explored. The main obtained analytical results showed that the uncontrolled shaft may respond with forward and backward whirling motion. However, the proposed controller illustrated its feasibility in eliminating the nonlinear behaviours of the studied system and forcing it to behave like the linear systems. Moreover, the obtained results confirmed that the proportional control gain plays a dominant role in destabilizing the studied rotor system. Finally, the safe operation of the studied system with avoiding the rub-impact force occurrence is discussed.