Nonlinear dynamics of a Jeffcott Rotor with imperfections
An in-depth analytical, numerical and experimental study investigating the vibrational characteristics of a rotor system with a clearance is the main objective of this thesis. The mathematical modelling of a two degrees-of-freedom rotor system was done based on the Jeffcott rotor model. The physical model assumes a situation where gyroscopic forces are neglected and concentrates on the dynamic responses caused by interactions between a whirling rotor and a massless snubber ring, which has much higher stiffness than the rotor. Two analytical methods for calculating nonlinear dynamic responses of the rotor system are devised in order to obtain robust analytical solutions maintaining high computational accuracy. To unveil the global dynamics of the rotor system different nonlinear dynamics analysis techniques in the form of time trajectories, phase portraits, bifurcation diagrams, Poincaré maps, power spectrum analysis, basins of attraction and parameter planes are employed. In particular, the effect of preloading on the system dynamics was also investigated. Based on analysis of the nonlinearity of the restoring forces, the Jeffcott rotor model was justified in comparison with the squeeze film damping journal using the short bearing approximation. Design and basic modification to the existing experimental rig was carried out in order to create a ‘smart’ structure to effectively control the system responses using an ER damper, Shape Memory Alloys composite beams, eccentricity controllers and forcing frequency. Extensive experimental studies are undertaken to explore the system dynamics and justify the computational model.