Bifurcation and Chaos of a Nonlinear Whirl Cracked Rotor

The dynamic responses of a cracked rotor affected by nonlinear whirl speed are investigated, with particular focus on the behaviors of bifurcation and chaos. A large number of numerical simulations show that the system has many nonlinear dynamic behaviors, such as period doubling bifurcation, quasi-periodic responses and chaotic motions at speed ratios near M2Qc and 2/3Qc. When the stiffness change ratio AK is large enough, periodic vibrations turn to quasi-period motions with two different ways at speed ratio V2Qc and 2/3 Qc , one way bifurcates a low frequency precession component, and the other bifurcates from fraction harmonic component. With a further increase of AK , chaotic vibration occurs first at the speed ratio of 2/3Qc , and the response turns to chaos along various routes. It may be from period doubling to chaos, from quasi-period to chaos, or relating to period-3 response which may turn to other kinds of periodic motions as initial values change. When AK is sufficient large, chaos from quasi-period is found near speed ratio I/2Qc. The results of this chapter show that some signals which are always taken as random noise and filtered away may represent the chaotic characteristics of the system, and can be used in rotating machinery fault diagnosis.