Bifurcation and Chaos Response of a Nonlinear 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 great deal of numerical simulations show that the system has many nonlinear dynamic behaviors, such as period doubling bifurcation, quasiperiodic responses and chaotic motions at the speed ratio near 1/2Ωc and 2/3Ωc when the stiffness change ratio ΔK is large. Periodic vibrations turn to quasiperiodic motions by two different ways at speed ratio 1/2Ωc and 2/3Ωc, one bifurcates a low frequency precession component, and the other bifurcates from fraction harmonic component. With further increasing of ΔK, chaotic vibration occurs first at the speed ratio of 2/3Ωc, the response turns to chaos along various routes, it may be from period doubling to chaos, from quasiperiod to chaos, or relating to period-3 response which may turn to other kinds of periodic motions as initial values changed. When ΔK is very large, chaos from quasiperiod is found near speed ratio 1/2Ωc. The results of this paper show that some signals which were always considered as random noise and filtered off may represent the chaotic characteristics of system, and can be used in future fault diagnosing of rotating machinery.