Cracked A Single Rotor System Dynamics Analysis

Non-linear dynamics characters of a rotor system for an elastic shaft-disk with a crack are examined by introducing the geometric non-linearity and equivalent line-spring model. Firstly, in order to treat the local weakened effect of the crack on the shaft, the equivalent line-spring model is built. Then the constitutive equations are derived and the flexibility model of the rotating shaft is discussed. Based on the Lagrange equations, the non-linear dimensionless differential equations of the single rotor system with the disk and crack located at an arbitrary position of the shaft are obtained. In chapter 3, the non-linear dynamic stabilities of the system are investigated. In the former, the linear dynamic stability with one degree is studied and compared with the correlated reference. It is yielded that the equivalent line-spring model is correct and has high precision. In the latter, the non-linear dynamic stabilities of the single rotor system with a crack are researched. The non-linear differential equations have periodic coefficients. And using the stability theory of the periodic motion, it is discussed that the thickness of the disk, the position of the disk and the position of the crack have effects on the dynamic stabilities. In chapter 4, the non-linear dynamic responses are investigates. In the first part, the linear dynamic responses with two degrees are studied and solved by the harmonic balance theory. It is discussed that the variations of the depth of the crack, the position of the crack on the shaft, the thickness of the disk and the eccentricity of the disk all affect on the dynamic responses. In the second part, the non-linear dynamic responses with one degree are studied and solved by the multiple-scale method and Newton-Raphson method. The prime resonance vibrations are discussed. It is analyzed that the values of external excitation, the internal damping of the shaft and the depth of the crack have effects on the amplitude frequency response curves. In chapter 5, the bifurcation and chaos of a rotor system are studied. The bifurcation parameter sets of the motion equation are determined by using the theoretical method. It is concluded that the results are consistent with that of the numerical method. Meanwhile, the critical condition that the system enters chaotic states is given by the Melnikov method. Finally, the numerical method is used to study the dynamic properties of the whirling rotor system.