Nonlinear Dynamic Study For Cracked Rotor System With Viscoelastic Supported

Large rotating machines are one of the most key and important equipments in the national basic industries. It has given more and more attention to the research of mechanical properties for large rotating machines. Through the theoretical analysis and numerical calculation, this paper, systematically, studies the nonlinear vibration, nonlinear dynamic response, nonlinear dynamic stability, bifurcation and chaos behaviours of the elastic disc-shaft rotor system with viscoelastic supported and transverse crack. This paper has more profound theoretical significances and important engineering application values, which provides contributions to the development and application of the nonlinear rotor dynamics.Adopting the Rayleigh beam model and the dissipation Lagrange equation, the nonlinear dynamic equations of an elastic disc-shaft rotor system with viscoelasticity supported under the axial periodic force are derived, and the masses and elastic deformations of the disc and shaft, the geometric nonlinearity of the shaft are considered.According to Lyapunov stability basic theory, Floquet theory and the numerical method for the stability theory of the periodic coefficients, the effects of the disc position, the disc thickness, the static load factor and asymmetric viscous and elastic supported on the principal regions of dynamic instability of the system are analyzed.The local flexibility coefficients of the shaft with transverse crack are derived by employing a line-spring model, using the fracture mechanics theory and the relation between the stress intensity factor and strain energy. The additional flexibility matrix is denoted by truncated cosine series when the shaft is rotating. The nonlinear dynamic equations of the elastic disc-shaft rotor system with viscoelastic supported and transverse crack, considering the mass of the disc and shaft, the nonlinearity of the shaft, under the action of axial periodic force are obtained by using the dissipation Lagrange equations. The vibration frequencies of the transverse cracked shaft are studied and the influences of the crack depth and crack close-open degree on the front three orders vibration frequencies are investigated in detail. Based on the Lyapunov stability theory and the Floquet criterion and applying the harmonic balance method, the linear and nonlinear dynamic stabilities of the cracked rotor system are analyzed. Finally, the effects of the multi-factors including the crack depth, the crack position, the viscoelastic and asymmetric supported, the disc position, the disc thickness, the disc centrifugal force and the static load factor on the principal regions of dynamic instability of the system are discussed.Furthermore, the nonlinear vibration and nonlinear dynamic response of the elasticdisc-shaft rotor system with the transverse crack are investigated. The effects of the crack depth and the crack position on the amplitude response, the time-history response and the frequency spectrum response are studied, which provides the theoretical foundation for the on-line diagnosis of the crack faults in time and effectively.The bifurcation and chaos of the cracked rotor system are researched by employing the numerical integration method. The dynamic properties of the system are analyzed under the various crack depth and the viscous damping coefficients. It is concluded that the crack is the principal reason causing the bifurcation and chaos for this system.Considering the nonlinear oil-film force, the nonlinear dynamic model of the rotor-bearing system is founded. In general , the nonlinear dynamic equations of the rotor-bearing system are derived included the multiple oil-film supported, the nonlinear oil-film forces, the masses and the elastic deformations of the shaft and disc and geometric nonlinearity of the shaft. Two oil-film bearings are taken in the examples and numerical method is used to study the bifurcation and chaos of the nonlinear dynamic system. The effects of the shaft's rotating speed and the mass eccentricity of the di...