Study On Nonlinear Vibration And Stability Of Rotor With A Transverse Crack

In modern industry,such as steam turbine generators,gas turbines,high-speed compressors and other large rotating machinery are subjected to high temperature,high pressure and various alternative stresses.For a long time,the rotor is apt to emerge small cracks due to the accumulation of fatigue damage.As the rotor is one of the most important parts of rotating machinery,rotor crack gradually expanded and may lead to vibration that will affect the efficiency or the rotor fracture resulting in casualties.Therefore,the study of cracked rotor system not only has very important academic value,but also has great significance to the safe of national economy and people's life.Several stiffness models and their advantages and disadvantages are introduced in this paper.On this basis,a stiffness model considering mass eccentric angle(angle between mass eccentricity and direction of crack)is established.For different eccentric angles,the variety of crack rotor stiffness in one cycle is analyzed.Based on the Jeffcott rotor,the established stiffness model is substituted into the differential equation of motion,and a crack rotor dynamic model with eccentricity is established.The inherent Runge-Kutta numerical method in Matlab apt to occur problems when solve complex differential equations.According to the definition of fourth-order Runge-Kutta,a numerical simulation method is proposed,which is easy to be solved.Crack rotor system dynamics model has carried on thorough meticulous research.The nonlinear characteristics of the cracked rotor system are analyzed by using bifurcation diagram,spectrum diagram,Poincare cross-section diagram,axial orbit diagram and time-domain waveform diagram.The influence of eccentricity and crack depth on the nonlinear vibration characteristics is analyzed as well as the evolution of non-linear behavior such as period-doubling bifurcation,quasi-period and chaos.Based on the theory of Floquet stability,the stability of crack rotor is studied,and the stability can be quantitatively analyzed without the help of analytical solution or difficult measurement of disturbance.The stability of the rotor under different system parameters was numerically simulated.The rotor instability zone corresponding to different rotational speed,eccentricity and crack depth is solved.The vibration simulation test bed of crack rotor was built,and the rotor with different crack depth and eccentricity was tested.The results show that both the power frequency and the second harmonic frequency increase with the increase of the crack depth and decrease with the increase of the eccentric angle.