Comparasion Of The Vibration Characteristics Of Fault Rotor System With Integer Order Damping And Fractional Order Damping

The damping force is always calculated by the cx￠ in a rotor system traditionally, however, the fractional calculus is used to calculate the damping force due to the advantage of the fractional calculus expressing damping properties of a material in this paper. A single span rotor with double discs is built in this paper, and a crack on the shaft and a rub-impact in the stator and rotor are introduced respectively. The four-DOF damping equations with the integer order is numerically simulated by the Runge-Kutta method. The fractional order damping system is studied by using the CFE-Euler method combining with the Runge-Kutta method, the vibration characteristics of the fractional order damping system and the integer order damping system are showed contrastively. The main contents are as follows:Considering the crack in three different position on the shaft, the four-DOF fractional order damping dynamic system and the integer order damping system was established by using the of the breathing crack stiffness model and the equations is numerically solved. For the integer order damping crack rotor system, the vibration amplitude-frequency response has peaks the under critical condition when 0w/ n,n =2,3,4... and the eccentricity and the speed of the r otor’s influence to the vibration response is considered. For the fractional order damping crack system, the vibration responses of the fractional order damping crack system and the integer order damping crack system are compared respectively. When r =1, the CFE-Euler method combining with the Runge-Kutta method is verified by contrast with the Runge-Kutta method. Then shaft center orbits, the Poincare map, frequency spectrogram and the bifurcation diagram are used to analyze the infl uence of the speed and the order to the system under the three situations. The results show that the integer order damping crack system and the fractional order damping crack system both has the high-frequency components and the obvious frequency doubling phenomenon under critical condition when 0w/ n,n =2,3,4... And the fractional order damping crack system can reveal more information of the high-frequency components than the integer order damping crack system.In the study of the rub-impact rotor system, the single span double-disc rotor model with the rub-impact fault is built. Considering one disc with a local rub-impact, the four-DOF fractional order damping dynamic system and the integer order damping system are established respectively, the equations are solved by the numerical method. In the study of the integer order damping rub-impact system, the Runge-Kutta method is used to get the shaft center orbits、the Poincare map、frequency spectrogram and the bifurcation diagram under different spe eds, and to analyze the nonlinear vibration characteristics,such as the bifurcation phenomenon, the process from the periodic motion to the quasi-periodic motion, fractional frequency and so on. In the study on the fractional order damping rub-impact system, the influence of the speed and the order to the system is considered, the process to the periodic motion 、 double period motion and the quasi-periodic motion is analyzed, we found the different order has different influence on the state of motion of the system.