Fault Diagnosis Method Of Cracked Rotor Based On Fractional Calculus

This dissertation was supported by the National Natural Science Foundation ofChina(No.51075372,50775208,51265039), Science and Technology Projects ofEducation Department of Jiangxi Province, China(No. GJJ12405) and the Open Fund ofKey Laboratory of Machanical Equipment Health of Hunan Province (201204). Basedon the deficiencies of the traditional integer order calculus in the modeling of crackedrotor system, a fault diagnosis method of cracked rotor based on fractional calculus isproposed. The nonlinear dynamics characteristics of cracked rotor system withfractional order damping is studied. And its main contents include the following aspects:1.The paper illuminates the definitions and natures of fractional calculus, thediscretization methods of fractional calculus operators and the difference between thefractional calculus and integral calculus.2. Nonlinear dynamics model of cracked rotor system with fractional order dampingunder the condition of nonlinear eddy is investigated. The effects of derivative order,rotating speed ratio, crack depth on the fractional order damping nonlinear dynamiccharacteristics of cracker rotor system are discussed. The research results show that thederivative order of damping has great influence to the dynamics characteristics of rotorsystem. Therefore, the nonlinear dynamic characteristics can be adjusted by adjusting ofderivative order. The cracked rotor system with fractional order damping gets chaotic,period-doubling and periodic as the rotating speed ratio increases. When the crack depthis very small, the rotor system doesn’t present complex bifurcation and chaosphenomena. With the increasing of the crack depth, the stiffness of rotor reduces and therotor system presents the complex vibration characteristics. The crack fault featurebecomes more obvious. The rotor system gets periodic, period-doubling respectively.The double frequency component is dominant, simultaneously other frequencymultiplication component also appears.The correctness of this model is verified by theexperiment. Using the cracked rotor as an example, compared with the vibrationcharacteristics of cracked rotor system with integer order damping and fractional orderdamping by numerical method. The simulation results show that more abundant theinformation of crack fault in the fractional damping cracked rotor system can beobtained by adjusting the fractional order. 3. Combining the model of cracked rotor system based on the fractional calculusand wavelet scalogram, a fault diagnosis method of cracked rotor system with fractionalorder damping based on wavelet scalogram is proposed. The characteristics of waveletscalogram and reassigned scalogram from different crack depth in rotor system withfractional order damping are discussed. The simulation results show that the proposedmethod is sensitive to crack fault. It can accurately extract the crack fault information inthe rotor system.4.The stiffness of a slant-cracked rotor is obtained by SIF0method. Thedynamics model of slant-cracked rotor system with fractional order damping isinvestigated. The proposed model is simulated by the Runge kutta method andcontinued fractional expansion Euler method. The effects of derivative order, rotatingspeed ratio, crack depth on the fractional order damping nonlinear dynamiccharacteristics of slant-cracked rotor system are discussed. The research results showthat the amplitude of torsional excitation frequency becomes larger with the increasingof the derivative order. With the increasing of the rotating speed,1X componentbecomes larger,2X and the other coupling frequency components change a little. Thetrajectory change from double ring type to elliptic without overlapping. With theincreasing of the crack depth, in the transversal responses of the slant-cracked rotorsystem, the amplitudes become larger. The torsional excitation frequency and combinedfrequencies appear. And the results are verified by experiment.