| With the development of electric power, the problem of vibration on turbogenerator shafts stands out. A deep research on vibration mechanism is carried out. And valid method for preventing and diagnosing fault is explored. But the fact is that analysis method and conclusion can't be used for diagnosing some faults exactly. Research on coupled flexural and torsional vibrations and nonlinear characteristics will help to reveal dynamics property of shafts more perfectly and strengthen analysis technique of vibration and improve the accuracy of fault diagnosis.Based on a Jeffcott rotor system with rigid support, the differential equations of coupled vibrations are established. Different from previous methods, litter parameter method is used for analyzing the characteristic of coupled vibrations. And the analytical results are validated through numerical simulation. Mass unbalance is necessary condition of coupling. The possibility of shaft damage led by coupled resonance is litter. Useful information for fault diagnosis is provided by the coupled characteristics.The differential equations of coupled vibrations for rubbing rotor are established. Numerical analysis for rubbing characteristics is processed using standard four-step Runge-kutta method. Main differences and torsional property of system response are compared with and without considering torsional vibration. And the influences of several factors on rubbing rotor are discussed thoroughly. The feasibility that torsional vibration characteristic and nonlinear characteristic are used for the faults diagnosis of rubbing rotor is proved by the analysis results fully. From the happen time of rotor rubbing, fraction and multiple frequencies of torsional vibration always concomitant appear. As the speed is slow, 1/2X frequency is the main component. With the speed increment, not only 1/2X and 2/3X frequency component appear in low frequency segment, but also 4/3X frequency component begin to appear in high frequency segment. The amplitude of fraction frequency is usually larger than that of multiple frequencies. The nonlinear characteristic of torsion for rubbing rotor is similar with that of flexural vibration completely. Torsion can restrain the complex motion of flexural vibration.A breathing crack controlled by weight is the study object. Transient characteristics of coupled vibrations and influence factors are analyzed with the shaft accelerated. The properties of 1/3X and 1/2X sub-syntonic resonance are discussed. Nonlinear characteristics such as bifurcation and chaos under three kinds of models are compared. And nonlinear characteristics of coupled vibrations under the model supporting with bearings are analyzed detailedly. The acquired torsion properties and nonlinear characteristics ofcracked rotor have good assistant effect on diagnosing cracked fault. 1/3X and 1/2X sub-syntonic resonance of torsional vibration occur with the cracked rotor accelerated. The ωphases of torsional resonance peak of IX, 2X and 3X components change 180 degree. And the phases corresponding to ωt0, 1/2ωt0, 1/3ωt0, 2/3ω0 and ω0 fluctuate too. The phase of ω0 frequency fluctuates tempestuously. The resonance peaks of flexural and torsional vibrations response are present at 2/3ω0 1/2ω0 1/3ω0 and 1/4ω0 with three kinds cracked rotor models. Near 1/2ω0 frequency, quasi-periodic and chaotic motions maybe appear. Periodic, quasi-periodic and chaotic motions show on alternately when the rotating speed is near to 2/3ω0.Combined step-by-step integral method with traditional transfer matrix method, an increment transfer matrix method is put forward. Based on Riccati method, the increment transfer matrix method is used in a multi-mass model. And matrix equations calculating the responses of coupled vibrations are deduced. A set of software analyzing coupled vibrations is developed. The responses of flexural vibration, torsional vibration and torsional torque are analyzed under some fault cases, including mass escaping of low-pressure and generator rotors...
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