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Based on the elasticity theory, a differential equation of forced oscillation of the blade-casing system with rub-impact excitation was deduced, and the steady analytic solution was derived. The analytic solution was verified with the FE (finite element) method, the results indicated that the eigenvalues of dynamical equation by FE method are larger than the semi-analytical method's, while the vibration modes are identical. Due to the characteristics of rub-impact excitation between the blade and casing, it is not suitable to solve impacting vibrational response for rotating blade with the steady analytic solution. Therefore, the semi-analytical solution was adopted to solve these dynamic problems, which can get the vibration response of any position for its continuity characteristic. Then, the FE and semi-analytical method is used. The comparison of dynamical response with changing speed, rub-impact depth and the friction coefficient was investigated in details. It is found that the speed has the greater effect on the dynamical vibration response, but other parameters affect the response slightly at the same rotational speed. When the friction coefficient and rub-impact depth unchanging, with the increasing speed, the contribution of each multi-frequency component to the resonant response grows obviously, especially the high-harmonic components should be pay more attention. Blade-casing model is easy to form a new resonance system, which will appear different resonant response with the increasing friction coefficient. When the friction coefficient reaches to a certain value, the response amplitude tends to be stable. [ABSTRACT FROM AUTHOR]

Considering spin softening and centrifugal stiffening effect of blades, the parameterized finite element model of rotating blades with moving rub-impact loads is established. Time domain response and frequency domain response are analyzed along with the change of speed and local vibration characteristic of the blade is studied under the different harmonic components. With investigation of the rotating blades, some conclusions have been found: The displacement caused by centrifugal effect has a maximum amplitude at blade tip and appears a smaller amplitude at blade root. And the stress change is just the opposite, which is basically a linear relation with location, and stress value caused by the centrifugal effect is basically in direct proportion to square of rotation speed within a certain range. Rub-impact can induced a variety of frequency multiplication components of the rotating blades, which cause different levels vibration response of the blade. The corresponding high-frequency components of the local stress mostly appear at angular position and root position of blade, which is easy to cause local fatigue damage of blade. Therefore, it need pay more attention to avoid frequency multiplication components caused by rub-impact approaching the natural frequency of the blade in order to prevent from local vibration. The results of the study in this paper will provide theoretical reference for the characteristic analysis and fault diagnosis of similar rotating blades. [ABSTRACT FROM AUTHOR]

In this paper, a finite element model of a nonlinear rotor-bearing system with two rub-impact faults is established, and the bifurcation and instability characteristics are analyzed along with the changing of rubbing clearance. To verify the results of the theoretical analysis, a rotorstator rubbing experimental system is established, which contains a pair of oil lubrication cylinder bearing and two disks. With monitoring the rubbing state by a designed electronic device, some qualitative analysis have been done on the rubbing response with different rotor-stator clearance. With investigation of the experimental response in time and frequency domain, some conclusions have be found: for the low eccentricity, when the rubbing clearance decreases, the rubbing fault makes the oil whirl take place earlier, the system of instability speed will decrease slightly, and lost instability through a period-doubling bifurcation. When the rubbing clearance increases, the instability speed will increase slightly, and the rotor system shows a quasi-periodic bifurcation. when the system is in a low speed state, due to the existence of the rubbing fault, the frequency domain appeared multiple frequency components, when the rotating speed is higher, because of the strong "oil whip", multiple frequency components are not obvious. In addition, due to the existence of the rubbing fault, the "oil whirl" and "oil whip" of the system become more obvious. The results of the study in this paper will provide some theoretical reference for the characteristic analysis and vibration control of similar rotor-bearing system. [ABSTRACT FROM AUTHOR]

In order to investigate the nonlinear characteristics of gear transmission system under the action of external and internal excitations, a dynamic model of a spur gear pair was established involving the backlash, damping, transmission error and the meshing stiffness. Based on the incremental harmonic balance method (IHBM), the general forms of the periodic solution with arbitrary precision are deduced. The vibration response obtained by IHBM compare very well with the results obtained by New-Mark method, which verifies the accuracy and electiveness of the analytical methodology (IHBM) and provide information on the dynamic characteristic of spur gear. The simulation results revealed that several types of steady-state periodic solution are identified and determined by employing the IHBM. Due to the effect of backlash, the nonlinear characteristics of jump discontinuity phenomena and multiple stable solutions coexist and the meshing impact phenomenon are obvious. In addition, the influences of the system damping, transmission error and excitation amplitude on the amplitude frequency characteristic are illustrated by a series of diagrams. The results implicate that increasing the external excitation amplitude and system damping can effectively decrease the system resonant amplitude and control the nonlinear vibration response of the gear system and the effect of hardening spring behavior becomes weaker. The transmission error excitation amplitude variation also tends to worse the degree of nonlinearity. Therefore, it presents some useful information to reduce the vibration and noise of gear system. [ABSTRACT FROM AUTHOR]