Traditional rotor dynamics mainly focuses on the steady- state behavior of the rotor and shafting. However, for systems such as hydro turbine generating sets (HTGS) where the control and regulation is frequently applied, the shafting safety and stabilization in transient state is then a key factor. The shafting transient state inevitably involves multiparameter domain, multifield coupling, and coupling dynamics. In this paper, the relative value form of the Lagrange function and its equations have been established by defining the base value system of the shafting. Taking the rotation angle and the angular speed of the shafting as a link, the shafting lateral vibration and generator equations are integrated into the framework of generalized Hamiltonian system. The generalized Hamiltonian control model is thus established. To make the model more general, additional forces of the shafting are taken as the input excitation in proposed model. The control system of the HTGS can be easily connected with the shafting model to form the whole simulation system of the HTGS. It is expected that this study will build a foundation for the coupling dynamics theory using the generalized Hamiltonian theory to investigate coupling dynamic mechanism among the shafting vibration, transient of hydro turbine generating sets, and additional forces of the shafting.

/pdf/the-generalized-hamiltonian-model-for-the-shafting-transient-2zw2uw12ht.pdf

The generalized Hamiltonian model for the shafting transient analysis of the hydro turbine generating sets

The influence of blade vibration on the nonlinear characteristics of rotor–bearing system is non-ignorable in estimating system performance. The extensive studies simplify the rotor system as lumped mass points. The influence of shaft’s bending and shear and the flexibility are usually ignored. The present paper is aim to analyze the nonlinear dynamic behavior of a continuum model. The continuum model of flexible blade–rotor–bearing coupling system is established, simplifying the shaft as Timoshenko beam. The Lagrange method is utilized to derive the differential equation of motion of system. Then, the nonlinear equations of coupling system are numerically solved using the Newmark-
 $$\upbeta $$
 method. The results obtained through the proposed model are compared with the rotor–bearing system without the blades. The effect of several parameters such as rotational speed, the damping coefficient and the length of blade on the nonlinear dynamics of rotor system have been investigated. Inclusive of the analysis methods of bifurcation diagram, three-dimensional spectral plots, time-base analysis, Poincare maps and spectral plots are used to analyze the behavior of the coupling system under different operating conditions, which exhibits rich dynamic behavior of the system.

The effect of blade vibration on the nonlinear characteristics of rotor–bearing system supported by nonlinear suspension

To minimize leakage and maintain the efficiency of turbomachinery, brush seal can be installed with zero clearance or interference as the flexibility. This leads to contact between the rotor and bristle pack, and may cause self-excited vibration, even instability. In this study, to establishment a mathematical model of the rotor system, a seal force model with bristle interference is proposed and the nonlinear oil-film force is applied in view of short bearing assumption. The influences of main factors containing rotor rotational speed, installing interval, disc mass, and disk eccentricity on the nonlinear characteristics of the rotor-bearing-brush seal system are conducted by adopting bifurcation diagram, spectrum cascade, axis orbit, and Poincare map. The results indicate that the vibration amplitude of the system with bristle interference is a bit larger than that without interference. The system stability is enhanced with smaller disk mass at a higher rotational speed. The proposed model could provide valuable reference for the design of a rotor-bearing-seal system.

Numerical analysis of the dynamic behavior of a rotor-bearing-brush seal system with bristle interference

Nonlinear dynamic analysis of a rotor-bearing-seal system under two loading conditions

This study deals with numerical analysis and experimental investigations where the nonlinear dynamic behaviors of an asymmetric double-disk rotor-bearing system are reproduced considering rub-impact and oil-film instability. A dedicated experimental setup was designed to validate the interaction between rubs and oil-film vibration. A model considering nonlinear rub-impact forces and nonlinear oil-film forces is put forward to analyze the complicated nonlinear vibrations of the rotor-bearing system. The experimental study focuses on the interaction of oil-whirl/whip and rub-impact faults, and the results show that the oil-whirl is restrained or even removed, but the whip is uninfluenced when the rub becomes heavy contact. The numerical simulation focuses on the effect of eccentricity and the stator stiffness on the onset of instability and nonlinear responses of the rotor-bearing system by using bifurcation diagrams, Poincare maps, frequency spectrum and three-dimension spectral plots. Agreeing with the experimental results, the results from simulation indicate that the motion of system becomes simple and the oil-whirl gets diminished or even disappeared, but the whip keeps unchanged when the eccentricity or the stator stiffness increases. The research discloses the worthy energy exchange phenomenon of multi-fault system and presents the nonlinear dynamical characteristics of the interaction between rub-impact and oil-film instability for such a rotor-bearing system.

https://link.springer.com/content/pdf/10.1007%2Fs11071-015-2513-3.pdf

Dynamic simulation and experimental study of an asymmetric double-disk rotor-bearing system with rub-impact and oil-film instability

Nonlinear dynamics and stability of the rotor–bearing–seal system are investigated both theoretically and experimentally. An experimental rotor–bearing–seal device is designed and corresponding tests are carried out. The experimental rotor system is simplified as the Jeffcott rotor. The nonlinear oil–film forces are obtained under the short bearing theory and Muszynska nonlinear seal force model is used. Numerical method is utilized to solve the nonlinear governing equations. Bifurcation diagrams, waterfall plots, Poincare maps, spectrum plots and rotor orbits are drawn to analyze various nonlinear phenomena and system unstable processes. Theoretical results from numerical analysis are in good agreement with results from experiments. Conclusions are drawn and prove that this study will contribute to the further understanding of nonlinear dynamics and stability of the rotor system with the fluid-induced forces from oil–film bearings and the seals.

Experimental and numerical analysis of nonlinear dynamics of rotor–bearing–seal system

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Experimental and numerical analysis of nonlinear dynamics of rotor–bearing–seal system