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Rotor systems are widely used in industrial power generation and propulsion. Once the nonlinear contact stiffness and oil film force are taken into account, the dynamics and stability of rotor systems become quite complex, often accompanied by super-harmonic and chaotic motions. Furthermore, conventional methods face limitations in real-time detection of the bifurcations and complex nonlinear motions. This research investigates the bifurcations and stability induced by nonlinear factors in a rotor-bearing system from an energy perspective. Dynamic equations of a rotor-bearing system considering cubic term stiffness are established, the steady responses are obtained by the fourth-order Runge–Kutta method. The relationship between the bifurcations and energy transfers is analyzed numerically, the proposed stability criterion is validated by comparing the Lyapunov exponents. The bistable phenomenon of period-3 m (m = 0 , 1) motion is discussed in terms of numerical results and experiments which corresponds to the asymmetric jumps of the generalized energy. It is found that bifurcations and unstable motions of the nonlinear system can be captured accurately by detecting the energy transfers, the proposed generalized energy curve exhibits more detailed information than the conventional speed-up curve. These findings provide a new perspective on studying bifurcations and stability of rotating systems, which can be further applied in the condition monitoring, stability prediction as well as the design of nonlinear energy sink, representing significant progress in converting theory into engineering applications for rotor systems. [ABSTRACT FROM AUTHOR]

In rotating machinery, aerodynamic forces and oil film forces often lead to cross-coupling stiffness. This paper is aimed at studying the stick-slip whirling vibrations induced by the piecewise smooth rotor/stator frictions in a modified flexible rotor subjected to cross-coupling stiffness. Governing equations determining the sliding region and boundaries of piecewise discontinuous friction are defined. This analytical study was conducted to discuss the complex vibrations and bifurcations. Various types of sliding motions (continuous pure rolling, continuous crossing, and grazing–sliding) were observed in this research. Further, as for discussing the impacts of the parameters on nonlinear sliding vibrations, a parametric study was conducted. The obtained results reveal that with an increase in the cross-coupling stiffness coefficient, continuous pure rolling occurs earlier, and the disk vibration time around the contact regime becomes shorter. For studying the self-excited backward whirling vibration of stick–slip nonlinear motions, analytical formulations are established. Detailed vibration amplitude and frequency studies of friction-induced backward whirling vibrations were carried out. Numerical simulations were performed to compare them with the analytical solutions and to validate the results as well. The proposed theory and results provide fresh perspectives for predicting friction-induced whirlings and creating proper designs for turbo machinery. [ABSTRACT FROM AUTHOR]

A brush seal has the advantages of adapting to different vibration conditions and increasing the stability of the nonlinear rotor system. In this research, the stability and bifurcations of complex vibrations in a brush-seal rotor system are studied. An analytical seal force model is obtained through the beam theory and mutual coupling dynamics of the bristles and the rotor. The interaction between the bristles and the rotor is clearly depicted by a geometric map. Periodic and chaotic vibrations as well as the corresponding amplitude–frequency characteristics are first predicted by a numerical bifurcation diagram and 3D waterfalls. Discrete dynamic eigenvalue analysis is adopted for a detailed investigation of the stability and bifurcations of nonlinear vibrations. Jumping, quasi-periodic, and half-frequency vibrations are warned during the speeding up and down process. Four separate nonlinear vibration evolving routes are discovered. Two period-doubling bifurcation trees evolving to chaos are illustrated for the observation of global and independent periodic vibrations. Nonlinear vibration illustrations are presented through displacement orbits as well as harmonic amplitudes and phases. Chaotic vibration and unstable semi-analytical vibration solutions are compared. The obtained results and analysis methods provide new perspectives on nonlinear vibrations in the brush-seal rotor system. [ABSTRACT FROM AUTHOR]

In this paper, periodic motions in a nonlinear rotor system are predicted through an implicit mapping method. The bifurcation trees of different period-1 to period-2 motion are presented, and there are many segments for different period-1 and period-2 motions. Harmonic frequency-amplitude characteristics of periodic motions are discussed for analysis and design of nonlinear rotor systems. Numerical simulations of periodic motions are completed for comparison of predicted and numerical results. The predictions of periodic motions in the nonlinear rotor system can provide guides for practical measurements of rotor systems, and one can have a better understanding of nonlinear rotor dynamics compared to the traditional perturbation analysis. Such studies presented in this paper just throw out some guides and ideas to predict complex motions in nonlinear rotor systems. The authors hope one can follow what presented in this paper to do further studies in nonlinear rotor dynamical systems and to improve design and control of nonlinear rotor systems. Image, graphical abstract [ABSTRACT FROM AUTHOR]

[Display omitted] • A multi-scale contact model is deduced to describe the contact effect more accurately. • Such modelling method practically guides the high-precision modeling of actual rotor system. • The increase in preloads leads to the period-doubling bifurcation moving toward low speed. • A multi-disk rotor test bench is built to verify the accuracy of the contact model and obtained results. Bolted disk structure has the advantages of easy production and assembly and it is widely adopted in the design of gas turbine rotors. However, the discontinuity of bolted structure and the contact effects between the disks produce complex nonlinear properties to the rotor system, resulting in difficulties in solving the vibration dynamics of the rotors. In this paper, in order to reflect the contact effect between the rotor disks more accurately, a multi-scale contact mechanics model considering the whole deformation process of the material is deduced based on the skewed distribution theory. The contact effect between disks is considered by introducing an equivalent material layer. Newmark- β method is applied to obtain the dynamic response of the rotor system under different preloads. A multi-disk rotor-bearing test bench is designed to conduct dynamic tests to verify the accuracy of the contact modeling method and obtained dynamic results. Numerical and experimental results show that adjusting the preloads has the effect to change the bifurcation state of the rotor system and the increase in the preloads leads to the period-doubling bifurcation phenomenon moving toward low speed, and leads to the early appearance of some combined frequency components (such as 2 fn - fr , where fn is the working frequency and fr is the oil film whirl frequency). This research provides a theoretical reference for the modeling, dynamic behavior prediction as well as fault diagnosis of rod-fastened gas turbine rotor systems. [ABSTRACT FROM AUTHOR]