Stability and Bifurcation of Nonlinear Bearing-Flexible Rotor System with a Single Disk

2010 ◽  
Vol 148-149 ◽  
pp. 141-146
Author(s):  
Di Hei ◽  
Yong Fang Zhang ◽  
Mei Ru Zheng ◽  
Liang Jia ◽  
Yan Jun Lu
Keyword(s):  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
Rotor System ◽  
Dynamic Responses ◽  
Flexible Rotor ◽  
Runge Kutta Method ◽  
Stability And Bifurcation ◽  
Single Disk ◽  
The Stability ◽  
Predictor Corrector

Dynamic model and equation of a nonlinear flexible rotor-bearing system are established based on rotor dynamics. A local iteration method consisting of improved Wilson-θ method, predictor-corrector mechanism and Newton-Raphson method is proposed to calculate nonlinear dynamic responses. By the proposed method, the iterations are only executed on nonlinear degrees of freedom. The proposed method has higher efficiency than Runge-Kutta method, so the proposed method improves calculation efficiency and saves computing cost greatly. Taking the system parameter ‘s’ of flexible rotor as the control parameter, nonlinear dynamic responses of rotor system are obtained by the proposed method. The stability and bifurcation type of periodic responses are determined by Floquet theory and a Poincaré map. The numerical results reveal periodic, quasi-periodic, period-5, jump solutions of rich and complex nonlinear behaviors of the system.

On an Independent Period-1 Motion in a Flexible Rotor System

2019 ◽  
Author(s):  
Yeyin Xu ◽  
Albert C. J. Luo
Keyword(s):  
Numerical Simulations ◽  
Internal Resonance ◽  
Mapping Method ◽  
Rotor System ◽  
Flexible Rotor ◽  
Periodic Motions ◽  
Phase Trajectories ◽  
Stability And Bifurcation ◽  
The Stability ◽  
Nonlinear Rotor System

Abstract This paper investigates stable and unstable period-1 motions in a rotor system through the discrete mapping method. The discrete mapping of a nonlinear rotor system is for stable and unstable period-1 motions. The stability and bifurcation of periodic motions are determined. Numerical simulations of periodic motions are completed and phase trajectories, displacement orbits and velocity plane are illustrated. The period-1 motion near the internal resonance is determined with large vibration in the nonlinear rotor system.

The Lower Bound of the Stability Threshold Speed of a Flexible Rotor System in Fluid-Film Bearings

1989 ◽  
Vol 111 (3) ◽  
pp. 351-353
Author(s):  
Wen Zhang
Keyword(s):  
Lower Bound ◽  
Theoretical Foundation ◽  
Simple Approach ◽  
Rotor System ◽  
Fluid Film ◽  
Flexible Rotor ◽  
Stability Threshold ◽  
Fluid Film Bearings ◽  
Single Disk ◽  
The Stability

The paper is devoted to the estimation of the lower bound of the stability threshold speed (STS) of a flexible rotor system supported in fluid-film bearings. It is proved theoretically that the STS of any multi-degree-of-freedom flexible rotor system is always higher than the STS of the corresponding equivalent single disk rotor. The conclusion offers us a simple approach to estimate the STS of any actual rotor system and provides a theoretical foundation for the approach.

Effect of Thrust Magnetic Bearing on Stability and Bifurcation of a Flexible Rotor Active Magnetic Bearing System

2003 ◽  
Vol 125 (3) ◽  
pp. 307-316 ◽  
Author(s):  
Y. S. Ho ◽  
H. Liu ◽  
L. Yu
Keyword(s):  
Periodic Motion ◽  
Magnetic Bearing ◽  
Rotor System ◽  
Magnetic Bearings ◽  
Active Magnetic Bearing ◽  
Flexible Rotor ◽  
Periodic Motions ◽  
Stability And Bifurcation ◽  
Mass Eccentricity ◽  
The Stability

This paper is concerned with the effect of a thrust active magnetic bearing (TAMB) on the stability and bifurcation of an active magnetic bearing rotor system (AMBRS). The shaft is flexible and modeled by using the finite element method that can take the effects of inertia and shear into consideration. The model is reduced by a component mode synthesis method, which can conveniently account for nonlinear magnetic forces and moments of the bearing. Then the system equations are obtained by combining the equations of the reduced mechanical system and the equations of the decentralized PID controllers. This study focuses on the influence of nonlinearities on the stability and bifurcation of T periodic motion of the AMBRS subjected to the influences of both journal and thrust active magnetic bearings and mass eccentricity simultaneously. In the stability analysis, only periodic motion is investigated. The periodic motions and their stability margins are obtained by using shooting method and path-following technique. The local stability and bifurcation behaviors of periodic motions are obtained by using Floquet theory. The results indicate that the TAMB and mass eccentricity have great influence on nonlinear stability and bifurcation of the T periodic motion of system, cause the spillover of system nonlinear dynamics and degradation of stability and bifurcation of T periodic motion. Therefore, sufficient attention should be paid to these factors in the analysis and design of a flexible rotor system equipped with both journal and thrust magnetic bearings in order to ensure system reliability.

Stability and bifurcation of a non-linear bearing-flexible rotor coupling dynamic system

2008 ◽  
Vol 223 (4) ◽  
pp. 835-849 ◽  
Author(s):  
Y J Lu ◽  
R Dai ◽  
D Hei ◽  
Y F Zhang ◽  
H Liu ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Iteration Process ◽  
Flexible Rotor ◽  
Oil Film ◽  
Hydrodynamic Bearing ◽  
Computational Costs ◽  
Stability And Bifurcation ◽  
Non Linear ◽  
Coupling Dynamic ◽  
The Stability

The non-linear coupling dynamic behaviour of a hydrodynamic bearing-flexible rotor system is analysed. A local iteration method consisting of the improved Wilson-θ method, the predictor—corrector mechanism, and the Newton—Raphson method is proposed to calculate the non-linear dynamic response. Using the proposed method, the iterations are executed only on non-linear degrees of freedom. The iteration process shows improved convergence by taking the prediction value as the initial value. The stability and bifurcation type of periodic responses are determined by the Floquet theory. According to the physical characteristics of the oil film, a variational constraint approach is proposed to revise continuously the variational form of the Reynolds equation at each step of the iterative process. Non-linear oil film forces and their Jacobians are calculated simultaneously without an increase in computational costs, and compatible accuracy is obtained. Numerical results reveal periodic, quasi-periodic, coexisting, and jump solutions of rich and complex non-linear behaviours of the system and show that the proposed methods not only save computational costs but also have high precision.

SINGULARITY, SWITCHABILITY AND BIFURCATIONS IN A 2-DOF, PERIODICALLY FORCED, FRICTIONAL OSCILLATOR

2013 ◽  
Vol 23 (03) ◽  
pp. 1330009 ◽  
Author(s):  
ALBERT C. J. LUO ◽  
MOZHDEH S. FARAJI MOSADMAN
Keyword(s):  
Dynamical Systems ◽  
Bifurcation Analysis ◽  
Degrees Of Freedom ◽  
Eigenvalue Analysis ◽  
Analytical Dynamics ◽  
Periodic Motions ◽  
Stability And Bifurcation ◽  
Mapping Structures ◽  
Stability And Bifurcation Analysis ◽  
The Stability

In this paper, the analytical dynamics for singularity, switchability, and bifurcations of a 2-DOF friction-induced oscillator is investigated. The analytical conditions of the domain flow switchability at the boundaries and edges are developed from the theory of discontinuous dynamical systems, and the switchability conditions of boundary flows from domain and edge flows are presented. From the singularity and switchability of flow to the boundary, grazing, sliding and edge bifurcations are obtained. For a better understanding of the motion complexity of such a frictional oscillator, switching sets and mappings are introduced, and mapping structures for periodic motions are adopted. Using an eigenvalue analysis, the stability and bifurcation analysis of periodic motions in the friction-induced system is carried out. Analytical predictions and parameter maps of periodic motions are performed. Illustrations of periodic motions and the analytical conditions are completed. The analytical conditions and methodology can be applied to the multi-degrees-of-freedom frictional oscillators in the same fashion.

scholarly journals Quasi-Static Characteristics and Vibration Responses Analysis of Helical Geared Rotor System with Random Cumulative Pitch Deviations

2020 ◽  
Vol 10 (12) ◽  
pp. 4403
Author(s):  
Bing Yuan ◽  
Geng Liu ◽  
Lan Liu
Keyword(s):  
Degrees Of Freedom ◽  
Transmission Error ◽  
Rotor System ◽  
Dynamic Responses ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Long Period ◽  
Light Load ◽  
Vibration Responses ◽  
Loaded Tooth Contact Analysis

As one of the long period gear errors, the effects of random cumulative pitch deviations on mesh excitations and vibration responses of a helical geared rotor system (HGRS) are investigated. The long-period mesh stiffness (LPMS), static transmission error (STE), as well as composite mesh error (CMS), and load distributions of helical gears are calculated using an enhanced loaded tooth contact analysis (LTCA) model. A dynamic model with multi degrees of freedom (DOF) is employed to predict the vibration responses of HGRS. Mesh excitations and vibration responses analysis of unmodified HGRS are conducted in consideration of random cumulative pitch deviations. The results indicate that random cumulative pitch deviations have significant effects on mesh excitations and vibration responses of HGRS. The curve shapes of STE and CMS become irregular when the random characteristic of cumulative pitch deviations is considered, and the appearance of partial contact loss in some mesh cycles leads to decreased LPMS when load torque is relatively low. Vibration modulation phenomenon can be observed in dynamic responses of HGRS. In relatively light load conditions, the amplitudes of sideband frequencies become larger than that of mesh frequency and its harmonics (MFIHs) because of relatively high contact ratio. The influences of random cumulative pitch deviations on the vibration responses of modified HGRS are also discussed.

STUDY ON NONLINEAR DYNAMIC BEHAVIOURS AND STABILITY OF A FLEXIBLE ROTOR SYSTEM WITH HYDRODYNAMIC SLIDING BEARING SUPPORTS

2007 ◽  
pp. 1761-1765
Author(s):  
Yanjun Lu ◽  
Yongfang Zhang ◽  
Heng Liu ◽  
Lie Yu ◽  
Dexin Li ◽  
...  
Keyword(s):  
Nonlinear Dynamic ◽  
Rotor System ◽  
Flexible Rotor ◽  
Sliding Bearing

Stability and Bifurcation of Unbalanced Response of a Squeeze Film Damped Flexible Rotor

1994 ◽  
Vol 116 (2) ◽  
pp. 361-368 ◽  
Author(s):  
J. Y. Zhao ◽  
I. W. Linnett ◽  
L. J. McLean
Keyword(s):  
Power Spectra ◽  
Squeeze Film ◽  
Integration Scheme ◽  
Flexible Rotor ◽  
Jump Phenomenon ◽  
Stability And Bifurcation ◽  
Trigonometric Collocation ◽  
Numerical Integration Scheme ◽  
The Stability ◽  
Nonsynchronous Vibrations

The stability and bifurcation of the unbalance response of a squeeze film damper-mounted flexible rotor are investigated based on the assumption of an incompressible lubricant together with the short bearing approximation and the “π” film cavitation model. The unbalanced rotor response is determined by the trigonometric collocation method and the stability of these solutions is then investigated using the Floquet transition matrix method. Numerical examples are given for both concentric and eccentric damper operations. Jump phenomenon, subharmonic, and quasi-periodic vibrations are predicted for a range of bearing and unbalance parameters. The predicted jump phenomenon, subharmonic and quasi-periodic vibrations are further examined by using a numerical integration scheme to predict damper trajectories, calculate Poincare´ maps and power spectra. It is concluded that the introduction of unpressurized squeeze film dampers may promote undesirable nonsynchronous vibrations.

The Dynamic Response and Sensitivity Analysis of the SFD-Sliding Bearing Flexible Rotor System

2012 ◽  
Vol 472-475 ◽  
pp. 1460-1464
Author(s):  
Ji Yan Wang ◽  
Yu Cheng Zhao ◽  
Chao Wang
Keyword(s):  
Dynamic Response ◽  
Periodic Motion ◽  
Period Doubling ◽  
Rotor System ◽  
Flexible Rotor ◽  
Sliding Bearing ◽  
Runge Kutta Method ◽  
Design Variables ◽  
Design Cycle ◽  
Stable Periodic

The paper established the mechanical model of SFD-sliding bearing flexible rotor system, adopting Runge-Kutta method to solve nonlinear differential equation, thus acquiring the dynamic response and the unbalanced response curve. The study has shown: from stable periodic motion, the route of the flexible rotor system to go into chaos is: periodic motion—quasi-periodic motion—chaos—period doubling bifurcation—chaos. The paper analyzed the sensitivity of the first two critical speeds of flexible rotor system, offering design variables for optimization analysis, improving the efficiency of optimization and shortening the design cycle.

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