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.

Periodic Solutions in Rotor Dynamic Systems With Nonlinear Supports: A General Approach

1989 ◽  
Vol 111 (2) ◽  
pp. 187-193 ◽  
Author(s):  
C. Nataraj ◽  
H. D. Nelson
Keyword(s):  
Dynamic Systems ◽  
Original Problem ◽  
Squeeze Film ◽  
Algebraic Equations ◽  
Trigonometric Collocation ◽  
Nonlinear Algebraic Equations ◽  
The Stability ◽  
Future Work ◽  
Rotor Dynamic ◽  
Large Rotor

A new quantitative method of estimating steady state periodic behavior in nonlinear systems, based on the trigonometric collocation method, is outlined. A procedure is developed to analyze large rotor dynamic systems with nonlinear supports by the use of the above method in conjunction with Component Mode Synthesis. The algorithm discussed is seen to reduce the original problem to solving nonlinear algebraic equations in terms of only the coordinates associated with the nonlinear supports and is a big improvement over commonly used integration methods. The feasibility and advantages of the procedure so developed are illustrated with the help of an example of a typical rotor dynamic system with an uncentered squeeze film damper. Future work on the investigation of the stability of the periodic response so obtained is outlined.

The Effects of Main-Flow Radial Velocity on the Stability of Developing Laminar Pipe Flow

1976 ◽  
Vol 43 (2) ◽  
pp. 209-212 ◽  
Author(s):  
F. C. T. Shen ◽  
T. S. Chen ◽  
L. M. Huang
Keyword(s):  
Radial Velocity ◽  
Main Flow ◽  
Integration Scheme ◽  
Neutral Stability ◽  
Radial Velocity Component ◽  
Numerical Integration Scheme ◽  
Critical Reynolds Numbers ◽  
The Stability ◽  
Direct Numerical Integration ◽  
Sommerfeld Equation

In studying the stability due to axisymmetric disturbances of the developing flow of an incompressible fluid in the entrance region of a circular tube, a generalized version of the Orr-Sommerfeld equation was derived which takes account of the radial velocity component in the main flow. The new terms in the generalized Orr-Sommerfeld equation are inversely proportional to the Reynolds number. The resulting eigenvalue problem consisting of the disturbance equation and the boundary conditions was solved by a direct numerical integration scheme along with an iteration procedure. Neutral stability curves and critical Reynolds numbers at various axial locations are presented. A comparison of the present results with those from the conventional Orr-Sommerfeld equation in which the effect of the main-flow radial velocity is neglected, shows that inclusion of the radial velocity contributes to a destabilization of the main flow.

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.

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.

Nonlinear Dynamic Effect of Thrust Bearing on a Flexible Rotor Bearing System

2012 ◽  
Author(s):  
Heng Liu ◽  
Yi Liu ◽  
Xuebin Song ◽  
Jun Yi ◽  
Minqing Jing ◽  
...  
Keyword(s):  
Thrust Bearing ◽  
Synthesis Method ◽  
Great Influence ◽  
Dynamic Effect ◽  
Flexible Rotor ◽  
Stability Margins ◽  
Resonant Amplitude ◽  
Stability And Bifurcation ◽  
Mass Eccentricity ◽  
The Stability

This article is concerned with the effect of nonlinearities on the stability and bifurcation of a flexible rotor system subjected to the influences of thrust bearing and mass eccentricity. The shaft is modeled by using the finite element method and then the model is reduced by a component mode synthesis method which can account for nonlinear forces and moment of the bearing. The periodic motions and their stability margins are obtained by using shooting method and path-following technique. The numerical results indicate that thrust bearing and mass eccentricity have great influence on stability and bifurcation of the motion of system. Thrust bearing can postpone the bifurcation of the periodic motion of system, heighten the critical speed and the stability threshold speed, and lower the resonant amplitude of the rotor.

scholarly journals An Investigation Into the Effect of Side-Plate Clearance in an Uncentralized Squeeze-Film Damper

1983 ◽  
Author(s):  
R. A. Cookson ◽  
L. J. Dainton
Keyword(s):  
Experimental Investigation ◽  
Rolling Contact ◽  
Squeeze Film ◽  
Radial Clearance ◽  
Flexible Rotor ◽  
Jump Phenomenon ◽  
Side Plate ◽  
Squeeze Film Damper ◽  
Squeeze Film Dampers ◽  
Experimental Rig

An experimental investigation has been carried out into the influence of side-plate flow restrictors on the performance of a squeeze-film damper bearing. The experimental rig used was a flexible rotor with a disc positioned mid-way between two squeeze-film damper bearings. One of the squeeze-film dampers was fitted with side-plates which could be adjusted and accurately located with respect to the squeeze-film damper journal. It has been found that the influence of the side-plate clearance on the ability of the squeeze-film damper to reduce the amplitude of the central disc can be considerable if the side-plate clearance is less than the radial clearance. As the side-plate clearance reduces towards zero, the effectiveness of the squeeze-film damper diminishes until the amplitudes obtained are the same as those measured when the rolling-contact bearing is rigidly supported. An interesting type of precessing elliptical orbit was discovered for conditions where the ‘jump’ phenomenon was operating.

Subharmonic and Quasi-Periodic Motions of an Eccentric Squeeze Film Damper-Mounted Rigid Rotor

1994 ◽  
Vol 116 (3) ◽  
pp. 357-363 ◽  
Author(s):  
J. Y. Zhao ◽  
I. W. Linnett ◽  
L. J. McLean
Keyword(s):  
Numerical Integration ◽  
Least Square ◽  
Harmonic Series ◽  
Squeeze Film ◽  
Maximum Speed ◽  
Rigid Rotor ◽  
Squeeze Film Damper ◽  
Squeeze Film Dampers ◽  
The Stability ◽  
Nonsynchronous Vibrations

When a squeeze-film damper is operated eccentrically, the nonlinear damper forces are no longer radially symmetric and subharmonic and quasi-periodic vibrations may be excited by the rotor unbalance. In this study, the unbalance response of a rigid rotor, supported on an eccentric squeeze film damper, is first approximated by a harmonic series whose coefficients are determined by the collocation method, together with a nonlinear least-square regression. The stability of the resulting periodic solution is then examined using the Floquet transition matrix method. For sufficiently large values of the unbalance and the damper static radial misalignment, it is shown that the approximate harmonic motion loses its stability and bifurcates into a stable subharmonic motion and a quasi-periodic motion at speeds above twice the system critical speed. This analytical finding is verified by a numerical integration in forms of the Poincare´ map, the rotor trajectory, the bifurcation diagram, and the power spectrum. It is suggested that stability analysis and numerical integration should always be incorporated into an approximate analytical method to achieve an adequate approximation. The results of this study show that the introduction of squeeze-film dampers may give rise to the undesirable nonsynchronous vibrations, which limits the maximum speed at which dampers should be used.

scholarly journals Bifurcation Behavior of a Flexible Rotor Supported on Nonlinear Squeeze Film Dampers without Centralized Springs

2000 ◽  
Vol 6 (4) ◽  
pp. 301-312 ◽  
Author(s):  
Zhu Changsheng ◽  
Heinz Ulbrich
Keyword(s):  
Power Spectra ◽  
Rotor System ◽  
Squeeze Film ◽  
Almost Periodic ◽  
Flexible Rotor ◽  
Bifurcation Diagrams ◽  
Operation Speed ◽  
Squeeze Film Dampers ◽  
Bifurcation Behavior ◽  
Periodic Bifurcation

In this paper, the bifurcation behavior of a flexible rotor supported on nonlinear squeeze film dampers without centralized springs is analyzed numerically by means of rotor trajectories, Poincar maps, bifurcation diagrams and power spectra, based on the short bearing and cavitated film assumptions. It is shown that there also exist two different operations (i.e., socalled bistable operations) in some speed regions in the rotor system supported on the nonlinear squeeze film dampers without centralized springs. In the bistable operation speed regions, the rotor system exhibits synchronous, sub-synchronous, sub-super-synchronous and almost-periodic as well as nonperiodic motions. The periodic bifurcation behaviors of the rotor system supported on nonlinear squeeze film dampers without centralized springs are very complex and require further investigations.

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.

An Investigation Into the Effect of Side-Plate Clearance in an Uncentralized Squeeze Film Damper

1983 ◽  
Vol 105 (4) ◽  
pp. 935-940
Author(s):  
R. A. Cookson ◽  
L. J. Dainton
Keyword(s):  
Rolling Contact ◽  
Squeeze Film ◽  
Radial Clearance ◽  
Flexible Rotor ◽  
Jump Phenomenon ◽  
Side Plate ◽  
Squeeze Film Damper ◽  
Central Disk ◽  
Squeeze Film Dampers ◽  
Experimental Rig

An experimental investigation has been carried out into the influence of side-plate flow restrictors on the performance of a squeeze film damper bearing. The experimental rig used was a flexible rotor with a disk positioned midway between two squeeze film damper bearings. One of the squeeze film dampers was fitted with side plates that could be adjusted and accurately located with respect to the squeeze film damper journal. It has been found that the influence of the side-plate clearance on the ability of the squeeze film damper to reduce the amplitude of the central disk can be considerable if the side-plate clearance is less than the radial clearance. As the side-plate clearance reduces towards zero, the effectiveness of the squeeze film damper diminishes until the amplitudes obtained are the same as those measured when the rolling-contact bearing is rigidly supported. An interesting type of precessing elliptical orbit was discovered for conditions where the “jump” phenomenon was operating.

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