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.

Nonlinear Dynamic Analysis of a Flexible Rod Fastening Rotor Bearing System

2010 ◽  
Author(s):  
Heng Liu ◽  
Chen Li ◽  
Weimin Wang ◽  
Xiaobin Qi ◽  
Minqing Jing
Keyword(s):  
Periodic Motion ◽  
Great Influence ◽  
Periodic Motions ◽  
Stability And Bifurcation ◽  
Mass Eccentricity ◽  
Rotor Bearing ◽  
Rod Fastening Rotor ◽  
The Stability ◽  
Tie Rods ◽  
Bearing System

This paper is concerned the stability and bifurcation of a flexible rod-fastening rotor bearing system (FRRBS). Here the shaft is considered as an integral or continuous structure and be modeled by using Timoshenko beam-shaft element which can take the effects of axial load into consideration. And using Hamilton’s principle, model tie rods distributed along the circumference as a constant stiffness matrix and an add-moment which caused by unbalanced pre-tightening forces. Then the model is reduced by a component mode synthesis method, which can conveniently account for nonlinear oil film forces of the bearing. This study focuses on the influence of nonlinearities on the stability and bifurcation of T periodic motion of the FRRBS subjected to the influence of mass eccentricity. The periodic motions and their stability margin are obtained by shooting method and path-following technique. The local stability and bifurcation behaviors of periodic motions are obtained by Floquet theory. The results indicate that mass eccentricity and unbalanced pre-tightening forces of tie rods 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.

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.

Investigation on the Stability and Bifurcation of a 3D Rotor-Bearing System

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Yi Liu ◽  
Heng Liu ◽  
Jun Yi ◽  
Minqing Jing
Keyword(s):  
Path Following ◽  
Rotor System ◽  
Periodic Motions ◽  
Stability Margins ◽  
Rotating Speed ◽  
Stability And Bifurcation ◽  
Mass Eccentricity ◽  
3D Elements ◽  
Order Of Magnitude ◽  
The Stability

The stability and bifurcation of a flexible 3D rotor system are investigated in this paper. The rotor is discretized by 3D elements and reduced by using component mode synthesis. Periodic motions and stability margins are obtained by using the shooting method and path-following technique, and the local stability of the periodic motions is determined by using the Floquet theory. Comparisons indicate that 3D and 1D systems have a general resemblance in the bifurcation characteristics while mass eccentricity and rotating speed are changed. For both systems, the orbit size of the periodic motions has the same order of magnitude, and the vibration response has identical frequency components when typical bifurcations occur. The stress distribution and location of the maximum stress spot are determined by the bending mode of the rotor. The type of 3D element has a slight effect on the stability and bifurcation of the rotor system. Generally, this paper presents a feasible method for analyzing the stability and bifurcation of complex rotors without much structural simplification.

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 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.

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.

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.

Release Profile of a Model Protein Drug Depending on the Stability of Microspheres Based on Polyelectrolyte Complex

2007 ◽  
Vol 342-343 ◽  
pp. 505-508
Author(s):  
Sung Won Kim ◽  
Yun Sik Nam ◽  
Yeon Jin Min ◽  
Jong Ho Kim ◽  
Kwang Meyong Kim ◽  
...  
Keyword(s):  
Polyelectrolyte Complex ◽  
Coating Layer ◽  
Great Influence ◽  
Release Profile ◽  
Core Material ◽  
Glycol Chitosan ◽  
The Core ◽  
Key Factor ◽  
Model Protein ◽  
The Stability

Stability and disintegration of natural polyelectrolyte complex microspheres for protein drugs delivery have been extensively investigated because of their great influence on the drug release patterns. In this study, we tested stability of microspheres with alginate (Alg) core layered by either chitosan (Chi) or glycol chitosan (GChi) by examining release profiles of fluorophorelabeled bovine serum albumin (BSA) and lysozyme (Lys) from the microspheres. While GChi shell was disintegrated quickly, Chi-shell microspheres showed good stability in PBS. Disintegration of the coated layer induced the core material instable. The results indicated that while the charges of the shell material provided additional diffusion barrier against the protein release, the key factor to hold the proteins inside the microspheres was the integrity of the outer coating layer.

Influence of Interaction Between Torsion and Bending on Long-Term Nonlinear Rotor Dynamics

1999 ◽  
Author(s):  
Jiazhong Zhang ◽  
Bram de Kraker ◽  
Dick H. van Campen
Keyword(s):  
Critical Speed ◽  
Floquet Theory ◽  
Rotor Dynamics ◽  
Steady State Response ◽  
Bending Vibrations ◽  
Bending Vibration ◽  
State Response ◽  
Stability And Bifurcation ◽  
The Stability

Abstract An elementary system with gears and excited by unbalance mass has been constructed for analyzing the interaction between torsion and bending vibration in rotor dynamics. For this system, only the interaction caused primarily by unbalance mass has been investigated. The stability and bifurcation characteristics of the system have been studied by numerical computation based on Hopf bifurcation and Floquet theory. The results show that the interaction between torsion and bending vibrations can affect the stability and bifurcation of the unbalance response, in particular the onset speed of instability. In addition to the above, the interaction also affects the steady-state response. To investigate the influence of unbalance mass, the periodic solution and its stability have been studied near the first bending critical speed of the decoupled system. All the results show that the coupling of torsion and bending vibrations can have a significant influence on the nonlinear dynamics of the whole system.

Bifurcation and stability of resonance of electric vehicle powertrain: Focus on the influence of electromagnetic parameters

2021 ◽  
pp. 095440702110450
Author(s):  
Qingzhen Han ◽  
Shiqin Niu ◽  
Lei He
Keyword(s):  
Electric Vehicle ◽  
Electromechanical Coupling ◽  
Equilibrium Points ◽  
Resonance Curve ◽  
Drive Shaft ◽  
Electromagnetic Parameters ◽  
Stability And Bifurcation ◽  
Fold Bifurcation ◽  
The Stability ◽  
Vehicle Powertrain

The influence of the electromagnetic parameters on the torsional dynamics of the electric vehicle powertrain is studied by considering the electromechanical coupling effect. By adding the electromagnetic torque on the drive side, the powertrain is simplified as nonlinear drive-shaft model. The number, stability, and bifurcation conditions of the equilibrium points of the nonlinear drive-shaft model are deduced. Based on the averaged equations and the amplitude-frequency response equation, the stability and bifurcation conditions, such as fold bifurcation and Hopf bifurcation, of the resonance curve are discussed. The influence of electromagnetic parameters on the torsional dynamics is studied by simulation. It is shown that with the change of the parameters, the number as well as the stability of the equilibrium points may be changed which is affected by fold bifurcation. It is also shown that the resonance curve may lose its stability when fold bifurcation happens. By limiting the parameters in the region without fold bifurcation, the unstable dynamics of the resonance curve can be controlled.

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