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.

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.

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.

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.

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.

scholarly journals Improvement of flexible rotor/active magnetic bearings system performance using pi-d control

2020 ◽  
Vol 40 (2) ◽  
pp. 112-123
Author(s):  
Adis Muminovic ◽  
Sanjin Braut ◽  
Adil Muminovic ◽  
Isad Saric ◽  
Goranka Štimac Rončević
Keyword(s):  
Pid Control ◽  
Real Life ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Active Magnetic Bearing ◽  
System Response ◽  
Active Magnetic Bearings ◽  
Flexible Rotor ◽  
Notch Filters ◽  
Common Control

Proportional–integral–derivative (PID) control is the most common control approach used to control active magnetic bearings system, especially in the case of supporting rigid rotors. In the case of flexible rotor support, the most common control is again PID control in combination with notch filters. Other control approaches, known as modern control theory, are still in development process and cannot be commonly found in real life industrial application. Right now, they are mostly used in research applications. In comparison to PID control, PI-D control implies that derivate element is in feedback loop instead in main branch of the system. In this paper, performances of flexible rotor/active magnetic bearing system were investigated in the case of PID and PI-D control, both in combination with notch filters. The performances of the system were analysed using an analysis in time domain by observing system response to step input and in frequency domain by observing a frequency response of sensitivity function.

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.

Unbalance response of a magnetic suspended dual-rotor system

2019 ◽  
Vol 233 (15) ◽  
pp. 5758-5772
Author(s):  
Dongxiong Wang ◽  
Nianxian Wang ◽  
Kuisheng Chen
Keyword(s):  
Magnetic Bearing ◽  
Rotor System ◽  
Magnetic Bearings ◽  
Active Magnetic Bearing ◽  
Active Magnetic Bearings ◽  
Maximum Displacement ◽  
Critical Speeds ◽  
Unbalance Response ◽  
Rotor Imbalance ◽  
Aero Engine

The magnetic suspended dual-rotor system applied in more electric aero-engine can eliminate the wear and lubrication system of mechanical bearings and solve the vibration control issue of system effectively, which provides the possibility to improve the performance of aero-engine significantly. This research focuses on the unbalance response of the magnetic suspended dual-rotor system. First, a structure of dual-rotor system supported by two active magnetic bearings and two permanent magnetic bearings is presented. With proportional derivative (PD) control adopted, the bearing characteristics of active magnetic bearings are modeled as the equivalent stiffness and equivalent damping, and the permanent magnetic bearings are modeled as elastic support. Then, the Riccati transfer matrix method with good numerical stability is used to establish the model of the magnetic suspended dual-rotor system unbalance response. Subsequently, the validity of the present formulation has been tested against some known results available in literature and the simulation results obtained by finite element method (FEM). Finally, the dynamic characteristics of the unbalance response are investigated. The results reveal that the influence of the inner rotor imbalance excitation on the magnetic suspended dual-rotor system unbalance response is much larger than that of the outer rotor imbalance excitation. In addition, the critical speeds increase with the proportional coefficient, and the derivative coefficient can affect the amplitudes of the unbalance response, but not critical speeds. From the perspectives of the maximum bearing capacity and maximum displacement of active magnetic bearing-rotor system, the possibility of the magnetic suspended dual-rotor system safely crossing the critical speeds of the first three orders is investigated.

Existence, Stability and Bifurcation of Periodic Motions in a Periodically Forced, Piecewise, Linear Oscillator With Impacts

2004 ◽  
Author(s):  
Albert C. J. Luo ◽  
Lidi Chen
Keyword(s):  
Nonlinear Dynamics ◽  
Periodic Motion ◽  
Piecewise Linear ◽  
Linear Oscillator ◽  
Analytical Prediction ◽  
Periodic Motions ◽  
Perfectly Plastic ◽  
Stability And Bifurcation ◽  
Mapping Structures ◽  
The Stability

The nonlinear dynamics of a generalized, piecewise linear oscillator with perfectly plastic impacts is investigated. The generic mappings based on the discontinuous boundaries are constructed. Furthermore, the mapping structures are developed for the analytical prediction of periodic motions of such a system. The stability and bifurcation conditions for specified periodic motions are obtained. The periodic motions and grazing motion are demonstrated. This model is applicable to prediction of periodic motion in nonlinear dynamics of gear transmission systems.

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