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.

Dynamic Response of SFD-Sliding Rigid Bearing Rotor -System

2013 ◽  
Vol 706-708 ◽  
pp. 1310-1313
Author(s):  
Ji Yan Wang
Keyword(s):  
Dynamic Response ◽  
Dynamic Model ◽  
Periodic Motion ◽  
Rotor System ◽  
Rigid Rotor ◽  
Kutta Method ◽  
Sliding Bearing ◽  
Runge Kutta Method ◽  
Stable Periodic ◽  
Runge Kutta

This paper establishes a linking dynamic model of SFD-sliding bearing rigid rotor system by employing Runge-Kutta method to solve dynamic question of the above systems. The study has shown: rigid rotor system can keep stable periodic motion in a certain scope with the following quasi-periodicity bifurcation.

The Dynamic Analysis of SFD-Sliding Bearing Flexible Rotor System Based on Optimization Design

2012 ◽  
Vol 159 ◽  
pp. 355-360
Author(s):  
Ji Yan Wang ◽  
Rong Chun Guo ◽  
Xu Fei Si
Keyword(s):  
High Speed ◽  
Optimization Design ◽  
Critical Speed ◽  
Structural Parameters ◽  
Rotor System ◽  
Flexible Rotor ◽  
Optimization Analysis ◽  
Sliding Bearing ◽  
Critical Speeds ◽  
Design Variables

The paper establishes the mechanical model of SFD-sliding bearing flexible rotor system, adopting Runge-Kutta method to solve nonlinear differential equation, thus acquiring the unbalanced response curve and then gaining the first two critical speeds of the system. Meanwhile, the paper analyzes the sensitivity of the system on the first two critical speeds towards structural parameters, offering design variables to optimization analysis. Based on sensitivity analysis, genetic algorithm is employed to give an optimization analysis on critical speed, which aims to remove critical speed from working speed as much as possible. The critical speed ameliorates after the optimization which supplies theoretical basis as well as theoretical analysis towards the dynamic stability of high-speed rotor system and provides reference for the design of such rotor system.

scholarly journals Influence of radial clearance on nonlinear dynamics of a two-span three-support rotor system

2021 ◽  
Vol 233 ◽  
pp. 04012
Author(s):  
HE Xing ◽  
WU Yi-ming ◽  
LI Mo ◽  
ZENG Fan
Keyword(s):  
Periodic Motion ◽  
Rotor System ◽  
System Model ◽  
Radial Clearance ◽  
Structural Form ◽  
Single Cycle ◽  
Rolling Bearings ◽  
System A ◽  
Runge Kutta Method ◽  
Nonlinear Dynamic Characteristics

Aiming at the structural form of a certain rotor system, a double-span three-support rotor system model is established. It is supported by three rolling bearings and has a typical nonlinear characteristic. The fourth-order Runge-Kutta method is used to solve the differential equations and analyze the nonlinear dynamic characteristics of the rotor system when the radial clearance of the bearing changed. The research results: with the increase of the rear bearing radial clearance, the rotor system performs single cycle, periodic two and pseudo-periodic motion. With the three location bearing radial clearance increases, the rotor system performs single cycle, periodic two and periodic four motion. When the radial clearance is bigger, the rotor system performs two periodic motion. The influence law of radial clearance on double span three - braced rotor system is shown.

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

scholarly journals Nonlinear Dynamic Analysis of Rotor Rub-Impact System

2019 ◽  
Vol 2019 ◽  
pp. 1-20
Author(s):  
Youfeng Zhu ◽  
Zibo Wang ◽  
Qiang Wang ◽  
Xinhua Liu ◽  
Hongyu Zang ◽  
...  
Keyword(s):  
Periodic Motion ◽  
Chaotic Motion ◽  
Nonlinear Dynamic Analysis ◽  
Period Doubling ◽  
Time History ◽  
Rotor System ◽  
Quasiperiodic Motion ◽  
Rotor Bearing ◽  
Motion Period ◽  
Bearing System

A dynamic model of a double-disk rub-impact rotor-bearing system with rubbing fault is established. The dynamic differential equation of the system is solved by combining the numerical integration method with MATLAB. And the influence of rotor speed, disc eccentricity, and stator stiffness on the response of the rotor-bearing system is analyzed. In the rotor system, the time history diagram, the axis locus diagram, the phase diagram, and the Poincaré section diagram in different rotational speeds are drawn. The characteristics of the periodic motion, quasiperiodic motion, and chaotic motion of the system in a given speed range are described in detail. The ways of the system entering and leaving chaos are revealed. The transformation and evolution process of the periodic motion, quasiperiodic motion, and chaotic motion are also analyzed. It shows that the rotor system enters chaos by the way of the period-doubling bifurcation. With the increase of the eccentricity, the quasi-periodicity evolution is chaotic. The quasiperiodic motion evolves into the periodic three motion phenomenon. And the increase of the stator stiffness will reduce the chaotic motion period.

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.

Optimal Vibration Reduction of Flexible Rotor Systems by the Virtual Bearing Method

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Shibing Liu ◽  
Bingen Yang
Keyword(s):  
Optimization Problem ◽  
Rotor System ◽  
Flexible Rotor ◽  
Rotor Systems ◽  
Rotor Design ◽  
Design Variables ◽  
Real Coded Genetic Algorithm ◽  
Minimum Number ◽  
Unique Method ◽  
Distributed Transfer Function

This paper presents a new approach to optimal bearing placement that minimizes the vibration amplitude of a flexible rotor system with a minimum number of bearings. The thrust of the effort is the introduction of a virtual bearing method (VBM), by which a minimum number of bearings can be automatically determined in a rotor design without trial and error. This unique method is useful in dealing with the issue of undetermined number of bearings. In the development, the VBM and a distributed transfer function method (DTFM) for closed-form analytical solutions are integrated to formulate an optimization problem of mixed continuous-and-integer type, in which bearing locations and bearing index numbers (BINs) (specially defined integer variables representing the sizes and properties of all available bearings) are selected as design variables. Solution of the optimization problem by a real-coded genetic algorithm yields an optimal design that satisfies all the rotor design requirements with a minimum number of bearings. Filling a technical gap in the literature, the proposed optimal bearing placement approach is applicable to either redesign of an existing rotor system for improvement of system performance or preliminary design of a new rotor system with the number of bearings to be installed being unforeknown.

Period-1 Motion to Chaos in a Nonlinear Flexible Rotor System

2020 ◽  
Vol 30 (05) ◽  
pp. 2050077 ◽  
Author(s):  
Yeyin Xu ◽  
Zhaobo Chen ◽  
Albert C. J. Luo
Keyword(s):  
Period Doubling ◽  
Rotor System ◽  
Harmonic Amplitude ◽  
Flexible Rotor ◽  
Periodic Motions ◽  
Bifurcation Tree ◽  
Rotor Systems ◽  
Saddle Node ◽  
Jeffcott Rotor ◽  
And Control

In this paper, a bifurcation tree of period-1 motion to chaos in a flexible nonlinear rotor system is presented through period-1 to period-8 motions. Stable and unstable periodic motions on the bifurcation tree in the flexible rotor system are achieved semi-analytically, and the corresponding stability and bifurcation of the periodic motions are analyzed by eigenvalue analysis. On the bifurcation tree, the appearance and vanishing of jumping phenomena of periodic motions are generated by saddle-node bifurcations, and quasi-periodic motions are induced by Neimark bifurcations. Period-doubling bifurcations of periodic motions are for developing cascaded bifurcation trees, however, the birth of new periodic motions are based on the saddle-node bifurcation. For a better understanding of periodic motions on the bifurcation tree, nonlinear harmonic amplitude characteristics of periodic motions are presented. Numerical simulations of periodic motions are performed for the verification of semi-analytical predictions. From such a study, nonlinear Jeffcott rotor possesses complex periodic motions. Such results can help one detect and control complex motions in rotor systems for industry.

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.

Sign in / Sign up

Export Citation Format

Share Document