NONLINEAR STABILITY OF BALANCED ROTOR DUE TO EFFECT OF BALL BEARING INTERNAL CLEARANCE
Stability and dynamic characteristics of a bail bearing-rotor system are investigated under the effect of the clearance in the ball bearing. Different clearance values are assumed to calculate the nonlinear stability of periodic solution with the aid of the Flo- quet theory. Bifurcation and chaos be...
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| Published in | Applied mathematics and mechanics Vol. 27; no. 2; pp. 175 - 186 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, P. R. China%School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, P. R. China
01.02.2006
Mechanical and Electrical Engineering College, Xi'an University of Architecture & Technology,Xi'an 710055, P. R. China |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0253-4827 |
| DOI | 10.1007/s10483-006-0205-1 |
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| Abstract | Stability and dynamic characteristics of a bail bearing-rotor system are investigated under the effect of the clearance in the ball bearing. Different clearance values are assumed to calculate the nonlinear stability of periodic solution with the aid of the Flo- quet theory. Bifurcation and chaos behavior are analyzed with variation of the clearance and rotational speed. It is found that there are three routes to unstable periodic solution. The period-doubling bifurcation and the secondary Hopf bifurcation are two usual routes to instability. The third route is the boundary crisis, a chaotic attractor occurs suddenly as the speed passes through its critical value. At last, the instable ranges for different internal clearance values are described. It is useful to investigate the stability property of ball bearing rotor system. |
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| AbstractList | O347.6; Stability and dynamic characteristics of a ball bearing-rotor system are investigated under the effect of the clearance in the ball bearing. Different clearance values are assumed to calculate the nonlinear stability of periodic solution with the aid of the Floquet theory. Bifurcation and chaos behavior are analyzed with variation of the clearance and rotational speed. It is found that there are three routes to unstable periodic solution.The period-doubling bifurcation and the secondary Hopf bifurcation are two usual routes to instability. The third route is the boundary crisis, a chaotic attractor occurs suddenly as the speed passes through its critical value. At last, the instable ranges for different internal clearance values are described. It is useful to investigate the stability property of ball bearing rotor system. Stability and dynamic characteristics of a bail bearing-rotor system are investigated under the effect of the clearance in the ball bearing. Different clearance values are assumed to calculate the nonlinear stability of periodic solution with the aid of the Flo- quet theory. Bifurcation and chaos behavior are analyzed with variation of the clearance and rotational speed. It is found that there are three routes to unstable periodic solution. The period-doubling bifurcation and the secondary Hopf bifurcation are two usual routes to instability. The third route is the boundary crisis, a chaotic attractor occurs suddenly as the speed passes through its critical value. At last, the instable ranges for different internal clearance values are described. It is useful to investigate the stability property of ball bearing rotor system. Stability and dynamic characteristics of a ball bearing-rotor system are investigated under the effect of the clearance in the ball bearing. Different clearance values are assumed to calculate the nonlinear stability of periodic solution with the aid of the Floquet theory. Bifurcation and chaos behavior are analyzed with variation of the clearance and rotational speed. It is found that there are three routes to unstable periodic solution. The period-doubling bifurcation and the secondary Hopf bifurcation are two usual routes to instability. The third route is the boundary crisis, a chaotic attractor occurs suddenly as the speed passes through its critical value. At last, the instable ranges for different internal clearance values are described. It is useful to investigate the stability property of ball bearing rotor system. |
| Author | 白长清 许庆余 张小龙 |
| AuthorAffiliation | School of Aerospace, Xi＇an Jiaotong University, Xi＇an 710049, P. R. China Mechanical and Electrical Engineering College, Xi＇an University of Architecture ＆ Technology, Xi＇an 710055, P. R. China |
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| Cites_doi | 10.1006/jsvi.1999.3109 10.1016/S0020-7403(03)00064-X 10.1006/jsvi.1993.1134 |
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| Keywords | rotor clearance bifurcation chaos ball bearing stability |
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| Notes | rotor bifurcation chaos clearance ball bearing; clearance; rotor; stability; bifurcation; chaos 31-1650/O1 O347.6 ball bearing stability ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
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| References | N. Aktürk (205_CR7) 1993 M. Tiwari (205_CR4) 2000; 238 B. Mevel (205_CR6) 1993; 162 Y. Liu (205_CR9) 2001 S. P. Harsha (205_CR5) 2003; 45 A. Harris Tedric (205_CR8) 1984 H. Tamura (205_CR2) 1983; 43 Edward. Ott (205_CR11) 1993 205_CR1 Anonynous (205_CR3) 2002; 54 J. Zhou (205_CR10) 1998 |
| References_xml | – volume: 54 start-page: 87 issue: 2 year: 2002 ident: 205_CR3 publication-title: Industrial Lubrication and Tribology – volume-title: Rolling Bearing Analysis[M] year: 1984 ident: 205_CR8 – volume-title: Chaos in Dynamical Systems[M] year: 1993 ident: 205_CR11 – ident: 205_CR1 – volume: 238 start-page: 723 issue: 5 year: 2000 ident: 205_CR4 publication-title: Journal of Sound and Vibration doi: 10.1006/jsvi.1999.3109 – volume: 45 start-page: 725 issue: 4 year: 2003 ident: 205_CR5 publication-title: International Journal of Mechanical Sciences doi: 10.1016/S0020-7403(03)00064-X – volume-title: Chen Liqun. Nonlinear Vibrations[M] year: 2001 ident: 205_CR9 – volume-title: Nonlinear Vibrations[M] year: 1998 ident: 205_CR10 – volume: 43 start-page: 285 issue: 4 year: 1983 ident: 205_CR2 publication-title: Memoirs of the Faculty of Engineering, Kyushu University – volume: 162 start-page: 471 issue: 3 year: 1993 ident: 205_CR6 publication-title: Journal of Sound and Vibration doi: 10.1006/jsvi.1993.1134 – volume-title: Dynamics of a Rigid Shaft Supported by Angular Contact Ball Bearings[D] year: 1993 ident: 205_CR7 |
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| Snippet | Stability and dynamic characteristics of a bail bearing-rotor system are investigated under the effect of the clearance in the ball bearing. Different... Stability and dynamic characteristics of a ball bearing-rotor system are investigated under the effect of the clearance in the ball bearing. Different... O347.6; Stability and dynamic characteristics of a ball bearing-rotor system are investigated under the effect of the clearance in the ball bearing. Different... |
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| SubjectTerms | Ball bearings Bifurcations Chaos theory Clearances Mathematical analysis Nonlinearity Rotors Stability 平衡转子 混沌理论 球轴承 间隙 非线性稳定性 |
| Title | NONLINEAR STABILITY OF BALANCED ROTOR DUE TO EFFECT OF BALL BEARING INTERNAL CLEARANCE |
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