Nonlinear Stability of Balanced Rotor Due to the Effect of Ball Bearing Internal Clearance
-
摘要: 研究滚动轴承平衡转子系统在不同轴承内间隙量,不同转速下系统的稳定性及其分岔特性和混沌．考虑Hertz接触力、 滚动体通过振动和轴承径向内间隙等非线性因素建立数学模型，根据Floquet理论分析不同间隙量下滚动轴承转子系统的周期解稳定性， 找到了3种导致周期解失稳的方式：倍周期分岔失稳、拟周期分岔失稳和边界激变导致混沌失稳．通过对各间隙量下转子系统拓扑特性变化和失稳区域的研究，表明滚动轴承间隙量是影响转子系统动力稳定性的一个重要因素．Abstract: 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 were assumed to calculate the nonlinear stability of periodic solution with the aid of the Floquet theory. Bifurcation and chaos behavior were 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 were described. It is useful to investigate the stability property of ball bearing-rotor system.
-
Key words:
- ball bearing /
- clearance /
- rotor /
- stability /
- bifurcation /
- chaos
-
[1] Gustafsson O G,Tallian T,et al.Research report on study of the vibration characteristics of bearing[R]. Report:AL631023,Reg:585 14:422 3 SKF Ind,Inc，1963. [2] Tamura H,Gad E H,Kondou T,et al.The static running accuracy of ball bearing,memoirs of the faculty of engineering[J].J Kyushu University,1983,43(4)：285—316. [3] Anonynous.NSK explains about internal clearance in rolling bearings[J].Industrial Lubrication and Tribology,2002,54(2)：87—88. [4] Tiwari M,Gupta K,Prakash O.Effect of radial internal clearance of a ball bearing on the dynamics of a balanced horizontal rotor[J].Journal of Sound and Vibration,2000,238(5)：723—756. doi: 10.1006/jsvi.1999.3109 [5] Harsha S P,Sandeep K,Prakash R.The effect of speed of balanced rotor on nonlinear vibrations associated with ball bearings[J].International Journal of Mechanical Sciences,2003,45(4)：725—740. doi: 10.1016/S0020-7403(03)00064-X [6] Mevel B,Guyader J L.Routes to chaos in ball bearings[J].Journal of Sound and Vibration,1993,162(3)：471—487. doi: 10.1006/jsvi.1993.1134 [7] Aktürk N.Dynamics of a rigid shaft supported by angular contact ball bearings[D].Ph D thesis.London U K:Imperial College of Science, Technology and Medicine,1993. [8] Harris Tedric A.Rolling Bearing Analysis[M].New York:John Wiley & Sons,1984. [9] 刘延柱，陈立群.非线性振动[M].北京：高等教育出版社，2001. [10] 周纪卿，朱因远.非线性振动[M].西安：西安交通大学出版社，1998. [11] Ott Edward.Chaos in Dynamical Systems[M].Cambridge:Cambridge University Press,1993. -
计量
- 文章访问数: 2302
- HTML全文浏览量: 103
- PDF下载量: 781
- 被引次数: 0
下载:
渝公网安备50010802005915号