Applied Mathematics and Mechanics (English Edition) ›› 2006, Vol. 27 ›› Issue (2): 175-186 .doi: https://doi.org/10.1007/s10483-006-0205-1

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NONLINEAR STABILITY OF BALANCED ROTOR DUE TO EFFECT OF BALL BEARING INTERNAL CLEARANCE

BAI Chang-qing, XU Qing-yu, ZHANG Xiao-long   

    1. School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, P. R. China;
    2. Mechanical and Electrical Engineering College, Xi'an University of Architecture & Technology, Xi'an 710055, P. R. China
  • Received:2004-06-28 Revised:2005-10-11 Online:2006-02-18 Published:2006-02-18
  • Contact: BAI Chang-qing

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 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.

Key words: ball bearing, clearance, rotor, stability, bifurcation, chaos

2010 MSC Number: 

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