Neimark-Sacker Bifurcation of Rolling Bearing System with Fault in Outer Ring

Abstract:

Piecewise non-smooth model of three-degree-of-freedom rolling bearing system with fault in outer Ring is established by the method of the nonlinear theory. The Neimark-Sacker bifurcation of bearing system is first studied in this paper. The switching matrixes of system are obtained at the switching boundaries, and theNeimark-Sacker bifurcation of non-smooth bearing system is analyzed by combining the switching matrixes with the Floquet theory for smooth systems. The numerical method is used to further reveal the Neimark-Sacker bifurcation of bearing system through establishing the Poincare mapping on the collision plane. When the rotating frequency is increased to reach the critical bifurcation point, a pair of complex conjugate Floquet multipliers is on the unit circle and others into a unit circle , and the Neimark-Sacker bifurcation appears.The study of bifurcation of the fault bearing system provides reliable basis for the design and fault diagnosis and provides theoretical guidance and technical support for the actual design in the safe and stable operation of large high-speed rotating machinery.

• Periodical: Applied Mechanics and Materials (Volume 723)
• Pages: 54-59
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.723.54
• Online since: January 2015
• Authors: Qiang Wang, Yong Bao Liu, Hui Dong Xu*, Xing He
• Keywords: Bearing, Floquet Theory, Neimark-Sacker Bifurcation

References

[1] F.J. Franklin, I. Widiyarta and A. Kapoor, Computer simulation of wear and rolling contact fatigue, Wear, Vol. 251(2001), p.949–955.

DOI: 10.1016/s0043-1648(01)00732-3

[2] S. Ericsson, N. Grip, E. Johansson, L.E. Persson, R. Sjoberg and J.O. Stromberg, Towards automatic detection of local bearing defects in rotating machines, Mechanical Systems and Signal Processing, Vol. 19 (2005), p.509–535.

DOI: 10.1016/j.ymssp.2003.12.004

[3] W. Sun, J. Chen and J. Li, Decision tree and PCA-based fault diagnosis of rotating machinery, Mechanical Systems and Signal Processing. Vol. 21(2007), p.1300–1317.

DOI: 10.1016/j.ymssp.2006.06.010

[4] P. Pennacchi, A. Vania, S. Chatterton and E. Tanzi, Detection of unsteady flow in a Kaplan hydraulic turbine using machine mechanical model and rotor measured vibrations, Proceedings of the ASME Turbo Expo2012–GT2012, Paper GT2012- 69995, Copenhagen, Denmark, June 11–15, (2012).

DOI: 10.1115/gt2012-69995

[5] Z.X. He and H. Gan, The study of rolling system dynamics behavior including the bearing shaft clearance Journal of vibration and shock, Vol. 28(9) (2009), pp.120-124.

[6] W.G. Zhang, S.H. Gao, X.H. Long and G. Meng, Nonlinear analysis for a machine-tool spindle system supported with ball bearing, Journal of vibration and shock, Vol. 27(9) (2008), pp.72-75.

[7] Y. B. Tang, D. P. Gao and G. H. Luo, Non-Linear Bearing Force of the Rolling Ball Bearing and Its Influence on Vibration of Bearing System, Journal of Aerospace Power, Vol. 21(2)(2006), pp.366-373.

[8] S.H. Gao, X.H. Long and G. Meng, Three types of bifurcation in a spindle-ball bearing system. Journal of Vibration and Shock, Vol. 28(4)(2009), pp.59-63.

[9] R.I. Leine and H. Nijmeijer, Dynamics and Bifurcation of Non-Smooth Mechanical Systems. Berlin; Springer, 2004: 101-118.