Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis.

Proceedings. Mathematical, Physical, and Engineering Sciences
Karin MoraM I Friswell

Abstract

The dynamics associated with bouncing-type partial contact cycles are considered for a 2 degree-of-freedom unbalanced rotor in the rigid-stator limit. Specifically, analytical explanation is provided for a previously proposed criterion for the onset upon increasing the rotor speed Ω of single-bounce-per-period periodic motion, namely internal resonance between forward and backward whirling modes. Focusing on the cases of 2 : 1 and 3 : 2 resonances, detailed numerical results for small rotor damping reveal that stable bouncing periodic orbits, which coexist with non-contacting motion, arise just beyond the resonance speed Ω p:q . The theory of discontinuity maps is used to analyse the problem as a codimension-two degenerate grazing bifurcation in the limit of zero rotor damping and Ω = Ω p:q . An analytic unfolding of the map explains all the features of the bouncing orbits locally. In particular, for non-zero damping ζ, stable bouncing motion bifurcates in the direction of increasing Ω speed in a smooth fold bifurcation point that is at rotor speed O ( ζ ) beyond Ω p:q . The results provide the first analytic explanation of partial-contact bouncing orbits and has implications for prediction and avoidance of unwanted machine vib...Continue Reading

References

Nov 11, 2014·Proceedings. Mathematical, Physical, and Engineering Sciences·Karin MoraPatrick Keogh
Sep 13, 2016·Proceedings. Mathematical, Physical, and Engineering Sciences·A D ShawM I Friswell

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