Hysteresis and the bifurcation mechanism of 1/2 order subharmonic resonances in varying compliance vibration of a ball bearing

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Journal of Vibration and Shock ›› 2022, Vol. 41 ›› Issue (2) : 1-10.

ZHU Yujie1，ZHANG Zhiyong1,2,3，CHEN Yiheng2，RUI Xiaoting2，SATTEL Thomas3，CHEN Yushu4，YANG Shaopu5#br#

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Abstract

Rolling bearing varying compliance (VC) vibration is an inevitable excitation to its rotor system, which is a basic scientific problem in the field of bearing-rotor dynamics. Due to the couplings of the nonlinearities from Hertzian contact, clearance (bearing clearance) effect and time-varying VC excitation, remarkable VC hysteretic resonances can be aroused, which may affect the stability and safety of the rolling bearing and even its supporting rotor system, and this subject has always received extensive attentions. According to the basic theory of nonlinear vibration, a parametric excited system often contains various kinds of resonances, such as primary/internal, super/sub harmonic, and combination resonance behaviors. However, compared to many studies on VC primary resonances, there are few works about other resonance types for rolling bearings. Therefore, the paper is addressed on the VC subharmonic resonances in a ball bearing-rigid Jeffcott rotor system. HB-AFT method is adopted to track the VC periodic motion branches, and Floquet theory is employed to analyze the evolutions of subharmonic resonances. It is found that the 1/2 order subharmonic resonance of the system also has hysteresis and jump behaviors. Furtherly, it is found that 1/2 order subharmonic resonant motions contain complex 1:2 and 1:4 internal resonances, which can lead strong couplings between different degrees of freedom of the system. In addition, hysteretic combination resonances triggered by the second Hopf bifurcation is found between the subharmonic resonance intervals. Finally, the paper discusses the influences from bearing radial clearance and damping coefficient on VC subharmonic resonances. The results may have some reference values for dynamic control of ball bearing VC resonances.

Key words

ball bearing / varying compliance vibration / subharmonic resonance / internal resonance / combination resonance / bifurcation

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ZHU Yujie1，ZHANG Zhiyong1,2,3，CHEN Yiheng2，RUI Xiaoting2，SATTEL Thomas3，CHEN Yushu4，YANG Shaopu5. Hysteresis and the bifurcation mechanism of 1/2 order subharmonic resonances in varying compliance vibration of a ball bearing[J]. Journal of Vibration and Shock, 2022, 41(2): 1-10

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