球轴承变柔度1/2阶亚谐共振的滞后特性及其分岔机理

朱宇杰1,张智勇1,2,3,陈毅恒2,芮筱亭2,SATTEL Thomas3,陈予恕4,杨绍普5

振动与冲击 ›› 2022, Vol. 41 ›› Issue (2) : 1-10.

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (2) : 1-10.
论文

球轴承变柔度1/2阶亚谐共振的滞后特性及其分岔机理

  • 朱宇杰1,张智勇1,2,3,陈毅恒2,芮筱亭2,SATTEL Thomas3,陈予恕4,杨绍普5
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Hysteresis and the bifurcation mechanism of 1/2 order subharmonic resonances in varying compliance vibration of a ball bearing

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

滚动轴承变柔度(varying compliance,VC)振动是转子系统不可避免的激励形式,属于轴承-转子动力学领域的基本科学问题。由于Hertzian接触非线性、间隙(轴承游隙)非线性和时变柔度参激非线性的耦合作用,系统具有显著的VC滞后共振特性,影响轴承自身乃至其支承转子系统运动的稳定性和安全性,相关问题得到持续关注。根据非线性振动基本理论,参激系统往往具有丰富的主共振、内共振、超谐、亚谐和组合共振行为。然而,相对于国内外大量有关滚动轴承VC参激主共振的研究,其他共振类型的研究甚少。基于此,本文将针对球轴承-刚性Jeffcott转子系统VC振动亚谐共振问题展开研究。论文采用HB-AFT方法追踪系统的VC周期运动分枝,并结合Floquet理论分析了系统亚谐共振行为的演化机制,发现系统1/2阶亚谐共振同样具有滞后跳跃行为。在此基础上,指出系统1/2阶亚谐运动包含复杂的1:2和1:4内共振现象,会引起球轴承不同自由度方向强烈的耦合振动。另外,研究发现在亚谐共振区间之间存在由二次Hopf分岔触发的滞后组合共振行为。最后,论文探讨了轴承径向游隙和阻尼系数对系统VC亚谐共振的影响。相关结果对于球轴承VC共振的动力学控制具有一定的参考意义。

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.

关键词

球轴承 / 变柔度振动 / 亚谐共振 / 内共振 / 组合共振 / 分岔

Key words

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

引用本文

导出引用
朱宇杰1,张智勇1,2,3,陈毅恒2,芮筱亭2,SATTEL Thomas3,陈予恕4,杨绍普5. 球轴承变柔度1/2阶亚谐共振的滞后特性及其分岔机理[J]. 振动与冲击, 2022, 41(2): 1-10
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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