球轴承变柔度1/2阶亚谐共振的滞后特性及其分岔机理  

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

作　　者：朱宇杰 张智勇 陈毅恒 芮筱亭[2] SATTEL Thomas 陈予恕[4] 杨绍普[5] ZHU Yujie;ZHANG Zhiyong;CHEN Yiheng;RUI Xiaoting;SATTEL Thomas;CHEN Yushu;YANG Shaopu(School of Science,Nanjing University of Science and Technology,Nanjing 210094,China;Institute of Launch Dynamics,Nanjing University of Science and Technology,Nanjing 210094,China;Department of Mechanical Engineering,Technische Universit t Ilmenau,Ilmenau 98684,Germany;School of Astronautics,Harbin Institute of Technology,Harbin 150001,China;State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University,Shijiazhuang 050043,China)

机构地区：[1]南京理工大学理学院,南京210094 [2]南京理工大学发射动力学研究所,南京210094 [3]伊尔默瑙工业大学机械工程学院,伊尔默瑙98684 [4]哈尔滨工业大学航天学院,哈尔滨150001 [5]石家庄铁道大学省部共建交通工程结构力学行为与系统安全国家重点实验室,石家庄050043

出　　处：《振动与冲击》2022年第2期1-10,共10页Journal of Vibration and Shock

基　　金：中国博士后科学基金(2019M661849);江苏省博士后科研资助计划项目(2018K164C);中央高校基本科研业务费专项资金(30920021155);省部共建交通工程结构力学行为与系统安全国家重点实验室开放基金(KF2020-30);国家留学基金(201906845022)。

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,该研究将针对球轴承-刚性Jeffcott转子系统VC振动亚谐共振问题展开研究。采用谐波平衡-频时转换(harmonic balance and alternating frequency/time domain,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,该研究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。相关结果对球轴承VC共振的动力学控制有一定的参考意义。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 supported rotor system,and this subject has always received extensive attention.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 of rolling bearings.Therefore,the paper was addressed on the VC subharmonic resonances in a ball bearing-rigid Jeffcott rotor system.The harmonic balance and alternating frequency/time domain(HB-AFT)method was adopted to track the VC periodic motion branches,and the Floquet theory was employed to analyze the evolution 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 motions of 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 influences of bearing radial clearance and damping coefficient on VC subharmonic resonances were discussed.The results may have some reference value for the dynamic control of ball bearing VC resonances.

关 键 词：球轴承 变柔度(VC)振动 亚谐共振 内共振 组合共振 分岔 

分 类 号：O322[理学—一般力学与力学基础]