| Intermittent vibration refers to the state in which the laminar flow in fluid is interrupted by turbulent outbreaks at irregular intervals.In the field of nonlinear dynamics,the intermittent motions is termed the pseudo random alternating motion between regular motion and irregular motion.Traditionally intermittent mechanisms are classified into three different types as I,II and III intermittency chaos,which are induced by fold,subcritical Hopf and subcritical period doubling bifurcations respectively,with the condition of reorganization of the global structure of the system.Intermittency is a typical route to chaotic motions for nonlinear dynamical systems.However,for the behaviors of intermittency chaos,the research methods have yet to be enriched due to the parametric sensitivity and evolution complexity of the nonlinear dynamic responses.The semi-analytical and semi-numerical harmonic balance and alternating frequency/time domain(HB-AFT)method can avoid the traditional integral or series expansion of complex nonlinear terms,which make it obtain a harmonic solution of the system quickly and accurately.Based on the HB-AFT method and Floquet stability theory,this paper will present a new semi-analytical method for the evolution of intermittency chaos in nonlinear dynamical systems.With the above method,the classic harmonic excitation Duffing system is taken as the research object.Based on the classic work of Thompson JMT,Hu Haiyan on the intermittent chaotic vibration of Duffing system,the excitation characteristics,multi-solution characteristics as well as the mechanism of intermittent chaotic evolution has been studied deeply.Besides,ball bearings are the main supporting parts of rotating machinery.In recent years,a large number of investigations have pointed out that bearing nonlinearity can abounds nonlinearities to the rotor system,such as hysteretic jumping vibrations and even chaotic vibration behaviors,which has huge effects on the stability and fatigue life of the rotor system's operations,and the related research is still an open question.Varying compliance(VC)of ball bearings is coming from the revolution of ball elements with the bearing cage in and out of the loaded areas,hence it is an inevitable source of parametric vibration of the rolling bearing rotor system.In this paper,the HB-AFT method will be used to further analyze the evolution of complex VC vibration and even its inherent trigger mechanism to intermittency chaos of ball bearings.Therefore,this study has important basic theoretical significance and engineering values. |
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