Study On Dynamic Mechanism Of Complex Subharmonic Resonances In Ball Bearings

The time-varying compliance(VC)vibration is an inevitable excitation form of the rotor system,which is a basic scientific problem in the field of bearing-rotor dynamics.Due to the coupling effect of Hertzian contact nonlinearity,clearance(bearing clearance)nonlinearity,and time-varying compliance parametrically excited nonlinearity,the system has a significant VC hysteresis resonance characteristic,which affects the stability and safety of the bearing and even the movement of supporting rotor system,and its related issues have received continuous attention.According to the basic theory of nonlinear vibration,parametric systems often have abundant main resonance,internal resonance,superharmonic,subharmonic and combined resonance behavior.However,compared to a large number of studies on the VC parametric primary resonance of rolling bearings at home and abroad,there are few studies on other resonance types.This article will focus on the sub-harmonic resonance of ball bearing VC vibration.The semi-numerical and semi-analytical Harmonic balance and alternating frequency/time domain(HB-AFT)method has the advantage of avoiding traditional methods such as series expansion or integration of complex nonlinear terms.The harmonic solution of the system can be obtained quickly and accurately.Using the HB-AFT method combined with Floquet stability theory,this paper studies the trigger mechanism and hysteresis response characteristics of ball bearing VC parametric 1/2-order subharmonic resonance.It is found that under the excitation of VC parameters,the system can arouse1/2-order subharmonic resonance behavior in the direction of two degrees of freedom from subcritical and supercritical period-doubling bifurcation instability.It also points out that the soft and hard hysteresis types of the 1/2-order subharmonic resonance response triggered in different degrees of freedom are consistent with the corresponding main resonance hysteresis types.On this basis,it is found that the internal resonance phenomenon of the1/2-order subharmonic motion of the system will cause strong coupling vibration of the ball bearing in different degrees of freedom.In addition,the study found that there is a hysteresis combination resonance behavior triggered by the second Hopf bifurcation between subharmonic resonance intervals.Finally,the paper discusses the influence of bearing radial clearance,damping coefficient and heavy load on the system VC sub-resonance,and points out that adjusting the bearing clearance can control the resonance amplitude and position.In conclusion,for the time-varying stiffness parametric system of rolling bearing,the superharmonic,subharmonic,internal resonance and combined resonance behavior that the system may trigger should be fully considered in the dynamic design process.This paper has certain reference significance for the study of the evolution mechanism of the complex nonlinear vibration response behavior of rolling bearings.