Study On Hysteretic Resonance Characteristics Of Power Nonlinear Systems

Power-form nonlinear contact force models are widely adopted in relatively moving parts of macro(e.g.,rolling bearings considering Hertzian contact restoring force between rolling elements and bearing raceways)or micro scales(e.g.,the micro cantilever probe system of atomic force microscopy)mechanical systems,and contact resonance could cause serious problems of wear,contact fatigue,vibration and noise,which has attracted widespread attentions.In the present paper,the softening/hardening stiffness characteristics of continuous and one-sided contact power-form nonlinear models are addressed,respectively,by analysis of the monotone features of resonant frequency-response skeleton lines.Herein,the period-n solution branch and its stability characteristics are obtained by the harmonic balance and alternating frequency/time domain(HB–AFT)method and Floquet theory.Compared with previous studies,this paper will furtherly clarifies the influence of constant loads on the softening/hardening stiffness characteristics of general power-form systems.In addition,for a power-form system with one-sided contact,the phenomenon of primary and super/sub-harmonic hysteretic resonances inducing period doubling,folding bifurcation,coexistence of multiple solutions is demonstrated.Besides,it gives the evolution mechanism of two types of intermittency chaos in one-sided contact system.And on that basis,this paper will investigate the hysteretic characteristics of the Hertzian contact resonances of a ball bearing system under VC excitations.Moreover,the linearized dynamic bearing stiffnesses of the system will be presented for assessing the locations of VC resonances.Our analysis indicates that the system possesses many types of VC resonances such as the primary,internal,super-harmonic and even combination resonances,and the evolutions of these resonances are presented.Finally,the suppression of resonances and hysteresis of the system will be proposed by adjusting the bearing clearance.The overall results may have certain basic theoretical significance and engineering values for control of vibration and noise in contact mechanical systems,and may have certain reference value for the engineering research and test of resonance control of rolling bearing system and even the optimization of bearing life.