Bifurcations And Parameter Matching Of Mechanical Vibration Systems With Plastic Impact

Mechanical components with gaps often experience shock and vibration during operation.Because the existence of shock vibration will reduce the use efficiency and operational reliability of some mechanical equipment,the dynamic research of vibro-impact system with gaps is of great significance for solving practical engineering problems.This paper takes the two-degree-of-freedom vibro-impact system and the impact-progressive vibration system as the research objects,discusses the relationship between dynamic parameters and the dynamic characteristics of the system and matching rules,and provides a theoretical basis for the parameter selection and dynamic performance matching design of vibro-impact system.The main research work of this thesis is as follows.The mechanical model of a two-degree-of-freedom vibro-impact system with a gap is considered.Under the condition of the Poincare mapping to identify the reference parameters,the periodic motion mode and existence domain of the system in the(ω,δ)plane are studied.The non-smooth bifurcations such as grazing and sliding of the periodic motion,as well as the existence(1,0,0)motion and(1,1,0)motion,are studied.The dynamics in the hysteresis domain and subharmonic inclusion domain reveal the characteristics of the transition from single-impact periodic n motion to periodic n+1 motion.In the hysteresis domain,the initial displacement and initial velocity of the system are assigned different values,resulting in different types of shock and vibration responses of the system.The periodic vibration types in the subharmonic inclusion domain show a certain regularity.In the low-frequency and small gap region,the parameter domains of(1,1,1)and(1,2,1)periodic sticking motions are distributed alternately,and the two types of periodic motions transfer to each other through switching-sliding bifurcations.Through the multi-parameter numerical simulation method,the matching relationship between the dynamic characteristics of the two-degree-of-freedom vibro-impact system with gaps and the key parameters m,ξ,ki(i=1,2),ci(i=1,2),f is studied.Among them,the mass distribution ratio m has the greatest impact on the distribution area and transition characteristics of the periodic motion of the system.When m increases,the range of the parameter domain of sticking periodic motions decreases and shifts to the area where ω andδ decrease.When k2 increases,more types of periodic sticking motion emerge in the low-frequency and small gap area.When k2=0.9,the bifurcation behaviors of periodic sticking motion such as crossing-sliding,switching-sliding and multi-sliding bifurcation as well as grazing and saddle node bifurcation presented by the system reveal the non-smooth bifurcation characteristics of periodic viscous motion in the region of low frequency and small gap.System dynamics parameters not only affect the distribution of sticking periodic motions in the two-dimensional parameter plane,but also affect the size and development trend of the system’s impact velocity.Among them,ci(i=1,2)has the least influence on the impact velocity.On the(ω,f)plane,the amplitude change of the impact velocity is symmetrically distributed along f=0.5.A dynamic model of an impact-progressive system is established.By constructing local mapping and Poincare mapping,the type and transition law of the periodic motion of the system are identified.When the frequency is low,(n,1,Ⅰ)motion and(n,1,Ⅱ)motion transfer through crossing-sliding.When the system response transitions from a single-impact period n motion to a period n+1 motion,although period doubling bifurcation appears,due to the existence of grazing bifurcation or Hopf bifurcation,no period doubling sequence is formed.There is a hysteresis zone between the grazing and the bifurcation point of the saddle node,and there is a phenomenon of coexistence of multiple attractors in the hysteresis zone.Under the condition of the benchmark parameters,when the excitation frequency is taken near ω=0.4,the system behaves as a cycle one movement,and the drilling amount of the slider is the largest.The influence of the dimensionless parameters of the percussion drilling vibration system on the system dynamics is studied,and the coupling relationship between the system parameters and the frequency range of period-to-motion and the impact velocity is revealed.