| The existence of constraints and gaps makes the vibro-impact system a typical nonsmooth system,which has complex bifurcation characteristics and transition laws.Many mechanical systems can be simplified into vibro-impact systems with gaps and constraints.Studying the mode types,bifurcation characteristics,and transition mechanisms of impact vibration in such systems can provide an important theoretical basis for the dynamic optimization of system parameters and fault diagnosis.Many researches on such problems often focus on one-sided or two-sided constraints and adopt the single parameter research method.However,it is difficult to realize the dynamic optimization of parameters,and can not deeply understand the dynamic characteristics of impact vibration system under the combined action of multiple clearances and constraints.The research on the hunting motion characteristics of railway vehicles is an important direction in dynamics research.The current research is generally aimed at the stable hunting motion without wheel rail impact.The complex environmental conditions and increasing running speed of railway vehicles may lead to the hunting instability of railway vehicles.It has become an urgent problem to study the hunting motion characteristics of railway vehicle system in a large speed domain and to explore the dynamic characteristics of vehicle system after wheel rail impact.This paper studies the two-degree-of-freedom forced vibration system with multiple gaps and constraints,and its application in the hunting motion of railway vehicles under the nonlinear wheel-rail relationship including wheel-rail impact vibration.The following aspects are mainly carried out.First,the two-degree-of-freedom forced vibration system with multiple one-sided rigid constraints and gaps is studied.By extracting the key parameters of the excitation force frequencyωand the gapδbetween the two masses for dual-parameter co-simulation,the mode types and existence areas of the periodic motions of the system are obtained in the(ω,δ)-parameter plane associated with each constraint.At the same time,in the corresponding three-dimensional space,the three-dimensional surface diagram of the maximum impact velocity and the three-dimensional bifurcation graph of the system are obtained.In this way,taking the mode types and existing regions of periodic motions in the two parameter plane as the main research means,combined with the three-dimensional surface diagram of maximum impact velocity,the three-dimensional bifurcation diagram can have an all-round and in-depth understanding of the mode types,existing regions maximum impact velocity and bifurcation characteristics of periodic motions in the whole two parameter plane.Through research,the transition laws of the fundamental impact motions,the incomplete chatting motions,and the sticking motions are revealed.The irreversibility of the mutual transition between adjacent fundamental periodic motions was discovered,and two types of transition domains were produced:tongue-like regions and hysteresis regions.The four boundary lines surrounding the tongue-like regions and hysteresis regions intersect at the singular point.Under the condition of multiple gaps and constraints,the boundary lines of the tongue-like regions are broken due to the superimposition of impact vibration at each constrained surface.The tongue-like regions are mainly composed of subharmonic motions and unrecognized gray areas.The modes of subharmonic motions are mainly(np+1)/n or(np+2)/n(p=1,2,...;n=2,3,...),and are not affected by the destruction of the tongue-like region boundary lines.The peaks of the maximum impact velocity generally appear in the existence areas of fundamental periodic motion 1/1,the existence area of subharmonic motions and small part of the unidentified gray areas.Based on the reference parameters,the influence of changing the system parameters on the system dynamics is discussed.Through the above research methods,a general research method is provided for the vibro-impact system with multiple constraints and gaps,and the required information can be effectively extracted according to the research needs.Secondly,the two-degree-of-freedom forced vibration system with one-sided and two-sided rigid limit constraints is studied.Using the research method proposed above,it is found that when the exciting force is all acting on the masses restricted by the two-sided constraints,the system exhibits complex periodic motion transitions in the low frequency domain and at multiple constraints and sticking motions appear at multiple constraints.The focus is on the effects of changing the damping coefficientζ,mass distribution ratioμ_m,and stiffness distribution ratioμ_k on the mode types,distribution areas,transition law,and maximum impact velocity of the system’s periodic motions.Finally,the research method of solving the non-smooth factors in the vibro-impact system is applied to the hunting motion characteristics and parameter dynamic optimization of the high-speed train bogie system including wheel-rail impact.The dynamic characteristics under the condition of straight track and curved track are studied respectively.In the research,the nonlinear wheel rail relationship closer to the reality is mainly considered,and the non smooth force of flange force is introduced when the bogie system is greatly hunting unstable.Under the condition of straight track and curved track,respectively,through the research method of dual-parameter co-simulation,the pattern types and existence areas of periodic motions on the parameter plane formed by the system parameters and the running speed of the bogie system are obtained.These include the areas of stable hunting motions,the stable limit cycle motions without wheel-rail impact vibration when the small amplitude hunting instability occurs,and the periodic motions including wheel-rail impact vibration.At the same time,the three-dimensional surface diagrams of the maximum impact velocity when the wheelsets impact with the tracks are obtained.The optimal value ranges of primary longitudinal and transverse suspension stiffness and secondary suspension stiffness are obtained,and the effects of wheel rail friction coefficient and track curvature radius on the dynamic characteristics of the system are obtained. |
