The Research Of Dynamic Performance And Parameter Matching Law For Mechanical System With Clearance

In recent years, most studies of nonlinear dynamics are based on single-parameter bifurcation analysis. Therefore, it is urgent to put forward a new calculation method for researching the correlation between dynamic performance and system parameters and their feasible matching law of the nonlinear dynamical system. Based on detail research of Cell-Mapping Method, a multi-parameter collaborative simulation method, which is used to discretize the parameter plane into parameter cell space for researching the complexity of nonlinear dynamics with multiple parameters, revealing the diversity, correlation, interaction of periodic-impact motions and their competition law, and determining the existence regions of different types of periodic-impact motions of the system, is presented in this paper. The dynamic performances and its correlation with system parameters of the system with clearance and rigid(or soft) constraints are studied in this paper by using the new method. The diversity and evolution characteristic of periodic-impact motions in the parameter plane are revealed in detail. The results provide a basis for feasible parameter matching law of the vibro-impact system.Firstly, the dynamic characteristics and its correlation with system parameters of a two-degree-of-freedom system with clearance and rigid impacts by using the new method are studied. As for low frequency excitation, the transition irreversibility between any two adjacent fundamental impact motions, which creates a series of singular points and two types of transition regions(hysteresis and tongue-shaped regions), are found. The generation mechanism of complete and incomplete chattering-impact vibration of the system is studied.According to the results, as for small clearance, with decrease in ω, a series of grazing bifurcations of p/1 motions occur successively so that the number p of impacts of such motions increases one by one. As p becomes big enough, the system exhibits an incomplete chattering-impact motion. The complete chattering-impact motion with sticking occurs as ω decreasingly passes though the sliding bifurcation boundary of incomplete chatter.The Real-grazing and Bare-grazing bifurcations of p/1 motion, located in both sides of the singular point, occur with decrease in ω or δ. The Period doubling and Saddle-node bifurcations of(p+1)/1 motion, located in both sides of the singular point, occur with increase in ω or δ. These four bifurcation boundaries alternately intersect at singular points so that two kinds of transient zones between p/1 and(p+1)/1 motions, hysteresis and tongue-shaped, are created inevitably due to the irreversibility of mutual transitions.The numerical calculation results show that chaos and a series of complex and regular subharmonic impact motions, such as(2p+1)/2,(3p+1)/3,(4p+1)/4, ……,(np+1)/n,…, impact orbits(p≥0, n≥2), etc., are found to appear in the tongue-shaped regions that are surrounded at the bottom by the period doubling bifurcation boundaries PD(p+1)/1 of(p+1)/1 motion and at the top by the bare-grazing bifurcation boundaries b p 1G of p/1 motion. In the specific tongue-shaped region, associated with 0/1 and 1/1 motions, subharmonic 1/n motions and Period-adding cascade dominate.The hysteresis regions between p/1 and(p+1)/1 motions are totally limited from the lower bound by the real-grazing bifurcation boundaries 1Gp of p/1 motion and from the upper bound by the saddle-node bifurcation boundaries SN(p+1)/1 of(p+1)/1 motion. Neighboring p/1 and(p+1)/1 motions can coexist in the hysteresis regions in the dependence on the initial conditions. The continuous transition between neighbouring p/1 and(p+1)/1 motions can exist only through the singular points.Secondly, the rigid stop A is replaced by a linear spring with stiffness 0K and the dynamic model of a two-degree-of-freedom system with clearance and soft impacts is considered. The differences of effect on dynamic characteristic between elastic and rigid constraints are analyzed emphatically. As the stiffness distribution of elastic restraint k0μ is large enough, the dynamic properties of the system with soft impact are essentially similar in comparison to those with rigid impact, no major differences can be observed.The corresponding vibro-impact systems, in which the stop A is replaced by a rigid constraint or elastic constraint with a pre-compressed clearance B, are detailed studied in dynamic properties. The periodic-impact motions and its existence regions of these systens are extended in the negative clearance interval due to the pre-compressed clearance B.Finally, the multi-parameter co-simulation method is put into the complex practical engineering application. A mechanical model of wheel-rail system with clearance and soft impact is built to study the existence regions of periodic-impact motions of the system. The correlation between dynamic performance and structural parameters is analyzed emphatically. The relations between critical instability speed of hunting motions of wheel set and chief constructive parameters such as the stiffness of suspension device. The results can be applied to optimizing the dynamic characteristic, improving critical instability speed of hunting motions of the wheel-rail system with soft impact and it also provides theoretical basis for analyzing the feasible matching law between dynamic performance and structural parameters of vibro-impact system with clearance, e.g., railway vehicles, train-bridge coupling system, train-rail coupling system, etc.