| The vibration of impact and friction not only greatly reduces the service life of mechanical system,stability and work efficiency,but also causes serious noise pollution.The research of dynamic characteristics of vibro-impact system under dynamic friction has important theoretical significance and practical engineering value for the accomplishment of dynamic response analysis,stability control and optimization of engineering parameters of mechanical systems.Based on the single DOF mass-belt system,two DOF symmetrical vibro-impact system with friction and two DOF system with symmetrical restraint and friction are established respectively,comprehensively considering the friction environment,supporting and boundary conditions of the system,and the Dankowicz and Lu Gre friction models are used as the sources of dynamic friction.The dimensionless equations of systems are given,with the help of R-K algorithm,we can get the numerical solution.By the analysis of results of numerical simulation which phases diagram,time history diagram,bifurcation diagram,sliding bifurcation diagram,exploring the dynamic bifurcation evolution,stick-slip and chattering vibration of systems.And researching the influence of key parameters to the stick-slip and chattering vibration by analysis of distribution of parameters field on the two-parameter plane.Under the given system parameters,the Dankowicz and LuGre friction models are used as the dynamic friction sources of two DOF symmetrical vibro-impact system,the nonlinear dynamic behavior and vibration characteristics of the systems are analyzed by numerical simulation.Under the influence of dynamic friction,it is found that the main area of stick-slip and chattering vibration is located in the low-frequency field,and there is corrugated bifurcation structure,amplitude jumping,periodic bifurcation,complete and incomplete chattering-impact vibration in both system.With the increasing of the excitation frequency,the system stick-slip is gradually weakened,and the complete chattering-impact vibration is weakening to the incomplete chattering-impact vibration,gradually transiting into the intermediate frequency field of single impact vibration.The intermediate frequency field usually exists single impacting which is stable and without stick-slip and chattering vibration,and also exits amplitude jumping.In the high frequency vibration region,the systems exists abundant dynamics bifurcation evolution forms which are Hopf bifurcation,periodic doubling and degradation bifurcation,amplitude jumping,intermittent chaos,periodic bubble.The impacting causes saltation of velocity and friction force.During the process of sticking,the system is in a state of dynamic equilibrium and without acceleration.And there are variety kinds of sliding bifurcation caused by the transformation of traversing track and the region of sticking vibration,such as crossing-sliding,grazing-sliding,switching-sliding,and multi-sliding bifurcation.On the selected parameters plane,the parameters field of stick-slip and chattering increasing and decreasing with the change of parameters.The stick-slip and chattering vibration has different strength of the sensitivity towards different parameters.And under certain parameters,there are cross vibration field between two adjacent vibration regions,which makes the system vibration complicated and sensitive.For the two DOF vibro-impact system with symmetrical restraint and dynamic friction,the non-linear dynamic bifurcation behavior and stick-slip and chattering vibration characteristics of system under the Dankowicz and LuGre friction models are explored.The results show that the system bifurcation presents same regional segmentation characteristics under the control of excitation frequency.There is a complete chattering vibration in the rigid constraints on both sides.The stick-slip and chattering vibration has different strength of the sensitivity of different parameters,and there are also variety cross-vibration behavior. |
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