The Dynamics Research Of A Mechanical System With Clearance

In mechanical system, vibro-impact of system will be happen during the movement for the clearance of system boundary or internal, when momentum is transfered in a very short period of time and tremendous force is generated, so that the vibro-impact has pros and cons of two sides for mechanical system with clearance in engineering practice. On the one hand, the vibro-impact can cause deformation and damage on equipment system, such as the vibro-impact that exists in cars, trains, aircraft and other transportation tools and the bridges, nuclear power plant and other engineering structure or gear meshing and transmission system, etc. On the other hand, the vibro-impact can be take full use of, such as the DTH drill, stone crusher, pile hammer, forging hammer, punch press and so on, which all utilize the vibro-impact principle to complete mechanical works. Therefore, the study of mechanical system with clearance has very important theoretical signification and practical application significance. Three mechanical models with rigid constraint vibro-impact system are abstracted and simplified from the engineering practice in this paper, and the dynamic characteristics of vibro-impact of the models are studied respectively as follows.(1) Mechanics models of two-degree-of-freedom impact system with unilateral rigid constraints, two-degree-of-freedom impact system with bilateral rigid constraints and three-degree-of-freedom relative impact system are set up respectively in this paper. Physical equations of the models are established by using Newton’s laws of motion and momentum theorem, and then physical equations are transformed to differential equations through the dimensionless. The systems are decoupled by using regular modal matrix method and the analytical solutions of the periodic motion of the systems are finished.(2) The stabilities of periodic motion of systems are analyzed through the conditions of periodic motion existence and bifurcation theory. The Poincare map and the linear matrix of the system are solved.(3) Numerical simulation was carried out on the systems respectively through the MATLAB programming. The evolution ways of the systems from various bifurcations to chaos under appropriate parameters are found out and the Poincare mapping sections of the systems in specific parameters are simulated.Through the simulation, it is found that the stable periodic motions of systems will become instability and bifurcations will occur when the eigenvalues of the linearization matrixes of systems across the unit circle, near the fixed point of system’s periodic motion. And the systems can evolve into chaos though the paths of Hopf bifurcation, doubling bifurcation, torus-doubling bifurcation, codimension-two bifurcation, phase-locked and so on as the parameters change gradually. In addition, through simulation we also found that the influence of vibration frequencies of the systems is greater on the dynamic characteristics of systems, during a number of factors. Consequently, all of these studies can provide a certain theoretical basis for the optimization of vibro-impact system with clearance in practice.