Analysis Of Discontinuous Dynamical Behaviors For A Class Of Friction And Impact Systems

Discontinuous phenomena widely exist in mechanical engineering.Collisions or friction often occurs in different mechanical components due to design or operating conditions.Establishing a suitable physical model to study the dynamic behaviors of friction and impact systems with clearances has been the focus for scholars at home and abroad.It has important significance and practical value for noise suppression,and the studies of friction and impact systems are also conducive to improving the practical application of the systems in the engineering field.Recently,a new result,i.e.,the theory of flow switchability,has been proposed in discontinuous dynamical systems.The transformation mechanisms of motions are analyzed by means of G-functions.According to this theory,the discontinuous dynamical behaviors in the mechanical systems and the motion transformation occurring on the discontinuous boundary can be explained more intuitively.In this paper,the dynamics of a two-degree-of-freedom impact oscillator with friction and a periodically forced excitation simplified by a single row cylindrical roller bearing system are investigated via using the flow switchability theory in discontinuous dynamical systems.Based on friction and bilateral rigid barriers,the phase space is divided into different domains and boundaries to study all possible motions in the system.And the related research results of the transition motion and the periodic motion in the two-degree-of-freedom system are given.The main contents of this paper are as follows:In Chapter 1,the background and current status of research on the friction and impact system with clearances are stated.And the concepts of G-functions and the lemmas of motion transformation in the theory of flow transformation in discontinuous systems are also discussed.In Chapter 2,the physical model of a two-degree-of-freedom impact oscillator with friction and a periodically forced excitation is introduced.Because of the change of external periodic excitation,all possible motions of the system are taken into account: free-flight motion or non-stick motion;impact motion;sliding motion and side-stick motion or stick motion.Further,according to the discontinuity resulted from the rigid constraints and friction in the system,different boundaries and regions are described in absolute and relative coordinates,respectively.Then,the G-functions are defined on the corresponding velocity and displacement boundaries on the basis of the flow switchability theory in discontinuous dynamical systems,and the analytical conditions of the motion switching in the two-degree-offreedom system are obtained.The corresponding physical explanations are given.The switching sets and appropriate mapping structures are defined by using the mapping dynamics theory,and the general structures and governing equations of different periodic motions are predicted.Lastly,the passable motion,sliding motion,stick motion,impact motion,grazing motion and two periodic motions are numerically simulated by using MATLAB software,which can better explain the complex motion transformation mechanism in the two-degree-of-freedom impact oscillator with friction and a periodically forced excitation.Chapter 3 summarizes this paper and looks forward to the problems and theories that can be studied in the future.