Analysis of dynamical behaviors of a 2-DOF friction-induced oscillator with one-sided impact on a conveyor belt

In this paper, the flow switchability theory of discontinuous dynamical systems is used to illustrate the dynamical behavior of a 2-DOF (two degrees of freedom) friction-induced oscillator with one-sided impact on a conveyor belt. All the possible motion states such as stick and non-stick motions, impact motion, and stuck motion for such an oscillator are introduced. The phase space in system can be divided into different domains and boundaries according to the discontinuity caused by the friction force jumping and the impact between the mass and the rigid obstacle. The vector field in each domain is continuous and different from that in its adjacent domain. The flow barrier on the separation boundary is considered in this paper. Once the boundary flow leaves the boundary, the boundary flow barrier on the velocity boundary may exist and the leaving flow barriers on the velocity boundary may also exist. The G-functions on different separation boundaries are defined to illustrate the flow switching on the corresponding boundaries. The analytical conditions of the passable, stick, grazing, impact, and stuck motions are developed through G-functions and analysis of vector fields. Since the motions of the two masses interact with each other, the four-dimensional switching sets are given by the form of direct product and the four-dimensional mappings are given to describe periodic motions with different mapping structures. The analytical prediction of different periodic motions is performed through the mapping dynamics. For a better understanding of the motion switching mechanism in such a 2-DOF oscillator , the time histories of displacement, velocity, G-function and the trajectories in phase space for the passable motion, stick motion, impact motion, grazing motion, stuck motion, and periodic motion in system are given by simulation numerically. This investigation has important significance in the optimization design of machinery with friction and impact etc.