Periodic and chaotic motions of an impact forming machinery with double masses

An impact-forming machinery with double masses is considered. Dynamics of the impact-forming machinery, in perfectly plastic impact case, is studied by using a three-dimensional map. The map is of piecewise property due to synchronous or non-synchronous motion of two masses immediately after the impact, and singularities caused by the grazing contact motions of two masses. The influence of the piecewise property and singularities on global bifurcations and transitions to chaos is elucidated. The impact-forming system exhibits two different types of period n single-impact motions in different forcing frequency regions, respectively. The results from simulation show that period-doubling bifurcations of single-impact periodic orbits of the impact-forming machinery are commonly existential. However, no period-doubling cascade occurs because of the piecewise and discontinuous nature of the map. The periodic motions with grazing contact of two masses lead complex sequences of transitions to chaos.