The Dynamics of an Impact Print Hammer

Abstract

A mathematical model is developed to describe the characteristic behavior of an impact print hammer of the stored energy type. The armature of the impact print hammer is represented by a rigid mass held against a backstop by a preloaded linear spring with negative stiffness which characterizes the net effect of a permanent magnet and a prestressed flexible beam acting on the armature. Periodic sine pulses are adopted to represent currents which release the armature to strike the ribbon and paper which is represented by a linear spring and a linear viscous dashpot. A coefficient of restitution is employed to characterize the instantaneous behavior of impact and rebound at the backstop. In this paper, periodic motions with n impacts against the backstop per forcing cycle, period doubling bifurcations, and chaotic motions are found. The stability of the periodic motions is investigated as is the influence of various parameters on the performance of the impact print hammer. With this simple model we can predict much of the qualitative behavior of the actual physical system.