We present an electro-mechanical system with finite delay whose construction was motivated by delay differential equations used to describe machine tool vibrations [Johnson, 1996; Moon & Johnson, 1998]. We show that the electro-mechanical system is capable of exhibiting periodic, quasiperiodic and chaotic vibrations. We provide a novel experimental technique for creating real-time Poincaré sections for systems with delay. This experimental technique was also applied to machine tool vibrations [Johnson, 1996]. Experimental Poincaré sections clearly show the existence of tori, and reveal the tori bifurcation sequence which leads to chaotic vibrations. The electro-mechanical system can be modeled by a single second-order differential equation with delay and a cubic nonlinearity. We show that the simple mathematical model fully replicates the bifurcation sequence seen in the electro-mechanical system.
Influence of machine tool vibrations on geometric specifications of balls
