Effects of built-up edge-induced oscillations on chip formation during turning

Built-up edge (BUE) is the accumulation of the cut material on the rake face that is close to the tip of the cutting tool. As the BUE periodically develops and breaks off, the thickness of the cut layer changes, which leads to poor surface quality. We developed a thermo-mechanical model for the description of the chip formation during turning that takes into account the variation of the depth of the cut. The model comprises a set of delay-differential equations; thus, the phase-space of the system has an infinite dimension. The formation of the BUE provides an excitation for the cutting dynamics. According to our experimental and numerical investigations, the resulting vibrations can be chaotic. To prove the occurrence of chaos, we determined the largest Lyapunov exponent using two different methods.