Front Instabilities and Cutting Processes

We present an equation for the evolution of a surface of a workpiece which is cut by beam cutting techniques such as abrasive waterjet cutting, ion sputtering or laser jet cutting. This evolution equation exhibits a Hopf bifurcation leading to patterns similar to the striation patterns observed in real cutting processes. We demonstrate that temporal modulations of various process control parameters such as feed rate, beam intensity or beam width as well as modulations of the path geometry can be used to suppress unwanted ripple formation. We propose to apply these strategies to real cutting processes.