Modeling Machining at High Speeds as a Fluid Mechanics Problem

Even though many models for machining exist, most of them are for low-speed machining, where momentum is negligible and material behavior is well approximated by quasi-static plastic constitutive laws. In machining at high speeds, momentum can be important and the strain rate can be exceedingly high. For these reasons, a fluid mechanics approach to understanding high-speed, very high-speed, and ultra-high-speed machining is attempted here. Namely, a potential flow solution is used to model the behavior of the material around a sharp tool tip during machining at high speeds. It is carefully argued that the potential flow solution is relevant and can be used as a first approximation to model the behavior of a metal during high-speed, very high-speed, or ultra-high-speed machining events; and at a minimum, the potential flow solution is qualitatively useful in understanding mechanics of machining at high speeds and above. Interestingly, the flow solution predicts that there is a stagnation point on the rake face, not at the tool tip as is usually assumed. Because the stagnation point is not at the tool tip, the flow solution predicts a significant amount of deformation in the workpiece resulting in large residual strains that may lead to a temperature rise on the finished surface.