Extension of process damping to milling with low radial immersion

This paper investigates the stabilizing effect of process damping at low cutting speeds for regenerative machine tool vibrations of milling processes. The process damping is induced by a velocity-dependent cutting force model, which takes into account that the actual cutting velocity is different from the nominal one during machine tool vibrations. The chip thickness and the cutting force are calculated according to the direction of the actual cutting velocity. This results in an additional damping term in the governing delay-differential equation, which is time-periodic for milling and inversely proportional to the cutting speed. In the literature, this term is often assumed to be constant and is considered to improve stability properties at low spindle speeds. In this paper, it is shown that the velocity-dependent cutting force model captures the improvement in the low-speed stability only for turning operations and milling with large radial immersion, while it results in a negative process damping term for low-immersion milling. Consequently, an extended process damping model is needed to explain the low-speed stability improvement for low radial immersion milling.