Stability of Turning Process with a Continuous Delay Model

An alternative physical explanation for process damping where a distributed cutting force model, along with a function distribution over the tool-chip interface, is assumed, is described. An exponential shape function is used to approximate the force distribution on the tool-chip interface. The distributed force model results in a more complicated governing equation, a second-order delayed integrodifferential equation, which involves both a discrete and distributed delay. An approach to transform and normalize the governing equation of motion into a third-order discrete system is described and the state-space representation of the new system is obtained. The semi-discretization method is then used to chart the stability boundaries for turning operation.