Analytical Prediction of Interrupted Cutting Periodic Motions in a Machine Tool

The methodology for prediction of interrupted cutting periodic motions in a machining system is developed. The interrupted cutting mappings in the vicinity of the system constraints are defined. The criteria for the interrupted cutting periodic motions are developed through the state variables and mapping forms. The periodic interrupted cutting motions in a two-degree-of-freedom model are predicted numerically and analytically via closed form solutions. The chip and tool-piece seizure in the machine-tool system is also discussed. The bifurcations are caused by interactions of continuous dynamical systems in the neighborhood of the boundary.