Milling Bifurcations: A Numerical Study

Abstract

In this work, a new model for predicting the dynamic behavior of the milling process is developed. Modeling of the discontinuous cutting forces now takes into account the motion of the cutting tool. The chip thickness is determined by using a search algorithm at each simulation step that determines when the tool cutting edge is in contact with the work piece and how far below the surface the cutting edge is. This new model has lead to a new, more precise, understanding of the stability of the dynamic milling system. For example, the new model is able to predict hysteresis effects in the point at which stability bifurcations occur. The bifurcation point depends on the direction of the change of the control parameter, depth of cut. The hysteresis effect was first seen in experimental results. The model details are presented with the aid programming flow charts. Simulation results show that the tool motion is unstable at large depth of cut and becomes stable as the depth of cut is slowly decreased. If the simulation begins with a small depth of cut stable behavior is exhibited. As the depth of cut slowly increases, the behavior becomes unstable. The depth of cut parameter value at which the bifurcation occurs depends on whether the depth of cut is increasing or decreasing. Simulation results show that an impulse can be given to the simulation to cause the system to jump from one attractor to another.