Mathematical Modeling of Metal Cutting Process

In the practice of metal treatment by cutting it is frequently necessary to deal with selfexcited oscillations of the cutting tool, treated detail and units of the machine tool. In this paper are presented differential equations with the delay of self-excited oscillations. The linear analysis is performed by the method of D-expansion. There is chosen an area of asymptotically stability and area D2. It is prove that, in the area D2 the stable periodical solution appears. The non-linear analysis is performed by the theory of bifurcation. The computational experiment of metal cutting process and results of these experiments are presented.