Analytical analysis of stability in turning

Chatter in cutting process is harmful to the productivity by its harmful effects such as poor surface quality and reduced productivity. Modeling and analyzing machining stability become necessary to understand the process dynamics and especially to predict the stability in machining operations. Stability lobe diagrams are among the methods that have been adopted to analyze system stability by indicating the boundary between stable and unstable zone. The diagrams are generated function of the depth or width of cut and the spindle speed. In this paper we will present a 3-DOFs analytical analysis of a turning cutting process stability of a steel 42 CD 4 workpiece (hollow cylinder) at low cutting speed including generation of stability lobe diagrams, workpiece displacements and cutting efforts time-variation curves.