Analysis of the General Tool Life Function of Cutting Tools by Application of the Catastrophe-Theory
Abstract Production technology planning requires information on tool life T and its relation to cutting speed v. As the Taylor formula often cannot be linearized on an lg-lg scale, a general tool life function has been developed for describing a v-T function with a convex-concave part. Using catastrophe theory, an analogy is established between the general tool life function and the cusp catastrophe, allowing topological mapping of the general v-T function. Results were verified by machinability tests in the turning of C35 and C60 conventional and specially deoxidized C-steels during steelmaking. It was found that in the convex-concave section of this function, 2–3 cutting speeds can be selected for a given tool life, which is advantageous for harmonizing tool changes in multi-operation technology.