A Transport-Diffusion Equation in Metal Cutting and its Application to Analysis of the Rate of Flank Wear

A two-dimensional transport-diffusion equation is derived for diffusion in metal cutting by an extension of Fick’s second law. The analysis considers the dynamics of the cutting process and thus offers a comprehensive representation of the diffusing species in the workpiece and the chip. A relationship for the rate of flank wear is derived considering adhesion and diffusion as the major modes of wear on the tool flank. It is based on the mechanics of the wear process, friction and diffusion, taking into account the regenerative effects of wear, temperature, and friction force. Based on the simulated results of the analysis, a new criterion is proposed for determining tool life.