Analytical thermal model of orthogonal cutting process for predicting the temperature of the cutting tool with temperature-dependent thermal conductivity

High temperatures generated in cutting processes significantly affect the surface integrity of machined parts and tool wear, leading to workpiece thermal damage, tensile residual stresses in the workpiece and a reduction in tool life. In recent years, different analytical thermal models to predict cutting temperatures have been developed in literature based on 2D modeling of the cutting process and the assumption that thermal conductivities of work piece and chip are not dependent on temperature. However, this dependence of conductivity on temperature may have a significant influence on predicted temperatures and must be taken into account. In this paper, a thermal model of the orthogonal cutting process that considers thermal conductivity of materials (chip and tool) to be dependent on temperature is developed. A linear variation of thermal conductivity with temperature is assumed for chip (workpiece) and tool materials. The model is based on application of: (1) the Kirchhoff transformation in order to convert the nonlinear heat conduction problem into a linear one, (2) the theory of moving and stationary heat sources in semi-infinite and infinite mediums in order to model primary and secondary deformation zones and (3) imaginary heat sources to meet adiabatic boundary conditions in the chip and tool. Imaginary heat sources were defined in the thermal model proposed in this paper in such a way that the effect of the tool-chip interface dimensions and of cutting tool width on the tool temperature could be taken into account. This allows the temperature on the rake face and lateral faces of the tool to be predicted. To this end, a new methodology that considers the temperature-dependent thermal conductivity of materials was developed in order to estimate heat partition ratio along the secondary heat source (tool-chip interface), which is assumed to be non-uniform. Orthogonal cutting tests were also performed in order to verify model predictions by comparing them to tool temperature distributions measured using an IR camera.