Non-Linear Numerical Analysis in Transient Cutting Tool Temperatures

Abstract

A numerical analysis, using a control volume approach, is conducted to study the transient cutting tool temperatures with temperature dependent thermal properties. With temperature dependent thermal properties, the governing conduction equation is non-linear and thus, the standard analytical solutions are no longer valid. In any cutting processes, the temperature distribution is intrinsically three-dimensional and very steep temperature gradient may be generated in the vicinity of the tool-chip interface. In this region, where the maximum temperature occurs, the effect of variable thermal properties may become important. The full three-dimensional non-linear transient heat conduction equation is solved numerically to study these non-linear effects on cutting tool temperatures. The extremely small size of the heat input zone (tool-chip interface), relative to the tool insert rake surface area, requires the mesh to be dense enough in order to obtain accurate solutions. This usually requires very intensive computational efforts. Due to the size of the discretized domain, an efficient algorithm is desirable in the solution of the problem. Four different iterative schemes are explored, and an optimized numerical scheme is chosen to significantly reduce the required computing time. This numerical model can be used for process development in an industrial setting. The effect of two different heat flux input profiles, a spatially uniform plane heat flux and a spatially non-uniform plane heat flux at the tool-chip interface, on the tool temperatures are also investigated in the present study. Some recommendations are given regarding the condition when these non-linear effects can not be ignored.