BEM approach to thermal aspects of machining processes and their design sensitivities

Elevated temperatures generated in machining operations influence the process efficiency, surface quality, and chip formation mechanics. This paper presents a boundary element method (BEM) formulation for the determination of design sensitivities of temperature and flux distributions for several shape and process parameters in machining operations. This approach is based on direct differentiation (DDA) of the relevant BEM formulation of the problem. The heat transfer and its sensitivities within the tool, the chip, and the workpiece are first calculated separately. A complete model for steady-state machining is then obtained by matching the boundary conditions across the tool-chip, chip-workpiece, and tool-workpiece interfaces. An exact expression for matching is developed to avoid any iterations. The temperature fields and their sensitivities within the workpiece, the chip, and the tool are obtained for various processing conditions. The situation of progressive flank wear and progressive crater wear with continued machining is considered, and its effects on the temperature and flux fields are investigated. The BEM is found to be very robust and efficient for this class of steady-state conduction-convection problems. The application of DDA in conjunction with BEM allows efficient determination of design sensitivities and avoids strongly singular kernels. This approach provides a new avenue toward efficient optimization of the thermal aspects of machining processes.