A new thermal model for bone drilling with applications to orthopaedic surgery
This paper presents a new thermal model for bone drilling with applications to orthopaedic surgery. The new model combines a unique heat-balance equation for the system of the drill bit and the chip stream, an ordinary heat diffusion equation for the bone, and heat generation at the drill tip, arising from the cutting process and friction. Modeling of the drill bit-chip stream system assumes an axial temperature distribution and a lumped heat capacity effect in the transverse cross-section. The new model is solved numerically using a tailor-made finite-difference scheme for the drill bit-chip stream system, coupled with a classic finite-difference method for the bone. The theoretical investigation addresses the significance of heat transfer between the drill bit and the bone, heat convection from the drill bit to the surroundings, and the effect of the initial temperature of the drill bit on the developing thermal field. Using the new model, a parametric study on the effects of machining conditions and drill-bit geometries on the resulting temperature field in the bone and the drill bit is presented. Results of this study indicate that: (1) the maximum temperature in the bone decreases with increased chip flow; (2) the transient temperature distribution is strongly influenced by the initial temperature; (3) the continued cooling (irrigation) of the drill bit reduces the maximum temperature even when the tip is distant from the cooled portion of the drill bit; and (4) the maximum temperature increases with increasing spindle speed, increasing feed rate, decreasing drill-bit diameter, increasing point angle, and decreasing helix angle. The model is expected to be useful in determination of optimum drilling conditions and drill-bit geometries.