Mechanistic model to predict temperature in bone end milling: A study intended for bone grafting surgery

Temperature control during bone maachining is critical to prevent thermal osteonecrosis and ensure post-operative success in orthopaedic procedures. Despite extensive research on force and surface integrity in bone milling, predictive temperature models tailored to cortical bone remain scarce. This study proposes a mechanistic model to predict the workpiece surface temperature during end milling of cortical bone using the bottom cutting edge. The model integrates moving heat source theory with dynamic cutting force modelling to calculate heat generated at the shear plane and tool-workpiece rubbing zones. The complex geometry of the bottom cutting edge and transient heating time effects was incorporated to reflect actual end milling conditions. A dynamic cutting force model, based on a mechanistic force prediction approach for cortical bone, was applied to determine the instantaneous heat generated at each discrete element along the cutting edge. To validate the model, a series of end milling experiments was performed on bovine cortical bone specimens using a four-fluted, 2.50 mm diameter tungsten carbide flat end mill cutter. The developed mechanistic model predicted cortical bone surface temperature with an average absolute error of 13.91% and a maximum error of 19.60% across 31 validation experiments. The heat partition ratio was found to range between 0.57 and 0.64, showing a near-linear dependence on thermal number. The results further demonstrate that the incorporation of finite heating-time effects improves prediction accuracy, particularly during the transient heating phase.