Experimental study and sensitivity analysis of force behavior in cortical bone milling

Bone milling force is a key factor to be controlled during the orthopedic surgery. Cutting force has significant influence on the breaking of the tools or causing bone cracks. The cutting force depends on machining parameters, cutting tools and the cortical bone tissue. In this paper, rotational speed, feed rate, cutting depth, tool diameter and the osteon orientation are considered as input parameters. For statistical modeling and experimental study, the response surface method was used. Moreover, using the Sobol statistical sensitivity analysis method the effect of each input parameter on the process force is investigated both qualitatively and quantitatively. Results revealed that bone milling force decreases with increasing rotational speed while it increases with feed rate due to an increase in the thickness of the deformed chip as well as an escalation of friction. Moreover, increasing cutting depth due to increased thickness of the deformed chip, increases friction and thus increases cutting force. Additionally, as the diameter of the blade increases, the cutting force increases. Finally, in the perpendicular direction to the osteon, less force is applied to the bone tissue than that of parallel to osteon. Based on Sobol sensitivity analysis, cutting depth (51.4%), feed rate (21.9%), tool rotational speed (19%), milling direction (4.8%) and tool diameter (1.9%) are the most effective respectively. Response optimization was also presented using Derringer algorithm, which provided a minimum cutting force of 3.76 N, when tool diameter of 4 mm, rotational speed of 3000 rpm and feed rate of 100 mm/min and cutting depth of 1 mm were selected in milling perpendicular to the osteon orientation. This research can be used to optimize milling parameters in order to assist robotic surgery and orthopedic tool design.