Mathematical Modelling of the Cutting Edge of a Tri-Flute Drill

Machining of precision holes is one of the most important area of advanced manufacturing. Precision boring with a diameter of up to 30 mm are processed using reaming or grinding operations with polishing heads. The most promising way of obtaining holes with up to 7-8 accuracy class is the use of three-flute drills. The load distribution among the three flutes and the positive geometry allows improving self-centering and reducing deviation from the specified axis of the hole. The complexity of the development of an analytical approach to the modelling of the cutting edge and gash arises from non-smoothness of changes in the angle of inclination of the cutting edge, which is caused by the presence of points, where the angle of inclination suddenly changes, while transiting from the helical groove to the chisel edge in the drill center. The new approach developed in this paper possesses the ability to create multiple designs of three-flute drills for machining various materials with different values of the rake angle throw the cutting edge in the helical groove section and different values of the angle of inclination of the transverse cutting edge in the center of the drill. Moreover, the special shape of the cutting edge eliminates sharp changes in the angle of inclination of the tangent to the cutting edge and provides a constant contact zone with the material being processed that decreases the size of the stress concentration zone on the cutting part. The present study has shown that productivity gains can be achieved by increasing feed rates using the drill design with a smooth transitions between the cutting edge regions and with the optimal gash shape. The increase in the feed rate from 0.063 to 0.15 mm / rev due to the use of tri-flute drill instead of two-flute more than doubles the productivity at the same internal stress during cutting.