Mathematical Modeling of a Complex Helical Drill Point

Helical drill points provide a superior cutting performance, particularly when drilling microholes. Complex helical drill points retain the advantages of conventional helical drills while providing a further strengthening of the cutting edge. However, no methods currently exist for systematically modeling drills of this type. The proposed method has three distinct features. First, the mathematical model of the complex helicoid grinding surface enables the normal and tangential vectors of the abrasive wheel to be explicitly derived. Second, the mathematical models of the flute and flank surfaces are integrated, and thus the cutting edges and chisel edges can be obtained using a simple numerical calculation procedure. Finally, the derivation of the model is straightforward and expresses the drill’s characteristics (e.g., the chisel edge, the lip clearance angle, the heel clearance, the normal rake angle, and the normal clearance angle) in accordance with International Organization for Standardization standards. When integrated with appropriate computer numerical control (CNC) software, the modeling approach presented in this study provides a powerful tool for the design and manufacturing of complex helical drill points with a variety of geometrical designs.