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Research Papers

# Mathematical Modeling of a Complex Helical Drill Point

[+] Author and Article Information
Jung-Fa Hsieh

Department of Mechanical Engineering, Far East University, Tainan 744, Taiwan, R.O.C.

J. Manuf. Sci. Eng 131(6), 061006 (Nov 10, 2009) (11 pages) doi:10.1115/1.4000438 History: Received October 07, 2008; Revised October 04, 2009; Published November 10, 2009; Online November 10, 2009

## Abstract

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.

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## Figures

Figure 1

Generating curve and corresponding unit outward normal and unit tangent vectors

Figure 2

Cutting the helical groove of a complex helical drill

Figure 3

Transverse section of a complex helical drill at riz=0

Figure 4

Generating curve of a bevel-type grinding wheel

Figure 5

Grinding of a drill flank surface using a form-grinding tool

Figure 6

Frontal view of major cutting edges of three drill types

Figure 7

Variation in normal clearance angle and normal rake angle along the cutting edge

Figure 8

Variation in normal clearance angle and normal rake angle along the chisel edge

Figure 9

Variation in the lip clearance angle along the cutting edge

Figure 10

Variation in the lip clearance angle along the chisel edge

Figure 11

Variation in the heel clearance angle along the cutting edge

Figure 12

Variation in the heel clearance angle along the chisel edge

## Errata

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