# Mathematical model of multiflute drill point

Jung Fa Hsieh, Psang-Dain Lin

Research output: Contribution to journalArticle

24 Citations (Scopus)

### Abstract

Multiflute drilling is an efficient means of making high accuracy holes without reaming. Because of the current lack of a comprehensive mathematical model for this kind of drilling, this paper presents a complete and simple method for designing multiflute drills. There are three special features of the proposed model. The first is that rotational axial-type cutting tools and disk-type abrasive wheels are modeled by revolution geometry, so that the normals and tangent vectors of flute and flank surfaces can be obtained explicitly. Consequently, rake and clearance angles of cutting and chisel edges can be investigated according to recommended ISO standards. The second feature is that the mathematical models of flute and flank surfaces are integrated, so that cutting and chisel edges and their various characteristic angles can be obtained by numerical calculation. Finally, a simple way to determine the rake angles and wedge angles and clearance angles is presented by using the unit normals of the ISO-recommended reference planes. To verify the validity of this methodology, a designed three-fluted drill was machined on a 6-axis tool-grinding machine. This model is comprehensive, simple, easy to use, and capable of describing a wide range of drill design features.

Original language English 1181-1193 13 International Journal of Machine Tools and Manufacture 42 10 https://doi.org/10.1016/S0890-6955(02)00044-5 Published - 2002 Jan 1

### Fingerprint

Mathematical models
Drilling
Reaming
Grinding machines
Grinding wheels
Cutting tools
Geometry

### All Science Journal Classification (ASJC) codes

• Mechanical Engineering
• Industrial and Manufacturing Engineering

### Cite this

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title = "Mathematical model of multiflute drill point",
abstract = "Multiflute drilling is an efficient means of making high accuracy holes without reaming. Because of the current lack of a comprehensive mathematical model for this kind of drilling, this paper presents a complete and simple method for designing multiflute drills. There are three special features of the proposed model. The first is that rotational axial-type cutting tools and disk-type abrasive wheels are modeled by revolution geometry, so that the normals and tangent vectors of flute and flank surfaces can be obtained explicitly. Consequently, rake and clearance angles of cutting and chisel edges can be investigated according to recommended ISO standards. The second feature is that the mathematical models of flute and flank surfaces are integrated, so that cutting and chisel edges and their various characteristic angles can be obtained by numerical calculation. Finally, a simple way to determine the rake angles and wedge angles and clearance angles is presented by using the unit normals of the ISO-recommended reference planes. To verify the validity of this methodology, a designed three-fluted drill was machined on a 6-axis tool-grinding machine. This model is comprehensive, simple, easy to use, and capable of describing a wide range of drill design features.",
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Mathematical model of multiflute drill point. / Hsieh, Jung Fa; Lin, Psang-Dain.

In: International Journal of Machine Tools and Manufacture, Vol. 42, No. 10, 01.01.2002, p. 1181-1193.

Research output: Contribution to journalArticle

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AU - Hsieh, Jung Fa

AU - Lin, Psang-Dain

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Y1 - 2002/1/1

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AB - Multiflute drilling is an efficient means of making high accuracy holes without reaming. Because of the current lack of a comprehensive mathematical model for this kind of drilling, this paper presents a complete and simple method for designing multiflute drills. There are three special features of the proposed model. The first is that rotational axial-type cutting tools and disk-type abrasive wheels are modeled by revolution geometry, so that the normals and tangent vectors of flute and flank surfaces can be obtained explicitly. Consequently, rake and clearance angles of cutting and chisel edges can be investigated according to recommended ISO standards. The second feature is that the mathematical models of flute and flank surfaces are integrated, so that cutting and chisel edges and their various characteristic angles can be obtained by numerical calculation. Finally, a simple way to determine the rake angles and wedge angles and clearance angles is presented by using the unit normals of the ISO-recommended reference planes. To verify the validity of this methodology, a designed three-fluted drill was machined on a 6-axis tool-grinding machine. This model is comprehensive, simple, easy to use, and capable of describing a wide range of drill design features.

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