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Research Papers

Geometric Modeling of Fluted Cutters

[+] Author and Article Information
Puneet Tandon1

 Indian Institute of Information Technology, Design & Manufacturing, Jabalpur 482011, Indiaptandon@iiitdm.in

Phalguni Gupta

Computer Science and Engineering Department,  I.I.T. Kanpur, Kanpur 208016, India

Sanjay G. Dhande

Department of Mechanical Engineering, I.I.T. Kanpur, Kanpur 208016, India

1

Corresponding author.

J. Comput. Inf. Sci. Eng 8(2), 021007 (May 16, 2008) (15 pages) doi:10.1115/1.2908025 History: Received May 16, 2006; Revised September 29, 2007; Published May 16, 2008

Geometries of cutting tools are usually represented by two-dimensional models. This paper outlines the construction of detailed computer aided design models for a variety of fluted cutters that includes slab mills, end mills, and drills; and establishes a new three-dimensional definition for the geometry of fluted cutters in terms of biparametric surface patches. This work presents unified models of both plain and helical slab mills, end mills (with different end geometries), and drills (with a variety of point styles). The surfaces meant for cutting operations, known as flutes, are modeled as helicoidal surfaces. To model the flutes, sectional geometry of tip-to-tip profile is developed and then it is swept according to a sweeping rule, determined by the type of the cutter under consideration. The slab mill consists of flutes and two planar end surfaces, while the end mills and drills have shanks and end geometries also (in addition to the flutes). The geometric models of shank and end geometries are separately developed. The transitional surfaces of these cutters are modeled as bicubic Bézier surfaces or biparametric sweep surfaces. The proposed models employ a novel nomenclature that defines the form of cutting tools in terms of three-dimensional rotational angles. The relations required to map the proposed three-dimensional angles to conventional angles (forward mapping) and their reverse relations (inverse mapping) are also developed for all three types of fluted cutters. The new paradigm offers immense technological advantages in terms of numerous downstream applications.

Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Surface patches of slab mill tooth

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Figure 2

Sectional curve of a slab mill

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Figure 3

Modeling of slab mill cutter body

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Figure 4

Conventional tool geometry for slab mill

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Figure 5

2D projected geometry of end mill

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Figure 6

Modeling of an end mill tooth

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Figure 7

Composite sectional curve

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Figure 8

2D projected geometry of twist drill

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Figure 9

Composite section curve for a twist drill

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Figure 10

Various types of drill end

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Figure 11

Conical drill end

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Figure 12

Double-angle point drill

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Figure 13

Rendering of a helical slab mill

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Figure 14

Surface-point cloud comparison of a fluted cutter surfaces

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Figure 15

Loading of slab mill teeth

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Figure 16

First four mode shapes of slab mill

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Figure 17

Stress distribution on slab mill

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