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Research Papers

Geometric Modeling of Cutter/Workpiece Engagements in Three-Axis Milling Using Polyhedral Representations

[+] Author and Article Information
Eyyup Aras

Department of Mechanical Engineering, University of British Columbia, 1000 University Boulevard, Vancouver, BC, V6T 1Z4, Canadaaraseyy@interchange.ubc.ca

Derek Yip-Hoi

Department of Engineering Technology, Western Washington University, 312 Ross Engineering Building, 512 Main Street, Bellingham, WA 98225derek.yip-hoi@wwu.edu

VERICUT is developed and marketed by CGITech Inc.

ACIS is a geometric/solid modeling kernel developed by Spatial Technologies a subsidiary of Dessault Systemes.

MAGICS X is a process planning system for rapid prototyping developed by Dimensionalize.

J. Comput. Inf. Sci. Eng 8(3), 031007 (Aug 19, 2008) (13 pages) doi:10.1115/1.2960490 History: Received July 19, 2007; Revised June 10, 2008; Published August 19, 2008

Modeling the milling process requires cutter/workpiece engagement (CWE) geometry in order to predict cutting forces. The calculation of these engagements is challenging due to the complicated and changing intersection geometry that occurs between the cutter and the in-process workpiece. This geometry defines the instantaneous intersection boundary between the cutting tool and the in-process workpiece at each location along a tool path. This paper presents components of a robust and efficient geometric modeling methodology for finding CWEs generated during three-axis machining of surfaces using a range of different types of cutting tool geometries. A mapping technique has been developed that transforms a polyhedral model of the removal volume from the Euclidean space to a parametric space defined by the location along the tool path, the engagement angle, and the depth of cut. As a result, intersection operations are reduced to first order plane-plane intersections. This approach reduces the complexity of the cutter/workpiece intersections and also eliminates robustness problems found in standard polyhedral modeling and improves accuracy over the Z-buffer technique. The CWEs extracted from this method are used as input to a force prediction model that determines the cutting forces experienced during the milling operation. The reported method has been implemented and tested using a combination of commercial applications. This paper highlights ongoing collaborative research into developing a virtual machining system.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Z-map calculation errors when the grid size is large

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Figure 4

Final machined surfaces with cusps

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Figure 5

Faceted representation of a model

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Possible (a) cutter/facet engagements and (b) chordal error

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Figure 7

Point sets CWEK(t), CWE(t), and bCWE(t) used in defining engagements

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Figure 8

Constituent surfaces of (a) milling cutters and (b) some typical milling cutter surfaces

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Figure 9

Description of a point on a cutter moving along a tool path

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Figure 10

Three-axis linear tool motions with a BNEM

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Engagement regions of the (a) front and (b) back contact faces

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Figure 12

Procedure for performing mapping MG:E3→P(φ,d,L)

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Cylindrical contact face CWEK,C(t) of BNEM

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Figure 16

STL file structure and facets

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Implementation of CWE extraction methodology

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Figure 18

CWEs for ball nose end mill performing a linear three-axis move

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CWEs for flat end mill performing a linear three-axis move

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CWEs for flat end mill performing a circular move

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CWEs for ball end mill performing a linear three-axis move

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Figure 22

CWE for flat end mill performing a circular move

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Figure 23

(a) and (b) removal volumes and (c)–(f) CWEs for different resolutions

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Figure 24

The effect of the facet resolutions

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Figure 25

Engagement regions of the (a) cylindrical and (b) flat contact faces for the flat end mill

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Engagement regions of the (a) front and (b) back contact faces for the tapered flat end mill

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Figure 27

Engagement regions of the (a) front and (b) back toroidal contact faces for the toroidal end mill

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Figure 28

Cutter interferences with points in space

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Figure 13

Different cutter locations for I∊CWEK(t)

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Figure 15

Moving coordinate frame for the circular tool path

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