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Research Papers

An Efficient, Accurate Approach to Representing Cutter-Swept Envelopes and Its Applications to Three-Axis Virtual Milling of Sculptured Surfaces

[+] Author and Article Information
Zezhong C. Chen1

Department of Mechanical and Industrial Engineering, Concordia University, Montreal, Quebec H3G 1M8, Canadazcchen@encs.concordia.ca

Wei Cai

Department of Mechanical and Industrial Engineering, Concordia University, Montreal, Quebec H3G 1M8, Canada

1

Corresponding author.

J. Manuf. Sci. Eng 130(3), 031004 (May 02, 2008) (12 pages) doi:10.1115/1.2823218 History: Received December 30, 2005; Revised November 05, 2007; Published May 02, 2008

To address a major technical challenge in simulating geometric models of machined sculptured surfaces in three-axis virtual machining, this paper presents an efficient, accurate approach to representing the 3D envelopes of a cutter sweeping sequentially through cutter locations; these envelopes embody the furrow patches of the machined surfaces. In our research, the basic mechanism of removing stock material in three-axis computer numerically controlled (CNC) milling of sculptured surfaces is investigated, and, consequently, an effective model is proposed to represent the 3D envelopes (or furrow patches). Our main contribution is that a new directrix (or swept profile) of the furrow patches (mathematically, ruled surfaces) is identified as a simple 2D envelope of cutting circles and is formulated with a closed-form equation. Therefore, the 3D cutter-swept envelopes can be represented more accurately and quickly than the existing swept-volume methods. With this innovative approach, a method of accurate prediction of the machining errors along tool paths in three-axis finish machining is provided, which is then applied to the optimization of tool-path discretization in two examples. Their results demonstrate the advantages of our approach and verify that the current machining-error-prediction methods can cause gouging in three-axis sculptured surface milling.

Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Illustration of the furrows of a machined surface

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Figure 2

(a) APT, (b) torus end mill (α1=0 and α2=0), (c) ball end mill (α1=0, α2=0, and R1=0), and (d) flat end mill (α1=0, α2=0, and R2=0)

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Figure 3

Geometric model of a furrow patch: (a) an APT step, (b) the envelope of cutting circles on layer Ω, and (c) the envelope of cutting circles on layer Π

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Figure 4

APT in the part and cutter coordinate systems

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Figure 5

Cutting circles on different cutting surfaces in the cutter coordinate system

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Figure 6

Illustration of machining-error predictions: (a) cutter-swept surface between two CC points, (b) surface contour and an envelope of cutting circles on a layer, and (c) projection of the envelope and the surface contour

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Figure 7

Illustration of the chordal deviation method

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Figure 8

Model of machining errors in the circular arc approximation method

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Figure 9

Geometric characteristics of sculptured surface milling

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Figure 10

Semicylindrical surface part with iso-parametric tool paths

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Figure 11

CC points on a tool path determined by (a) the circular arc approximation method or the optimization system and (b) the chordal deviation method

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Figure 12

Machined surface of the semicylinder in simulation

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Figure 13

Predicted machining errors at the sample points along one tool path from the two regions

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Figure 14

(a) Machined semicylindrical surface part and (b) the semicylindrical surface part measured on a CMM

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Figure 15

Measured machining errors of the left-hand region

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Figure 16

Measured machining errors of the right-hand region

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Figure 17

CC points on isoparametric tool paths of the sculptured surface determined by (a) the circular arc approximation method and (b) the CC point optimization system

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Figure 18

Sculptured surface machined with the CC points determined with the chordal deviation method

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Figure 19

Sculptured surface machined with the CC points determined with the circular arc approximation method

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Figure 20

Sculptured surface machined with the CC points optimized with the CC point optimization system

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Figure 21

Predicted machining errors along the outmost tool path using the three methods

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