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Research Papers

An Accurate and Efficient Approach to Three-Dimensional Geometric Modeling of Undeformed Chips for the Geometric and the Physical Simulations of Three-Axis Milling of Complex Parts

[+] Author and Article Information
Zhiyong Chang

Department of Mechanical Engineering,
Northwestern Polytechnical University,
Xi’an 710072, Shaanxi, China
e-mail: changzy@nwpu.edu.cn

Zezhong C. Chen

Department of Mechanical Engineering,
Northwestern Polytechnical University,
Xi’an 710072, Shaanxi, China;
Department of Mechanical and
Industrial Engineering,
Concordia University,
Montreal, QC H3G 1M8, Canada
e-mail: zcchen@encs.concordia.ca

1Dr. Chen currently is on sabbatical leave at the Northwestern Polytechnical University, Xi'an, China.

Manuscript received July 21, 2015; final manuscript received November 6, 2015; published online December 16, 2015. Assoc. Editor: Laine Mears.

J. Manuf. Sci. Eng 138(5), 051010 (Dec 16, 2015) (16 pages) Paper No: MANU-15-1360; doi: 10.1115/1.4032086 History: Received July 21, 2015; Revised November 06, 2015

To pursue high-performance computer numerical control (CNC) milling of complex parts, it is crucial to simulate their machining process geometrically and physically with high fidelity beforehand. The geometric simulation is to construct three-dimensional (3D) models of the finished parts and to compute geometric deviation between the models and the part designs, in order to verify the planned tool paths. The physical simulation is to build undeformed chips geometric models and in-process workpiece models and to compute instantaneous cutting forces, in order to optimize the machining parameters. Therefore, it is essential to accurately and efficiently model undeformed chips geometry in machining complex geometric parts. Unfortunately, this work is quite challenging, and no well-established method for this work is available. To address this problem, our work proposes an accurate and effective approach to 3D geometric modeling of undeformed chips geometry in three-axis milling of complex parts. The outstanding feature of this approach is that undeformed chip models and in-process workpiece models can be effectively constructed. This approach lays a theoretical foundation for the geometric and the physical simulations of three-axis milling. It advances the technique of machining simulation and promotes high-performance machining of complex parts.

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Figures

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Fig. 1

The APT tool profile, its parameters, and the cutting circles

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Fig. 2

(a) The original workpiece profile on the layer Π and (b) the undeformed chip geometry of a cut and the new workpiece profile on the layer Π

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Fig. 3

The relationship between the part (X, Y, Z) and the local (x, y, z) coordinate systems

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Fig. 4

Formulation of the cutting circle envelope in the local coordinate system

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Fig. 5

(a) Three cutting circle envelopes in blue (See online version for color) when the cutter moves upward and (b) the cutting circle envelopes in blue when the cutter moves downward

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Fig. 6

Illustration of multiple engagements between the cutter and the workpiece

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Fig. 7

(a) The design of a sculptured surface part and its workpiece with stairs after roughing and (b) the layer-based in-process workpiece geometric model

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Fig. 8

A B-Rep data structure for the workpiece profile on a layer

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Fig. 9

The undeformed chip geometry on the layer Π and the cutter–workpiece engagement

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Fig. 10

The principle algorithm of the well-established mechanistic model

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Fig. 11

A part with an NURBS surface and its control polyhedron in the u and v directions

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Fig. 12

(a) The in-process workpiece model after roughing and (b) the 3D solid model of the workpiece after roughing

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Fig. 13

The preplanned tool paths for finishing the sculptured surface

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Fig. 14

The virtually finished part model

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Fig. 15

The geometric deviation between the virtually finished part model and the part design

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Fig. 16

(a) The in-process workpiece model after the cut at cutter location [−88.368−149.585125.575] and (b) the in-process workpiece model after the cut at cutter location [−88.035−146.257124.045]

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Fig. 17

(a) The discrete chip sections at the first moment of this step and (b) the corresponding chip geometric model

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Fig. 18

(a) The discrete chip sections at the second moment of this step and (b) the corresponding chip geometric model

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Fig. 19

(a) The discrete chip sections at the third moment of this step and (b) the corresponding chip geometric model

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Fig. 20

(a) The discrete chip sections at the fourth moment of this step and (b) the corresponding chip geometric model

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Fig. 21

(a) The discrete chip sections at the fifth moment of this step and (b) the corresponding chip geometric model

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Fig. 22

The chips cut in this step

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Fig. 23

(a) The CNC machining center and the dynamometer used in the tests and (b) the end-mill with a chipped cutting edge

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Fig. 24

(a) The machined workpiece geometric model and the machined part, (b) the undeformed chip geometry of the first cut, the corresponding measured and the predicted cutting forces, and (c) the undeformed chip geometry of the second cut, the corresponding measured and predicted cutting forces

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Fig. 25

(a) The surface part model and the curved paths for finishing the surface, (b) the workpiece model after roughing, and (c) the machined surface part

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Fig. 26

(a) The measured cutting forces along the path 2 and (b) the predicted cutting forces along the path 2

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Fig. 27

(a) The undeformed chip geometry of a cut between 1.18 and 1.24 s along the path 1, (b) the plot of the corresponding measured cutting forces in the dashed line and the plot of the predicted ones in the solid line along the x-, y-, and z-axis directions, and (c) the plot of the measured resultant cutting forces in the dashed line and the plot of the predicted one in the solid line in this cut

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Fig. 28

(a) The undeformed chip geometry of a cut between 1.07 and 1.13 s along the path 2, (b) the plot of the corresponding measured cutting forces in the dashed line and the plot of the predicted ones in the solid line along the x-, y-, and z-axis directions, and (c) the plot of the measured resultant cutting forces in the dashed line and the plot of the predicted one in the solid line in this cut

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