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Research Papers

Modeling and Theory of Intermittent Motions in a Machine Tool With a Friction Boundary

[+] Author and Article Information
Brandon C. Gegg1

Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123brandon-gegg@tamu.edu

Steve C. S. Suh

Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123

Albert C. J. Luo

Department of Mechanical Engineering, Southern Illinois University at Edwardsville, Edwardsville, IL 62026-1805

1

Corresponding author.

J. Manuf. Sci. Eng 132(4), 041001 (Jul 21, 2010) (9 pages) doi:10.1115/1.4001643 History: Received October 28, 2008; Revised February 09, 2010; Published July 21, 2010; Online July 21, 2010

In this paper the simplified mechanical model for a machine-tool system is presented. The state and domains are defined with respect to the (contact and frictional force) boundaries in this system. The switching sets for this machine-tool will be defined for all the boundaries considered herein. The forces and force product components at the switching points are determined according to discontinuous systems theory. The forces and force product govern the passability of the machine-tool through the respective boundary. Mapping definitions and notations are developed through the switching sets for the boundaries. A mapping structure and notation for one type of intermittent cutting periodic motion is defined as an example.

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Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 2

Force definitions for this machine-tool system: (a) domain 1 and domain 2 force condition, (b) domains 2–4 force condition, and (c) loading and unloading paths

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Figure 4

Partitions in phase space for the displacement and velocity discontinuities of this machine-tool system: (a) D1 phase plane and (b) D2 phase plane

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Figure 5

Partitions in phase space for the displacement and velocity discontinuities of this machine-tool system: (a) ỹ phase plane, (b) D4 phase plane, and (c) ∂Ω24 boundary in the ỹ phase plane

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Figure 6

Vector fields for (a) passable and (b) nonpassable motion

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Figure 7

Vector fields for (a) passable and nonpassable with appearance and vanishing points and (b) specific example of nonpassable motion and vanishing point

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Figure 8

Mappings according to (a) D1 and (b) D2, phase planes

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Figure 9

Mappings according to (a) D3 and (b) D4, phase planes

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Figure 10

Nonstick periodic motion in the absolute phase plane

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Figure 1

Cutting tool mechanical model: (a) external forces and (b) mechanical analogy

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Figure 3

Chip and tool-piece: (a) effective force contact, (b) route to loss of effective force contact, and (c) loss of effective force contact

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