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TECHNICAL PAPERS

Effects of Clamping on the Laser Forming Process

[+] Author and Article Information
A. J. Birnbaum

Department of Mechanical Engineering,  Columbia University, New York, NY 10027ajb2118@columbia.edu

P. Cheng, Y. L. Yao

Department of Mechanical Engineering,  Columbia University, New York, NY 10027

J. Manuf. Sci. Eng 129(6), 1035-1044 (Jun 05, 2006) (10 pages) doi:10.1115/1.2375140 History: Received August 02, 2005; Revised June 05, 2006

Although considerable effort has gone into characterizing the laser forming process in terms of process parameters and conditions, there has been little emphasis on the effects of the mechanical and thermal constraints introduced by the clamping method utilized for a desired application. This research suggests means for investigating and predicting the resulting geometry of a specimen due to laser operation in close proximity to an array of imposed thermo-mechanical constraints for both the single and multiple scan cases; specifically, the resulting average bending angle as well as bending angle variations throughout the part. This is accomplished by initially only considering these effects on the thermal field. Conclusions are then drawn about the nature of the mechanical effects. These conclusions are validated through numerical simulation as well as physical experimentation. An analytical solution of the thermal problem is also presented for further validation of the temperature field as a constrained edge is approached.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 3

Experimental, average bending angle as a function of operating distance (Q=800W, v=50mm∕s)

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Figure 4

Numerical, average bending angle as a function of operating distance (Q=800W, v=50mm∕s)

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Figure 5

Clamped, experimental bending angle distribution (Q=800W, v=50mm∕s)

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Figure 6

Clamped, numerical bending angle distribution (Q=800W, v=50mm∕s)

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Figure 7

Unclamped, experimental bending angle distribution (Q=800W, v=50mm∕s)

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Figure 8

Unclamped, numerical bending angle distribution (Q=800W, v=50mm∕s)

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Figure 9

Comparison of elastic constraint for three operating distances (unclamped, Q=960W, v=70mm∕s)

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Figure 10

Clamped, elastic constraint as a function of power and operating distance for three velocities

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Figure 11

Unclamped, elastic constraint as a function of power and operating distance for three velocities

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Figure 12

Clamped, numerical, average bending angle as a function of operating distance and power for three velocities

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Figure 13

Unclamped, numerical, average bending angle as a function of operating distance and power for three velocities

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Figure 14

Comparison of clamped and unclamped σyy (constraint) distribution (P=800W, v=60mm∕s, a=40mm)

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Figure 15

Typical comparison of total elastic constraint in the top surface between clamped and unclamped configurations (left scale) (Q=800, v=60mm∕s). Also shown is the instantaneous stress at the bottom layer of the part, showing a dramatic increase in effective bending rigidity as operating distance decreases (right scale).

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Figure 16

Portrayal of major and minor regions, sampling path locations, major and minor bending angles, and local Z displacement w(x)

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Figure 17

Representative curvature comparison between clamped and unclamped configurations (Q=640W, v=60mm∕s)

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Figure 18

Plastic strain in the Y direction as a function of X. Note the decrease in magnitude at both edges.

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Figure 19

(Numerical results) Comparison of relative displacement curvatures in minor region. Sampling paths are defined in Fig. 1 (a=40mm, Q=640W, v=60mm∕s).

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Figure 20

Comparison of temperature distribution for three operating distances (numerically obtained). Note: Distributions taken at times accentuating asymmetries.

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Figure 26

Contour plot for selected operating distance. Note the transition to an asymmetric temperature distribution with respect to the scanning path (analytically obtained).

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Figure 25

Schematic representation of dual source reflection process in analytical formulation

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Figure 24

Comparison of temperature time histories between the insulated and highly conductive clamp case. Also shown is plastic strain PE22 in the Y direction (right scale) (a=10mm, Q=800W, v=50mm∕s).

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Figure 23

Unclamped-multiple scan, experimental bending angle distribution (Q=800W, v=50mm∕s)

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Figure 22

Clamped-multiple scan, experimental bending angle distribution (Q=800W, v=50mm∕s)

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Figure 21

Multiple scan, experimental average bending angle (Q=800W, v=50mm∕s)

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Figure 2

Schematic of clamped specimen specifying coordinate system and operating distance

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Figure 1

Schematic of clamped and unclamped configurations

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