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RESEARCH PAPERS: Heat Transfer in Manufacturing

Effects of Multiple Reflections on Hole Formation During Short-Pulsed Laser Drilling

[+] Author and Article Information
Michael F. Modest

Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA 16802mfmodest@psu.edu

J. Heat Transfer 128(7), 653-661 (Dec 20, 2005) (9 pages) doi:10.1115/1.2194035 History: Received April 07, 2005; Revised December 20, 2005

Beam guiding effects during laser drilling due to multiple specular reflections inside the hole are analyzed for the case of very short laser pulses (nanosecond range). Specular reflections are valid for materials that retain a smooth surface during laser evaporation (small optical roughness compared to the laser wavelength). The problem is assumed to be two-dimensional axisymmetric (unpolarized laser), with the hole geometry defined by nodal values connected through a cubic spline. The net radiative flux onto a surface node is determined through ray tracing methods. The resulting absorbed laser flux is combined with a simple quasi-one-dimensional conduction model (to assess the minor conduction losses) and an Arrhenius evaporation rate model, to predict hole development as a function of time through iteration. To stabilize this highly nonlinear and thus unstable problem (in numerical analysis as well as in experiments) the laser beam is diffused a small amount from the specular direction (to also account for the limitation that no beam can be focused down to a point), and by periodic slight smoothing of the irradiation levels. Results show that drilling rates are increased dramatically due to beam trapping for highly reflective materials, resulting in a more pointed hole profile.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Laser drilling setup and coordinate system

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Figure 2

Temporal laser pulse shapes: top-hat and clipped-Gaussian profiles

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Figure 3

Specular reflection cone with Gaussian decay of strength away from specular direction

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Figure 4

Influence of time step, cell number, and ray number on accuracy of solution during nanosecond laser drilling

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Figure 5

Influence of pulse strength and pulse temporal shape on conduction losses during nanosecond laser drilling

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Figure 6

Influence of specularity angle on distribution of reflected energy inside laser-drilled hole

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Figure 7

Typical laser ray reflection paths for varying hole depths (Ste=4.71,Nc=0.25,αn=0.15,θsp=5deg); (a) hole after eight pulses (without reflection effects), (b) after 16 pulses (with bulging due to reflections), and (c) after burn-through (with strong beam trapping). Dimensions are to scale (with a material thickness of 10w0).

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Figure 8

Hole development as a function of pulse number (Ste=4.71,Nc=0.25,αn=0.15,θsp=5deg); left: hole cross section, right: absorbed, multiple-reflected laser power

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Figure 9

Hole development as a function of pulse number (Ste=4.71,Nc=0.25,αn=0.15,θsp=10deg); left: hole cross section, right: absorbed, multiple-reflected laser power

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Figure 10

Hole development as a function of pulse number (Ste=4.71,Nc=0.25,αn=0.15,θsp=3deg); left: hole cross section, right: absorbed, multiple-reflected laser power

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Figure 11

Hole development as a function of pulse number (Ste=4.71,Nc=0.25,αn=0.20,θsp=5deg); left: hole cross section, right: absorbed, multiple-reflected laser power

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Figure 12

Hole development as a function of pulse number (Ste=4.71,Nc=0.25,αn=0.10,θsp=5deg); left: hole cross section, right: absorbed, multiple-reflected laser power

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