Hindawi Publishing Corporation
Advances in Materials Science and Engineering
Volume 2011, Article ID 137407, 5 pages
doi:10.1155/2011/137407
Research Article
Precise Hole Drilling in PMMA Using 1064 nm Diode Laser CNC
Machine
Jinan A. Abdulnabi,
1
Thaier A. Tawfiq,
1
Anwaar A. Al-Dergazly,
2
Ziad A. Taha,
1
and Khalil I.
Hajim
1
1
Institute of Laser for Postgraduste Studies, University of Baghdad, P.O. Box 47314, Jadriha, Baghdad, Iraq
2
Laser and Optoelctronics Engineering Department, Al-Nahrain university, Jadriha, Baghdad, Iraq
Correspondence should be addressed to Ziad A. Taha, zddiesel@yahoo.com
Received 30 December 2010; Accepted 21 February 2011
Academic Editor: J. Dutta Majumdar
Copyright © 2011 Jinan A. Abdulnabi et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
This paper represents the outcome of efforts that intended to achieve laser hole drilling execution in polymethylmethacrylate
(PMMA) of 2.5 mm thickness using 1064 nm diode laser of 5 W output power. Different laser beam powers, exposure time, and
positions of the laser spot were taken into consideration with respect to the workpiece. The workpieces were tested in the existence
of low-pressure assist gas (20–60 mmHg of air). The experimental results were supported by the predicted results of the analytical
model.
1. Introduction
The conduction of heat in a three-dimensional solid is given
by the solution of the following equation:
ρC
P
∂T
∂t
=
∂
∂x
K
∂T
∂x
+
∂
∂y
K
∂T
∂y
+
∂
∂z
K
∂T
∂z
+ A
(
x, y, z, t
)
,
(1)
where, the thermal conductivity K (Wcm
−1
K
−1
), the den-
sity ρ (g cm
−3
), and the specific heat C
P
(Jkg
−1
K
−1
) are
dependent on the temperature and position. The rate of the
applied heat to the solid is A(x, y, z, t) per unit time per
unit volume, and t is the time [1].
Using the cylindrical coordinates r and z (Figure 1), the
temperature distribution is [1, 2]
T (r , z, t)
=
Pε
2π aK
∞
0
J
0
(mr )J
1
(ma)
×
exp( − mz) erfc
z
2(kt)
1/2
−m
− (kt)
1/2
−e(mz) erfc
z
2(kt)
1/2
+ m(kt)
1/2
dm
m
+ T
0
,
(2)
where, r is the radial coordinate (hole radius), z is the axial
coordinate (thermal penetration depth), J
o
and J
1
are Bessel
functions of the first kind, P is the constant power during a
laser pulse, a is the radius of the laser spot at the surface, K
is the thermal conductivity of the material, k is the thermal
diffusivity, ε is the fraction of incident radiation absorbed, m
is an integer that represents the limit of integration, t is the
exposure time, and T
o
is the initial temperature.
The numerical solution of (2) for determining the
temperature distribution as a function of time at any point