1. Modeling of LASER
Micromachining Process
Debkalpa Goswami
Department of Production Engineering
Jadavpur University
B. Prod. E. III
Roll: 001011701033
2. Light
Amplification by • Population
Inversion
Stimulated
• Stimulated
Albert Einstein
Emission
Emission of
• Amplification
Radiation
2
T. H. Maiman
3. Population Inversion
E2 E1
Boltzmann Distribution Law
kT
N2 N1e (Thermal Equilibrium) 3
8. Laser Materials Interactions
Laser Parameters Material Parameters
• intensity • absorptivity
• wavelength • thermal conductivity
• spatial and temporal • specific heat
coherence
• density
• angle of incidence
• latent heat
• polarization
8
• illumination time
9. Thermal Effects
2
T z, t T z, t
; T z,0 T0 for 0 z
t z2
T 0, t 1 0 t tp
k H 0 t tp
z
H 12 z
4 t ierfc 12
0 t tp heating
k 4 t
T z, t
12
2H z 12 z
t1 2ierfc 12
t tp ierfc 12
t tp cooling
k 4 t 4 t tp
1
ierfc x exp x2 x 1 erf x
x 9
2 2
where erf x e d .
0
13. Important Practical Considerations
• Beam Shapes
2r 2
I r I 0 exp
w2
2 2 2
T x, y , z , t T x, y , z , t T x, y , z , t T x, y , z , t
t x2 y2 z2
13
15. • Moving Source of Heat
x vt
2 2 2
T , y, z , t T , y, z , t T , y, z , t T , y, z , t T , y, z , t
v 2
t y2 z2
T , y, z, t (quasi-stationary heat flow)
0
t
v
T T0 e , y, z (trial function)
2 2 2 2
v , y, z , y, z , y, z
, y, z 2
15
2 y2 z2
16. • Temperature dependent properties
• Thermal conductivity
• Thermal diffusivity f(T)
• Absorptivity
Etc.
16
17. Laser Micromachining Mechanisms
• Laser Ablation • Laser Assisted Chemical
Etching
material removal processes
by photo-thermal or photo- carried out by using
chemical interactions. suitable etchant
(precursors).
multiphoton
gaseous precursors: Cl2
mechanism: even
and Br2
though the energy
(dry etching)
associated with each
photon is less than the
liquid precursors: HCl,
dissociation energy of
HNO3, H2SO4, NaCl,
bond, the bond breaking
and K2SO4 (wet
is achieved by
etching) 17
simultaneous absorption
of two or photons.
20. Relevant Research and Recent Trends
• Experimental
Kuar et. al (2006)
Models
• Semi-analytical Gospavic et. al
Models (2004)
• Numerical or Ding et. al (2012)
Computer Models
Kuar, A. S., B. Doloi and B. Bhattacharyya (2006). "Modelling and analysis of pulsed Nd:YAG laser machining characteristics
during micro-drilling of zirconia (ZrO2)." International Journal of Machine Tools and Manufacture 46(12-13): 1301-1310.
Gospavic, R., M. Sreckovic and V. Popov (2004). "Modelling of laser-material interaction using semi-analytical approach."
Mathematics and Computers in Simulation 65(3): 211-219. 20
Ding, H., N. Shen and Y. C. Shin (2012). "Thermal and mechanical modeling analysis of laser-assisted micro-milling of
difficult-to-machine alloys." Journal of Materials Processing Technology 212(3): 601-613.
22. • Gospavic et. Semi-analytical model
al (2004)
Particular cases with
cylindrical geometry
Alternative
method Laplace Transform and
Fourier Method of Variable
Separation
Differential PDE ODE
Transform
22
Mukherjee, S., D. Goswami and B. Roy (2012). "Solution of Higher-Order Abel
Equations by Differential Transform Method." International Journal of Modern
Physics C 23(09): 1250056.
24. Laser-Assisted Nano-wire Growth and Harvest
Laser Thermal Lab, UC Berkeley
Nanoplasians harvesting their nanowires selectively grown on a field by a laser-assisted
method. (SEM image)
24
