modeling of laser micromachining

8/18/2019 Modeling of Laser Micromachining

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Modeling of LASER

Micromachining Process

Debkalpa GoswamiDepartment of Production

Engineering Jadapur !niersit"

#$ Prod$ E$ %%%

Roll& ''('(()'('33


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Light

Amplification by

Stimulated

Emission of

Radiation

•Population

Inversion

•Stimulated

Emission

• Amplification

Albert Einstein

T. H. Maiman


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Population Inversion

Boltzmann Distribution Law

(Thermal Equilibrium)

2 1

2 1

E E

kT N N e

− − ÷ =


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Stimulated Emission

2 1h E E ν = −


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Amplification

( )21 1 2 0

k L I r r I e

γ −=

( )21 2 1

thk Lr r e γ − =

1 2

1 1

ln2thk L r r γ

= + ÷


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Properties of Laser Radiation

• Monochromaticity

• Collimation

• Beam Coherence

• Temporal Modes

• Frequency

Multiplication


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Types of Industrial Lasers

•

Solid-state Lasers

• Gas Lasers

• Semiconductor Lasers

• Liquid dye Lasers

Nd:YAG (1064 nm)

Ruby (694 nm)

Nd:glass (1062 nm)

HeNe (632.8 nm)

CO2 (10,600 nm)

Argon (488, 514.5 nm)

InGaAs (980 nm)

Rhodamine 6G (570-640 nm)

Coumarin 102 (460-515 nm)

Stilbene (403-428 nm)

Kumar Patel


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Laser Materials Interactions

Laser Parameters Material Parameters

• intensity

• wavelength

• spatial and

temporal coherence

•angle of incidence

• polarization

• illumination time

• absorptivity

• thermal

conductivity

• specific heat

•density

• latent heat


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Thermal Effects

; for( ) ( )

2

2, ,T z t T z t

t z α ∂ ∂=∂ ∂ ( )

0,0T z T = 0 z ≤ ≤ ∞

( )0,T t k H

z δ

∂− =

∂

1 0

0

p

p

t t

t t

δ ≤ ≤

= >

( )

( )( )

( ) ( ) ( )( )

1 2

1 2

1 21 2

1 2

1 2 1 2

4 ierfc 0 heating4

,

2

ierfc ierfc cooling4 4

p

p p

p

H z t t t

k t

T z t

H z z

t t t t t k t t t

α α

α

α α

≤ ≤ ÷

÷ ∆ = ÷− − > ÷ ÷ ÷ ÷−

( ) ( ) ( )( ){ }

( )

2

2

0

1ierfc exp 1 erf

2

where erf .

x

x x x x

x e d

ξ

π

ξ π

−

= − − −

= ∫


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a


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b b

Hz T

kT T π π

= ÷ ÷


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Important Practical Considerations

• Beam Shapes

( )2

0 2

2exp

r I r I

w

−=

( ) ( ) ( ) ( )2 2 2

2 2 2

, , , , , , , , , , , ,T x y z t T x y z t T x y z t T x y z t

t x y z α

∂ ∂ ∂ ∂= + + ∂ ∂ ∂ ∂


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• Pulse Shapes


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• Moving Source of Heat

(quasi-stationary heat flow)

(trial function)

x vt ξ = −

( ) ( ) ( ) ( ) ( )2 2 2

2 2 2

, , , , , , , , , , , , , , ,T y z t T y z t T y z t T y z t T y z t v

t y z

ξ ξ ξ ξ ξ α

ξ ξ

∂ ∂ ∂ ∂ ∂− + = + +

∂ ∂ ∂ ∂ ∂

( ), , ,0

T y z t

t

ξ ∂=

∂

( )0 , ,vT T e y z λ ξ ϕ ξ −= +

( ) ( ) ( ) ( )

2 2 2 2

2 2 2

, , , , , ,, ,

2

y z y z y z v y z

y z

ϕ ξ ϕ ξ ϕ ξ ϕ ξ

α ξ

∂ ∂ ∂ − = + + ÷ ∂ ∂ ∂


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• Temperature dependent properties

• Thermal conductivity

•

Thermal diffusivity

• Absorptivity

Etc.

f(T)


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Laser Micromachining Mechanisms

• Laser Ablation • Laser AssistedChemical Etching

material removal processes

by photo-thermal or photo-

chemical interactions.

multiphoton

mechanism: even

though the energy

associated with each

photon is less than thedissociation energy of

bond, the bond breaking

is achieved by

simultaneous absorption

of two or photons.

carried out by using

suitable etchant

(precursors).

gaseous precursors:

Cl2 and Br2(dry etching)

liquid precursors: HCl,

HNO3, H2SO4, NaCl,

and K2SO4(wet

etching)


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Laser Micromachining Applications

•

MicroviaDrilling

• Drilling of

Inkjet

NozzleHoles


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• Fuel

Injector

Drillin

g

• Laser

Scribing

Bio-medical applications:


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Relevant Research and Recent Trends

•

ExperimentalModels

• Semi-analytical

Models

• Numerical or

Computer Models

Kuar et. al (2006)

Gospavic et. al(2004)

Ding et. al (2012)

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 Manufacture46(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 Simulation65(3): 211-219.

Ding, H., N. Shen and Y. C. Shin (2012). "Thermal and mechanical modeling analysis of laser-assisted micro-milling ofdifficult-to-machine alloys." Journal of Materials Processing Technology212(3): 601-613.


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• Kuar et. al

(2006)


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• Gospavic et.

al (2004)

Semi-analytical model

Particular cases with

cylindrical geometry

Laplace Transform and

Fourier Method of

Variable Separation

PDE ODE

Alternative

method

Differential

Transform

Mukherjee, S.,D. Goswami and B. Roy (2012). "Solution of Higher-Order

Abel Equations by Differential Transform Method." International Journal ofModern Physics C23(09): 1250056.


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• Ding et. al

(2012)


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Laser Thermal Lab, UC Berkeley

Laser-Assisted Nano-wire Growth and Harvest

Nanoplasians harvesting their nanowires selectively grown on a field by a laser-

assisted method. (SEM image)


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Thank You

modeling of laser micromachining

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