Final Calculation Once D 02 is calculated, 2 could be found 2 4 - - PowerPoint PPT Presentation

Final Calculation

• Once D02 is calculated, Θ2 could be found
• Depth of focus where focal spot size changes by ±5%.

02 2

. . . 4 D M π λ = Θ

2 2 2 02 2 2

Θ + = z D D z

ME 677: Laser Material Processing Instructor: Ramesh Singh

• Depth of focus where focal spot size changes by ±5%.
• Approximate solution for focused beam diameter if lens is

placed at z from the beam waist If unfocused beam diameter at z, is Dz.

z

D M f D . . . . 4

2 02

π λ =

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Aberrations

• Spherical Aberration
• Thermal Distortion
• Astigmatism

Damage

ME 677: Laser Material Processing Instructor: Ramesh Singh

• Damage

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Spherical Aberration

• There are two reasons why a lens will not

focus to a theoretical point

– Diffraction limited problem – Spherical lens is not a perfect shape.

ME 677: Laser Material Processing Instructor: Ramesh Singh

– Spherical lens is not a perfect shape.

• Most lenses are made with a spherical shape since this

can be accurately manufactured economically

• The alignment of the beam is not so critical as with a

perfect aspheric shape

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Thermal Distortion

• High power laser beams are absorbed by

lenses/optics

– Selection of right optics ZnSe with CO2 – The power distribution in TEM00 causes more

ME 677: Laser Material Processing Instructor: Ramesh Singh

– The power distribution in TEM00 causes more severe gradients than Donut

• Shape change of lens
• Varies the refractive index, specially in ZnSe

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Astigmatism and Damage

• Due to optical misalignment
• Damage

– Due to dirt accumulation and burning on lens surface

ME 677: Laser Material Processing Instructor: Ramesh Singh

surface

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Summary

• Absorption
• Beam Modes
• Propagation
• Focusing

ME 677: Laser Material Processing Instructor: Ramesh Singh

Focusing

• Aberrations

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Analytical Modeling of Laser Moving Sources Moving Sources

Contains:

• Heat flow equation
• Analytic model in one dimensional heat flow
• Heat source modeling

– Point heat source – Line heat source – Plane heat source – Surface heat source

• Finite difference formulation
• Finite elements

Heat flow equation

For developing basic heat flow equation, consider the differential element . Heat balance in element is given by,

Heat in – Heat out + Heat generated = Heat accumulated

Heat in and out rates depends on conduction and convection.

Heat flow through differential element

2 p p

T k T C C U T H t ρ ρ ∂ ∇ − − ∇ = − ∂

Analytic model in one dimensional heat flow:

If the heat flow in only one direction and there is no convection or heat generation, the basic equation becomes where α = diffusivity, t = time. It is assumed that there is constant thermal properties, with no radiant heat loss or melting, then the BC ‘s are The solution is,

Heat source modelling: Introduction:

• Why modeling?
• 1. Semi-quantitative understanding of the process mechanism for the

design of experiments.

• 2. Parametric understanding for control purpose. E.g. statistical charts.
• 3. Detailed understanding to analyse the precise process mechanisms

for the purpose of prediction, process improvement . for the purpose of prediction, process improvement . Types of heat sources: Point heat source. Line heat source. Plane heat source. (e.g. circular , rectangular)

1.Instantaneous point heat source:

The differential equation for the conduction of heat in a stationary medium assuming no convection or radiation, is This is satisfied by the solution for infinite body,

( )

2 2 2 3 2

( ') ( ') ( ') ' , , , exp[ ] 4 ( ') (4 ( ')) inf q x x y y z z dT x y z t a t t C a t t semi inite δ ρ π − + − + − = − − − −

δq = instantaneous heat generated, C = sp. heat capacity, α = diffusivity, ρ = Density, t = time, K = thermal conductivity. gives the temperature increment at position (x, y, z) and time t due to an instantaneous heat source δq applied at position (x’, y’, z’) and time t’.

( )

2 2 2 3 2

2 ( ') ( ') ( ') ' , , , exp[ ] 4 ( ') (4 ( ')) q x x y y z z dT x y z t a t t C a t t δ ρ π − + − + − = − − −