1. NUMERICAL SIMULATION OF LASER
BEAM MICRO MACHINING OF304
STAINLESS STEEL
Summer Internship report
BY
ABHISHEK KUMAR
( B.Tech, NIT CALICUT)
Under the guidance of
Dr. M. RAVI SANKAR
DEPARTMENT OF MECHANICAL ENGINEERING
INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI
15 MAY 2015 – 08 JULY 2015

2. CERTIFICATE
The work contained in this report titled “Numerical Simulation of laser beam
machining of 304 Stainless Steel” by ABHISHEK KUMAR, student of the
Department of Mechanical Engineering, NIT CALICUT has been carried out
under my supervision. This work has not been submitted elsewhere.
Dr. M. RAVI SANKAR,
Asst. Professor, Department of Mechanical Engineering,
Indian Institute of Technology, Guwahati
PIN-781039

3. ACKNOWLEDGEMENT
I would like to express my gratitude to my guide Dr. M. Ravi Sankar for his
valuable guidance, nice and patient teaching, motivation and encouragement
throughout the period of my summer stay here in IIT Guwahati.
I have taken efforts in this project. However, it would not have been possible
without the kind supportand help of many individuals and organizations. I would
like to extend my sincere thanks to all of them.
I am highly indebted toMr. RasmiRanjanBehera for his guidance and constant
supervision as well as for providing necessary information regarding the project &
also for his supportin completing the project.
I would like to express my gratitude towards my parentsfor their kind co-operation
and encouragement which help me in completion of this project.
My thanks and appreciations also go to my groupmates in developing the project
and people who have willingly helped me out with their abilities.
ABHISHEK KUMAR
Date: July 08, 2015
Place: IIT Guwahati

4. CONTENTS
SL.NO TOPIC PAGE NO.
1. Certificate i
2. Acknowledgement ii
3. List of Figures iii
4. List of Tables iv
5. Abstract v
6. Introduction 1
7. Literature Review 4
8. Finite Element Simulation 5
9. Results & Discussion 15
10. Conclusion 30
11. References 31

5. List of Figures
Fig1: Basic model outline for continuous wave 08
Fig2: Partition made in the assembly module 09
Fig3: Load applied to the work piece 09
Fig4:The meshed work piece showing finer mesh 10
Fig5: Basic model outline for pulsed beam 11
Fig6:Variation of power with time for square pulsed wave 12
Fig7:Basic model outline for moving laser source 13
Fig8:Variation of power with time for single pulsed wave 15
Fig9:Temperature profile for different Y coordinates 16
Fig10:Temperature Vs Time plot for different Y coordinates 17
Fig11:Temperature Vs Time plot for different x coordinates 18
Fig12:Temperature distribution at a point on 304 Stainless steel 18
Fig13:Melted region in ABAQUS 19
Fig14:Temperature variation with different laser power 20
Fig15:Temperature variation with different laser cutting speed 21
Fig16:Temperature profile at the center of the 304 Stainless Steel. 22
Fig17:Temperature Vs Time plot for different x coordinates 23
Fig18:Temperature Vs Time plot for the center of the workpiece 24
Fig19:Melted region for multi pulsed static laser source25
Fig20:Temperature profile at different Y coordinates 26
Fig21:Temperature Vs Time plot for different Y coordinates 27
Fig22:Melted region for multi pulsed moving laser source28
Fig23: Temperature profile at a specific point on the workpiece 29
Fig24: Temperature Vs Time plot at a specific point on the workpiece 29
Fig25:Melted region at a point on the workpiece 30

6. List of Tables
Table1: Variation of thermal & mechanical properties of 304 Stainless steel 06
with temperature
Table2: Laser power optimization 20
Table3: Laser speed optimization 21

7. ABSTRACT
Laser Beam Micromachining (LBμM) is one of the most widely used thermal energy based non-
contact type advance machining process which can be applied for almost whole range of
materials.The process has applications across many industries and has been the subject of
experimental, analytical, and numerical research. The objective is to generate a model of laser
machining and use the model to identify the mechanisms of laser beam machining. Laser beam is
focused for melting and vaporizing the unwanted material from the parent material. It is suitable
for geometrically complex profile cutting and making miniature holes in sheetmetal. Among
various type of lasers used for machining in industries, CO2 and Nd:YAG lasers are most
established because of their high energy densities. The thermal analysis of laser beam machining
on304 Stainless Steelissimulated in this report using ABAQUS software. The type of laser taken
is a high-power Nd:YAG laser, emitting at 1064nmand operating in thePulsedMode
(millisecond) as well as continuous wave.For multi pulsed beam both static and moving laser
sources have been considered. Main objective is to find the Kerf width & depthin all the cases.
The Kerf width and depth are calculated from the results obtained from the numerical analysis.
The temperature fields and the maximum temperature are calculated from the results obtained by
the numerical analysis. The finite element analysis using ABAQUS is done here so as to
understand the temperature distributions during laser machining of Stainless Steel. For a
continuous wave, the parameters like laser power and laser cutting speedare varied to observe
their effect on the maximum temperature. The temperature dependent material properties are
taken into account for the both cases.It is observed that as the laser power increases, the
maximum temperature also increases and fine meshing takes longer time for simulation but gives
acceptable results.
KEYWORDS: SS 304, ND:YAG, Kerf width, Kerf depth, Pulsed Laser

8. 1. INTRODUCTION
Laser micro machining is a direct machining method and is based on the interaction of laser light
with solid matter. It uses intense ultraviolet (UV) or infrared radiation that is provided by a laser
to remove the material. The removal mechanism is affected by the radiation wavelength used. It
is a thermal energy based advanced machining process in which material is removed by melting,
vaporization and/or chemical degradation. When high energy density laser beam is focused on
work surface, the thermal energy is absorbed which heats and transforms the work volumes in to
molten, vaporized or chemically changed state that can easily be removed by flow of high
pressure assist gas jet which accelerates the transformed materials and ejects it from machining
zone. The above process is affected by temperature distribution in the sheet, change in material
properties during the heating and cooling process.The characteristic of a pulsed laser is that in
each cycle it is accompanied with a laser stage and a spacing stage.Typical problems that may be
faced with laser micromachining are Irregular kerf width, high surface roughness [1].
To perform a simulation of the laser cutting process using the finite element method, parameters,
such as boundary conditions, mechanical and thermal properties of the material are considered.
304 Stainless Steel is selected as the workpiece material. ABAQUS software is used for heat
transfer analysis. The thermal & mechanical properties are considered to be varying with
temperature& hence linear interpolation is used.During pulsed laser heating, the material is
heated intermittently with a succession of short duration pulses to produce a series of
overlapping spots. Consequently, the material is subjected to a large number of thermal cycles.
Predictions of accurate heating and cooling rates using analytical methods are very difficult to
obtain. Therefore, a three-dimensional numerical model employing the finite element technique
is developed Thus, the output energy of the laser beam is uneven and has two obvious processes,
the rise and drop zones [2].
Laser beam Micromachining (LBμM) is one of the advanced machining processes, which is used
for shaping almost whole range of materials thatdepends on the thermal properties of the material
rather than the mechanical properties.Major application of laser beam is mainly cutting of metals
and non- metals, soft and difficult to machine materials. Laser comprises of three principal
components, namely the lasing medium, means of exciting the lasing medium into its amplifying

9. state (lasing energy source), and optical delivery/feedback system. Additional provisions of
cooling the mirrors, guiding the beam and manipulating the target are also important. The laser
medium may be a solid (e.g. Nd:YAG or neodymium doped yttrium–aluminium–garnet), liquid
(dye) or gas (e.g. CO2, He, Ne) [3].HAZ is the effect of heat conduction into the work piece,
which in turn, influences bulk phenomena such as grain refinement, carbide formation and other
sulfide and phosphide impurities that might exist due to the alloying elements used in stainless
steel. These phenomena result in the formation of small HAZ. It is often associated with
undesirable effects such as distortion, surface cracking, embrittlement, decrease in weldability,
decrease in corrosion, fatigue resistance, etc. [4].Hence it is of great importance to bring
modifications in laser micro-machining process so as to reduce the problems associated with it.
Frequently, high quality components are obtained by chance or at the expense of time and money
due to inaccessible machining dimension, improper set of process parameter and large
uncertainty in the process itself. To tackle these problems, virtual laser micromachining with the
aid of computational model is important. Furthermore, now with the development
CAD/CAM/CAE system many realistic designs, analysis and simulations can be done on the
computer prior to actual manufacturing.
The heat transfer analysis is based on solving the three-dimensional heat conduction equation in
the cross section of the x-yplane. The initial condition is that the whole specimen is at the room
temperature (298K). Since the left and right boundaries as well as the bottom surface are far
away from the laser beam, the boundary conditions at theselocations are prescribed as the room
temperature. The boundarycondition of the top surface irradiated by the laser beam needssome
special considerations. Besides conduction, convection with air as a surrounding medium is also
considered while radiation has been neglected. Instead of prescribing the heat flux onthe top
surface, the laser flux is handled as surface heat flux absorbed by a small region in the target.The
pulsed laser beam is generally handled as a heat source with Gaussian intensity distributions in
both x-direction and y-direction [5]. The thermal & mechanical properties are temperature
dependent. Fine meshing takes more computational time but the results are more accurate
[6,7,13].
Most of its applications are found in the electronics industry and in high-volume production
industries. Lasers used for micromachining are characterized by short pulse lengths ranging from
millisecond for applications like micro welding to Pico-second and even femto-second area for

10. ablation of metals. Laser micromachining has many technological advantages compared to
conventional technologies, including design flexibility, production of complex shape and
possibility of rapid prototyping. Lasers are great tool for fabricating extremely precise features
quickly and repeatedly. In addition to the laser source, most micromachining systems are
configured with highly accurate optics and motion control systems. Some of the critical
advantages of laser micromachining include contactless machining with no tool wear and load
bearing, very sharp features with minimal or no burrs, material build-up or heat affected zone.
The type of analysis depends upon the objective of the simulation. If the objective is to find
temperature distribution only then non coupled thermal analysis is used. For calculating stress &
plastic deformation after heat treatment, sequentially or fully coupled analysis is used [8,9].
SS304 micromachining can be done in various other mechanical methods such as milling and
diamond cutting. Irregular cut path, poor surface finish, chip formation are some of the problems
associated with this type of glass cutting. In order to overcome these problems, laser
micromachining is becoming increasingly popular. The advantages include smooth surface
finish, less consumption of time etc.The finite element method (FEM) is a numerical
technique for finding approximate solutions to boundary value problemsfor differential
equations. It uses variation methods (the calculus of variations) to minimize an error function
and produce a stable solution [14].
As the temperature of the workpiece rises on the application of heat flux, there are some
elements in the model that are having temperature greater than the melting temperature (1873K).
ABAQUS enables feature to remove those elements. But the removal of elements take place only
at a particular laser position. Hence, in the post processing process it is not possible to obtain the
whole molten channel.
The objective of the following project is to simulate the laser micromachining of pulsed as well
as continuous mode laser beamon SS304using ABAQUS. For multi pulses both moving & static
laser sources have been considered. For single pulsed beam only static source has been
considered. For continuous wave a moving volumetric heat source with a Gaussian distribution,
i.e. the laser beam is analyzed here and the maximum temperature reached during the machining
is found out. Kerf width & depth have been found for all the cases.

11. 2. LITERATURE REVIEW
Shia[1] found that the above process is affected by temperature distribution in the sheet, change
in material properties during the heating and cooling process. The characteristic of a pulsed laser
is that in each cycle it is accompanied with a laser stage and a spacing stage.There have been
several research work done in this field. Xu et al.[2] used triangular pulse & power of the pulse
was varied with time. They also found that each laser pulse causes a sharp rise and drop in
temperature at the pulsed laser spot. The pulsed laser beam was handled as a heat source with
Gaussian intensity distributions in both x-direction and y-direction.The material was assumed to
be elastic-perfectly plastic material with no strain-hardening/softening behaviours, with
properties varying with temperature. The thermal conductivity, specific heat, Young’s modulus,
yield stress, and thermal expansion coefficient of silicon are considered by means of linear
interpolation.Majumdar et al.[3] discussed that laser comprises of three principal components,
namely the lasing medium, means of exciting the lasing medium into its amplifying state (lasing
energy source), and optical delivery/feedback system.Choi et al.[4] have used Nd:YLF laser
beam (λ=349 nm, full-width half-maximum (FWHM) pulse width as 4 ns, pulse repetition rate as
1 kHz which was focused by a UV objective lens (f=19 mm).They have considered the
attenuation of the laser beam as it penetrates into the GaN layer along the negative z direction.
They have considered the reflectivity of the GaN surface that reflects some of the incident power
resulting in the power loss.Milos et al.[5] used the FEM analysis to study the heat affected zone
in CO2 laser cutting of stainless steel. They concluded that cutting speed has maximum influence
on the width of HAZ followed by the laser power, focus position and assist gas pressure.Nisaret
al.[6] studied the effect of thermal stresses on chip free diode laser cutting of glassand used a
laser beam with a CW mode and uniform distribution. The controlled fracture technique for the
cutting of glass was used which is initiated by the laser beam and it was found that the absorption
length was greater than the diffusion length.Liu et al.[7] used temperature dependent properties
and fine meshing at machining zone. And they concluded temperature dependent properties and
fine meshing has maximum influence on HAZ. Pence et al.[8] have considered relation between
laser velocity and pulse frequency. Depending upon the overlapping ratio they have varied above
parameters.The laser-induced shock wave pressures predicted using the hydrodynamics model

12. were applied as user-defined distributed time-dependent pressure loads in ABAQUS.Fully
coupled thermo-mechanical ABAQUS/Explicit analysis was first carried out for a timestep of
2,000 ns. The resultant solution was then imported to the following implicit step, which
calculates the steady-state deformation by the ABAQUS/Standard solver to save computation
cost.Chen et al. [9] have done finite element analysis of the pulsed laser-bending process with
a single, line-shape laser pulse. They have considered FWHM pulse with a pulse width of 10
ns.In this work, a pulsed, diode-pumped Nd:YLF laser is used as the energy source. The laser
beam with a Gaussian distribution is focused into a line shape irradiating on the stainless steel
specimen to induce bending. In an actual pulsed laserbending operation, the Gaussian laser beam
is scanned in the x-direction, thus, the temperature and stress/strain development in the target are
three-dimensional.A finite element code, ABAQUS is used for both heat transfer and thermal
stress analyses with a twodimensionalplane-strainassumption.Pulsed Nd:YAG laser was used by
Khalil et al.[10] in their study of experimental and numerical simulation of laser ablation in
stainless steel. The energy per pulse in their project is 270mJ per pulse with a repetition rate of
10Hz and pulse duration is 6ns. They took laser beam mode to be a Gaussian one.Ramkumaret
al. [11] studied the simulations and experiments on excimer laser micro machining of metal and
polymer where they used temperature dependent material properties for simulation. They used a
specific formula for determining the thermal conductivity of the material at various
temperatures.𝜅 = 14.6 + 0.0127𝑇 , where 𝜅 is the thermal conductivity of the material. They
also determined that specific heat capacity (𝐶 𝑃) of steel i.e. a metal remains fairly unaffected by
temperature and hence a constant specific heat was taken into account.Singhet al.[12] did
extensive study on Laser Beam Machining (LBM) and the effect of its process parameters as in
laser power and cutting speed on the Heat Affected Zone (HAZ). They found that the effect of
laser power on HAZ is more as compared to the effect of cutting speed and therefore laser power
is more important factor that controls the HAZ.
3. FINITE ELEMENT ANALYSIS
FEM (Finite element method) is most flexible and powerful numerical method for analyzing heat
transfer problems of general interest [14]. FEM however, is an approximate numerical method

13. and care has to be taken in setting up aproblem for FEM analysis. The quality of the solution
obtaineddepends upon various factors including mainly thedistribution of the space discretization
(meshing) throughoutthe domain, time discretization for transient problem,proper application of
the boundary conditions and selectionof suitable material properties.
In the following project ABAQUS was used to carry out the thermal analysis. Temperature
dependent thermal and physical properties were used in the analysis given in Table 1.The density
of the work piece was taken as independent of temperature and has a value of𝜌 = 7896𝐾𝑔/𝑚3
.
Table1.Temperature dependent physical properties of SS304 used in our calculation [13]
Mechanical Properties:-
T(𝑘) 400 600 800 1000
𝛼(1/𝐾) 1.49E-05 1.56E-05 1.69E-05 1.8E-05
𝐸(𝐺𝑃𝑎) 190 170 160 180
Poisson’s ratio 0.29 0.324 0.335 0.34
Thermal Properties :-
T(k) 500 1000 1500 2000
Cp(J/KgK) 540 600 670 790
K(W/mK) 16 24 32 19
Here, T(𝐾): Temperature
𝛼(1/𝐾):Thermal expansion coefficient
𝐸(𝐺𝑃𝑎): Young’s Modulus
𝜅(𝑊/𝑚𝐾): Thermal conductivity of the material
𝐶 𝑃(𝐽/𝐾𝑔𝐾): Specific heat

14. 3.1 NUMERICAL SIMULATION OF CONTINUOUS WAVE
Assumptions: In the simulation of laser machining of SS304, the following assumptions were
made for the thermal analysis by ABAQUS.
1. The laser heat source is a continuous wave type.
2. The laser intensity follows a Gaussian distribution.
3. Heat conduction in the specimen and free convection in the surrounding air are considered, but
thermal radiation is neglected.
4. The heating phenomena due to phase changes are neglected.
5. The material was homogenous and isotropic.
Modeling Approaches: The meshing used the specimen isindependent type which was selected
in the assembly module of ABAQUS. For the equivalent continuous power analysis, a constant
time step was used while traversing the part. With Q being constant the time step was no longer
restricted by the pulsing function but rather by the radius of the laser. The time increment was set
such that during each step the laser does not travel a distance longer than a quarter of the laser
radius. In the step module the heat transfer was taken as transient with a time period of 2sec. The
increment type is fixed and the maximum number of increments is 40. The increment size was
taken as 0.05sec. In the interaction module, surface film condition was selected and the areas
which were in air are marked. The heat convection coefficient of air (10–100 W/m2 K). The heat
convection coefficient of air was set as 100 W/m2 K. The heat convection was applied on all the
surfaces of the model as an interaction property where sink temperature is same as the ambient
temperature. A Gaussian laser beam with a uniform distribution passes through a cylindrical lens
condensing into a line beam and its intensity distribution 𝐼( 𝑥, 𝑦), can be expressed as:
𝐼𝑠( 𝑥, 𝑦) = 𝐼0exp(
−2( 𝑥2
+ 𝑦2)
𝑟𝑓
2 )
Where 𝐼0 =
2𝑃
𝜋𝑟 𝑓
2
𝑑
and that
𝐼0is the laser intensity at the centre point (W/m2) ,

15. 𝑃is the laser power (W)
𝑟𝑓is the laser spot radius
𝑑is the material thickness
The work piece used for the project was SS304. The parameters used for three dimensional
thermal analysis with a moving heat source are summarized below:
1. Type of laser used: high-power ND:YAGlaser
2. Laser power used: 100W
3. Work piece dimension: 50mm X 30mm X 2mm
4. Laser scanning speed: 15 mm/sec
5. Laser spot size: 300 um diameter
6. Wavelength of the laser used: 1024nm
30mm
2mm
50mm
Fig.1. Basic model outline with global coordinate system
The dimension of the specimen is 50mmX30mmX2mm. A continuous wave diode laser beam
was then delivered forming a line shaped beam onto the upper surface of the specimen as shown
Laser propagation
Laser spot
Z
X
Y

16. in the figure below. S.I units are considered throughout the analysis. The laser propagation takes
place in y direction. A 3-D model has been considered because there is some power dissipated
along the thickness of the workpiece
An 8-node linear heat transfer brick DC3D8 was considered in the mechanical model and the
meshed specimen is shown in the fig below, where a fine meshing was applied around the laser
beam to analyze the steep temperature gradients around the heating zone.The specimen consists
of 144000elements. The material was treated as isotropic.In the assembly module a partition of
width 750μm is made. The laser spot diameter is 300μm. The extra 450μm is used to consider
the effects of HAZ. Partition is done to specify the machining zone. Load is given using DFLUX
subroutine file.
f j f kj
Fig.2.Partition made in the assembly module
Fig.3. Load applied to the work piece

17. The meshing of the work piece was done in the mesh module. If a dependent type mesh is
chosen, then the meshing is done in the part module and in the assembly module, independent
meshing is done. In the mesh controls, the element type was chosen as hexahedral DC3D8 heat
transfer brick and the technique used was structured. The various edges were then seeded and
part meshing was done. The concept behind the number of seeds to be chosen for the partition
plane where the laser beam is passed is that, 4 to 5 elements must lie inside the laser spot.The
type of mesh chosen was independent type. The size of the element in the machining zone was
selected to be 75μm x 150μm x 75μm.
Fig.4. The meshed work piece showing finer mesh in the plane where laser beam is passed.
3.2. NUMERICAL SIMULATION OF MULTI PULSED BEAMFOR STATIC SOURCE
Assumption: In the simulation of laser machining of SS304, the following assumptions were
made for the thermal analysis by ABAQUS.
1. The laser heat source is a pulsed (millisecond) type.

18. 2. The laser intensity follows a Gaussian distribution.
3. Heat conduction in the specimen and free convection in the surrounding air are considered but
thermal radiation is neglected.
4. The heating phenomena due to phase changes are neglected.
5. The material was homogenous and isotropic.
6. The position of the laser is kept constant.
Y
30mm
1515
2mm
50mm
Fig.5. Basic model outline with global coordinate system
The dimension of the specimen is 50mmX30mmX2mm. The position of the laser is kept
constant at 𝑥 = 25𝑚𝑚, 𝑦 = 15𝑚𝑚, 𝑧 = 2𝑚𝑚 . A pulsed wave diode laser beam was then
delivered forming a spot onto the upper surface of the specimen as shown in the figure above. S.I
units are considered throughout the analysis.
15mm
Z
X
Position of laser
source
25mm

19. The work piece used for the project was SS304. The parameters used for three dimensional
thermal analysis with a moving heat source are summarized below:
1. Type of laser used: high-power ND:YAGlaser
2. Laser power used: 100W
3. Work piece dimension:50mm X 30mm X 2mm
4. Laser spot diameter: 200 um diameter
5. Wavelength of the laser used: 1024nm
Modeling Approaches: The meshing used the specimen isindependent type which was selected
in the assembly module of ABAQUS. In the step module the heat transfer was taken as transient
with a time period of 0.5sec. The increment type is fixed and the maximum number of
increments is 500. The increment size was taken as 1ms. The graph shows the variation of power
with time for a single pulse. The pulse width is taken as 1ms. The frequency is taken as 100Hz.
The total number of pulses are50. The type of pulse is squarepulse wave.
Fig.6. Variation of power with time for square pulsed wave
The Gaussian heat distribution was used. Interaction module was also similar to that for the
continuous wave. But DFLUX subroutine was modified to include a time varying factor. The
position of the laser beam was kept constant. Fine mesh size was used for the simulation.The
type of mesh chosen was independent type. The size of the element in the machining zone was
selected to be 75μm x 150μm x 75μm.

20. 3.3. NUMERICAL SIMULATION OF PULSED BEAMFOR MOVING HEAT SOURCE
Assumption: In the simulation of laser machining of SS304, the following assumptions were
made for the thermal analysis by ABAQUS .
1. The laser heat source is a pulsed (millisecond) type.
2. The laser intensity follows a Gaussian distribution.
3. Heat conduction in the specimen and free convection in the surrounding air are considered but
thermal radiation is neglected.
4. The heating phenomena due to phase changes are neglected.
5. The material was homogenous and isotropic.
6. The position of the laser keeps on changing with time.
Y
30mm
Fig.7. Basic model outline with global coordinate system
2mm
Z
X
Laser propagation
Laser spot
50mm

21. The dimension of the specimen is 50mmX30mmX2mm.A pulsed wave diode laser beam was
then delivered forming a spotand the position of the laser spot changes with time as shown in the
above figure. S.I units are considered throughout the analysis.
Modeling Approaches: The meshing used the specimen isindependent type which was selected
in the assembly module of ABAQUS. In the step module the heat transfer was taken as transient
with a time period of 0.5sec. The increment type is fixed and the maximum number of
increments is 500. The increment size was taken as 1ms. The graph shows the variation of power
with time for a single pulse. The pulse width is taken as 2ms. The frequency is taken as 100Hz.
The total number of pulses are50. The type of pulse is squarepulse wave.
The Gaussian heat distribution was used. Interaction module was also similar to that for the
continuous wave. But DFLUX subroutine was modified to include a time varying factor. The
position of the laser beam was kept constant. Fine mesh size was used for the simulation.The
type of mesh chosen was independent type. The size of the element in the machining zone was
selected to be 75μm x 150μm x 75μm.
3.4. NUMERICAL SIMULATION OF SINGLE PULSED BEAM
Assumption: In the simulation of laser machining of SS304, the following assumptions were
made for the thermal analysis by ABAQUS .
1. The laser heat source is a pulsed (millisecond) type.
2. The laser intensity follows a Gaussian distribution.
3. Heat conduction in the specimen and free convection in the surrounding air are considered but
thermal radiation is neglected.
4. The heating phenomena due to phase changes are neglected.
5. The material was homogenous and isotropic.
6. The position of the laser does not change with time.
7. Heat is applied in the form of a single pulse.

22. Fig.8. Variation of power with time for single pulsed wave
The dimension of the specimen is 50mmX30mmX2mm. The position of the laser is kept
constant at 𝑥 = 25𝑚𝑚, 𝑦 = 15𝑚𝑚, 𝑧 = 2𝑚𝑚 . A pulsed wave diode laser beam was then
delivered forming a spot onto the upper surface of the specimen.
Modeling Approaches: The meshing used the specimen isindependent type which was selected
in the assembly module of ABAQUS. In the step module the heat transfer was taken as transient
with a time period of 0.05sec. The increment type is fixed and the maximum number of
increments is 50. The increment size was taken as 1ms. The graph shows the variation of power
with time for a single pulse. The pulse width is taken as 2ms. The total number of pulse is 1. The
type of pulse is squarepulse wave.
The Gaussian heat distribution was used. Interaction module was also similar to that for the
continuous wave. But DFLUX subroutine was modified to include a time varying factor. The
position of the laser beam was kept constant. Fine mesh size was used for the simulation.The
type of mesh chosen was independent type. The size of the element in the machining zone was
selected to be 75μm x 150μm x 75μm.
4. RESULTSAND DISCUSSIONS
4.1 CONTINUOUS BEAM

23. For thermal analysis of the passing of laser beam on work piece, the laser power considered was
100W. To find proper results, four points with varying y coordinates were selected. The
temperature profile at these points were shown. The temperature vs time graph for these points
were plotted.
The coordinates of four points with their maximum temperatures are as follows:
1. 𝑥 = 25𝑚𝑚, 𝑦 = 29.4𝑚𝑚, 𝑧 = 2𝑚𝑚Tmax=2203.1K
2. 𝑥 = 25𝑚𝑚, 𝑦 = 29.1𝑚𝑚, 𝑧 = 2𝑚𝑚Tmax=2201.2K
3. 𝑥 = 25𝑚𝑚, 𝑦 = 28.8𝑚𝑚, 𝑧 = 2𝑚𝑚Tmax=2229.8K
4. 𝑥 = 25𝑚𝑚, 𝑦 = 28.75𝑚𝑚, 𝑧 = 2𝑚𝑚Tmax=2159.3K
Fig.9. Temperature profiles at coordinates 1. 𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 = 𝟐𝟗. 𝟒𝒎𝒎, 𝒛 = 𝟐𝒎𝒎, 2.𝒙 =
𝟐𝟓𝒎𝒎, 𝒚 = 𝟐𝟗. 𝟏𝒎𝒎, 𝒛 = 𝟐𝒎𝒎, 3.𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 = 𝟐𝟖. 𝟖𝒎𝒎, 𝒛 = 𝟐𝒎𝒎,4.𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 =
𝟐𝟖. 𝟕𝟓𝒎𝒎, 𝒛 = 𝟐𝒎𝒎.
A
B
C
D

24. Fig.10shows that the maximum temperature gets shifted as the time changes. This is because the
laser position is changing. Also, irrespective of the laser position the maximum temperature
value remains same. This is because the interaction time of laser beam with the SS304 for all the
laser positions remains same.
Fig.10. Comparison of maximum temperature obtained at 1. 𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 =
𝟐𝟗.𝟒𝒎𝒎, 𝒛 = 𝟐𝒎𝒎, 2. 𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 = 𝟐𝟗. 𝟏𝒎𝒎, 𝒛 = 𝟐𝒎𝒎, 3. 𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 =
𝟐𝟖.𝟖𝒎𝒎, 𝒛 = 𝟐𝒎𝒎, 4.𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 = 𝟐𝟖. 𝟕𝟓𝒎𝒎, 𝒛 = 𝟐𝒎𝒎.
Fig.11 shows the temperature distribution at ( 𝑥 = 25𝑚𝑚, 𝑦 = 29.4𝑚𝑚, 𝑧 = 2𝑚𝑚). The red
region marks the region of maximum temperature. Since laser intensity follows Gaussian
distribution as we keep moving away from the red region the temperature decreases. This can be
easily shown by calculating the maximum temperature at varying x coordinates. Fig.10 shows
the maximum temperature for different x coordinates. The maximum temperature at 𝑥 =
25.15𝑚𝑚, 𝑦 = 29.4𝑚𝑚, 𝑧 = 2𝑚𝑚&𝑥 = 24.85𝑚𝑚, 𝑦 = 29.4𝑚𝑚, 𝑧 = 2𝑚𝑚 is less than that at
the central point ( 𝑥 = 25𝑚𝑚, 𝑦 = 29.4𝑚𝑚, 𝑧 = 2𝑚𝑚). This is because the laser intensity is
assumed to be Gaussian.
0
500
1000
1500
2000
2500
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
Temperature(K)
Step Time (s)
A
B
C
D

25. Fig.11. Comparison of maximum temperature obtained at 1. 𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 =
𝟐𝟗. 𝟒𝒎𝒎, 𝒛 = 𝟐𝒎𝒎, 2. 𝒙 = 𝟐𝟓. 𝟏𝟓𝒎𝒎, 𝒚 = 𝟐𝟗. 𝟒𝒎𝒎, 𝒛 = 𝟐𝒎𝒎, 3. 𝒙 =
𝟐𝟒. 𝟖𝟓𝒎𝒎, 𝒚 = 𝟐𝟗. 𝟒𝒎𝒎, 𝒛 = 𝟐𝒎𝒎
Fig.12. Temperature distribution at the upper surface of the SS304 work piece at point
( 𝒙 = 𝟐𝟓𝒎𝒎,𝒚 = 𝟐𝟗. 𝟒𝒎𝒎, 𝒛 = 𝟐𝒎𝒎), where element dimensions are taken as
0.07mmX0.15mmX0.07mm.
0
500
1000
1500
2000
2500
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
Temperature(K)
Step Time (s)
X1
X2
X3
X3
X2
X1

26. After getting the temperature distribution the kerf width & depth were obtained. This was done
by using display group in the visualization mode. All the elements having temperature greater
than that of the melting point of SS304 (1873K) were identified. The width & the depth can be
obtained only for a particular laser position. One dimension of the object is taken equivalent to a
specific length of the scale. The channel dimensions are measured using that scale & using ratio
methodKerf width & depth are obtained. The laser power was 100W & laser speed was 15mm/s.
The obtained kerf width & depth are 145.31μm&84.37μm respectively.
Fig.13. MeltedRegionat point ( 𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 = 𝟐𝟗. 𝟒𝒎𝒎, 𝒛 = 𝟐𝒎𝒎)
Laser Power Optimization: In this section the laser power was optimized by considering
various input power values. Then the maximum temperature obtained at the centralpoint (𝑥 =
25𝑚𝑚, 𝑦 = 29.4𝑚𝑚, 𝑧 = 2𝑚𝑚)was calculated by simulating the laser propagation on a SS304
work piece.The table below shows the maximum temperature obtained at various power levels
taken.
Kerf depth
Kerf width

27. Table 2.Variation of maximum temperature with different laser power levels.
Laser power Maximum temperature obtained at
(𝑥 = 25𝑚𝑚, 𝑦 = 29.4𝑚𝑚, 𝑧 = 2𝑚𝑚)
100W 2203.9K
200W 3656.14K
300W 6142.56K
Fig.10 shows that with the increase in input laser power, the maximum temperature obtained at a
point 𝑥 = 25𝑚𝑚, 𝑦 = 29.4𝑚𝑚, 𝑧 = 2𝑚𝑚increases.
Fig.14. Comparison of temperature variation with different laser power levels
Laser speed optimization: Laser propagation speed or cutting speed is an essential parameter
for determining the maximum temperature obtained at the central point chosen. Here cutting
speed was optimized to analyze the changes in temperature when cutting speed is varied. Then
the graph of temperature vs time was plotted to obtain the value of the maximum temperature
obtained at 𝑥 = 25𝑚𝑚, 𝑦 = 29.4𝑚𝑚, 𝑧 = 2𝑚𝑚.
0
1000
2000
3000
4000
5000
6000
7000
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
Temperature(K)
Step Time (s)
100W
200W
300W

28. Table 3.Variation of maximum temperature with changing lasercutting speed.
Laser speed Maximum temperature obtained at
(𝑥 = 25𝑚𝑚, 𝑦 = 29.4𝑚𝑚, 𝑧 = 2𝑚𝑚)
10mm/s 2216K
15mm/s 2209K
30mm/s 1809K
Fig.15. Comparison of temperature variation with different laser cutting speed
Fig.15 shows that with increase in cutting speed the maximum temperature decreases because the
interaction time of the laser beam with the SS304 decreases.
4.1MULTI PULSED BEAM FOR STATIC HEAT SOURCE
For thermal analysis of the passing of laser beam on a work piece, the laser power considered
was 100W. To find proper results, a point at the work piece with coordinates (𝑥 = 25𝑚𝑚, 𝑦 =
0
500
1000
1500
2000
2500
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61
Temperature(K)
Step Time (s)

29. 15𝑚𝑚, 𝑧 = 2𝑚𝑚) was chosen and the temperature of the work piece was calculated. The figure
below indicates the temperature distribution during laser machining of SS304.
Fig.16. Temperature distribution at the center of the SS304 considered
Fig.16 shows the temperature distribution at ( 𝑥 = 25𝑚𝑚, 𝑦 = 15𝑚𝑚, 𝑧 = 2𝑚𝑚) . The red
region marks the region of maximum temperature. Since laser intensity follows Gaussian
distribution as we keep moving away from the red region the temperature decreases. This can be
easily shown by calculating the maximum temperature at varying x coordinates. Fig.17 shows
the maximum temperature for different x coordinates. The maximum temperature at 𝑥 =
25.15𝑚𝑚, 𝑦 = 15𝑚𝑚, 𝑧 = 2𝑚𝑚&𝑥 = 25.30𝑚𝑚, 𝑦 = 15𝑚𝑚, 𝑧 = 2𝑚𝑚 is less than that at the
center( 𝑥 = 25𝑚𝑚, 𝑦 = 15𝑚𝑚, 𝑧 = 2𝑚𝑚). The purple lines correspond to the central point
while the green and red lines represent the 𝑥 = 25.15𝑚𝑚, 𝑦 = 15𝑚𝑚, 𝑧 = 2𝑚𝑚 & 𝑥 =
25.30𝑚𝑚, 𝑦 = 15𝑚𝑚, 𝑧 = 2𝑚𝑚 respectively. Clearly it can be seen that the values of
maximum temperature is very much less for the other coordinates.
X1X2 X3

30. Fig.17. Comparison of maximum temperature obtained at 1.𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 = 𝟏𝟓𝒎𝒎, 𝒛 =
𝟐𝒎𝒎, 2.𝒙 = 𝟐𝟓. 𝟏𝟓𝒎𝒎, 𝒚 = 𝟏𝟓𝒎𝒎, 𝒛 = 𝟐𝒎𝒎, 3.𝒙 = 𝟐𝟓. 𝟑𝟎𝒎𝒎, 𝒚 = 𝟏𝟓𝒎𝒎, 𝒛 = 𝟐𝒎𝒎
The variation of temperature with time for (𝑥 = 25𝑚𝑚, 𝑦 = 15𝑚𝑚, 𝑧 = 2𝑚𝑚)is shown in
fig.18. The time gap between pulses is constant whereas the values of maximum temperature for
pulses are almost similar. As the pulse energy varies with time, so does the temperature
variations. The pulse consists of a rise & fall zone. Therefore, there is a maxima. Similarly the
temperature also has a rise & fall zone.
0
500
1000
1500
2000
2500
3000
3500
4000 1
17
33
49
65
81
97
113
129
145
161
177
193
209
225
241
257
273
289
305
321
337
353
369
385
401
417
433
449
465
481
497
Temperature(K)
Time (ms)
X1
X2
X3

31. Fig.18. Temperature Vs Time plot for ( 𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 = 𝟏𝟓𝒎𝒎, 𝒛 = 𝟐𝒎𝒎)point
After getting the temperature distribution the kerf width & depth were obtained. This was done
by using display group in the visualization mode. All the elements having temperature greater
than that of the melting point of SS304 (1873K) were identified.The width & the depth can be
obtained only for a particular laser position. One dimension of the object is taken equivalent to a
specific length of the scale. The channel dimensions are measured using that scale & using ratio
method Kerf width & depth are obtained. The width & the depth can be obtained only for a
particular laser position. The laser power was 100W. The obtained kerf width & depth are
103.31μm& 40.11μmrespectively.
0
500
1000
1500
2000
2500
3000
3500
4000
1 31 61 91 121 151 181 211 241 271 301 331 361 391 421 451 481
Temperature(K)
Time (ms)

32. Fig.19. MeltedRegion at point ( 𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 = 𝟏𝟓𝒎𝒎, 𝒛 = 𝟐𝒎𝒎)
4.3 MULTI PULSED BEAM WITH MOVING HEAT SOURCE
For thermal analysis of the passing of laser beam on work piece, the laser power considered was
100W. To find proper results, four points with varying y coordinates were selected. The
temperature profile at these points were shown. The temperature vs time graph for these points
were plotted.
The coordinates of four points with their maximum temperatures are as follows:
1. 𝑥 = 25𝑚𝑚, 𝑦 = 16.5𝑚𝑚, 𝑧 = 2𝑚𝑚 Tmax=3058.3K Step Time=160ms
2. 𝑥 = 25𝑚𝑚, 𝑦 = 13.5𝑚𝑚, 𝑧 = 2𝑚𝑚 Tmax=3057.3K Step Time=112ms
3. 𝑥 = 25𝑚𝑚, 𝑦 = 10.5𝑚𝑚, 𝑧 = 2𝑚𝑚 Tmax=3118.5K Step Time=43ms
Kerf depth
Kerf width

33. Fig.20. Temperature profiles at coordinates 1. 𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 = 𝟏𝟔. 𝟓𝒎𝒎, 𝒛 = 𝟐𝒎𝒎, 2.𝒙 =
𝟐𝟓𝒎𝒎, 𝒚 = 𝟏𝟑. 𝟓𝒎𝒎, 𝒛 = 𝟐𝒎𝒎, 3.𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 = 𝟏𝟎. 𝟓𝒎𝒎, 𝒛 = 𝟐𝒎𝒎
Fig.21 shows that the maximum temperature gets shifted as the time changes. This is because the
laser position is changing. Also, irrespective of the laser position the maximum temperature
value remains same. This is because the interaction time of laser beam with the SS304 for all the
laser positions remains same.
B
A
C

34. Fig.21. Comparison of maximum temperature obtained at 1. 𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 =
𝟏𝟔. 𝟓𝒎𝒎, 𝒛 = 𝟐𝒎𝒎, 2. 𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 = 𝟏𝟑. 𝟓𝒎𝒎, 𝒛 = 𝟐𝒎𝒎, 3. 𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 =
𝟏𝟎. 𝟓𝒎𝒎, 𝒛 = 𝟐𝒎𝒎
After getting the temperature distribution the kerf width & depth were obtained. This was done
by using display group in the visualization mode. All the elements having temperature greater
than that of the melting point of SS304 (1873K) were identified. The width & the depth can be
obtained only for a particular laser position.The width & the depth can be obtained only for a
particular laser position. One dimension of the object is taken equivalent to a specific length of
the scale. The channel dimensions are measured using that scale & using ratio method Kerf
width & depth are obtained. The laser power was 100W& laser speed was 24mm/s. The
obtained kerf width & depth are 126.62μm&45.84μm respectively.
0
500
1000
1500
2000
2500
3000
3500
1
21
41
61
81
101
121
141
161
181
201
221
241
261
281
301
321
341
361
381
401
421
441
461
481
501
Temperature(K)
Time (ms)
B
A
C

35. Fig.22. MeltedRegion
at point ( 𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 = 𝟏𝟔. 𝟓𝒎𝒎, 𝒛 = 𝟐𝒎𝒎)
4.4 SINGLE PULSED BEAM WITH STATIC HEAT SOURCE
For thermal analysis of the passing of laser beam on a work piece, the laser power considered
was 100W. To find proper results, a point at the work piece with coordinates (𝑥 = 25𝑚𝑚, 𝑦 =
5𝑚𝑚, 𝑧 = 2𝑚𝑚) was chosen and the temperature of the work piece was calculated. Fig.23
indicates the temperature distribution during laser machining of work piece. Fig.24 shows the
variation of temperature with for ( 𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 = 𝟓𝒎𝒎, 𝒛 = 𝟐𝒎𝒎).
Fig.23. Temperature distribution at (𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 = 𝟓𝒎𝒎, 𝒛 = 𝟐𝒎𝒎)
Kerf depth
Kerf width

36. Fig.24. Temperature Vs Time plot for ( 𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 = 𝟓𝒎𝒎, 𝒛 = 𝟐𝒎𝒎)point
After getting the temperature distribution the kerf width & depth were obtained. This was done
by using display group in the visualization mode. All the elements having temperature greater
than that of the melting point of SS304 (1873K) were identified. The width & the depth can be
obtained only for a particular laser position.The width & the depth can be obtained only for a
particular laser position. One dimension of the object is taken equivalent to a specific length of
the scale. The channel dimensions are measured using that scale & using ratio method Kerf
width & depth are obtained. The laser power was 100W. The obtained kerf width & depth are
98.43μm&23.43μm respectively.
0
500
1000
1500
2000
2500
1 6 11 16 21 26 31 36 41 46 51
Temperature(K)
Time (ms)

37. Fig.25. MeltedRegion at point ( 𝒙 = 𝟐𝟓𝒎𝒎, 𝒚 = 𝟓𝒎𝒎, 𝒛 = 𝟐𝒎𝒎)
CONCLUSION
Thermal analysis of laser beam machining of 304 stainless steel has been studied in this project.
Laser machining on 304 stainless steel using pulsed & continuous wave mode has been
simulated. Both cases of static & moving laser source has been considered. The main objective
of this project was to find the temperature profile, Kerf width, Kerf depth in different cases. The
optimization aspects of laser machining parameters, the variation in temperature of the work
piece when laser machining is done using different laser sources where convection is neglected is
also studied here. Another objective was to specify the importance of meshing in determining the
desired results.
A commercial FE package ABAQUS was used for thermal analysis in this project. From the
following study it is clear that in laser sources with Gaussian heat distribution the temperature
decrease as distance from the center of laser increases. The variation of temperature with
changing laser parameters such as laser input power, laser propagation speed is studied here and
graphs were plotted to obtain the desired results. It is observed that the Kerf width & depth in
case of single pulsed laser beam is the minimum among all the cases. This can be due to very
small interaction time of laser with the material.
Kerf depth
Kerf width

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