Transcript No Slide Title

Neural Network Approach to Modeling the
Laser Material-Removal Process
By
Basem. F. Yousef
London, Canada, N6A 5B9
December 2001
Organization
• Introduction
• Experimental setup and data acquisition
• Neural networks concepts and models
• Model outputs and results
• Model validation
• Conclusions and recommendations
INTRODUCTION
Introduction
What is laser micro-machining ?
Laser micro-machining is the
process of manufacturing parts of
dimensions from 0.1 m to 1000 m
using the laser beam as a cutting
tool.
laser-drilled
orifices (all less
than 100 µm in
diameter) in
catheter tubing.
Why “laser micro-machining”?
•
•
The global trend of industry is moving
toward miniaturization
Micro-scale parts are used in diverse
fields such as medical bio-medical,
microelectronics,
opto-electronics,
space and others.
Microgear of Al2O3
with 120 m m
diameter, produced
by laser ablation
(Courtesy of
Microlas).
Laser Micro-Machining System and
Controlling Parameters
LASER
Internal disturbances in the
laser/optics subsystem
Prescribed laser beam
parameters
Laser subsystem
Actual laser beam parameters
within process zone
Control
vector
Kinematic & dynamic
disturbances
Process noise
Volume of
material
removed
Thermodynamic
disturbances
Laser-beam-material
interaction process
Final surface
profile
Workpiece subsystem
Workpiece
Objectives

To investigate and analyze how the geometry of the final
surface profile forms and depends on the laser pulse
energy.

To develop an artificial neural network model, which can
predict the laser pulse energy needed to produce a crater
with specific depth and diameter on the surface of a specific
material, and the expected variation in the produced crater
depth and diameter associated with the modeled pulse
energy.
Procedure
Utilizing a neural network involves:
 Conducting experiments and acquiring data
 Developing the neural network models
 Training the networks using the experimental data
 Recreating outputs by the trained model
EXPERIMENTS
Experimental Setup and Data Acquisition
a : 41.1 μm
a: 21.7 μm
Crater depth - hc (µm)
“a”-Profile
b
hc
μm
Crater parameters
“b” profile
Sample picture
provided by the
surface profiler
a
“a”-Profile
μm
Crater depth – hc (µm)
μm
“b”-Profile
“a” profile
b: 40.6
μm
b: 24.2
μm
The crater volume is
calculated by
V=

2
μm
abhc
Crater depth - hc (μm)
Variation of Depth for Craters Produced by Pulses
with Pulse Energy of 40.4 µJ
0
5
10
15
20
25
30
35
40
45
50
0
5
10
15
20
25
30
35
40
45
50
-4
-5
-6
-7
Pulse number
Crater Depth vs. Pulse Energy
(Brass)
0
100
200
300
400
500
600
500
6 00
0
-5
-1 0
Mean + 2 
-1 5
Mean
-2 0
Mean - 2 
-2 5
-3 0
0
100
200
300
400
Pulse energy - E (J)
Crater Average Diameter vs. Pulse Energy
(Brass)
30
Mean + 2 
25
20
Mean
15
Mean- 2 
10
5
0
0
100
200
300
400
Pulse energy - E (J)
500
600
Mechanism of Material Removal by
a Laser Pulse
Laser beam flux
Material surface
Surface formed by photons of
1st portion of the of flux
Surface formed by photons of
last portion of the flux
Surface formed by photons of
2nd portion of the flux
NEURAL NETWORKS
Typical Multi-layer Neural Network
Input
signals
First
hidden
layer
Second
hidden
layer
Output
layer
Crater depth -hc
Laser Pulse
Energy-E
Crater diameter -dc
Neurons
Basic Operation Performed by a Neuron
Neural Processing
Element
X  n
y  
1
INPUT
SIGNALS
(x i )
hc
BIAS
w jo
w j2
u j   w ji x i
Mapping
dc
X  n
w j2
yj
OUTPUT
0
uj
yj
y  1
Neural input space
Neural output space
(vector)
(scalar)
Nonlinear mapping function
Ne : X   n
1
y  1
Crater depth -hc
Crater diameter -dc
Laser Pulse
Energy-E
Neural Network Model in Training Phase
Inputs
Neural Network
Modeler
CORRECTION
Modeled output
COMPARISON
Actual output
In order to reduce the (error) difference between the modeled output and the
desired output, the neural network updates its weight values by the backpropagation algorithm. In this method, the error signal originating at the output layer
neurons is back-propagated through the network in the direction of the first layer
and the weights are updated to reduce that error.
Approximating a Continuous Function
+1
1
w 10
x1
1
w 11

y1
1
+1
1
Data points used
for training
2
w 11
0.8
2
d1
w 10
2
+1

1
y1
+
_
y
0.6
0.4
w 20
0.2
1
1
w 21

y2
2
w 12
Approximate
function
e
0
0
2
4
6
x
•A two-layer neural network can form an approximation to any continuous
nonlinear mapping
•Training set consists of input-output pairs (x,d)
8
10
The Interconnection of the Artificial Neural
Networks for the Operation Mode.
Crater depth -hc
Laser Pulse
Energy-E
Crater diameter -dc
ANN1
ANN2
 depth
 diameter
MODEL OUTPUTS
Crater Depth and Diameter vs. Modeled and Actual Energy
(Brass)
Crater depth – hc (μm)
30
25
20
15
Modeled
pulse
S im u lated p u lse
en erg y energy
10
A ctu al p u lse en erg y
Actual
pulse energy
5
0
0
100
200
300
400
500
600
Pulse energy - E (μJ)
Crater diameter - dc (μm)
30
25
20
15
S im ulated p ulse pulse
energy
Modeled
energy
A ctual p ulse energy
Actual
pulse energy
10
5
0
0
100
200
300
400
Pulse energy - E (μJ)
500
600
Modeling the Variance of Depth and Diameter
(Brass)
1.2
1
 depth
0.8
Depth standard deviation
vs. pulse energy.
0.6
S im ulated

Modeled
0.4
A ctual
Actual
0.2
depth
 depth
0
0
100
200
300
400
500
600
Pulse energy (μJ)
1.2
S im ulated  diameter
Modeled
1
 diameter
 diameter
A ctual
Actual
Diameter standard
deviation vs. pulse energy.
0.8
0.6
0.4
0.2
0
0
100
200
300
400
Pulse energy (μJ)
500
600
Change in Diameter Under the Effect of Change in Energy
Model outputs overlapping
with experimental data
Crater diameter – dc (μm)
Mean depth-mean
diameter curve
dc1 = dc+10%
Model outputs superimposed on
experimental data points for
verification and comparison
purpose.
dc
Experimental
data points
dc2 = dc-10%
Model outputs falling outside
experimental data region are
Modeled E for 80% dc.
Modeled E for 50% dc.
Diameter
increase
E2
E
E1
Pulse energy- E (μJ)
Nonlinearity is obvious when
comparing when E2-E with EE1.
MODEL VALIDATION
3D Data Visualization
22
diameter
CraterDent
– (µm)
dc (μm)
diameter
Elliptical regions confining
the experimental data
areas associated with 3
energy levels.
Energy= 207µJ
20
Energy=144 µJ
18
6*
 diameter
16
Energy=107 µJ
6*
14
 depth
12
20
15
Dent depth
Crater depth
– hc (µm)
(μm)
180
10
100
120
140
200
160
Pulse
(µJ)E (μJ)
Pulseenergy
energy-
220
Mesh Confining Experimental Data
Mesh representing volume
of experimental data
Energy ellipses
Model Validation
All simulation curves are
inside the mesh except 80%
mean-diameter curve. Curve
“A” corresponds to craters
having depth =19.84 μm.
110% mean diameter
105% mean diameter
Mean diameter
95% mean diameter
90% mean diameter
80% mean diameter
Curve “A”
Curve “A” intersects with
simulation curve “80% mean
diameter” at the anticipated
point of intersection with a
corresponding error of 2 %.
Details of anticipated
intersection point between
extended curve “A” and
simulation curve 80% mean
diameter.
Model Validation
22μm
Verification curves corresponding
to
same-depth
pulses
are
intersecting with model-output
curve” 80 % mean diameter”.
(Numbers on the figure show the
depths of craters - hc, which
belong to each curve).
19.84 μm
17.09μm
14.98μm
12.86μm
9.94μm
Multi-Material Model
Depth – (hc)
Diameter – (dc)
ANN1
Pulse energy – (E)
Material
property – (k)
ANN2
 depth
 diameter
Theoretical Equation for Volume of Material Melt
by a Laser Pulse
[c p (T f  T0 )  L f ]V ρ  (1  R)E
V 
π
abh
2
f
Tf = Melting point.
T0 = Ambient temperature.
Lf = Latent heat of fusion.
ρ = Density.
R = Surface reflectivity
CP = Heat capacity
Material
Property
Sensible Heat of Melting = ρ c p (T f  T0 )
Multi-Material Model Outputs
Crater mean depth – hc (μm)
30
copper
25
20
15
Modeled
energy
(brass)
S im ulated energy
(b rass)
A ctual energy
(b rass)
Actual
energy
(brass)
S im ulated energy
(stainless
steel)steel)
Modeled
energy
(stainless
A ctual energy
(stainless
steel) steel)
Actual
energy
(stainless
S im ulated energy
(co(copper)
p p er)
Modeled
energy
A ctual energy
(co(copper)
p p er)
Actual
energy
brass
10
Stainless steel
5
0
0
100
200
300
400
Pulse energy – E (μJ)
500
600
Multi-Material Model Outputs
Crater mean diameter – dc (μm)
30
copper
25
brass
20
15
energy(b(brass)
SModeled
im ulated energy
rass)
10
Actual
energy
(brass)
A
ctual energy
(b rass)
energy(stainless
(stainless
steel)
SModeled
im ulated energy
steel)
5
A
ctual energy
(stainless
steel)
Actual
energy
(stainless
steel)
Stainless steel
SModeled
im ulated energy
p p er)
energy(co
(copper)
A
ctual energy
(co(copper)
p p er)
Actual
energy
0
0
100
200
300
400
Pulse energy – E (μJ)
500
600
Neural Network Approach to Modeling the
Laser Material-Removal Process
Conclusions
•
The developed neural network successfully modeld the actual
process behavior to high degree of accuracy.
•
The successful research results set the stage for valuable
and promising future work in the field and for further
improvement in process performance.
Future Work
•
•
Model the process outputs in terms of different input
parameters such as focal spot, frequency and feed rate.
Test the neural network capabilities to model the process
when new materials (other than those used for training) are
considered.
THANK YOU