Neural Network Approach to Modeling the Laser Material-Removal Process By Basem. F. Yousef London,...

Neural Network Approach to Modeling the Laser Material-Removal Process

By

Basem. F. Yousef

London, Canada, N6A 5B9 December 2001

Organization

• Conclusions and recommendations

• Introduction

• Experimental setup and data acquisition

• Neural networks concepts and models

• Model outputs and results

• Model validation

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.

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.

laser-drilled orifices (all less than 100 µm in diameter) in catheter tubing.

Microgear of Al2O3

with 120 m m diameter, produced by laser ablation (Courtesy of Microlas).

Introduction

Laser Micro-Machining System and Controlling Parameters

Laser subsystem

Laser-beam-material interaction process

Workpiece subsystem

Kinematic & dynamic disturbances

Final surface profile

Volume of material removed

Control vector

Actual laser beam parameters within process zone

Internal disturbances in the laser/optics subsystem

Prescribed laser beam parameters

Process noise

Thermodynamic disturbances

LASER

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

V = abhc 2

Crater parameters

The crater volume is calculated by

b

hc

a

b: 24.2

b: 40.6

Crater depth – hc (µm)

μm“b” profile

μm

μm

“a”-Profile

a: 21.7

Crater depth - hc (µm)

a : 41.1“a” profile

μm

μmμm

“a”-Profile

“b”-

Pro

file

μm

μm

Sample picture provided by the surface profiler

Variation of Depth for Craters Produced by Pulses with Pulse Energy of 40.4 µJ

-7

-6

-5

-4

0 5 10 15 20 25 30 35 40 45 50

Crater depth - hc (μm)

Pulse number

0 5 10 15 20 25 30 35 40 45 50

Crater Depth vs. Pulse Energy (Brass)

-30

-25

-20

-15

-10

-5

0

0 100 200 300 400 500 600

0 100 200 300 400 500 600

Mean -

Mean +

Mean

Pulse energy - E (J)

2

Cra

ter

d ept

h -

h c (m

)

2

Crater Average Diameter vs. Pulse Energy(Brass)

0

5

10

15

20

25

30

0 100 200 300 400 500 600

Mean-

Mean

Mean +

Pulse energy - E (J)

2

2C

rate

r a v

erag

e di

ame t

e r -

dc

( m

)

Laser beam flux

Surface formed by photons of 1st portion of the of flux Surface formed by photons of

2nd portion of the flux

Material surface

Surface formed by photons of last portion of the flux

Mechanism of Material Removal by a Laser Pulse

NEURAL NETWORKS

Typical Multi-layer Neural Network

First hidden layer

Second hidden layer

Output layer

Crater depth -hc

Crater diameter -dc

Laser Pulse Energy-E

Neurons

Input signals

Crater depth -hc

Crater diameter -dc


Basic Operation Performed by a Neuron

INPUT SIGNALS

(xi)

ijij xwu

j2w

j2w

BIAS

hc

dc

ju

jy

0

1

jy

X n

Mapping

y 1

Neural input space

(vector)

Neural output space

(scalar)

Neural Processing Element

X ny 1

X n y 1Ne :

Nonlinear mapping function

OUTPUT

jow

Neural Network Model in Training Phase

Neural Network Modeler Modeled output

COMPARISON

Actual output

CORRECTION

Inputs

In order to reduce the (error) difference between the modeled output and the desired output, the neural network updates its weight values by the back-propagation 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

•A two-layer neural network can form an approximation to any continuous nonlinear mapping

•Training set consists of input-output pairs (x,d)

+1

1

11w

1x1d

_ +

1

1y

+1

+1

e0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

x

y

Approximate function

Data points used for training

1

10w

1

21w

1

20w

1

2y

2

11w

2

12w

2

10w

2

1y

depthdiameter

Crater depth -hc

Crater diameter -dc


ANN1 ANN2

The Interconnection of the Artificial Neural Networks for the Operation Mode.

MODEL OUTPUTS

Crater Depth and Diameter vs. Modeled and Actual Energy(Brass)

0

5

10

15

20

25

30

0 100 200 300 400 500 600

Simulated pulse energy

Actual pulse energy

Crater depth – hc (μm)

Pulse energy - E (μJ)

Modeled pulse energy

Actual pulse energy

0

5

10

15

20

25

30

0 100 200 300 400 500 600

Simulated pulse energy

Actual pulse energy

Crater diameter - dc (μm)

Modeled pulse energyActual pulse energy

Pulse energy - E (μJ)

Depth standard deviation vs. pulse energy.

Diameter standard deviation vs. pulse energy.

Modeling the Variance of Depth and Diameter(Brass)

0

0.2

0.4

0.6

0.8

1

1.2

0 100 200 300 400 500 600

Simulated

Actual

Pulse energy (μJ)

depthdepth

depthModeled

Actual

0

0.2

0.4

0.6

0.8

1

1.2

0 100 200 300 400 500 600

Simulated

Actual

Pulse energy (μJ)

diameterdiameter

diameterModeled

Actual

Change in Diameter Under the Effect of Change in Energy

Crater diameter – dc (μm)

Experimental data points

Model outputs falling outside experimental data region are

Modeled E for 80% dc.Modeled E for 50% dc.

Model outputs overlapping with experimental data

Diameter increase

dc1 = dc+10%

dc

dc2 = dc-10%

E1EE2

Pulse energy- E (μJ)

Mean depth-mean diameter curve

Model outputs superimposed on experimental data points for verification and comparison purpose.

Nonlinearity is obvious when comparing when E2-E with E-E1.

MODEL VALIDATION

3D Data Visualization

100 120 140 160180 200 220

10

15

2012

14

16

18

20

22

Pulse energy (µJ)

Dent depth (µm)

De

nt d

iam

ete

r (µ

m)

Energy= 207µJ

Energy=107 µJ

Energy=144 µJ

6*

6*

Crater depth – hc (μm)

depth

diameterCrater diameter – dc (μm)

Pulse energy- E (μJ)

Elliptical regions confining the experimental data areas associated with 3 energy levels.

Energy ellipses

Mesh representing volume of experimental data

Mesh Confining Experimental Data

Details of anticipated intersection point between extended curve “A” and simulation curve 80% mean diameter.

110% mean diameter 105% mean diameter Mean diameter 95% mean diameter 90% mean diameter

80% mean diameter

Curve “A”

Model Validation

Curve “A” intersects with simulation curve “80% mean diameter” at the anticipated point of intersection with a corresponding error of 2 %.

All simulation curves are inside the mesh except 80% mean-diameter curve. Curve “A” corresponds to craters having depth =19.84 μm.

Model Validation

9.94μm12.86μm

14.98μm

22μm

19.84 μm 17.09μm

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).

ANN1

ANN2

Depth – (hc)

Diameter – (dc) Pulse energy – (E)

Material property – (k)

depth

diameter

Multi-Material Model

R)E(1]L)T(T[c f0fp Vρ

fabh2

πV

Tf = Melting point.

T0 = Ambient temperature.

Lf = Latent heat of fusion.

ρ = Density.

R = Surface reflectivity

CP = Heat capacity

Theoretical Equation for Volume of Material Melt by a Laser Pulse

Sensible Heat of Melting = )T(Tc 0fp ρMaterial Property

Multi-Material Model Outputs

0

5

10

15

20

25

30

0 100 200 300 400 500 600

Simulated energy (brass)

Actual energy (brass)

Simulated energy (stainless steel)

Actual energy (stainless steel)

Simulated energy (copper)

Actual energy (copper)

copper

brass

Stainless steel

Pulse energy – E (μJ)

Crater mean depth – hc (μm)

Modeled energy (brass)


Modeled energy (stainless steel)


Modeled energy (copper)


Multi-Material Model Outputs

0

5

10

15

20

25

30

0 100 200 300 400 500 600

Simulated energy (brass)


Simulated energy (stainless steel)


Simulated energy (copper)


Pulse energy – E (μJ)

Crater mean diameter – dc (μm)

copper

brass

Stainless steel

Modeled energy (brass)


Modeled energy (stainless steel)


Modeled energy (copper)


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.

Neural Network Approach to Modeling the Laser Material-Removal Process

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Neural Network Approach to Modeling the Laser Material-Removal Process By Basem. F. Yousef London,...

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