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 Al 2 O 3 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 = abh c Crater parameters The crater volume is calculated by b hchc a b: 24.2 b: 40.6 Crater depth – h c (µm) “b” profile “a”-Profile a: 21.7 Crater depth - h c (µm) a : 41.1 “a” profile “a”-Profile “b”-Profile Sample picture provided by the surface profiler

Variation of Depth for Craters Produced by Pulses with Pulse Energy of 40.4 µJ Crater depth - h c (μm) Pulse number

Crater Depth vs. Pulse Energy (Brass) Mean - Mean + Mean Pulse energy - E (  J) Crater depth - h c (  m)

Crater Average Diameter vs. Pulse Energy (Brass) Mean- Mean Mean + Pulse energy - E (  J) Crater average diameter - d c (  m)

Laser beam flux Surface formed by photons of 1 st portion of the of flux Surface formed by photons of 2 nd 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 -h c Crater diameter -d c Laser Pulse Energy-E Neurons Input signals

Crater depth -h c Crater diameter -d c Laser Pulse Energy-E Basic Operation Performed by a Neuron INPUT SIGNALS ( x i ) BIAS hchc dcdc 0 1 X Mapping y Neural input space (vector) Neural output space (scalar) Neural Processing Element X y Xy Ne : Nonlinear mapping function OUTPUT

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 _ + e Approximate function Data points used for training

Crater depth -h c Crater diameter -d c Laser Pulse Energy-E 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) Crater depth – h c (μm) Pulse energy - E (μJ) Modeled pulse energy Actual pulse energy Crater diameter - d c (μm) Modeled pulse energy Actual 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) Pulse energy (μJ) Modeled Actual Pulse energy (μJ) Modeled Actual

Change in Diameter Under the Effect of Change in Energy Crater diameter – d c (μm) Experimental data points Model outputs falling outside experimental data region are Modeled E for 80% d c. Modeled E for 50% d c. Model outputs overlapping with experimental data Diameter increase d c1 = d c +10% dc dc d c2 = d c -10% E1E1 EE2E2 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 E 2 -E with E- E 1.

MODEL VALIDATION

3D Data Visualization 6* Crater depth – h c (μm) Crater diameter – d c (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 9.94μm 12.86μm 14.98μm 22μm 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 - h c, which belong to each curve).

ANN1 ANN2 Depth – (h c ) Diameter – (d c ) Pulse energy – (E) Material property – (k) Multi-Material Model

T f = Melting point. T 0 = Ambient temperature. L f = Latent heat of fusion. = Density. R = Surface reflectivity C P = Heat capacity Theoretical Equation for Volume of Material Melt by a Laser Pulse Sensible Heat of Melting = Material Property

Multi-Material Model Outputs copper brass Stainless steel Pulse energy – E (μJ) Crater mean depth – h c (μm) Modeled energy (brass) Actual energy (brass) Modeled energy (stainless steel) Actual energy (stainless steel) Modeled energy (copper) Actual energy (copper)

Multi-Material Model Outputs Pulse energy – E (μJ) Crater mean diameter – d c (μm) copper brass Stainless steel Modeled energy (brass) Actual energy (brass) Modeled energy (stainless steel) Actual energy (stainless steel) Modeled energy (copper) Actual 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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