Gustavo Augusto RengifoThesis Presentation
Advisor: Dr. Hazim ElAdvisor: Dr. Hazim El--MounayriMounayri
Advanced Engineering Manufacturing Laboratory (AEML)Advanced Engineering Manufacturing Laboratory (AEML)Mechanical Engineering DepartmentMechanical Engineering Department
Purdue School of Engineering & Technology, IUPUIPurdue School of Engineering & Technology, IUPUI
April 13April 13thth, 2007, 2007
DEVELOPMENT OF AN INNOVATIVE NEURAL NETWORK MODEL FOR MILLING BASED ON A SYSTEMATIC APPROACH FOR STATISTICAL
DESIGN OF EXPERIMENTS
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 22
OutlineProblem Definition
Previous Work
Current Work
• Overview
• Experiments
• More general ANN model for end milling
• New DOE technique for optimal data collection/sets
• Systematic approach for optimizing process modeling
Results
Conclusions and Future Research
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Problem Definition
The End Milling OperationProcessCutting Conditions & Process ParametersUsability
GoalComprehensiveEfficientInexpensive Practical
R.D.C.
A.D.C.
Tool
Workpiece
Spindle Speed
Feed rate
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Previous Work Traditional vs. Non-Traditional Techniques
Mathematical/Analytical models:
- Kline [1]: Predicted cutting forces and cutter/workpiece deflection
- Sutherland [2]: Determined chip load for surface error prediction
ANN:
- Elanayar [3]: Predicted surface roughness
- El-Mounayri [4]: Predicted cutting forces using feed, speed and axial depth of cut
Generality: Cutting Conditions & Process Parameters
- Oktem [5]: Predicted surface roughness using cut. speed, and ADC and RDC
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Previous Work
Training and Collection of Data
Optimization
Lack of systematic approach
- Oktem [5] used a full factorial DOE to study the effects of cutting parameters on AL end milling
- Ghani [6] performed a three factor full factorial to minimize cutting forces and surface roughness
- Baris [7] investigated the impact of cutting parameters on surface finish using fractional factorial
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 66
Experimental Setup
Data Collection
Optimum Data Set
Training Validation
Trained ANNOptimization
of Cutting Parameters
F & Ra
Process Model
Systematic Approach
DOE HGLInput Parameters
Tool DiameterAxial Depth f Cut
Radial Depth of CutFeed per toothCutting Speed
Overview
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 77
Overview - Summary
Efficient application of BP ANN to model End Milling
Unique Cutting Force and Surface Roughness Model
Simulation of Cutting Force Components
Implementation of Fractional Factorial DOE
Development of a Systematic Approach based on reliability to train the ANN Model
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ExperimentsExperimental Setup for Cutting Force Measurement
3-Component Force Dynamometer
Shielded Connecting cable LabVIEW Application
PC
Charge Amplifier
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Experiments Cont’Surface Profile Measurement
Non contact Profilometer: Proscan 2000
Chromatic SensorRes. 0.1 µm
Measurement of Surface Profile at two levels
L1L2
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 1010
Experimental Setup
Data Collection
Optimum Data Set
Training Validation
Trained ANNOptimization
of Cutting Parameters
F & Ra
Process Model
Systematic Approach
DOE HGLInput Parameters
Tool DiameterAxial Depth f Cut
Radial Depth of CutFeed per toothCutting Speed
Overview
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 1111
Experiments Cont’Cutting Experiments
Control Factors
1. Tool diameter
2. Radial depth of cut
3. Axial depth of cut
4. Feed per tooth
5. Cutting speed
System Responses
1. Cutting Forces
2. Surface Profiles
Cutters:
½” & 1” – 1 flute end mill for AL
→ RUNOUT
Material
AL-7075
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 1212
Experiments Cont’Run Out Effect
Surface Profile using 2 flute cutter[0.2 mm/tooth & 0.5 mm RDC]
0.2 mm
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Experiments Cont’Run Out Effect
Surface Profile using 1 flute cutter[0.4 mm/tooth]
0.2 mm
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Experiments Cont’Cutting Experiments
Control Factors
1. Tool diameter: ½”, 1”
2. Axial depth of cut: 25%, 50%, 75%, 100%
3. Radial depth of cut: 0.5, 2, 4, 6 [mm]
4. Feed per tooth: 0.1, 0.15, 0.2, 0.25 [mm/tooth]
5. Cutting speed: 90, 110, 150 [mm/min]
2 X 3 X 43
384
experiments
Dv
**1000S
π= SNF **FR =
F…feed per tooth
N…# of flutes
S…Spindle Speed
F.R…Feed Rate
v…Cutting Speed
D…Cutter Diameter
S…Spindle Speed
LevelV1 X LevelV5 X Level V23
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Experiments Cont’Cutting Force Measurement
1.27 1.28 1.29 1.3 1.31 1.32 1.33
-250
-200
-150
-100
-50
0
Cutting Forces: Experiment #60: t1a2r1f4v3
Second
Cut
ting
Forc
es [N
ewto
n]
FxFyFz
Force Measurement: Exp# 60:t1=1/2”, a2=50%, r1=0.5mm,
f4=0.25mm/tooth, v3=150mm/min
Force FFT: Exp# 60
20 40 60 80 100 120 140 160 180 2000123
x 107
FFT and Power Spectrum: Experiment#60: t1a2r1f4v3
Forces X
Pow
er
50 100 150 200 2500
5
10
15x 10
5 FFT Forces Y
Pow
er50 100 150 200 250
0
1
2x 10
5 FFT Forces Z
Frequency [Rad/sec]P
ower
62.65 rad/sec3759.6 RPM
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Experiments Cont’Surface Profile Measurement
Surface Profile measured: 1L
Photo using CCD CameraScaling Techniques
[0.25mm/tooth]
Approx.
Distance0.5 1 1.5 2 2.5
-5
-4
-3
-2
-1
0
1
2
3
Surface Profile: Experiment #60: t1a2r1f4v3 Level #1
Distance [mm]
Mic
ron
0.5 mm1 µm
Distance
Rou
ghne
ss
Surface Profile measured: 2L0.5 1 1.5 2 2.5
-4
-3
-2
-1
0
1
2
3
Surface Profile: Experiment #60:t1a2r1f4v3 Level #2
Distance mm
Mic
ron
0.5 mm
1 µm
Rou
ghne
ss
Distance
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 1717
Experimental Setup
Data Collection
Optimum Data Set
Training Validation
Trained ANNOptimization
of Cutting Parameters
F & Ra
Process Model
Systematic Approach
DOE HGLInput Parameters
Tool DiameterAxial Depth f Cut
Radial Depth of CutFeed per toothCutting Speed
Overview
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 1818
ANN End Milling ModelBack Propagation Artificial Neural Network: (BP ANN)
BP ANN General Topology
Feed-Forward Phase
Processing Element “PE”Architecture
∑==
n
iiijj IWa
0
)( jl
j aSFY = Yj…Predicted output
SF…Squashing FunctionBack-Propagation Phase
2)(21
jjj Yte −=
IJJJWW T
Told
ijnew
ij ⋅+⋅
−= ⋅
⋅
µδ
E = (e1,…, ej,…ek )
Adaptation: Levenberg-Marquardt
Aj…information
W…Weight
I…Input vector
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Experimental Data for Training and Validation
Full Factorial
Experimental Data 384 experiments
75% Training Set (288 exp.)
25% Validation Set (96 exp.)
Data Preprocessing
Cutting Forces: (each component)
1. Amplitude: “Amp”
2. Mean: “Mean”
3. Standard Deviation: “Std”
4. Period (Avg.): “Period”
0 2000 4000 6000 8000 10000 12000 14000-400
-300
-200
-100
0
100
200
300
400
Reading #
Forc
es [N
]
Cutting Forces Fx: Exp#112: t1a3r2f2v1
0 1000 2000 3000 4000 5000 6000-450
-400
-350
-300
-250
-200
-150
-100
-50
0
50
Reading #
Forc
es [N
]
Cutting Forces Fy: Exp.#80: t1a2r3f3v2
Raw DataAdjusted Data
ANN End Milling Model
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Experimental Data for Training and Validation (Cont’)
Surface Profiles
1. Surface Roughness: “Ra”
2. Feed Marks: “FeedM”
n
yRa
n
ii∑
= =1
86 86.5 87 87.5 88 88.5 89-5
0
5
10
15
20
25
Position [mm]
Sur
face
Rou
ghne
ss -
Hei
ght [
10-6
m]
Surface Profile: Exp. #80: t1a2r3f3v2
Raw Data2nd order Pol.Adjusted DataFiltered Data
ANN End Milling Model
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Experimental Data for Training and Validation (Cont’)
Normalization minmin)max(
min)max(*min)( NRR
NNRRN +−
−−=
ANN End Milling Model
Topology: End Milling ANN model
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Validation Results
0.976035.58Feed Marks
0.4732832.59Ra
0.994846.11Period
0.986969.23Std
0.9848110.43Mean
0.988118.50Amp
Fz
0.995337.38Std
0.991408.72Mean
0.991618.32Amp
Fy
0.992738.53Std
0.9901912.78Mean
0.991538.54AmpFx
R valueAvg. Error ej [%]Output Variable
0 10 20 30 40 50 60 70 80 90 1000
500
1000
1500
2000
2500
3000
Experiment Indices in Testing Set
Forc
e [N
]
Measured vs. Simulated Amplitude Fx in Testing
Error [%] = 8.5422
MeasuredSimulated
Amplitude Fx
ANN End Milling Model
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 2323
Experimental Setup
Data Collection
Optimum Data Set
Training Validation
Trained ANNOptimization
of Cutting Parameters
F & Ra
Process Model
Systematic Approach
DOE HGLInput Parameters
Tool DiameterAxial Depth f Cut
Radial Depth of CutFeed per toothCutting Speed
Overview
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 2424
DOE for Optimal Data Sets
Design of Experiments (DOE)
Process of planning the experiments appropriate data
Full Factorial 2 X 3 X 43 = 384 experiments
Screening methodInvestigate effects on the responsesMore efficient High amount of experiments c2
c1
b2
b1a2a1
C
B
A
Full Factorial 2 level DOE: Design Factors: A, B, C
Full Factorial 2k-level DOE
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Fractional Factorials
Number of design factors is high
Provides efficient exploration of space – Process behavior
Experimental constraints
Three key ideas:
• Sparsity of effects principle
• Projection property
• Sequential experimentation
DOE for Optimal Data Sets
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Hyper Greco Latin DOE (HGL DOE)
Balanced and orthogonal DOETabular grid “p x p”, p being the # of levelsThree Latin Squares superimposedEach level occurs once and only once in each row/column
Factor: X
CBAD4
BADC3
ADCB2
DCBA1
Factor: Y4321
• Additive model• Effect model
Latin Square Design
DOE for Optimal Data Sets
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Hyper Greco Latin DOE (HGL DOE) (Cont’)
4-level 5 design factor DOE: 16 vs. 45 runs (1024 experiments)
Factor: UA β 3B α 4C δ 1D γ 24B γ 1A δ 2D α 3C β 43C α 2D β 1A γ 4B δ 32D δ 4C γ 3B β 2A α 11
Factor: V4321
What if the design is mixed?
2 X 3 X 43
DOE for Optimal Data Sets
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 2828
Hyper Greco Latin DOE (HGL DOE): Layout Rules
Rules:1. Column Axial depth of cut 2. Row Radial depth of cut3. Latin letter Feed per tooth 4. Greek letters Cutting speed5. Numbers Tool Diameter 6. Greek letter equal 0: no fraction7. Number 1-3, 2-4 are same levels 8. Random definition of levels
Radial Depth of Cut
A β 1B α 2C δ 1D γ 24B γ 1A δ 2D α 1C β 23C α 2D β 1A γ 2B δ 12D δ 2C γ 1B β 2A α 11
Axial Depth of Cut4321
DOE for Optimal Data Sets
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 2929
Hyper Greco Latin DOE (HGL DOE): Sample Fraction
Cutter diameter: t = 25.4*[0.5 1.0] = [1, 2]Axial depth of cut: a = [0.25 0.5 0.75 1.0] = [1, 2, 3, 4] Radial depth of cut: r = [0.5 2.0 4.0 6.0] = [1, 2, 3, 4]Feed per tooth: f = [0.1 0.15 0.2 0.25] = [A, B, C, D] Cutting speed: v = [0 90 110 150] = [α, β, γ, δ]
1100.20.50.7512.72
900.150.50.525.41
Cutting Speed
Feed per tooth
Radial depth of
cut
Axial depth of cut
Cutter DiameterExp. #
D δ 2C γ 1B β 2A α 11
Axial Depth of Cut4321
DOE for Optimal Data Sets
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 3030
Hyper Greco Latin DOE (HGL DOE): Sample Fraction
900.16112.712
1500.260.512.711
1100.2560.2525.410
1100.154112.79
1500.140.7525.48
900.240.2525.47
900.2520.7512.76
1100.120.525.45
1500.1520.2512.74
1500.250.5125.43
1100.20.50.7512.72
900.150.50.525.41
Cutting SpeedFeed per tooth
Radial depth of cut
Axial depth of cut
Cutter DiameterExperiment #
DOE for Optimal Data Sets
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 3131
Fractional Factorial Back Propagation ANNIdentify optimal fraction sets to successfully train the modelFull Factorial as a benchmark
DOE for Optimal Data Sets
Topology: End Milling ANN model
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 3232
Fractional Factorial Back Propagation ANN
Results: Validation (Overall E)
Fraction Performance Comparison
%100*
)(1
nt
Yt
e
n
iji
jiji
j
∑−
==
%100*12
12
1∑
== jje
E
1510.5522-22-22288 F. F.
1312.1327 - 27252
3612.5426 - 26240
1312.7326 - 26 228
2412.9523 - 23216
1512.9223 - 23204
3113.1922 - 22192
3112.9920 - 20180
2414.1220 - 20168
6213.1218 - 18156
5415.8619 - 19144
2416.3618 - 18132
2117.1218 - 18120
2523.516 - 1696
EpochsE [%]# PE per Hidden Layers# of runs
DOE for Optimal Data Sets
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 3333
Validation Results: Fraction of 156 exp.
0.9726.23Feed Marks
0.54244.98Ra
0.99710.95Period
0.99014.95Std
0.98616.21Mean
0.98911.36AmpFz
0.9938.03Std
0.98714.21Mean
0.9909.21Amp
Fy
0.9949.26Std
0.99212.61Mean
0.9939.03Amp
Fx
R valueAvg.Error ej
[%]
Output Variable
0 50 100 150 200 2500
500
1000
1500
2000
2500
3000
Experiment Indices in Testing Set
Forc
e [N
]
Measured vs. Simulated Amplitude Fx in Testing
Error [%] = 9.031
MeasuredSimulated
Amplitude Fx
DOE for Optimal Data Sets
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 3434
How do we know the selected fraction is the optimum set to train and validate the ANN?
Is the fraction set capable to fully represent the end milling process behavior?
Statistical DOE Validation Approach
• Determine best DOE fraction to be statistically comparable to the full factorial fraction
“Process Response Distributions”
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 3535
Probability Density Function “PDF”: (Fraction of 96 experiments)
0 260.9 575.4 889.8 1204.3 1518.7 1833.2 2147.60
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
Amplitude of Forces in X direction 'Fx'
Freq
uenc
y 'N
(t)'
Frequency distribution of Fx
2625
19
12
6 5
3
Delta(t)=260.9
t1 t2 t3 t4 t5 t6 t7 200 400 600 800 1000 1200 1400 1600 1800 2000 22000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1x 10-3
Force [N]
Pro
babi
lity
Den
sity
Fun
ctio
n (p
df)
Data Distribution "pdf" of Amplitude of Force in X Direction
96 exps
PDFFrequency Distribution at t = 7
Statistical DOE Validation Approach
tNttCumNtCumNtfpdf
∆∆−−
==*
)()()(
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 3636
PDF of the End Milling Process
0 500 1000 1500 2000 25000
0.2
0.4
0.6
0.8
1
1.2
1.4x 10-3
Forces [N]
Pro
babi
lity
Den
sity
Fun
ctio
n (p
df)
Data Distribution of Amplitude Force in X direction
12 exps24 exps36 exps48 exps60 exps72 expsFull Factorial
0 500 1000 1500 2000 25000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1x 10-3
Forces [N]
Pro
babi
lity
Den
sity
Fun
ctio
n (p
df)
Data Distribution of Amplitude Force in X direction
84 exps96 exps108 exps120 exps132 exps144 expsFull Factorial
0 500 1000 1500 2000 25000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1x 10-3
Forces [N]
Pro
babi
lity
Den
sity
Fun
ctio
n (p
df)
Data Distribution of Amplitude Force in X direction
156 exps168 exps180 exps192 exps204 exps216 expsFull Factorial
Amplitude Fx
Experimental fraction size increases
Statistical DOE Validation Approach
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 3737
PDF of the End Milling Process
0.2 0.4 0.6 0.8 1 1.2 1.4 1.60
0.5
1
1.5
2
2.5
3
Ra
Pro
babi
lity
Den
sity
Fun
ctio
n (p
df)
Data Distribution of Surface Rouhgness
12 exps24 exps36 exps48 exps60 exps72 expsFull Factorial
0.2 0.4 0.6 0.8 1 1.2 1.4 1.60
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Ra
Pro
babi
lity
Den
sity
Fun
ctio
n (p
df)
Data Distribution of Surface Rouhgness
84 exps96 exps108 exps120 exps132 exps144 expsFull Factorial
0.2 0.4 0.6 0.8 1 1.2 1.4 1.60
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Ra
Pro
babi
lity
Den
sity
Fun
ctio
n (p
df)
Data Distribution of Surface Rouhgness
156 exps168 exps180 exps192 exps204 exps216 expsFull Factorial
Surface Roughness
Statistical DOE Validation Approach
Experimental fraction size increases
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 3838
Chi-Square Goodness of Fit Test: Distribution Comparison
∑=
−=
−++
−+
−=
k
j j
jj
k
kk
eeo
eeo
eeo
eeo
1
22
2
222
1
2112 )()(
...)()(χ
Comparison between two distributions:1: Observed (o) 2: Expected (e)
95% confidence level
(χ2) ≤ (χ2)1-α,f1−−= mkf
Statistical DOE Validation Approach
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 3939
Distribution Comparison: Fraction vs. Full Factorial Fraction
10.841812.1618
18.861720.7617
21.571626.2116
27.701438.8214
36.131254.2412
57.98983.309
80.207105.257
102.275132.975
126.333159.843
152.941
Ra(χ2)0.95.5=11.1
192.791
Amp Fx(χ2)0.95.6=12.6
χ2Observed Fractionf = 5χ2Observed
Fractionf = 6
Statistical DOE Validation Approach
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0 500 1000 1500 2000 25000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1x 10-3
Force [N]
Pro
babi
lity
Den
sity
Fun
ctio
n (p
df)
Data Distribution of Amplitude of Force in X direction
18th FractionFull Factorial
0.2 0.4 0.6 0.8 1 1.2 1.4 1.60
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Ra
Pro
babi
lity
Den
sity
Fun
ctio
n (p
df)
Data Distribution of Surface Roughness
18th FractionFull Factorial
Distribution Comparison: 18th vs. Full Factorial Fractions
Amplitude Fx Surface Roughness
Statistical DOE Validation Approach
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 4141
Experimental Setup
Data Collection
Optimum Data Set
Training Validation
Trained ANNOptimization
of Cutting Parameters
F & Ra
Process Model
Systematic Approach
DOE HGLInput Parameters
Tool DiameterAxial Depth f Cut
Radial Depth of CutFeed per toothCutting Speed
Overview
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 4242
Basic Idea
Systematic Approach for Optimizing the Modeling
1. Assume the End Milling Process is reliable (based on the definition of Reliability shown below)
2. Determine the Law Probability Distribution of the process (i.e. distribution of the process parameters)
3. Track the distributions of the data set
4. Identify the minimum set as the data set with distribution that fits closely the process distribution as determined in step 2.
Definition of Reliability:
Probability that a system will adequately perform under stated environmental conditions for a specific time.
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 4343
Law Probability Distributions considered
β
θβ
θθβ ⎟
⎠⎞
⎜⎝⎛−
−
⎟⎠⎞
⎜⎝⎛=
tyt
t ey
ypdf1
)(
⎟⎠⎞
⎜⎝⎛−
= θ
θ
ty
t eypdf 1)(
( ) tyrtt ey
rypdf µµµ −−
Γ= 1
)()(
Weibull
Exponential
Gamma
Systematic Approach for Optimizing the Modeling
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 4444
Fitting Process Parameters to a Law Probability Distribution
600 800 1000 1200 1400 1600 1800 2000 2200 24000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1x 10-3
Force [N]
Pro
babi
lity
Den
sity
Fun
ctio
n (p
df)
Data Distribution Fitting of Amplitude Fx
Response pdfFull FactorialExponential pdfWeibull pdfGamma pdf
200 300 400 500 600 700 8000
0.5
1
1.5
2
2.5
3x 10-3
Force [N]
Pro
babi
lity
Den
sity
Fun
ctio
n (p
df)
Data Distribution Fitting of Std Fx
Response pdfFull FactorialExponential pdfWeibull pdfGamma pdf
Amplitude Fx Standard Deviation Fx
Systematic Approach for Optimizing the Modeling
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 4545
400 500 600 700 800 900 1000 1100 12000
0.5
1
1.5x 10-3
Force [N]
Pro
babi
lity
Den
sity
Fun
ctio
n (p
df)
Data Distribution Fitting of Amplitude Fy
Response pdfFull FactorialExponential pdfWeibull pdfGamma pdf
80 100 120 140 160 180 200 220 240 260 2800
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10-3
Force [N]
Pro
babi
lity
Den
sity
Fun
ctio
n (p
df)
Data Distribution Fitting of Mean Fy
Response pdfFull FactorialExponential pdfWeibull pdfGamma pdf
Amplitude Fy Standard Deviation Fy
Fitting Process Parameters to a Law Probability Distribution
Systematic Approach for Optimizing the Modeling
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 4646
200 300 400 500 600 700 8000
0.5
1
1.5
2
2.5x 10-3
Force [N]
Pro
babi
lity
Den
sity
Fun
ctio
n (p
df)
Data Distribution Fitting of Amplitude Fz
Response pdfFull FactorialExponential pdfWeibull pdfGamma pdf
50 100 150 200 250 3000
1
2
3
4
5
6
7x 10-3
Force [N]
Pro
babi
lity
Den
sity
Fun
ctio
n (p
df)
Data Distribution Fitting of Std Fz
Response pdfFull FactorialExponential pdfWeibull pdfGamma pdf
Amplitude Fz Standard Deviation Fz
Fitting Process Parameters to a Law Probability Distribution
Systematic Approach for Optimizing the Modeling
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 4747
36.2647.5010.9314.17Std Fz
43.3055.5013.9514.17Mean Fz
21.8631.787.6514.17Amp. Fz
40.6653.4910.7311.15Std Fy
51.7164.9223.7611.15Mean Fy
37.5649.5812.6711.15Amp. Fy
20.3730.283.9414.17Std Fx
41.0252.6314.0214.17Mean Fx
17.1026.094.8214.17Amp. Fx
GammaWeibullExponential
χ2
χ21-α,f
Degrees of freedom
“f”Response
End Milling Reliability Analysis: Distribution Comparisons
Chi-Square test
95% Confidence Level
Systematic Approach for Optimizing the Modeling
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 4848
Identifying Optimum Fraction
600 800 1000 1200 1400 1600 1800 2000 2200 24000
0.2
0.4
0.6
0.8
1
1.2
1.4x 10-3
Force [N]
Pro
babi
lity
Den
sity
Fun
ctio
n (p
df)
Systematic Approach to find the optimun fraction
Frac #1: ActualFrac #1: ExpFrac #2: ActualFrac #2: ExpFrac #6: ActualFrac #6: ExpFrac #10: ActualFrac #10: Exp
Systematic Approach for Optimizing the Modeling
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 4949
600 800 1000 1200 1400 1600 1800 2000 2200 24000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1x 10-3
Force [N]
Pro
babi
lity
Den
sity
Fun
ctio
n (p
df)
Systematic Approach to find the optimun fraction
Frac #12: ActualFrac #12: ExpFrac #15: ActualFrac #15: ExpFrac #17: ActualFrac #17: ExpFrac #18: ActualFrac #18: Exp
Identifying Optimum Fraction
Systematic Approach for Optimizing the Modeling
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 5050
ResultsFull Factorial ANN:
Extended end milling ANN model (Force + Ra)Training and validation successfully completed. R > 0.9. Improvement with respect to literature. 32% vs. (20% and 53%) (only Ra)
DOE for Optimal Data Sets & Validation
HGL DOE: efficient method of selecting fractions (balanced/orthogonal) Validation 13th fraction: E = 13.12% (Compromise: accuracy, cost and time)End milling behavior captured progressively
Systematic approach for optimizing process modeling
End milling: statistical similarity behavior to exponential distribution (95%)Selection of the optimum fraction can be systematizedSimilar correlation found using AL6061
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 5151
ConclusionsDevelopment of an efficient and accurate predictive end milling model
• Prediction of cutting force and surface roughness• Reconstruction of force signal components
Implementation of DOE techniques: HGL • Optimization of the data collection process• More design factor levels / orthogonal & balanced experiments
Systematization of the optimum fraction data set selection• Exponential behavior: Chi-Square test + 95% confidence level
Proposed technique is applicable for machining other material types.
Extensive collection of accurate data
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 5252
Future Work
Extension of the ANN: (Attractive for implementation in industry)• Cutting Parameters: # of cutting flutes, tool geometry• Similar cutting tools: ball end mill, taper end mill
Incorporation of additional process responses (development of self monitoring and control systems)• Flatness, chatter, tool wear
Integration of dynamic effects: • Cutter/workpiece deflection and runout
Extension of the reliability analysis:• Tool/workpiece material and end milling cutter types
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 5353
AcknowledgementAcknowledgement
Hazim El-Mounayri, Advisor, ME department, IUPUI
Committee Members, ME department, IUPUI
Behnam Imani and Affan Badar
School of Dentistry, Oral Health Research Institute
Colleagues from the AEML, ME department, IUPUI
Family members
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 5454
ReferencesReferences1. Kline, W. A., DeVor, R. E., and Shareef, I. A., “The prediction of surface accuracy in end milling,”
Journal of Engineering for Industry, Vol. 104, 1982, pp. 272-279.
2. Sutherland, J., and DeVor, R. E., “An improved method for cutting force and surface error prediction in flexible end milling system,” Journal of Engineering for Industry, Vol. 108, 1986, pp. 269-279.
3. Elanayar, S. and Shin, Y. C., “Design and implementation of tool wear monitoring with radial basis function neural networks,” Proceedings of the American Control Conference, Part 3, 1995, pp. 1722 - 1726
4. El-Mounayri, H. and Tandon, V., “An AI-based model for predicting instantaneous cutting force in end milling,” 2002 ASME International Mechanical Engineering Congress & Exposition, 2002
5. Oktem, H., Erzurumlu, T., and Erzincanli, F., “Prediction of minimum surface roughness in end milling mold parts using neural network and genetic algorithm,” Journal of Materials and Design, Vol. 27, 2006, pp. 735-744.
6. Ghani, J.A., Choudhury I.A., and Hassan, H.H., “Application of Taguchi method in the optimization of end milling parameters,” Journal of Materials Processing Technology, 2004, Vol. 145, pp. 84-92.
7. Baris, K., Investigation of the Impact of Cutting Parameters on Surface Finish for a Discontinuous Machining Process, Master’s Thesis, School of Industrial Engineering, University of Tennessee, Knoxville, 2004
Gustavo Augusto RengifoThesis Presentation
Advisor: Dr Hazim ElAdvisor: Dr Hazim El--MounayriMounayri
Advanced Engineering Manufacturing Laboratory (AEML)Advanced Engineering Manufacturing Laboratory (AEML)Mechanical Engineering DepartmentMechanical Engineering Department
Purdue School of Engineering & Technology, IUPUIPurdue School of Engineering & Technology, IUPUI
April 13April 13thth, 2007, 2007
Question SessionQuestion Session
Gustavo Augusto RengifoThesis Presentation
Advisor: Dr Hazim ElAdvisor: Dr Hazim El--MounayriMounayri
Advanced Engineering Manufacturing Laboratory (AEML)Advanced Engineering Manufacturing Laboratory (AEML)Mechanical Engineering DepartmentMechanical Engineering Department
Purdue School of Engineering & Technology, IUPUIPurdue School of Engineering & Technology, IUPUI
April 13April 13thth, 2007, 2007
Thanks!!!Thanks!!!
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 5757
EXTRA!!!!
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 5858
Training Results
%100*288
)(288
1∑
−
==i
ji
jiji
j
tYt
e
0.987574.21Feed Marks
0.999551.45Ra
0.998931.54Period
0.999963.82Std
0.999076.78Mean
0.998943.78Amp
Fz
0.999222.87Std
0.998375.84Mean
0.998473.29Amp
Fy
0.999443.38Std
0.998966.38Mean
0.999283.18Amp
Fx
R valueAvg. Error ej [%]Output Variable
ANN End Milling Model
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 5959
Training Results (Cont’)
0 50 100 150 200 250 3000
500
1000
1500
2000
2500
Experiment Indices in Training Set
Forc
e [N
]
Measured vs. Simulated Amplitude Fx in Training
Error [%] = 3.1783
MeasuredSimulated
0 50 100 150 200 250
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Experiment Indices in Training Set
Sur
face
Rou
ghne
ss [1
0- 6 m
]
Measured vs. Simulated Surface Roughness Ra in Training
Error [%] = 1.4486 Measured
Simulated
Amplitude Fx Surface Roughness
ANN End Milling Model
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 6060
Validation Results (Cont’)
0 10 20 30 40 50 60 70 80 90 100-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
Experiment Indices in Testing Set
Sur
face
Rou
ghne
ss [1
0- 6 m
]
Measured vs. Simulated Surface Roughness Ra in Testing
Error [%] = 32.5918
MeasuredSimulated
0 10 20 30 40 50 60 70 80 90 100
0.1
0.15
0.2
0.25
Experiment Indices in Testing Set
Feed
per
toot
h [m
m/to
oth]
Measured vs. Simulated Feed Marks Testing
Error [%] = 5.5818
MeasuredSimulated
Surface Roughness Feed Marks
ANN End Milling Model
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 6161
Training Results: Fraction of 156 exp.
0.9993.99Feed Marks
0.9990.63Ra
0.9991.38Period
0.9993.91Std
0.9996.86Mean
0.9993.87Amp
Fz
0.9992.60Std
0.9987.34Mean
0.9983.30Amp
Fy
0.9993.20Std
0.9996.61Mean
0.9993.43AmpFx
R valueAvg.Error ej [%]
Output Variable
0 20 40 60 80 100 120 140 1600
500
1000
1500
2000
2500
Experiment Indices in Training Set
Forc
e [N
]
Measured vs. Simulated Amplitude Fx in Training
Error [%] = 3.4323MeasuredSimulated
Amplitude Fx
DOE for Optimal Data Sets
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 6262
Training Results: Fraction of 156 exp. (Cont’)
0 20 40 60 80 100 120 140 1600
0.5
1
1.5
Experiment Indices in Training Set
Sur
face
Rou
ghne
ss [1
0- 6 m
]
Measured vs. Simulated Surface Roughness Ra in Training
Error [%] = 0.63207MeasuredSimulated
0 20 40 60 80 100 120 140 1600.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
Experiment Indices in Training SetFe
ed p
er to
oth
[mm
/toot
h]
Measured vs. Simulated Feed Marks in Training
Error [%] = 3.9864Measured
Simulated
Surface Roughness Feed Marks
DOE for Optimal Data Sets
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 6363
Validation Results: Fraction of 156 exp. (Cont’)
0 50 100 150 200 250-0.5
0
0.5
1
1.5
2
2.5
3
3.5
Experiment Indices in Testing Set
Sur
face
Rou
ghne
ss [1
0- 6 m
]
Measured vs. Simulated Surface Roughness Ra in Testing
Error [%] = 44.9807
MeasuredSimulated
0 50 100 150 200 2500.05
0.1
0.15
0.2
0.25
0.3
Experiment Indices in Testing SetFe
ed p
er to
oth
[mm
/toot
h]
Measured vs. Simulated Feed Marks in Testing
Error [%] = 6.2295
MeasuredSimulated
Surface Roughness Feed Marks
DOE for Optimal Data Sets
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 6464
Reliability:
Probability that a system will adequately perform under stated environmental conditions for a specific time.
Reliability, operational reliability, inherent reliability, probability of survival
Probability of failure
)()( tFtTP =≤ 0≥t
)()(1)( tTPtFtR >=−=
Statistical DOE Validation Approach
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 6565
Probability Density Function “PDF”
∫∫∞
=−=−=t
tdfdftFtR ττττ )()(1)(1)(
0
tNttCumNtCumNtfpdf
∆∆−−
==*
)()()(
tNttNtNtfpdf
∆∆+−
==*
)()()(
Statistical DOE Validation Approach
7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 6666
0.4718170.781817
0.5517160.751716
1.0411101.471110
1.48982.0598
1.73872.6087
13.27761.7276
1.58542.4454
3.354316.1743
2.82324.8932
6.0821
Ra(χ2)0.95.5=11.1
-21
Amp Fx(χ2)0.95,6=12.6
χ2Exp. F.Obs. Ff = 5χ2Exp. F.Obs. Ff = 6
Distribution comparison between consecutive fractions
Statistical DOE Validation Approach