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![Page 1: Fast Discovery of the Best Designs - AES Home · Fast Discovery of the Best Designs November 2004 Random Number Generation ... Excel and the equations: ... Ackerman Steering Mechanism.](https://reader031.fdocuments.us/reader031/viewer/2022022017/5b8378cb7f8b9a7d3a8ce472/html5/thumbnails/1.jpg)
Fast Discovery of the Best Designs November 2004
byAndreas Vlahinos, Ph.D.
Principal,Advanced Engineering Solutions, LLC
4547 N. Lariat Dr., Castle Rock, CO 80104Phone: 303-814-0455; email: [email protected]
www.aes.nu
Fast Discovery of the Best Designs
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Fast Discovery of the Best Designs November 2004
Learning Outcomes
• Understand the basics of designed experiments and robust design
• Enable designs to be driven by their product specifications
• Know how to use simple graphical techniques to analyze multi-objective study data
• Perform automated design space exploration• Optimize automatically the design for a set of
performance attributes• Design for Six-sigma quality levels
![Page 3: Fast Discovery of the Best Designs - AES Home · Fast Discovery of the Best Designs November 2004 Random Number Generation ... Excel and the equations: ... Ackerman Steering Mechanism.](https://reader031.fdocuments.us/reader031/viewer/2022022017/5b8378cb7f8b9a7d3a8ce472/html5/thumbnails/3.jpg)
Fast Discovery of the Best Designs November 2004
Application Activity # 1
Identification of the most influentialPro/E parameters (DOE)
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Fast Discovery of the Best Designs November 2004
Application activity #1:Identification of the most influential Pro/E parameters
• Problem Statement:Using 2 level 3 factor design of experiments determine the Pro/E parameters W, H, t that are the most influential on the performance attribute(Ixx/A) for the aluminum extruded section shown.
where:
80 < W < 120160 < H < 2404 < t < 6
• Learning Goals:– Understanding the fundamentals
of Designs Of Experiments
![Page 5: Fast Discovery of the Best Designs - AES Home · Fast Discovery of the Best Designs November 2004 Random Number Generation ... Excel and the equations: ... Ackerman Steering Mechanism.](https://reader031.fdocuments.us/reader031/viewer/2022022017/5b8378cb7f8b9a7d3a8ce472/html5/thumbnails/5.jpg)
Fast Discovery of the Best Designs November 2004
Design Exploration for Full Factorial,2 level - 3 factor design
-1
0
1
-1
0
1
-1
0
1
W
Normalized Design Space
H
t
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Fast Discovery of the Best Designs November 2004
Multi-Objective Design Study – Full Factorial
![Page 7: Fast Discovery of the Best Designs - AES Home · Fast Discovery of the Best Designs November 2004 Random Number Generation ... Excel and the equations: ... Ackerman Steering Mechanism.](https://reader031.fdocuments.us/reader031/viewer/2022022017/5b8378cb7f8b9a7d3a8ce472/html5/thumbnails/7.jpg)
Fast Discovery of the Best Designs November 2004
Response Table for Three-factor Experiment
min 80 max 120 min 160 max 240 min 4 max 6
1 R1 R1 R1 R1
2 R2 R2 R2 R2
3 R3 R3 R3 R3
4 R4 R4 R4 R4
5 R5 R5 R5 R5
6 R6 R6 R6 R6
7 R7 R7 R7 R7
8 R8 R8 R8 R8
AVERAGE R W1 W2 H1 H2 t1 t2
t (thickness)
EFFECT W2-W1 H2-H1 t2-t1
Experiment Number
Response Value
W (Width) H (Height)
![Page 8: Fast Discovery of the Best Designs - AES Home · Fast Discovery of the Best Designs November 2004 Random Number Generation ... Excel and the equations: ... Ackerman Steering Mechanism.](https://reader031.fdocuments.us/reader031/viewer/2022022017/5b8378cb7f8b9a7d3a8ce472/html5/thumbnails/8.jpg)
Fast Discovery of the Best Designs November 2004
Response Table for Three-factor Experiment
min 80 max 120 min 160 max 240 min 4 max 6
1 2558 2558 2558 2558
2 2527 2527 2527 2527
3 5598 5598 5598 5598
4 5555 5555 5555 5555
5 2636 2636 2636 2636
6 2700 2700 2700 2700
7 5976 5976 5976 5976
8 5927 5927 5927 5927
AVERAGE 4184.6 4059.5 4309.8 2605.3 5764.0 4192.0 4177.3
Experiment Number
250.25 3158.75 -14.75EFFECT
W (Width) H (Height) t (thickness)Response Value
![Page 9: Fast Discovery of the Best Designs - AES Home · Fast Discovery of the Best Designs November 2004 Random Number Generation ... Excel and the equations: ... Ackerman Steering Mechanism.](https://reader031.fdocuments.us/reader031/viewer/2022022017/5b8378cb7f8b9a7d3a8ce472/html5/thumbnails/9.jpg)
Fast Discovery of the Best Designs November 2004
Graphical Representation of Main Effects
1 2 32500
3000
3500
4000
4500
5000
5500
6000
Parameter
Res
pons
e V
alue
Graphical Representation of main effects
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Fast Discovery of the Best Designs November 2004
Automatic Design Exploration
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Fast Discovery of the Best Designs November 2004
Scatter Plot for two of Design Variables
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Fast Discovery of the Best Designs November 2004
Scatter Plot of Ixx versus Area
cost
![Page 13: Fast Discovery of the Best Designs - AES Home · Fast Discovery of the Best Designs November 2004 Random Number Generation ... Excel and the equations: ... Ackerman Steering Mechanism.](https://reader031.fdocuments.us/reader031/viewer/2022022017/5b8378cb7f8b9a7d3a8ce472/html5/thumbnails/13.jpg)
Fast Discovery of the Best Designs November 2004
Application activity # 2
Minimum Cost Container
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Fast Discovery of the Best Designs November 2004
Application activity # 6Minimum Cost Container
Problem Statement:Consider the open top circular storage bin container
shown. Choose the height h, the width d, and the slope θ such that the bin holds a prescribed volume V = 10 m3 and it is of a minimum cost. The cost of the base per unit area is C1=1.00 $/m2 and the cost of the side per unit area is C2 =1.50 $/m2
BMX Learning Goals:– Create an optimization study that holds a prescribed
value constant and minimizes a cost function.
![Page 15: Fast Discovery of the Best Designs - AES Home · Fast Discovery of the Best Designs November 2004 Random Number Generation ... Excel and the equations: ... Ackerman Steering Mechanism.](https://reader031.fdocuments.us/reader031/viewer/2022022017/5b8378cb7f8b9a7d3a8ce472/html5/thumbnails/15.jpg)
Fast Discovery of the Best Designs November 2004
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Fast Discovery of the Best Designs November 2004
Volume, Area and Cost Analyses Features
• Insert a model analysis feature to compute the volume
• Insert a measure analysis feature to compute the base area
• Insert a measure analysis feature to compute the side area
• Insert a Relation Analysis Feature to compute the cost:cost=1.00*AREA:FID_BASE_AREA+1.5*AREA:FID_SIDE_AREA
![Page 17: Fast Discovery of the Best Designs - AES Home · Fast Discovery of the Best Designs November 2004 Random Number Generation ... Excel and the equations: ... Ackerman Steering Mechanism.](https://reader031.fdocuments.us/reader031/viewer/2022022017/5b8378cb7f8b9a7d3a8ce472/html5/thumbnails/17.jpg)
Fast Discovery of the Best Designs November 2004
Optimization of storage container
• Goal:– Minimize cost
• Constraints:– Volume = 10
• Design Variables:– 0.5 < RADIUS < 3– 0.5 , HEIGHT < 3– 10 < ANGLE < 90
• Optimum Solution:– RADIUS = 1.63– HEIGHT = 0.50– ANGLE = 53.35
![Page 18: Fast Discovery of the Best Designs - AES Home · Fast Discovery of the Best Designs November 2004 Random Number Generation ... Excel and the equations: ... Ackerman Steering Mechanism.](https://reader031.fdocuments.us/reader031/viewer/2022022017/5b8378cb7f8b9a7d3a8ce472/html5/thumbnails/18.jpg)
Fast Discovery of the Best Designs November 2004
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Fast Discovery of the Best Designs November 2004
Application activity # 3Cell Phone speaker - Spacing Sensitivity
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Fast Discovery of the Best Designs November 2004
Spacing Sensitivity on Area Ratio
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Fast Discovery of the Best Designs November 2004
Robust Design Using Multi Objective Design Study
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Fast Discovery of the Best Designs November 2004
Random Number Generation
• Random numbers for common distributions can be obtained using Box-Muller method in Excel and the equations:– Standard Normal Distribution – Xi= µ+σ*Rn– Where:
• Rn = √(-2*ln(Ru) * cos(2πRu)• Ru a uniform random number generator • In Excel =SQRT(-2*LN(RAND()))*COS(2*PI()*RAND())
– Distribution of 10,000 random input variables generated in Excelwith a mean of 10 and standard deviation of 2
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Fast Discovery of the Best Designs November 2004
Random spacing Input and Area Ratio Output
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Fast Discovery of the Best Designs November 2004
Application activity # 4BMX - Pro/MECHANICA Integration
• Set up an analysis in Pro/MECHANICA,
• Set up a BMX Analysis feature.– tag the list of quantified
results from the Mechanicaanalysis as a computed parameter.
• Use these computed parameters for relations, Sensitivity, Global Optimization and Multi-Objective Design Studies.
![Page 25: Fast Discovery of the Best Designs - AES Home · Fast Discovery of the Best Designs November 2004 Random Number Generation ... Excel and the equations: ... Ackerman Steering Mechanism.](https://reader031.fdocuments.us/reader031/viewer/2022022017/5b8378cb7f8b9a7d3a8ce472/html5/thumbnails/25.jpg)
Fast Discovery of the Best Designs November 2004
Set up an analysis in Pro/MECHANICA
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Fast Discovery of the Best Designs November 2004
Tag the list of quantified results from the Mechanica analysis as a computed parameter
• .
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Fast Discovery of the Best Designs November 2004
Sensitivity of Rib’s length on Max Displacement
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Fast Discovery of the Best Designs November 2004
Sensitivity of Rib’s length on Max stress
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Fast Discovery of the Best Designs November 2004
BMX-Modal analysis
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Fast Discovery of the Best Designs November 2004
Sensitivity of Hole Diameter on Natural Frequency
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Fast Discovery of the Best Designs November 2004
Application activity # 5
Mechanism Optimization
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Fast Discovery of the Best Designs November 2004
Ackerman Steering Optimization
Find optimum Ackerman angle that minimizes the steering error
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Fast Discovery of the Best Designs November 2004
Ackerman Steering Mechanism
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Fast Discovery of the Best Designs November 2004
Ackerman Steering Optimization
• Assumptions:– Low speed steering is achieved by pure rolling of
wheels– For low speed the slip angles are negligible small
• Goals:– Identify the instantaneous center of rotation– Establish measures for the steering error– Plot the steering error versus time for a given
Ackerman angle– Using Behavioral Modeling plot the maximum
steering error versus the Ackerman angle– Find the optimum Ackerman angle that minimizes the
steering error
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Fast Discovery of the Best Designs November 2004
Steering error versus time for Ackerman angle = 16 deg
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Fast Discovery of the Best Designs November 2004
Create a Vision,Adopt it,
Adapt to Achieve it
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Fast Discovery of the Best Designs November 2004