Post on 29-Dec-2015
Robust DesignIntegrated Product and Process Development
MeEn 475/476
“Great Product, Solid, and just always works.”- CNET user review of MacBook Pro
Objectives
1. Define Robust Design
2. Explore how it fits in the context of product and process development
3. Identify why people do robust design
4. Learn how to do robust design
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Main Conceptual Message
3
• Noise – Uncontrolled variations that may affect performance; such as manufacturing variations or operating conditions.
• Robust Product (or process) – performs as intended even in the presence of noise.
• Robust Design – product development activity of improving desired performance while minimizing the effect of noise.
Motorola Razr
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Class Challenge
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Your Design
Output(Functionality, Performance)
Noise Factors
Control Factors
Team 31, for example
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Your Design
Drilling Rate(in/min)
Speed of TurnSoil Type
Down PressurePump Flow
Pump Pressure
Main Conceptual Message
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Objective Function = F(x) + G(y)
Design Option 1 = F(X1) + G(Y2)Design Option 2 = F(X2) + G(Y1)
Main Conceptual Message
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Robust Design Methodology1. Identify control factors, noise factors, performance metrics
2. Formulate an objective function
3. Develop an experimental plan
4. Run the experiment
5. Conduct the analysis
6. Select and confirm designs
7. Reflect and repeat
An I/O look at design…
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?
F(x), G(y)
Simple Example
1. Geometry2. Material3. Loading
?Known or derived from Functional Specification
Simple Example
1. Geometry2. Material3. Loading
3
3
4PL
Ebh
?
Vertical Deflection at Tip,
Safety Factor on Yield due to Bending,
0.15T
1yN
Vertical Deflection at Tip,
Safety Factor on Yield due to Bending,
Simple Example
1. Geometry2. Material3. Loading
0.15T
1yN
3
3
4PL
Ebh
2
6y
y
S bhN
PL
Simple Example
3
3
4PL
Ebh
2
6y
y
S bhN
PL
, , , yP L E S
,b h
Fixed Factors
Control Factors
Vertical Deflection at Tip,
Safety Factor on Yield due to Bending,
0.15T
1yN 0.20 0.50
0.01 0.20
b
h
Important Observation #1
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3
4PL
Ebh
0.20 0.50
0.01 0.04
b
h
Design Space: b vs. h
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0 0.1 0.2 0.3 0.4 0.5 0.6
b (in)
h (
in)
Design Space: b vs. h
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0 0.1 0.2 0.3 0.4 0.5 0.6
b (in)
h (
in)
Observation: More than one combination of b and h satisfy the performance metrics
Terminology
Setpoint – a particular set of values for input parameters
Design Space: b vs. h
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0 0.1 0.2 0.3 0.4 0.5 0.6
b (in)
h (
in)
0.44
0.03
0.5
3
30,000,000
55,000
0.15
2.44
y
y
b
h
P
L
E
S
N
Any guesses on which setpoint is most robust?
Important Observation #2
0.20 0.50
0.01 0.04
b
h
Performance Model: Deflection vs b
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 0.1 0.2 0.3 0.4 0.5 0.6
b (in)
def
lect
ion
(in
)
Performance Model: Deflection vs. h
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.01 0.02 0.03 0.04 0.05
h (in)
def
lect
ion
(in
)
Observation: Transmission of noise to the performance model may vary with different setpoints
Comparing two Setpoints
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Terminology Review
• Noise – Uncontrolled variations that may affect performance; such as manufacturing variations or operating conditions.
• Robust Product (or process) – performs as intended even in the presence of noise.
Performance Model: Deflection vs b
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 0.1 0.2 0.3 0.4 0.5 0.6
b (in)
def
lect
ion
(in
)
Performance Model: Deflection vs. h
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.01 0.02 0.03 0.04 0.05
h (in)
def
lect
ion
(in
)
Terminology Review
Robust Design – product development activity of improving desired performance while minimizing the effect of noise.
1. Where does Robust Design fit in the product development process?
2. What benefits could come from Robust Design?
How to do Robust Design
• Geometry• Material• Loading• Noise
?Known or derived from Functional Specification
What factors are needed to evaluate the performance
metrics?What are the things we
want to measureregarding the design’s
performance?
Do we want to maximize,minimize, hit a target, or
some combinationthereof?
More on Performance Metrics
• We have known differentiable equations• Single variable cases• Multiple variable cases
• We have known non-differentiable equations
• We have time-consuming equations or experiments
Single Variable Case
Transmission of Noise
3
3
4PL
Ebh
2
6y
y
S bhN
PL
3
4
12PL
h Ebh
22hh
2
6y yN S bh
h PL
2
2
y
yN h
N
h
Single Variable Case
Transmission of Noise
22hh
2
2
y
yN h
N
h
Performance Model: Deflection vs. h
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.01 0.02 0.03 0.04 0.05
h (in)
def
lect
ion
(in
)
Single Variable Case
Form an Objective
Function
Problem Objective
Hit the Target Deflection
While keeping the Safety Factor at or
above 1
Subject to
2min Th
1yN
0.01 0.04h
Subject to
2min minTh h
and
1yy NN
0.01 0.04h
Traditional Optimization Robust Design Optimization
h
Would result in…
Performance Model: Deflection vs. h
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.01 0.02 0.03 0.04 0.05
h (in)
def
lect
ion
(in
)
Multiple Variable Cases
Transmission of Noise
22xx
2
2
1j i
nj
xi ix
( )j j x Assumptions• Independent variables• Variation in x is small
• Objectives and constraints are differentiable
Non-differentiable Equations
Monte Carlo Simulation1. Generate a large number
slightly differing setpoints
2. Execute performance metrics for each generated setpoint
3. Characterize the mean and standard deviation of the execution data
2
2
1j i
nj
xi ix
Performance Model: Deflection vs. h
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.01 0.02 0.03 0.04 0.05
h (in)
def
lect
ion
(in
)
Monte Carlo Simulation Results
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Time Consuming Eqs or Experiments
Time Consuming Eqs or Experiments
Response Surface Methodology•Select a starting design•Run a screening experiment•Build a response surface model•Optimize•Refine response surface
Screening Design
Number of runs
Full Factorial: R = 3F
Box Behnken: R = 2*F2 + 1
Example: 12 factors531,441 runs for Full Factorial289 runs for Box Behnken
Screening Model
C = 73.20%
C = 71.89%
Theoretical
Experimental
Does RD really work?
C = 73.20%
C = 71.89%
Theoretical
Experimental
Weight, B. L., Mattson, C. A., Magleby, S. P., and Howell, L. L., “Configuration Selection, Modeling, and Preliminary Testing in Support of Constant Force Electrical Connectors,” ASME Journal of Electronic Packaging.
Only a small percentage of contacts were tested due to manufacturing variations
Does RD really work?
C = 98.02% Favg = 0.83 N
C = 73.20%
Does RD really work?
Optimized Percentage
Monte Carlo Average Percentage
Monte Carlo Standard Deviation
Previous Work
Case 1
Case 2 92.30% 91.94% 1.66%
98.02% 94.84% 2.57%
73.20% 66.98% 2.04%
Class Objectives and Summary
1. What is Robust Design?
2. How it fits in the context of product and process development?
3. What benefits could come from robust design?
4. How do we do robust design?
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Class Objectives and Summary
1. What is Robust Design?
2. How it fits in the context of product and process development?
3. What benefits could come from robust design?
4. How do we do robust design?
37
Class Objectives and Summary
1. What is Robust Design?
2. How it fits in the context of product and process development?
3. What benefits could come from robust design?
4. How do we do robust design?
38
Class Objectives and Summary
1. What is Robust Design?
2. How it fits in the context of product and process development?
3. What benefits could come from robust design?
4. How do we do robust design?
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