Robust Design Integrated Product and Process Development MeEn 475/476 “Great Product, Solid, and...

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

5

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


7

Objective Function = F(x) + G(y)

Design Option 1 = F(X1) + G(Y2)Design Option 2 = F(X2) + G(Y1)


8

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


3

3

4PL

Ebh

?

Vertical Deflection at Tip,

Safety Factor on Yield due to Bending,

0.15T

1yN



Simple Example


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



0.15T

1yN 0.20 0.50

0.01 0.20

b

h

Important Observation #1

3

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)


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


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

)


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



22hh

2

2

y

yN h

N

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

)


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…


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


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


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


C = 98.02% Favg = 0.83 N

C = 73.20%


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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