ME317 dfM at Stanford
Design for Manufacturability
ME317 dfM
Robust Design: Case Study
“Beware of Confounding--analyze the physical behavior
and understand the interactions”
Barkan, 1990
Kos Ishii, Professor
Department of Mechanical Engineering
Stanford University
ishii@stanford.edu
http://me317.stanford.edu
©2006 ME317 at Stanford
ME317 dfM at Stanford
Agenda
 Robust Design: ME317 Example
 Case Study (Developed by Ken Seki, Sony)
Robust Design for Dynamic Performance
Optical Pick-up Actuator Structure Design
 Confounding: A simple example
Use common sense!
 Interacting Noise Factors
Manufacturing Variation Patterns
 Next Lecture: Platform Design
©2006 ME317 at Stanford
ME317 dfM at Stanford
Robust Design Example
ME217 2001: Sun Carrier Plate Example
Multiple CPAs
(Removable)
CPU
CPA
I/O
Pin Connection
Failure
Center-Plane
Interface Board
©2006 ME317 at Stanford
ME317 dfM at Stanford
CPA Major Components
Structural Support
Computer Boards
- CPU (20 Ib)
- I / O (7.5 lb)
- Expander (23 Ib)
CPU
I/O
Expander
- 1 Vertical Stiffener
- 2 Horizontal Guides
Pin Connections
(25 Pins / Inch)
Carrier Plate
(22” W x 37.5” H)
©2006 ME317 at Stanford
ME317 dfM at Stanford
DoE Analysis: 1st Attempt
 Control Factors: Stiffener
3 variables
Thickness, Height, Width
3 Levels
Low, Medium, High
L
L
H
H
L
H
L
H
Trials
1
2
3
4
5
6
7
8
9
L
L
L
M
M
M
H
H
H
L
M
H
L
M
H
L
M
H
L
M
H
M
H
L
H
L
M
4
4
4
4
4
4
4
4
4
©2006 ME317 at Stanford
Responses
 Orthogonal Arrays
Inner L9
Outer L4
Total of 36 Experiments
Inner Array
Experiments
 Noise Factors: Board Design
2 variables
Location and Weight
Assume Centralized Load
Outer Array
ME317 dfM at Stanford
Robust Objective: System Cost
System Cost
System Cost
45
40
Material Cost
50
35
Defect Cost
30
Cost
45
Defect Cost
Material Cost
System Cost
25
40
20
35
15
10
30
Cost
5
0
0
Material Cost
25
0.005
20
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Inertia
15
10
5
Defect Cost
0
Possible 0OPTIMAL
DESIGN!!!
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Inertia
©2006 ME317 at Stanford
ME317 dfM at Stanford
Robust Optimization Results
Mean System Cost
50.00
T - Cost - Big
W - Cost - Big
H - Cost -Big
System Cost
40.00
30.00
20.00
10.00
0.00
0
1
2
3
4
Thickness
5
6
7
MIN - MEAN - MAX
Width
8
9
10
Height
Cost: S / N Ratio
-15
0
1
2
3
4
5
6
7
8
9
Thickness
Width
Height
S / N Ratio
-20
10
 Optimal Design
Thickness (Mid)
Width (High)
Height (High)
 So the Robust design is:
Design:
0.06” x 1.5” x 0.18”
+Deflection 0.0013”
-Deflection 0.0040”
Cost: $20.9
-25
-30
-35
MIN - MEAN - MAX
 Note:
Variation in this example
characterized as S/N
ratio (larger the better)
©2006 ME317 at Stanford
ME317 dfM at Stanford
Robust Design at Sony
Sony uses Robust Design for Mfg. Process
DOE in CRT Manufacturing Process
"Deflection Yoke"
Deflection Yoke (DY)
"Gun"
"CRT"
Seeking Application to Product Design
Need a good demonstration example
Look at CD Optical Pick-up Actuator
Focus on “Shape Synthesis” in Detail Design
Use Frequency Response as Performance Metric
Use Available Numerical Models
©2006 ME317 at Stanford
ME317 dfM at Stanford
Robust Design of Optical Pick-up
 Motivation at Sony: minimize the effect of variation
Variations in dynamic performance in mass prod.
Difficult to find optimal solution by empirical method
 Optical Pick-up Design
Typical “Electro-mechanical systems” at Sony
Must address interactions
Servo Circuits
Mechanical vibrations
Robustness in servo stability
Product Competitiveness
©2006 ME317 at Stanford
ME317 dfM at Stanford
What is an Optical pick-up ?
 Like a “needle” in record player
consists of lens & leaf spring
focus error
 Disc not perfectly level or centered
tracking error
 Lens has to follow the disc to keep
focus and tracking
precise positioning servo
©2006 ME317 at Stanford
ME317 dfM at Stanford
Pick-up Actuator Design
Required Dynamic characteristics:
Magnet
Lens
Fixture
Leaf Spring
Coil
Bobbin
Lens holder
Yoke
1-axis pick-up actuator
Single-DOF behavior is essential !
©2006 ME317 at Stanford
ME317 dfM at Stanford
Problems in “Mass production trial”
 Sometimes we see variations
Response gain and natural frequency
Undesirable peaks, etc.
Undesirable peak due to torsional mode
©2006 ME317 at Stanford
ME317 dfM at Stanford
Robust Design Strategy
STEP 1: Definition of robustness problem
Performance requirements & Design constraints
Selection of Quality Characteristics
STEP 2: Parameter design
Cause and Effect Analysis
Search for the error sources
Identification of Control factor & Blocking
STEP 3: Experiments & Analysis of Results
©2006 ME317 at Stanford
ME317 dfM at Stanford
[ STEP 1 ]
Definition of robustness problem
Performance requirements
Minimum frequency response gain at 2nd mode
Gain
(to guarantee the servo stability even if noise exists)
Design constraints
Frequency
Total weight < M max
1st natural frequency = f 0 (design spec.)
©2006 ME317 at Stanford
ME317 dfM at Stanford
[ STEP 1 ] Cont.
Definition of robustness problem
Quality Characteristics
Response gain {yi} at the resonance frequency of
torsional mode
k
yi   
r 1
 r   f  r 
T
kr  jcr  mr
2
2
2
Robust Objective S/N = -10 log ( S + yi )
©2006 ME317 at Stanford
ME317 dfM at Stanford
[STEP 2]
Parameter Design
Variations affecting dynamic response
Part-to-part variation
* thickness in spring
* warping, pre-strain of spring
* other parts dimensions
Material condition
* E, G modulus
* density
* damping
Assembly errors
* misalignment of magnet
--- “imbalance actuator forces”
Environmental variables
©2006 ME317 at Stanford
ME317 dfM at Stanford
[STEP 2] Cont: Parameter Design
Cause and effect analysis
Identification of Control Factors and Blocking
EXCITING FORCE
CONDITION
PART DIMENSION
CONDITION
Magnitude
Direction
Phase
MATERIAL
(leaf spring)
Thickness
Elastic Modulus
Density
Width
Pre-strain
Warping
Length
(other parts)
Alignment
Connecting
stiffness
ASSEMBLY
CONDITION
Fixing
condition
Non-linearity
BOUNDARY
CONDITION
DYNAMIC
RESPONSE
Loss factor
stiffness
DAMPING
CONDITION
Environmental
Easily
Controllable
©2006 ME317 at Stanford
ME317 dfM at Stanford
[STEP 3]
Conduct experiments & Analysis of Results
 Use the simulation model with DOE
Find optimum values for the control factors
Parameter Arrays
Numerical Simulation
Sensitivity &
Robustness
Frequency
FEM
Model Resp. Analysis
Control
Noise
Experimental
Modal Analysis
©2006 ME317 at Stanford
ME317 dfM at Stanford
[STEP 3]
Conduct experiments & Analysis of Results
 Control Parameters
Target width of leaf spring (8 sections)
1
2
3
4
5
6
7
8
 Environmental Parameters
thickness of leaf spring)
modulus of elasticity)
magnet misalignment)
©2006 ME317 at Stanford
ME317 dfM at Stanford
Set up the DOE Array
L18 Array Control factor array
Run CF1 CF2 CF3 CF4 CF5 CF6 CF7 CF8
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
2
2
2
3
1
1
3
3
3
3
3
3
4
1
2
1
1
2
2
3
3
5
1
2
2
2
3
3
1
1
6
1
2
3
3
1
1
2
2
7
1
3
1
2
1
3
2
3
8
1
3
2
3
2
1
3
1
9
1
3
3
1
3
2
1
2
10 2
1
1
3
3
2
2
1
11 2
1
2
1
1
3
3
2
12 2
1
3
2
2
1
1
3
13 2
2
1
2
3
1
3
2
14 2
2
2
3
1
2
1
3
15 2
2
3
1
2
3
2
1
16 2
3
1
3
2
3
1
2
17 2
3
2
1
3
1
2
3
18 2
3
3
2
1
2
3
1
Environmental
Factor
Array
Noise factor
array
NF1
NF2
NF3
L
L
L
1
0.832
0.584
0.237
0.394
0.636
0.547
0.441
0.636
0.64
0.56
0.413
0.565
0.44
0.533
0.478
0.555
0.39
0.478
L
H
H
2
0.682
0.419
0.263
0.345
0.535
0.408
0.407
0.437
0.441
0.457
0.381
0.474
0.364
0.375
0.435
0.383
0.373
0.431
H
H
L
H L4 Array
H
L
3
4
S/N
2
2.07 -3.73
1.33 1.28 0.08
0.538 0.731 6.2
0.942 0.972 2.79
1.572 1.6 -1.55
1.23 1.24 0.56
1.04 1.11 1.75
1.42 1.34 -0.42
1.42 1.37 -0.51
1.39
1.4 -0.43
0.981 1.05 2.25
1.4
1.42 -0.53
1.02 1.06 2.06
1.2
1.15 0.99
1.11
1.2
1.12
1.24 1.17 0.76
0.911 1.01 2.71
1.09 1.18 1.26
©2006 ME317 at Stanford
ME317 dfM at Stanford
Parameter Sensitivity: 2nd Mode Amplitude
Gain
 Minimize variation
Adjust width 1,6,7 & 8
Proportionally to S/N
"y"
Frequency
1
2
3
4
5
6
Robust Sensitivity of 2nd mode freq. response gain
(S/N measure: higher the better)
©2006 ME317 at Stanford
7
8
ME317 dfM at Stanford
 Match target natural frequency
Adjust width 2 &3
Gain
Parameter Sensitivity: 1st Mode Frequency
Frequency
f0
Mean sensitivity of 1st mode frequency
©2006 ME317 at Stanford
ME317 dfM at Stanford
Robust Design Modifications
Change in peak gain & natural frequency
Original
Target
Modification (A)
Modification (B)
"Mean Frequency" of 1st mode
23.5 Hz
around 24 Hz
26.6 Hz
25.1 Hz
New design of leaf spring
©2006 ME317 at Stanford
ME317 dfM at Stanford
Effect of Noise on Dynamic Performance
Original:
Lens disp.
2
1
0
200
400
Lens disp.
800
1000
Frequency [Hz]
2
Optimal:
600
1
0
200
400
600
800
1000
Frequency [Hz]
©2006 ME317 at Stanford
ME317 dfM at Stanford
CD Pick-up Head Scorecarding
Magnet
Lens
Fixing
Leaf Spring
Yoke
Lens holder
Gain
 Objective Measures (Y)
Frequency Response
 Control Factors (Vital X)
Leaf Spring Design
Coil
 Noise Factors (V's:
sources of variation) Bobbin
Manufacturing
Variation (Fabrication
and Assembly)
 Transfer function
FEM-based Dynamic
Simulation Model
Frequency
©2006 ME317 at Stanford
ME317 dfM at Stanford
Some Cautions in Robust Design
Beware of Confounding!
x
 Maximize Torque
 T= W (x-L)
W
L
L=1.2
BLACK
BOX
 Test Parameters
 Weight W
[10,20]
 Position X [0.9, 1.3]
 Color of Beam {Blue, Yellow}
©2006 ME317 at Stanford
ME317 dfM at Stanford
Let’s run DOE (L4)
Test
1
2
3
4
W
10
10
20
20
X
0.9
1.3
0.9
1.3
Color
Blue
Yellow
Yellow
Blue
T orque
-3
1
-6
2
2
1
0
-1
-2
-3
-4
-5
©2006 ME317 at Stanford
ME317 dfM at Stanford
Interpretation
 The tests tells us to use
Largest X (OK)
Smaller W (Whaaat?)
Blue Beam (Why??)
2
1
0
-1
-2
-3
-4
 When common sense
suggests there’s
something wrong...
-5
x
W
There IS!
L
L=1.2
BLACK
BOX
©2006 ME317 at Stanford
ME317 dfM at Stanford
There’s Interaction!
 X and W are Interacting
 The range of X covers the pivot point
50
40
30
20
60
B2
B1
B2
B1
Response
Response
60
50
40
B1
B2
30
20
B1
B2
10
10
A1
A2
Factor A
No interaction
A1
A2
Factor A
Interaction
©2006 ME317 at Stanford
ME317 dfM at Stanford
We really need to consider XW!
 The third column really shows X and W are interacting
NOT the effect of color on torque
 XW interaction confounded with Color
2
1
0
This effect really
due to
XW Interaction
-1
-2
-3
-4
-5
©2006 ME317 at Stanford
ME317 dfM at Stanford
Significance of Interaction XW
 Confounding between XW and Color!
Significant interaction between X and W
3rd column represent the effect of interaction XW
L4 has only 3 degrees of freedom (DOF)
Currently, C and XW are CONFOUNDING
Need to use a larger array to test the effect of C
Trial
A
Columns
B
1
2
3
4
1
1
2
2
1
2
1
2
C
AB
1
2
2
1
©2006 ME317 at Stanford
ME317 dfM at Stanford
Adjust the Range of X to [1.3, 1.4]
x
Test
1
2
3
4
W
10
10
12
12
X
1.3
1.4
1.3
1.4
Color
Blue
P urple
P urple
Blue
T orque
1
2
1.2
2.4
W
L
L=1.2
BLACK
BOX
2.5
2
1.5
1
0.5
0
©2006 ME317 at Stanford
ME317 dfM at Stanford
DOE for Interaction
 Main factors A, B, C, and D; interaction AB.
Assign the Column as follows
Avoid Confounding
Columns with Factors and Interactions
Trial
1
2
3
4
5
6
7
8
A
BCD
+
+
+
+
B
ACD
+
+
+
+
AB
CD
+
+
+
+
-
C
ABD
+
+
+
+
AC
BD
+
+
+
+
-
AD
BC
+
+
+
+
-
D
ABC
+
+
+
+
 Use common sense, if you suspect interaction
Change the range or use larger array
©2006 ME317 at Stanford
ME317 dfM at Stanford
Noise Can be Interacting too!
Manufacturing Variation Pattern (MVP)
 Injection molded plastic switch box (Lexan 141)
x1 exhibits primarily shrinkage
x2 exhibits both linear shrinkage and warpage.
2 .6 2 1
2 .6 2 0
2 .6 1 9
2 .6 1 8
x 2 ( inch)
2 .6 1 7
x2
1.5"
2 .6 1 5
2 .6 1 4
2 .6 1 3
2 .6 1 2
x1
2.4"
2 .6 1 6
2.7"
2 .6 1 1
2 .6 1 0
2 .6 0 9
2 .3 5 4 5 2 .3 5 5 5 2 .3 5 6 5 2 .3 5 7 5 2 .3 5 8 5 2 .3 5 9 5 2 .3 6 0 5
x 1 ( inch)
©2006 ME317 at Stanford
ME317 dfM at Stanford
Negatively Correlated Noise
Heat Treated Shafts
 Interested in more details?
Yu, J.C. and Ishii, K. (1998), “Design for Robustness Based
on Manufacturing Variation Patterns,” ASME Journal of
Mechanical Design, Vol. 120, pp.196-202. ISSN 1050-0472
©2006 ME317 at Stanford
ME317 dfM at Stanford
Robust Design Summary
 Cause and Effects Diagram: IMPORTANT!!!
Identify quality metrics, blocks and control factors
Be as thorough as you can, focus in later
 Parameter Design using Orthogonal Arrays
Simple, yet very effective
 Up-front Robust Design saves TIME and MONEY!!
 Start at conceptual design stage
Develop guiding principles, apply in Pugh Selection
Next Lecture!
©2006 ME317 at Stanford