ME317 dfM at Stanford
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Transcript ME317 dfM at Stanford
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
[email protected]
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