ME317 dfM at Stanford
Design for Manufacturability
ME317 dfM
Robust Design Fundamentals
“Robust means product & process
insensitive to noises”
Genichi Taguchi, 1985
Kos Ishii, Professor
Department of Mechanical Engineering
Stanford University
ishii@stanford.edu
http://me317.stanford.edu
©2006 K. Ishii
ME317 dfM at Stanford
Today’s Agenda
 Next Four Lectures: ROBUST DESIGN
1. Robust Design Introduction--simple examples
2. Design of Experiments (DoE) / Taguchi Method
3. Variation Patterns / Confounding, Case Study
4. Robust Conceptual Design (Dr. Russell Ford)
 Today: Robust Design Fundamentals
Concept of Robustness
DoE Basics
Cantilever Example: Using Analytical Models
©2006 K. Ishii
ME317 dfM at Stanford
What’s Robustness?
 Seek candidate design whose performance is
insensitive to variation
 Focus on variation that affect performance
Manufacturing variation
Deterioration of parts/materials
Environmental variables
 Illustrative Examples
Kos’ Rectangular Cookie
Force Sensor (Cantilever Beam Structure)
Profile Modified Helical Gears
CD Pickup Mechanism (Dynamic Performance)
©2006 K. Ishii
Robust Dimensional Fit
 EXAMPLE
Design a hood hinge with excellent alignment
Low manufacturing and assembly cost
 SOURCES OF VARIANCE
Manufacturing variation
Assembly errors
ME317 dfM at Stanford
Robustness Optimization
TIP
Objective Function L
 Peak vs.
Robust
Optimum
AMT. OF
RELIEF
Pl
START
ROLL
ANGLE
ROOT
R
Rl
Rh
Ph
P
Parameter X
3s
3s
3s
©2006 K. Ishii
ME317 dfM at Stanford
Robust Design Philosophy
System--Parameter--Tolerance
 SYSTEM DESIGN
Function Requirements  System Configuration
Russell Ford’s Lecture
 PARAMETER DESIGN
System Configuration Detailed Design
Hit Target Response while Minimize Variation
 TOLERANCE DESIGN
Detailed Design Tolerance Specification
Tighten tolerances sensitive to performance
variation but insensitive to cost
©2006 K. Ishii
ME317 dfM at Stanford
Robust Design Approach
 The Principles of Parameter Design
Use a limited set of experiments to determine the
design sensitivities
Design the product and process to minimize the
sensitivity of the quality measures to noise
f
f (X )  f (X0) 
X
X  R
X0
 Tolerance Design
Tightening tolerance induces higher control cost
Applied after parameter design
Tighten the tolerance of most sensitive variables
©2006 K. Ishii
ME317 dfM at Stanford
Noise and Loss
 Control Factors:
Designers have control, e.g., parameter set points
 Noise Factor:
Designers do not have control
Need to minimize effects on performance
 Types of Noise Factors:
External (outer): environmental noise
Unit to Unit (product): mfg. variations
Deterioration (inner): changes in the product
©2006 K. Ishii
ME317 dfM at Stanford
Example: Noise Factors
 Noise Factors for braking distance of a car
External
wet or dry road
Unit-to-Unit Variation
friction characteristics of brake pads
Deterioration
wear of brake pads
©2006 K. Ishii
ME317 dfM at Stanford
Loss Function
 Various Form of Loss Functions
m-²
0
m
m+²
0
m-²
Step
0
m
m+²
0
Quadratic
 Quadratic Loss functions:
Nominal-is-Best: k(y-m)2
Smaller-is-Best: ky2
Larger-is-Best: k(1/y2)
©2006 K. Ishii
ME317 dfM at Stanford
Robustness Objective Criteria
 Many forms of criteria (Nominal-is-Best Case)
2
2
Average Loss = k[S  (y  m) ]
y = mean
S2 = variance, m = target performance
L(y)
Quality Loss
Distribution of y
m-² 0
m
y
m+² 0
y
©2006 K. Ishii
ME317 dfM at Stanford
Robust Design Basics
1. Establish the concept configuration
Dr. Russell Ford’s Lecture
2. Define performance goals
3. Identify factors which influence performance
Classify into categories
Draw Cause-and-effect diagram
Select factors that form the basis of experiments
 Important to consider all possible factors
May need to identify significant factors and iterate
 Utilize analytical / numerical models if available
©2006 K. Ishii
ME317 dfM at Stanford
Force Sensor Example
 Step 1: Design Concept
Cantilever Bar + Strain Gauge
 Step 2: Robust objective
Hit the target stiffness!
©2006 K. Ishii
ME317 dfM at Stanford
Identify pertinent variables
 Step 3: Cause & Effects Diagram
(Ishikawa Dia.)
List all the variables that
influence performance
Classify significant control and
noise parameters
Causes
Material
Effects
Dimensions
Type
Am ount
b
L
Shape
Material
Clamp
h
Tolerance
h
b
L

Uniform
Stiffnesss
©2006 K. Ishii
ME317 dfM at Stanford
Factors in the Force Sensor Example
 Control Factors: b, h, L ( L < 2 inch)
 Noise Factors:
Strain
Thickness h: +0.0001 inch Gauge
Width b: +0.001 inch
Length L: +0.005 inch
Material: Aluminum
E = 1.25x10 7 psi
h±h
L±L
b±b
 Goal
Minimize variation on stiffness
Target Objective: K0=0.05 lb/in
©2006 K. Ishii
ME317 dfM at Stanford
Closed Form Approach
The “Rectangular Cookie” Problem
 If there is a closed form expression
Could lead to analytical solutions
E.g. for the force sensor:
Ebh 3
K
3
4L
X
 Very simple example:
A = X • Y
Y
Target A0
Noise on X and Y
Find target X and Y that Minimize Variation
A
©2006 K. Ishii
ME317 dfM at Stanford
Derive the Robustness Criteria
 Relate performance variation to noise
A0  XY
A0  A  (X  X)(Y  Y)
A0  A  XY  XY  YX  XY
A XY X Y XY
1




A0 XY X
Y
XY
1
0
A X Y


A0
X
Y
©2006 K. Ishii
ME317 dfM at Stanford
Find the robust optimum
 Find the value of X that minimizes variation on A
A0
A0  XY  Y 
X
A X XY


A0
X
A0
A 
  
 A0 
X
X Y
 2 
0
X
A0
X2
A0

X Y
XO p t 
X
A0
Y
©2006 K. Ishii
ME317 dfM at Stanford
An Example Cookie
 A0 = 8; x = 0.2; y = 0.1
X
0.2
A0
 8
 4.0
Y
0.1
XO p t 
4
2
X
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
13.00
14.00
15.00
16.00
Y
8.00
4.00
2.67
2.00
1.60
1.33
1.14
1.00
0.89
0.80
0.73
0.67
0.62
0.57
0.53
0.50
Delta A
1.72
1.02
0.85
0.82
0.84
0.89
0.95
1.02
1.10
1.18
1.27
1.35
1.44
1.53
1.63
1.72
©2006 K. Ishii
ME317 dfM at Stanford
How about Numerical Optimization
 Use simulation and optimization methods
1.80
1.60
1.40
1.20
1.00
0.80
4
0.60
2
0.40
0.20
16.00
15.00
14.00
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
©2006 K. Ishii
ME317 dfM at Stanford
Force Sensor Example
Closed Form Approach
 Define a “cost function” = variation in K
VERY IMPORTANT STEP
2
2
2

2  K 
2  K 
2  K  
2
V  S h    S b    S L   
 b 
 L  
  h 
 Monotonicity Analysis of V
Determines L
 Use expression for target K and relate b and h
Expression of V on one variable, b of h
Set dV/dh = 0 or dV/dh = 0 and find the optimum
©2006 K. Ishii
ME317 dfM at Stanford
Robust Design of Helical Gears
Using Computational Models
 Objectives
Minimize transmission error
Indication of noise and vibration
Use gear profile modification
 Design variables in profile modification
AMT. OF
RELIEF
TIP
START
ROLL
ANGLE
ROOT
©2006 K. Ishii
Performance Contour Plots
of Transmission Error
Peak to Peak Transmission Error
Weighted Objective Function
F(X, )   y    sy
ME317 dfM at Stanford
Helical Gear Example
 Variations (Simulated with DoE matrix*)
 0.00015” in tip relief
1.5 degrees in roll angle
Shaft misalignment of 0.0005”
Torque variations of 25%
PPTE in micro inches
*L8 is one type of DoE matrix, to be explained in next lecture
45
Wors t of L8
Target
30
15
0
Peak
Statis tical
©2006 K. Ishii