Pin-Joint Test Rig Design and Scaling Laws
by
Micah David Smith
B.S., Mechanical Engineering
United States Naval Academy, 1998
SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING
IN PARTIAL FULFILLMENT OF THE DEGREE OF
MASTER'S OF SCIENCE IN MECHANICAL ENGINEERING
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2000
D 2000 Massachusetts Institute of Technology
All rights reserved
Signature of Author .......................
Department of Mechanical Engineering
May 5, 2000
Certified by ...........................
ProfessoFA~Klexander H. Slocum
Th~ei
ev
Accepted by .............................
Professor Ain Sonin
airman, Department Graduate Committee
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
SEP 2 0 2000
LIBRARIES
MiTLibraries
Document Services
Room 14-0551
77 Massachusetts Avenue
Cambridge, MA 02139
Ph: 617.253.2800
Email: docs@mit.edu
http://libraries.mit.edu/docs
DISCLAIMER OF QUALITY
Due to the condition of the original material, there are unavoidable
flaws in this reproduction. We have made every effort possible to
provide you with the best copy available. If you are dissatisfied with
this product and find it unusable, please contact Document Services as
soon as possible.
Thank you.
Some pages in the original document contain pictures,
graphics, or text that is illegible.
Pages 121-150 (Appendix B-Design Prints) contain illegible
text. Best image quality available.
2
4
Pin-Joint Test Rig Design and Scaling Laws
by
MICAH DAVID SMITH
Submitted to the Department of Mechanical Engineering
on May 5th, 2000 in Partial Fulfillment of the
Requirements for the Degree of Master's of Science in Mechanical Engineering
at the Massachusetts Institute of Technology
ABSTRACT
A novel test apparatus is described which allows for the testing of pin-joints of varying
sizes. The test-apparatus allows for measuring the applied load, reactionary torque, friction coefficient, lubricant temperature, rotation speed and acceleration, and failure time of
a pin-joint system. The apparatus is capable of simulating a full scale load of a pin-joint
system as well as being able to accommodate optical analysis of the fluid flow through the
joint. Optical analysis cannot be conducted on a highly loaded pin-joint due to the inability of most optically clear elements to withstand high loading. To overcome this problem,
scaling laws are introduced which allow for the modeling of pin deformation of typical
opaque metallic joints using plastic pins and transparent ceramic or plastic bushings with
much lower loadings. A method of optical analysis using the Laser Induced Fluorescence
technique is described to dynamically measure the thickness of fluid in the contact region
of the joint. This apparatus, including the scaling laws and optical techniques, is an invaluable tool in the investigation of the affect of surface features on the lubrication and wear
mechanisms of pin-joint systems.
Thesis Supervisor:
Prof. Alexander H. Slocum
Dept. of Mechanical Engineering
4
ABSTRACT
A CKNOWLEDGMENTS
I would like to thank my parents David and Jeanie Smith for the love and support they
have given me in all my endeavors. Without their encouragement and constant reassurance
I could have never accomplished the things I have done.
I would like to thank my brother Joshua for always being there to joke around with and
help me keep my schooling in perspective.
I would be remiss if I did not thank my beautiful girlfriend, Nancy Newton. Darling,
thank you for your patience, love, and encouragement as I did my work. I love you.
I would like to thank all my friends at the United States Naval Academy for helping me
strive and achieve the privilege of even attempting this degree. You are all too numerous
to mention, but you know who you are.
I would like to thank all my friends I have made here at M.I.T. that have helped me learn
that school isn't only a memorization of facts. George and Carlos although I often complained about your pestering me, without you I would have made errors that would have
gone unnoticed. Ebbe your computer consulting saved me in many of my darkest hours.
Sami, Roger, James, Alex, Joachim, Jin, Don, Mark, and Nate, your humor and joking
around, helped me to relax and really enjoy my work, especially this last semester. Marty
I will never forget that "cracks don't go around corners" although my massaga soap never
really did work.
I would like to thank Caterpillar for funding this research and I sincerely hope that one day
the pin-joint problem is fixed. I would like to specially thank Kristy Johnson from Caterpillar for her tireless efforts to make all our lives a little easier. Kristy you are truly a brilliant and talented engineer, who is a great asset to any company. Most of all you are a
good friend. I would also like to thank Joe Vanecko from Caterpillar for always being
there to find a number or get that information that we so desperately needed.
I would like to thank the United States Navy for allowing me a leave of absence to pursue
my Master's Degree.
I would like to give special thanks to Professor Robert Grainger of the United States Naval
Academy. It is because of his instruction that I chose to go to graduate school. His love of
science and care for his students inspired me to strive for academic excellence. The day
he had the most impact on me was when he threw me out of class for dozing off. He
warned me once to wake up, then told me to leave the class. He then told me I couldn't
even listen outside the door. I then realized that it was a privilege for me to learn, and that
I really wanted to go back into that classroom. It was at that moment that I realized that I
wanted to go to M.I.T. and really enjoy the learning process.
Next, I would like to thank the man who has had the biggest impact on my experience here
at M.I.T., Professor Slocum. Alex, I will never forget the first moment I met you, wild
eyed with ruffled hair, wearing a suit, a tie, and tennis shoes rushing off to some meeting
somewhere. You gave me a new perspective on learning, thinking, and most of all life.
You believed in me when no one else did and you always stood behind me when I thought
the world was against me. You always watched out for my interests and you always
5
6
ACKNOWLEDGMENTS
wanted what was best for me and everyone else in the lab. I will never forget the things
you have taught me and I promise I will return after my time under water is through.
Finally, I would like to thank God for giving me the talents I have and for the opportunities
He has given me so far in this life. It is God who deserves the glory for the accomplishments and work I have completed, because without Him none of this could have been possible.
7
A bstract . . . . . . . . . . . . . . . . . . . . . .
Acknowledgments
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
Chapter 1.
Background
1.1 What is a Pin-Joint? . . . . . . . . . . . . .
1.1.1 Pin-Joint Beginnings . . . . . . . . .
1.1.2 Pin-Joints Today . . . . . . . . . . .
1.1.3 Pin-Joint Geometry . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
17
17
18
18
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
19
20
21
21
22
1.2 A Brief Overview of Failure Mechanisms
1.2.1 Micro-Welding . . . . . . . . . .
1.2.2 Delamination Wear . . . . . . . .
1.2.3 Common Design Parameters . . .
1.2.4 Lubrication Solutions . . . . . .
.
.
.
.
1.3 State of the Art of Pin-Joint Testing . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .
1.3.1 Design and Testing Parameters
. . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2 Testing and Results
22
22
24
1.4 Selection of a Test Joint . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
Chapter 2.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
28
28
28
28
Level Functional Requirements . . .
FRI-Apply Loading . . . . . . . . .
FR2-Apply Rotation . . . . . . . . .
FR3-Conduct Optical Analysis . . .
FR4- Rest on Floor . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
29
29
29
29
30
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
2.1 Design Constraints . . . .
2.1.1 C1- Low Cost . . .
2.1.2 C2- Small . . . . .
2.1.3 C3- Scalable . . . .
2.2 Upper
2.2.1
2.2.2
2.2.3
2.2.4
27
Test machine design . . . . . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
2.3 Design Concepts . . . . . . . . . .
2.3.1 Four-Bar Linkage . . . . .
2.3.2 Double Clevis Design . . .
2.3.3 Big Clevis Design . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
2.4 Level Two Functional Requirements and Design Parameters
2.4.1 DPI Decomposition (Hydraulic Cylinder) . . . . .
2.4.2 DP2 Decomposition (Hydraulic Motor) . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
30
30
33
36
. . .
38
38
39
8
2.4.3 DP3 Decomposition (Ample Space Below Bushing) . . . . . . . . . 40
2.4.4 DP4 Decomposition (Steel Plate) . . . . . . . . . . . . . . . . . . . 42
2.4.5 Level Two Design Matrix . . . . . . . . . . . . . . . . . . . . . . . 42
2.5 Level Three Functional Requirements and Design Parameters
2.5.1 DP 1I Decomposition (Properly Size Cylinder) . . . .
2.5.2 DP12 Decomposition (Load Cell) . . . . . . . . . . .
2.5.3 DP13 Decomposition (Loading Clevis) . . . . . . . .
2.5.4 DP14 Decomposition (Bushing Mount) . . . . . . . .
2.5.5 DP15 Decomposition (Press Fit Ring) . . . . . . . . .
2.5.6 DP22 Decomposition (Motor Sizing) . . . . . . . . .
2.5.7 DP23 Decomposition (Coupling Shaft) . . . . . . . .
2.5.8 DP24 Decomposition (Torque Sensor) . . . . . . . .
2.5.9 DP31 Decomposition (Sizing of Mounting Legs) . . .
2.5.10 DP25 Decomposition (Motor Mount) . . . . . . . . .
2.5.11 DP32 Decomposition (Optical Slots) . . . . . . . . .
2.5.12 DP33 Decomposition (Scaling Laws) . . . . . . . . .
2.5.13 DP34 Decomposition (Damping Pad) . . . . . . . . .
2.5.14 DP41 Decomposition (Size of Plate) . . . . . . . . .
2.5.15 DP42 Decomposition (Height and Position of Risers)
2.5.16 DP43 Decomposition (Thickness of Plate) . . . . . .
2.5.17 Level Three Design Matrix . . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
45
45
46
46
49
52
54
56
59
59
61
62
63
64
64
65
65
66
Four Decomposition . . . . . . . . . . . . . . . . . . . .
DP131 Decomposition-Bolts . . . . . . . . . . . . . . .
DP132 Decomposition (Pin Clamps) . . . . . . . . . . .
DP133 Decomposition (Detach Mount) . . . . . . . . . .
DP134 Decomposition (No Failure or Plastic Deformation)
DP135 Balanced . . . . . . . . . . . . . . . . . . . . . .
DP141 (Clamping Mechanism) . . . . . . . . . . . . . .
DP151 Decomposition (Large Diameter Bearing) . . . . .
DP152 Decomposition (Bolt Holes and Press Fit) . . . . .
DP153 Decomposition (Angled Blocks) . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
67
67
69
72
72
74
74
76
77
78
2.7 Hydraulics and Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . .
80
2.8 Manufacturing and Assembly . . . . . . . . . . . . . . . . . . . . . . . . .
2.8.1 Notes on Manufacturing . . . . . . . . . . . . . . . . . . . . . . . .
2.8.2 Notes on Assembly . . . . . . . . . . . . . . . . . . . . . . . . . .
81
81
82
2.6 Level
2.6.1
2.6.2
2.6.3
2.6.4
2.6.5
2.6.6
2.6.7
2.6.8
2.6.9
Chapter 3.
Scaling laws
. . . . . . . . . . . . . . . . . . .
3.1 Desired Properties to Replicate
. . . . . . . . . . . . .
.
.
.
.
.
87
87
9
3.2 Physical Laws Governing Scaling . . . .
3.2.1 Hertzian Contact Mechanics . . . .
3.2.2 Four Point Bending . . . . . . . .
88
89
91
3.3 Material Matching . . . . . . . . . . . . .
3.3.1 Combinatorial Complexity . . . . .
3.3.2 Solution Materials . . . . . . . . .
92
92
93
3.4 Problems with Scaling . . . . . . . . . . .
96
Chapter 4.
4.1
Optical Analysis
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
. . . . . . . . . . . . . . . . .
99
Dual Emission Laser Induced Fluorescence
4.2 Optical Setup
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.3 Other Types of Optical Analysis
. . . . . . . . . . . . . . . . . . . . . . . 104
Future Pin Joint Studies
. . . . . . . . . . . . . . . . . . . . . . . 107
Chapter 5.
5.1 General Surface Geometry Studies
. . . . . . . . . . . . . . . . . . . . . . 107
5.2 Modeling, Machining, and Testing
. . . . . . . . . . . . . . . . . . . . . . 108
5.3
Other Dye Applications and Particle Tracking
. . . . . . . . . . . . . . . . 108
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Appendix A.
Hertzian Contact Mechanics
. . . . . . . . . . . . . . . . . . . . 113
A. 1 Hertzian Contact Calculations for Steel Contact
. . . . . . . . . . . . . . . 113
A.2 Hertzian Contact Calculations for Matching Materials
Appendix B.
. . . . . . . . . . . . 116
Design Prints . . . . . . . . . . . . . . . . . .1 . . . . . . . . . .. 121
10
11
Figure 1.1
Pin-Joint Nomenclature
. . . . . . . . . . . . . . . .
. . . .
19
Figure 1.2
Galled Pin-Joint
. . . . . . . . . . . . . . . . . . . .
. . . .
20
Figure 1.3
Isometric View of Industrial Testing Apparatus . . . .
. . . .
23
Figure 2.1
Isometric View of Four Bar Linkage Design
. . . . .
. . . .
31
Figure 2.2
Side View of Four Bar Linkage Design . . . . . . . .
. . . .
32
Figure 2.3
Isometric View of Double Clevis Design . . . . . . .
. . . .
34
Figure 2.4
Side View of Double Clevis Design . . . . . . . . . .
. . . .
35
Figure 2.5
Front View of Final Design
. . . . . . . . . . . . . .
. . . .
37
Figure 2.6
Side View of Cylinder (in)
. . . . . . . . . . . . . .
. . . . 45
Figure 2.7
Drawing of Load Cell (in.)
. . . . . . . . . . . . . .
. . . . 46
Figure 2.8
Isometric View of Clevis/Cylinder Attachment . . . .
. . . . 48
Figure 2.9
Isometric View of Pin Clamp
. . . . . . . . . . . . .
. . . . 48
Figure 2.10
Isometric View of Clevis and Weights
Figure 2.11
Isometric View of Bushing Mount
. . . . . . . .
. . . .
50
. . . . . . . . . .
. . . .
51
. . . . . . . . . . .
. . . .
53
. . . . . . . . .
. . . .
54
Figure 2.14 Isometric View of Base plate to Load Cell Connection
. . . .
55
Figure 2.15
Shaft/Torque Cell Connection . . . . . . . . . . . . .
. . . .
57
Figure 2.16
Length of Shaft Affect on Allowable Error . . . . . .
. . . .
57
Figure 2.17
Simple Beam Bending Diagram . . . . . . . . . . . .
. . . .
58
Figure 2.18
Isometric View of Motor Mount
Figure 2.19
Width of Window
Figure 2.12 Mounting Block/Ring Schematic
Figure 2.13
Isometric View of Mounting Blocks
. . . . . . . . . . .
. . . . 63
. . . . . . . . . . . . . . . . . . .
. . . .
64
Figure 2.20 Level Three Axiomatic Design Summary . . . . . . .
. . . .
66
Figure 2.21 Further Decomposition Design Matrix
. . . . . . . .
Figure 2.22 Close-Up View Sealing Surface . . . . . . . . . . . .
Figure 2.23 Connection Piece
. . . . . . . . . . . . . . . . . . .
. . . . 67
. . . .
69
. . . . 79
Figure 2.24 Isometric View of Final Design . . . . . . . . . . . .
. . . .
81
Figure 2.25 Isometric View of Assembled Final Design . . . . . .
. . . .
84
Figure 2.26 Front View of Assembled Final Design . . . . . . . .
. . . .
85
Figure 3.1
Axial Sketch of Pin Showing Lobes
. . . .
89
Figure 3.2
Circumferential Sketch of Pin Showing Flowers
. . . . . . . . .
. . . . 90
12
Figure 3.3
Sketch of Loading Configuration
. . . . . . . . . . . . . . . . . . . .
90
Figure 3.4
Hertzian Contact Area . . . . . . . . . . . . . . . . . . . . . . . . . .
91
Figure 3.5
Re-enforced Pin Overview
. . . . . . . . . . . . . . . . . . . . . . .
94
Figure 3.6
Optical Pin and Bushing . . . . . . . . . . . . . . . . . . . . . . . . .
96
Figure 4.1
Bottom View of Sapphire Window and Bushing Mount
Figure 4.2
Dichroic Mirror Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Figure 4.3
Optical Setup
Figure 5.1
Manufactured Optically Accessible Pin-Joint Test Rig . . . . . . . . . 110
. . . . . . . . 102
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
13
TABLE 1.1
Field Conditions of Model Pin-Joint ..................
25
TABLE 2.1
Axiomatic Design Matrix for Four Bar Linkage Design ..........
32
TABLE 2.2
Axiomatic Design Matrix of Upper Level FR's and DP's of Double Clevis
D esign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
TABLE 2.3
Axiomatic Design Matrix for DPI Decomposition
TABLE 2.4
Axiomatic Design Matrix of DP2 Decomposition
TABLE 2.5
Axiomatic Design Matrix for DP3 Decomposition
..........
41
TABLE 2.6
Axiomatic Design Matrix for DP4 Decomposition
..........
42
TABLE 2.7
Coupled Axiomatic Design Matrix for Level Two Decomposition
.
43
TABLE 2.8
Revised Axiomatic Design Matrix For Level Two Decomposition
.
44
TABLE 2.9
Axiomatic Design Matrix of DP13 Decomposition
..........
39
...........
40
. . . . . . . . . .
50
TABLE 2.10 Axiomatic Design Matrix for DP14 Decomposition . . . . . . . . . .
51
TABLE 2.11 Axiomatic Design Summary for DP15 Decomposition
. . . . . . . .
55
TABLE 2.12 Axiomatic Summary Design Matrix for DP23 Decompositions . . . .
59
TABLE 2.13 Axiomatic Design Summary Matrix for DP31 Decomposition
. . . .
61
TABLE 2.14 Axiomatic Design Summary Matrix for DP25 Decomposition
. . . .
63
Stresses in Sapphire/Delrin . . . . . . . . . . . . . . . . . . . . . . .
95
TABLE 3.1
14
NOMENCLATURE
A
Area [m2]
At
c
c
C
C
d
d
Cross Sectional Area of Bolt [in]
Shaft Radius [in]
Major Hertz Diameter [in]
Design Constraint
Molar Concentration [Mole/Liter]
Diameter of Bolts [in]
Minor Hertz Diameter [in]
Press Interference Ratio [in/in]
Diameter of Oil Reservoir
Design Parameter
Diameter of Pin [in]
Diameter of Steel Insert
Molar Absorptivity
Modulus of Elasticity [psi]
Modulus of Elasticity of Plasticity [in 4 ]
Elastic Modulus of Steel [psi]
Property of SAE Bolts
Angle of Twist [rad]
Quantum Efficiency [%]
Total Force Placed on a Pin [lbf.]
Force on One Lobe [lbf]
Necessar Force in Bolt [lbf]
Press Fit Force [lbf]
Design Functional Requirement
Shearing Force [lbf]
Modulus of Ridgidity [psi]
Height Box Beam [in]
Height of Legs [in]
Bending Moment of Inertia [in 4 ]
Dye Emission Intensity [Candle Watt]
Laser Intensity [Candle Watt]
Property of SAE Bolts
6
Do;;
DP
Dp
DSteei
EE
Ep
Esteel
Esmin
0
(D
F
FL
Fpreload
Fpressfit
FR
FS
G
hbox
hiegs
I
If
10
Knmax
Xlaser
PIng
Lbeam
'clamp
LD
Le
if
Laser Emmission Wavelength
4
Moment of Inertia of the Pin [in ]
Beam Length [in]
Clamp Length [in]
Local Hertzian Deformation [in]
Effective Length of Threads [in]
Distance Between Loading Points
15
16
NOMENCLATURE
Lpgi
LRiser
LShaft
'weld
tp
p
n
p
r
rbushing
rmb
t
T
tbox
tclamp
tfluid
thlegs
Ttighten
ttp
CY
Ghoop
Gmaxbending
Yproof
Gultimate
CYy
w
W
Wbox
Wclamp
Wlegs
WPlate
Wtp
Az
Length of the Pin [in]
Unsupported Length Between Risers [in]
Connecting Shaft Length [in]
Unsupported Length of the Top Plate [in]
Length of Weld Bead
friction Coefficient
Threads Per Inch
Clamp Pressure [psi]
radius of pin [in]
Outer Radius of Bushing [in]
Bolt Radius for Connecting Block [in]
Clamp Thickness [in]
Torque [in-lbf]
Thickness of Box Beam [in]
Clamp Thickness [in]
Fluid Thickness [in]
Thickness of Legs [in]
Torque to Tighten Bolts [in-lb]
Thickness of Top Plate [in]
stress[psi]
Hoop Stress [psi]
Maximum Bending Stress [psi]
Proof Strength of Bolts [psi]
Shear Stress [psi]
Ultimate Tensile Strength [psi]
Yield Strength [psi]
Distance Applied Loading and Edge of Bushing [in]
Weld Bead Diameter [in]
Width of Box Beam [in]
Width of Clamp [in]
Width of Legs [in]
Width of Plate [in]
Width of Top Plate [in]
Bending Displacement [in]
Chapter 1
BACKGROUND
1.1 What is a Pin-Joint?
A pin-joint is a means of coupling one member to another to restrict lateral translation
while still allowing rotation about the axis of the pin. Pin-joints are used in almost all of
the products in the world today in many different types of applications ranging from children's toys to heavy industrial applications. Before beginning the design of a test for these
seemingly simple devices it is necessary to examine the beginnings and evolution of the
pin-joint system.
1.1.1 Pin-Joint Beginnings
Pin-joints have been around since the dawn of man's industrial endeavours. It was not
long after man discovered the wheel that he realized he must somehow attach the wheel to
his cart. Thus the first pin-joint was developed. The first pin-joint system was probably no
more than a shaft made of wood or cast metal placed through a bushing made from either
wood or cast metal. Shortly after this, man introduced lubricant into the joint as a way to
reduce friction. This simple design served man's industrial designs almost up to the twentieth century. It was not until the industrial revolution took place that great advances
started to be made. The discoveries of different lubricants and material processing techniques extended the life of pin-joints and made them suitable for the increased loading
applications that man's large industrial feats required. Improved sealing methods and elas17
18
BACKGROUND
tomeric materials allowed for better lubricant retention within the joint. The preferred
material for industrial applications became steel. Steel was very tough and had the ductility and strength necessary for applications such as the tracks of large earth moving vehicles. It seemed that the only design parameter necessary for increasing the size of a
machine was increasing the size of the steel pin-joint used. Unfortunately, this did not
prove true.
1.1.2 Pin-Joints Today
As the 20th century progressed, the desire for larger machinery became greater and greater
as the scope of man's imagination and engineering capabilities grew to unheard of proportions. Projects such as the "Big Dig" in Boston, Massachusetts and the Three River
Gorges Dam on the Yangtzee River in China required production of the largest industrial
machines in all of man's history. These machines are required to perform under extreme
loading applications. For example, a track link on a large earth moving vehicle is expected
to withstand 100,000 lbf. of loading, while only being 2.5 inches in diameter and roughly
a foot long! Looking at this example from a simple mechanical loading situation, this pin
should function properly, well below the yield strength of steel, but pin-joints still fail at
an alarmingly high rate and at random times. This alludes to the fact that industry is at a
point where simply increasing the size of the pin-joint to insure the yield stress is never
exceeded may no longer suffice as a design principle. It is now necessary to take a deeper
look inside pin-joints and examine the tribological and lubrication issues that are taking
place.
1.1.3 Pin-Joint Geometry
As previously stated, pin-joints are used in a wide variety of applications which in turn has
led to a wide variety of terminology. Although terminology may vary most industry personnel use or are familiar with the configuration and terminology show in Figure 1.1. This
schematic shows the typical pin-joint configuration of a pin passing through a bushing.
Section A-A of Figure 1.1 shows the axial view of the pin. The pin is normally press fit
A Brief Overview of Failure Mechanisms
Bus ing
19
A
1A
Bus ing
F/2
F/F/
Section A-A
Figure 1.1 Pin-Joint Nomenclature
into a fixture on both ends through which load is applied. The bushing is pressed into a
fixture which resists the loads applied by the pin. In Figure 1.1 these loading fixtures have
been replaced with point loadings, which are used when modeling the joint as a four point
bending application.
1.2 A Brief Overview of Failure Mechanisms
Most pin-joints fail by a method of seizure referred to throughout industry as "galling"
which cannot be qualitatively observed due to the inherent opaque nature of most pinjoints. The current way of observing the phenomena is to disassemble a failed joint and
observe the failed surfaces of the pin and the bushing. It can be seen from a picture of a
failed pin in Figure 1.2 that material is "smeared" around the pin and that material has
been transferred between the pin and bushing surface. How this failure occurs is a point of
much debate, throughout industry and academia. Two of the most popular theories of failure are the "micro-weld" theory Archard, J., "Contact and Rubbing of Flat Surfaces", J. of
20
BACKGROUND
Figure 1.2 Galled Pin-Joint
Applied Physics 24, pp. 981-988, July 1953.[Archard, 1953] and the "delamination" theory of wear [Suh, 1973] .
1.2.1 Micro-Welding
The micro-weld theory postulates that throughout rotation, asperity tips of the pin and
bushing come into contact and reach temperatures high enough to cause the metals to
"weld" together. Once the materials have welded together they are immediately ripped
apart, destroying the surfaces of the metals and creating wear particles. These wear parti-
A Brief Overview of Failure Mechanisms
21
cles increase the friction force in the joint which in turn generates more heat which leads
to an increase in micro-welding between the surfaces. Eventually this process reaches a
point where the friction coefficient created by the wear particles and micro-welds is so
high that the joint can no longer rotate.
1.2.2 Delamination Wear
The delamination theory of wear starts with the premise that very small wear particles will
be generated when materials contact no matter what tribological precautions are implemented. These tiny wear particles act as stress risers as they are circulated throughout the
joint. This increased stress causes cracks to propagate below the surface of the pin and
bushing. These microcracks reach a critical length where entire sheets of material are
sheared off of the surfaces. These "delaminated" strips cause larger stress risers that cause
more micro-cracks to develop and delaminate material. This process grows exponentially
until the joint can no longer rotate.
1.2.3 Common Design Parameters
Neither theory has been conclusively proved, and evidence can be drawn from failed
joints to support both theories. The smeared look of failed pin-joints in Figure 1.2 serves
to validate the micro-weld theory, while the visible wear tracks and embedded particles
support the delamination theory. The actual wear mechanism is probably a function of
both mechanisms, but the important thing is to formulate design parameters that can serve
to prevent both mechanisms.
The most obvious way to prevent both methods is to increase lubricant flow to the contact
area of the joint. Increased lubricant will not only prevent the micro-welding contact but
will also carry harmful wear particles away from the contact area preventing delamination
wear. This seems like a simple functional requirement, but effective design parameters are
elusive and hard to validate.
22
BACKGROUND
1.2.4 Lubrication Solutions
Experimental and analytical work has been done in both industry and academia over the
past twenty years trying to address the problem of increasing lubricant and removing wear
particles. Many papers have been written that present mathematical modeling of lubricant
flow within pin-joints [Tamre, 1995] , but these papers can present no visual justification
for their modeling.
Some of the most interesting experimental work has been done by Suh, et al, on adding
surface geometries to the pin in order to "trap" wear particles [Budinski, 1988] . Suh
found that adding very small axial grooves served to reduce both the wear rate and friction
coefficient of pin-joint applications. The theory behind the grooves was that as the joint
would rotate the wear particles would fall into the grooves and not contribute to further
delamination wear. The mystifying point of Suh's research was that when the joint was
disassembled, no wear particles could be found in the grooves! The necessary tool to validate both the mathematical models and work similar to Suh's experimental surface geometries is a means of visually verifying the lubricant and wear particle flow inside a joint
while under full load and operation. This is the hole that the new pin-joint tester will fill.
1.3 State of the Art of Pin-Joint Testing
1.3.1 Design and Testing Parameters
Testing of fully loaded pin-joints is a very expensive endeavor and is only conducted by a
few of the largest industrial firms and universities. Testing is expensive due to both the
equipment involved and the fact that a perfectly good part that could be sold must be
destroyed. A particular large industrial firm has spent the last twenty years investigating
and testing pin joints. They have tested over five thousand pin-joints. With a cost per pin/
bushing set of $500 that adds up to 2.5 million dollars in test pins alone! The test machine
used by the company is shown in Figure 1.3 and costs an additional 10 million dollars.
The rig also occupies a large amount of space with a work volume of 14' by 10' by 8' for
State of the Art of Pin-Joint Testing
23
Figure 1.3 Isometric View of Industrial Testing Apparatus
the rotating machinery and an entire separate room for the hydraulics system and controls.
The problem with the current machine used is that for the large volume and cost it is able
to gather very little data about the testing environment.
The rig is capable of measuring the applied load, by measuring the pressure in the loading
cylinders. It is able to measure the speed of rotation by the use of an encoder. It is able to
measure the pressure in the joint by the use of a transducer mounted inside the pin. It is
able to measure temperature at three locations by using thermocouples mounted on each
side of the bushing and one inside the oil reservoir of the pin. The rig is also capable of
measuring the acceleration of the pin as it rotates by the use of an accelerometer mounted
on the outside of the pin. This last parameter is used to measure when the joint is about to
fail, based on the presumption that as the surfaces wear and particles are formed, the pin
will not rotate smoothly leading to sharp spikes in acceleration.
24
BACKGROUND
These measured parameters are all very interesting but some critical data such as coefficient of friction is currently unattainable.
1.3.2 Testing and Results
A test is conducted by rotating the pin and applying and removing load to simulate field
conditions of a joint. The load is incrementally increased until safety limitations based on
oil temperature and pressure inside the joint are reached. When these safety switches are
triggered the accelerometer is typically registering very large spikes indicating a failed
pin. The pin and bushing are then removed and when disassembled usually show signs of
galling. The problem with this method of testing is that the only information gained is at
what loading a joint failed. Temperature and pressure data are gained but they are bulk
values and not directly applicable to modeling. From a designer's point of view, this
method gives little feedback of which direction to proceed with the next generation design
because no information is available on the old design except that it didn't work! The goal
of this work was to design a new test rig that would be both size and cost effective while
being able to gain more pertinent data for the future design and modeling of pin-joint systems.
1.4 Selection of a Test Joint
Before a new design could be conceived a test joint had to be chosen from which calculations could be made and concepts tested. The selected joint was a track joint from a large
industrial earth moving vehicle. This joint was chosen for several reasons, the most obvious of which was that substantial research had already been done on the joint by the aforementioned industrial firm. This provided not only a current test apparatus to compare the
design improvements to, but also a wealth of experimental and field data to incorporate
into the functional requirements of a test machine for industry. The track joint chosen is
subject to the conditions given in Table 1.1.
Selection of a Test Joint
TABLE 1.1 Field Conditions of Model Pin-Joint
Normal Load
0-100,000 lbf.
Angle of Rotation
0 - 30 degrees
Speed of Rotation
0 - 20 rpm
25
26
BACKGROUND
Chapter 2
TEST MACHINE DESIGN
The industrial design was worked on by a team of professional engineers that had a large
budget and a design time frame of two years. The current design effort was not nearly as
well equipped. The design personnel included one graduate student and one professor that
were given the task to build a new test rig from start to finish in just under 6 months time.
This left very little room for errors or re-works in the design, so the design methodology
used had to be very methodical and exact. There was still room for free flowing creativity,
but the overall design had to be analyzed in a succinct and efficient way in order to guarantee success.
Good engineers have practiced this type of design for many decades, but many have conducted this design in their head and been able to be successful because they are very experienced and good at what they do. Professor Nam P. Suh has presented a very efficient
framework in which to standardize these techniques and design processes that have been
used for so many years [Suh, 1990] .
The technique, Axiomatic Design, presents a nice framework to not only work through a
design but present the results to others. This methodology was used on the pin-joint test
rig design and is presented here. The thrust of the method is that functional requirements
are presented that the machine must accomplish. A list of design parameters are then formulated that meet these functional requirements. The best design parameters are chosen to
meet the functional requirements by insuring that the same two functional requirements do
27
28
TEST MACHINE DESIGN
not depend on the same two design parameters. The design parameters are then further
decomposed into smaller function requirements that must be designed for. This process
continues until a level is reached where the design parameters can be directly linked to the
decomposed functional requirements by a physical law. This method is presented below.
2.1 Design Constraints
2.1.1 Cl- Low Cost
The first constraint is on the cost of the machine. The cost of the current test rig is 10 million dollars which precludes smaller companies and academic institutions from conducting testing. This cost includes both the machine as well as the labor costs involved in
assembling and disassembling the machine for one test. For example, if the improved rig
costs a tenth of the current design but is so complex that is takes an expert operator ten
times as long to run a test, no savings has been made. In fact in the long run, operator
expenses will probably outweigh the cost of the machine. Based on the cost of other loading type machines a cost constraint of $500,000 was set for the new test rig.
2.1.2 C2- Small
The second constraint is on the size of the machine. The current machine is very large and
unwieldy. It not only occupies a large work volume, but also inhibits repositioning. Both
of these characteristics are undesirable for smaller companies and universities where
space is a premium and the ability to reposition equipment is a must. As a first pass design
constraint, a constraint of fitting the new test rig including all the hydraulics and controls
into the work volume of the current test rig (14' by 10' by 8') was set.
2.1.3 C3- Scalable
The third constraint is that the machine must have the ability to be scalable to different
pin-joint systems. This requires the ability to scale the design to accommodate different
Upper Level Functional Requirements
29
pin-joints that are of different sizes, undergo different loadings, pass through different
angles of rotation, and realize different speeds.
2.2 Upper Level Functional Requirements
2.2.1 FR1-Apply Loading
The first upper level functional requirement is that the machine be able to apply a normal
force that simulates the loading of a real world pin-joint system. This requires the ability
to apply up to 100,000 pounds of normal force. This functional requirement not only
entails the choice of a proper design parameter, but an overall design that can accommodate the stresses and strains placed on the machine by the design parameter.
2.2.2 FR2-Apply Rotation
The second upper level functional requirement is that the machine be able to rotate at
speeds that simulate the rotation of the real-world test joint. This entails being able to
rotate through a 30 degree rotation at speeds up to 20 rpms. Again, this not only entails the
design parameter, but an overall structural design that is capable of withstanding the
induced stresses and strains with sufficient factors of safety.
2.2.3 FR3-Conduct Optical Analysis
The third upper level functional requirement is the ability to conduct optical analysis on a
pin-joint. Lower level functional requirements and design parameters for the optical analysis will be discussed later in this text. For the time being the only necessary design
parameter to satisfy this functional requirement will be that there be ample space left
beneath the bushing for the placement of optical elements.
30
TEST MACHINE DESIGN
2.2.4 FR4- Rest on Floor
The fourth functional requirement was simply that the machine had to be able to securely
rest on the floor without distortion that would affect the experimentation.
2.3 Design Concepts
2.3.1 Four-Bar Linkage
The first design concept attempted to continue with the design used by the industrial firm
of using a four-bar linkage to apply both the normal load and joint rotation. This design
shown in Figure 2.1 and Figure 2.2 simplified the industrial design by using cross-members to brace the machine so that the pistons pulled against themselves and the body of the
machine, instead of the large steel fixtures in Figure 1.3.
This concept satisfies the first two design constraints by eliminating some of the bulk of
the machine which makes it less expensive, lighter, and smaller. The third design constraint was satisfied by the design parameter that all of the parts of the machine were
replacable components. To test different pin-joint systems the modular parts of the
machine could be resized. This re-tooling would still incur some cost, but a few of the
parts such as the base plate could be re-used. The design satisfies the first two functional
requirements by applying the normal load and rotation with the four bar linkage. The third
functional requirement was met by supplying ample space beneath the bushing for optical
access. The fourth functional requirement was satisfied by the use of a steel base plate that
could be sized appropriately.
Although this design satisfies all of the functional requirements it still has many flaws.
The first major problem is the complex controls system that will be necessary to apply a
constant load and rotation using two cylinders. This complexity drives the cost of the
machine higher and provides a breeding ground for malfunctions and errors to arise in the
future. The complexity of the four bar-mechanism design stems from the coupled nature
of the design and can be seen by examining the design matrix shown in Table 2.1.
ffi~-~
____
Design Concepts
31
Figure 2.1 Isometric View of Four Bar Linkage Design
The axiomatic design matrix denotes the influence of design parameters by an "X" in the
matrix. For example FR3(Optical Analysis) is only influenced by DP3(Ample Space
Below Bushing), because ample space below the bushing is not affected by the cylinders
or the base plate. On the other hand FR1(Apply Force) and FR2(Apply Rotation) are both
affected by both DP1(Cylinder) and DP2(Cylinder). This is due to the fact that as the second cylinder attempts to provide rotation, the first cylinder must change the force applied
in order to maintain constant loading on the pin, because the line of force has been
32
TEST MACHINE DESIGN
Figure 2.2 Side View of Four Bar Linkage Design
TABLE 2.1 Axiomatic Design Matrix for Four Bar Linkage Design
FR1-Apply Loading
FR2-Rotate
FR3-Enable Optical Analysis
FR4-Rest Securely on Floor
X
X
X
X
0
0
0
0
0
0
X
0
DPi-Hydraulic Piston
DP2-Second Hydraulic Piston
DP3-Ample Space Below Bushing
X
X
X
X
DP4-Steel Plate
changed. Once the force in the first cylinder has changed, the force applied by the second
cylinder must change in order to maintain the desired position. It can quickly be seen that
this is a circular solution that will require a complex controls system in order to reach the
desired performance. This design is a coupled design due to this inter-dependence.
This design also has other conceptual problems. First, although the design has become
lighter it still occupies a large work volume due to the supporting cage. Secondly, although
some parts are interchangeable the design will still cost a substantial re-investment to be
Design Concepts
33
scalable. Third, the design does not lend itself easily to the mounting of load cells and
torque cells to gain data from the testing. This inability to gain vital testing data is one of
the shortcomings of the current industrial design. The final negative attribute is that the
height of the bushing placement creates safety hazards when conducting optical analysis.
For these reasons another design had to be formulated.
2.3.2 Double Clevis Design
The major point that had to be corrected in the second design iteration was the coupled
nature of the two cylinder system. One of the cylinders had to be replaced. The first design
parameter was kept as a hydraulic piston, because the most efficient way of providing a
normal force is with a linear actuator. The second design parameter seemed to be the problem, because it was attempting to provide rotary motion with a linear actuator. To solve
this problem a new design parameter of a hydraulic motor was used to provide the joint
rotations. Although this design parameter seemed inherently obvious, it developed a new
challenge, "How could the cylinder apply a load while the hydraulic motor applied rotation?" The answer to this problem came by placing the cylinder between two clevises.
The smaller clevis was attached to ends of the pin, while the larger clevis was pinned to
joints attached to the floor. The bushing was housed in a steel sleeve that was mounted to
the floor. Thus the piston could extend and apply load to the pin, while the motor could be
attached to the outer clevis and apply rotation, as can be seen in the models of the design
in Figure 2.3 and Figure 2.4. This also eliminated the large cage of previous designs by
taking advantage of the sturdiest reinforcement in the lab area, the floor. The design
matrix in Table 2.2 now shows that the design is de-coupled due to the influence of the
size of the components on the size of the base plate.
This design also allows for the gathering of friction, torque, and load data by mounting
both a load cell and torque sensor in line with the design. The load cell is mounted
between the hydraulic piston and the small loading clevis in order to measure the applied
force in the line of action of the cylinder. This is much more accurate than inferring the
34
TEST MACHINE DESIGN
Figure 2.3 Isometric View of Double Clevis Design
loading of the pin by calculating the pressure in each cylinder as done in the industrial
experimentation. A torque sensor is also mounted in the shaft coupling between the
hydraulic motor and the large rotating clevis. This in line sensor allows for accurate gathering of the torque necessary to rotate the pin. From these two pieces of information it is
possible to calculate the coefficient of friction between the pin and the bushing by
Equation 2.1.
=
Fr
(2.1)
The third functional requirement is still fulfilled by leaving over a foot of clearance below
the bushing mount for optical access to the joint. This design is safer than the previous
design, however, because all optical analysis is conducted near the floor and away from
eye-level of the operator.
Design Concepts
35
Figure 2.4 Side View of Double Clevis Design
TABLE 2.2 Axiomatic Design Matrix of Upper Level FR's and DP's of Double Clevis Design
FR1-Apply Loading
FR2-Rotate
X
0
0
0
DPi-Hydraulic Cylinder
0
X
0
0
FR3- Enable Optical Access
0
0
X
0
DP2-Hydraulic Motor
DP3-Ample Space Below Bushing
FR4-Rest Securely on Floor
X
X
X
X
DP4-Steel Plate
The fourth functional requirement is fulfilled in the same manner as before and this design
parameter will be used in all future designs and will not be reiterated again.
The double clevis design is even more compact and less bulky than the previous design
and thus better satisfies Cl(Low Cost) and C2(Small). It also better satisfies constraint
three by being more modular than the four bar linkage design. Instead of having two loading cylinders with different stroke lengths, this design incorporates only one cylinder with
a short stoke and one hydraulic motor. These two components can be sized accordingly to
the largest loading and torque and then re-used on all smaller joint applications. Eliminat-
36
TEST MACHINE DESIGN
ing the cage design also allows for testing of pins with large rotations of up to 180 degrees.
The only parts that must be replaced on the design to accommodate a different joint configuration are the small loading clevis and the steel bushing mount.
Although this design made great improvements on the previous four-bar linkage design, it
still left much to be desired. The first major drawback was that although the design volume had been minimized, it still had some large rotating parts. For example the outer large
clevis swept through a very large arc, which required ample space and posed a safety hazard to the operator. The second major problem was that the part count was still very high,
because two clevis were needed and the outer clevis required pillow blocks and mounting
fixtures. This large part count adversely affected both the manufacturing costs as well as
the time necessary for assembly. All these factors pointed to the fact that a more compact,
simpler design still had to be formulated. The problem that arose through the search for a
new design was that it was not obvious how the cylinder could push off the floor with out
being attached to the floor through the pillow blocks. This led to the final "Big Clevis"
design.
2.3.3 Big Clevis Design
The part count problem and swinging are problem seemed to be inter-related. Having two
clevis made the arc of swing farther away from the axis of rotation of the pin, posing a
safety hazard, and requiring the use of pillow blocks and mounts. An ideal solution would
be to eliminate the smaller loading clevis and use the outer clevis to clamp right on to the
ends of the pin and receive loading from the cylinder. This solution had merit, but the
question still remained, "How could the cylinder push off of the floor and still provide
rotation with the bushing mount in the way?" The solution was conceived by undergoing a
paradigm shift by which the bushing mount was not "in the way", but rather "there to
help."
Drawing some analogies from the machine tool industry [Slocum, 1993] , it was discovered that a large diameter bearing could be pressed onto the bushing mount. This bearing
Design Concepts
37
could then be press fit into a steel ring that could be threaded onto the cylinder. Using this
configuration the cylinder is threaded into the pressed ring and bolted onto the single loading arm as can be seen in Figure 2.5. The cylinder actuates and attempts to extend which
Figure 2.5 Front View of Final Design
causes the stroke to push against the pressed ring, which presses through the bearing,
which presses down against the bushing mount and base plate and into the floor which
will be assumed rigid. Since the stroke cannot extend, the pressure causes the cylinder to
push up, which pulls on the loading clevis, which in turn loads the pin. Through this
method not only does the arc of swing diminish, but the need for extraneous pillow blocks
and mounts is eliminated. The rotation can then be transmitted from the hydraulic motor to
the loading arm by a flange mount and a keyed shaft as can be seen in Figure 2.5.
38
TEST MACHINE DESIGN
This design is a de-coupled design and satisfies the functional requirements set forth, but
so does the double clevis design. The design matrix in Table 2.2 that was used for the double clevis design remains the same for this design. This design has the same modularity as
the double clevis and the same space under the bushing mount, so its solution of FR3
(Optical Analysis) and C3(Scalability) is the same. The difference in this design is that it
has rectified all the inefficiencies that existed in the previous design. The large part count
that consisted of two loading clevises, two pillow blocks, and two mounting blocks, has
been replaced by one loading clevis, and one large bearing with a pressed ring. The design
is also more efficient because the large moment arm has been decreased reducing the
strain on the hydraulic motor. The big clevis design is also more compact and safer for the
operator. Based on these reasons the big clevis design is the optimum out of the two decoupled designs.
Now that an overall de-coupled design was formulated, it became necessary to set forth
lower level functional requirements and corresponding design parameters to complete the
design.
2.4 Level Two Functional Requirements and Design
Parameters
2.4.1 DP1 Decomposition (Hydraulic Cylinder)
The decomposition of DPI resulted in several second level functional requirements. First
the load had to be generated by the hydraulic cylinder. This functional requirement came
with a corresponding constraint that typical hydraulic cylinders have a limiting pressure of
3500 psi. The second requirement is the ability to monitor the applied force. The third
requirement was that there had to be some way of transmitting the load from the cylinder
to the pin. The fourth requirement was that the cylinder had to have some way of pushing
off of the floor. The fifth requirement was that the bushing had to be held in place.
Level Two Functional Requirements and Design Parameters
39
The corresponding DP for FR11(Generate Force) is the proper sizing of the hydraulic cylinder. The corresponding DP for FR12 (Measure Force) is a load cell in series with the
applied force. The corresponding DP for FR13(Transmit Force) is the loading clevis
shown in Figure 2.5. The corresponding DP for FR14(Support Bearing) is a mounting fixture that secures the bushing to the floor. The corresponding DP for FR15 (Push off of
Floor) is the press fit ring on the large diameter bearing. This design parameter is constrained by the fact that the bearing can not be more than 1.5 in. wide or it will inhibit optical access to the joint. A design matrix of DP1's decomposition is given in Table 2.3,
which reveals that the design is de-coupled because the size of the cylinder and load cell
will affect the loading clevis and the size of the bearing mount is going to affect the diameter of the bearing chosen.
TABLE 2.3 Axiomatic Design Matrix for DP1 Decomposition
FR 11-Generate Force
FR12-Measure Force
FR13-Transmit Force
FR14-Support Bearing
FR15-Push off of Floor
X
0
X
0
0
0
X
X
0
0
0
0
X
0
0
0
0
0
X
X
0
0
0
0
X
DP 1-Properly Size Cylinder
DP12- Load Cell
DP13-Loading Clevis
DP14-Bushing Mount
DP15-Press Fit Ring
2.4.2 DP2 Decomposition (Hydraulic Motor)
The decomposition of DP2 resulted in several second level functional requirements. The
first requirement was that the pin be able to rotate a minimum of 30 degrees. The second
requirement was that the motor be able to rotate the pin at 20 rpms. The third requirement
was that the rotation of the motor had to be transmitted to the pin. The fourth requirement
was to be able to measure the torque necessary to rotate the pin. The fifth requirement was
that the motor rotate along the axis of the pin in order to avoid any binding moments that
may affect rotation.
The corresponding DP for FR21(Rotate 30 Degrees) was satisfied as a result of the upper
level design. Using an open frame design to provide scalability according to C3 (Scalabil-
40
TEST MACHINE DESIGN
ity) has in turn already satisfied FR21 (Rotate 30 Degrees). Therefore no further decomposition is necessary. The corresponding DP for FR22 (Rotate at 20 rpm) was the proper
sizing of the hydraulic motor based on pressure and flow that could be provided. The corresponding DP for FR23 (Transmit Rotation) is a keyed coupling shaft from the motor that
flange mounts to the loading clevis. The corresponding DP for FR24 (Measure Torque) is
a torque sensor mounted in series with the coupling shaft. The corresponding DP for FR25
(Align Motor) is a raised mounting platform that aligns the motor axis with the axis of
rotation. A design matrix is given inTable 2.4, and shows that the design is un-coupled.
TABLE 2.4 Axiomatic Design Matrix of DP2 Decomposition
FR21-30 degree rotation
FR22-Rotate at 20 wpm
FR23-Transmit Rotation
FR24-Measure Torque
FR25-Align Motor
X
0
0
0
0
0
X
0
0
0
0
0
X
0
0
0
0
0
X
0
0
0
0
0
X
DP21-No Obstructions
DP22-Motor Sizing
DP23-Coupling Shaft
DP24-Torque Sensor
DP25-Motor Mount
2.4.3 DP3 Decomposition (Ample Space Below Bushing)
The decomposition of DP3 yielded several lower level functional requirements. The first
requirement was that there be sufficient room underneath the bushing for the mounting of
optical elements. Based on optical mirrors and lenses and observing other experimental
setups for conducting optical imaging, a height of one foot was established as a criteria.
The second requirement was that there be optical access through the steel bushing mount.
The third criteria was that there be optical access to the contact area of the joint while
under full loading that was accessible to laser light and optical imaging. The final requirement was that the oscillations and chatter of the machine be minimized in order to increase
the resolution and decrease the error of the images gathered.
The corresponding DP for FR31 (Optical Clearance) is proper sizing of the legs of the
bushing support to allow for the optical analysis. FR32 (Mounting Access) is satisfied by
cutting a viewing window in the bottom of the steel bushing mount. The slot for viewing
Level Two Functional Requirements and Design Parameters
41
could be sized appropriately small and would have little affect on the stress in both the
bending and compressive stress of the mount.
FR33 (Internal Joint View) was the most challenging to solve because the very nature of
optical imaging is not conducive to the loads experienced in this application. Typically
optical analysis is conducted by making one of the surfaces transparent to facilitate the
viewing of the lubricant flow within the joint. This could not be done in this case, however, because the required 100,000 lbf. loading would crack any transparent material of
reasonable thickness. The design parameter that presented itself was the introduction of
scaling laws into the design. It was postulated that the exact same behavior of surface features, such as deformations and deflections experienced by a steel pin and steel bushing
under 100,000 lbf. of loading, could be replicated on two different materials under a much
lower loading. If this was true and if one of the materials could be transparent, the lower
loading would allow the use of optical analysis to characterize the affects of surface geometries and pin configurations on lubricant flow. This hypothesis turned out to be correct
and is explained in detail in Chapter 3. For now the design parameter will simply be listed
as scaling laws and further decomposition will be postponed until Chapter 3.
FR34 (Reduce Chatter) was satisfied by designing a damping floor mat beneath the base
plate to damp the oscillations and chatter created by the machine and hydraulics. A design
matrix is shown in Table 2.5, and shows that the design is un-coupled.
TABLE 2.5 Axiomatic Design Matrix for DP3 Decomposition
FR3 1-Optical Clearance
FR32-Mounting Access
X
0
0
0
DP3 1-Sizing of Mounting Legs
0
X
0
0
DP32-Optical Slots
FR33-Internal Joint View
0
0
X
0
DP33-Scaling Laws
FR34-Reduce Chatter
0
0
0
X
DP34-Damping Pad
42
TEST MACHINE DESIGN
2.4.4 DP4 Decomposition (Steel Plate)
The decomposition of DP4 led to three lower level functional requirements. First the base
plate had to be large enough to accommodate all the components of the apparatus. The
second requirement was that the plate had to allow for easy transportation and positioning
of the equipment. The third requirement was that the plate should avoid plastic deformations under loading of the cylinder.
The corresponding DP for FR41(Accomodate All Parts) is proper sizing of the plate to
accommodate all experimental elements. The corresponding DP for FR42 (Accommodate
Palate Jack) is that the base plate be mounted on riser mounts capable of accommodating a
standard lab palate jack. FR43 (No Plastic Deformation) is satisfied by sizing the thickness of the plate to avoid plastic deformation under loading.
The design matrix in Table 2.6, shows that the design is de-coupled due to the fact that
FR43 is affected by the surface area of the plate, its loading points, as well as its thickness.
This is still a viable design because DP41 and DP42 can be set, and then DP43 can be
appropriately chosen.
TABLE 2.6 Axiomatic Design Matrix for DP4 Decomposition
FR41-Accommodate All Parts
FR42-Accommodate Palate
Jack
FR43-No Plastic Deformation
X
0
0
X
0
0
DP41-Size of Plate
X
X
X
DP43-Thickness of Plate
DP42-Height and Position of Risers
2.4.5 Level Two Design Matrix
Before the design progressed any further it was necessary to examine the entire level two
design matrix in Table 2.7 to ensure nothing had become coupled in the decomposition.
From the full design matrix we can see that the design has become coupled by the fact that
the height of the mounting legs necessary for optical access affects the necessary height of
the motor mount to ensure axis alignment. An easy solution to this problem however is to
switch the rows of the matrix and the design becomes de-coupled as can be seen in
43
Level Two Functional Requirements and Design Parameters
TABLE 2.7 Coupled Axiomatic Design Matrix for Level Two Decomposition
FRIl
FR12
X
O
OO
O
X
0
FR13
X
X
FR14
FR15
OO
0 0
FR22
FR23
OO
FR24
FR25
FR31
FR32
FR33
FR34
FR41
FR42
FR43
O
O
O
OO
0
0
0
0
0
X
O
OO
O
O
O
0
X O0 0 0
X X O O
O
OO
O
O
O
OO
O O
DP11
0
0
0
0
0
OO
O O
DP12
O
0
0
0
0
0
OO
O O
DP14
0
0
0
0
0
OO
O O
DP15
OO
O O
0 0 0 0
DP22
0
0
0
0
0
0
0
0
0
0
0
0
0
O
O
0
X OO
O
O X OO
O0 0
O O0
0
0
0
O OO
OO
O
O0 0
O
O
X
OO
O
0
0
X OO
X OO
X O
0
OO
0
X
0
O
OO
O
O
OO
X X
O
X
OO
O
O O0 0 0 0 0 0 0 0
X X X X X X X X X X
O O O OO
O O O
OO
OO
O
O
0
0
0
DP13
0
0
O
O
0
O0 0 0 0 0
OO
O O OO
O
0 0 0
0
X 0
0
O
0
0
0
0
0
0
0
0
X
X
0
0
0
0
0
DP23
DP24
0
0
0
0
DP25
DP31
0 0
0 0 0
0 0 0
0 0 0
X O O
0
X
DP32
DP33
DP34
DP41
X0
DP42 I
X X DP43
Table 2.8. In plain terms this means that the height of the legs to allow optical access will
first be determined, and then the height of the motor mount will subsequently be chosen.
The second level design parameters will be treated in this order during the rest of this discussion. DP21(No Obstructions) has already been fully decomposed and a connection "X"
solved therefore it will not be discussed in further decompositions.
--
I
*
II
I
I'
TLIILJr1r11*
-
TEST MACHINE DESIGN
44
TABLE 2.8 Revised Axiomatic Design Matrix For Level Two Decomposition
FR11
FR12
FR13
FR14
FR15
O O O OO
O
O OO
O X OO
X X X 0 0 0 0 0
0 0 0 X 0 0 0 0
O O O X X O OO
X
OO
FR22
FR23
O0 0
FR24
FR31
FR25
0
FR32
FR33
O OO
FR34
FR41
FR42
FR43
______________I
0 0
0
O O OO
OO
O O O O O
O O O O O
0 0 0 0 0
0 0 0 0 0
O O
O OO
X O OO
O OO
O X OO
O OO
X 0 0 0 0
X 0 0 0
0 0 0 0 0 0 0 0 0
X X OO
o0 0 0 0 0 0 0 0
0
O O
0 0
X X
0 0
0 0
0
0
0
0
0
0
O O O O O OO
O O OO
0 0 0 0 0
X X X X X
0 0 0 0 0
0 0 0 0 0
OO
O
O O O
0 0 0 0
X X X X
0 0 0 0
0 0 0 0
0
o
DP11
0
o
DP12
0 0
0 0
0
o
DP13
0
DP14
0 0
0
o
o
o
DP22
o
o
DP23
0
0
0
0
N0 0
0 0 0
0 0 0
X O
O X
0 0
X X
0
0
0
0
X
X
0
O
0
X
0
X
DP15
DP24
o DP31
o DP25
o DP32
o DP33
0 o DP34
0 o DP41
X o DP42
X X DP43
Level Three Functional Requirements and Design Parameters
45
2.5 Level Three Functional Requirements and Design
Parameters
2.5.1 DP11 Decomposition (Properly Size Cylinder)
DP11 is already fully decomposed. The "X" that connects FR11 (Apply Loading) and
DP11 (Sizing of Cylinder) is given in Equation 2.2.
A = F
(2.2)
From this equation and a conservative estimate of only applying 2,500 psi of pressure to
the system it becomes apparent that a diameter slightly larger than 7 in. is necessary for
the cylinder. For this design a diameter of 8 in. was used in order to further reduce the
pressure demands on the system. Furthermore, a 2 in. stroke was specified for the cylinder.
Such a long stroke was not necessary as the cylinder would only deflect the pin a few
thousandths of an inch, but the play in the stroke facilitated installation. These were given
to a manufacturer and an appropriate cylinder was created. A print of the cylinder used is
included in Figure 2.6.
321.62)
If
Figure 2.6 Side View of Cylinder (in)
46
TEST MACHINE DESIGN
2.5.2 DP12 Decomposition (Load Cell)
DP12 is already fully decomposed. The "X" that connects FR11 (Measure Force) and
DP11 (Load Cell) is selecting a load cell from a manufacturer that is able to measure
100,000 lbf. while at the same time being able to connect to both the cylinder and the
mounting ring. The load cell also had the added constraint that it had to be as slim as possible because it had to be placed in line with the piston. This is due to the fact that the
thicker the load cell was, the farther the heavy piston was away from the center of rotation
which would require more torque from the motor to rotate the assembly.
A suitable load cell was found that was comparably thin and had a hole in the center which
could be threaded onto the stroke of the cylinder. The load cell also had a bolt hole pattern
around the circumference in order to attach to the press fit ring. The "Pancake" load cell
S.00
0
(2.50'II
0
Figure 2.7 Drawing of Load Cell (in.)
that was chosen is shown in Figure 2.7.
2.5.3 DP13 Decomposition (Loading Clevis)
The decomposition of DP13 yields several level three functional requirements. The first is
that the loading arm must be able to attach to the cylinder. The second requirement is that
Level Three Functional Requirements and Design Parameters
47
it must be able to securely attach to the pin and allow no slip while still allowing ease of
assembly and disassembly. The third functional requirement is that the loading clevis had
to have a flange mounted to its arm that allows the torque sensor to bolt onto the axis of
rotation of the joint The fourth functional requirement is that the arm must not plastically
deform under full loading and rotation. The final functional requirement is that it must be
perfectly balanced around the axis of rotation so that the only torque required by the motor
is that required to overcome the friction between the pin and bushing. This requirement
will ensure the coefficient of friction measurements are functions solely of the friction
force within the joint and not influenced by a moment arm.
An additional constraint on the design of the arm is that it must be made as short and light
as possible. This is for two reasons. The first reason is that the more weight put in the arm
places a higher pre-load on the pin. The second reason is the same given for the load cell
being thin, the more weight placed farther away from the axis of rotation creates a greater
moment that must be overcome by a counterweight or motor torque.
The corresponding DP for FR131 (Attach to Cylinder) is placing four threaded holes into
the cylinder around the stroke and four corresponding clearance holes in the top of the clevis surrounding a clearance hole for the stroke. Thus the stroke can slide through the large
hole cut in the clevis and the clevis can be bolted to the cylinder as shown in Figure 2.8
Finding a design parameter for FR132 (Attach to Pin) was not easy because the constraint
of "easy to assemble and disassemble" ruled out the common practice of press fitting the
pin into its mating piece. Another solution had to be found.
Through a study of flexure design it was conceived that the arms of the clevis could be
clamps that would allow the pin to slide through with ease upon assembly and disassembly, but could be tightened closed with bolts before operation. This design parameter not
only facilitates easy assembly but allows the operator to adjust the "psuedo" press fit
based on the pin being tested. A isometric view of the "pin clamps" is given in Figure 2.9.
FR133 (Attach to Torque Sensor) was a tricky requirement to satisfy. The torque sensor
48
TEST MACHINE DESIGN
Figure 2.8 Isometric View of Clevis/Cylinder Attachment
Figure 2.9 Isometric View of Pin Clamp
Level Three Functional Requirements and Design Parameters
49
cannot bolt right onto the clamp because it would interfere with the clamping. An attachment could be welded on, but then it would not allow removal of the pin, Figure 2.8. A
solution to these problems was the designing of a removable mounting that attached to the
loading arm above the axis of rotation, but had a "dog-leg" down to align the sensor with
the axis of rotation. An isometric view of the proposed design parameter is shown in
Figure 2.10.
FR134 (No Failure of Plastic Deformation) is satisfied by properly sizing the dimensions
of the loading clevis in order to avoid plastic deformation and failure. FR135 (Balanced) is
satisfied by providing counterweight posts attached to the arm on the opposite end of the
hydraulic cylinder. These posts can be loaded with counterweights similar to those used in
weight rooms in order to compensate for the weight of the arm and cylinder.
In order to reduce the weight of the overall arm, the lengths of the arm were made out of
two thin-walled box beams. This adjustment costs little as far as tensile strength and bending strength are concerned, but pays large dividends in weight savings. An isometric view
of the overall clevis design with counterweights is given in Figure 2.10. A design matrix
summary for the DP13 decomposition is also given in Table 2.9, which reveals that the
design is de-coupled due to the dependence of the amount of counterweights on the size of
the arm.
2.5.4 DP14 Decomposition (Bushing Mount)
DP14 was composed into several level three functional requirements. The first requirement is that the mount be able to firmly hold and support the bushing in place while at the
same time allowing ease of assembly and disassembly. The second functional requirement
for the mount is that it elevate the bushing off of the base plate in order to allow the loading clevis to swing by with the counterweights upon rotation.
FR141(Hold on to Bushing) sounds very similar to FR131 (Hold on to Pin), and thus
receives a similar design parameter. DP141 is to use a clamping device that is the same
50
TEST MACHINE DESIGN
Figure 2.10 Isometric View of Clevis and Weights
TABLE 2.9 Axiomatic Design Matrix of DP13 Decomposition
FR13 1-Attach to Cylinder
FR132-Attach to Pin
FR133-Attach to Torque Sensor
X
0
0
0
0
0
X
0
0
0
DP131-Bolts
DP132-Pin Clamps
0
0
X
0
FR134-No Failure or Plastic Deformation
0
0
0
X
0
0
DP132-Detach Mount
DP134-Sizing of Arm
FR135-Balanced
0
0
0
X
X
DP135-Counterweights
length as the bushing in order to hold it in place. When the mount is unclamped, the bushing can slide freely in and out of the mount, but when the mount is clamped the bushing is
locked in place. DP142 satisfies FR142 (Elevate Bushing) by using two legs that are connected to the mount and the base plate and set in away from the rotating clevis. An over-
Level Three Functional Requirements and Design Parameters
51
view of the mounting assembly is given in Figure 2.11. A summary of the mount
Figure 2.11 Isometric View of Bushing Mount
decomposition is given in Table 2.10, which shows that the sub-design is un-coupled.
TABLE 2.10 Axiomatic Design Matrix for DP14 Decomposition
FR141-Fix Bushing
X
0
FR142-Elevate Bushing
0
X
DP141-Clamping Mechanism
FR142-Two Thin Legs
52
TEST MACHINE DESIGN
2.5.5 DP15 Decomposition (Press Fit Ring)
The decomposition of the press fit design yielded several functional requirements. The
first requirement was that the press fit onto the bushing mount had to allow rotation of the
joint. The second requirement was that it had to be able to interface between the load cell
and the design parameter used to provide rotation. Thus this functional requirement was
de-coupled to the first design parameter of this decomposition. The last and most challenging functional requirement that was generated was the ability to press fit the entire
part onto the bushing mount when the clamp was open and when the clamp was closed!
The design parameter chosen to fulfill FR151 (Provide Rotation) was a large diameter
bearing. Bearings were developed for the machine tool industry that are very narrow and
can carry very high loadings on a large diameter race [Slocum, 1993] . These were ideally
suited for this application. The second design parameter was simply a piece of steel that on
one surface was able to bolt to the load cell, while on the other it was able to be press fit
onto the large bearing.
The final design parameter to allow the press fit onto the bushing mount, was the trickiest
to design because a simple press fit would not work due the changing diameter of the
bushing mount as the clamp was tightened. A clamp could not be used as in previous solutions because the outer surface of this element had to be pressed into the inner diameter of
the bearing, which was constant. The parameter that was finally devised was to use four
mating blocks and a mating ring. The ring would be cut with a 45 degree face and press fit
into the bearing. The four mounting blocks would be cut with corresponding 45 degree
faces and sized slightly wider than the ring, bushing combination. The four blocks would
then be welded to the outer diameter of the bushing mount. Both the bearing ring and the
four blocks would have oversized clearance holes drilled through them. Thus the faces of
Level Three Functional Requirements and Design Parameters
53
the blocks and ring could be bolted together to achieve a pre-load on the bushing mount.
As the bushing mount was clamped down on the bushing, the bolts on the block/ring interface could be tightened which would cause the ring to slide up the faces of the block and
maintain a tight "pseudo" press fit.
There is an axial error that is incurred which is equivalent to the amount the radius of the
bushing mount changes. Based on the assumption that the clamping force will be the same
as the interference of a medium press fit which is 0.0035 in. on the radius, the mounting
will have a "delta x" equivalent to 0.0035 inches, Figure 2.12. This is negligible, due to
delta x=.015 in.
Pressed Ring
--1.
Mounting Block
delta y=.015 in.
Figure 2.12 Mounting Block/Ring Schematic
the compliance that exists in the mountings between the clevis and the cylinder, as well as
the bolted coupling between the load cell and the mating piece. A solid model of the
mounting configuration is given in Figure 2.13, followed by an overview of the entire
54
TEST MACHINE DESIGN
Figure 2.13 Isometric View of Mounting Blocks
assembly that connects the load cell to the ground in Figure 2.14. The summary design
matrix in Table 2.11 reveals that the design is de-coupled.
2.5.6 DP22 Decomposition (Motor Sizing)
DP22 was set forth as the correct sizing of the hydraulic motor in order to rotate the pin.
Therefore a motor had to be chosen that met the following functional requirements. The
first was to be able to overcome the torque necessary to rotate the pin under full load. This
was estimated by solving Equation 2.1 for the torque it would take to rotate a pin with
r=1.31 in. F=100,000lbf. and [=.07 for lubricated contact. The torque necessary to rotate
the pin under these conditions turns out to be 9,000 in-lbf. The second requirement is that
the motor be able to rotate at 20 rpm under these conditions.
The corresponding DP for both of these functional requirements is the selection of an off
the shelf motor capable of meeting these criteria. A low-speed, high torque hydraulic
motor was found capable of meeting both of these criteria and able to provide 13,500 inlbf of torque and 20 rpm under maximum pressure and flow. This left little room for error
Level Three Functional Requirements and Design Parameters
55
Figure 2.14 Isometric View of Base plate to Load Cell Connection
TABLE 2.11 Axiomatic Design Summary for DP15 Decomposition
FR15 1-Allow Rotation
FR152-Load Cell/Mount Connector
X
0
0
DP151-Large Bearing
X
X
0
FR153- Press and Clamp Bushing
X
0
X
DP152-Bolt Holes/Press Fit
DP153-Angled Blocks
and the motor could be ineffective if the coefficient of friction rose substantially above
0.07 during a failure mode. This scenario was a worst case scenario and since most of the
testing would be conducted well below the 100,000 lbf maximum loading it was decided
that the current off the shelf motor was a better solution than ordering a specialty motor.
As a worst case scenario, another identical motor could be coupled to the shaft in series,
56
TEST MACHINE DESIGN
with little trouble, and easily rotate the pin. A design matrix is not included here because
the design parameters and connecting matrix are simply to choose an off the shelf motor.
2.5.7 DP23 Decomposition (Coupling Shaft)
The problem of connecting the motor to the loading clevis seemed simple but actually
proved to be rather challenging, presenting several lower level functional requirements.
The first is that the coupling shaft had to allow for mis-alignments between the loading
clevis and the motor so true rotation could be achieved while at the same time being able
to transmit the 9,000 in-lbf of torque necessary. The second requirement was that the shaft
had to connect to the motor. The third requirement was that the shaft had to connect to a
flange mounted torque sensor. The fourth requirement was that the shaft had to prevent
side loads from being transmitted from the loading clevis to the motor shaft to avoid damage to the motor. The final requirement was that the shaft had to have a torsional deformation of less than one degree to minimize backlash.
The DP that solved FR231 (Allow for Mis-Alignments) was a flexible coupling. A gear
tooth coupling was found that was able to account for 1.5 degrees of misalignment. FR232
(Connect to Motor) was satisfied by a keyed slot in both the shaft and flexible coupling so
that the flexible coupling joins the motor shaft and coupling shaft together. Off the shelf
shaft keys were purchased capable of transmitting the desired torque.
The DP that satisfied FR233 (Attach to Torque Sensor) was a short cylinder that had a
keyed way in the center to connect to the coupling shaft and bolt holes for a flange mount
around the circumference. This member is shown in Figure 2.15
At first FR234 (Prevent Side Loads) appeared to be satisfied by the flexible coupling, but
after further examination, it became apparent that if the loading clevis deflected down
enough to deflect the shaft by more than 1.5 degrees side forces would still be transmitted
to the motor. Simple geometry in Figure 2.16 reveals that this is more of a problem if the
flexible coupling is close to the loading clevis than if it is far away. Therefore an effective
tsm
Level Three Functional Requirements and Design Parameters
57
Figure 2.15 Shaft/Torque Cell Connection
L2
L1
denl
z13de
CD
Figure 2.16 Length of Shaft Affect on Allowable Error
design parameter is to insure that the shaft is long enough to allow for the worst displacement of the loading clevis. This is done by figuring out the maximum displacement of the
loading clevis and solving the geometry for the corresponding length. The maximum displacement of the loading clevis was approximated by subjecting half of the pin to a simple
point load of 50,000 lbf. as can be seen in Figure 2.17. The solution for maximum deflec-
58
TEST MACHINE DESIGN
F
L
Figure 2.17 Simple Beam Bending Diagram
tion of this simple beam bending scenario is well documented and is given in
Equation 2.3, For this scenario FL=50,000 lbf., Lpgn=14 in., ESteel=30E 6 psi., bI,=1.916
in 4 , and the resulting Az= 0.046in. Through simple trigonometry it can be
FL(L~
Az = 24.
3
24.- ESteel Ipin
(2.3)
calculated that length of the beam has to be approximately 1.5 inches. This value was
given a safety factor of 15 for further calculations which results in a connection length of
22.5 inches. This increased length actually improves the design, because it gives the operator more room to work around the machine as well as keeping the hydraulic elements of
the motor away from the large rotating clevis.
The final functional requirement was satisfied by appropriately sizing the diameter of the
shaft to resist twisting. The equation governing twist angle of a shaft is given in
Equation 2.4 [Hibbeler, 1993] .
Level Three Functional Requirements and Design Parameters
59
TL~hf
Shaft(2.4)
0 =
G)
(j(c4.
T is a torque of 9,000 in-lbf. LShaft is the shaft length of 22.5 in. G is the modulus of rigidity equal to 1 1E
6
psi. Solving the above equation results in a minimum shaft radius (c) of
0.75 in. Therefore the shaft will be sized to the closest flexible coupling that has a shaft
diameter greater than 1.5 in. A summary design matrix is included in Table 2.12
TABLE 2.12 Axiomatic Summary Design Matrix for DP23 Decompositions
FR23 1-Allow For Mis-Alignment
FR232-Connect to Motor
FR233-Connect to Sensor
FR234-Prevent Side Loads
FR235-Limit Angle of Twist
X
0
0
0
0
0
X
0
0
0
0
0
X
0
0
0
0
0
X
X
0
0
0
0
X
DP23 1-Flexible Coupling
DP232-Keyed Shaft
DP233-Keyed/Flange Mount
DP234-Length of Shaft
DP235-Diameter of Shaft
2.5.8 DP24 Decomposition (Torque Sensor)
The decomposition of DP24 yielded three lower level functional requirements. The torque
sensor had to be able to record torque loads of up to 10,000 in-lbf. It also had to be small
enough to be reasonably mounted on the coupling shaft. Finally it had to be flange mountable to both the coupling connector and the loading clevis.
Like many of the other off the shelf parts the connection between the functional requirements and design parameters was merely selecting a supplier that could provide the
desired instrument.
2.5.9 DP31 Decomposition (Sizing of Mounting Legs)
DP31 is decomposed into several lower level design parameters. The first requirement to
allow optical access has already been satisfied by setting the distance from the bushing
mount to the floor as at least 1 ft. The second functional requirement is that the legs minimize rocking of the machine. The third functional requirement is that the legs avoid buck-
60
TEST MACHINE DESIGN
ling. The fourth functional requirement is that the legs attach to the bushing mount. The
final functional requirement is that the legs attach to the floor.
The DP that satisfies FR312 (Minimize Rocking) is that the legs form an angle with the
base plate that is less than 90 degrees with smaller angles being more stable to resist rocking motion. An angle of 60 degrees was chosen as a compromise between more stability
and space conservation. FR313 (Avoid Buckling) was satisfied by choosing the thickness
of the legs to resist buckling based on Equation 2.5 [Hibbeler, 1993] . Based on this equation and using a length of 12 in. and a width of only the diameter of the bushing mount (6
in.) as a worst case scenario, the thickness must be at least 0.73 in. to avoid buckling.
2
BucklingLoad =
I
3
- ESteel Wlegs -thlegs
96- hegs
(2.5)
A thickness of 0.75 in. was chosen, based on the assumption that a factor of safety was
already built in due to the increase inertia of the wide-angled legs as opposed to the 6 in.
wide beams.
FR314 (Attach to Bushing Mount) is satisfied by welding the mounting legs to the bushing mount. Tensile stress is not a factor when designing the welds because the bushing
mount is in compressive contact with the mounting legs during operation. The parameter
that is important is that the welds be sufficient enough to withstand the 9,000 in-lbf of
torque that will be applied to the bushing. Based on the fact that the shear force decreases
with distance away from the axis of rotation, the actual force experienced by the entire
weld is a mere 2,500 lbf. if a diameter of the bushing mount of 4 in. is assumed. Continuing with the assumption that the final diameter of the bushing mount will be 8 in., that the
leg thickness is 0.75 in.,and that the welds will extend half way around the bushing mount
the surface area of the weld as a function of weld bead size can be calculated as 51W in
Equation 2.6. Plugging this value for surface area into the shear stress formula given in
Equation 2.7
61
Level Three Functional Requirements and Design Parameters
surfacearea =
2H8+4 -
US
W = 51W
Fs
51
S51 W
(2.6)
(2.7)
and using a shear force of 2,500 lbf. and a maximum shear stress of 1.4E 5 psi, a minimum
value for W is found of 0.017 in. Therefore a weld bead diameter of 0.25 inches will be
more than sufficient to secure the mounting legs to the bushing mount.
The final functional requirement was satisfied by welding mounting plates to the bottom
of the legs that would be bolted to the base plate. Although the bolts should always be in
compression, it was necessary to size the bolts as if the machine were mis-operated and
the cylinder pulled away from the floor. Assuming 8 bolts, it was determined that a 0.75
in. SAE 5 steel bolt could easily handle the 12,500 lbf. of force generated under maximum
loading. A summary design matrix is included in Table 2.13.
TABLE 2.13 Axiomatic Design Summary Matrix for DP31 Decomposition
FR311-Allow Optical Analysis
FR312-Minimize Rocking
FR313-Avoid Buckling
FR314-Attach to Bushing Mount
FR315-Attach to Base plate
X
0
0
0
0
0
X
0
0
0
0
0
X
0
0
0
0
0
X
0
0
0
0
0
X
DP3 11-Height of Legs
DP312-Angle of Legs
DP313-Thickness of Legs
DP314-Welds
DP315-Mounting Blocks
2.5.10 DP25 Decomposition (Motor Mount)
DP25 is decomposed into several lower level functional requirements. The first is that it
must elevate the motor to the correct height and support the weight of the motor. The second is that it must attach to the motor. The third requirement is that it must secure to the
base plate. The final requirement is that it must minimize vibrations from the motor.
The design parameter that satisfies FR251 (Elevate Motor) is the appropriate sizing of the
legs. The height of the legs would be determined by the final height of the bushing mount.
62
TEST MACHINE DESIGN
Due to the fact that there was little force placed on the legs by the weight of the motor,
failure and plastic deformation were not a factor. The thickness of the legs was chosen as 1
in. due to material availability. They are attached by a 1" mounting plate to the motor.
FR252 (Attach to the Motor) is satisfied by a mount that bolts to the motor and in turn
bolts to the legs. FR253 (Secure to Base plate) is similar to the functional requirement of
securing the bushing mount legs to the base plate. In order to lower cost and simplify the
assembly process, the same mounting blocks that are welded to the legs of the bushing
mount and bolted to the floor are used here.
The final functional requirement was satisfied by placing a piece of 0.75 in. hard rubber
between the motor mounting plate and the plate that was welded to the legs. The mounting
plate and the hard rubber are fitted with clearance holes while the plate attached to the legs
has threaded holes. Therefore long bolts are passed through the motor mounting plate,
then the rubber, and finally threaded into the leg mount. This rubber is hard enough to support the load of the motor while soft enough to absorb a great deal of the vibrations. An
isometric view of the entire motor mount assembly is included in Figure 2.18. A summary
design matrix is included in Table 2.14.
2.5.11 DP32 Decomposition (Optical Slots)
DP32 is fully decomposed and only needs a connecting equation to connect DP32 (Optical
Slots) to FR32 (Mount Access). The connection between the two is the width of the slots.
Knowing that the joint undergoes 30 degrees of rotation, this seems like the obvious candidate for window size. Therefore the chord length of the outer diameter of the bushing
subtended by a a 30 degree angle should be the width of the optical slot as shown in
Level Three Functional Requirements and Design Parameters
63
Figure 2.18 Isometric View of Motor Mount
TABLE 2.14 Axiomatic Design Summary Matrix for DP25 Decomposition
FR25 1 -Elevate Motor
X
0
0
0
FR252-Attach to Motor
FR253-Attach to Base
plate
FR254-Reduce Vibration
0
X
0
0
DP25 1-Match Height of Legs
DP252-Motor Mount Interface
0
0
X
0
DP253- Mounting Blocks
0
0
0
X
DP254-Rubber Pad
Figure 2.19. Using 2.322 in. for the radius of the bushing the necessary width of the window can be solved for by trigonometry as 1.2 in.
2.5.12 DP33 Decomposition (Scaling Laws)
DP33 needs to be further decomposed but this decomposition is covered in Chapter 3.
64
TEST MACHINE DESIGN
Wdt~h
of
Wndcyw
30 deg.
Figure 2.19 Width of Window
2.5.13 DP34 Decomposition (Damping Pad)
DP34 no needs no further decomposition but only to select a proper damping pad to eliminate vibrations. In this case a sandwich damping device was constructed using two 1/8"
sheets of buna rubber surrounding one 1/2" piece of particle board to damp out vibrations
and chatter. This pad was placed underneath the base plate riser mounts and the hydraulic
system mounts to reduce vibrations in the test cell.
2.5.14 DP41 Decomposition (Size of Plate)
DP41 has already been decomposed, but can now be sized based upon the lengths of all
the major components in the two directions. The length of the plate must be greater than
the lengths of the pin, the coupling device, and the motor combined. The width of the plate
had to be wider than the width of the legs. These critical dimensions were then rounded to
the next whole foot, to allow for a margin of error and machining simplicity, resulting in a
plate with dimensions of 4 ft. by 5 ft.
Level Three Functional Requirements and Design Parameters
65
2.5.15 DP42 Decomposition (Height and Position of Risers)
DP42 has already been decomposed and can be connected to FR42 (Accommodate Palate
Jack) by measuring the minimum height of standard palate jacks. This height was found to
be 3 in., therefore the riser mounts were made 4 in. tall out of 3 in. diameter, round stock.
Clearance holes were drilled through the base plate, and corresponding holes were tapped
into each riser. The mounts were thus bolted to the plate and fixed in place. Ten instances
was selected as ample support for the base plate, with three risers on each side and one in
the center to prevent bending of the base plate. Compressive stress considerations were
not a consideration, because of the large surface area of support of the ten risers. Stress in
the bolts was negligible due to the fact that there were no shear loads placed on the risers.
Deflection of the base plate was then limited by proper selection of the thickness of the
plate in DP43 (Thickness of Plate).
2.5.16 DP43 Decomposition (Thickness of Plate)
DP43 is fully decomposed and is connected to FR43 (Avoid Plastic Deformation) by the
equation for bending moment in a beam fixed at both ends. This is given in equation
Equation 2.8. Obviously the larger of the two dimensions of the plate controls the minimum
Gmaxbending =Riser
4
-
(2.8)
2
Wplate - (Thickness
)
thickness of the plate. Using lE 6 psi as the yield strength for medium-carbon steel,
F=100,000lbf, LRiser = 30 in., Wplate= 48 in., a minimum thickness of 0.685 in. Based on
this calculation a thickness of 0.75 in. was chosen. This estimate includes an additional
factor of safety because the 100,000 lbf. does not act in the center of the un-supported
length but actually acts closer to the supported surfaces, giving an even lower bending
moment. This thickness also gives the base plate substantial weight, 825 lbs., to prevent
the machine from tipping over during operation.
66
TEST MACHINE DESIGN
2.5.17 Level Three Design Matrix
The level three summary design matrix is given in Figure 2.20, with the fully decomposed
r-rim JA~
FR132 X X
FR133 X X
FR134 X X
JFR1351X X
A
0
0
0
0
U
X
0
0
0
UUU
0 0
X a
X X
0 0
IFRI41 10101010100
U u u
0 00
-1~'0 0101
0 01010101010101010101010101010101010101010Io
X,0101
01 X 01
0 0101010 DP131
2
00
00000
DP132
DP133
00 0 00 OP135
0 22
00 000
O.DP135
DP141
Figure 2.20 Level Three Axiomatic Design Summary
and solved FR's highlighted. Since the design is de-coupled the bottom of the design
matrix can be ignored, and the design matrix left for level four decomposition is given in
Figure 2.21.
Level Four Decomposition
N
C
01 01 01 01 01 01 0101 ODP131-Bolts
FR131-Attach to Cylinder
X1 X X
FR132-Attach to Pin
X X 0 X 0 0 0 0 0 0 0 0 DP132-Pis Clamps
a FR133-Attach to Torque Sensor
X X O O X 0 0 0 0 0 0 0 0P133-Detacb Mount
0 0 0 00 DP134-Siming of Arm
FR134-No FailurelPlastic Def.
X X O 0
FR135-Balanced
X X 0 0 0 X X O 0
FRI41-Fix Bushing o
67
XOO
0 0 0 0 0 X
Connco
FRI42-No FailurelPlastic Def
0 00 DP135-Counterweights
0P152-Clamping Mecaism
X 0 0 0 0
DPI42-Size
of Clamp
DPI5I-Larga
Beariog
LA
IFRI5S=Allow Rotation
0000
00
OOOXI
0 G
0 0
IFRI52-Load CellfMoust Connector 0 0 0 0 0 0 0 0 0 X X 0 DPI52-Bait LoleslPress Fit
FR53-Press and
Clamp
Bashing
j1IOj0I0LOOO XX
DP153-Angled
Blocks
Figure 2.21 Further Decomposition Design Matrix
2.6 Level Four Decomposition
2.6.1 DP131 Decomposition-Bolts
The use of four bolts was assumed to secure the cylinder to the top of the loading clevis in
order to provide an even and distributed loading against the loading clevis. The two functional requirements that decomposed from DP13 is that the bolts be sufficient to avoid
failure as the cylinder extends and that the threads into the cylinder be sufficient to avoidfailure.
68
TEST MACHINE DESIGN
The corresponding DP for FR1311 (Avoid Failure in Bolts) is that the bolts be of sufficient
diameter to avoid plastic deformation. The physics that governs the selection of the diameter (d) of each bolt is given in Equation 2.9 [Oberg, 1996] .
16 -F(aY) = (0.55 -d) - (0.25 -d)
(2.9)
Using an F=100,000 lbf., and cY,=92,000 psi. as the minimum for SAE 7 bolts, a d= 0.966
is found. Therefore the bolts will be sized as 1 in. diameter, SAE grade 7 bolts [Oberg,
1996] . This gives a factor of safety by the fact that the bolts will never experience plastic
deformation. Solving the same equation for force using d= 1 in. indicates that the maximum loading pressure before plastic deformation is F= 110,400 lbf. This value should
never be exceeded, but if it is, the bolts will not fail until F= 144,000 lbf. is reached based
upon a aultimate=120,000 psi. A further note on installation is that no preload should be
applied between, the cylinder and the loading clevis. It is only necessary that the members
be drawn flush. Increasing the preload on the bolts will diminish the allowable loading
pressure of the cylinder before failure.
The resulting de-coupled DP for FR1312 (Avoid Stripping Bolts) is that given a diameter
of bolt, in this case 1 in., that the type of thread and depth of thread be sufficient to avoid
failure. This is governed by Equation 2.10 [Oberg, 1996].
2 -A
Le=3112-A
Le= 3.1416- Knmax - (0.5 + 0.57735 - n - (Esmin - Knmax))
(2.10)
Using Knmax=.9098, n=14 (Fine Thread), Esmin=0.9459, and At=0.663 [Oberg, 1996], a
necessary depth of 0.56 in. was found. Imposing a reasonable factor of safety, a depth of
1.5 in. will be used. Therefore the cylinder should be tapped at least 1.5 in. in depth with
UNC 1-14 threads. The bolts should accordingly be fully threaded and have a threaded
length greater then 1.5 in. plus the thickness of the loading clevis top mount.
Level Four Decomposition
69
2.6.2 DP132 Decomposition (Pin Clamps)
The decomposition of DP132 results in three lower level functional requirements. The
first is that the clamping mount must seal the joint. The second functional requirement is
that the clamps not fail or plastically deform. The final requirement is that the clamps be
able to apply a medium press fit of 0.001 in. of interference on the diameter.
FR1321 (Seal Joint) is satisfied by counter boring holes around the clamp to allow for
standard oscillating seals to be installed. This is accomplished by sizing the holes according to the current seals used in field tests, as can be seen in Figure 2.22.
Figure 2.22 Close-Up View Sealing Surface
The DP for FR1322 (No Failure or Plastic Deformation) is to properly size the thickness
of the walls in order to not allow the cylinder to plastically deform. This was done by
examining the hoop stress of a thin walled pressure vessel in Equation 2.11 [Marks, 1978]
. This equation is valid as long as the prescribed wall thickness to diameter ratio is less
70
TEST MACHINE DESIGN
than 0.1. In this equation p is assumed to be a function of the applied force distributed
over
yhoop
t
(2.11)
the surface area of half the pin. The value of pressure (p) was a combination of two factors: the pressure due to the press fit, and the pressure due to the loading. The pressure
due to the press fit can be found using Equation 2.12 assuming a medium press fit interference of .001 in. In this equation 8 is equal to the ratio of the press fit to the diameter of the
pin, in this case .00038 in/in., and Estee is the elastic modulus of steel,
p = 6 - Esteel
(2.12)
30E 6 psi. Using these value a press pressure of 11,420 psi. is found. Using a force of
50,000 lbf. per clamp and distributing it over half the surface area of the pin, an inner pressure due to loading was calculated as 6,552 psi. Adding these two estimates together a
total inner wall pressure of 17,980 psi. was found. Using this value and a value for maximum yield strength of 100 ksi., a value for wall thickness of .25 in. was found. A factor of
safety of 6 was imposed and a clamp thickness of 1.5 inches was used.
FR1323 (Apply Press Fit) is satisfied by properly sizing the bolts to be able to apply the
necessary clamping press-fit and withstand the loading of the clevis. The force to achieve
the necessary hoop stress for the press fit loading is calculated according to
Equation 2.13. Using p= 17,980 psi., r=1.313 in. and 1c-amp=1.85 (length of the clamp with
insets for seals), a value of 43,660 lbf. of clamping force is necessary. This force was
Fpressit = Ghoop * t - 1clamp = p - r * 'clamp
(2.13)
spread over two bolts. The area of each bolt was evaluated according to Equation 2.14
[Oberg, 1996]
Abol,
(FPreload)
-0.75
- proof
Level Four Decomposition
71
using Fpreload= 2 1,8 3 0 , and cproof =95,000 psi. for SAE 7 bolts. The necessary diameter of
the bolt was found to be .625 in. The factor of 0.75 in Equation 2.14 is a factor of safety
based on the fatigue type application of the clamps. Due to the fact that the proof strength
was used and the loading was considered a maximum, when the majority of the testing
will be conducted at much lower levels, this diameter of .625 inches was deemed sufficient. The torque necessary to turn the bolt to this tension was calculated using
Ttighten = 0. 2 - Fpreload- d
(2.15)
Equation 2.15 [Oberg, 1996] , and turns out to be 3,469 in-lb. This requires an input force
of 144 lbs. using a 24 in. wrench. A experienced machinist is capable of generating this
force alone or with the assistance of pneumatic tools or lever bars.
The next component that had to be sized based on these results was the thickness of the
upper clamping piece. This part has a clearance hole to allow the bolt to draw it down
towards the bottom clamping piece creating the press fit. The thickness of this piece was
sized to avoid plastic defomation due to bending. The model for a simple cantilevered
beam in Figure 2.17 shows that the maximum stress occurs at the support and is given by
Equation 2.16 [Oberg, 1996] . Using Lbeam=. 7 5 in. to accomodate a wrench, a width of
2.26 in. , Fpresft= 43,660 lbf., and a amaxbending= 100 ksi, a necessary thickness of .932
in. was found. Thus an actual
6
Umaxbending
-Fpressfit -Lbeam
2
Wlamp - tclamp
(2.16)
'6
thickness of 1 in. was used for the upper clamping piece.
The last necessary parameter to evaluate for the bolts is the necessary length of thread to
avoid stripping. This can be calculated using Equation 2.10, and turns out to be .305 in.
using n=20 threads/inch, At=.1599 in 2 , Knmax=.4459 in., and Esmin=.4675 in [Oberg,
1996] .
72
TEST MACHINE DESIGN
2.6.3 DP133 Decomposition (Detach Mount)
The detachable mount needed little structural calculations. It was arbitrarilty sized with
the same width as the overall clevis walls and same depth. It had a gap of .25 inches
between the inner face of the mount and the loading clevis and extended down so the center of the torque sensor bolting pattern was in line with the axis of rotation of the pin. To
be removable the mount had to be bolted onto the arm with two large bolts. A steel block
was welded inside one of the loading arms to allow for two corresponding holes to be
tapped. The only calculation that had to be made was to insure that the bolts be able to
withstand the shear-force applied by the hydraulic motor as it rotated the arm. This diameter was solved for in Equation 2.19. Using T=10000 in-lbf, rmb= 7 in. (axis of rotation to
center of bolt), and
d
2 T
b '
(2.17)
shear
yshear = 50,000 psi., a d of .15 in. is found. A factor of safety of 5 was used and two .75 in.
diameter bolts were chosen.
2.6.4 DP134 Decomposition (No Failure or Plastic Deformation)
The problem of sizing the clamps had alredy been accomplished but the loading clevis still
had two more parts that had to be de-composed in order to avoid failure or plastic deformation. The first functional requirement was that the arms connecting between the top of
the clevis and the pin should not plastically deform or rupture. The second functional
requirement was that the top of the clevis not fail from bending or tensile stress. The
design parameter for both of these cases was that the components be properly sized. A
isometric view of the entire loading clevis is shown in Figure 2.8.
The first component to size was the side arms, which had been designed as box beams that
were welded to the clamping mechanisms as well as to the top of the clevis. The governing equation for their sizing was to choose the thickness of the walls to avoid plastic defor-
73
Level Four Decomposition
mation according to Equation 2.18. Using values for width and height of the arm of 1.313
in and 5.625 in. respectively along with a force of 100,000 lbf. and a acy=100,000 psi. the
minimum wall thickness is equal to .032 in. Applying a factor of safety of 7 a thickness of
.25 in. was used.
2 (wbox + hbox) - 2 Jwbox + hbox) 2 -
8
t-oxwalls
2
(
(2.18)
The second component that had to be sized was the thickness of the top clevis. The length
of the top clevis will be made more rigid by having the 8 inch, steel hydraulic cylinder
bolted to the center of it, but as a worst case scenario, the beam was considered simply
supported at the ends and free to rotate. By combining the maximum moment at the center
of the beam into the beam bending stress equation in Equation 2.19, an expression was
arrived at giving the minumum thickness of the top plate. Using values of Ltp= 11.292 in,
wtp=5.625 in, F=100,000 lbf., and acy=100,000 psi., a minimum thickness of 1.735 in. was
found. This is rounded to give a
t
=
tp
3 -F*L
w
* tp ' y
(2.19)
thickness of 2 in. This does not provide an incredible factor of safety, but it is helped by
the fact that the cylinder will provided the beam with more rigidity and reduce the bending
moment and displacement. As an extra precaution gusset plates were welded across each
corner of the loading clevis. This also served to connect the top clevis to the loading arms.
The arms were then subsequently welded to the clamping pieces. The welded joints have
a higher tensile strength than the steel parts and were deemed substantial enough for the
connections.
74
TEST MACHINE DESIGN
2.6.5 DP135 Balanced
Balancing the design is accomplished by providing counterweight posts. The counterweights and posts have the constraint that they cannot strike the floor as rotation occurs.
Based on this constraint the maximum diameter of the of the weights to be used was set at
10 in. and the distance between the axis of rotation and the center of the weights was set to
be 10.812 in. to avoid striking the floor. This was done by utilizing a solid model of the
design and adjusting the distance between the two until the moment arm was maximized
without the weights striking the floor. Since deflection of the loading arms was not a consideration, the diameter of the weight bars was sized according to typical weight room
equipment, which is 1.5 in. diameter, medium grade steel.
The only other dimension to calculate was the width of the weight bars to be used. This
was calculated by computing what the total width of the weights had to be in order attain
the desired force to balance the machine using this moment arm. This was done by modeling the entire machine in a solid modeling program and having the program calculate the
center of mass of the machine. The width of the weight was then adjusted until the center
of mass was perfectly aligned with the axis of rotation of the pin. The final width of the
total weight was found to be slightly over 16 in., therefore 8, 10 in. diamter, 2 in. wide
steel weights were used with four on each side as shown in Figure 2.10. Finer adjustments
can be made to precisely balance the arm by manufacturing smaller adjustment weights.
2.6.6 DP141 (Clamping Mechanism)
The design and decompositon of the clamping mechanism for the bearing mount is similar
to those that resulted from the decomposition of the pin clamps. The first functional
requirement was to avoid plastic deformation and failure while appying the press fit and
loading. The second functional requirement was to be able to apply a medium press fit of
.001 in. on the bushing.
Level Four Decomposition
75
The DP for FR1411 (Avoid Plastic Deformation) is to properly size the thickness of the
walls in order to not allow the cylinder to plastically deform. This was done by examining
the hoop stress of a thin walled pressure vessel in Equation 2.11. The value of pressure
was a combination of two factors: the pressure due to the press fit, and the pressure due to
the loading. The pressure due to the press fit can be found using Equation 2.12, where 8 is
equal to the ratio of the press fit to the diameter of the pin, in this case .00022 in/in., and
Estee is the elastic modulus of steel, 30E 6 psi. Using these values a press pressure of
6,460 psi. was found. Using a force of 100,000 lbf. , an inner radius of 2.322 in. and a
total bushing length of 9.292 in, an inner pressure due to loading was calculated as 1,475
psi. Adding these two estimates together a total inner wall pressure of 7,935 psi. was
found. Using this value and a value for maximum yield strength of 100 ksi., a value for
wall thickness of 0.184 in. was found. A smaller factor of safety of only 3 was used here
due to the negative affect on the center of mass of the machine by increasing diameter.
Based on these reasons a final outer diameter of 6 in. was chosen.
FR1412 (Apply a Medium Press Fit) is satisfied by properly sizing the bolts to be able to
apply the necessary clamping press fit and withstand the loading of the clevis. The force
to achieve the necessary hoop stress for the press fit loading is calculated according to
Equation 2.13. Using p= 7,935 psi., rbushing=4 .64 4 in. and 1=1.8 in., a value of 33,180 lbf.
is necessary. A value of 1= 1.8 in. was used as opposed to the entire bushing length
because it is only necessary to have a press at four points along the length to keep the
bushing from rotating. A value of 1.8 in. results in an identical surface area to that used to
clamp the two ends of the pin in place, which is sufficient. This lowers the amount of
force required for the clamp. This force was spread over four bolts. The area of each bolt
was evaluated according to Equation 2.14 using Fpressfit=33,180, and cproof =95,000 psi
for SAE 7 bolts [Oberg, 1996] . The necessary diameter of the bolt was found to be .366
in. The factor of 0.75 in Equation 2.14 is a factor of safety based on the fatigue type application of the clamps. Due to the fact that the proof strength was used and the loading was
considered a maximum, when the majority of the testing will be conducted at much lower
levels, this diameter of .366 in. was deemed sufficient and rounded to 0.5 in.
76
TEST MACHINE DESIGN
The torque necessary to turn the bolt to this tension was calculated using n Equation 2.15,
and turns out to be 2,702 in-lbf. This requires an input force of 113 lbf. using a 24 in.
wrench. An experienced machinist is capable of generating this force alone or with the
assistance of pneumatic tools or lever bars.
The next component that had to be sized based on these results was the thickness of the
upper clamping piece. This part has a clearance hole to allow the bolt to draw it down
towards the opposite clamping piece. The thickness of this piece was sized to avoid plastic defomation due to bending. The model for a simple cantilver beam in Figure 2.17
shows that the maximum stress occurs at the support and is given by Equation 2.16. Using
Lbearn=.65 in. to accomodate a wrench, a width of 4.646 in. (half the length of the bushing
for each clamp), F= 33,180 lbf., and a a-maxbending= 100 ksi, a necessary thickness of .75
in. was found. This is distributed over two equally sized clamps so each clamping side
will deflect half of the total amount. Thus an actual thickness of .5 in. was used for the for
each clamping piece.
The last necessary parameter to evaluate for the bolts is the necessary length of thread to
avoid stripping. This can be calculated using Equation 2.10, and turns out to be .385 in.
using n=18 threads/inch, At=.256 in 2 , Knmax=.5649 in., and Esmin=-5889 in. Therefore the
clamping piece that is threaded must be fully threaded to 0.5 in.
2.6.7 DP151 Decomposition (Large Diameter Bearing)
DP151 is fully decomposed with the connecting piece between DP151 and FR151 (Allow
rotation) being correct sizing of the bearing. The sizing of the bearing came with two constraints. The first constraint was that the outer diameter of the bearing could not be too
large because this would move the center of mass away from the center of rotation resulting in increased torque necessary from the motor. The second limitation was that the
width of the bearing could not exceed 1.5 in. or it would make optical access to the pin
impossible. In searching for bearings to accomplish this task the most promising result
was a Torrington XLS bearing that had a 8.25 in. bore and and a 11 in. outer diameter. The
Level Four Decomposition
77
width of the bearing was only 1.375 in. and would not interfere with optical access. The
only drawback was that the bearing was only capable of an L' 0 life of 55,000 lbf. of static
loading and 45,500 lbf. of dynamic loading. This was obviously not sufficient to support
the loading of the full 100,000 lbf. It was possible to place two bearings face to face and
achieve a 110,000 lbf. of static load and 90,000 lbf. of dynamic load, but this doubling of
width would interfere with the desired optical access. Because the main purpose of this
first machine was to test the optical analysis set up, it was decided to only use a single
bearing and be limited in the ability to apply full loading to a steel pin. Due to the modularity of this design the test rig could be upgraded later with a dual bearing mount assembly for about $7,000. Another major factor influencing this decision was that most pinjoints of this size fail between 50,000 and 60,000 lbf. of loading, so substantial research
could still be done on steel joints using this configuration.
2.6.8 DP152 Decomposition (Bolt Holes and Press Fit)
The decomposition of DP152 led to three lower level functional requirements. The first
was that the connection piece had to be able to bolt to the load cell while avoiding failure
in the bolts. The second requirement was that the connection piece had to press fit onto
the bearing without failure or plastic deformation in the connecting piece.
DP1521 is the proper sizing of the bolts to bolt onto the load cell. The load cell is prethreaded with bolt holes, so a simple calculation was done to see what bolt diameter was
necessary to prevent failure in the bolts. The assumed load per bolt was 833 lbf. Using
equation Equation 2.14 and solving for the necessary area, it can be seen that the minimum diameter per bolt is .13 in. assuming SAE 7 grade bolts.
Therefore the given bolt
hole diameter of 0.625 in. is more than sufficient.
FR1522 (Press Fit to Bearing) is satisfied by sizing the width dimensions of the pressing
piece to avoid failure or plastic deformation. This was done by assuming the mounting
piece will be a thin walled cylinder. The calculations for a thin walled cylinder are given
in Equation 2.11 and Equation 2.12. The pressure generated by the press fit can be calcu-
78
TEST MACHINE DESIGN
lated by specifying a heavy press fit of .006 in. on the 11 in. bearing diameter, which
results in a 6 of .00545 in/in. This in turn was used in Equation 2.11 to calculate a pressure of 16,360 psi. The pressure due to the loading was found by distributing the full loading of the machine over half the surface area of the bearing resulting in 4,029 psi.
Therefore the entire pressure for the hoop stress calculation is 20,570 psi. Plugging this
value into Equation 2.12 with a maximum hoop stress of 100 ksi. revealed that a necessary thickness of 1.131 in. was necessary for the ring. Although this cylinder now seems
thick walled it still falls under the category of thin walled because the ratio of t/D is still
less than 0.1. Based on these results the mounting piece was made out of a square of steel
with an 11 in. diameter hole cut in the center. The thickness on the sides of the piece was
made to 1.25 in. The thickness on the top was made 0.25 in. but was welded onto a 0.75
inch plate which bolted to the load cell. This 1 in. thickness augmented by the strength of
the load cell would be more than sufficient to withstand the stress. The critical bottom
thickness of the connection was sized at 1.5 in. thick to allow for a larger factor of safety.
The only parameter that was left to specify and check was the thickness of the weld bead
diameter that must be used to secure the load cell plate to the press fit plate. Based on
using two weld beads, each the length of the load cell plate, the minimum bead diameter
of the weld to be used is given in Equation 2.20, which results in a .056 in. diameter. A
factor of safety
W =
(2.20)
weld
max
of 5 was used to give a minimum bead diameter of .25 in. The completed load cell bearing
connection piece is shown in Figure 2.23.
2.6.9 DP153 Decomposition (Angled Blocks)
DP153 can be decomposed into two lower level functional requirements. The first is that
the blocks must be able to allow for diametrical changes in the bushing mount cylinder.
Level Four Decomposition
79
Figure 2.23 Connection Piece
The second functional requirement is that the mounting bolts be able to apply a sufficient
press fit without failure.
FR1531 (Allow for Diameter Change) is met by sizing the blocks appropriately so that as
the mount closes its diameter the blocks can have the mounting ring slide over. This was
done by cutting a 45 degree angle into a steel ring that was pressed into the bushing. A
corresponding 45 degree angle was cut into the four mounting blocks. Using a 45 degree
angle meant that for every increment the clamp changed radius, the ring would have to
move the same increment over onto the mounting blocks in order to find a fit point. Since
the maximum clamping distance for the press fit was .0035 in. the radial direction, the
80
TEST MACHINE DESIGN
maximum lateral shift of the ring onto blocks would be .0035 in. Therefore to allow for a
sufficient factor of safety, the block were oversized .25 in. as can be seen in Figure 2.12.
To properly size the bolts, the necessary pressure and corresponding force for the
"pseudo" press fit had to be calculated. It is not necessary to generate a press fit to stop
rotation, because the bolts going through the two blocks will prevent rotation. The only
requirement of the bolts is to keep the two faces snugly mounted so as to allow even pressure distribution. Therfore a reasonable design parameter was that the four bolts be capable of applying a clamping force equal to the normal loading of the cylinder. This was
evaluated using Equation 2.14 with a factor of .9 instead of .75 due to the fact that the
bolts would not be heavily cycled [Oberg, 1996] . This resulted in a minimum diameter of
0.58 in. so a diameter of 0.625 in. was used.
The last design parameter that had to be investigated was how to mount the blocks to the
bushing mount. Based on previous weld calculations, it was apparent that a 0.25 in. diameter weld bead would keep the blocks in place and not fail in shear. The blocks are
mounted at 45 degree angles from each other and offset from the bottom of the mount so
as to not interfere with optical analysis as can be seen in Figure 2.12.
2.7 Hydraulics and Controls
The hydraulics and controls packages used for this design were off the shelf packages. The
only functional requirements placed on the hydraulics system is that it be able to supply
3,500 psi. working pressure at 30 gpm. This can be attained by the use of most typical
hydraulic power units that are correctly sized.
A controls system can be purchased that can fulfill varying degrees of automation depending on the testing conditions. For instance, by the use of the more expensive servo-controlled proportional feedback valves, the entire system can be run by a computer that
receives feedback from the load cell and an encoder mounted on the hydraulic motor. For
substantially less money the system can be run manually by simply using manual propor-
Manufacturing and Assembly
81
tional valves to control pressure to the cylinder and pressure and flow to the hydraulic
motor. The motor rotation angle can be controlled using mechanical limit switches that
reverse the flow in the motor when they are tripped by some mechanical switch attached
to the rotating shaft.
The degree of automation depends on the application to be tested and the financial budget
of the testing facility.
2.8 Manufacturing and Assembly
2.8.1 Notes on Manufacturing
The new test rig was designed with manufacturing simplicity in mind. The most complicated part that had to be manufactured was the bearing assembly and large diameter bearing mounts. Looking at an isometric view of the test rig, it can easily be seen that the large
Figure 2.24 Isometric View of Final Design
82
TEST MACHINE DESIGN
diameter bearing cannot be placed over the bearing assembly after the legs have been
welded to the bushing mount. Therefore it is necessary to weld the mounting blocks onto
the bushing mount and slide the bearing and all of its press fit components onto the bearing assembly before the second of the two legs is welded onto the mount.
The second consideration that must be accounted for in manufacturing is the affect of
welding deformation on the concentricity of the bushing mount bore. To avoid this, the
bore of the bushing mount should be rough cut and then have all the welded components
affixed to the bushing mount. After the welds have deformed the bushing mount, the entire
mount can be placed on a machine tool to finish cut the bore and insure proper concentricity along the length of the mount. This will ensure a proper fit between the bushing and the
bushing mount.
The rest of the parts can be easily manufactured by an experienced machine shop.
2.8.2 Notes on Assembly
The assembly of the majority of the machine is fairly straight forward. It was designed
with a modular "lego" type assembly system. The majority of the parts simply bolt
together with the torques specified in the beginning of this chapter. The trickiest part of the
assembly is when the pin and bushing are to be inserted into the machine for a test.
The first step in this process is to insert the bushing into the bushing mount. The ends of
the bushing should be aligned with the end of the bushing mount and then the 4 bolts
should be progressively tightened to insure a uniform pressure across the bushing. The
loading clevis should then be elevated with adjustable jack stands in order to align the pinclamps with the hole in the bushing. The pin should then be slid through the loading clevis
and the bushing and the pin clamps should then be progressively tightened in the same
manner as the bushing clamp. The counterweights should then be placed on the loading
clevis in order to keep the loading clevis in an upright position. The weights should then
be locked onto the weight bars by means of a weight bar clamp or an interference using a
Manufacturing and Assembly
83
binding adhesive tape. The press fit ring and large diameter bushing should then be
clamped to the angled blocks to form the "psuedo" press fit. The load cell should be bolted
to the connection piece prior to assembly. The next step of the process is to hoist the
hydraulic cylinder above the assembly by the use of either an overhead hoist or several
experienced operators. An additional operator must then steady the large diameter bearing
and subsequent connection piece in an upright position so that the other operator may
thread the cylinder into the load cell. Once the cylinder is fully threaded on the load cell
the four large diameter bolts should then be used to bolt the cylinder to the top of the loading clevis. After this step is complete the pin-joint is fully assembled and ready for the
addition of lubricant and testing.
The connection of the motor mount to the loading clevis is straight forward and only
entails bolting and fastening obvious parts together, that can easily be inferred from the
isometric view in Figure 2.24. This completes the design, manufacturing and assembly
procedures of the new pin joint test rig. A completed actual assembly can be seen in
Figure 2.25 and Figure 2.26. A complete set of prints for all parts is included in
Appendix B.
84
TEST MACHINE DESIGN
Figure 2.25 Isometric View of Assembled Final Design
-1
Manufacturing and Assembly
Figure 2.26 Front View of Assembled Final Design
85
86
TEST MACHINE DESIGN
Chapter 3
SCALING LAWS
Optical analysis can easily be conducted on small, lightly loaded pin-joints, but this is not
the application scenario that experiences the most wear. The heaviest wear occurs in pinjoints subjected to large loadings that undergo loss of lubricant, particle abrasion, and
severe wearing. Unfortunately, the very nature of these heavy pin-joint applications are
preclusive to optical analysis. This is mainly due to the fact that the heavy loads used in
these applications would crack any clear materials that are used as a bushing to allow optical analysis. Based on these facts, it was determined that a fully loaded joint could not be
observed, but perhaps scaling laws and dimensional analysis could be used to conduct
optical analysis on different materials and extrapolate these results to a steel on steel pinjoint.
3.1 Desired Properties to Replicate
In a search for scaling laws, it was necessary to identify a mechanical behavior of the pin
that would be useful to observe. The most obvious parameter that can be observed with
optical analysis is the thickness and motion of lubricant within a pin-joint. This is clearly
an important parameter, because fluid thickness and its impact on lubrication and particle
wear has a direct influence on life of the pin-joint [Suh, 1986].
One of the most promising methods of positively influencing fluid thickness and lubrication behavior is to add some type of surface feature to the surface of the pin. Surface fea87
88
SCALING LAWS
tures can be used in a variety of ways to improve the tribological behavior of the pin-joint.
One of the proposed concepts is to crown the surface of the pin in order to avoid stress risers due to the interaction of the bushing/pin clamp interface. Another promising design is
to place straight grooves on the surface of the pin to "trap" wear particles as they are
formed [Suh, 1973]. Yet another design is to place a flowered surface around the circumference of the pin in order to re-wet the contact surface upon each rotation.
All of these concepts share one common design parameter. The surface of the pin is somehow changed to increase the fluid film and somehow influences the flow of both lubricants and particles. It would be beneficial to study how these different surface geometries
affect the flow of both lubricants and particles within the joint. During loading and rotation, these surface geometries undergo deformation and bending that further change the
flow of lubricants and particles through the joint. Based on this idea and the desire to conduct optical analysis it was postulated that two different materials could experience the
same type of deformation and bending in surface geometries with a lower loading. With
this lower loading and the proper selection of optically compliant elements, fluid and particle flows could be optically observed. In order to validate this hypothesis it was necessary to examine the physics that govern such deformations and bending.
3.2 Physical Laws Governing Scaling
Surface geometries undergo two types of deformation under loading: local deformation
governed by Hertzian Contact Deformation, and bending deformation based on a four
point bending model. In order to examine the size of these deformations for scaling it was
necessary to gain some baseline data based on a steel on steel bushing loaded at 100,000
lbf. The pin is made of SAE 50B38 steel that has been heat treated to provide a tensile
yield strength of 290,000 psi. The pin is 13.812 in. long and has a nominal diameter of
2.626 in. The bushing is made of a comparable material and has a length of 9.343 in. and a
nominal diameter of 2.645 in. A 50,000 lbf. load was assumed to be applied in the middle
Physical Laws Governing Scaling
89
of the unsupported pin ends of each side and the bushing was assumed to contact at two
points inside the bushing.
As a generic test of surface features to develop scaling laws, it was assumed that the pin
had been manufactured with two lobes each with a 50 in. radius of curvature along the axis
of the pin, and that the pin had a flowered pattern around its circumference consisting of
12 "bumps" each with a radius of curvature of 1.127 in. Sketches of the pin geometry and
loading configuration are given in Figure 3.1, Figure 3.2, and Figure 3.3.'
Figure 3.1 Axial Sketch of Pin Showing Lobes
3.2.1 Hertzian Contact Mechanics
At the end of the 19th century Heinrich Hertz mathematically solved the contact mechanics problem of two curved contacting bodies. The solution to this problem is well documented and accepted throughout the engineering community and was used to model the
deformation and stresses generated by the surface features on the pin [Slocum, 1993]. The
model sets forth that when two curved surfaces are brought into contact, the contact area
looks like a parabola having two diameters of curvature as can be seen in Figure 3.4. This
contact area also has a local deformation associated with it as the two bodies press against
1. This work is not yet documented, but is part of experimental work currently being conducted by Professor Alexander H. Slocum, MIT, and Micah David Smith, MIT, in order to increase pin-joint performance.
SCALING LAWS
90
Trough
Bump
Figure 3.2 Circumferential Sketch of Pin Showing Flowers
F/2
F/2
U
U
1~
r
I
Va-
M
M-
I P100, "Ii
.1
A
AIL
F/2
1-
U
A
AIL
F/2
Figure 3.3 Sketch of Loading Configuration
Physical Laws Governing Scaling
91
Figure 3.4 Hertzian Contact Area
each other. The model also sets forth that the maximum contact pressure and local deformation occur at the center of the contact area and that the mode of failure is shear failure
below the surface. The Hertzian contact mechanics equations are rather lengthy and thus
have been placed in Appendix A. 1.
Using the aforementioned equations and assuming that the entire 100,000 lbf. loading is
subjected to just one lobe as a worst case scenario, the results of a steel on steel bushing
are as follows:
- c= 0.783 in.
- d= 0.253 in.
- Local Deformation = 0.028 in.
The only deformation left to model is that due to bending of the pin.
3.2.2 Four Point Bending
The deflection of the pin was modeled by looking at the deflection under the applied loads
placed on the ends of the pin. The equation for bending at the ends of the pin is given in
Equation 3.1[Marks, 1978]
Az =
(F -W2
>-(2
12 - ESteel' IPin)
w + 3 -lf)
(3.1)
92
SCALING LAWS
Using this equation a maximum deflection for the steel pin is calculated as 0.028 in. The
calculations for this number are also included in Appendix A. 1.
3.3 Material Matching
In order to find materials to match the properties above, a softer pin had to be chosen.
Based on this, the obvious material choice for the pin became a hard plastic. A list of 250
possible plastics was chosen that showed promise in terms of elastic modulus.
The bushing on the other hand had to be relatively hard compared to the pin in order to
assure that the plastic pin was the deflecting member and that the bushing was not bending. This is typical of real world steel applications, due to the fact that the bushing is
housed in an outer ring of steel, giving it a much higher bending moment of inertia than
that of the pin. The bushing also had the added constraint of having to be optically accessible. Thus based on this a much smaller list of five materials was chosen.
Now that the database of materials was chosen it became necessary to find combinations
of materials that when loaded not only matched the deformed dimensions of the real pin,
but also avoided failure in shear and bending.
3.3.1 Combinatorial Complexity
The task of combining materials and then finding what loading causes them to match the
steel pin exactly is quite a daunting task. If the loading range used as a test case on the
materials is given as 1-10,000 lbf, and a 250 by 5 matrix of material combinations is
assumed, the number of total combinations is 12.5 million. Now adding the fact that each
Hertzian and bending solution requires five equations, the number of total calculations
rockets to 62.5 million. The use of a spreadsheet was thus needed to ease the calculation
burden.
Thus a spreadsheet was constructed that calculated all the Hertzian and bending parameters for each loading case. The spreadsheet records the load when the parameters are
Material Matching
93
within 1% of the steel parameters and records the load when the parameters leave this
range. Hence, a table is constructed giving all the usable material combinations and their
corresponding load range that matches the steel parameters to within 1%.
Upon using the spreadsheet it was found that many combinations of materials met the criteria of the Hertzian deformation, but very few satisfied the bending criteria. This is due to
the fact that most plastics have very poor flexural stiffness. To compensate for this it was
necessary to change the mass moment of inertia of the pin. This variable has a strong
affect on the amount of deflection experienced, but has no affect on the Hertzian calculations. This was accomplished by placing a steel cylinder inside of the pin, in order to
decrease bending. The previous term for "El" is given in Equation 3.2 [Hibbeler, 1993],
while the steel cylinder "El" is given in Equation 3.3, where Doi, is the diameter of the
center oil reservoir, Dp is the diameter of the outside of the pin, and Dsteei is the outer
diameter of the steel re-enforcing cylinder. A sketch of the re-enforced plastic cylinder is
shown in
EI= E
EI =
E
(( EN44
(3.2)
4
(D - Dstee)) + Esteei -
4
(Dsteel - Do)
(3.3)
Using the above equations it is also possible to have the spreadsheet specify the necessary
diameter of the steel to be used to provide the desired bending deformation.
3.3.2 Solution Materials
Using the described computer software a matrix was generated of all the possible material
combinations, loading combinations, and steel centers that could be used to scale the
behavior of the steel pin. Out of the list of possible materials, the combination of DelrinTM
500AF pin pressed against a sapphire bushing was chosen. DelninTM was chosen due to its
94
SCALING LAWS
7
Ii Re!e rvor
Figure 3.5 Re-enforced Pin Overview
availability and easy machinability. It also has good flow resistance at higher temperatures. Sapphire was chosen for its optical quality and excellent hardness characteristics.
Sapphire also has the added bonus of sharing the same crystalline structure and material
properties as Aluminum Oxide (A1 2 0 3 ). This fact allowed the bushing to be manufactured
out of Aluminum Oxide with Sapphire inserts lapped in.
This combination creates the same loading configuration as the steel on steel application
by only applying 2,881 lbf. The prescribed steel center diameter to match bending deflecting is 1.027 in. Due to the fact that the scaling methods cannot match all the properties
exactly there is an error in each parameter to achieve the best fit. The error in each dimension is given as follows:
- error in "c" dimension = 0.074%
- error in "d" dimension = 0.00781%
- error in local deformation= 0.056%
- error in bending deflection= 0.07%
The single set of equations to obtain this solution is given in Appendix A.2.
The small errors show that the prescribed loading gives very good accuracy, but that exact
loading may be hard to maintain over time. The benefit of using the spreadsheet is that it
provides a range of loadings that are within a certain percent of the desired values. For
Material Matching
95
instance loadings of 2,735 lbf. to 3,023 lbf. will result in errors in all dimensions +/- 5%.
This range greatly decreases the demands on the controls system.
The maximum contact pressure between the parts is calculated using the Hertzian Contact
formulas included in Appendix A.2. The maximum bending stress in the pin occurs in the
center of the pin and is governed by Equation 3.4 [Marks, 1978]. Bending stress is
neglected in the
maxbending
4
.
4-Pin
Sapphire because it is housed in the bushing clamping mount which will be assumed rigid
at this loading. This is also necessary due to the low flexural strength of Sapphire. The
results of these calculations are shown Table 3.1, and reveal that all the materials are in
their elastic region.
TABLE 3.1 Stresses in Sapphire/Delrin
Stress Condition
Contact Pressure
Bending Stress
Deirin
7481 psi.
1,831 psi
Maximum Contact Pressure
% Contact Pressure
%Bending Stress
10,440 psi.
71.6
22.9
Sapphire
7481 psi.
N/A
196,400 psi.
3.8
N/A
On a percentage basis the only stress that is near plastic deformation is the contact pressure of the DelrinTM pin. This calculation, however, already has a factor of safety built in
because the entire loading was assumed to be at only one point as a worst case scenario.
Thus only 1,440 lbf. will be placed at each lobe of the pin and the maximum contact pressure will be only 36% of the maximum for DelrinTM
The only other precautionary note on the use of Sapphire is that care must be taken when
clamping the Sapphire bushing into the bushing mount. Due to the low loading and the
aw
96
SCALING LAWS
inherent low friction nature of the ceramic/DelrinTM interface, the friction torque will be
fairly small, thus a heavy press fit is not necessary to keep the bushing from rotating.
Therefore, in order to prevent the bushing from cracking under compressive force, the
bolts should simply be snugged to provide a very light interference fit between the clamp
and bushing. It is better to err on the side of caution in this respect and have to re-tighten
the clamps and re-test, rather than cracking a very expensive bushing.
A picture of the manufactured optical pin and bushing is shown in Figure 3.6.
Figure 3.6 Optical Pin and Bushing
3.4 Problems with Scaling
As with most scaling problems every parameter cannot be perfectly simulated. The purpose of this scaling is to study the affect of surface features on lubrication and wear particle behavior. Simply matching the deflected contact areas does present some problems,
however.
Problems with Scaling
97
The most obvious difference between DelrinTM and steel is that DelrinTM has a much lower
coefficient of friction than steel and will perform better in a sliding friction sense. The second major thing is that DelrinTM wear particles are not as abrasive as steel and will not
form cutting grooves. Other differences exist and will have to be studied, but this does not
make these scaling laws invalid. The results of experimental work using this technique to
observe the affect of surface features is simply one piece of a larger tribological puzzle.
The information gathered from this work should be combined with other experiments such
as those investigating the coefficient of friction between DelrinTM and Sapphire in order to
better understand the behavior inside the joint.
98
SCALING LAWS
Chapter 4
OPTICAL ANALYSIS
The ability to conduct optical analysis is one of the major improvements of this design.
For many years modeling and hypothesis about the fluid flow in pin-joint applications
have been put forth, but there has been no way to verify these results. Now with the use of
this test machine and some modem types of optical analysis these models can be verified,
and new ones can be put forth.
Optical analysis is a very broad term and encompasses many techniques that can be used
to study different phenomena inside the joint. The first and most basic type of optical analysis that can be conducted is "white light" analysis. This technique simply entails illuminating the optical window to observe the pin rotating through the joint. This method can
be used to verify that the predicted Hertzian contact size is correct and that the fluid flow
is qualitatively correct. This method is good as a first pass verification of predicted performance, but more in depth analysis is necessary to get quantitative data. One of the most
promising techniques to gain quantitative data about fluid flow is Dual Emission Laser
Induced Fluorescence [Hidrovo, 2000].
4.1 Dual Emission Laser Induced Fluorescence
Laser Induced Fluorescence (LIF) is a technique that capitalizes on the light energy emitted by certain dyes when excited by a laser pulse. Using this principle, dyes with know
emission properties are mixed into the lubricant between two surfaces and then excited
99
100
OPTICAL ANALYSIS
with a laser of corresponding wavelength. The emission of the dye can be calculated from
Equation 4.1, where I, is the intensity of the laser, (D is the quantum efficiency, F is the
molar absorption of the dye, C is the molar concentration of the dye, and t is the thickness.
From this equation it can be seen that by knowing the intensity of the laser
If tfluid)
= I0 - (D -
{1I - e (-6((Xlaser) - C - Ifluid))
being used and the properties of the dye that is mixed with the lubricant it is possible to
correlate the intensity of emitted light to the fluid thickness being observed. This technique has been used extensively to get qualitative data on fluid flow. It gives very clear
pictures with good distinction as to where there is fluid and where there is not fluid. This is
a great improvement over white light which often leaves many question marks on where
the contact area transitions actually occurs and is unable to show thin fluid layers. Also,
because a thicker fluid film results in more intensity, a computer can be used to analyze
digital pictures to form gradient profiles of light intensity. This allows the operator to get a
very clear qualitative picture about fluid thickness in the joint during rotation. These pictures can also be streamed together to form a movie of fluid flow throughout a joint. This
technique can be extremely beneficial when trying to verify a hypothesis about the affect
of surface features on fluid thickness and flow.
To this point the use of LIF has been limited to these type of qualitative analysis mostly
because of the fact that along with fluid thickness, the emission intensity is affected by the
initial intensity of the laser (I,). With an ideal laser beam this would not be a problem, but
typical lasers are not able to produce a repeatable laser intensity over the entire beam
width from pulse to pulse. This can obviously be a problem, because if a laser intensity is
correlated to height in the first picture, it may not be able to be correlated to the same
height the next picture. This leads to problems when trying to calibrate the setup as well as
analyze the results. To combat this problem a new technique has been developed based on
the concept of using two dyes that have different emissive properties. This concept is
called Dual Emission Laser Induced Fluorescence (DELIF). The dyes both emit light
101
Optical Setup
based on Equation 4.1, which means that they both emit, based on the same thickness and
the same initial intensity of the laser. Now the problem becomes one with two equations
and two unknowns. Therefore by taking the ratio of the two emission intensities measured,
the thickness of the fluid layer can be found, regardless of initial laser intensity variations
as can be seen in Equation 4.2.
I
R(tfluid) - I Id2
C
C, - (p -El - (C - E) -
2 ' (P2 * E2 - (C - E+ C 2
- eXp[-(C -E + C2 -2
2) {1 - ep [-(C -E -tfluid)] }
-
(4.2)
Using this technique it is possible to gain invaluable data on the quantitative affects of surface features on fluid film thickness and flow inside pin-joint systems.
4.2 Optical Setup
Many different types of hardware setup can be used to gain optical images from the pin
joint. One of these setup techniques is presented here that covers the basic principles
involved in all the techniques.
The first element that must be used is obviously the dyes that must be excited to produce
emission. The dyes must be carefully mixed to known molar concentrations in the oil used
to lubricate the joint. The current dyes used in testing are Pyromethane and Rhodamine,
but other dyes can be chosen based on known emissive properties. Once the dyes are properly mixed they should be inserted into the assembled pin joint consisting of the DelrinTM
pin and Sapphire insert bushing. The Sapphire inserts should be aligned with the optical
slots in the bottom of the bushing mount as shown in Figure 4.1.
The next major component that must be placed is the laser. The laser must be able to emit
light at a wavelength that excites the dye. Other than that constraint any laser may be used
regardless of profile, due to the concept of using two dyes presented in Equation 4.2. The
laser must be mounted on a vibration free platform in order to protect the optical elements
from mis-alignment. In this scenario it will be placed on the base plate on a vibration free
mount. The beam emitted by the laser is then passed through a series of mirrors to direct
102
OPTICAL ANALYSIS
Figure 4.1 Bottom View of Sapphire Window and Bushing Mount
the beam up through the optical window. The beam then excites the dyes which in turn
emit the desired intensities based on fluid thickness.
In order to capture the images it is necessary to bounce the image off a different set of mirrors to a camera system. The problem with this is that in order to place mirrors below the
optical window, the incoming laser light is prohibited. This problem is solved by the use
of a dichroic mirror in the path of the laser beam. A dichroic mirror is one that allows certain wavelengths of light to pass through while reflecting other wavelengths. Since the
light emitted by the dyes is different than the light emitted by the laser the appropriate
selection of a dichroic mirror can provide the "traffic cop" necessary to direct flow of light
below the window. A schematic of the dichroic mirror is shown in Figure 4.2.
The final component necessary for optical analysis is a means of capturing the emitted
light profile of the dyes. To accomplish this the emitted light intensity is captured by using
a 16 bit CCD camera that sends images to a computer for storage and analysis. The camera
system must be fast enough to capture images at the desired frequency. Once the images
Optical Setup
103
Figure 4.2 Dichroic Mirror Setup
are captured in the computer they can be manipulated to map the emitted intensity profiles
for each picture. These pictures can then be correlated and streamed together to provide a
movie of fluid thickness and flow as the joint rotates. An overview of the entire optical
setup is shown in Figure 4.3.
This setup is not the only one available and other systems can be adapted based on individual lab criteria. For instance the laser and camera system do not have to be mounted on
the base plate, but can rather be mounted in a vibration proof room, if necessary, with the
assistance of the proper optics. As long as the basic concepts of optical analysis are
retained, any comparable system will work.
104
OPTICAL ANALYSIS
Figure 4.3 Optical Setup
4.3 Other Types of Optical Analysis
The immediate use of optical analysis is to study the thickness of the fluid layer between
the pin and bushing but the possibilities for future research are seemingly infinite. There
are over 1,000 different dyes currently on the market all of which have different emissive
properties. Some dyes emissive characteristics are sensitive to pressure, while still others
are sensitive to temperature. All these characteristics are important parameters involved in
the modeling and behavior of pin-joints systems. Therefore using the same type of analysis described above with different selections of dyes will allow researchers of the future to
gain data on the inner workings of pin joints that was once unthinkable. The key to this
Other Types of Optical Analysis
105
future success has been made possible by the development of the optical capabilities of the
new pin joint test rig design.
106
OPTICAL ANALYSIS
Chapter 5
FUTURE PIN JOINT STUDIES
The development of this new pin-joint test rig stemmed from the research done by Professor Alexander H. Slocum on the benefit of surface geometries on pin joint performance.
The exploration of the full use of this machine has been left for future research, but some
of the desired future work is briefly described in the following sections.
5.1 General Surface Geometry Studies
Extensive work has been done in testing the affect of simple surface geometries on wear
and joint performance [Budinski, 1988]. The first application of this machine will be to
further validate this work by the use of optical analysis.
One of the most intriguing designs was presented by Suh, et al, with regards to the addition of micron level axial grooves to "trap" wear debris before they could further wear the
pin through "delamination" and particle abrasion [Burgess, 1983]. The grooves proved
successful, but when the joint was disassembled particles were not found "trapped" in the
grooves. This is not to say that they were never trapped there and in fact they were most
likely washed away as the joint was disassembled. This test machine is a perfect tool to
observe the particles being trapped in the grooves if this is what indeed happens.
The machine will also be used to look at other such simple geometries such as circumferential grooves, spirals, and dimpled patterns. Valuable qualitative data can be gathered by
107
108
FUTURE PIN JOINT STUDIES
the use of optical analysis that will allow designers to further catalog what surface features
lead to positive results with regard to fluid thickness and flow within a joint.
5.2 Modeling, Machining, and Testing
Based on the results of the above fundamental investigations, designers will be able to
pose more accurate models of fluid thickness and flow within a pin-joint. Based on these
models designers will be able to design more effective pin joint systems that incorporate
one or several of the above design parameters in order to improve joint performance.
Once designs are formulated and results predicted, the trial pins can be easily machined
out of Delrin and tested to observe performance and compare results to predicted models.
Once the results have been analyzed the models can be adjusted to match results and
improved designs can be postulated. This process can be repeated until viable designs are
discovered. This entire process is much more efficient and expeditious than the previous
way of testing pin joints. The first and most obvious reason for this is that more relevant
data, including optical models, are available to further educate designers. The second
major advantage is that hypothesis can be tested on Delrin which is easily machinable and
provides much shorter times for test parts to go from paper to reality at a much lower cost
than steel. Promising designs can then be manufactured out of steel and tested on the same
apparatus to verify the validity of the model on real-world steel applications.
5.3 Other Dye Applications and Particle Tracking
As mentioned in Chapter 4 the primary use of the optical analysis at first will be measuring the fluid film thickness and flow between the pin and the bushing, but many other
techniques can be used with the proper selection of dyes. Some of the most interesting
dyes are sensitive to pressure difference and temperature difference. It is also possible to
use all of these dyes at once since they all emit at different wavelengths. Therefore by
using multiple cameras all set to filter different wavelengths of light, it is possible to gain
Conclusion
109
all the pertinent factors that govern fluid flow simultaneously. This technique, once perfected could prove to be one of the most powerful tools available to engineers.
Aside from studying the resulting properties of the fluid layer, it is also important to
observe the behavior of wear particles that are formed in the joint. To do this it is proposed
that a grouping of wear particles be doped with a fluorescent dye and introduced to a pin
joint system. The particles could then be tracked as they move through the joint and the
affect of surface geometries on wear particle behavior could then be studied.
5.4 Conclusion
This paper presents the concept, design, and manufacture details necessary to construct a
novel test apparatus that is capable of providing vital data for the study and design of pinjoint systems. This test rig design also provides the optical analysis capability necessary to
validate the modeling hypothesis related to fluid and particle flow within the joint.
This design accomplishes all the functional requirements set forth by being able to replicate the field loading of a heavily loaded pin-joint. The design is also scalable to different
pin-joint geometries by using a modular design that is able to re-use parts on different configurations. The cost savings of this machine is impressive with a final design price of
$150,000 which includes engineering time and design, as compared to an industry estimate of $10 million. The design is also an improvement by being able to fit the entire test
rig, hydraulic unit, and controls package into a work volume that is smaller than the actual
industry test machine alone. In addition to these monetary and space improvements, the
design is able to gain vital data such as coefficient of friction which the industry apparatus
cannot. The new test rig design is also capable of attaining higher speeds of rotation for
very little increase cost due to the shift to a rotary actuator. All these improvements are on
top of the fact that this design is capable of conducting vital optical analysis while at the
same time being able to conduct fully loaded joint testing.
-
I EU
in11E1ViI1
EE iii
110
f~
-
FUTURE PIN JOINT STUDIES
Based on this improved design and improvements in the DELIF technique the field of pinjoint research is poised to make major breakthroughs. Hypothesis and models that have
existed for years can now be validated. Designs can be improved and optimized based on
optical analysis and improved joint models. Prototypes can be quickly machined out of
Delrin to evaluate the validity of new designs, leading to shorter lead times in solving joint
problems. All these qualities would not be possible without this new test rig concept and
design. Therefore the optically accessible pin-joint test rig could be responsible for some
amazing future improvements in one of man's most useful design elements.
Figure 5.1 Manufactured Optically Accessible Pin-Joint Test Rig
REFERENCES
[Archard, 1953] Archard, J., "Contact and Rubbing of Flat Surfaces", J. ofApplied Physics 24, pp. 981-988, July 1953.
[Budinski, 1988] Budinski, K., Surface Engineeringfor Wear Resistanc, Prentice Hall,
Englewood Cliffs, 1988.
[Burgess, 1983] Burgesss, S., Friction and Wear of Composites, MIT M.S. Thesis in
Mechanical Engineering, June 1983.
[Hibbeler; 1993] Hibbeler, R., Mechanics of Materials, Prentice Hall, Englewood Cliffs,
1994.
[Hidrovo, 2000] Hidrovo, C., and Hart, D., "Dula Emission Laser Induced Fluorescence
Technique (DELIF) for Oil Film Thickness and Temperature Measurent", Proceedings of ASME FEDSM'00 , Boston, 2000.
[Marks, 1978] Marks, L., and Baumeister, T., Marks' Standard Handbookfor Mechanical Engineers,McGraw-Hill, New York, 1978.
[Oberg, 1996] Oberg, E., Jones, F., Horton, H., and Ryffel, H., Machinery's Handbook,
Industrial Press, New York, 1996.
[Slocum, 1993] Slocum, A., PrecisionMachine Design, Society of Manufacturing Engineers, Dearborn, 1992.
[Suh, 1973] Suh, N., "The Delamination Theory of Wear", Wear 25, pp. 111-124, 1973 .
[Suh, 1986] Suh, N., Tribophysics, Prentice Hall, Englewood Cliffs, 1986.
[Suh, 1990] Ueha, S., and Tomikawa, Y., The Principles of Design, Oxford University
Press, New York, 1990.
[Tamre, 1995] Tamre, M., "Mis-Aligned Journal Bearings", Proceedingsof the Estonian
Academy of Sciences, 1, pp. 87-97, 1995.
111
112
REFERENCES
Appendix A
HERTZIAN CONTACT MECHANICS
A.1 Hertzian Contact Calculations for Steel Contact
Nomenclature:
DP
R1P
R2P
LP
EP
vp
Ftotal
a maxtensile
o maxflexural
Nominal Diameter of Pin
Radius of Curvature of Lobes
Radius of Curvature of Bumps
Length of Pin
Elastic Modulus of Pin
Poisson's Ratio of Pin
Total Applied Length
amaxtensilesaph
Maximum tensile strength ofpin
Maximum flexural yield strength
Maximum tensile strenght of saphire
w
Distance from bushing end to loading
len
Distance between loading points
Radius of curvature of bushing
Nominal radius of bushing
Length of bushing
R1B
R2B
LB
EB
vb
Fperlobe
OilD
Elastic modulus of bushing
Poisson's ratio of bushing
Loading per lobe for deflection
Diameter of oil reservoir in center of pin
Moment of Inertia
Requiv
Eequiv
theta
CPSteel
cST
dST
LDSteel
MDSteel
dS
ES
IS
IP
Equivalent Radius of Curvature
Equivalent Elastic Modulus
Angle of Contact (0)
Contact Pressure of Steel
"c" major diameter of steel contact
"d" minor diameter of steel contact
Local Deformation of steel contact
Maximum Deflection of steel contact
Steel Center to Increase Stiffness
Elastic Modulus of Steel
Moment of Inertia of Steel
Moment of Inertia of Plastic
113
114
APPENDIX A
Input Parameters:
DP =2.626in
RiB :=100000000000000000
RP:=50 in
R2B
R2P :=1.127in
LB := 9 .3 3 4 in
LP =13.812in
EP
:=-1.3135in
EB := 3 00 0 0 0 0 0 psi
=30000000psi
vb:=.3
vp:=.3
Ftotal :=lOOOOOlbf
Fperlobe
290000
cnnaxtensile: =
2
psi
oiiD:=. 8O 7 O9in
*-(LP- LB)
w.-
2
len :=LB+2 w
theta
=0 deg
Calculation Variables:
1
Requiv'
1
E e q u iv
v )) (1-
1-vb2
RP/
Requiv = 6.85in
cosO:=Requiv
coso = 0.726
Eequiv = 1.648-1
-
(1
_E2P
\R2B/
\1B/
2+
(ilB-
]2+
2
-
-cos(2
opsi
-theta)
115
APPENDIX A
Oa:= 0.996720 if cose<0.9
Aop:= 1.0 if COSe<0.9
(-4522791.052060 otherwise
la:= 1.278600 if COSe<0.9
2a:= -6.7201 if coso<0.9
3a:= 27.379 if COSe<0.9
4a= [41.827 if
Alp:=
A2p :=
A4P:=
23.472 if coso<0.9
0.589090 if cose<0.9
A2T :=
otherwise
I(-865562.5 otherwise
A4'P:= 2.6781 if cose<0.9
1.770600 if coso<0.9
(462760.43 otherwise
-0.998870 if cose<0.9
A5T:= -1.5533 if cose<0.9
I(-98958.33
1-70684.52 otherwise
(Alp -COSO)-+ (A2p -COSo2) + (A3p -COS3) +
0.295260 if cose<0.9
A3:= -1.7567 if coso<0.9
a :=AOa-f+(Ala -COSO) + (A2a COS02) + (A3a COS03) + (A4a COS04)
p :=AoP +
otherwise
1(809436.14 otherwise
1(331436.01) otherwise
A5p :=
-0.042130 if COSO<0.9
j(-378446.23
1-621625.0 otherwise
coso<0.9
1(6269014.53
APP :=
A3p:= -1.327700 if coso<0.9
(-29371139.00 otherwise
5a:=
-0.688650 if cosE<0.9
(582926.0 otherwise
otherwise
0.750180 if cose<0.9
170770.7 otherwise
I(-273306.21 otherwise
otherwise
(-51557740.0)
155036391.0
1(51254.01) otherwise
otherwise
1(24146275.9
AO'P:=
+
otherwise
(A5a'-COS05)
(A4p -COSo4) + (A5p -COS5)
T :=AOT +( AlT -COSO) + A2T -COS02) +(A3T -COS03) + (A4T -COS04 + (A5T -COSO 5)
a = 1.974
p = 0.593
c :=a *-( 3-Ftotal-Requiv)]
2-Eequiv
2[
ContactPressure
3 total)
T
=0.634
d.'=@ -(3-Ftotal-Requiv)3
2-Eequiv
LocalDeformation:=T -
S
2-Ftota2)
i
I2
3-Requiv-Eequiv 2 _
Deflection at Ends
-5
ContactPressure=2.59510 -psi
MaxContactPressure:- (3nmaxtensile)
2
MaxContactPressure= 4.35-10 psi
c = 0.7831n
d
=
0.2354n
LocalDeformation
=9.69610 -3 -in
(Fperlobe-w2)
6-EP -I
A =0.028n
- 2w±3Ien)
116
APPENDIX A
A.2 Hertzian Contact Calculations for Matching Materials
Initial Conditions of Steel
CPSteel
:=259500 psi
dS
:=1.027
in
ES :=30000000 psi
cST :=0.783 in
dST :=0.235 in
LDSteel
:=.009696 in
MDSteel
:=.028 in
Bushing Parameters:
Pin Parameters:
DP
:=2.626 in
RIB :=1000000O000000000
in
R1P :=50 in
R2B :=-1.3135 in
R2P :=1.127 in
LB :=9.334 in
LP :=13.812 in
EB :=53954039.28 psi
EP :=420609.446 psi
vb :=.22
vp :=.35
Ftotal :=2881 lbf
amaxflexural
Fperlobe
Ftotal
2
:=8000 psi
oilD :=.80709
-LB)
w ,-(LP
.
2
'pP
len :=LB -- 2 w
:=[,a
Q
-dS)4]][n
4
=37999.88729 psi
amaxtensilesaph
:=6961.811 psi
amaxtensile
is
-
ID )4]]
4
[L
(.)4]][
in
S(~.)]
APPENDIX A
117
Calculation Variables:
1
Eequiv
Requiv
2
1-v2
EP
EB
Requiv = 6.85in
COSO-:=Requiv
coSe
=
-
Eequiv
theta :=0 deg
-
2l-
-
= 4.75 340
1 psi
-
I
-cos(2-theta)
0.726
AOa := 0.996720if coso<0.9
AOP:= 1.0 if COSO<0.9
1(51254.Ob
1(-4522791.052060 otherwise
Ala := 1.278600 if coso<0.9
A2a:= -6.7201 if coso<0.9
I(-51557740.0)
(-273306.21 otherwise
A2p:= 0.589090 if cose<0.9
1(582926.0 otherwise
otherwise
A3a:= 27.379 if coso<0.9
A3p:= -1.327700 if coso<0.9
1-621625.0 otherwise
55036391.0 otherwise
A4a:= -41.827 if coso<0.9
I(-29371139.09 otherwise
A5a:= 23.472 if coso<0.9
1(6269014.53 otherwise
otherwise
Al:= -0.688650 if cose<0.9
1(24146275.9 otherwise
A40:=
AOT:= 0.750180 if coso<0.9
1.770600 if coso<0.9
(331436.Ob otherwise
A5p:= -0.998870 if coso<0.9
1-70684.52 otherwise
170770.7 otherwise
Al:=
-0.042130 if cose<0.9
1(-378446.23 otherwise
A2T:= 0.295260 if coSo<0.9
1(809436.14 otherwise
A3T:= -1.7567 if COSO<0.9
1(-865562.5 otherwise
A4T:= 2.6781 if coso<0.9
(462760.4Z otherwise
A5V:= -1.5533 if cose<0.9
(-98958.335 otherwise
118
APPENDIX A
a =A0a t (Ala -COSO ) + (A2a COSo2) + (A3a -COSO3) + (A4ac -COS04) + (A5a -COS05)
p =AOP
+(Alp
-COSO)+ (A2p -COSO2
+
(A3
-COSO) + (A4p -COS04) + (A5p -COS 5)
T : =AO' +(A1T -COSO)+ (A2' COS02) + (A3T -COSo3) + (A4 -COSO) + A5
a = 1.974
c:=c
p =0.593
[(3-Ftotal-Requiv)
3
S= 0.634
(3-Ftotal-Requiv)
2-Eequiv
2-Eequiv
3
MaxContactPressurepin
ContactPressure= 7.481-103-psi
MaxContactPressurepin
R2-Ftota2)
LocalDeformation :=T
I
ContactPressure _( 3-Ftotal)
2-t -c-d
c = 0.782Pin
-COSO5)
.3-Requiv -Eequiv2_
_
3
-omaxtensile)
2
=
1.04410 Opsi
_
MaxContactPressureSaph
-55000 psi)
1-2-vb
d =0.23-5in
MaxContactPressureSaph
=
1.96410
50
psi
LocalDeformation = 9.69 1-10 -in
Deflection at Ends
I)
Fperlobe-wj
Fperlobe-w 2)_
-2-wt3-len)
IS))] (
amaxbending
2
:
A6-((EP-IP)+(ES
A = 0.028in
-3
omaxbending
=
1.831-10
30
psi
/J
119
APPENDIX A
Results:
percenterrorc:=[ c-cST) -100
FcST
percenterrorLD:.
percenterrord:=
[( LocalDeformationLLDSteel
PercentPressurePin:
[
LDStee)
( d - dST)
1.10
-100
(MaxContactPressurepin- ContactPressure)
MaxContactPressurepin
-S100
SteefnsertDiameter.-dS
J
100
100
PercentPressurefshing= 1- (MaxContactPressureSaph- ContactPressure)
I
MaxContactPressureSaph
I
percenterroA =F (A
LMDSteel
I
.100
-MSteel)
-
percentflexuralstresspin
SteelnsertDiameter= 1.027'in
percenterrorct -0.074
-3
6
PercentwressurePiu= 71. 36
percenterrord=7.8110
PereentPresureBushing = 3.808
percenterrorLD=-0.056
percentflexuralstresspin = 22.882
percenterrov = 0.07
amaxbending
amaxflexur
(c maxflexural -
)100
120
APPENDIX A
Appendix B
DESIGN PRINTS
.... . ..
..
.0
[I
IJ
D
..............
. ................
......
.....
....
....
'A
e
I'
E&
aa
aa
0
*
-.9
a
..........
.............
*
'A
L
-
.
a
U
121
122
"PENDIX
B
......
....
...
.......
Ap. Abp
....
..........
oppoOD&C-am IN POA- as %.Iulp
"Pub.
."b %.Mp.mpM
N 00 AP. 9 PAUPWH4
- - - --- --------............
. .....
......
...................
LLL
.............
...........
JAI
(D
.......
.... ..
..............................
....... ..................
.............
............
..............
...............
"PENDIX
B
APPENDIX B
a
~ .....~ww
.....S...
...
123
123
... .
~
/
------------
~
~x~m ~ ~
-
I
~t0
-__11
9
_IL.I
-.
~1
o
uOflI.Iyl
3.........
A
124
PIENDIX B
AP
...4M.
Aw .*p:D.6c-w"
.N p~t.
a," 4WO~
.lw
nnwn. rhaAnwr
ml.
Is
4
~3~
-3
A Shantholeof fi25 dareler
a
a
Iia
7zc2
6
j
I
?2
7 272
A3
Kt...ti.
...
772
...
n
wr..
s rz
flhIM =tdIIw
a - - -...
a-
-K--
.
.
- -
125
APPENDIX B
rrJL
.~D
Jtrt~s~K
1-~---~-
-
-,
-~
______
DI
a'.
C
C.
0
o
Iij
-
. -
0
.
.
iiiiiV
s
___________________________
___________________
ff
I
-Aa
126
APPENDIX B
.'u. Aphfl
.
.Pp
Th.
7
FOSBWW :,I ~~a " ~ b
NWHG
UhUeaWMWHM.3WA'nrkhiFflfWW'U
l&w:0thc-mH
"9P.IMP
.
1e
ID ;ia presZ
O
A
:zco
2
0
-WE
...
...
........
......
..........
.. D....
..
........
..
h er e are Iwo parIs naCh;ned Itt h'.
O ne lel and one r ghl. O n lhe lefl o ne
Ihe 003' reg~on.srernoved on lhe rghl
of I he end and Ihe drinensonsfor lhe holes
are from Ihe lei W;l lhe hole end faC.ng away
rr o rni he rmach;n~sl.O n Ihe rghI end 1.sreversec
froin you
T
-lolesare
0.5-20
Quanl ly:2
See nole lo letI
astarn'w
Ul.l bC Ml4IK
~rr
ases
C
-
-
IN
lhreaded
F2A
AK
5
~
4.......
-
....-..
~
-
--
-
-
..-............s
...
~
.
~
T*------4
...
.
J
...
APPENDIX B
127
..
......
...
...
....
....
.. U. OJO owsaftc-EN
;7
B
IN p0j. an "PaM
vtob.
3
......
.......
.....
...........................
.......
.........
.......
....
..........................
......
.....
.......
. .......
.....
.....
..........
.
..
........
....
... .....
....
...........
.
....
..........
.....
....
. ..
......
..
............
..
..
....................
......
mcmi-mmi-M
m dA p
M-."p
'11:11 -
uo
......
..T
...............
...
..
....
......
........
..........
- r &.....
Do
.............
...
.......
id- vr- tlm-p
5cl
M. KcAll. Dso.%IOC
...
........
.....
...........
1.....
I ........
..
...........
7 1 -
.....
I'll -- 11,11-.1 ............
128
APPENDIX B
PAu.pap ow.lBaft~clo"
04 POA- Do "Voll.
up A.. a Pan3lm
pnb4M.
0
.
..
..
...
T here are Iwo par li very
;rn.Iar.
T he Il hai Ihe hole: d.me 3o0ed
rm Ihe leI edge w;Ih Ihe curved 3urface
Iowar d the tnach;nsI w th the (klal de uV.
T he r~g h 1:1 oV CPole.
r
..........
-.
0 uanl ly:2
frifgWVeuar
Mmm
~
- -
~-.---
......
-s..
2 -1
5'ccI
S
-
4
T
T
-
I
129
APPENDIX B
a
.......
.
....
---- --------. .....
...........
.....
....
.............
wpoh.
ED&C-ON " PAM. so
" a$. .. U. a Paul-mm
,Pp* 1"90,p IINW:ww
01
.......
...
........
.............
... ....................................
.......
........
...........
........
..........
...
......
. ......
. ...
......................
. ...
..............
...
.........
I
-- 7
VwrR
nTa
wr
.
......
..............
..
. ................
A
3-wk Ar.
.Ccl
.......
.....
........
..
.......
....
130
APPENDIX B
'1
c m.....
a
,la
ma. ,rnu0B06.Naw aeu'rt
m
S3
wcb
,-I
4 hoLesIhreadedwilh
1.000- 8 L)NC 2A
7I
ij,
(J-vm)
'I
*-1
n __
W1
rn irunrws:FmsT:r,
*~
-A
-
-
Ioe a
CC
s
7,
OA
131
APPENDIX B
Ia a a
--------------
--------------- ------------
a r1r.0
Cell Plare IS Ce rirem(i (k nci Wel.3e.3
r, 1 a C3 Cell lrereftC.2
0
0
0
0
...................
....
.........................
.....
.......................
...
.......
-.......
.....
....
............
............
....
..........................................
I
r
11
Kai"
10
...........................
...........................
.....
..
.....
.....
...................
I.....................
........
...
- -......
....
132
132
APPENDIX B
APPENDIX B
- -------
.
0
I
U-
a
12 mOles eQe"ilysocCoa
aria u'irireoaea
lr rsa MD in.alaurperer
-
- -
IT
I
..
7.
iI
Ma orrlry:I
-
£-7 . -
to M-'L----------
--
-
L
i-
APPENDIX B
II
1.
D.at UaT
El~
MA________
isO afQ o i t art sreel tolera rce
C~uotirlry:I
.6a
-
~
.
. .-
.- ..
.........
133
134
APPENDIX B
D
~A
-
U
~
&
6
~N.
/
/2
/
F
-47
V
/1
\
"N
15,
I
S.,
Quao Irry: 2
tarr
....
.
..
- ~r
~ U
t
7....
t
...
....
APPENDIX B
3
...
...........
. ..
........
..
M. Aff, movaumc-mm of VAM.
P W.IIIIIIIIHOI-AP.
::
135
...
. ........
----------........
..
106-MM
I
cl
i
2 rj
In n e r raCe of I he c k3 In p:i rnaC h: ned c3l a 4 5 degree
43 n g le lo ma IC h I he rno u n 1; ng b loc ts.
.................................
- 1 ...........
...
RIP
. ....
...........
4o leiare all.5;n d;arneler 3.hant hOL-3.
0
'--
0 D of
Ihe
t)arl;3,o
.......................
...........
............
....
...........
.....
........................
ua n
wr
..........
. ......
I........
Ckw-PVD
Piccc
3-ccl
...........
...............
Du m - moil. MOL m
...
........
J- 1-1-..............
...... ............
.........
...
..............
.............
........
136
136
APPENDIX B
APPENDIX B
N
D
U
--
-0
N
U
~L.
~
- 1.18.
all
.. 1110-30. c M
40
L~awmw4
V
4
ifbn
4om
w
Icy: I
Qw4I
I-..__
.
Ffk
--
-
4
137
137
APPENDIX B
APPENDIX B
a
A
D
jwlij
a
+ +
4
dm.=mi
a 6.6===e6= T o-e med =
.a H
-onen
1-
+4IVAN
4
to
+
4,,
I
4
4
Ql4n i
y: I
am pl&,B~m~Ph"
r4 .4
138
138
APPENDIX B
APPENDIX B
0
It
0
D
+'A
S r n acra A 4S1J3/
7'M
~,
~
cey o
no r , e nas
Eorn E4as SI',ilror
2
0
-
ua
r --
s.U..C.....
a
---
-
ill
a
APPENDIX B
S
139
7
2LLII
01
c
1
md Ihreaded W;I h
C 2Aon a 2.125'rad-us
0
0
2K
.
*~zm
EhIbhr4AAI
5-cPPE
3.E-A
Y: 1
__
Do M.CllFGO
_
06
140
APPENDIX B
.M
-.
m. -------------
0
'p
-..a m am .- . ... r .
0
C
-r
b
o
Qre eVe MOy s pocea
nreaara wirn
-1.6
a2.1 ~ raciw
CC
dIdNC 2A
T
I
I
0
0
/3/a
sra
aCOM A NS I cey
[fT
way
Cia ariry: I
b-al
-J
treu Swar C.LQIUr
0
-0 ~--~r
~r~~~~
~r---
-r--
r...-..
...
-"
141
APPENDIX B
N
N
N,
0
0
0
4
~~~
hI
liii
WE
I
-I
5%
-
I
~J
0
V 0
Ckic ijrlry: 2
a1
A
r
rarui
4
4
142
APPENDIX B
0..
..
.,_
.. ..... .....
0
0
~
-
-
U
Ii
.....
.....
....
..
. J.......
,,-
In
o IDat'rnrls ow is a silo nr
[~I~it:
a
rerlry:
LI
-
a--
-
-a-
-~c-
,
..
.....
7a
143
APPENDIX B
a
.................. .....
.._
.................
-
FK
d
_
_
....
.........
144
APPENDIX B
.......
..
........
N
N
N
1.
H
I-
II
Aarrp%%k&
0
11
±am
145
145
APPENDIX B
APPENDIX B
-- D----
0
-----------
.1,1
.-l.-.....
a-.......
ci7
C
-m
F
Hse.
I
I
-
IJ
~s
-'
p-".--
=11
Wrr
146
APPENDIX B
0
U
wee
lp'l
0
..
......
...
.................
.........
...
........
..
-~ -- ---
C1-- yjry7On
t-a
-t--y-U
t
-
-
-
--
"PENDIX
B
..
............. .......
....
..........
--....
...
. ..
........
-9................
._,"L ...............
I"7_1.....
..............
. ........
........
..
.......
__- ..........
.........
....
-A
aim
...
.......
Ikkkkkkkkikkkollilillow"
SIB'd WC 2A r rjMQC.2Q rjolej a sl rplior a n ?.S CIO rperer
cagrees lya rp r ne Ce nreril rie
rw
Cuo rlrlry,. I
....
...........
...
..
...
...............
... .......
Womb wo-or w&wr
wffm,
1-1
.................
OL
.. .. .......
....
..
147
148
APPENDIX B
..
....
........ . .......
..........
......
---.......
.........
...........
..........
All molas an r rils vlaw are
orraig rjr s no n t noles
....
........
................
...........
....
....... ...........
....
..................
- Cii- j
CDua nrlry:
......
.
..........
wr
..........
-
-t
..
....................
149
APPENDIX B
..........
..
...........
....
. ......
0
-......
-----------........... -------............
--------a
-
.-
...
.......
- -..- ---.....................
.- -
wlew are
Ail males art r rils
fir s ria ri K riales
f1fain
IPA;%
IPLM
0-
4
NOWWWWWWWAMM
I
-
11
ii
!
Cuo rorlry: I
r
LA3b&r b&ropdr
- - - ------...
....................................................
.. ... ............
......
........
....
. ........
.
............
. .......
. ...
.....
..
..........
....
... -------------.....
150
APPENDIX B
0
.........
..............
......
. .....
.
...
....
..........
.. ..
.....
..
.............
.. ------------.......
.............
0
..................
....
............
-I ......
.............
......
. ......
..........
.........
i.
42*2
on
Q"ngicp d
Mir
J.641
......
.
.........
14 .
..
...........
Marko 11641
...........
...............
...
....
............
.................
.........
..............
1,11-11--.1 ....................
........
...
. .....
.............