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TRANSCRIPT
Reprinted with permission from the
Winter 2003 edition of
Driving Performance with Optimization
Leverage the
Power of
Linux Clusters
CAD/CAE
Integration:
Making the Grade
7
14
Wire Harness
Design Powers Up
18
Conducting
Computing
Performance
2
Page10
Ideas and Strategies in Product Development
Ideas and Strategies in Product Development
An Publication
WI N
TE
R 2
0 0
3
Altair Engineering, Inc.
DrivingPerformance
with Optimization
DrivingPerformance
with Optimization
12
Concept To Reality/ W
inter 2003
www.altair.co
m/c2
r
ing bodies, reducing the mo-
mentum
transferred from
one body to another. For ex-
ample, if the deform
ation
were perfect without energy
losses, a ball dropped on the
floor would bounce up to its
original height. If a ball of artist clay were dropped
on the floor, it would deform and stick to the floor.
In most impacts, bodies act somewhere between
these two extremes.
COR is the parameter used in rigid body dynamics to
distinguish between these extremes. For now, consider
the ball bouncing off the fixed floor. If a body bounces
to the same height from which it was dropped, it has a
COR of 1. A body that hits and sticks has a COR of 0.
The height a body bounces up is defined by the COR
between the two bodies (e.g., ball and floor). When the
floor is stationary, a collision having a 0.822 COR
value will cause the ball to bounce up 82.2 % of the
height from which it is dropped.
When both bodies are moving, the COR defini-
tion requires a more precise analysis. Remember, the
COR depends on the deformation in both bodies.Here is the full blown definition of COR: The COR is
the negative ratio of relative post-impact velocities to rela-
tive pre-impact velocities.
What exactly is meant by relative velocities? If
two balls move towards one another at 100 mph, the
relative velocity is 200 mph. In our simple case from
the previous paragraph, one velocity was zero.
Hence, the relative velocity is just that of the moving
body. Relative velocity reflects the vector nature of
velocities.To measure the COR for a club head and ball colli-
sion, the pre- and post-impact velocities for both the
club and the ball must be measured. COR is then a
simple calculation. As the ball approaches the club, it
passes through a pair of ballistic screens measuring the
time elapsed to travel a fixed distance. Thus, the in-
bound velocity is measured. As the ball rebounds, the
ballistic screens work the same way in reverse order.
The club head is at rest before impact, so the club
head’s post-impact velocity is all that’s needed to
compute the ball-club head COR. Use of physics’
conservation of momentum allows for the computa-
tion of the COR from the ball’s pre- and post-impact
velocities. This little trick makes for a more econom-
ical experiment, but it also confuses some because
the resulting formula has mass terms. Recall the def-
inition of COR is mass-independent.
Here is the bottom line on COR: Increasing COR
for a given club head velocity and ball will increase
the ball’s initial rebound velocity. Thus, the golf shot
should travel farther.
Getting to the COR with CAE
Designing golf clubs with a COR of less than 0.830
can be tricky. However, employing simulation soft-
ware enables manufacturers to evaluate a multitude
of designs without having to cast a single part.
One such simulation package is Altair Hyper-
Study, an open architecture optimization tool that
can be used in conjunction with any finite-element
solver. Using HyperStudy, with LS-Dyna3D soft-
ware, our objective was to obtain the maximum pos-
sible COR of the club head while maintaining a club
head mass of 200 g and keeping club head stress lev-
els below the material yield of 150 ksi.
The optimization problem is defined by the specifi-
cation of an objective function, constraints and design
variables. The model responses that are used for the ob-
jective and constraints are limited only to quantities
that can be obtained in the solver output. Through the
notation convention of HyperStudy, any value in the
input deck can be defined as a design variable. Thus,
the procedure involved is extremely general.
Figure 1. Definitions of regions on the golf club head.
Figure 2. Resulting
driver shapes for
maximum shape
variable values.
Hosel
FaceSmile
Sole
Toe
Crown
Skirt
Heel
Longer
Wider
Taller
OOn golf c
ourse
s arou
nd the w
orld,
plenty
of gre
at go
lf
has be
en pl
ayed
this s
ummer
at th
e prof
ession
al an
d am-
ateur
levels
. Off t
he links,
an on
going d
rama r
elatin
g to
golf c
lub pe
rform
ance
also
has be
en pl
aying o
ut.
At issu
e is t
he perf
orman
ce of
golf
club d
rivers
.
Specif
ically
, golf
’s ruli
ng bod
ies hav
e inde
pende
ntly
deter
mined a
rule t
hat set
s a un
iform
, worl
dwide
stan
-
dard
for “
sprin
g-like
” effe
ct in
drivi
ng club
s. The o
r-
ganiza
tions w
ill rig
orousl
y test
golf e
quipm
ent fo
r con
-
formity
to th
is and t
he oth
er Rule
s of G
olf.
What
this
means f
or eq
uipmen
t man
ufactu
rers i
s
that
they
must
deve
lop th
eir pr
oduc
ts to
meet t
he ap-
propri
ate st
anda
rds. W
hat’s m
ore, th
e club
s hav
e to b
e
pleasi
ng in th
e eye
s of th
e con
sumers
yet b
e trad
ition
al
and p
lain in
shap
e in th
e eye
s of g
olf’s r
uling b
odies
.
One way
equip
ment m
anufa
cturer
s can
achiev
e
thes
e goals
is th
rough
the u
se of c
omputatio
nal
analy
ses, in
cludin
g rec
ent a
dvan
cemen
ts in
optim
i-
zation
softw
are an
d meth
ods. A
rece
nt eva
luatio
n of
a golf
drive
r hea
d dem
onstr
ates t
hat usi
ng suc
h simu-
lation
tech
nology
can im
prov
e the d
esign
, resu
lting
in dr
ivers
that
are st
ructu
rally
optim
ized t
o the p
er-
forman
ce lim
it all
owed
by th
e Rule
s of G
olf.
Equipped for E
xcellence
Golf heri
tage h
as pr
oduc
ed tw
o ruli
ng bod
ies: t
he
Royal a
nd Anci
ent G
olf Clu
b of S
t. A
ndrews
(R&
A) and th
e Unite
d Sta
tes G
olf Asso
ciatio
n
(USGA).
The USGA is
, in a
way, t
he you
nger o
ff-
sprin
g of t
he R&
A. For
med on
Dec
embe
r 22,
1894
,
the U
SGA is a n
onpro
fit, m
embe
rship-
drive
n orga
n-
izatio
n that
gove
rns t
he gam
e of g
olf in
Nort
h Amer-
ica. E
ven th
ough
Can
ada h
as its
own go
lf ass
ocia-
tion, t
he Roy
al Can
adian
Golf
Asso
ciatio
n, it de
fers
to th
e USGA on
man
y matt
ers. F
or th
e mos
t part
,
the r
est of
the w
orld i
s gov
erned
by th
e R&A.
In te
rms o
f fac
ilitie
s, th
e USGA h
as tak
en su
b-
stantia
l step
s to s
uppo
rt its
equip
ment s
tanda
rds r
e-
by Tom M
ase
Michigan State
Universi
ty
Ea
op
et
Golf D
river
s
Golf D
river
sGo t
he D
is
10
Conce
pt To
Realit
y / W
inter 20
03
TH
E A
RT
OF
I NN
OV
AT
I ON
Enginee
ring en
thusia
sts
and s
oftwar
e tee-o
ff to
optimize
club d
river
perfo
rman
cewhil
e
ensu
ring co
nform
ance
to
he R
ules o
f Golf
.
stan
ce
spon
sibili
ties.
A state
-of-t
he-art,
14,00
0-sq
-ft te
st
center
was
open
ed in
1984
and i
s staf
fed by
a ca
dre of
engin
eers
and s
cientis
ts. T
he test
center
stud
ies th
e
whole ga
mbit of
golf e
quipm
ent a
nd dev
ices.
Behind t
he buil
ding i
s a le
vel, i
nstrum
ented
range
onto
which go
lf rob
ots hit
shots
. In th
e past
, most
of
the t
ime w
as sp
ent o
n testi
ng ball
confor
mation
to
the r
ules a
nd pub
lishin
g a lis
t of a
ccep
table
balls
. In
the m
id-19
70s,
the l
ist fi
t on on
e typ
ewrit
ten pa
ge;
now it
is a
book
of th
ousan
ds of
balls
.
The USGA W
eb si
te indic
ates t
hat ap
proxim
ately
20,00
0 ball
s are
tested
each
year.
Biom
echan
ics sc
i-
ence
s are
emplo
yed t
o unde
rstan
d how
the h
uman
as-
pect
of th
e gam
e is c
hangin
g. Rec
ent y
ears
have s
hown
an in
crease
in dr
iver c
lub hea
d test
ing and t
he form
a-
tion of
assoc
iated
regu
lation
s. Tod
ay, b
all an
d equ
ip-
ment m
anufac
ture
rs su
bmit th
eir pro
ducts t
o the
USGA to va
lidate
that
the e
quipm
ent c
onfor
ms to t
he
Rules o
f Golf
.
Why d
oes th
e USGA m
ake e
quipm
ent ru
les? U
SGA
Preside
nt Ree
d Mac
kenzie
says
for th
ree re
asons1 :
1.The o
verw
helmin
g majo
rity o
f golf
ers be
lieve
there
shou
ld be
rules
abou
t equ
ipmen
t.
2.Equ
ipmen
t rule
s hav
e bee
n the r
espon
sibilit
y of
the U
SGA for o
ver a
centur
y.
3.As a
n inde
pende
nt ruli
ng bod
y, th
e USGA has
no finan
cial in
terest
and c
an lo
ok ou
t for t
he goo
d of
the g
ame.
Dynamics R
ule
The Rule
s of G
olf is
a con
cise a
nd eloq
uent se
t of 3
4
rules.
Rule
4 is
titled
“Club
s,” fo
r the o
bviou
s rea
son.
Muc
h of th
is rule
has to
do w
ith th
e play
ing of a
roun
d.
For insta
nce, h
ow man
y clu
bs may
a play
er ca
rry?
Four
teen. F
urth
er, it
state
s, in
genera
l, these
club
s
shall
confor
m to A
ppen
dix II
of th
e Rule
s.
Appen
dix II
spell
s out
the m
eaning o
f USGA co
n-
forming c
lubs r
egard
ing shaft
strai
ghtn
ess, o
ffset,
grip,
groov
es (re
membe
r that
one?)
and a
newer
criter
ion
know
n as “c
oeffic
ient o
f resti
tution
” (COR).
This last
criter
ion is
in App
endix
II, 4
-1e, a
nd is c
ommon
ly re-
ferred
to as
“4-1
e” or
“COR.”
Curren
tly, t
he USGA
limits
golf c
lubs t
o hav
e a C
OR less
than
0.83
0.
The conce
pt of C
OR rests
in th
e engin
eerin
g
realm
of ri
gid bo
dy dy
namics
, the s
tudy
of how
rigid
bodies m
ove and ac
celer
ate u
nder th
e act
ions o
f
forc
es. T
he oper
ativ
e word
her
e is “
rigid
.” In
the
real w
orld,
defor
mation
take
s plac
e betw
een co
llid-
Conce
pt To
Realit
y / W
inter 20
03
OOn golf courses around the world, plenty of great golfhas been played this summer at the professional and am-ateur levels. Off the links, an ongoing drama relating togolf club performance also has been playing out.
At issue is the performance of golf club drivers.Specifically, golf’s ruling bodies have independentlydetermined a rule that sets a uniform, worldwide stan-dard for “spring-like” effect in driving clubs. The or-ganizations will rigorously test golf equipment for con-formity to this and the other Rules of Golf.
What this means for equipment manufacturers isthat they must develop their products to meet the ap-propriate standards. What’s more, the clubs have to bepleasing in the eyes of the consumers yet be traditionaland plain in shape in the eyes of golf’s ruling bodies.
One way equipment manufacturers can achievethese goals is through the use of computationalanalyses, including recent advancements in optimi-zation software and methods. A recent evaluation ofa golf driver head demonstrates that using such simu-lation technology can improve the design, resultingin drivers that are structurally optimized to the per-formance limit allowed by the Rules of Golf.
Equipped for ExcellenceGolf heritage has produced two ruling bodies: the
Royal and Ancient Golf Club of St. Andrews(R&A) and the United States Golf Association(USGA). The USGA is, in a way, the younger off-spring of the R&A. Formed on December 22, 1894,
the USGA is a nonprofit, membership-driven organ-ization that governs the game of golf in North Amer-ica. Even though Canada has its own golf associa-tion, the Royal Canadian Golf Association, it defersto the USGA on many matters. For the most part,the rest of the world is governed by the R&A.
In terms of facilities, the USGA has taken sub-stantial steps to support its equipment standards re-
by Tom MaseMichigan StateUniversity
EaopetGolf DriversGolf Drivers
Go the Dis
10Concept To Reality / Winter 2003
Reprinted with permission from the
Winter 2003 edition of
T H E A R T O F I N N O V A T I O N
Engineering enthusiastsand software tee-off tooptimize club driverperformance whileensuring conformance tohe Rules of Golf.
stance
sponsibilities. A state-of-the-art, 14,000-sq-ft testcenter was opened in 1984 and is staffed by a cadre ofengineers and scientists. The test center studies thewhole gambit of golf equipment and devices.
Behind the building is a level, instrumented rangeonto which golf robots hit shots. In the past, most ofthe time was spent on testing ball conformation tothe rules and publishing a list of acceptable balls. Inthe mid-1970s, the list fit on one typewritten page;now it is a book of thousands of balls.
The USGA Web site indicates that approximately20,000 balls are tested each year. Biomechanics sci-ences are employed to understand how the human as-pect of the game is changing. Recent years have shownan increase in driver club head testing and the forma-tion of associated regulations. Today, ball and equip-ment manufacturers submit their products to theUSGA to validate that the equipment conforms to theRules of Golf.
Why does the USGA make equipment rules? USGAPresident Reed Mackenzie says for three reasons1:
1. The overwhelming majority of golfers believethere should be rules about equipment.
2. Equipment rules have been the responsibility ofthe USGA for over a century.
3. As an independent ruling body, the USGA hasno financial interest and can look out for the good ofthe game.
Dynamics RuleThe Rules of Golf is a concise and eloquent set of 34
rules. Rule 4 is titled “Clubs,” for the obvious reason.Much of this rule has to do with the playing of a round.For instance, how many clubs may a player carry?Fourteen. Further, it states, in general, these clubsshall conform to Appendix II of the Rules.
Appendix II spells out the meaning of USGA con-forming clubs regarding shaft straightness, offset, grip,grooves (remember that one?) and a newer criterionknown as “coefficient of restitution” (COR). This lastcriterion is in Appendix II, 4-1e, and is commonly re-ferred to as “4-1e” or “COR.” Currently, the USGAlimits golf clubs to have a COR less than 0.830.
The concept of COR rests in the engineeringrealm of rigid body dynamics, the study of how rigidbodies move and accelerate under the actions offorces. The operative word here is “rigid.” In thereal world, deformation takes place between collid-
Concept To Reality / Winter 2003
12Concept To Reality / Winter 2003 www.altair.com/c2r
ing bodies, reducing the mo-mentum transferred fromone body to another. For ex-ample, if the deformationwere perfect without energylosses, a ball dropped on thefloor would bounce up to itsoriginal height. If a ball of artist clay were droppedon the floor, it would deform and stick to the floor.In most impacts, bodies act somewhere betweenthese two extremes.
COR is the parameter used in rigid body dynamics todistinguish between these extremes. For now, considerthe ball bouncing off the fixed floor. If a body bouncesto the same height from which it was dropped, it has aCOR of 1. A body that hits and sticks has a COR of 0.The height a body bounces up is defined by the CORbetween the two bodies (e.g., ball and floor). When thefloor is stationary, a collision having a 0.822 CORvalue will cause the ball to bounce up 82.2 % of theheight from which it is dropped.
When both bodies are moving, the COR defini-tion requires a more precise analysis. Remember, theCOR depends on the deformation in both bodies.
Here is the full blown definition of COR: The COR isthe negative ratio of relative post-impact velocities to rela-tive pre-impact velocities.
What exactly is meant by relative velocities? Iftwo balls move towards one another at 100 mph, therelative velocity is 200 mph. In our simple case fromthe previous paragraph, one velocity was zero.Hence, the relative velocity is just that of the movingbody. Relative velocity reflects the vector nature ofvelocities.
To measure the COR for a club head and ball colli-
sion, the pre- and post-impact velocities for both theclub and the ball must be measured. COR is then asimple calculation. As the ball approaches the club, itpasses through a pair of ballistic screens measuring thetime elapsed to travel a fixed distance. Thus, the in-bound velocity is measured. As the ball rebounds, theballistic screens work the same way in reverse order.
The club head is at rest before impact, so the clubhead’s post-impact velocity is all that’s needed tocompute the ball-club head COR. Use of physics’conservation of momentum allows for the computa-tion of the COR from the ball’s pre- and post-impactvelocities. This little trick makes for a more econom-ical experiment, but it also confuses some becausethe resulting formula has mass terms. Recall the def-inition of COR is mass-independent.
Here is the bottom line on COR: Increasing CORfor a given club head velocity and ball will increasethe ball’s initial rebound velocity. Thus, the golf shotshould travel farther.
Getting to the COR with CAEDesigning golf clubs with a COR of less than 0.830
can be tricky. However, employing simulation soft-ware enables manufacturers to evaluate a multitudeof designs without having to cast a single part.
One such simulation package is Altair Hyper-Study, an open architecture optimization tool thatcan be used in conjunction with any finite-elementsolver. Using HyperStudy, with LS-Dyna3D soft-ware, our objective was to obtain the maximum pos-sible COR of the club head while maintaining a clubhead mass of 200 g and keeping club head stress lev-els below the material yield of 150 ksi.
The optimization problem is defined by the specifi-cation of an objective function, constraints and designvariables. The model responses that are used for the ob-jective and constraints are limited only to quantitiesthat can be obtained in the solver output. Through thenotation convention of HyperStudy, any value in theinput deck can be defined as a design variable. Thus,the procedure involved is extremely general.
Figure 1. Definitions of regions on the golf club head.
Figure 2. Resultingdriver shapes formaximum shapevariable values.
Hosel
Face
SmileSole
Toe
Crown
SkirtHeel
Longer Wider Taller
Reprinted with permission from the
Winter 2003 edition of
T H E A R T O F I N N O V A T I O N
Structural optimization problems are distinguishedby the type of design variables utilized. Generally, sizeoptimization considers the effect of thickness whileshape optimization refers to the modification of geo-metric shape. For a golf driver, which is typically a hol-low structure, the key thickness variables are in theface of the club, but the other wall thicknesses alsocontribute to performance. In optimizing a driverhead, both size and shape optimizations should be con-sidered simultaneously.
In our recent CAE study to evaluate the COR for agolf head, three different shape variables were defined:longer in the toe-to-heel sense, wider in the face-to-back sense and taller. (See Figure 1 for golf club headnomenclature.) As part of the evaluation process, thesoftware alters the model slightly without distorting itor affecting the accuracy of the computation. A linearinterpolation is used to define the shape variables of allinternal nodes lying within the domain. The shapevariable changes can be animated to provide visualverification of the vectors and nodes selected. Figure 2shows the altered shapes of the three shape variablesdefined in the present study.
In addition to the three shape variables, 10 size vari-ables were defined in the optimization problem. Theclub face was divided up into five regions in a bulls-eyepattern while the remainder of the club head was di-vided into five other regions. All regions were defined asoptimization variables. The skirt and hosel thicknessvalues were not considered in the optimization problem.
The power of the optimization process can be seenin looking at the objective function as the design vari-ables are perturbed. Figure 3 shows the design variableevolution and the corresponding objective functionand constraint evolutions. Here, the COR signifi-cantly increases once the response surface has beendefined by initial iterations.
One caveat about the simulated optimization re-sults shown here: The ball model used did not haverate-dependent rubber properties. Rate-dependentmaterials would exhibit damping, which could possi-bly reduce the COR predicted. To get predictive CORnumbers, it is essential to have representative, accu-rate, validated material properties. However, a majorequipment manufacturer recently told me it has meas-ured club heads having COR as high as 0.91.
One final optimization result to point out is thatthe optimized shape has not radically been alteredinto something that doesn’t look like a golf club
head. The combination of shape and size variableshas given the program enough design room to greatlyenhance COR—resulting in a golf ball that travelsfarther—while maintaining a good golf head shape.
With the maturity and sophistication of CAE, op-timization software can now drive the design processversus its historical role of design evaluation and re-finement. As this program demonstrates, robust opti-mization tools, like HyperStudy, can play a key rolein the product development cycle, enabling manu-facturers to virtually design, optimize and validatenumerous concepts as well as save time and money inthe downstream prototype build and test phases.What’s more, optimization software can be appliedto a range of engineering problems, from golf driversto space craft, making it a “must-have” tool in manu-facturing’s arsenal of technological solutions.
Tom Mase is a Visiting Associate Professor at MichiganState University and is affiliated with its CompositeMaterials and Structures Center.
Acknowledgement: The author would like to acknowledgethe help of Eric A. Nelson, Altair Engineering, in theHyperStudy work herein.
LS-Dyna3D solver technology was developed by and isowned by LSTC. For more information visit www.lstc.com.
1 Referencewww.usga.org/about/Perspective/march_april_2002.html
13www.altair.com/c2r Concept To Reality / Winter 2003
C.O.R. Club Mass Peak Stress
Coef
ficie
nt o
f Res
titut
ion
0.92
0.91
0.9
0.89
0.88
0.87
0.86
0.85
0.84
0.830 4 8 12 16 20
Iteration #
Mas
s (g
)
270
260
250
240
230
220
210
200
1900 4 8 12 16 20
Iteration #
Stre
ss (k
si)
200
190
180
170
160
150
140
130
110
120
0 4 8 12 16 20Iteration #
Problem Statement:Objective - Maximize C.O.R.UB Constraint - Peak Stress < 150 ksiUB Constraint - Mass < 200 g
Figure 3. Resultingdriver shapes formaximum shapevariable values.
To request a complimentary copy of the technicalpaper of this case study, visit www.altair.com/c2r or
check 3 on the reply card.
Reprinted with permission from the
Winter 2003 edition of
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