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a” Aluminum Beryllium alloy '—
Tb increase
compliance
ofs‘trong
materials
use them in
the form of
thin hollow
shells. 34 Ti6Al4V 174PH' LVitre’loy' Solid
copper stainless ' ' hardwood Fig. 6— Percent recovered energy for various hollowmetal club head materials and
for a solid persimmon hardwood club head 8 % mass available A Aluminum Beryllium TiGAIAr
alloy , Fig. 7— Percent mass available for perimeter weighting of the club for various club face materials impact increases mildly as the ratio of m2 (repre \ senting the club head) to 1111 (representing the ball) increases. The maximum impact. force increases
more rapidly as the ratio of Fe to E1 increases Figure
5 indicates that the key to decreasing the maximum
impact force between a ball and a striking object is to reduce the elastic modulus of the strildng object!
Thus, the strikin gobject needs to be more comphant ' to lower the maximum impact force and reduce the
amount of strain energy lost during the compres sion and recovery of shape of the ball. , »
1 The effective elastic modulus of a golf ball is about three orders of magnitude lower than that of any of f the metals that are used to construct club heads for drivers. The effective elastic modulus of a baseball is much lower than even that of a golf ball. An ef1 fective value of E for a baseball' 18 7 ksi (50 MPa) _ The wayto drastically, increase the compliance
of strong materials is to use them in the form of‘thin
hollow shells Hollow shells are the basis for the
design strategies used to improve the ball launch performance characteristics of modern hightech 1 club heads and bats. Modeling hollow driver club heads , . ,
The last part of this article examines the predic Eons of a simple design model for the from face of
driver club head The model treats the face of the driva as a rectangular plate: with fixed edges sub jected to a load over a small concentric circle of ra— 7
dius r0 (in other words, as a membrane consumed 3 in. (75 mm), or greater. Under such conditions the
deﬂection, 8, in the center of the club face as a func
tion of the load, P, generatedduring impact is given
by Eq. 3.3 5 = 0.079b2P
E . 13‘ (Eq 3) The compliance of the driver face (5/ P) Varies ' linearly with the reciprocal of the elastic modulus of the material used in itsconstruction, and to the third 1 power of its reciprocal thickness, 1 / t. Equation 3 clearly indicates that the face of a driver can be
made very compliant if its thickness is reduced to a
very low value. However, as the thickness of the
face decreases, the maximum stress, 0, on its sur
face increases, as indicated by Eq. 4:3 'o=‘ 3P
'21tt2 2b 75°70 E1 + v)1n + 0.067] (Eq. 4) In this equation, v is Poisson’s ratio for the ma ‘ terial used for the club face. Clearly, the club face is not functional if a, exceeds a valuenear the ﬂow .
stress, of, of the material used in its construction.
With the stress limited by the yield strength of
the material, Eq. 4 establishes the minimum thick
ness of the club face as a function of applied load. The minimum club face thickness defines the max
_ 1mum compliance for a given material through Eq.
1 1 3. The maximum compliance IS obtained by a ma terial that maximizes the 6f 15 / E mechanical prop
erty index Using Eq. 3 and the load / displacement
relationship fer compression of a golf ball, the
lowest Value for the maximum force that could be ,
generated when a driver club face traveling at 100
mph (160 km/ h) impacts a golf ball was deter
mined for the materials listed in the table. Comparing candidate club facematerials ,
The maximum impact force values are listed' in the table A club face made of Vitreloy metallic glass * prciduce‘s the lewest maxirhum impact force, while
the aluminum alloy produces the highest max imum impact force. That order of result would be
1 expected based upon the Gf1'5/ E property index values. However, the magnitude of the variations
between the property index values and the max
imum impact ferce values among the materials 18
very different The property index Value for Vit \
reloy' IS 6. 7 times that of the aluminum alloy, but
its maximum impact force 15 only 17% lower than
that of the aluminum alloy The relative 1nsensi—
tivity of the maximum impyact force to the compli
ance of the club face is due to the compliances of
all of the club face materialsbeing much lower than ‘
that of the golf ball. For all of the materials tested, ‘
the majority of the defamation and buildup of force
during impact is dependent upon the properties of the golf ball. As a t of contrast, the impact force generated 1. for the 100 mp h (160 km / h) impact of a 7 oz (200 ’ , g) solid block of persimmon hardwood with a golf " _' 11 "‘ _ ,_ g , ball was detemuned; The impactforoe is quite sim *
‘ face, b, is taken as 1: 5 111.2(40 min) and its Width is". ilar to those of the hollow metal (membrane design) ADVANCED MATERIALS & PROCESSES/ SEPTEMBER 2001 ...
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 Spring '08
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