golfclub-2_img_3 - 6‘ 00 VI 01 an t 5 i g 1s 2 a”...

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Unformatted text preview: 6‘ 00 VI 01 . an t 5 i g 1s 2 a” Aluminum Beryllium- alloy '— Tb increase compliance ofs‘trong materials use them in the form of thin hollow shells. 34 Ti-6Al-4V 17-4PH' LVitre’loy' Solid copper stainless ' ' hardwood Fig. 6— Percent recovered energy for various hollow-metal club head materials and for a solid persimmon hardwood club head 8 % mass available A Aluminum Beryllium- Ti-GAI-Ar 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 ef-1 fective value of E for a baseball' 18 7 ksi (50 MPa) _ The way-to 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 high-tech 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 '21t-t2 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 " _' 1-1 "‘ _ ,_ 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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