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[0001] The present invention concerns a new shaft, in which the bending stiffness of the shaft is controlled by a pre-stress in the shaft, which is readily adjustable.
[0002] A golf club shaft is described in detail as an example. The choice of bending stiffness of golf shaft is limited, which is fixed in the factory. From the most stiff to the most soft, there are only five stiffness grades, being offered to the public.
[0003] For metal wood clubs of a standard length, the softest L grade shaft deflects about 210 mm and the stiffest XS grade deflects 135 mm, which is a 36% difference. At present there is no golf club shaft whose stiffness can be adjusted.
[0004] In theory of mechanics, it is known that the end deflection of a cantilever beam under end load is changed when it has a simultaneous internal axial force. It is because under the simultaneous loading, the neutral axis of the beam is no longer at its mid-plane. It is shifted up or down, so that the total potential of the shaft is a minimum.
[0005] A shaft can be made stiffer in bending by having a tensile pre-stress, and less stiff by a compressive pre-stress. A difficulty of application of the invention is in the arrangement of the pre-stress and the lacking of a way to estimate the changed stiffness.
[0006] The invention suggests a self-equilibrating internal force system, establishes rules governing the design and a simple procedure to estimate the changed bending stiffness.
[0007] The invention has applications besides golf club shaft. It can be used in other kind of shafts, such as fishing rods, instrument parts, machine parts, etc.
[0008]
[0009]
[0010]
[0011]
[0012]
[0013] The principle of the design of a pre-stressed shaft is as follows:
[0014] (1), The shaft includes concentric, longitudinal structural members, the majority of them joined at their two ends. The majority of members are pre-stressed permanently, in tension or in compression respectively, at least along a significant part of their length. The part of the member, which carries pre-stress, does not enter into the part of the body, which does not participate in the bending process, such as the head part of the club.
[0015] (2), If the adjustment of the axial force is either increasing or decreasing, and if the shaft deflection is to be reduced with increasing pre-stress, the sum of the bending rigidity of its tension members should be significantly greater than that of the compression members; and if the shaft deflection is to be increased with increasing pre-stress, the sum of the bending rigidity of its compression members should be significantly greater than that of the tension members.
[0016] (3), The internal axial force is substantial, and is self-equilibrating.
[0017]
[0018] To maintain a constant force, a spring device
[0019] In
[0020] The following lists geometry and physical data of the
[0021] Shaft length L=107 cm. Outside diameter=1.30 cm. Inside diameter.=1.00 cm.
[0022] 10-ply wall thickness=0.15 cm. Vol.=58 cc. Shaft weight=67.0 g.
[0023] Material density=1.15 g per c.c. Young's modulus E=1,310,000 kg/sq.cm.
[0024] The bending rigidity EI of the shaft is 119,200 kg-sq.cm, where E is the material's Young's modulus and I its sectional moment of inertia. Assume the outer member has 6 plies, which is 69% of the EI, and the inner has 4, which is 31%. Without the axial force, the members share the bending load W at the ratio of 69% to 31%, as the ratio of their respective bending stiffness. With axial force, the load ratio changes more to the stiffer.
[0025] Assume the inner member is able to sustain the axial compressive force P and its Deflection Ratio d*/d remains a constant 1.67 as shown in
[0026] where
[0027] C=ratio of d*/d of the tension member to d*/d of the compression member,
[0028] D=ratio of the compression member's EI to the tension member's EI.
[0029] The same equation also gives the final deflection ratio d*/d of the shaft, denoted as R,
[0030] where
[0031] U=ratio of EI of the tension member to the EI of the total shaft.
[0032] V=d*/d of the tension member under the axial tension force P.
[0033] H=d*/d of the compressed member under the axial compressive force P.
[0034] As an example, assume the axial force P is 10 kg. We get C=0.65/1.67, D=0.31/0.69, U=0.69, V=0.65, and H is taken from the
[0035] From Eq. (1) and (2), the load ratio X is 0.85 and the shaft deflection ratio R is 0.80.
[0036] Compute for more P points, one gets the Curve B of
[0037] An analysis is done also for the case of having a compressed outer member with a tensioned inner member as shown in
[0038] To get the fill range of deflection reduction 36% between the XS stiff state to the final L state, the desired d*/d ratio is 1.56, which yields the Force & Rigidity Coef. of 0.94 from the
[0039] The base shaft may begin as a stiff shaft, XS, and then the axial force in the inner element is increased as intended to control the stiffness of the shaft.
[0040] As seen from the data presented in
[0041] For bending stiffness increment of the shaft device which derives from the tensioned outer member, the axial compression force applied to the inner member may begin at approximately 4.0 kg (8.8 lb) and upward, and the Deflection Reduction Coef. d*/d of the shaft may begin from 0.94; and
[0042] For bending stiffness reduction of the shaft device which derives from the compression outer member, the axial tension force applied to the inner member may begin at approximately 2.0 kg (4.4 lb) and upward, and the Deflection Reduction Coef. d*/d of the shaft may begin from 1.10.
[0043] Finally, one may suggest that for the bending stiffness reduction mode mentioned above, a conversion kit may be adapted to be incorporated into a hollow shaft device, such as a golf club, for controlling the deflection when the shaft is under a bending load. The kit comprises at least a wire-like elongated, structural element and means for connecting the structural element to the ends of the hollow shaft device and producing adjustable stresses to control the bending of the shaft device.