Patent Publication Number: US-2003224870-A1

Title: Shaft having axial pre-stress

Description:
BACKGROUND OF THE INVENTION  
       [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. 
     
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
     [0008]FIG. 1 shows the Table 9a, Reaction and Deflection coefficients for beams under simultaneous loading, taken from p. 157, Roark&#39;s Formulas for Stress &amp; Strain, by Warren C. Young, sixth Edition, McGraw-Hill, Inc.  
     [0009]FIG. 2A shows a cantilever beam having an end load W, and a deflection denoted as d. The deflection is reduced to d* with a simultaneous axial tension force P.  
     [0010]FIG. 2B curve A plots the Force and Rigidity Coefficient of a pre-tensioned beam versus the Deflection Reduction, d*/d, based on FIG. 1 table data. Curve B is the force P versus d*/d of the pre-stressed shaft shown in FIG. 3.  
     [0011]FIG. 3 shows a golf club shaft its inner member is in compression  
     [0012]FIG. 4 shows a golf club shaft its inner member is in tension. 
    
    
     A PRINCIPLE TO ARRANGE THE PRE-STRESS  
     [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.  
     A GOLF CLUB SHAFT EMBODIMENT  
     [0017]FIG. 3 is the embodiment of a golf club shaft  1 , having a length L, and two ends: a handle end  2  and an opposite end  3 , which leads to the golf club head. The golf shaft consists of a cylindrical outer member  4  and an inner member  5 . The two members as shown have a threaded joint  7  at the handle end and a fixed joint at the opposite end  6 . When the smaller inner member is being pushed down from the grip end, joint  6  will pull the outer member with an equal force P. It is to be noted that the structural end of the shaft at end  2  may be extended beyond  2 . The end point  2  and the length L begins where the force engagement of the two members actually begins, which is the length that counts in the invention. In this embodiment the outer member has the predominate bending rigidity. Such an internal force system is a self-equilibrating system. If the applied force P is to be adjustable, a screw and thread device such as  7 , which engages  4  to  5  at the handle end  2 , may be used. A screwdriver is sufficient to adjust the force P from the outside through a small recoverable opening made at  2 .  
     [0018] To maintain a constant force, a spring device  8  is optional. The interfaces between contacting members may be free, may have cushions; or fixed, such as by adhesives.  
     [0019] In FIG. 3, the bending stiffness of the shaft is increased by the axial tension of the outer member through the compressed inner member. For the case of a shaft to be softened by the pre-stress, the inner member is in tension, and the outer member is in compression. The inner member may be a wire-like structural element or a small bar as shown in FIG. 4. Other configurations may have more than two members. In general, some members may be only partially stressed, or not stressed at all, or its length may be shorter than full.  
     NUMERICAL EXAMPLE  
     [0020] The following lists geometry and physical data of the FIG. 3 carbon-fiber golf shaft:  
     [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&#39;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&#39;s Young&#39;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.  
     SHAFT STIFFNING THROUGH AXIMAL PRE-STRESS  
     [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 FIG. 1 table. An equation that the deflections of the two ends are equal yields Eq. (1), where X is the percentage of the load on the tension member:  
       X= 1.0/[1.0+( C×D )],   (1)  
     [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&#39;s EI to the tension member&#39;s EI.  
     [0029] The same equation also gives the final deflection ratio d*/d of the shaft, denoted as R,  
       R= 1.0/[( U/V )+(1 −U )/ H],    (2)  
     [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 FIG. 1 compression table as 1.67.  
     [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 FIG. 2B. It shows the stiffening effect obtained if the sample shaft of FIG. 3 has 6 plies for the outer member and 4 plies for the inner member. The result shows at an axial compression force of 19 kg (42 lb), the deflection ratio d*/d reaches 0.64. This corresponds to a 36% deflection reduction, the full range of stiffness change. This point is marked in FIG. 2B curve B. If the base shaft begins as a soft grade L shaft, the 36% deflection reduction makes the shaft to become the stiffest XS shaft. A player can adjust the stiffness by a screwdriver to get any stiffness within that 36% range.  
     SHAFT SOFTENING THROUGH PRE-STRESS  
     [0037] An analysis is done also for the case of having a compressed outer member with a tensioned inner member as shown in FIG. 4. In this arrangement, the inner member is a wire-like structural element and the outer member is structurally the main shaft, which takes the full load. The advantage is that the inner member&#39;s rigidity and weight are almost negligible.  
     [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 &amp; Rigidity Coef. of 0.94 from the FIG. 1 compression data. The required P to yield the Coef of 0.94 is found as 9.30 kg (20 lb). The analysis is simple, because the outer member is practically the complete shaft. This greatly simplifies the analysis.  
     [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.  
     COMMENT  
     [0040] As seen from the data presented in FIG. 1 tables and FIG. 2B curves that, for the pre-stress begins to have noticeable and meaningful bending stiffening or softening effect on a shaft device, especially as applied to golf club shaft with comparable bending rigidities as given in the sample problem, it is reasonable to suggest that:  
     [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.