U.S. patent application number 09/822701 was filed with the patent office on 2003-01-23 for golf club shaft with superelastic tensioning device.
Invention is credited to Jessiman, Alexander W., Masters, Brett P., Schoor, Marthinus C. van.
Application Number | 20030017884 09/822701 |
Document ID | / |
Family ID | 25236731 |
Filed Date | 2003-01-23 |
United States Patent
Application |
20030017884 |
Kind Code |
A1 |
Masters, Brett P. ; et
al. |
January 23, 2003 |
Golf club shaft with superelastic tensioning device
Abstract
A shaft for a golf club or other sporting equipment is
disclosed, wherein the shaft is hollow and contains a wire or cable
placed under tension therein, the wire being made of a superelastic
material. The wire is connected at one end to a variation device
such as a cam which varies the tension on the wire and thus the
bending stiffness of the golf club. Because the wire is made of a
superelastic material, for example Nitinol, it can reversibly
elongate in response to pre-tensioning and dynamic stresses
encountered during swinging the golf club, in order to
counterbalance and accommodate, the stress encountered during
normal use of the golf club, thus ensuring a long life and
preventing damage to the golf club shaft.
Inventors: |
Masters, Brett P.; (Belmont,
MA) ; Schoor, Marthinus C. van; (Medford, MA)
; Jessiman, Alexander W.; (Scituate, MA) |
Correspondence
Address: |
Dike, Bronstein, Roberts & Cushman
Intellectual Property Practice Group
EDWARDS & ANGELL
P.O. Box 9169
Boston
MA
02209
US
|
Family ID: |
25236731 |
Appl. No.: |
09/822701 |
Filed: |
March 30, 2001 |
Current U.S.
Class: |
473/316 |
Current CPC
Class: |
A63B 60/06 20151001;
A63B 60/16 20151001; A63B 60/08 20151001; A63B 59/00 20130101; A63B
60/22 20151001; A63B 53/10 20130101; A63B 60/42 20151001; A63B
53/00 20130101; A63B 53/12 20130101; A63B 60/24 20151001; A63B
2209/14 20130101; A63B 60/10 20151001; A63B 60/002 20200801; A63B
53/14 20130101; A63B 60/0081 20200801 |
Class at
Publication: |
473/316 |
International
Class: |
A63B 053/12; A63B
053/16 |
Claims
What is claimed is:
1. A sporting device having a variable stiffness shaft, comprising:
a hollow shaft; a length of a superelastic alloy placed under
tension within the hollow shaft and affixed thereto at two points
on the shaft, the alloy capable of reversibly elongating to
accommodate an applied stress; and variation means for adjusting
the tension of the tensioning device, whereby increasing the
tension reduces the bending stiffness of the shaft.
2. The sporting device of claim 1, wherein the superelastic alloy
is Nitinol.
3. The sporting device of claim 1, wherein the superelastic alloy
can reversibly elongate by up to approximately 8% to accommodate
the applied stress.
4. The sporting device of claim 1, wherein the applied stress
includes a pre-stress applied to the length of superelastic alloy
by the variation means.
5. The sporting device of claim 1, wherein the applied stress
includes a dynamic stress produced during a swing.
6. The sporting device of claim 1, wherein the length of
superelastic alloy comprises a wire affixed at one end to the
shaft, and affixed at the opposing end to the variation means, the
variation means transmitting the tension of the wire to the
shaft.
7. The sporting device of claim 1, wherein the length of
superelastic alloy comprises a plurality of wires affixed at one
end to the shaft, and affixed at the opposing end to the variation
means, the variation means transmitting the tension of the wires to
the shaft.
8. The sporting device of claim 1, wherein the variation means is a
cam.
9. The sporting device of claim 1, wherein the variation means is a
pinned retractable piece.
10. The sporting device of claim 1, wherein the variation means is
a lockable lead screw.
11. The sporting device of claim 9, wherein the lead screw is
varied by an external actuator.
12. The sporting device of claim 1, wherein the variation means is
a pump.
13. The sporting device of claim 1, wherein the variation means is
a sleeve screw.
14. The sporting device of claim 1, wherein the variation means is
a displacement actuator powered by an external source.
15. The sporting device of claim 1, and further comprising a
constraint insert for preventing dynamic vibration of the length of
superelastic alloy.
16. The sporting device of claim 15, wherein the constraint insert
comprises a material selected from the group consisting of low
density foam, plastic, and elastomers.
17. The sporting device of claim 15, and further comprising a
plurality of discrete inserts.
18. The sporting device of claim 15, wherein the constraint insert
is a single constraint insert extending substantially along the
length of the shaft.
19. The sporting device of claim 15, wherein the constraint insert
is held in the shaft by compression.
20. The sporting device of claim 15, wherein the constraint insert
is held in the shaft by adhesive.
21. The sporting device of claim 1, wherein the sporting device is
selected from the group consisting of a golf club, a tennis racket,
a ski pole, a hockey stick, a baseball bat, a fishing pole, a
hurling stick, a lacrosse stick, and a vaulting pole.
22. A golf club having a variable stiffness shaft, comprising: a
hollow shaft; a wire disposed within the hollow shaft and affixed
thereto at two points on the shaft, wherein the wire is made of a
superelastic alloy which reversibly elongates to accommodate an
applied stress; and variation means for varying the tension of the
wire, whereby increasing the tension of the wire reduces the
bending stiffness of the shaft.
23. The golf club of claim 22, wherein the superelastic alloy is
Nitinol which can reversibly elongate by up to approximately
8%.
24. The sporting device of claim 22, wherein the applied stress
includes a pre-stress applied to the length of superelastic alloy
by the variation means.
25. The sporting device of claim 22, wherein the applied stress
includes a dynamic stress produced during a swing.
24. The golf club of claim 21, wherein the superelastic alloy is
selected from the group consisting of nickel and aluminum (Ni--Al);
copper and zinc and another element Cu--Zn--X (where the other
element X is silicon (Si), tin (Sn), or aluminum (Al)); copper and
zinc (Cu--Zn); copper and tin (Cu--Sn); copper and aluminum and
nickel (Cu--Al--Ni); iron and platinum (Fe--Pt); iron and manganese
and silicon (Fe--Mn--Si); and manganese and copper (Mn--Cu).
25. The golf club of claim 21, wherein the wire is affixed at one
end to the shaft, and affixed at the opposing end to the variation
means, the variation means transmitting the tension of the wire to
the shaft.
26. The golf club of claim 25, wherein the tensioning device
comprises a plurality of wires affixed at one end to the shaft, and
affixed at the opposing end to the variation means, the variation
means transmitting the tension of the wires to the shaft.
27. The golf club of claim 21, wherein the variation means is a
cam.
Description
FIELD OF INVENTION
[0001] The present invention relates to shape memory alloys, which
are materials capable of recovering their original shape after
being deformed under stress, and more particularly relates to the
use of such materials in sporting equipment such as a golf club or
a hockey stick.
BACKGROUND OF THE INVENTION
[0002] Shape memory alloys (SMAs) are metal alloy materials that
have the ability to return to their original shape after being
deformed. All SMAs have two distinct crystal structures, or phases,
with the phase present being dependent on the temperature and the
amount of stress applied to the SMA. The two phases are martensite,
which exists at lower temperatures, and austenite at higher
temperatures. The exact structure of these two phases depends on
the type of SMA, where the most commonly used type is called
Nitinol. Nitinol is a mixture of two component metals, nickel (Ni)
and titanium (Ti), which are mixed in an approximate ratio of 55%
by weight Ni and 45% by weight Ti, and annealed to form a part in
the desired shape.
[0003] Shape memory alloys possess two material properties that
work together to provide shape memory. The first material property
is an austenite to martensite transition in the SMA. This is a
solid-to-solid phase transition from an austenite phase with high
symmetry (such as a cubic molecular structure) to a martensite
phase with lower symmetry (such as tetragonal or monoclinic
structures). The second property of a shape memory alloy is the
ability of the low-symmetry martensite structure to be deformed by
twin boundary motion. A twin boundary is a plane of mirror symmetry
in the material. If the twin boundary is mobile, as in certain
martensite structures, the motion of the boundary can cause the
crystal to rearrange and thus accommodate strain.
[0004] The coupling of the above two properties produces two
distinct types of mechanical behavior in shape memory alloys. These
two behaviors are referred to as "shape memory effect" and
"superelasticity."
[0005] The shape memory effect occurs when deformation incurred in
the martensite phase via twin boundary motion is recovered by
heating the material past a transition temperature to the high
temperature austenite phase. The following three-stage model
illustrates the changes undergone by a shape change alloy according
to this effect:
[0006] In stage 1, the alloy is in the austenite phase. As the
alloy is cooled below the transition temperature, T.sub.m, the
material tends to retain its original shape by inducing twin
boundaries that allow the newly deformed (stage 2) crystal
structure to occupy approximately the same volume as the stage 1
structure. Now, if stress is applied to the structure, it can
deform by twin boundary motion. The twin boundaries move to
rearrange the crystalline asymmetry to accommodate strain (thereby
reaching stage 3). This rearrangement can occur in several
directions, allowing the crystal structure to handle strain in
multiple directions. Finally, when the material is re-heated, the
asymmetry that permitted strain in the crystal structure disappears
in the transformation, and the material recovers to its original
(stage 1) shape. The particular orientation of the crystal
structure in stage 2 is unimportant, as the material returns to
only one structure, i.e. the original austenite structure of stage
1. Hence, such a material exhibits the shape memory effect.
Thermally actuated shape memory materials such as Nitinol (NiTi)
include an elastic range of up to 8% reversible elongation in some
materials, and the yield stress is very low, thus allowing the
material to deform easily in the martensite state.
[0007] Superelasticity uses the same deformation mechanisms as
shape memory, but occurs without a change in temperature. Instead,
the transformation is induced by stress alone. Applied stress can
overcome the natural driving force which keeps the material at
equilibrium in the austenite phase. By applying stress to the
material, it can be converted into the martensite phase, and the
crystal structure will strain to accommodate the applied stress.
When this stress-energy is greater than the chemical driving force
of stabilization in the austenite phase, the material will
transform to the martensite phase and be subject to a large amount
of strain. When the stress is removed, the material returns to its
original shape in the austenite phase, since martensite cannot
exist above the transition temperature. This superelastic behavior
is fully reversible and does not require any change in
temperature.
[0008] The full stress recovery of a superelastic material can
occur with up to approximately 8% elongation in Nitinol (NiTi).
Because of this large elastic range, superelastic materials are
used in applications such as cardiovascular stents, mobile
telephone antennas, and eyeglass frames. Superelastic materials
have not previously been used in sporting equipment such as golf
clubs or hockey sticks.
[0009] U.S. Ser. No. 09/158,172, commonly owned with the present
application, discloses a variable stiffness shaft for use in a golf
club, and is incorporated by reference in the present disclosure.
As taught in the '172 application, a golf club includes a hollow
shaft having a wire placed under tension inside the shaft, the
tension being adjustable to a desired level. Such an invention is
useful for varying the stiffness of the shaft to accommodate
individual users and different anticipated levels of stress.
However, the internal wire is customarily made of a material that
does not have shape memory, such as steel (piano wire), titanium,
aluminum, or a corrosion resistant plastic such as nylon, all of
which are non-SMAs. Such materials can reversibly elongate by
typically 0.33%-0.34%, and even as much as 1% for spring steel, but
dynamic strains realized in a golf club shaft commonly range from
0.33% to about 1%, thus resulting in material failure. Accordingly,
conventional materials are subject to damage after repeated blows
on the golf course.
SUMMARY OF THE INVENTION
[0010] A hollow shaft for use in a golf club or other sporting
equipment having a shaft is disclosed, wherein the shaft contains a
tensioning device comprising a wire or cable made of a superelastic
alloy. The tension level of the wire can be varied in order to
reduce the bending stiffness of the shaft, in accordance with
particular anticipated loads or to accommodate the player's
individual stroke. Initially, the wire is pre-tensioned by
mechanically tightening the wire using a variation means. As a
result of being tightened, the wire elongates by approximately 0-7%
(i.e. any amount within the wire's elastic range of up to 8%)
against the shaft stiffness, which is known as a pre-stress or
pre-tension level of the wire. The shaft is pre-tensioned by an
amount less than the maximum strain level of 8% in the wire, so as
to accommodate dynamically induced strain encountered during a
swing and contact with the ball.
[0011] As a result of pre-stressing, the shaft is compressed to the
tension level produced by the wire elongation. By pre-compressing
the shaft, the bending frequency of the shaft is reduced which
reduces the net flex rating and improves performance of the golf
club. Shaft pre-compression also tends to offset centrifugally
induced shaft tension encountered during a swing, such that, upon
impact of the golf club with a ball, a lower net strain level is
present in the shaft as compared with uncompressed composite
shafts. Thus, when coupled with preset strains, strain levels
present in the shaft at impact do not exceed yield and failure
strains of the shaft.
[0012] During the swing, centrifugal loads of the accelerating golf
club head mass result in approximately 50-100 pounds of dynamic
tension force being placed on the shaft. On top of this are
short-term dynamic stresses and strains in the shaft that result
from ball impact. Conventional composite golf club shafts degrade
over time when used by hard swingers because the net dynamic strain
(i.e. the large dynamic strain that results from swing centripetal
acceleration forces coupled with impact dynamic strains) causes the
material situated near the hosel end of the shaft to fail. By
incorporating in the shaft a wire made of a superelastic shape
memory alloy, measured levels of swing and impact-induced dynamic
strain, which can reach approximately 0.33-1%, will not result in
significant degradation of the shaft due to stress, as
substantially all of the stress is absorbed by the wire. Whereas a
composite shaft incorporating a wire made of a conventional
material produces large stress changes in the shaft which accompany
relatively small changes in strain, thus resulting in premature
fatigue and failure.
[0013] Superelastic wires exhibit a large recoverable strain
capability, and can recover approximately 0-8% of strain, or
substantially the entire range of deformation produced in the wire.
Since the superelastic wire can recover over a large strain range,
even for nominal dynamic stresses above the pre-tension amount, the
wire made of a superelastic alloy has superior fatigue and failure
properties, and is also an extremely hard, corrosion-resistant
material.
[0014] A preferred superelastic alloy is Nitinol (NiTi), which can
reversibly elongate over an elastic range of up to approximately
8%, allowing the golf club to be swung repeatedly without damaging
the shaft. As used herein, the terms "shape memory alloy" and
"superelastic alloy" refer to a material having (i) an austenite to
martensite solid-to-solid phase transition, and (ii) an ability for
the martensite structure to be deformed by twin boundary motion.
The preferred materials to be used in the present invention are
superelastic alloys, which are further defined as materials that
undergo the martensite to austenite phase transition without a
significant change in temperature. In superelastic alloys, the
martensite to austenite transition occurs due to the dynamically
applied stress forces which overcome the natural driving force that
keeps the material at equilibrium in the austenite phase.
[0015] The golf club with a wire made of Nitinol incorporated in
the hollow shaft can respond to each swing by returning to its
original preset shape. The wire can reversibly elongate under
strain over an elastic range of up to approximately 8% of
reversible strain. The use of a superelastic alloy in the golf club
yields unexpected results in terms of high performance and
long-lasting durability of the golf club. As taught in the '172
application, by placing a wire under tension inside a hollow shaft
of the club, bending stiffness of the club can be reduced, thereby
improving trajectory for each stroke. However, when the internal
wire is made of conventional materials, it tends to stretch
whenever the total stress exceeds the maximum level of
approximately 0.33-1% tolerated by the wire material, and the wire
becomes damaged over time. Such stretching and damage is minimized
by the use of a wire made of a superelastic alloy, in accordance
with the present invention. The applied stress produces elongation
in the wire which is well within the recoverable strain of the
superelastic wire and which causes only minimal variations in the
pre-stressed wire. Thus, a golf club with a hollow shaft
incorporating a superelastic wire (e.g. made of Nitinol)
demonstrates high stroke performance but also a long term
durability not present in golf club shafts made of a conventional
material.
[0016] The stiffness of the hollow shaft is initially set by using
a variation means to adjust the tension on a tensioning device
disposed in the hollow shaft. The tensioning device is attached to
the shaft at two points. Thus, applying tension to the tensioning
device causes compression in the shaft region between the two
points. The tensioning device, as explained above, can be a wire or
cable made of a superelastic alloy, or a plurality of wires or
cables. Many variation means are possible, including a cam, a
pinned retractable piece, a lockable lead screw (which may be
adjusted by an external actuator), a pump, a sleeve screw, or a
"set and forget" displacement actuator. The shaft can have one or
more constraint inserts, which can be made, for example, of low
density foam, plastic, or an elastomer. The constraint inserts
impede dynamic variation of the tensioning device. They can be held
in the shaft by compression fit or by adhesive. The sporting
equipment can be, for example, a golf club, a tennis racket, a ski
pole, a hockey stick, a baseball bat, a fishing pole, a hurling
stick, a lacrosse stick, or a vaulting pole.
BRIEF DESCRIPTION OF THE DRAWINGS
[0017] For a fuller understanding of the nature of the present
invention, reference is made to the following detailed description
taken in conjunction with the accompanying drawing figures wherein
like reference characters denote corresponding parts throughout the
several views and wherein:
[0018] FIG. 1 is a cross-sectional view of a preferred embodiment
of a golf club shaft according to the present invention;
[0019] FIG. 2 is a cross-sectional view of another preferred
embodiment of a golf club shaft;
[0020] FIG. 3 is a cross-sectional view of a further preferred
embodiment of a golf club shaft; and
[0021] FIGS. 4A-4F are cross-sectional views of six alternative
preferred embodiments of a variation means according to the present
invention.
DETAILED DESCRIPTION OF THE INVENTION INCLUDING THE PREFERRED
EMBODIMENT(S)
[0022] The present invention discloses a golf club or other
sporting equipment with a hollow shaft inside the golf club, where
a wire or cable is placed under tension, allowing the bending
stiffness of the golf club to be varied. In a particular aspect of
this invention, the wire is made of a superelastic alloy, such that
the wire recovers to its original pre-stressed state after a
dynamically applied stress is released (i.e. after the club head
strikes the ball). Accordingly, after repeated swings, the wire
retains its original shape, with little variation from the
pre-tensioned state, and does not suffer significant damage, thus
prolonging the life of the golf club.
[0023] Such a design utilizes the well known concept that a beam's
bending stiffness can be varied by preloading the beam along its
longitudinal axis. The present invention involves the use of this
principle to provide a variation mechanism for golf club shafts and
other sporting equipment. The preloading device is the wire or
cable (mentioned above) which is placed under tension in the hollow
shaft of a golf club. Tensioning the wire/cable compresses the
shaft along its bending axis, reducing the effective bending
stiffness as compared to that of the unloaded shaft. An advantage
of the present invention is that it allows production of a shaft
having a high torsional stiffness, enabling a rapid response to
player wrist turnover action, but having a low bending stiffness,
so that the player achieves the best ball trajectory for a given
swing speed. A detailed explanation of the above principle is
provided later in this description.
[0024] FIG. 1 illustrates a preferred embodiment of a golf club
shaft 10 having a butt end 12 and a hosel end 14, with a tensioning
wire or cable 16 secured at both ends of the shaft. A variation
mechanism 18 is located at the butt end 12 of the shaft, where it
is readily accessible to the user of the club. FIG. 2 shows an
alternate preferred embodiment of the golf club shaft, further
comprising a wire termination insert 20 in the interior of the
shaft. In this embodiment, the wire 16 extends only part way into
the shaft, reaching from the butt end 12 to the termination insert
20. FIG. 3 shows a further preferred embodiment of the golf club
shaft, wherein the shaft includes a plurality of constraint inserts
22, made for example from low density foam, which restrain lateral
motion of the wire 16.
[0025] The internal tensioning wire/cable 16 is preferably made of
a superelastic alloy which can reversibly elongate under an applied
dynamic stress by an amount in excess of the normal expected strain
of approximately 0.33-1% experienced in a golf club upon impact
with the ball. A preferred superelastic alloy is Nitinol (NiTi),
which exhibits an elastic range of up to 8% deformation, and is
therefore able to fully recover from the expected strain
experienced in a golf club. Such an elastic range provides
significant advantages over conventional metals and alloys which
generally exhibit strain levels very close to the expected level of
0.33-1%.
[0026] A problem encountered in conventional composite shaft golf
clubs is that the dynamic stresses often produce unacceptable
strain levels in the wire 16, leading to premature fatigue and
failure. Using such materials, the wire is often pre-tensioned to
approximately its elastic limit, resulting in damage if any
additional dynamic strain is applied during swinging. Repeated
swings can lead to permanent damage of the golf club and a reduced
useful life. Use of a superelastic alloy such as Nitinol enables
the golf club to be swung repeatedly without damaging the
shaft.
1TABLE 1 Comparison of Material Properties of Nitinol With Other
Materials 304 NiTi 6061 Cast AM100A 4140 Stainless Material SMA Al
Iron Mg Steel Steel Wood Recoverable 8% 0.34% 0.23% 0.33% 0.33%
0.11% 0.42% Strain (%) Recoverable .about.7000 147 41 137 142 15 51
Energy (J/kg) Density (kg/m.sup.3) 6450 2770 7064 1800 7830 7830
500 Modulus (GPa) 75 aus. 70 90 45 205 197 12.1 28 mart. Yield
Stress 600 241 250 150 675 215 13.1 (MPa) Melting Temp. (.degree.
C.) 1240 582 -- 540 1400 1427 --
[0027] As shown in Table 1 above, Nitinol provides properties
superior to those of conventional materials and is ideal for use in
the wire/cable 16. The recoverable strain in Nitinol is
approximately 8%, which is significantly greater than Al (0.34%),
Mg (0.33%), and steel (0.33%). Spring steel (not shown) can recover
up to approximately 1% of recoverable strain. Iron and stainless
steel, the most common materials for golf club shafts, exhibit even
lower percentages of recoverable strain, and thus are not practical
for use in a composite shaft, where expected levels of strain can
produce approximately 0.33-1% elongation. Even using aluminum,
magnesium, or steel in the hollow shaft 10 can result in damage to
the shaft because the recoverable strain of such materials is very
close to the expected strain experienced in a golf club and can be
exceeded whenever a large amount of stress is applied. Wood (0.42%)
has a higher percentage of recoverable strain, but is not practical
for use in the golf shaft due to its low yield stress.
[0028] Also as demonstrated in Table 1, the recoverable energy of
Nitinol is extremely high compared to conventional materials, a
property which stems from the ability of Nitinol and other
superelastic alloys to convert from the austenite to the martensite
phase, and then return to its original shape upon returning to the
austenite phase.
[0029] While the preferred material for the wire 16 is a Nitinol
alloy, other superelastic alloys and shape memory alloys can be
used, including but not limited to mixtures of: nickel and aluminum
(Ni--Al), copper and zinc and another element Cu--Zn--X (where the
other element X can be silicon (Si), tin (Sn), or aluminum (Al)),
copper and zinc (Cu--Zn), copper and tin (Cu--Sn), copper and
aluminum and nickel (Cu--Al--Ni), iron and platinum (Fe--Pt), iron
and manganese and silicon (Fe--Mn--Si), or manganese and copper
(Mn--Cu).
[0030] When the wire 16 is made of one of the above superelastic
alloys, e.g. Nitinol, the wire is subject to stress at three
different stages: (1) when the wire is pre-tensioned by a desired
amount, where the pre-tension amount is within the range of 8%
maximum allowable strain so as to allow room for dynamically
induced strain occurring during the swing and impact; (2) during
the downswing as the result of tension forces loaded onto the shaft
by the accelerating club head; and (3) as the golf club strikes the
ball. Accordingly, the wire 16 is converted from austenite to
martensite during stressing, and the martensite structure deforms
by twin boundary motion in an elastic range of up to approximately
8% elongation to accommodate the stress. After the stress is
released, the wire 16 returns to its original zero-strain,
austenite state. The wire 16 is able to reversibly elongate under
strain to accommodate the full amount of stress encountered during
a golf swing.
[0031] A number of wire/cable tension variation systems are
suitable for use with the invention. Several such systems are shown
in FIGS. 4A-4F as applied to a golf club. FIG. 4A depicts a cammed
lever variation system having four settings that span the accepted
stiffness range for golf club shafts. As a cam 30 is rotated in the
direction of the arrow, the tension is increased on the wire 16,
resulting in a softening of the shaft. There are four settings for
the illustrated cam 30, corresponding to the four faces of the cam,
each of which is at a different distance from an attachment point
32 of the wire. As shown, the wire tension is at its lowest
setting, corresponding to the stiffest shaft setting. It will be
apparent to those skilled in the art that this type of variation
system is not limited to a four-faced cam, but can be used with a
cam having a different number of faces or with a continuous cam, as
long as the variation system is capable of holding its setting. The
illustrated cam 30 is held in any of the four settings by pressure
on the flat face of the cam; a continuous cam can use a set screw
or the like (not shown) to achieve the same end.
[0032] FIG. 4B depicts a plunger clevis/cotter pin variation system
having four settings that span the accepted stiffness range for
golf club shafts. In this arrangement, a plunger clevis 40 passes
through a plug 42, which is attached to the butt end of the shaft
12. The clevis 40 is provided with several holes 44 perpendicular
to its axis, and is attached to the wire 16 at point 46. A cotter
pin 48 is adapted to slide into any of the holes, thereby varying
the position of the plunger clevis 40 relative to the plug 42. It
will be apparent to those skilled in the art that this type of
variation system is not limited to having four levels, nor are the
illustrated shapes of the clevis and cotter pin intended to be
limiting.
[0033] FIG. 4C depicts a pneumatic or hydraulic variation system,
where a constant force is applied to a piston 50 by a working fluid
52 which applies a constant tension to the wire 16. A pumping
mechanism 54 allows a golfer to vary the tension by pumping working
fluid 52 through a one-way valve (not shown). The tension can be
relieved by opening the valve to allow back flow. This type of
system is continuously variable over a range of tensions.
[0034] FIG. 4D depicts a lead screw variation system comprising a
threaded lead screw 60, a threaded lock fitting 62, and a guide 64
attached to the butt end 12 of the shaft. The threads of the lead
screw 60 engage the lock 62, which can thus be set at any point on
the length of the lead screw 60. The lock is held in compression
fit with the guide 64, allowing the lead screw to apply a tension
to the wire 16. The attachment point 66 is preferably designed not
to twist the wire when the lead screw 60 is turned. This type of
system is continuously variable over a range of tensions. The lead
screw can be turned by hand, or can be activated by an external
actuator such as a battery powered electric screwdriver or the
like. This type of system is continuously variable over a range of
tensions.
[0035] FIG. 4E depicts a threaded sleeve variation system. A plug
70 is affixed to the butt end 12 of the shaft, the plug 70 having
an outer thread. An inner threaded turn sleeve 72 is engaged with
the plug 70. The turn sleeve supports a head 74, and can be adapted
to slip relative to the head at their point of contact 76. The head
is connected to the wire 16 at point 78. It will be seen that
rotation of the turn sleeve 72 will raise or lower the head 74 to
vary the wire tension over a continuous range.
[0036] FIG. 4F depicts an active set and forget displacement
actuator variation system. A head 80 is connected to the wire 16 at
point 82, and a standard set and forget actuator 84 is inserted
between the butt end of the shaft 12 and the head 80. Such
actuators are commonly known in the art, and generally are
activated by connection of a separate power source. Once the
actuator has been set to the desired length (and corresponding wire
tension and shaft stiffness), the power source (not shown) can be
removed for the swing. This variation system can vary the wire
tension over a continuous range.
[0037] A detailed explanation will now be provided with respect to
behavior of the golf club shaft according to the present invention.
The fundamental behavior that this invention leverages is described
by the general, unforced, one dimensional equation of motion for a
beam,
(EIw")"+(Pw')'+m{overscore (w)}=0 (1)
[0038] where EI is the elastic modulus times the shaft cross
section area moment of inertia that can vary along the length of
the golf club shaft, P is the axial compression applied to the
shaft that can also vary along the length of the shaft, m is the
mass per unit length that can vary along the length of the shaft,
and w is the lateral deflection which is a function of time and
position along the length of the shaft. The first term of Equation
(1) relates how the beam bending stiffness is affected by inertial
loads through the second spatial derivative of the shaft internal
moment (the bracketed term that includes second order spatial
derivative of the deflection) with respect to the axial coordinate.
The second term of Equation (1) is generally small and is typically
neglected. The last term in Equation (1) represents inertial load
(per unit length) resulting from motion, where force equals mass
times the second derivative of the deflection with respect to
time.
[0039] When a beam is under compression, the compressive load
reduces the apparent bending stiffness of the beam by amplifying
the lateral deflection. This effect can be visualized by
considering a ruler being compressed along its measurement axis by
pressing opposing ends together. When the center of the ruler is
slightly perturbed laterally, the deflection is enhanced by the
compression and the ruler bends.
[0040] This behavior can be seen mathematically, to first order, by
assuming a deflection as a function of time, t, and position on the
shaft, x, 1 w = A sin ( t ) sin ( x L ) ( 2 )
[0041] where .omega. is the natural frequency of motion, L is the
shaft length and A is an arbitrary constant. This simplifying
assumption is a good one since Fourier theory states that any
bounded analytic function can be approximated by a series of sines
and cosines. Placing this deflection shape into the equation of
motion and assuming that the bending stiffness, EI, and mass per
unit length, m, can be represented by constant averaged values over
the length of the shaft, EI and m, and that P is uniform, yields 2
[ 4 L 4 E I _ - P 2 L 2 - m _ 2 ] A sin ( t ) sin ( x L ) = 0 ( 3
)
[0042] which, when solved for the natural frequency by setting the
square bracketed term equal to zero, gives 3 = 4 E I _ ( 1 - P L 2
2 E I _ ) m L 4 ( 4 )
[0043] To first order, Equation (4) shows how the apparent
stiffness, the numerator of the quotient under the square root
sign, decreases with increased static compression. For reference,
the general buckling load for a uniform beam under uniform
compression is 4 P buckling = 2 E I _ L 2 ( 5 )
[0044] so that a compressive load equal to 20% of the buckling load
results in a 20% decrease in stiffness and a corresponding 10%
decrease in natural frequency.
[0045] It is important to note that the shaft load P changes during
the downswing, that is, the centrifugal force generated by the
accelerating club head counters the precompression and results in
general shaft stiffening. Without precompression, the centrifugal
load would merely serve to stiffen the dynamic behavior of the
shaft, since the shaft load P would by definition be negative.
[0046] For beams of general cross sections, moduli, mass per unit
length, and preloading that vary with the axial coordinate,
expressions analogous to Equations (2)-(5) do not exist in closed
form, and full analysis is necessary for accurate predictions.
However, the behavior for more complicated geometries and loading
is generally similar to the simple case illustrated above.
[0047] This invention may be applied to metal, wood, and composite
shafts as long as the shafts are hollow or hollowed to allow the
insertion of the invention. The tensioning member may be affixed to
any point along the shaft's length. This allows tailoring of the
variable stiffness length of the shaft. For full length golf club
shaft embodiments a tensioning wire/cable assembly may be
integrated into the butt and hosel ends of the shaft. The
tensioning device may comprise a single wire or cable, or multiple
(twisted or untwisted) wires.
[0048] The wire can be restrained from dynamic vibration within the
shaft by filling the enclosed volume, either entirely or partially,
with low density foam or a similar material. The wire can also be
restrained from dynamic vibration by placing form fitting inserts
down the length of the wire and affixing them to the shaft, by glue
or compression resulting from expansion, thus allowing the wire to
run freely through the insert while restraining its lateral
motion.
[0049] Although the invention has been described in detail
including the preferred embodiments thereof, such description is
for illustrative purposes only, and it is to be understood that
changes and variations including improvements may be made by those
skilled in the art without departing from the spirit or scope of
the following claims.
* * * * *