U.S. patent application number 10/156470 was filed with the patent office on 2003-12-04 for shaft stiffened by axial pre-stress.
Invention is credited to Soong, Tsai C..
Application Number | 20030224869 10/156470 |
Document ID | / |
Family ID | 29582271 |
Filed Date | 2003-12-04 |
United States Patent
Application |
20030224869 |
Kind Code |
A1 |
Soong, Tsai C. |
December 4, 2003 |
Shaft stiffened by axial pre-stress
Abstract
A long shaft comprising a number of axially pre-stressed
members, one inside the other, the sum of the bending rigidities of
the axially tensioned members is greater than the sum of the
bending rigidities of the compression members, is enhanced in
bending stiffness such that the end deflection of the shaft under a
simultaneous transverse load and the axial force has an end
deflection less than the end deflection of the same shaft, which
has no pre-stress. The long shaft may be a golf club shaft. An
example shows a flex "s" golf shaft, which ordinarily has an end
deflection of 3.5 inch, measured from the deflection board, is
stiffened into a super stiff shaft with end deflection of 1.54
inch, without having a weight increase or a change of material.
Inventors: |
Soong, Tsai C.; (Penfield,
NY) |
Correspondence
Address: |
TSAI C. SOONG
1839 Jackson Rd
Penfield
NY
14526
US
|
Family ID: |
29582271 |
Appl. No.: |
10/156470 |
Filed: |
May 28, 2002 |
Current U.S.
Class: |
473/318 |
Current CPC
Class: |
A63B 53/10 20130101;
A63B 60/0081 20200801; A63B 60/10 20151001; A63B 60/06 20151001;
A63B 60/08 20151001; A63B 60/00 20151001; A63B 2209/02 20130101;
A63B 60/16 20151001 |
Class at
Publication: |
473/318 |
International
Class: |
A63B 053/10; A63B
053/12 |
Claims
What is claimed is:
1. A shaft, comprising two or more long, concentric, cylindrical
members, being joined together at their common end regions, said
sleeves are permanently pre-stressed along its axis, in compression
or in tension, constitutes a self equilibrating internal force
system.
2. The shaft as defined in claim 1 wherein each of said concentric
members has its own bending rigidity, and the sum of the bending
rigidities of all tension members is greater than the sum of the
compression members' bending rigidities.
3. The shaft as defined in claim 2 wherein the outmost member is in
tension.
4. The shaft as defined in claim 2 wherein when the shaft is held
as a cantilever beam having its free end under a transverse load,
the end deflection will be less as compared to the same shaft under
the same load but its internal pre-stress is removed; and said end
deflection would be further reduced when the pre-stress in the
members is further increased.
5. The shaft as defined in claim 2 wherein the shaft has three
concentric members and at least the outer member is in tension.
6. The shaft as defined in claim 2 wherein there is a spring device
installed at the grip end to create the required axial force to the
compression members.
7. The shaft as defined in claim 1 wherein the pre-stress is
adjustable after it was first installed in the factory.
8. The shaft as defined in claim 1 is a golf club shaft.
9. The shaft as defined in claim 1 is a part of a fishing rod.
10. The shaft as defined in claim 1 wherein a said cylindrical
member for compression may be a slender shaft with spacers, which
remains concentric but is not necessarily having surface to surface
contact with the outer member.
11. The shaft as defined in claim 2 wherein at least one of the
compression members has a physical arrangement made during
manufacturing process such that its bending rigidity is
significantly reduced because of the arrangement so that the ratio
of the bending rigidity of the tension members to that of the
compression members can be increased.
12. The shaft as defined in claim 11 wherein said physical
arrangement is shallow cuttings on the member's surface along a
major part of the length of the member.
13. The shaft as defined in claim 6 wherein the force at the spring
device is adjustable.
Description
BACKGROUND OF THE INVENTION
[0001] The invention concerns a new shaft, in which the bending
stiffness of the shaft is enhanced by properly arranged pre-stress
in the shaft. Shafts like golf clubs, fishing rod, arms used in
precision equipment, etc. may find use of the invention.
[0002] In theory of mechanics, it was known that when a cantilever
beam is in bending due to a transverse load, its end deflection
would be reduced if the beam has simultaneous axial tension force.
It is because under the simultaneous load, the neutral axis of the
beam will be shifted upward and the axial tension force will
produce a counter moment to offset the external bending moment, and
consequently the deflection of the end of the beam will be reduced.
Axial compression force will have the opposite effect.
[0003] A difficulty of application is the involved complicated
mechanics, which is not popularly understood; and the net gain in
performance regarding the new technology is not quantitatively
clear.
[0004] The invention suggests a self-equilibrating internal force
system, establishes rules governing the stiffness change, and a
procedure to estimate the enhanced stiffness.
BRIEF DESCRIPTIONS OF THE DRAWING
[0005] FIG. 1 shows the cover page of a reference book titled
Roark's Formulas for Stress & Strain, by Warren C. Young, sixth
Edition, McGraw-Hill, Inc.
[0006] FIG. 2 shows p. 157, Table 9a, Reaction and deflection
coefficients for beams under simultaneous loading, taken from the
FIG. 1 reference book.
[0007] FIG. 3 curve A shows the force and rigidity coefficient
plotted against the deflection ratio coefficient based on FIG. 2
tension data. Curve B is a plot related to the data applicable only
to the sample shaft of FIG. 4.
[0008] FIG. 4 shows a sample shaft constructed according to the
findings of the invention.
A PREFERRED EMBODIMENT
[0009] We conclude that the new enhanced shaft should follow these
rules:
[0010] (1), the internal axial force system is
self-equilibrating.
[0011] (2), the shaft comprises concentric, longitudinal shaft
members joined at the ends, which are either in compression or in
tension, wherein each member bends according to its own bending
rigidity, as affected by the internal stress and constraints.
[0012] (3), the sum of the bending rigidities of its tension
members should be greater than that of the compression members.
[0013] A fourth rule concerning estimation of the stiffness
increment will be described later.
[0014] FIG. 2 table shows quantitatively that the tension beam
becomes stiffer in bending and the compression beam becomes weaker
in stiffness and deflects more.
[0015] In FIG. 3, the curve A is plotted from the tension table in
FIG. 2. In the vertical coordinate of curve A, EI is the beam
bending rigidity, wherein E is its Young's modulus, I the bending
moment of inertia of the cross-section of the tensioned portion, P
is the axial tension force in kg, and L the beam's length in cm.
The horizontal axis is the deflection ratio d*/d, where d* is the
reduced end deflection under the axial tension P, and d is the
conventional beam deflection of the tensioned part, without the
axial force. Curve B is specific for the sample shaft in FIG. 4,
which shall be explained later.
[0016] To illustrate the invention, a golf club shaft is shown in
FIG. 4:
[0017] The shaft 1 has a length L, having a grip end 2 and a small
end 3, which is joined to the golf club head. The shaft consists of
an outer member 4 and an inner member 5; one inside the other and
each bends accordingly. They are joined at the common end 6. A
screw device 7 joins 4 to 5 at the grip end. The axial force P,
created by turning the screw, compresses the inner member, which in
turn drags the outer member into tension, because the end of 4
restraints the axial movement of 5. Other forcing arrangement is
possible. The bending rigidity EI of the tension member is greater
than that of the compression member. The spring device 8 is
optional. Through the spring, the axial force may be maintained
constant at all times.
[0018] To increase the ratio of bending rigidities, one may also
choose to reduce the bending rigidity of the compression member. An
example is to cut light, parallel transverse surface lines on the
surface of a compression member, which does not affect its
compressive strength but reduces its bending rigidity.
[0019] Other embodiments are possible. For example, there may be
three or more co-axial members, or there may be honeycomb-like
inner member, or a slender member with discrete spacers for bracing
purpose. The outer member is preferred to be in tension.
NUMERICAL EXAMPLE OF A PRE-STRESSED SHAFT
[0020] A conventional graphite golf shaft is used as an example.
All relevant calculations are presented in detail so that we can
follow the progressing steps closely.
[0021] The shaft length L is 100 cm, weighs 58 g, outer diameter
1.23 cm, inner diameter 0.96 cm, wall thickness 0.135 cm, which has
9 plies of prepreg fiber-reinforced resin tapes. Specific weight of
the material is 1.25 g per c.c, and the Young's modulus E of the
tape is 1,339,000 kg/sq.cm. The constant diameter shaft may
represent a corresponding, conventional tapered golf club shaft of
the same weight and length.
[0022] The 9-ply wall is divided into a 6-ply outer member and a
3-ply inner member. They fit snugly, each can bend independently.
Having the same end deflection makes compatibility easier between
various members' slightly different curvatures.
[0023] In this shaft, the total bending rigidity EI of the shaft is
94,700 kg-sq.cm, the EI of the tension member is 70,600, and that
of the inner member is a much smaller 24,100.
[0024] In general, beam deflection is proportional to its load, but
is inversely proportional to its bending rigidity EI. Since the
outer and the inner shaft share the same bending load W, and both
deflect the same at the end, the outer shaft should take
70,600/94,700=75% of the load W and the inner shaft 25%, in the
absence of axial force. Now, having the axial force P, the tension
shaft should have less deflection and the compression shaft more.
Therefore, the percentages of W on the two component shafts should
be adjusted so that their ends can deflect equally. The adjustment
depends on P. That's where the mechanics of the combined load on a
beam comes into the picture.
[0025] The tension member of the FIG. 4 shaft has EI/L-square=7.06
kg. Using curve A, we can construct a new P-versus d*/d curve,
which is shown as curve B in FIG. 3, which is specific only to this
tension member of this sample shaft. The dependency of the reduced
deflection d* upon the axial force P is very clear.
[0026] Given a P value, say 30 kg, curve B yields d*/d=0.33. This
means having the tension force P, the deflection d* of the outer
member is reduced to 33% of d.
[0027] In Ref. 2, the corresponding table for the compression shaft
is limited to have the force & rigidity coef. up to 1.0 only.
So we have to take d*=1.67d as the effect of axial compression for
all ranges of P.
[0028] So, with the deflection d* reduced to 0.33d for the tension
shaft, and the compression shaft's deflection d* increased to
1.67d, the share of the W load should be changed, more to the
tension member, so that their end deflections can remain the same
as before.
[0029] Simple calculation leads to the answer: the tension shaft
should take 94% of the W load and the weakened compression shaft
takes only 6% of the W load.
[0030] Studies show that such overwhelming one-sided load
distribution is generally true.
[0031] Therefore, we now have the fourth rule for the design as
follows:
[0032] (4), the shaft's bending rigidity comprises of its tensioned
member only, and its deflection is the deflection of the tensioned
member under the combined load W and P.
[0033] To get the deflection, the EI of the tensioned part is
70,600 and P is 30 kg, curve A yields d*/d=0.33. Convert d of the
tension shaft to d of the original shaft, both without the axial
force P, we should increase d by a factor of 94700/70600=1.34.
Therefore, the final estimated deflection according to rule (4) is
d==0.33.times.1.34=0.44.
[0034] In this example, assume the shaft is a golf club shaft of
stiffness "s". The stiff golf shaft of length 100 cm, having "s",
will have an end deflection about 3.5-inch measured on a standard
Deflection Measurement Board. Multiplied by a reduction factor of
0.44, the new deflection becomes 1.54 inch. This is a very stiff
number. The enhanced shaft now becomes so stiff that it is way
beyond the range of the calibration chart of a conventional
Measuring Board.
[0035] Of course, stiffening is not the only merit of the
invention. We also can make a much lighter shaft, keeping the same
stiffness. That is what most players are looking for, and that
probably has the most appeal. We also can have shaft whose
stiffness can be changed by the turn of a screw at the grip end.
This on spot adjustment is allowed by USGA. Its rules said that
adjustment is allowed if the adjustment is done in a simple way,
having the handle end sealed easily, and the process completed
before the tournament.
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