The present invention relates to a variable diameter
fastener for a railway rail fastening assembly and
particularly, although not exclusively, relates to a
5 variable diameter fastener with a convex portion between
ends of the fastener.
Background
10 Figure 1 shows a railway rail fastening assembly 10 to
which the present invention may be applied. The rail
fastening assembly 10 comprises a base plate 12, which
extends beneath a rail 13 and is configured to receive
railway rail fastening clips 14 either side of the rail.
15 The railway rail fastening assembly 10 further comprise a
pair of fasteners 30, such as studs, bolts or screws. The
fasteners fasten the base plate 12 to an underlying
foundation 16, such as a railway sleeper or slab. A
resilient pad 15 and/or a further plate 18 may be provided
20 between the base plate 12 and the underlying foundation 16.
The clips 14 retained by the base plate 12 bear on a rail
base or foot 17 of the rail 13. The clips 14 secure the
railway rail 13 to the underlying foundation 16 by virtue
of forces exerted by the clip on the base plate 12 and the
25 rail 13.
During use the baseplate 12 is subjected to a combination
of vertical and lateral loads. The vertical load component
is directed down through the base plate 12 and resilient
30 pad 15 into the underlying foundation 16. By contrast, the
lateral loads are transmitted into the underlying
foundation 16 through a combination of: (a) shear forces at
the interface between the lowest layer of the railway rail
5
3
fastening assembly 10 and the upper surface of the
underlying foundation 16; and (b) lateral forces applied
through the fasteners 30 used to fix down the base plate
12.
Where a resilient pad 15 is provided under the baseplate 12
and the fasteners 30 pass through this soft layer, there is
potentially less capacity to transmit shear force. In this
case, the fasteners 30 may need to take a greater
10 proportion of the lateral load than in the case without the
resilient pad. As a result, the fasteners 30 for a railway
rail fastening assembly 10 with a resilient pad may need to
be larger in diameter to withstand the higher lateral
loads. However, such larger fasteners increase the amount
15 of material required, which in turn increases the weight
and cost of the fastening assembly. As the number of
fasteners required over a length of rail can be high, the
additional costs can be significant.
20 Statements of Invention
According to an aspect of the present disclosure there is
provided a variable diameter fastener for a railway rail
fastening assembly, wherein the fastener comprises a shaft,
25 a first end of the shaft being configured for placement in
an underlying foundation, a second end of the shaft being
configured for engagement with the fastening assembly,
wherein the shaft comprises a variable diameter portion
extending longitudinally and disposed between the first and
30 second ends, the variable diameter portion having a
diameter that varies along a longitudinal axis of the shaft
such that at least a portion of an outer surface of the
variable diameter portion is convex in a plane containing
4
the longitudinal axis of the shaft so as to define a convex
portion or section of the shaft.
The diameter of the shaft may thus be reduced (e.g.
5 compared to a constant diameter shaft) and material may be
saved as a result.
A lateral load may be applied to the shaft at a location
between the convex portion and the second end. The shaft
10 may be secured, e.g. by the underlying foundation, at the
start of the convex portion opposite the second end.
The convex portion may vary in diameter such that upon
application of a lateral load to the fastener the maximum
15 stress in a cross-section of the variable diameter fastener
may be substantially or approximately constant along the
length of the convex portion. The convex portion may vary
in diameter such that, upon application of the lateral
load, the stress in the shaft may be greater than a linear
20 reduction in stress from the start of the convex portion to
the location at which the lateral load is applied. For
example, the convex portion may vary in diameter such that,
upon application of the lateral load, the stress in the
shaft may be between a constant value and the linear
25 reduction in stress from the start of the convex portion to
the location at which the lateral load is applied.
The shaft may have a substantially circular cross-section,
30 e.g. throughout the variable-diameter portion.
The diameter of the convex portion may reduce as the axial
position moves closer to the second end.
5
The diameter of the convex portion may vary as a function
of the axial position with an absolute gradient that
becomes steeper as the axial position moves closer to the
5 second end.
The convex portion may begin with a substantially zero
gradient (at point closest to the first end). Preceding
the convex portion (i.e. on a side of the convex portion
10 closer to the first end) may be another portion that is not
convex.
The diameter of the convex portion may vary as a function
of the axial position with an absolute gradient that may be
15 substantially zero at an end of the convex portion that may
be closest to the first end of the shaft. The end of the
convex portion that is closest to the first end of the
shaft may be substantially parallel to a longitudinal axis
of the shaft.
20
The diameter of the convex portion may (e.g. approximately
or substantially) vary as a function of the axial position
with an inverse cubic relationship.
25 The diameter of the convex portion may vary in the axial
direction with a curvature having a substantially constant
radius of curvature.
The shaft may comprise a substantially constant diameter
30 portion, which may be disposed between the convex portion
and the second end of the shaft. The constant diameter
portion may be adjacent, e.g. immediately adjacent, to the
convex portion.
6
The shaft may comprise a further substantially constant
diameter portion, which may be provided between the convex
portion and the first end of the shaft. The further
5 substantially constant diameter portion may be adjacent,
e.g. immediately adjacent, to the convex portion.
The shaft may comprise a concave portion, which may be
disposed between the convex portion and the second end of
10 the shaft. The concave portion may be provided between the
convex portion and the constant diameter portion. The
convex portion may be longer than the concave portion in
the axial direction of the shaft.
15 The second end may comprise a threaded portion for
receiving a nut.
The shaft may comprise a further convex portion disposed
between the convex portion and the first end of the shaft.
20 The diameter of the further convex portion may vary along
the longitudinal axis of the shaft such that an outer
surface of the further convex portion may be convex in the
plane containing the longitudinal axis of the shaft. The
diameter of the further convex portion may reduce as the
25 axial position moves closer to the first end of the shaft.
The further convex portion may be adjacent, e.g.
immediately adjacent, to the convex portion.
Alternatively, the further substantially constant diameter
30 portion may be provided between the convex portion and the
further convex portion.
7
The variable diameter fastener may comprise an anchor
portion provided at the first end of the shaft. The anchor
may be configured to anchor the variable diameter fastener
in the underlying foundation. The variable diameter
5 fastener may be cast into the underlying foundation. The
anchor may be cast into the underlying foundation and may
secure the fastener in place.
The variable diameter fastener may be configured such that
10 the convex portion begins from a top level of the
underlying foundation and the convex portion extends
towards the second end therefrom.
The variable diameter fastener may comprise a maximum
15 diameter between the first and second ends of the shaft.
20
The maximum diameter may occur between the convex portion
and the further convex portion. The convex portion may
start at the maximum diameter and may extend therefrom
towards the second end of the shaft.
The convex portion may have a length that may be more than
5% of the distance between the first and second ends of the
shaft. The convex portion may have a length that is more
than 10% of the distance between the first and second ends
25 of the shaft.
30
The convex portion may have a length that may be more than
20mm or 30mm. The convex portion may have a length that is
approximately 37mm.
A fastener assembly may comprise the above-mentioned
variable diameter fastener and a cooperating sleeve. The
cooperating sleeve may have an inner concave surface
8
corresponding to the convex portion of the variable
diameter fastener. The sleeve may further comprise an
inner constant diameter portion, e.g. corresponding to the
constant diameter portion of the fastener shaft. The
5 sleeve may comprise an internal threaded portion for
engaging a corresponding thread on the variable diameter
fastener. An outer diameter of the sleeve may be
substantially constant.
10 According to a further aspect of the present disclosure
there is provided a sleeve for a variable diameter fastener
of a railway rail fastening assembly, wherein the sleeve
comprises:
a cylindrical outer surface; and
15 a through bore having an inner surface at least a
portion of which is concave in a plane containing the
longitudinal axis of the sleeve so as to define a concave
portion of the sleeve.
20 The concave portion may be configured to correspond with
and abut a convex portion of the variable diameter
fastener, e.g. such as that mentioned above.
The sleeve through bore may further comprise an inner
25 constant diameter portion. The sleeve through bore may
further comprise an internal threaded portion for engaging
a corresponding thread on the variable diameter fastener.
A fastener assembly may comprise the above-mentioned
30 variable diameter fastener and the above-mentioned sleeve.
A railway rail fastening assembly may comprise the abovementioned
variable diameter fastener or the above-mentioned
5
9
fastener assembly. The railway rail fastening assembly may
further comprise the underlying foundation. For example,
the variable diameter fastener may be cast, screwed or
otherwise secured into the underlying foundation.
The railway rail fastening assembly may further comprise a
baseplate and/or an anchoring device for receiving a rail
clip to bear down on a rail.
10 The underlying foundation may comprise a sleeper or a slab,
e.g. as used in track slab application. The underlying
foundation may be formed from concrete, cement or any other
suitable material.
15 Brief Description of the Drawings
Reference will now be made to the accompanying drawings in
which:
20 Figure 1 is a perspective view showing the railway rail
fastening assembly according to an example of the present
disclosure;
Figure 2 is a sectional perspective view showing the
25 railway rail fastening assembly according to the example of
the present disclosure;
Figure 3 is an enlarged sectional view showing the railway
rail fastening assembly according to the example of the
30 present disclosure;
10
Figure 4 is a sectional view showing the railway rail
fastening assembly according to the example of the present
disclosure; and
5 Figure 5 is a partial side sectional view showing the
profile of the fastener according to examples of the
present disclosure.
10
Detailed Description
With reference to Figures 1, 2, 3 and 4, a railway rail
fastening assembly 10, according to an example of the
present disclosure, comprises an anchoring device, such as
a base plate 12. The base plate 12 may be configured to
15 receive one or more railway rail fastening clips 14, which
bear on a base or foot 17 of a rail 13. The base plate 12
is in turn connected to an underlying foundation 16, such
as a railway sleeper or slab, by virtue of a fastener 30,
such as a stud, bolt or screw, which passes through an
20 opening 11 in the base plate 12. In the example shown, a
pair of fasteners 30 is provided, one on each side of the
rail 13.
The base plate 12 extends beneath a rail 13 and is
25 configured to receive the railway rail fastening clips 14
either side of the rail, although in alternative
arrangements, respective anchoring devices may be provided
on either side of the rail.
30 A resilient rail pad 19 may be provided between the rail 13
and base plate 12. In addition, in the example shown, a
resilient pad 15 and a further plate 18 are provided
between the base plate .12 and the underlying foundation 16,
11
although either or both of these components may be omitted.
The further plate 18 may function as a spacing shim.
Accordingly, as depicted in Figure 4, the thickness of the
further plate and/or number of further plates may be varied
5 to adjust the height of the base plate 12 relative to the
underlying foundation 18. The resilient pad 15 and further
plate 18 may be securely located in the installed
configuration thanks to respective openings in the
resilient pad 15 and further plate 18 through which the
10 fasteners 30 may pass.
The clip 14 may be configured such that it can be deflected
from a non-operative configuration to at least one
operative configuration in which a toe portion 14a of the
15 clip bears indirectly on the rail via an insulator 22. (In
an alternative arrangement, the insulator may be omitted
such that the clip bears directly on the rail.) A heel
portion 14b of the clip may be received in a receiving
portion 21 on the base plate. The clip 14 may be resilient
20 and may be made from a rod of resilient material.
The clip 14 may be of the type that is inserted into
engagement with the base plate 12 and rail 13 in a
substantially longitudinal direction relative to a
25 longitudinal axis of the rail. However, other clip types
are also envisaged, e.g. clips that are inserted in a
direction perpendicular to the longitudinal axis of the
rail. Furthermore, although a particular anchoring device,
which cooperates with a corresponding clip, is shown in
30 Figures 1 to 3, it is envisaged that the present invention
may apply to any other type of anchoring device, clip
and/or anchoring devices without clips.
12
The railway rail fastening assembly 10 may further comprise
one or more electrically insulating wear pieces, such as
the insulator 22 mentioned above. As described above, the
insulator 22 may bear against the rail foot 17 in an
5 installed configuration. The insulator 22 may electrically
insulate the rail from the clip and/or limit wear between
the rail and the clip. The insulator 22 may also be
positioned between the receiving portion 21 and the rail
foot 17 in an installed configuration and the insulator 22
10 may extend along the width of the receiving portion. The
insulator 22 and/or rail pad 19 may electrically insulate
the rail from the base plate 12 and/or limit wear between
15
the rail and the base plate. (The insulators 22 are not
shown in Figure 4 for clarity.)
With reference to Figures 2, 3, 4 and 5, the fastener 30
comprises a shaft 32. A first end 32a of the shaft is
configured for placement in the underlying foundation 16
and a second end 32b of the shaft is configured for
20 engagement with the fastening assembly 10.
In the particular example shown, the fasteners 30 may be
cast into the underlying foundation 16. For example, the
fastener 30 may comprise an anchor portion 33 provided at
25 the first end 32a of the shaft. The anchor portion 33 may
be cast into the underlying foundation 16 and may secure
the fastener 30 in place. The anchor portion 33 may
comprise a wavy profile to increase the resistance to
lateral loads and to increase pull-out resistance. The
30 first end 32a of the shaft may be shaped in other ways to
achieve a similar effect.
13
The second end 32b of the shaft may comprise a threaded
portion 34 for receiving a nut 20. A washer 27 may be
provided next to the nut 20 and the washer 27 may be
integral or separate from the nut 20. A surface of the
5 washer 27 may engage a spring 23, which in turn bears on a
collar 24 provided in the opening 11 on the base plate 12.
The spring 23 may instead bear directly on the base plate
12 and the collar 24 may be omitted.
10 The shaft 32 may have a substantially circular crosssection
between the first and second ends 32a, 32b.
However, the diameter of the cross-section may vary along
at least a lengthwise portion of the shaft so as to define
a variable diameter portion. In particular, the shaft 32
15 comprises a first convex portion 35, over which an outer
surface of the shaft is convex in the longitudinal
direction of the shaft.
The diameter of the first convex portion 35 may reduce as
20 the axial position on the shaft 32 moves closer to the
second end 32b. In particular, the diameter of the first
convex portion 35 may vary as a function of the axial
position with a gradient that becomes steeper as the axial
position moves closer to the second end 32b. As depicted,
25 the gradient may be substantially zero at an end of the
first convex portion 35 that is closest to the first end
32a of the shaft. Accordingly, the end of the first convex
portion 35 that is closest to the first end 32a of the
shaft may be substantially parallel to the longitudinal
30 axis 2 9 of the shaft 32.
The shaft 32 may comprise a maximum diameter between the
first and second ends 32a, 32b of the shaft. The first
14
convex portion 35 may start at the maximum diameter and may
extend therefrom towards the second end 32b of the shaft.
The first convex portion 35 may extend over a significant
5 lengthwise portion of the shaft 32. For example, the first
convex portion 35 may have a length, Lb, which is more than
10%, e.g. approximately 13%, of the length of the fastener.
In particular, the first convex portion 35 may have a
length, Lb, which is approximately 37mm.
10
The shaft 32 may comprise a first substantially constant
diameter portion 36, which may be disposed between the
first convex portion 35 and the second end 32b of the
shaft. The threaded portion 34 may be provided on or at
15 the end of the first constant diameter portion 36.
The shaft 32 may comprise a second substantially constant
diameter portion 37, which may be provided between the
first convex portion 35 and the first end 32a of the shaft.
20 The second substantially constant diameter portion 37 may
be adjacent, e.g. immediately adjacent, to the first convex
portion 35.
As depicted in Figures 2, 3 and 4, the first convex portion
25 35 may begin from a top level 16' of the underlying
foundation 16 and the convex portion extends towards the
second end therefrom. In other words, the end of the first
convex portion 35 that is closest to the first end 32a of
the shaft may coincide with the underlying foundation top
30 level 16'. However, in alternative arrangements, the
fastener 30 may be positioned (e.g. set) in the underlying
foundation at a different vertical position relative to the
top level 16'. For example, the underlying foundation top
15
level 16' may intersect a point in the second constant
diameter portion 37.
The shaft 32 may comprise a second convex portion 38
5 disposed between the first convex portion 35 and the first
end 32a of the shaft. The diameter of the second convex
portion 38 may vary along the longitudinal axis 29 of the
shaft 32 such that an outer surface of the second convex
portion may be convex in the plane containing the
10 longitudinal axis of the shaft. In a manner similar to the
first convex portion 35, the diameter of the second convex
portion 38 may reduce as the axial position moves closer to
the first end 32a of the shaft. In particular, the diameter
of the second convex portion 38 may vary as a function of
15 the axial position with a gradient that becomes steeper as
the axial position moves closer to the first end 32a. As
depicted, the gradient may be substantially zero at an end
of the second convex portion 35 that is closest to the
second end 32b of the shaft, i.e. the end that is adjacent
20 to the first convex portion 35. Accordingly, the end of
the second convex portion 38 that is closest to the first
convex portion 35 may be substantially parallel to the
longitudinal axis 29 of the shaft 32.
25 As depicted, the second substantially constant diameter
portion 37 may be provided between the first convex portion
35 and the second convex portion 38. Alternatively, in the
event that the second constant diameter portion 37 is
omitted, the second convex portion 38 may be immediately
30 adjacent to the first convex portion 35. In either case,
the maximum shaft diameter may occur between the first and
second convex portions 35, 38.
5
16
The shaft 32 may comprise a third substantially constant
diameter portion 39, which may be provided between the
second convex portion 38 and the first end 32a of the
shaft.
The shaft 32 may additionally comprise a first concave
portion 40, which may be disposed between the first convex
portion 35 and the first constant diameter portion 36.
Likewise, the shaft 32 may comprise a second concave
10 portion 41, which may be disposed between the second convex
portion 38 and the third constant diameter portion 39. As
for the convex portions 35, 38, the concave portions 40, 41
may be concave in the shaft longitudinal direction/plane.
15 The concave portions 40, 41 may transition from the
gradient of the convex portions 35, 38 to the neighbouring
constant diameter portions 36, 39. Such a smooth
transition in the gradient of the shaft outer surface may
assist in reducing the concentration of stress in the
20 fastener 30.
Each of the concave portions 40, 41 may be curved with a
radius of curvature (in the longitudinal direction) that is
smaller than a radius of curvature for its neighbouring
25 convex portion 35, 38. Also, each of the convex portions
35, 38 may be longer than its neighbouring concave portion
40, 41 in the axial direction of the shaft 32.
The fastener assembly 10 may further comprise a cooperating
30 sleeve 50. The cooperating sleeve 50 has a through bore 51
having an inner surface 52. At least a portion of the
inner surface 52 is concave in a plane containing the
longitudinal axis of the sleeve so as to define a concave
17
portion 53 of the sleeve. The concave portion 53 is
configured to correspond in shape with and abut the first
convex portion 35 of the fastener 30.
5 The inner surface 52 of the sleeve may further comprise an
inner constant diameter portion 54 corresponding to the
constant diameter portion 36 of the fastener shaft. At
least a portion of the constant diameter portion 54 of the
sleeve may comprise an internal threaded portion 55 for
10 engaging the threaded portion 34 on the fastener.
The sleeve 50 may comprise a substantially cylindrical
outer surface 56. As such, an outer diameter of the sleeve
50 may be substantially constant along the length of the
15 sleeve.
The sleeve 50 and fastener 30 may mate such that the sleeve
50 substantially covers the first convex portion 35 of the
fastener 30. The combination of the fastener 30 and sleeve
20 50 presents a cylindrical outer surface such that the
vertical position of the base plate 12 relative to the
fastener 30 may be varied without affecting the horizontal
spacing between the fastener 30 and the base plate opening
11 (or opening in collar 24).
25
30
Referring now to Figure 5, the diameter, d, of the first
convex portion 35 may vary as a function of the axial
position, x, in particular so as to minimise the amount of
material required for the fastener.
The maximum lateral force applied to the fastener will be
F0 and the assembly may be designed such that this force
can be applied at a maximum height Lo above a top level 16'
5
10
18
of the underlying foundation 16. Therefore the maximum
bending moment, M, that can be applied to the fastener when
in use is:
Mo Fo. Lo,
which occurs where the fastener intersects the
underlying foundation top level 16'. The stress, o0 , in
the fastener at this position of maximum bending moment is:
ao Mo. ro/Io,
where r 0 and 10 are the radius of the fastener and the
second moment of area of the shaft's cross-section (about
15 an axis perpendicular to the longitudinal direction) at the
underlying foundation top level respectively.
A material for the fastener is selected that is strong
enough that its fatigue strength is greater than o0 with a
20 given safety factor, so that it will survive in track when
this level of stress is applied to it in a cyclic fashion.
Effectively, along with F0 and L0 , o0 becomes another fixed
value in the design (and is determined in turn by the
diameter, d 0 , of the fastener at the top level of the
25 underlying foundation, which is a value that may be
selected as appropriate).
If the fastener was cylindrical, the bending moment and
therefore the bending stress would reduce as you progress
30 up the fastener from the underlying foundation top surface
16' towards the height, L0 , above the underlying foundation
at which the lateral load, F0 , is applied. At a given
position, at a height x above the top surface of the
5
19
underlying foundation 16, the stress in a cylindrical shaft
is:
a M. ro/Io
F0 • (Lo-x). ro/Io.
The bending moment and stress would thus reduce in a linear
fashion as you move up the shaft of the fastener.
10 However, this is wasteful of material. The amount of
material required may be reduced by providing a fastener
for which the stress is greater than that determined by the
above expression, e.g. with a stress that stays
substantially the same as you move up the fastener. As a
15 result, the safety factor may remain constant but the
diameter may instead vary. That is, such that:
ao Fo. (Lo - x) .r/I,
20 where r and I are now variables but the stress, c 0 , is
25
constant. In fact r and I are both related to the diameter,
d, of the shaft since,
r=d/2, and
I=nd4 I 64.
As such there is only one variable, d, which represents the
desired cross sectional diameter at a given height, x,
30 above the top level 16' of the underlying foundation.
Substituting in for r and I gives,
co= Fo. (Lo-x) .32/rrd3
•
20
Thus you can relate d to x by rearranging to give:
5
After back substitution and rearrangement this becomes:
d/do
10 where do is the diameter of the fastener at the
underlying foundation top level.
Applying this to the case where x = L0 , would result in the
desired diameter dropping to zero which would be
15 impractical. So we apply another condition that the above
variation in fastener diameter only applies where the
calculated diameter exceeds some predefined limit value d1 •
So you get:
20 if (d0 • { (L 0-x) /L0 }
113 > d1 ) then
d = do. { (L 0-x) /L0 }
113
else
25 where d 1 is the diameter of the fastener after the
convex portion 35, i.e. at the first constant diameter
portion 36.
The first convex portion 35 may thus have a diameter that
30 varies with axial distance that is determined using the
above-described methodology. In other words, the diameter
of the first convex portion 35 may vary as a function of
the axial position with an inverse cubic relationship. The
21
shape of such a variation is shown by the dotted line 35'
in Figure 5. With such a variation in diameter, it follows
from the above equations that the stress caused by the
lateral load may be substantially constant along the length
5 of the first convex portion 35.
However, to provide a smoother transition with the second
constant diameter portion 37, the first convex portion 35
may instead vary in diameter with a shape that closely
10 approximates the inverse cubic relationship described
above. For example, the diameter of the first convex
portion 35 may vary in the axial direction with a curvature
having a substantially constant radius of curvature. The
shape of such a variation is shown by the solid line 35''
15 in Figure 5. For example, the outer surface of the first
convex portion 35 may have an arcuate shape with a radius
of curvature Ra.
a point that is
The radius ot curvature may be centred on
in line with the start of the first convex
portion 35 (e.g. where the first convex portion 35 and
20 second constant diameter portion 37 meet). As such, the
gradient of the first convex portion 35 will be zero at the
intersection with the second constant diameter portion 37,
thereby ensuring a smooth transition. The shape 35'' may
also be easier to manufacture than the shape 35' resulting
25 from the inverse cubic relationship.
As depicted in Figure 5, the first convex portion 35 formed
by line 35'' closely matches the line 35' resulting from
the inverse cubic relationship. The radius of curvature Ra
30 may be selected to provide such a close match. (The radius
of curvature Ra may also be selected so that the diameter
of the fastener exceeds that of line 35' at all points.)
Due to this close match, the stress in the first convex
22
portion formed by line 35'' resulting from the lateral load
may be approximately constant along the length of the first
convex portion 35.
5 In any case, with either variation of the first convex
portion diameter 35' or 35'', the stress in the shaft may
be greater than that resulting from a linear reduction in
stress from the start of the convex portion to the location
at which the lateral load is applied. Or in other words,
10 the stress has been optimised so as to reduce the amount of
material required.
As mentioned above, the first convex portion 35 (regardless
of how it is formed) may transition to the first constant
15 diameter portion 36 by virtue of the intervening first
concave portion 40. As depicted in Figure 5, the first
concave portion 40 may have an arcuate shape with a radius
of curvature Rb. The radius of curvature Rb may be centred
on a point that is in line with the start of the first
20 constant diameter portion 36 (e.g. where the first constant
diameter portion 36 and first concave portion 40 meet). As
such, the gradient of the first concave portion 40 will be
zero at the intersection with the first constant diameter
portion 36, thereby ensuring a smooth transition. The
25 radius of curvature Rb may be selected to ensure a smooth
transition with the first convex portion 35, e.g. with
matching gradients where they meet.
To use the fastener 30 to its maximum effect, the fastener
30 may be positioned (e.g. set) in the underlying foundation
16 at a height that corresponds to that on which the design
is based. For example, the first convex portion 35 may
begin from a top level 16' of the underlying foundation 16.
23
However, in alternative arrangements, the fastener 30 may
be positioned in the underlying foundation at a different
vertical position relative to the top level 16', e.g. with
the underlying foundation top level 16' intersecting a
5 point below the start of the first convex portion 35. The
length, La, of the second constant diameter portion 37 may
be sized to accommodate such variation. For example,
length, La, of the second constant diameter portion 37 may
be approximately 5mm.
10
Furthermore, the height of the fastening assembly 10 may
vary, e.g. due to different thicknesses of the further
plate 18. As a result the height at which the lateral load
is applied may also vary. The above-described design
15 process to determine the shape of the first convex portion
35 is based on a maximum height, L0 , at which the lateral
load may be applied. However, in practice, the lateral
load height may be lower. In this case, the stresses in
the fastener will be lower than when the lateral load is
20 applied at the maximum height and the safety factor will in
effect increase.

We claim:
1. A variable diameter fastener for a railway rail
fastening assembly, wherein the fastener has a first end
5 configured for placement in an underlying foundation and a
second end of configured for engagement with the fastening
assembly,
wherein the fastener comprises a shaft with a variable
diameter portion extending longitudinally and disposed
10 between the first and second ends, the variable diameter
portion having a diameter that varies along a longitudinal
axis of the shaft such that at least a portion of an outer
surface of the variable diameter portion is convex in a
plane containing the longitudinal axis of the shaft so as
15 to define a convex portion of the shaft.
2. The variable diameter fastener of claim 1, wherein the
convex portion varies in diameter such that upon
application of a lateral load to the fastener the maximum
20 stress in a cross-section of the variable diameter fastener
is approximately constant along the length of the convex
portion.
3. The variable diameter fastener of claim 1 or 2, wherein
25 the diameter of the convex portion reduces as the axial
position moves closer to the second end.
4. The variable diameter fastener of any of the preceding
claims, wherein the diameter of the convex portion varies
30 as a function of the axial position with an absolute
gradient that becomes steeper as the axial position moves
closer to the second end.
25
5. The variable diameter fastener of any of the preceding
claims, wherein the diameter of the convex portion varies
as a function of the axial position with an absolute
gradient that is substantially zero at an end of the convex
5 portion that is closest to the first end.
6. The variable diameter fastener of any of the preceding
claims, wherein the diameter of the convex portion
approximately varies as a function of the axial position
10 with a substantially inverse cubic relationship.
7. The variable diameter fastener of any of the preceding
claims, wherein the diameter of the convex portion varies
in the axial direction with a curvature having a
15 substantially constant radius of curvature.
8. The variable diameter fastener of any of the preceding
claims, wherein the shaft comprises a substantially
constant diameter portion disposed between the convex
20 portion and the second end.
9. The variable diameter fastener of any of the preceding
claims, wherein the shaft comprises a further substantially
constant diameter portion provided between the convex
25 portion and the first end.
30
10. The variable diameter fastener of any of the preceding
claims, wherein the shaft comprises a concave portion
disposed between the convex portion and the second end.
11. The variable diameter fastener of claims 8 and 10,
wherein the concave portion is provided between the convex
portion and the constant diameter portion.
5
26
12. The variable diameter fastener of claim 10 or 11,
wherein the convex portion is longer than the concave
portion in the axial direction of the shaft.
13. The variable diameter fastener of any of the preceding
claims, wherein the second end comprises a threaded portion
for receiving a nut.
10 14. The variable diameter fastener of any of the preceding
claims, wherein the shaft comprises a further convex
portion disposed between the convex portion and the first
end.
15 15. The variable diameter fastener of claim 14, wherein the
diameter of the further convex portion reduces as the axial
position moves closer to the first end.
16. The variable diameter fastener of claim 14 or 15 when
20 dependent on claim 9, wherein the further substantially
constant diameter portion is provided between the convex
portion and the further convex portion.
17. The variable diameter fastener of any of the preceding
25 claims, wherein the variable diameter fastener comprises an
anchor portion provided at the first end, the anchor
configured to anchor the variable diameter fastener in the
underlying foundation.
30 18. The variable diameter fastener of any of the preceding
claims, wherein the variable diameter fastener is
configured such that the convex portion begins from a top
27
level of the underlying foundation and extends towards the
second end therefrom.
19. The variable diameter fastener of any of the preceding
5 claims, wherein the variable diameter fastener comprises a
maximum diameter between the first and second ends.
20. The variable diameter fastener of claim 19, when
dependent on claim 14, wherein the maximum diameter occurs
10 between the convex portion and the further convex portion.
15
20
21. The variable diameter fastener of claim 19 or 20,
wherein the convex portion starts at the maximum diameter
and extends therefrom towards the second end.
22. The variable diameter fastener of any of the preceding
claims, wherein the convex portion has a length that is
more than 5% of the distance between the first and second
ends.
23. The variable diameter fastener of any of the preceding
claims, wherein the convex portion has a length that is
more than 20mm.
25 24. A sleeve for a variable diameter fastener of a railway
rail fastening assembly, wherein the sleeve comprises:
a cylindrical outer surface; and
a through bore having an inner surface at least a
portion of which is concave in a plane containing the
30 longitudinal axis of the sleeve so as to define a concave
portion of the sleeve.
28
25. The sleeve of claim 24, wherein the sleeve through bore
further comprises an inner constant diameter portion.
26. The sleeve of claim 24 or 25, wherein the sleeve
5 through bore further comprises an internal threaded portion
for engaging a corresponding thread on the variable
diameter fastener.
27. A fastener assembly comprising the variable diameter
10 fastener of any of claims 1 to 23 and the sleeve of any of
claims 24 to 26.
28. A railway rail fastening assembly comprising the
variable diameter fastener of any of claims 1 to 23 or the
15 fastener assembly of any of claims 24 to 27.
20
25
29. The railway rail fastening assembly of claim 28,
wherein the railway rail fastening assembly further
comprises the underlying foundation.
30. The railway rail fastening assembly of claim 28 or 29,
wherein the railway rail fastening assembly further
comprises a baseplate and/or an anchoring device for
receiving a rail clip to bear down on a rail.
31. The variable diameter fastener, fastener assembly or
railway rail fastening assembly substantially as described
herein with reference to and as shown in the accompanying