Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
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A ~ETH~D FOR PROVIDING A CY~INDRICAL MEM~ER WITH
INCREASED RESISTANCE TO TORSIONAL ST~ESSES AND A
CYLINDRICAL MEMBER CONSTRUCTED IN ACCORDANCE
WITH SAID METHOD
BACKGROUND OF THE INVENTION
Field of the Invention
The present invention relates to a method for
reinforcing a cylindrical memher such as a transmission
shaft which is intended to be subjected to a torque.
The invention is also directed to a cylindrical
member which is endowed with increased torsional strength
and which can be constructed in accordance with the
method aforesaid.
Description of the Prior Art
A typieal transmission shaft is constituted by
a solid or hollow cylindrical member such as a metal
tube (usually of steel) whieh is subjeeted to torque
under serviee conditions. The torque in turn produces
shearing stresses in the eylindrieal member.
Depending on the eharaeteristies of the
material constituting the eylindrical member and on the
value of torque, the member is subjected to a rotational
displacement through a torsional angle of greater or
lesser value.
In order to endow the transmission shaft with
resistance to shearing stresses while assuming a limited
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torsional angle under the action of the maximum torque
to be exerted on the cylindrical member, the thickness
and diameter of said member must be of sufficient value.
In consequence, when said cylindrical member is coupled
to a motor having high maximum torque, the member is
relatively heavy and cumbersome.
Moreover, as the weight of a transmission
shaft is greater, so it becomes more essential to devote
greater care and accuracy to dynamic balancing of the
shaft in order to guard against vibrations. It may
prove necessary in addition to provide intermediate
bearings for this purpose.
For these reasons, it is a desirable objective
to minimize the weight of transmission shafts without,
however, reducing their torsional strength and torque-
transmitting capacity.
The precise aim of the present invention is to
accomplish this objective by providing a method for re-
inforcing a cylindrical member such as a transmission
shaft which is intended to be subjected to a torque
while limiting its diameter and/or its weight as well as
the torsional angle.
SUMMARY OF THE INVENTION
In accordance with the method of the present
invention, a composite small-section strip is wound
helically around the cylindrical member aforesaid under
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a pre~etermined tension so as to form in a predetermined
direction a first helical winding which completely sur-
rounds the cylindrical member. A second winding is then
formed in the opposite direction so as to pass symmetric~
ally across the first winding, whereupon the direction of
winding is again reversed in order to obtain a third
winding having the same direction which is parallel to
the first winding, and so on in sequence. The operation
is continued until the entire surface of the cylindrical
member is covered by a whole number of windings in one
direction, said whole number being equal to the number of
windings in the opposite direction. The tension exerted
on the strip is such that a winding formed in one
direction exerts on the cylindrical member a low torque
which is equal and of opposite direction to the torque
exerted by the winding formed in the other direction.
The sum of these torques is at least equal to the maximum
torque to be exerted on the cylindrical member in order
to ensure that the windings acting in opposition to the
torque are never in compression and that the permissible
stress in the strip is not exceeded.
The torque exerted by the strip windings formed
in one direction consequently balances the torque exerted
by the strip windings formed in the opposite direction,
with the result that the cylindrical supporting member
is subjected to zero torsion.
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When a torque is applied to the cylindrical
member, tensile stresses induced by the torque in the
windings formed in the same direction as said torque
prevent twisting of the cylindrical member whereas, in
the windings formed in the opposite direction, this
torque produces a reduction in tension, the difference
between the two being equal to the applied torque.
The effect thereby achieved is to limit the
torsional angle of said cylindrical member. It is thus
possible to reduce the diameter of said cylindrical
member or its thickness in the case of a tubular member
in order to make it lighter in weight.
In an advantageous embodiment of the invention,
the angle at which the strip is wound on the cylindrical
member is reversed each time there is a change from
winding in one direction to winding in an opposite
direction in order to ensure that the turns in one
direction of winding pass across the turns in the other
direction symmetrically with respect to a generator-
line of the cylindrical msmber.
Moreover, by reason of the tension appliedto the strip during the winding operation, each turn of
strip exerts on the cylindrical member a circumferential
stress and a longitudinal stress which increases with
each successive turn. On the other hand, the torsional
stress induced by winding is constant and becomes zero
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when the winding operation stops by reason of the
equilibrium between the opposite windings which are in
equal number. The resultant of these stresses gives rise
to a circu~lferential compression and to an axial com-
pression which do not produce any torsional stress inthe cylindrical member. These compressions are not
modified at the time of application of a torque of lower
value than the maximum design torque since an increase
in tension in one direction is compensated by a reduction
by the same value in the other direction.
Preferably, the angle at which the strip is
wound around the cylindrical member is equal to plus or
minus 45 with respect to the axis of the tube.
This angle is of optimum value when the
cylindrical member is intended to withstand torsional
stresses alone. However, said angle may be smaller or
larger than 45 in cases where the tube is also intended
to withstand bending stresses or an internal pressure in
addition to the torsional stresses.
According to another aspect of the invention,
the cylindrical member such as a tran~mission shaft which
is intended to be subjected to a torque as constructed
in accordance with the method of the invention is re-
inforced by windings of a strip consisting of continuous
fibers embedded in a resin and e~tending in the direction
of the strip.
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By way of example, the strip under consider~
ation is fabricated in accordance with the method
described in French patent N 2,51~,441.
A strip of this type is remarkable both for
its great flexibility, its low specific gravity, its
high breaking strength and its high modulus of elasticity,
with the result that the strip is particularly well-
suited for the present application.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 iS a fragmentary plan view which shows
a cylindrical member constituting a transmission shaft
and illustrates the practical application of the method
in accordance with the invention.
FIG. 2 is a developed view of the cylindrical
member in the plane of the figure and showing on the left
the stress equilihrium with zero torque and on the right
the state of stresses under the action of a torque.
DETAILED DESCRIPTION OF TIIE INVENTION
FIG. 1 illustrates the method in accordance
with the invention for reinforcing a cylindrical member
1 which may be a tubular member of metal and is intended
to be subjected to a torque. By way of example, this
cylindrical member 1 can be a transmission shaft for an
automotive vehicle.
In accordance with this method, a strip 2 i5
wound completPly around said cylindrical memher 1 under
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a predetermined tension and in a predetermined
direction F1 so as to form a first helical winding 2a.
A second windin~ 2b is then formed in the opposite
direction F2 so as to pass across the first winding.
The direction of winding is then reversed in order to
obtain a winding 2c which is in juxtaposed relation
with the first winding 2a or separated from this latter
by a spatial interval equal to a whole number of strips.
The direction of windiny is again reversed in order to
obtain a winding 2d which is in juxtaposed relation with
the second winding 2b or separated from this latter by
a spatial interval equal to a whole number of strips.
The operation is thus continued until the entire surface
of the cylindrical member is covered by a number of
lS windings in a direction F1 equal to the number of
windings in the opposite direction F2.
In order to carry out the aforementioned
winding operations, the cylindrical member 1 is rotated
about its axis X-X' and the strip 2 is displaced lateral-
ly by making use of means known per se in a directionparallel to the axis of the cylindrical member 1 (as
shown by the arrow F in FIG. 1).
The tension exerted on the strip 2 is such
that the windings 2a, 2c formed in the direction of the
arrows Fl exert on the cylindrical member 1 a torque
which is equal and of opposite direction to the torque
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exerted by the windings 2b, 2d which are formed in the
other direction F2 and which is calculated so that the
sum of said torques is at least equal to the maximum
design torque to be exerted on the cylindrical member 1.
In order to satisfy this condition, the number
of windings which have a given direction such as F1 must
clearly be equal to the number of windings which have a
reverse direction such as F2.
As will be readily apparent, it is necessary
to ensure that the cylindrical member l affords
resistance to the circumferential and longitudinal com-
pressive stresses induced by the windings under tension
of the strip 2 without exceeding its permissible stress.
Similarly, the tension exerted on the strip 2
must be lower than its maximum permissible stress with
a view to ensuring that said strip 2 is capable of
accepting the additional tensile stress produced at the
time of application of the maximum torque on the cylin-
drical member 1 without exceeding the value of permissible
stress.
It is apparent from FIG. l that the angle a at
which the strip is wound on the cylindrical member 1 is
reversed each time a winding 2a, 2c in the direction F
changes over to a winding 2b, 2d in the opposite
direction F2, thereby ensuring that the windings of
the strips in one direction pass across the windings
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in the opposite dir~ction and symmetrically with respect
to a generator-line of the c~lindrical member.
In the example illustrated in FIGS. 1 and 2,
the angle a at which the strip 2 is wound on the cylin-
drical member 1 is equal to plus or minus 45, thisangle being considered as an optimum value within the
scope of the application considered ln the present
invention.
The nature of the strips, the number of layers
of windings and their total thickness are defined as a
function of the torque to be applied to the cylindrical
member 1. These values may be readily calculated from
the known mechanical characteristics of the strip and
in particular its elastic limit as well as those of the
cylindrical member.
It is understood that the strip windings are
attached at least to the ends of the cylindrical member
1. This attachment can be carried out by mechanical
clamping, welding or bonding according to the nature of
the material which forms the strip 2.
Said strip 2 is preferably made from continu-
ous fibers. Non-limitative examples include glass,
carbon, aramide fibers embedded in a thermoplastic resin
such as a polyamide resin. Said strip 2 is preferably
obtained in accordance with the method described in
~rench patent N 2,516,441 cited earlier.
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The attachment of a fiber-resin composite strip
to the ends of the cylindrical member 1 or to the entire
surface of this latter can readily be performed by
thermoplastic welding, that is to say by heating the
composite strip during winding on the cylindrical member
l to a sufficient temperature to obtain surface melting
of the strip surface which is intended to be applied on
the cylindrical member l, this member having previously
been coated in the hot state with the same thermoplastic
resin. This technology is described in French patent
N 2,491,044.
Referring now to FIG. 2, the technical effects
and advantages of the method in accordance with the
invention and of the reinforced cylindrical member
obtained by this method will now be explained.
The developed view in the plane of this
figure illustrates a steel tube 1 having a diameter
equal to D and a circumference equal to ~D.
The successive windings of the strip 2 have
been carried out with an angle a equal to plus 45, for
example in the case of the odd-numbered layers 2' (shown
in dashed lines in FIG. 2),and equal to minus 45 in the
case of the even-numbered layers 2 (shown in full lines
in the figure).
It will be assumed that the strips 2 and 2'
have been wound on the cylindrical tube 1 under a
~.Z~76~L~8
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tension such that the resultant stress T in the strip
is equal to 2/3 of the maximum permissible stress S in
said strip : T = 2S/3.
The thickness of the windings is calculated
so as to afford resistance to the torque Mt with a
stress equal to S. When the torque Mt is applied to the
tube 1, an additional stress equal to Tj2 is developed
in the strips 2 and a stress reduction equal to T/2 is
produced in the strips 2'. The difference in stress
between the windings 2 and 2' is therefore equal to
3T/2 - T/2 = T corresponding to a torque having a value
Mt which acts in opposition to the applied torque and
balances this latter.
The stress in the winding 2 is accordingly
equal to 3/2 x 2S/3 = S, which is the permissible stress
in the strip.
In FIG. 2, it is observed that the longitudinal
and circumferential components of T in each winding,
namely sl/2 and sc/2,give rise in both situations to a
longitudinal compression equal to sl and to a radial
compression equal to sc.
These stresses in the cylindrical member
permit dimensioning of this latter in accordance with
conventional rules established in strength of materials
analysis. Furthermore, the fact of obtaining torsional
prestress by means of a succession of multiple small-
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section windings which balance each other in pairs
permits the use of a cylindrical member having low
torsional resistance and therefore of lightweight con-
struction.
If the windings had been formed under zero
tension, the stress produced in one of the windings
under the action of a torque Mt would have been equal to
T, thus producing a torsional angle having double the
value obtained in the case of windings formed under
tension in accordance with the invention and the wind-
ings of opposite direction would have been in compression,
thus entailing the risk of flexural deformation or
buckling of the fibers.
In consequence, by utilizing the method in
accordance with the invention, it is possible to reduce
the torsional angle of the tube 1 by one-half the angle
which would have been required for windings performed
under zero tension.
The cylindrical member which is thus reinforced
in accordance with the invention therefore exhibits a
behavior which is totally different from that of a
conventional shaft of metal or of composite materials
since the applied torque is absorbed by a differential
tractive force in the composite windings and longi-
tudinal and circumferential compressive forces in thecylindrical supporting member with a reduced torsional
stress arising from a torsional angle having a value of
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27895-1
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one-half and a high value of tensile modulus of the
composite winding compared with that of the torsional
modulus of the cylindrical member.
The possibility of reducing the torsional
angle of a transmission shaft offers a very significant
advantage in certain applications such as load-handling
robots.
Furthermore, the invention makes it possible
in respect of a given maximum torque to reduce the dia-
meter and especially the weight of a transmission shàftas shown by the numerical example given below.
For the transmission of a torque having a
value of 400 mN, it is necessary to make use of a steel
tube having a breaking strellgth of 800 MPa, an external
lS diameter of 29 mm and an internal diameter of 23 mm,
namely a thickness of 3 mm and weighing 1923 g per meter
in length.
In accordance with the method of the preaent
invention, the same torque of 400 mN can be transmitted
by a steel tube of identical strength having an external
diameter equal to 27 mm and an internal diameter equal
to 25 mm, namely a thickness of 1 mm covered by a
winding equal in thickness to l.S mm and formed by means
of a strip of Kevla~ fibers embedded in a polyamide
resin, the total weight of tube and winding being
830 q per meter in length.
*Trade Mark
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The fact of being able to reduce the weight
and/or the diameter of the transmission shaft makes it
possible not only to produce a relatively lightweight
vehicle or installation equipped with a transmission
shaft of this type and thus to increase performances
but also to reduce the difficulties presented by the
need to obtain perfect dynamic balance of a transmission
shaft of large diameter which rotates at high speed~
thus often making it possible to suppress one or a number
of intermediate bearings.
