DOUBLE-LAYER MULTI-STRAND CABLE HAVING IMPROVED BENDING ENDURANCE

Abstract

The invention relates to a multi-strand cord (50) comprising an internal layer (CI) of the cord made up of K=1 three-layer (C1, C2, C3) internal strand (TI), with the internal layer (C1) being made up of Q internal metallic threads (F1), the intermediate layer (C2) being made up of M intermediate metallic threads (F2) and the external layer (C3) being made up of N external metallic threads (F3), and an external layer (CE) of the cord made up of L>1 three-layer (C1′, C2′, C3′) external strands (TE) wound around the internal layer (CI) of the cord, with the internal layer (C1′) being made up of Q′ internal metallic threads (F1′), the intermediate layer (C2′) being made up of M′ intermediate metallic threads (F2′) and the external layer (C3′) being made up of N′ external metallic threads (F3′).

The cord (50) has: an endurance criterion SL≤40 000 MPa.Math.mm with

[00001]$SL=\max \left(\frac{\Delta {\sigma }_{\mathrm{bending}\_\mathrm{CI}}}{\mathrm{Cp}};\frac{\Delta {\sigma }_{\mathrm{bending}\_\mathrm{CE}}}{C_r\times \mathrm{Cp}}\right);$  and a size criterion Ec≥0.46 with Ec=Sc/Se.

Claims

1.-15. (canceled)

16. A two-layer multi-strand cord (50) comprising: an internal layer (CI) of the cord made up of K=1 three-layer (C1, C2, C3) internal strand (TI) comprising: an internal layer (C1) made up of Q=1, 2, 3 or 4 internal metallic threads (F1) of diameter d1; an intermediate layer (C2) made up of M intermediate metallic threads (F2) of diameter d2 wound around the internal layer (C1); and an external layer (C3) made up of N external metallic threads (F3) of diameter d3 wound around the intermediate layer (C2); and an external layer (CE) of the cord made up of L>1 three-layer (C1′, C2′, C3′) external strands (TE) wound around the internal layer (CI) of the cord comprising: an internal layer (C1′) made up of Q′=1, 2, 3 or 4 internal metallic threads (F1′) of diameter d1′; an intermediate layer (C2′) made up of M′ intermediate metallic threads (F2′) of diameter d2′ wound around the internal layer (C1′); and an external layer (C3′) made up of N′ external metallic threads (F3′) of diameter d3′ wound around the intermediate layer (C2′), wherein the cord (50) has a bending endurance criterion SL≤40 000 MPa.Math.mm with $\mathrm{SL}=\max \left(\frac{\Delta {\sigma }_{\mathrm{bending}\_\mathrm{CI}}}{\mathrm{Cp}};\frac{\Delta {\sigma }_{\mathrm{bending}\_\mathrm{CE}}}{C_r\times \mathrm{Cp}}\right),$  and a size criterion Ec≥0.46 with Ec=Sc/Se, where: Δσ.sub.bending CI=Msteel×Max(d1; d1′; d2; d2′)/2 in MPa.Math.mm is a maximum bending stress per unit curvature seen by the internal threads (F1; F1′) of the internal and external strands or intermediate threads (F2; F2′) of the internal and external strands, Δσ.sub.bending_CE=Msteel×Max(d3; d3′)/2 in MPa.Math.mm is a maximum bending stress per unit curvature seen by the external metallic threads (F3; F3′) of the internal and external strands, M.sub.steel— 210 000 MPa is the modulus of the steel, d1, d1′, d2, d2′, d3 and d3′ are expressed in mm, $\mathrm{Cp}=\frac{\mathrm{CpIT}+\mathrm{CpTE}}{2},$ Cp is a penetration coefficient for the cord with Cp.sub.IT an inter-strand penetration coefficient and Cp TE a penetration coefficient for the external strands with: Cp.sub.IT=0.4 when the inter-strand distance E of the external strands (TE) of the external layer (CE) E<30 μm; or Cp.sub.IT=1.0 when E>70 μm; or CP.sub.IT=0.015×E−0.05 when 30 μm≤E≤70 μm; and $\mathrm{CpTE}=\frac{\mathrm{CpC}{3}^{\prime }+\min \left(\mathrm{CpC}{2}^{\prime };\mathrm{CpC}{3}^{\prime }\right)}{2},$ where CpC2′ is a penetration coefficient for the intermediate layer (C2′) of the external strand (TE) and CpC3′ is a penetration coefficient for the external layer (C3′) of the external strand (TE) such that: Cp C2′=0.4 when the inter-thread distance I2′ of the intermediate metallic threads (F2′) of the intermediate layer (C2′) I2′<10 μm; or Cp C2′=1.0 when I2′>40 μm; or Cp C2′=0.02×I2′+0.2 when 10 μm≤I2′≤40 μm; and Cp C3′=0.4 when the inter-thread distance I3′ of the external metallic threads (F3′) of the external layer (C3′) I3′<10 μm; or Cp C3′=1.0 when I3′>40 μm; or Cp C3′=0.02×I3′+0.2 when 10 μm≤I3′≤40 μm; Cr is a dimensionless performance coefficient of the cord (50) with $C_r=1-\left(\frac{\sin \left({\propto }_f\right)}{d3\times d{3}^{\prime }}\times \frac{\left({.Math.}_{i=1}^{Q^{\prime }+M^{\prime }+N^{\prime }}{F}_{\mathrm{mi}}\right)\times \sin \left(\alpha t\right)}{N\times \mathrm{Cste}}\right)$  where: d3 and d3′ are expressed in mm, αf is an angle of contact between the external metallic threads (F3) of the internal strand (TI) and the external metallic threads (F3′) of the external strands (TE) expressed in radians, αt is a helix angle of each external strand (TE) expressed in radians; Σ.sub.i=1.sup.Q′+M′'N′F.sub.mi is a sum of forces at break for the Q′+M′+N′ threads of an external strand in Newtons; Cste=1500 N.Math.mm.sup.−2; D is a diameter of the cord in mm; and Sc is a compacted surface area in mm.sup.2 with Sc=[Q×(d1/2).sup.2+M×(d2/2).sup.2+N×(d3/2).sup.2+L×(Q′×(d1′/2).sup.2+M′×(d2′/2).sup.2+N′×(d3′/2).sup.2)]×π and Se is the surface area of the cord (50) in mm.sup.2 Se=π×(D/2).sup.2.

17. The cord (50) according to claim 16, wherein SL≤37 500 MPa.Math.mm.

18. The cord (50) according to claim 16, wherein SL≥25 000 MPa.Math.mm.

19. The cord (50) according to claim 16, wherein Ec≥0.47.

20. The cord (5) according to claim 16, wherein Ec≤0.65.

21. The cord (50) according to claim 16, wherein αf is greater than or equal to 0°.

22. The cord (50) according to claim 16, wherein αf is less than or equal to 25°.

23. The cord (50) according to claim 16, wherein at is greater than or equal to 0°.

24. The cord according to claim 16, wherein at is less than or equal to 20°.

25. The cord (50) according to claim 16, wherein the external layer (CE) of the cord is desaturated so that an inter-strand distance of the external strands, defined, on a section of the cord perpendicular to the main axis of the cord (50), as being the shortest distance separating, on average, circular envelopes in which two adjacent external strands (TE) are inscribed, is greater than or equal to 30 μm.

26. The cord (50) according to claim 16, wherein the external layer (C3′) of each external strand (TE) is desaturated.

27. The cord (50) according to claim 16, wherein the penetration coefficient for the cord Cp is greater than or equal to 0.60.

28. The cord (50) according to claim 16, wherein the cord (50) is extracted from a polymer matrix.

29. A reinforced product (100) comprising a polymer matrix (102) and at least one cord (50) according to claim 16.

30. A tire comprising at least one cord (50) according to claim 16.

Description

[0165] A better understanding of the invention will be obtained on reading the examples which will follow, given solely by way of non-limiting examples and with reference to the drawings, in which:

[0166] FIG. 1 is a view in cross section perpendicular to the circumferential direction of a tyre according to the invention;

[0167] FIG. 2 is a detail view of the region II of FIG. 1;

[0168] FIG. 3 is a view in cross section of a reinforced product according to the invention;

[0169] FIG. 4 is a schematic view in cross section perpendicular to the axis of the cord (which is assumed to be straight and at rest) of a cord (50) according to a first embodiment of the invention;

[0170] FIG. 5 is a schematic view in cross section perpendicular to the axis of the cord (which is assumed to be straight and at rest) of an extracted cord (50′) according to a first embodiment of the invention;

[0171] FIG. 6 is a schematic depiction of the angle αf of the cord (50) of FIG. 4;

[0172] FIG. 7 is a photograph of a cord (50) according to a first embodiment of the invention, and

[0173] FIG. 8 is a schematic view of various geometric parameters of the cord.

EXAMPLE OF A TYRE ACCORDING TO THE INVENTION

[0174] A frame of reference X, Y, Z corresponding to the usual respectively axial (X), radial (Y) and circumferential (Z) orientations of a tyre has been depicted in FIGS. 1 and 2.

[0175] The “median circumferential plane” M of the tyre is the plane that is normal to the axis of rotation of the tyre and that is located equidistantly from the annular reinforcement structures of each bead.

[0176] FIGS. 1 and 2 depict a tyre according to the invention and denoted by the general reference 10.

[0177] The tyre 10 is for a heavy vehicle of construction plant type, for example of “dumper” type. Thus, the tyre 10 has a dimension of the type 53/80 R 63.

[0178] The tyre 10 has a crown 12 reinforced by a crown reinforcement 14, two sidewalls 16 and two beads 18, each of these beads 18 being reinforced with an annular structure, in this instance a bead wire 20. The crown reinforcement 14 is surmounted radially by a tread 22 and connected to the beads 18 by the sidewalls 16. A carcass reinforcement 24 is anchored in the two beads 18 and in this instance wound around the two bead wires 20 and comprises a turnup 26 positioned towards the outside of the tyre 20, which is shown here fitted onto a wheel rim 28. The carcass reinforcement 24 is surmounted radially by the crown reinforcement 14.

[0179] The carcass reinforcement 24 comprises at least one carcass ply 30 reinforced by radial carcass cords 50 according to the invention (not depicted). The carcass cords 50 are positioned substantially parallel to one another and extend from one bead 18 to the other so as to form an angle comprised between 80° and 90° with the median circumferential plane M (plane perpendicular to the axis of rotation of the tyre which is situated midway between the two beads 18 and passes through the middle of the crown reinforcement 14).

[0180] The tyre 10 also comprises a sealing ply 32 made up of an elastomer (commonly known as “internal liner”) which defines the radially internal face 34 of the tyre 10 and which is intended to protect the carcass ply 30 from the diffusion of air coming from the space inside the tyre 10.

[0181] The crown reinforcement 14 comprises, radially from the outside towards the inside of the tyre 10, a protective reinforcement 36 arranged radially on the inside of the tread 22, a working reinforcement 38 arranged radially on the inside of the protective reinforcement 36 and an additional reinforcement 40 arranged radially on the inside of the working reinforcement 38. The protective reinforcement 36 is thus interposed radially between the tread 22 and the working reinforcement 38. The working reinforcement 38 is interposed radially between the protective reinforcement 36 and the additional reinforcement 40.

[0182] The protective reinforcement 36 comprises first and second protective plies 42, 44 comprising protective metal cords, the first ply 42 being arranged radially on the inside of the second ply 44. Optionally, the protective metal cords make an angle at least equal to 10°, preferably in the range from 10° to 35° and more preferably from 15° to 30°, with the circumferential direction Z of the tyre.

[0183] The working reinforcement 38 comprises first and second working plies 46, 48, the first ply 46 being arranged radially on the inside of the second ply 48.

[0184] The additional reinforcement 40, also referred to as a limiting block, the purpose of which is to absorb in part the mechanical stresses of inflation, comprises, for example and as known per se, additional metallic reinforcing elements, for example as described in FR 2 419 181 or FR 2 419 182, making an angle at most equal to 10°, preferably in the range from 5° to 10°, with the circumferential direction Z of the tyre 10.

[0185] Example of a Reinforced Product According to the Invention

[0186] FIG. 3 depicts a reinforced product according to the invention and denoted by the general reference 100. The reinforced product 100 comprises at least one cord 50, in this instance a plurality of cords 50, embedded in the polymer matrix 102.

[0187] FIG. 3 depicts the polymer matrix 102, the cords 50 in a frame of reference X, Y, Z, in which the direction Y is the radial direction and the directions X and Z are the axial and circumferential directions. In FIG. 3, the reinforced product 100 comprises a plurality of cords 50 arranged side-by-side in the main direction X and extending parallel to one another within the reinforced product 100 and collectively embedded in the polymer matrix 102. In this instance, the polymer matrix 102 is an elastomer matrix based on an elastomer composition.

[0188] Cord According to a First Embodiment of the Invention

[0189] FIGS. 4 and 5 respectively depict the cord 50 and the cord 50′ according to a first embodiment of the invention.

[0190] The cords 50 and 50′ have the same geometric structure. The cord 50′ is obtained after extraction from the tyre 10.

[0191] FIG. 7 shows a photograph of the cord 50.

[0192] The cord 50 and the extracted cord 50′ are made of metal and are of the multi-strand type with two cylindrical layers. Thus, it will be understood that there are two layers, not more, not less, of strands of which the cord 50 or 50′ is made.

[0193] The cord 50 or the cord 50′ comprises an internal layer CI of the cord which is made up of K=1 internal strand TI. The external layer CE is made up of L>1 external strands TE wound around the internal layer CI of the cord. In this particular instance, L=6, 7 or 8; for preference L=6 or 7 and more preferably, L=6 and here L=6.

[0194] The cord has a bending endurance criterion

[00006]$\mathrm{SL}=\max \left(\frac{\Delta {\sigma }_{\mathrm{bending}\_\mathrm{CI}}}{\mathrm{Cp}};\frac{\Delta {\sigma }_{\mathrm{bending}\_\mathrm{CE}}}{C_r\times \mathrm{Cp}}\right)$

[0195] Δσ.sub.bending_CI=M.sub.steel×Max(d1; d1′; d2; d2′)/2=210 000×0.26/2=27 300 MPa.Math.mm and Δσ.sub.bending_CE=M.sub.steel×Max(d3; d3′)/2=210 000×0.26/2=27 300 MPa.Math.mm.

[0196] The inter-strand distance E=80 μm>70 μm, thus Cp.sub.IT=1.00

[0197] The inter-thread distance I3′=43 μm, thus Cp C3′=1.00 when 40 μm

[0198] The inter-thread distance I2′=36 μm, thus Cp C2′=0.02×36+0.2=0.92

CpTe=(1+0.92)/2=0.96

Cp=(0.96+1.00)/2=0.98

[00007]$C_r=1-\left(\frac{\sin \left({\propto }_f\right)}{d3\times d{3}^{\prime }}\times \frac{\left({.Math.}_{i=1}^{Q^{\prime }+M^{\prime }+N^{\prime }}{F}_{\mathrm{mi}}\right)\times \sin \left(\alpha t\right)}{N\times \mathrm{Cste}}\right)=1-\left(\frac{\mathrm{Sin}\left(6.6\times \frac{\pi }{180}\right)}{0.26\times 0.26}\times \frac{3387\times \sin \left(8.1\times \frac{\pi }{180}\right)}{14\times 1500}\right)=0.96.$

[00008]$SL=\max \left(\frac{27300}{0.98};\frac{27300}{0.98\times 0.96}\right)=\max \left(28857;29017\right)=29017$

MPa.Math.mm which is well below 40 000 MPa.Math.mm. SL≤37 500 MPa.Math.mm, preferably SL≤35 000 MPa.Math.mm and SL≥25 000 MPa.Math.mm and preferably SL≥27 500 MPa.Math.mm.

[0199] The compacted surface area Sc=[4×(0.26/2).sup.2+9×(0.26/2).sup.2+14×(0.26/2).sup.2+6×(3×(0.26/2).sup.2+9×(0.2372).sup.2+14×(0.23/2).sup.2)]×π=8.10

[0200] The surface area Se=π×(4.6/2).sup.2=16.88.

[0201] Ec=Sc/Se=8.10/16.88=0.48 Ec≥0.47, Ec≥0.48 and Ec≤0.65 and preferably Ec≤0.55.

[0202] The penetration coefficient for the cords 50 and 50′ is equal to 0.98, which is greater than or equal to 0.60 and preferably greater than or equal to 0.70.

[0203] The external layer of the cords 50 and 50′ is desaturated. Thus, the inter-strand distance E of the external strands is strictly greater than 20 μm. Here, E=80 μm.

[0204] αf is greater than or equal to 0° and preferably greater than or equal to 3° and less than or equal to 25° and preferably greater than or equal to 20°. Here αf=6.6°.

[0205] αt is greater than or equal to 0° and preferably greater than or equal to 3° and less than or equal to 20°, preferably less than or equal to 15° and more preferably less than or equal to 10°. Here αt=8.1°.

[0206] Internal Strands TI of the Cords 50 and 50′

[0207] Each internal strand TI is a three-layer strand and comprises an internal layer C1 made up of Q=2, 3 or 4 internal metallic threads F1, an intermediate layer C2 made up of M intermediate metallic threads F2 wound around the internal layer C1 and an external layer C3 made up of N external metallic threads F3 wound around the intermediate layer C2.

[0208] Here, Q=4.

[0209] M=7, 8, 9 or 10 and for preference M=7, 8 or 9. Here M=9.

[0210] N=12, 13, 14 or 15 and for preference N=12, 13 or 14. Here N=14.

[0211] The external layer C3 of each internal strand TI is desaturated. The inter-thread distance of the external layer of the internal strand is greater than or equal to 30 μm, and in this case equal to 46 μm. The sum SI3 of the inter-thread distances I3 of the external layer C3 is greater than the diameter d3 of the external threads F3 of the external layer C3. Here, the sum S13=0.046×14=0.64 mm, which is a value greater than d3=0.26 mm.

[0212] d1, d2 and d3 range, independently of one another, from 0.12 mm to 0.38 mm and preferably from 0.15 mm to 0.35 mm. Here d1=d2=d3=0.26 mm.

[0213] External Strands TE of the Cords 50 and 50′

[0214] Each external strand TE has three layers and comprises an internal layer C1′ made up of Q′=2, 3 or 4 internal metallic threads F1′, an intermediate layer C2′ made up of M′ intermediate metallic threads F2′ wound around the internal layer C1′ and an external layer C3′ made up of N′ external metallic threads F3′ wound around the intermediate layer C2′.

[0215] Here, Q′=3.

[0216] M′=7, 8, 9 or 10 and for preference M′=7, 8 or 9. Here M′=9.

[0217] N′=12, 13, 14 or 15 and for preference N′=12, 13 or 14. Here N′=14.

[0218] The external layer C3′ of each external strand TE is desaturated. Because it is desaturated, the inter-thread distance I3′ of the external layer C3′ which on average separates the N′ external threads is greater than or equal to 10 μm. The inter-thread distance I3′ of the external layer of each external strand is greater than or equal to 30 μm, and in this case equal to 43 μm. The sum SI3′ of the inter-thread distances I3′ of the external layer C3′ is greater than the diameter d3′ of the external threads F3′ of the external layer C3′. Here, the sum SI3′=0.043×14=0.60 mm, which is a value greater than d3′=0.23 mm.

[0219] Each external layer C3′ of the external strand TE is wound in a direction of winding that is the opposite to the direction of winding of the cord and the external layer C3 of the internal strand TI is wound in the same direction of winding as the direction of winding of the cord. And each internal C1′ and intermediate C2′ layer of each external strand TE is wound in the direction of winding that is the opposite to the direction of winding of the cord, and the internal C1 and intermediate C2 layers of the internal strand TI are wound in the direction of winding of the cord. In this case, the direction of winding of the layers C1, C2, C3 and of the cord is Z and that of the layers C1′, C2′ and C3′ is S.

[0220] Method for Manufacturing the Cord According to the Invention

[0221] One example of a method for manufacturing the multi-strand cord 50 will now be described.

[0222] Each aforementioned internal strand is manufactured according to known methods involving the following steps, preferably performed in line and continuously:

[0223] first of all, a first step of assembling, by cabling or by twisting, the Q=4 internal threads F1 of the internal layer C1 at the pitch p1 and in the Z-direction to form the internal layer C1 at a first assembling point;

[0224] followed by a second step of assembling, by cabling or by twisting, the M=9 intermediate threads F2 around the Q internal threads F1 of the internal layer C1 at the pitch p2 and in the Z-direction to form the intermediate layer C2 at a second assembling point;

[0225] followed by a third step of assembling, by cabling or by twisting, the N=14 external threads F3 around the M intermediate threads F2 of the intermediate layer C2 at the pitch p3 and in the Z-direction to form the external layer C3 at a third assembling point;

[0226] preferably a final twist-balancing step.

[0227] Each aforementioned external strand is manufactured according to known methods involving the following steps, preferably performed in line and continuously:

[0228] first of all, a first step of assembling, by cabling or by twisting, the Q′=3 internal threads F1′ of the internal layer C1′ at the pitch p1′ and in the S-direction to form the internal layer C1′ at a first assembling point;

[0229] followed by a second step of assembling, by cabling or by twisting, the M′=9 intermediate threads F2′ around the Q′ internal threads F1′ of the internal layer C1′ at the pitch p2′ and in the S-direction to form the intermediate layer C2′ at a second assembling point;

[0230] followed by a third step of assembling, by cabling or by twisting, the N′=14 external threads F3′ around the M′ intermediate threads F2′ of the intermediate layer C2′ at the pitch p3′ and in the S-direction to form the external layer C3′ at a third assembling point;

[0231] preferably a final twist-balancing step.

[0232] What is meant here by “twist balancing” is, as is well known to those skilled in the art, the cancellation of the residual torque (or the elastic return of the twist) applied to each thread of the strand, in the intermediate layer as in the external layer.

[0233] After this final twist-balancing step, the manufacture of the strand is complete. Each strand is wound onto one or more receiving reels, for storage, prior to the later operation of assembling the elementary strands by cabling in order to obtain the multi-strand cord.

[0234] In order to manufacture the multi-strand cord of the invention, the method, as is well known to those skilled in the art, is to cable or twist together the strands previously obtained, using cabling or twisting machines rated for assembling strands.

[0235] Thus, the L=6 external strands TE are assembled around the internal strand TI at the pitch pe and in the Z-direction to form the cord 50. Possibly, in a last assembly step, the wrapper F is wound, at the pitch pf and in the S-direction, around the assembly previously obtained.

[0236] The cord 50 is then incorporated by calendering into composite fabrics formed from a known composition based on natural rubber and carbon black as reinforcing filler, conventionally used for manufacturing crown reinforcements of radial tyres. This composition essentially contains, in addition to the elastomer and the reinforcing filler (carbon black), an antioxidant, stearic acid, an extender oil, cobalt naphthenate as adhesion promoter, and finally a vulcanization system (sulfur, accelerator and ZnO).

[0237] The composite fabrics reinforced by these cords have an elastomer composition matrix formed from two thin layers of elastomer composition which are superposed on either side of the cords and which have a thickness ranging between 1 and 4 mm, respectively. The calendering pitch (spacing at which the cords are laid in the elastomer composition fabric) ranges from 4 mm to 8 mm.

[0238] These composite fabrics are then used as carcass ply in the carcass reinforcement during the method for manufacturing the tyre, the steps of which are otherwise known to a person skilled in the art.

[0239] Cord According to a Second Embodiment of the Invention

[0240] Unlike in the first embodiment described hereinabove, the cord 60 according to the second embodiment is such that Q=1, M=4 and N=9 and Q′=1, M′=3 and N′=9.

[0241] Table 2 below summarizes the characteristics of the various cords 50, 50′ and 60 according to the invention.

TABLE-US-00002 TABLE 2 Cords 50 50′ 60 TI Q/M/N 4/9/14 4/9/14 1/4/9 d1/d2/d3 (mm) 0.26/0.26/0.26 0.26/0.26/0.26 0.12/0.26/0.26 direction for C1/pitch p1 (mm) Z/6 Z/6 Z/inf direction for C2/pitch p2 (mm) Z/12 Z/12 Z/6 direction for C3/pitch p3 (mm) Z/18 Z/18 Z/12 I2(μm)/SI2(mm)   38/0.34   38/0.34   6/0.02 I3(μm)/SI3(mm)   46/0.64   46/0.64   42/0.38 TE Q′/M′/N′ 3/9/14 3/9/14 1/3/9 d1′/d2′/d3′ (mm) 0.26/0.23/0.23 0.26/0.23/0.23 0.10/0.23/0.23 direction for C1′/pitch p1′ (mm) S/6 S/6 S/inf direction for C2′/pitch p2′ (mm) S/12 S/12 S/6 direction for C3′/pitch p3′ (mm) S/18 S/18 S/12 I2′(μm)/SI2′(mm)   36/0.32   36/0.32   53/0.15 I3′(μm)/SI3′(mm)   43/0.60   43/0.60   36/0.32 Direction of cord/pi/pe Z/inf/60 Z/inf/60 Z/inf/60 K 1 1 1 L 6 6 6 E (μm) 80 80 69 D (mm) 4.6 4.6 3.2 Δσ.sub.bending_CI 27 300 27 300 27 300 Δσ.sub.bending_CE 27 300 27 300 27 300 Cp.sub.IT 1.00 1.00 0.98 Cp C2′ 0.92 0.92 1.00 Cp C3′ 1.00 1.00 0.91 CpTE 0.96 0.96 0.91 Cp 0.98 0.98 0.94 αf (°) 6.6 6.6 4.8 αt (°) 8.1 8.1 6.5 Σ.sub.i=1.sup.Q′+M′+N′ F.sub.mi (N) 3427 3427 1551 Cr 0.96 0.96 0.98 SL (MPa .Math. mm) 29 017 29 017 29 635 Sc (mm.sup.2) 8.01 8.01 3.69 Se (mm.sup.2) 16.88 16.88 8.02 Ec 0.48 0.48 0.46

[0242] Comparative Tests

[0243] Evaluation of the Bending Endurance Criterion and of the Size Criterion

[0244] Various control cords and cords of the prior art were simulated.

[0245] Table 3 summarizes the characteristics of the control cord C1 and of the cord of the prior art EDT (the 189.23 cord).

TABLE-US-00003 TABLE 3 Cords EDT C1 TI Q/M/N 3/9/15 4/10/16 d1/d2/d3 (mm) 0.23/0.23/0.23 0.23/0.23/0.23 direction for C1/pitch p1 Z/6.5 Z/6 (mm) direction for C2/pitch p2 Z/12 Z/12 (mm) direction for C3/pitch p3 Z/16 Z/18 (mm) I2(μm)/SI2(mm) 14/0.13 9/0.09 I3(μm)/SI3(mm) 10/0.15 TE Q′/M′/N′ 3/9/15 4/10/16 d1′/d2′/d3′ (mm) 0.23/0.23/0.23 0.23/0.23/0.23 direction for C1′/pitch p1′ Z/6.5 Z/6 (mm) direction for C2′/pitch p2′ Z/12 Z/12 (mm) direction for C3′/pitch p3′ Z/16 Z/18 (mm) I2′(μm)/SI2′(mm) 14/0.13 9/0.09 I3′(μm)/SI3′(mm) 10/0.15 8/0.13 Direction of cord/pi/pe S/inf/60 S/inf/60 K 1 1 L 6 6 E (μm) 0 0 D (mm) 4.2 4.4 Δσ.sub.bending_CI 23 730 23 940 Δσ.sub.bending_CE 23 730 23 940 Cp.sub.IT 0.40 0.40 Cp C2′ 0.48 0.40 Cp C3′ 0.41 0.40 CpTE 0.41 0.40 Cp 0.41 0.40 αf (º) 34.2 31.9 αt (º) 8.4 1.5 Σ.sub.i=1.sup.Q′+M′+N′ F.sub.mi (N) 3110 3785 Cr 0.78 0.79 SL (MPa .Math. mm) 74 202 75 759 Sc (mm.sup.2) 7.58 8.57 Se (mm.sup.2) 13.78 15.30 Ec 0.55 0.56

[0246] Tables 2 and 3 show that the cords 50, 50′ and 60 have a relatively low bending endurance criterion compared with the cord of the prior art EDT and the control cord C1 while at the same time having a sufficient size criterion. Specifically, the cords EDT and C1 have a relatively high bending endurance criterion that does not make it possible to effectively reduce the stresses in the cord during a bending stress loading. Thus the cords according to the invention have a bending endurance criterion SL≤40 000 MPa.Math.mm low enough to remedy these drawbacks while at the same time maintaining a satisfactory size.

[0247] The invention is not limited to the above-described embodiments.