Tire with improved belt structure

Abstract

A tire comprises at least first and second working plies (16, 18) respectively comprising first and second reinforcing elements (50, 52) in which at least one of the following relationships is satisfied:
−4053×E1+4720≤(D1.sup.4×d1×1000)/E1  (I)
−4053×E2+4720≤(D2.sup.4×d2×1000)/E2  (II)
where D1, D2 are the diameter of each reinforcing element (50, 52) made up of a metallic monofilament (66, 68), and D1 and/or D2 ranges from 0.34 to 0.38 mm, d1, d2 are the density of the reinforcing elements (50, 52), expressed in monofilaments per decimetre, and E1, E2 are the mean thickness of the working ply (16, 18), expressed in mm.

Claims

1. A tire, defining three main directions circumferential, axial and radial, comprising a crown comprising a tread, two sidewalls, and two beads, each sidewall connecting each bead to the crown, a carcass reinforcement anchored in each of the beads and extending in the sidewalls and in the crown, a crown reinforcement extending in the crown in the circumferential direction and situated radially between the carcass reinforcement and the tread, the crown reinforcement comprising a working reinforcement comprising at least first and second working plies, each first and second working ply respectively comprising first and second reinforcing elements arranged substantially parallel to one another in each first and second working ply, wherein both of the following relationships I and II are satisfied:
−4053×E1+4720≤(D1.sup.4×d1×1000)/E1  (I) where D1 is a diameter of each first reinforcing element made up of a metallic monofilament, expressed in mm, with D1 ranging from 0.34 to 0.38 mm, d1 is a density of the first reinforcing elements in the first working ply, expressed in monofilaments per decimeter and measured in a direction perpendicular to the main axis of the metallic monofilaments, and E1 is a mean thickness of the first working ply, expressed in mm and measured in the radial direction; and
−4053×E2+4720≤(D2.sup.4×d2×1000)/E2  (II) where D2 is a diameter of each second reinforcing element made up of a metallic monofilament, expressed in mm, with D2 ranging from 0.34 to 0.38 mm, d2 is a density of the second reinforcing elements in the second working ply, expressed in monofilaments per decimeter and measured in a direction perpendicular to the main axis of the metallic monofilaments, and E2 is a mean thickness of the second working ply, expressed in mm and measured in the radial direction, wherein each of D1 and D2 are identical, wherein each of E1 and E2 are identical, and less than 0.75 mm, wherein each of d1 and d2 are identical, and range from 70 to 180 monofilaments per decimeter, and wherein the characteristics D1, D2, d1, d2, E1, E2 being measured in a central part of the crown reinforcement of the tire in the vulcanized state, on each side of a midplane over a total axial width of 4 cm.

2. The tire according to claim 1, wherein both of the following relationships are satisfied:
(D1.sup.4×d1×1000)/E1≤−7997×E1+9027
and
(D2.sup.4×d2×1000)/E2<−7997×E2+9027.

3. The tire according to claim 1, wherein both of the following relationships are satisfied:
(D1.sup.4×d1×1000)/E1≤−6800×E1+7850
and
(D2.sup.4×d2×1000)/E2<−6800×E2+7850.

4. The tire according to claim 1, wherein both of the following relationships are satisfied:
(D1.sup.4×d1×1000)/E1<5300 and (D2.sup.4×d2×1000)/E2<5300.

5. The tire according to claim 1, wherein both of the following relationships are satisfied:
−4053×E1+4720<(D1.sup.4×d1×1000)/E1<−4140×E1+5300
and
−4053×E2+4720<(D2.sup.4×d2×1000)/E2<−4140×E1+5300.

6. The tire according to claim 1, wherein both of the following relationships are satisfied:
−4053×E1+4720<(D1.sup.4×d1×1000)/E1<−4430×E1+5120
and
−4053×E2+4720<(D2.sup.4×d2×1000)/E2<−4430×E2+5120.

7. The tire according to claim 1, wherein both of the following relationships are satisfied:
−4430×E1+5120≤(D1.sup.4×d1×1000)/E1<−4140×E1+5300
and
−4430×E2+5120<(D2.sup.4×d2×1000)/E2<−4140×E2+5300.

8. The tire according to claim 1, wherein both of the following relationships are satisfied:
2050<(D1.sup.4×d1×1000)/E1 and 2050<(D2.sup.4×d2×1000)/E2.

9. The tire according to claim 1, wherein both of the following relationships are satisfied:
2500<(D1.sup.4×d1×1000)/E1 and 2500<(D2.sup.4×d2×1000)/E2.

10. The tire according to claim 1, wherein both of the following relationships are satisfied:
2700<(D1.sup.4×d1×1000)/E1 and 2700<(D2.sup.4×d2×1000)/E2.

11. The tire according to claim 1, wherein
(D1.sup.4×d1×1000)/E1<3500 and/or (D2.sup.4×d2×1000)/E2<3500.

12. The tire according to claim 1, wherein each of E1 and E2 is greater than or equal to 0.40 mm.

13. The tire according to claim 1, wherein a mean thickness Ey radially separating a first reinforcing element and a second reinforcing element, measured in the radial direction, ranges from 0.05 to 0.40 mm.

14. The tire according to claim 13, wherein Ey and D1 satisfy the following relationship:
0.15≤Ey/(Ey+D1)≤0.50.

15. The tire according to claim 13, wherein Ey and D2 satisfy the following relationship:
0.15≤Ey/(Ey+D2)≤0.50.

16. The tire according to claim 1, wherein the first reinforcing elements make an angle ranging from 10 to 45 degrees with the circumferential direction.

17. The tire according to claim 1, wherein the second reinforcing elements make an angle ranging from 10 to 45 degrees with the circumferential direction.

18. The tire according to claim 1, wherein the first and second reinforcing elements are crossed relative to one another between the first working ply and the second working ply.

19. The tire according to claim 1, wherein a force at break of the first working ply and/or a force at break of the second working ply ranges from 18000 N.Math.dm.sup.−1 to 32000 N.Math.dm.sup.−1.

20. The tire according to claim 1 further comprising a hoop reinforcement comprising at least one hooping ply comprising textile reinforcing elements arranged substantially parallel to one another in the hooping ply.

21. The tire according to claim 20, wherein the textile reinforcing elements form an angle at most equal to 10° with the circumferential direction.

22. The tire according to claim 1, wherein the tread has a thickness ranging from 3 mm to 6 mm.

23. The tire according to claim 1, wherein the tread has a thickness ranging from 5.5 mm to 7 mm.

24. The tire according to claim 1, wherein the tread has a thickness ranging from 7 mm to 10.5 mm.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention and the advantages thereof will be easily understood in the light of the detailed description and entirely nonlimiting exemplary embodiments which follow, and also of the figures in which:

(2) FIG. 1 illustrates a view in radial section (namely in section on a plane containing the axis of rotation of the tyre) of a tyre according to the invention, and

(3) FIG. 2 is a detail view of the crown reinforcement of the tyre of FIG. 1.

DETAILED DESCRIPTION

Tyre According to a First Embodiment of the Invention

(4) A frame of reference X, Y, Z corresponding to the usual respectively axial (X), radial (Y) and circumferential (Z) directions of a tyre has been depicted in the figures.

(5) FIG. 1 depicts a tyre, in this case a pneumatic tyre, in accordance with a first embodiment of the invention and denoted by the general reference 10. The tyre 10 substantially exhibits revolution about an axis substantially parallel to the axial direction X. The tyre 10 here is intended for a passenger vehicle.

(6) The tyre 10 is of the radial type and comprises a crown 12 comprising a tread 20 and a crown reinforcement 14 extending in the crown 12 in the circumferential direction Z. The crown reinforcement 14 comprises a working reinforcement 15 comprising first and second working plies 16, 18 and a hoop reinforcement 17 comprising a hooping ply 19. The crown reinforcement 14 is surmounted by the tread 20. In this case, the hoop reinforcement 17, in this case the hooping ply 19, is radially interposed between the working reinforcement 15 and the tread 20.

(7) The tyre comprises two sidewalls 22 extending the crown 12 radially inwards. The tyre 10 further comprises two beads 24 radially on the inside of the sidewalls 22 and each comprising an annular reinforcing structure 26, in this instance a bead wire 28, surmounted by a mass of filling rubber 30, and also a radial carcass reinforcement 32. The crown reinforcement 14 is situated radially between the carcass reinforcement 32 and the tread 20. Each sidewall 22 connects each bead 24 to the crown 12.

(8) The carcass reinforcement 32 preferably comprises a single carcass ply 34 of radial textile reinforcing elements. The carcass reinforcement 32 is anchored in each of the beads 24 by being turned up around the bead wire 28, so as to form, within each bead 24, a main strand 38 extending from the beads 24 through the sidewalls 22 as far as into the crown 12, and a turnup strand 40, the radially outer end 42 of the turnup strand 40 being radially on the outside of the annular reinforcing structure 26. The carcass reinforcement 32 thus extends from the beads 24 through the sidewalls 22 as far as into the crown 12. In this embodiment, the carcass reinforcement 32 also extends axially through the crown 12.

(9) In this embodiment, the tread 20 has a thickness Hb ranging from 7 mm to 10.5 mm, preferably from 8 mm to 10 mm. In this instance Hb=9 mm. This thickness Hb is the mean of 10 measurements taken on each side of the midplane over a total axial width of 4 cm, on the tyre 10 when new, between the external surface of the tread 20 that is intended to come into contact with the ground, and the radially external surface of the crown reinforcement 14, in this instance the radially external surface of the hoop reinforcement 17 that acts as an interface with the radially internal surface of the tread 20. As an alternative, it would be possible to conceive of smaller thicknesses Hb, for example thicknesses ranging from 3 mm to 6 mm, preferably from 3.5 mm to 4.5 mm, or also thicknesses Hb ranging from 5.5 mm to 7 mm.

(10) Each working ply 16, 18, hooping ply 19 and carcass ply 34 comprises an elastomer matrix in which reinforcing elements of the corresponding ply are embedded. Each elastomer matrix of the working plies 16, 18, hooping ply 19 and carcass ply 34 is based on a conventional composition for the skimming of reinforcing elements conventionally comprising a diene elastomer, for example natural rubber, a reinforcing filler, for example carbon black and/or silica, a crosslinking system, for example a vulcanization system, preferably comprising sulfur, stearic acid and zinc oxide, and possibly a vulcanization accelerator and/or retarder and/or various additives.

(11) In this particular instance and with reference to FIG. 2, each first and second working ply 16, 18 respectively comprises first and second reinforcing elements 50, 52 arranged substantially parallel to one another in each first and second working ply 16, 18 and respectively embedded in first and second elastomeric matrices 54, 56. The first reinforcing elements 50 make an angle ranging from 10 to 45 degrees with the circumferential direction Z of the tyre 10. Similarly, the second reinforcing elements 52 make an angle ranging from 10 to 45 degrees with the circumferential direction Z of the tyre 10. The first and second reinforcing elements 50, 52 are crossed relative to one another between the first working ply 16 and the second working ply 18. Thus, the angle formed by the first reinforcing elements 50 and the circumferential direction Z is equal here to +23°, whereas the angle formed by the second reinforcing elements 52 and the circumferential direction Z is equal here to −23°. In an alternative form, it might be conceivable to have angles respectively equal to +38° and −38°.

(12) The hooping ply 19 comprises textile reinforcing elements 58 arranged substantially parallel to one another in the hooping ply 19 and embedded in a third elastomeric matrix 60. The textile reinforcing elements 58 form an angle at most equal to 10°, preferably ranging from 5° to 10°, with the circumferential direction Z of the tyre 10. In this case, each textile reinforcing element is made from a heat-shrinkable material, here made of polyamide 66. Each textile reinforcing element comprises two multifilament strands made from a heat-shrinkable material, here made of polyamide 66, which are individually overtwisted at 250 twists.Math.m.sup.−1 in one direction then twisted together at 250 twists.Math.m.sup.−1 in the opposite direction. The two multifilament strands are helically wound around one another. Each multifilament strand has a titre equal to 140 tex. The thermal contraction CT of each hooping textile reinforcing element is approximately equal to approximately 7%.

(13) The carcass ply 34 comprises radial carcass textile reinforcing elements arranged substantially parallel to one another and that form an angle ranging from 65° to 90° with the circumferential direction Z of the tyre 10. In this case, each carcass textile reinforcing element comprises two multifilament strands made of polyester, here made of PET, which are individually overtwisted at 420 twists.Math.m.sup.−1 in one direction then twisted together at 420 twists.Math.m.sup.−1 in the opposite direction. The two multifilament carcass strands are helically wound around one another. Each multifilament carcass strand has a titre equal to 144 tex. The radial textile reinforcing elements are embedded in an elastomeric matrix.

(14) Each first and second reinforcing element 50, 52 is made up of a metallic monofilament respectively denoted by the reference 66, 68. Each metallic monofilament 66, 68 comprises a steel core coated with a layer of metallic coating, for example brass or zinc. Each metallic monofilament 66, 68 has a respective diameter D1, D2, expressed in mm, ranging from 0.34 mm to 0.38 mm, according to the invention, preferably from 0.35 mm to 0.37 mm and here less than or equal to 0.36 mm. In this first embodiment, D1=D2=0.35 mm. The steel is a carbon steel of the HT type having a strength Rm equal to 2838 MPa for a diameter of 0.35 mm (namely 273 N).

(15) Each density d1, d2 of the first and the second reinforcing elements 50, 52 in each first and second working ply 16, 18, expressed in monofilaments per decimetre and measured in a direction perpendicular to the main axis of the metallic monofilaments, ranges from 70 to 180 monofilaments per decimetre, preferably from 70 to 120 monofilaments per decimetre. Here, the main axis of the metallic monofilaments of each working ply makes an angle equal to ±23° with the circumferential direction Z. Here, because each diameter D1, D2 is less than or equal to 0.36 mm, each density d1, d2 ranges from 90 to 110 monofilaments per decimetre, preferably from 95 to 105 monofilaments per decimetre, and is here such that d1=d2=100 monofilaments per decimetre.

(16) The force at break of each first and second working ply 16, 18 ranges from 18000 N.Math.dm.sup.−1 to 32000 N.Math.dm.sup.−1, preferably from 20000 N.Math.dm.sup.−1 to 30000 N.Math.dm.sup.−1. Here, because each diameter D1, D2 is less than or equal to 0.36 mm, the force at break of each first and second working ply 16, 18 ranges from 24000 N.Math.dm.sup.−1 to 29000 N.Math.dm.sup.−1, and in this instance is equal to 27300 N.Math.dm.sup.−1.

(17) The mean thickness Ey radially separating a first reinforcing element 50 and a second reinforcing element 52, measured in the radial direction Y, ranges from 0.05 to 0.40 mm, preferably from 0.10 to 0.30 mm, and more preferably from 0.12 to 0.28 mm. In this instance, Ey=0.15 mm. Ey and D1 satisfy the following relationship 0.15≤Ey/(Ey+D1)≤0.50, for preference 0.22≤Ey/(Ey+D1)≤0.45, and more preferably 0.25≤Ey/(Ey+D1)≤0.42. In this instance, Ey/(Ey+D1)=0.29. Similarly, Ey and D2 satisfy the following relationship 0.15≤Ey/(Ey+D2)≤0.50, for preference 0.22≤Ey/(Ey+D2)≤0.45, and more preferably 0.25≤Ey/(Ey+D2)≤0.42. In this instance, Ey/(Ey+D2)=Ey/(Ey+D1)=0.29.

(18) Each mean thickness E1, E2 of each first and second working ply 16, 18, respectively, expressed in mm and measured in the radial direction Y is less than 0.75 mm, preferably less than or equal to 0.70 mm, more preferably less than or equal to 0.60 mm, and more preferably still less than or equal to 0.55 mm, and greater than or equal to 0.40 mm, preferably greater than or equal to 0.45 mm. In this case E1=E2=0.50 mm.

(19) With the values described above, (D1.sup.4×d1×1000)/E1=(D2.sup.4×d2×1000)/E2=3024. Thus, (D1.sup.4×d1×1000)/E1≥2050 and (D2.sup.4×d2×1000)/E2≥2050. Even (D1.sup.4×d1×1000)/E1≥2500 and (D2.sup.4×d2×1000)/E2≥2500 and even better (D1.sup.4×d1×1000)/E1≥2700 and (D2.sup.4×d2×1000)/E2≥2700. In this first embodiment, also 3500≥(D1.sup.4×d1×1000)/E1 and 3500≥(D2.sup.4×d2×1000)/E2.

(20) According to the invention, relationships I and II are satisfied:
−4053×E1+4720≤(D1.sup.4×d1×1000)/E1≤−4140×E1+5300  (I)
−4053×E2+4720≤(D2.sup.4×d2×1000)/E2≤−4140×E2+5300  (II)

(21) The following relationships are also satisfied:
−4430×E1+5120≤(D1.sup.4×d1×1000)/E1≤−4140×E1+5300
−4430×E2+5120≤(D2.sup.4×d2×1000)/E2≤−4140×E2+5300

(22) The characteristics D1, D2, d1, d2, E1, E2 and Ey are measured in the central part of the crown reinforcement 14 of the tyre 10 in the vulcanized state, on each side of the midplane M over a total axial width of 4 cm. All of the measurements are averaged over a total axial distance between −2.0 cm and +2.0 cm with respect to the centre of the working reinforcement.

Tyre According to a Second Embodiment of the Invention

(23) A second embodiment of the invention will now be described with reference to the first embodiment. Thus, for the sake of conciseness, unless mentioned otherwise, only those features that differ from those of the tyre according to the first embodiment will be described.

(24) Unlike in the first embodiment, each metallic monofilament 66, 68 respectively has a diameter ranging from 0.34 mm to 0.38 mm, preferably from 0.35 mm to 0.37 mm, and greater than or equal to 0.36 mm and here D1=D2=0.37 mm. The steel used is of the HT type and has a strength Rm equal to 2718 MPa for a diameter of 0.37 mm (namely 292 N).

(25) Each density d1, d2 of the first and the second reinforcing elements 50, 52 ranges from 70 to 90 monofilaments per decimetre and preferably from 70 to 80 monofilaments per decimetre and is here such that d1=d2=74 monofilaments per decimetre. The mean thickness Ey radially separating a first reinforcing element 50 and a second reinforcing element 52 is Ey=0.13 mm. Ey, D1 and D2 are such that Ey/(Ey+D1)=Ey/(Ey+D2)=0.26.

(26) Because d1≥0.36 mm and d2≥0.36 mm, the force at break of each first and second working ply 16, 18 ranges from 20000 N.Math.dm.sup.−1 to 24000 N.Math.dm.sup.−1 and is here equal to 21630 N.Math.dm.sup.−1.

(27) With the values described above, (D1.sup.4×d1×1000)/E1=(D2.sup.4×d2×1000)/E2=2779. Relationships I and II are satisfied in accordance with the invention:
−4053×E1+4720≤(D1.sup.4×d1×1000)/E1≤−4140×E1+5300  (I)
−4053×E2+4720≤(D2.sup.4×d2×1000)/E2≤−4140×E2+5300  (II)

(28) Unlike in the first embodiment, the following relationships are also satisfied:
−4053×E1+4720≤(D1.sup.4×d1×1000)/E1≤−4430×E1+5120
−4053×E2+4720≤(D2.sup.4×d2×1000)/E2≤−4430×E2+5120

Tyre According to a Third Embodiment of the Invention

(29) A third embodiment of the invention will now be described with reference to the first embodiment. Thus, for the sake of conciseness, unless mentioned otherwise, only those features that differ from those of the tyre according to the first embodiment will be described.

(30) Unlike in the first embodiment, each metallic monofilament 66, 68 respectively has a diameter ranging from 0.34 mm to 0.38 mm, preferably from 0.35 mm to 0.37 mm, and greater than or equal to 0.36 mm and here D1=D2=0.37 mm. The steel used is of the HT type and has a strength Rm equal to 2718 MPa for a diameter of 0.37 mm (namely 292 N).

(31) Each density d1, d2 of the first and the second reinforcing elements 50, 52 ranges from 70 to 90 monofilaments per decimetre and preferably from 70 to 80 monofilaments per decimetre and is here such that d1=d2=80 monofilaments per decimetre. The mean thickness Ey radially separating a first reinforcing element 50 and a second reinforcing element 52 is Ey=0.12 mm. Ey, D1 and D2 are such that Ey/(Ey+D1)=Ey/(Ey+D2)=0.24.

(32) Because d1>0.36 mm and d2>0.36 mm, the force at break of each first and second working ply 16, 18 ranges from 20000 N.Math.dm.sup.−1 to 24000 N.Math.dm.sup.−1 and is here equal to 23360 N.Math.dm.sup.−1.

(33) With the values described above, (D1.sup.4×d1×1000)/E1=(D2.sup.4×d2×1000)/E2=3085. Relationships I and II are satisfied in accordance with the invention:
−4053×E1+4720≤(D1.sup.4×d1×1000)/E1≤−4140×E1+5300  (I)
−4053×E2+4720≤(D2.sup.4×d2×1000)/E2≤−4140×E2+5300  (II)

(34) As in the first embodiment, the following relationships are also satisfied:
−4430×E1+5120≤(D1.sup.4×d1×1000)/E1≤−4140×E1+5300
−4430×E2+5120≤(D2.sup.4×d2×1000)/E2≤−4140×E2+5300

Tyre According to a Fourth Embodiment of the Invention

(35) A fourth embodiment of the invention will now be described with reference to the first embodiment. Thus, for the sake of conciseness, unless mentioned otherwise, only those features that differ from those of the tyre according to the first embodiment will be described.

(36) Unlike in the first embodiment, each metallic monofilament 66, 68 respectively has a diameter such that D1=D2=0.37 mm. The steel used is of the HT type and has a strength Rm equal to 2718 MPa for a diameter of 0.37 mm (namely 292 N).

(37) Each density d1, d2 is, here, such that d1=d2=111 monofilaments per decimetre. The mean thickness Ey radially separating a first reinforcing element 50 and a second reinforcing element 52 is Ey=0.13 mm. Ey, D1 and D2 are such that Ey/(Ey+D1)=Ey/(Ey+D2)=0.26.

(38) The force at break of each first and second working ply 16, 18 is here equal to 32444 N.Math.dm.sup.−1.

(39) With the values described above, (D1.sup.4×d1×1000)/E1=(D2.sup.4×d2×1000)/E2=4169. The following relationships are satisfied:
−4140×E1+5300<(D1.sup.4×d1×1000)/E1
−4140×E2+5300<(D2.sup.4×d2×1000)/E2

(40) As in the first embodiment, the following relationships are also satisfied:
(D1.sup.4×d1×1000)/E1≤−7997×E1+9027
(D2.sup.4×d2×1000)/E2≤−7997×E2+9027

Tyre According to a Fifth Embodiment of the Invention

(41) A fifth embodiment of the invention will now be described with reference to the first embodiment. Thus, for the sake of conciseness, unless mentioned otherwise, only those features that differ from those of the tyre according to the first embodiment will be described.

(42) Unlike in the first embodiment, each metallic monofilament 66, 68 has a diameter such that D1=D2=0.37 mm. The steel used is of the HT type and has a strength Rm equal to 2718 MPa for a diameter of 0.37 mm (namely 292 N).

(43) Each density d1, d2 of the first and the second reinforcing elements 50, 52 is here such that d1=d2=122 monofilaments per decimetre. The mean thickness Ey radially separating a first reinforcing element 50 and a second reinforcing element 52 is Ey=0.12 mm. Ey, D1 and D2 are such that Ey/(Ey+D1)=Ey/(Ey+D2)=0.25.

(44) The force at break of each first and second working ply 16, 18 is here equal to 35610 N.Math.dm.sup.−1.

(45) With the values described above, (D1.sup.4×d1×1000)/E1=(D2.sup.4×d2×1000)/E2=4654. The following relationships are satisfied:
−4140×E1+5300<(D1.sup.4×d1×1000)/E1
−4140×E2+5300<(D2.sup.4×d2×1000)/E2

(46) As in the first embodiment, the following relationships are also satisfied:
(D1.sup.4×d1×1000)/E1≤−7997×E1+9027
(D2.sup.4×d2×1000)/E2≤−7997×E2+9027

Comparative Tests

(47) The following tests demonstrate that the working plies of tyres according to the invention make it possible to obtain, on the one hand, better resistance to buckling than the second prior art and, on the other hand, a better compromise between the resistance to buckling and the mass of the or each ply than the first and second prior arts, thanks to the specific combination of monofilaments having diameters chosen according to their density and according to the thickness of the corresponding working ply.

(48) In these comparative tests, the resistance to buckling of the working reinforcements of the tyres T1, T2 introduced in the preamble of the present application and of tyres P1 to P12 and Q1 to Q12 according to the invention, and notably of tyres P10, P3 and P4 according to the first, second and third embodiments respectively and of tyres Q5 and Q6 respectively according to the fourth and fifth embodiments, was tested.

(49) The conditions of use liable to generate buckling of the crown reinforcement of the tyre correspond to stress loadings on cornering with relatively high accelerations of at least 0.7 g. These accelerations may be greater in certain usage scenarios of the competitive type because in such cases aerodynamic effects may make it possible to generate vertical aerodynamic loadings that make it possible to generate lateral loadings in excess of 1 g. The tyre that is the most highly stressed is therefore the one that is on the outside of the corner and the lateral loading generated on the tyre is generally considered to be proportional to the vertical loading.

(50) This vertical loading comprises the vertical load borne by the tyre when stationary or in a straight line, plus the load transfer. The vertical loading generated on the tyre is expressed using the following relationship:

(51) $\mathrm{Fz}=\mathrm{Fz}0\left(1+\frac{{\gamma }_T}{g}.Math.\frac{H}{V}\right)$ in which Fz0 is the vertical load and FZ0.Math.γ.sub.T/g.Math.H/V is the load transfer.

(52) The lateral loading generated on the tyre is proportional to the vertical loading and is therefore expressed by the following relationship:

(53) $\mathrm{Fy}=\mathrm{Fz}0.Math.\frac{{\gamma }_T}{g}\left(1+\frac{{\gamma }_T}{g}.Math.\frac{H}{V}\right)$

(54) In order to evaluate the buckling, runs are performed considering a reference load and applying loading pairs (Fy, Fz) on a machine or on a vehicle incrementally after various distances covered. An analysis of the tyres as a function of these stress loadings and of the distances covered makes it possible to determine whether buckling has been able to cause breakages in the working plies. The performance level is measured in terms of the distance covered without breakage.

(55) The results of the buckling test are indicated in base 100 with respect to a tyre comprising working plies comprising reinforcing elements made up of assemblies of 2 filaments measuring 0.30 mm of the HT type at a density of 83 threads per decimetre. A value above 100 means that the ply has an improved resistance to buckling, namely has covered a longer distance, and a value below 100 means that the ply has a deteriorated resistance to buckling, namely has covered a shorter distance.

(56) With regard to mass, the results are indicated in base 100 with respect to the working plies of the tyre T1. A value above 100 means that the ply has a mass higher than the mass of a ply of the tyre T1, and a value below 100 means that the ply has a mass lower than the mass of a ply of the tyre T1.

(57) The results of this buckling test are collated in Tables 1 and 2 below (row RF) together with the diameter D of the metallic monofilaments of each working ply (which are identical), the thickness E of each working ply (which are identical), the thickness Ey, the indicator (D.sup.4×d)/E for each working ply (which are identical), where appropriate, the calculated values of −4053×E+4720, −4430×E+5120 and −4140×E+5300, as well as −4140×E+5300, −6800×E+7850, −7997×E+9027, and the force at break for each working ply (which are identical).

(58) A comparison of tyres T1 and T2 confirms that tyre T2 has a lower mass than tyre T1 but at the expense of the resistance to buckling RF for which tyre T1 is far better.

(59) All the tyres according to the invention exhibit a better compromise between resistance to buckling and mass than the tyres T1 and T2. Furthermore, the resistance to buckling of tyres P1 to P12 according to the invention is vastly superior to that of tyre T2. In the case of the tyres according to the invention for which −4430×E1+5120≤(D1.sup.4×d1×1000)/E1≤−4140×E1+5300 and/or −4430×E2+5120≤(D2.sup.4×d2×1000)/E2≤−4140×E2+5300, the resistance to buckling is equal or even superior to that of tyre T1. The other tyres according to the invention nevertheless exhibit largely satisfactory resistance to buckling.

(60) In the case of the tyres according to the invention for which −4140×E1+5300<(D1.sup.4×d1×1000)/E1 and/or −4140×E2+5300<(D2.sup.4×d2×1000)/E2, the mass is close to that of tyre T1 and the gain in terms of resistance to buckling is significantly greater.

(61) The invention is not limited to the embodiments described above. Specifically, it is possible to envisage embodiments in which just one of the two working plies satisfies the conditions described.

(62) TABLE-US-00001 TABLE 1 T1 T2 P1 P2 P3 P4 P5 D (mm) 0.32 0.30 0.37 0.37 0.37 0.37 0.37 E (mm) 0.75 0.48 0.45 0.43 0.50 0.49 0.60 Ey (mm) 0.43 0.18 0.09 0.07 0.14 0.12 0.23 d (unit/dm) 143 111 74 80 74 80 74 −4053 × E + 4720 1660 2780 2898 2953 2695 2750 2290 (D.sup.4 × d × 1000)/E 1984 1881 3087 3439 2779 3085 2315 −4430 × E + 5120 1776 3000 3143 3188 2922 2967 2479 −4140 × E + 5300 2175 3319 3453 3495 3246 3288 2832 RF 107 63 97 105 97 105 98 Mass of the ply 100 68 69 75 69 75 69 Fr of the ply (N .Math. dm.sup.−1) 33143 23000 21630 23360 21630 23360 21630 P6 P7 P8 P9 P10 P11 P12 D (mm) 0.37 0.37 0.37 0.35 0.35 0.35 0.35 E (mm) 0.59 0.70 0.69 0.45 0.50 0.60 0.70 Ey (mm) 0.22 0.33 0.32 0.09 0.14 0.25 0.35 d (unit/dm) 80 74 80 100 100 100 100 −4053 × E + 4720 2345 1884 1940 2898 2695 2290 1884 (D.sup.4 × d × 1000)/E 2559 1984 2186 3363 3024 2517 2155 −4430 × E + 5120 2524 2036 2081 3143 2922 2479 2036 −4140 × E + 5300 2874 2418 2460 3453 3246 2832 2418 RF 105 98 105 105 105 105 105 Mass of the ply 75 69 75 84 84 84 84 Fr of the ply (N .Math. dm.sup.−1) 23360 21630 23360 27300 27300 27300 27300

(63) TABLE-US-00002 TABLE 2 T1 T2 Q1 Q2 Q3 Q4 Q5 Q6 D (mm) 0.32 0.30 0.37 E (mm) 0.75 0.48 0.45 0.50 Ey (mm) 0.43 0.18 0.08 0.12 d (unit/dm) 143 111 100 111 122 100 111 122 −4140 × E + 5300 2175 3319 3447 3267 (D.sup.4 × d × 1000)/E 1984 1881 4188 4633 5181 3767 4169 4654 −6800 × E + 7850 2717 4596 4807 4467 −7997 × E + 9027 2990 5200 5448 5048 RF 107 63 131 145 159 131 145 159 Mass of the ply 100 68 94 104 114 94 104 114 Fr of the ply (N .Math. dm.sup.1) 33143 23000 29200 32444 35610 29200 32444 35610 Q7 Q8 Q9 Q10 Q11 Q12 D (mm) 0.37 E (mm) 0.60 0.70 Ey (mm) 0.23 0.33 d (unit/dm) 100 111 122 100 111 122 −4140 × E + 5300 2826 2412 (D.sup.4 × d × 1000)/E 3137 3474 3866 2687 2977 3307 −6800 × E + 7850 3774 3107 −7997 × E + 9027 4249 3449 RF 131 146 160 132 147 161 Mass of the ply 94 104 114 94 104 114 Fr of the ply (N .Math. dm.sup.1) 29200 32444 35610 29200 32444 35610