Method for determining the structure parameters of a meridian tire bead and meridian tire bead

Abstract

The present application belongs to the technical field of radial aviation tire, and particularly relates to a method for determining structure parameters of a radial tire bead and a radial tire bead. In the method for determining structure parameters of the radial tire bead, a bending neutral layer of a bending beam of a bead section is introduced, the bending neutral layer of the radial tire bead is obtained by using an area weighted average method, then the distance between the midpoint of the intersection interface of the bead reinforcing rubber and the positive wrapping cord and the Y axis is designed to be equal to the distance between the bending neutral layer and the Y axis, and the obtained structure parameters of the radial tire bead can improve the bead fatigue performance, thereby effectively avoiding cracks and delamination of the rubber and the cord at the bead in the overloading sliding of the radial tire. Meanwhile, the present application provides a method for forward design of the radial tire bead by using an iterative method, greatly improves the design efficiency of the radial tire bead, and has wide industrial application value.

Description

Technical Field

[0001] The invention belongs to the technical field of radial aircraft tires, and in particular relates to a method for determining structural parameters of a radial tire bead and the radial tire bead. Background Art

[0002] With the development of aerospace technology, high requirements are placed on radial aircraft tires, such as high load bearing, fatigue resistance and light weight.

[0003] However, in recent years, 80% of the damage to radial aircraft tires during overload sliding in dynamic simulation tests is as follows: Figure 1 The damage to the interface between the cord and rubber shown in the figure restricts the improvement of the performance of radial aircraft tires. Summary of the Invention

[0004] The object of the present invention is to provide a method for determining the structural parameters of a radial tire bead and a radial tire bead. The structural parameters of the radial tire bead obtained by the method provided by the present invention can effectively improve the fatigue performance of the bead and prevent delamination of the rubber and cord at the bead, thereby solving the problem of delamination between the bead cord and rubber interface commonly occurring in radial aviation tires during overload sliding in dynamic simulation tests.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] The present invention provides a method for determining structural parameters of a radial tire bead, comprising the following steps:

[0007] (1) The bead structure of a radial tire is modeled using the area equality method to obtain a simplified model, wherein the simplified model includes: a bead reinforcing rubber in the shape of a parallelogram, a positive cord in the shape of a parallelogram, a reverse cord in the shape of a parallelogram and a rectangle, a apex rubber in the shape of a right triangle, and a sealing layer rubber in the shape of a rectangle;

[0008] (2) establishing a two-dimensional coordinate system with the edge of the sealant layer in the simplified model that is away from the wire ring and does not contact the turn-up cord as the coordinate origin and the long side of the rectangle of the sealant layer in the simplified model as the Y axis;

[0009] (3) In the two-dimensional coordinate system:

[0010] Calculate the distance x between the bending neutral layer and the Y axis in the simplified model according to formula 1;

[0011]

[0012] In formula 1: E r1 is the elastic modulus of the tire bead reinforcement, E r2is the elastic modulus of the apex, E r3 is the elastic modulus of the sealing layer glue, E r4 is the elastic modulus of the positive cord, E r5 is the elastic modulus of the turn-up cord, S y1 To simplify the static moment of the tire bead reinforcement on the Y axis in the model, S y2 To simplify the static moment of the triangle on the Y axis in the model, S y3 In order to simplify the static moment of the sealing layer glue on the Y axis in the model, S y4 To simplify the static moment of the positive cord to the Y axis in the model, S y5 is the static moment of the turn-up cord about the Y axis in the simplified model; A1 is the area of ​​the bead reinforcement rubber in the simplified model; A2 is the area of ​​the apex rubber in the simplified model; A3 is the area of ​​the sealing layer rubber in the simplified model; A4 is the area of ​​the positive cord in the simplified model; A5 is the area of ​​the turn-up cord in the simplified model;

[0013] Then, determining whether the distances x and x0 between the bending neutral layer and the Y axis in the simplified model are equal, wherein x0 is the distance between the midpoint of the intersection interface between the bead reinforcement rubber and the positive cord in the simplified model and the Y axis;

[0014] When the distances x and x0 between the bending neutral layer and the Y axis in the simplified model are equal, step (5) is executed;

[0015] When the distances x and x0 between the bending neutral layer and the Y axis in the simplified model are not equal, executing step (4);

[0016] (4) modifying the simplified model, wherein the modification comprises: modifying the model parameters of at least one of the bead reinforcement rubber, the front cord, the back cord, the apex rubber, and the sealant rubber in the simplified model, wherein the model parameters include elastic modulus information and / or graphic size information; and then executing step (3);

[0017] (5) Obtaining the structural parameters of the radial tire bead, wherein the structural parameters of the radial tire bead include: elastic modulus information and graphic size information of the bead reinforcing rubber, positive cord, reverse cord, apex rubber and sealing layer rubber in the simplified model.

[0018] Preferably, in step (4), the correction is: modifying the elastic modulus information of the positive cord in the simplified model, and simultaneously modifying the graphic size information of the bead reinforcing rubber, the positive cord, the turn-up cord, the apex rubber and the sealing layer rubber in the simplified model;

[0019] In step (1), the construction is as follows: simplifying the shape of the bead reinforcing rubber in the bead located on the upper part of the radial tire wire ring into a parallelogram, simplifying the shape of the positive cord into a parallelogram, simplifying the shape of the turn-up cord into a parallelogram and a rectangle, simplifying the shape of the apex rubber into a right triangle, and simplifying the shape of the sealing layer rubber into a rectangle; the absolute value of the area change rate of the bead reinforcing rubber, positive cord, turn-up cord, apex rubber and sealing layer rubber before and after the simplified model is constructed is ≤5%.

[0020] Preferably, the elastic modulus of the apex rubber, the elastic modulus of the sealing layer rubber, the elastic modulus of the front covered cords and the elastic modulus of the turn-up covered cords are uniaxial tensile moduli.

[0021] Preferably, the elastic modulus of the apex glue and the elastic modulus of the sealing layer glue adopt the tensile elastic modulus when the strain is 1.

[0022] Preferably, the method for determining the tensile elastic modulus when the strain is 1 comprises the following steps:

[0023] Stretching a sample of the apex glue or the sealing layer glue in a tensile testing machine until the apex glue or the sealing layer glue breaks, thereby obtaining a tensile stress-strain curve;

[0024] According to the compressive stress-strain curve, the tensile elastic modulus when the strain is 1 is calculated by formula 2;

[0025]

[0026] In formula 2, σ1 is the stress value when the strain is 1, and ε1 = 1.

[0027] Preferably, the elastic modulus of the tire bead reinforcing rubber is a compressive elastic modulus.

[0028] Preferably, the compressive elastic modulus is the compressive elastic modulus when the strain is -0.4.

[0029] Preferably, the method for determining the compressive elastic modulus when the strain is -0.4 comprises the following steps:

[0030] The tire bead reinforcement rubber sample is placed in a compression testing machine and compressed until the strain reaches 25% or the compression force reaches 18 kN, and a compression stress-strain curve is obtained;

[0031] According to the compressive stress-strain curve, the compressive elastic modulus at a strain of -0.4 is calculated by formula 3;

[0032]

[0033] In formula 3: σ -0.4is the stress value when the strain is -0.4, ε -0.4 =-0.4.

[0034] Preferably, the elastic modulus of the front cord and the elastic modulus of the turn-up cord are the tensile elastic modulus when the strain is 0.1.

[0035] Preferably, the method for determining the tensile elastic modulus when the strain is 0.1 comprises the following steps:

[0036] The stress-strain performance test of the cord was carried out according to GB / T 9101-2017 "Nylon 66 Dipped Cord Fabric" and GB / T 32108-2015 "Test Method for Tensile Properties of Dipped Cords, Yarns and Cords", and the stress-strain curve of the cord fabric was obtained.

[0037] According to the stress-strain curve of the cord, the tensile elastic modulus when the strain is 0.1 is calculated by formula 4;

[0038]

[0039] In formula 4: σ 0.1 is the stress value when the strain is 0.1, ε 0.1 =0.1.

[0040] The present invention provides a radial tire bead, the structural parameters of the radial tire bead are determined by the method described in the above technical solution.

[0041] The present invention provides a method for determining the structural parameters of the bead of a radial tire. Figure 1The primary cause of interface failure between the cord (positive wrap cord) and rubber (bead reinforcement) shown is significant deformation at the cord-rubber interface when the bead is subjected to reciprocating bending loads. The present inventors discovered that within the bead bending deformation model, a neutral bending layer exists that is neither tensile nor compressive, preventing deformation of the bead cord and rubber. Consequently, the present inventors propose the concept of a neutral bending layer in the radial tire bead to address the common problem of delamination at the bead cord-rubber interface during overloaded taxiing in dynamic simulation tests of radial aircraft tires. The present invention introduces the bead bending neutral layer into the method for determining the structural parameters of the radial tire bead, uses the area-weighted average method to calculate the bending neutral layer at the radial tire bead, and then designs the distance between the midpoint of the intersection interface of the positive cord and the bead reinforcing rubber and the Y axis to be equal to the distance between the bending neutral layer and the Y axis (that is, the interface between the bead reinforcing rubber and the positive cord is set at the bending neutral layer position). The obtained structural parameters of the radial tire bead can improve the fatigue performance of the bead, thereby effectively preventing cracks and delamination between the rubber and the cord at the bead of the radial tire during overload sliding. At the same time, the present invention uses an iterative method to provide a method for forward designing the radial tire bead, greatly improving the efficiency of radial tire bead design and having broad industrial application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a radial tire bead crack;

[0043] Figure 2 It is a simplified schematic diagram of the tire bead;

[0044] Figure 3 This is the force analysis diagram of the model;

[0045] Figure 4 The shape and size of the I-type cutter;

[0046] Figure 5 is the tensile stress-strain curve;

[0047] Figure 6 is the compression stress-strain curve of rubber;

[0048] Figure 7 is the tensile stress-strain curve of the cord;

[0049] Figure 8 A flow chart of a method for determining structural parameters of a radial tire bead provided by the present invention;

[0050] Figure 9 This is a simplified schematic diagram of an aircraft tire in an embodiment;

[0051] Figure 10 Schematic diagram of the tire bead size after adjustment in the embodiment;

[0052] In the figure: 1 is the positive cord, 2 is the reverse cord, 3 is the apex rubber, 4 is the sealing layer rubber, and 5 is the tire bead reinforcement rubber. DETAILED DESCRIPTION

[0053] The present invention provides a method for determining structural parameters of a radial tire bead, comprising the following steps:

[0054] (1) The bead structure of a radial tire is modeled using the area equality method to obtain a simplified model, wherein the simplified model includes: a bead reinforcing rubber in the shape of a parallelogram, a positive cord in the shape of a parallelogram, a reverse cord in the shape of a parallelogram and a rectangle, a apex rubber in the shape of a right triangle, and a sealing layer rubber in the shape of a rectangle;

[0055] (2) establishing a two-dimensional coordinate system with the edge of the sealant layer in the simplified model that is away from the wire ring and does not contact the turn-up cord as the coordinate origin and the long side of the rectangle of the sealant layer in the simplified model as the Y axis;

[0056] (3) In the two-dimensional coordinate system:

[0057] Calculate the distance x between the bending neutral layer and the Y axis in the simplified model according to formula 1;

[0058]

[0059] In formula 1: E r1 is the elastic modulus of the tire bead reinforcement, E r2 is the elastic modulus of the apex, E r3 is the elastic modulus of the sealing layer glue, E r4 is the elastic modulus of the positive cord, E r5 is the elastic modulus of the turn-up cord, S y1 To simplify the static moment of the tire bead reinforcement on the Y axis in the model, S y2 To simplify the static moment of the triangle on the Y axis in the model, S y3 In order to simplify the static moment of the sealing layer glue on the Y axis in the model, S y4 To simplify the static moment of the positive cord to the Y axis in the model, S y5 is the static moment of the turn-up cord about the Y axis in the simplified model; A1 is the area of ​​the bead reinforcement rubber in the simplified model; A2 is the area of ​​the apex rubber in the simplified model; A3 is the area of ​​the sealing layer rubber in the simplified model; A4 is the area of ​​the positive cord in the simplified model; A5 is the area of ​​the turn-up cord in the simplified model;

[0060] Then, determining whether the distances x and x0 between the bending neutral layer and the Y axis in the simplified model are equal, wherein x0 is the distance between the midpoint of the intersection interface between the bead reinforcement rubber and the positive cord in the simplified model and the Y axis;

[0061] When the distances x and x0 between the bending neutral layer and the Y axis in the simplified model are equal, step (5) is executed;

[0062] When the distances x and x0 between the bending neutral layer and the Y axis in the simplified model are not equal, executing step (4);

[0063] (4) modifying the simplified model, wherein the modification comprises: modifying the model parameters of at least one of the bead reinforcement rubber, the front cord, the back cord, the apex rubber, and the sealant rubber in the simplified model, wherein the model parameters include elastic modulus information and / or graphic size information; and then executing step (3);

[0064] (5) Obtaining the structural parameters of the radial tire bead, wherein the structural parameters of the radial tire bead include: elastic modulus information and graphic size information of the bead reinforcing rubber, positive cord, reverse cord, apex rubber and sealing layer rubber in the simplified model.

[0065] In the present invention, unless otherwise specified, all preparation raw materials / components are commercially available products well known to those skilled in the art.

[0066] In the present invention, the radial tire bead is preferably a radial aircraft tire bead. In the present invention, the cross-sectional schematic diagram of the radial tire bead portion is as follows Figure 2 As shown in the left image, the bead reinforcement rubber contacts the wheel rim and is a compression-bearing material. The apex rubber is placed on top of the bead ring and is a tension-bearing material. The sealant rubber contacts the air inside the tire, ensuring airtightness and is a tension-bearing material. The positive cord is the cord that wraps from the outside of the tire to the inside and does not need to wrap over the top of the bead ring. The reverse cord is the cord that wraps from the inside of the tire to the outside and needs to wrap over the top of the bead ring to ensure stable load-bearing. Figure 2 The various materials in the left figure are all irregularly shaped, hindering the subsequent calculation of the bead's neutral bending layer. Therefore, this paper uses the equal area method to model the cross-sectional structure of the radial tire located above the bead ring (i.e., simplification), resulting in a simplified model. In this invention, the simplified model includes a neutral bending layer.

[0067] In the present invention, Figure 2As shown in the right figure in the figure, the present invention constructs a model of the radial tire bead structure using the area equality method to obtain a simplified model. The simplified model includes: a bead reinforcing rubber in the shape of a parallelogram, a positive cord in the shape of a parallelogram, a turn-up cord in the shape of one parallelogram and one rectangle, a apex rubber in the shape of a right triangle, and a sealant in the shape of a rectangle. In a specific embodiment of the present invention, from the outside to the inside of the radial tire bead, the simplified model includes, in order: a bead reinforcing rubber in the shape of a parallelogram, a positive cord in the shape of a parallelogram, a turn-up cord in the shape of one parallelogram, a apex rubber in the shape of a right triangle, a turn-up cord in the shape of one rectangle, and a sealant in the shape of a rectangle.

[0068] In the present invention, the model is constructed by simplifying the shape of the bead reinforcement rubber in the tire bead located above the radial tire bead ring into a parallelogram, the shape of the front cord into a parallelogram, the shape of the turn-up cord into a parallelogram and a rectangle, the shape of the apex rubber into a right triangle, and the shape of the sealant rubber into a rectangle. In the present invention, the absolute value of the area change rate of the bead reinforcement rubber, front cord, turn-up cord, apex rubber, and sealant rubber before and after the model is constructed (i.e., simplified) is preferably ≤5%. Figure 2 This is a schematic diagram of the model construction of the tire bead cross-section structure located above the bead ring of a radial tire according to the present invention.

[0069] like Figure 3 The force analysis diagram of the model shown is Figure 3 The "M" in the simplified model represents the bending moment. After obtaining the simplified model, the present invention uses the edge of the sealant layer in the simplified model that is away from the wire ring and does not contact the turn-up cord as the coordinate origin, and uses the long side of the rectangle of the sealant layer in the simplified model as the Y axis to establish the following: Figure 3 The two-dimensional coordinate system shown.

[0070] After establishing the two-dimensional coordinate system, the present invention uses the two-dimensional coordinate system as follows:

[0071] The distance between the bending neutral layer and the Y axis in the simplified model is calculated according to formula 1;

[0072]

[0073] In formula 1: E r1 is the elastic modulus of the tire bead reinforcement, E r2 is the elastic modulus of the apex, E r3 is the elastic modulus of the sealing layer glue, E r4 is the elastic modulus of the positive cord, E r5 is the elastic modulus of the turn-up cord, S y1To simplify the static moment of the tire bead reinforcement on the Y axis in the model, S y2 To simplify the static moment of the triangle on the Y axis in the model, S y3 In order to simplify the static moment of the sealing layer glue on the Y axis in the model, S y4 To simplify the static moment of the positive cord to the Y axis in the model, S y5 The static moment of the turn-up cord about the Y-axis in the simplified model is given by: A1, the area of ​​the bead reinforcement rubber in the simplified model; A2, the area of ​​the apex rubber in the simplified model; A3, the area of ​​the sealing layer rubber in the simplified model; A4, the area of ​​the positive cord in the simplified model; and A5, the area of ​​the turn-up cord in the simplified model.

[0074] In the present invention, S y5 To simplify the static moment of the turn-up cord about the Y axis in the model, that is, S y5 To simplify the model, the sum of the static moments of the turn-up cord with a parallelogram shape and the turn-up cord with a rectangular shape about the Y axis.

[0075] In the present invention, A5 is the area of ​​the turn-up cord in the simplified model, that is, A5 is the sum of the areas of the turn-up cord in the shape of a parallelogram and the turn-up cord in the shape of a rectangle relative to the Y axis in the simplified model.

[0076] In the present invention, the determination of the bead's neutral bending layer position is primarily related to the bead material's elastic modulus, the material's static moment in the compressive direction, and the material's cross-sectional area. Therefore, the present invention uses Equation 1 to calculate the neutral bending layer position. In the present invention, since the rubber material in the radial tire bead (including the bead reinforcing rubber, apex rubber, and sealant rubber) is anisotropic, the bead reinforcing rubber is mostly in compression, while the apex rubber and sealant rubber are both in tension. Therefore, the compression modulus is used for the bead reinforcing rubber, while the tensile modulus is used for the apex rubber and sealant rubber.

[0077] In the present invention, the elastic modulus of the apex rubber, the elastic modulus of the sealant rubber, the elastic modulus of the front cord, and the elastic modulus of the turn-up cord are preferably uniaxial tensile moduli. The elastic modulus of the apex rubber and the sealant rubber are preferably the tensile modulus at a strain of 1. The elastic modulus of the front cord and the turn-up cord are preferably the tensile modulus at a strain of 0.1. The elastic modulus of the bead reinforcing rubber is preferably a compressive modulus. The compressive modulus is preferably the compressive modulus at a strain of -0.4.

[0078] In the present invention, the method for determining the tensile elastic modulus when the strain is 1 preferably comprises the following steps:

[0079] Stretching a sample of the apex glue or the sealing layer glue in a tensile testing machine until the apex glue or the sealing layer glue breaks, thereby obtaining a tensile stress-strain curve;

[0080] According to the compressive stress-strain curve, the tensile elastic modulus when the strain is 1 is calculated by formula 2;

[0081]

[0082] In formula 2, σ1 is the stress value when the strain is 1, and ε1 = 1.

[0083] The present invention stretches the sample of the apex glue or the sealing layer glue in a tensile testing machine until the apex glue or the sealing layer glue breaks, and obtains a tensile stress-strain curve. In the present invention, the sample of the apex glue or the sealing layer glue is preferably vulcanized into a sheet sample using a flat vulcanizer, and the sheet sample is preferably cut using an I-type cutter. During the cutting, the length direction of the sample of the apex glue or the sealing layer glue is parallel to the length direction of the sample. The sample of the apex glue or the sealing layer glue is preferably dumbbell-shaped, and the number is preferably 3. In the present invention, the structural schematic diagram of the I-type cutter is as shown below. Figure 4 As shown. The present invention preferably clamps the sample of the apex or the sealant symmetrically on the upper and lower clamps of the tensile testing machine, and then fixes the extensometer on the marking lines at both ends of the narrow and long part, wherein the spacing between the marking lines is 25mm; then the tensile testing machine is started, and the stretching is preferably to stretch the clamp at a rate of 200mm / min±20mm / min until the rubber breaks. In a specific embodiment of the present invention, the tensile stress-strain curve of the sample of the apex or the sealant is calculated as shown Figure 5 shown.

[0084] In the present invention, the apex rubber or the sealing layer rubber is a highly nonlinear large deformation elastic body, and the strain at the apex rubber or the sealing layer rubber of the radial tire bead (especially the radial aircraft tire bead) is often no more than 1, so the present invention obtains a tensile stress-strain curve;

[0085] According to the compressive stress-strain curve, the tensile elastic modulus when the strain is 1 is calculated by formula 2;

[0086]

[0087] In formula 2, σ1 is the stress value when the strain is 1, and ε1 = 1.

[0088] In the present invention, the method for measuring the compressive elastic modulus when the strain is -0.4 preferably comprises the following steps:

[0089] The tire bead reinforcement rubber sample is placed in a compression testing machine and compressed until the strain reaches 25% or the compression force reaches 18 kN, and a compression stress-strain curve is obtained;

[0090] According to the compressive stress-strain curve, the compressive elastic modulus at a strain of -0.4 is calculated by formula 3;

[0091]

[0092] In formula 3: σ -0.4 is the stress value when the strain is -0.4, ε -0.4 =-0.4.

[0093] The present invention places the tire bead reinforcing rubber sample in a compression testing machine for compression until the strain reaches 25% or the compression force reaches 18kN, and obtains a compression stress-strain curve. In the present invention, the tire bead reinforcing rubber sample is in the shape of a cylinder, and the diameter of the tire bead reinforcing rubber sample is preferably 29.0mm±0.5mm, and the height is preferably 12.5mm±0.5mm. The tire bead reinforcing rubber sample is preferably prepared by a molding method, and the surface of the tire bead reinforcing rubber sample is preferably flat, and the upper and lower surfaces are parallel to each other. The present invention preferably places the assembly of the tire bead reinforcing rubber sample in the center of the compression testing machine, and the compression is preferably to compress the tire bead reinforcing rubber sample at a speed of 10mm / min until the strain reaches 25% or the compression force reaches 18kN. In a specific embodiment of the present invention, the compression stress-strain curve is as follows Figure 6 According to the compression stress-strain curve, the present invention calculates the compression elastic modulus when the strain is -0.4 using Formula 3.

[0094] In the present invention, the method for determining the tensile elastic modulus when the strain is 0.1 preferably comprises the following steps:

[0095] The stress-strain performance test of the cord was carried out according to GB / T 9101-2017 "Nylon 66 Dipped Cord Fabric" and GB / T 32108-2015 "Test Method for Tensile Properties of Dipped Cords, Yarns and Cords", and the stress-strain curve of the cord fabric was obtained.

[0096] According to the stress-strain curve of the cord, the tensile elastic modulus of the positive cord or the reverse cord when the strain is 0.1 is calculated using Formula 4;

[0097]

[0098] In formula 4: σ 0.1 is the stress value when the strain is 0.1, ε 0.1 =0.1.

[0099] In a specific embodiment of the present invention, the stress-strain curve of the cord is as follows: Figure 7 shown.

[0100] After obtaining the distance x between the bending neutral layer and the Y axis in the simplified model, the present invention then determines whether the distance x between the bending neutral layer and the Y axis in the simplified model is equal to x0, where x0 is the distance between the midpoint of the intersection interface between the bead reinforcement rubber and the positive cord in the simplified model and the Y axis.

[0101] In the present invention, when the distance x between the bending neutral layer and the Y axis in the simplified model is equal to x0, the structural parameters of the radial tire bead are obtained, and the structural parameters of the radial tire bead include: when the distance between the bending neutral layer and the Y axis in the simplified model is equal to x0, the elastic modulus information and graphic size information of the bead reinforcement rubber, positive cord, turn-up cord, apex rubber and sealing layer rubber in the simplified model.

[0102] In the present invention, when the distance x between the bending neutral layer and the Y axis in the simplified model is not equal to x0, the present invention modifies the model parameters of at least one of the bead reinforcement rubber, positive cord, reverse cord, apex rubber and sealing layer rubber in the simplified model, and the model parameters include elastic modulus information and / or graphic size information.

[0103] In the present invention, the correction is preferably: modifying the elastic modulus information of the positive cord in the simplified model, and modifying the graphic size information of the bead reinforcement rubber, positive cord, turn-up cord, apex rubber and sealing layer rubber in the simplified model.

[0104] In the present invention, when the distance x between the bending neutral layer and the Y axis in the simplified model is less than x0, the correction is preferably: increasing the elastic modulus information of the positive cord, increasing the thickness of the tire bead reinforcement rubber, reducing the thickness of the positive cord, increasing the thickness of the reverse cord, reducing the thickness of the apex rubber, and increasing the thickness of the sealing layer rubber.

[0105] In the present invention, when the distance x between the bending neutral layer and the Y axis in the simplified model is greater than x0, the correction is preferably: reducing the elastic modulus information of the positive cord, reducing the thickness of the tire bead reinforcement rubber, increasing the thickness of the positive cord, reducing the thickness of the reverse cord, increasing the thickness of the apex rubber, and reducing the thickness of the sealing layer rubber.

[0106] The thickness of the bead reinforcement rubber is the length of the short side of the parallelogram forming the bead reinforcement rubber in the simplified model. The thickness of the front cord is the length of the short side of the parallelogram forming the front cord in the simplified model. The thickness of the turn-up cord is the length of the short side of the parallelogram forming the turn-up cord in the simplified model and the length of the wide side of the rectangle forming the turn-up cord in the simplified model. The thickness of the apex rubber is the length of the short straight side of the right triangle forming the apex rubber in the simplified model. The thickness of the sealant rubber is the length of the wide side of the rectangle forming the sealant rubber in the simplified model.

[0107] After modifying the model parameters of at least one of the bead reinforcement rubber, the front cord, the turn-up cord, the apex rubber, and the sealant rubber in the simplified model, the present invention repeats the above steps of "calculating the distance between the bending neutral layer and the Y axis in the simplified model according to Formula 1 in the two-dimensional coordinate system" and "then determining whether the distances x and x0 between the bending neutral layer and the Y axis in the simplified model are equal" until the distances x and x0 between the bending neutral layer and the Y axis in the simplified model are equal, thereby obtaining the structural parameters of the radial tire bead.

[0108] The present invention provides a radial tire bead, the structural parameters of the radial tire bead are determined by the method described in the above technical solution.

[0109] This invention, for the first time, proposes the concept of a neutral bending layer in the radial aircraft tire bead to address the common problem of delamination between the bead cord and the rubber interface during overloaded taxiing in dynamic simulation tests. This invention also incorporates the calculation method for the neutral bending layer of a cross-sectional bending beam into radial tire bead design, proposing a forward-thinking approach to radial tire bead design that significantly improves the iterative efficiency of radial tire bead design.

[0110] In order to further illustrate the present invention, the technical solutions provided by the present invention are described in detail below in conjunction with the embodiments, but they should not be construed as limiting the scope of protection of the present invention.

[0111] The following embodiments provide methods for determining the structural parameters of radial tire beads, including a bead simplification method, a bead structure calculation method, and a bead material parameter determination method. The steps include: first, roughly drawing a schematic diagram of the bead structure; then, using the area equality method to simplify the bead structure, converting the simplified diagram into a regular shape that is easy to calculate. Then, the elastic modulus, cross-sectional area, and static moment of each material are calculated and applied to the area-weighted average formula to calculate the position of the bead's neutral bending layer. Finally, after multiple iterations, the final bead structure diagram is obtained.

[0112] Figure 8 Flowchart of the method for determining the structural parameters of the radial tire bead provided by the present invention, Figure 8"Adjusting the neutral layer position" is the step of correcting the simplified model.

[0113] Example 1

[0114] This embodiment provides a method for determining the structural parameters of a radial aircraft tire bead, the flow chart of which is as follows: Figure 8 As shown. In this embodiment, the following should be drawn first. Figure 2 The left figure in the middle shows a schematic diagram of the structure of the radial aircraft tire bead. Then, the cross-sectional structure of the bead located on the upper part of the radial tire bead is modeled using the area equality method (i.e., simplified processing) to obtain a simplified model. The simplified processing is as follows: the shape of the bead reinforcement rubber in the bead located on the upper part of the radial tire bead is simplified to a parallelogram, the shape of the positive cord is simplified to a parallelogram, the shape of the reverse cord is simplified to a parallelogram and a rectangle, the shape of the apex rubber is simplified to a right triangle, and the shape of the sealing layer rubber is simplified to a rectangle, as shown in the figure. Figure 2 As shown in the right figure in the figure, the area change rate of the bead reinforcement rubber, the front cord, the back cord, the apex rubber and the sealing layer rubber before and after the simplified treatment in this embodiment is ≤5%.

[0115] After obtaining the simplified model, this embodiment uses the edge of the sealant layer in the simplified model that is away from the wire ring and does not contact the turn-up cord as the coordinate origin, and uses the long side of the rectangle of the sealant layer in the simplified model as the Y axis to establish the following coordinate system: Figure 3 The two-dimensional coordinate system shown.

[0116] Then measure the elastic modulus of the rubber (bead reinforcement rubber, triangular cross and sealing layer rubber) and cords (positive cords and reverse cords) used in the bead;

[0117] The elastic modulus of the apex rubber and the sealant rubber is the tensile modulus at a strain of 1. The elastic modulus of the front and turn-up cords is the tensile modulus at a strain of 0.1. The elastic modulus of the bead reinforcement rubber is the compressive modulus at a strain of preferably -0.4.

[0118] The methods for determining the elastic modulus of the apex adhesive or the elastic modulus of the sealing layer adhesive include:

[0119] Use a flat vulcanizer to vulcanize sheet samples. The samples are dumbbell-shaped. The number is 3. Use an I-type cutter to cut (make the length direction of the sample parallel to the length direction of the sample) to obtain dumbbell-shaped samples. Figure 4 As shown:

[0120] Clamp the sample symmetrically on the upper and lower clamps of the tensile testing machine, then fix the extensometer on the marking lines at both ends of the narrow part (marking line spacing 25mm); start the testing machine and stretch the clamps at a rate of 200mm / min±20mm / min until the rubber breaks. Calculate the rubber tensile stress-strain curve as follows Figure 5 As shown:

[0121] The elastic modulus of the apex rubber or the sealing layer rubber is a highly nonlinear large deformation elastic body, and the strain at the bead rubber of the radial aircraft tire is often no more than 1. Therefore, the elastic modulus of the apex rubber or the sealing layer rubber is calculated using Formula 2:

[0122]

[0123] In formula 2: σ1 is the stress value when the strain is 1, ε1 = 1;

[0124] Methods for determining the elastic modulus of the bead reinforcement include:

[0125] The rubber material compression specimen for tire bead reinforcement is a cylinder with a diameter of 29.0mm±0.5mm and a height of 12.5mm±0.5mm. The specimen is prepared by molding, and its surface should be flat and the upper and lower surfaces should be parallel to each other. The specimen assembly is placed in the center of the compression tester and compressed at a speed of 10mm / min until the strain reaches 25% or the compression force reaches 18kN. The compression stress-strain curve is as follows: Figure 6 As shown, the rubber compression modulus should be calculated using Formula 3:

[0126]

[0127] In formula 3: σ -0.4 is the stress value when the strain is -0.4, ε -0.4 =-0.4;

[0128] Methods for determining the elastic modulus of a positive cord or a reverse cord include:

[0129] The stress-strain performance test of the cord was carried out according to GB / T 9101-2017 "Nylon 66 Dipped Cord Fabric" and GB / T 32108-2015 "Test Method for Tensile Properties of Dipped Cords, Yarns and Cords". The stress-strain curve is as follows: Figure 7 As shown, the cord modulus should be calculated using Formula 4:

[0130]

[0131] In formula 4: σ 0.1 is the stress value when the strain is 0.1, ε 0.1 =0.1.

[0132] exist Figure 3 The cross-sectional area and static moment of rubber and cord are measured and calculated in the two-dimensional coordinate system shown. Figure 9 This is a simplified model diagram of a radial aircraft tire. The calculation formula for the static moment of rubber and cord is: Static moment = A × Y c , A is the area of ​​the material, Yc is the distance from the centroid of the material to the Y axis, and the calculated dimensions and parameters of the simplified model of a radial aircraft tire are shown in Table 1.

[0133] Table 1 Dimensional parameters of a simplified model of a radial aircraft tire

[0134] <![CDATA[E r1 ]]> <![CDATA[E r2 ]]> <![CDATA[E r3 ]]> <![CDATA[E r4 ]]> <![CDATA[E r5 ]]> 7.25 4.0 0.956 1300 1300 <![CDATA[S y1 ]]> <![CDATA[S y2 ]]> <![CDATA[S y3 ]]> <![CDATA[S y4 ]]> <![CDATA[S y5 ]]> 9884 2232 31 1024 2160 <![CDATA[A1]]> <![CDATA[A2]]> <![CDATA[A3]]> <![CDATA[A4]]> <![CDATA[A5]]> 416 248 62 64 252

[0135] Substituting the parameters in Table 1 into Formula 1, we can get the result x = 10.17 mm. Figure 9 The distance x0 between the midpoint of the interface where the bead reinforcement rubber and the positive cord intersect and the Y axis is measured. x0 = 17.2 mm, x ≠ x0, so the bead structure is adjusted. The diagram of the adjusted bead size is as follows: Figure 10 The calculated and adjusted tire bead size parameters are shown in Table 2.

[0136] Table 2 Bead size parameters after adjustment

[0137] <![CDATA[E r1 ]]> <![CDATA[E r2 ]]> <![CDATA[E r3 ]]> <![CDATA[E r4 ]]> <![CDATA[E r5 ]]> 7.25 4 0.956 6000 1300 <![CDATA[S y1 ]]> <![CDATA[S y2 ]]> <![CDATA[S y3 ]]> <![CDATA[S y4 ]]> <![CDATA[S y5 ]]> 10166 1488 139.5 450 1960 <![CDATA[A1]]> <![CDATA[A2]]> <![CDATA[A3]]> <![CDATA[A4]]> <![CDATA[A5]]> 480 186 93 31 189

[0138] Then substitute the parameters in Table 2 into Formula 1 to obtain the bending neutral layer x, x = 12.22 mm, from Figure 10 Measure the distance x0 between the midpoint of the interface where the bead reinforcement rubber and the positive cord intersect and the Y axis, x0 = 13mm, x-x0 ≤ 1mm. Due to the limitations of the aircraft tire manufacturing process, a process error of 1mm is allowed.

[0139] The interface is located at the bending neutral layer. The tire bead structure is redrawn according to the bending neutral layer x. After two or three iterations, the final tire bead structure diagram is obtained.

[0140] As can be seen from the above examples, the present invention provides a novel tire bead design method based on a material-weighted average algorithm. This method uses an area-weighted average method to calculate the neutral bending layer at the bead of a radial tire. The rubber-cord interface is then positioned at this neutral bending layer, thereby improving bead fatigue performance and preventing rubber-cord delamination at the bead. This method can effectively improve the fatigue performance of the bead of radial aircraft tires and significantly enhance the efficiency of aircraft tire bead structures.

[0141] Although the above embodiment provides a detailed description of the present invention, it is only a part of the embodiments of the present invention, not all of the embodiments. Other embodiments can be obtained based on this embodiment without creativity, and these embodiments all fall within the scope of protection of the present invention.

Claims

1. A method for determining the structural parameters of a radial tire bead, characterized in that: The following steps are involved: (1) The bead structure of a radial tire is modeled using the area equality method to obtain a simplified model, wherein the simplified model includes: a bead reinforcing rubber in the shape of a parallelogram, a positive cord in the shape of a parallelogram, a reverse cord in the shape of a parallelogram and a rectangle, a apex rubber in the shape of a right triangle, and a sealing layer rubber in the shape of a rectangle; (2) establishing a two-dimensional coordinate system with the edge of the sealant layer in the simplified model that is away from the wire ring and does not contact the turn-up cord as the coordinate origin and the long side of the rectangle of the sealant layer in the simplified model as the Y axis; (3) In the two-dimensional coordinate system: Calculate the distance x between the bending neutral layer and the Y axis in the simplified model according to formula 1; In formula 1: E r1 is the elastic modulus of the tire bead reinforcement, E r2 is the elastic modulus of the apex, E r3 is the elastic modulus of the sealing layer glue, E r4 is the elastic modulus of the positive cord, E r5 is the elastic modulus of the turn-up cord, S y1 To simplify the static moment of the tire bead reinforcement on the Y axis in the model, S y2 To simplify the static moment of the triangle on the Y axis in the model, S y3 In order to simplify the static moment of the sealing layer glue on the Y axis in the model, S y4 To simplify the static moment of the positive cord to the Y axis in the model, S y5 is the static moment of the turn-up cord about the Y axis in the simplified model; A1 is the area of ​​the bead reinforcement rubber in the simplified model; A2 is the area of ​​the apex rubber in the simplified model; A3 is the area of ​​the sealing layer rubber in the simplified model; A4 is the area of ​​the positive cord in the simplified model; A5 is the area of ​​the turn-up cord in the simplified model; The elastic modulus of the apex adhesive and the elastic modulus of the sealing layer adhesive adopt the tensile elastic modulus when the strain is 1; the method for measuring the tensile elastic modulus when the strain is 1 includes the following steps: Stretching the sample of the apex glue or the sealing layer glue in a tensile testing machine until the apex glue or the sealing layer glue breaks, thereby obtaining a tensile stress-strain curve; According to the tensile stress-strain curve, the tensile elastic modulus when the strain is 1 is calculated by formula 2; In formula 2: σ1 is the stress value when the strain is 1, ε1 = 1; Then, determining whether the distances x and x0 between the bending neutral layer and the Y axis in the simplified model are equal, wherein x0 is the distance between the midpoint of the intersection interface between the bead reinforcement rubber and the positive cord in the simplified model and the Y axis; When the distances x and x0 between the bending neutral layer and the Y axis in the simplified model are equal, step (5) is executed; When the distances x and x0 between the bending neutral layer and the Y axis in the simplified model are not equal, executing step (4); (4) modifying the simplified model, wherein the modification comprises: modifying the model parameters of at least one of the bead reinforcement rubber, the front cord, the back cord, the apex rubber, and the sealant rubber in the simplified model, wherein the model parameters include elastic modulus information and / or graphic size information; and then executing step (3); (5) Obtaining the structural parameters of the radial tire bead, wherein the structural parameters of the radial tire bead include: elastic modulus information and graphic size information of the bead reinforcing rubber, positive cord, reverse cord, apex rubber and sealing layer rubber in the simplified model.

2. The method for determining the structural parameters of a radial tire bead according to claim 1, wherein: In step (4), the correction is: modifying the elastic modulus information of the positive cord in the simplified model, and modifying the graphic size information of the bead reinforcement rubber, the positive cord, the turn-up cord, the apex rubber and the sealing layer rubber in the simplified model; In step (1), the model is constructed as follows: the shape of the bead reinforcing rubber in the bead located on the upper part of the radial tire wire ring is simplified to a parallelogram, the shape of the positive cord is simplified to a parallelogram, the shape of the turn-up cord is simplified to a parallelogram and a rectangle, the shape of the apex rubber is simplified to a right triangle, and the shape of the sealing layer rubber is simplified to a rectangle; the absolute value of the area change rate of the bead reinforcing rubber, positive cord, turn-up cord, apex rubber and sealing layer rubber before and after the simplified model is constructed is ≤5%.

3. The method for determining the structural parameters of a radial tire bead according to claim 1, wherein: The elastic modulus of the apex rubber, the elastic modulus of the sealing layer rubber, the elastic modulus of the front cord and the elastic modulus of the turn-up cord are uniaxial tensile moduli.

4. The method for determining the structural parameters of a radial tire bead according to claim 1, wherein: The elastic modulus of the tire bead reinforcing rubber is a compressive elastic modulus.

5. The method for determining the structural parameters of a radial tire bead according to claim 4, characterized in that: The compressive elastic modulus is the compressive elastic modulus when the strain is -0.

4.

6. The method for determining the structural parameters of a radial tire bead according to claim 5, characterized in that: The method for measuring the compressive elastic modulus when the strain is -0.4 comprises the following steps: The tire bead reinforcement rubber sample is placed in a compression testing machine and compressed until the strain reaches 25% or the compression force reaches 18 kN, and a compression stress-strain curve is obtained; According to the compressive stress-strain curve, the compressive elastic modulus at a strain of -0.4 is calculated by formula 3; In formula 3: σ -0.4 is the stress value when the strain is -0.4, ε -0.4 =-0.

4.

7. The method for determining the structural parameters of a radial tire bead according to claim 3, wherein: The elastic modulus of the front cord and the elastic modulus of the turn-up cord are the tensile elastic modulus when the strain is 0.

1.

8. A radial tire bead, characterized in that: The structural parameters of the radial tire bead are determined by the method according to any one of claims 1 to 7.

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