Design method of densely arranged circular cross-section wire ring and circular cross-section wire ring

Abstract

The present application belongs to the field of tire bead rings, and in particular relates to a design method for densely arranged circular cross-section bead rings and a circular cross-section bead ring. The design method for densely arranged circular cross-section bead rings can more accurately calculate the maximum number of steel wires that can be arranged in each layer, as well as the wire gaps of various steel wire arrangement schemes, quickly determine the design scheme for dense arrangement of steel wires of different diameters, and improve the overall performance of the circular cross-section bead ring and the tire.

Description

Technical Field

[0001] The present application relates to the technical field of tire bead rings, and in particular to a design method for densely arranged circular cross-section bead rings and a circular cross-section bead ring. Background Art

[0002] Bead rings are critical load-bearing components of tires, and their performance significantly impacts the tire's load-bearing capacity. To achieve higher load-bearing capacity, circular bead rings typically require a dense arrangement of wound wires. However, current theoretical design methods for circular bead rings are still incomplete, making modeling of these densely packed wires time-consuming for engineers. Due to the complex structure of circular bead rings, changes in bead ring size make it difficult for engineers to quickly analyze the maximum number of wires that can be arranged in each layer and the gaps between layers under varying parameters.

[0003] The current theoretical calculation of the arrangement of steel wires in a circular cross-section wire ring assumes that the projection of the steel wire on a plane perpendicular to the cross-section of the ring core is a circle. However, due to the winding angle, the projection of the steel wire on this plane is not actually a circle, which will cause a certain calculation error. The greater the degree of twisting of the steel wire on the ring core, the greater the error. Therefore, the current theory cannot quickly and accurately determine the dense arrangement of steel wires of different diameters on the ring core, nor can it accurately calculate the gaps between each layer of steel wires. Summary of the Invention

[0004] The embodiments of the present application provide a design method for densely arranged circular cross-section steel wire rings and a circular cross-section steel wire ring, which aims to quickly and accurately calculate the maximum number of steel wires that can be arranged in each layer without the need for 3D modeling, so as to achieve the minimum gap between the steel wires in each layer, thereby reducing the development cycle and improving development efficiency.

[0005] The present application provides a method for designing a densely packed circular cross-section steel wire ring. The steel wire ring comprises a ring core and multiple layers of steel wires wound layer by layer around the outer circumference of the ring core. The method for designing a circular cross-section steel wire ring comprises the following steps:

[0006] S1. Calculate the theoretical number of wires in contact in each layer based on the core diameter and cross-sectional radius, the cross-sectional radius of the wires, the number of layers in which the wires are located, the winding angle of the circular cross-sectional wire ring, and the number of leads of the circular cross-sectional wire ring. Round this value down to the nearest integer.

[0007] S2. Based on the maximum number of steel wires in each layer obtained by rounding, calculate the projected gap between the steel wires in each layer on the cross section of the coil core, taking into account the influence of the winding angle, and calculate the actual gap between the steel wires in each layer.

[0008] In some embodiments, when the diameters of the steel wires in each layer are the same, the maximum number of steel wires that can be accommodated in each layer [N2i is determined by the following equation:

[0009]

[0010] where D is the diameter of the core, R1 is the cross-sectional radius of the core, R2 is the cross-sectional radius of the wire, N1 is the number of leads of the wire loop with a circular cross-section, α is the winding angle of the wire loop with a circular cross-section, i is the layer where the wire is located, and N 2i is the theoretical value of the number of wires when the wires in the i-th layer contact each other.

[0011] In some embodiments, when the diameters of the wires in each layer are different, the maximum number of wires [N 2i is determined by the following equation:

[0012]

[0013] where D is the diameter of the core, R1 is the cross-sectional radius of the core, R2 is the cross-sectional radius of the wire, N1 is the number of leads of the wire loop with a circular cross-section, α is the winding angle of the wire loop with a circular cross-section, i is the layer where the wire is located, R 2i is the radius of the wire in the i-th layer, and R n is the radius of the wire in the n-th layer, and i < n, n ≥ 2, and both i and n are positive integers. N 2i is the theoretical value of the number of wires when the wires in the i-th layer contact each other.

[0014] In some embodiments, the projected gap δ0 between the wires in each layer is calculated by the following formula:

[0015]

[0016] The actual gap δ between the wires in each layer is calculated by the following formula:

[0017]

[0018] where θ is the angle formed by the line connecting the centers of the wire and the core and the tangent line to the cross-sectional profile passing through the core on the cross-sectional profile of the wire, x0 is the abscissa of the tangent point, and α is the winding angle of the wire loop with a circular cross-section.

[0019] In some embodiments, when the diameters of the wires in each layer are the same, θ and x0 are calculated by the following formula:

[0020]

[0021] When the diameters of the wires in each layer are different, θ and x0 are calculated by the following formula:

[0022]

[0023] In the formula, R1 is the cross-sectional radius of the core, R2 is the cross-sectional radius of the steel wire, α is the winding angle of the steel wire ring with a circular cross-section, and i is the layer where the steel wire is located. R 2i is the radius of the steel wire in the i-th layer, and R n is the radius of the steel wire in the n-th layer, where i < n, n ≥ 2, and both i and n are positive integers.

[0024] The present application also provides a steel wire ring with a circular cross-section, which includes a core and multiple layers of steel wires wound layer by layer on the outer peripheral surface of the core. When the winding directions between the layers of steel wires are opposite, the steel wire ring with a circular cross-section is prepared by using the above design method of the steel wire ring with a circular cross-section.

[0025] In some embodiments, the steel wire ring with a circular cross-section has 2 - 6 layers of steel wires. The diameter of the steel wire ring with a circular cross-section is 350 - 635 mm, the cross-sectional diameter of the core is 3 - 5 mm, and the cross-sectional diameter of the steel wire is 1 - 2 mm.

[0026] The beneficial effects of the design method of the closely arranged steel wire ring with a circular cross-section and the steel wire ring with a circular cross-section provided by the present application are as follows: Compared with the prior art, the design method of the closely arranged steel wire ring with a circular cross-section provided by the present application can more accurately calculate the maximum number of steel wires that can be arranged in each layer and the gaps of various steel wire arrangement schemes, quickly determine the design scheme of the dense arrangement of steel wires with different diameters, and improve the overall performance of the steel wire ring with a circular cross-section and the tire. Description of the Drawings

[0027] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts. Among them:

[0028] Figure 1 is a flowchart of the design method of the closely arranged steel wire ring with a circular cross-section in the embodiment of the present application;

[0029] Figure 2 is a definition diagram of the winding angle α in the steel wire ring in the embodiment of the present application;

[0030] Figure 3 is the projection profile and mathematical model of the core and the steel wire of the steel wire ring with a circular cross-section in the core plane in the embodiment of the present application;

[0031] Figure 4 is a cross-sectional view of the steel wire ring in the embodiment of the present application;

[0032] Figure 5 is a three-dimensional view of the steel wire ring in the embodiment of the present application.

[0033] Description of main component symbols:

[0034] 1. Ring core; 2. Steel wire. DETAILED DESCRIPTION

[0035] In order to make the technical problems, technical solutions and advantages to be solved by the present invention clearer, a detailed description will be given below with reference to the accompanying drawings and specific embodiments.

[0036] The embodiment of the present application provides a method for designing a densely packed circular cross-section wire ring, wherein, Figure 3 As shown, the wire ring includes a ring core 1 and multiple layers of steel wires 2 wound layer by layer on the outer circumference of the ring core 1. The diameters of the steel wires 2 in the same layer are the same, and the diameters of the steel wires 2 in different layers can be the same or different. Figure 1 As shown, the circular cross-section ring design method includes the following steps:

[0037] S1. According to the diameter and cross-sectional radius of the coil core 1, the cross-sectional radius of the wire 2, the number of layers of wire 2, the winding angle and the lead number of the circular cross-sectional wire ring, the theoretical value of the number of wires in each layer 2 when they are in contact with each other is calculated and rounded down;

[0038] S2. Based on the rounded number of steel wires in each layer, calculate the projected gap between the steel wires 2 in each layer on the cross section of the coil core 1, taking into account the influence of the winding angle, and calculate the actual gap.

[0039] Specifically, the steps are as follows: based on the lead number N1 of the circular cross-section steel wire ring, the diameter D of the ring core 1 and the cross-sectional radius R2 of the steel wire 2, the winding angle expression of each layer of steel wire 2 under this condition is calculated; then, based on the projection of the ring core 1 and the steel wire 2 on any plane perpendicular to the cross-sectional area of ​​the ring core 1, a coordinate system is established to calculate the mathematical conditions when the steel wires 2 in each layer are exactly in contact.

[0040] By combining the above two equations and rounding down the theoretical value of the maximum number of steel wires 2 in each layer, the maximum number of steel wires 2 wound in each layer can be obtained.

[0041] According to the defined gap calculation formula, the actual gap value between the two steel wires in each layer is calculated.

[0042] Assume that the radius R2 of the wound wire 2 in each layer is the same:

[0043] like Figure 2 As shown, the winding wire 2 and the circle where the center of the wire 2 is located are expanded into a triangle as shown in the figure, and the winding angle α can be obtained as:

[0044]

[0045] Where D is the diameter of the ring core 1, R1 is the cross-sectional radius of the ring core 1, R2 is the cross-sectional radius of the steel wire 2, N1 is the number of steel wire ring leads, and i is the layer number where the steel wire 2 is located (i = 1, 2, 3, 4, 5, 6).

[0046] like Figure 3 As shown, since the projection of the steel wire 2 on the cross section of the coil core 1 is approximately an ellipse, a coordinate system is established with the center of the steel wire 2 as the origin, the major axis of the ellipse as the x-axis, and the line where the minor axis is located as the y-axis. Point A is the origin of the coil core 1, and the equation of the ellipse is:

[0047]

[0048] The slope of the tangent line at any point of the ellipse is:

[0049]

[0050] Obviously, the length of the OA segment is:

[0051]

[0052] Line AB is the tangent line of the ellipse passing through point A. Let the tangent point be (x0, y0). Then the equation of the line is:

[0053]

[0054] The simultaneous equations of the ellipse and the line at the point (x0, y0) are as follows:

[0055]

[0056] The solution is:

[0057]

[0058] like Figure 3 As shown, the tangent of the angle θ between the tangent line and the y-axis is:

[0059]

[0060] Substituting the above x0 and y0 into the equation, we get:

[0061]

[0062] Then θ is:

[0063]

[0064] like At this time, the steel wires 2 in the same layer just touch each other, that is, the critical contact condition is:

[0065]

[0066] Among them, N 2i is the theoretical value of the number of steel wires in the i-th layer when the steel wires are in contact with each other.

[0067] The simultaneous equations are:

[0068]

[0069] Solve for N 2i Then, round down:

[0070] [N 2i ]≤N 2i

[0071] [N 2i ] is the maximum number of steel wires 2 arranged in the i-th layer.

[0072] like At this time, the steel wires 2 in the same layer do not contact each other, that is:

[0073]

[0074] and The tangent of the ellipse of the two adjacent steel wire cross sections passing through point A is β, which can be calculated by the following formula:

[0075]

[0076] Since β is usually very small, for the steel wires 2 that are not in contact with each other, the gap value δ0 between the two ellipses on the cross section is:

[0077]

[0078] Since the steel wire 2 is wound on the coil core 1, the actual gap value is:

[0079]

[0080] Assume that the radius R of the wrapped steel wire 2 in each layer is 2i Not the same:

[0081] like Figure 2 As shown, the winding wire 2 and the circle where the center of the wire 2 is located are expanded into a triangle as shown in the figure, and the winding angle α can be obtained as:

[0082]

[0083] Where D is the diameter of the ring core, R1 is the cross-sectional radius of the ring core, R2 is the cross-sectional radius of the steel wire 2, N1 is the lead number of the circular cross-sectional steel wire ring, α is the winding angle of the circular cross-sectional steel wire ring, and i is the number of layers in which the steel wire 2 is located. 2i is the radius of the ith layer of steel wire 2, Rn is the radius of the wire 2 in the nth layer, where i < n, n ≥ 2, and both i and n are positive integers.

[0084] As Figure 3 shown, since the projection contour of the wire 2 on the cross-section of the coil core 1 is approximately an ellipse, a coordinate system is established with the center of the wire 2 as the origin, the major axis of the ellipse as the x-axis, and the line where the minor axis is located as the y-axis. Point A is the origin of the coil core 1, and the ellipse equation is:

[0085]

[0086] The tangent slope of any point on the ellipse is:

[0087]

[0088] Obviously, the length of the OA segment is:

[0089]

[0090] The straight line AB is the tangent of the ellipse passing through point A. Let the tangent point be (x0, y0), then the straight line equation is:

[0091]

[0092] The ellipse equation of the point (x0, y0) and the straight line equation are联立 as follows:

[0093]

[0094] The solution is:

[0095]

[0096] As Figure 3 shown, the tangent value of the angle θ between the tangent and the y-axis is:

[0097]

[0098] Substituting x0 and y0, we get:

[0099]

[0100] Then θ is:

[0101]

[0102] If then the wires 2 in the same layer just touch each other at this time. That is, the contact critical condition is:

[0103]

[0104] The critical condition equations for the wires 2 to just touch each other:

[0105]

[0106] Solve for N 2i Then, round down:

[0107] [N 2i ]≤N 2i

[0108] [N 2i ] is the maximum number of steel wires 2 arranged in the i-th layer.

[0109] like At this time, the steel wires 2 in the same layer do not contact each other, that is:

[0110]

[0111] For the steel wires 2 that are not in contact with each other, the gap between the two ellipses on the cross section is:

[0112]

[0113] Since the steel wire 2 is wound on the coil core 1, the actual gap value is:

[0114]

[0115] When the radius R2 of the winding wire 2 is the same, the circular cross-section wire ring is densely arranged as follows:

[0116] Taking a ring core with a diameter of 5 mm, a circular cross-section steel wire ring with a diameter of 540 mm, a circular cross-section steel wire ring with a lead number of 6, and steel wires with preset diameters of 1.5 mm, 1.6 mm, 1.7 mm, 1.8 mm, and 1.9 mm as an example, the gap obtained by the algorithm in the present invention is compared with the gap measured by UG modeling as follows:

[0117]

[0118] Compared with the existing technology, the advantages of the present invention are: the design method of the present invention can more accurately calculate the maximum number of steel wires that can be accommodated in each layer of steel wires, and accurately calculate the gap value between steel wires of different diameters, helping engineers to quickly determine the design scheme for dense arrangement of steel wires of different diameters, thereby improving the overall performance of the tire.

[0119] The embodiment of the present application also provides a circular cross-section wire ring, such as Figure 4-Figure 5 As shown, the circular cross-section steel wire ring includes a ring core 1 and multiple layers of steel wire 2 wound layer by layer on the outer circumference of the ring core 1. When the winding directions (twist directions) of the layers of steel wire 2 are opposite, the circular cross-section steel wire ring is prepared using the circular cross-section steel wire ring design method in the above embodiment.

[0120] The circular cross-section steel wire ring has 2-6 layers of steel wires 2, the diameter of the circular cross-section steel wire ring is 350-635 mm, the cross-section diameter of the ring core 1 is 3-5 mm, and the cross-section diameter of the steel wire 2 is 1-2 mm.

[0121] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0122] The above embodiments merely represent several implementation methods of the present application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the application. A person skilled in the art would be able to make various modifications and improvements without departing from the spirit of the present application, and all such modifications and improvements fall within the scope of protection of the present application, which shall be subject to the appended claims.

Claims

1. A method for designing a densely packed circular cross-section steel wire ring, wherein the circular cross-section steel wire ring comprises a ring core and multiple layers of steel wire wound layer by layer around the outer circumference of the ring core, characterized in that: The circular cross-section wire ring design method comprises the following steps: S1. Calculate the theoretical number of wires in contact in each layer based on the core diameter and cross-sectional radius, the cross-sectional radius of the wires, the number of layers in which the wires are located, the winding angle of the circular cross-sectional wire ring, and the number of leads of the circular cross-sectional wire ring. Round this value down to the nearest integer. S2. Based on the maximum number of steel wires in each layer obtained by rounding, calculate the projected gap between the steel wires in each layer on the cross section of the coil core, taking into account the influence of the winding angle, and calculate the actual gap between the steel wires in each layer; When the diameters of the steel wires in each layer are the same, the maximum number of steel wires that can be accommodated in each layer Determined by the following equation: ； Where, is the diameter of the coil core, is the cross-sectional radius of the coil core, is the cross-sectional radius of the steel wire, is the lead number of the circular cross-section wire ring, is the winding angle of the circular cross-section wire ring, is the number of layers where the steel wire is located, For the The theoretical value of the number of steel wires in a layer when the steel wires are in contact with each other; When the diameters of the steel wires in each layer are different, the maximum number of steel wires that can be accommodated in each layer Determined by the following equation: ； Where, is the diameter of the coil core, is the cross-sectional radius of the coil core, is the cross-sectional radius of the steel wire, is the lead number of the circular cross-section wire ring, is the winding angle of the circular cross-section wire ring, is the number of layers where the steel wire is located, For the The radius of the layer wire, For the The radius of the layer wire, and , 、 are all positive integers, For the The theoretical value of the number of steel wires in a layer when the steel wires are in contact with each other; Projected gap between steel wires in each layer Calculated by the following formula: ； Considering the influence of winding angle, the actual gap between steel wires in each layer Calculated by the following formula: ； Where, The angle between the line connecting the center of the wire and the center of the coil core and the tangent line of the cross-sectional profile of the coil core is formed on the cross-sectional profile of the wire. is the horizontal coordinate of the tangent point, It is the winding angle of circular cross-section wire ring.

2. The circular cross-section ring design method according to claim 1, characterized in that: When the diameters of the steel wires in each layer are the same, and Calculated by the following formula: ； ； When the diameters of the steel wires in each layer are different, and Calculated by the following formula: ； ； Where, is the cross-sectional radius of the coil core, is the cross-sectional radius of the steel wire, is the winding angle of the circular cross-section wire ring, is the number of layers where the steel wire is located, For the The radius of the layer wire, For the The radius of the layer wire, and , 、 All are positive integers.

3. A circular cross-section wire ring, characterized in that: It comprises a ring core and multiple layers of steel wires wound layer by layer on the outer circumference of the ring core. When the winding directions of the steel wires in each layer are opposite, the circular cross-section steel wire ring is prepared by the circular cross-section steel wire ring design method according to any one of claims 1 or 2.

4. The circular cross-section wire ring according to claim 3, characterized in that: The circular cross-section steel wire ring has 2-6 layers of steel wires, the diameter of the circular cross-section steel wire ring is 350-635 mm, the cross-sectional diameter of the ring core is 3-5 mm, and the cross-sectional diameter of the steel wire is 1-2 mm.

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