Method for identifying the position of the neutral axis of bending deformation at the bead of a tire

Abstract

A method for identifying the location of the neutral axis of bending deformation at the tire bead, belonging to the field of radial tire technology. The specific solution is as follows: A method for identifying the location of the neutral axis of bending deformation at the tire bead includes the following steps: Step 1: Establish a finite element model of the tire, perform load simulation analysis on the tire, and output the principal strain of each rubber material element; Step 2: Calculate the volumetric strain of each rubber material element; Step 3: Calculate the volumetric strain divergence of each rubber material element; Step 4: Graphically display the volumetric strain divergence of the tire model's contact patch, find the boundary smooth line connecting the regions with values ​​close to 0, and determine the location of the neutral axis of bending at the tire bead. This invention provides a basis and guidance for tire structure design.

Description

Technical Field

[0001] This invention belongs to the field of radial tire technology, and particularly relates to a method for identifying the position of the neutral axis of bending deformation at the tire bead. Background Technology

[0002] Tires are organically composed of materials such as rubber, steel wire, and nylon. During vehicle operation, tires undergo repeated deformation, eventually leading to damage. For all-steel-wire tires, truck and bus tires, and engineering vehicle tires, the bead area is a high-risk area for damage. The main reason is that the bead area is composed of multiple layers of steel wire and nylon fabric, while also containing rubber materials of varying hardness. There are many interfaces between the carcass material and the rubber material, and between different rubber materials. When bending deformation occurs, significant shear deformation occurs between the rubber and the carcass material or within the rubber itself. Effectively controlling shear deformation in vulnerable areas is a key focus and challenge for tire design engineers. Currently, the main approach relies on engineers' experience to adjust the tire structure, followed by real-world tire testing or simulation analysis. However, this method lacks a clear basis and objective for structural adjustments, often requiring more than ten iterations to find the right direction. However, from a mechanical perspective, when the tire bead undergoes bending deformation, the closer it is to the neutral axis, the greater the shear deformation, and vice versa. If the position of the bending neutral axis of the tire bead can be obtained, it can provide direction for structural design adjustments. However, there are currently no reports on methods and technologies for identifying the bending neutral axis of the tire bead. Summary of the Invention

[0003] The purpose of this invention is to address the problems existing in the prior art, namely, how to effectively control the shear deformation of vulnerable areas is a key focus and challenge for tire design engineers. Currently, the main approach relies on engineers' experience to adjust the tire structure, followed by real-world tire testing or simulation analysis. This approach suffers from a lack of clear basis and objectives for structural adjustments, often requiring more than ten iterations to find the right direction. This invention provides a method for identifying the neutral axis position of bending deformation at the tire bead, offering a basis and guidance for tire structure design.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] A method for identifying the position of the neutral axis of bending deformation at the tire bead includes the following steps:

[0006] Step 1: Establish a finite element model of the tire, divide the rubber material into several rubber material elements, perform load simulation analysis on the tire, and output the principal strain of each rubber material element.

[0007] Step 2: Calculate the volumetric strain of each rubber material unit;

[0008] Step 3: Calculate the volumetric strain divergence of each rubber material element;

[0009] Step 4: Graphically display the volumetric strain divergence of the tire model's ground contact section, find the smooth boundary line connecting the regions with values ​​close to 0, and determine the position of the bending neutral axis at the tire bead.

[0010] Furthermore, in step one, the principal strains of each rubber material unit are denoted as LEP1, LEP2, and LEP3.

[0011] Furthermore, in step two, the formula for calculating the volumetric strain of each rubber material unit is:

[0012]

[0013] Where i is the number of each rubber material unit.

[0014] Furthermore, the formula for calculating volumetric strain divergence is:

[0015]

[0016] Where x, y, z are the Cartesian coordinate axes of the tire model space.

[0017] Furthermore, the rubber material unit is triangular or quadrilateral in shape.

[0018] Compared with the prior art, the beneficial effects of the present invention are:

[0019] This invention can fully guarantee the durability of the tire bead during the tire prototype design stage. The principle is as follows: the tire is very prone to damage at the bead, and the damage location is mainly concentrated at the interface between the cord and the rubber. The deformation mode here is mainly bending deformation. According to the principles of material mechanics, the structure has a bending neutral axis during bending deformation. The material above the neutral axis is subjected to tensile stress, and the material below the neutral axis is subjected to compressive stress. At the neutral axis, the tensile / compressive strain caused by bending deformation is basically zero, but the shear stress is the greatest at the neutral axis. The further away from the neutral axis, the smaller the shear stress. Shear stress is the main factor causing tire damage at the bead. Therefore, in tire design, the interface between the cord and the rubber should be avoided from being placed above or too close to the neutral axis, otherwise the tire's durability will be greatly reduced. The tire bead area is made of various materials with complex shapes, and the modulus of the materials (rubber and steel wire or nylon) varies greatly. Theoretical methods cannot accurately locate the position of the neutral axis at this location, making it impossible to determine whether the interface between the cord and the rubber is above or at a distance from the neutral axis. This invention can solve this problem and provide intuitive and accurate guidance for tire structure design. Attached Figure Description

[0020] Figure 1 This is a two-dimensional simulation model of a 305 / 70R22.5 tire and the location of the tire bead.

[0021] Figure 2 A 3D simulation model of a 305 / 70R22.5 tire;

[0022] Figure 3 The volumetric strain divergence contour map and neutral axis position of the bead area at the grounding center location;

[0023] Figure 4 The volumetric strain divergence contour map and neutral axis position of the bead area offset by 2 degrees from the grounding center;

[0024] Figure 5 The volumetric strain divergence cloud map and neutral axis position of the bead area offset by 3 degrees from the grounding center;

[0025] Figure 6 This shows the actual location of damage to a 305 / 70R22.5 tire.

[0026] Figure 7 The diagram shows the original and improved versions of the 305 / 70R22.5 tire. Detailed Implementation

[0027] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings and embodiments. Obviously, the described embodiments are only some embodiments of the invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0028] Example 1:

[0029] Taking 305 / 70R22.5 tires as an example:

[0030] A method for identifying the position of the neutral axis of bending deformation at the tire bead includes the following steps:

[0031] The first step is to establish a finite element model of the tire and perform load simulation analysis: Establish a finite element model of the tire, such as... Figure 1 The rubber material is divided into several triangular and / or quadrilateral rubber material elements, and load simulation calculations are performed, such as... Figure 2 The output data shows the principal strains of the rubber material elements, arranged in ascending order as LEP1, LEP2, and LEP3. Some data are shown in Table 1 below (the first column is the rubber material element number, the second column is LEP1, the third column is LEP2, and the fourth column is LEP3):

[0032] Table 1

[0033]

[0034] The second step is to extract the simulation result data: using a Python program, extract the principal strain of each rubber material element (1380 rubber material elements in this example) from the calculation results, and calculate the volumetric strain ε of each rubber material element. Vi :

[0035]

[0036] Where i represents the rubber material unit number, as shown in Table 2 below:

[0037] Table 2

[0038]

[0039] Because tires undergo not only bending deformation but also stretching or compression during rolling deformation, stretching or compression deformation causes a uniform change in strain throughout the entire part, while bending deformation causes non-uniform strain. Therefore, finding a location with constant strain cannot accurately determine the neutral axis position; the region with uniform strain is the neutral axis position. Volumetric strain can characterize the magnitude of volume change or strain of a unit. If a point is located at the neutral axis of bending, its volumetric strain is essentially constant or its change is minimal. Therefore, in the case of coupled stretching, compression, and bending deformation, the location where the volumetric strain is the same can be found; this location is the bending neutral axis position.

[0040] The third step, to find the point where the volumetric strain remains essentially constant, can be achieved by calculating the divergence of the volumetric strain at each point. A divergence close to 0 indicates that the volumetric strain at that point has neither increased nor decreased. The volumetric strain divergence div(ε) for each rubber material element is calculated using a Python program. vi The formula is:

[0041]

[0042] Where x, y, and z are the Cartesian coordinate axes of the tire model space, and the calculation results are shown in Table 3 below:

[0043] Table 3

[0044]

[0045] The fourth step is to graphically display the volumetric strain divergence of the tire model's contact patch section to determine the neutral axis position: A Python program is used to graphically display the mesh and volumetric strain divergence of the section. The minimum displayed value ranges from -0.00005 to -0.00001, and the maximum displayed value ranges from 0.00001 to 0.00005. Smoothly connecting the boundaries of regions with values ​​close to 0 in the graphical representation can determine the location of the bending neutral axis at the tire bead. Figures 3 to 5 .from Figures 3 to 5 It can be seen that the horizontal axis position of the cross-section bending is basically the same at different tire positions (i.e., different degrees of bending), which is consistent with the bending theory, and the horizontal axis position is also consistent with the actual tire failure position (e.g., Figure 6 This matches. When the tire triangle rubber is thickened (e.g.) Figure 7 When the cord-rubber interface is positioned away from the horizontal axis, the durability is improved from 62 hours to 75 hours. This demonstrates that the present invention can not only predict the location of tire bead failure but also provide guidance for tire design improvements.

[0046] The above technical solutions enable the identification of the neutral axis position of the bending deformation at the tire bead, providing guidance for tire design and durability improvement.

[0047] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for identifying the position of the neutral axis of bending deformation at the tire bead, characterized in that: Includes the following steps: Step 1: Establish a finite element model of the tire, divide the rubber material into several rubber material elements, perform load simulation analysis on the tire, and output the principal strain of each rubber material element. Step 2: Calculate the volumetric strain of each rubber material unit; Step 3: Calculate the volumetric strain divergence of each rubber material element; Step 4: Graphically display the volumetric strain divergence of the tire model's ground contact section, find the smooth boundary line of the region with a value of 0, and determine the position of the bending neutral axis at the tire bead.

2. The method for identifying the neutral axis position of bending deformation at the tire bead according to claim 1, characterized in that: In step one, the principal strains of each rubber material unit are denoted as LEP1, LEP2, and LEP3.

3. The method for identifying the neutral axis position of bending deformation at the tire bead according to claim 2, characterized in that: In step two, the formula for calculating the volumetric strain of each rubber material unit is: Where i is the number of each rubber material unit.

4. The method for identifying the neutral axis position of bending deformation at the tire bead according to claim 3, characterized in that: The formula for calculating volumetric strain divergence is: Where x, y, z are the Cartesian coordinate axes of the tire model space.

5. The method for identifying the neutral axis position of bending deformation at the tire bead according to claim 1, characterized in that: The rubber material unit is triangular or quadrilateral in shape.

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