A method and system for precise modeling of tire belt based on dual-curvature driving and edge compensation

Abstract

This invention relates to the field of tire structure simulation design technology, and particularly to a method and system for accurate modeling of tire belt layers based on dual curvature drive and edge compensation. The method first establishes a finite element model of the tire and extracts the local radii at each axial position of the belt layer. Then, it calculates the radial elongation and axial elongation, calculates the finished belt angle distribution and belt spacing distribution based on the dual rates, and introduces an edge compensation term related to the axial position. Finally, the obtained parameters are written into the finite element model for inflation and ground contact simulation. This invention can more accurately reflect the continuous deformation of the belt layer caused by the manufacturing process, significantly improving the prediction accuracy of tire profile and ground contact shape.

Description

Technical Field

[0001] This invention relates to the field of tire structure simulation design technology, and in particular to a method and system for accurate modeling of tire belt layers based on dual curvature drive and edge compensation. Background Technology

[0002] The belt layer of a semi-steel radial tire is one of the key reinforcing structures that determines the tire's inflation profile, contact patch shape, high-speed stability, handling performance, and durability. During tire product development, the belt layer angle, belt spacing, and their distribution along the tread width directly affect the tire crown stiffness distribution, shoulder stress concentration, contact patch pressure uniformity, and profile forming accuracy. Therefore, accurately describing the true geometric state of the belt layer in the finished tire has always been a core technical issue affecting the reliability of simulation results in tire finite element analysis and structural optimization design. Although the finite element method has been widely adopted in existing tire design processes, the modeling methods for belt layer parameters still generally suffer from oversimplification, insufficient process response, and distortion of the shoulder region description, leading to a long-standing systematic deviation between simulation predictions and actual prototype tire test results.

[0003] From the perspective of tire manufacturing mechanisms, the belt layer does not maintain its original geometric state as a semi-finished product in the finished tire. The belt layer is typically first bonded to the forming drum with a predetermined cut angle and initial spacing. Then, through multiple manufacturing stages such as carcass forming, belt wrapping, tread bonding, inflation shaping, and vulcanization, the belt layer undergoes complex geometric reconstruction in space. Especially during the transformation from a planar or near-cylindrical surface to the curved surface of the finished tire crown, the belt layer cords experience non-uniform deformation due to factors such as local radius changes, axial contraction or expansion, and differences in process loading in the shoulder area. The final finished belt angle and belt spacing often differ significantly from the cut angle and design pitch of the semi-finished product, and this difference is not a simple constant but varies continuously along the belt width direction. The variation patterns between the crown center area and the shoulder transition area are usually significantly different, and this is precisely the part most easily overlooked by existing modeling techniques.

[0004] In existing technologies, some literature has begun to focus on the determination of belt layer angles. For example, Chinese patent CN110455555A discloses a method for determining the layup angle of a tire belt layer. Its technical approach mainly involves scanning the tire's outer contour, mapping the belt layer outline, obtaining the steel wire distribution, and then combining the elongation rate and steel wire spacing to infer the layup angle distribution. This document demonstrates that the belt layer angle in a finished tire does indeed change relative to the initial design state, and also shows that the belt layer angle distribution has practical engineering value for measurement and analysis. Furthermore, this document has revealed from a testing perspective that the true angle of the belt layer is not a fixed constant, but is related to the spatial position of the tire after molding. However, the core focus of CN110455555A remains on measurement rather than modeling. Its technical solution mainly relies on scanning, mapping, and statistical analysis of the finished tire contour and belt layer contour, requiring the actual distribution information of the belt layer steel wires before the layup angle can be further calculated. In other words, this approach is essentially closer to a post-hoc detection or measurement method than a modeling method that can directly predict the distribution of belt layer parameters at the simulation front end. For tire development companies, obtaining accurate belt layer distribution data across a large number of product designs still requires cutting, scanning, or other precise measurement operations on finished tires. This is costly, cumbersome, and unsuitable for frequent use in the early iteration stages of design. Especially when tire specifications, materials, crown structures, or molding processes change frequently, relying solely on measurement methods cannot meet the needs of rapid development. More importantly, while this type of method can output belt angles or distribution results at certain locations, it does not establish a continuous predictive relationship that can be directly coupled with the finite element model. Therefore, it cannot directly solve the fundamental problem of how to accurately define the model input parameters in tire finite element analysis.

[0005] On the other hand, in the field of tire simulation modeling, Chinese patent CN107103119B discloses an automated modeling method for tire finite element analysis. This patent focuses on identifying, naming, meshing, quality checking, and establishing contact surfaces of the tire cross-section rubber and cord regions, starting from the tire material distribution map, ultimately achieving automated generation of the tire finite element model. This technology is significant for shortening tire finite element preprocessing time, lowering the modeling threshold, and improving R&D efficiency, indicating that automated tire finite element model creation has become an important development direction in the industry. However, CN107103119B mainly addresses the problem of how to quickly establish finite element models, without deeply solving the problem of how to accurately assign values ​​to the belt layer parameters. While its automated modeling can improve modeling efficiency, the model accuracy still depends on whether the input parameters themselves are realistic and reasonable. For the belt layer, if the traditional method of assigning only fixed layup angles and fixed spacing is still used, or if only a simple segmented assignment method is used in the finite element preprocessing, then even with high automated modeling efficiency, only a quickly established but inaccurate simulation model can be obtained. Especially in the tire shoulder area, due to the influence of factors such as molding, bulging, and process rolling, the local angle increase and cord dispersion of the belt layer are often more pronounced. However, traditional automated modeling methods do not provide a parameter generation mechanism that can reflect this non-uniform width-direction deformation. Therefore, there is still a significant disconnect between existing automated modeling methods and actual manufacturing processes, resulting in discrepancies between simulation results and measured results for tire inflation profiles, ground contact marks, and local stiffness distribution.

[0006] In engineering practice, existing tire finite element software or conventional simulation processes typically suffer from the following shortcomings in handling the finished state of the belt layer: First, the belt layer angle is simplified to a constant, assuming that the belt angle at any axial position of the finished tire is consistent with the layup angle of the semi-finished product, ignoring the belt direction deflection caused by local radius changes during manufacturing. Second, the geometric changes of the belt layer are estimated through empirical formulas or software-built-in approximate equations. However, these methods are usually based on strong assumptions of uniform deformation, only roughly describing the average trend after overall bulging, and failing to characterize the continuous gradient changes from the center of the tire crown to the edge of the tire shoulder. Third, the belt parameters are assigned piecewise constant values ​​according to several width segments. While seemingly considering regional differences, this actually introduces unrealistic abrupt changes at the boundaries of adjacent segments, thus affecting the accuracy of local stress, strain, and ground pressure distribution. Fourth, parameters are obtained by relying on cutting sections, X-rays, or other a posteriori methods, and then manually written back into the model. This is not only labor-intensive but also detrimental to forming a unified and repeatable algorithm process.

[0007] It is particularly noteworthy that the tire shoulder region and the belt center region exhibit completely different process response characteristics. During tire manufacturing, the tire shoulder region is typically more significantly affected by local bending, folding, outward expansion, and related process loading, resulting in greater angular deflection and more pronounced spacing of the belt layer cords. Using only the overall average radius, single elongation rate, or uniform expansion assumptions often only provides an acceptable approximation for the center region, while introducing significant errors for the tire shoulder region. Since the tire shoulder region is precisely the key area affecting tire contact shoulder width, contact edge shape, local wear characteristics, and durability and safety, existing methods distort its description of this region, further amplifying the discrepancy between whole-tire simulation and actual measurements. In other words, the fundamental deficiency of existing technology is not merely insufficient accuracy, but rather the lack of a unified modeling framework capable of simultaneously characterizing local radial deformation, axial deformation, and edge process compensation effects.

[0008] Furthermore, as tire companies' R&D models gradually shift from prototyping-testing-modification to simulation-driven and experimental verification, modeling methods no longer merely serve the function of geometric representation but require stronger process mapping and predictive capabilities. Especially in the rapid iterative development of new tire specifications, new tread patterns, and multiple solutions, if the actual angle and spacing distribution of the finished tire's belt layers cannot be accurately predicted during the finite element preprocessing stage, even with a complete subsequent analysis process, it will be difficult to provide a sufficiently reliable input basis for inflation profiles, ground contact marks, ground pressure, and even durability performance. Currently, no existing technology provides a precise modeling scheme that addresses tire manufacturing process deformation, allows direct embedding of finite element parameter definitions, and can continuously output belt angle and spacing distribution along the belt width direction.

[0009] Therefore, existing technologies still face the following pressing technical challenges: First, there is a lack of a continuous prediction model that effectively correlates the state of the formed drum with the state of the finished tire; second, there is a lack of a parameter solution mechanism that can simultaneously reflect the combined effects of radial elongation and axial deformation of the belt layer; third, there is a lack of a compensatory description method for the dispersion and increased angle of the cords in the shoulder edge region; and fourth, there is a lack of an engineering implementation path that can directly incorporate the predicted belt angle and belt spacing distribution into the finite element model for analysis of inflation, grounding, and other operating conditions. Against this backdrop, developing a new method based on the deformation mechanism of the manufacturing process, capable of continuously and accurately calculating the belt layer angle and spacing of semi-steel radial tires, and adapted to the finite element modeling process, has become a crucial technical issue urgently needing to be addressed in this field. Summary of the Invention

[0010] The technical objective of this invention is to address the common problems in existing semi-steel radial tire belt layer modeling processes, such as neglecting manufacturing process deformation, difficulty in accurately describing the continuous changes in belt angle and spacing in the tire shoulder area, and the resulting insufficient simulation accuracy of inflation profile and ground contact shape. This invention proposes a precise belt layer modeling method based on dual curvature driving and edge compensation to achieve continuous and accurate prediction of the angle and spacing distribution of the finished tire belt layer. The prediction results are then directly used for finite element model parameter definition, thereby improving the accuracy and development efficiency of tire structure design and performance simulation.

[0011] Firstly, in order to achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0012] A method for accurate modeling of tire belt layers based on dual curvature drive and edge compensation includes the following steps: S1. Establish an axisymmetric finite element model of the tire to be analyzed. The belt layer is characterized by skeleton reinforcement unit or equivalent reinforcement definition. Determine the belt drum radius, semi-finished belt laying angle, initial spacing of semi-finished belt, total width of semi-finished belt, total width of finished belt, angle correction coefficient and spacing correction coefficient. S2. Read the node coordinate information of the belt skeleton unit and calculate the axial position and local radius of the midpoint of each belt skeleton unit. S3. Based on the radius of the belt drum, the total width of the finished belt, the total width of the semi-finished belt, and the local radius, determine the radial elongation, axial elongation, and normalized axial position at each axial position respectively. S4. The combined correction result of radial elongation and axial elongation on the semi-finished product belt layup angle is used as the base angle, and an edge angle compensation amount that increases with the normalized axial position is added to the base angle to obtain the belt angle distribution. S5. The initial spacing of the semi-finished belt bundle, after being corrected by the axial elongation and angular change, is used as the base spacing. The base spacing is then corrected by the edge spacing compensation factor that increases with the normalized axial position to obtain the belt bundle spacing distribution. S6. Write the belt angle distribution and belt spacing distribution into the belt layer reinforcement definition of the finite element model, and perform inflation analysis or load grounding analysis to obtain the predicted results of tire inflation profile or grounding shape.

[0013] As a further improvement, in step S2, the local radius is obtained by reading the coordinates of the adjacent nodes of the belt frame unit and calculating the distance from the geometric midpoint of the belt frame unit to the tire rotation axis.

[0014] And / or, in step S3, the radial elongation is determined by the ratio of the local radius to the belt drum radius; the axial elongation is determined by the belt drum radius, the total width of the finished belt, the local radius, and the total width of the semi-finished belt; the normalized axial position is determined by the dimensionless positional relationship of the axial position relative to the total width of the finished belt.

[0015] As a further improvement, in step S4, the belt angle distribution is based on the combined driving result of radial elongation and axial elongation on the semi-finished belt layup angle, and a secondary edge compensation term related to the normalized axial position is added to the basic angle; the angle correction coefficient is taken as 0.5 to 2.0, which is used to adjust the increase in the belt angle in the tire shoulder area relative to the center area.

[0016] As a further improvement, in step S5, the belt spacing distribution is based on the spacing variation result determined by the initial spacing of the semi-finished belt, axial elongation, belt angle distribution, and semi-finished belt laying angle, and multiplied by a fourth-order edge compensation factor related to the normalized axial position; the spacing correction coefficient is taken as 0.05 to 0.20, and is used to adjust the dispersion of the belt spacing in the tire shoulder area relative to the central area.

[0017] As a further improvement, step S4 uses an additive quadratic edge compensation term to characterize the gradual edge increase effect of the belt angle, and step S5 uses a multiplicative quartic edge compensation factor to characterize the rapid dispersion effect of the belt spacing in the edge region, so that the belt angle distribution and belt spacing distribution change gently in the belt center region and change more strongly in the tire shoulder region.

[0018] As a further improvement, in step S6, the belt angle distribution and belt spacing distribution are written into the reinforcement direction parameters and reinforcement arrangement parameters of the finite element calculation file element by element, so that the belt layer forms a continuous gradient definition in the axial width direction; the inflation analysis includes tire internal pressure conditions, the load grounding analysis includes vertical load conditions, and the prediction results include at least the coordinate difference of key points on the tire outer contour, the grounding long axis parameter, and the shoulder width parameter.

[0019] As a further improvement, the method is applicable to semi-steel radial tires, and the belt layer parameter prediction results are used to correct the belt angle and belt spacing distribution in the tire shoulder area of ​​the finite element model, so as to improve the prediction accuracy of inflation profile and grounding mark; the tire shoulder area is the area close to the belt edge along the belt width direction.

[0020] Secondly, the present invention also provides a tire finite element simulation system, which is used to implement the method, including:

[0021] The modeling input module is used to input tire specifications, belt drum radius, semi-finished belt laying angle, initial spacing of semi-finished belt, total width of semi-finished belt, total width of finished belt, angle correction factor, and spacing correction factor.

[0022] The finite element model generation module is used to establish an axisymmetric finite element model of the tire to be analyzed, and to characterize the belt layer by defining skeleton reinforcement elements or equivalent reinforcement.

[0023] The local geometry extraction module is used to read the node coordinate information of the belt skeleton element and to calculate the axial position and local radius of the midpoint of each belt skeleton element.

[0024] The dual-rate calculation module is used to determine the radial elongation, axial elongation, and normalized axial position at each axial position.

[0025] Angle prediction module, used to obtain the belt angle distribution of the finished tire;

[0026] The belt spacing prediction module is used to obtain the belt spacing distribution of the finished tire;

[0027] The parameter write-back module is used to write the belt angle distribution and belt spacing distribution into the belt layer enhancement definition of the finite element model;

[0028] The working condition solution and result evaluation module is used to perform inflation analysis or load grounding analysis and output the predicted results of tire inflation profile or grounding shape.

[0029] Thirdly, the present invention also provides an electronic device, including a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the method described above.

[0030] Fourthly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described thereon.

[0031] This invention establishes a hyperbolic driving model based on the local radius variation of the belt layer and introduces an edge compensation mechanism in the belt width direction to address the non-uniform process deformation in the tire shoulder region. This enables continuous and accurate prediction of the true distribution of belt layer angles and cord spacing in the finished tire, significantly improving the modeling distortion problems caused by traditional fixed angle, fixed spacing, or segmented empirical assignment methods. The belt layer parameters obtained based on this method can more realistically reflect the geometric evolution caused by molding, inflation shaping, and local process effects in the tire shoulder region during manufacturing, and can especially effectively improve the increase in belt angle and cord spacing in the tire shoulder region. The invention improves the accuracy of distance dispersion prediction, thereby making the finite element model more closely resemble the measured results in terms of inflation profile, key point dimensions, ground contact major axis, shoulder width, and ground contact imprint edge shape. At the same time, the invention directly writes the calculated results of the belt layer parameters into the finite element model, reducing the reliance on cumbersome measurement methods such as cutting analysis and X-ray scanning, shortening the tire structure parameter verification and simulation correction cycle, and improving the modeling efficiency, simulation reliability, and scheme iteration speed in the tire design and development stage. Therefore, it has significant engineering application value for the refined design, performance prediction, and rapid development of semi-steel radial tires. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the axisymmetric finite element model and direction markings of a 255 / 45ZR20 semi-steel radial tire in an embodiment of the present invention.

[0033] Figure 2 This is a schematic diagram comparing the conventional method and the method of this invention with the X-ray scan of the inflation profile.

[0034] Figure 3 A magnified view of a key point A in the middle.

[0035] Figure 4 A magnified view of key point B in the middle.

[0036] Figure 5 A magnified view of the key point C.

[0037] Figure 6 This is a schematic diagram of the measured grounding pressure shape.

[0038] Figure 7 This is a schematic diagram of the grounding shape calculated using traditional methods.

[0039] Figure 8 This is a schematic diagram of the grounding shape calculated using the method of the present invention. Detailed Implementation

[0040] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the protection scope of the present invention.

[0041] This invention proposes an accurate modeling method for the belt layer of semi-steel radial tires based on bicurvature driving and edge compensation. The core of this method is not to simply assign a fixed angle or fixed spacing to the belt layer, but to take the local geometric state of the finished tire belt layer at different axial positions as the starting point for modeling. The radial elongation and axial elongation driven by the local radius are used to describe the geometric evolution of the belt layer. Then, combined with the edge compensation term that changes with the belt width position, the angle distribution and spacing distribution of the finished tire belt layer are continuously predicted. The continuous distribution results are written into the finite element model element by element so as to further perform inflation analysis and load grounding analysis.

[0042] Traditional finite element preprocessing typically treats the belt layer as a reinforcement layer with constant parameters along the width direction, or assigns constant angles and constant spacing only to a few zones. While this approach can provide a rough approximation of the central region of the tire crown, it significantly deviates from the actual belt layer state of the finished tire in the shoulder and shoulder transition areas. Especially after the tire undergoes molding drum bonding, crown wrapping, inflation shaping, and vulcanization processes, the belt layer cords undergo non-uniform changes related to local curvature and process effects: the changes are relatively gradual in the central region of the crown, while the shoulder region often exhibits increased belt angles and more pronounced spacing dispersion. Because of this continuous non-uniform change along the width direction, this invention does not employ piecewise constant processing but instead establishes a continuously distributed model to improve the input realism of tire simulation.

[0043] For ease of explanation, the following detailed description uses the 255 / 45ZR20 semi-steel radial tire as an example. However, the present invention is not limited to this tire specification, but is also applicable to other semi-steel radial passenger car tires, SUV tires, or tire products with similar belt ply structures.

[0044] I. Terminology Explanation

[0045] To make the technical solution of this application clearer and more explicit, the main terms appearing in the specification are explained below.

[0046] Semi-finished belt layer: refers to the belt layer state after it has been cut and bonded on the molding drum but has not yet undergone molding drum expansion, tire molding and vulcanization. Its geometric parameters can be directly given by design drawings, cutting process or semi-finished product process parameters.

[0047] Finished belt layer: refers to the belt layer inside the final finished tire after the tire has been formed, inflated and vulcanized. Its angle and spacing are usually different from those of the semi-finished product.

[0048] Belt angle: refers to the angle between the belt layer cords at a certain local position and the tire circumference, denoted as in this article. The layup angle of the belt in the semi-finished state is denoted as . .

[0049] Belt spacing: refers to the center-to-center distance between adjacent cords in the same belt layer, denoted as [insert value here] in the finished product state in this article. In the semi-finished state, it is recorded as .

[0050] Local radius: refers to the local radial distance of a certain axial position of the belt layer relative to the tire's axis of rotation, denoted as in this article. or .

[0051] Radial elongation: refers to the ratio of the local radius of the belt layer at a certain location in the finished state to the radius of the belt drum, characterizing the degree of change of that location in the radial direction relative to the drum surface state. In this paper, it is denoted as . .

[0052] Axial elongation: refers to the axial deformation characteristic calculated based on the belt drum radius, finished belt width, semi-finished belt width, and local radius. In this paper, it is denoted as... .

[0053] Edge compensation term: refers to the additional correction term related to the normalized axial position added to the angle model and spacing model to reflect the non-uniform process deformation of the tire shoulder and edge areas.

[0054] Normalized axial position: refers to the normalization of axial position Based on the total width of the finished belt The dimensionless variables are used to uniformly express the edge position effect in tires of different specifications.

[0055] Write-back per element: This refers to writing the angle and spacing values ​​corresponding to each belt skeleton element into the belt enhancement definition or related input file of the finite element model, instead of using a single average value for the entire belt layer.

[0056] II. System Structure

[0057] The method of this invention can be implemented using a tire finite element simulation system. The system, in terms of its functional structure, includes at least the following modules:

[0058] 1. Modeling Input Module

[0059] This module is used to input the basic structural and manufacturing parameters of the tire, including but not limited to: tire specifications and belt drum radius. , semi-finished belt laying angle Initial spacing of semi-finished product belt bundles Total width of semi-finished belt Total width of finished belt bundle Angle correction factor Spacing correction factor Inflation pressure under simulated working conditions and vertical load .

[0060] 2. Finite element model generation module

[0061] This module is used to build an axisymmetric tire model or a corresponding 3D model in Abaqus or other equivalent finite element platforms. The belt layer can be expressed in this module through skeleton reinforcement elements, surface reinforcement definitions, embedded reinforcement definitions, or equivalent anisotropic lamination parameters. This embodiment uses an axisymmetric finite element model, and the cord direction and spacing are characterized by skeleton reinforcement definitions in the belt layer region.

[0062] 3. Local geometry extraction module

[0063] This module is used to read the node coordinate information of the bundled skeleton element and calculate the axial coordinates corresponding to the midpoints of each element. and local radius The results of local radius extraction serve as the primary basis for subsequent dual-rate calculations.

[0064] 4. Dual-rate calculation module

[0065] This module is based on the local radius. With belt drum radius Calculate radial elongation And combined with the belt width parameter , Calculate axial elongation .

[0066] 5. Angle Prediction Module

[0067] This module calculates the finished belt angle distribution at different axial positions based on dual-rate results and edge compensation terms. .

[0068] 6. Spacing Prediction Module

[0069] This module calculates the finished belt spacing distribution at different axial positions based on dual-rate results, angular distribution, and edge sparsity compensation terms. .

[0070] 7. Parameter write-back module

[0071] This module writes the angle distribution and spacing distribution element by element into the Abaqus input file or modeling database, forming a finite element definition of the belt layer that changes continuously along the width direction.

[0072] 8. Working Condition Solution and Result Evaluation Module

[0073] After the model parameters are updated, this module performs inflation condition analysis and load grounding condition analysis on the tire, and outputs results such as inflation profile, key point difference, grounding major axis, shoulder width and grounding edge shape, which are used to compare and verify with the measured data.

[0074] The above modules can be integrated into a single software system, or they can be implemented collaboratively by a Python script and the Abaqus solver. For those skilled in the art, using Python to read model data, execute formula calculations, and write back the input file is a mature and feasible engineering approach.

[0075] III. Specific Technical Route for Implementing the Method of the Invention

[0076] The specific technical approach of this invention can be summarized as follows: First, establish an axisymmetric finite element model of the tire; then, read the local radius of the midpoint of the belt layer skeleton unit to form a local radius data series reflecting the geometric state of the finished product; calculate the two driving quantities, radial elongation and axial elongation, based on the local radius; then, obtain the belt angle distribution and belt spacing distribution based on the hyperbolic driving model; subsequently, write the obtained continuous parameter distribution back into the belt layer reinforcement definition element by element; finally, solve the problem under inflation and load conditions, and evaluate the model accuracy by comparing it with the X-ray scan profile and the measured grounding imprint.

[0077] The following section will provide a detailed explanation of steps S1 to S6 in sequence.

[0078] (a) Step S1: Establish the axisymmetric finite element model of the tire and determine the basic process parameters

[0079] Step S1 serves as the input foundation for the entire method. Its purpose is to establish a finite element model environment capable of accurately assigning subsequent belt layer parameters and to clarify the geometric and process parameters required for subsequent calculations.

[0080] In this embodiment, a 255 / 45ZR20 semi-steel radial tire is used as the object, and its axisymmetric finite element model is established in Abaqus, as follows: Figure 1As shown, the model includes at least the main structural regions such as tread rubber, belt layer, carcass ply, sidewall rubber, bead filler, and steel wire bead. In the model, the rubber region can be discretized using axisymmetric continuum elements, while the belt layer is represented by surface reinforcement definitions or equivalent skeleton reinforcement elements that can express the reinforcement direction. To facilitate subsequent positional assignment, this embodiment retains axially continuously distributed skeleton reinforcement elements at the belt layer, so that each axial position can correspond to one or a set of independent parameter definition objects.

[0081] When building the model, the coordinate orientation must first be unified. In this embodiment, Figure 1 In The direction is defined as the radial direction. The direction is defined as the axial direction, and the tire's rotation axis lies on the axis of symmetry of the axisymmetric model. For each belt skeleton element, its local geometric position can be mapped to this global coordinate system through nodal coordinates. Therefore, in subsequent steps, the so-called axial position... Essentially, it refers to the position of the midpoint of the bundled skeleton element in the global coordinate system. Coordinate values; so-called local radius Then it can be determined from the midpoint of the belt skeleton unit at... The distance relative to the axis of rotation in the direction is obtained.

[0082] After the model is established, the basic process parameters in the method of this invention need to be determined. For this embodiment, the parameters are as follows: belt drum radius. ; semi-finished belt laying angle Initial spacing of semi-finished product belts Total width of semi-finished belt Total width of finished belt bundle Angle correction factor Spacing correction factor .

[0083] In traditional technologies, this step often results in a fixed angle and pitch being assigned to the entire belt layer. However, this invention argues that the above approach does not truly utilize the information provided by the geometry of the finished tire. Therefore, it is necessary to further analyze the local geometric changes of the belt layer along the width direction in the finished tire state as a basis for continuous prediction of angles and pitch.

[0084] (ii) Step S2: Extract the local radius and axial position of the midpoint of the belt skeleton unit.

[0085] Step S2 transforms the actual geometry of the finished tire into local parameter inputs that can be used by the algorithm. Unlike traditional methods that use the average radius of the entire layer or empirical radius, this invention directly extracts local radius information at the element level from the belt skeleton elements of the finite element model, thereby establishing subsequent angle and spacing predictions on a real geometric basis of continuous spatial distribution.

[0086] Specifically, after the Abaqus model is built, a Python program is used to access the node and unit information from the model database or input file, and the bundled layer enhancement unit number is read. The coordinates of the nodes. For any quadrilateral skeleton element, the coordinates of its four nodes can be set as follows:

[0087] ;

[0088] in, Indicates the first Unit 1 The radial coordinates of each node, Indicates the first Unit 1 The axial coordinates of each node.

[0089] The coordinates of the points in this unit can be obtained as follows:

[0090] ;

[0091] ;

[0092] in, For the first The radial coordinates of the midpoint of a bundled skeleton element For the first The axial coordinates of the midpoints of each bundled skeleton unit.

[0093] In an axisymmetric model, the radial coordinate of a point in the bundled skeleton element is the local radius at that location; therefore, the following definition applies:

[0094] ;

[0095] in, For the first The midpoint of each belted skeleton unit is located in the axial position. The corresponding local radius, .

[0096] In this way, each skeleton unit along the width direction of the belt can obtain a set of paired data. These data essentially describe the continuous variation of the finished tire belt layer profile along the axial width direction, and form the basis for constructing the hyperbolic drive model in this invention.

[0097] In this embodiment, the program extracts local radius data unit by unit from the left shoulder to the right shoulder according to the axial position, forming the discrete position sequence used in Table 1.

[0098] Table 1

[0099]

[0100] For example, the local radius changes little near the center of the tread; however, the local radius shows a significantly larger gradient with axial position near the shoulder. This phenomenon indicates that the shoulder region and the tread region have significant differences in geometric evolution, and using a single average radius or segmented empirical values ​​cannot accurately reflect these differences.

[0101] It should be noted that the reason this invention uses the local radius of the midpoint of the belt skeleton unit, rather than the radius of the tire's outer surface contour point or the average radius of the entire belt layer, is that: the outer surface contour is greatly affected by the tread blocks, grooves, and tread rubber thickness, and cannot directly represent the true local radius of the belt layer; the average radius of the entire layer would smooth out the most critical local variation features of the tire shoulder area. By directly extracting the local radius of the midpoint of the belt layer skeleton unit, both surface tread pattern interference and the loss of local information caused by overall averaging are avoided, allowing subsequent calculations to accurately point to the geometric state of the belt layer itself.

[0102] Although this step is a data extraction step from an implementation perspective, from the technical logic of this invention, it actually builds a bridge between the finite element finished product geometry, local deformation driving, and continuous parameter distribution of the belt layer. It is an important foundation that distinguishes the entire technical solution from the traditional empirical assignment method.

[0103] (III) Step S3: Calculate the radial elongation and axial elongation, and construct the normalized axial position parameters.

[0104] Step S3, the so-called dual curvature drive, refers to no longer using a single dimensional change to explain the changes in belt layer parameters. Instead, it simultaneously introduces radial elongation, which reflects radial geometric changes, and axial elongation, which reflects changes in width-direction geometric coupling. These two driving factors jointly determine the evolution of the finished belt layer angle and spacing. Compared to traditional approximate models that only consider a single bulging effect, this invention argues that the state of the belt layer after tire forming depends not only on the degree of radial lifting of a certain position from the bulge surface, but also on the local axial deformation in the width direction caused by crown contraction, shoulder unfolding, and other effects. Therefore, only the synergistic effect of deformation in both directions can reasonably reflect the true reorientation process of the belt layer cords.

[0105] 1. Calculation of radial elongation

[0106] For axial position The radial elongation of the belt skeleton unit at that location is defined as the ratio of the local radius of the finished product at that location to the radius of the belt drum:

[0107] ;

[0108] in: Indicates axial position Radial elongation at the location; Indicates the first Local radius of the midpoint of a bundled skeleton unit; Indicates the radius of the belt drum.

[0109] This formula reflects the dimensional change of the finished belt layer in the radial direction relative to the semi-finished product's drum-attached state. When When the value is high, it indicates that the location has undergone radial outward geometric expansion relative to the tread surface; the larger the value, the more significant the radial change after the surface unfolds. This is typically seen in the tread plateau region. The changes are relatively small; however, in the shoulder transition area, the changes are more pronounced due to the stronger contour bending and forming effect of the process.

[0110] 2. Calculation of axial elongation

[0111] Unlike traditional methods, this invention does not simply equate the influence in the width direction to an empirical reduction factor, but instead constructs the following axial elongation:

[0112] ;

[0113] in: Indicates axial position Axial elongation at the location; Indicates the radius of the belt drum; Indicates the total width of the finished belt layer; Indicates axial position The local radius at that location; This indicates the total width of the semi-finished product's belt layer.

[0114] The physical meaning of this formula is: when the belt layer transitions from the drum-shaped state to the finished product state, if the local radius changes, while the overall belt width changes from... Change to Therefore, the axial geometry at different locations is no longer a simple linear scaling, but needs to be considered in conjunction with the local radius. By constructing the above form, the overall width variation and the local radius variation can be unified into an axial characterization quantity, making it a dual-rate model together with the radial elongation.

[0115] For those skilled in the art, this can be understood as follows: In a semi-finished state, the cords on the belt layer have a predetermined spatial orientation and spacing. When the tire changes from a drum state to a finished product state, the local curved surface to which the cords are attached changes, and the cord orientation is readjusted due to in-plane geometry. If only the increase in local radius is considered while ignoring the redistribution of the width direction, only a rough directional projection can be obtained. However, by introducing axial elongation, the changes in the local curved surface in two principal directions are simultaneously introduced, making it more suitable for describing the synchronous evolution of cord orientation and cord density.

[0116] 3. Construction of normalized axial position parameters

[0117] Since the belt width varies across different tire specifications, this invention also introduces a normalized axial position parameter to ensure that the edge compensation term maintains a consistent mathematical expression across different specifications:

[0118] ;

[0119] in: Indicates axial position Normalized position parameters; Indicates axial position; This indicates the total width of the finished belt layer.

[0120] when When approaching the center of the belt, The absolute value is small; when When approaching the edge of the belt, The absolute value gradually increases. Through the use of... This allows us to directly incorporate the engineering principle that the edge effect becomes more pronounced the farther away from the center into subsequent models.

[0121] The technical value of this step lies not only in providing two formulas, but more importantly, in establishing a new modeling approach: the parameters of the finished belt layer are no longer driven by a single empirical quantity, but rather by two rates derived from the local geometric extraction results. This approach directly addresses the problem of traditional methods neglecting non-uniform deformation in the width direction.

[0122] In the actual program implementation, the Python script will perform the above calculations cyclically for each bundled skeleton unit, resulting in a column that corresponds one-to-one with the axial position. , and These data are then fed into the angle prediction module and the spacing prediction module. Since the axial positions of each element are continuously distributed, the final calculated angles and spacings naturally exhibit a continuous distribution, rather than an artificially divided piecewise constant.

[0123] (iv) Step S4: Calculate the angle distribution of the finished belt and introduce a secondary edge compensation term.

[0124] The task of step S4 is to calculate the angular distribution of the belt layer of the finished tire at different axial positions based on the dual-rate results, and to specifically correct the belt angle increase effect in the tire shoulder area through an edge compensation term. Compared with the traditional fixed angle assignment method and simple segmentation method, this invention forms a composite prediction model of basic geometric transformation + edge non-uniform compensation in this step, which can more accurately reflect the continuous change of the belt angle along the width direction after the molding process.

[0125] 1. Finished product belt angle distribution model

[0126] This invention uses the following formula to calculate the angle distribution of the finished belt bundle:

[0127] ;

[0128] in: Indicates the axial position of the finished tire The belt angle at the location; Indicates axial position Axial elongation at the location; Indicates axial position Radial elongation at the location; Indicates the angle at which the semi-finished product belt is laid; Indicates the angle correction factor; Indicates axial position The normalized position parameters.

[0129] 2. Understanding the Formula Structure

[0130] This formula can be broken down into two parts:

[0131] The first part reflects the main terms of the fundamental geometric transformations:

[0132] ;

[0133] This part means: under the combined effects of local radius changes and axial geometric changes, the original semi-finished product laying angle... A reprojection occurs in the local coordinates of the finished product, forming a new base angle. If only this main term is retained, it is already closer to reality than the traditional fixed angle or single elongation model, because it takes into account changes in both radial and axial directions.

[0134] The second part is the edge compensation item:

[0135] ;

[0136] This term describes the tendency for increased angle in the tire shoulder edge region due to special manufacturing processes. A quadratic term is chosen instead of a linear term because, in actual manufacturing, the angle change from the belt center to the edge is usually not a linear abrupt change, but rather a gradual increase after a relatively gentle transition. The quadratic term better characterizes this pattern of small changes at the center and gradually amplified changes at the edge, while maintaining a simple functional form, facilitating engineering calculations and parameter calibration.

[0137] 3. Edge compensation item

[0138] During tire manufacturing, the shoulder region often undergoes more complex geometric reconstruction and technological processes compared to the center region. For example, during bulging and tire shape formation, the local curvature of the shoulder region changes more rapidly, and the belt layer is more prone to outward expansion. In subsequent bonding and contour stabilization, the shoulder region is further affected by the tread rubber, sidewall transition, and structural support conditions, potentially causing additional deflection of the cord direction relative to the center region. Therefore, relying solely on basic geometric parameters, while reflecting general trends, may still underestimate the increase in belt angle in the shoulder region.

[0139] This is more clearly seen in the comparison results in Table 1. In Table 1, the measured belt angle is significantly higher in the axial position near the tire shoulder than in the crown region, while the angle curve given by the traditional method shows a smaller variation and cannot follow the upward trend of the measured curve's edge. This invention, by adding secondary edge compensation in addition to the basic main term, allows the angle curve to rise further near the tire shoulder, thus getting closer to the measured results. Especially in areas where the traditional method has a large deviation, the gap between the predicted and measured values ​​of this invention is significantly reduced.

[0140] 4. Parameters Settings

[0141] In this invention, the angle correction coefficient The results can be determined based on tire type, molding characteristics, shoulder transition shape, and sample tire ratio. In this embodiment, This parameter is not an arbitrarily added free quantity, but rather an engineering parameter used to characterize the degree of additional angular offset of the shoulder area relative to the center area. Generally, the more significant the shoulder process effect and the more pronounced the increase in edge angle, the more appropriate it is to select a larger value. .

[0142] For those skilled in the art, The determination can be made in the following way: First, select a number of prototype tires and obtain some measured values ​​of the belt angle; then, fix the dual-rate principal terms and select a suitable one through least squares fitting or the principle of minimum error. This parameter is then used in modeling tires of the same type or series. This ensures both physical plausibility and engineering repeatability.

[0143] 5. Program implementation for this step

[0144] In the actual implementation, the Python program performs the following process for each bundled skeleton unit:

[0145] 1) Read the corresponding unit , and ;

[0146] 2) Lay the semi-finished products at the corner Convert to radians;

[0147] 3) Substituting into the above formula, we get the result. ;

[0148] 4) Store the results in an array and establish a mapping relationship with the corresponding cell number.

[0149] Received The sequence is continuous and can be directly used to define the reinforcement direction of the belt layer in the finite element model. Since each element has a different angle value, the angular distribution of the belt layer along the entire width is no longer a single value, but a discretized result of a function that changes continuously with the axial position.

[0150] 6. Technical effects of this step

[0151] The direct effect of this step is a significant improvement in the accuracy of belt angle prediction. Based on the results shown in Table 1, in the crown region, both the method of this invention and the traditional method can provide relatively close predictions; however, in the edge region near the shoulder, the deviation between the predicted and measured values ​​of the traditional method increases significantly, while the method of this invention significantly reduces this deviation through secondary edge compensation. Therefore, this step not only improves the overall angle distribution fitting but also effectively addresses the most challenging problem of distortion in the shoulder region.

[0152] (v) Step S5: Calculate the finished belt spacing distribution and introduce a fourth-order edge compensation term.

[0153] Step S5 primarily addresses the issue of how the distance between the cords changes. In actual manufacturing, the tire shoulder area not only exhibits an increased belt angle but also often shows a more dispersed belt spacing compared to the crown area, meaning the local cord arrangement is sparser. If the angle model is very accurate, but the spacing still uses a fixed value or simple linear scaling, the stiffness and density distribution of the belt layer in the finite element model will still be unrealistic, ultimately affecting the inflation profile, grounding marks, and local stress analysis results. Therefore, in step S5, this invention further constructs a continuous prediction model for the belt spacing.

[0154] 1. Finished product belt spacing distribution model

[0155] This invention uses the following formula to calculate the spacing distribution of the finished belt bundle:

[0156] ;

[0157] in: Indicates the axial position of the finished tire The belt spacing at the location; Indicates the initial spacing of the semi-finished product belt bundle; Indicates axial position Axial elongation at the location; Indicates axial position The angle of the finished belt at the location; Indicates the angle at which the semi-finished product belt is laid; Indicates the spacing correction factor; Indicates axial position The normalized position parameters.

[0158] 2. Physical understanding of the formula

[0159] This formula can also be divided into two parts: the principal term and the compensation term. The principal term is:

[0160] ;

[0161] in, It is the initial spacing in the semi-finished product state. Used to reflect the influence of axial geometric changes on the spacing, This indicates the change in the projection of the belt spacing due to changes in the direction of the cord. In other words, this main term embodies the idea that the final value of the belt spacing is related not only to the geometric stretching or compression in the width direction, but also to the change in the projection of the cord from its original angle. Transform into finished product perspective It is related to the projection relationship afterward.

[0162] The compensation items are:

[0163] ;

[0164] This term amplifies the cord sparsity effect in the edge region. This invention uses a quartic term in the spacing model instead of a quadratic term in the angle model because, in actual engineering, the belt spacing typically changes little in the crown region, but tends to exhibit a more pronounced accelerated dispersion trend as it approaches the shoulder edge. Using a quartic term makes the compensation in the central region almost insignificant, while rapidly enhancing it in the edge region, more closely resembling the actual sparsity phenomenon of the belt cords at the shoulder position.

[0165] 3. Spacing compensation uses a fourth-order term.

[0166] Observing the measured data in the tire shoulder area reveals that the change in belt angle is typically a relatively smooth increase, while the change in belt spacing is more likely to exhibit a magnified characteristic in the peripheral area. In other words, in most of the range from the crown to the shoulder, the spacing increase is not very drastic; however, once it enters the area adjacent to the outer side of the shoulder, the local cord dispersion trend becomes significantly stronger. Therefore, this invention uses quadratic terms in the angle model and quartic terms in the spacing model precisely to match the different spatial variation patterns of the two.

[0167] As can be seen from Table 1, the belt spacing predicted by the method of this invention is close to the measured value in the middle region, while it increases significantly with the measured curve at the tire shoulder position. In contrast, traditional methods often underestimate the edge spacing and cannot fully reflect the sparsity effect in the tire shoulder region. Therefore, the fourth edge compensation term is not arbitrarily selected, but is a directional construction based on the spatial distribution characteristics of the belt spacing.

[0168] 4. Parameters The determination

[0169] In this embodiment, the spacing correction coefficient This parameter is used to adjust the compensation level for edge sparseness. It can be determined through cross-sectional statistics, X-ray scanning-assisted measurements, or calibration with a small number of sample tires. Generally, when a certain type of tire has a steeper shoulder transition and more pronounced edge cord sparseness due to manufacturing processes, a larger compensation level should be used. Conversely, a smaller one can be used. .

[0170] In engineering applications, The appropriate method can be used to determine the belt spacing: first, fix the parameters of the angle model and the dual-rate calculation method, and collect the measured belt spacing at several typical axial positions; then, use the error minimization method to fit and obtain a suitable belt spacing. This model is then used to predict tires of the same structural series. This approach maintains the repeatability of the model while also taking into account the manufacturing differences between different tire families.

[0171] 5. Program Implementation Method

[0172] In implementation, the program first calls the value obtained in step S4. Then , , , and Substituting into the above formula, we can calculate the result unit by unit. The generated The array corresponds one-to-one with the number of the belt skeleton element, so it can be directly used to define the belt reinforcement arrangement parameters in the finite element model.

[0173] If the finite element platform uses a representation of reinforcement density per unit width or number of cords per unit area, the spacing can also be expressed first. The values ​​are converted to the corresponding reinforcement density values ​​and then written back into the model. For those skilled in the art, this is an equivalent expression conversion of the belt parameters in different finite element software, and it does not change the core idea of ​​this invention to perform accurate modeling through continuous spacing distribution.

[0174] 6. Technical effects of this step

[0175] The direct effect of this step is to make the belt layer stiffness distribution and reinforcement arrangement closer to the actual state of the finished tire. Since the belt spacing directly affects the local reinforcement density and structural stiffness, especially in the shoulder edge region, if the predicted spacing is too small, it will cause excessive local reinforcement in that area in the model, leading to a stiffer crown shoulder profile, a wider ground contact shoulder, or a distorted ground contact edge shape. Conversely, if the predicted spacing is too large, it will cause insufficient local support. The continuous spacing distribution model of this invention, especially by describing the rapid sparsification process of the shoulder region through a fourth-order edge compensation term, can significantly improve the realism of ground contact and profile simulation.

[0176] (vi) Step S6: Write the belt angle and spacing into the finite element model element by element and perform working condition simulation.

[0177] Step S6 is the implementation step of converting the aforementioned algorithm results into engineering simulation results. Without this step, the aforementioned dual-rate and edge compensation models remain at the theoretical level; only by actually incorporating the calculated angle distribution and spacing distribution into the finite element model and using it for inflation and load grounding condition analysis can the application value of this invention in tire design and development be truly realized.

[0178] 1. Parameter write-back method

[0179] In this embodiment, after completing steps S4 and S5, the Python program will obtain two sets of data corresponding to the belt skeleton unit numbers: one set is the belt angle distribution. The other group has a belt spacing distribution. Subsequently, the program modifies the bandgap enhancement definitions in the Abaqus input file one by one according to the cell number.

[0180] For the angle parameter, the reinforcement direction of each skeleton unit can be set to its corresponding... For the spacing parameter, it can be set to the corresponding cord spacing value, or converted to an equivalent reinforcement density before being written. If the finite element platform uses a local coordinate system to describe the reinforcement direction, the program can generate the corresponding local coordinate definition for each group of elements; if the platform uses the method of directly providing angle values, the angle array can be written directly. For the spacing value, if the software requires the input to be the number of cords per unit width, then it can be used. Perform the conversion.

[0181] This unit-by-unit writing method enables the parameters of the belt layer in the model to form a continuous gradient distribution along the width direction. Compared with the traditional single-value assignment of the entire layer or a small number of partition assignments, the model generated by this invention can have different local reinforcement directions and local reinforcement densities in different regions such as the center of the tire crown, the transition of the tire shoulder, and the edge of the tire shoulder, thus better conforming to the internal structure of the real tire.

[0182] 2. Inflation Calculation

[0183] After the parameters are written back, the tire inflation condition analysis is performed first. In this embodiment, the inflation pressure is set as follows:

[0184] ;

[0185] in, The inflation pressure inside the tire.

[0186] After solving the inflation condition, the outer contour of the tire is extracted and compared with the actual inflation contour obtained by X-ray scanning to obtain... Figure 2 The results are shown. Figure 2 In the diagram, the pink outline represents the measured outline, the black outline represents the simulation result of the method of this invention, and the blue outline represents the simulation result of the traditional method. Looking at the overall outline, the outer contour simulated by the method of this invention basically matches the measured outline, while the traditional method shows significant deviations in the crown plateau area, the area adjacent to the tread grooves, and the tire shoulder area.

[0187] Furthermore, such as Figures 3-5 As shown, keypoints A, B, and C were selected, and the local differences were magnified for comparison. The corresponding differences are shown in Table 2.

[0188] Key point A: The difference in traditional methods is The difference in the method of this invention is ;

[0189] Key Point B: The difference in the traditional method is The difference in the method of this invention is ;

[0190] Key point C: The difference in the traditional method is The difference in the method of this invention is .

[0191] The above comparison shows that the contour prediction error of the method of the present invention is significantly smaller than that of the traditional method at the three key locations, especially in the crown plateau and tire shoulder regions. This demonstrates that continuous and accurate modeling of the belt layer angle distribution and spacing distribution can indeed directly improve the prediction accuracy of the finished tire's outer contour.

[0192] 3. Calculation of load grounding conditions

[0193] After completing the inflation condition analysis, a vertical load is further applied to the tire, and the ground contact condition is solved. In this embodiment, the tire load is: ,in, This represents the vertical load on the tire during grounding analysis.

[0194] Under this operating condition, the measured grounding imprint, the simulated grounding shape using the traditional method, and the simulated grounding shape using the method of this invention were obtained respectively, as follows: Figures 6 to 8 As shown in the diagram. The red center line indicates the direction of the long axis of contact with the ground, and the yellow circled area highlights the area with differences in the shape of the tire shoulder edge.

[0195] Based on the comparison results shown in Table 2:

[0196] The measured major axis of the grounding is The traditional method is The deviation is The method of this invention is as follows: The deviation is ;

[0197] Actual shoulder width is The traditional method is The deviation is The method of this invention is as follows: The deviation is .

[0198] The data above shows that the method of the present invention is significantly superior to the traditional method in terms of both the long axis and shoulder width of the grounding. Furthermore, from... Figures 6 to 8 As can be seen from the grounding edge shape, the shoulder edge contour calculated by the method of this invention is closer to the measured imprint, while the traditional method shows more obvious outward expansion or edge distortion at the tire shoulder. This further proves that accurately describing the increase in belt angle and the dispersion of belt spacing in the tire shoulder region plays an important role in predicting the grounding shape.

[0199] IV. Specific Application Examples

[0200] (a) Purpose of application examples

[0201] To verify the effectiveness of the proposed method for accurate modeling of the belt layer of semi-steel radial tires based on dual curvature drive and edge compensation in predicting tire belt layer parameters and performing whole-tire finite element simulation, a 255 / 45ZR20 semi-steel radial passenger car tire was selected as the research object. Finite element models of the belt layer were established using both traditional modeling methods and the method of this invention. The simulation results obtained by the two methods were compared with the test results of the actual sample tire to examine the improvement effect of this invention in predicting belt angle, belt spacing, inflation profile, and ground contact shape.

[0202] This application example focuses on verifying the following three aspects: (1) whether the present invention can more accurately predict the continuous distribution of the angle and spacing of the belt layer along the width direction; (2) whether the present invention can improve the consistency between the inflation profile and the actual X-ray scan profile; (3) whether the present invention can improve the consistency between the tire grounding shape and the main grounding parameters and the measured results.

[0203] (II) Test subjects and test conditions

[0204] 1. Test subjects

[0205] The test tire was a 255 / 45ZR20 semi-steel radial tire. This tire has a typical belt layer structure, which is suitable for verifying the angle and spacing changes of the belt layer after tire manufacturing due to molding, bulging, and shoulder processes.

[0206] 2. Simulation Modeling Platform

[0207] The finite element modeling and solution platform used was Abaqus. Data extraction, local parameter calculation of the belt layer, and the process of writing back the belt parameters were implemented using Python.

[0208] 3. Basic parameters for experimentation and modeling

[0209] In this application example, the following basic process and structural parameters are used: belt drum radius ; semi-finished belt laying angle Initial spacing of semi-finished product belts ; width of semi-finished product belt Finished belt width Angle correction factor Edge sparsity correction coefficient .

[0210] 4. Operating conditions

[0211] Inflation conditions are set as follows: ;in, This refers to the inflation pressure inside the tire.

[0212] Grounding condition settings: ;in, This refers to the vertical load on the tire.

[0213] (III) Test Methods

[0214] 1. Finite element model establishment

[0215] First, according to Figure 1 An axisymmetric finite element model of a 255 / 45ZR20 tire was established based on the structure shown. The model includes major components such as the tread compound, belt layer, carcass layer, bead, and sidewall. The belt layer is characterized with a reinforced structure to allow for the incorporation of angle and spacing parameters at different axial positions into the finite element model in subsequent steps.

[0216] Figure 1 The tire axisymmetric model and orientation markings are shown, in which The direction is radial. The direction is axial. The belt skeleton elements are continuously arranged along the axial direction, providing a basis for subsequent extraction of local radii and assignment of values ​​to each element.

[0217] 2. Traditional Modeling Methods

[0218] In contrast, traditional methods use conventional belt layer parameter modeling, which uses a fixed belt angle and fixed belt spacing along the width direction, or uses simple empirical approximations, without considering the continuous gradient changes caused by local manufacturing process deformation in the tire shoulder area.

[0219] 3. Modeling using the method of this invention

[0220] The method of the present invention is implemented according to the following steps:

[0221] Step 1: Extract local radius

[0222] The Python program reads the node information of the belt skeleton unit and extracts the axial coordinates and local radius of the midpoints of each belt skeleton unit. Let the axial position be... Then the local radius at the corresponding position is .

[0223] Step 2: Calculate the two-rate parameters

[0224] The formula for calculating radial elongation is:

[0225] ;

[0226] in, Axial position Radial elongation at the location; The local radius; The radius of the belt drum.

[0227] The formula for calculating axial elongation is:

[0228] ;

[0229] in, Axial position Axial elongation at the location; This refers to the width of the finished belt bundle; This refers to the width of the semi-finished product belt.

[0230] Step 3: Calculate the belt angle distribution

[0231] The belt angle distribution is calculated using the following formula:

[0232] ;

[0233] in, For the finished tire in axial position The belt angle at the location; For laying angles of semi-finished product belts; This is the angle correction factor.

[0234] Step 4: Calculate the belt spacing distribution

[0235] The belt spacing distribution is calculated using the following formula:

[0236] ;

[0237] in, For the finished tire in axial position The belt spacing at the location; This represents the initial spacing of the semi-finished product belt bundle; This is the edge sparsity correction coefficient.

[0238] Step 5: Input the finite element model and solve it.

[0239] The belt angle calculated unit by unit and belt spacing The parameters are written into the Abaqus model, replacing the fixed parameter definitions in the traditional method, and then the gas filling analysis and load grounding analysis are performed respectively.

[0240] (iv) Testing methods

[0241] 1. Belt angle and spacing test

[0242] Actual tests were conducted on the finished tire sample to obtain the angle and spacing distribution of the belt layer at different positions along the axial direction. The test results were compared with the prediction results of the conventional method in Table 1 and the prediction results of this invention.

[0243] 2. Inflation contour test

[0244] For the prototype X-ray scanning was performed under inflation pressure to obtain the actual inflated outer contour of the tire. (Selection) Figure 2 The key points A, B, and C shown are used to compare the differences between the simulated contour and the measured contour.

[0245] 3. Grounding shape test

[0246] For tire inflation pressure Vertical load Grounding tests were conducted under operating conditions to collect the actual grounding pressure shape and main grounding dimensions, including the grounding long axis and shoulder width, and the results were compared with the simulation results of traditional methods and the method of this invention.

[0247] (V) Experimental Results and Data Analysis

[0248] 1. Prediction effect of belt angle and spacing distribution

[0249] As shown in Table 1, there are significant differences in the distribution trends of belt angle and belt spacing between the traditional method, the method of this invention, and the actual test values. The traditional method can approximate the trend in the central region of the belt, but the deviation increases significantly in the shoulder region, and it cannot accurately describe the edge increase effect of the belt angle and the edge dispersion effect of the belt spacing.

[0250] In comparison, the belt angle and belt spacing curves predicted by the method of this invention are highly close to the measured values, especially in the tire shoulder region where the traditional method has the largest error, the method of this invention significantly improves the fitting of the changing trend. According to the test analysis results: in the tire shoulder region, the maximum deviation of the belt angle of the traditional method is greater than 4°; the maximum deviation of the belt angle of the method of this invention in the tire shoulder region can be reduced to less than 1°.

[0251] Meanwhile, the maximum deviation of the belt spacing in the traditional method is greater than 0.3 mm; the maximum deviation of the belt spacing in the method of the present invention can be reduced to less than 0.1 mm.

[0252] This result demonstrates that the present invention, through a continuous prediction model driven by double curvature and compensated by edge, can effectively describe the nonlinear variation of the belt layer in the tire shoulder region caused by the manufacturing process, and significantly improve the prediction accuracy of the local structural parameters of the belt layer.

[0253] 2. Inflation profile prediction effect

[0254] Inflation pressure Under the conditions described above, tires were simulated using both traditional methods and the method of this invention, and the results were compared with the actual inflation profile obtained from X-ray scanning. The results are as follows: Figure 2 As shown in Table 2.

[0255] Table 2 Comparison of key point differences between traditional methods and the method of this invention with X-ray scan contours.

[0256]

[0257] As can be seen from Table 2, the method of the present invention is significantly superior to the traditional method in three key aspects.

[0258] 1. Key Point A

[0259] At key point A, the difference between the traditional method and the measured profile is 3.8463 mm, while the difference using the method of this invention is only 0.1246 mm. The error reduction is: The error reduction rate is approximately:

[0260] ;

[0261] 2. Key Point B

[0262] At key point B, the error of the traditional method is 1.1471 mm, while the error of the method of this invention is 0.1608 mm.

[0263] The error reduction rate is approximately:

[0264] %=85.98%;

[0265] 3. Key Point C

[0266] At key point C, the error of the traditional method is 2.6522 mm, while the error of the method of this invention is 0.1535 mm.

[0267] The error reduction rate is approximately:

[0268] ;

[0269] Therefore, it is evident that the method of this invention significantly outperforms traditional methods in predicting tire inflation profiles, especially in the tire shoulder area and key profile transition points, where the improvement in prediction accuracy is even more pronounced. Combined with... Figure 2 As can be seen from the magnified images of key points, the simulated contour obtained by the method of the present invention basically coincides with the actual contour of the X-ray scan, while the traditional method shows obvious deviations in the crown and shoulder areas.

[0270] (III) Prediction effect of grounding shape

[0271] Inflation pressure Vertical load Under these conditions, a ground contact test was performed on the tires, and the results were compared with those of the two simulation methods. The results are as follows: Figure 6 , Figure 7 , Figure 8 As shown in Table 3.

[0272] Table 3 Comparison of key parameters of traditional method, method of the present invention, and measured grounding shape.

[0273]

[0274] 1. Grounding Long Axis Analysis

[0275] The measured major axis of the grounding profile is 192 mm. Traditional methods predict 218 mm, a deviation of 13.5%; the method of this invention predicts 198 mm, a deviation of 3.1%. It is evident that this invention reduces the major axis deviation from 13.5% to 3.1%, a reduction of 10.4 percentage points. This indicates that the method of this invention is closer to the actual situation in predicting the overall length of the grounding profile.

[0276] 2. Shoulder width analysis

[0277] The measured shoulder width was 150mm. Traditional methods predicted 169mm, a deviation of 12.6%; the method of this invention predicted 155mm, a deviation of 3.3%. It is evident that this invention reduces the shoulder width deviation from 12.6% to 3.3%, a reduction of 9.3 percentage points. Since shoulder width is mainly affected by the belt angle and belt spacing distribution in the tire shoulder region, this result further proves that the modeling of the tire shoulder region by this invention is more accurate.

[0278] 3. Grounding Shape Edge Profile Analysis

[0279] from Figures 6 to 8 As can be seen from the comparison, the ground contact shape obtained by the traditional method differs significantly from the actual ground contact imprint in the tire shoulder edge area, with the ground contact edge expanding outwards significantly, failing to accurately reflect the stress state of the tire shoulder; while the ground contact shape obtained by the method of this invention is more consistent with the measured imprint, especially in the yellow circled area in the figure, where the edge contour is closer to the actual test results.

[0280] This result demonstrates that the present invention not only improves the prediction accuracy of macroscopic parameters such as the major axis and shoulder width, but also improves the fitting effect of the local shape of the grounding edge, thereby making the finite element model more reliable in tire grounding performance analysis.

[0281] (vi) Technical effects

[0282] The above application examples and experimental data clearly demonstrate that, compared with traditional belt layer parameter modeling methods, this invention has the following significant technical advantages:

[0283] 1. Significantly improves the accuracy of belt layer parameter prediction

[0284] This invention can continuously predict the angular and spacing distribution of the belt layer along the width direction. Especially in the tire shoulder area, the maximum deviation of the belt angle is reduced from more than 4° to less than 1°, and the maximum deviation of the belt spacing is reduced from more than 0.3 mm to less than 0.1 mm.

[0285] 2. Significantly improves the accuracy of inflation profile prediction.

[0286] At key points A, B, and C, the contour error of the method of the present invention is reduced by approximately 96.76%, 85.98%, and 94.21% respectively compared with the traditional method, indicating that the present invention can significantly improve the prediction accuracy of the inflatable contour.

[0287] 3. Significantly improves the accuracy of grounding shape prediction.

[0288] The ground contact long axis deviation decreased from 13.5% to 3.1%, and the shoulder width deviation decreased from 12.6% to 3.3%, indicating that the present invention can significantly improve the simulation results of tire ground contact characteristic parameters.

[0289] 4. Improve the engineering usability of whole tire finite element modeling

[0290] Because this invention can more realistically reflect the geometric deformation of the belt layer caused by the manufacturing process in the finite element modeling stage, it reduces the errors caused by relying on empirical assignments in traditional methods. Therefore, it helps to reduce the number of prototype tire trials and mold repairs, and improve tire development efficiency. Based on the experimental analysis results provided by this invention, the design iteration speed can be increased by approximately 40%.

[0291] This application example demonstrates that the proposed method for accurate modeling of the belt layer of semi-steel radial tires based on dual curvature drive and edge compensation can effectively solve the problem that traditional methods cannot accurately reflect the increase in belt angle and dispersion in the tire shoulder area. By introducing local geometric deformation into the calculation of belt layer parameters and writing the prediction results into the finite element model element by element, this invention significantly improves the prediction accuracy of belt layer parameters, inflation profile, and ground contact shape, thus providing reliable technical support for the refined design, performance analysis, and rapid development of semi-steel radial tires.

[0292] The foregoing description of embodiments of the present invention, through which those skilled in the art are able to implement or use the present invention, will be readily apparent to those skilled in the art. Various modifications to these embodiments will be readily apparent to those skilled in the art. The general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novelty disclosed herein.

[0293] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0294] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0295] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0296] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0297] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0298] Memory may include non-persistent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0299] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

Claims

1. A method for accurate modeling of tire belt layers based on dual curvature drive and edge compensation, characterized in that, Includes the following steps: S1. Establish an axisymmetric finite element model of the tire to be analyzed. The belt layer is characterized by skeleton reinforcement unit or equivalent reinforcement definition. Determine the belt drum radius, semi-finished belt laying angle, initial spacing of semi-finished belt, total width of semi-finished belt, total width of finished belt, angle correction coefficient and spacing correction coefficient. S2. Read the node coordinate information of the belt skeleton unit and calculate the axial position and local radius of the midpoint of each belt skeleton unit. S3. Based on the radius of the belt drum, the total width of the finished belt, the total width of the semi-finished belt, and the local radius, determine the radial elongation, axial elongation, and normalized axial position at each axial position respectively. S4. The combined correction result of radial elongation and axial elongation on the semi-finished product belt layup angle is used as the base angle, and an edge angle compensation amount that increases with the normalized axial position is added to the base angle to obtain the belt angle distribution. S5. The initial spacing of the semi-finished belt bundle, after being corrected by the axial elongation and angular change, is used as the base spacing. The base spacing is then corrected by the edge spacing compensation factor that increases with the normalized axial position to obtain the belt bundle spacing distribution. S6. Write the belt angle distribution and belt spacing distribution into the belt layer reinforcement definition of the finite element model, and perform inflation analysis or load grounding analysis to obtain the predicted results of tire inflation profile or grounding shape.

2. The method according to claim 1, characterized in that, In step S2, the local radius is obtained by reading the coordinates of the adjacent nodes of the belt frame unit and calculating the distance from the geometric midpoint of the belt frame unit to the tire rotation axis. And / or, in step S3, the radial elongation is determined by the ratio of the local radius to the belt drum radius; the axial elongation is determined by the belt drum radius, the total width of the finished belt, the local radius, and the total width of the semi-finished belt; the normalized axial position is determined by the dimensionless positional relationship of the axial position relative to the total width of the finished belt.

3. The method according to claim 1, characterized in that, In step S4, the belt angle distribution is based on the combined driving result of radial elongation and axial elongation on the belt layup angle of the semi-finished product, and a secondary edge compensation term related to the normalized axial position is added to the basic angle; the angle correction coefficient is taken as 0.5 to 2.0, which is used to adjust the increase in belt angle in the tire shoulder area relative to the center area.

4. The method according to claim 1, characterized in that, In step S5, the belt spacing distribution is based on the spacing variation result determined by the initial spacing of the semi-finished belt, axial elongation, belt angle distribution, and semi-finished belt laying angle, and multiplied by a fourth-order edge compensation factor related to the normalized axial position; the spacing correction coefficient is taken from 0.05 to 0.20 and is used to adjust the dispersion of the belt spacing in the tire shoulder area relative to the central area.

5. The method according to claim 1, characterized in that, Step S4 uses an additive quadratic edge compensation term to characterize the gradual edge increase effect of the belt angle, and step S5 uses a multiplicative quartic edge compensation factor to characterize the rapid dispersion effect of the belt spacing in the edge region, so that the belt angle distribution and belt spacing distribution change gently in the belt center region and change more strongly in the tire shoulder region.

6. The method according to claim 1, characterized in that, In step S6, the belt angle distribution and belt spacing distribution are written element by element into the reinforcement direction parameters and reinforcement arrangement parameters of the finite element calculation file, so that the belt layer forms a continuous gradient definition in the axial width direction; the inflation analysis includes tire internal pressure conditions, the load grounding analysis includes vertical load conditions, and the prediction results include at least the coordinate difference of key points on the tire outer contour, the grounding major axis parameter, and the shoulder width parameter.

7. The method according to claim 1, characterized in that, The method is applicable to semi-steel radial tires, and the belt layer parameter prediction results are used to correct the belt angle and belt spacing distribution in the tire shoulder area of ​​the finite element model to improve the prediction accuracy of inflation profile and grounding mark; the tire shoulder area is the area close to the belt edge along the belt width direction.

8. A tire finite element simulation system, characterized in that, The system is used to implement the method according to any one of claims 1 to 7, comprising: The modeling input module is used to input tire specifications, belt drum radius, semi-finished belt laying angle, initial spacing of semi-finished belt, total width of semi-finished belt, total width of finished belt, angle correction factor, and spacing correction factor. The finite element model generation module is used to establish an axisymmetric finite element model of the tire to be analyzed, and to characterize the belt layer by defining skeleton reinforcement elements or equivalent reinforcement. The local geometry extraction module is used to read the node coordinate information of the belt skeleton element and to calculate the axial position and local radius of the midpoint of each belt skeleton element. The dual-rate calculation module is used to determine the radial elongation, axial elongation, and normalized axial position at each axial position. Angle prediction module, used to obtain the belt angle distribution of the finished tire; The belt spacing prediction module is used to obtain the belt spacing distribution of the finished tire; The parameter write-back module is used to write the belt angle distribution and belt spacing distribution into the belt layer enhancement definition of the finite element model; The working condition solution and result evaluation module is used to perform inflation analysis or load grounding analysis and output the predicted results of tire inflation profile or grounding shape.

9. An electronic device, characterized in that, The method includes a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method described in any one of claims 1 to 7.

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