A method for rapidly dividing a finite element grid of a tire tread pattern containing shoulder reverse arcs

Abstract

This invention discloses a rapid finite element mesh generation method for tread patterns with a reverse shoulder arc, comprising: axially mapping the inner and outer contour lines of the meridional plane of the tread pattern with a reverse shoulder arc; establishing layer lines within the mapped inner and outer contour lines according to the pattern structure characteristics; geometrically cleaning the tread pattern unfolded diagram to complete the two-dimensional mesh generation and grouping; axially restoring the two-dimensional mesh to a three-dimensional curved surface mesh, and axially restoring the layer lines; determining the projection direction of each node of the three-dimensional curved surface mesh, and solving the three-dimensional node coordinates in the non-reverse arc region; solving the three-dimensional node coordinates in the reverse arc region using the reverse arc equation; numbering and connecting all three-dimensional nodes to obtain the three-dimensional mesh; and circumferentially restoring the mesh to obtain a single-pitch tread pattern finite element mesh with a reverse shoulder arc that conforms to the actual shape. This invention achieves rapid finite element mesh generation for tread patterns with a reverse arc shape in the outer contour of a two-dimensional cross-section, improving mesh generation efficiency and quality.

Description

Technical Field

[0001] This invention relates to tire tread patterns, and particularly to a finite element mesh generation method for tread patterns with a reverse shoulder arc. Specifically, it relates to a method for rapidly generating finite element meshes for tread patterns with a reverse arc shape in the outer contour of a two-dimensional cross-section. Background Technology

[0002] Tires are the only part of a vehicle that comes into contact with the road surface, bearing the core functions of supporting loads, transmitting driving force, braking force, and cushioning shocks. Their performance directly affects the vehicle's safety, handling, and comfort. The tread pattern is the part of the tire that directly contacts the ground, and it has a decisive impact on braking, handling stability, noise control, hydroplaning performance, rolling resistance, and durability. The tire shoulder area, as the transition structure between the tire crown and the sidewall, bears the maximum shear stress during cornering (accounting for 35%-40% of the overall stress distribution), and is prone to stress concentration and heat accumulation due to abrupt curvature changes, making it a high-risk area for tire failure. Traditional flat tire shoulders are prone to "shoulder gap" failure under high-load conditions, resulting in the separation of the rubber and ply layers. The reverse-curve design (an inwardly concave arc profile) significantly improves heat dissipation efficiency and structural strength by increasing the arc length, with a typical curvature radius of 140-500mm. However, the geometric nonlinearity of the reverse curve greatly increases the complexity of finite element modeling, requiring high-precision meshes to capture the mechanical behavior at the abrupt curvature changes.

[0003] The complex structure of tire tread patterns, including grooves of varying shapes and depths, chamfered edges at different angles, and beveled edges, leads to challenges in efficiency and quality during 3D finite element mesh generation. Traditional fabrication methods are inefficient, requiring the creation of a 3D solid model followed by manual mesh generation in finite element preprocessing software, taking 5-8 hours per model and resulting in a high proportion of distorted elements (Jacobi matrix < 0.3). Therefore, to address these issues, the industry has developed methods to improve mesh generation efficiency and quality, such as flattening the tread cross-section through axial mapping, projecting the 2D mesh, and then restoring it to 3D space axially and circumferentially. While this avoids manual 3D modeling, it lacks automation, requiring manual intervention to correct distorted elements. Furthermore, the 2D-to-3D conversion relies on the topological relationships of discrete points, making it difficult to guarantee mesh consistency.

[0004] Chinese invention patent application CN119830646A discloses a method for generating a three-dimensional finite element mesh based on a two-dimensional mesh of a tire tread pattern development diagram. This method first maps the two-dimensional cross-section of the tread meridional plane axially, then divides the mapped cross-section into layer lines according to tread feature parameters, followed by two-dimensional mesh generation. Next, the layer lines are axially restored to obtain restored layer lines, and the two-dimensional mesh is axially restored to obtain a three-dimensional curved surface mesh. The three-dimensional curved surface mesh is then projected onto the restored layer lines along different directions to obtain a three-dimensional mesh. Finally, circumferential restoration is performed to obtain a three-dimensional mesh of the true shape of the tire tread pattern. This method effectively avoids three-dimensional modeling while solving the element distortion problem caused by excessively small curvature of the tire tread outer contour, and can efficiently generate tread pattern meshes with continuous curvature of the two-dimensional cross-section without abrupt changes (outward convexity of the tire shoulder). However, when dealing with tires that use a reverse arc structure (concave shoulder) in the shoulder area, the axial mapping process fails because the center of the discrete points of the reverse arc is located outside the outer contour, which does not satisfy the conformal mapping principle. As a result, it is impossible to generate a flattened two-dimensional cross section, which in turn affects the subsequent mesh generation operation. Furthermore, it makes it very difficult to establish the local polar coordinate system of the discrete points on the outer contour during the restoration process, making it impossible to restore the mesh axially and circumferentially to generate a three-dimensional mesh of the tread pattern with the real shape. Summary of the Invention

[0005] To address the problem that existing automatic finite element mesh generation methods for complex tread patterns cannot describe the reverse arc structure of two-dimensional cross-sections, this invention proposes a rapid finite element mesh generation method for tread patterns containing reverse arcs on the tire shoulder. By performing a novel axial mapping on the two-dimensional cross-section containing the reverse arc and using different projection methods on the two-dimensional mesh of the tread pattern unfolded diagram, a three-dimensional finite element mesh of the tread pattern is directly generated. This solves the problem of automatic generation of the reverse arc pattern model, improves the efficiency and quality of mesh generation, and makes the simulation analysis results more accurate.

[0006] The objective of this invention is achieved through the following technical solution.

[0007] A rapid finite element mesh generation method for tire tread patterns with a reverse shoulder arc includes the following steps:

[0008] S1. According to the conformal mapping principle, the inner and outer contour lines of the tread pattern meridional surface containing the shoulder reverse arc are axially mapped. The outer contour line area is mapped to a straight line except for the reverse arc, and the reverse arc is mapped to an arc, ensuring that the thickness of the two-dimensional section remains unchanged before and after the mapping.

[0009] S2. Based on the structural feature parameters in the pattern design drawing, establish layered lines within the mapped inner and outer contour lines to represent different pattern groove feature information.

[0010] S3. Extract the tread pattern development diagram from the tire structure design drawing and perform geometric cleanup. Then, divide the tread pattern development diagram into two-dimensional meshes and group the two-dimensional meshes according to the tread structure characteristics to obtain information on different components.

[0011] S4. Based on the parameters obtained in the axial mapping stage, unfold the tread pattern. Figure 2 The axial restoration of the 3D mesh yields a 3D curved surface mesh within the outer surface of the pattern obtained by stretching the original outer contour along the Z-axis in the non-reverse arc region.

[0012] S5. Calculate the discrete point set of the layer line based on the layer line information and the inner and outer contour discrete point information of the corresponding sequence number after mapping, and perform axial restoration calculation on the discrete point set to obtain the axially restored discrete point set of the layer line.

[0013] S6. For each node of the three-dimensional curved surface mesh except for the left and right boundary lines, in its meridional plane, let the node project onto the inner contour along the direction perpendicular to the outer contour and onto the inner contour along the direction perpendicular to the inner contour respectively, to obtain two feature projection points. Determine the projection direction of the node based on the distance between the two projection points.

[0014] S7. Project the 3D curved surface mesh nodes, excluding the left and right boundary lines, onto the axially restored layer and the inner surface of the tread pattern along the projection direction, and solve for the coordinates of the 3D mesh nodes of the tread pattern in the non-reverse arc region.

[0015] S8. Solve for the intersection of the inverse arc equations corresponding to the left and right boundary node sets of the three-dimensional surface mesh and the axially restored layer lines to obtain the coordinates of the three-dimensional mesh nodes of the tread pattern in the inverse arc region.

[0016] S9. Number all three-dimensional nodes, connect all nodes according to the right-hand rule to form the corresponding three-dimensional finite element mesh and establish the corresponding tread pattern features. Write the node and element information into the INP file to obtain the complete single-pitch tread pattern finite element mesh with the shoulder reverse arc.

[0017] S10. Perform circumferential restoration on the tread pattern finite element mesh to obtain a single-pitch tread pattern finite element mesh containing the shoulder reverse arc that matches the actual shape.

[0018] To further achieve the objective of this invention, preferably, in step S1, the process of axial mapping of the inner contour line and the outer contour line is as follows:

[0019] 1) Determine the number of discrete points in the non-reverse arc region based on the length of the outer contour of the non-reverse arc region in the X-axis direction, and discretize the inner and outer contour lines of the non-reverse arc region;

[0020] 2) Calculate the ratio of the X-direction span of the reverse arc region to the X-direction span of the non-reverse arc region. Multiply this ratio by five times the product of the number of discrete points in the non-reverse arc region to obtain the number of discrete points in the reverse arc region. Discretize the corresponding inner and outer contour lines of the reverse arc region.

[0021] 3) Keeping the position of the discrete point at the center of the tread unchanged, the discrete points of the outer contour of the non-reverse arc region are mapped to equidistant scattered points on a straight line according to the arc length of adjacent discrete points, so as to obtain the flattened outer contour discrete points of the non-reverse arc region.

[0022] 4) Keep the discrete points of the flattened tire shoulder unchanged, and map the discrete points of the outer contour of the reverse arc region to the discrete points of the arc line according to the relationship between the distance and angle with the discrete points of the tire shoulder.

[0023] 5) Based on the principle that the distance and angle of the corresponding discrete points of the original inner and outer contour lines remain unchanged, the inner contour is axially mapped using the mapped outer contour as the basis, so as to realize the axial mapping of the inner and outer contour lines containing the reverse arc.

[0024] Preferably, in step S2, the structural feature parameters in the pattern design drawing include the shape, axial length, width, and depth of each groove segment of the pattern, as well as the chamfer structural feature points of the pattern.

[0025] The layered lines represent the projection points of the starting and ending points of the bottom of the groove in the pattern meridian plane and the outer contour line, which are composed of multiple straight or arc segments connected end to end.

[0026] In step S3, the geometric cleanup includes:

[0027] 1) Delete the annotation lines, dimension lines, and auxiliary lines in the tread pattern unfolding diagram;

[0028] 2) Clean up the endpoint connection problems of the feature lines of the pattern outline. Ensure that the endpoints of each feature line are precisely closed by extending, trimming or connecting them, eliminating small gaps and overlaps, and ensuring the continuity and integrity of the pattern geometry; the feature lines refer to the geometric lines that define the boundary of the pattern.

[0029] When performing two-dimensional meshing on the tread pattern unfolding diagram, ensure that the mesh node density on the front and rear pitch boundary lines of a single pitch tread unit is the same and that the X-axis coordinates are consistent. This allows the three-dimensional meshes of different pitches to be arranged through shared nodes to obtain the tire circumference model. Finally, the generated two-dimensional meshes are grouped according to the shape of each groove segment, axial length, and chamfer structure feature points. Pitch is the length of a single tread unit along the circumferential direction of the tread. Pitch boundary lines refer to the front and rear boundary lines of the tread pitch unit in the positive Z-axis direction. Mesh node density is the number of mesh nodes per unit length.

[0030] Preferably, in step S4, the parameters obtained in the axial mapping stage include the center, radius, arc length, and central angle of the discrete point.

[0031] Axial restoration involves searching for the nearest discrete point on the outer contour of the flattened, non-reverse arc region to the left of each mesh node's X-coordinate as a reference point, and calculating the distance between the mesh node and the reference point. Then, using the axial mapping parameters of the discrete point with the same number as the reference point before flattening, including the center, radius, arc length, and central angle, a local coordinate system is established with the reference point and its corresponding center as the polar axis. Finally, based on the distance between the mesh node and the reference point, and the corresponding numbered central angle, the axially restored three-dimensional spatial coordinates of the node are calculated according to the principle of inverse mapping. The planar two-dimensional mesh node is then restored and fitted onto the outer surface of the tread pattern formed by stretching the original outer contour of the non-reverse arc region circumferentially along the Z-axis, generating a three-dimensional curved surface mesh for the tread pattern.

[0032] In step S5, the method for obtaining the set of discrete points of the axially restored layered line is as follows:

[0033] 1) Determine the layer line equations and layer numbers: First, count the endpoint coordinates of each arc or straight line segment. Connect the arc and straight line segments that are connected end to end in sequence. Then, use the interpolation function to fit the obtained layer line equations. Next, calculate the average Y-coordinate of all endpoints on each complete layer line. Finally, assign layer numbers according to the magnitude of the average Y-coordinate. The larger the average Y-coordinate, the closer it is to the outer contour, and the smaller the layer line number. The smaller the average Y-coordinate, the closer it is to the inner contour, and the larger the layer line number.

[0034] 2) Based on the discrete point information of the inner and outer contours within the non-reverse arc region excluding the tire shoulder after axial mapping, connect the inner contour discrete points and outer contour discrete points with the same number in pairs to construct a corresponding set of straight line equations.

[0035] 3) Solve for the intersection points of each straight line equation and the equations of each layer line to obtain the set of discrete points on each layer line;

[0036] 4) For any discrete point on the layer line, solve for the distance h between the discrete point and the corresponding numbered discrete point on the outer contour;

[0037] 5) Take a point with a distance of h along the vertical downward direction from the original outer contour discrete point with the corresponding number. This is the discrete point of the layer line after axial restoration of the corresponding number. This gives the set of all discrete points of the layer line after axial restoration.

[0038] Preferably, in step S6, the method for determining the projection direction of a node based on the distance between two projection points is as follows: For each three-dimensional curved surface mesh node except for the left and right boundary lines, projection point A is obtained by projecting along the direction perpendicular to the outer contour onto the inner contour, and projection point B is obtained by projecting along the direction perpendicular to the inner contour onto the inner contour; the distance s between the two feature projection points A and B is calculated: if the distance s is greater than a threshold, then the vector a formed by projection point B and the current node is used as the projection direction of the node; if the distance s is less than or equal to the threshold, then the vector b formed by projection point A and the current node is used as the projection direction of the node.

[0039] The threshold is calculated as follows: the discrete points of the original outer contour of the non-reverse arc region are numbered in ascending order to solve the projection points of each discrete point on the inner contour line along the direction perpendicular to the outer contour. The distance between all adjacent projection points is calculated, and half of the arithmetic mean of the distance is set as the discrimination threshold.

[0040] In step S6, the reason for excluding the mesh nodes on the left and right boundary lines of the three-dimensional curved surface mesh is that the three-dimensional mesh node sets corresponding to the nodes on the left and right boundaries are all located on the inverse arc line, so there is no need to determine the node projection direction.

[0041] Preferably, in step S7, the layered surface refers to the curved surface obtained by stretching the axially restored layered lines along the tire circumference; the inner surface of the tread pattern refers to the curved surface obtained by stretching the inner contour lines along the tire circumference.

[0042] The method for solving the 3D mesh node coordinates of the tread pattern in the non-reverse arc region is as follows:

[0043] 1) For each 3D surface mesh node except for the left and right boundary lines, take the XY plane corresponding to the Z coordinate of the node as the plane containing the original 2D section, the layer lines after axial restoration, and the projection lines;

[0044] 2) Establish the projection line equation corresponding to the node based on the node coordinates and the node projection vector determined in step S6;

[0045] 3) Intersect the projection line equation with the curve fitted to the set of discrete points of the layer line after axial restoration of each layer in turn to obtain the projection points of the grid node on different layer surfaces after axial restoration.

[0046] 4) Intersect the projection line equation with the inner contour line to obtain the projection point of the mesh node on the inner surface of the pattern.

[0047] Preferably, in step S8, the coordinates of the three-dimensional mesh nodes of the tread pattern in the reverse arc region are obtained through the following steps:

[0048] 1) For each 3D surface mesh node of the left and right boundary lines, take the XY plane corresponding to the Z coordinate of the node as the plane where the original 2D section and the layer lines of each layer are located after axial restoration;

[0049] 2) Intersect the original reverse arc with the curve formed by fitting the discrete point set of the layer line after axial restoration of each layer in turn, and obtain the projection of the grid node on different layer surfaces after axial restoration;

[0050] 3) Take the intersection of the original reverse arc and the inner contour line in the projection plane as the projection point of the grid node on the inner surface of the pattern.

[0051] Preferably, in step S9, the method for numbering all three-dimensional nodes is as follows: first, define a constant value greater than the total number of three-dimensional surface mesh nodes to avoid overlapping of projection point numbers; for each surface mesh node and its projection point, add the source node number to the product of the projection point layer number and the defined constant to obtain the number of the three-dimensional mesh node.

[0052] The right-hand rule refers to the arrangement of mesh nodes during the construction of finite element meshes. Extend your right hand with your thumb perpendicular to the other four fingers; keep your thumb still and bend the other four fingers into a semi-clenched shape; the direction of your thumb is the direction of the element normal, and the direction of the bending of your four fingers is the sorting direction of the node numbers; the right-hand rule is applicable to the construction of hexahedral elements and wedge-shaped pentahedral elements; the tread pattern features include the establishment of grooves and chamfers.

[0053] Preferably, the grooves are created by deleting corresponding grid cells during the grid construction process based on component information and preset layer number information to obtain patterned groove features;

[0054] The chamfer is established after solving the three-dimensional mesh nodes. The chamfer plane is calculated based on the component information and the preset chamfer angle. During the mesh construction process, the initial projection points are projected onto the chamfer plane to obtain the pattern chamfer feature.

[0055] Preferably, in step S10, the circumferential restoration corresponds to the transformation process of the tread pattern finite element mesh from the rectangular coordinate system to the cylindrical coordinate system in the circumferential direction.

[0056] Compared with the prior art, the present invention has the following advantages and effects:

[0057] The method of this invention can perform axial mapping on a two-dimensional cross section containing a reverse arc of the tire shoulder, and proposes a new three-dimensional mesh element node projection method. This method can solve the problem that the existing technology fails to perform axial mapping on reverse arc type pattern models and cannot automatically generate a three-dimensional mesh of the tread pattern with a real shape. It realizes the rapid generation of finite element meshes for tread patterns with reverse arc shapes in the outer contour of a two-dimensional cross section, and improves the efficiency and quality of mesh generation. Attached Figure Description

[0058] Figure 1 This is a schematic diagram illustrating the discretization process of the inner and outer contour lines of the two-dimensional cross-section of the right half of the tire tread pattern in an embodiment.

[0059] Figure 2 This is a schematic diagram showing the axial mapping of discrete points of the inner and outer contour lines of the right half of the tread pattern in an embodiment before and after the two-dimensional cross-section.

[0060] Figure 3 This is an enlarged schematic diagram of the front and rear areas of the two-dimensional cross-section of the right half of the tire tread pattern, showing the discrete points of the inner and outer contour lines axially mapped before and after the embodiment.

[0061] Figure 4 This is a schematic diagram of a two-dimensional cross-section of the tread pattern after the layer lines are established for an example.

[0062] Figure 5 The tread pattern unfolds before and after geometric cleaning, as shown in the example.

[0063] Figure 6 This is a schematic diagram of a two-dimensional grid of a single-pitch pattern after grouping in an embodiment.

[0064] Figure 7 A schematic diagram of a three-dimensional curved surface mesh obtained by axial restoration of a two-dimensional mesh in an example embodiment;

[0065] Figure 8 This is a schematic diagram showing the axial restoration of the discrete point set of the layered line before and after the implementation example.

[0066] Figure 9 This is a schematic diagram of the different projection directions of a curved mesh node that is not on the left or right boundary in its meridional plane, as shown in the example.

[0067] Figure 10 This is a schematic diagram illustrating the projection solution process of the three-dimensional mesh nodes of the tread pattern in the reverse arc region and the non-reverse arc region in an embodiment.

[0068] Figure 11 This is a schematic diagram of all three-dimensional nodes of the finite element mesh for the tire tread pattern in an embodiment.

[0069] Figure 12 This is a schematic diagram of the three-dimensional unit node connection process in an embodiment.

[0070] Figure 13 A schematic diagram of a single-pitch tread pattern with a shoulder reverse arc formed by node connection in an embodiment;

[0071] Figure 14 This is a schematic diagram illustrating the circumferential reconstruction process of the finite element mesh for the tire tread pattern in an embodiment.

[0072] Figure 15This is a schematic diagram showing the changes in the finite element mesh of the tire tread pattern before and after circumferential reconstruction, as illustrated in the example.

[0073] Figure 16 This is a schematic diagram of a single-pitch tread pattern with a reversed shoulder arc, which conforms to the actual shape after circumferential restoration, as an example. Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be systematically described below in conjunction with the accompanying drawings and specific embodiments. The embodiments below are merely representative embodiments of the technical solutions of this invention, and not all possible embodiments; any other embodiments derived from the embodiments of this invention without creative effort by those skilled in the art are within the scope of protection claimed by this invention.

[0075] Example

[0076] This embodiment uses a tread pattern of the 315 / 70R22.5 TRD06 tire as an example. This tire model is a heavy-duty radial tire, mainly used in heavy trucks and buses. Its tread pattern features a reverse-arc structure (concave shoulder) in the shoulder area. This concave design helps improve the tire's contact pressure distribution, increases tire lifespan under high load conditions, and effectively reduces stress concentration in the shoulder area. However, the geometric characteristics of this reverse-arc structure present technical challenges for traditional automatic treading methods when processing the shoulder transition area.

[0077] To address the shortcomings of existing technologies, this invention proposes a finite element mesh generation method for tread patterns with a reverse arc on the tire shoulder. By establishing a novel axial mapping mechanism, it solves the problem of automatic generation of the reverse arc model, enabling rapid generation of finite element meshes for tread patterns with reverse arc shapes in the outer contour of the two-dimensional cross-section of the tread pattern, thereby improving the efficiency and quality of mesh generation.

[0078] A rapid finite element mesh generation method for tire tread patterns with a reverse shoulder arc, comprising the following steps:

[0079] (1) Axial mapping of the inner and outer contour lines of the tread pattern with the reverse arc of the shoulder.

[0080] First, the 2D cross-section of the tire tread pattern in the XY plane is extracted using AutoCAD software. Since the tire structure is symmetrical about the centerline, only one side of the cross-section needs axial mapping. Here, the right half of the 2D cross-section is processed. In this embodiment, the right half of the 2D cross-section before axial mapping is shown below. Figure 1As shown in the upper middle section. Taking the tire's center point as the origin O, the tire's axial direction as the X-axis, and the meridional profile symmetry line as the Y-axis, the number of discrete points n1 in the non-reverse arc region is determined based on the length of the right half of the two-dimensional cross-section outer contour (excluding the reverse arc region) along the X-axis (generally n1 ≥ 30; the more points, the higher the accuracy of curve fitting after axial mapping). The X-axis coordinate range [X...] of the right half of the two-dimensional cross-section outer contour (excluding the reverse arc region) is extracted. out_min X out_max] Within this interval, n1 X coordinate values ​​are generated according to the principle of equal spacing.

[0081] Based on these X-coordinate values, corresponding discrete points are determined on the outer and inner contour lines of the non-reverse arc region, respectively. The discrete points on the inner and outer contours are then numbered in ascending order of their X-coordinate values ​​(numbered from 1 to n1, with the outer contour numbered 1). out to n1 out The inner contour is numbered 1 in to n1 in This ensures that discrete points with the same number on the inner and outer contour lines within the non-reverse arc region have the same X-coordinate value. Next, the inner and outer contour lines of the reverse arc region are discretized. First, the X-direction span (X...) of the reverse arc region is calculated. fh_max- X fh_min ) and the X-direction span of the non-reverse arc region (X out_max -X out_min The ratio of the number of discrete points in the non-reverse arc region to the number of discrete points in the reverse arc region (n1) is multiplied by five to obtain the number of discrete points in the reverse arc region (n2). Subsequently, using the same discretization method as for the inner and outer contours of the non-reverse arc region, the inner and outer contour arc segments of the reverse arc region are discretized respectively, and numbered in ascending order of X-coordinate value (numbered from n1+1 to n1+n2, where the outer contour is numbered (n1+1)). out To (n1 + n2) out The inner contour is numbered (n1+1). in To (n1 + n2) in This ensures that discrete points with the same number on the inner and outer contour lines of the reverse arc region have the same X-coordinate value. The correspondence and numbering of the discrete points on the inner and outer contours of the right half before axial mapping are as follows: Figure 1 As shown in the lower part, the number of discrete points n1 in the non-reverse arc region is 30, and the number of discrete points n2 in the reverse arc region is 6.

[0082] Subsequently, the discrete points of the outer contour of the non-reverse arc region are numbered in ascending order (1... out to n1 out The geometric method of determining a circle using three points is employed to sequentially flatten and map each discrete point on the outer contour line of the non-reverse arc region. For the point numbered i... out discrete points (i) out∈ [1 out n1 out Select the two adjacent discrete points (numbered (i-1)) before and after it. out and(i+1) out Using the coordinates of these three points as auxiliary points, the center coordinates and radius of the circle formed by these three points are determined, and the current discrete point i is calculated. out And the next discrete point (i+1) out The arc length and corresponding central angle between the points are used as parameters for flattening the outer contour of the non-reverse arc region and for subsequent axial reconstruction of the two-dimensional mesh into a three-dimensional curved surface mesh. Then, the outer contour discretization point at the center of the tire crown (numbered 1) is used as the parameter. out Using the tire crown center as the starting reference point, the arc length values ​​corresponding to each discrete point of the outer contour in the non-reverse arc region are accumulated and superimposed along the tire axis (positive X-axis direction) in ascending order of their numbers to obtain the X-coordinate values ​​mapped after flattening all discrete points of the outer contour in the non-reverse arc region; at the same time, the Y-coordinate values ​​of all discrete points of the outer contour in the non-reverse arc region are uniformly set as the discrete point of the outer contour of the tire crown center (numbered 1). out The Y-coordinate value of the tire (equal to the tire radius) is used to obtain the flattened coordinates of all discrete points on the outer contour of the non-reverse arc region (numbered 1). out’ to n1 out’ ).

[0083] Next, we need to sequentially discrete the outer contour points of the reverse arc region (numbered (n1+1)). out To (n1 + n2) out Mapping is performed. The specific mapping steps are as follows: For a discrete point numbered t (t ∈ [(n1+1)]... out ,(n1+ n2) out ]), calculate the current discrete point t and the discrete point of the outer contour of the tire shoulder before flattening mapping (numbered n1) out The distance h between them t And the current discrete point t and the discrete point of the outer contour of the tire shoulder before flattening mapping (numbered n1) out The angle θ between the line connecting the two axes and the Y-axis. t Based on the principle that the distance between the discrete points of the outer contour shoulder and the discrete points of the outer contour of the reverse arc region before and after mapping, and the angle with respect to the Y-axis remain unchanged, the axial coordinate transformation of each discrete point of the outer contour of the reverse arc region is performed accordingly, so as to obtain the axial coordinates of all discrete points of the outer contour of the reverse arc region after axial mapping (numbered as (n1+1)). out’ To (n1 + n2) out’ ).

[0084] Finally, the discrete points of the mapped outer contour (numbered 1) can be used as a basis. out’ To (n1 + n2) out’ ) sequentially discrete points of the original inner contour (numbered 1)in To (n1 + n2) in Perform axial mapping. The specific mapping steps are as follows: For the number i in Discrete points of the inner contour (i) in ∈ [1 in ,(n1+ n2) in ]), calculate the current discrete point i in Discrete point i with the same number as the outer contour before flattening and mapping out The distance h between them i and the current discrete point i in with i out and i out The next adjacent discrete point of the outer contour (i) +1) out The angle θ between the two lines i Based on the principle that the distance and angle between the corresponding discrete points of the outer and inner contours remain unchanged before and after mapping, the axial coordinates of each discrete point of the inner contour are transformed accordingly to obtain the axial coordinates of all discrete points of the inner contour (including the reverse arc region) after axial mapping (numbered 1). in ’ To (n1 + n2) in ’ ).

[0085] After completing the axial mapping process of all outer and inner contours, a two-dimensional cross section composed of the mapped inner and outer contour curves can be obtained by curve fitting, and the cross section thickness has the same distribution as the original cross section thickness.

[0086] Discrete points of the inner and outer contours of the right half before and after axial mapping are obtained from Figure 2 As shown in the upper and middle parts, the final axially mapped two-dimensional cross section obtained through curve fitting can be obtained from... Figure 2 The lower part is shown. Simultaneously, during the axial mapping process, the processes before and after axial mapping of the outer contour of the non-reverse arc region and the entire inner contour (including the reverse arc region) are... Figure 3 The enlarged views of regions A and B in the image are shown; the process of axial mapping of the outer contour of the reverse arc region before and after is as follows: Figure 3 The enlarged view of regions C and D is shown in the figure.

[0087] (2) Based on the pattern structure feature parameters, establish layer lines within the mapped inner and outer contour lines.

[0088] Based on the characteristic parameters in the pattern structure design drawing, layered lines are established within the two-dimensional cross-section composed of the mapped inner and outer contour lines. The characteristic parameters include the shape, axial length, width, depth of each groove segment of the pattern, and the characteristic points of the pattern's chamfer structure. The layered lines represent the projection points of the groove bottom start and end points onto the inner and outer contour lines of the pattern's meridional plane, and are formed by connecting multiple straight or arc segments end-to-end. Six layers of layered lines are defined based on the aforementioned pattern structure characteristic parameters, as follows: Figure 4 As shown, the Y-coordinate differences at different X-coordinates between the layer lines, between the highest layer layer line (closest to the outer contour) and the outer contour, and between the lowest layer layer line (closest to the inner contour) and the inner contour are the control parameters for the mesh cell height and trench depth in the Y-axis direction during automatic 3D mesh generation. Figure 4 The code marks the Y-coordinate differences between each layer line and between the layer lines and the inner and outer contours when the X-coordinate is zero. The layer lines are then output as DXF files, and the program reads the endpoint information of the straight line segments and the center coordinates, radius, and start and end angles of the arc segments related to the layer lines, providing accurate geometric parameters for subsequent 3D mesh generation.

[0089] (3) Extract the tread pattern development diagram from the tire structure design drawing, perform geometric cleanup, and then perform two-dimensional mesh division and grouping.

[0090] First, AutoCAD software is used to extract the tread pattern unfolded drawing from the tire structure design drawing (the tread pattern unfolded drawing is a two-dimensional planar drawing obtained by flattening the tread pattern on the circumference of the tire to a certain scale, containing the geometric boundary of the complete tread pattern). Then, the tread pattern unfolded drawing is geometrically cleaned, specifically including the following two aspects: (1) deleting the annotation lines, dimension lines, auxiliary lines, etc. in the drawing. These lines do not participate in the geometric definition of the tread pattern; (2) cleaning up the endpoint connection problem of the feature lines of the tread pattern outline (feature lines refer to the geometric lines that define the tread pattern boundary). Through operations such as extension, trimming, and connection, the endpoints of each feature line are ensured to be precisely closed, eliminating small gaps and overlaps, and ensuring the continuity and integrity of the tread pattern geometry. After the geometric cleanup is completed, the complete tread pattern unfolded drawing DXF file format data can be output. Figure 5 This diagram illustrates the tread pattern development before and after geometric cleaning. As shown, the tread pattern development consists of tread units with three different pitches (i.e., the length of a single tread unit along the circumferential direction of the tread). Each pitch tread unit has the same topological shape, but the dimensions of the tread features differ.

[0091] The tread pattern unfolded DXF file is then imported into HYPERMESH. A three-dimensional coordinate system is established, with the center point of the tire as the origin O, the axial direction X-axis as the tire axis, the radial direction Y-axis as the tire axis, and the circumferential direction Z-axis as the tire axis. A rectangular plane (the plane size should be larger than the maximum outline size of the tread pattern unfolded) that can cover the entire tread pattern unfolded area is constructed in the XZ plane with the Y-coordinate being the tire radius. Then, the imported tread pattern unfolded image is projected and embedded into the rectangular plane through Boolean operations to obtain a rectangular plane containing the geometric boundary of the complete tread pattern.

[0092] Next, meshing is performed on a rectangular plane for individual pitch pattern elements. During the meshing process, ensure that the mesh node density (number of mesh nodes per unit length) on the front and rear pitch boundary lines of the single pitch pattern element (referring to the front and rear boundary lines of the pattern pitch element in the positive Z-axis direction) is the same and that the X-axis coordinates are consistent. Figure 6 This is a schematic diagram of a two-dimensional mesh for a single-pitch tread pattern element. The mesh node density is the same on the front and rear pitch boundary lines, and the X-coordinates of any corresponding mesh nodes on the front and rear pitch boundary lines are equal (x1=x1', x2=x2', x3=x3'). This consistency ensures that when generating a full-circumference tire tread pattern model using pitch arrangement (the partitioning method described in this paper does not involve pitch arrangement), the boundary nodes between adjacent pitch elements can be successfully merged, avoiding node duplication, gaps, or mesh quality issues, and ensuring the continuity and integrity of the full-circumference model.

[0093] After mesh generation, based on the pattern's geometric characteristics, the two-dimensional mesh is divided into different components according to the groove shape, axial length, and chamfer structure features. The final result is as follows: Figure 6 The single-pitch pattern two-dimensional mesh shown has all nodes located in the XZ plane where the Y-coordinate is equal to the tire radius. The groove component and chamfer component are marked in the figure.

[0094] (4) The 2D mesh of the tread pattern is axially restored to obtain the 3D curved surface mesh of the tread pattern.

[0095] First, the 2D mesh is output as an INP file. The program then iterates through all nodes of the 2D mesh. For each node, it searches for the nearest discrete point on the outer contour of the flattened, non-inverted arc region to the left of that node's X-coordinate as a reference point (numbered at 1). out’ to n1 out’ The distance between the grid node and the reference point is calculated using discrete points with the same number as the reference point before flattening (numbered between 1 and 2). out to n1 out The axial mapping parameters (between) include the center coordinates, radius, arc length and central angle, and a local coordinate system with the reference point and the corresponding center as the polar axis is established.

[0096] Finally, based on the distance between the mesh nodes and the reference point, and the corresponding central angle, the axially restored 3D spatial coordinates of the nodes can be calculated according to the principle of inverse mapping. Using the above method, the axially restored 3D spatial coordinates of all nodes can be obtained, thereby restoring the planar 2D mesh nodes to the outer surface of the tread pattern formed by stretching the original outer contour of the non-reverse arc region circumferentially along the Z-axis, generating a 3D curved surface mesh of the tread pattern.

[0097] Figure 7 The upper part shows the process of restoring the tread pattern grid in the XY plane from a side view. The flattened straight lines are restored to curves that fit the original outer contour of the non-reverse arc area. Figure 7 The lower part shows the 3D curved surface mesh of the axially restored tire tread pattern in the XYZ coordinate system from top view. This surface perfectly fits the original outer contour of the non-reverse arc region, which is stretched radially along the Z-axis to form the outer surface of the tread pattern.

[0098] (5) Discretize and restore the axial layering lines of the patterned meridional plane to obtain the discrete points of the axially restored layering lines.

[0099] First, using the endpoint information of the straight line segments and the center coordinates, radius and start and end angle information of the arc segments read by the program in step (2), geometric calculations are performed to determine the layer number of each arc segment or straight line segment and the layer line equation of each layer, so as to perform three-dimensional mesh node projection and identify the layer number corresponding to the mesh projection point.

[0100] The method for determining the layer line equations and layer numbering is as follows: First, count the endpoint coordinates of each arc or straight line segment. Connect the arc and straight line segments that are connected end to end in sequence. Then, use the interpolation function to fit the obtained layer line equations. Next, calculate the average Y-coordinate of all endpoints on each complete layer line. Finally, assign layer numbers according to the magnitude of the average Y-coordinate. The larger the average Y-coordinate (closer to the outer contour), the smaller the layer line number. The smaller the average Y-coordinate (closer to the inner contour), the larger the layer line number.

[0101] Then, according to the discrete point numbering order of the non-reverse arc region after axial mapping (1) ’ to (n1) ’ -1), connect the inner contour discrete points with the same number to the outer contour discrete points in pairs after mapping to construct (n1-1) straight line equations, and then find the intersection of each straight line equation with the fitted layer line equations to obtain the set of discrete points on each layer line.

[0102] Finally, the discrete points on each layer's dividing line can be reconstructed axially. The specific steps for axial reconstruction are as follows: For the equation of the line numbered i (i ∈ [1, (n1-1)]), calculate the discrete points (i...) of each layer's dividing line under that number. pk’(where k is the layer line number where the discrete point is located) and the discrete point on the outer contour of that number (i out’ The distance h between them pk And the corresponding numbered original outer contour discrete points (i out Take a distance h along the direction perpendicular to the downward direction. pk The point, i.e., the coordinates of the discrete points of each layer of the axially reconstructed layer line, numbered i, are obtained. pk This method can obtain the set of discrete points of all axially restored layer lines. By fitting the set of discrete points of each layer, the axially restored layer lines of each layer can be obtained.

[0103] like Figure 8 The upper part is labeled with the number of the original layer lines in the two-dimensional section of the right half after axial mapping, and a schematic diagram of the set of discrete points of the original layer lines obtained by intersecting the equations of (n1-1) straight lines; Figure 8 The enlarged views of regions E and F in the image show in detail the axial reconstruction of the discrete points of each layer line obtained by intersecting the equation of the line numbered i with the layer lines of each layer (i). pk’ →i pk The process of (where k is the layer line number where the discrete point is located); Figure 8 The lower part shows the set of discrete points of all the layered lines after axial restoration of the original right half two-dimensional cross section, as well as the axially restored layered lines of each layer obtained by fitting the set of discrete points.

[0104] (6) For the three-dimensional curved surface mesh except for the left and right boundary lines, determine the projection direction of each node in the meridional plane.

[0105] The three-dimensional surface mesh and the discrete point set of the layered lines after axial reconstruction have been obtained. Subsequently, the three-dimensional mesh nodes of the tread pattern in the non-reverse arc region can be solved. Before this, the projection directions of all three-dimensional surface mesh nodes except for the left and right boundary lines need to be determined. The left and right boundary lines of the three-dimensional surface mesh are visible. Figure 7 The lower part (since the three-dimensional mesh node sets corresponding to the nodes of the left and right boundaries are all located on the reverse arc, it is not necessary to determine the node projection direction, see step (8)).

[0106] First, the program calculates two characteristic projections of the 3D surface mesh nodes excluding the left and right boundary lines: For each 3D surface mesh node excluding the left and right boundary lines (the reason for excluding mesh nodes on the left and right boundary lines is that the set of 3D mesh nodes corresponding to the nodes on the left and right boundaries are all located on the inverse arc line, so there is no need to determine the node projection direction), projection point A is obtained by projecting along the direction perpendicular to the outer contour onto the inner contour, and projection point B is obtained by projecting along the direction perpendicular to the inner contour onto the inner contour. Then, the original outer contour discrete points in the non-inverse arc region are numbered in ascending order (1... out to n1out The process involves sequentially calculating the projection points of each discrete point onto the inner contour line along a direction perpendicular to the outer contour, and then calculating the distances between all adjacent projection points. Half of the arithmetic mean of these distances is set as the discrimination threshold. Finally, the projection direction is determined based on the threshold: For each 3D surface mesh node except for the left and right boundary lines, the distance s between its two feature projection points A and B is calculated. If the distance s is greater than the threshold, the vector a formed by projection point B and the current node is used as the projection direction of that node; if the distance s is less than or equal to the threshold, the vector b formed by projection point A and the current node is used as the projection direction of that node.

[0107] like Figure 9 The diagram shows different projection directions of a curved mesh node (not bounded by left or right boundaries) on the right half of a two-dimensional cross-section composed of the original outer and inner contours in the XY plane. The node is projected onto the inner contour along a direction perpendicular to the outer contour to obtain projection point A, and the projection vector a is determined. Similarly, it is projected onto the inner contour along a direction perpendicular to the inner contour to obtain projection point B, and the projection vector is determined. The distance s between points A and B is used to determine the projection direction of the node.

[0108] (7) Project the three-dimensional curved surface mesh nodes, except for the left and right boundary lines, onto the axially restored layer and the inner surface of the pattern along the projection direction, and solve for the coordinates of the three-dimensional mesh nodes of the tread pattern in the non-reverse arc region.

[0109] First, the program iterates through all 3D surface mesh nodes except for the left and right boundary lines. For each 3D surface mesh node except for the left and right boundary lines, the XY plane corresponding to the node's Z coordinate is taken as the plane containing the original 2D cross section, the layer lines after axial restoration, and the projection lines. Based on the node coordinates and the node projection vector determined in step (6), the parametric equation of the projection line corresponding to the node is established. Then, the projection line is intersected with the curve formed by fitting the discrete point set of the layer lines after axial restoration of each layer to obtain the projection points of the mesh node on different layer surfaces after axial restoration (the layer surface represents the surface obtained by stretching the layer lines after axial restoration along the tire circumference, i.e., the Z-axis). Then, the projection line is intersected with the inner contour line of the tire to obtain the projection points of the mesh node on the inner surface of the tread pattern (the inner surface of the tread pattern represents the surface obtained by stretching the inner contour line along the tire circumference, i.e., the Z-axis).

[0110] Using the method described above, the sets of projection points for each layer corresponding to all three-dimensional surface mesh nodes outside the left and right boundary lines can be obtained. The three-dimensional surface mesh nodes outside the left and right boundary lines, and the sets of projection points for each layer obtained by the above method, constitute the coordinate data of the three-dimensional mesh nodes of the tread pattern in the non-reverse arc region.

[0111] like Figure 10It shows a three-dimensional curved mesh that is attached to the original outer contour and stretched along the tire circumference to form the outer surface of the pattern. It also shows the layer lines of each layer and the layer layers and inner surface of the pattern formed by stretching the inner contour lines along the circumference. Figure 10 The enlarged view of region C in the image shows in detail the projection solution process of a 3D mesh node of a certain tread pattern in the non-reverse arc region: Let a certain internal 3D curved surface mesh node, excluding the left and right boundary lines, be... Its source node Represents grid nodes The projection point on the patterned meridian plane, the projection line corresponding to the source node is... By finding the intersections of the projection lines with the layer lines and inner contour lines of each layer, all mesh projection points corresponding to the source node can be obtained. Then project all grid points Translate to grid node Below, you can obtain accurate internal 3D mesh nodes. This method can be used to solve for the set of all projection points in the non-inverted arc region.

[0112] (8) Solve for the coordinates of the three-dimensional mesh nodes of the tread pattern in the reverse arc region according to the reverse arc equation.

[0113] First, the program iterates through all 3D surface mesh nodes on the left and right boundaries. For each 3D surface mesh node on the left and right boundary lines, the XY plane corresponding to the node's Z coordinate is taken as the plane containing the original 2D cross section and the layer lines after axial restoration. Then, the original reverse arc is intersected with the curve formed by fitting the discrete point set of each layer line after axial restoration to obtain the projection points of the mesh node on different layer surfaces after axial restoration. Then, the intersection point of the original reverse arc and the inner contour line in the projection plane is taken as the projection point of the mesh node on the inner surface of the pattern.

[0114] The above method is used to solve for the set of projection points corresponding to all three-dimensional surface mesh nodes on the left and right boundary lines. The three-dimensional surface mesh nodes on the left and right boundary lines, and the set of projection points obtained by the above method, constitute the coordinate data of the three-dimensional mesh nodes of the tread pattern in the reverse arc region.

[0115] like Figure 10 The enlarged view of region C shows in detail the projection solution process of a 3D mesh node of a certain tread pattern in the reverse arc region: Let P be a certain internal 3D curved surface mesh node in the left and right boundary lines. jf Its source node P′ jf Represents grid node P jf At the projection point on the patterned meridian plane, take the inverted arc within the meridian plane as the projection line L. jfBy finding the intersection of the inverted arc with the layer lines of each layer and taking the intersection of the inverted arc with the inner contour, all mesh projection points P′ corresponding to the source node can be obtained. jf,k Then project all grid points P′ jf,k Translate to grid node P jf Below, the accurate internal 3D mesh node P′′ can be obtained. jf,k This method can be used to solve for the set of all projection points in the inverse arc region.

[0116] Figure 11 The diagram shows all the three-dimensional nodes of the finite element mesh for the tread pattern, and displays the solution results of the projection points in steps (7) and (8): the three-dimensional curved surface mesh nodes of the tread pattern and the corresponding three-dimensional projection points of the tread pattern, and the reverse arc region and the non-reverse arc region are marked.

[0117] (9) Number all three-dimensional nodes and connect all nodes in sequence to form pentahedral or hexahedral elements to obtain a single-pitch tread pattern finite element mesh containing the shoulder reverse arc.

[0118] After solving for the projection points of all 3D surface meshes, it is necessary to number all 3D nodes (including 3D surface mesh nodes and the projection points of each layer corresponding to the 3D surface mesh nodes).

[0119] First, a constant value greater than the total number of nodes in the 3D surface mesh is defined to avoid overlapping projection point numbers (e.g., when the total number of 3D surface mesh nodes is 1800, the constant is 2000). Then, the node numbers of the 3D mesh generated by projection are calculated. By writing a program to traverse all 3D surface mesh nodes, the following numbering rule is adopted for each surface mesh node and its projection point: 3D mesh node number = source node number + (projection point layer number × constant), where the source node number is the corresponding number in the 3D surface mesh. For example, the surface mesh node numbered 1800 has projection point numbers of 3800 (1800+1×2000) and 5800 (1800+2×2000) in the first and second layers, respectively, and 15800 (1800+7×2000) in the last layer.

[0120] After calculating all node numbers, the node connection order is determined using the 3D node numbering information according to the right-hand rule. All 3D nodes are then connected to form vertically arranged hexahedral or wedge-shaped pentahedral elements, thus generating a complete 3D mesh model. When constructing the finite element mesh, the right-hand rule must be followed to determine the node sorting direction: extend your right hand, with your thumb perpendicular to the other four fingers; keep your thumb still and bend the other four fingers into a semi-clenched position. At this point, the thumb points in the direction of the element normal, and the direction the four fingers bend indicates the node numbering direction.

[0121] For example, the definition format of a hexahedral element in an INP file is as follows: 1, 1801, 1802, 1803, 1804, 1, 2, 3, 4; where the first number is the element number, the 2nd to 5th numbers (1801-1804) are the four numbering nodes at the bottom layer of the element, and the 6th to 9th numbers (1-4) are the four numbering nodes at the top layer of the element. The first four numbers are the next layer projection points corresponding to the positions of the last four numbering nodes. Connecting these eight numbering nodes according to the right-hand rule forms a complete hexahedral element. The connection method for wedge pentahedral elements is similar, except that the quadrilateral faces in the hexahedral element are replaced with the triangular faces in the wedge pentahedron. For example, this element can be defined as 1, 1801, 1802, 1803, 1, 2, 3. The connection process for the above hexahedral and wedge pentahedral elements can be as follows: Figure 12 As shown.

[0122] Next, using the components defined in step (3), the three-dimensional mesh elements located within the groove component are deleted to establish the groove region. Existing three-dimensional mesh nodes are projected onto the chamfer plane defined by the chamfer component to establish the chamfer structure, thus completing the full modeling of the tread pattern. Finally, the program outputs an INP format file to obtain a finite element mesh model of a single-pitch tread pattern containing the shoulder reverse arc, as shown below. Figure 13 As shown, where Figure 13 The lower part shows the grooved areas and chamfered structures in the mesh model.

[0123] (10) The circumferential restoration of the tread pattern finite element mesh is performed to obtain a single-pitch tread pattern finite element mesh with shoulder reverse arc that matches the actual shape.

[0124] At this point, the axial reconstruction of the tread pattern 3D mesh has been completed (achieved by projecting the 3D curved surface mesh onto the 2D mesh and layer lines in the aforementioned steps to generate the tread pattern 3D mesh), but the circumferential reconstruction has not yet been performed. Circumferential reconstruction refers to the geometric transformation process of converting the tread pattern finite element mesh from a Cartesian coordinate system to a tire cylindrical coordinate system in the circumferential direction.

[0125] The specific implementation method of circumferential restoration is as follows: First, the Y and Z coordinates of the 3D mesh nodes restored by the axis are used to determine the YZ plane where the coordinate transformation is located. Then, according to the tire radius, the angle between the current 3D node and the Y axis in this plane is calculated. Finally, the overall restoration of the 3D finite element mesh of the tread pattern can be achieved by calculating the cosine of the angle.

[0126] like Figure 14 This demonstrates the process of circumferential reconstruction of the tire tread pattern using a finite element mesh. The center point of the tire is taken as the origin O, with the axial direction (X-axis) as the tire axis, the radial direction (Y-axis) as the tire axis, and the circumferential direction (Z-axis) as the tire axis. Assuming point... These are the finite element nodes after axial restoration, based on The Z-coordinate of the node and the outer contour radius R outer It can be calculated Angle with the Y-axis Then, according to the following formulas (1)-(3), the points are... Circumferential reduction to points This achieves the overall reconstruction of the finite element mesh of the tire tread pattern, where t = 1, 2, 3, ..., N, and N is the total number of nodes in the three-dimensional mesh of the tire tread pattern.

[0127] (1)

[0128] cos (2)

[0129] (3)

[0130] like Figure 15 This diagram illustrates the changes in the finite element mesh of the tire tread pattern before and after circumferential reconstruction. The mesh exhibits a significant change in curvature along the tire circumferential direction. Figure 16 The image shows a schematic diagram of a single-pitch tread pattern with a reversed shoulder arc, which is circumferentially restored to match the actual shape.

[0131] In summary, this invention can axially map a two-dimensional cross-section containing a reverse arc on the tire shoulder, and axially restore and fit the two-dimensional mesh of the planar tread pattern onto the plane extending from the outer contour. It can automatically project and generate all three-dimensional mesh nodes through different projection methods. This invention can solve the problems of failure of axial mapping function for reverse arc type tread pattern models, automatic generation of reverse arc models, and inability to generate three-dimensional meshes of tread patterns with realistic shapes in the existing technology. It realizes the rapid generation of finite element meshes for tread patterns containing reverse arc shapes in the outer contour of a two-dimensional cross-section, and improves the efficiency and quality of mesh generation.

[0132] It should be noted that the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for fast dividing finite element mesh of tire tread pattern with shoulder reverse curvature, characterized in that Including the following steps: S1. According to the conformal mapping principle, the inner and outer contour lines of the tread pattern meridional surface containing the shoulder reverse arc are axially mapped. The outer contour line area is mapped to a straight line except for the reverse arc, and the reverse arc is mapped to an arc, ensuring that the thickness of the two-dimensional section remains unchanged before and after the mapping. S2. Based on the structural feature parameters in the pattern design drawing, establish layered lines within the mapped inner and outer contour lines to represent different pattern groove feature information. S3. Extract the tread pattern development diagram from the tire structure design drawing and perform geometric cleanup. Then, divide the tread pattern development diagram into two-dimensional meshes and group the two-dimensional meshes according to the tread structure characteristics to obtain information on different components. S4. Based on the parameters obtained in the axial mapping stage, the two-dimensional mesh of the tread pattern unfolding diagram is axially restored to obtain a three-dimensional curved surface mesh in the outer surface of the pattern obtained by stretching the original outer contour along the Z-axis in the non-reverse arc region. S5. Calculate the discrete point set of the layer line based on the layer line information and the inner and outer contour discrete point information of the corresponding sequence number after mapping, and perform axial restoration calculation on the discrete point set to obtain the axially restored discrete point set of the layer line. S6. For each node of the three-dimensional curved surface mesh except for the left and right boundary lines, in its meridional plane, let the node project onto the inner contour along the direction perpendicular to the outer contour and onto the inner contour along the direction perpendicular to the inner contour respectively, to obtain two feature projection points. Determine the projection direction of the node based on the distance between the two projection points. S7. Project the 3D curved surface mesh nodes, excluding the left and right boundary lines, onto the axially restored layer and the inner surface of the tread pattern along the projection direction, and solve for the coordinates of the 3D mesh nodes of the tread pattern in the non-reverse arc region. S8. Solve for the intersection of the inverse arc equations corresponding to the left and right boundary node sets of the three-dimensional surface mesh and the axially restored layer lines to obtain the coordinates of the three-dimensional mesh nodes of the tread pattern in the inverse arc region. S9. Number all three-dimensional nodes, connect all nodes according to the right-hand rule to form the corresponding three-dimensional finite element mesh and establish the corresponding tread pattern features. Write the node and element information into the INP file to obtain the complete single-pitch tread pattern finite element mesh with the shoulder reverse arc. S10. Perform circumferential restoration on the tread pattern finite element mesh to obtain a single-pitch tread pattern finite element mesh containing the shoulder reverse arc that matches the actual shape.

2. The method of claim 1, wherein, In step S1, the process of axial mapping of the inner contour line and the outer contour line is as follows: 1) Determine the number of discrete points in the non-reverse arc region based on the length of the outer contour of the non-reverse arc region in the X-axis direction, and discretize the inner and outer contour lines of the non-reverse arc region; 2) Calculate the ratio of the X-direction span of the reverse arc region to the X-direction span of the non-reverse arc region. Multiply this ratio by five times the product of the number of discrete points in the non-reverse arc region to obtain the number of discrete points in the reverse arc region. Discretize the corresponding inner and outer contour lines of the reverse arc region. 3) Keeping the position of the discrete point at the center of the tread unchanged, the discrete points of the outer contour of the non-reverse arc region are mapped to equidistant scattered points on a straight line according to the arc length of adjacent discrete points, so as to obtain the flattened outer contour discrete points of the non-reverse arc region. 4) Keep the discrete points of the flattened tire shoulder unchanged, and map the discrete points of the outer contour of the reverse arc region to the discrete points of the arc line according to the relationship between the distance and angle with the discrete points of the tire shoulder. 5) Based on the principle that the distance and angle of the corresponding discrete points of the original inner and outer contour lines remain unchanged, the inner contour is axially mapped using the mapped outer contour as the basis, so as to realize the axial mapping of the inner and outer contour lines containing the reverse arc.

3. The method of claim 1, wherein, In step S2, the structural feature parameters in the pattern design drawing include the shape, axial length, width, and depth of each groove segment of the pattern, as well as the chamfer structural feature points of the pattern. The layered lines represent the projection points of the starting and ending points of the bottom of the pattern grooves onto the inner and outer contour lines of the pattern meridional plane, and are composed of multiple straight or arc segments connected end to end. In step S3, the geometric cleanup includes: 1) Delete the annotation lines, dimension lines, and auxiliary lines in the tread pattern unfolding diagram; 2) Clean up the endpoint connection problems of the feature lines of the pattern outline. Ensure that the endpoints of each feature line are precisely closed by extending, trimming or connecting them, eliminating small gaps and overlaps, and ensuring the continuity and integrity of the pattern geometry; the feature lines refer to the geometric lines that define the boundary of the pattern. When performing two-dimensional meshing on the tread pattern unfolding diagram, ensure that the mesh node density on the front and rear pitch boundary lines of a single pitch tread unit is the same and that the X-axis coordinates are consistent. This allows the three-dimensional meshes of different pitches to be arranged through shared nodes to obtain the tire circumference model. Finally, the generated two-dimensional meshes are grouped according to the shape of each groove segment, axial length, and chamfer structure feature points. Pitch is the length of a single tread unit along the circumferential direction of the tread. Pitch boundary lines refer to the front and rear boundary lines of the tread pitch unit in the positive Z-axis direction. Mesh node density is the number of mesh nodes per unit length.

4. The method of claim 1, wherein, In step S4, the parameters obtained in the axial mapping stage include the center, radius, arc length, and central angle of the discrete point. Axial restoration involves searching for the nearest discrete point on the outer contour of the flattened, non-reverse arc region to the left of each mesh node's X-coordinate as a reference point, and calculating the distance between the mesh node and the reference point. Then, using the axial mapping parameters of the discrete point with the same number as the reference point before flattening, including the center, radius, arc length, and central angle, a local coordinate system is established with the reference point and its corresponding center as the polar axis. Finally, based on the distance between the mesh node and the reference point, and the corresponding numbered central angle, the axially restored three-dimensional spatial coordinates of the node are calculated according to the principle of inverse mapping. The planar two-dimensional mesh node is then restored and fitted onto the outer surface of the tread pattern formed by stretching the original outer contour of the non-reverse arc region circumferentially along the Z-axis, generating a three-dimensional curved surface mesh for the tread pattern. In step S5, the method for obtaining the set of discrete points of the axially restored layered line is as follows: 1) Determine the layer line equations and layer numbers: First, count the endpoint coordinates of each arc or straight line segment. Connect the arc and straight line segments that are connected end to end in sequence. Then, use the interpolation function to fit the obtained layer line equations. Next, calculate the average Y-coordinate of all endpoints on each complete layer line. Finally, assign layer numbers according to the magnitude of the average Y-coordinate. The larger the average Y-coordinate, the closer it is to the outer contour, and the smaller the layer line number. The smaller the average Y-coordinate, the closer it is to the inner contour, and the larger the layer line number. 2) Based on the discrete point information of the inner and outer contours within the non-reverse arc region excluding the tire shoulder after axial mapping, connect the inner contour discrete points and outer contour discrete points with the same number in pairs to construct a corresponding set of straight line equations. 3) Solve for the intersection points of each straight line equation and the equations of each layer line to obtain the set of discrete points on each layer line; 4) For any discrete point on the layer line, solve for the distance h between the discrete point and the corresponding numbered discrete point on the outer contour; 5) Take a point with a distance of h along the vertical downward direction from the original outer contour discrete point with the corresponding number. This is the discrete point of the layer line after axial restoration of the corresponding number. This gives the set of all discrete points of the layer line after axial restoration.

5. The method of claim 1, wherein, In step S6, the method for determining the projection direction of a node based on the distance between two projection points is as follows: For each three-dimensional curved surface mesh node except for the left and right boundary lines, projection point A is obtained by projecting along the direction perpendicular to the outer contour onto the inner contour, and projection point B is obtained by projecting along the direction perpendicular to the inner contour onto the inner contour; the distance s between the two feature projection points A and B is calculated: if the distance s is greater than a threshold, the vector a formed by projection point B and the current node is used as the projection direction of the node; if the distance s is less than or equal to the threshold, the vector b formed by projection point A and the current node is used as the projection direction of the node. The threshold is calculated as follows: the discrete points of the original outer contour of the non-reverse arc region are numbered in ascending order to solve the projection points of each discrete point on the inner contour line along the direction perpendicular to the outer contour. The distance between all adjacent projection points is calculated, and half of the arithmetic mean of the distance is set as the discrimination threshold.

6. The method of claim 1, wherein, In step S7, the layered surface refers to the curved surface obtained by stretching the layered lines along the tire circumference after axial restoration; the inner surface of the tread pattern refers to the curved surface obtained by stretching the inner contour lines along the tire circumference. The method for solving the 3D mesh node coordinates of the tread pattern in the non-reverse arc region is as follows: 1) For each 3D surface mesh node except for the left and right boundary lines, take the XY plane corresponding to the Z coordinate of the node as the plane containing the original 2D section, the layer lines after axial restoration, and the projection lines; 2) Establish the projection line equation corresponding to the node based on the node coordinates and the node projection vector determined in step S6; 3) Intersect the projection line equation with the curve fitted to the set of discrete points of the layer line after axial restoration of each layer in turn to obtain the projection points of the grid node on different layer surfaces after axial restoration. 4) Intersect the projection line equation with the inner contour line to obtain the projection point of the mesh node on the inner surface of the pattern.

7. The method of claim 1, wherein, In step S8, the coordinates of the three-dimensional mesh nodes of the tread pattern in the reverse arc region are obtained through the following steps: 1) For each 3D surface mesh node of the left and right boundary lines, take the XY plane corresponding to the Z coordinate of the node as the plane where the original 2D section and the layer lines of each layer are located after axial restoration; 2) Intersect the original reverse arc with the curve formed by fitting the discrete point set of the layer line after axial restoration of each layer in turn, and obtain the projection of the grid node on different layer surfaces after axial restoration; 3) Take the intersection of the original reverse arc and the inner contour line in the projection plane as the projection point of the grid node on the inner surface of the pattern.

8. The method of claim 1, wherein, In step S9, the method for numbering all three-dimensional nodes is as follows: first, define a constant value greater than the total number of three-dimensional surface mesh nodes to avoid overlapping of projection point numbers; for each surface mesh node and its projection point, add the source node number to the product of the projection point layer number and the defined constant to obtain the number of the three-dimensional mesh node. The right-hand rule refers to the arrangement of mesh nodes during the construction of finite element meshes. Extend your right hand with your thumb perpendicular to the other four fingers; keep your thumb still and bend the other four fingers into a semi-clenched shape; the direction of your thumb is the direction of the element normal, and the direction of the bending of your four fingers is the sorting direction of the node numbers; the right-hand rule is applicable to the construction of hexahedral elements and wedge-shaped pentahedral elements; the tread pattern features include the establishment of grooves and chamfers.

9. The method of claim 8, wherein, The grooves are created by deleting corresponding grid cells during the grid construction process based on the component information and preset layer number information, thus obtaining the patterned groove features. The chamfer is established after solving the three-dimensional mesh nodes. The chamfer plane is calculated based on the component information and the preset chamfer angle. During the mesh construction process, the initial projection points are projected onto the chamfer plane to obtain the pattern chamfer feature.

10. The method of claim 1, wherein, In step S10, the circumferential restoration corresponds to the transformation process of the tread pattern finite element mesh from the rectangular coordinate system to the cylindrical coordinate system in the circumferential direction.

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