CN115809582A - Method for judging tire durability through tire grounding pressure distribution - Google Patents
Method for judging tire durability through tire grounding pressure distribution Download PDFInfo
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Abstract
A method for judging the durability of a tire through the distribution of the tire grounding pressure belongs to the technical field of tire structure computer simulation design. The scheme is as follows: establishing a 3D model after the matching of the tire and the rim; outputting a stress cloud picture of a grounding area; dividing the grounding area into n sections according to the stress of the grounding area, wherein the tire pressure is P, delta ij For the stress value of each node of the crown, the area S of each section K And total area of ground S t Evaluation index of tire durability
The value of M is indicative of the endurance of the tire at the contact pressure of each zone, and the two are negatively correlated. The method provides a method capable of accurately judging the durability of the tire andand the endurance performance improving direction is given, and direction guidance is provided for a tire design engineer.
Description
Technical Field
The invention relates to the technical field of tire structure computer simulation design, in particular to a method for judging tire durability through tire ground pressure distribution, application and a computer program product.
Background
The durability of the tire is not only closely related to low carbon and environmental protection, but also is concerned with driving safety. China puts forward definite requirements on the durability of tires, and simultaneously, enterprises respectively set more severe enterprise standards on the basis of national standards for meeting customer requirements. However, all current methods for obtaining tire endurance performance only involve bench testing. The bench testing machine occupies a large area, is high in purchase cost and is long in testing period.
In order to solve the above-mentioned shortcomings of the bench test, a great deal of research has been conducted by experts of domestic and foreign scholars, and it is expected that the durability of the tire is reflected by a numerical simulation method or by establishing a relationship between the characteristics of other aspects of the tire and the durability performance. At present, a virtual crack propagation method is mainly adopted at home and abroad, the durable damage of the tire is caused by structural failure after the intrinsic microcrack of the rubber expands to a certain size, the method needs to measure the relation between the initial crack of the rubber and the periodic load and the intrinsic microcrack size, the early-stage material testing workload and the working difficulty are large, the testing period is long, and the method is not easy to popularize. The method for representing the durability of the tire by strain energy density gradient is provided by scholars in China, the relationship between the strain energy density gradient and the tire is obtained by numerical fitting, a large number of bench tests are required to be carried out on the tire in the early stage, and the relationship between the strain energy density gradient and the tire is obtained by functional fitting according to test results, so that the defects of the bench tests still exist.
At present, the problems of high cost, long cycle and large workload and difficulty in working of the tire durability evaluation method are solved, so that the suitable physical quantity and evaluation method are required to be further searched in the aspect of tire durability prediction, and the improvement direction of the durability performance can be provided.
Disclosure of Invention
In order to solve the above technical problems, an object of the present invention is to provide a method for determining tire durability through tire ground contact pressure distribution, which establishes a relationship between tire durability and other physical properties of a tire, provides a method capable of accurately determining tire durability and provides a direction for improving durability, and provides a direction guide for a tire design engineer.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for judging tire endurance performance from a tire ground contact pressure distribution, the method comprising the steps of:
step one, establishing a two-dimensional tire finite element analysis model according to a tire material distribution map;
step two, on the basis of the step one, enabling the two-dimensional tire finite element analysis model to rotate 360 degrees along the circumferential direction of the tire rotating shaft, and generating a 3D model after the tire and the rim are matched; establishing a rigid straight road model, and enabling the rigid straight road to displace towards a tire until the contact load of the rigid straight road model and the tire reaches the standard load of the tire; carrying out tire load analysis and outputting stress value delta of each node of the tire crown contacting with the ground ij Synchronously outputting a stress cloud picture of the grounding area;
step three, carrying out sectional analysis on the stress cloud picture of the tire tread grounding area extracted in the step two: the tire pressure is P, delta ij Dividing a grounding area into n sections according to the stress of the grounding area for each node stress value of a tire crown, respectively drawing a plane contour line of a node stress extreme value (namely two end point values of the node stress section) in the n sections, and forming a closed area in an area between two adjacent plane contour lines; the area of a closed area enclosed by the contour lines of two adjacent planes in the Kth stress section is marked as S K K＝1,2,3,…,n；
Step four, according to the tire pressure P, the tire load L and the total grounding area S t The relation between them is S t ＝L/P；
Step five, according to the area S of each section K Stress value delta of each node of the tire crown ij And total area of grounding S t The average value of the actual grounding pressure can be obtained as follows:
step six, defining the tire durability evaluation index
The endurance performance of the tire under the grounding pressure of each zone can be represented by the M value, and the endurance performance and the grounding pressure of the tire are in negative correlation.
Preferably, in the first step, the specific steps of establishing the tire finite element analysis model are as follows: firstly, establishing a tire two-dimensional axial symmetry analysis model, carrying out grid division on a tire material distribution diagram, carrying out region division on grids according to types of all components, giving corresponding material attributes to all the components, establishing a rigid rim 2D model, enabling a tire and a rim to be located in the same coordinate system, arranging contact pairs, and enabling a tire bead and the rim to be combined together to obtain a tire finite element analysis model. And applying rated inflation pressure on the boundary layer of the inner surface of the tire to perform inflation analysis.
Preferably, in the sixth step, when M is reduced by 0.1, the endurance level is improved by 13-15%; when the pressure difference between the inside and the outside of each grounding section of the tire tends to 0, the durability can reach the best.
Preferably, in the third step, the grounding area is divided into 10 sections according to the stress, n =10, and the method of segment analysis is as follows:
a first stage: delta. For the preparation of a coating ij < 0.1P; and a second stage: delta is not less than 0.1P ij ＜0.3P；
A third stage: delta is not less than 0.3P ij < 0.5P; a fourth stage: 0.5P is less than or equal to delta ij ＜0.7P；
A fifth stage: 0.7P≤δ ij less than 0.9P; a sixth stage: 0.9P is less than or equal to delta ij ＜1.1P；
A seventh stage: 1.1P is less than or equal to delta ij < 1.3P; an eighth stage: 1.3P is less than or equal to delta ij ＜1.5P；
A ninth stage: 1.3P is less than or equal to delta ij < 1.7P; a tenth stage: 1.7P is less than or equal to delta ij ；
And respectively drawing a plane contour line of the node stress in the ten sections to form 10 closed areas.
More preferably, | M | ≦ 0.1 is set as the target value, in which case δ ij ∈[0.9P,1.1P](ii) a The area of a closed area defined by the contour lines of the two planes of the node stress section is S 6 | M | with S 6 The durability is improved when the size is increased and decreased; if | M | is greater than 0.1, there is room for improvement in tire durability, and optimization can be performed until | M | reaches a target value.
As a further preference, from the conclusions drawn above, the nodal stress δ can be derived ij Is [0.9P,1.1P ]]Is enclosed by two plane isolines 6 The durability of the tire is determined by the ratio of the total ground contact area, and S is increased to improve the durability of the tire 6 。
Furthermore, the invention also discloses application of the method for judging the durability of the tire through the tire ground contact pressure distribution in tire simulation design.
Further, the invention also discloses computer equipment which comprises a memory, a processor and a computer program or instruction stored on the memory, wherein the processor executes the computer program or instruction to realize the method for judging the endurance performance of the tire through the tire ground contact pressure distribution.
Further, the present invention also discloses a computer readable storage medium having stored thereon a computer program or instructions which, when executed by a processor, implement the method for determining durability performance of a tire from a ground contact pressure distribution of a tire.
Further, the invention also discloses a computer program product comprising a computer program or instructions, which when executed by a processor, implement the method for determining the endurance performance of a tire through the ground contact pressure distribution of the tire.
By adopting the technical scheme, the invention provides a method for accurately judging the durability of the tire and a durability improving direction by establishing the relationship between the durability of the tire and other physical properties of the tire, and provides direction guidance for tire design engineers.
Drawings
FIG. 1 is a two-dimensional axisymmetric analysis model of a tire;
FIG. 2 is a 3D model of a tire and rim after mating;
FIG. 3 is a stress cloud diagram of a ground region;
FIG. 4 is a diagram of an area of a closed area surrounded by contour lines of two adjacent planes in a K-th stress section;
FIG. 5 is a graph of the inflation analysis performed by the Abaqus software for the tire of example 1;
FIG. 6 is a graph showing a specific angle distribution in step 3 of example 1;
FIG. 7 is a view showing the contour distribution of each node in the ground contact area of the tire of example 1;
FIG. 8 is a graph of the inflation analysis performed by the tire Abaqus software of example 2;
FIG. 9 is a profile distribution shape diagram of each node in the ground contact area of the tire according to example 2;
FIG. 10 is a diagram of the improved footprint of example 2.
Detailed Description
The invention will be described in further detail below with reference to the accompanying drawings: the present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation is given, but the scope of the present invention is not limited to the following embodiments.
A method for judging the endurance quality of a tire from a ground contact pressure distribution of the tire, the method comprising the steps of:
1) Establishing two-dimensional tire finite element analysis model according to tire material distribution diagram
Firstly, establishing a tire two-dimensional axial symmetry analysis model, as shown in fig. 1, performing grid division on a tire material distribution diagram, performing area division on grids according to types of all parts, giving corresponding material attributes to all parts, establishing a rigid rim 2D model, enabling a tire and a rim to be located in the same coordinate system, arranging contact pairs, and enabling a tire bead and the rim to be combined together to obtain the tire finite element analysis model. And applying rated inflation pressure on the boundary layer of the inner surface of the tire, wherein the direction of the inflation pressure is consistent with the normal direction of the inner surface of the tire, and performing inflation analysis.
2) On the basis of the first step, the tire finite element analysis model is rotated 360 degrees along the circumferential direction of the tire rotating shaft, and a 3D model after the tire and the rim are matched is generated, as shown in fig. 2. And (3) establishing a rigid straight road surface model at a position 1mm away from the surface of the tire, and enabling the rigid straight road surface to displace towards the tire until the contact load of the rigid straight road surface and the tire reaches the standard load of the tire. Carrying out tire load analysis and outputting stress value delta of each node of the tire crown contacting with the ground ij And synchronously outputting a stress cloud map of the grounding region as shown in fig. 3.
3) And (3) carrying out sectional analysis on the stress cloud picture of the tire tread grounding area extracted in the step 2). The tire pressure is P, delta ij The method for the segmental analysis of the stress value of each node of the tire crown comprises the following steps:
the ground area is divided into 10 sections according to the stress size:
a first stage: delta ij < 0.1P; and a second stage: 0.1P is less than or equal to delta ij ＜0.3P；
A third stage: delta is not less than 0.3P ij < 0.5P; a fourth stage: delta is not less than 0.5P ij ＜0.7P；
A fifth stage: delta is not less than 0.7P ij < 0.9P; a sixth stage: delta is not less than 0.9P ij ＜1.1P；
A seventh stage: 1.1P is not more than delta ij < 1.3P; an eighth stage: 1.3P is less than or equal to delta ij ＜1.5P；
A ninth stage: 1.3P is less than or equal to delta ij < 1.7P; a tenth stage: 1.7P is less than or equal to delta ij ；
And respectively drawing a plane contour line of the node stress in the ten sections to form 10 closed areas. Two adjacent nodesThe area of the region surrounded by the isolines of the stress plane is recorded as S K K =1,2,3,4,5,6,7,8,9,10, which represents the area of the closed area enclosed by the contours of two adjacent planes in the K-th stress section, as shown in fig. 4.
4) According to the tire pressure P, the tire load L and the total grounding area S t The relation between them is S t ＝L/P；
5) According to the area S of each section K Stress value delta of each node of the tire crown ij And total area of ground S t The average value of the actual grounding pressure can be obtained as follows:
6) Defining tire endurance evaluation index
The endurance performance of the tire under the grounding pressure of each zone can be represented by the M value, and the endurance performance and the grounding pressure of the tire are in negative correlation. When the M is reduced by 0.1, the endurance level is improved by 13-15%. When the pressure difference between the inside and the outside of each grounding section of the tire tends to 0, the durability can reach the best. However, the pressure difference between the inside and the outside of each section cannot be all 0, that is, the area of a closed area defined by a plane contour line with the node stress of P cannot be equal to S t 。
7) Setting M | ≦ 0.1 as the target value, at this time, delta ij ∈[0.9P,1.1P]. The area of a closed region surrounded by the contour lines of the two planes of the node stress section is S 6 M with S 6 And increases and decreases, and durability is improved. If | M | is greater than 0.1, there is room for improvement in tire durability, and optimization can be performed until | M | reaches a target value.
8) From the conclusion of 7), the node pressure δ can be derived ij Is [0.9P,1.1P ]]Is enclosed by the two plane isolines 6 The durability of the tire is judged by the ratio of the total ground contact area, and S is increased to improve the durability of the tire 6 。
Further, in the step of establishing the tire finite element analysis model, carrying out grid division on a tire material distribution diagram, wherein a rubber material without a framework material and a steel wire ring material are divided into quadrilateral units or triangular units; the units containing the framework material are divided into quadrilateral units; (2) and defining the cell type of the divided cells: the framework material is defined as a rebar unit type, and other units are defined as CGAX4; (3) according to the tire material distribution diagram, defining the material attribute of the divided tire grids; (4) and defining relevant parameters such as rim specification, standard air pressure and the like according to the analyzed tire specification type.
The method for judging the durability of the tire through the tire ground contact pressure distribution is applied to tire simulation design.
A computer apparatus comprising a memory, a processor and a computer program or instructions stored on the memory, the processor executing the computer program or instructions to implement the method of determining tire endurance performance from a tire ground contact pressure profile.
A computer-readable storage medium on which a computer program or instructions are stored, which when executed by a processor, implement the method of determining durability performance of a tire from a ground contact pressure distribution of a tire.
A computer program product comprising a computer program or instructions for implementing the method for determining the endurance performance of a tire from a ground contact pressure distribution of a tire when executed by a processor.
Example 1
The tire of 12r22.5 standard will be described as an example.
Step 1, carrying out mesh division on a tire material distribution map. And performing grid division on the tire material distribution diagram, dividing the rubber material into triangular units or quadrilateral units, dividing the rubber material where the framework material is located into quadrilateral units, and dividing the framework material into 2-node one-dimensional units.
And 2, defining material properties. And (3) on the basis of the step 1, giving material properties to the divided grid areas according to actual conditions. The rubber material is selected from a linear elastic constitutive model, and the framework material is selected from a MALLOW model. And the model parameters of each part are obtained by fitting according to the material test data.
And step 3, setting boundary conditions. On the basis of the step 2, applying air pressure of 0.9MPa to the inner surface of the tire inner liner; and establishing a 2D (two-dimensional) model of a rigid rim to carry out position constraint on the tire bead, wherein the rim uses a standard rim with the model number of 9.00 multiplied by 22.5. Aeration analysis was performed using the Abaqus software and the results are shown in figure 5.
And 4, establishing a 3D model. And 3, on the basis of the step 3, rotating the tire section in the circumferential direction for 360 degrees to obtain a 3D model after the tire and the rim are matched, and dividing the section in the circumferential direction. In order to improve the calculation efficiency and ensure the calculation accuracy, a circle is divided into 74 sections, wherein the included angle between the sections of the grounding region is 2 degrees, the included angle between the sections far away from the grounding region is 5-9 degrees, the specific angle distribution is shown in fig. 6, wherein 5 × 12 in the region 1 and the region 3 means that the region 1 and the region 3 are divided into 12 sections, and the included angle between two adjacent sections is 5 degrees; 2 x 30 degrees in the region 2 means that the region 2 is divided into 30 sections, and the included angle between every two adjacent sections is 2 degrees; 2 x 30 degrees in regions 4 and 5 means that regions 4 and 5 are each divided into 10 sections, and the angle between two adjacent sections is 9 degrees. The rim of the analytic rigid body is restrained to displace the road surface, and the load applied to the tire is set to be 35500N.
And 5, extracting grounding characteristic data. On the basis of the step 4, partial node stress distribution data (shown as table 1) and a contour distribution shape chart (shown as figure 7) in the tire grounding area are extracted, and plane contour line division (shown as figure 7) is carried out according to the extracted data. Calculating the area S of each segment region K Total area S of ground region t (see table 2).
TABLE 1 partial nodal stress distribution data in the ground contact area of a tire
TABLE 2 area S of the enclosed area surrounded by the contour lines of two adjacent planes of each stress segment K Total area S of the ground region t
And 6, calculating the durability evaluation index. On the basis of the step 5, calculating the area S of a closed area surrounded by the contour lines of the two planes of each stress section K Occupying the total area S of the grounding region t The ratio of (a) to (b). Further, a durability evaluation index M (table 2) was calculated. According to the calculation result, the | M | =0.09 ≦ 0.1, and the target value is reached. The durability of the tire reaches the qualified standard of 107h through the actual measurement of a bench test. The coincidence degree of the calculation result and the actual test result is high, and the endurance level of the tire can be accurately represented.
Example 2
A tire of 12.00r20 standard will be described as an example.
Step 1, carrying out meshing on a tire material distribution map. And performing grid division on the tire material distribution diagram, dividing the rubber material into triangular units or quadrilateral units, dividing the rubber material where the framework material is located into quadrilateral units, and dividing the framework material into 2-node one-dimensional units.
And 2, defining material properties. And (3) on the basis of the step 1, giving material properties to the divided grid areas according to actual conditions. The rubber material is selected from a linear elastic constitutive model, and the framework material is selected from a MALLOW model. And fitting parameters of each part model according to the material test data.
And step 3, setting boundary conditions. On the basis of the step 2, applying air pressure of 0.9MPa to the inner surface of the tire inner liner; and establishing a rigid rim 2D model to carry out position constraint on the tire bead, wherein the rim uses a standard rim with the model of 8.5 multiplied by 20. The results of the aeration analysis using the Abaqus software are shown in fig. 8.
And 4, establishing a 3D model. And 3, on the basis of the step 3, rotating the tire section by 360 degrees in the circumferential direction to obtain a 3D model after the tire and the rim are matched, and dividing the section in the circumferential direction. In order to improve the calculation efficiency and ensure the calculation accuracy, one circle is divided into 74 sections, wherein the included angle between the sections of the grounding area is 2 degrees, the included angle between the sections far away from the grounding area is 5-9 degrees, and the specific angle distribution is shown in a table of fig. 6. The rim of the analytic rigid body was restrained to displace the road surface, and the load applied to the tire was set to the standard load 37500N.
And 5, extracting grounding characteristic data. On the basis of the step 4, partial node stress distribution data (table 3) and a contour distribution shape chart in the tire grounding area are extracted, as shown in fig. 9, and plane contour line division is carried out according to the extracted data. Calculating the area S of each segment region K Total area S of ground region t (Table 4).
TABLE 3 stress distribution data of tire inner part of tire contact patch in example 2
Table 4 example 2 enclosed area S of the enclosed area enclosed by the two-plane contours of each stress section K Total area S of ground region t
Step 6, on the basis of the step 3, calculating the area S of a closed area surrounded by the contour lines of two adjacent planes of each stress section K Occupying the total area S of the grounding region t Ratio (table 4). Further, the durability evaluation index M was calculated, and it was shown from the calculation result that | M | =0.28 > 0.1, which did not reach the target value. The actual measurement of the bench test shows that the endurance quality of the tire does not reach the qualified standard of 97h. The coincidence degree of the calculation result and the actual test result is high, and the endurance level of the tire can be accurately represented.
And 7, improving the durability. Designing and optimizing the tire with the specification on the basis of the step 4, and increasing the area S of a closed area formed by the isolines of the two planes of the stress section 6 Occupying the total area S of the grounding region t The ratio of (table 5) was increased from 72% to 91%, and the improved footprint pattern is shown in fig. 10. At this time, the durability evaluation index M =0.09 (table 5) was calculated, and the target value of | M | < 0.1 was reached.
TABLE 5 increase of the area S of the closed area surrounded by the contour lines of two adjacent planes of the rear stress section 6 Occupying the total area S of the grounding region t Data of (2)
Further, the actual measurement is carried out through a bench test, and the durability of the tire reaches the qualified standard of 125h. The M value is reduced by 0.19, and the endurance time is improved by 28 percent. The calculation result and the actual test result have high goodness of fit, and the relationship between the change of the M value and the tire durability level can be accurately represented.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention, including any reference to the above-mentioned embodiments. 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. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (10)
1. A method for judging the durability of a tire through the distribution of the tire grounding pressure is characterized in that: the method comprises the following steps:
step one, establishing a two-dimensional tire finite element analysis model according to a tire material distribution diagram;
step two, on the basis of the step one, rotating the two-dimensional tire finite element analysis model by 360 degrees along the circumferential direction of a tire rotating shaft to generate a 3D model after the tire and the rim are matched; establishing a rigid straight road surface model, and enabling the rigid straight road surface to displace towards a tire until the contact load of the rigid straight road surface and the tire reaches the standard load of the tire; analyzing the tire load, and outputting stress values delta of each node of the tire crown contacting with the ground ij Synchronously outputting a stress cloud picture of the grounding area;
step three, aligning the wheel extracted in the step twoAnd (3) carrying out sectional analysis on a stress cloud picture of a tire tread grounding area: the tire pressure is P, delta ij Dividing a grounding area into n sections according to the stress of the grounding area for each node stress value of the tire crown, respectively drawing plane isolines of extreme values of the node stresses in the n sections, and forming a closed area in an area between two adjacent plane isolines; the area of a closed area enclosed by the contour lines of two adjacent planes in the Kth stress section is marked as S K ，K＝1,2,3,…,n；
Step four, according to the tire pressure P, the tire load L and the total grounding area S t The relation between them is S t ＝L/P；
Step five, according to the area S of each section K Stress value delta of each node of tire crown ij And total area of grounding S t The average value of the actual grounding pressure can be obtained as follows:
step six, defining the durability evaluation index of the tire
The endurance performance of the tire under the grounding pressure of each zone can be represented by the M value, and the endurance performance and the grounding pressure of the tire are in negative correlation.
2. The method for judging the endurance quality of the tire according to the ground contact pressure distribution of the tire as claimed in claim 1, wherein: the method comprises the following specific steps of establishing a tire finite element analysis model in the first step: firstly, establishing a two-dimensional axial symmetry analysis model of the tire, carrying out grid division on a tire material distribution map, carrying out region division on grids according to types of all components and endowing all components with corresponding material attributes; establishing a rigid rim 2D model, enabling the tire and the rim to be located in the same coordinate system, arranging a contact pair, combining the tire bead and the rim together to obtain a tire finite element analysis model, and then applying rated inflation pressure on a boundary layer of the inner surface of the tire to perform inflation analysis.
3. The method for judging the endurance quality of the tire according to the ground contact pressure distribution of the tire as claimed in claim 1, wherein: in the sixth step, when the M is reduced by 0.1, the endurance level of the tire is improved by 13-15%; when the pressure difference between the inside and the outside of each grounding section of the tire tends to 0, the durability can reach the best.
4. The method for judging the endurance quality of the tire according to the ground contact pressure distribution of the tire as claimed in claim 1, wherein: in the third step, the grounding area is divided into 10 sections according to the stress magnitude, namely n =10, and the method of segment analysis is as follows: a first stage: delta. For the preparation of a coating ij Less than 0.1P; and a second stage: 0.1P is less than or equal to delta ij ＜0.3P；
A third stage: 0.3P is less than or equal to delta ij < 0.5P; a fourth stage: delta is not less than 0.5P ij ＜0.7P；
A fifth stage: delta is not less than 0.7P ij Less than 0.9P; a sixth stage: delta is not less than 0.9P ij ＜1.1P；
A seventh stage: 1.1P is not more than delta ij < 1.3P; an eighth stage: 1.3P is less than or equal to delta ij ＜1.5P；
A ninth stage: 1.3P is less than or equal to delta ij < 1.7P; a tenth stage: 1.7P is less than or equal to delta ij ；
And respectively drawing a plane contour line of the node stress in the ten sections to form 10 closed areas.
5. The method for judging the endurance quality of the tire according to the ground contact pressure distribution of the tire as claimed in claim 4, wherein: setting M | ≦ 0.1 as target value, at this time, δ ij ∈[0.9P,1.1P](ii) a The area of a closed region surrounded by the contour lines of the two planes of the node stress section is S 6 | M | with S 6 The durability is improved when the size is increased and decreased; if | M | is greater than 0.1, there is room for improvement in tire durability, and optimization can be performed until | M | reaches a target value.
6. The method of claim 5, wherein the tire durability is judged according to the tire ground contact pressure distributionIs characterized in that: from the conclusions drawn, the nodal stress δ can be derived ij Is [0.9P,1.1P ]]Is enclosed by two plane isolines 6 The ratio of the total ground contact area is used to determine the endurance of the tire, and S is increased to improve the endurance 6 。
7. Use of the method of any one of claims 1 to 6 in the design of a tyre simulation.
8. A computer device comprising a memory, a processor and a computer program or instructions stored on the memory, wherein the processor executes the computer program or instructions to implement the method of any one of claims 1 to 6.
9. A computer-readable storage medium, on which a computer program or instructions are stored, which, when executed by a processor, carries out the method of any one of claims 1 to 6.
10. A computer program product comprising a computer program or instructions, characterized in that the computer program or instructions, when executed by a processor, implements the method of any one of claims 1 to 6.
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