CN115809582B - Method for judging durability of tire through tire ground pressure distribution - Google Patents
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Abstract
A method for judging the durability of a tire through the distribution of the ground pressure of the tire belongs to the technology of the computer simulation design of the tire structureThe field of surgery. The scheme is as follows: establishing a 3D model of the tire and the rim after matching; outputting a stress cloud picture of the grounding area; dividing the ground contact area into n sections according to the stress of the ground contact area, wherein the tire pressure is P, delta ij For the stress value of each node of the crown, each section area S K Total ground area S t Index of evaluation of durability of tire
The M value may be indicative of tire endurance performance at each segment ground contact pressure, both of which are negatively correlated. The method provides a method capable of accurately judging the durability of the tire and provides a direction for improving the durability performance, and provides direction guidance for tire design engineers.
Description
Technical Field
The invention relates to the technical field of tire structure computer simulation design, in particular to a method, application and computer program product for judging tire durability through tire ground contact pressure distribution.
Background
The durability of the tire is not only related to low carbon and environmental protection, but also related to the driving safety. China has made clear demands on the durability of tires, and enterprises respectively set more severe enterprise standards on the basis of national standards for meeting the demands of clients. However, all current methods for achieving tire endurance performance have only been bench testing. The bench test machine has large occupied area and high acquisition cost, and meanwhile, the test period is longer.
In order to solve the above-described deficiency of the bench test, a great deal of research has been conducted by the scholars at home and abroad, and it is desired to reflect the durability of the tire by a numerical simulation method or by establishing a relationship between the characteristics of other aspects of the tire and the durability. At present, a virtual crack expansion method is mainly adopted at home and abroad, and the method needs to measure the relation between the initial crack and the periodic load of the rubber and the size of the intrinsic crack by assuming that the durable damage of the tire is caused by the structural failure after the intrinsic crack of the rubber is expanded to a certain size, so that the early-stage material testing workload and the working difficulty are large, the testing period is long, and the popularization is not easy. The method for representing the endurance performance of the tire by using the strain energy density gradient is proposed by domestic scholars, and the relationship between the strain energy density gradient and the tire is obtained through numerical fitting.
At present, the problems of high cost, long period, large workload and large working difficulty of the tire durability evaluation method are solved, so that proper physical quantity and evaluation method are further explored in the aspect of tire durability prediction, and the improvement direction of the durability performance can be given.
Disclosure of Invention
In order to solve the technical problems described above, an object of the present invention is to provide a method for determining endurance performance of a tire by tire ground contact pressure distribution, which establishes a relationship between endurance performance of the tire and other physical properties of the tire, provides a method capable of accurately determining endurance of the tire and provides endurance performance improvement direction, and provides direction guidance for tire design engineers.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a method of determining tire durability by tire ground contact pressure distribution, the method comprising the steps of:
step one, building a two-dimensional tire finite element analysis model according to a tire material distribution diagram;
step two, on the basis of the step one, enabling the two-dimensional tire finite element analysis model to rotate for 360 degrees along the circumferential direction of a tire rotation shaft, and generating 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 the tire until the contact load of the rigid straight road surface model and the tire reaches the standard load of the tire; performing tire load analysis, and outputting stress value delta of each node of the crown which is in contact with the ground ij Synchronously outputting a stress cloud picture of the grounding area;
step three, carrying out sectional analysis on the stress cloud image 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 the crown, respectively drawing plane contour lines of node stress extreme values (namely two end point values of the node stress sections) in the n sections, and forming a closed area in the area between two adjacent plane contour lines; the area of a closed area surrounded by the contour lines of two adjacent planes in the Kth stress section is recorded 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 gets S t ＝L/P；
Step five, according to the area S of each section K Stress value delta of each node of crown ij Total ground area S t The actual ground pressure average value can be obtained as follows:
step six, defining the durability evaluation index of the tire
Tire endurance performance at each segment ground contact pressure can be characterized by the M value, both of which are negatively correlated.
Preferably, in the first step, the specific step of building a tire finite element analysis model is as follows: firstly, a two-dimensional axisymmetric analysis model of the tire is established, a tire material distribution diagram is subjected to grid division, grids are subjected to regional division according to the types of all parts, corresponding material properties of all parts are given, a 2D model of a rigid rim is established, the tire and the rim are located in the same coordinate system, contact pairs are arranged, and the tire bead and the rim are combined together to obtain the finite element analysis model of the tire. Then applying rated inflation pressure on the boundary layer of the inner surface of the tire for inflation analysis.
Preferably, in the sixth step, the endurance level is raised by 13% -15% every time M is reduced by 0.1; the durability of the tire is optimized when the pressure difference between the inside and the outside of each section of the tire which is in contact with the ground tends to be 0.
Preferably, in the third step, the ground area is divided into 10 sections according to the stress, n=10, and the method of the segmentation analysis is as follows:
the first section: delta ij < 0.1P; and a second section: 0.1P is less than or equal to delta ij ＜0.3P；
Third section: 0.3P is less than or equal to delta ij < 0.5P; fourth section: 0.5P is less than or equal to delta ij ＜0.7P；
Fifth section: 0.7 P.ltoreq.delta ij < 0.9P; sixth section: 0.9P is less than or equal to delta ij ＜1.1P；
Seventh section: 1.1P.ltoreq.delta ij < 1.3P; eighth section: 1.3 P.ltoreq.delta ij ＜1.5P；
Ninth section: 1.3 P.ltoreq.delta ij < 1.7P; tenth section: 1.7P.ltoreq.delta ij ；
And respectively carrying out plane contour line drawing on the node stresses in the ten sections to form 10 closed areas.
As a further preferable mode, delta is obtained when |M| is not more than 0.1 as the target value ij ∈[0.9P,1.1P]The method comprises the steps of carrying out a first treatment on the surface of the The area of a closed area surrounded by two plane contour lines of the node stress section is S 6 (M) with S 6 Increase and decrease, at which time durability is improved; if |M| > 0.1, indicating that there is room for improvement in tire durability, optimization may be performed until |M| reaches the target value.
As a further preference, the node stress delta can be determined from the above-mentioned conclusion ij Is [0.9P,1.1P]Is a closed area S enclosed by two plane contours 6 The ratio of the total ground contact area is used for judging the durability of the tire, and the 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 the tire simulation design.
Further, the invention also discloses a computer device, which comprises a memory, a processor and a computer program or instructions stored on the memory, wherein the processor executes the computer program or instructions to realize the method for judging the durability performance of the tire through the ground contact pressure distribution of the tire.
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 of determining tire endurance performance from tire ground contact pressure distribution.
Further, the invention also discloses a computer program product comprising a computer program or instructions which, when executed by a processor, implements the method for judging the endurance performance of a tire through the tire ground contact pressure distribution.
By adopting the technical scheme, the invention provides a method capable of accurately judging the durability of the tire and provides the direction for improving the durability by establishing the relation 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 of the ground region;
FIG. 4 is a graph of the area of a closed region bounded by contour lines of two adjacent planes in a Kth stress section;
FIG. 5 is a graph of the inflation analysis performed by the tire Abaqus software of example 1;
FIG. 6 is a specific angle distribution diagram in step 3 of example 1;
FIG. 7 is a profile distribution shape of each node in the footprint 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 of each node in the footprint of the tire of example 2;
fig. 10 is a graph of the improved footprint of example 2.
Detailed Description
The invention will be described in further detail 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 protection of the present invention is not limited to the following embodiments.
A method of determining tire durability by tire ground contact pressure distribution, the method comprising the steps of:
1) Building a two-dimensional tire finite element analysis model according to a tire material distribution diagram
Firstly, a two-dimensional axisymmetric analysis model of the tire is established, as shown in fig. 1, a tire material distribution diagram is subjected to grid division, the grid is subjected to region division according to the types of all parts, corresponding material properties of all parts are given, a rigid rim 2D model is established, the tire and the rim are located in the same coordinate system, contact pairs are arranged, and the tire bead and the rim are combined together, so that the finite element analysis model of the tire is obtained. And then 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 for 360 degrees along the circumferential direction of the tire rotation axis, and a 3D model after the tire and the rim are matched is generated, as shown in fig. 2. A rigid flat road surface model is built at a position 1mm away from the surface of the tire, and the rigid flat road surface is displaced towards the tire until the contact load of the rigid flat road surface model and the tire reaches the standard load of the tire. Performing tire load analysis, and outputting stress value delta of each node of the crown which is in contact with the ground ij And synchronously outputting the stress cloud diagram of the grounding area as shown in fig. 3.
3) For the tire tread ground contact area extracted in step 2)And carrying out sectional analysis on the stress cloud picture. The tire pressure is P, delta ij For the stress value of each node of the crown, the method for analyzing the segments is as follows:
the ground area is divided into 10 sections by stress magnitude:
the first section: delta ij < 0.1P; and a second section: 0.1P is less than or equal to delta ij ＜0.3P；
Third section: 0.3P is less than or equal to delta ij < 0.5P; fourth section: 0.5P is less than or equal to delta ij ＜0.7P；
Fifth section: 0.7 P.ltoreq.delta ij < 0.9P; sixth section: 0.9P is less than or equal to delta ij ＜1.1P；
Seventh section: 1.1P.ltoreq.delta ij < 1.3P; eighth section: 1.3 P.ltoreq.delta ij ＜1.5P；
Ninth section: 1.3 P.ltoreq.delta ij < 1.7P; tenth section: 1.7P.ltoreq.delta ij ；
And respectively carrying out plane contour line drawing on the node stresses in the ten sections to form 10 closed areas. The area of the region surrounded by the contour lines of the stress planes of two adjacent nodes is denoted as S K K=1, 2,3,4,5,6,7,8,9,10, represents the area of the enclosed area enclosed by the contours of adjacent planes in the kth stress zone, as shown in fig. 4.
4) According to the tire pressure P, the tire load L and the total ground contact area S t The relation between them gets S t ＝L/P；
5) According to the area S of each section K Stress value delta of each node of crown ij Total ground area S t The actual ground pressure average value can be obtained as follows:
6) Definition of tire durability evaluation index
Tire endurance performance at each segment ground contact pressure can be characterized by the M value, both of which are negatively correlated. When M is reduced by 0.1, the durability level is improved by 13% -1%5%. The durability of the tire is optimized when the pressure difference between the inside and the outside of each section of the tire which is in contact with the ground tends to be 0. But the pressure difference between the inside and the outside of each section cannot be all 0, namely the area of a closed area surrounded by a plane contour line with the node stress of P cannot be equal to S t 。
7) Let |M| be less than or equal to 0.1 as the target value, delta at this time ij ∈[0.9P,1.1P]. The area of a closed area surrounded by two plane contour lines of the node stress section is S 6 (M) with S 6 And increases and decreases, and durability is improved. If |M| > 0.1, indicating that there is room for improvement in tire durability, optimization may be performed until |M| reaches the target value.
8) From the conclusion of 7), the node pressure delta can be derived ij Is [0.9P,1.1P]Is a closed area S enclosed by two plane contours 6 The ratio of the total ground contact area is used for judging the durability of the tire, and S is increased to improve the durability of the tire 6 。
Further, in the step of establishing the tire finite element analysis model, the tire material distribution diagram is subjected to grid division, wherein the rubber material without the framework material and the bead ring material are divided into quadrilateral units or triangular units; the units containing the framework materials are divided into quadrilateral units; (2) defining unit types of the divided unit cells: the framework material is defined as a rebar unit type, and other units are defined as CGAX4; (3) defining material properties of the divided tire grids according to the tire material distribution diagram; (4) and defining the related 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 the design of the tire simulation.
A computer device 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 having stored thereon a computer program or instructions which, when executed by a processor, implement the method of determining tire durability performance from tire ground contact pressure distribution.
A computer program product comprising a computer program or instructions which, when executed by a processor, implements the method of determining tire endurance performance from a tire ground contact pressure profile.
Example 1
A tire of 12r22.5 standard will be described as an example.
Step 1, meshing a tire material distribution map. And (3) carrying out grid division on the tire material distribution diagram, wherein the rubber material is divided into triangular units or quadrilateral units, the rubber material with the framework material is divided into quadrilateral units, and the framework material is divided into 2-node one-dimensional units.
And 2, defining material properties. And on the basis of the step 1, endowing the divided grid areas with material properties 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 the model parameters of each part according to the material test data.
And 3, setting boundary conditions. Applying 0.9MPa air pressure to the inner surface of the tire inner liner layer on the basis of the step 2; the rigid rim 2D model was built to position the beads and a standard rim model 9.00 x 22.5 was used. The inflation analysis was performed using Abaqus software and the results are shown in fig. 5.
And 4, establishing a 3D model. And (3) on the basis of the step (3), rotating the tire section in the circumferential direction by 360 degrees to obtain a 3D model of the tire and the rim after matching, and dividing the section in the circumferential direction. In order to improve the calculation efficiency and ensure the calculation precision, a 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, the specific angle distribution is shown in fig. 6, wherein 5 x 12 in the area 1 and the area 3 refer to that the area 1 and the area 3 are divided into 12 sections, and the included angle between the adjacent two 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 two adjacent sections is 2 degrees; the 2 x 30 degrees in the region 4 and the region 5 means that the region 4 and the region 5 are divided into 10 sections, and the included angle between two adjacent sections is 9 degrees. The rim of the analytical rigid body is restrained and displaced by the road surface to bring the load applied to the tire to standard load 35500N.
And 5, extracting the grounding characteristic data. On the basis of step 4, partial node stress distribution data (as shown in table 1) and a profile distribution shape chart (as shown in fig. 7) in the tire ground contact area are extracted, and plane contour line division (fig. 7) is performed according to the extracted data. Calculating the area S of each segmented region K Total area S of ground region t (as in Table 2).
TABLE 1 partial node stress distribution data in tire footprint
TABLE 2 area S of the closed region defined by the contour lines of two adjacent planes of each stress zone K Total area S of ground area t
And 6, calculating a durability evaluation index. On the basis of the step 5, calculating the area S of a closed area surrounded by two plane contour lines of each stress section K Occupy the total area S of the grounding area t Is a ratio of (2). Further, durability evaluation index M (table 2) was calculated. And according to the calculation result, displaying that the absolute value M is less than or equal to 0.09 and less than or equal to 0.1, and reaching the target value. The actual measurement is carried out through a bench test, and the durability of the tire reaches the qualified standard 107h. The calculated result has high coincidence degree with the actual test result, and the endurance level of the tire can be accurately represented.
Example 2
A 12.00R20 tire will be described as an example.
Step 1, meshing a tire material distribution map. And (3) carrying out grid division on the tire material distribution diagram, wherein the rubber material is divided into triangular units or quadrilateral units, the rubber material with the framework material is divided into quadrilateral units, and the framework material is divided into 2-node one-dimensional units.
And 2, defining material properties. And on the basis of the step 1, endowing the divided grid areas with material properties 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 the model parameters of each part according to the material test data.
And 3, setting boundary conditions. Applying 0.9MPa air pressure to the inner surface of the tire inner liner layer on the basis of the step 2; the rigid rim 2D model was built to position constrain the beads, with a standard rim model 8.5×20. The inflation analysis was performed using Abaqus software and the results are shown in fig. 8.
And 4, establishing a 3D model. And (3) on the basis of the step (3), rotating the tire section in the circumferential direction by 360 degrees to obtain a 3D model of the tire and the rim after matching, and dividing the section in the circumferential direction. In order to improve the calculation efficiency and ensure the calculation precision, a 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 analytical rigid body is constrained to displace the road surface to bring the load applied to the tire to standard load 37500N.
And 5, extracting the grounding characteristic data. On the basis of step 4, partial node stress distribution data (table 3) and a profile distribution shape chart in the tire ground contact area are extracted, as shown in fig. 9, and plane contour line division is performed according to the extracted data. Calculating the area S of each segmented region K Total area S of ground region t (Table 4).
Table 3 example 2 partial node stress distribution data in the tire footprint
TABLE 4 area S of the closed region enclosed by the two planar contours of each stress segment of example 2 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 Occupy the total area S of the grounding area t Is a ratio (Table 4). Further, the durability evaluation index M was calculated, and it was shown that |m|=0.28 > 0.1, based on the calculation result, did not reach the target value. The actual measurement by the bench test shows that the durability of the tire does not reach the qualified standard 97h. The calculated result has high coincidence degree with the actual test result, and the endurance level of the tire can be accurately represented.
And 7, improving durability. On the basis of the step 4, the design optimization is carried out on the tire with the specification, and the area S of a closed area surrounded by two plane contour lines of a stress section is increased 6 Occupy the total area S of the grounding area t The ratio (table 5) was increased from 72% to 91%, and the improved footprint graph was shown in fig. 10. The endurance evaluation index m=0.09 (table 5) was calculated at this time, reaching the target value of |m| < 0.1.
TABLE 5 increasing the area S of the closed region bounded by the contour lines of two adjacent planes of the post-stress section 6 Occupy the total area S of the grounding area 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 125h. The M value is reduced by 0.19, and the endurance time is improved by 28%. The calculated result has high coincidence degree with the actual test result, and the relationship between the change of the M value and the endurance level of the tire 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. Various modifications to these embodiments will be readily apparent to those skilled in the art. The generic principles defined herein may be applied to 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 (8)
1. A method for determining tire durability through tire ground contact pressure distribution, characterized by: the method comprises the following steps:
step one, building a two-dimensional tire finite element analysis model according to a tire material distribution diagram;
step two, rotating the two-dimensional tire finite element analysis model for 360 degrees along the circumferential direction of a tire rotation shaft on the basis of the step one 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 the tire until the contact load of the rigid straight road surface model and the tire reaches the standard load of the tire; performing tire load analysis, and outputting stress value delta of each node of the crown which is in contact with the ground ij Synchronously outputting a stress cloud picture of the grounding area;
step three, carrying out sectional analysis on the stress cloud image 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 the crown, respectively drawing plane contour lines of node stress extreme values in the n sections, and forming a closed area in the area between two adjacent plane contour lines; the area of a closed area surrounded by the contour lines of two adjacent planes in the Kth stress section is recorded 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 gets S t ＝L/P；
Step five, according to the area S of each section K Stress value delta of each node of crown ij Total ground area S t The actual ground pressure average value can be obtained as follows:
step six, fixingDurability evaluation index of sense tire
Tire endurance performance at each segment ground contact pressure can be characterized by the M value, both of which are negatively correlated.
2. A method of determining tire durability by tire ground contact pressure distribution according to claim 1, wherein: the specific steps of building the tire finite element analysis model in the first step are as follows: firstly, building a two-dimensional axisymmetric analysis model of the tire, carrying out grid division on a tire material distribution diagram, carrying out region division on grids according to the types of all parts, and endowing corresponding material properties of all parts; and (3) establishing a rigid rim 2D model, enabling the tire and the rim to be located in the same coordinate system, arranging contact pairs, enabling the tire bead and the rim to be combined together to obtain a tire finite element analysis model, and then applying rated inflation pressure on the boundary layer of the inner surface of the tire to perform inflation analysis.
3. A method of determining tire durability by tire ground contact pressure distribution according to claim 1, wherein: in the sixth step, when M is reduced by 0.1, the endurance level of the tire is improved by 13% -15%; the durability of the tire is optimized when the pressure difference between the inside and the outside of each section of the tire which is in contact with the ground tends to be 0.
4. A method of determining tire durability by tire ground contact pressure distribution according to claim 1, wherein: in the third step, the grounding area is divided into 10 sections according to the stress, namely n=10, and the method of the segmentation analysis is as follows: the first section: delta ij < 0.1P; and a second section: 0.1P is less than or equal to delta ij ＜0.3P；
Third section: 0.3P is less than or equal to delta ij < 0.5P; fourth section: 0.5P is less than or equal to delta ij ＜0.7P；
Fifth section: 0.7 P.ltoreq.delta ij < 0.9P; sixth section: 0.9P is less than or equal to delta ij ＜1.1P；
Seventh section: 1.1P.ltoreq.delta ij < 1.3P; eighth section：1.3P≤δ ij ＜1.5P；
Ninth section: 1.3 P.ltoreq.delta ij < 1.7P; tenth section: 1.7P.ltoreq.delta ij ；
And respectively carrying out plane contour line drawing on the node stresses in the ten sections to form 10 closed areas.
5. A method of determining tire durability by tire ground contact pressure distribution according to claim 4, wherein: let |M| be less than or equal to 0.1 as the target value, delta at this time ij ∈[0.9P,1.1P]The method comprises the steps of carrying out a first treatment on the surface of the The area of a closed area surrounded by two plane contour lines of the node stress section is S 6 (M) with S 6 Increase and decrease, at which time durability is improved; if |M| > 0.1, indicating that there is room for improvement in tire durability, optimization may be performed until |M| reaches the target value.
6. A method of determining tire durability by tire ground contact pressure distribution according to claim 5, wherein: from the conclusion, the node stress delta can be calculated ij Is [0.9P,1.1P]Is a closed area S enclosed by two plane contours 6 The ratio of the total ground contact area is used for judging the durability of the tire, and the S is increased to improve the durability of the tire 6 。
7. 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 1-6.
8. A computer readable storage medium having stored thereon a computer program or instructions, which when executed by a processor, implements the method of any of claims 1-6.
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| US11498364B2 (en) * | 2017-12-30 | 2022-11-15 | Compagnie Generale Des Etablissements Michelin | Tire with improved handling performance and speed durability |
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| CN114297891A (en) * | 2021-12-27 | 2022-04-08 | 中策橡胶集团股份有限公司 | Method, device and computer program for calculating ratio of bending energy to compression energy of tread |
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