A method, application and program product for calculating the effect of rubber material modulus on tire rolling resistance

Abstract

The present invention relates to the field of intelligent design technology for tires, and in particular to a method, application and program product for calculating the influence of rubber material modulus on tire rolling resistance. The present invention can quickly obtain the influence law of component modulus on tire rolling resistance through the above three simulation calculations combined with the proposed mixed deformation model formula of tire rubber material rolling, which can improve efficiency by hundreds of times compared with the experimental method. If the tire contains 10 components, the time spent by the method proposed in this patent (3 simulation calculations) can be at least 17 times higher than that of the pure simulation method (50 simulation calculations), which can provide guidance for quickly determining reasonable component moduli and improve development efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent design of tires, and in particular to a method, application and program product for calculating the influence of rubber material modulus on tire rolling resistance. Background Art

[0002] With the popularity of electric vehicles and the demand for high mileage, coupled with the introduction of tire labeling laws in the United States, the European Union, Japan and China, higher requirements have been placed on the rolling resistance of tires. How to reduce rolling resistance is a key issue that all tire companies urgently need to solve. The factors that affect tire rolling resistance mainly include structure, materials, working conditions and road surfaces. Among them, working conditions and road surfaces are uncontrollable factors, and structure and materials are the two main entry points for reducing rolling resistance. The effects of structure and material on tire rolling resistance are not independent. Different structural tires require reasonable modulus matching to obtain ideal rolling resistance effects. How to quickly obtain reasonable and accurate component modulus under the premise that the tire structure is basically finalized is related to the development efficiency and quality of the product. At present, the main methods for studying the influence of material modulus on tire rolling resistance are experimental methods and simulation methods. The experimental method requires the development of materials with different moduli and the production of tires, which has the disadvantages of long cycle and high cost. Although the simulation method can quickly obtain the rolling resistance of a single tire, since the tire has more than ten components, the calculation using the simulation method alone must first be performed DOE, which requires at least hundreds of schemes to be calculated, with huge calculation volume and low efficiency. In fact, there is a specific physical relationship between tire rolling resistance and modulus. Based on this, this patent proposes a method for quickly calculating the influence of rubber material modulus on tire rolling resistance. The method combining simulation and theory can quickly obtain the influence of modulus on rolling resistance, and then clearly indicate how to adjust the material modulus of various parts of the tire, providing a basis for tire design engineers and material development engineers. Summary of the invention

[0003] The purpose of the present invention is to solve the problems existing in the above-mentioned prior art, and further provide a method for calculating the influence of rubber material modulus on tire rolling resistance. The method combining simulation and theory can quickly obtain the influence law of modulus on rolling resistance, and then clearly indicate how to adjust the material modulus of various parts of the tire, providing a basis for tire design engineers and material development engineers.

[0004] In order to achieve the above-mentioned purpose, the present invention adopts the following technical solutions:

[0005] A method for calculating the effect of rubber material modulus on tire rolling resistance, the method comprising the following steps:

[0006] The first step is to conduct static simulation analysis on the tire, establish the tire structure mesh geometry, assign material properties, apply rated inflation pressure to the internal boundary layer of the tire, conduct two-dimensional axisymmetric inflation analysis, and on the basis of the inflation analysis, rotate the two-dimensional axisymmetric model for one circle to generate a three-dimensional tire model. Fix the tire rim at a distance from the tire surface, apply rated load to the drum, conduct tire load analysis, and output stress and strain values ​​of the tread.

[0007] In the second step, the program is used to extract the true stress and strain values ​​of the units at the same position and different angles around the tire in the first step, which are recorded as σ ij Value and ε ij The value is x, with the tire circumferential angle in radians. The 400th-order trigonometric series is used to calculate σ. ij , ε ij The values ​​are fitted:

[0008]

[0009]

[0010] Step 3: Use the fitted parameter data to calculate the energy loss density e of the rubber material unit under stress and strain in different directions ij , tanδ is the loss tangent of the rubber material,

[0011]

[0012] Add the energy loss density under stress and strain and multiply it by the volume V of the unit el , which is the energy loss W of unit m m :

[0013]

[0014] The energy loss of the rubber material unit divided by the circumference of the tire is the rolling resistance w of the rubber material unit. The modulus of the rubber material at this time is recorded as E 100,j , j is the part number:

[0015] i is the unit number

[0016] r 0 Extracted from the calculation result in the first step, that is, the distance from the tire axle to the road surface after loading;

[0017] Step 4: Increase the modulus of the rubber material in the two-dimensional axisymmetric model in the first step by 10-30%, which is E 120,j , j is the set number, and then repeat the first step to the third step to obtain the rolling resistance of the tire rubber material unit with a modulus increase of 10-30%, which is recorded as w 120，i, i is the unit number;

[0018] Step 5: Reduce the modulus of the rubber material in the two-dimensional axisymmetric model in the first step to 70-90%, which is E 80,j , j is the set number, and then repeat the first to third steps to obtain the unit rolling resistance of the tire rubber material with a modulus of 70-90%, recorded as w 80，i , i is the unit number;

[0019] Step 6: Decompose the rolling resistance of the rubber material according to the following formula:

[0020]

[0021] where a j , b j , c j is the coefficient, Q j is the rolling resistance of unit set number j, E j is the material modulus of the unit set number j, where Q j The calculation method is as follows:

[0022]

[0023] Where i is the unit number of unit set j, and n is the number of all rubber units in unit set j;

[0024] According to the third to fifth steps, the 100 , E 120 , E 80 Each unit w in the case i , and then use the above formula in this step to obtain the Q of each unit set j , a j , b j 、c j The calculation of is obtained by solving the following formula:

[0025] Q 80，j =a j E 80，j +b j / E 80，j +c j

[0026] Q 100，j =a j E 100，j +b j / E 100，j +c j

[0027] Q 120，j =a j E 120，j +b j / E 120，j +c j

[0028] In the above formula, Q 80,j , Q 100,j , Q 120,j and E 80,j , E 100,j , E 120,j All are known. The three unknowns a can be obtained through the above three equations. j , b j 、c j .

[0029] Preferably, in the first step, a 1.7-meter or 2-meter diameter tire rim is placed at a distance of 1 mm from the tire surface to fix the tire rim.

[0030] Preferably, the stress and strain values ​​include 6 stress components and 6 strain components, and the directions are 11 direction, 22 direction, 33 direction, 12 direction, 13 direction and 23 direction respectively.

[0031] Preferably, in the fourth step, the modulus of the rubber material in the two-dimensional axisymmetric model in the first step is increased by 20%; in the fourth step, the modulus of the rubber material in the two-dimensional axisymmetric model in the first step is reduced to 80%.

[0032] Furthermore, the present invention also provides application of the method in tire design.

[0033] Preferably, the tire is a radial tire.

[0034] Preferably, the rolling resistance of the sidewall rubber of the tire increases with increasing modulus, the rolling resistance of the tread rubber decreases with increasing modulus, increases sharply with increasing modulus within a smaller modulus range, and then decreases slowly, and the rolling resistance of the base rubber decreases with increasing modulus.

[0035] Furthermore, the present invention also provides a computer device, comprising a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the method.

[0036] Furthermore, the present invention also provides a computer-readable storage medium having a computer program or instruction stored thereon, and the method is implemented when the computer program or instruction is executed by a processor.

[0037] Furthermore, the present invention also provides a computer program product, comprising a computer program or instructions, which implement the method when executed by a processor.

[0038] The present invention can quickly obtain the influence of component modulus on tire rolling resistance through the above three simulation calculations combined with the proposed mixed deformation model formula of tire rubber material rolling. Compared with the experimental method, the efficiency can be improved by hundreds of times. If the tire contains 10 components, the time spent by the method proposed in this patent (3 simulation calculations) can be at least 17 times higher than that of the pure simulation method (50 simulation calculations). It can provide guidance for quickly determining reasonable component modulus and improve development efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is the 21550R15 tire section mesh and material components;

[0040] Figure 2 The deformation result of 21550R15 tire inflation;

[0041] Figure 3 The three-dimensional circumferential mesh division result of the 21550R15 tire;

[0042] Figure 4 The three-dimensional load results and direction identification of the 21550R15 tire;

[0043] Figure 5 To output the partial stress values ​​of the tire component elements in the second step;

[0044] Figure 6 To output the partial strain values ​​of the tire component elements in the second step;

[0045] Figure 7 This is the curve of unit LE11 No. 3 changing with the circumferential angle;

[0046] Figure 8 It is the trigonometric series fitting curve of unit LE11 of No.3 and the circumferential angle curve;

[0047] Fig. 9 Partial unit volume data obtained for calculation;

[0048] Fig.10 The variation law of the rolling resistance of the sidewall rubber with the modulus;

[0049] Fig.11 is the variation law of rolling resistance of tread rubber with modulus;

[0050] Fig.12 This is the variation law of base rubber rolling resistance with modulus. DETAILED DESCRIPTION

[0051] The present invention will be further described in detail below in conjunction with the accompanying drawings: This embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation method is given, but the protection scope of the present invention is not limited to the following embodiments.

[0052] Take 21550R15 tire as an example:

[0053] The first step is to use Abaqus software to perform static simulation analysis on the tire. Establish the tire structure mesh geometry (such as Figure 1 ), assign material properties (as shown in Table 1), apply a rated inflation pressure of 0.21 MPa to the tire internal boundary layer, and perform a two-dimensional axisymmetric inflation analysis (as shown in Table 1). Figure 2 ), based on the inflation analysis, the two-dimensional axisymmetric model is rotated for one circle to generate a three-dimensional tire model, and a rigid road surface with a diameter of 1 mm is placed at a distance of 1 mm from the tire surface (such as Figure 3 ), fix the tire rim, apply a rated load of 2882N to the drum, and perform tire load analysis (such as Figure 4 ), output the stress value of the tread part (S11, S22, S33, S12, S13, S23, such as Figure 5 ) and strain values ​​(LE11, LE22, LE33, LE12, LE13, LE23, such as Figure 6 ).

[0054] Table 1 shows the material properties of various components of the 21550R15 tire. 100

[0055]

[0056]

[0057] In the second step, the program is used to extract the true stress (S11, S22, S33, S12, S13, S23) and strain value (LE11, LE22, LE33, LE12, LE13, LE23) of the unit at the same position and different angles in the first step and the middle tire circle, respectively, and record them as σ ij Value and ε ij Value, with the tire circumferential angle as x value (x in radians) (such as Figure 7 ), using the 400th-order trigonometric series to calculate σ ij and ε ij Fitting (such as Figure 8 , the fitting coefficients are shown in Table 2):

[0058]

[0059]

[0060] Table 2 shows the trigonometric series fitting coefficients of unit 3

[0061] Degree <![CDATA[ε nc ]]> <![CDATA[ε ns ]]> n＝1 0.048677128161277006 -0.01178 n＝2 0.005762 0.034562 n＝3 -0.02496 0.006944 n＝4 -0.01306 -0.01652 n＝5 0.010247 -0.0155 n＝6 0.009846 0.008189 n＝7 -0.00664 0.005613 n＝8 -0.00468 -0.00443 n＝9 0.00364 -0.00312 n＝10 0.000865 0.003969

[0062] Step 3: Use the fitted parameter data to calculate the energy loss density e of the rubber material unit under different stresses (strains) ij , tanδ is the loss tangent of the rubber material (as shown in Table 1),

[0063]

[0064] Add the energy loss densities under the six stresses (strains) and multiply by the volume V of the unit el (The calculation result is output from the second step, such as Fig. 9 ), which is the energy loss W of unit m m :

[0065]

[0066] The energy loss of the rubber material unit divided by the circumference of the tire is the rolling resistance w of the rubber material unit. 100 , the modulus of the rubber material at this time is recorded as E 100,j , j is the part number, tire load radius r 0 287.7mm:

[0067] i is the unit number

[0068] The calculated partial unit w 100 The values ​​are shown in Table 3.

[0069] Table 3 shows the 100 The rolling resistance value of some units

[0070]

[0071]

[0072] Step 4: Increase the modulus of the rubber material in the two-dimensional axisymmetric model in the first step by 20%, which is E 120,j (as shown in Table 4), j is the set number, and then repeat the first step to the third step, and when the modulus is increased by 20%, r 0 The rolling resistance of the tire rubber material unit with a modulus increased by 20% is 286.66 mm, which is recorded as w 120，i , i is the unit number, as shown in Table 5.

[0073] Table 4 shows the material parameters of the tire components after the modulus is increased by 20%

[0074]

[0075]

[0076] Table 5 shows the 120The rolling resistance value of some units

[0077]

[0078]

[0079] Step 5: Reduce the modulus of the rubber material in the two-dimensional axisymmetric model in the first step to 80%, which is E 80,j (as shown in Table 6), j is the set number, and then repeat the first step to the third step to obtain the unit rolling resistance of the tire rubber material with a modulus of 80%, which is recorded as w 80，i , i is the unit number, as shown in Table 7.

[0080] Table 6 shows the material parameters of the tire components after the modulus is reduced by 20%

[0081]

[0082]

[0083] Table 7 shows the 80 The rolling resistance value of some units

[0084]

[0085]

[0086] Step 6: Traditionally, the deformation of rubber materials in different parts of the tire is considered to be in a single mode. However, since the tire rubber material is in a three-dimensional stress state, the deformation of the rubber material in each part is in a mixed deformation mode. Therefore, the rolling resistance of the rubber material needs to be decomposed according to the following formula:

[0087]

[0088] where a j , b j , c j is the coefficient, Q j is the rolling resistance of unit set number j, E j is the material modulus of the unit set number j, where Q j The calculation method is as follows:

[0089]

[0090] Where i is the unit number of unit set j, and n is the number of all rubber units in unit set j.

[0091] Take the tread rubber as an example. At this time, the unit set number j is the tread. The tread unit set contains 140 units. 80 The w of each unit in this set isi Add together to get Q 胎面 , is 12.371N, as shown in Table 8.

[0092] Table 8 shows the rolling resistance values ​​of tire tread assembly units and assemblies

[0093]

[0094]

[0095] According to the third to fifth steps, the 100 , E 120 , E 80 Each unit w in the case i , and then use the above formula in this step to obtain the Q of each unit set j , a j 、b j 、c j The calculation of is obtained by solving the following formula:

[0096] Q 80，j =a j E 80，j +b j / E 80，j +c j

[0097] Q 100，j =a j E 100，j +b j / E 100，j +c j

[0098] Q 120，j =a j E 120，j +b j / E 120，j +c j

[0099] Taking the tread unit set as an example, Q in the above formula 80,胎面 , Q 100,胎面 , Q 120,胎面 They are 12.237, 12.558, and 12.739 respectively. 80,胎面 , E 100,胎面 , E 120,胎面 6, 7.5, and 9 are all known, and the above three equations are:

[0100] 12.237 = a 胎面 6+b 胎面 / 6+c 胎面

[0101] 12.558 = a胎面 7.5+b 胎面 / 7.5+c 胎面

[0102] 12.739 = a 胎面 9+b 胎面 / 9+c 胎面

[0103] Through the above three equations, we can get the unknown number a 胎面 , b 胎面 、c 胎面 The coefficients a, b, and c of all tire sets are obtained by the same method as above, as shown in Table 9. According to the values ​​of a, b, and c of each unit set, the variation law of the rolling resistance of the unit set with the modulus can be quickly plotted, as shown in Table 9. Fig.10 , Fig.11 , Fig.12 shown.

[0104] Table 9 shows the a, b, c values ​​of each unit set

[0105] gather a b c Tread -0.065902523 -12.5922039 14.73121109 Base glue -0.204762644 -0.016776139 6.822686867 Lining layer 0.237840877 -1.375450276 1.056529499 Sidewall rubber 0.308360753 -0.132386557 2.075845428 Protective glue 0.02563698 0.581869853 1.300729846 Triangle 0.000215369 -1.451010513 0.431897646 First crown layer -0.007037645 0.933740522 1.678117138 Second belt layer 0.001708898 -0.600577652 1.460504406 The second crown layer -0.001187314 0.513310956 0.558951584 First belt layer 0.012032281 2.034442868 0.422313118

[0106] from Fig.10 It can be seen that the rolling resistance of the sidewall rubber increases with the increase of modulus. Fig.11 It can be seen that the rolling resistance of the tread rubber decreases with the increase of modulus. In a smaller modulus range, it increases sharply with the increase of modulus, and then decreases slowly. Fig.12 It can be seen that the rolling resistance of the base rubber decreases as the modulus increases.

[0107] Through the above three simulation calculations combined with the proposed mixed deformation model formula of tire rubber material rolling, the influence of component modulus on tire rolling resistance can be quickly obtained. According to the calculated law, the simulation method is used to increase the base rubber modulus to 6.5, and the rolling resistance of the base rubber is reduced from 5.898N to 5.39N, verifying the effectiveness of this patented method.

[0108] A single simulation calculation of this embodiment takes 40 minutes, and this patent only calculates 3 simulation results. If the method of this patent is not adopted, at least 50 simulation calculations are required, which is at least 17 times higher than the pure simulation method (50 simulation calculations). Even if 50 results are calculated, there are only 5 data points for the influence law of each component, which may not necessarily reflect a more complete law. This reflects the effectiveness and innovation of this patent application.

[0109] The above is a description of the embodiments of the present invention. Through the above description of the disclosed embodiments, professionals and technicians in the field can implement or use the present invention. Various modifications to these embodiments will be apparent to professionals and technicians in the field. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown in this article, but will conform to the widest range consistent with the principles and novelties disclosed herein.

Claims

1. A method for calculating the effect of rubber material modulus on tire rolling resistance, characterized in that: The method comprises the following steps: The first step is to conduct static simulation analysis on the tire, establish the tire structure mesh geometry, assign material properties, apply rated inflation pressure to the internal boundary layer of the tire, and conduct a two-dimensional axisymmetric inflation analysis. Based on the inflation analysis, the two-dimensional axisymmetric model is rotated one circle to generate a three-dimensional tire model. A rigid road surface is placed 1 mm away from the tire surface, the tire rim is fixed, and a rated load is applied to the drum. The tire load analysis is performed to output the stress and strain values ​​of the tread. In the second step, the program is used to extract the true stress and strain values ​​of the units at the same position and different angles around the tire in the first step and record them as σ ij Value and ε ij Value, in tire circumferential angle x value, x In radians, using a 400-order trigonometric series σ ij , ε ij The values ​​are fitted: Step 3: Use the fitted parameter data to calculate the energy loss density of the rubber material unit under stress and strain in different directions e ij , tanδ is the loss tangent of the rubber material, Add the energy loss densities under stress and strain and multiply by the volume of the element , which is the unit m Energy loss : The energy loss of the rubber material unit divided by the circumference of the tire is the rolling resistance of the rubber material unit. , the modulus of the rubber material at this time is recorded as E 100 , j , j For the part number: ， i is the unit number, r 0 Extracted from the calculation result in the first step, that is, the distance from the tire axle to the road surface after loading; Step 4: Increase the modulus of the rubber material in the two-dimensional axisymmetric model in the first step by 10-30%, which is E 120,j , j Number the set, and then repeat the first to third steps to obtain the rolling resistance of the tire rubber material unit with a modulus increase of 10-30%, recorded as , i is the unit number; Step 5: Reduce the modulus of the rubber material in the two-dimensional axisymmetric model in the first step to 70-90%, which is E 80,j , j Number the set, and then repeat the first to third steps to obtain the unit rolling resistance of the tire rubber material with a modulus of 70-90%, recorded as , i is the unit number; Step 6: Decompose the rolling resistance of the rubber material according to the following formula: in a j , b j , c j is the coefficient, Q j The unit set number is j The rolling resistance, E j The unit set number is j The material modulus of Q j The calculation method is as follows: in i For unit collection j The unit number of n For unit collection j The number of all rubber units; According to the third to fifth steps, E 100 ，E 120 ，E 80 Each unit in the case w i , and then use the above formula in this step to obtain the value of each unit set Q j , a j , b j , c j The calculation of is obtained by solving the following formula: In the above formula Q 80,j , Q 100,j , Q 120,j and E 80,j , E 100,j , E 120,j All are known. The three unknowns can be obtained through the above three equations. a j , b j , c j .

2. The method according to claim 1, characterized in that Place a rigid road surface with a diameter of 1.7m or 2m at a distance of 1mm from the tire surface and fix the tire rim.

3. The method according to claim 1, characterized in that The stress and strain values ​​include 6 stress components and 6 strain components, and the directions are 11 direction, 22 direction, 33 direction, 12 direction, 13 direction and 23 direction respectively.

4. The method according to claim 1, characterized in that: In the fourth step, the modulus of the rubber material in the two-dimensional axisymmetric model in the first step is increased by 20%; in the fourth step, the modulus of the rubber material in the two-dimensional axisymmetric model in the first step is reduced to 80%.

5. Application of the method according to any one of claims 1 to 4 in tire design.

6. Application of the method according to claim 5 in tire design, characterized in that: The tires are radial tires.

7. The use according to claim 5, characterized in that: The rolling resistance of the sidewall rubber of the tire increases with the increase of modulus, while the rolling resistance of the tread rubber decreases with the increase of modulus. Within a smaller modulus range, it increases sharply with the increase of modulus and then decreases slowly. The rolling resistance of the base rubber decreases with the increase of modulus.

8. A computer device comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the method according to any one of claims 1 to 4.

9. A computer-readable storage medium having a computer program or instruction stored thereon, characterized in that: When the computer program or instruction is executed by a processor, the method described in any one of claims 1 to 4 is implemented.

10. A computer program product comprising a computer program or instructions, characterized in that When the computer program or instruction is executed by a processor, the method described in any one of claims 1 to 4 is implemented.

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