An analysis method, application and program product for the influence of rubber modulus on tire rolling resistance

Abstract

The present invention relates to the technical field of intelligent design of tires, and in particular to an analysis method, application and program product of the influence degree of rubber modulus on tire rolling resistance. The calculation process of the present invention can obtain the influence trend of modulus on rolling resistance. Since the deformation mode of the rubber material is refined and decomposed, that is, when the deformation index is greater than 0, it is considered to be a strain and energy mixed control mode, and when the deformation index is less than 0, it is considered to be a stress and energy mixed control mode. By solving a and b parameters, the influence trend and influence degree of the rubber material modulus on rolling resistance can be accurately judged according to the positive and negative sum of m, a and b values, which can provide effective guidance for tire design engineers and material development engineers.

Description

Technical Field

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

[0002] Tires are essential components of automobiles. During their service, the viscoelastic properties of rubber materials will cause rolling energy loss, i.e. rolling resistance. Rolling resistance will consume energy and reduce the mileage of the car. Low rolling resistance is the common pursuit of all tire companies. From the perspective of tire structure, the factors that affect tire rolling resistance are mainly materials and structural design. The two are not independent. The requirements of the structure for materials are mainly reflected in the matching of the modulus of the materials of each part. However, tire design engineers cannot directly propose how to adjust the modulus of each part. The concept of "deformation index" proposed by Futamura et al. (reference: Futamura S, Goldstein A A. Rubber Chemistry and Technology, 2015: 15.84853.; Ebbott T, Futamura S, Goldstein A, et al. Tire Society 17th Annual Meeting and Conference, March 1998, Akron, OH. 1998.; Futamura, Shingo. Rubber Chemistry & Technology, 1991, 64 (1): 57-64.) provides a convenient indicator for adjusting the material modulus. That is, when the "deformation index" is equal to 1, the material is strain-controlled deformation, and reducing the material modulus can reduce the rolling resistance. When the "deformation index" is equal to -1, it is stress-controlled deformation, and increasing the material modulus can reduce the rolling resistance. When the "deformation index" is equal to 0, it is energy-controlled deformation, and the rolling resistance can only be reduced by reducing the material loss factor. At this time, the material modulus has little effect on the rolling resistance of the tire. However, the "deformation index" of the materials in various parts of the tire is rarely exactly equal to 1, -1 or 0, and is basically between -1 and 1 (there are also cases where the absolute value is greater than 1), that is, it is in a mixed deformation state of "strain control" and "energy control" or "stress control" and "energy control". At this time, the indication direction of the "deformation index" is not clear enough, and even gives wrong guidance. Therefore, this patent provides an analysis method for the influence of rubber modulus on the rolling resistance of radial tires. By refining the deformation index, the influence of rubber modulus adjustment on rolling resistance is obtained, and then clear instructions are given on 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 to provide an analysis method for the influence of rubber modulus on tire rolling resistance. By refining the deformation index, the influence of rubber modulus adjustment on rolling resistance is obtained, and then clear instructions are given on 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 analyzing the influence of rubber 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 E100,j , j is the part number:

[0015] i is the unit number

[0016] r0 is 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: Calculate the deformation index of the rubber material unit set:

[0019] Compute the energy loss of a collection of elements for different moduli:

[0020]

[0021]

[0022]

[0023] Where i is the unit number of unit set j, n is the number of all rubber units in unit set j, and the deformation index of each set is calculated by the above formula;

[0024] Step 6: Decompose the deformation index into the following three cases:

[0025] 1) When m j >0, the rubber material deformation is considered to be in the strain and energy joint control mode, a j represents the percentage of strain control, c j Represents the percentage of energy control, the sum of the two is 100%, then solve the equation:

[0026]

[0027] 1=a j +c j

[0028] Due to E 100,j , m j are all known, and a can be obtained through the above two formulas j and c j ;

[0029] 2) When m j<0, the rubber material deformation is considered to be in a stress and energy joint control mode, b j represents the percentage of stress control, c j Represents the percentage of energy control, the sum of the two is 100%, then solve the equation:

[0030]

[0031] 1 = b j +c j

[0032] Similarly, we can find b j and c j ;

[0033] 3) When m j =0, set a j , b j All are 0;

[0034] Step 7: Based on the calculated a j , b j and c j The relationship between the modulus of each component in the tire and the rolling resistance is determined by the value:

[0035] 1) When m j >0:a j >0, the rolling resistance increases with the increase of modulus, and the modulus of the component material should be reduced to reduce the rolling resistance. j <0, the rolling resistance decreases with the increase of modulus, and the modulus of the component material should be increased to reduce the rolling resistance. j The larger the absolute value of , the greater the influence of the material modulus on rolling resistance;

[0036] 2) When m j <0:b j >0, the rolling resistance loss modulus increases and decreases, and the component material modulus should be increased to reduce the rolling resistance, b j <0, at this time, the rolling resistance increases with the increase of modulus, and the modulus of the component material should be reduced to reduce the rolling resistance. The larger the absolute value of bj, the greater the influence of the material modulus on the rolling resistance;

[0037] 3) When m j =0, the rolling resistance is independent of the modulus, and the rolling resistance of the component cannot be affected by adjusting the material modulus.

[0038] 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.

[0039] 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.

[0040] 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%.

[0041] Furthermore, the present invention also provides application of the method in tire design.

[0042] Preferably, the tire is a radial tire.

[0043] Preferably, the tire apex rubber, tread, base rubber, second belt layer, carcass, inner liner, sidewall and protective rubber have a deformation index m j >0, and a j >0, at this time, the rolling resistance increases with the increase of modulus, and the modulus of the component material should be reduced to reduce the rolling resistance; the first belt layer, the first cap layer and the second cap layer, m j <0, b j <0, at this time, the rolling resistance increases with the increase of modulus, and the modulus of the component material should be reduced to reduce the rolling resistance.

[0044] 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.

[0045] 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.

[0046] 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.

[0047] The present invention can obtain the influence trend of modulus on rolling resistance through the above calculation process. Since the deformation mode of the rubber material is refined and decomposed, that is, when the deformation index is greater than 0, it is considered to be a strain and energy mixed control mode, and when the deformation index is less than 0, it is considered to be a stress and energy mixed control mode. By solving the a and b parameters, the influence trend and degree of the modulus of the rubber material on the rolling resistance can be accurately judged according to the positive and negative sum of the m, a, and b values, which can provide effective guidance for tire design engineers and material development engineers. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is the 21550R15 tire section mesh and material components;

[0049] Figure 2 The deformation result of 21550R15 tire inflation;

[0050] Figure 3 The three-dimensional circumferential mesh division result of the 21550R15 tire;

[0051] Figure 4 The three-dimensional load results and direction identification of the 21550R15 tire;

[0052] Figure 5 To output the partial stress values ​​of the tire component elements in the second step;

[0053] Figure 6 To output the partial strain values ​​of the tire component elements in the second step;

[0054] Figure 7 This is the curve of unit LE11 No. 3 changing with the circumferential angle;

[0055] Figure 8 It is the trigonometric series fitting curve of unit LE11 of No.3 and the circumferential angle curve;

[0056] Fig. 9 Partial unit volume data obtained for calculation. DETAILED DESCRIPTION

[0057] 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.

[0058] Take 21550R15 tire as an example:

[0059] 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 ).

[0060] Table 1 shows the material properties of the components of the 21550R15 tire

[0061] Part Name Material modulus (MPa) Poisson's ratio <![CDATA[Density (10 -9 t / mm 3 )]]> tanδ Carcass 3.968 0.49 1 0.1 Protective glue 6.48 0.49 1 0.12 Lining 3.968 0.49 1 0.14 Base glue 4 0.49 1 0.08 Cap layer 5.536 0.49 1 0.13 Second belt layer 8.416 0.49 1 0.12 First belt layer 8.416 0.49 1 0.12 Tread 3.6 0.49 1 0.16 Sidewall 2.336 0.49 1 0.17 Triangle 18.56 0.49 1 0.15 Traveller 21000 0.3 7 0.0 The crown layer skeleton 1000 0.3 1.2 0.0 Carcass frame 2000 0.3 1.2 0.0 Belt skeleton 100000 0.3 6 0.0

[0062] 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):

[0063]

[0064]

[0065] Table 2 shows the trigonometric series fitting coefficients of unit 3

[0066] 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

[0067] 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),

[0068]

[0069] 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 :

[0070]

[0071] 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, and the tire load radius r0 is 286.26 mm:

[0072] i is the unit number

[0073] The calculated partial unit w100 The values ​​are shown in Table 3.

[0074] Table 3 shows the 100 The rolling resistance value of some units

[0075]

[0076]

[0077] 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, when the modulus is increased by 20%, r0 is 286.66mm, and the rolling resistance of the tire rubber material unit with the modulus increased by 20% is obtained, which is recorded as w 120，i , i is the unit number, as shown in Table 5.

[0078] Table 4 shows the material parameters of the tire components after the modulus is increased by 20%

[0079]

[0080]

[0081] Table 5 shows the 120 The rolling resistance value of some units

[0082]

[0083]

[0084] Step 5: Calculate the deformation index of the rubber material unit set:

[0085] Compute the energy loss of a collection of elements for different moduli:

[0086]

[0087]

[0088]

[0089] Where i is the unit number of unit set j, n is the number of all rubber units in unit set j, and Q calculated by the above formula 100 As shown in Table 6, Q 120 As shown in Table 7, the deformation index of each set is obtained, and the deformation index is shown in Table 8.

[0090] Table 6 shows the E of each tire component 100 Rolling resistance value at

[0091] Part Name <![CDATA[Rolling resistance contribution (N) Q 100 > Triangle 0.325 First belt layer 0.907 Second belt layer 1.518 First crown layer 1.741 The second crown layer 0.635 Carcass 1.791 Lining 1.127 Protective glue 1.677 Sidewall 2.663 Tread 12.096 Base glue 5.391

[0092] Table 7 shows the E of each tire component 120 Rolling resistance value at

[0093]

[0094]

[0095] Table 8 shows the deformation index values ​​of various tire components

[0096] Part Name Deformation index m Triangle 0.359253 First belt layer -0.10378 Second belt layer 0.071792 First crown layer -0.03794 The second crown layer -0.02597 Carcass 0.483363 Lining 0.949478 Protective glue 0.145237 Sidewall 0.284937 Tread 0.172733 Base glue 0.012195

[0097] Step 6: Decompose the deformation index into the following three cases:

[0098] (1) In this example, when the deformation index m of the apex rubber, the second belt layer, the carcass, the inner liner, the protective rubber, the sidewall, the tread, and the base rubber is greater than 0, it is considered that the deformation of the rubber material is in the strain and energy joint control mode. Taking the apex rubber as an example, the equation is solved at this time:

[0099] 18.56 0.005926724 =a*18.56+c

[0100] 1=a+c

[0101] Through the above two formulas, we can get a as 0.000994461.

[0102] (2) When m j <0, the deformation of the rubber material is considered to be in a stress and energy joint control mode. Taking the first cap layer as an example, its deformation index is -0.01083851. At this time, solve the equation:

[0103] 5.536 -0.01083815 =b / 5.536+c

[0104] 1 = b + c

[0105] It can be calculated that b is -0.022427254.

[0106] (3) m does not appear in this example j = 0, so it is not considered.

[0107] The calculated a and b values ​​of each component are shown in Table 9.

[0108] Fig. 9 a and b are the values ​​of each tire component

[0109] Part Name a b Triangle 0.000994461 0 First belt layer 0 -0.024142864 Second belt layer 0.003454859 0 First crown layer 0 -0.022427254 The second crown layer 0 -0.00564587 Carcass 0.105909087 0 Lining 0.269953732 0 Protective glue 0.012233123 0 Sidewall 0.220190919 0 Tread 0.381050411 0 Base glue 0.007004042 0

[0110] Step 7: Based on the calculated aj , b j The relationship between the modulus of each component in the tire and the rolling resistance is determined by the value:

[0111] (1) For the apex rubber, tread, base rubber, second belt layer, carcass, inner liner, sidewall, and rubber guard, the deformation index m j >0, and a j >0, in which case the rolling resistance increases with the increase of modulus, and the modulus of the component material should be reduced to reduce the rolling resistance;

[0112] (2) For the first belt layer, the first cap layer and the second cap layer, m j <0, b j <0, at this time, the rolling resistance increases with the increase of modulus, and the modulus of the component material should be reduced to reduce the rolling resistance.

[0113] According to the above analysis, if the tire modulus is adjusted according to the deformation index, then for the first cap layer, since its deformation index is negative, increasing the modulus of the first cap layer will reduce the tire rolling resistance. On the basis of Table 1, the cap layer modulus is increased to 7, and the tire rolling resistance is analyzed using the first to fourth steps of this patent. The tire rolling resistance is 29.904N, and when the cap layer modulus is 5.536, the tire rolling resistance is 29.871N. From the results, it can be seen that increasing the cap layer modulus increases the tire rolling resistance, which is the same as the result of the analysis method of this patent and contrary to the result of the deformation index evaluation method, which proves the effectiveness of the method provided by this patent.

[0114] 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 analyzing the influence of rubber 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 and 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 e of the rubber material unit under stress and strain in different directions 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: 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: Calculate the deformation index of the rubber material unit set: Compute the energy loss of a collection of elements for different moduli: in i For unit collection j The unit number of n For unit collection j The number of all rubber units in the set is calculated by the above formula to obtain the deformation index of each set; Step 6: Decompose the deformation index into the following three cases: 1) When m j >0, the rubber material deformation is considered to be in the strain and energy joint control mode. a j represents the percentage of strain control, c j Represents the percentage of energy control, the sum of the two is 100%, then solve the equation: because E 100,j , m j are all known, and can be obtained through the above two formulas a j and c j ; 2) When m j <0, the rubber material deformation is considered to be in a stress and energy joint control mode. b j Represents the percentage of stress control, c j Represents the percentage of energy control, the sum of the two is 100%, then solve the equation: Similarly, we can find b j and c j ; 3) When m j =0, set a j , b j All are 0; Step 7: According to m j , a j , b j The positive and negative values ​​and the value can be used to determine the trend and degree of influence of the rubber material modulus on rolling resistance.

2. The method according to claim 1, characterized in that In the first step The method includes the following steps: establishing the mesh geometry of the tire structure, assigning material properties, applying rated inflation pressure to the internal boundary layer of the tire, performing a two-dimensional axisymmetric inflation analysis, and based on the inflation analysis, rotating the two-dimensional axisymmetric model for one circle to generate a three-dimensional tire model, fixing the tire rim at a distance from the tire surface, applying a rated load to the drum, and performing a tire load analysis.

3. The method according to claim 1, characterized in that Place a 1.7m or 2m diameter tire rim 1mm away from the tire surface and fix it.

4. 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.

5. 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%.

6. The method according to claim 1, characterized in that In the seventh step, according to the calculated a j , b j and c j The relationship between the modulus of each component in the tire and the rolling resistance is as follows: 1) When m j >0: a j >0, the rolling resistance increases with the increase of modulus, and the modulus of the component material should be reduced to reduce the rolling resistance. a j <0, at this time, the rolling resistance decreases with the increase of modulus, and the modulus of the component material should be increased to reduce the rolling resistance, a j The larger the absolute value of , the greater the influence of the material modulus on rolling resistance; 2) When m j <0: b j >0, the rolling resistance loss modulus increases and decreases, and the component material modulus should be increased to reduce the rolling resistance. b j <0, at this time, the rolling resistance increases with the increase of modulus, and the modulus of the component material should be reduced to reduce the rolling resistance. The larger the absolute value of bj, the greater the influence of the material modulus on the rolling resistance; 3) When m j =0, the rolling resistance is independent of the modulus, and the rolling resistance of the component cannot be affected by adjusting the material modulus.

7. A tire designed by the method according to any one of claims 1 to 6.

8. The tire according to claim 7, characterized in that The tires are radial tires.

9. The tire according to claim 7, characterized in that Tire's apex rubber, tread, base rubber, second belt layer, carcass, inner liner, sidewall and rubber guard, deformation index m j >0, and a j >0, at this time, the rolling resistance increases with the increase of modulus, and the modulus of the component material should be reduced to reduce the rolling resistance; the first belt layer, the first cap layer and the second cap layer, m j <0, b j <0, at this time, the rolling resistance increases with the increase of modulus, and the modulus of the component material should be reduced to reduce the rolling resistance.

10. 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 described in any one of claims 1-6.

11. 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 6 is implemented.

12. 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 6 is implemented.

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