Method and system for predicting torsional rigidity of tire and computer software

Abstract

The invention relates to the technical field of tire finite element simulation analysis, in particular to a method and system for predicting the torsional rigidity of a tire and computer software. The method comprises the following steps: firstly, acquiring experimental data under different tire models and working conditions, and identifying key factors influencing the torsional rigidity of the tire, such as air pressure, load, tire size and the like; and then, establishing a mathematical model by using a statistical analysis method, and fitting experimental data with the model so as to accurately predict the torsional rigidity of the tire. The method not only simplifies the prediction process of the tire torsional rigidity, but also greatly reduces the cost and time consumption. Compared with a traditional laboratory test and simulation analysis method, the method has the advantages of being easy and convenient to operate, free of high-skill operation, high in calculation speed and the like, an efficient and accurate prediction tool can be provided for tire designers, and improvement of performance optimization of tires and controllability and comfort of vehicles is facilitated.

Description

Technical Field

[0001] The present invention relates to the technical field of tire finite element simulation analysis, and in particular to a method, system and computer software for predicting tire torsional stiffness. Background Art

[0002] The torsional rigidity of a tire refers to the ratio of torsional torque to the rotation angle when the tire is subjected to torsional torque (k=N*m / deg). It is an important parameter that reflects the tire's ability to resist deformation during steering.

[0003] The torsional rigidity of a tire affects the handling of a vehicle when turning. Higher torsional rigidity allows the vehicle to respond more quickly to the driver's input, improving the flexibility and precision of steering, thereby improving the driving experience and safety of the vehicle.

[0004] The torsional rigidity of a tire can be tested in a professional laboratory, which requires professional equipment and time; it can also be predicted through finite element simulation analysis. Compared with experimental methods, simulation analysis can greatly reduce the testing cost and cycle. The torsional rigidity of a tire can be measured experimentally or predicted through simulation analysis.

[0005] Such as the Chinese invention patent applications applied by the applicant (publication numbers: CN115422806A, CN116805129A, CN116680952A). However, the use of finite element analysis requires a deep understanding of its principles, materials used, and boundary conditions, and a slight setting error may lead to extremely inaccurate results. The simulation analysis of tires requires professional software and complex operations, which is demanding and time-consuming for designers and developers. Summary of the invention

[0006] In order to solve the above-mentioned technical problems, the present invention proposes a new method for predicting tire torsional stiffness. The method is based on experimental data and adopts a simple mathematical model to predict the torsional stiffness of the tire, thereby avoiding the tedious and professional simulation analysis process and effectively improving the efficiency of tire design.

[0007] In order to achieve the above-mentioned purpose, the present invention adopts the following technical solutions:

[0008] A method for predicting tire torsional stiffness, the method uses an exponential function mathematical expression to directly calculate and obtain the tire torsional stiffness, the exponential function is as follows:

[0009] k=6.978*P -0.662 *L 1.0121 *W 0.3777 *D 0.0189 *R 0.2555 *e -1.1893 ;

[0010] Where k is the predicted tire torsional stiffness value, k0 is the coefficient, tire inflation pressure P, load L, section width W, rim diameter and width D, R, and effective section aspect ratio e.

[0011] Furthermore, the present invention also provides a method for establishing the exponential function, which comprises the following steps:

[0012] 1) selecting tire-related variable factors, wherein the variable factors include tire inflation pressure P, load L, and multiple parameters of tire size, wherein the size parameters include section width W, rim diameter D, rim width R, and effective section aspect ratio e;

[0013] 2) Assume that the relationship between the tire torsional stiffness k and the factor is in the form of an exponential function, k = k0*P m *L n *W x *D y *R q *e z , where m, n, x, y, q, z, k0 are unknown coefficients;

[0014] 3) Based on the experimental data, the torsional stiffness of the tire under different air pressures, loads, rim diameters, rim widths and effective section aspect ratios was investigated, the coefficients m, n, x, y, q, z, k0 were obtained, and the torsional stiffness of the tire was calculated;

[0015] 4) Using the obtained coefficients, the torsional stiffness of the tire is predicted by using the mathematical expression of the exponential function after substituting the coefficients m, n, x, y, q, z, and k0.

[0016] Preferably, the undetermined coefficients in step 2) are determined by the following method:

[0017] a. Incorporating the factors related to the tire model in the relationship into a constant term;

[0018] b. Under the same conditions of air pressure, load, rim diameter, rim width and effective section aspect ratio, calculate the value of the unknown coefficient through experimental data.

[0019] Preferably, the coefficient m is obtained by examining the torsional stiffness test data of the same model of tire at different inflation pressures;

[0020] And / or, the coefficient n is obtained by examining torsional stiffness test data under different loads;

[0021] And / or, the coefficient y is obtained by examining torsional stiffness test data under different rim diameters;

[0022] And / or, the coefficient q is obtained by examining torsional stiffness test data under different rim widths;

[0023] And / or, the coefficient z is obtained by examining torsional stiffness test data under different effective section aspect ratios.

[0024] As a preferred method, the coefficient m is obtained as follows:

[0025] When k=k0*P m *L n *W x *D y *R q *e z In the m =k0*L n *W x *D y *R q *e z As a quantity related to the tire model, the torsional stiffness of the tire k = P m *C m ; When other conditions are the same, the data k1 and k2 under two different air pressures are measured, and the relationship is: k1=(P1) m *C m , k2=(P2) m *C m , then:

[0026] m = ln(k1 / k2) / ln(P1 / P2);

[0027] The coefficient n is obtained as follows:

[0028] When k=k0*P m *L n *W x *D y *R q *e z In the above example, Cn=k0*P m *W x *D y *R q *e z As a whole, the torsional stiffness of the tire k = L n *C n ; When other conditions are the same, the data k1 and k2 under two different loads are measured, and the relationship is: k1 = (L1) n *C n , k2=(L2) n *X n , then we have the following formula:

[0029] n=ln(k1 / k2) / ln(L1 / L2);

[0030] The coefficient y is obtained as follows: when k = k0*P m *L n *W x *D y *R q *e z In the y =k0*P m *L n *W x *R q *e z As a whole, the torsional stiffness of the tire is k = D y *C y ; When other conditions are the same, the test data k1 and k2 of two different rim diameters D are examined, and the relationship is: k1 = (D1) y *C y , k2=(D2) y *C y , then: y = ln(k1 / k2) / ln(D1 / D2)

[0031] The coefficient q is obtained as follows: when k = k0*P m *L n *W x *D y *R q *e z In the q =k0*P m *L n *W x *D y *e z As a whole, the torsional stiffness of the tire is k = R q *C q ; When other conditions are the same, the test data k1 and k2 of two different rim widths R are examined, and the relationship is: k1 = (R1) q *C q , k2=(R2) q *C q , then:

[0032] q = ln(k1 / k2) / ln(R1 / R2);

[0033] The coefficient z is obtained as follows: when k = k0*P m *L n *W x *D y *R q *e zIn the z =k0*P m *L n *W x *D y *R q As a whole, the torsional stiffness of the tire is k = e z *C z ; When other conditions are the same, we examine the test data k1 and k2 with two different e values ​​(e1 and e2), and we have the relationship: k1 = (e1) z *C z , k2=(e2) z *C z , then:

[0034] z = ln(k1 / k2) / ln(e1 / e2);

[0035] The coefficient x is obtained as follows: Since e = 100*(h / W), the change of e needs to be considered when examining the change of W. m *L n *W x *D y *R q *e z In the x =k0*P m *L n *D y *R q As a whole, the torsional stiffness of the tire is k = W x *C x *e z ; The coefficient z has been determined, e for a specific tire model z is a known quantity, e z =cons; When other conditions are the same, the test data k1 and k2 of two different section widths W1 (cons1) and W2 (cons2) are examined, and the relationship is: k1 = (W1) x *C x *cons1, k2 = (W2) x *C x *cons2, then we have:

[0036] x=ln((k1*cons2 / k2*cons1)) / ln(W1 / W2);

[0037] The method for obtaining the constant coefficient k0 is as follows: the coefficients m, n, x, y, q, z have been obtained in the previous data processing. In the expression k = k0*P m *L n *W x *Dy *R q *e z Only K0 is unknown; based on the test data, the test results of different tire models are extracted, k0 = k / (P m *L n *W x *D y *R q *e z ).

[0038] Furthermore, the present invention also provides a system for implementing the method for predicting tire torsional stiffness, which implements the method described above, and the system comprises:

[0039] a. A data acquisition module for collecting data on tire inflation pressure P, load L, tire size parameters W, D, R and e;

[0040] b. A prediction module for predicting the torsional stiffness of the tire based on the exponential function.

[0041] Preferably, the data acquisition module includes a sensor for collecting tire pressure, load and dimensional parameters in real time.

[0042] Preferably, the system also includes a data analysis module for calculating the predicted tire torsional stiffness k based on the experimental data and the parameters, and obtaining the coefficients m, n, x, y, q, z, k0; the data analysis module includes a computer processing unit for performing data analysis and calculating the tire torsional stiffness and its related coefficients.

[0043] 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.

[0044] 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.

[0045] The present invention has the following technical effects due to the adoption of the above technical solution:

[0046] 1. Simplified prediction process: Through experimental data analysis, simple mathematical formulas are used to predict tire torsional stiffness, avoiding complex simulation analysis processes. This method is more user-friendly and efficient than existing technologies, especially for tire design and optimization stages.

[0047] 2. Reduce costs and time consumption: Compared with traditional laboratory testing methods, the present invention can quickly obtain the predicted value of torsional stiffness through the comparison of simple mathematical models and experimental data, which significantly reduces the test cycle and cost.

[0048] 3. No need for high-skilled operation: Compared with the simulation analysis method, the present invention does not require engineering and technical personnel to have complex software operation and modeling skills, which greatly reduces the requirements for personnel's professional skills and improves the universality and convenience of the design process.

[0049] 4. Efficient prediction of torsional stiffness: By analyzing experimental data under multiple tire models and working conditions, the present invention can accurately obtain multiple variable factors that affect the torsional stiffness of the tire, such as air pressure, load, tire size, etc., and then use these factors to predict the torsional stiffness of the tire.

[0050] By accurately predicting the torsional stiffness of the tire, the present invention allows designers to quickly evaluate the effects of different design solutions, providing a scientific basis for the optimal design of the tire, thereby improving the overall performance of the tire. Accurately predicting the torsional stiffness of the tire can help optimize the tire design, thereby improving the vehicle's handling, safety and comfort, and improving the overall driving experience. This method is simple and easy to implement, can greatly improve the efficiency and accuracy of tire design, reduce costs, and provide strong support for tire performance optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Schematic diagram of tire sizes W, R, D, e, e0. DETAILED DESCRIPTION

[0052] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0053] The first step is to select tire-related variable factors. Research results in existing literature: Factors affecting tire torsional stiffness include:

[0054] 1-Inflation pressure: The torsional stiffness of a tire increases as the air pressure increases.

[0055] 2-Tire size: Larger tires generally have higher torsional stiffness than smaller tires.

[0056] 3-Tire Load: High-load tires generally have higher torsional stiffness than low-load tires.

[0057] There is a nonlinear relationship between the above three influencing factors and the tire torsional stiffness, and they are coupled with each other.

[0058] 4-Tire structure and materials: Studies have shown that the structure and materials of the tire have relatively little effect on torsional stiffness.

[0059] Based on the above research results, the influencing factors of tire torsional stiffness are determined. Tire inflation pressure P (pressure) and load L (load) are used as working conditions and can be adjusted separately as needed. Because the tire cross-section is approximately elliptical, its size needs to be characterized by several parameters: the tire size is expressed in terms of section width W (mm), and rim diameter and width D (inch), R (mm); the rim is a rigid body, and the deformed part of the tire is above the rim, so the effective section aspect ratio e (dimensionless) is taken, e = 100*(h / W). h is the height above the rim in the tire section (mm), and H is the tire section height (mm), see for details. Figure 1 .

[0060] The second step is to consider the influence of various influencing factors on the tire torsional stiffness and the nonlinear relationship, assuming that the corresponding relationship is in the form of an exponential function, that is:

[0061] k=k0*P m *L n *W x *D y *R q *e z Where k0, m, n, x, y, q, z are unknown coefficients.

[0062] The third step is to examine the test results of multiple tire models based on the test data and obtain the coefficient m. m *L n *W x *D y *R q *e z In the m =k0*L n *W x *D y *R q *e z As a quantity related to the tire model, the torsional stiffness of the tire k = P m *C m When other conditions are the same, the data k1 and k2 under two different air pressures are measured, and the relationship is: k1 = (P1) m *C m , k2=(P2) m *C m , then:

[0063] m=ln(k1 / k2) / ln(P1 / P2), see Table 1 for details

[0064] Table 1 Analysis of torsional stiffness and air pressure data

[0065]

[0066] Take the arithmetic mean of m, m=-0.662.

[0067] Similarly, the coefficients n, x, y, q, z, and k0 are obtained through the changes in single factors and the test results of the corresponding tire torsional stiffness.

[0068] Obtaining coefficient n: When k = k0*P m *L n *W x *D y *R q *e z In the above example, Cn=k0*P m *W x *D y *R q *e z As a whole, the torsional stiffness of the tire k = L n *C n When other conditions are the same, the data k1 and k2 under two different loads are measured, and the relationship is: k1 = (L1) n *C n , k2=(L2) n *C n , then we have the following formula:

[0069] n=ln(k1 / k2) / ln(L1 / L2), see Table 2 for details

[0070] Table 2 Torsional stiffness and load data analysis

[0071]

[0072]

[0073] Take the arithmetic mean of n, n=1.0121.

[0074] The coefficient y is obtained when k = k0*P m *L n *W x *D y *R q *e z In the y =k0*P m *L n *W x *R q *e z As a whole, the torsional stiffness of the tire is k = D y *C yWhen other conditions are the same, the test data k1 and k2 of two different rim diameters D are examined, and the relationship is: k1 = (D1) y *C y , k2=(D2) y *C y , then:

[0075] y=ln(k1 / k2) / ln(D1 / D2), see Table 3 for details

[0076] Table 3 Torsional stiffness and rim diameter data analysis

[0077]

[0078] Take the arithmetic mean of y, y=0.0189.

[0079] The coefficient q is obtained when k = k0*P m *L n *W x *D y *R q *e z In the q =k0*P m *L n *W x *D y *e z As a whole, the torsional stiffness of the tire is k = R q *C q When other conditions are the same, the test data k1 and k2 of two different rim widths R are examined, and the relationship is: k1 = (R1) q *C q , k2=(R2) q *C q , then:

[0080] q=ln(k1 / k2) / ln(R1 / R2), see Table 4 for details

[0081] Table 4 Torsional stiffness and rim width data analysis

[0082]

[0083] Take the arithmetic mean of q, q=0.2555.

[0084] The coefficient z is obtained when k = k0*P m *L n *W x *D y *R q *e z In the z=k0*P m *L n *W x *D y *R q As a whole, the torsional stiffness of the tire is k = e z *C z When other conditions are the same, we examine two test data k1 and k2 with different e values ​​(e1 and e2), and we have the relationship: k1 = (e1) z *C z , k2=(e3) z *C z , then:

[0085] z=ln(k1 / k3) / ln(e1 / e2), see Table 4 for details

[0086] Table 5 Data analysis of torsional stiffness and effective section aspect ratio

[0087]

[0088] Take the arithmetic mean of z, z = -1.1893.

[0089] The coefficient x is obtained because e = 100*(h / W). When examining the change of W, it is necessary to consider the change of e. m *L n *W x *D y *R q *e z In the x =k0*P m *L n *D y *R q As a whole, the torsional stiffness of the tire is k = W x *C x *e z The coefficient z = -1.1893 has been determined, e for a specific tire model z is a known quantity, e z =cons. When other conditions are the same, the test data k1 and k2 of two different section widths W1 (cons1) and W2 (cons2) are examined, and the relationship is: k1 = (W1) x *C x *cons1, k2 = (W2) x *C x *cons2, then we have:

[0090] x=ln((k1*cons2 / k2*cons1)) / ln(W1 / W2), see Table 6 for details

[0091] Table 6 Torsional stiffness and section width data analysis

[0092]

[0093] Take the arithmetic mean of x, x=0.3777.

[0094] The constant coefficient k0 is obtained. The coefficients m, n, x, y, q, z have been obtained in the previous data processing. In the expression k = k0*P m *L n *W x *D y *R q *e z Only K0 is unknown. Based on the test data, the test results of different tire models are extracted, k0 = k / (P m *L n *W x *D y *R q *e z ), and the coefficient k0 is obtained. See Table 7 for details.

[0095] Table 7 Torsional stiffness and constant coefficient data analysis

[0096]

[0097]

[0098] Take the arithmetic mean of k0, k0=6.978.

[0099] Step 4: Use the coefficients obtained above to replace the coefficients in the assumed expression. Substitute m = -0.662, n = 1.0121, y = 0.0189, q = 0.2555, z = -1.1893, x = 0.3777, k0 = 6.978 into k = k0*P m *L n *W x *D y *R q *e z Then we have:

[0100] k=6.978*P -0.662 *L 1.0121 *W 0.3777 *D 0.0189 *R 0.2555 *e -1.1893

[0101] The above tire torsional stiffness expression is used to estimate the tire torsional stiffness and compare it with the test results to verify its effectiveness. See Table 8 for details.

[0102] Table 8 Comparison of tire torsional stiffness prediction and measured results

[0103]

[0104] As can be seen from Table 8, the error between the tire torsional rigidity predicted by the patented method and the actual measured result is within 9.64%, and there is also a good corresponding trend when applied to tires of different tire models and different working conditions, which proves the effectiveness of the patented method.

[0105] The above are only preferred specific embodiments of the present invention, which are all different implementations based on the overall concept of the present invention, and the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for predicting tire torsional stiffness, characterized in that: This method uses an exponential function mathematical expression to directly calculate and obtain the torsional stiffness of the tire. The exponential function is as follows: k=6.978*P- 0.662 *L 1.0121 *W 0.3777 *D 0.0189 *R 0.2555 *e- 1.1893 ; Where k is the predicted tire torsional stiffness value, k0 is the coefficient, tire inflation pressure P, load L, section width W, rim diameter and width D, R, and effective section aspect ratio e.

2. The method for establishing an exponential function according to claim 1, characterized in that: The method comprises the following steps: 1) selecting tire-related variable factors, wherein the variable factors include tire inflation pressure P, load L, and multiple parameters of tire size, wherein the size parameters include section width W, rim diameter D, rim width R, and effective section aspect ratio e; 2) Assume that the relationship between the tire torsional stiffness k and the factor is in the form of an exponential function, k = k0*Pm*L n *W x *D y *R q *e z , where m, n, x, y, q, z, k0 are unknown coefficients; 3) Based on the experimental data, the torsional stiffness of the tire under different air pressures, loads, rim diameters, rim widths and effective section aspect ratios was investigated, the coefficients m, n, x, y, q, z, k0 were obtained, and the torsional stiffness of the tire was calculated; 4) Using the obtained coefficients, the torsional stiffness of the tire is predicted by using the mathematical expression of the exponential function after substituting the coefficients m, n, x, y, q, z, and k0.

3. The method according to claim 2, characterized in that The undetermined coefficients in step 2) are determined by the following method: a. Incorporating the factors related to the tire model in the relationship into a constant term; b. Under the same conditions of air pressure, load, rim diameter, rim width and effective section aspect ratio, calculate the value of the unknown coefficient through experimental data.

4. The method according to claim 2, characterized in that: The coefficient m is obtained by examining the torsional stiffness test data of the same type of tire at different inflation pressures; And / or, the coefficient n is obtained by examining torsional stiffness test data under different loads; And / or, the coefficient y is obtained by examining torsional stiffness test data under different rim diameters; And / or, the coefficient q is obtained by examining torsional stiffness test data under different rim widths; And / or, the coefficient z is obtained by examining torsional stiffness test data under different effective section aspect ratios.

5. The method according to claim 4, characterized in that The coefficient m is obtained as follows: When k=k0*P m *L n *W x *D y *R q *e z In the m =k0*L n *W x *D y *R q *e z As a quantity related to the tire model, the torsional stiffness of the tire k = P m *C m ; When other conditions are the same, the data k1 and k2 under two different air pressures are measured, and the relationship is: k1=(P1) m *C m , k2=(P2) m *C m , then: m = ln(k1 / k2) / ln(P1 / P2); The coefficient n is obtained as follows: When k=k0*P m *L n *W x *D y *R q *e z In the above example, Cn=k0*P m *W x *D y *R q *e z As a whole, the torsional stiffness of the tire k = L n *C n ; When other conditions are the same, the data k1 and k2 under two different loads are measured, and the relationship is: k1 = (L1) n *C n , k2=(L2) n *C n , then we have the following formula: n=ln(k1 / k2) / ln(L1 / L2); The coefficient y is obtained as follows: when k = k0*P m *L n *W x *D y *R q *e z In the y =k0*P m *L n *W x *R q *e z As a whole, the torsional stiffness of the tire is k = D y *C y ; When other conditions are the same, the test data k1 and k2 of two different rim diameters D are examined, and the relationship is: k1 = (D1) y *C y , k2=(D2) y *C y , then: y=ln(k1 / k2) / ln(D1 / D2) The coefficient q is obtained as follows: when k = k0*P m *L n *W x *D y *R q *e z In the q =k0*P m *L n *W x *D y *e z As a whole, the torsional stiffness of the tire is k = R q *C q ; When other conditions are the same, the test data k1 and k2 of two different rim widths R are examined, and the relationship is: k1 = (R1) q *C q , k2=(R2) q *C q , then: q = ln(k1 / k2) / ln(R1 / R2); The coefficient z is obtained as follows: when k = k0*P m *L n *W x *D y *R q *e z In the z =k0*P m *L n *W x *D y *R q As a whole, the lateral stiffness of the tire k = e z *C z ; When other conditions are the same, we examine the test data k1 and k2 with two different e values ​​e1 and e2, and we have the relationship: k1 = (e1) z *C z , k2=(e2) z *C z , then: z = ln(k1 / k2) / ln(e1 / e2); The coefficient x is obtained as follows: Since e = 100*(h / W), the change of e needs to be considered when examining the change of W. m *L n *W x *D y *R q *e z In the x =k0*P m *L n *D y *R q As a whole, the lateral stiffness of the tire k = W x *C x *e z ; The coefficient z has been determined, e for a specific tire model z is a known quantity, e z =cons; when other conditions are the same, the test data k1, k2 of two different section widths W1, cons1 and W2, cons2 are examined, and the relationship is: k1 = (W1) x *C x *cons1, k2 = (W2) x *C x *cons2, then we have: x=ln((k1*cons2 / k2*cons1)) / ln(W1 / W2); The method for obtaining the constant coefficient k0 is as follows: the coefficients m, n, x, y, q, z have been obtained in the previous data processing. In the expression k = k0*P m *L n *W x *D y *R q *e z Only K0 is unknown; based on the test data, the test results of different tire models are extracted, k0 = k / (P m *L n *W x *D y *R q *e z ).

6. A system for implementing a method for predicting tire torsional stiffness, characterized in that: The method implements the method described in claim 1, wherein the system comprises: a. A data acquisition module for collecting data on tire inflation pressure P, load L, tire size parameters W, D, R and e; b. A prediction module for predicting the torsional stiffness of the tire based on the exponential function.

7. The system according to claim 8, characterized in that The data acquisition module includes sensors for collecting tire pressure, load and size parameters in real time.

8. The system according to claim 8, characterized in that The system also includes a data analysis module for calculating the predicted tire torsional stiffness k based on the experimental data and the parameters, and obtaining the coefficients m, n, x, y, q, z, k0; the data analysis module includes a computer processing unit for performing data analysis and calculating the tire torsional stiffness and its related coefficients.

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 according to any one of claims 1 to 5 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 according to any one of claims 1 to 5 is implemented.

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