Method and system for quickly comparing tire rolling resistance and computer program product

Abstract

The invention relates to the technical field of tire simulation design, in particular to a method and system for quickly comparing tire rolling resistance and a computer program product. The method comprises the following steps: selecting main structure factors such as a pattern groove depth and a grounding width, obtaining rolling resistance data through an orthogonal test, and establishing a relationship between each factor and rolling resistance by using a polynomial function; based on known rolling resistance of a reference tire, the rolling resistance of different design schemes can be quickly predicted and compared by directly substituting the structural variation into the model. Compared with traditional CAE modeling and complex simulation, the method has the advantages that the research and development period is greatly shortened, the calculation cost is reduced, and efficient reference is provided for optimization of the tire rolling resistance.

Description

Technical Field

[0001] The present invention relates to the technical field of tire simulation design, and particularly to a method, a system, and a computer program product for quickly comparing the rolling resistance of tires. Background Art

[0002] Tire rolling resistance is one of the important indicators for measuring tire performance, which not only has a significant impact on the fuel consumption of traditional fuel vehicles but is also crucial for the driving range of new energy vehicles. In the prior art, in order to optimize tire rolling resistance, it is usually necessary to model, simulate, and process data of the tire through finite element analysis (CAE) to predict the rolling resistance performance of the tire under different structural or material change conditions. Although this method can theoretically obtain relatively accurate results, in practical engineering applications, it often faces difficulties such as complex modeling, large simulation calculation volume, and long iteration cycle, and it is difficult to meet the requirements of rapid design and optimization.

[0003] For example, Patent CN115659625A and ZL 2023 1 0472577.1 respectively disclose a method for predicting tire rolling resistance based on a CAE model, and its steps include:

[0004] 1) Establish a tire CAE model;

[0005] 2) Conduct a rolling simulation analysis on the tire;

[0006] 3) Perform data processing and calculation of rolling resistance.

[0007] The above-mentioned technology improves the efficiency in the data processing link by improving the material model and algorithm, but still needs to repeatedly perform modeling and rolling simulation analysis when using this method. For situations with more structural changes and frequent iteration of optimization schemes, this process will significantly increase the calculation cost and time investment.

[0008] In engineering practice, R & D personnel often need to improve the tire structure or material based on an existing tire (with known rolling resistance) to achieve the expected rolling resistance target. However, the internal components of the tire are complex, and there are many factors affecting rolling resistance, such as tread groove depth, contact width, belt width, cushion gum thickness, etc.; when adjusting these factors, if relying on the traditional CAE simulation prediction method, it is necessary to separately establish or modify the CAE model for each improvement scheme and conduct a rolling simulation analysis, resulting in an extremely large calculation volume and workload. Summary of the Invention

[0009] Based on the above situation, the present invention proposes a method for quickly comparing the rolling resistance of tires. This method is based on the known rolling resistance of a reference tire and combines a polynomial model of the relationship between various structural variables (such as tread groove depth, apex height, etc.) and rolling resistance. The structural change amounts in different schemes are directly substituted into the model for rapid estimation and comparison of rolling resistance. Thereby, the process of repeatedly establishing CAE models and performing complex rolling simulations is avoided, significantly reducing the computational and experimental workload, and providing an efficient and feasible technical approach for the rapid evaluation and optimization of tire rolling resistance.

[0010] To achieve the above object, the present invention adopts the following technical solutions:

[0011] A method for quickly comparing the rolling resistance of tires, which is based on the structure and rolling resistance of a reference tire. By comparing the structural difference changes of the tires and using polynomials to directly compare and calculate the rolling resistance changes, rapid estimation of the tire rolling resistance is realized. The functional relationship for estimation is as follows:

[0012] RR = (1 + 0.0143 * Δa + 0.0238 * Δb + 0.008 * Δc + 0.0067 * Δd

[0013] + 0.1176 * Δe + 0.0026 * Δf) * RRC;

[0014] In the formula, RR is the estimated tire rolling resistance value, RRC is the rolling resistance value of the reference tire, and Δa to Δf are the structural parameter change amounts of the tread groove depth a, the rubber thickness at the bottom of the tread groove b, the contact width c, the width of the steel belt layer d, the thickness of the cushion rubber e, and the apex height f in sequence.

[0015] The method for establishing the functional relationship according to claim 1, characterized in that the method comprises the following steps:

[0016] 1) Select common tire structure factors as variables, including the tread groove depth a, the rubber thickness at the bottom of the tread groove b, the contact width c, the width of the steel belt layer d, the thickness of the cushion rubber e, and the apex height f;

[0017] 2) Use experimental design software to perform experimental design on the above 6 structural variables. The structural variables have at least 5 levels to form an orthogonal design experimental scheme, and perform rolling resistance tests to obtain the rolling resistance values corresponding to each experimental scheme;

[0018] 3) Based on the results of the experimental design, analyze the main effects or influence trends of each structural factor, and determine the functional type of the influence of each factor on rolling resistance;

[0019] 4) Establish a rolling resistance polynomial model according to the function type, and solve the undetermined coefficients of the model by using the least squares method or other mathematical methods;

[0020] 5) Take the rolling resistance value of the reference tire as the benchmark, input the change amounts of each factor based on the obtained polynomial model, quickly compare the changes in the tire rolling resistance, and verify the prediction results with the measured results.

[0021] Preferably, in step 3), the main effects of the factors are obtained from the main effect diagram generated in the experimental design software or relevant statistical analysis results, and the function types include linear, parabolic or horizontal line relationships.

[0022] Preferably, in step 4), the established rolling resistance polynomial model is in the following form:

[0023] RR = (1 + k 1 *Δa + k 2 *Δb + k 3 *Δc + k 4 *Δd + k 5 *Δe + k 6 *Δf)*RRC;

[0024] k1 to k6 are undetermined coefficients;

[0025] Preferably, the least squares method obtains k1 to k6 by solving an overdetermined system of equations, specifically by jointly forming a system of equations with the experimental data and the polynomial model, and using the generalized inverse or pseudo-inverse algorithm of the matrix to calculate the unknown coefficients.

[0026] Preferably, in step 5), by adjusting the design values of at least one structural factor, input the corresponding change amounts Δa to Δf into the polynomial model, quickly predict or compare to obtain the rolling resistance value of the tire, and compare and verify it with the corresponding test results.

[0027] Preferably, the reference tire is a tire with a known rolling resistance value and the same or similar specifications and models, and the change amounts of the structural factors are set according to tire design requirements or different specifications and models, so as to quickly compare the rolling resistances of different tire specifications and models.

[0028] Preferably, the experimental design software includes Minitab, JMP or other software with orthogonal design and main effect analysis functions, and the data processing and polynomial coefficient solving process are implemented by Matlab, Python or other mathematical analysis software;

[0029] Preferably, the test data of the tire rolling resistance is sourced from the rolling resistance test methods specified in ISO 28580, GB / T 15082 or other relevant test standards to ensure the accuracy and comparability of the test results.

[0030] Preferably, after the polynomial model is established, the coefficients of the polynomial model are corrected or calibrated again by introducing additional experimental points or measuring the rolling resistance using tires of other specifications to improve the model prediction accuracy.

[0031] Furthermore, the present invention also provides a system for quickly comparing the rolling resistance of tires. This system implements the method described above and includes:

[0032] Input module: used to input the rolling resistance value of the reference tire, the change range and change amount of each tire structure factor;

[0033] Experimental design and data acquisition module: uses experimental design software to generate experimental schemes and records the rolling resistance corresponding to each experiment;

[0034] Data processing module: uses mathematical analysis software to statistically analyze the experimental data, establish a polynomial model and solve its undetermined coefficients;

[0035] Rolling resistance comparison module: quickly calculates and outputs the rolling resistance comparison results of the target tire according to the polynomial model and the input change amount of the structure factor.

[0036] Furthermore, the present invention also provides a computer-readable storage medium, on which a computer program or instruction is stored. When the computer program or instruction is executed by a processor, the method described above is implemented.

[0037] Furthermore, the present invention also provides a computer program product, including a computer program or instruction. When the computer program or instruction is executed by a processor, the method described above is implemented.

[0038] Due to the adoption of the above technical solutions, the present invention has the following technical effects:

[0039] 1. Realize the quick prediction and comparison of rolling resistance: Based on the structure and rolling resistance of the existing tire (reference tire), the present invention directly constructs and applies a polynomial relationship to characterize the relationship between structural changes and rolling resistance, eliminating the need to repeatedly establish CAE models and conduct rolling simulation analyses for each new structural scheme, thus significantly shortening the design and verification cycle.

[0040] 2. Reduced computational complexity and testing costs: Compared with traditional CAE modeling and rolling simulation methods, the present invention directly calculates the tire rolling resistance relying on the polynomial prediction model, avoiding the cumbersome finite element modeling process and the consumption of high computing resources, and only needs to complete the fitting and verification of the model coefficients based on a small amount of experimental design and testing, significantly reducing the R & D costs.

[0041] 3. Applicable to various tire structures and specifications: During the implementation of the present invention, by flexibly selecting the main influencing factors such as the depth of the tread groove, the thickness of the rubber at the bottom of the tread groove, the contact width, the width of the steel belt layer, the thickness of the cushion rubber, and the height of the apex rubber, and using the orthogonal experiment or similar experimental design methods to obtain diversified structural data, it is possible to quickly evaluate and compare the rolling resistance of tires with different specifications or within different structural change ranges, with strong versatility and adaptability.

[0042] 4. High prediction accuracy: By combining the rolling resistance data of the reference tire with the test results of other specification tires, and using the least square fitting of polynomial coefficients or other mathematical methods to correct and optimize the model, it is possible to predict the tire rolling resistance within a high-precision range; the test results show that the prediction error of the method of the present invention can be stably controlled within a certain reasonable range, verifying its effectiveness and reliability.

[0043] 5. Provide direct reference for the structural optimization of tire rolling resistance: Using the polynomial model of the present invention, during the design process, R & D personnel only need to make corresponding settings for the structural factors to be adjusted (such as the depth of the tread groove, the width of the belt layer, etc.), and then can quickly obtain the influence direction and approximate amplitude on the rolling resistance, providing a direct and efficient reference basis for further structural optimization or improvement. Description of the Drawings

[0044] Figure 1 Schematic diagram of tire design factors. a, b, c, d, e, f.

[0045] Figure 2 Main effect diagram of each factor in Taguchi design.

[0046] Figure 3 Comparison of prediction and measurement results for different tire models. Detailed Embodiment

[0047] Next, in combination with the embodiments of the present invention, the technical solutions in the embodiments will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0048] This embodiment is implemented on the premise of the technical solution of the present invention. Taking the tire 205 / 55R16 as an example (the rolling resistance RRc = 50N corresponding to the reference structure is known), a detailed implementation manner is given, but the protection scope of the present invention is not limited to the following embodiments.

[0049] First step, select common tire structure factors. Considering the standardization of the design and the influencing factors of rolling resistance reported in the literature, the selected tire structure variables are: tread groove depth (a), rubber thickness at the bottom of the tread groove (b), contact width (c), steel belt width (d), cushion gum thickness (e), and height of the apex rubber (f). See Figure 1 .

[0050] Second step, use Minitab software to conduct experimental design. The selected structure variables are 6, and the variation range is 5 levels, that is, the experimental plan L25. The variation range of each factor needs to be screened according to the limitations of the engineering practice. The designed variation of the tread groove depth is ±2mm, the designed variation of the rubber thickness at the bottom of the tread groove is ±0.6mm, the designed variation of the contact width is ±8mm, the designed variation of the steel belt width is ±6mm, the designed variation of the cushion gum thickness is ±0.8mm, and the designed variation of the height of the apex rubber is ±10mm. Then, record the experimental results of the corresponding tire rolling resistance. See Table 1.

[0051] Table 1 Taguchi design plan and experimental results

[0052] Solution Δa (mm) Δb (mm) Δc (mm) Δd (mm) Δe (mm) Δf (mm) RR (N) 1 -1 -0.6 -8 -6 -0.8 -10 37.35 2 -1 -0.3 -4 -3 -0.4 -5 43.32 3 -1 0 0 0 0 0 49.29 4 -1 0.3 4 3 0.4 5 55.25 5 -1 0.6 8 6 0.8 10 61.22 6 -2 -0.6 -4 0 0.4 10 49.93 7 -2 -0.3 0 3 0.8 -10 52.6 8 -2 0 4 6 -0.8 -5 46.81 9 -2 0.3 8 -6 -0.4 0 47.78 10 -2 0.6 -8 -3 0 5 45.74 11 0 -0.6 0 6 -0.4 5 49.59 12 0 -0.3 4 -6 0 10 50.56 13 0 0 8 -3 0.4 -10 53.24 14 0 0.3 -8 0 0.8 -5 51.21 15 0 0.6 -4 3 -0.8 0 45.41 16 1 -0.6 4 -3 0.8 0 55.31 17 1 -0.3 8 0 -0.8 5 49.51 18 1 0 -8 3 -0.4 10 47.48 19 1 0.3 -4 6 0 -10 50.16 20 1 0.6 0 -6 0.4 -5 51.12 21 2 -0.6 8 3 0 -5 54.26 22 2 -0.3 -8 6 0.4 0 52.22 23 2 0 -4 -6 0.8 5 53.19 24 2 0.3 0 -3 -0.8 10 47.4 25 2 0.6 4 0 -0.4 -10 50.07

[0053] Third step, according to the analysis results of Minitab software, extract the main effect of each factor on the tire rolling resistance. See Figure 2 . Considering the influence of experimental error and the graphical trend of the main effect, construct the relationship between the tire rolling resistance and each factor as a linear change and have the following relationship:

[0054] RR = (1 + k 1 *Δa + k 2 *Δb + k 3 *Δc + k 4 *Δd + k 5 *Δe + k 6 *Δf) * RRC

[0055] Fourth step, according to each test plan and the corresponding result data (Table 1) and the relationship of the constructed function, there are the following 25 equations:

[0056]

[0057] The above system of equations can be expressed in the matrix form of: X * k = b, where X is a 25-row and 6-column matrix:

[0058]

[0059] The vector k[k1, k2, k3, k4, k5, k6]’ is an unknown column vector, which can be obtained by pre-multiplying the inverse matrix X-1 on both sides of the equation. Since the number of equations is greater than the number of unknowns, it is an overdetermined system of equations, and the least squares method of the built-in function pinv in Matlan is used to solve it, k = Pinv(X)*b;

[0060] It is obtained that k1 = 0.0143, k2 = 0.0238, k3 = 0.008, k4 = 0.0067, k5 = 0.1176, k6 = 0.0026; Substitute k1 to k6 into the constructor expression, that is:

[0061] RR = (1 + 0.0143*Δa + 0.0238*Δb + 0.008*Δc + 0.0067*Δd

[0062] + 0.1176*Δe + 0.0026*Δf)*RRC.

[0063] In the fifth step, adjust the design values of the 6 factors and use the expression obtained in the fourth step to predict (compare) the rolling resistance of the tire model 205 / 55R16, as shown in Table 2;

[0064] Table 2 Comparison between the predicted results and experimental results of the rolling resistance of tire model 205 / 55R16

[0065]

[0066]

[0067] In addition, select tire models 185 / 60R15 (model 2), 235 / 60R17 (model 3), 234 / 45R18 (model 4), 255 / 45R19 (model 5) respectively to predict (compare) and measure the tire rolling resistance, see details in Figure 3 .

[0068] From Table 2, Figure 3 it can be seen that the error between the tire rolling resistance predicted (compared) by the method of this patent and the measured results is within 7.9%, and there is also a good corresponding trend in the applications of different tire models, which proves the effectiveness of the method of this patent.

[0069] The foregoing is a description of embodiments of the present invention. Through the above description of the disclosed embodiments, those skilled in the art can implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. 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 the embodiments shown herein, but rather to the broadest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for quickly comparing tire rolling resistance, characterized in that: This method takes the structure and rolling resistance of the reference tire as the benchmark, compares the structural differences of the tires, and uses polynomials to directly compare and calculate the rolling resistance changes to achieve a rapid estimation of the tire rolling resistance. The estimated functional relationship is as follows: Where RR is the estimated rolling resistance value of the tire, RRC is the rolling resistance value of the reference tire, and Δa~Δf are the changes in structural parameters of groove depth a, groove bottom rubber thickness b, ground contact width c, steel belt layer width d, cushion rubber thickness e, and apex rubber height f.

2. The method for establishing a functional relationship according to claim 1, characterized in that: The method comprises the following steps: 1) Commonly used tire structural factors are selected as variables, including groove depth a, groove bottom rubber thickness b, ground contact width c, steel belt layer width d, cushion rubber thickness e, and apex rubber height f; 2) using experimental design software to conduct experimental design on the above 6 structural variables, wherein the structural variables have at least 5 levels, to form an orthogonal design experimental scheme, and conducting a rolling resistance test to obtain a rolling resistance value corresponding to each experimental scheme; 3) Based on the results of the experimental design, the main effect or influence trend of each structural factor is analyzed to determine the function type of the influence of each factor on rolling resistance; 4) establishing a rolling resistance polynomial model according to the function type, and solving the undetermined coefficients of the model using the least square method or other mathematical methods; 5) Taking the rolling resistance value of the reference tire as a benchmark, the change of each factor is input based on the obtained polynomial model, the change of the tire rolling resistance is quickly compared, and the predicted results are verified with the measured results.

3. The method according to claim 2, characterized in that: In the step 3), the main effect of each factor is obtained by a main effect diagram or related statistical analysis results generated in the experimental design software, and the function type includes a linear, parabolic or horizontal line relationship.

4. The method according to claim 2 or 3, characterized in that: In step 4), the established rolling resistance polynomial model is in the following form: RR=(1+k1*Δa+k2*Δb+k3*Δc+k4*Δd+k5*Δe+k6*Δf)*RRC; k1~k6 are unknown coefficients.

5. The method according to claim 4, characterized in that: The least square method obtains k1-k6 by solving an overdetermined set of equations. Specifically, the test data and the polynomial model are combined into a set of equations, and the generalized inverse or pseudo-inverse algorithm of the matrix is ​​used to calculate the unknown coefficients.

6. The method according to claim 2, characterized in that: In step 5), by adjusting the design value of at least one structural factor, the corresponding variation Δa-Δf is input into the polynomial model, the rolling resistance value of the tire is quickly predicted or compared, and then compared and verified with the corresponding test result.

7. The method according to claim 2, characterized in that: The reference tire is a tire with a known rolling resistance value and the same or similar specifications and models. The variation of the structural factor is set according to the tire design requirements or different specifications and models, so as to achieve a rapid comparison of the rolling resistance of different tire specifications and models; and / or, The experimental design software includes Minitab, JMP or other software with orthogonal design and main effect analysis functions, and the data processing and polynomial coefficient solution process are implemented by Matlab, Python or other mathematical analysis software; and / or, The tire rolling resistance test data is derived from the rolling resistance test method specified in ISO 28580, GB / T 15082 or other relevant test standards to ensure the accuracy and comparability of the test results; and / or, After the polynomial model is established, the coefficients of the polynomial model are corrected or calibrated again by introducing additional experimental points or using tires of other specifications to measure rolling resistance, so as to improve the prediction accuracy of the model.

8. A system for quickly comparing tire rolling resistance, characterized in that: The method implements the method described in claims 1-7, and the system comprises: Input module: used to input the rolling resistance value of the reference tire, the range and amount of change of each tire structural factor; Test design and data acquisition module: use the test design software to generate the test plan and record the rolling resistance corresponding to each test; Data processing module: Use mathematical analysis software to perform statistical analysis on test data, establish polynomial models and solve their unknown coefficients; Rolling resistance comparison module: according to the polynomial model and the input structural factor variation, the rolling resistance comparison result of the target tire is quickly calculated and output.

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 7 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 7 is implemented.

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