A method, system, and computer program product for quickly comparing tire rolling resistance

Abstract

The present application relates to the technical field of tire simulation design, and particularly relates to a method, system and computer program product for quickly comparing tire rolling resistance. The method comprises: selecting main structure factors such as groove depth and ground contact width, obtaining rolling resistance data through orthogonal test, and establishing the relationship between each factor and rolling resistance by using a polynomial function. Based on the known rolling resistance of a reference tire, the structure change amount is directly substituted into the model to quickly predict and compare the rolling resistance of different design schemes. Compared with traditional CAE modeling and complex simulation, the method greatly shortens the research and development cycle and reduces the calculation cost, and provides an efficient reference for the optimization of tire rolling resistance.

Description

Technical Field

[0001] This invention relates to the field of tire simulation design technology, and in particular to a method, system, and computer program product for rapidly comparing tire rolling resistance. Background Technology

[0002] Tire rolling resistance is a crucial indicator of tire performance, significantly impacting fuel consumption in traditional gasoline vehicles and significantly affecting the driving range of new energy vehicles. Current technologies typically employ finite element analysis (CAE) to model, simulate, and process data to predict tire rolling resistance under varying structural or material conditions, aiming to optimize rolling resistance. While this method theoretically yields relatively accurate results, practical engineering applications often face challenges such as complex modeling, extensive simulation calculations, and long iteration cycles, making it difficult to meet the demands of rapid design and optimization.

[0003] For example, patents CN115659625A and ZL 2023 1 0472577.1 disclose a method for predicting tire rolling resistance based on a CAE model, the steps of which include:

[0004] 1) Establish a tire CAE model;

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

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

[0007] The aforementioned techniques improve efficiency in data processing by refining material models and algorithms; however, repeated modeling and rolling simulation analyses are still required when using this method. For situations with numerous structural changes and frequent optimization iterations, this process significantly increases computational costs and time investment.

[0008] In engineering practice, R&D personnel often need to improve the structure or materials of existing tires (with known rolling resistance) to achieve the desired rolling resistance target. However, the internal components of a tire are complex, and many factors affect rolling resistance, such as tread groove depth, contact patch width, belt layer width, and rubber pad thickness. When adjusting these factors, relying on traditional CAE simulation prediction methods requires building or modifying a separate CAE model and performing rolling simulation analysis for each improvement scheme, resulting in an extremely large amount of computation and workload. Summary of the Invention

[0009] Based on the above situation, this invention proposes a method for rapidly comparing tire rolling resistance. This method uses the known rolling resistance of a reference tire as a foundation, and combines it with a polynomial model of the relationship between various structural variables (such as tread groove depth and tread height) and rolling resistance. The structural changes in different designs are directly substituted into the model for rapid estimation and comparison of rolling resistance. This avoids the need for multiple CAE model building and complex rolling simulations, significantly reducing the workload of calculations and experiments, and providing an efficient and feasible technical approach for the rapid evaluation and optimization of tire rolling resistance.

[0010] To achieve the above objectives, the present invention adopts the following technical solution:

[0011] A method for rapidly comparing tire rolling resistance is proposed. This method uses the structure and rolling resistance of a reference tire as a benchmark. By comparing changes in tire structural differences, it directly calculates the changes in rolling resistance using a polynomial, achieving a rapid estimation of tire rolling resistance. The estimated functional relationship is as follows:

[0012] ;

[0013] In the formula, RR is the estimated tire rolling resistance value, and RRC is the rolling resistance value of the reference tire. ~ The structural parameters are as follows: a) groove depth, b) rubber thickness at the bottom of the groove, c) grounding width, d) steel wire bundle layer width, e) padding thickness, and f) triangular rubber height.

[0014] The method for establishing a functional relation as described in claim 1 is characterized by comprising the following steps:

[0015] 1) Select commonly used tire structure factors as variables, including tread groove depth a, tread groove bottom rubber thickness b, ground contact width c, steel belt bundle width d, pad rubber thickness e, and triangular rubber height f;

[0016] 2) Experimental design software was used to design experiments for the above 6 structural variables, which have at least 5 levels, to form an orthogonal design experimental scheme. Rolling resistance tests were conducted to obtain the rolling resistance values ​​corresponding to each experimental scheme.

[0017] 3) Based on the results of the experimental design, analyze the main effects or influence trends of each structural factor, and determine the function type of each factor's influence on rolling resistance;

[0018] 4) Based on the function type, establish a polynomial model of rolling resistance, and solve for the undetermined coefficients of the model using the least squares method or other mathematical methods;

[0019] 5) Using the rolling resistance value of the reference tire as a benchmark, input the changes of each factor based on the obtained polynomial model, quickly compare the changes in tire rolling resistance, and verify the predicted results with the measured results.

[0020] Preferably, in step 3), the main effects of each factor are obtained by generating a main effects plot or relevant statistical analysis results in the experimental design software, and the function type includes linear, parabolic or horizontal relationship.

[0021] Preferably, the rolling resistance polynomial model established in step 4) has the following form:

[0022] ;

[0023] k1~k6 are undetermined coefficients;

[0024] Preferably, the least squares method obtains k1~k6 by solving an overdetermined system of equations. Specifically, the experimental data and the polynomial model are combined to form a system of equations, and the generalized inverse or pseudo-inverse algorithm of the matrix is ​​used to calculate the unknown coefficients.

[0025] Preferably, in step 5), by adjusting the design value of at least one structural factor, the corresponding change Δa~Δf is input into the polynomial model to quickly predict or compare the rolling resistance value of the tire, and then compare and verify it with the corresponding test results.

[0026] Preferably, the reference tire is a tire with a known rolling resistance value and the same or similar specifications. The variation of the structural factor is set according to the tire design requirements or different specifications, thereby enabling a rapid comparison of the rolling resistance of different tire specifications.

[0027] 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 solution process is implemented by Matlab, Python, or other mathematical analysis software.

[0028] Preferably, the test data for tire rolling resistance are derived 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.

[0029] Preferably, 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 model prediction accuracy.

[0030] Furthermore, the present invention also provides a system for rapidly comparing tire rolling resistance, the method implementing the above method, the system comprising:

[0031] Input module: Used to input the rolling resistance value of the reference tire, the variation range and amount of each tire structure factor;

[0032] Experimental design and data acquisition module: Experimental design software is used to generate experimental plans and record the rolling resistance corresponding to each experiment;

[0033] Data processing module: Uses mathematical analysis software to perform statistical analysis on experimental data, establish polynomial models, and solve for their undetermined coefficients;

[0034] Rolling resistance comparison module: Based on the polynomial model and the input structural factor change, quickly calculate and output the rolling resistance comparison results of the target tire.

[0035] Furthermore, the present invention also provides a computer-readable storage medium having a computer program or instructions stored thereon, which, when executed by a processor, implement the method.

[0036] Furthermore, the present invention also provides a computer program product, including a computer program or instructions that, when executed by a processor, implement the method.

[0037] The present invention, by adopting the above-described technical solution, has the following technical effects:

[0038] 1. Achieve rapid prediction and comparison of rolling resistance: This invention directly constructs and applies a polynomial relationship to characterize the relationship between structural changes and rolling resistance based on the structure and rolling resistance of an existing tire (reference tire). This eliminates the need to repeatedly build CAE models and perform rolling simulation analysis for each new structural scheme, significantly shortening the design and verification cycle.

[0039] 2. Reduced computational load and testing costs: Compared with traditional CAE modeling and rolling simulation methods, this invention directly calculates tire rolling resistance based on a polynomial prediction model, avoiding the cumbersome finite element modeling process and high computational resource consumption. Furthermore, it only requires a small amount of experimental design and testing to complete the fitting and verification of model coefficients, significantly reducing R&D costs.

[0040] 3. Applicable to various tire structures and specifications: In the implementation of this invention, by flexibly selecting key influencing factors such as tread groove depth, tread groove bottom rubber thickness, ground contact width, steel belt layer width, pad rubber thickness, and triangular rubber height, and by using orthogonal experiments or similar experimental design methods to obtain diverse structural data, it is possible to quickly evaluate and compare the rolling resistance of tires of different specifications or with different structural variations, thus exhibiting strong versatility and adaptability.

[0041] 4. High prediction accuracy: By combining the rolling resistance data of the reference tire with the test results of other tire specifications, and using the least squares fitting of polynomial coefficients or other mathematical methods to correct and optimize the model, the rolling resistance of the tire can be predicted within a high accuracy 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, which verifies its effectiveness and reliability.

[0042] 5. Provides direct reference for structural optimization of tire rolling resistance: Using the polynomial model of this invention, researchers only need to set the structural factors to be adjusted (such as tread groove depth, belt layer width, etc.) during the design process to quickly obtain the direction and approximate magnitude of the influence on rolling resistance, providing a direct and efficient reference for further structural optimization or improvement. Attached Figure Description

[0043] Figure 1 A schematic diagram of tire design factors. a, b, c, d, e, f.

[0044] Figure 2 Design the main effect plots for each factor for Taguchi.

[0045] Figure 3 Comparison of predicted and measured results for different tire models. Detailed Implementation

[0046] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not 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 effort are within the protection scope of the present invention.

[0047] This embodiment is implemented based on the technical solution of the present invention. Taking a 205 / 55R16 tire as an example (the rolling resistance RRc=50N corresponding to the reference structure is known), a detailed implementation method is given. However, the scope of protection of the present invention is not limited to the following embodiment.

[0048] The first step is to select commonly used tire structural factors. Considering design standardization and the influencing factors of rolling resistance reported in the literature, the tire structural variables selected are: tread groove depth (a), rubber thickness at the bottom of the tread groove (b), contact patch width (c), steel belt layer width (d), gasket thickness (e), and tread height (f). See details... Figure 1 .

[0049] The second step involved designing an experiment using Minitab software. Six structural variables were selected, with five levels of variation, resulting in experimental scheme L25. The variation range for each factor needed to be determined based on actual engineering constraints: ±2mm for tread groove depth, ±0.6mm for the rubber thickness at the bottom of the tread groove, ±8mm for the ground contact width, ±6mm for the steel belt layer width, ±0.8mm for the pad rubber thickness, and ±10mm for the triangular rubber height. The corresponding tire rolling resistance experimental results were then recorded. See Table 1 for details.

[0050] Table 1 Taguchi's design scheme and experimental results

[0051] plan 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

[0052] The third step is to extract the main effects of each factor on tire rolling resistance based on the analysis results from the Minitab software. See details. Figure 2 Considering the influence of experimental error and the graphical trend of the main effect, the relationship between tire rolling resistance and each factor is constructed to be linear and has the following relationship:

[0053]

[0054] Fourthly, based on the relationship between each experimental scheme, the corresponding result data (Table 1), and the constructor, the following 25 equations are obtained:

[0055]

[0056] The above system of equations can be expressed in matrix form as X*k=b, where X is a 25x6 matrix.

[0057]

[0058] The vector k[k1,k2,k3,k4,k5,k6]' is an unknown column vector. It can be obtained by multiplying both sides of the equation by the inverse matrix X-1. Since the number of equations is greater than the number of unknowns, it is an overdetermined system of equations. It is solved using the least squares method of the built-in function pinv in MATLAB, k=Pinv(X)*b;

[0059] We obtain k1=0.0143, k2=0.0238, k3=0.008, k4=0.0067, k5=0.1176, and k6=0.0026; substituting k1~k6 into the constructor expression, we get:

[0060] .

[0061] Fifth, adjust the design values ​​of the six factors and use the expression obtained in step 4 to predict (compare) the rolling resistance of tire model 205 / 55R16, see Table 2;

[0062] Table 2 Comparison of predicted and experimental results of rolling resistance for tire model 205 / 55R16

[0063] plan Δa Δb Δc Δd Δe Δf RR(N) prediction Actual RR(N) measurement error% 1 -0.7 -0.3 -5 -5 -0.5 -8 38.2 41.48 -7.90% 2 0.9 -0.5 -2 -2 -0.6 -6 42.3 44.26 -4.50% 3 1.2 0 1 1 -0.3 -2 50.2 49.56 1.30% 4 1.5 0.2 3 2 0.4 4 54.6 56.05 -2.60% 5 1.1 0.4 6 3 0.6 8 55.4 59.24 -6.50%

[0064] Additionally, tire models 185 / 60R15 (model 2), 235 / 60R17 (model 3), 234 / 45R18 (model 4), and 255 / 45R19 (model 5) were selected for predicted (comparison) and actual measurements of tire rolling resistance. See details below. Figure 3 .

[0065] 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 actual measurement result is within 7.9%, and there is also a good corresponding trend in the application of different tire models, which proves the effectiveness of the method of this patent.

[0066] The foregoing description of embodiments of the present invention, through which those skilled in the art are able to implement or use the present invention, will be readily apparent to those skilled in the art. Various modifications to these embodiments will be readily apparent to those skilled in the art. The general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novelty disclosed herein.

Claims

1. A method of rapidly comparing the rolling resistance of tires, characterized in that, The method takes the structure and rolling resistance of a reference tire as a benchmark, compares the structural differences of the comparison tire, and directly compares and calculates the rolling resistance changes using a polynomial to quickly estimate the tire rolling resistance. The function relationship of the estimation is as follows: ； where RR is the estimated rolling resistance value of the tire, RRC is the rolling resistance value of the reference tire, The structure parameter variation amounts are, in order, groove depth a, groove bottom rubber thickness b, ground contact width c, steel belt width d, pad thickness e, and apex height f.​ 2. The method of claim 1, wherein, The method for establishing the function relationship comprises the following steps: 1) Select commonly used tire structure factors as variables, including pattern groove depth a, pattern groove bottom rubber thickness b, ground contact width c, steel belt width d, pad thickness e, and triangular rubber height f; 2) Use a test design software to design tests on the above-mentioned six structure variables, which have at least five levels, to form an orthogonal design test scheme, and perform rolling resistance tests to obtain the rolling resistance values corresponding to each test scheme; 3) Based on the results of the test design, analyze the main effects or trends of each structure factor to determine the function type of the influence of each factor on the rolling resistance; 4) According to the function type, establish a rolling resistance polynomial model, and use the least squares method or other mathematical methods to solve the undetermined coefficients of the model; 5) Take the rolling resistance value of the reference tire as a benchmark, input the change amount of each factor based on the obtained polynomial model, quickly compare the changes of the rolling resistance of the comparison tire, and verify the prediction results with the actual test results.

3. The method of claim 2, wherein: In the step 3), the main effects of each factor are obtained through the main effect chart generated in the test design software or related statistical analysis results, and the function type includes linear, parabolic or horizontal line relationship.

4. The method of claim 2 or 3, wherein: In the step 4), the established rolling resistance polynomial model is as follows: ； k1~k6 are undetermined coefficients.

5. The method of claim 4, wherein: The least squares method obtains k1~k6 by solving an overdetermined equation system, specifically by forming an equation system with the test data and the polynomial model, and using the generalized inverse or pseudo-inverse algorithm of a matrix to calculate the unknown coefficients.

6. The method of claim 2, wherein: In the step 5), by adjusting the design value of at least one structure factor, inputting the corresponding change amount Δa~Δf to the polynomial model, quickly predicting or comparing to obtain the rolling resistance value of the tire, and comparing it with the corresponding test results.

7. The method of claim 2, wherein: The reference tire is a tire with known rolling resistance value and same or similar specifications, and the change amount of the structure factor is set according to the tire design requirements or different specifications, so as to quickly compare the rolling resistance of different tire specifications; And / or, The test 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 is realized through Matlab, Python or other mathematical analysis software; And / or, the test data of the tire rolling resistance is obtained from the rolling resistance test method specified in ISO 28580, GB / T 15082 or other related 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 revised or calibrated again by introducing additional experimental points or using other specifications of tires to measure the rolling resistance, so as to improve the prediction accuracy of the model.

8. A system for quickly contrasting the rolling resistance of tyres, characterised in that, The method realizes the method of any one of claims 1-7, and the system comprises: An input module for inputting the rolling resistance value of the reference tire, the variation range and variation amount of each tire structure factor; A test design and data acquisition module for generating a test scheme by using a test design software and recording the rolling resistance corresponding to each test; A data processing module for statistically analyzing the test data by using a mathematical analysis software, establishing a polynomial model and solving the undetermined coefficients of the polynomial model; A rolling resistance comparison module for quickly calculating and outputting the rolling resistance comparison result of the target tire according to the polynomial model and the input structure factor variation amount.

9. A computer readable storage medium having stored thereon a computer program or instructions, characterized in that, The computer program or instructions are executed by the processor to realize the method of any one of claims 1-7.

10. A computer program product comprising computer programs or instructions, characterized in that, The computer program or instructions are executed by the processor to realize the method of any one of claims 1-7.

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