Method for predicting macroscopic friction coefficient of tire based on micro-friction performance of tread rubber

Abstract

This invention discloses a method for predicting the macroscopic friction coefficient of tires based on the microscopic friction properties of tread rubber, belonging to the field of tire friction coefficient prediction technology. The method first obtains the shape and pressure distribution of the tire contact patch through experiments or simulations, establishing a three-dimensional complex contact patch model considering longitudinal grooves. Then, by conducting friction tests on tread rubber blocks, a microscopic friction model is established to show how the friction coefficient varies with contact pressure and slip velocity. Next, the slip velocity distribution within the contact patch is calculated, and combined with the contact pressure and the microscopic friction model, the friction coefficient at each point within the patch is determined. Finally, by integrating the stress over the entire contact patch area, the longitudinal dynamic friction coefficient of the tire is obtained, achieving accurate prediction from the microscopic properties of the tread rubber material to the overall macroscopic friction coefficient of the tire. This invention improves prediction accuracy, shortens the development cycle, and provides an effective tool for tire design and virtual vehicle matching.

Description

Technical Field

[0001] This invention belongs to the field of tire friction coefficient prediction technology, specifically relating to a method for predicting the macro friction coefficient of tires based on the micro-friction properties of tread rubber. Background Technology

[0002] The tire friction coefficient is a core indicator for measuring the mechanical performance between the tire and the road surface, directly affecting vehicle handling stability, ride comfort, and fuel economy. Tire friction characteristics depend not only on the adhesion and hysteresis properties of the tread rubber material but also on operating conditions such as vehicle speed, vertical load, and slip velocity. Accurately obtaining the tire friction coefficient is crucial in vehicle dynamics modeling, active safety control systems, and the development of virtual vehicle matching; therefore, it is necessary to study methods for obtaining the friction coefficient.

[0003] Traditional methods for obtaining tire friction coefficients primarily rely on real-vehicle road tests or tire bench tests. However, these methods have long development cycles, high testing costs, and are sensitive to test conditions, making them difficult to meet short-cycle development goals. Furthermore, friction characteristics exhibit significant nonlinearity under high tire slip rates, rendering simplified, experience-based models inadequate for high-precision simulation requirements. Therefore, establishing methods and models capable of accurately predicting tire friction characteristics is crucial for tire dynamics research and virtual tire-vehicle matching.

[0004] There are still obvious shortcomings in the existing related technologies: for example, the existing literature [1] requires a reference tire to predict the longitudinal dynamic friction coefficient of the tire, and predicts the longitudinal dynamic friction coefficient of the target tire by establishing an empirical ratio of the lateral and longitudinal peak friction coefficients of the reference tire. The establishment of this method has achieved the prediction of the longitudinal dynamic friction coefficient of the tire to a certain extent. However, this method lacks a theoretical basis for predicting the longitudinal dynamic friction coefficient of the tire, and assumes that the influence of the slip speed change of different tires on the friction coefficient is consistent, resulting in inaccurate prediction results. In addition, the accurate description of the ground imprint characteristics in the theoretical model is the key to realizing the prediction of the overall friction coefficient of the tire. However, the two-dimensional arbitrary ground imprint pressure distribution model commonly used in the literature [1, 2, 3, 4, 5] is overly simplified and fails to fully consider key factors such as the shape of the ground imprint, tire width and grooves, thus limiting the simulation accuracy of the model. Therefore, a method for predicting the macroscopic friction coefficient of the tire based on the micro-friction properties of the tread rubber is proposed. This method establishes a three-dimensional complex ground imprint model, systematically considering the geometry, pressure distribution, and longitudinal grooves of the non-contact area of ​​the ground imprint. This allows for a more accurate characterization of the contact pressure and slip velocity characteristics within the ground imprint, enabling the solution of the tire's macroscopic friction coefficient based on the microscopic friction properties of the tread rubber. This significantly improves the simulation accuracy of the model, compensates for the lack of theoretical basis, and provides support for shortening the virtual matching cycle between the tire and the vehicle.

[0005] [1] Xia Danhua. Research on prediction of steady-state lateral slip and longitudinal slip mechanical characteristics of tires [D]. Changchun: Jilin University, 2023. [2] Liu Qing, Guo Konghui, Chen Bingcong. Tire brush model analysis I. Steady-state lateral brush model [J]. Transactions of the Chinese Society for Agricultural Machinery, 2000, 31(1): 19-22. [3] Liu Qing, Guo Konghui. Tire brush model analysis II. Steady-state longitudinal slip and longitudinal slip lateral slip brush model [J]. Transactions of the Chinese Society for Agricultural Machinery, 2000, 31(2): 4-8. [4] Guo Konghui. UniTire unified tire model [J]. Journal of Mechanical Engineering, 2016, 52(12): 90-99. [5] Guo Konghui, Liu Qing. Theoretical model of tire steady-state lateral slip characteristics considering complex tire body deformation [J]. Journal of Mechanical Engineering, 1999, 35(2): 15-18. Summary of the Invention

[0006] The purpose of this invention is to provide a method for predicting the macro-friction coefficient of a tire based on the micro-friction properties of the tread rubber, so as to solve the technical problem that the simplified empirical models and simplified contact patch models used in the prior art are difficult to accurately obtain the friction characteristics and slip velocity distribution within the tire contact patch, which affects the accurate prediction of the overall friction coefficient. The purpose of this invention is also to shorten the virtual matching cycle between the tire and the vehicle, and to provide technical support for tire performance design and development.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for predicting the macroscopic friction coefficient of a tire based on the microscopic friction properties of the tread rubber includes the following steps: S1. Obtain the ground contact information of the target tire, including the shape of the ground contact, pressure distribution, and longitudinal tread groove information; S2. Based on the grounding imprint information, establish a three-dimensional grounding imprint model considering longitudinal patterned grooves; the grounding imprint model is used to determine the position coordinates and vertical contact pressure of each point within the grounding imprint. S3. Obtain the frictional characteristic data of the tread rubber material and establish a micro-friction model of the tread rubber material. The micro-friction model characterizes the functional relationship between the rubber friction coefficient and the contact pressure and slip velocity. S4. Based on the grounding imprint model, obtain the longitudinal slip deformation of each point within the grounding imprint, thereby calculating the local slip velocity distribution of each point within the grounding imprint. S5. For each point within the grounding imprint, based on the vertical contact pressure and sliding velocity at that point, the local friction coefficient at that point is determined using the micro-friction model, and then the longitudinal shear stress at that point is calculated. S6. Establish a longitudinal dynamic friction prediction model, integrate the longitudinal shear stress at each point within the grounding imprint, and realize the prediction of the macroscopic longitudinal dynamic friction coefficient of the tire.

[0008] Further, in step S2, the ground imprint model is constructed jointly by a ground imprint shape function and a pressure distribution function; the ground imprint shape function is: , In the formula, This represents the shape function of the ground imprint, used to characterize the contour shape of the tire when it touches the ground. This represents the outer radius of the tire when it is inflated and unloaded. and These are the radius of curvature and the curvature index of the tire's cross-sectional width profile, respectively. For tire load radius, , The coordinates of each point on the grounding imprint; The pressure distribution function includes a longitudinal pressure distribution function and a lateral pressure distribution function. The vertical contact stress at each point within the grounding imprint is a combined result of the longitudinal pressure distribution and the lateral pressure distribution.

[0009] Further, in step S2, the longitudinal pressure distribution function characterizes the vertical grounding pressure distribution at each point within the grounding imprint along the longitudinal direction, and its expression is: , The lateral pressure distribution function characterizes the vertical grounding pressure distribution along the lateral direction at each point within the grounding imprint, and its expression is: , In the formula, For the position ( , Vertical ground pressure distribution function along the longitudinal direction at point ( ); For the position ( , The vertical ground pressure distribution function along the lateral direction at point ( ); for Location grounding imprint length, for Location grounding imprint width, for The location is the lateral coordinate of the geometric center of the ground imprint. For the lateral distribution of grounding imprint pressure concavity factor, , and Here are the parameters for the ground imprint model, and n is the pressure distribution index.

[0010] Further, in step S2, the vertical contact pressure at each point within the grounding imprint is calculated using the following formula: In the formula, To contact pressure, For the vertical load on the tire, The area of ​​the ground imprint micro-element region. This is the longitudinal pressure distribution function. Let be the lateral pressure distribution function. This is the comprehensive pressure distribution function.

[0011] Furthermore, in step S2, the specific location of the longitudinal tread groove is determined by the lateral coordinate value of the tire ground contact mark feature, and the contact area and the non-contact longitudinal groove area are distinguished by the ground contact mark shape function.

[0012] Further, in step S3, the micro-friction model is established as follows: the tread rubber block sample is tested to obtain its friction coefficient data under various contact pressures and various sliding speeds; based on the test data, model parameters characterizing the functional relationship between the friction coefficient and the contact pressure and sliding speed are obtained by fitting.

[0013] Further, in step S3, the micro-friction model is: , In the formula, The coefficient of dynamic friction of the tire. The coefficient of friction during full sliding is . The peak friction coefficient, To control the parameter that the friction coefficient varies with the slip velocity, This is the actual sliding speed. The slip velocity corresponding to the peak friction coefficient. The parameter used to control the increase in the coefficient of friction during small slippage.

[0014] Further, in step S4, the local slip velocity distribution within the grounding imprint is obtained by solving for the longitudinal slip deformation of the tread, and the expression is: , In the formula, Let be the sliding velocity of a point within the grounding imprint. This represents the longitudinal component of the tire speed. For the ground imprint half length, , This represents the slip displacement of a point within the grounding imprint. For longitudinal slip ratio, For the vertical load on the tire, This refers to the longitudinal slip stiffness of the tire tread. The coefficient of friction, This is the pressure distribution coefficient.

[0015] Furthermore, in step S6, the overall longitudinal force of the tire is obtained by summing the longitudinal shear stresses at all contact points within the grounding imprint. The integration is performed over the entire contact area defined by the grounding imprint model.

[0016] Furthermore, in step S6, the longitudinal dynamic friction prediction model is: In the formula, For the longitudinal force of the tire, For the longitudinal shear stress in the micro-element region within the grounding imprint, The area of ​​the ground imprint micro-element region. This refers to the longitudinal slip stiffness of the tire tread. This refers to the longitudinal slip deformation of the tire tread. The longitudinal frictional stress is denoted as .

[0017] The beneficial effects of the above scheme are as follows: This invention fundamentally improves the accuracy and reliability of prediction results. By combining a microscopic rubber friction model with a physical path of spatial integration, a deterministic mapping relationship from the inherent properties of materials to system performance is established, eliminating reliance on historical tire data. This ensures that new tire designs also possess high accuracy and reliability. The introduction of a "three-dimensional grounding imprint model with longitudinal grooves" accurately characterizes the true geometry of the grounding imprint, pressure gradient, and contact / non-contact areas caused by the grooves. Integrating on this model ensures that the boundary conditions of the mechanical analysis closely match the actual situation, eliminating inaccurate predictions caused by oversimplification of the model and improving the expressive accuracy of the prediction model.

[0018] 2. This invention can significantly shorten the development cycle of tire products and greatly reduce the costs of prototyping and testing during the R&D process. Traditional tire performance development processes heavily rely on multiple physical iterations of "design-prototyping-testing," each involving expensive mold manufacturing and bench testing, resulting in a lengthy cycle. This method only requires obtaining basic information such as the friction performance of the tread rubber sample and the ground contact imprint of the target tire to complete the prediction and comparative analysis of the overall tire's macroscopic coefficient of friction in a virtual environment. This means that before mold opening and physical tire production, R&D personnel can accurately evaluate and optimize different formulations and specifications, thus supporting rapid and low-cost tire performance design and development.

[0019] 3. This invention possesses excellent adaptability to various operating conditions and technical versatility. Some existing prediction methods rely on complete test data from specific reference tires, making them unapplicable to entirely new tire specifications without comparable references. This method constructs a prediction system based on universal physical principles, its applicability unrestricted by tire specifications or compounds, achieving truly universal prediction capabilities. More importantly, existing complex simulation analyses often focus on the evaluation and optimization of rolling resistance, while this invention constructs a complete and proprietary physical integral model from the microscopic to the macroscopic level. Its output directly addresses the grip characteristic curve, crucial for vehicle handling stability and braking safety, meeting the demand for high-precision tire friction characteristics in tire design and development, as well as tire-vehicle matching. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the method for predicting the macroscopic friction coefficient of tires according to the present invention; Figure 2 This invention relates to a tire testing bench and finite element model; Figure 3 This is a schematic diagram of the grounding imprint test or simulation results of the present invention; Figure 4 This is a schematic diagram illustrating the verification results of the grounding imprint shape model of the present invention; Figure 5 This is a schematic diagram of the verification results of the grounding imprint pressure distribution model of the present invention; Figure 6 This is a schematic diagram of the application method of the longitudinal patterned groove of the present invention; Figure 7 This is a schematic diagram of the simulation results of a three-dimensional complex tire ground contact mark considering longitudinal tread grooves in this invention; Figure 8 This is a schematic diagram of the rubber friction test bench of the present invention; Figure 9 This is a schematic diagram comparing the friction coefficient identification results of this invention with experimental results; Figure 10 This is a schematic diagram of the slip velocity distribution within the grounding imprint of the present invention; Figure 11 This is a schematic diagram of the friction coefficient distribution that takes into account both contact pressure and sliding speed in this invention; Figure 12 This is a schematic diagram illustrating the coordinate system definition and motion analysis of the tire dynamic friction prediction model of this invention; Figure 13 This is a schematic diagram comparing the predicted results of the tire dynamic friction coefficient of this invention with experimental data (load is 2705N); Figure 14 This is a schematic diagram comparing the predicted tire dynamic friction coefficient of the present invention with experimental data (load of 5410N); Figure 15This is a schematic diagram comparing the predicted results of the tire dynamic friction coefficient of this invention with the test data (load is 6762N). Detailed Implementation Detailed Implementation

[0021] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0022] It should be noted that, unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0023] like Figure 1 As shown, a method for predicting the macroscopic friction coefficient of a tire based on the microscopic friction properties of the tread rubber is presented. This method predicts the tire's friction coefficient through the friction properties of the tread rubber. The method includes the following steps: S1. Obtain the ground contact information of the target tire, including the shape of the ground contact, pressure distribution, and longitudinal tread groove information; S2. Based on the grounding imprint information, establish a three-dimensional grounding imprint model considering longitudinal patterned grooves; the grounding imprint model is used to determine the position coordinates and vertical contact pressure of each point within the grounding imprint. S3. Obtain the frictional characteristic data of the tread rubber material and establish a micro-friction model of the tread rubber material. The micro-friction model characterizes the functional relationship between the rubber friction coefficient and the contact pressure and slip velocity. S4. Based on the grounding imprint model, obtain the longitudinal slip deformation of each point within the grounding imprint, thereby calculating the local slip velocity distribution of each point within the grounding imprint. S5. For each point within the grounding imprint, based on the vertical contact pressure and sliding velocity at that point, the local friction coefficient at that point is determined using the micro-friction model, and then the longitudinal shear stress at that point is calculated. S6. Establish a longitudinal dynamic friction prediction model, integrate the longitudinal shear stress at each point within the grounding imprint, obtain the macroscopic longitudinal dynamic friction coefficient of the tire, and realize the prediction of the macroscopic friction coefficient of the tire.

[0024] The core of this method lies in establishing a refined three-dimensional ground contact imprint model and combining it with microscopic frictional properties obtained from tests on the tire tread rubber material itself. This allows for the calculation of the slip velocity and friction coefficient at each contact point within the ground contact imprint, ultimately predicting the overall longitudinal dynamic friction performance of the tire through integral synthesis. The testing and simulation are conducted using a tire-based test bench or finite element model, as follows: Figure 2 As shown, the characteristics of the tire contact patch are obtained as follows: Figure 3 As shown.

[0025] The implementation process of each of the above steps will be explained in detail below.

[0026] Step S1: Obtain the ground contact information of the target tire.

[0027] First, it is necessary to obtain the contact patch information of the tire to be predicted under a specific load. The contact patch information includes the shape (outline) of the contact patch, the vertical pressure distribution within the contact patch area, and the layout information of the longitudinal tread grooves on the tire tread.

[0028] The results can be obtained through either physical experiments or computer simulations. Test acquisition: The target tire is mounted on a tire testing rig (e.g., Figure 2 (a) As shown, a specified vertical load is applied to the grounding imprint, and the shape and pressure distribution are directly measured using a pressure distribution measurement system. The location of the longitudinal trench is also recorded. The test results are as follows: Figure 3 As shown in (a).

[0029] Simulation acquisition: Establish a detailed finite element model of the target tire (e.g., Figure 2 (b) shows that static simulation analysis was performed under the same load conditions to extract the shape and pressure distribution data of the grounding area. The simulation results are as follows: Figure 3 As shown in (b).

[0030] Step S2: Establish a three-dimensional grounding imprint model that takes into account longitudinal patterned grooves.

[0031] Based on the grounding imprint information obtained in step S1, a three-dimensional grounding imprint model is established that can accurately characterize the geometry, pressure distribution, and longitudinal groove patterns of the grounding imprint. This model is used to determine the position coordinates (x, y) of any contact point within the grounding imprint and the vertical contact stress experienced at that point.

[0032] The grounding imprint model is constructed using a grounding imprint shape function and a pressure distribution function; the grounding imprint shape function is: , In the formula, This represents the shape function of the ground imprint, used to characterize the contour shape of the tire when it touches the ground. This represents the outer radius of the tire when it is inflated and unloaded. and These are the radius of curvature and the curvature index of the tire's cross-sectional width profile, respectively. For tire load radius, , These are the coordinates of the locations of each point on the grounding imprint.

[0033] The model parameters are obtained based on the tire's outer contour coordinates according to geometric relationships. satisfy: , The radial deformation of the tire is calculated using the following formula: In the formula, This is the vertical distance from the wheel center to the road surface.

[0034] The relationship between the effective rolling radius and radial deformation is as follows: .

[0035] In the formula, , and For model parameters, The effective rolling radius of the tire is defined. Based on the obtained ground imprint characteristics, the parameters of the ground imprint shape model are identified, and the simulation results of the theoretical model are compared with the experimental results. Figure 4 As shown.

[0036] The pressure distribution function includes a longitudinal pressure distribution function and a lateral pressure distribution function. The vertical contact stress at each point within the grounding imprint is a combined result of the longitudinal pressure distribution and the lateral pressure distribution.

[0037] The longitudinal pressure distribution function is expressed as follows: , The expression for the lateral pressure distribution function is: , In the formula, For the position ( , Vertical ground pressure distribution function along the longitudinal direction at point ( ); For the position ( , The vertical ground pressure distribution function along the lateral direction at point ( ); for Location grounding imprint length, for Location grounding imprint width, for The location is the lateral coordinate of the geometric center of the ground imprint. For the lateral distribution of grounding imprint pressure concavity factor, , and For ground imprint model parameters, n This is the pressure distribution index.

[0038] The longitudinal pressure distribution function characterizes the vertical ground pressure distribution at each point within the grounding imprint along the longitudinal direction, while the lateral pressure distribution function characterizes the vertical ground pressure distribution at each point within the grounding imprint along the lateral direction. Lateral refers to the tire width direction, and longitudinal refers to the tire rolling direction. , These represent the vertical coordinate and the lateral coordinate, respectively.

[0039] Based on the overall pressure distribution within the grounding imprint, the expression for the contact pressure at each point within the imprint is: .

[0040] In the formula, To contact pressure, For the vertical load on the tire, The area of ​​the ground imprint micro-element region. This is the longitudinal pressure distribution function. Let be the lateral pressure distribution function. This is the comprehensive pressure distribution function.

[0041] Based on the obtained grounding imprint characteristics, the parameters of the grounding imprint pressure distribution model are identified, and the simulation results of the theoretical model are compared with the experimental results. Figure 5 As shown.

[0042] Based on the location of the tire's longitudinal grooves, four longitudinal grooves are set along the tire width in the contact patch model. The specific location of the longitudinal grooves is determined by the lateral coordinates of the tire finite element model, which includes a total of 8 key coordinate values. When, it is represented as a non-contact longitudinal groove area, while When, it represents the contact area within the imprint, the application method of longitudinal pattern grooves is as follows: Figure 6 As shown.

[0043] Based on the established grounding imprint shape model, grounding imprint pressure distribution model, and longitudinal tread groove application method, the characteristics of a three-dimensional complex tire grounding imprint considering the longitudinal tread groove can be obtained, such as... Figure 7 As shown.

[0044] Step S3: Obtain the micro-friction coefficient of the tread rubber material and establish a micro-friction model.

[0045] Figure 8 A rubber friction testing rig was used to conduct friction tests on tire tread rubber blocks to obtain the friction coefficients of the rubber blocks under different contact pressures and sliding velocities. A microscopic friction model considering contact pressure and sliding velocity was established as shown below: , In the formula, The coefficient of dynamic friction of the tire. The coefficient of friction during full sliding is . The peak friction coefficient, To control the parameter that the friction coefficient varies with the slip velocity, This is the actual sliding speed. The slip velocity corresponding to the peak friction coefficient. The parameter used to control the increase in the coefficient of friction during small slippage.

[0046] , In the formula, , , and For model parameters, This refers to the contact pressure of the contact unit.

[0047] Based on the established friction model considering sliding velocity and contact pressure, the friction coefficient obtained from the test was parameterized. The friction coefficient identification results were compared with experimental results. Figure 9 As shown. Figure 9 The comparison between the friction coefficient curve predicted by the model and the experimental measurement data is shown, which verifies the effectiveness of the model.

[0048] Step S4: Calculate the local slip velocity distribution within the grounding imprint.

[0049] The slip velocity distribution within the contact patch is obtained by measuring the longitudinal slip deformation of the tire tread, as shown in the following formula: , , , In the formula, Let be the sliding velocity of a point within the grounding imprint. This represents the longitudinal component of the tire speed. For the ground imprint half length, , This represents the slip displacement of a point within the grounding imprint. For longitudinal slip ratio, For the vertical load on the tire, This refers to the longitudinal slip stiffness of the tire tread. The coefficient of friction, This is the pressure distribution coefficient.

[0050] The results of the slip velocity distribution within the grounding imprint are as follows Figure 10 As shown.

[0051] Step S5: Determine the local friction coefficient and longitudinal shear stress at each point within the grounding imprint.

[0052] The core objective of this step is to combine the model and data obtained in the previous steps to calculate the actual longitudinal frictional force contributed by each contact point within the grounding imprint.

[0053] First, for each contact point obtained after discretizing the three-dimensional grounding imprint model established in step S2, the vertical contact pressure data of that point is extracted from the model; at the same time, the local slip velocity data corresponding to that point is extracted from the calculation results of step S4.

[0054] Next, the vertical contact pressure and sliding velocity obtained above are used as input parameters and substituted into the micro-friction model of the tread rubber established in step S3. The friction coefficient of the contact unit under the specific contact pressure and sliding velocity conditions can then be calculated using this model.

[0055] Then, based on the longitudinal shear stress when the tire tread slips from the road surface and when it does not slip, the actual longitudinal shear stress generated by the unit is calculated.

[0056] Finally, following the above logic, the actual longitudinal shear stress of all contact elements within the grounding imprint is traversed and calculated. This yields not only the longitudinal shear stress distribution across the entire grounding region but also the friction coefficient distribution determined by the micro-friction model, which varies with contact pressure and sliding velocity. This accurately characterizes the microscopic non-uniformity of the friction state within the grounding surface. This distribution result forms the basis for subsequent macroscopic force integration.

[0057] Based on the contact pressure and slip velocity distribution within the grounding imprint, the friction coefficient distribution within the grounding imprint is obtained as follows: Figure 11 As shown.

[0058] Step S6: Integrate to obtain the macroscopic longitudinal dynamic friction coefficient of the tire.

[0059] The following formula is used to establish a dynamic friction prediction model based on the tire's motion deformation: In the formula, This represents the position vector of any contact point during tire movement. Indicates the contact center Location in space, This indicates the position of the contact point relative to the contact center.

[0060] in, Expressed as: , , , , , , , , , .

[0061] In the formula, For the longitudinal force of the tire, For the longitudinal shear stress in the micro-element region within the grounding imprint, The area of ​​the ground imprint micro-element region. This refers to the longitudinal slip stiffness of the tire tread. This refers to the longitudinal slip deformation of the tire tread. The longitudinal frictional stress is denoted as .

[0062] Based on the established dynamic friction prediction model, the longitudinal shear stress at each point within the ground contact imprint is integrated to predict the macroscopic longitudinal dynamic friction coefficient of the tire.

[0063] Figure 12 This diagram illustrates the coordinate system definition and motion analysis of the tire dynamic friction prediction model. By analyzing the ratio of longitudinal force to vertical force and the relationship between longitudinal slip ratio and longitudinal slip velocity, the curve of the tire's longitudinal dynamic friction coefficient versus longitudinal slip velocity is obtained. The predicted tire dynamic friction coefficient under a 2705N load is compared with experimental data. Figure 13 As shown, the predicted tire dynamic friction coefficient under a 5410N load is compared with the experimental data. Figure 14 As shown, the predicted tire dynamic friction coefficient under a load of 6762N is compared with the experimental data. Figure 15 As shown.

[0064] The comparative results show that, under different loads, the friction characteristic curves predicted by the method of this invention are in good agreement with the experimental data, and the prediction results are highly consistent with the experimental data, verifying the feasibility of the technical solution and the reliability of the prediction accuracy. This fully demonstrates the accuracy and effectiveness of the macroscopic characteristic prediction based on the micro-friction coefficient of tread rubber and the three-dimensional ground imprint model of this invention, providing technical support for the virtual design and performance development of tires.

[0065] Finally, it should be noted that any parts of this invention not described in detail are prior art. Those skilled in the art will understand that the above descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A method for predicting the macroscopic friction coefficient of tires based on the microscopic friction properties of tread rubber, characterized in that, Includes the following steps: S1. Obtain the ground contact information of the target tire, including the shape of the ground contact, pressure distribution, and longitudinal tread groove information; S2. Based on the grounding imprint information, establish a three-dimensional grounding imprint model considering longitudinal patterned grooves; the grounding imprint model is used to determine the position coordinates and vertical contact pressure of each point within the grounding imprint. S3. Obtain the frictional characteristic data of the tread rubber material and establish a micro-friction model of the tread rubber material. The micro-friction model characterizes the functional relationship between the rubber friction coefficient and the contact pressure and slip velocity. S4. Based on the grounding imprint model, obtain the longitudinal slip deformation of each point within the grounding imprint, thereby calculating the local slip velocity distribution of each point within the grounding imprint. S5. For each point within the grounding imprint, based on the vertical contact pressure and sliding velocity at that point, the local friction coefficient at that point is determined using the micro-friction model, and then the longitudinal shear stress at that point is calculated. S6. Establish a longitudinal dynamic friction prediction model, integrate the longitudinal shear stress at each point within the grounding imprint, and realize the prediction of the macroscopic longitudinal dynamic friction coefficient of the tire.

2. The method for predicting the macroscopic friction coefficient of a tire based on the microscopic friction properties of tread rubber according to claim 1, characterized in that, In step S2, the ground imprint model is constructed using a ground imprint shape function and a pressure distribution function; the ground imprint shape function is: ， In the formula, This represents the shape function of the ground imprint, used to characterize the contour shape of the tire when it touches the ground. This represents the outer radius of the tire when it is inflated and unloaded. and These are the radius of curvature and the curvature index of the tire's cross-sectional width profile, respectively. For tire load radius, , The coordinates of each point on the grounding imprint; The pressure distribution function includes a longitudinal pressure distribution function and a lateral pressure distribution function. The vertical contact pressure at each point within the grounding imprint is a combined result of the longitudinal pressure distribution and the lateral pressure distribution.

3. The method for predicting the macroscopic friction coefficient of a tire based on the microscopic friction properties of tread rubber according to claim 2, characterized in that, In step S2, the longitudinal pressure distribution function characterizes the vertical grounding pressure distribution at each point within the grounding imprint along the longitudinal direction, and its expression is: ， The lateral pressure distribution function characterizes the vertical grounding pressure distribution along the lateral direction at each point within the grounding imprint, and its expression is: ， In the formula, For the position ( , Vertical ground pressure distribution function along the longitudinal direction at point ( ); For the position ( , The vertical ground pressure distribution function along the lateral direction at point ( ); for Location grounding imprint length, for Location grounding imprint width, for The location is the lateral coordinate of the geometric center of the ground imprint. For the lateral distribution of grounding imprint pressure concavity factor, , and Here are the parameters for the ground imprint model, and n is the pressure distribution index.

4. The method for predicting the macroscopic friction coefficient of a tire based on the microscopic friction properties of tread rubber according to claim 3, characterized in that, In step S2, the vertical contact pressure at each point within the grounding imprint is calculated using the following formula: In the formula, To contact pressure, For the vertical load on the tire, The area of ​​the ground imprint micro-element region. This is the longitudinal pressure distribution function. Let be the lateral pressure distribution function. This is the comprehensive pressure distribution function.

5. The method for predicting the macroscopic friction coefficient of a tire based on the microscopic friction properties of tread rubber according to claim 1, characterized in that, In step S2, the specific location of the longitudinal tread groove is determined by the lateral coordinate value of the tire ground contact mark feature, and the contact area and the non-contact longitudinal groove area are distinguished by the ground contact mark shape function.

6. The method for predicting the macroscopic friction coefficient of a tire based on the microscopic friction properties of tread rubber according to claim 1, characterized in that, In step S3, the micro-friction model is established as follows: the tread rubber block sample is tested to obtain its friction coefficient data under various contact pressures and various sliding speeds; based on the test data, model parameters characterizing the functional relationship between the friction coefficient and the contact pressure and sliding speed are obtained by fitting.

7. The method for predicting the macroscopic friction coefficient of a tire based on the microscopic friction properties of tread rubber according to claim 1, characterized in that, In step S3, the micro-friction model is: ， In the formula, The coefficient of dynamic friction of the tire. The coefficient of friction during full sliding is . The peak friction coefficient, To control the parameter that the friction coefficient varies with the slip velocity, This is the actual sliding speed. The slip velocity corresponding to the peak friction coefficient. The parameter used to control the increase in the coefficient of friction during small slippage.

8. The method for predicting the macroscopic friction coefficient of a tire based on the microscopic friction properties of tread rubber according to claim 4, characterized in that, In step S4, the local slip velocity distribution within the grounding imprint is obtained by solving for the longitudinal slip deformation of the tread, and the expression is: ， In the formula, Let be the sliding velocity of a point within the grounding imprint. This represents the longitudinal component of the tire speed. For the ground imprint half length, , This represents the slip displacement of a point within the grounding imprint. For longitudinal slip ratio, For the vertical load on the tire, This refers to the longitudinal slip stiffness of the tire tread. The coefficient of friction, This is the pressure distribution coefficient.

9. The method for predicting the macroscopic friction coefficient of a tire based on the microscopic friction properties of tread rubber according to claim 1, characterized in that, In step S6, the overall longitudinal force of the tire is obtained by summing the longitudinal shear stresses at all contact points within the grounding imprint. The integration is performed over the entire contact area defined by the grounding imprint model.

10. The method for predicting the macroscopic friction coefficient of a tire based on the microscopic friction properties of tread rubber according to claim 1, characterized in that, In step S6, the longitudinal dynamic friction prediction model is: In the formula, For the longitudinal force of the tire, For the longitudinal shear stress in the micro-element region within the grounding imprint, The area of ​​the ground imprint micro-element region. This refers to the longitudinal slip stiffness of the tire tread. This refers to the longitudinal slip deformation of the tire tread. The longitudinal frictional stress is in the micro-element region.

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