Wheel-ground force estimation method based on elastic half-space contact model and in-tire monitoring

Abstract

The application discloses a wheel-ground force estimation method based on an elastic half-space contact model and tire internal monitoring, which comprises the following steps: step one, stress analysis of an elastic half-space body; step two, introduction of an empirical formula of tire-pavement displacement, and establishment of a wheel-ground contact deformation stress theoretical model; and step three, establishment of a functional relationship between vertical load F and deformation variable ε x of the tire, and estimation of the tire wheel-ground force. The method can effectively estimate the tire wheel-ground force by analyzing the internal stress and strain relationship of the elastic half-space body when the elastic deformation of the elastic half-space body occurs, and establishing the functional relationship between the vertical load F and the deformation variable ε x of the tire, and has the characteristics of high precision and strong real-time performance.

Description

Technical Field

[0001] This invention relates to the field of vehicle stability technology, specifically to a wheel-ground force estimation method based on an elastic half-space contact model and in-tire monitoring. Background Technology

[0002] With the rapid development of my country's highway infrastructure, the types and number of cars owned by people have increased rapidly, leading to a continuous increase in the transportation volume that highways need to bear. Along with the rapid development of the highway transportation industry, some problems have gradually emerged, such as: overloading occurs frequently, with some drivers breaking the law and disregarding the safety hazards that overloading poses to driving; prolonged operation under overload conditions will shorten the lifespan of the vehicle, accelerate the aging of parts and damage the engine, cause tire wear and deformation, make steering heavier, increase centrifugal force, reduce braking performance, affect the vehicle's handling stability, and lead to accidents such as tire blowouts and loss of brake control. This not only seriously damages the lifespan of highways but also easily causes serious traffic accidents, resulting in unnecessary loss of life and property.

[0003] When a vehicle is driving on the road, its operating state is closely related to the contact deformation between the tire and the ground. The kinematic properties of the tire are further affected by the relationship between the vertical load and the tire body deformation during tire deformation. Improving the stability and comfort of vehicles is a major area of ​​continuous exploration and development in the current automotive industry, which is inseparable from the research support of tire-ground kinematic contact mechanics. Many scholars at home and abroad have studied the changes in tire body deformation under the action of external forces when the tire is rolling by creating wheel-ground contact force models, and calculated the deformation and stress relationship in the deformation area.

[0004] The forces acting on the tire in contact with the ground are closely related to the safety and stability of a vehicle. Therefore, research on tire-wheel contact models is of great practical significance. In recent years, research on tire-ground contact mechanics by scholars both domestically and internationally has revealed two main research methods for wheel-ground contact mechanics models: 1. Solving for the pressure exerted on the tire in contact with the ground based on finite element theory to establish a wheel-ground contact force model; 2. Studying the forces acting on the tire in contact with the ground.

[0005] The methods mentioned above are unable to explore the relationship between stress and deformation displacement when elastic half-space bodies are in contact, resulting in low detection accuracy and the inability to monitor tire pressure in real time. Therefore, it is urgent to design a wheel-ground force estimation method based on elastic half-space contact model and in-tire monitoring to solve the problems of the existing technologies. Summary of the Invention

[0006] To address the aforementioned problems, this invention aims to provide a wheel-ground force estimation method based on an elastic half-space contact model and in-tire monitoring. This method analyzes the internal stress-strain relationship of an elastic half-space body under elastic deformation through the theory of elastic contact, establishing the vertical load on the tire. With deformation The functional relationship between them can effectively estimate the tire-ground force, and has the characteristics of high accuracy and strong real-time performance.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] Wheel-to-ground force estimation method based on elastic half-space contact model and in-tire monitoring, including

[0009] Step 1: Perform force analysis on the elastic half-space.

[0010] S1.1 When the tire is in rolling contact with the ground, a simplified tire-ground contact mechanics model is used;

[0011] S1.2 Performs force analysis on the elastic half-space;

[0012] S1.3 Perform normal force analysis on the elastic half-space;

[0013] S1.4 Perform tangential force analysis on the elastic half-space;

[0014] S1.5 Analyze the force conditions of the elastic half-space;

[0015] Step 2: Introduce the empirical formula for tire-road displacement to establish a theoretical model of wheel-ground contact deformation and force.

[0016] S2.1 Analyzes the deformation of the curved surface of an elastically contacting object;

[0017] S2.2 Analysis of the wheel-ground contact area boundary;

[0018] S2.3 Establish a wheel-ground elastic contact model;

[0019] Step 3: Establish the vertical load on the tire With deformation The functional relationship between the tire and the ground is used to estimate the tire-ground force.

[0020] Preferably, the process of performing force analysis on the elastic half-space body in step S1.2 includes:

[0021] (1) When the tire and the ground are in contact, there is a contact band. When the contact band is subjected to load, the ground is regarded as an elastic half-space body for force analysis. A three-dimensional rectangular coordinate system is established, in which the x-axis is parallel to the tangent of the tire rotation, the y-axis is parallel to the long side of the contact band, and the z-axis is perpendicular to the narrow band pointing to the elastic half-space body. A two-dimensional rectangular coordinate system is established by taking a section perpendicular to the y-axis at the tire-ground rolling contact point.

[0022] (2) First, stress calculation is performed on the stress points within the deformation region of the elastic half-space. The stress state of each stress point consists of six components, and the stress components are: The displacements occurring in each direction are The strain that occurs is: In an elastic half-space, the relationship between the stress and strain changes inside a tire when subjected to elastic deformation at a selected point in the xz plane is as follows:

[0023] (1)

[0024] When studying an elastic half-space subjected to an external vertical load, the elastic modulus of each part and point of the elastic half-space, as an isotropic body, is measured. Since it is a constant, the relationship between strain and stress can be derived:

[0025] (2)

[0026] in, The lateral deformation coefficient is... Shear modulus is defined as:

[0027] (3)

[0028] (3) Substituting into equation (2), we get:

[0029] (4)

[0030] (4) When analyzing the force at the point of application on the wheel-ground contact section, we have Constraints, given a stress function stress and Regarding the stress function given by the following formula: :

[0031] (5)

[0032] Let the stress function be... Satisfying the biconcordance equations:

[0033] (6)

[0034] Using cylindrical coordinates Solving for the elastic strain relationship, we give the relationship between stress components and deformation displacement in cylindrical coordinates;

[0035] In stress function The relationship between strain and displacement is as follows:

[0036] (7)

[0037] The relationship between stress and function is as follows:

[0038] (8).

[0039] Preferably, the process of performing normal force analysis on the elastic half-space body in step S1.3 includes:

[0040] (1) Suppose that when the elastic half-space is subjected to a normal perpendicular pressure distributed along the y-axis, the perpendicular pressure is uniformly distributed according to the magnitude of P; the elastic half-space undergoes elastic deformation and generates stress components under the action of a tangential normal force, and the polar coordinate stress function is defined. Perform stress analysis:

[0041] (9)

[0042] In the stress function formula, A is an arbitrary constant;

[0043] (2) Substituting the stress function formula (9) into the stress change formula of the stress function is shown below:

[0044] (10)

[0045] (3) Determine the effect on the For the radius located at Force on the positive axis semicircle ,when With normal force When they are equal in size, we have:

[0046] (11)

[0047] get:

[0048] (12)

[0049] (4) Given the transformation relationship between polar coordinates and rectangular coordinates, the stress... Converted into right-angle stress The stress components are obtained:

[0050] (13)

[0051] Having obtained the functional relationship of the stress components, we substitute this relationship into Hooke's law to calculate the strain and normal force. Relationship with deformation displacement:

[0052] (14)

[0053] Based on the relationship between deformation displacement and normal force in (14), we can obtain:

[0054] (15)

[0055] When studying the deformation of an elastic half-space under stress, considering the actual deformation of a tire in rolling contact with the ground, the elastic half-space does not sway left and right during a collision, thus obtaining... , ,get:

[0056] (16)

[0057] Take any point outside the contact surface area and determine the constant. Let the distance between the reference point and the contact deformation surface be... ,constant for:

[0058] (17).

[0059] Preferably, the process of performing tangential force analysis on the elastic half-space body in step S1.4 includes:

[0060] (1) When the elastic half-space is subjected to a tangential force distributed along the y-axis, assuming the tangential force is uniformly distributed and has a magnitude of Q, it acts on... Point; When an elastic half-space is subjected to a tangential force, stress components are generated in the contact deformation region of the half-space; the form of the stress expression is the same as that when a normal force is applied, that is:

[0061] (18)

[0062] (2) Within the region where the elastic half-space deforms, The range of values ​​is Transforming the stress relationship in polar coordinates into the stress relationship in rectangular coordinates, we get:

[0063] (19)

[0064] (3) When the elastic half-space does not undergo rigid rotation, and in If no vertical displacement occurs in the axial direction, then the deformation-displacement relationship is:

[0065] (20).

[0066] Preferably, the process of analyzing the stress state of the elastic half-space in step S1.5 includes...

[0067] (1) Let Represents the contact surface Point and origin distance, The unit area representing the area of ​​an elastic half-space subjected to force is then... In terms of area, the forces acting on the elastic half-space are: forces acting in the normal direction on the contact surface of the elastic half-space, with magnitudes of , to the origin use After point replacement, there is ,Will Point due to its effect on Integrating the stress generated in the tangential direction at a unit area yields the stress on the deformation of the elastic half-space. Stress components generated by point action:

[0068] (twenty one)

[0069] In equation (21), when analyzing the plane strain relationship equation of the elastic half-space, the functional relationship between stress components and surface forces was analyzed;

[0070] (2) Using an analysis method similar to that of stress components, the deformation displacement of the elastic half-space body under the action of tangential and normal forces is obtained;

[0071] (twenty two)

[0072] Regarding the left and right sides of equation (22) Perform differentiation to eliminate constants ,get:

[0073] (twenty three).

[0074] Preferably, the process of analyzing the surface deformation of the elastically contacting object described in step S2.1 includes:

[0075] Analyzing the tire as an elastic cylinder, the curve containing the contact surface is a continuous curve. The first and second derivatives at any point on the curve have geometric meaning within the contact region. Here is the general definition of the curve:

[0076] (twenty four).

[0077] Preferably, the process of analyzing the boundary of the wheel-ground contact area in step S2.2 includes...

[0078] (1) Let the expression for the vertical pressure distribution of the tire be:

[0079] (25)

[0080] have:

[0081] (26)

[0082] For the vertical load distribution function Introducing an nth-order polynomial function:

[0083] (27)

[0084] in The relative displacement has a magnitude of ;

[0085] From equation (23), we know that the vertical load distribution is closely related to the constant n. Only by determining the value of n can we obtain the magnitude of the contact point pressure. Here, we perform finite element analysis to obtain the magnitude of n under different loads, and know the relationship of n values:

[0086]

[0087] The results were obtained through finite element analysis. The relational expression is:

[0088] (28)

[0089] Introducing given boundary conditions and Substituting the expression into equation (23), we obtain the vertical load within the elastic half-space. With deformation The functional relationship is:

[0090] (29).

[0091] Preferably, the process of establishing the wheel-ground elastic contact model in step S2.3 includes:

[0092] set up

[0093] (30)

[0094] For the equivalent elastic modulus, the following holds:

[0095]

[0096] but:

[0097] (31)

[0098] Will Substituting into equation (27) yields the relationship between vertical load and deformation.

[0099] The beneficial effects of this invention are: This invention discloses a method for estimating wheel-ground force based on an elastic half-space contact model and in-tire monitoring. Compared with the prior art, the improvement of this invention lies in:

[0100] This invention presents a method for estimating wheel-ground force based on an elastic half-space contact model and in-tire monitoring. First, the method simplifies the wheel-ground contact deformation force model, approximating the tire and ground as a cylinder and an elastic half-space, respectively. Using elastic contact theory, the internal stress and strain relationships of the elastic half-space under elastic deformation are studied. Force analysis is performed on both the surface force (normal pressure) and tangential friction force experienced by the tire during rolling, yielding the functional relationship between tire displacement and surface force during deformation. Then, surface deformation analysis of the elastic contact object is conducted. Given the contact curve equation, relevant parameter expressions from elastic contact theory are introduced, ultimately establishing the vertical load on the tire. With deformation The functional relationship between them can effectively estimate the tire-ground force, with the advantages of high accuracy and strong real-time performance. Attached Figure Description

[0101] Figure 1 This is a flowchart of the evaluation process for the wheel-ground force estimation method based on the elastic half-space contact model and in-tire monitoring of the present invention.

[0102] Figure 2 This is a diagram of the tire-ground contact coordinate system of the present invention.

[0103] Figure 3 This is a diagram showing the internal deformation of the elastic half-space body of the present invention.

[0104] Figure 4 This is a diagram of an elastic half-space under the normal pressure P of the present invention.

[0105] Figure 5 This is a diagram of an elastic half-space under the action of tangential force Q according to the present invention.

[0106] Figure 6 This is a diagram of an elastic half-space under the simultaneous action of tangential and normal forces according to the present invention.

[0107] Figure 7 This is a force diagram of the cross-section of the elastic deformation region of the present invention. Detailed Implementation

[0108] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0109] Example 1: Refer to Appendix Figure 1-7 The method shown is a wheel-ground force estimation method based on an elastic half-space contact model and in-tire monitoring, including...

[0110] Step 1: Perform force analysis on the elastic half-space when the tire rolls into contact with the ground.

[0111] S1.1 Based on the elastic contact theory, a simplified tire-ground contact mechanical model is constructed.

[0112] When a tire rolls into contact with the ground, it undergoes elastic deformation under the action of a normal perpendicular force. Upon contact with the ground, deformation occurs, and simultaneously, a tangential force drives the tire to rotate. The deformation caused by the elastic contact between the tire and the ground is influenced by two forces. Furthermore, within the tire-ground contact area, there are two deformation models: an adhesion zone and a sliding zone. In the sliding zone, contact points will experience regular contact and separation, while the stress changes in the adhesion zone maintain a uniform pattern. The surface profile of the wheel-ground contact section approximates a parabolic curve. In actual contact problems, the size of the tire-ground contact surface is often much smaller than the tire-ground surface size and relative radius of curvature. Therefore, the results obtained from deformation stress and displacement analysis using elastic contact theory are close to the actual results.

[0113] Due to the influence of other factors on the tire-ground contact problem, in order to reduce the difficulty of the problem, the tire is approximated as an elastic cylinder with uniform material distribution in the analysis process, and the ground is approximated as an elastic body constrained by the contact surface in one direction and infinitely large in other directions, called an elastic half-space. The deformation of the tire-ground contact is regarded as elastic contact deformation; therefore, the linear small deformation theory can be used to analyze and calculate the strain and stress at any point in the contact surface area.

[0114] The contact deformation stress of the tire carcass under vertical load is mainly distributed in the contact area between the tire carcass and the ground, and its size decreases rapidly with the increase of distance from the contact point. Therefore, in the tire carcass deformation analysis, the stress value change near the contact point is the focus of the study and analysis, and the trend of deformation stress change in this area is more convincing.

[0115] S1.2 Force analysis of the elastic half-space

[0116] (1) When the tire and the ground are in contact, there is a narrow contact band. When the narrow band is subjected to a load, if the ground is regarded as an elastic half-space body for force analysis, the wheel-ground contact deformation force analysis problem is a three-dimensional contact force analysis problem. A three-dimensional rectangular coordinate system (o-xyz system) is established, in which the x-axis is parallel to the tangent direction of the tire rotation, the y-axis is parallel to the long side of the narrow contact band, and the z-axis is perpendicular to the narrow band pointing to the elastic half-space body; the coordinate system is established as follows: Figure 2 As shown;

[0117] A cross-section perpendicular to the y-axis at the tire-ground rolling contact point is taken to analyze the functional relationship between strain and stress at a point within the elastic half-space under load; a two-dimensional rectangular coordinate system is established, and the forces inside the elastic half-space are as follows: Figure 3 As shown;

[0118] Figure 3 This demonstrates the relationship between stress and strain when an elastic half-space is simultaneously subjected to tangential and normal forces, resulting in deformation within the half-space. When the elastic half-space is subjected to load, the strain generation and changes are concentrated along the x-axis. Within the range, the forces acting on the object within the deformation range are: , The force is related to x and there is a functional relationship between them; located at Outside the range (elastic deformation range), there is no external force, no related deformation, and no stress or strain changes;

[0119] (2) First, stress calculation is performed on the stress points within the deformation region of the elastic half-space. The stress state of each stress point consists of six components, and the stress components are: The displacements occurring in each direction are The strain that occurs is: ;

[0120] In analyzing an elastic half-space, we select a point on the cross section xz-plane to analyze the relationship between stress and strain changes inside the tire when it undergoes elastic deformation (stress is divided into normal strain and shear strain). The relationship between strain and displacement is as follows:

[0121] (1)

[0122] The elastic deformation that occurs upon contact conforms to the generalized Hooke's law. When studying an elastic half-space subjected to an external vertical load, the elastic half-space can be solved as an isotropic body, i.e., the elastic modulus of each part and point undergoing deformation is determined. It is a constant, and the relationship between strain and stress is derived from Hooke's Law:

[0123] (2)

[0124] in, This is the lateral deformation coefficient (Poisson's ratio). Shear modulus is defined as:

[0125] (3)

[0126] (3) When studying the plane strain of the tire-ground contact section, Substituting into equation (2), we can obtain:

[0127] (4)

[0128] (4) When analyzing the force at the point of application on the wheel-ground contact section, we have For ease of solving in-plane stress, a stress function is given as a constraint condition. stress and Regarding the stress function given by the following formula: :

[0129] (5)

[0130] Assuming stress function Satisfying the biconcordance equations:

[0131] (6)

[0132] Using cylindrical coordinates It is more convenient to solve the elastic strain relationship, and the relationship between stress components and deformation displacement in cylindrical coordinates is given;

[0133] In stress function The relationship between strain and displacement is as follows:

[0134] (7)

[0135] The relationship between stress and function is as follows:

[0136] (8);

[0137] S1.3 Normal force analysis of the elastic half-space.

[0138] (1) Assume that when the elastic half-space is subjected to a normal perpendicular pressure distributed along the y-axis, the perpendicular pressure is uniformly distributed according to the magnitude of P; the elastic half-space undergoes elastic deformation and generates stress components under the action of a tangential normal force, and the deformation and stress situation inside the elastic half-space is as follows. Figure 4 As shown, the polar coordinate stress function is defined. Perform stress analysis:

[0139] (9)

[0140] In the stress function formula, A can be any constant;

[0141] (2) Substituting the stress function formula (9) into the stress change formula of the stress function is shown below:

[0142] (10)

[0143] Figure 4 This is a force diagram of an elastic half-space body under a vertical pressure P, with P concentrated at point O. The stress is almost zero when the body moves away from point O, and is maximum at point O. According to the strain function, the stress increases with... The increase in The rate decreases;

[0144] (3) Determine the effect on the For the radius located at Force on the positive axis semicircle ,when With normal force When they are equal in size, we have:

[0145] (11)

[0146] get:

[0147] (12)

[0148] (4) Given the transformation relationship between polar coordinates and rectangular coordinates, the stress... Converted into right-angle stress The stress components are obtained:

[0149] (13)

[0150] The functional relationship of the stress components has been obtained. Substituting the stress function relationship into Hooke's law, the strain and normal force can be calculated. Relationship with deformation displacement:

[0151] (14)

[0152] Based on the relationship between deformation displacement and normal force in (14), and according to elasticity theory, we can obtain:

[0153] (15)

[0154] When studying the deformation of an elastic half-space under stress, considering the actual deformation of a tire in rolling contact with the ground, the elastic half-space does not sway left and right during a collision, thus obtaining... When studying contact surfaces, Right now( ),get:

[0155] (16)

[0156] constant It cannot be obtained from plane strain; to determine the constant... It is necessary to select any point outside the contact surface area and determine the constant. Assume the distance between the reference point and the contact deformation surface is... Then the constant for:

[0157] (17);

[0158] S1.4 Tangential force analysis of the elastic half-space.

[0159] (1) When the elastic half-space is subjected to a tangential force distributed along the y-axis, assuming the tangential force is uniformly distributed and has a magnitude of Q, it acts on... Point; When an elastic half-space is subjected to a tangential force, stress components are generated in the contact deformation region of the half-space. The stress situation of the elastic half-space is as follows: Figure 5 As shown;

[0160] A radial force field is generated under the action of tangential force, which is similar to the stress field generated by normal force rotated by 90°. Size from The measurement of the axis begins, and the method for analyzing the stress generated in the elastic half-space is the same as that for the application of a normal force. The resulting stress expression also has the same form as that for the application of a normal force, namely:

[0161] (18)

[0162] (2) Within the region where the elastic half-space deforms, The range of values ​​is Transforming the stress relationship in polar coordinates into the stress relationship in rectangular coordinates, we get:

[0163] (19)

[0164] (3) When the elastic half-space does not undergo rigid rotation, and in If no vertical displacement occurs in the axial direction, then the deformation-displacement relationship is:

[0165] (20);

[0166] S1.5 Analysis of the force conditions of the elastic half-space

[0167] (1) In steps S1.3 and S1.4, stress analysis is performed on the normal force and tangential force individually applied to the elastic half-space. The stress and deformation obtained under the action of two mutually perpendicular forces are the same, but the measurement methods are very different. However, when analyzing the stress analysis problem of deformation caused by tire contact with the ground, in addition to the normal perpendicular load, the tire-ground contact surface is always subject to friction due to the roughness of the contact surface when the tire rolls and comes into contact with the ground. This leads to the transmission of tangential force due to friction. Therefore, when analyzing the stress model of tire-ground contact, it is necessary to comprehensively consider the influence of the two forces on the stress change of the elastic half-space. In this embodiment, it is necessary to solve the problem of determining the stress and deformation caused by surface force at any point in the tire-ground contact area. , The resulting changes in stress and strain, and the elastic deformation displacement occurring at that point; Figure 6 This indicates that the elastic half-space is subjected to surface forces within the region where elastic deformation occurs. , Force diagram of the action;

[0168] exist Figure 6 middle, Represents the contact surface Point and origin distance, The unit area representing the area of ​​an elastic half-space subjected to force is then... In terms of area, the forces acting on the elastic half-space are: forces acting in the normal direction on the contact surface of the elastic half-space, with magnitudes of , to the origin use After point replacement, there is ,Will Point due to its effect on Integrating the stress generated in the tangential direction at a unit area yields the stress response to the deformation of the elastic half-space. Stress components generated by point action:

[0169] (twenty one)

[0170] In equation (21), when analyzing the plane strain relationship equation of the elastic half-space, the functional relationship between stress components and surface forces was analyzed;

[0171] By employing an analysis method similar to that of stress components, the deformation displacement of the elastic half-space body under the action of tangential and normal forces was obtained;

[0172] (twenty two)

[0173] Regarding the left and right sides of equation (22) Perform differentiation to eliminate constants ,get:

[0174] (twenty three);

[0175] Step 2: Introduce the empirical formula for tire-road displacement to establish a theoretical model of wheel-ground contact deformation and force.

[0176] S2.1 Analysis of the deformation of the curved surface of an elastically contacting object

[0177] When analyzing the forces acting on elastic deformation, we first analyze the forces acting on the cylinder and the elastic half-space in the normal direction. The two objects undergo elastic deformation upon contact. During the deformation process of the cylinder and the elastic half-space, the deformation changes from a line to a surface, satisfying the premise of the elastic deformation stress analysis in step one. The deformation force relationship between the two elastic objects is theoretically derived and numerically calculated. In establishing the tire-ground contact model, we regard the tire and the ground as a cylinder and an elastic half-space, respectively. The cylinder is a symmetrical object rotating about the rotation center axis. Other irrelevant factors are ignored, and the two objects are in contact with each other under force.

[0178] From the force-contact deformation image of the cylinder, the surface in contact between the cylinder and the elastic half-space is still a continuous curve, which can be approximated as an ellipse. The stress and deformation displacement analysis in the deformation area requires calculating the deformation displacement of the force points on the contact surface between the tire and the ground where the contact deformation occurs. For an axisymmetric figure like a cylinder, there is a symmetrical relationship between the force range in contact with the elastic half-space.

[0179] Force analysis was performed on any section of the contact deformation area between the cylinder and the elastic half-space. The force conditions of the other sections were the same. The surface curve of the cylinder was circular when it was not in contact, and became elliptical after contact compression deformation. Figure 7 Force diagram of the cross section in the elastic deformation region;

[0180] For force analysis of elastic contact surfaces, the tire is treated as an elastic cylinder. The curve containing the contact surface is a continuous curve. The first and second derivatives at any point on the curve have geometric meaning within the contact region. Here, the general definition of the curve is given:

[0181] (twenty four)

[0182] S2.2 Analysis of the wheel-ground contact area boundary

[0183] (1) In step one, we discuss and analyze the surface forces of the elastic half-space. , The relationship between stress and deformation displacement during elastic deformation in the contact area under the combined action of forces is investigated. Theoretical analysis is conducted using elastic contact theory, assuming no stress or deformation displacement exists outside the elastic contact area. By setting boundary conditions for deformation, different combinations of boundary conditions lead to changes in the final stress-strain relationship. The mechanical model of tire-ground rolling deformation we are investigating involves adhesion and rolling states, and corresponding deformation displacement, strain, and force are selected accordingly. , combination;

[0184] In the tire-ground contact problem, the testing device used in this embodiment can measure the positive vertical load, stress-deformation displacement, and stress magnitude. To facilitate further theoretical analysis, both adhesion and sliding states are unified here. and Given as boundary conditions; in the study When considering the functional relationship with vertical load, let the expression for the vertical pressure distribution of the tire be:

[0185] (25)

[0186] Then we have:

[0187] (26)

[0188] (2) For the vertical load distribution function We introduce an nth-order polynomial function to represent it:

[0189] (27)

[0190] in The relative displacement has a magnitude of ;

[0191] From equation (23), it can be seen that the vertical load distribution is closely related to the constant n. Only by determining the value of n can the magnitude of the contact point pressure be obtained. Here, finite element analysis is performed to obtain the magnitude of n under different loads, and the relationship of the value of n can be known:

[0192]

[0193] The results were obtained through finite element analysis. The relational expression is:

[0194] (28)

[0195] Here we introduce the given boundary conditions and Substituting the expression into equation (23), we can obtain the vertical load within the elastic half-space. With deformation The functional relationship is:

[0196] (29);

[0197] S2.3 Establishing a wheel-ground elastic contact model

[0198] In the analysis of wheel-ground contact deformation stress, the tire is subjected to vertical pressure, which causes many parameter variables to change. In order to obtain the relationship between vertical pressure and deformation, other related variables need to be expressed by known quantities.

[0199] In the study of tangential and normal forces, the contact half-width between the tire and the ground was obtained through actual measurements based on previous laboratory experimental data.

[0200] (30)

[0201] Here For the equivalent elastic modulus, the following holds:

[0202]

[0203] but:

[0204] (31)

[0205] In this embodiment, the strain gauge used measures the circumferential strain. Here, we take a specific point to study the relationship between deformation and vertical load. When the strain gauge moves with the tire to its lowest point (i.e., the normal deformation reaches its maximum, the deformation is...), the strain is... this (At point 1), the circumferential deformation of the strain gauge at this point is the point where the strain gauge is located. The tangential deformation of the point will Substituting into equation (27) yields the relationship between vertical load and deformation.

[0206] That is, by studying the relationship between strain and force in the contact area between the tire and the ground, the relationship between tangential and normal strain and force was established. In order to further study the correlation between vertical load and strain, the point with the largest deformation when the tire rotates was selected as the reference point for the study. The equation relationship between the circumferential deformation of the strain gauge and the tangential deformation at that point was established, and the relationship between strain and vertical load at the characteristic point was obtained.

[0207] Step 3: Establish the vertical load on the tire With deformation The functional relationship between the tire and the ground is used to estimate the tire-ground force.

[0208] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for estimating wheel-ground force based on an elastic half-space contact model and in-tire monitoring, characterized in that: include Step 1: Perform force analysis on the elastic half-space. S1.1 When the tire is in rolling contact with the ground, a simplified tire-ground contact mechanics model is used; S1.2 Performs force analysis on the elastic half-space; S1.3 Perform normal force analysis on the elastic half-space; S1.4 Perform tangential force analysis on the elastic half-space; S1.5 Analyze the force conditions of the elastic half-space; Step 2: Introduce the empirical formula for tire-road displacement to establish a theoretical model of wheel-ground contact deformation and force. S2.1 Analyzes the deformation of the curved surface of an elastically contacting object; S2.2 Analysis of the wheel-ground contact area boundary; S2.3 Establish a wheel-ground elastic contact model; Step 3: Establish the vertical load on the tire With deformation The functional relationship between the tire and the ground is used to estimate the tire-ground force; Step S2.2, the process of analyzing the boundary of the wheel-ground contact area, includes... (1) Let the expression for the vertical pressure distribution of the tire be: （25） have: （26） For the vertical load distribution function Introducing an nth-order polynomial function: （27） in The relative displacement has a magnitude of , For vertical loads within an elastic half-space. Represents the contact surface Point and origin The distance; The vertical load distribution is closely related to the constant n. Only by determining the value of n can the magnitude of the contact point pressure be obtained. Here, finite element analysis is performed to obtain the magnitude of n under different loads, thus revealing the relationship between the values ​​of n: ； The results were obtained through finite element analysis. The relational expression is: （28） Obtain the vertical load within the elastic half-space With deformation The functional relationship is: （29）； The process of establishing the wheel-ground elastic contact model described in step S2.3 includes: set up （30） For the equivalent elastic modulus, the following holds: ； but: （31） Will Substituting into equation (27) yields the relationship between vertical load and deformation; in, This is the lateral deformation coefficient.

2. The wheel-ground force estimation method based on the elastic half-space contact model and in-tire monitoring according to claim 1, characterized in that: The process of performing force analysis on the elastic half-space body as described in step S1.2 includes: (1) When the tire and the ground are in contact, there is a contact band. When the contact band is subjected to load, the ground is regarded as an elastic half-space body for force analysis. A three-dimensional rectangular coordinate system is established, in which the x-axis is parallel to the tangent of the tire rotation, the y-axis is parallel to the long side of the contact band, and the z-axis is perpendicular to the contact band and points to the elastic half-space body. A two-dimensional rectangular coordinate system is established by taking a section perpendicular to the y-axis at the tire-ground rolling contact point. (2) First, stress calculation is performed on the stress points within the deformation region of the elastic half-space. The stress state of each stress point consists of six components, and the stress components are: The displacements occurring in each direction are The strain that occurs is: In an elastic half-space, the relationship between the stress and strain changes inside a tire when subjected to elastic deformation at a selected point in the xz plane is as follows: （1） When studying an elastic half-space subjected to an external vertical load, the elastic modulus of each part and point of the elastic half-space, as an isotropic body, is measured. Since it is a constant, the relationship between strain and stress can be derived: （2） in, The lateral deformation coefficient is... Shear modulus is defined as: （3） (3) Substituting into equation (2), we get: （4） (4) When analyzing the force at the point of application on the wheel-ground contact section, we have Constraints, given a stress function stress and Regarding the stress function given by the following formula: : （5） Let the stress function be... Satisfying the biconcordance equations: （6） Using cylindrical coordinates Solving for the elastic strain relationship, we give the relationship between stress components and deformation displacement in cylindrical coordinates; In stress function The relationship between strain and displacement is as follows: （7） The relationship between stress and function is as follows: （8）。 3. The wheel-ground force estimation method based on the elastic half-space contact model and in-tire monitoring according to claim 2, characterized in that: The process of performing normal force analysis on the elastic half-space body as described in step S1.3 includes: (1) Suppose that when the elastic half-space is subjected to a normal perpendicular pressure distributed along the y-axis, the perpendicular pressure is uniformly distributed according to the magnitude of P; the elastic half-space undergoes elastic deformation and generates stress components under the action of a tangential normal force, and the polar coordinate stress function is defined. Perform stress analysis: （9） In the stress function formula, A is an arbitrary constant; (2) Substituting the stress function formula (9) into the stress change formula of the stress function is shown below: （10） (3) Determine the effect on the For the radius located at Force on the positive axis semicircle ,when With normal force When they are equal in size, we have: （11） get: （12） (4) Given the transformation relationship between polar coordinates and rectangular coordinates, the stress... Converted into right-angle stress The stress components are obtained: （13） Having obtained the functional relationship of the stress components, we substitute this relationship into Hooke's law to calculate the strain and normal force. Relationship with deformation displacement: （14） Based on the relationship between deformation displacement and normal force in (14), we can obtain: （15） When studying the deformation of an elastic half-space under stress, considering the actual deformation of a tire in rolling contact with the ground, the elastic half-space does not sway left and right during a collision, thus obtaining... , ,get: （16） Take any point outside the contact surface area and determine the constant. Let the distance between the reference point and the contact deformation surface be... ,constant for: （17）。 4. The wheel-ground force estimation method based on the elastic half-space contact model and in-tire monitoring according to claim 3, characterized in that: The process of performing tangential force analysis on the elastic half-space body as described in step S1.4 includes: (1) When the elastic half-space is subjected to a tangential force distributed along the y-axis, assuming the tangential force is uniformly distributed and has a magnitude of Q, it acts on... Point; When an elastic half-space is subjected to a tangential force, stress components are generated in the contact deformation region of the half-space; the form of the stress expression is the same as that when a normal force is applied, that is: （18） (2) Within the region where the elastic half-space deforms, The range of values ​​is Transforming the stress relationship in polar coordinates into the stress relationship in rectangular coordinates, we get: （19） (3) When the elastic half-space does not undergo rigid rotation, and in If no vertical displacement occurs in the axial direction, then the deformation-displacement relationship is: （20）。 5. The wheel-ground force estimation method based on the elastic half-space contact model and in-tire monitoring according to claim 4, characterized in that: The process of analyzing the force state of the elastic half-space body described in step S1.5 includes... (1) Let Represents the contact surface Point and origin distance, The unit area representing the area of ​​an elastic half-space subjected to force is then... In terms of area, the forces acting on the elastic half-space are: forces acting in the normal direction on the contact surface of the elastic half-space, with magnitudes of , to the origin use After point replacement, there is ,Will Point due to its effect on Integrating the stress generated in the tangential direction at a unit area yields the stress on the deformation of the elastic half-space. Stress components generated by point action: （21） In equation (21), when analyzing the plane strain relationship equation of the elastic half-space, the functional relationship between stress components and surface forces was analyzed; (2) Using an analysis method similar to that of stress components, the deformation displacement of the elastic half-space body under the action of tangential and normal forces is obtained; （22） Regarding the left and right sides of equation (22) Perform differentiation to eliminate constants ,get: （23）。 6. The wheel-ground force estimation method based on the elastic half-space contact model and in-tire monitoring according to claim 5, characterized in that: Step S2.1, the process of analyzing the deformation of the surface of an elastically contacting object, includes... Analyzing the tire as an elastic cylinder, the contact surface lies on a continuous curve. The first and second derivatives at any point on this curve have geometric meaning within the contact region. Here is the general definition of the curve: （24）。

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