A method for estimating mechanical characteristics of a tire on a pothole road based on a simplified flexible ring model

Abstract

The application discloses a kind of pit road surface tire mechanics characteristic estimation method based on simplified flexible ring model, this method includes establishing meridian tire high fidelity finite element benchmark model, obtains the displacement data of wheel rim center point under the contact state of tire in pit road surface, while constructing two-dimensional flexible ring physical model reflecting the actual stress characteristics of tire;The dynamics equation of two-dimensional flexible ring physical model is reduced, the complex tire continuum deformation problem under the contact state of tire in pit road surface is converted into the vibration problem of finite low-order mode and is solved, obtains the vibration response coordinates of each order mode that can characterize the overall deformation law of tire;Utilize the displacement data of wheel rim center point and each order mode vibration response coordinates, combine modal orthogonal characteristics to carry out wheel rim center mapping, utilize the displacement change of wheel rim center point to obtain the longitudinal force and vertical force transient response of tire acting on wheel rim, realize the rapid estimation of tire mechanics characteristic under pit road surface.

Description

Technical Field

[0001] This invention belongs to the field of vehicle engineering technology, and in particular relates to a method for estimating the mechanical properties of tires on pothole roads based on a simplified flexible ring model. Background Technology

[0002] Tires are the key components that come into direct contact with the road surface, and their mechanical properties directly determine the vehicle's driving safety and handling stability. When a vehicle travels over unstructured road surfaces such as potholes, the tires experience severe radial compression, longitudinal slippage, and transient impact deformation.

[0003] Current mainstream tire mechanics estimation methods have significant shortcomings, as follows:

[0004] Steady-state empirical tire models such as the Dugoff model and the Magic Formula, in pursuit of computational speed, significantly simplify the tire envelope mechanism and are only applicable to smooth paved roads, making it difficult to accurately characterize the transient impact forces on tires under pothole conditions. Traditional rigid ring models have insufficient envelope adaptability, resulting in large calculation errors for short-wavelength pothole surfaces. While refined finite element simulation can faithfully reproduce large tire deformations and transient stress states, the large number of model meshes and high computation time limit restrict it to offline simulation, failing to meet the real-time computing power requirements of onboard controllers. Although conventional flexible ring theory offers excellent accuracy in road envelope calculation, the solution of complete flexible ring partial differential equations is complex and computationally expensive, making it difficult to apply to online real-time force estimation for intelligent chassis.

[0005] Therefore, there is an urgent need to develop a method for estimating the mechanical properties of tires on pothole roads that balances mechanical fidelity and real-time computational efficiency. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention proposes a method for estimating the tire mechanical properties of pothole roads based on a simplified flexible ring model.

[0007] The technical solution of the present invention is as follows:

[0008] A method for estimating tire mechanical properties on pothole surfaces based on a simplified flexible ring model includes:

[0009] A high-fidelity finite element benchmark model of a radial tire was established to obtain the displacement data of the rim center point of the tire under the contact state of the tire on the pitted road surface. At the same time, a two-dimensional flexible ring physical model reflecting the actual stress characteristics of the tire was constructed.

[0010] The dynamic equations of the two-dimensional flexible ring physical model are reduced in order, and the complex tire continuum deformation problem under the contact state of the tire with the road surface is transformed into a vibration problem with a finite number of low-order modes and solved to obtain the vibration response coordinates of each mode that can characterize the overall deformation law of the tire.

[0011] By utilizing the displacement data of the rim center point and the coordinates of the vibration response of each mode, combined with the orthogonality of the modes, the rim center is mapped, and the transient response of the longitudinal and vertical forces acting on the rim by the displacement change of the rim center point is obtained, so as to realize the rapid estimation of the mechanical properties of the tire under the road surface of potholes.

[0012] Furthermore, the specific method for establishing a high-fidelity finite element benchmark model of a radial tire includes:

[0013] A high-fidelity finite element model of a 205 / 55R16 radial tire was established using ABAQUS simulation software. The rubber matrix adopted a Neo-Hookean hyperelastic constitutive model, and its strain energy is shown below:

[0014] ;

[0015] In the formula, It is the initial shear modulus; It is the incompressible parameter of the material; These are strain tensor invariants;

[0016] An implicit-explicit sequential coupling solution strategy is adopted. First, the tire inflation and static vertical loading are pre-analyzed using an implicit solver. Then, the state import technique is used to map the results to explicit dynamic analysis, and transient impact simulation of the pothole road surface is performed to obtain the time history data of the rim center displacement field. Quasi-static load-displacement tests are conducted on a flatbed tire test bench, and the model accuracy is verified by comparing the results with the simulation results.

[0017] Furthermore, the specific method for constructing a two-dimensional flexible ring physical model that reflects the actual stress characteristics of a tire includes:

[0018] Establish a fixed rectangular coordinate system and a rotating coordinate system that rotates with the tire at the center point of the rim; decouple the tire's physical structure into an elastic ring with mass distribution, bending stiffness and circumferential pretension, and a radial and tangential distributed spring damping system representing inflation pressure and sidewall support force; establish a partial differential equation for the dynamics of the elastic ring containing Coriolis force terms and centrifugal stiffening effect terms.

[0019] Furthermore, the specific method for reducing the order of the dynamic equations of the two-dimensional flexible ring physical model includes:

[0020] The radial and tangential displacement fields of the flexible ring are spatially discretized using Fourier series, as shown in the following expressions:

[0021] ;

[0022] ;

[0023] In the formula, and For the generalized coordinates of the nth mode; These are higher-order modal quantities; Let any point on the ring and the rotating coordinate system X * The included angle of the axis;

[0024] and The corresponding included angles are respectively Tangential and radial deformation at time t;

[0025] Substituting into the dynamic equations and utilizing the modal orthogonality, we obtain the system of second-order differential equations satisfied by the coordinates of each mode, as shown below:

[0026] ;

[0027] By employing Galerkin projection transformation, the high-dimensional distribution parameters of the original physical space are discretized into an orthogonal modal subspace, thereby effectively mapping the above modal evolution equations into the following generalized coordinate matrix expression:

[0028] ;

[0029] , , , , , ;

[0030] In the formula, Modal mass; Modal damping; For gyroscopes; Modal stiffness; The coordinates are for the first mode. The coordinates are for the second mode. For the first generalized force; For the second generalized force;

[0031] Here is the modal mass matrix; This is a gyroscope matrix; Here is the modal damping matrix; y is the modal stiffness matrix; Q is the generalized modal force vector; y is the generalized modal coordinate vector;

[0032] This can then be transformed into a first-order state-space equation, expressed as follows:

[0033] ;

[0034] in, , , , ;

[0035] In the formula, This is the system state vector; The overall quality matrix of the system; For generalized gyroscope damping matrix; It is a generalized excitation vector;

[0036] By introducing the first-order matrix perturbation theory, and using the complex eigensol of the undamped gyroscope system as a benchmark, a damping correction term is added to solve for the vibration response coordinates of each mode.

[0037] Furthermore, the specific method for combining modal orthogonality characteristics to map the rim center and using the displacement change of the rim center point to obtain the transient response of the longitudinal and vertical forces acting on the rim by the tire includes:

[0038] The longitudinal and vertical forces at the tire center are determined by the circumferential integral resultant force of the sidewall spring damping system. Substituting the modal expansion into the resultant force integral equation, the higher-order modal contribution terms are eliminated based on the orthogonality of the circumferential trigonometric functions, leaving only the first-order mode. The transient envelope force of the tire is directly and linearly reconstructed from the first-order modal coordinates.

[0039] Furthermore, the specific method for combining modal orthogonality characteristics to map the rim center and using the displacement change of the rim center point to obtain the transient response of the longitudinal and vertical forces acting on the rim by the tire includes:

[0040] Based on force equilibrium, establish the definite integral resultant force equation of the sidewall spring-damped system on the circumference:

[0041] ;

[0042] ;

[0043] Substituting the modal expansion, all non-first-order high-frequency modes are filtered out by the orthogonality of trigonometric functions, directly obtaining the analytical expression of the wheel center force dominated by the first-order radial and tangential modal coordinates, thus completing the reduced-order mechanical mapping:

[0044] ;

[0045] ;

[0046] In the formula, This refers to the longitudinal force of the tire; This represents the longitudinal displacement of the wheel center; For b n First-order modal coordinates; The mass is converted to the neutral point of the rim; This represents the vertical displacement of the wheel center; The vertical force on the tire; For a n First-order modal coordinates;

[0047] A tire mechanical property estimation system for pothole road surfaces based on a simplified flexible ring model is provided for performing the tire mechanical property estimation method for pothole road surfaces based on a simplified flexible ring model as described in any of the preceding claims, including a modeling module, a reduced-order solution module, and a mapping estimation module.

[0048] The modeling module is used to establish a high-fidelity finite element benchmark model of a radial tire, obtain the displacement data of the rim center point of the tire in contact with a pothole road surface, and construct a two-dimensional flexible ring physical model that reflects the actual stress characteristics of the tire.

[0049] The order reduction solution module is used to reduce the order of the dynamic equations of the two-dimensional flexible ring physical model, transforming the complex tire continuum deformation problem under the contact state of the tire with the road surface into a vibration problem of a finite number of low-order modes and solving it to obtain the vibration response coordinates of each mode that can characterize the overall deformation law of the tire.

[0050] The mapping estimation module is used to perform rim center mapping by using the displacement data of the rim center point and the vibration response coordinates of each mode, combined with the orthogonality of the modes. It uses the displacement change of the rim center point to obtain the transient response of the longitudinal and vertical forces acting on the rim by the tire, so as to realize the rapid estimation of the tire mechanical properties under the road surface of potholes.

[0051] An electronic device includes a memory and a processor, the memory storing a computer program, the processor being configured to invoke and run the computer program stored in the memory to perform the method as described in any of the preceding methods.

[0052] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of any of the methods described above.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] This invention employs an implicit-explicit sequential coupling technique to establish a finite element reference model for radial tires. This technique solves the existing problems of numerous interferences in real vehicle testing environments, difficulty in accurately controlling test variables, and difficulty in obtaining true stress values. It can eliminate external noise interference, accurately apply key parameters such as load and indentation angle, and obtain high-precision, noise-free rim center displacement and tire stress reference data.

[0055] This invention constructs a two-dimensional flexible ring physical model, decoupling the tire into an elastic ring with mass distribution, bending stiffness, and circumferential pretension, as well as a radial and tangential distributed spring system representing inflation pressure and sidewall support force. This solves the problems of traditional steady-state tire models neglecting tire envelope and rigid ring models having insufficient short-wave road envelope accuracy, and can accurately describe the transient impact response characteristics of the tire under dent conditions.

[0056] This invention performs Fourier series modal expansion on the dynamic partial differential equations of flexible rings, and transforms them into finite-dimensional ordinary differential state-space equations by combining modal orthogonality for order reduction solution. This solves the problems of complex solution and high computational cost of complete flexible ring partial differential equation sets, significantly reduces the amount of computation, and realizes rapid solution of tire mechanical properties.

[0057] This invention utilizes the orthogonality of circumferential trigonometric functions to map the integrals of each mode back to the rim center, retaining only the first-order mode that contributes to the macroscopic resultant force at the rim center. This solves the problem of traditional methods relying on the integral of local tire deformation to calculate the resultant force, which is cumbersome and time-consuming. It directly reduces the complex in-plane distortion to the macroscopic mechanical parameters of the rim center point, completely breaking through the technical bottleneck that makes it impossible to achieve both mechanism fidelity and computational time.

[0058] This invention verifies the algorithm's performance through cross-simulation of multiple extreme working conditions, solving the problem of large estimation errors in existing algorithms under unstructured road conditions. It achieves an accuracy of over 92.3% in capturing extreme values ​​of longitudinal and vertical transient impacts generated at the edge of potholes, meeting the real-time high-frequency perception requirements of intelligent chassis domain controllers for complex road conditions. Attached Figure Description

[0059] Figure 1 Modeling process for tire finite element model;

[0060] Figure 2 This is a test bench for vertical stiffness.

[0061] Figure 3 Establish the tire coordinate system;

[0062] Figure 4 It is a two-dimensional flexible ring model structure;

[0063] Figure 5 A schematic diagram of the tire and the dent structure;

[0064] Figure 6 The longitudinal force of the tire under variable angular velocity;

[0065] Figure 7 The vertical force on the tire under varying angular velocity;

[0066] Figure 8 The longitudinal force of the tire under the sidewall of the dent;

[0067] Figure 9 The vertical force on the tire under the sidewall of the dent;

[0068] Figure 10 The longitudinal force of the tire under varying friction coefficients;

[0069] Figure 11 This represents the vertical force of the tire under varying friction coefficients. Detailed Implementation

[0070] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0071] Example 1:

[0072] The present invention provides a method for estimating tire mechanical properties on pothole surfaces based on a simplified flexible ring model, comprising:

[0073] A high-fidelity finite element benchmark model of a radial tire is established using an implicit-explicit sequential coupling analysis method. The displacement data of the rim center point of the tire under the contact state of the tire on the road surface with potholes is obtained. The displacement data of the rim center point includes at least the tire center point displacement and the true value data of transient impact. At the same time, a two-dimensional flexible ring physical model reflecting the actual force characteristics of the tire is constructed. The physical structure of the tire is decoupled into an elastic ring with mass distribution, bending stiffness and circumferential pretension, as well as a radial and tangential distributed spring system representing the inflation pressure and the sidewall support force.

[0074] The dynamic equations of the two-dimensional flexible ring physical model are reduced in order, and the complex tire continuum deformation problem under the contact state of the tire with the road surface is transformed into a vibration problem with a finite number of low-order modes and solved to obtain the vibration response coordinates of each mode that can characterize the overall deformation law of the tire.

[0075] By utilizing the displacement data of the rim center point and the vibration response coordinates of each mode, and combining the orthogonality of the modes, the rim center is mapped. The transient response of the longitudinal and vertical forces acting on the rim by the tire is obtained by utilizing the displacement change of the rim center point, so as to realize the rapid estimation of the tire mechanical properties under pothole road surface.

[0076] Example 2:

[0077] This embodiment, based on Embodiment 1, further designs the following: The specific method for establishing a high-fidelity finite element reference model of a radial tire in this example includes:

[0078] A high-fidelity finite element model of a 205 / 55R16 radial tire was established using ABAQUS simulation software. The rubber matrix adopted a Neo-Hookean hyperelastic constitutive model, and its strain energy is shown below:

[0079] ;

[0080] In the formula, It is the initial shear modulus; It is the incompressible parameter of the material; These are strain tensor invariants, upon which the elastic strain potential energy function of this model is based; when the material is assumed to be incompressible... That is, the second term is 0; For strain energy, It is a volume ratio;

[0081] Specifically, a static vertical stiffness test bench was used to apply a load of 4000 N with a tire pressure of 0.25 MPa. Stiffness parameters were obtained to verify the accuracy of the finite element static characteristics.

[0082] An implicit-explicit sequential coupling solution strategy is adopted. First, an implicit solver is used for pre-analysis of tire inflation and static vertical loading to obtain the initial steady-state stress field. Then, using state import technology, the stress-displacement field is mapped as initial conditions to the explicit solver for explicit dynamic analysis, performing transient impact simulation of the pothole pavement. Specifically, an analytical rigid body is used to describe the geometric contour of the pothole for transient impact calculation, providing a reliable numerical benchmark for subsequent order-reduced models. The modeling process is as follows: Figure 1 As shown, the time history data of the rim center displacement field were obtained; a quasi-static load-displacement test was conducted on a flatbed tire test bench, and the model accuracy was verified by comparing the results with simulation results. In the explicit dynamic analysis, a two-dimensional indentation was defined analytically by rigid body definition and stretched along the axial direction to generate a three-dimensional surface. The initial tire velocity was controlled, with the initial longitudinal velocity set to 0. By controlling the angular velocity, for example, 27.7 rad / s, the starting and getting out of trouble was simulated. Compared with the actual vehicle test, this finite element method eliminates the interference of external environmental noise and achieves more precise variable control.

[0083] Specifically, it can be accessed through Figure 2 The displacement control system of the flatbed tire testing bench adjusts the initial vertical position of the tire and applies different loads to the tire in a quasi-static manner to obtain the tire's vertical displacement. and tire vertical force Simultaneously, a simulation experiment was conducted in ABAQUS under the same working conditions to extract the load-displacement response data of the simulation model. The two data were then compared to verify the accuracy of the tire finite element model. Specifically, Figure 2The specific structure and hardware composition of the vertical stiffness test bench used to verify the accuracy of the finite element model are shown. The entire test bench equipment mainly consists of two parts: a sensor system responsible for data acquisition and a signal receiving system responsible for data processing and monitoring. The mechanical assembly structure and the installation positions of each component can be clearly observed from the front view, flip view of the bench base, and rear view of the test bench shown in the figure. During the test operation, the system uses a high-precision laser displacement sensor to accurately measure the vertical displacement deformation of the tire, uses an attitude angle sensor to obtain accurate rim attitude information in real time, and relies on a multi-dimensional force sensor to simultaneously measure the road reaction force and the force state at the center of the rim during the test. The various raw physical signals collected by the sensor system are transmitted and processed at high speed through a dedicated Ethernet force measurement module. The relevant mechanical and displacement values ​​are presented in real time and intuitively on a digital display. Finally, all test monitoring data are completely summarized and transmitted to the host computer for subsequent data storage and comparative verification analysis with simulation results.

[0084] Example 3:

[0085] This embodiment, based on Embodiment 2, further incorporates the following method for constructing a two-dimensional flexible ring physical model that reflects the actual force characteristics of the tire:

[0086] Establish a fixed rectangular coordinate system and a rotating coordinate system that rotates with the tire at the center point of the rim, such as... Figure 3 As shown, a rectangular coordinate system is established at the center point of the rim, with the longitudinal displacement direction set as the X-axis and the vertical displacement set as the Z-axis. To simulate the rotational characteristics of the tire, in addition to the rectangular coordinate system, a rotating coordinate system X is also needed. * OZ * ,like Figure 3 As shown. The angle between any point on the ring and the X-axis is φ, and the angle between the X-axis and the X-axis is... * The angle between the axes is θ. The difference in angle between them is Ωt, where Ω is the rotational velocity of the ring. This point lies in both the fixed coordinate system XOZ and the rotating coordinate system X. * OZ * The coordinates on the upper part are (x, z) and (x, z) respectively. * ,z * ); x * and z * These represent the longitudinal and vertical spatial displacements under coordinate transformation; the tire's physical structure is decoupled into an elastic ring with mass distribution, bending stiffness, and circumferential pretension, and a radially and tangentially distributed spring-damped system representing inflation pressure and sidewall support force; a partial differential equation for the dynamics of the elastic ring, explicitly containing Coriolis force terms (gyroscopic terms) and centrifugal stiffening effect terms, is established. Specifically, as follows... Figure 4As shown, based on the inextensibility assumption, a coupled partial differential dynamic equation for the radial and tangential displacements at any point on the elastic ring of the belt layer is established. The equation explicitly includes the Coriolis force (gyroscopic term) generated by the tire rotation and the centrifugal stiffening effect term, as expressed below:

[0087] ;

[0088] ;

[0089] In the formula, Young's modulus; Let be the moment of inertia of the cross section; The average radius of the sidewall; Radial deformation, representing the deformation amount; Let any point on the ring and the rotating coordinate system X * The included angle of the axis; For vertical deformation, it represents the deformation amount; This represents the initial circumferential stress of the tire; The cross-sectional area; Radial stiffness; The rotational speed of the ring; This refers to the radial external force acting on the ring; Tangential stiffness; Initial tire pressure; The width of the ring; The tangential external force acting on the ring;

[0090] Example 4:

[0091] This embodiment, based on Embodiment 3, further incorporates the following method for reducing the order of the dynamic equations of the two-dimensional flexible ring physical model:

[0092] The radial and tangential displacement fields of the flexible ring are spatially discretized using Fourier series, as shown in the following expressions:

[0093] ;

[0094] ;

[0095] In the formula, and For the generalized coordinates of the nth mode; These are higher-order modal quantities; Let any point on the ring and the rotating coordinate system X * The included angle of the axis;

[0096] and The corresponding included angles are respectively Tangential and radial deformation at time t;

[0097] By eliminating the spatial dimension using the Galerkin method, substituting it into the dynamic equations, and utilizing modal orthogonality, we obtain the system of second-order differential equations satisfied by the coordinates of each mode, as shown below:

[0098] ;

[0099] By employing Galerkin projection transformation, the high-dimensional distribution parameters of the original physical space are discretized into an orthogonal modal subspace, thereby effectively mapping the above modal evolution equations into the following generalized coordinate matrix expression:

[0100] ;

[0101] , , , , , ;

[0102] In the formula, Modal mass; Modal damping; For gyroscopes; Modal stiffness; The coordinates are for the first mode. The coordinates are for the second mode. For the first generalized force; For the second generalized force; a parameter with one dot indicates the first derivative, and two dots indicate the second derivative.

[0103] Here is the modal mass matrix; This is a gyroscope matrix; Here is the modal damping matrix; y is the modal stiffness matrix; Q is the generalized modal force vector; y is the generalized modal coordinate vector;

[0104] This can then be transformed into a first-order state-space equation, expressed as follows:

[0105] ;

[0106] in, , , , ;

[0107] In the formula, This is the system state vector; The system's overall quality matrix is ​​a block matrix formed by diagonalizing the original system's modal quality matrix and modal stiffness matrix. This is the generalized gyro damping matrix, which integrates the modal damping effect of the tire system, the gyroscopic effect (Coriolis force) generated by tire rotation, and the modal stiffness characteristics. It is a generalized excitation vector, reconstructed from the generalized modal forces acting on the tire from the outside.

[0108] Given the relatively small damping of tire rubber, a first-order matrix perturbation theory is introduced. Based on the complex eigenvalue of the undamped gyroscope system, a damping correction term is added to solve for the vibration response coordinates of each mode.

[0109] Example 5:

[0110] This embodiment, based on Embodiment 4, further designs the following: In this example, by combining modal orthogonality characteristics to perform rim center mapping, the specific method for obtaining the transient response of the longitudinal and vertical forces acting on the rim by utilizing the displacement change of the rim center point includes:

[0111] The longitudinal and vertical forces at the tire center are determined by the circumferential integral resultant force of the sidewall spring damping system. Substituting the modal expansion into the resultant force integral equation, and based on the orthogonality of the circumferential trigonometric functions, higher-order modal contribution terms that do not directly contribute to the macroscopic resultant force at the tire center are eliminated, leaving only the first-order mode. The transient envelope force of the tire can be directly and linearly reconstructed from the first-order modal coordinates without relying on local tire deformation. The transient response of the longitudinal and vertical forces can be obtained solely through the displacement change of the rim center point.

[0112] Example 6:

[0113] This embodiment, based on Embodiment 5, further incorporates a method for mapping the rim center using modal orthogonality characteristics. The specific method for obtaining the transient response of the longitudinal and vertical forces acting on the rim by utilizing the displacement change of the rim center point includes:

[0114] Based on force equilibrium, establish the definite integral resultant force equation of the sidewall spring-damped system on the circumference:

[0115] ;

[0116] ;

[0117] Substituting the modal expansion, all non-first-order high-frequency modes are filtered out by the orthogonality of trigonometric functions, directly obtaining the analytical expression of the wheel center force dominated by the first-order radial and tangential modal coordinates, thus completing the reduced-order mechanical mapping:

[0118] ;

[0119] ;

[0120] In the formula, This refers to the longitudinal force of the tire; This represents the longitudinal displacement of the wheel center under coordinate transformation; For b n First-order modal coordinates; The mass converted to the neutral point of the rim is derived from the initial static vertical load of a single wheel; This represents the vertical displacement of the wheel center under coordinate transformation; The vertical force on the tire; For a n First-order modal coordinates;

[0121] ABAQUS software is used as the truth output to achieve stable variable control, thereby obtaining a more accurate and reliable wheel center trajectory. Simultaneously, based on the analytical reaction forces on the rigid land surface, the longitudinal and vertical forces on the tire are derived. A schematic diagram of the overall structure is shown below. Figure 5 As shown.

[0122] To further verify the robustness and generalization ability of the rapid guidance method for tire transient contact force based on the hub center bearing field input proposed in this invention, this example also conducts cross-simulation and accuracy verification of tire transient impact response under different extreme operating conditions and complex tire conditions.

[0123] The baseline condition is defined as follows: a tire rolls at a constant angular velocity Ω = 27.7 rad / s through a trapezoidal pit with a depth h = 100 mm and a horizontal projection length L = 100 mm for the sidewalls. The road surface friction coefficient is f = 0.8 to simulate the adhesion conditions of a dry asphalt road surface. By controlling the wheel angular velocity, pit sidewall inclination angle, and road surface friction coefficient, the longitudinal and vertical forces of the tire under different conditions are estimated. The calculated values ​​are compared with the simulation values ​​in ABAQUS. Figures 6-11 As shown.

[0124] Figure 6 and Figure 7 These figures illustrate the conditions under a baseline trapezoidal pothole (depth). Horizontal projection length of sidewall coefficient of friction The wheels move at different constant angular velocities ( , and When the tire rolls over a pothole, the longitudinal force at the center of the tire rim... With vertical force The algorithmic calculations and finite element simulations of the time-evolution curves are compared. This test case aims to verify the accuracy of the method of the present invention in capturing the contact force oscillation characteristics when faced with centrifugal stiffening effects and Coriolis forces (gyroscopic effects) of different intensities.

[0125] The results analysis shows that: with the wheel angular velocity As the speed increases (corresponding to increased vehicle speed), the transient impact peak values ​​of both longitudinal and vertical forces generated by the tire impacting the edge of the dent show a significant amplification trend, and the high-frequency oscillation characteristics after the impact become more intense. The fundamental reason for this mechanical phenomenon is that the centrifugal stiffening effect of the elastic belt layer ring and the Coriolis force (gyroscopic effect) caused by rotation are significantly enhanced at high speeds, leading to a nonlinear evolution of the dynamic stiffness of the continuous system. The comparison curves clearly show that, under the three conditions of low speed, medium speed, and high speed with strong dynamic differences, the transient response curves calculated by the algorithm of this invention and the true value curves of the ABAQUS finite element simulation maintain a very high degree of overlap in the impact front response, extreme point capture, and the damped oscillation phase after escaping the dent. This strongly demonstrates that when performing modal order reduction processing on the dynamic equations, this invention can accurately preserve and calculate the centrifugal stiffening and gyroscopic terms in the explicit wheel center displacement term.

[0126] Figure 8 and Figure 9 They respectively demonstrated at a constant speed ( ) and standard attachment conditions ( When the geometric features of a dent change abruptly, the longitudinal force of the tire... With vertical force The transient evolution process was simulated. The horizontal projection length L of the pit sidewall was controlled at 50mm, 100mm, and 150mm to simulate transient pavement excitation under three different slopes: steep, standard, and gentle. This test case modified the pavement pit geometry parameters defined by the analytical rigid body to verify the consistency of the model's dynamic response to different spatial excitation frequencies and transient large earthquake step inputs.

[0127] The results analysis shows that the horizontal projected length L of the sidewall has a decisive influence on the transient large deformation impact experienced by the tire. When At the moment of contact (representing an extremely steep sidewall of the pit), due to the large geometric jump, the tire experiences severe radial and longitudinal step disturbances at the contact edge, resulting in extremely high transient peaks in both vertical and longitudinal forces, and the nonlinear reaction force of the spring damping in the contact area reaches its maximum value. However, as L increases to 150mm (the sidewall slope becomes gentler), the spatial excitation frequency decreases, the impact process on the tire becomes smoother, and the peak of the mechanical response curve shifts significantly backward with a decrease in amplitude. Even under these extreme conditions of severe short-circuiting and step input in the effective contact imprint area caused by large-scale non-indentation deformation, the algorithm of this invention still exhibits excellent tracking performance. It not only in… The model has extremely high accuracy in capturing the extreme values ​​of impacts under steep impacts, and can accurately reconstruct the response characteristics under different spatial excitation frequencies, highlighting the strong generalization robustness of the model to spatial geometric changes of unstructured road surfaces.

[0128] Figure 10 andFigure 11 The following are examples of the same trapezoidal pit geometry and rolling angular velocity. Under extreme changes in road surface adhesion conditions, the longitudinal force of the tire... With vertical force The analytical estimates and simulation values ​​were compared. The friction coefficient f was set to 0.3 (simulating low-adhesion road surfaces such as wet / icy surfaces), 0.5 (simulating medium-adhesion road surfaces such as wet asphalt in rainy weather), and 0.8 (simulating high-adhesion road surfaces such as dry asphalt).

[0129] The results analysis shows that the change in the road surface friction coefficient f mainly affects the tire longitudinal force. ( Figure 10 The amplitude limit of ) has a significant impact on the local adhesion-slip evolution characteristics. Under these conditions, sufficient traction allows the tire to generate significant spatial friction and shear forces during impacts and traction recovery, resulting in a wide curve fluctuation range accompanied by high-frequency micro-oscillations; however, when the coefficient of friction degrades to At this time, the longitudinal force is significantly subjected to severe shearing due to the physical limits of local adhesion, resulting in a sharp drop in the peak longitudinal force and a smoothing waveform due to overall slippage. In contrast, the vertical force ( Figure 11 The global macroscopic trend of friction is relatively less affected by the friction coefficient, mainly manifested as the local load redistribution phenomenon during contact transients. The fast solver constructed in this invention, through accurate linear reconstruction of first-order modal coordinates, can calculate the friction distortion caused by nonlinearity of road surface adhesion with high accuracy under various friction coefficients.

[0130] In summary, Figures 6-11 The results of cross-simulation and multi-condition comparison fully demonstrate that the tire force acquisition method for complex road surfaces proposed in this invention, based on flexible ring theory and modal order reduction, completely breaks through the technical bottleneck of the trade-off between mechanism fidelity and computational time. While ensuring millisecond-level computational efficiency to meet the real-time perception requirements of intelligent chassis domain controllers, it accurately captures the extreme values ​​of longitudinal and vertical transient impacts under complex unstructured impacts, and has extremely high engineering practical value.

[0131] Example 7:

[0132] The present invention provides a tire mechanical property estimation system for pothole road surfaces based on a simplified flexible ring model, which is used to execute the tire mechanical property estimation method for pothole road surfaces based on the simplified flexible ring model of the present invention, including a modeling module, a reduced-order solution module, and a mapping estimation module.

[0133] The modeling module is used to establish a high-fidelity finite element benchmark model of a radial tire, obtain the displacement data of the rim center point of the tire in contact with a pothole road surface, and construct a two-dimensional flexible ring physical model that reflects the actual stress characteristics of the tire.

[0134] The order reduction solution module is used to reduce the order of the dynamic equations of the two-dimensional flexible ring physical model, transforming the complex tire continuum deformation problem under the contact state of the tire with the road surface into a vibration problem of a finite number of low-order modes and solving it to obtain the vibration response coordinates of each mode that can characterize the overall deformation law of the tire.

[0135] The mapping estimation module is used to perform rim center mapping by using the displacement data of the rim center point and the vibration response coordinates of each mode, combined with the orthogonality of the modes. It uses the displacement change of the rim center point to obtain the transient response of the longitudinal and vertical forces acting on the rim by the tire, so as to realize the rapid estimation of the tire mechanical properties under the road surface of potholes.

[0136] Example 8:

[0137] An electronic device includes a memory and a processor. The memory stores a computer program, and the processor is used to invoke and run the computer program stored in the memory to perform the methods of any of the above embodiments.

[0138] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of any of the above embodiments.

[0139] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for estimating tire mechanical properties on pothole surfaces based on a simplified flexible ring model, characterized in that, include: A high-fidelity finite element benchmark model of a radial tire was established to obtain the displacement data of the rim center point of the tire under the contact state of the tire on the pitted road surface. At the same time, a two-dimensional flexible ring physical model reflecting the actual stress characteristics of the tire was constructed. The dynamic equations of the two-dimensional flexible ring physical model are reduced in order, and the complex tire continuum deformation problem under the contact state of the tire with the road surface is transformed into a vibration problem with a finite number of low-order modes and solved to obtain the vibration response coordinates of each mode that can characterize the overall deformation law of the tire. By utilizing the displacement data of the rim center point and the coordinates of the vibration response of each mode, combined with the orthogonality of the modes, the rim center is mapped, and the transient response of the longitudinal and vertical forces acting on the rim by the displacement change of the rim center point is obtained, so as to realize the rapid estimation of the mechanical properties of the tire under the road surface of potholes.

2. The method for estimating tire mechanical properties of pothole roads based on a simplified flexible ring model according to claim 1, characterized in that, The specific methods for establishing a high-fidelity finite element baseline model of a radial tire include: A high-fidelity finite element model of a 205 / 55R16 radial tire was established using ABAQUS simulation software. The rubber matrix adopted a Neo-Hookean hyperelastic constitutive model, and its strain energy is shown below: ； In the formula, It is the initial shear modulus; It is the incompressible parameter of the material; These are strain tensor invariants; An implicit-explicit sequential coupling solution strategy is adopted. First, the tire inflation and static vertical loading are pre-analyzed using an implicit solver. Then, the state import technique is used to map the results to explicit dynamic analysis, and transient impact simulation of the pothole road surface is performed to obtain the time history data of the rim center displacement field. Quasi-static load-displacement tests are conducted on a flatbed tire test bench, and the model accuracy is verified by comparing the results with the simulation results.

3. The method for estimating tire mechanical properties of pothole roads based on a simplified flexible ring model according to claim 2, characterized in that, The specific method for constructing a two-dimensional flexible ring physical model that reflects the actual stress characteristics of a tire includes: Establish a fixed rectangular coordinate system and a rotating coordinate system that rotates with the tire at the center point of the rim; decouple the tire's physical structure into an elastic ring with mass distribution, bending stiffness and circumferential pretension, and a radial and tangential distributed spring damping system representing inflation pressure and sidewall support force; establish a partial differential equation for the dynamics of the elastic ring containing Coriolis force terms and centrifugal stiffening effect terms.

4. The method for estimating tire mechanical properties of pothole roads based on a simplified flexible ring model according to claim 3, characterized in that, The specific method for reducing the order of the dynamic equations of the two-dimensional flexible ring physical model includes: The radial and tangential displacement fields of the flexible ring are spatially discretized using Fourier series, as shown in the following expressions: ； ； In the formula, and For the generalized coordinates of the nth mode; These are higher-order modal quantities; Let any point on the ring and the rotating coordinate system X * The included angle of the axis; and The corresponding included angles are respectively Tangential and radial deformation at time t; Substituting into the dynamic equations and utilizing the modal orthogonality, we obtain the system of second-order differential equations satisfied by the coordinates of each mode, as shown below: ； By employing Galerkin projection transformation, the high-dimensional distribution parameters of the original physical space are discretized into an orthogonal modal subspace, thereby effectively mapping the above modal evolution equations into the following generalized coordinate matrix expression: ； ， ， ， ， ， ； In the formula, Modal mass; Modal damping; For gyroscopes; Modal stiffness; The coordinates are for the first mode. The coordinates are for the second mode. For the first generalized force; For the second generalized force; Here is the modal mass matrix; This is a gyroscope matrix; Here is the modal damping matrix; y is the modal stiffness matrix; Q is the generalized modal force vector; y is the generalized modal coordinate vector; This can then be transformed into a first-order state-space equation, expressed as follows: ； in, , , , ; In the formula, This is the system state vector; The overall quality matrix of the system; For generalized gyroscope damping matrix; For generalized excitation vectors; By introducing the first-order matrix perturbation theory, and using the complex eigensol of the undamped gyroscope system as a benchmark, a damping correction term is added to solve for the vibration response coordinates of each mode.

5. The method for estimating tire mechanical properties of pothole roads based on a simplified flexible ring model according to claim 4, characterized in that, The specific method for mapping the rim center using modal orthogonality characteristics and obtaining the transient response of the longitudinal and vertical forces acting on the rim by the tire through the displacement change of the rim center point includes: The longitudinal and vertical forces at the tire center are determined by the resultant force of the circumferential integral of the sidewall spring damping system. Substituting the modal expansion into the resultant force integral equation, the higher-order modal contribution terms are eliminated based on the orthogonality of the circumferential trigonometric functions, leaving only the first-order mode. The transient envelope force of the tire is directly and linearly reconstructed from the first-order modal coordinates.

6. The method for estimating tire mechanical properties of pothole roads based on a simplified flexible ring model according to claim 5, characterized in that, The specific method for mapping the rim center using modal orthogonality characteristics and obtaining the transient response of the longitudinal and vertical forces acting on the rim by the tire through the displacement change of the rim center point includes: Based on the principle of force equilibrium, establish the definite integral resultant force equation of the sidewall spring-damped system on the circumference: ； ； Substituting the modal expansion, all non-first-order high-frequency modes are filtered out by the orthogonality of trigonometric functions, directly obtaining the analytical expression of the wheel center force dominated by the first-order radial and tangential modal coordinates, thus completing the reduced-order mechanical mapping: ； ； In the formula, This refers to the longitudinal force of the tire; This represents the longitudinal displacement of the wheel center; For b n First-order modal coordinates; The mass is converted to the neutral point of the rim; This represents the vertical displacement of the wheel center; This refers to the vertical force on the tire. For a n The first-order modal coordinates.

7. A tire mechanical property estimation system for pothole roads based on a simplified flexible ring model, used to execute the tire mechanical property estimation method for pothole roads based on a simplified flexible ring model as described in any one of claims 1 to 6, characterized in that, It includes a modeling module, a reduction-order solution module, and a mapping estimation module; The modeling module is used to establish a high-fidelity finite element benchmark model of a radial tire, obtain the displacement data of the rim center point of the tire in contact with a pothole road surface, and construct a two-dimensional flexible ring physical model that reflects the actual stress characteristics of the tire. The order reduction solution module is used to reduce the order of the dynamic equations of the two-dimensional flexible ring physical model, transforming the complex tire continuum deformation problem under the contact state of the tire with the road surface into a vibration problem of a finite number of low-order modes and solving it to obtain the vibration response coordinates of each mode that can characterize the overall deformation law of the tire. The mapping estimation module is used to perform rim center mapping by using the displacement data of the rim center point and the vibration response coordinates of each mode, combined with the orthogonality of the modes. It uses the displacement change of the rim center point to obtain the transient response of the longitudinal and vertical forces acting on the rim by the tire, so as to realize the rapid estimation of the tire mechanical properties under the road surface of potholes.

8. An electronic device, characterized in that, The electronic device includes a memory and a processor, the memory storing a computer program, and the processor being used to call and run the computer program stored in the memory to perform the method as described in any one of claims 1 to 6.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 6.

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