Tire failure judgment method based on grounding marks

Abstract

The invention discloses a tire failure judgment method based on grounding marks, and relates to the technical field of tire failure judgment. Comprising the steps that a grounding mark of a to-be-detected tire is obtained, and the grounding mark comprises a grounding shape and grounding pressure distribution; projecting the grounding imprint into a rectangular plane coordinate system, and describing the grounding shape by adopting a binary bifingering function to obtain a grounding imprint mathematical model; performing numerical solution on the grounding mark mathematical model through Euler integral, and taking the grounding pressure distribution as a weight factor in the numerical solution process to obtain an equivalent inertia moment failure coefficient; constructing a tire instability critical criterion by adopting a pressure bar stability theory to obtain a critical failure load; and comparing the actual load of the to-be-tested tire with the critical failure load to obtain a failure judgment result of the to-be-tested tire. According to the method, the non-uniformity of pressure distribution can be quantified into key parameters influencing the structural stability, so that the tire failure analysis is upgraded from static geometric description to dynamic bearing evaluation.

Description

Technical Field

[0001] This invention relates to the field of tire failure assessment technology, and in particular to a tire failure assessment method based on ground contact marks. Background Technology

[0002] Tires are the only point of contact with the ground for aircraft and automobiles, and tire failure is crucial to their safety. The contact patch between the tire and the ground is a key factor in tire design, significantly impacting vehicle handling stability, driving safety, and tire performance optimization. Currently, most tire structural engineers rely solely on the shape of the contact patch to judge the quality of the structural design. In practical applications, in addition to the shape of the contact patch, the distribution of ground pressure is also a very important influencing factor, and the coupling effect of the two is a key factor determining tire failure.

[0003] In the prior art, for example, there is a method for describing the tire contact patch shape using a binary biexponential function, as described in application number CN202211658047.8. First, the contact patch pattern is expressed using a binary biexponential function. Second, the major axis length, minor axis length, and area of ​​the closed region enclosed by the binary biexponential function curve are extracted. Finally, the extracted parameters are calculated as follows: a) the ratio of the minor axis to the major axis, i.e., the rectangularity coefficient of the tire contact patch; b) the ratio of the area of ​​the closed region enclosed by the binary biexponential function to the area of ​​the rectangle with sides equal to the major and minor axes, i.e., the rectangularity ratio of the tire.

[0004] This existing technology expresses the shape of the ground contact mark using a binary double exponential function, and can obtain the variation of geometric parameters such as the ground contact shape with the structural design scheme, resulting in shape description parameters. Although the shape description parameters are indirectly related to tire performance, they cannot consider the variation of ground contact pressure distribution with the structural design scheme, thus making this existing technology unable to effectively predict tire failure. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a method to solve the technical challenge of incorporating the coupling effect of ground contact shape and ground pressure distribution into tire failure assessment. This method introduces ground pressure distribution as a weighting factor into the calculation of the cross-sectional moment of inertia (usually referring to the area moment of inertia about its geometric center or pressure center) of the tire ground contact mark, and constructs the critical failure load of the tire based on the compression bar stability theory. Furthermore, the frictional force of the tire during starting or braking is compared with the critical failure load as the actual load to determine whether the tire has failed.

[0006] This invention provides a tire failure determination method based on grounding marks, comprising: Obtain the ground contact mark of the tire under test. The ground contact mark includes: the ground contact shape when the tire contacts the ground and the ground pressure distribution that reflects the stress distribution characteristics when the tire contacts the ground. The ground contact mark of the tire under test is projected onto a Cartesian coordinate system, and the ground contact shape is described by a binary double-finite function to obtain a mathematical model of the ground contact mark. The mathematical model of the ground contact mark is used to describe the deformation characteristics of the ground contact shape of the tire under different loads and different tire pressures. The mathematical model of the grounding imprint is numerically solved by Euler integral, and the grounding pressure distribution is used as a weighting factor in the numerical solution process. The weighting coefficient is introduced into the calculation of the cross-sectional moment of inertia of the tire grounding imprint to obtain the equivalent moment of inertia failure coefficient. A critical criterion for tire instability based on the equivalent moment of inertia failure coefficient was constructed using the strut stability theory, and the critical failure load of the tire under test was obtained. The frictional force of the tire under test during startup or braking is used as the actual load and compared with the critical failure load to obtain the failure judgment result of the tire under test.

[0007] Optionally, the ground contact mark of the tire under test is projected onto a Cartesian coordinate system, and a bivariate exponential function is used to describe the grounding shape of the ground contact mark, resulting in a mathematical model of the ground contact mark, which specifically includes: Taking the horizontal position of the grounding imprint in the Cartesian coordinate system as the horizontal vector and the vertical position of the grounding imprint in the Cartesian coordinate system as the vertical vector, the mathematical model of the grounding imprint is obtained based on the following formula: in, m and n This is an exponential parameter used to control the curvature characteristics of the grounding shape; u and v These are scale parameters used to describe the dimensions of the grounding shape on the horizontal and vertical axes of a Cartesian coordinate system. x The horizontal position of the grounding imprint in a Cartesian coordinate system. y This refers to the longitudinal position of the grounding imprint in a Cartesian coordinate system.

[0008] Optionally, the mathematical model of the grounding imprint is numerically solved using Euler integrals, and the grounding pressure distribution of the grounding imprint is used as a weighting factor in the numerical solution process. This weighting coefficient is then introduced into the calculation of the cross-sectional moment of inertia of the tire grounding imprint, and the equivalent moment of inertia failure coefficient is obtained based on the following formula: ; ; ; in, S The equivalent moment of inertia failure factor.K These are weighting coefficients. Let the stress be at any point within the grounding imprint. This represents the maximum internal stress of the grounding imprint. I x The moment of inertia of the ground imprint.

[0009] Optionally, based on the following formula, a critical criterion for tire instability is constructed using the bar stability theory, with the equivalent moment of inertia failure coefficient as the basis, to obtain the critical failure load of the tire under test: ; in, F pcr The critical failure load, E This refers to the Young's modulus of the tire material. S The equivalent moment of inertia failure factor. μ This is the length coefficient. l This is the equivalent height of the tire.

[0010] Optionally, the frictional force of the tire under test during starting or braking is compared with the critical failure load to obtain the failure judgment result of the tire under test, specifically including: If the actual load is greater than or equal to the critical failure load, the tire under test is deemed to have failed. If the actual load is less than the critical failure load, the tire under test is considered normal.

[0011] The tire failure determination method based on grounding marks provided in this invention has the following advantages compared with the prior art: This invention uses a mathematical model to uniformly describe the ground pressure distribution and ground shape in a Cartesian coordinate system, while also covering geometric and load distribution characteristics. By using Euler integrals to introduce the ground pressure distribution as a weighting factor into the calculation of the cross-sectional moment of inertia, an equivalent moment of inertia failure coefficient is obtained. This technical solution quantifies the non-uniformity of pressure distribution into a key parameter affecting structural stability, overcoming the shortcomings of the original method that ignores the changes in pressure distribution with structural design, thus upgrading tire failure analysis from static geometric description to dynamic load assessment.

[0012] Furthermore, this invention constructs an instability critical criterion based on the equivalent moment of inertia failure coefficient through the bar stability theory, and compares the critical failure load of the tire under test with the actual load to achieve the failure judgment of the tire under test; this process directly links the ground pressure distribution with the tire failure mechanism, and by quantifying the impact of pressure distribution on stability, it can accurately predict the tire failure risk, thereby improving the accuracy of tire failure judgment. Attached Figure Description

[0013] Figure 1This is a flowchart illustrating a tire failure determination method based on grounding imprints provided in one embodiment. Detailed Implementation

[0014] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0015] Current technologies for tire load stability calculation and application still face a series of theoretical limitations, technical bottlenecks, and engineering challenges. These problems directly affect prediction accuracy, real-time performance, and design optimization effects. Dynamic high-precision measurement failures due to sensor interference, embedded pressure films detach from the actual contact area due to shear deformation during high-speed rolling, and their durability is insufficient. Furthermore, transparent platform test benches cannot simulate real road surface textures, and water films / dust cause optical imaging blurring. The lack of full-condition coverage leads to pressure-sensitive material sensor failure under high temperatures and icy / snowy road conditions. The inability to simultaneously measure tire dynamic deformation, temperature field, and friction field results in a disconnect between moment of inertia calculation and stability. In recent years, with the advancement of computer technology and the development of numerical simulation methods, some studies have begun to explore methods for calculating tire contact marks based on mathematical models. These methods typically rely on factors such as geometry, material properties, and ground pressure distribution to predict tire contact marks and their moments of inertia by establishing mathematical models.

[0016] This invention provides a tire failure determination method based on grounding marks, such as... Figure 1 As shown, the method includes: Obtain the ground contact mark of the tire under test. The ground contact mark includes the ground contact shape when the tire contacts the ground and the ground pressure distribution that reflects the stress distribution characteristics when the tire contacts the ground.

[0017] The ground contact mark of the tire under test is projected onto a Cartesian coordinate system, and a binary double-finite function is used to describe the ground contact shape to obtain a mathematical model of the ground contact mark. The mathematical model of the ground contact mark is used to describe the deformation characteristics of the ground contact shape of the tire under different loads and different tire pressures.

[0018] The mathematical model of the grounding imprint is numerically solved by Euler integral, and the grounding pressure distribution is used as a weighting factor in the numerical solution process. The weighting coefficient is introduced into the calculation of the cross-sectional moment of inertia of the tire grounding imprint to obtain the equivalent moment of inertia failure coefficient.

[0019] A critical criterion for tire instability based on the equivalent moment of inertia failure coefficient was constructed using the compression bar stability theory, and the critical failure load of the tire under test was obtained.

[0020] The frictional force of the tire under test during startup or braking is used as the actual load and compared with the critical failure load to obtain the failure judgment result of the tire under test.

[0021] Preferably, the ground contact mark of the tire under test is projected onto a Cartesian coordinate system, and a bivariate exponential function is used to describe the ground contact shape, resulting in a mathematical model of the ground contact mark, specifically including: Taking the horizontal position of the grounding imprint in the Cartesian coordinate system as the horizontal vector and the vertical position of the grounding imprint in the Cartesian coordinate system as the vertical vector, the mathematical model of the grounding imprint is obtained based on the following formula: in, m and n This is an exponential parameter used to control the curvature characteristics of the grounding shape; u and v These are scale parameters used to describe the dimensions of the grounding shape on the horizontal and vertical axes of a Cartesian coordinate system. x The horizontal position of the grounding imprint in a Cartesian coordinate system. y This refers to the longitudinal position of the grounding imprint in a Cartesian coordinate system.

[0022] Preferably, a critical criterion for tire instability based on the equivalent moment of inertia failure coefficient is constructed using the compression bar stability theory based on the following formula, thereby obtaining the critical failure load of the tire under test: ; in, F pcr The critical failure load, E This refers to the Young's modulus of the tire material. S The equivalent moment of inertia failure factor. μ This is the length coefficient. l This is the equivalent height of the tire.

[0023] In tire design, E This is the ratio of tire stiffness to contact area. Tire stiffness is obtained through experiments or simulation calculations.

[0024] In tire stability analysis, the length coefficient μ The value is usually selected based on the tire's geometry, mounting method, and deformation. Common value ranges are as follows:

[0025] For ordinary passenger car tires: the length factor is 1.3.

[0026] For truck tires or tires that bear heavy loads: the length factor is 1.6 to accommodate greater deformation.

[0027] For high-performance or sport tires: the length factor may be 1.0, because these tires are typically designed to be more rigid and less prone to deformation.

[0028] Preferably, the frictional force of the tire under test during starting or braking is compared with the critical failure load to obtain the failure judgment result of the tire under test, specifically including: If the actual load is greater than or equal to the critical failure load, the tire under test is deemed to have failed. If the actual load is less than the critical failure load, the tire under test is considered normal.

[0029] In simple terms, the tire contact patch curve, tire contact pressure distribution, and equivalent moment of inertia coefficient are considered tire failure indicators. The tire contact patch closed curve is obtained through simulation or experiment, and the equivalent moment of inertia failure coefficient controlling the tire contact pressure distribution is calculated based on the simulation or experiment. S Then, the critical criterion for tire instability is constructed using the bar stability theory, and the critical failure load is obtained. The actual load is compared with the critical failure load to determine tire failure.

[0030] A specific embodiment of the present invention is provided: By analyzing the geometric characteristics of tire contact marks, a mathematical model of the contact marks is constructed using a bivariate exponential function to accurately describe the shape of the tire when in contact with the ground. A weighting coefficient for the ground pressure distribution is also introduced. K The weighting coefficient is larger in areas of high pressure and smaller in areas of low pressure. It can not only adapt to failure assessments of different types of tires, but also flexibly adjust to different working conditions.

[0031] 1. Failure coefficient of equivalent moment of inertia of grounding imprint S The calculation method.

[0032] By applying integral calculation and numerical analysis methods, combined with the established bivariate double-exponential function model, the equivalent moment of inertia failure coefficient of tire contact marks is derived. S This formula takes into account changes in tire contact patch shape and variations in contact pressure distribution, thus enabling efficient assessment of tire failure.

[0033] The equivalent moment of inertia failure coefficient is obtained based on the following formula: ; ; ; in, S The equivalent moment of inertia failure factor. K These are weighting coefficients. Let the stress be at any point within the grounding imprint. This represents the maximum internal stress of the grounding imprint. I x The moment of inertia of the ground imprint.

[0034] 2. Grounding imprint curve and grounding pressure distribution A weighting factor for grounding pressure distribution is introduced based on the grounding imprint. K The weighting coefficient is larger where the pressure is high and smaller where the pressure is low. This method can not only adapt to the design requirements of different types of tires, but also be flexibly adjusted for different working conditions.

[0035] 3. Critical loads for column stability and instability A method for judging tire failure is established by using the principle of strut stability and critical load for instability, based on the pressure distribution of tire contact marks, contact surface, and moment of inertia, as shown in Table 1.

[0036] Table 1 establishes tire failure mechanisms based on tire contact patch pressure distribution, contact area, and moment of inertia. The core of column stability (Euler buckling): The critical buckling load of the column is given by Euler's formula, and the critical load... F cr It is proportional to the moment of inertia of the cross section. I The larger the value, the less likely the member is to buckle and become unstable.

[0037] The ability of a tire to resist rollover moments (tilt / pitch) is essentially to resist rotational instability around the X-axis or Y-axis.

[0038] Stabilizing torque M It can be represented as: M ≈ F z * d ,in F z This is the vertical load on the tire (equivalent to the axial pressure of the pressure bar). d The equivalent force arm (related to the shape and size of the grounding imprint) is determined by the moment of inertia of the grounding imprint.

[0039] 3.1 Compression Member: Moment of Inertia of Section I Larger → Larger bending stiffness → Critical buckling load F cr The higher the value, the stronger the stability.

[0040] 3.2 Moment of inertia of tire contact patch.

[0041] Lateral stability about the X-axis: Imprint lateral moment of inertia Ixx The larger the value, the further the load is distributed laterally from the centerline (Y-axis), thus increasing the equivalent force arm against roll.d Larger → stabilizing torque M The larger the value, the stronger its ability to resist lateral tilting instability.

[0042] Pitch stability about the Y-axis: longitudinal moment of inertia of the imprint Heyy The larger the value, the further the load is distributed longitudinally from the centerline (X-axis), thus increasing the equivalent force arm against pitch. d Larger → stabilizing torque M The larger the value, the stronger its ability to resist pitch instability.

[0043] There is a critical overturning moment M cr Critical overturning moment M cr Including: critical roll moment ( M cr，roll ) and critical pitching moment ( M cr，pitch ).

[0044] As a feasible approach, the formulas for calculating the critical roll moment and critical pitch moment are as follows: Critical roll moment ( M cr，roll The torque that makes the vertical load on the inner wheel zero is: M cr，roll = ( mg * T ) / (2 * h ); m Total vehicle mass g Gravitational acceleration, T Wheelbase, h Vehicle center of gravity height.

[0045] Critical pitch moment ( M cr，pitch The pitching moment occurs in the longitudinal direction. The formula for the static critical pitching moment (that lifts the rear wheels off the ground) is:

[0046] M cr，pitch = ( m * g * L ) / ( h ); L The distance from the center of gravity to the axle of the tire off the ground. When the front wheel is off the ground, L This is the distance from the center of gravity to the rear axle (when the front wheels are off the ground, the distance between the off-ground tires and the rear axle is the center of gravity); when the rear wheels are off the ground, L It is the distance from the center of gravity to the front axle (when the rear wheel is off the ground, the tire off the ground is relative to the front axle).

[0047] 3.3 External torque → load transfer → change in tire vertical load → change in stress and shape of ground contact mark.

[0048] Tires are the only component connecting a vehicle to the ground, and almost all loss of vehicle dynamic control ultimately manifests as a loss of tire force. Therefore, tire failure is a key intermediate indicator and direct sign for judging whether a vehicle is about to roll over or become unstable.

[0049] When a vehicle is cornering or subjected to lateral disturbances, centrifugal or lateral forces attempt to rotate the vehicle around the contact point of the outer tire. If this torque exceeds the restoring torque (i.e., the critical rollover moment) determined by the center of gravity height and track width, the vehicle will roll over. M cr，roll If this happens, the vehicle will lift its inner tire, eventually causing it to roll over.

[0050] Instability here refers to directional instability, meaning the driver is unable to control the vehicle's trajectory through the steering wheel (such as understeer, oversteer, fishtailing, etc.). The root cause is that the tires cannot provide sufficient longitudinal or lateral force to meet the driver's input requirements.

[0051] When tilting: The pressure on the outer tire tracks increases and is distributed more outwards; the pressure on the inner tires decreases and is distributed more inwards, even partially lifting off the ground. When pitching: When braking (nodding), the pressure on the front tire tracks increases and is distributed more forwards; the pressure on the rear tires decreases and is distributed more rearwards.

[0052] Whether it is the compression rod I Still tire tracks I xx / I yy The physical essence of both describes the "dispersion" of mass or load distribution relative to a certain axis of rotation. This dispersion directly contributes to the magnitude of stability.

[0053] Because the critical tilting moment and the longitudinal moment of inertia of the imprint are related to the longitudinal moment of inertia and the longitudinal inertia of the imprint, respectively, as follows: ; ; in, The axial pressure in the compression bar is the load that leads to instability. I xx Let the lateral moment of inertia of the imprint be... I yy Let the longitudinal moment of inertia of the imprint be... It provides crucial geometric resistance (equivalent to the compression bar). I This determines the amount of torque required to overcome this geometric stability. M cr，rollThe critical roll moment, M cr，pitch This is the critical pitching moment. C 1 and C 2 is a coefficient related to tire characteristics, encompassing the effects of tire lateral / longitudinal stiffness, suspension stiffness, center of gravity height, and other factors, similar to the boundary condition coefficient of a strut. K Therefore, the longitudinal moment of inertia of the imprint can be determined by reversing the calculation formulas for the critical roll moment and the critical pitch moment.

[0054] In summary, whether it's the strut resisting buckling or the tire contact patch resisting rollover, the moment of inertia of the cross section or area relative to the axis of rotation... I It is a core geometric parameter for measuring an object's inherent resistance to instability. It quantifies the degree to which the material or load distribution is far from the axis of rotation, thus providing a lever effect (stabilizing moment) against rotation. Stability improvement: Increasing the moment of inertia is a direct geometric approach to improving stability. Tires: Using wider tires (increasing...) Ixx To resist tilting, the optimized design allows the imprint to extend appropriately in the longitudinal direction (increasing...). Heyy To resist pitch and ensure uniform load distribution on the imprint (maximizing the effectiveness of the moment of inertia). Critical state: There exists a state determined by the moment of inertia. I The critical state (buckling load / overturning moment) is determined by the load and constraints. Exceeding the critical state will cause instability (rollover / uncontrolled pitching and nose-up), which will lead to tire failure.

[0055] This invention innovatively applies the principles of bar stability theory to tire failure analysis, emphasizing that the moment of inertia of the tire contact patch is not merely a geometric quantity describing its shape, but a core physical quantity connecting tire geometry with vehicle load-bearing stability (resistance to rollover instability). Its mechanism of action shares a profound isomorphism with the moment of inertia of the cross-section during bar buckling in terms of enhancing stability. Furthermore, it innovatively combines the contact patch curve with the contact pressure distribution. In addition, this invention optimizes traditional calculation methods by introducing efficient Euler integrals (such as the Gamma function and Beta function), thereby improving calculation accuracy and speed while reducing resource consumption. This not only improves the calculation accuracy and efficiency of the tire contact patch moment of inertia but also broadens the application areas of tire performance analysis, demonstrating significant technological innovation and practical application value.

[0056] As a feasible approach, the specific implementation is as follows: 1. Construction of a bivariate two-finite function model.

[0057] First, define a binary two-finger function. f ( x , yThis is used to describe the geometric characteristics of tire contact marks. Among them, x and y These represent the lateral and longitudinal positions of the contact patch in a planar coordinate system, respectively. This function reflects the deformation characteristics of the tire's contact patch shape under different loads and tire pressures.

[0058] This model can realistically simulate the contact marks left by tires. The modeling process is as follows: 1.1 A binary double-finite function model of tire contact marks is established, which describes the tire's geometric features, material properties, and load conditions.

[0059] The bivariate two-finite-function model considers the following factors: a. the lateral and longitudinal shape characteristics of the tire. b. the load and air pressure conditions borne by the tire. c. the influence of ambient temperature and road surface type on the contact patch.

[0060] 1.2 Based on the bivariate double-finite function, the geometry of the tire ground contact mark is integrally calculated, and the formula for the moment of inertia of the ground contact mark is derived.

[0061] 1.3 Apply numerical analysis methods to optimize the calculation process in order to improve calculation accuracy and speed.

[0062] 1.4 Compare and verify the calculation results with experimental data to ensure the reliability of the calculation method.

[0063] 2. Mathematical derivation of the ground imprint moment of inertia.

[0064] Based on the established bivariate double-finite function model, the formula for the moment of inertia of the grounding imprint is derived. According to the definition of moment of inertia, the following integral formula is used:

[0065] ; The Beta function and the Gamma function are both special functions in mathematics, each with its own specific definition and properties: 2.1 The Beta function, also known as the Euler integral of the first kind, is defined as follows: ; This definite integral can be solved using integration by parts or integration by substitution. The Beta function has symmetry, i.e. B ( x,y )= B ( y, x Furthermore, there is a close relationship between the Beta function and the Gamma function; the Beta function can be expressed in the form of the Gamma function:

[0066] ; 2.2 The Gamma function, also called Euler's second integral, is an extension of the factorial function to real and complex numbers. Its definition is:

[0067] ; The Gamma function is continuous and defined for both integers and non-integers, making it crucial for computational problems. The Gamma function also exhibits a recursive relationship, i.e. This property greatly simplifies the calculation of the Gamma function. Furthermore, the values ​​of the Gamma function at specific points have been extensively studied, for example:

[0068] ; like At this point, the bivariate exponential function is the unit circle, then: ; like At this point, the bivariate exponential function is If a closed curve is formed by two axial symmetries, then: ; Continue to explore the relationship between the moments of inertia of circles, ellipses, and quadrilaterals of the same area.

[0069] like At this point, the equation of the circular curve is: ; Area is Area of ​​the ellipse Then it is necessary .Pick The equation of the elliptic curve is:

[0070] ; The equation of a quadrilateral in the first quadrant is: ,at this time Then the circle, ellipse, and quadrilateral are respectively:

[0071] ; ; ; Numerical methods (such as Euler integrals of the first and second kind) are used to solve the above integral formulas. These methods can effectively handle complex geometries and irregular boundaries, improving the accuracy and efficiency of the calculations. During the calculation process, optimized algorithms are designed to reduce computation time and resource consumption, adapting to the needs of various tire designs.

[0072] 3. Grounding imprint curve and grounding pressure distribution.

[0073] The ground pressure distribution is analyzed, and a weighting coefficient K is introduced. The weighting coefficient is larger where the pressure is high and smaller where the pressure is low. The tire ground pressure is calculated based on the tire ground pressure distribution, and then divided by the maximum value to obtain the weighting coefficient. K Calculated using the following formula: ; in, Let the stress be at any point within the grounding imprint. This represents the maximum internal stress of the grounding imprint.

[0074] 4. Critical failure load.

[0075] ; in, F pcr The critical failure load, E This refers to the Young's modulus of the tire material. S The equivalent moment of inertia failure factor. μ This is the length coefficient. l This is the equivalent height of the tire.

[0076] The frictional force of the tire under test during startup or braking is used as the actual load and compared with the critical failure load to obtain the failure judgment result of the tire under test.

[0077] This invention proposes a method combining grounding imprint curves and grounding pressure distribution, along with the concepts of lever stability and tire implementation. Based on a bivariate double-exponential function, it calculates the tire's equivalent moment of inertia failure coefficient using tire grounding imprints. S The technical effects that can be achieved include, but are not limited to:

[0078] 1. The calculation accuracy has been significantly improved.

[0079] By constructing a bivariate, two-finite-function model, the geometric characteristics and material effects of tire contact marks can be described more accurately, thereby improving the accuracy of moment of inertia calculation. Compared with traditional experimental methods and simplified models, this provides a more comprehensive and detailed calculation approach, ensuring the reliability of the results.

[0080] 2. Computational efficiency is significantly improved.

[0081] Optimized numerical calculation algorithms, such as the first and second Euler integrals of the kind, were employed, significantly improving computational speed. Through efficient algorithm design, engineers can obtain the moment of inertia of the tire contact patch in a shorter time, thereby accelerating design iteration and verification processes and reducing development costs.

[0082] 3. Highly adaptable and flexible.

[0083] This invention can adapt to the analysis of various tire types and different operating conditions. Whether it is different tire size, material properties, or changing load and air pressure conditions, it can be flexibly adjusted through corresponding input parameters. This high adaptability enables the invention to meet the needs of a wide range of industrial applications.

[0084] 4. Support scientific decision-making and design optimization.

[0085] By providing accurate contact patch moment of inertia data, engineers and designers can make more informed decisions regarding tire design, performance optimization, and safety analysis. Precise moment of inertia calculations can help identify potential design problems, optimize tire performance, and improve vehicle handling and safety.

[0086] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for tire failure determination based on grounding imprints, characterized in that, include: The ground contact imprint of the tire under test is obtained, and the ground contact imprint includes: the ground contact shape when the tire contacts the ground and the ground pressure distribution reflecting the stress distribution characteristics when the tire contacts the ground; The ground contact mark of the tire under test is projected onto a Cartesian coordinate system, and the ground contact shape is described by a binary double-finite function to obtain a mathematical model of the ground contact mark. The mathematical model of the ground contact mark is used to describe the deformation characteristics of the ground contact shape of the tire under different loads and different tire pressures. The mathematical model of the grounding imprint is numerically solved by Euler integral, and the grounding pressure distribution is used as a weighting factor in the numerical solution process. The weighting coefficient is introduced into the calculation of the cross-sectional moment of inertia of the tire grounding imprint to obtain the equivalent moment of inertia failure coefficient. A critical criterion for tire instability based on the equivalent moment of inertia failure coefficient was constructed using the strut stability theory, and the critical failure load of the tire under test was obtained. The frictional force of the tire under test during startup or braking is used as the actual load and compared with the critical failure load to obtain the failure judgment result of the tire under test.

2. The tire failure judgment method based on grounding imprint as described in claim 1, characterized in that, The process involves projecting the ground contact mark of the tire under test onto a Cartesian coordinate system, using a bivariate exponential function to describe the ground contact shape, and obtaining a mathematical model of the ground contact mark, specifically including: Taking the horizontal position of the grounding imprint in the Cartesian coordinate system as the horizontal vector and the vertical position of the grounding imprint in the Cartesian coordinate system as the vertical vector, the mathematical model of the grounding imprint is obtained based on the following formula: in, m and n This is an exponential parameter used to control the curvature characteristics of the grounding shape; u and v These are scale parameters used to describe the dimensions of the grounding shape on the horizontal and vertical axes of a Cartesian coordinate system. x The horizontal position of the grounding imprint in a Cartesian coordinate system. y This refers to the longitudinal position of the grounding imprint in a Cartesian coordinate system.

3. The tire failure judgment method based on grounding imprint as described in claim 1, characterized in that, The mathematical model of the grounding imprint is numerically solved using Euler integrals, and the grounding pressure distribution of the grounding imprint is used as a weighting factor in the numerical solution process. This weighting coefficient is introduced into the calculation of the cross-sectional moment of inertia of the tire grounding imprint, and the equivalent moment of inertia failure coefficient is obtained based on the following formula: ； ； ； in, S The equivalent moment of inertia failure factor. K These are weighting coefficients. Let the stress be at any point within the grounding imprint. This represents the maximum internal stress of the grounding imprint. I x The moment of inertia of the ground imprint.

4. The tire failure judgment method based on grounding imprint as described in claim 3, characterized in that, Based on the following formula, a critical criterion for tire instability is constructed using the bar stability theory and the equivalent moment of inertia failure coefficient, thus obtaining the critical failure load of the tire under test: ； in, F pcr The critical failure load, E This refers to the Young's modulus of the tire material. S The equivalent moment of inertia failure factor. μ This is the length coefficient. l This is the equivalent height of the tire.

5. The tire failure judgment method based on grounding imprint as described in claim 1, characterized in that, The step of comparing the frictional force of the tire under test during startup or braking as the actual load with the critical failure load to obtain the failure judgment result of the tire under test specifically includes: If the actual load is greater than or equal to the critical failure load, the tire under test is deemed to have failed. If the actual load is less than the critical failure load, the tire under test is considered normal.

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