Steel rail irregularity limit value determination method considering impact dynamics and material stability

Abstract

The invention relates to the technical field of railway engineering wheel-rail relationship, and provides a steel rail irregularity limit value determination method considering impact dynamics and material stability, which comprises the following steps: step 1, establishing a geometric irregularity model of any steel rail surface, and solving wheel-rail impact force at the irregularity of the steel rail surface by combining a vehicle-rail coupling system dynamics model; 2, establishing a wheel-rail rolling contact numerical model, and calculating normal and tangential stress distribution during wheel-rail contact; 3, determining a material constitutive model, establishing a rolling contact two-dimensional finite element model, calculating stress-strain time history data of the steel rail, and determining a material stability state of the steel rail; and 4, comprehensively considering the steel rail material, the traction coefficient, the friction coefficient and the wheel-rail contact state, considering the impact dynamics and the material stability service behavior, and forming a steel rail surface geometric irregularity limit value table. According to the method, the irregularity limit value of the steel rail can be well determined.

Description

Technical Field

[0001] The invention relates to the technical field of wheel-rail relationship in railway engineering, and in particular to a method for determining a limit value of rail irregularity taking into account impact dynamics and material stability. Background Art

[0002] With the increase of train speed, train load and vehicle axle weight, the interaction between wheels and rails has also intensified. The geometric unevenness of the rail surface will intensify the impact between wheels and rails, affecting the safe operation of trains and the comfort of passengers. Under long-term effects, it may also cause corrugation, cracks, broken rails and other defects, which seriously restrict the service life and driving safety of rails. On the one hand, the occurrence of rail defects is related to the strong impact of wheels and rails under the geometric unevenness of the rail surface, and on the other hand, it is related to the material of the rail and the local response of the material. Under cyclic reciprocating loads, the material response is divided into four types: elasticity, elastic stability, plastic stability and ratchet effect. The main reasons that affect the mutual conversion of local material responses of wheels and rails are the size of contact load, the hardening characteristics of wheel-rail materials, the residual stress-strain state, and the change of wheel-rail contact state caused by plastic deformation.

[0003] A detailed description of the dynamic action law of wheel-rail under the excitation of track surface geometric irregularity should fully consider the influence of vehicle system, track system and their interaction. Vehicle-track coupling dynamics is one of the commonly used methods in the process of studying the limit of rail geometric irregularity. For the vehicle model, the vehicle is usually simulated as a multi-rigid body system composed of rigid body, spring and damping, the rail is regarded as an Euler beam or Timoshenko beam, and the rail foundation is simulated as a 1-3 layer structure with continuous or discrete support along the longitudinal direction. The interaction between the wheel and the track is the key to the coupling system, which is usually simulated by Hertz linear or nonlinear elastic contact theory. Some scholars applied the vehicle-track coupling dynamics model and simulation analysis software TTISIM to study the influence characteristics of the rail welding zone irregularity on the dynamic response of the wheel and rail, and on this basis proposed the safety limit of the rail welding zone irregularity amplitude. Some scholars simulated the single wave irregularity of the track in a single harmonic way, and applied the vehicle-track coupling dynamics theory and SIMPACK software to study the train dynamic performance and the limit of the irregularity index under different track geometric irregularities. Some scholars have taken actual turnouts as the research object, and proposed the limit values ​​of track geometric irregularity in the turnout area under various management levels by establishing a rigid-flexible coupling dynamic model of the vehicle-turnout system.

[0004] Quantifying the geometric irregularity limit of rails is a very quick way to ensure safe, stable and economical operation of railways. Among them, determining the straightness of rails and the change of geometric gradient are two more representative evaluation parameters. Straightness is often used to characterize the degree of damage of geometric irregularity of rails through the depth of irregularity wave. In order to more comprehensively consider the influence of the geometric shape of rail irregularity on the dynamic response of wheel-rail, some scholars have proposed a method to evaluate the irregularity limit using geometric gradient, which assumes that there is a linear relationship between the geometric gradient of rail irregularity and the maximum fluctuation amplitude of the vertical force of wheel-rail that it excites.

[0005] For the wheel-rail rolling contact problem, the repeated stress on the wheel-rail contact interface can easily cause fatigue damage to the wheel-rail material, and this damage cannot be simply evaluated by the vehicle-track coupled vertical dynamics, but it will have a great impact on the stability and safety of the normal operation of the vehicle. Therefore, a method for determining the limit of rail geometric irregularity that considers both impact dynamics and material stability behavior is needed. Summary of the invention

[0006] The present invention provides a method for determining rail irregularity limit taking into account impact dynamics and material stability, which can overcome certain or some defects of the prior art.

[0007] The method for determining the rail irregularity limit value considering impact dynamics and material stability according to the present invention comprises the following steps:

[0008] Step 1: Establish a geometric irregularity model of any rail surface, and combine it with the vehicle-track coupling system dynamics model to solve the wheel-rail impact force at the irregularity of the rail surface;

[0009] Step 2: Establish a numerical model of wheel-rail rolling contact and calculate the normal and tangential stress distribution during wheel-rail contact;

[0010] Step 3: Determine the material constitutive model, establish a rolling contact two-dimensional finite element model, calculate the rail stress-strain time history data and clarify its material stability state;

[0011] Step 4: Comprehensively consider the rail material, traction coefficient, friction coefficient, wheel-rail contact state, and take into account the impact dynamics and material stable service behavior to form a table of limit values ​​for rail surface geometric irregularity.

[0012] Preferably, in step 1, specifically:

[0013] 1.1) The rail geometric irregularity that causes severe locomotive and vehicle vibration is converted into two-dimensional geometric data, and a rail surface short-wave geometric irregularity model is established;

[0014] 1.2) Establish a vehicle-track coupling system dynamics model, where the vehicle model considers the car body, frame, wheelset and suspension components, and the track model includes rails, fastener system and ballast; the car body and bogie are considered as rigid bodies, and the suspension and fastener system are simulated using spring-damper units;

[0015] According to Hertz nonlinear elastic contact theory, the wheel-rail vertical force p(t) is calculated as:

[0016]

[0017] Where G is the rail contact constant, δZ(t) is the elastic compression between the wheel and rail;

[0018] The vehicle-track coupled dynamics equation is expressed in the following basic form:

[0019] [M]{A}+[C]{v}+[K]{X}={P} (2)

[0020] Where [M], [C], [K] are the mass, damping and stiffness matrices of the vehicle-track coupling system, respectively; {X}, {v}, {A} are the generalized displacement vector, velocity vector and acceleration vector of the coupling system, respectively; {P} is the generalized load vector of the vehicle-track coupling system;

[0021] 1.3) The short-wave geometric irregularity model of the rail surface is written into the dynamic model of the vehicle-track coupling system to obtain the wheel-rail dynamic response under geometric irregularity.

[0022] Preferably, in step 1.1), the rail geometric irregularity includes cosine irregularity, sine irregularity and triangle irregularity.

[0023] Preferably, in step 2, specifically:

[0024] 2.1) When the vehicle is running, when the wheel and the rail are in contact under the static wheel load, assuming that the normal pressure on the wheel-rail contact patch is Hertzian distribution, the normal pressure distribution p(x, y) is:

[0025]

[0026]

[0027] Where a and b are the half-widths of the contact patch in the x and y directions, respectively, p0 is the maximum contact pressure on the contact patch, and P is the total normal contact force;

[0028] When the cylindrical wheel rolls, b is much larger than a. At this time, the normal pressure distribution p(x) and the half-width of the contact patch are:

[0029]

[0030]

[0031]

[0032] Where P z is the normal force per unit length in the transverse direction, R1 and R2 are the radii of curvature, E1, E2 and u1, u2 represent the elastic modulus and Poisson’s ratio of the material respectively;

[0033] 2.2) The wheel-rail vertical force generated when the vehicle passes through different rail geometric irregularities in step 1 is written into the wheel-rail rolling contact calculation model to obtain the normal and tangential stress distribution at the wheel-rail contact spot during operation.

[0034] Preferably, in step 3, specifically:

[0035] 3.1) The Chaboche nonlinear isotropic-hardening model is used as the material constitutive model of the rail, which takes into account the yield criterion, flow criterion and hardening criterion of the material;

[0036] The yield criterion is the condition for judging whether the material enters plastic yield, where the yield surface is used to describe the stress state when the material begins to enter the plastic deformation state, as shown in formula (8):

[0037]

[0038] Where f() is the yield function, σ is the stress tensor, α is the back stress tensor, s is the deviatoric stress tensor, h is the deviatoric back stress tensor, and k is the size of the yield surface;

[0039] The flow criterion is a theory that can determine the normal direction of the plastic strain increment. It links the plastic strain increment with the yield criterion and establishes the plastic flow equation, as shown in formula (9):

[0040]

[0041] Where, dε p is the plastic strain increment, λ is the plastic multiplier;

[0042] The hardening criterion is a criterion used to define the change of the subsequent yield function in the stress space after the material enters the plastic deformation state; the hardening criterion corresponding to the back stress component is:

[0043]

[0044] The total back stress tensor α is composed of the back stress components α i It is superimposed and expressed as:

[0045]

[0046] Where: C i and γ i is the material parameter, M represents the total number, and dp is the cumulative plastic strain, which can be expressed as:

[0047]

[0048] The rails were subjected to uniaxial tensile tests to obtain stress-strain curves, and finally the relevant material parameters used in the Chaboche nonlinear isotropic-hardening model were obtained;

[0049] 3.2) Combined with the material constitutive model, a two-dimensional rolling contact finite element model is established; assuming that the track is a semi-infinite body, the periphery of the two-dimensional finite element model is defined by infinite elements to take into account the semi-infinite characteristics of the structure and prevent the reflection of stress waves generated on the boundary from causing inaccurate results;

[0050] 3.3) Using the method obtained in step 2, the translation of the tangential stress distribution in the rolling direction is used to simulate the cyclic rolling process;

[0051] 3.4) The stress-strain time history data of the rail when the vehicle rolls back and forth is calculated through the finite element model to form a stress-strain relationship curve to determine the material stability of the rail.

[0052] Preferably, in step 3.4), the material stable state includes elasticity, elastic stability, plastic stability and ratchet effect.

[0053] Preferably, in step 4, specifically:

[0054] By changing the rail material, traction coefficient, friction coefficient, wheel-rail contact state, running speed, geometric irregularity wavelength and wave depth parameters, and comprehensively considering the calculation methods of steps 1 and 3, and taking the local deformation results of the wheel and rail under the non-ratchet effect state under the premise of meeting the dynamic requirements, we finally summarize and form a table of rail geometric irregularity limit values ​​that considers impact dynamics and material stability behavior.

[0055] The present invention proposes a method for determining the geometric irregularity limit of rails that can simultaneously consider impact dynamics and material stability behavior. On the one hand, the constraints on the dynamic contact force of wheels and rails in the traditional evaluation method of the geometric irregularity limit of rails through vehicle-track coupling dynamics theory and the like are retained to meet the maintenance rules of existing lines; on the other hand, considering parameters such as rail material, traction coefficient, friction coefficient, running speed, geometric irregularity shape (wavelength, wave depth), a finite element model capable of solving the relationship between the contact stress and deformation of rails under reciprocating rolling of vehicles is established, the stability state of the rail material is clarified through the stress-strain curve, the geometric irregularity characteristics of the rails under the non-ratchet effect state are summarized, and finally a numerical table of the geometric irregularity limit of rails under different parameters is formed. The present invention can better determine the rail irregularity limit. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 This is a flow chart of a method for determining rail irregularity limit value considering impact dynamics and material stability in Example 1;

[0057] Figure 2 Schematic diagram of the distribution of short-wave geometric irregularities on the rail surface in Example 1;

[0058] Figure 3 Schematic diagram of the vehicle-track coupling system dynamics model in Example 1;

[0059] FIG4( a ) is a schematic diagram of the wheel-rail vertical force under the action of uneven wave depth in Example 1;

[0060] FIG4( b ) is a schematic diagram of the wheel-rail vertical force under the action of the uneven wavelength in Example 1;

[0061] Figure 5 Schematic diagram of stress-strain curve of uniaxial tensile test in Example 1;

[0062] Figure 6 Schematic diagram of the two-dimensional rolling contact finite element model in Example 1;

[0063] Figure 7 This is a schematic diagram of the material stable state under cyclic reciprocating load in Example 1;

[0064] FIG8( a ) is a schematic diagram of the dynamic response between the wheel and the rail when a vehicle passes through an ideal geometric unevenness of a rail with a wavelength of 40 mm and a wave depth of 0.1 mm in Example 1;

[0065] FIG8( b ) is an equivalent stress-strain relationship curve of a point in the rolling contact two-dimensional finite element model in Example 1;

[0066] Fig. 9 Schematic diagram showing the comparison of calculation results between the method of this embodiment and the traditional method in Example 1;

[0067] Fig.10 Schematic diagram of the vertical wheel-rail force in Example 2;

[0068] FIG11( a ) is a schematic diagram of normal stress distribution in the contact area within a specified vertical force range in Example 2;

[0069] FIG11( b ) is a schematic diagram of the tangential stress distribution in the contact area within the specified vertical force range in Example 2;

[0070] Fig.12 It is the stress cloud diagram of the two-dimensional rolling contact finite element model in Example 2;

[0071] Fig.13 This is the von Mises equivalent stress-strain relationship curve in Example 2. DETAILED DESCRIPTION

[0072] In order to further understand the content of the present invention, the present invention is described in detail in conjunction with the accompanying drawings and embodiments. It should be understood that the embodiments are only for explaining the present invention and are not intended to limit it.

[0073] Example 1

[0074] like Figure 1 As shown, this embodiment provides a method for determining the rail irregularity limit value considering impact dynamics and material stability, which includes the following steps:

[0075] Step 1: Establish a geometric irregularity model of any rail surface, and combine it with the vehicle-track coupling system dynamics model to solve the wheel-rail impact force at the irregularity of the rail surface;

[0076] In step 1, specifically:

[0077] 1.1) The rail geometric irregularities (cosine irregularities, sine irregularities and triangle irregularities) that cause severe vibration of locomotives and vehicles are converted into two-dimensional geometric data, and a short-wave geometric irregularity model of the rail surface is established, such as Figure 2 As shown;

[0078] 1.2) Establish the vehicle-track coupling system dynamics model, such as Figure 3 As shown, the vehicle model considers the car body, frame, wheelset and suspension components, and the track model includes rails, fastener system and ballast; the car body and bogie are considered as rigid bodies, and the suspension and fastener system are simulated using spring-damper units;

[0079] According to Hertz nonlinear elastic contact theory, the wheel-rail vertical force p(t) is calculated as:

[0080]

[0081] Where G is the rail contact constant, δZ(t) is the elastic compression between the wheel and rail;

[0082] The vehicle-track coupled dynamics equation is expressed in the following basic form:

[0083] [M]{A}+[C]{v}+[K]{X}={P} (2)

[0084] Where [M], [C], [K] are the mass, damping and stiffness matrices of the vehicle-track coupling system, respectively; {X}, {v}, {A} are the generalized displacement vector, velocity vector and acceleration vector of the coupling system, respectively; {P} is the generalized load vector of the vehicle-track coupling system;

[0085] 1.3) The short-wave geometric irregularity model of the rail surface is written into the dynamic model of the vehicle-track coupling system, and the wheel-rail dynamic response under geometric irregularity is obtained, as shown in Figure 4(a) and Figure 4(b).

[0086] Step 2: Establish a numerical model of wheel-rail rolling contact and calculate the normal and tangential stress distribution during wheel-rail contact;

[0087] In step 2, specifically:

[0088] 2.1) When the vehicle is running, when the wheel and the rail are in contact under the static wheel load, assuming that the normal pressure on the wheel-rail contact patch is Hertzian distribution, the normal pressure distribution p(x, y) is:

[0089]

[0090]

[0091] Where a and b are the half-widths of the contact patch in the x and y directions, respectively, p0 is the maximum contact pressure on the contact patch, and P is the total normal contact force;

[0092] When the cylindrical wheel rolls, the contact patch is very thin and long, resulting in b being much larger than a. At this time, the normal pressure distribution p(x) and the half-width of the contact patch are approximately:

[0093]

[0094]

[0095]

[0096] Where P z is the normal force per unit length in the transverse direction, R1 and R2 are the radii of curvature, E1, E2 and u1, u2 represent the elastic modulus and Poisson’s ratio of the material respectively;

[0097] 2.2) The wheel-rail vertical force generated when the vehicle passes through different rail geometric irregularities in step 1 is written into the wheel-rail rolling contact calculation model to obtain the normal and tangential stress distribution at the wheel-rail contact spot during operation.

[0098] Step 3: Determine the material constitutive model, establish a rolling contact two-dimensional finite element model, calculate the rail stress-strain time history data and clarify its material stability state;

[0099] In step 3, specifically:

[0100] 3.1) The Chaboche nonlinear isotropic-hardening model (Chaboche model for short) is used as the material constitutive model of rails. This model takes into account the yield criterion, flow criterion and hardening criterion of the material, and can better describe the ratcheting effect and stress relaxation phenomenon of cyclic plastic strain of the material under repeated rolling contact conditions;

[0101] The yield criterion is a condition for judging whether a material enters plastic yield. The yield surface is used to describe the stress state when the material begins to enter the plastic deformation state. The von Mises yield condition is often used in finite element analysis. For example, formula (8):

[0102]

[0103] Where f() is the yield function, σ is the stress tensor, α is the back stress tensor, s is the deviatoric stress tensor, h is the deviatoric back stress tensor, and k is the size of the yield surface, which is a constant in the Chaboche model;

[0104] The flow criterion is a theory that can determine the normal direction of the plastic strain increment. It links the plastic strain increment with the yield criterion and establishes the plastic flow equation, as shown in formula (9):

[0105]

[0106] Where, dε p is the plastic strain increment, λ is the plastic multiplier;

[0107] The hardening criterion is a criterion used to define the change of the subsequent yield function in the stress space after the material enters the plastic deformation state; the hardening criterion corresponding to the back stress component is:

[0108]

[0109] The total back stress tensor α is composed of the back stress components α i It is superimposed and expressed as:

[0110]

[0111] Where: Ci and γ i is the material parameter, M represents the total number, and dp is the cumulative plastic strain, which can be expressed as:

[0112]

[0113] In this embodiment, it is assumed that the rail material is U71Mn, and a uniaxial tensile test is performed on the rail to obtain a stress-strain curve, such as Figure 5 As shown, the relevant material parameters used in the Chaboche nonlinear isotropic-hardening model are finally obtained;

[0114] 3.2) Combined with the material constitutive model, a two-dimensional rolling contact finite element model is established, such as Figure 6 As shown in the figure, assuming that the track is a semi-infinite body, the periphery of the two-dimensional finite element model is defined by infinite elements to take into account the semi-infinite characteristics of the structure and prevent the reflection of stress waves generated on the boundary from causing inaccurate results.

[0115] 3.3) The cyclic rolling process is simulated by using the method obtained in step 2 and the translation of the tangential stress distribution in the rolling direction; the cyclic moving load on the top surface of the rail is realized by self-programming and combining the modification of the inp file in abaqus. In this embodiment, the total rolling distance is set to 40 mm, and 5 load cycles are considered;

[0116] 3.4) The stress-strain time history data of the rail when the vehicle reciprocates is calculated by the finite element model to form a stress-strain relationship curve, so as to determine the material stability state of the rail (elasticity, elastic stability, plastic stability and ratchet effect), such as Figure 7 shown.

[0117] Step 4: Comprehensively consider the rail material, traction coefficient, friction coefficient, wheel-rail contact state, and impact dynamics and material stable service behavior to form a table of rail surface geometric irregularity limit values;

[0118] In step 4, specifically:

[0119] By changing the rail material, traction coefficient, friction coefficient, wheel-rail contact state, running speed, geometric irregularity wavelength and wave depth parameters, and comprehensively considering the calculation methods of steps 1 and 3, and taking the local deformation results of the wheel and rail under the non-ratchet effect state under the premise of meeting the dynamic requirements, we finally summarize and form a table of rail geometric irregularity limit values ​​that considers impact dynamics and material stability behavior.

[0120] This embodiment takes into account the stability behavior of rail materials and expands the traditional evaluation method of rail geometric irregularity limits. The original analysis and constraints on the impact force generated by rail geometric irregularity during vehicle operation based on vehicle-track coupling dynamics ignore the influence of rail materials. For the wheel-rail rolling contact problem, the reciprocating stress of the wheel on the contact interface can easily cause fatigue damage to the rail, so it is also necessary to discuss the material stability of the rail when judging the geometric irregularity limit.

[0121] Figure 8(a) shows the dynamic response between the wheel and rail when the vehicle passes through the ideal geometric unevenness of the rail with a wavelength of 40mm and a wave depth of 0.1mm. Figure 8(b) shows the equivalent stress-strain relationship curve of a certain point in the two-dimensional finite element model of rolling contact under certain contact conditions. It is easy to see from the figure that after meeting the impact dynamics requirements between the wheel and rail, the geometric unevenness of the rail may still cause the ratcheting effect of the rail material, thereby causing fatigue damage to the material. Through calculation summary, the limit value calculation results of the method of this embodiment are compared with those of the traditional vertical impact dynamics method, as shown in Figure 8(a). Fig. 9 shown.

[0122] Example 2

[0123] Assuming that a subway type B car is used, the wheel profile is LMA, the rail profile is CN60, and considering that the rail and wheel materials are consistent, the elastic modulus E=206GPa, the shear elastic modulus G=79231Mpa, the Poisson's ratio v=0.3, the pure shear yield strength k=265Mpa, and the friction coefficient f=0.2.

[0124] The invention method is described by taking an ideal two-dimensional geometric irregularity of a rail surface as an example. The typical dimensions of the two-dimensional geometric irregularity are: wavelength and wave depth are 40 mm and 0.1 mm respectively. When a subway vehicle passes by, the vertical force between the wheel and the rail is as follows: Fig.10 shown.

[0125] pass Fig.10 It can be seen that when running at a speed of 40 km / h, under the ideal unevenness excitation of 40 mm wavelength and 0.1 mm wave depth, the impact dynamics safety limit is met.

[0126] When exploring the material stable state, for the convenience of calculation, only the wavelength of the [0.2m, 0.25m] interval is intercepted to calculate the stress distribution. Assuming that the vehicle is in pure rolling operation, that is, there is no adhesion area in the contact patch, the normal stress distribution and tangential stress distribution of the contact area within the specified vertical force range can be calculated, as shown in Figure 11 (a) and Figure 11 (b).

[0127] The above stress distribution is repeated 5 times by self-written matlab program and the results are written into inp file to simulate the reciprocating motion of the train on the rail. The von Mises stress cloud diagram of the rail after 5 rolling (the finite element model part is intercepted) is displayed in Fig.12 .

[0128] Take the stress-strain time history data at the position corresponding to the maximum von Mises equivalent stress, such as Fig.13 It can be clearly seen from the figure that the rail is in a plastic stable state at this time, meeting the requirements of material stable behavior.

[0129] By modifying the geometric irregularity of the rail, changing the operating parameters, and repeating the above calculations, we can obtain a table of results that takes both impact dynamics and material stability behavior into account, thereby summarizing the corresponding rail geometric irregularity limits.

[0130] The present invention and its embodiments are described schematically above, and the description is not restrictive. The drawings show only one embodiment of the present invention, and the actual structure is not limited thereto. Therefore, if a person skilled in the art is inspired by it and designs a structural method and an embodiment similar to the technical solution without creativity without departing from the purpose of the invention, they shall all fall within the protection scope of the present invention.

Claims

1. A method for determining rail irregularity limits considering impact dynamics and material stability, characterized in that: The following steps are involved: Step 1: Establish a geometric irregularity model of any rail surface, and combine it with the vehicle-track coupling system dynamics model to solve the wheel-rail impact force at the irregularity of the rail surface; Step 2: Establish a numerical model of wheel-rail rolling contact and calculate the normal and tangential stress distribution during wheel-rail contact; Step 3: Determine the material constitutive model, establish a rolling contact two-dimensional finite element model, calculate the rail stress-strain time history data and clarify its material stability state; Step 4: Comprehensively consider the rail material, traction coefficient, friction coefficient, wheel-rail contact state, and take into account the impact dynamics and material stable service behavior to form a table of limit values ​​for rail surface geometric irregularity.

2. The method for determining rail irregularity limit considering impact dynamics and material stability according to claim 1, characterized in that: In step 1, specifically: 1.1) The rail geometric irregularity that causes severe locomotive and vehicle vibration is converted into two-dimensional geometric data, and a rail surface short-wave geometric irregularity model is established; 1.2) Establish a vehicle-track coupling system dynamics model, where the vehicle model considers the car body, frame, wheelset and suspension components, and the track model includes rails, fastener system and ballast; the car body and bogie are considered as rigid bodies, and the suspension and fastener system are simulated using spring-damper units; According to Hertz nonlinear elastic contact theory, the wheel-rail vertical force p(t) is calculated as: Where G is the rail contact constant, δZ(t) is the elastic compression between the wheel and rail; The vehicle-track coupled dynamics equation is expressed in the following basic form: [M]{A}+[C]{v}+[K]{X}={P} (2) Where [M], [C], [K] are the mass, damping and stiffness matrices of the vehicle-track coupling system, respectively; {X}, {v}, {A} are the generalized displacement vector, velocity vector and acceleration vector of the coupling system, respectively; {P} is the generalized load vector of the vehicle-track coupling system; 1.3) The short-wave geometric irregularity model of the rail surface is written into the dynamic model of the vehicle-track coupling system to obtain the wheel-rail dynamic response under geometric irregularity.

3. The method for determining rail irregularity limit considering impact dynamics and material stability according to claim 2, characterized in that: In step 1.1), the rail geometric irregularity includes cosine irregularity, sine irregularity and triangle irregularity.

4. The method for determining rail irregularity limit considering impact dynamics and material stability according to claim 3, characterized in that: In step 2, specifically: 2.1) When the vehicle is running, when the wheel and the rail are in contact under the static wheel load, assuming that the normal pressure on the wheel-rail contact patch is Hertzian distribution, the normal pressure distribution p(x, y) is: Where a and b are the half-widths of the contact patch in the x and y directions, respectively, p0 is the maximum contact pressure on the contact patch, and P is the total normal contact force; When the cylindrical wheel rolls, b is much larger than a. At this time, the normal pressure distribution p(x) and the half-width of the contact patch are: Where P z is the normal force per unit length in the transverse direction, R1 and R2 are the radii of curvature, E1, E2 and u1, u2 represent the elastic modulus and Poisson’s ratio of the material respectively; 2.2) The wheel-rail vertical force generated when the vehicle passes through different rail geometric irregularities in step 1 is written into the wheel-rail rolling contact calculation model to obtain the normal and tangential stress distribution at the wheel-rail contact spot during operation.

5. The method for determining rail irregularity limit considering impact dynamics and material stability according to claim 4, characterized in that: In step 3, specifically: 3.1) The Chaboche nonlinear isotropic-hardening model is used as the material constitutive model of the rail, which takes into account the yield criterion, flow criterion and hardening criterion of the material; The yield criterion is the condition for judging whether the material enters plastic yield, where the yield surface is used to describe the stress state when the material begins to enter the plastic deformation state, as shown in formula (8): Where f() is the yield function, σ is the stress tensor, α is the back stress tensor, s is the deviatoric stress tensor, h is the deviatoric back stress tensor, and k is the size of the yield surface; The flow criterion is a theory that can determine the normal direction of the plastic strain increment. It links the plastic strain increment with the yield criterion and establishes the plastic flow equation, as shown in formula (9): Where, dε p is the plastic strain increment, λ is the plastic multiplier; The hardening criterion is a criterion used to specify the change of the subsequent yield function in the stress space after the material enters the plastic deformation state; The hardening criterion corresponding to the back stress component is: The total back stress tensor α is composed of the back stress components α i It is superimposed and expressed as: Where: C i and γ i is the material parameter, M represents the total number, and dp is the cumulative plastic strain, which can be expressed as: The rails were subjected to uniaxial tensile tests to obtain stress-strain curves, and finally the relevant material parameters used in the Chaboche nonlinear isotropic-hardening model were obtained; 3.2) Combined with the material constitutive model, a two-dimensional rolling contact finite element model is established; assuming that the track is a semi-infinite body, the periphery of the two-dimensional finite element model is defined by infinite elements to take into account the semi-infinite characteristics of the structure and prevent the reflection of stress waves generated on the boundary from causing inaccurate results; 3.3) Using the method obtained in step 2, the translation of the tangential stress distribution in the rolling direction is used to simulate the cyclic rolling process; 3.4) The stress-strain time history data of the rail when the vehicle rolls back and forth is calculated through the finite element model to form a stress-strain relationship curve to determine the material stability of the rail.

6. The method for determining rail irregularity limit considering impact dynamics and material stability according to claim 5, characterized in that: In step 3.4), the material stability states include elasticity, elastic stability, plastic stability and ratchet effect.

7. The method for determining rail irregularity limit considering impact dynamics and material stability according to claim 6, characterized in that: In step 4, specifically: By changing the rail material, traction coefficient, friction coefficient, wheel-rail contact state, running speed, geometric irregularity wavelength and wave depth parameters, and comprehensively considering the calculation methods of steps 1 and 3, and taking the local deformation results of the wheel and rail under the non-ratchet effect state under the premise of meeting the dynamic requirements, we finally summarize and form a table of rail geometric irregularity limit values ​​that considers impact dynamics and material stability behavior.

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