Subway elastic strip matching method based on friction self-excited vibration and resonance mechanism

Abstract

The invention discloses a subway elastic strip matching method based on friction self-excited vibration and a resonance mechanism, and relates to the technical field of railway engineering. Comprising the following steps: establishing a vehicle-rail system rigid-flexible coupling dynamic simulation model based on rail design parameters and vehicle parameters, and obtaining axle box suspension force, a wheel-rail contact angle and wheel-rail creep force based on the dynamic simulation model; establishing a wheel-rail friction coupling finite element model based on the axle box suspension force, the wheel-rail contact angle, the track design parameters and the vehicle parameters; based on a friction self-excited vibration theory, combined with wheel-rail creep force, predicting steel rail corrugation by utilizing a wheel-rail friction coupling finite element model, and extracting a characteristic dominant frequency of the steel rail corrugation; based on the characteristic dominant frequency of rail corrugation, an elastic strip suitable for the rail is selected in combination with the resonance avoidance principle. According to the method, the adaptability and robustness of a matching strategy are improved, the fatigue fracture risk of the elastic strip is effectively reduced, and the operation safety and reliability of a subway track system are enhanced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of railway engineering, and particularly relates to a subway spring bar matching method based on friction self-excitation vibration and resonance mechanism. BACKGROUND

[0002] Steel rails are usually fixed on sleepers through a fastening system, in which a spring bar assembly is used to provide the necessary clamping force to ensure the stability of the rail direction and position. In subway lines, the setting of curved tracks is inevitable due to the limitations of terrain conditions and line layout. A large number of studies and actual operation data show that rail wavy wear (hereinafter referred to as rail corrugation) is more likely to occur in curved track sections than in straight track sections. Rail corrugation is a periodic wave-shaped wear, and its typical characteristics are short waves (25-80 mm) and long waves (>80 mm), and the excitation frequency generally ranges from 50 to 1200 Hz. Although rail corrugation can be temporarily eliminated by grinding, it often quickly reappears at the same location, making it difficult to completely eliminate. Its existence will lead to sharp fluctuations in wheel-rail contact force, thereby increasing the stress fluctuations and fatigue damage of the spring bar in the fastening system, and ultimately inducing the spring bar to break.

[0003] Statistics have shown that the number of broken spring bars in curved track sections is much higher than that in straight track sections, and in severe cases, it can cause large-scale failure of the fastening system, affect the stability of the track structure, and even endanger the safety of train operation. However, the differences in different train models and line parameters (such as curve radius, track widening, etc.) and the influence of rail corrugation development on the fatigue life of the spring bar are often not fully considered during the design stage of the subway track. Therefore, it is urgent to propose a rapid and effective subway spring bar matching method to adapt to the service conditions of curved tracks, reduce the risk of spring bar breakage, and improve the overall operation safety and reliability of the track system.

[0004] Although a large number of studies have been conducted on the spring bar breakage mechanism, and the influence of internal and external factors on its fatigue failure has been thoroughly discussed, the related work is mostly based on the premise that rail corrugation has already formed, and focuses on post-damage assessment and local structure improvement under the action of corrugation. For the formation mechanism and prior prediction of the complete evolution chain of "rail corrugation generation - wheel-rail vibration excitation - spring bar fatigue damage", there is still a lack of systematic analysis and effective modeling, and the related research has not fully revealed the essential influence of the inducing conditions of rail corrugation and its evolution process on the spring bar life.

[0005] Existing models generally cannot accurately predict the fatigue risk of the spring bar that may be caused by rail corrugation at the stage when rail corrugation has not yet formed, resulting in that the selection and parameter matching of the subway fastening system still mainly rely on engineering experience. The existing matching method generally lacks the ability of rapid adaptation and parameter optimization when facing different curve radius tracks, and it is difficult to achieve early warning of the fatigue life of the spring bar in extreme working conditions, and it is also impossible to achieve an effective balance between safety margin and economic cost. SUMMARY

[0006] To achieve the above object, the application provides a metro spring strip matching method based on friction self-excited vibration and resonance mechanism, which comprises the following steps: S1, a rigid-flexible coupling dynamics simulation model of a vehicle-track system is established based on track design parameters and vehicle parameters, and based on the dynamics simulation model, axle box suspension force, wheel-rail contact angle and wheel-rail creep force are obtained; S2, a wheel-rail friction coupling finite element model is established based on the axle box suspension force, the wheel-rail contact angle, the track design parameters and the vehicle parameters; S3, based on the friction self-excited vibration theory, the wheel-rail creep force is combined, the wheel-rail friction coupling finite element model is used to predict rail corrugation, and the characteristic main frequency of the rail corrugation is extracted; S4, based on the characteristic main frequency of the rail corrugation, the spring strip suitable for the track is selected in combination with the resonance avoidance principle.

[0007] The application has the beneficial effects that the application integrates the friction self-excited vibration theory and the modal resonance characteristics, constructs an integrated modeling framework of wheel-rail dynamics-wear-resonance response, innovatively introduces the resonance avoidance mechanism of the spring strip modal frequency and the corrugation excitation frequency, combines visual recognition and dynamic simulation technology, realizes rapid matching and individual dynamic adjustment of the spring strip before the corrugation is formed. The method improves the adaptability and robustness of the matching strategy, effectively reduces the risk of spring strip fatigue fracture, and enhances the operation safety and reliability of the metro track system. BRIEF DESCRIPTION OF DRAWINGS

[0008] In order to more clearly illustrate the technical solutions of the application, the following will briefly introduce the drawings needed to be used in the embodiments. Obviously, for those skilled in the art, other drawings can also be obtained without creative labor based on these drawings.

[0009] Figure 1 It is a rigid-flexible coupling dynamics model of a vehicle-track system containing a flexible rail; Figure 2 It is a wheel-rail contact schematic diagram of a wheel-rail friction coupling finite element model; Figure 3 It is a prediction result of rail corrugation frequency of a certain metro curve track; Figure 4 It is a prediction result of unstable vibration mode of a wheel-rail system at a certain metro curve track. DETAILED DESCRIPTION

[0010] With reference to the drawings of the embodiments of the present application, the technical solutions in the embodiments of the present application will be clearly described below. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments of the present application, other embodiments obtained by a person of ordinary skill in the art without creative effort should fall within the protection scope of the present application.

[0011] Hereinafter, the terms "first", "second" and the like are used only for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the technical features indicated. Therefore, the features defined with "first", "second" and the like can explicitly or implicitly include one or more features. In the description of the present application, unless otherwise specified, the meaning of "a plurality of" is two or more.

[0012] The subway spring strip matching method based on friction self-excited vibration and resonance mechanism comprises: S1, based on track design parameters and vehicle parameters, a rigid-flexible coupling dynamics simulation model of a vehicle-track system is established, and based on the dynamics simulation model, axle box suspension force, wheel-rail contact angle and wheel-rail creep force are obtained; In this step, the track design parameters include superelevation, curve track radius, slope and easement curve length; the vehicle parameters include the mass and moment of inertia of the car body, frame and wheelset, and the stiffness and damping of the suspension; these parameters are common design parameters in the art. At the same time, it is a common means in the art to establish a rigid-flexible coupling dynamics simulation model of a vehicle-track system through these parameters. For a vehicle, according to the railway line configuration, it is usually an A-type vehicle or a B-type vehicle, and the vehicle parameters are relatively easy to obtain; at the same time, according to the design parameters of the vehicle, the wheelbase of the bogie and the center distance between the front and rear bogies can be obtained, and the wheel profile, rolling circle radius and rolling circle lateral span can also be obtained. For track design parameters, the standard track gauge is usually set as 1435mm, of course, a person skilled in the art can also design the line as wide track or narrow track according to the actual situation.

[0013] In this embodiment, the established dynamics simulation model includes a single car and a flexible steel rail, as shown in Figure 1 .

[0014] Further, in this embodiment, the Kik-Piotrowski contact model is used for the flexible contact wheel-rail non-Hertz contact analysis, which has a faster calculation speed and high reliability.

[0015] In the actual setting process, the first step is to determine the penetration area, assuming that the wheel profile and the rail profile are located in two orthogonal coordinate systems oxyz1 and oxyz2, x , yLet be the local rectangular coordinates of the wheel and rail, with the contact point O as the origin, located within the common tangent plane: where x The axle is positive along the direction of wheel rolling (rail direction, forward movement). y The axis is positive along the transverse direction of the track gauge (from the inner rail to the outer rail), and is used to describe the position of the major and minor axes and stress distribution of the contact ellipse in the tangent plane; z 1 and z 2 represents the geometric coordinates of the wheel and rail surfaces in the z-direction, respectively. z Axis perpendicular to x – y The plane, pointing outwards in the normal direction, is used to describe the relative height, deformation, and normal pressure distribution between the wheel and rail. The penetration function of the wheel and rail sections... h ( y ) is defined as: In the formula, f ( y () represents the minimum distance between the wheel profile and the rail profile. delta 0 is the virtual penetration value, a known quantity obtained through a large number of experiments.

[0016] Through formula The coordinates of the front and rear edges of the contact area can be determined, where, x l ( y ) indicates along the track direction ( x (Direction) in different lateral positions y The coordinates of the front boundary of the wheel-rail contact area; x t ( y () represents the coordinates of the rear boundary of the contact area; R Indicates the radius of the wheel.

[0017] Since the wheel is a rotating body, when solving the wheel-rail normal contact problem, it is assumed that the normal pressure on the wheel is ( p ( x , y The distribution is semi-elliptical. In the formula, p m This represents the maximum normal force, which is a known quantity. x l ( 0 () indicates the contact area between the wheel and the rail along the rolling direction. x The leading edge coordinates of the axle correspond to the initial position of the wheel entering contact. Integrating the above equation yields the normal load of the wheel-rail contact: y l and y r These represent the contact ellipse in the horizontal direction ( yN is the normal load.

[0018] Assume that the intersection of the two orthogonal coordinate systems oxyz1, oxyz2 in which the wheel profile and the rail profile are located is point O, which is the geometric contact point (common point) between the wheel and the rail when there is no load. The wheel profile or the rail profile is in the plane of x =0, and when the rail bears the normal load from the wheel, the wheel and the rail produce deformation, w w w r is the displacement of each point on the wheel (rail) in the Oz1 (Oz2) direction due to the deformation under force.

[0019] For any point in the elastic half-space: Use delta to represent the amount of cutting, so the point distance between the wheel and the rail when transmitting the load is: In the formula, s x y indicates the distance between point x and point y ; z x y indicates the geometric height or separation distance function of any point x , y in the contact area of the wheel and the rail in the normal z direction. For any point on the contact area: When x, y all take the value of 0, and the separation distance between the wheel and the rail in the z-axis z (0,0)=0, In the formula, w 0 is recorded as the normal initial displacement of the wheel and the rail in contact at the geometric contact point O; to accurately estimate the maximum pressure and ensure that the method is absolutely reliable, it is set that only at the geometric contact point (0,0) the contact condition is met, and the normal displacement of the point is calculated by the Boussinesq function w x y : Where, sigma is the Poisson's ratio, E is the elastic modulus. Further calculation gives the following results: Through the above calculation, the normal load of the wheel and rail contact N is obtained, and the wheel and rail creep force is calculated by the method in document 1, which can be directly output by the rigid-flexible coupled dynamics simulation model of the vehicle-rail system; the maximum normal force P ​​​​​​​m determines the limit friction of wheel-rail contact, which is used to determine whether the contact between wheel and rail enters the full sliding state. Further, it can be used as a prerequisite condition for whether the wheel-rail system generates friction self-excited vibration.

[0020] The above document 1 is as follows: Kalker J J. On the rolling contact of two elastic bodies in the presence of dry friction [D]. Delft: Delft University of Technology, 1967.

[0021] In this step, the axle box suspension force includes the axle box lateral suspension force and the axle box vertical suspension force, and the wheel-rail contact angle includes the outer wheel and high rail contact angle and the inner wheel and low rail contact angle. They can be directly output by the rigid-flexible coupling dynamics simulation model of the vehicle-rail system.

[0022] S2, based on the axle box suspension force, the wheel-rail contact angle, the track design parameters and the vehicle parameters, a wheel-rail friction coupling finite element model is established; Based on the dynamics simulation results obtained in step 1, including the axle box lateral suspension force, the axle box vertical suspension force, the outer wheel and high rail contact angle and the inner wheel and low rail contact angle, etc., a wheel-rail friction coupling model containing wheel set, rail and rail pad and other solid components is further constructed, and a spring-damper unit is used to simulate the spring bar. The wheel-rail contact diagram of the finite element model is shown in Figure 2 In this embodiment, the model contains two standard profile rails, the rail density is set to 60 kg / m, and the length of a single rail is 18 m; the super-high value h The structure or parameters of the rail pad and the iron pad are set according to the actual track selection and the vehicle running speed, and the lateral, longitudinal and vertical constraints of the sleeper are simulated by using the spring-damper unit.

[0023] S3, based on the friction self-excited vibration theory, combining the wheel-rail creep force, using the wheel-rail friction coupling finite element model to predict the rail corrugation, and extracting the characteristic frequency of the rail corrugation; In this step, first, according to the wheel-rail creep force, it is judged whether the wheel-rail sliding needs to be introduced in the calculation process of the finite element model: when the wheel-rail creep force tends to be saturated, the wheel-rail sliding is introduced, otherwise not. This is mainly because, when the vehicle is running, the saturated creep force between the wheel and the rail causes the relative sliding of the wheel and the rail, which further causes the generation of friction self-excited vibration of the wheel-rail system, and finally leads to the generation of rail corrugation of the curve track.

[0024] Subsequently, based on the S2 finite element model, the theory of frictional self-excited vibration was introduced to study the unstable vibration characteristics of the system model under frictional sliding state. In the research process, the characteristic dominant frequency of rail corrugation was mainly calculated using the following formula.

[0025] S31. Establish the system's equations of motion: In the formula, M r Represents the system's quality matrix; K r Represents the stiffness matrix of the system; C r Represents the damping matrix of the system; Represents the acceleration of a node; Indicates the speed of the node; x Represents the displacement of the node; f Indicates the coefficient of friction between the wheel and the rail; K t Indicates wheel-rail contact stiffness; Characteristic analysis of the equation of motion yields its characteristic equation: , In the formula, λ is the eigenvalue; φ is the eigenvector, corresponding to the mode shape of the eigenvalue λ.

[0026] S32. Based on the wheel-rail friction coupled finite element model, the equations of motion are calculated and solved to obtain the general solution: In the formula, x (t) represents the general solution at time t; These are the eigenvalues ​​of the general solution; The eigenvectors corresponding to the complex eigenvalues; Due to the system's mass matrix M r Damping matrix C r and stiffness matrix K Both are asymmetric, which makes it possible for the above general solution to be a complex number.

[0027] S33. Obtain the characteristic dominant frequency of rail corrugation based on the eigenvalues ​​of the general solution: When the eigenvalue of the general solution is a positive real part, it indicates that rail corrugation exists. omega i The characteristic frequency of rail corrugation at time t is represented.

[0028] The system's equivalent damping ratio ( xi ) is defined as xi i = ‒2 α i / omega i When complex eigenvalues When the real part is positive, the equivalent damping ratio is negative, and the system may be unstable. That is, under very small disturbances, the system may have increasingly large vibrations over time t , eventually leading to the generation and accumulation of rail corrugation. Finally, the system's unstable vibration frequency under the unstable vibration mode is extracted, which is the characteristic main frequency of the rail corrugation.

[0029] S4, based on the characteristic main frequency of the rail corrugation, combined with the resonance avoidance principle, to select the appropriate elastic strip for the track In engineering system design, the resonance avoidance principle is to adjust the natural frequency of the structure or the excitation frequency to avoid the resonance region, so as to avoid the amplification of the amplitude, fatigue damage or structural failure caused by resonance. The formula for the vibration transmissibility is T wherein f e is the excitation frequency, f n is the natural frequency of the system, and ζ is the damping ratio.

[0030] In the design selection, if the system components or structures are to achieve resonance avoidance conditions, it is usually required that , at this time T <1> to achieve vibration reduction of the system. If the structure of the designed system cannot meet the above avoidance conditions, as long as formula is met, the amplitude of the component can be significantly reduced to achieve the purpose of reducing structural damage and improving fatigue life.

[0031] Common fasteners include Cologne egg fasteners, elastic strip I, II, and III type fasteners, DTⅥ2 type fasteners, double-layer nonlinear vibration reduction fasteners, and pioneer fasteners. The types of elastic strips used by each type of fastener are different, and the modalities of the elastic strips are also different. The first five modalities of each type of elastic strip are measured and extracted based on modal experiments and finite element simulations, and a database is recorded and arranged. The main frequency is compared with the predicted main frequency of the rail corrugation, and the elastic strip suitable for a certain curve track section of the newly built subway line is quickly matched based on the resonance avoidance principle. As long as any one of the frequencies of the elastic strip meets the above requirements, the elastic strip can be considered to be well applied to the track and has a longer life and better stability.

[0032] Through the above method, a better elastic strip can be selected.

[0033] In particular, the above method of selecting the elastic strip is based on the selection before the track is in operation. After the track has been in operation for a period of time, the wheel-rail contact situation will inevitably change due to wear and tear, etc. Therefore, in this embodiment, S5 is also provided for selecting the elastic strip during the subsequent operation. ​

[0034] S5, after the track is put into operation, every interval, based on visual recognition technology, the wear of the track is obtained, and it is substituted into the dynamic simulation model of S1 and the wheel-rail friction coupling finite element model of S2 and updated, and the operation of S1-S4 is repeated to update the elastic strip suitable for the track.

[0035] For the wheel, when it is worn, it can be directly replaced, therefore, in the actual operation process, we ignore the wear of the wheel, and only consider the wear of the track.

[0036] In the embodiment, the laser vision line scanning system is used to obtain the cross section of the steel rail, the core of which is "single line laser-camera triangulation method" and is assisted by step scanning along the line direction. The system is composed of a line laser projector, an industrial camera, a calibration target and a synchronous trigger unit. The line laser projects a light plane perpendicular to the extension direction of the steel rail, and the camera optical axis forms an angle with the light plane When the light plane intersects with the cross section of the steel rail, a bright line is generated, and the imaging plane coordinates of the camera are The camera internal parameter matrix K and the camera external parameter matrix obtained through calibration are obtained, then the pixel coordinates are mapped to the camera coordinate system, and then the three-dimensional coordinates of the space point P( , x , y , z ) in the world coordinate system are obtained by the laser plane equation: n . Wherein d represents the unit normal vector of the laser plane, the superscript T represents the matrix transpose operator, represents the distance (intercept) from the laser plane to the origin.

[0037] B Let the normal distance from the camera optical center to the laser plane be the baseline f , the optical axis focal length be Delta x , and the parallax of point P on the imaging plane relative to the reference pixel column be z , then the depth coordinate can be given by the classical triangulation formula: y The lateral coordinate k can be calculated by the product of the pixel row offset and the proportionality coefficient x converted from the image pixel to the actual size, and the longitudinal coordinate s is determined based on the encoder displacement along the rail direction. The measurement accuracy of the system satisfies the following formula: wherein is the pixel positioning error, z represents the measurement error (depth direction resolution).

[0038] During the scanning process, the camera is triggered synchronously with the line laser and with a fixed step distance Delta S The continuous frames are collected, and a complete three-dimensional point cloud section sequence is reconstructed through inter-frame registration. Then, a Canny-Hough combined algorithm is used to extract the rail head profile curve, and a least square fitting is performed on the standard section template to obtain parameters such as vertical wear, side wear, total wear, 45° wear, and rail head tread wear of the rail, and the worn rail profile is fed back to the vehicle-track dynamics model and the wheel-rail system friction coupling finite element model in real time to realize online updating and closed-loop control of the wear geometry data.

[0039] Taking the north section of a newly-built subway line in a city as the research object, the line uses B-type metro vehicles, the design running speed is 80 km / h, the curve radius of part of the section is 350 m, and the track structure is ballastless track. According to the past construction experience and the reference of the fastening selection of similar subway lines, the newly-built line uses the WJ-8 fastening system, and the elastic strip selects the type II elastic strip.

[0040] Firstly, according to the method of the application, the geometric parameters of the curve section (including curve radius, track gauge, sleeper spacing, etc.) and the vehicle parameters (including axle load 14 t, wheel diameter 830 mm, bogie wheelbase 2.2 m) are obtained. Based on the above parameters, a rigid-flexible coupling dynamics model of the vehicle-track system is established, and the wheel-rail contact force is simulated and analyzed to obtain the dynamic contact characteristics of the wheel-rail under the operation of the curve section.

[0041] Subsequently, a wheel-rail system friction self-excited vibration model is constructed according to the initial design requirements and based on the dynamics simulation results, and the possible rail corrugation wavelength and frequency characteristics are predicted. The simulation results show that there is a short-wave corrugation risk with a main excitation frequency of about 335 Hz in the line section, and the amplitude has a growth trend within a few weeks, and the prediction results are shown in Figure 3 and Figure 4 , wherein, Figure 3 is the prediction result of the rail corrugation frequency of the subway curve track, Figure 4 is the prediction result of the unstable vibration mode of the wheel-rail system at the subway curve track.

[0042] The first five order modal frequencies of different elastic strip types are shown in Table 1. According to the predicted corrugation frequency characteristics, the second order modal frequency of the existing matching elastic strip (type II elastic strip) is 340 Hz, which is close to the predicted corrugation frequency of 335 Hz, and the difference is about 5 Hz, which is close to the difference between the first and second order modal frequencies of the type II elastic strip, and the difference between the first and second order modal frequencies of the type II elastic strip is about 10 Hz. f e - f n |≈1.5% f n, which does not meet the resonance avoidance requirement. There is a resonance risk with the corrugation frequency. According to the resonance avoidance principle of the application, a type I elastic strip with a modal frequency of 380 Hz is selected for replacement configuration. Calculation shows that the relative deviation of the second-order modal frequency of the elastic strip from the dominant frequency of the rail corrugation is 11.8%, which meets the minimum frequency separation requirement (≥10%) of resonance avoidance and can effectively suppress the resonance response under the excitation of rail corrugation.

[0043] Table 1: The first five order modal frequencies of type I elastic strips and type II elastic strips

[0044] After the replacement installation of part of the type II elastic strips, comparative analysis after 3 months of operation shows that the data indicates that the number of broken elastic strips of the newly selected type I elastic strips in the curve section is significantly reduced. Through the actual measurement of the rail vibration information of the curve track section, combined with the linear fatigue cumulative damage theory, the theoretical service life of the elastic strips in the region is calculated, and compared with the original WJ-8 type fastener type II elastic strips, the theoretical fatigue life of the type I elastic strips is increased by more than 45%.

[0045] The case verifies the effectiveness and applicability of the method of the application in the rapid selection of elastic strips in the actual subway line design.

[0046] In summary, the application combines the subway curve track operation environment and the formation mechanism of rail corrugation, and proposes a rapid matching method of subway elastic strips based on the friction self-excited vibration theory and resonance principle, aiming at the limitations of the traditional elastic strip selection method, such as relying on experience and being difficult to predict fatigue risk. By constructing a rigid-flexible coupling dynamics model of the vehicle-track system, combining wheel-rail friction coupling vibration and elastic strip modal analysis, an integrated analysis framework of “excitation-response-failure” is established to realize the prediction of elastic strip fatigue damage in the stage when rail corrugation has not yet formed. And based on the modal characteristics of the elastic strip, a resonance avoidance mechanism is constructed to complete the intelligent selection of the elastic strip type. In the method, visual recognition technology is also introduced to collect the rail wear and geometric state in real time, update the original dynamics simulation model in real time, and iteratively update the wheel-rail friction coupling model, predict the evolution result of the rail corrugation, and dynamically adjust the elastic strip type or the modal frequency of the elastic strip according to the corrugation excitation frequency. The method has the advantages of strong predictability, high adaptability and high matching efficiency, significantly reduces the fatigue fracture risk of the elastic strip in the curve track section, and improves the safety and reliability of the track system operation.

[0047] It is to be understood that other embodiments of the application will be readily apparent to those skilled in the art from the disclosure herein. It is the intent, therefore, to be limited only as apparent in the patent and patent documents, and in the application as filed and issued. It must be noted that, as used in the specification and the appended claims, the singular form "a", "an" and "the" include plural referents unless the context clearly dictates otherwise.

[0048] It is to be understood that the application is not limited to the precise construction already described above and shown in the drawings, and that various modifications and changes can be made by those skilled in the art without departing from the scope thereof. The true scope of the application is set forth in the claims.

Claims

1. A subway elastic bar matching method based on frictional self-excited vibration and resonance mechanism, characterized in that, include: S1. Based on the track design parameters and vehicle parameters, establish a rigid-flexible coupling dynamic simulation model of the vehicle-track system. Based on the dynamic simulation model, obtain the axle box suspension force, wheel-rail contact angle, and wheel-rail creep force. S2. Based on the axle box suspension force, wheel-rail contact angle, track design parameters and vehicle parameters, establish a wheel-rail friction coupling finite element model; S3. Based on the theory of frictional self-excited vibration and combined with the wheel-rail creep force, the wheel-rail friction coupling finite element model is used to predict rail corrugation and extract the characteristic main frequency of rail corrugation. S4. Based on the characteristic main frequency of rail corrugation and combined with the principle of resonance avoidance, select a spring clip suitable for the rail.

2. The subway elastic bar matching method based on frictional self-excited vibration and resonance mechanism according to claim 1, characterized in that, In S1, the track design parameters include superelevation, curve radius, gradient, and transition curve length; the vehicle parameters include the mass and moment of inertia of the car body, frame, and wheelsets, as well as the stiffness and damping of the suspension; the axle box suspension force includes the axle box lateral suspension force and the axle box vertical suspension force; and the wheel-rail contact angle includes the contact angle between the outer wheel and the high rail and the contact angle between the inner wheel and the low rail.

3. The subway elastic bar matching method based on frictional self-excited vibration and resonance mechanism according to claim 1, characterized in that, In S2, when establishing the wheel-rail friction coupling finite element model, spring-damped elements are used to simulate the spring bar.

4. The subway elastic bar matching method based on frictional self-excited vibration and resonance mechanism according to claim 1, characterized in that, In S3, the characteristic dominant frequency of rail corrugation is calculated using the following method: S31. Establish the system's equations of motion: In the formula, M r Represents the system's quality matrix; K r Represents the stiffness matrix of the system; C r Represents the damping matrix of the system; Represents the acceleration of a node; Indicates the speed of the node; x Represents the displacement of the node; f represents the coefficient of friction between the wheel and the rail; K t Indicates wheel-rail contact stiffness; S32. Based on the wheel-rail friction coupled finite element model, the equations of motion are calculated and solved to obtain the general solution: In the formula, x(t) represents the general solution at time t; These are the eigenvalues ​​of the general solution; The eigenvectors corresponding to the complex eigenvalues; S33. Obtain the characteristic dominant frequency of rail corrugation based on the eigenvalues ​​of the general solution: When the eigenvalue of the general solution is a positive real part, it indicates that rail corrugation exists. ω i The characteristic frequency of rail corrugation at time t is represented.

5. The subway elastic bar matching method based on frictional self-excited vibration and resonance mechanism according to claim 1, characterized in that, In S4, the method for selecting a suitable spring for this track is as follows: obtain the fixed frequency of the spring. f n Select a pop-up bar that satisfies any of the following formulas: ,or, In the formula, f e This indicates the characteristic frequency of rail corrugation.

6. The subway elastic bar matching method based on frictional self-excited vibration and resonance mechanism according to claim 1, characterized in that, After selecting a suitable spring bar for the track, the following steps are also included: S5. After the track is put into operation, at regular intervals, the wear amount of the track is obtained based on visual recognition technology, and it is substituted into the dynamic simulation model of S1 and the wheel-rail friction coupling finite element model of S2 and updated. Repeat the operation of S1~S4 to update the spring bar suitable for the track.

7. The subway elastic bar matching method based on frictional self-excited vibration and resonance mechanism according to claim 6, characterized in that, In the aforementioned visual recognition technology, a line laser projector, an industrial camera, a calibration board, and a synchronous triggering unit are used as recognition devices. Continuous frames are acquired with a fixed step distance, and a complete three-dimensional point cloud cross-sectional sequence is reconstructed through inter-frame registration. Subsequently, the Canny-Hough combined algorithm is used to extract the rail head contour curve, and least-squares fitting is performed with a standard cross-section template to obtain the wear amount of the rail.

8. The subway elastic bar matching method based on frictional self-excited vibration and resonance mechanism according to claim 6 or 7, characterized in that, The wear of the track includes vertical wear, lateral wear, 45° wear, rail head tread wear, and total wear.

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