Metro line steel rail corrugation formation mechanism analysis method

Abstract

An analysis method for a metro line steel rail corrugation forming mechanism comprises the steps that numerical model input parameters are obtained, and a wheel-rail three-dimensional coupling numerical model suitable for a vehicle-rail / wheel set of a metro line is constructed; longitudinal and transverse half width lengths of wheel-rail contact spots in the stable running process of the vehicle / wheel are obtained so as to determine a creep force-creep rate relation curve; determining a creep rate saturation critical value to judge the creep saturation state of the wheel-rail system; a macroscopic determination program for determining the structural stability of the wheel-rail system; determining an analysis process of a steel rail corrugation forming mechanism; judging whether the contact interface creep is saturated or not, and analyzing the probability of occurrence of rail corrugation according to the judgment; and determining a wavelength fixing method for rail corrugation in an actual measurement interval, and verifying the effectiveness and applicability of the method. According to the method, the steel rail corrugation phenomenon on a subway line is focused, the analysis method is provided from the two aspects of microcosmic creep saturation and macroscopic structure stability, and therefore the occurrence probability of steel rail corrugation is reflected more accurately.

Description

Technical Field

[0001] The invention relates to a method for analyzing the formation mechanism of rail corrugation, in particular to a method for analyzing the formation mechanism of rail corrugation on a subway line, and belongs to the technical field of rail transportation. Background Art

[0002] Rail corrugation is a frequent structural damage phenomenon in railway systems, manifesting as periodic, wave-like wear on the longitudinal running surface of the rail. Rail corrugation occurs at the wheel-rail interface and is closely related to wheel-rail dynamic interaction. Therefore, all factors related to the wheel-rail system serve as the starting point for rail corrugation research. Generally speaking, rail corrugation occurs most frequently in curved sections, especially on small-radius curves with a radius of less than 350 meters. While rail corrugation can also occur on straight lines, it is most concentrated on specific track structures (high-elasticity tracks), such as Cologne Egg fasteners, Vanguard fasteners, and steel spring floating slabs. Because subway lines pass through urban residential areas and have limited available space both above and below ground, they inevitably contain numerous small-radius curves, making them a particularly vulnerable area for rail corrugation. Rail corrugation can cause abnormal vibration and high-frequency noise in the vehicle / rail / wheel-rail system, damaging structural components and adversely affecting ride comfort and safety. How to prevent and control rail corrugation has always been an important research topic in the railway industry, and understanding the formation mechanism of rail corrugation is the primary prerequisite for achieving effective control of rail corrugation.

[0003] The industry has made considerable and substantial progress in the study of the mechanism and characteristics of rail corrugation, and the theoretical framework of rail corrugation is constantly being improved. However, the diversity and complexity of the wheel-rail / wheel-rail system lead to many uncertainties in the mechanism of rail corrugation. Therefore, further analysis is still necessary.

[0004] Wear and periodicity are the two main manifestations of rail corrugation. The probability of wear depends on whether the creep rate / force is saturated, while periodicity reflects the degree of instability in the wheel-rail system. Most existing studies analyze corrugation characteristics from either the perspective of interface creep or system stability, lacking a comprehensive consideration of both.

[0005] Related patent document: CN116561849A discloses a method for calculating the development and evolution of railway rail corrugation. A multi-body dynamics model and a frequency-domain three-dimensional vehicle-track dynamics model are established. The multi-body dynamics model is used to calculate the quasi-static wheel-rail forces, and the frequency-domain three-dimensional vehicle-track dynamics model calculates the dynamic wheel-rail lateral and vertical forces. Based on the simulation of the wheel-rail lateral and vertical forces, the rail roughness change caused by the wheel-rail dynamic interaction is obtained. The calculated roughness change is added to the initial roughness, and the final rail corrugation state is calculated in an iterative manner.

[0006] The above technologies do not solve the problem of how to accurately reflect the probability of occurrence of rail corrugation. Summary of the Invention

[0007] The object of the present invention is to provide a method for analyzing the formation mechanism of rail corrugation on a subway line, which can more accurately reflect the occurrence probability of rail corrugation.

[0008] In order to solve the above technical problems, the technical solutions adopted by the present invention are as follows:

[0009] A method for analyzing the corrugation formation mechanism of subway rails, the technical solution of which comprises the following steps:

[0010] S1. Obtaining numerical model input parameters and constructing a three-dimensional wheel-track coupling numerical model suitable for the vehicle-track / wheelset of the subway line;

[0011] S2. Obtaining the longitudinal half-width length a and the transverse half-width length b of the wheel / rail contact patch during stable vehicle / wheel operation to determine a creep force-creep rate relationship curve;

[0012] S3, according to the longitudinal creep rate saturation value (i.e. longitudinal saturation creep rate) ξ sx and the saturation value of the transverse creep rate (i.e., the transverse saturated creep rate) ξ sy , determine the creep rate saturation critical value to judge the creep saturation state of the wheel-rail system (wheel-rail contact);

[0013] S4. Under creep saturation conditions, use complex modal analysis methods to determine the macroscopic determination procedure of the wheel-rail system structural stability;

[0014] S5. Determine the analysis process of the rail corrugation formation mechanism by combining the microscopic determination procedure of creep rate saturation and the macroscopic determination procedure of wheel-rail system structural stability;

[0015] S6. Use multi-body dynamics methods to determine whether the contact interface creep is saturated and analyze the probability of rail corrugation based on this;

[0016] S7. Perform macroscopic characterization of the structural stability of the wheel-rail system, determine the wavelength fixation method of rail corrugation in the measured interval, and verify the effectiveness and applicability of the proposed method.

[0017] In the above technical solutions, a preferred technical solution may be that in step S1, the method for constructing the three-dimensional coupled numerical model is as follows:

[0018] S11. First, determine the numerical model input parameters based on the subway line and operation conditions, including track structure parameters, vehicle structure parameters, and operating conditions;

[0019] S12. Based on the model input parameters, use multi-body dynamics or finite element methods to construct a three-dimensional vehicle-track / wheelset (wheel)-track coupling numerical model suitable for the subway line, and verify the validity and accuracy of the model by combining measured data and / or precise contact algorithms (such as CONTACT).

[0020] In the above technical solution, the preferred technical solution can also be that in step S2, the method for determining the creep force-creep rate relationship curve is as follows: taking a and b as input parameters, writing the creep force-creep rate two-dimensional tangential contact algorithm, such as using CONTACT, FASTSIM and self-programmed tangential contact algorithm, to obtain the creep force-creep rate relationship curve.

[0021] In the above technical solution, a preferred technical solution may also be that in step S3, the creep rate saturation critical value is determined according to the following formula:

[0022]

[0023] Where F represents the macro creep force, F x Indicates the longitudinal creep force, F y represents the lateral creep force;

[0024] ξ represents the composite creep rate, x represents the longitudinal creep rate, ξ y represents the lateral creep rate;

[0025] The longitudinal saturated creep rate ξ is then extracted sx and the transverse saturation creep rate ξ sy , the creep rate saturation critical value ξ is determined by the following formula sc :

[0026] ξ sc =max(ξ sx ,ξ sy ).

[0027] In step S3, the method for determining the creep saturation state of the wheel-rail system is as follows:

[0028] The calculated creep rate saturation critical value ξ sc , can be used as a basis for judging the creep saturation state of the wheel-rail system. sc To a certain extent, the creep saturation limit is increased. Therefore, in general, when ξ>ξ sc When , it can be considered that the wheel-rail creep has reached saturation, and the microscopic determination procedure of the creep saturation state of the wheel-rail system (wheel-rail contact) from step S1 to step S3 is completed.

[0029] In the above technical solution, a preferred technical solution may also be that, in step S4, the method for determining the macroscopic determination procedure of the wheel-rail system structural stability is as follows: According to the negative damping theory, the damping parameter of the material has an important influence on the stability of the structure. Therefore, in this step, the damping effect of the structural material is taken into account, and a numerical method is used to determine the damping ratio of the structural vibration mode. The finite element software ABAQUS is used to perform complex modal analysis to obtain the equivalent damping ratio corresponding to different structural vibration modes, thereby determining whether the wheel-rail system has an unstable vibration mode.

[0030] In step S4, the macroscopic determination procedure of the wheel-rail system structural stability includes the following steps:

[0031] S41. First, determine the wheel-rail structural parameters, which do not include material damping, as input data for the numerical model. Use the finite element method to establish a three-dimensional wheel-rail coupling numerical model suitable for the subway line.

[0032] S42. Then, a complex modal analysis is performed using the numerical model to obtain the vibration mode, characteristic frequency, and equivalent damping ratio of the wheel-rail system without material damping;

[0033] S43. Determine the natural frequency ω of any two vibration modes i and ω j , determine the damping ratio ψ between any two vibration modes i and ψ j , and substitute it into the formula to calculate the modal mass proportional coefficient α0 and the modal stiffness proportional coefficient α1; the calculation formulas for α0 and α1 are as follows:

[0034]

[0035] Where: ω i and ω j represents the natural frequencies of any two vibration modes,

[0036] ψ i and ψ j represents the damping ratio of any two vibration modes,

[0037] α0 and α1 represent the modal mass proportional coefficient and modal stiffness proportional coefficient;

[0038] S44. Combining the structural parameter data in step S41 and step S43, using the finite element method, establish a numerical model including the material damping effect, and perform complex modal analysis to obtain the vibration mode, characteristic frequency, and equivalent damping ratio of the wheel-rail system under the condition of material damping;

[0039] S45. Finally, in the frequency range ω i ~ω j Inside, determine whether there is ψ m <0(i≤m≤j), if it exists, it means that the wheel-rail system will have a corresponding ψ m The unstable vibration mode will occur, otherwise it will not. At this point, the macroscopic determination procedure of the wheel-rail system structural stability is completed.

[0040] In the above technical solution, a preferred technical solution may also be that in step S5, the analysis process for determining the rail corrugation formation mechanism includes the following steps:

[0041] S51. First, it is necessary to determine whether the wheel-rail creep calculated by the numerical model has reached saturation using the analysis method - microscopic determination procedure. If it has not reached saturation, the system will not produce rail corrugation. If it has reached saturation, the system will produce uneven wear on the rail surface, which means that the damage mechanism for corrugation has been established.

[0042] S52. Then, according to the analysis method - macroscopic determination procedure, determine whether the wheel-rail system has unstable vibration modes; if not, the uneven wear has the possibility of evolving into rail corrugation, but additional conditions are required to satisfy the wavelength-fixed mechanism for the occurrence of rail corrugation, such as pits on the rail surface, uneven welding, etc.; if it does exist, the uneven wear will gradually evolve into rail corrugation at a specific frequency, that is, the wavelength-fixed mechanism for the occurrence of rail corrugation is already present on the basis of the damage mechanism.

[0043] In the above technical solution, a preferred technical solution may also be that, in step S6, analyzing the probability of occurrence of rail corrugation includes the following steps:

[0044] S61. The operating vehicle type of a certain subway line is a B-type subway car with an operating speed of 60 km / h. On-site measurements found that the rail corrugation in the line section is quite serious, with a corrugation wavelength of approximately 25 mm. According to calculations, the passing frequency of rail corrugation in the measured section is 666.7 Hz.

[0045] In step S61, the calculation formula for the passing frequency of rail corrugation is as follows:

[0046]

[0047] Where: f is the rail corrugation frequency, unit Hz; v is the vehicle speed, unit km / h;

[0048] λ is the wavelength of rail corrugation, in mm.

[0049] S62. Build a three-dimensional numerical model of subway vehicle-track coupling;

[0050] S63, perform time domain simulation on the numerical model in step S62 to obtain the longitudinal half-width length a and the transverse half-width length b, and use the established wheel-rail tangential contact algorithm to obtain the creep rate saturation critical value ξ sc ;

[0051] S64, by setting the creep rate saturation critical value ξ sc The creep rate is compared with the calculated one to analyze the possibility of corrugation occurring in the measured interval.

[0052] In the above technical solution, a preferred technical solution may also be that, in step S7, macroscopic characterization of the structural stability of the wheel-rail system includes the following steps:

[0053] S71. Since no surface defects significantly abnormal to rail corrugation were observed in the measured corrugation interval, the wavelength fixation mechanism of rail corrugation may be related to the structural properties of the wheel-rail system. Using the complex modal analysis method of step S4, determine the wavelength fixation method for rail corrugation in the measured interval from the perspective of wheel-rail system structural stability (exploring the wavelength fixation mechanism for rail corrugation in the measured interval from the perspective of wheel-rail system structural stability).

[0054] S72. Based on the track conditions in the corrugation section, use the finite element software ABAQUS to establish a three-dimensional solid model of the wheelset-floating plate small radius curve track;

[0055] S73. In the finite element model, the wheel-rail contact adopts the Coulomb friction function, the normal contact is hard contact, the tangential contact is described using the penalty function method, and the friction coefficient is set to 0.35; the wheel-rail contact position is determined based on the calculation result of step S62, that is, the corresponding working condition is set and simulated based on the three-dimensional coupled numerical model in step S62 to determine the wheel-rail contact position under this working condition;

[0056] S74. Perform a first complex modal analysis without material damping using the finite element model. Set the initial analysis frequency range to 20 to 1000 Hz. The calculation results show that the frequency and equivalent damping ratio of the first-order vibration mode are 39.625 Hz and 0.0247078, respectively. The frequency and equivalent damping ratio of the last-order vibration mode are 997.51 Hz and 0.00623595, respectively.

[0057] S75, let ω i =39.625,ω j =997.51,ψ i =0.0247078 and ψ j=0.00623595, and substituting into the analytical expressions of α0 and α1 in step S43, we can obtain α0=1.94153 and α1=0.00001;

[0058] S76. Input α0 and α1 as material damping parameters into the finite element model and perform complex modal analysis again. By extracting the equivalent damping ratio of the modal vibration mode, the calculated results show that there are two vibration modes with negative equivalent damping ratios, corresponding to frequencies of 665.90 Hz and 666.11 Hz, respectively.

[0059] S77. The frequencies corresponding to the two unstable vibration modes obtained from the complex modal analysis are 665.90 Hz and 666.11 Hz, which are similar to or identical to the passing frequencies of rail corrugation on the measured line. In addition, the unstable vibration modes both manifest as bending vibrations of the inner wheel relative to the track, which is consistent with the serious inner rail corrugation on the measured line. It also shows that the macroscopic determination procedure of the wheel-rail system structural stability is effective.

[0060] The beneficial effects of the present invention are as follows: (1) The present invention deepens the theoretical understanding of the corrugation formation mechanism. By constructing a three-dimensional coupled numerical model including vehicle-track / wheelset (wheel)-track and a three-dimensional coupled numerical model including wheel-rail, the present invention can systematically reveal the dynamic interaction between wheel and rail and the coupling influence mechanism of train operation parameters in the process of subway rail corrugation formation, providing a basis for the study of existing theories under complex subway working conditions; (2) Rail corrugation is one of the main sources of high-frequency vibration and wheel-rail noise in subway operation. The analysis method of the present invention clearly shows that the corrugation wavelength is related to the structural properties of the wheel-rail system, and a vibration reduction and noise reduction scheme (such as the use of elastic wheels and floating slab roadbed) can be designed in a targeted manner, thereby reducing the impact of vibration on the surrounding environment and improving passenger comfort; (3) By identifying the key cause of corrugation formation (structural instability vibration at a specific frequency of the wheel-rail system under microscopic creep saturation conditions), targeted measures can be formulated in advance, such as: adjusting the train speed to avoid the vibration-sensitive range; optimizing the track structural parameters (such as replacing high-damping fasteners) to suppress high-frequency vibration; and using rail surface treatment technology (such as grinding and coating) to reduce the wear rate. Compared to the traditional "after-the-fact repair" model, this method significantly reduces maintenance costs and train downtime. By integrating microscopic and macroscopic determination procedures, this method can derive the formation mechanism of measured corrugation, providing a basis for understanding rail corrugation caused by structural instability vibrations at specific frequencies in the wheel-rail system under microscopic creep saturation conditions.

[0061] In summary, this paper focuses on the rail corrugation phenomenon on subway lines and proposes a new analytical method suitable for explaining the formation mechanism of rail corrugation from the two aspects of microscopic creep saturation and macroscopic structural stability, thereby more accurately reflecting the probability of rail corrugation. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 The present invention is a flow chart (block diagram) of the method for analyzing the corrugation formation mechanism of subway rails.

[0063] Figure 2 This is a schematic diagram of a microscopic determination procedure for creep rate saturation in the analysis method for the corrugation formation mechanism of subway rails of the present invention.

[0064] Figure 3 Schematic diagram of contact spot shapes under different stick-slip distribution states calculated using the three-dimensional transient wheel-rail rolling contact finite element method in the analysis method of the subway line rail corrugation formation mechanism of the present invention. Figure 3 (a) is a schematic diagram of the contact spot shape in the stick-slip state. Figure 3 (b) is a schematic diagram of the contact spot shape in the slip state.

[0065] Figure 4 This is a schematic diagram of the macroscopic determination procedure of structural stability in the analysis method of the corrugation formation mechanism of subway rails of the present invention.

[0066] Figure 5 The figure is a flow chart of the method for analyzing the corrugation formation mechanism of subway rails according to the present invention.

[0067] Figure 6 This is a schematic diagram (on-site photo) of rail corrugation in the analysis method of the formation mechanism of subway line rail corrugation of the present invention. Figure 6 (a) is the overall picture of the corrugated rail. Figure 6 Middle (b) is a partial view of the corrugated rail.

[0068] Figure 7 This is a schematic diagram of the wheel-rail contact model in the analysis method of the corrugation formation mechanism of subway rails of the present invention.

[0069] Figure 8 This is a schematic diagram of a three-dimensional coupled numerical model of subway vehicles and tracks in the analysis method of the corrugation formation mechanism of subway rails of the present invention.

[0070] Figure 9 This is a schematic diagram of the a / b time history curve of the inner and outer wheel-rail contact spots when a vehicle stably passes through a circular curve section in the analysis method of the subway line rail corrugation formation mechanism of the present invention.

[0071] Figure 10 This is a schematic diagram of the creep force-creep rate curve corresponding to the inner wheel-rail contact in the analysis method of the corrugation formation mechanism of subway line rails of the present invention. Figure 10 (a) is a schematic diagram of the longitudinal creep force-creep rate curve corresponding to the inner wheel-rail contact (F x -ξ x curve graph), Figure 10(b) is a schematic diagram of the lateral creep force-creep rate curve corresponding to the inner wheel-rail contact (F y -ξ y curve graph).

[0072] Figure 11 This is a schematic diagram of the creep force-creep rate curve corresponding to the outer wheel-rail contact in the analysis method of the corrugation formation mechanism of subway line rails of the present invention. Figure 11 (a) is a schematic diagram of the longitudinal creep force-creep rate curve corresponding to the outer wheel-rail contact (F x -ξ x curve graph), Figure 11 (b) is a schematic diagram of the lateral creep force-creep rate curve corresponding to the outer wheel-rail contact (F y -ξ y curve graph).

[0073] Figure 12 This is a schematic diagram of the distribution of initial corrugation (i.e., uneven wear) on the entire line in the analysis method of the corrugation formation mechanism of subway rails of the present invention. Figure 12 (a) is the inner wheel-rail contact creep curve. Figure 12 Middle (b) is the outer wheel-rail contact creep curve.

[0074] Figure 13 This is a schematic diagram of a three-dimensional solid model of a wheelset-floating plate small-radius curved track in the analysis method of the corrugation formation mechanism of subway rails of the present invention. Figure 13 (a) is a stereogram of the three-dimensional solid model. Figure 13 (b) is a cross-sectional view (sectional view), the cutting plane passes through Figure 13 (a) The centerline of the axle of the middle wheelset is projected from front to back (equivalent to the front view).

[0075] Figure 14 This is a schematic diagram of the boundary mode vibration shape of the wheel-rail system analysis frequency in the analysis method of the subway line rail corrugation formation mechanism of the present invention. Figure 14 (a) is a schematic diagram of the vibration mode corresponding to the frequency of 39.625Hz (the deformation scaling factor is 1000). Figure 14 (b) is a schematic diagram of the vibration mode corresponding to a frequency of 997.51 Hz (the deformation scaling factor is 500).

[0076] Figure 15 This is a schematic diagram of the modal vibration shape of the wheel-rail system in the analysis method of the corrugation formation mechanism of subway line rails of the present invention. Figure 15 (a) is a schematic diagram of the vibration mode corresponding to the frequency of 665.90Hz (the deformation scaling factor is 100). Figure 15 (b) is a schematic diagram of the vibration mode corresponding to the frequency of 666.11 Hz (the deformation scaling factor is 100).

[0077] Figure 7 、 Figure 8 、 Figure 13 , the corresponding reference numerals of the various components are as follows: wheelset 1, left wheel 101, right wheel 102, left rail 2 (left rail is outer rail), right rail 3 (right rail is inner rail), rail substructure 4 (including roadbed 401 and floating plate 402), primary suspension 5, bogie 6, secondary suspension 7, car body 8, outer wheel-rail contact 9, inner wheel-rail contact 10, (ZX-2) fastener 11. DETAILED DESCRIPTION

[0078] To make the purpose, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. Based on the following embodiments, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0079] Example 1: Figure 1 、 Figure 2 、 Figure 3 、 Figure 4 、 Figure 5 、 Figure 6 、 Figure 7 、 Figure 8 、 Figure 9 、 Figure 10 、 Figure 11 、 Figure 12 、 Figure 13 、 Figure 14 、 Figure 15 As shown, the method for analyzing the formation mechanism of subway rail corrugation of the present invention includes the following steps:

[0080] S1. Acquire numerical model input parameters and construct a vehicle-track / wheelset (wheel)-track three-dimensional coupled numerical model suitable for the subway line. In step S1, the method for constructing the three-dimensional coupled numerical model is as follows:

[0081] S11. First, determine the numerical model input parameters based on the subway line and operation conditions, including track structure parameters, vehicle structure parameters, and operating conditions;

[0082] S12. Based on the model input parameters, use multi-body dynamics or finite element methods to construct a three-dimensional vehicle-track / wheelset (wheel)-track coupling numerical model suitable for the subway line, and verify the validity and accuracy of the model by combining measured data and / or precise contact algorithms (such as CONTACT).

[0083] S2. Obtain the longitudinal half-width length a and the transverse half-width length b of the wheel / rail contact patch during stable operation of the vehicle / wheel to determine the creep force-creep rate relationship curve. In step S2, the method for determining the creep force-creep rate relationship curve is as follows: a and b are used as input parameters, and a creep force-creep rate two-dimensional tangential contact algorithm is written, such as CONTACT, FASTSIM, and self-programmed tangential contact algorithm, to obtain the creep force-creep rate relationship curve. Specifically, the creep force-creep rate relationship curve includes the longitudinal creep force F x - Longitudinal creep rate ξ x Curvilinear and lateral creep forces F y - Transverse creep rate ξ y Curve, extract the creep rate saturation value, including the longitudinal creep rate ξ sx and lateral creep rate ξ sy , where F x and F y The macro creep force F can be further expressed as x and ξ y It can be further expressed as the composite creep rate ξ.

[0084] S3, according to the longitudinal creep rate saturation value ξ sx and the saturation value of the transverse creep rate ξ sy , determine the creep rate saturation critical value to judge the creep saturation state of the wheel-rail system (wheel-rail contact). In step S3, the creep rate saturation critical value is determined according to the following formula:

[0085]

[0086] Where F represents the macro creep force, F x Indicates the longitudinal creep force, F y represents the lateral creep force;

[0087] ξ represents the composite creep rate, x represents the longitudinal creep rate, ξ y represents the lateral creep rate;

[0088] The longitudinal saturated creep rate ξ is then extracted sx and the transverse saturation creep rate ξ sy , the creep rate saturation critical value ξ is determined by the following formula sc :

[0089] ξ sc =max(ξ sx ,ξ sy ) (2).

[0090] In step S3, the method for determining the creep saturation state of the wheel-rail system is as follows: Calculate the creep rate saturation critical value ξ sc, can be used as a basis for judging the creep saturation state of the wheel-rail system. sc To a certain extent, the creep saturation limit is increased. Therefore, in general, when ξ>ξ sc When , it can be considered that the wheel-rail creep has reached saturation, and the microscopic determination procedure of the creep saturation state of the wheel-rail system (wheel-rail contact) from step S1 to step S3 is completed.

[0091] The microscopic determination procedure of creep rate saturation shown in steps S1 to S3 is as follows: Figure 2 In addition, it should be noted that the above program uses the wheel-rail contact patch parameters a and b during stable vehicle / wheel operation. At this time, the contact patch may be in a stick-slip state or a sliding state, and the values ​​of a and b depend only on the matching type of the wheel-rail profile and the normal load distribution on the contact patch. Figure 3 The contact patch shapes calculated using the finite element method for three-dimensional transient wheel-rail rolling contact under different stick-slip distribution states are given. It can be seen that Figure 3 (a) and Figure 3 The contact patch shape parameters a and b shown in (b) are similar, both about 8.4 mm and 3.3 mm ( Figure 3 The unit size is 1×1 mm), but they correspond to the stick-slip state and slip state respectively, which further indicates that the contact patch shape parameters a and b have no direct correlation with the stick-slip distribution state of the wheel-rail contact.

[0092] S4. Under creep saturation conditions, a complex modal analysis method is used to determine the macroscopic determination procedure for the wheel-rail system structural stability. In step S4, the method for determining the macroscopic determination procedure for the wheel-rail system structural stability is as follows: According to negative damping theory, the damping parameter of the material has a significant impact on the stability of the structure. Therefore, in this step, the damping effect of the structural material is considered, and a numerical method is used to determine the damping ratio of the structural vibration mode. Complex modal analysis is performed using the finite element software ABAQUS to obtain the equivalent damping ratio corresponding to different structural vibration modes, thereby determining whether the wheel-rail system has unstable vibration modes.

[0093] In step S4, the macroscopic determination procedure of the wheel-rail system structural stability includes the following steps:

[0094] S41. First, determine the wheel-rail structural parameters, which do not include material damping, as input data for the numerical model. Use the finite element method to establish a three-dimensional wheel-rail coupling numerical model suitable for the subway line.

[0095] S42. Then, a complex modal analysis is performed using the numerical model to obtain the vibration mode, characteristic frequency, and equivalent damping ratio of the wheel-rail system without material damping;

[0096] S43. Determine the natural frequency ω of any two vibration modesi and ω j , determine the damping ratio ψ between any two vibration modes i and ψ j , and substitute it into the formula to calculate the modal mass proportional coefficient α0 and the modal stiffness proportional coefficient α1; the calculation formulas for α0 and α1 are as follows:

[0097]

[0098] Where: ω i and ω j represents the natural frequencies of any two vibration modes,

[0099] ψ i and ψ j represents the damping ratio of any two vibration modes,

[0100] α0 and α1 represent the modal mass proportional coefficient and modal stiffness proportional coefficient;

[0101] S44. Combining the structural parameter data in step S41 and step S43, using the finite element method, establish a numerical model including the material damping effect, and perform complex modal analysis to obtain the vibration mode, characteristic frequency, and equivalent damping ratio of the wheel-rail system under the condition of material damping;

[0102] S45. Finally, in the frequency range ω i ~ω j Inside, determine whether there is ψ m <0(i≤m≤j), if it exists, it means that the wheel-rail system will have a corresponding ψ m The unstable vibration mode will occur, otherwise it will not. At this point, the macroscopic determination procedure of the wheel-rail system structural stability is completed.

[0103] Specifically, in the above program, α0 and α1 calculated from the equivalent damping ratio in the case of no material damping are used as the model input data in the case of material damping, and the equivalent damping ratio of the structural vibration mode in the case of material damping is further obtained, so as to determine whether there is an unstable vibration mode in the structure based on the equivalent damping ratio. The above program can further accurately simulate the frequency characteristics of the system structure in the actual case of material damping on the basis of retaining the original system structure frequency characteristics in the case of no material damping, and is therefore closer to the actual case. In addition, it should be explained that the original wheel-rail system in the case of no material damping includes the damping effects of other components, such as primary suspension, fasteners and foundation support, etc. It is for this reason that the equivalent damping ratio of the system structure in the original case of no material damping is not 0.

[0104] The calculation formulas for α0 and α1 in step S43 are derived as follows:

[0105] Since S4 only considers the structural stability of the wheel-rail system under a specific contact state (creep saturation), and does not involve the friction effect before complex modal analysis, the theoretical basis is different from the friction self-excited vibration theory. At the same time, according to the negative damping theory, the damping parameters of the material have a significant impact on the stability of the structure. Therefore, the damping effect of the structural material is considered. Rayleigh damping is used to describe the damping effect of the material, which assumes that the damping matrix C of the structure is a combination of the mass matrix M and the stiffness matrix K, that is:

[0106] C=α0M+α1K (4)

[0107] Where α0 and α1 can be determined by the measured structural damping ratio, or by the given values ​​of the damping ratio of two vibration modes. To do this, this formula needs to be converted into a form expressed in terms of damping ratio. Multiply this formula by the transpose of the vibration mode. and right-multiplied vibration mode ζ n , we can get:

[0108] C n =α0M n +α1K n (5)

[0109] Where C n 、M n and K n are the damping coefficient, modal mass and modal stiffness of the nth-order vibration mode, respectively, and their expressions are:

[0110]

[0111] If it is assumed that the damping of the structural system satisfies the orthogonal condition and the mode superposition method is used to solve it, it is not necessary to construct the overall damping, and the mode damping ratio ψ can be directly used. n The damping ratio can be directly given in actual structural damping measurements. The purpose of constructing the overall damping matrix is ​​to use it for step-by-step integration analysis in the time domain. In this case, the damping matrix satisfies the orthogonality condition, that is, the purpose of using Rayleigh damping is to facilitate matrix construction and to determine the coefficients α0 and α1 using the orthogonality condition.

[0112] Formula C n =2ψ n ω n M n and Substituting into formula (4), we can get

[0113]

[0114] If the damping ratio ψ of any two vibration modes is given i and ψ j (natural frequency ω i and ωj Assuming ψ i and ψ j Given, the matrix for calculating α0 and α1 can be written as:

[0115]

[0116] According to formula (8), the analytical expressions of α0 and α1 are:

[0117] From formula (8), we can get that α0 and α1 are in ψ i and ψ j Determined under known conditions, however, in practice, ψ i and ψ j It also needs to be determined in advance based on the structural conditions.

[0118] Specifically, the methods commonly used to determine the structural vibration damping ratio are the half-power point method, the free vibration attenuation method, the resonance frequency method and the amplification coefficient method. These methods are all based on actual on-site measurements and have high requirements for the measurement point layout and measurement equipment.

[0119] Specifically, the damping ratio of the structural vibration mode is determined by numerical methods, and the equivalent damping ratio corresponding to different structural vibration modes is obtained by performing complex modal analysis using the finite element software ABAQUS. Figure 4 shown.

[0120] S5. Determine the analysis process of the rail corrugation formation mechanism by combining the microscopic determination procedure of creep rate saturation and the macroscopic determination procedure of wheel-rail system structural stability. In step S5, the analysis process of determining the rail corrugation formation mechanism includes the following steps:

[0121] S51. First, it is necessary to determine whether the wheel-rail creep calculated by the numerical model has reached saturation using the analysis method - microscopic determination procedure. If it has not reached saturation, the system will not produce rail corrugation. If it has reached saturation, the system will produce uneven wear on the rail surface, which means that the damage mechanism for corrugation has been established.

[0122] S52. Then, according to the analysis method - macroscopic determination procedure, determine whether the wheel-rail system has unstable vibration modes; if not, the uneven wear has the possibility of evolving into rail corrugation, but additional conditions are required to satisfy the wavelength-fixed mechanism for the occurrence of rail corrugation, such as pits on the rail surface, uneven welding, etc.; if it does exist, the uneven wear will gradually evolve into rail corrugation at a specific frequency, that is, the wavelength-fixed mechanism for the occurrence of rail corrugation is already present on the basis of the damage mechanism.

[0123] S6. Using multi-body dynamics methods, determine whether the creep of the contact interface is saturated and analyze the probability of rail corrugation based on this. In step S6, analyzing the probability of rail corrugation includes the following steps:

[0124] S61. The operating vehicle type of a certain subway line is a B-type subway car with an operating speed of 60 km / h. On-site measurements found that the rail corrugation in the line section is quite serious, with a corrugation wavelength of approximately 25 mm. According to calculations, the passing frequency of rail corrugation in the measured section is 666.7 Hz.

[0125] In step S61, the calculation formula for the passing frequency of rail corrugation is as follows:

[0126]

[0127] Where: f is the rail corrugation frequency, unit is Hz; v is the vehicle speed, unit is km / h; λ is the rail corrugation wavelength, unit is mm.

[0128] S62. Build a three-dimensional numerical model of subway vehicle-track coupling;

[0129] S63, perform time domain simulation on the numerical model in step S62 to obtain the longitudinal half-width length a and the transverse half-width length b, and use the established wheel-rail tangential contact algorithm to obtain the creep rate saturation critical value ξ sc ;

[0130] S64, by setting the creep rate saturation critical value ξ sc The creep rate is compared with the calculated one to analyze the possibility of corrugation occurring in the measured interval.

[0131] Specifically, in step S61, the measured corrugation section is located on a subway line with a small-radius curve, a curve radius of 350m, an outer rail superelevation of 95mm, a track gauge of 1435mm, and a CN60 rail type. The subrail structure consists of a steel spring floating plate, the upper portion of which is connected to the rail via ZX-2 fasteners 11, and the lower portion is directly connected to the trackbed. In this embodiment, the three-dimensional subway vehicle-track coupling numerical model in step S62 includes the following components: Vehicle Model: The vehicle model consists of a carbody 8, two bogies 6, and four wheelsets 1. The carbody 8, bogies 6, and wheelsets 1 are all considered rigid bodies. The carbody 8 and bogies 6, as well as the bogies 6 and wheelsets 1, are connected via spring-damper units to simulate the secondary suspension 7 and primary suspension 5. The entire vehicle model has a total of 42 degrees of freedom, meaning that the carbody 8, bogies 6, and wheelsets 1 each have six degrees of freedom.

[0132] Track model: The track model is set as a continuous elastic support model. The rails are simulated using Euler beams, and the fasteners are simulated using spring-damper units to connect the rails and the sub-rail structure.

[0133] Wheel-rail contact model: For the wheel-rail contact model, Hertz nonlinear elastic contact theory is used to solve the normal contact problem, where the wheel-rail normal force p(t) is defined as:

[0134]

[0135] Where: G is the wheel-rail contact constant, ΔZ(t) is the normal elastic compression on the contact patch, and t is time. The tangential contact problem is first solved using the FASTSIM algorithm based on Kalker creep theory, and then corrected using Shen's theory. The wheel-rail contact model can consider the situation where three different contact surfaces are in contact at the same time. The contact model diagram is shown in the figure below. Figure 7 As shown, where k yrt and k zrt represents the lateral and vertical stiffness of the fastener, c yrt and c zrt represents the lateral and vertical damping of the fastener, k nwr represents the wheel-rail normal contact stiffness, c i (i=1,2,3) represents the i-th wheel-rail contact spot;

[0136] The established three-dimensional coupling numerical model of subway vehicle and track is as follows: Figure 8 shown.

[0137] In this embodiment, after performing time domain simulation on the numerical model in step S63, the obtained results are analyzed as follows:

[0138] Since the guide wheelset plays a decisive role in the formation of rail corrugation, only the interaction between the inner and outer wheels of the front bogie guide wheelset of the vehicle and the rail is considered in step S63. By setting the model centerline path type and performing calculations, the a / b time history curves of the inner and outer wheel-rail contact patches when the vehicle stably passes through the circular curve section can be obtained, as shown in FIG. Figure 9 As shown, the circular curve line condition is consistent with the line condition measured in step S61, the vehicle speed is 60 km / h, and the wheel-rail contact static friction coefficient is 0.35;

[0139] Depend on Figure 9 It can be seen that when the vehicle is running stably in the circular curve section, the a / b ratio of the inner wheel-rail contact patch is approximately constant at 2.43, while the a / b ratio of the outer wheel-rail contact patch is approximately constant at 2.13. Furthermore, by inputting the above a / b data into the wheel-rail tangential contact algorithm, the corresponding creep force-creep rate curve can be obtained, as shown in Figure 2. Figure 10 、 Figure 11 shown.

[0140] Depend on Figure 10 、 Figure 11 It can be obtained that for a / b=2.13, ξxs and ξ ys are 6.26‰ and 10.50‰ respectively; for a / b=2.43, ξ xs and ξ ys are 6.27‰ and 10.50‰ respectively; therefore, according to formula (2), ξ sc Based on this, the time domain simulation of the circular curve section is performed again to obtain the distribution of initial corrugation (i.e. uneven wear) on the entire line, as shown in the following example: Figure 12 As shown. Figure 12 It can be seen that the initial corrugation occurs mainly in the inner and outer rail sections of a small-radius circular curve (due to the different wheel-rail contact geometries, the outer rail is more prone to side wear). This is consistent with the occurrence of rail corrugation on actual lines, indicating that the microscopic determination procedure for creep saturation of the wheel-rail contact proposed in this paper is feasible.

[0141] S7. Perform macroscopic characterization of the structural stability of the wheel-rail system, determine a method for fixing the wavelength of rail corrugation in the measured interval, and verify the effectiveness and applicability of the proposed method. In step S7, the macroscopic characterization of the structural stability of the wheel-rail system includes the following steps:

[0142] S71. Since no surface defects significantly abnormal to rail corrugation were observed in the measured corrugation interval, the wavelength fixation mechanism of rail corrugation may be related to the structural properties of the wheel-rail system. Using the complex modal analysis method of step S4, determine the wavelength fixation method for rail corrugation in the measured interval from the perspective of wheel-rail system structural stability (exploring the wavelength fixation mechanism for rail corrugation in the measured interval from the perspective of wheel-rail system structural stability).

[0143] S72. Based on the track conditions in the corrugation section, use the finite element software ABAQUS to establish a three-dimensional solid model of the wheelset-floating plate small radius curve track;

[0144] Specifically, the three-dimensional solid model of the wheelset-floating plate small radius curve track, such as Figure 13As shown, the model primarily consists of a wheelset 1, rails (left rail 2 and right rail 3), ZX-2 fasteners, a floating plate 402, steel spring isolators, and a trackbed 401. The fasteners connect the rails to the floating plate, while the spring isolators connect the floating plate to the trackbed. The finite element model shows a circular curve with a radius of 350m. The outer rail superelevation is set at 95mm based on the actual track, the track gauge is 1435mm, and the track length is 25m. The rails and trackbed run along the entire length of the model, while four floating plates, each 6m long, are arranged continuously along the track centerline. The wheel profile is LM wear type, and the rail profile is CN60. The spacing between fasteners is 0.6m, and the spacing between spring isolators is 1.2m. Grounding springs are evenly distributed at the bottom of the trackbed, connecting it to the foundation. All these connecting components are simulated using spring-damper elements, which account for stiffness and damping characteristics in three directions. The physical structures of all simulated components are discretized using C3D8R units. The grid size of the wheel-rail structure is uniformly set to 30 mm, and the grid size of the floating plate and trackbed structure is uniformly set to 100 mm. The entire model has a total of 208,212 units and 279,047 nodes.

[0145] S73. In the finite element model, the wheel-rail contact adopts the Coulomb friction function, the normal contact is hard contact, the tangential contact is described using the penalty function method, and the friction coefficient is set to 0.35; the wheel-rail contact position is determined based on the calculation result of step S62, that is, the corresponding working condition setting and simulation are performed based on the three-dimensional coupling numerical model in step S62 to determine the wheel-rail contact position under this working condition; specifically, the model boundary conditions are set as follows: the longitudinal end faces of the track structure are fixedly constrained, the transverse end faces of the floating plate and the trackbed plate are constrained for lateral displacement, and other surfaces and structures are free of any constraints.

[0146] S74. Use the above finite element model to perform the first complex modal analysis without material damping, setting the initial analysis frequency range to 20-1000 Hz. The calculation results show that the frequency and equivalent damping ratio of the first-order vibration mode are 39.625 Hz and 0.0247078, respectively, and the frequency and equivalent damping ratio of the last-order vibration mode are 997.51 Hz and 0.00623595, respectively. Specifically, the first-order and last-order vibration modes are as follows: Figure 14 shown.

[0147] S75, let ω i =39.625,ω j =997.51,ψ i =0.0247078 and ψ j =0.00623595, and substituting into the analytical expressions of α0 and α1 in step S43, we can obtain α0=1.94153 and α1=0.00001;

[0148] S76. Input α0 and α1 as material damping parameters into the finite element model and perform complex modal analysis again. By extracting the modal vibration mode equivalent damping ratio, the calculated results show that there are two vibration modes with negative equivalent damping ratios, corresponding to frequencies of 665.90 Hz and 666.11 Hz, respectively. Specifically, Figure 15 As shown in the figure, it is shown that at the above frequency, the wheel-rail system experiences unstable vibration. In addition, it is easy to see that the frequencies corresponding to the above two unstable vibration modes are very close, but the vibration modes are inconsistent, which means that the wheel-rail system is also prone to modal coupling at this frequency, which in turn leads to instability of the wheel-rail system.

[0149] S77. The frequencies corresponding to the two unstable vibration modes obtained from the complex modal analysis are 665.90 Hz and 666.11 Hz, which are similar to or identical to the passing frequencies of rail corrugation on the measured line. In addition, the unstable vibration modes both manifest as bending vibrations of the inner wheel relative to the track, which is consistent with the serious inner rail corrugation on the measured line. It also shows that the macroscopic determination procedure of the wheel-rail system structural stability is effective.

[0150] To facilitate understanding of the above-mentioned technical solution of the present invention, the following detailed description of the working principle or operation method of the present invention in actual practice is provided: In response to the widespread rail corrugation phenomenon on subway lines, the present invention proposes a new analytical method for explaining the corrugation mechanism from the perspectives of microscopic creep saturation and macroscopic structural stability. This method includes two modules: a microscopic determination procedure for wheel-rail system creep saturation and a macroscopic determination procedure for wheel-rail system structural stability. By applying this analytical method and combining it with actual subway corrugation cases, the formation mechanism of rail corrugation was studied and the effectiveness and applicability of the method were verified. The main conclusions are as follows:

[0151] The microscopic determination procedure for creep saturation in wheel-rail systems can effectively determine the degree of creep saturation. Generally speaking, when the composite creep rate is greater than the creep rate saturation critical value, wheel-rail creep reaches saturation;

[0152] The macroscopic determination procedure of the wheel-rail system structural stability can take into account the frequency domain characteristics of the system structure under material damping, and when the equivalent damping ratio is negative, the structural vibration mode is unstable.

[0153] The creep characteristics and structural stability analysis show that the occurrence range of initial corrugation, the frequency and location of unstable vibration mode are consistent with the actual corrugation situation, which shows that the analysis method is feasible.

[0154] According to the corrugation mechanism analysis method, it is found that the measured corrugation is caused by the structural instability vibration at a specific frequency of the wheel-rail system under the condition of micro creep saturation.

[0155] In summary, this paper focuses on the rail corrugation phenomenon on subway lines and proposes a new analytical method suitable for explaining the formation mechanism of rail corrugation from the two aspects of microscopic creep saturation and macroscopic structural stability, thereby more accurately reflecting the probability of rail corrugation.

Claims

1. A method for analyzing the formation mechanism of rail corrugation on subway lines, characterized in that: It includes the following steps: S1. Obtaining numerical model input parameters and constructing a three-dimensional wheel-track coupling numerical model suitable for the vehicle-track / wheelset of the subway line; S2. Obtaining the longitudinal half-width length a and the transverse half-width length b of the wheel / rail contact patch during stable vehicle / wheel operation to determine a creep force-creep rate relationship curve; S3, according to the longitudinal creep rate saturation value ξ sx and the saturation value of the transverse creep rate ξ sy , determine the creep rate saturation critical value to judge the creep saturation state of the wheel-rail system; S4. Under creep saturation conditions, use complex modal analysis methods to determine the macroscopic determination procedure of the wheel-rail system structural stability; S5. Determine the analysis process of the rail corrugation formation mechanism by combining the microscopic determination procedure of creep rate saturation and the macroscopic determination procedure of wheel-rail system structural stability; S6. Use multi-body dynamics methods to determine whether the contact interface creep is saturated and analyze the probability of rail corrugation based on this; S7. Perform macroscopic characterization of the structural stability of the wheel-rail system, determine the wavelength fixation method of rail corrugation in the measured interval, and verify the effectiveness and applicability of the proposed method.

2. The method for analyzing the corrugation formation mechanism of subway rails according to claim 1, characterized in that: In step S1, the method for constructing the three-dimensional coupled numerical model is as follows: S11. First, determine the numerical model input parameters based on the subway line and operation conditions, including track structure parameters, vehicle structure parameters and operation conditions; S12. Based on the model input parameters, use multi-body dynamics or finite element methods to construct a three-dimensional wheel-track coupling numerical model suitable for the vehicle-track / wheelset of the subway line, and verify the validity and accuracy of the model by combining measured data and / or precise contact algorithms.

3. The method for analyzing the corrugation formation mechanism of subway rails according to claim 1, characterized in that: In step S2, the method for determining the creep force-creep rate relationship curve is as follows: a and b are used as input parameters, a creep force-creep rate two-dimensional tangential contact algorithm is written, and CONTACT, FASTSIM and self-programmed tangential contact algorithm are used to obtain the creep force-creep rate relationship curve.

4. The method for analyzing the corrugation formation mechanism of subway rails according to claim 1, characterized in that: In step S3, the creep rate saturation critical value is determined according to the following formula: Where F represents the macro creep force, F x Indicates the longitudinal creep force, F y represents the lateral creep force; ξ represents the composite creep rate, x represents the longitudinal creep rate, ξ y represents the lateral creep rate; The longitudinal saturated creep rate ξ is then extracted sx and the transverse saturation creep rate ξ sy , the creep rate saturation critical value ξ is determined by the following formula sc : x sc =max(ξ sx ,x sy )。 5. The method for analyzing the corrugation formation mechanism of subway rails according to claim 4, characterized in that: In step S3, the method for determining the creep saturation state of the wheel-rail system is as follows: The calculated creep rate saturation critical value ξ sc , as the basis for judging the creep saturation state of the wheel-rail system, when ξ>ξ sc When , it is considered that the wheel-rail creep has reached saturation, and the microscopic determination procedure of the wheel-rail system creep saturation state from step S1 to step S3 is completed.

6. The method for analyzing the corrugation formation mechanism of subway rails according to claim 1, characterized in that: In step S4, the macroscopic determination procedure for determining the structural stability of the wheel-rail system is as follows: a numerical method is used to determine the damping ratio of the structural vibration mode, and a complex modal analysis is performed using the finite element software ABAQUS to obtain the equivalent damping ratio corresponding to different structural vibration modes, thereby determining whether the wheel-rail system has unstable vibration modes.

7. The method for analyzing the corrugation formation mechanism of subway rails according to claim 1, characterized in that: In step S4, the macroscopic determination procedure of the wheel-rail system structural stability includes the following steps: S41. First, determine the wheel-rail structural parameters, which do not include material damping, as input data for the numerical model. Use the finite element method to establish a three-dimensional wheel-rail coupling numerical model suitable for the subway line. S42. Then, a complex modal analysis is performed using the numerical model to obtain the vibration mode, characteristic frequency, and equivalent damping ratio of the wheel-rail system without material damping; S43. Determine the natural frequency ω of any two vibration modes i and ω j , determine the damping ratio ψ between any two vibration modes i and ψ j , and substitute it into the formula to calculate the modal mass proportional coefficient α0 and the modal stiffness proportional coefficient α1; the calculation formulas for α0 and α1 are as follows: S44. Combining the structural parameter data in step S41 and step S43, using the finite element method, establish a numerical model including the material damping effect, and perform complex modal analysis to obtain the vibration mode, characteristic frequency, and equivalent damping ratio of the wheel-rail system under the condition of material damping; S45. Finally, in the frequency range ω i ~ω j Inside, determine whether there is ψ m <0(i≤m≤j), if it exists, it means that the wheel-rail system will have a corresponding ψ m The unstable vibration mode will occur, otherwise it will not. At this point, the macroscopic determination procedure of the wheel-rail system structural stability is completed.

8. The method for analyzing the corrugation formation mechanism of subway rails according to claim 1, characterized in that: In step S5, the analysis process for determining the rail corrugation formation mechanism includes the following steps: S51. First, it is necessary to determine whether the wheel-rail creep calculated by the numerical model has reached saturation using the analysis method - microscopic determination procedure. If it has not reached saturation, the system will not produce rail corrugation. If it has reached saturation, the system will produce uneven wear on the rail surface, which means that the damage mechanism for corrugation has been established. S52. Then, according to the analysis method - macroscopic determination procedure, determine whether the wheel-rail system has unstable vibration modes; if not, the uneven wear has the possibility of evolving into rail corrugation, but additional conditions are required to satisfy the wavelength-fixed mechanism for the occurrence of rail corrugation, such as pits on the rail surface and uneven welding; if it does exist, the uneven wear will gradually evolve into rail corrugation at a specific frequency, that is, the wavelength-fixed mechanism for the occurrence of rail corrugation is already present on the basis of the damage mechanism.

9. The method for analyzing the corrugation formation mechanism of subway rails according to claim 1, characterized in that: In step S6, analyzing the probability of rail corrugation includes the following steps: S61. The operating vehicle type of a certain subway line is a B-type subway car with an operating speed of 60 km / h. The rail corrugation in the line section is quite serious, with a corrugation wavelength of about 25 mm. According to calculations, the passing frequency of rail corrugation in the measured section is 666.7 Hz. S62. Build a three-dimensional numerical model of subway vehicle-track coupling; S63, perform time domain simulation on the numerical model in step S62 to obtain the longitudinal half-width length a and the transverse half-width length b, and use the established wheel-rail tangential contact algorithm to obtain the creep rate saturation critical value ξ sc ; S64, by setting the creep rate saturation critical value ξ sc The creep rate is compared with the calculated one to analyze the possibility of corrugation occurring in the measured interval.

10. The method for analyzing the corrugation formation mechanism of subway rails according to claim 9, characterized in that: In step S61, the calculation formula for the passing frequency of rail corrugation is as follows: Where: f is the rail corrugation frequency, unit Hz; v is the vehicle speed, unit km / h; λ is the wavelength of rail corrugation, in mm.

11. The method for analyzing the corrugation formation mechanism of subway rails according to claim 9, characterized in that: In step S7, macroscopic characterization of the structural stability of the wheel-rail system includes the following steps: S71. Using the complex modal analysis method of step S4, determine a method for fixing the wavelength of rail corrugation in the measured section from the perspective of wheel-rail system structural stability; S72. Based on the track conditions in the corrugation section, use the finite element software ABAQUS to establish a three-dimensional solid model of the wheelset-floating plate small radius curve track; S73. In the finite element model, the wheel-rail contact adopts the Coulomb friction function, the normal contact is hard contact, the tangential contact is described using the penalty function method, and the friction coefficient is set to 0.35; the wheel-rail contact position is determined based on the calculation result of step S62, that is, the corresponding working condition is set and simulated based on the three-dimensional coupled numerical model in step S62 to determine the wheel-rail contact position under this working condition; S74. Perform a first complex modal analysis without material damping using the finite element model. Set the initial analysis frequency range to 20 to 1000 Hz. The calculation results show that the frequency and equivalent damping ratio of the first-order vibration mode are 39.625 Hz and 0.0247078, respectively. The frequency and equivalent damping ratio of the last-order vibration mode are 997.51 Hz and 0.00623595, respectively. S75, let ω i =39.625,ω j =997.51,ψ i =0.0247078 and ψ j =0.00623595, and substituting into the analytical expressions of α0 and α1 in step S43, we can obtain α0=1.94153 and α1=0.00001; S76. Input α0 and α1 as material damping parameters into the finite element model and perform complex modal analysis again. By extracting the equivalent damping ratio of the modal vibration mode, the calculated results show that there are two vibration modes with negative equivalent damping ratios, corresponding to frequencies of 665.90 Hz and 666.11 Hz, respectively. S77. The frequencies corresponding to the two-order unstable vibration modes obtained from the complex modal analysis are 665.90 Hz and 666.11 Hz, which are similar to or identical to the frequencies of rail corrugation on the measured line. In addition, the unstable vibration modes both manifest as bending vibrations of the inner wheel relative to the track, which is consistent with the inner rail corrugation on the measured line.

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