A method and system for suppressing rail corrugation based on speed regulation

Abstract

This invention discloses a method for suppressing rail corrugation based on speed regulation, comprising the following steps: acquiring the wheel speed of the train; inputting the wheel speed into a pre-constructed wheel-rail mathematical model, and calculating the wheel torsional vibration angular velocity through the wheel-rail mathematical model; continuously inputting the wheel torsional vibration angular velocity into a pre-constructed feedback control module, and performing extreme value judgment and feedback control through the feedback control module, specifically: finding the maximum and minimum values ​​of the wheel torsional vibration angular velocity within a preset time period, and judging whether the sum of the maximum and minimum values ​​is greater than a preset threshold; if so, outputting an instruction to control the wheel speed to decrease by a preset value to the train, so as to reduce the train corrugation; if not, continuing the extreme value judgment. This invention can effectively reduce corrugation.

Description

Technical Field

[0001] This invention relates to the field of wheel-rail system speed regulation, and more particularly to a method and system for suppressing rail corrugation based on speed regulation. Background Technology

[0002] Rail corrugation refers to the longitudinal, regular, uneven wear phenomenon on the top surface of rails, classified into two types based on wavelength: corrugated and wavy. Rail corrugation has long been a widespread problem, causing not only infrastructure damage but also increased maintenance costs. Higher train speeds result in greater dynamic loads on the track, accelerating corrugation. Current main methods for suppressing and eliminating rail corrugation include grinding, lubrication, adjusting fastener stiffness and damping, and adding vibration dampers. Additionally, researchers are also exploring ways to mitigate rail corrugation by controlling the angle of train speed.

[0003] Subway lines are mostly composed of sections operating under different conditions. Generally, subways maintain a constant speed across different sections, but for lines with lower support stiffness and damping, the speed should not be kept too high. Therefore, it is necessary to rationally control the speed for sections with different track conditions to reduce the occurrence of corrugation. Summary of the Invention

[0004] The main objective of this invention is to provide a rail corrugation suppression method and system based on speed regulation that can effectively reduce train corrugation.

[0005] The technical solution adopted in this invention is:

[0006] A method for suppressing rail corrugation based on speed regulation is provided, comprising the following steps:

[0007] Obtain the speed of the train wheels;

[0008] The wheel speed is input into a pre-built wheel-rail mathematical model, and the wheel torsional vibration angular velocity is calculated through the wheel-rail mathematical model.

[0009] The wheel torsional vibration angular velocity is continuously input into a pre-built feedback control module. The feedback control module performs extreme value judgment, specifically: find the maximum and minimum values ​​of the wheel torsional vibration angular velocity within a preset time, and determine whether the sum of the maximum and minimum values ​​is greater than a preset threshold. If so, output an instruction to control the wheel speed to decrease by a preset value to the train so as to reduce the train's rutting; if not, continue to perform extreme value judgment.

[0010] Based on the above technical solution, the wheel-rail mathematical model is expressed as follows:

[0011] The specific mathematical model for wheel-rail systems is as follows:

[0012]

[0013] In the formula, m w J w m r c1, c2, and c3 represent the mass of the wheel, the moment of inertia of the wheel axle, and the mass of the track, respectively; c1, c2, and c3 represent the damping of the primary suspension, the torsional damping of the wheel axle, and the damping of the fastener system, respectively; k1, k2, and k3 represent the stiffness of the primary suspension, the torsional stiffness of the wheel axle, and the stiffness of the fastener system, respectively. y w These represent the vertical vibration acceleration, vertical vibration velocity, and vertical displacement of the wheel, respectively. θ w These are the torsional vibration angular acceleration, torsional vibration angular velocity, and torsional vibration angular displacement of the wheel, respectively. y r Let F be the vertical vibration acceleration, vertical vibration velocity, and vertical displacement of the wheel, respectively; P0 is the static force on the wheel; F is the static force acting on the wheel. N F T These are the normal force and longitudinal creep force between the wheel and rail, respectively.

[0014] Following the above technical solution, wherein:

[0015]

[0016] In the formula, k H Let μ(ξ) be the contact stiffness between the wheel and rail, and μ(ξ) be the adhesion coefficient related to the longitudinal adhesion ratio in the wheel-rail rolling contact, expressed as:

[0017]

[0018] Where, μ K (ξ) is the relative friction characteristic defined by Kraft, expressed as:

[0019]

[0020] Where μ0 is the static friction coefficient μ0; ξ' is the standardized longitudinal creep parameter.

[0021] Following the above technical solution, ξ' is represented as:

[0022]

[0023] In the formula, G is the elastic modulus of the wheelset material, G=E / 2(1+υ), and υ is Poisson's ratio; C 11 Longitudinal creep coefficient, a constant listed according to Kalker linear theory; a, b Hertz contact ellipse semi-major axis lengths in the rolling and lateral directions.

[0024] Following the above technical solution, the values ​​of a and b are calculated using a direct method to determine the wheel-rail contact ellipse, by introducing the following parameters:

[0025]

[0026] In the formula, r is the nominal rolling radius of the wheel, r w r is the radius of the cross-sectional shape of the wheel tread. t ρ is the radius of the cross-sectional shape of the rail top, and ρ represents the curvature of the wheel-rail contact ellipse.

[0027] The intermediate variable a is obtained from the parameter ρ / r. e b e This allows us to determine the semi-major axis of the contact ellipse.

[0028]

[0029] When ρ / r≤2

[0030]

[0031] When ρ / r>2

[0032]

[0033] In the formula m h and n h This is expressed as the coefficient related to the β angle, determined by the following formula in Hertzian theory:

[0034]

[0035] Following the above technical solution, in the process of continuously judging extreme values, the maximum and minimum values ​​are iteratively updated and stored each time.

[0036] Following the above technical solution, during the extreme value judgment process, three adjacent values ​​in continuous sampling are compared. If the extreme value condition is met, it is output; otherwise, 0 is output. After finding the results of the changes of the maximum and minimum values ​​over time, the results are imported into the extreme value memory. If the extreme value is not 0, the value replaces the previous extreme value and is stored. If the input data is 0, the previously stored extreme value is used.

[0037] Following the above technical solution, the train is in an unstable operating phase for an initial period of time, and the obtained wheel speeds of the train are not used for extreme value judgment.

[0038] The present invention also provides a rail corrugation suppression system based on speed regulation, comprising:

[0039] The data acquisition module is used to acquire the wheel speed of the train;

[0040] The wheel torsional vibration angular velocity calculation module is used to input the wheel velocity into a pre-built wheel-rail mathematical model and calculate the wheel torsional vibration angular velocity through the wheel-rail mathematical model.

[0041] The feedback control module is used to continuously input the wheel torsional vibration angular velocity into a pre-built feedback control module. The feedback control module performs extreme value judgment and feedback control. Specifically, it finds the maximum and minimum values ​​of the wheel torsional vibration angular velocity within a preset time period, and judges whether the sum of the maximum and minimum values ​​is greater than a preset threshold. If so, it outputs a command to control the wheel speed to decrease by a preset value to the train to reduce the train's rutting. If not, it continues to perform extreme value judgment and feedback control.

[0042] Based on the above technical solution, the wheel-rail mathematical model is expressed as follows:

[0043] The specific mathematical model for wheel-rail systems is as follows:

[0044]

[0045] In the formula, m w J w m r c1, c2, and c3 represent the mass of the wheel, the moment of inertia of the wheel axle, and the mass of the track, respectively; c1, c2, and c3 represent the damping of the primary suspension, the torsional damping of the wheel axle, and the damping of the fastener system, respectively; k1, k2, and k3 represent the stiffness of the primary suspension, the torsional stiffness of the wheel axle, and the stiffness of the fastener system, respectively. y w These represent the vertical vibration acceleration, vertical vibration velocity, and vertical displacement of the wheel, respectively. θ w These are the torsional vibration angular acceleration, torsional vibration angular velocity, and torsional vibration angular displacement of the wheel, respectively. y r Let F be the vertical vibration acceleration, vertical vibration velocity, and vertical displacement of the wheel, respectively; P0 is the static force on the wheel; F is the static force acting on the wheel. N F T These are the normal force and longitudinal creep force between the wheel and rail, respectively.

[0046] The present invention also provides a computer storage medium storing a computer program executable by a processor, the computer program executing the rail corrugation suppression method based on speed regulation as described in any of the above technical solutions.

[0047] The beneficial effects of this invention are as follows: This invention constructs a wheel-rail mathematical model based on rail corrugation caused by frictional self-excited torsional vibration. Using this model, the torsional vibration angular velocity of the wheel is calculated, and the maximum and minimum values ​​of the inner wheel torsional vibration angular velocity are continuously found. The two extreme values ​​are summed. If the sum is greater than a preset value, the wheel speed is controlled to decrease. Thus, by adjusting the wheel speed, the longitudinal creep force is controlled, thereby controlling the magnitude of the torsional vibration and effectively reducing corrugation.

[0048] Furthermore, the constructed wheel-rail mathematical model involves the wheel, track, and fastener system, and includes the nonlinear relationship between longitudinal creep and adhesion ratio. Parameters such as vertical damping and stiffness obtained from field investigations are also imported into the mathematical model to simulate different road conditions in subway lines, making the calculated wheel torsional vibration angular velocity more accurate.

[0049] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 This describes the contact mechanism of the wheelset on the curved track in an embodiment of the present invention.

[0052] Figure 2 This is a schematic diagram showing the interaction relationships between various structures in the wheel-rail system according to an embodiment of the present invention;

[0053] Figure 3 This is a schematic diagram of the Simulink model (including the wheel-rail mathematical model and the feedback control module) of an embodiment of the present invention;

[0054] Figure 4A This is a flowchart of the rail corrugation suppression method based on speed regulation according to an embodiment of the present invention;

[0055] Figure 4B yes Figure 4A The detailed flowchart of step S3;

[0056] Figure 5 This is a schematic diagram of the feedback control module in an embodiment of the present invention;

[0057] Figure 6 This is a schematic diagram of the extreme value memory according to an embodiment of the present invention. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0059] It should be noted that the illustrations provided in the embodiments of the present invention are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0060] In this invention, it should also be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application. Furthermore, the terms "first" and "second" are used only for descriptive and distinguishing purposes and should not be construed as indicating or implying relative importance.

[0061] When a train wheelset travels on a curved track, the outer wheel tends to roll steadily on the outer rail, while the inner wheel tends to slip, inducing torsional vibrations. For example... Figure 1 As shown, the inner track radius is R1, which is smaller than the outer track radius R2. After the wheelset has been running on the curved track for a certain period of time, since the inner and outer wheels are connected by the axle, the rolling distances of corresponding points on the inner and outer wheel treads are equal. However, the running distance L2 of the outer wheel on the outer track is greater than the running distance L1 of the inner wheel on the inner track. Assuming that the rolling distance of the outer wheel is equal to the running distance of the outer wheel on the outer track, that is, the outer wheel rolls stably on the outer track, then the inner wheel needs to produce slight slippage on the inner track surface to compensate for the difference in running distances between the inner and outer wheels on the track surface (ΔL = L2 - L1). Therefore, when the wheelset enters the curved track, the axle connecting the wheelset will undergo elastic deformation. Once this deformation exceeds a critical value, it will trigger frictional self-excited torsional vibration of the wheelset, leading to wear on the track surface.

[0062] To address the aforementioned corrugation phenomenon, this invention mitigates its occurrence by adjusting train speed. The principle behind this method is as follows: When a train travels at high speed over a curved track, the inner wheel experiences torsional vibration. Due to the longitudinal creep force, the maximum torsional vibration angular velocity amplitude in the positive direction is greater than that in the negative direction. This is because when the longitudinal creep force and the inner wheel's torsional vibration angular velocity are in the same direction, the longitudinal creep force inputs energy into the inner wheel's torsional vibration system, exacerbating the amplitude of the torsional vibration. Conversely, when the longitudinal creep force and the inner wheel's torsional vibration angular velocity are in opposite directions, the longitudinal creep force dissipates energy from the inner wheel's torsional vibration system, thereby reducing the amplitude of the torsional vibration. Mathematical models show that both the longitudinal creep force and relative speed are speed-dependent; therefore, adjusting the speed can control the longitudinal creep force, thereby controlling the magnitude of the torsional vibration and mitigating corrugation.

[0063] like Figure 4A As shown, the rail corrugation suppression method based on speed regulation in this embodiment of the invention includes the following steps:

[0064] S1, Obtain the train's wheel speed;

[0065] S2. Input the wheel speed into the pre-built wheel-rail mathematical model, and calculate the wheel torsional vibration angular velocity through the wheel-rail mathematical model;

[0066] S3. The wheel torsional vibration angular velocity is continuously input into the pre-built feedback control module, and the extreme value is judged and feedback control is performed through the feedback control module.

[0067] like Figure 4B As shown, step S3 specifically involves:

[0068] S31. Find the maximum and minimum values ​​of the wheel torsional vibration angular velocity within a preset time.

[0069] S32. Determine whether the sum of the maximum and minimum values ​​is greater than a preset threshold. If yes, proceed to step S33; otherwise, return to step S31 to continue the extreme value judgment within the next preset time period.

[0070] S33: Output a command to the train to reduce the wheel speed by a preset value, so as to reduce the train's rutting.

[0071] This invention constructs a wheel-rail mathematical model based on the principle of rail corrugation caused by frictional self-excited torsional vibration. This wheel-rail mathematical model includes the mechanical relationship between the wheel, rail and fastener system, and also includes the nonlinear relationship between longitudinal creep and adhesion ratio.

[0072] according to Figure 2 The kinematic relationships of the various structures in the wheel-rail system shown can be used to establish a wheel-rail mathematical model of the wheel, rail, and fastener system, which can be expressed as:

[0073]

[0074] In the formula, m w J w m r c1, c2, and c3 represent the mass of the wheel, the moment of inertia of the wheel axle, and the mass of the track, respectively; c1, c2, and c3 represent the damping of the primary suspension, the torsional damping of the wheel axle, and the damping of the fastener system, respectively; k1, k2, and k3 represent the stiffness of the primary suspension, the torsional stiffness of the wheel axle, and the stiffness of the fastener system, respectively. y w These represent the vertical vibration acceleration, vertical vibration velocity, and vertical displacement of the wheel, respectively. θ w These are the torsional vibration angular acceleration, torsional vibration angular velocity, and torsional vibration angular displacement of the wheel, respectively. y r F represents the vertical vibration acceleration, vertical vibration velocity, and vertical displacement of the wheel, respectively; P0 represents the static force acting on the wheel. N F T These are the normal force and longitudinal creep force between the wheel and rail, respectively, and can be expressed as:

[0075]

[0076] In the formula, k H Let μ(ξ) be the contact stiffness between the wheel and rail, and μ(ξ) be the adhesion coefficient related to the longitudinal adhesion ratio in the wheel-rail rolling contact, which can be expressed as:

[0077]

[0078] Where μ K (ξ) is the relative friction characteristic defined by Kraft, and can be expressed as:

[0079]

[0080] The static friction coefficient μ0 is 0.45. ξ' is a normalized longitudinal creep parameter proposed by Vermeulen and Johnson, which can be expressed as:

[0081]

[0082] In the formula, G is the elastic modulus of the wheelset material, G=E / 2(1+υ), and υ is Poisson's ratio; C 11 The longitudinal creep coefficient is a constant listed according to Kalker's linear theory; the semi-major axis lengths of the Hertz contact ellipse in the rolling and lateral directions are a and b. The values ​​of a and b can be calculated using a direct method for determining the wheel-rail contact ellipse.

[0083] By introducing parameters:

[0084]

[0085] In the formula, r is the nominal rolling radius of the wheel, r w r is the radius of the cross-sectional shape of the wheel tread. t Let ρ be the radius of the cross-sectional shape of the rail top, and ρ represent the curvature of the wheel-rail contact ellipse.

[0086] Then, the intermediate variable a can be obtained based on the parameter ρ / r. e b e This allows us to determine the semi-major axis of the contact ellipse:

[0087]

[0088] When ρ / r≤2

[0089]

[0090] When ρ / r>2

[0091]

[0092] In the formula m h and n h This is expressed as the coefficient related to the β angle, determined by the following formula in Hertzian theory:

[0093]

[0094] m corresponding to a typical β angle h and n h The values ​​are shown in Table 1 below.

[0095] Table 1. β angle and m h and n h Corresponding parameter values

[0096]

[0097] The parameters ρ / r and intermediate variable a were established based on the above relationship. e b e With a one-to-one correspondence, as long as the value of ρ / r is obtained, the shape and size of the wheel-rail contact elliptical contact spot can be obtained.

[0098] In the above formula, the Kalker coefficient C 11 It depends entirely on the ratio of the major and minor semi-axes of the wheel-rail contact ellipse, a / b, and the Poisson's ratio, υ, and can be obtained by linear interpolation according to Table 2 below.

[0099] Table 2 shows the relationship between C11 and a / b parameter values.

[0100]

[0101] like Figure 1 As shown, V0 is the rolling speed of the wheel, then the longitudinal sliding speed of the inner wheel is... It can be represented as:

[0102]

[0103] In the formula, D is the track gauge, R1 is the radius of the inner rail, and R2 is the radius of the outer rail.

[0104] Also in Figure 1 In the middle, the speed of the wheel's torsional vibration is Therefore, the longitudinal vibration velocity at the wheel-rail contact point can be expressed as: Therefore, the longitudinal creep at the wheel-rail contact point can be expressed as:

[0105]

[0106] The torsional stiffness k2 of the wheel axle reflects the material's resistance to torsional deformation and can be expressed as:

[0107]

[0108] In the formula, G is the polar moment of inertia of the axle cross section, L is the torsional length of the axle, and I... p Let be the polar moment of inertia of the axle cross section. Since the axle is a solid axle, its polar moment of inertia can be expressed as:

[0109]

[0110] In the formula, d is the diameter of the axle.

[0111] In one embodiment of the present invention, a wheel-track mathematical model consisting of equations (1)-(14) is established using the Simulink module in MATLAB software, and a feedback control module is constructed. The two models can form a Simulink model, such as... Figure 3 As shown, the wheel-rail mathematical model uses wheel speed as input and wheel torsional vibration angular velocity as output. A feedback control module can be established through the function module. The time-domain result of the output wheel torsional vibration angular velocity is imported into the feedback control module as input, and the adjusted wheel speed is then used as output and re-input into the wheel-rail mathematical model to achieve feedback control adjustment.

[0112] Furthermore, methods for implementing feedback control include: establishing a feedback control module such as... Figure 5 As shown, this feedback control module mainly consists of three parts: an extreme value searcher, an extreme value memory, and a speed regulator. Figure 5As shown, the Memory module is used to record the torsional vibration angular velocity of the previous moment. The extremum searcher processes the wheel torsional vibration angular velocity calculated by the mathematical model numerically. First, it compares three adjacent values ​​in continuous sampling. If the extremum condition is met, it is output; otherwise, 0 is output, as shown in the following code:

[0113]

[0114] This is a MATLAB function that accepts three input arguments 'w', 'w_sub1', and 'w_sub2', and returns two values ​​'big_value' and 'small_value'. The main purpose of this function is to compare the three arguments and assign the values ​​that meet certain conditions to 'big_value' and 'small_value'. First, 'big_value' and 'small_value' are initialized to 0. If 'w' is less than 'w_sub1' and 'w_sub1' is greater than 'w_sub2', then the value of 'w_sub1' is assigned to 'big_value'. 'big_value' represents the found maximum value, and similarly, 'small_value' represents the found minimum value.

[0115] The extremum searcher finds the results of how the maxima and minima change over time and imports them into the extremum memory. The extremum memory mainly consists of two function modules, such as... Figure 6 As shown.

[0116] The specific code is shown below. If the searched extreme value is not 0, then the value will replace the previously searched extreme value and be stored in the Memory module. If no extreme value is found, that is, the data passed in is 0, then the extreme value stored in the Memory module will be used.

[0117] (a) Maximum value memory code;

[0118]

[0119] This MATLAB code defines a function 'fcn' that accepts two input parameters, 'zero0Rbig_value' and 'big_value_sub1'. 'zero0Rbig_value' is the output of the extreme value searcher, which is not necessarily a maximum value. It then returns a value 'big_value'. If the value of 'zero0Rbig_value' is equal to 0, then the value of 'big_value' will be set to 'big_value_sub1'. If the value of 'zero0Rbig_value' is not equal to 0, then the value of 'big_value' will be set to 'zero0Rbig_value'.

[0120] (b) Minimum memory code

[0121]

[0122] This MATLAB code defines a function 'fcn' that accepts two input parameters, 'zero0Rsmall_value' and 'small_value_sub1'. 'zero0Rsmall_value' is the output of the extreme value searcher, which is not necessarily a minimum value. It then returns a value 'small_value'. If the value of 'zero0Rsmall_value' is equal to 0, then the value of 'small_value' will be set to 'small_value_sub1'. If the value of 'zero0Rsmall_value' is not equal to 0, then the value of 'small_value' will be set to 'zero0Rsmall_value'.

[0123] The obtained maximum and minimum values ​​are then input into the speed regulator module, as shown in the following code:

[0124]

[0125] This MATLAB code defines a function 'fcn' that accepts four input parameters: 'big_value', 'small_value', 'T', and 'V0_sun1', and returns a value 'V0'. If 'T' is greater than 0.2, it first checks if the sum of the maximum and minimum values ​​is greater than 0.03. If it is, it reduces the value of V0 by 0.05; otherwise, it keeps the original value of V0.

[0126] The minimum and maximum values ​​can be processed after the system has been running for a period of time (e.g., at least 0.2 seconds). This is because before this initial period, the system is in an unstable operating phase, with the wheel torsional vibration angular velocity amplitude fluctuating irregularly, which will affect the search for the minimum and maximum values, and consequently, the subsequent feedback adjustment. The speed regulator first adds the minimum and maximum values ​​and checks if the result is less than a preset threshold (e.g., 0.03 rad / s, which can be set according to specific circumstances). If the result is greater than the preset threshold, the wheel speed is reduced by a preset value (e.g., 0.05 m / s, which can be set according to specific circumstances), and feedback adjustment is repeated until the sum of the output minimum and maximum values ​​is less than the preset threshold.

[0127] Furthermore, subway staff can conduct on-site measurements and calculations on the corrugated section to obtain the data listed in Table 3 below, and then import the data into the Simulink model. By controlling the speed parameters, the sum of the maximum and minimum amplitudes of the inner wheel torsional vibration angular velocity is not greater than a preset threshold, thereby achieving the purpose of mitigating corrugation.

[0128] Table 3. Relevant parameters of the mathematical model for friction-induced torsional vibration.

[0129]

[0130]

[0131] The present invention also provides a rail corrugation suppression system based on speed regulation, comprising:

[0132] The data acquisition module is used to acquire the wheel speed of the train;

[0133] The wheel torsional vibration angular velocity calculation module is used to input the wheel velocity into a pre-built wheel-rail mathematical model and calculate the wheel torsional vibration angular velocity through the wheel-rail mathematical model.

[0134] The feedback control module is used to continuously input the wheel torsional vibration angular velocity into the pre-built feedback control module. The feedback control module performs extreme value judgment, specifically: find the maximum and minimum values ​​of the wheel torsional vibration angular velocity within a preset time, and determine whether the sum of the maximum and minimum values ​​is greater than a preset threshold. If so, output an instruction to control the wheel speed to decrease by a preset value to the train to reduce the train's rutting; if not, continue to perform extreme value judgment.

[0135] The wheel-rail mathematical model can be represented as:

[0136] The specific mathematical model for wheel-rail systems is as follows:

[0137]

[0138] In the formula, m w J w m r c1, c2, and c3 represent the mass of the wheel, the moment of inertia of the wheel axle, and the mass of the track, respectively; c1, c2, and c3 represent the damping of the primary suspension, the torsional damping of the wheel axle, and the damping of the fastener system, respectively; k1, k2, and k3 represent the stiffness of the primary suspension, the torsional stiffness of the wheel axle, and the stiffness of the fastener system, respectively. y w These represent the vertical vibration acceleration, vertical vibration velocity, and vertical displacement of the wheel, respectively. θ w These are the torsional vibration angular acceleration, torsional vibration angular velocity, and torsional vibration angular displacement of the wheel, respectively. y r Let F be the vertical vibration acceleration, vertical vibration velocity, and vertical displacement of the wheel, respectively; P0 is the static force on the wheel; F is the static force acting on the wheel. N F T These are the normal force and longitudinal creep force between the wheel and rail, respectively.

[0139] Each module is mainly used to implement the steps of the method embodiment, which will not be elaborated here.

[0140] This application also provides a computer-readable storage medium, such as flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, disk, optical disk, server, app store, etc., which stores a computer program. When the program is executed by a processor, it implements a corresponding function. In this embodiment, the computer-readable storage medium, when executed by a processor, implements the speed-adjustment-based rail corrugation suppression method of the method embodiment.

[0141] It should be noted that, depending on the implementation needs, the various steps / components described in this application can be broken down into more steps / components, or two or more steps / components or parts of the operation of steps / components can be combined into new steps / components to achieve the purpose of this invention.

[0142] The order of the steps in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0143] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A method for suppressing rail corrugation based on speed regulation, characterized in that, Includes the following steps: Obtain the speed of the train wheels; The wheel speed is input into a pre-built wheel-rail mathematical model, and the wheel torsional vibration angular velocity is calculated through the wheel-rail mathematical model. The wheel torsional vibration angular velocity is continuously input into a pre-built feedback control module. This module performs extreme value judgment and feedback control. Specifically, it finds the maximum and minimum values ​​of the wheel torsional vibration angular velocity within a preset time period, and determines whether the sum of the maximum and minimum values ​​is greater than a preset threshold. If so, it outputs a command to control the wheel speed to decrease by a preset value to the train to reduce train rutting. If not, it continues to perform extreme value judgment and feedback control.

2. The rail corrugation suppression method based on speed regulation according to claim 1, characterized in that, The wheel-rail mathematical model is expressed as: The specific mathematical model for wheel-rail systems is as follows: (1) In the formula, m w , J w ，m r These are the mass of the wheel, the moment of inertia of the wheel axle, and the mass of the track, respectively. c 1, c 2, c 3 represents the damping of the primary suspension, the torsional damping of the wheel axle, and the damping of the fastener system, respectively. k 1, k 2, k 3 represents the stiffness of the primary suspension, the torsional stiffness of the wheel axle, and the stiffness of the fastener system, respectively. , , These represent the vertical vibration acceleration, vertical vibration velocity, and vertical displacement of the wheel, respectively. , , These are the torsional vibration angular acceleration, torsional vibration angular velocity, and torsional vibration angular displacement of the wheel, respectively. , , These represent the vertical vibration acceleration, vertical vibration velocity, and vertical displacement of the wheel, respectively. P 0 represents the static force on the wheel; F N , F T These are the normal force and longitudinal creep force between the wheel and rail, respectively.

3. The rail corrugation suppression method based on speed regulation according to claim 2, characterized in that... in: (2) In the formula, k H For the contact stiffness between the wheel and the rail, μ ( ξ The adhesion coefficient, which is related to the longitudinal adhesion ratio in wheel-rail rolling contact, is expressed as: (3) in, μ K ( ξ The relative friction feature is defined by Kraft and is expressed as: (4) in, μ 0 represents the static friction coefficient; ξ' These are standardized longitudinal creep parameters; V 0 represents the rolling speed of the wheel.

4. The rail corrugation suppression method based on speed regulation according to claim 3, characterized in that, ξ' Represented as: (5) In the formula, E The elastic modulus of the wheelset material. G = E / 2(1+ v ), v Poisson's ratio; C 11 is the longitudinal creep coefficient, and is a constant listed according to Kalker's linear theory; a , b The length of the semi-major axis of the Hertz contact ellipse in the rolling and lateral directions.

5. The rail corrugation suppression method based on speed regulation according to claim 4, characterized in that, a , b The value is calculated using a direct method to determine the wheel-rail contact ellipse, by introducing the following parameters: (6) In the formula, r The nominal rolling radius of the wheel. r w The radius of the cross-sectional shape of the wheel tread. r t The radius of the cross-sectional shape of the rail top is given. The curvature of the wheel-rail contact ellipse; According to parameters ρ / r Obtain intermediate variables a e , b e This allows us to determine the semi-major axis of the contact ellipse. (7) when ρ / r When ≤2, (8) when ρ / r >2 hours, (9) In the formula m h and n h This is expressed as determined by the following formula in Hertzian theory. β Coefficients related to angles: (10)。 6. The rail corrugation suppression method based on speed regulation according to claim 1, characterized in that, In the process of continuously judging extreme values, the maximum and minimum values ​​are iteratively updated and stored each time.

7. The rail corrugation suppression method based on speed regulation according to claim 1, characterized in that, During the extreme value determination process, three adjacent values ​​in continuous sampling are compared. If the extreme value condition is met, it is output; otherwise, 0 is output. After finding the results of the changes of the maximum and minimum values ​​over time, the results are imported into the extreme value memory. If the extreme value is not 0, the value replaces the previous extreme value and is stored. If the input data is 0, the previously stored extreme value is used.

8. The rail corrugation suppression method based on speed regulation according to claim 1, characterized in that, For a period of time initially, the train is in an unstable operating phase, and the obtained wheel speeds of the train are not used for extreme value judgment.

9. A rail corrugation suppression system based on speed regulation, characterized in that, include: The data acquisition module is used to acquire the wheel speed of the train; The wheel torsional vibration angular velocity calculation module is used to input the wheel velocity into a pre-built wheel-rail mathematical model and calculate the wheel torsional vibration angular velocity through the wheel-rail mathematical model. The feedback control module is used to continuously input the wheel torsional vibration angular velocity into the pre-built feedback control module. The feedback control module performs extreme value judgment, specifically: find the maximum and minimum values ​​of the wheel torsional vibration angular velocity within a preset time, and determine whether the sum of the maximum and minimum values ​​is greater than a preset threshold. If so, output an instruction to control the wheel speed to decrease by a preset value to the train to reduce the train's rutting; if not, continue to perform extreme value judgment.

10. The rail corrugation suppression system based on speed regulation according to claim 9, characterized in that, The wheel-rail mathematical model is expressed as: The specific mathematical model for wheel-rail systems is as follows: (1) In the formula, m w , J w ，m r These are the mass of the wheel, the moment of inertia of the wheel axle, and the mass of the track, respectively. c 1, c 2, c 3 represents the damping of the primary suspension, the torsional damping of the wheel axle, and the damping of the fastener system, respectively. k 1, k 2, k 3 represents the stiffness of the primary suspension, the torsional stiffness of the wheel axle, and the stiffness of the fastener system, respectively. , , These represent the vertical vibration acceleration, vertical vibration velocity, and vertical displacement of the wheel, respectively. , , These are the torsional vibration angular acceleration, torsional vibration angular velocity, and torsional vibration angular displacement of the wheel, respectively. , , These represent the vertical vibration acceleration, vertical vibration velocity, and vertical displacement of the wheel, respectively. P 0 represents the static force on the wheel; F N , F T These are the normal force and longitudinal creep force between the wheel and rail, respectively.

Images