Railway rail corrugation development and evolution calculation method

Abstract

The present application relates to a kind of railway rail corrugation development and evolution calculation method, establish multi-body dynamics model and frequency domain three-dimensional vehicle track dynamics model, wherein the multi-body dynamics model is used to calculate the quasi-static force of wheel rail, the frequency domain three-dimensional vehicle track dynamics model calculates the dynamic wheel rail lateral force and vertical force;According to the lateral and vertical force of wheel rail, the roughness change caused by wheel rail dynamic interaction is simulated, the calculated roughness change is added to the initial roughness, and the final rail corrugation state is calculated by iterative method.The present application has the advantages of: fast calculation speed, can reveal the mechanism of corrugation generation;It has a wide range of application scenarios, and can be applied to the evaluation of newly-built line, rail corrugation management in existing line.

Description

Technical Field

[0001] This invention relates to the field of traffic testing technology, and in particular to a method for calculating the development and evolution of railway rail corrugation. Background Technology

[0002] In recent years, my country's urban rail transit has developed rapidly. As of January 2022, 51 cities had opened and operated 270 urban rail transit lines, with an operating mileage of 8,759 kilometers. With the completion and opening of these rail transit lines, the resulting vibration and noise problems have become increasingly prominent, leading to a rise in related complaints.

[0003] Rail corrugation refers to the abnormal, periodic wear of the rail surface in the longitudinal direction. It is one of the main causes of increased vibration and noise, and it also exacerbates wheel-rail interaction, causing damage to track and vehicle components. The presence of corrugation seriously affects the smoothness of train operation. To solve the corrugation problem, it is essential to first understand the generation and development patterns of corrugation, and the influence of track and vehicle dynamic parameters on corrugation. A quantitative calculation method is needed to accurately predict the wavelength of corrugation and its development rate, providing support for the development of corrugation mitigation measures and the formulation of maintenance plans. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the prior art by providing a calculation method for the development and evolution of railway rail corrugation. This method utilizes the design parameters of the vehicle, track, and line, as well as the initial roughness state of the rail surface, to perform iterative simulation calculations on the development process of rail corrugation, predict the wavelength of corrugation and its development trend, and provide support for rail corrugation mitigation measures and maintenance.

[0005] The objective of this invention is achieved through the following technical solutions:

[0006] A method for calculating the development and evolution of railway rail corrugation, characterized by the following steps:

[0007] A multibody dynamics model and a frequency domain three-dimensional vehicle track dynamics model are established. The multibody dynamics model is used to calculate the quasi-static forces between the wheel and the rail, and the frequency domain three-dimensional vehicle track dynamics model is used to calculate the dynamic lateral and vertical forces between the wheel and the rail.

[0008] The changes in rail roughness caused by the dynamic interaction between the wheel and rail are obtained by simulating the lateral and vertical forces between the wheel and rail. The calculated roughness changes are added to the initial roughness, and the final rail corrugation state is calculated by iterative method.

[0009] The multibody dynamics model is a simulation model established based on the profile of the rail and vehicle, the track stiffness, and the dynamic parameters of the vehicle.

[0010] A track model consisting of straight lines, transition curves, and circular curves is established. The curve radius, superelevation, and gradient of the track model are determined by the actual parameters of the area where the rail to be corrugated is located. The roughness of the wheel and rail is set to a smooth state.

[0011] The frequency domain three-dimensional vehicle track dynamics model is a finite element model or theoretical model established based on the dynamic parameters of the track and the vehicle. The wheel admittance, rail admittance and contact admittance of the whole vehicle model are calculated through this model.

[0012] The formula for calculating the change in rail roughness in the frequency domain is:

[0013]

[0014] In the formula, ΔZ(ω) is the change in rail roughness, nT is the number of vehicles passing through during the calculation period, N(ω) is the normal force, and η(ω) is the lateral force. and Let N(ω) be the partial derivative of the normal force and the lateral force, respectively; L(k) be the distance of the k-th wheel from the initial calculation point; and v be the vehicle speed. For the inner rail, which is prone to corrugation, N(ω) ≈ -F(ω).

[0015] The advantages of this invention are: it has the advantages of fast calculation speed and ability to reveal the mechanism of corrugation generation; it has a wide range of application scenarios and can be applied to the evaluation of new lines and the corrugation control of existing lines. Attached Figure Description

[0016] Figure 1 This is a flowchart of the calculation process of the present invention;

[0017] Figure 2 This is a diagram of the multibody dynamics calculation model established in this invention;

[0018] Figure 3 This is a diagram of the frequency domain vehicle-track dynamics model established in this invention;

[0019] Figure 4 This is a diagram showing the wear distribution of the inner rail wheel in the lateral direction in this invention.

[0020] Figure 5 This is a diagram showing the wear distribution of the inner rail wheel in the longitudinal direction in this invention.

[0021] Figure 6 The figure shows the development of inner rail corrugation of a typical curve over 7 months using the present invention. Detailed Implementation

[0022] The features and other related features of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments, so as to facilitate understanding by those skilled in the art:

[0023] Example: Figure 1 As shown, the calculation method for the development and evolution of railway rail corrugation in this embodiment is as follows:

[0024] Taking a single train car as the research object, an iterative method is used for calculation. A total calculation time T is set during the simulation, and this time is divided into several calculation cycles. For example, the calculation time can be set to 1 year, and the calculation cycle can be set to 30 days. Starting from the initial state, the calculation is performed every 30 days, and then the rail surface roughness and rail profile are updated and carried over to the next calculation cycle, until the total calculation time is reached.

[0025] In summary, the calculation method in this embodiment first establishes a multibody dynamics model and a frequency-domain three-dimensional vehicle-track dynamics model, respectively. The multibody dynamics model is used to calculate the quasi-static forces between the wheel and rail, while the frequency-domain three-dimensional dynamics model calculates the dynamic lateral and vertical forces between the wheel and rail. Then, the lateral and vertical forces between the wheel and rail are input into the calculation model to simulate the changes in rail roughness caused by the dynamic interaction between the wheel and rail. The calculated roughness changes are then added to the initial roughness to obtain the updated roughness. Iterative calculations are performed for each calculation cycle to obtain the final rail corrugation state.

[0026] Specifically, for each calculation cycle, a multibody dynamics simulation model is first established based on the rail and vehicle profile, rail stiffness, and vehicle dynamic parameters. For example... Figure 2 As shown, the multibody dynamics simulation model establishes a track model consisting of straight lines, transition curves, and circular curves to improve the accuracy and comprehensiveness of corrugation calculation. The curve radii, superelevation, and gradient in the track model are given by actual design data of the location of the rail section whose corrugation is to be calculated. The wheel-rail roughness is set to an initial smooth state to accurately determine the complete process of rail corrugation development trend.

[0027] The contact state parameters of the vehicle when passing through the circular curve are calculated by the multibody dynamics simulation model. These parameters include the magnitude of the wheel-rail normal contact force, the size and location of the contact patch, and the creep rate in each direction.

[0028] like Figure 3 As shown, a frequency domain model for vehicle-track coupled dynamics calculation is established using the dynamic parameters of the track and vehicle. This model can be a finite element model or a theoretical model. The wheel admittance, rail admittance, and contact admittance of the whole vehicle model are calculated using this model.

[0029] The initial roughness is input into the model, and the wheel-rail interaction force P(ω) is calculated using formula (1), where ω is the frequency and its relationship with wavelength λ and vehicle speed v is as follows: H W(ω), H R (ω), H C (ω) represent the wheel admittance matrix, rail admittance matrix, and contact admittance matrix, respectively. 0 (ω) is a matrix consisting of the initial roughness of the rails corresponding to each wheel.

[0030] P(ω)=[H W (ω)+H R (ω)+H C (ω)] -1 Z 0 (ω) (1)

[0031] Because the wheels are positioned differently, the rail roughness corresponding to each wheel has a phase difference. For the k-th wheel, its roughness can be expressed as:

[0032]

[0033] In the formula, L(k) is the distance of the kth wheel from the initial calculation point.

[0034] Further calculations are made of the lateral displacement of the wheel and rail at the contact point, and the additional lateral creep rate is calculated using the following formula:

[0035] η * =(v w -v r ) / υ (3)

[0036] In the formula, η * v represents the total lateral creep rate. w v is the actual lateral speed of the wheel. r v is the lateral velocity of the rail, and v is the vehicle speed.

[0037] like Figure 4 and Figure 5 As shown, the Arcard model is used to calculate the wear of the rail, and the calculation formula is shown in equation (4). In the equation, x and y are the coordinates of the calculation point within the contact patch, Δx is the size of the longitudinal grid, a and b are the longitudinal and transverse half-axis lengths of the contact patch, respectively, and ξ, η, ... These represent longitudinal, transverse, and spin creep rates, respectively. These parameters can be calculated using a multibody dynamics model. N is the normal contact force, and k... w H represents the wear constant and the hardness of the rail.

[0038]

[0039] Rail corrugation is decomposed into longitudinal uneven wear caused by normal force fluctuations and uneven wear caused by lateral vibration-induced creep. Assuming the roughness change is negligible within one calculation cycle, the formula for calculating the roughness change in the frequency domain is as follows.

[0040]

[0041] In the formula, ΔZ(ω) is the change in rail roughness, nT is the number of vehicles passing through during the calculation period, N(ω) is the normal force, and η(ω) is the lateral force. and Let N(ω) be the partial derivative of the normal force and the lateral force, respectively, where L(k) is the distance of the k-th wheel from the initial calculation point, and v is the vehicle speed. For the inner rail, which is prone to corrugation, N(ω) ≈ -F(ω). Since the normal force and creep rate cannot be explicitly represented in relation to wear, their partial derivatives can be calculated using numerical simulation methods. The normal force and creep rate are essentially linearly related to wear when the creep rate is low; therefore, these two partial derivatives can be obtained numerically.

[0042] The roughness of the first calculation cycle can be obtained by superimposing the initial roughness with the roughness variation, i.e.

[0043] Z1(ω)=Z0(ω)+ΔZ(ω) (6)

[0044] Following the previous process, with Z1(ω) as input, continue to calculate the roughness change in the next calculation cycle, iterating repeatedly until the calculation is completed.

[0045] like Figure 6 As shown in the figure, the circular mark represents the initial measured roughness, i.e., the starting point of the calculation; the dashed line represents the intermediate calculation results; the solid line marked with an asterisk represents the final simulation calculation result, i.e., 7 months later; and the triangle mark represents the measured corrugation roughness 7 months later. From the overall changes, the simulation results and the measured results show the same corrugation characteristics: the rail roughness in the wavelength range greater than 315mm hardly changed; obvious corrugation appeared in the two wavelength ranges of 200-250mm and 40mm; and slight corrugation appeared at the 16mm wavelength. This verifies the effectiveness of the calculation method in this embodiment.

[0046] Although the above embodiments have described the concept and embodiments of the present invention in detail with reference to the accompanying drawings, those skilled in the art will recognize that various improvements and modifications can still be made to the present invention without departing from the scope of the claims, and therefore will not be elaborated here.

Claims

1. A method for calculating the development and evolution of railway rail corrugation, characterized in that: Includes the following steps: A multibody dynamics model and a frequency domain three-dimensional vehicle track dynamics model are established. The multibody dynamics model is used to calculate the quasi-static forces between the wheel and the rail, and the frequency domain three-dimensional vehicle track dynamics model is used to calculate the dynamic lateral and vertical forces between the wheel and the rail. The changes in rail roughness caused by the dynamic interaction between the wheel and rail are obtained by simulating the lateral and vertical forces between the wheel and rail. The calculated roughness changes are added to the initial roughness, and the final rail corrugation state is calculated by iterative method. The multibody dynamics model is a simulation model established based on the profile of the rail and vehicle, the rail stiffness, and the dynamic parameters of the vehicle. The frequency domain three-dimensional vehicle track dynamics model is a finite element model or theoretical model established based on the dynamic parameters of the track and the vehicle. The wheel admittance, rail admittance and contact admittance of the whole vehicle model are calculated through this model. The formula for calculating the change in rail roughness in the frequency domain is: ； In the formula, Here, n represents the change in rail roughness, and nT represents the number of vehicles passing through during the calculation period. For normal force, It is a lateral force. and These are the partial derivatives of the normal force and the transverse force, respectively. For the first The distance of each wheel from the initial calculation point, v The speed is the vehicle speed.

2. The method for calculating the development and evolution of railway rail corrugation according to claim 1, characterized in that: A track model consisting of straight lines, transition curves, and circular curves is established. The curve radius, superelevation, and gradient of the track model are determined by the actual parameters of the area where the rail to be corrugated is located. The roughness of the wheel and rail is set to a smooth state.

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