Method and system for predicting dynamic performance evolution of ballast track structure

Abstract

The invention relates to the technical field of train track simulation, and discloses a ballast track structure dynamic performance evolution prediction method and system, and the method comprises the steps: determining a train load on a ballast track according to a train-ballast track system dynamic model, and calculating the dynamic stress and bias stress of a ballast track bed under the action of the train load; constructing a ballast track bed settlement empirical model, and calculating a ballast track bed settlement curve under a single train load based on the ballast track bed settlement empirical model; calculating the dynamic response of the train-ballast track structure under the non-uniform settlement condition of the ballast track bed based on the ballast track bed settlement curve; calculating a track structure and train system evaluation index under the ballast track settlement condition based on the train-ballast track structure dynamic response, and predicting the ballast track dynamic performance according to the track structure and train system evaluation index; the method solves the problems that an existing ballast track structure dynamic performance evolution method is low in calculation efficiency and poor in accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of train track simulation, and in particular to a method and system for predicting the evolution of dynamic performance of a ballasted track structure. Background Art

[0002] The ballasted track structure is one of the important structural forms of rail transit in my country. The ballast track bed supports the rails, disperses the stress of the sleepers, and maintains the shape and position of the track structure. However, due to the discreteness of the ballast track bed and the random characteristics of its materials, its mechanical behavior is quite complex, and it is impossible to accurately describe the mechanical behavior of the track bed using traditional mechanical methods. In addition, under the action of the dynamic load of the train, the ballast track bed will undergo compaction, crushing of gravel particles, and other processes, which will lead to permanent settlement of the ballast track bed and further accelerate the deterioration of the ballast track bed. Therefore, the evolution and prediction of the long-term dynamic performance of the ballasted track structure is still one of the major problems in the operation and maintenance of the ballasted track structure.

[0003] At present, indoor tests and on-site monitoring are important means to study the evolution of dynamic performance of ballasted trackbed. Among them, indoor tests cannot simulate real train loads, and the settlement of ballasted trackbed under real train loads is quite different; and on-site monitoring has high manpower, physical and time costs. In terms of numerical simulation analysis, the main method to study the dynamic performance of ballasted trackbed is to establish a dynamic simulation analysis model of track structure using finite element method. This method regards rails and sleepers as beam models, ballasted trackbed is simulated by solid units, and the connection between components is simulated by spring damping units, and train load is regarded as a moving load acting on the rail. In finite element simulation, the accurate stress and strain calculation of ballasted trackbed requires the use of extremely small unit size, which will reduce the calculation efficiency of ballasted track dynamic model; in addition, considering train load as moving load will ignore the dynamic stress amplification effect of ballasted trackbed caused by track unevenness and sleeper derailment, which will bring errors to the prediction of long-term dynamic performance of ballasted track structure. It can be seen that the existing methods for the evolution of dynamic performance of ballasted track structures have the problems of low computational efficiency and poor accuracy. Summary of the invention

[0004] The present invention provides a method and system for predicting the evolution of dynamic performance of a ballasted track structure, so as to solve the problems of low calculation efficiency and poor accuracy in the existing method for predicting the evolution of dynamic performance of a ballasted track structure.

[0005] In order to achieve the above object, the present invention is implemented by the following technical solutions: In a first aspect, the present invention provides a method for predicting the evolution of dynamic performance of a ballasted track structure, comprising: Construct the dynamic model of train-ballasted track system based on vehicle-track coupling dynamics theory; Determining the train load on the ballasted track according to the train-ballasted track system dynamics model, and calculating the dynamic stress and eccentric dynamic stress of the ballasted track bed under the train load; Constructing an empirical model for ballasted track bed settlement, and calculating a ballasted track bed settlement curve under a single train load based on the empirical model for ballasted track bed settlement; Calculating the dynamic response of the train-ballasted track structure under the condition of uneven settlement of the ballasted track based on the ballasted track settlement curve; Based on the dynamic response of the train-ballasted track structure, the track structure and train system evaluation indicators under the condition of ballasted track settlement are calculated, and the dynamic performance of the ballasted track is predicted according to the track structure and train system evaluation indicators.

[0006] Optionally, the construction of the train-ballasted track system dynamics model includes: The high-order finite element method is used for the ballasted track structure, and the high-order interpolation basis function is used to fit the track structure vibration to obtain the train-ballasted track system dynamics model. The shape function of the train-ballasted track system dynamics model adopts an orthogonal raised-order spectral polynomial, and the polynomial satisfies the following relationship: ; in: ; Where: express k Order Legendre polynomials; Represents a function variable and its value range is , k represents the order, represents the solution of a polynomial.

[0007] Optionally, the calculation of dynamic stress of the ballast track bed satisfies the following relationship: ; in: ; In the formula: represents Dynamic stress of ballast track bed; represents the strain matrix of the ballast bed; represents the displacement vector of the ballast bed; , and They represent the longitudinal, transverse and vertical dynamic stresses of the ballast track bed respectively; , and Respectively indicate the ballast bed xy -Towards, yz -Xiang He zx- Shear stress; Optionally, the calculation of the dynamic deviator stress of the ballast track bed satisfies the following relationship: ; Where: Indicates the dynamic deviator stress of the ballast bed.

[0008] Optionally, the empirical model of ballast bed settlement satisfies the following relationship: ; Among them: α represents the intermediate coefficient of the model calculation, ; Where: It represents the plastic strain of ballasted track structure; a , b and c It means that the empirical coefficients related to the settlement of the ballast track bed can be obtained through indoor tests. N Indicates the number of times the train load acts.

[0009] Optionally, the calculation of the settlement of the ballast track under a single train load satisfies the following relationship: ; Where: It indicates that there is settlement of the top surface of the ballast bed; n Indicates the number of vertical layers of the finite element of the roadbed, the subscript " i " indicates the i Layer ballast finite element; Indicates i Thickness of finite element of the ballast layer; Indicates i Finite element strain of the ballast layer; The ballast bed settlement at different points of the ballast bed is combined to obtain the ballast bed settlement curve.

[0010] Optionally, the calculation steps for calculating the dynamic response of the train-ballasted track structure under the condition of uneven settlement of the ballasted track bed based on the ballasted track bed settlement curve are as follows: S1: Set the incremental count symbol n =1, time step t The system dynamic response within , the system equivalent load vector The average is N share , , the initial train-ballasted track system stiffness matrix at this time step is expressed as ; S2: Calculation of deformation of the ballasted track structure at each loading stage : , and accumulate the deformation at each stage: , update the nonlinear parameters of the train-ballasted track system and regenerate the system stiffness matrix ; S3: Determine whether n=N If yes, then jump out of the loop and output the dynamic response of the train-ballasted track structure. If no, then let n=n+ 1, and return to S2 to recalculate.

[0011] Optionally, based on an evaluation index corresponding to the dynamic response of the train-ballasted track structure under the condition of uneven ballast bed settlement, and based on the evaluation index, the dynamic performance of the train-ballasted track system under the condition of ballast bed settlement is evaluated, including: The wheel load reduction rate and train vehicle stability index are used to evaluate the dynamic response of the train-ballasted track structure. The calculation method and limit of the wheel load reduction rate are as follows:

[0012] Where: Indicates wheel load reduction rate; Indicates the static wheel weight of the wheel; Indicates the change value of wheel-rail force.

[0013] The calculation method of train vehicle stability index is as follows:

[0014] Where W represents the train vehicle stability index, W i Indicates the index coefficient, subscript N Indicates the total number of calculated frequencies; in: ; Where: W i represents the index coefficient, A represents the vehicle body vibration acceleration, f represents the vibration frequency, Indicates the frequency correction factor.

[0015] In a second aspect, an embodiment of the present application provides a system for predicting the evolution of dynamic performance of a ballasted track structure, including a processor and a memory; Memory, used to store computer programs; The processor is used to implement any method step described in the first aspect when executing a program stored in the memory.

[0016] Beneficial effects: The method for predicting the evolution of dynamic performance of ballasted track structure provided by the present invention uses a high-order finite element method to simulate the ballasted track structure, so that the model calculation accuracy and calculation efficiency are higher, breaking through the limitations of the traditional finite element method, and is superior to the traditional method in methodology. It breaks through the assumption that the train load is regarded as a moving load in the traditional ballasted track bed settlement prediction method, and introduces the vehicle-track coupling dynamics theory, so that the train load is more realistic and the calculation error of the ballasted track bed settlement is smaller; In the static / dynamic calculation of train-ballasted track, the suspended sleepers caused by uneven settlement of the track bed are taken into account, and the incremental method is used to calculate the static / dynamic response of the system, making the calculation results more accurate. At the same time, by adopting the linear approximation method, the settlement of the ballasted track bed caused by one hundred train cycle loads is approximated by the linear superposition of the settlement of the ballasted track bed after a single train load, which greatly improves the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of a method for predicting the dynamic performance evolution of a ballasted track structure according to a preferred embodiment of the present invention; Figure 2 A schematic diagram of a train-ballasted track structure simulation analysis model according to a preferred embodiment of the present invention; Figure 3 The dynamic response of the train-ballasted track system of the preferred embodiment of the present invention; Figure 4 The stress distribution of the cross section of the ballasted track bed of the preferred embodiment of the present invention, wherein: (a) the deviator stress distribution diagram of the ballasted track bed, (b) the stress distribution diagram of the ballasted track bed in the X direction, (c) the stress distribution diagram of the ballasted track bed in the Y direction, (d) the stress distribution diagram of the ballasted track bed in the Z direction, (e) the stress distribution diagram of the ballasted track bed in the XY direction, (f) the stress distribution diagram of the ballasted track bed in the YZ direction, (g) the stress distribution diagram of the ballasted track bed in the ZX direction; Figure 5 The stress time history curve of the top surface of the ballasted track bed of the preferred embodiment of the present invention, wherein: (a) the deviator stress distribution diagram of the ballasted track bed, (b) the stress distribution diagram of the ballasted track bed in the X direction, (c) the stress distribution diagram of the ballasted track bed in the Y direction, (d) the stress distribution diagram of the ballasted track bed in the Z direction, (e) the stress distribution diagram of the ballasted track bed in the XY direction, (f) the stress distribution diagram of the ballasted track bed in the YZ direction, (g) the stress distribution diagram of the ballasted track bed in the ZX direction; Figure 6 The cumulative settlement prediction curve of the ballasted track bed according to the preferred embodiment of the present invention; Figure 7 Schematic diagram of a system incremental solution method according to a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0018] The technical solution of the present invention is described clearly and completely below. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0019] Unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the usual meanings understood by persons with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Similarly, words such as "one" or "one" do not indicate quantity restrictions, but indicate the existence of at least one. Words such as "connect" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship also changes accordingly.

[0020] See also Figure 1-7 The present application embodiment provides a method for predicting the evolution of dynamic performance of a ballasted track structure, comprising: A train-ballasted track system dynamics model is constructed based on the vehicle-track coupling dynamics theory, and train system parameters and ballasted track structure parameters are obtained according to the train-ballasted track system dynamics model; Establishing a vehicle-ballasted track system dynamics simulation analysis model based on the train system parameters and the ballasted track structure parameters; Calculate the dynamic stress and eccentric stress of the ballasted track bed under train loads; Constructing an empirical model for ballasted track bed settlement, and calculating the ballasted track bed settlement under a single train load based on the empirical model for ballasted track bed settlement; Constructing a ballast bed settlement curve according to the ballast bed settlement under a single train load, and calculating the dynamic response of the train-ballast track structure under the condition of uneven ballast bed settlement based on the ballast bed settlement curve; Based on the evaluation index corresponding to the dynamic response of the train-ballasted track structure under the condition of uneven roadbed settlement, the dynamic performance of the train-ballasted track system under the condition of ballasted roadbed settlement is evaluated based on the evaluation index.

[0021] The specific steps of the dynamic performance evolution prediction method of ballasted track structure in this example are as follows: Step 1: Based on the vehicle-track coupling dynamics theory, a dynamic simulation analysis model of the train-ballasted track system is established.

[0022] The train system and ballasted track structure parameters of this example are derived from the actual parameters of the CHR series high-speed trains and the measured ballasted track structure parameters, as shown in Table 1-2: Table 1 Train system parameters

[0023] Table 2 Ballast track structural parameters

[0024] In the present invention, the ballast bed structure adopts a high-order finite element method, that is, on the basis of the finite element method, a high-order interpolation basis function is used to fit the vibration of the track structure. In this example, an orthogonal ascending spectral function is used to enhance the sparsity of the matrix and improve the calculation efficiency. The specific calculation method is as follows:

[0025] in: , Where: express k Order Legendre polynomials; Represents a function variable, whose value range is .

[0026] Step 2: Calculate the dynamic stress and eccentric stress of the ballast track under train load The dynamic stress of the ballasted track bed is calculated using the following formula:

[0027] in: , In the formula: represents Dynamic stress of ballast track bed; represents the strain matrix of the ballast bed; represents the displacement vector of the ballast bed; , and They represent the longitudinal, transverse and vertical dynamic stresses of the ballast track bed respectively; , and Respectively indicate the ballast bed xy -Towards, yz -Xiang He zx- Shear stress; The dynamic deviator stress of the ballast track bed is calculated using the following formula:

[0028] Where: Indicates the dynamic deviator stress of the ballast bed.

[0029] Step 3: Calculate the settlement of the ballasted track bed under a single train load: The empirical formula for the ballasted track bed used in the present invention is as follows:

[0030] in: , Where: It represents the plastic strain of ballasted track structure; a , b and c It indicates the empirical coefficient related to the settlement of the ballast track bed, which can be obtained through indoor tests; N It indicates the number of times the train load acts; it indicates the deviatoric stress of the ballasted track bed; it indicates the compressive strength of the ballasted track bed under a confining pressure of 50kPa.

[0031] The overall settlement amplitude of the ballast bed is calculated using the following formula:

[0032] Where: It indicates that there is settlement of the top surface of the ballast bed; n Indicates the number of vertical layers of the finite element of the roadbed, the subscript " i " indicates the i Layer ballast finite element; Indicates i Thickness of finite element of the ballast layer; Indicates i Finite element strains of the ballast layer.

[0033] In this example, a CHR series high-speed railway train is used, which has a total of 16 vehicles. Figure 5 From the dynamic stress history of the ballast in , it can be seen that a single train will cause two ballast stress peaks. Therefore, the load of a single train is 16×2 cycles. Figure 4 The deviator stress distribution of the ballast track bed shown in , and the settlement value of the ballast track bed under a single train load, where the parameters of the ballast track bed used in this example are as follows: Table 3 Settlement parameters of ballast track bed

[0034] Step 4: Calculate the dynamic response of the train-ballasted track structure under the condition of uneven roadbed settlement: (1) Set the incremental count symbol n =1; time step t The system dynamic response within ; The system equivalent load vector The average is N share : ; The initial train-ballasted track system stiffness matrix at this time step is expressed as .

[0035] (2) Calculate the deformation of the ballasted track structure at each loading stage : , and accumulate the deformation at each stage: ; Update the nonlinear parameters of the train-ballasted track system and regenerate the system stiffness matrix ,It is worth noting that the system mass matrix is ​​a linear matrix and does not participate in the matrix update calculation.

[0036] (3) Determine whether n=N If yes, then exit the loop and output the stiffness matrix and track structure dynamic response; if no, then n=n+ 1, and return to step 2.

[0037] Step 5: Evaluate the dynamic performance of the train-ballasted track system under the condition of ballasted track settlement: In the present invention, the wheel weight reduction rate and the train vehicle stability index are used to evaluate the dynamic response of the train-ballasted track structure, wherein the calculation method and limit value of the wheel weight reduction rate are as follows:

[0038] Where: Indicates wheel load reduction rate; Indicates the static wheel weight of the wheel; Indicates the change value of wheel-rail force.

[0039] The calculation method of train vehicle stability (Sperling) index is as follows:

[0040] in:

[0041] Where: represents the vibration acceleration of the vehicle body (g); represents the vibration frequency; subscript N Indicates the total number of calculated frequencies; Indicates the frequency correction factor, as shown in the following table: Table 4 Frequency correction coefficient

[0042] The Sperling index limits for trains and vehicles are as follows: Table 5 Evaluation level of rolling stock stability

[0043] After different train load times, the wheel weight reduction rate and train stability index under the condition of cumulative roadbed settlement are as follows: Table 6 Train-ballasted track dynamic performance evaluation

[0044] The embodiment of the present application also provides a system for predicting the evolution of dynamic performance of a ballasted track structure, including a processor and a memory; Memory, used to store computer programs; The processor is used to implement any method step described in the method for predicting the evolution of dynamic performance of ballasted track structure when executing the program stored in the memory.

[0045] The above-mentioned ballasted track structure dynamic performance evolution prediction system can implement various embodiments of the above-mentioned ballasted track structure dynamic performance evolution prediction method and achieve the same beneficial effects, which will not be described in detail here.

[0046] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for predicting the evolution of dynamic performance of ballasted track structure, characterized in that: include: Construct the train-ballasted track system dynamics model based on vehicle-track coupling dynamics theory; Determining the train load on the ballasted track according to the train-ballasted track system dynamics model, and calculating the dynamic stress and eccentric dynamic stress of the ballasted track bed under the train load; Constructing an empirical model for ballasted track bed settlement, and calculating a ballasted track bed settlement curve under a single train load based on the empirical model for ballasted track bed settlement; Calculating the dynamic response of the train-ballasted track structure under the condition of uneven settlement of the ballasted track based on the ballasted track settlement curve; Based on the dynamic response of the train-ballasted track structure, the track structure and train system evaluation indicators under the condition of ballasted track settlement are calculated, and the dynamic performance of the ballasted track is predicted according to the track structure and train system evaluation indicators.

2. The method for predicting the evolution of dynamic performance of ballasted track structure according to claim 1, characterized in that: The construction of the train-ballasted track system dynamics model includes: The high-order finite element method is used for the ballasted track structure, and the high-order interpolation basis function is used to fit the track structure vibration to obtain the train-ballasted track system dynamics model. The shape function of the train-ballasted track system dynamics model adopts an orthogonal raised-order spectral polynomial, and the polynomial satisfies the following relationship: ； in: ； Where: express k Order Legendre polynomials; Represents a function variable and its value range is , k represents the order, represents the solution of a polynomial.

3. The method for predicting the evolution of dynamic performance of ballasted track structure according to claim 1, characterized in that: The calculation of dynamic stress of ballasted track bed satisfies the following relationship: ； in: ; In the formula: represents Dynamic stress of ballast track bed; represents the strain matrix of the ballast bed; represents the displacement vector of the ballast bed, , and They represent the longitudinal, transverse and vertical dynamic stresses of the ballast track bed respectively; , and Respectively indicate the ballast bed xy -Towards, yz -Xiang He zx- Shear stress.

4. The method for predicting the evolution of dynamic performance of ballasted track structure according to claim 1, characterized in that: The calculation of dynamic deviator stress of ballast track bed satisfies the following relationship: ； Where: represents the dynamic deviator stress of the ballast track bed, , and They represent the longitudinal, transverse and vertical dynamic stresses of the ballast track bed respectively; , and Respectively indicate the ballast bed xy -Towards, yz -Xiang He zx- Shear stress.

5. The method for predicting the evolution of dynamic performance of ballasted track structure according to claim 1, characterized in that: The empirical model of ballast bed settlement satisfies the following relationship: ； Among them: α represents the intermediate coefficient of the model calculation, ; Where: represents the plastic strain of the ballasted track structure, a , b and c It means that the empirical coefficients related to the settlement of the ballast track bed can be obtained through indoor tests. N represents the number of times the train load acts, represents the dynamic deviator stress of the ballast track bed, It represents the allowable stress of soil in the ultimate limit state and can be obtained through experiments.

6. The method for predicting the evolution of dynamic performance of ballasted track structure according to claim 1, characterized in that: The calculation of the settlement of the ballast track under a single train load satisfies the following relationship: ； Where: It indicates that there is settlement of the top surface of the ballast bed; n Indicates the number of vertical layers of the finite element of the roadbed, subscript " i " indicates the i Layer ballast finite element; Indicates i Thickness of finite element of the ballast layer; Indicates i Finite element strain of the ballast layer; The ballast bed settlement at different points of the ballast bed is combined to obtain the ballast bed settlement curve.

7. The method for predicting the evolution of dynamic performance of ballasted track structure according to claim 1, characterized in that: The calculation steps for calculating the dynamic response of the train-ballasted track structure under the condition of uneven settlement of the ballasted track bed based on the ballasted track bed settlement curve are as follows: S1: Set the incremental count symbol n =1, time step t The system dynamic response within , the system equivalent load vector The average is N share , , the initial train-ballasted track system stiffness matrix at this time step is expressed as ; S2: Calculation of deformation of the ballasted track structure at each loading stage : , and accumulate the deformation at each stage: , update the nonlinear parameters of the train-ballasted track system and regenerate the system stiffness matrix ; S3: Determine whether n=N If yes, then jump out of the loop and output the dynamic response of the train-ballasted track structure. If no, then let n=n+ 1, and return to S2 to recalculate.

8. The method for predicting the evolution of dynamic performance of ballasted track structure according to claim 1, characterized in that: Based on the dynamic response of the train-ballasted track structure, the track structure and train system evaluation indexes under the condition of ballasted track settlement are calculated, and the dynamic performance of the ballasted track is predicted according to the track structure and train system evaluation indexes, including: The wheel load reduction rate and train vehicle stability index are used to evaluate the dynamic response of the train-ballasted track structure. The calculation method and limit of the wheel load reduction rate are as follows: ； Where: Indicates wheel load reduction rate; Indicates the static wheel weight of the wheel; Indicates the change value of wheel-rail force. The calculation method of train vehicle stability index is as follows: ； Where W represents the train vehicle stability index, W i Indicates the index coefficient, subscript N Indicates the total number of calculated frequencies; in: ; Where: W i represents the index coefficient, A represents the vehicle body vibration acceleration, f represents the vibration frequency, Indicates the frequency correction factor.

9. A system for predicting the evolution of dynamic performance of ballasted track structure, characterized in that: Including processor and memory; Memory, used to store computer programs; A processor, for implementing the method steps described in any one of claims 1 to 8 when executing a program stored in a memory.

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