Train-ballasted track-roadbed system simulation method and system based on MBD-DEM-FDM coupling

Abstract

The present invention discloses a train-ballasted track-roadbed system simulation method based on MBD-DEM-FDM coupling, comprising: establishing a train model based on the multi-body dynamics (MBD) method, including: establishing a dynamic model of the train system, simplifying the train's suspension system through springs and dampers, and considering the interaction between the train and the track; establishing a three-dimensional ballasted trackbed model based on the discrete element method (DEM); establishing a roadbed finite difference model based on the finite difference method (FDM), including: treating the roadbed as a continuous medium and simulating the mechanical behavior and deformation characteristics of the roadbed under train loads based on the finite difference method (FDM); providing a coupling medium to couple the MBD-DEM-FDM and perform real-time information exchange between the MBD, DEM, and FDM systems; establishing a coupling model based on the MBD-DEM-FDM coupling, and verifying and applying the coupling model. Also disclosed are corresponding systems, electronic devices, and computer-readable storage media that consider the combined effects of the microscopic mechanical properties of the roadbed's internal particles and the train's dynamic effects on the track and roadbed.

Description

Technical Field

[0001] The present invention relates to the technical field of train-ballasted track-roadbed system simulation methods, and in particular to a train-ballasted track-roadbed system simulation method and system based on MBD-DEM-FDM coupling. Background Art

[0002] Railway lines are multi-layered, heterogeneous longitudinal structures composed of ballasted track, roadbed, bridges, and tunnels. To ensure stable operation, each structural layer must meet functional and technical requirements and work in tandem. However, existing research often separates the superstructure, track structure, and substructure, ignoring the interactions between them. This separation hinders the systematic evaluation and study of the impact of local structural defects on the dynamic response of other structural layers, and fails to fully characterize the overall mechanical properties of the coupled train-track-roadbed system and the cyclic effects of a real train.

[0003] Currently, research on the dynamic response of the train-ballasted track-subgrade relationship is primarily conducted through field testing, full-scale model tests, and theoretical numerical calculations. Due to the limited number of inspection points and low efficiency, field testing makes it difficult to detect internal defects in the ballast subgrade, preventing rapid real-time detection and hindering intervention studies. Full-scale model tests differ significantly from actual field conditions and cannot accurately reproduce the effects of train cycling. Theoretical numerical calculations primarily focus on modeling and studying the coupled train-ballasted track-subgrade system. Most of these are based on the traditional finite element method (FEM) and consider the substructure. These methods often simplify the ballast subgrade as a discrete mass or continuous medium, ignoring the numerous internal voids and point contacts between ballasts at the mesoscopic level. This inadequately accounts for hidden defects and the microscopic mechanical behavior of the ballast subgrade, hindering research on the overall structural dynamic response. To address these challenges, the discrete element method (DEM) effectively simulates the microscopic morphology and mechanical properties of ballast particles within the subgrade, providing a better approach for studying the microscopic dynamic mechanical behavior of the ballast subgrade. However, current numerical simulation research on ballasted trackbeds is still limited to the structural layer of the trackbed itself, ignoring the actual effect of the upper train.

[0004] In addition, the existing technical solutions mostly use multi-body dynamics methods to simulate the train vehicle subsystem, use the finite element method to simulate the track and roadbed subsystems respectively, and use spring-damper elements to simulate the interaction between the various structural layers. Figure 1 (a)- Figure 1 (b) shows the numerical model of the three-dimensional coupled system of train, ballast track and roadbed. Based on the multi-body dynamics theory, a multi-rigid body model of the train vehicle is established. The schematic diagram of the three-dimensional multi-body dynamics model of the train vehicle is shown in Figure 2 (a)- Figure 2 (c) shown.

[0005] The defects in the existing research on train-track-roadbed coupling system are mainly manifested in the following aspects:

[0006] (1) Existing studies often analyze the superstructure, track structure, and substructure separately, ignoring the interactions between them and failing to fully characterize the overall mechanical properties of the train-track-subgrade coupled system. This separation approach is not conducive to systematically evaluating the impact of local structural defects on the dynamic responses of other structural layers.

[0007] (2) Due to the small number of test points and low efficiency, it is difficult to obtain defects inside the ballasted trackbed during field testing, and it is impossible to detect them in real time and conduct human intervention; full-scale model tests are difficult to truly restore the circulation effect of the train and cannot effectively represent the actual working conditions; traditional theoretical numerical calculation methods simplify the simulation of the ballasted trackbed, ignoring the internal void structure of the ballasted trackbed and the microscopic mechanical behavior of the ballast particles, resulting in inaccurate research results on the overall dynamic response.

[0008] Therefore, developing a numerical model that comprehensively analyzes real-time train operation and the microscopic mechanical behavior of ballasted trackbed particles, while also accounting for the interaction between the ballasted track and roadbed, is crucial for studying the spatial dynamic interactions and overall mechanical performance evolution of the coupled train-track-roadbed system. This numerical simulation method can reproduce actual field conditions, reducing the burden of field measurements and ultimately ensuring safe railway operation and long-term service life. Summary of the Invention

[0009] The purpose of the present invention is to provide a train-ballasted track-roadbed system simulation method and system based on MBD-DEM-FDM coupling, which is used to simulate the mechanical response of the train-track-roadbed system under complex dynamic conditions. A three-dimensional numerical calculation model based on the coupling of Multi-Body Dynamics (MBD)-Discrete Element Method (DEM)-Finite-difference methods (FDM) is intended to conduct a comprehensive study on the macro- and micro-dynamic responses of the train-ballasted track-roadbed system. This model can make up for the shortcomings of the existing research on the analysis of the overall mechanical behavior of the coupled system, especially considering the micro-mechanical properties of the particles inside the roadbed and the comprehensive influence of the train dynamics on the track and roadbed. Through this method, the actual working conditions can be reproduced, and the burden of on-site measurements can be reduced, thereby providing a theoretical basis and technical support for the safe operation of high-speed and heavy-load railways.

[0010] The invention objectives and technical problems to be solved by the present invention include:

[0011] (1) A coupled model that can simultaneously consider the interaction between trains, tracks, and roadbed is established to study the dynamic behavior of the train-track-roadbed system under high-speed and heavy-load conditions.

[0012] (2) By real-time coupling of MBD, DEM, and FDM calculation methods, accurate simulation of the microscopic dynamic mechanical behavior of ballasted track bed particles is achieved, and their influence on the overall mechanical response of the system is revealed.

[0013] (3) Provide theoretical basis and technical guidance for the design and intelligent operation and maintenance of high-speed and heavy-load railways, and improve the safety and long-term service capability of the railway system.

[0014] A first aspect of the present invention is to provide a train-ballasted track-roadbed system simulation method based on MBD-DEM-FDM coupling, comprising:

[0015] S1, establishing a train model based on a multi-body dynamics (MBD) method, including: establishing a dynamic model of the train system based on the multi-body dynamics (MBD) method, wherein the train suspension system is simplified by using springs and dampers in the dynamic model of the train system, and interaction between the train and the track is considered;

[0016] S2, establish a three-dimensional ballasted trackbed model based on the discrete element method (DEM);

[0017] S3, establishing a finite difference model of the roadbed based on a finite difference method (FDM), including: treating the roadbed as a continuous medium, simulating the mechanical behavior and deformation characteristics of the roadbed under the action of a train load based on the finite difference method (FDM), thereby obtaining the finite difference model of the roadbed;

[0018] S4, setting up a coupling medium to couple MBD-DEM-FDM and perform real-time information exchange between MBD and DEM and FDM systems;

[0019] S5, establishing a coupling model based on MBD-DEM-FDM coupling and verifying and applying the coupling model, including: establishing a coupling model, obtaining simulation results based on the coupling model, and comparing and analyzing the simulation results with the on-site dynamic response to verify the correctness of the coupling model; establishing five ballast-deficient working conditions to calculate and obtain a particle contact force chain diagram and a sleeper displacement acceleration curve diagram to realize the application of the coupling model.

[0020] Preferably, the S1 includes:

[0021] S11, based on MBD theory, establish a rigid body consisting of a car body, a bogie, and a wheelset, wherein the car body and the two bogies are connected through a primary and a secondary suspension system, and the springs and dampers of the suspension system are simplified into linear models;

[0022] S12, in modeling the suspension system, simulating the connection between the vehicle body and the bogie, and between the bogie and the wheelset, by using linear springs and dampers;

[0023] S13, based on the Hamiltonian principle, starting from the total kinetic energy, total potential energy, and virtual work of the system, by constructing a generalized coordinate system, the mass matrix, stiffness matrix, damping matrix, and load matrix of the system are obtained, and finally the vibration dynamics equations of the train system are formed. The vibration dynamics equations are:

[0024]

[0025] Where: M v 、C v and K v are the mass matrix, damping matrix and stiffness matrix of the train vehicle, F v is the load vector, X v is the displacement matrix;

[0026] S14, establishing a three-dimensional train-track model, including: calculating the normal force between the wheel and rail based on Hertz nonlinear contact theory; simulating the wheel-rail tangential contact force based on Kalker creep theory; establishing a wheel-rail contact coupling model based on the normal force between the wheel and rail and the tangential contact force between the wheel and rail, wherein the wheel-rail contact coupling model can accurately calculate the dynamic changes of the wheel-rail contact during the train operation; further comprehensively considering four different types of track irregularities, wherein the four types of track irregularities include height irregularity, directional irregularity, horizontal irregularity, and gauge irregularity, including: different types of track irregularities obtained by simulation and analysis using a trigonometric series method are input as external excitations into the wheel-rail contact coupling model to obtain a first comprehensive sample of height irregularity and horizontal irregularity, and a second comprehensive sample of gauge irregularity and directional irregularity; establishing the three-dimensional train-track model based on the first comprehensive sample and the second comprehensive sample;

[0027] S15, calculating the dynamic model of the train system based on the Wilson-θ integration method, including: first discretizing the vibration dynamics equations of the train system, introducing a correction factor θ to adjust the response within each time step by setting equally spaced discrete time points, and adjusting the acceleration, velocity and displacement of the next time step to reflect the correction effect of the current time step; then, gradually correcting the response of the system through an iterative process within each time step until a given convergence condition is met.

[0028] Preferably, the S2 includes:

[0029] S21, constructing a mesoscopic mechanical model of ballast particles, including: simulating contact, friction, and rolling behaviors of ballast particles based on the discrete element method (DEM), and establishing a particle stacking model as the mesoscopic mechanical model of ballast particles by setting mesoscopic parameters such as particle gradation, size, and density;

[0030] S22, compacting the ballast particle micromechanical model to establish the three-dimensional ballasted track bed model.

[0031] Preferably, the S21 includes:

[0032] (1) Define the geometric parameters of ballast particles, determine the particle size distribution, and use PFC software to generate particles;

[0033] (2) Considering the contact model between particles, the contact model between particles is set as an anti-rolling linear contact model, and boundary conditions are set to simulate the dynamic behavior between particles and other structural components.

[0034] Preferably, the S22 includes:

[0035] (1) In the designated area, ballast is generated three times. After each generation, wall units are generated above the ballast particles and compacted using the servo control principle. The compressive stress is 200 kPa. A total of three compaction procedures are performed. The ballast slope is 1:1.75, and the thickness of the final roadbed model is 0.55 m. Then, walls are generated on the top surface of the roadbed and the ballast slopes on both sides, and the final compaction is performed. Finally, the particles in the sleeper area are removed and the sleepers are placed.

[0036] (2) By measuring the overall porosity of the roadbed, the ρ of the final roadbed model is calculated b About 1600kg / m 3 , meeting the requirements of the "Heavy Haul Railway Design Code" (TB 10625-2017).

[0037] Preferably, the S3 includes:

[0038] S31, the roadbed is regarded as a continuous medium, a roadbed grid division numerical model is established, and material properties and boundary conditions of the roadbed grid division numerical model are set;

[0039] S32, solving the subgrade grid numerical model using a finite difference method to simulate the mechanical behavior and deformation characteristics of the subgrade under the train load, thereby obtaining the subgrade finite difference model.

[0040] Preferably, the S4 includes:

[0041] S41, using the coupling relationship of track-ballast-subgrade interface to establish the coupling model between MBD-DEM and DEM-FDM;

[0042] S42, achieving real-time coupling between the train multi-body system and the discrete ballast particle system by defining a mechanical transfer relationship between the rail and the sleeper;

[0043] S43, by setting an artificial viscoelastic boundary in the discrete element numerical model, an equivalent simulation between the ballast mass and the discrete ballast particles is achieved, thereby realizing real-time information exchange between the MBD and DEM and FDM systems.

[0044] A second aspect of the present invention is to provide a train-ballasted track-roadbed system simulation system based on MBD-DEM-FDM coupling, which is used to implement the method of the first aspect, including:

[0045] A train model building module (101) is used to build a train model based on a multi-body dynamics (MBD) method, comprising: building a dynamic model of a train system based on the multi-body dynamics (MBD) method, wherein the train suspension system is simplified by using springs and dampers in the dynamic model of the train system, and the interaction between the train and the track is considered;

[0046] A three-dimensional ballast model establishment module (102) is used to establish a three-dimensional ballast model based on a discrete element method (DEM); the module comprises: simulating the contact, friction and rolling behavior of ballast particles based on the discrete element method (DEM), establishing a particle accumulation model by setting microscopic parameters such as particle gradation, size and density, and compacting the particle accumulation model to establish the three-dimensional ballast model;

[0047] A roadbed finite difference model establishment module (103) is used to establish a roadbed finite difference model based on a finite difference method (FDM), comprising: treating the roadbed as a continuous medium, simulating the mechanical behavior and deformation characteristics of the roadbed under train load based on the finite difference method (FDM), and thereby obtaining the roadbed finite difference model;

[0048] MBD-DEM-FDM coupling module (104), used to set a coupling medium to couple MBD-DEM-FDM and perform real-time information exchange between MBD and DEM and FDM systems;

[0049] A coupling model establishment and verification application module (105) is used to establish a coupling model based on MBD-DEM-FDM coupling and verify and apply the coupling model, including: establishing a coupling model, obtaining simulation results based on the coupling model, and comparing and analyzing the simulation results with the on-site dynamic response to verify the correctness of the coupling model; establishing five ballast-missing working conditions to calculate and obtain a particle contact force chain diagram and a sleeper displacement acceleration curve diagram to realize the application of the coupling model.

[0050] A third aspect of the present invention provides an electronic device, comprising a processor and a memory, wherein the memory stores a plurality of instructions, and the processor is configured to read the instructions and execute the method described in the first aspect.

[0051] A fourth aspect of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores a plurality of instructions, and the plurality of instructions can be read by a processor to execute the method described in the first aspect.

[0052] Beneficial effects of the method and system of the present invention:

[0053] This paper proposes a three-dimensional numerical simulation method based on MBD-DEM-FDM coupling, which significantly improves the accuracy of studying the dynamic behavior of the train-track-roadbed system. Compared with existing technologies, it has the following technical advantages:

[0054] 1. Accurate multi-scale coupling analysis

[0055] Deficiencies of existing technology: Traditional studies on train-track-roadbed systems mostly analyze the train, track, roadbed and roadbed separately, ignoring the interactions between them, making it difficult to accurately predict the overall mechanical behavior of the system.

[0056] Technical Advantages: This method, by coupling multi-body dynamics (MBD) with discrete element methods (DEM) and finite difference methods (FDM), accurately simulates the interactions between the train, track, roadbed, and subgrade. It simultaneously captures both the macroscopic dynamic response of the system and the microscopic mechanical behavior within the roadbed. This multi-scale coupled model comprehensively characterizes the dynamic characteristics of all levels of the system and reveals the load transfer paths and dynamic changes between different structural layers.

[0057] 2. Micro-dynamic simulation of roadbed particles

[0058] Deficiencies of existing technologies: In existing technologies, the ballast track bed is often treated as a continuous medium or discrete mass blocks through simplified methods, ignoring the complex contact, rolling and friction characteristics between ballast particles, and is unable to accurately simulate the microscopic mechanical behavior of the track bed.

[0059] Technical Advantages: This invention incorporates the discrete element method (DEM) to finely model the shape, size, and mechanical behavior of ballast particles. This method can simulate dynamic behaviors such as contact, sliding, wear, and crushing between particles, accurately reproducing the microscopic response of the roadbed under train loads. This approach effectively overcomes the shortcomings of traditional continuum models and can reveal the relationship between hidden defects within the roadbed and the overall dynamic response of the system.

[0060] 3. Real-time coupling calculation interface

[0061] Deficiencies of existing technologies: Existing studies usually simulate the dynamic behavior of trains, tracks, and roadbeds separately and manually input the results into other models, resulting in low computational efficiency and the inability to achieve real-time coupled dynamic simulation.

[0062] Technical Advantages: This method achieves real-time coupling of MBD, DEM, and FDM methods through a Python programming interface, enabling simultaneous calculation of the dynamic responses of different subsystems. This avoids the inaccuracy and inefficiency associated with manual input of results in traditional methods. This real-time calculation method not only improves simulation efficiency but also ensures the timeliness and accuracy of the system's dynamic response.

[0063] 4. More comprehensive system dynamic response

[0064] Deficiencies of existing technologies: Existing numerical simulation methods cannot simultaneously consider the macro- and micro-scale responses of the train, track, roadbed, and subgrade systems, making it difficult to predict the global dynamic behavior of the train under different operating conditions.

[0065] Technical Advantages: This invention analyzes the mechanical effects of train loads on track, roadbed, and subgrade at a macroscopic level, while simultaneously simulating the local behavior of ballast particles at a microscopic level. This multi-layered, integrated analysis provides a more comprehensive and accurate system dynamic response, offering significant advantages in predicting track settlement, ballast wear, and subgrade deformation.

[0066] 5. Efficient hidden disease simulation

[0067] Deficiencies of existing technologies: Traditional methods for detecting hidden roadbed defects mostly rely on on-site measurements, making it difficult to conduct real-time dynamic analysis and lacking microscopic mechanical analysis of hidden defects.

[0068] Technical Advantages: This invention uses the discrete element method to accurately simulate the impact of hidden roadbed defects on the overall mechanical response of the system. Combined with dynamic simulations of train loads, it can analyze in real time the dynamic effects of ballast degradation, crushing, and other defects on the train-track-roadbed system, providing a more accurate defect diagnosis tool.

[0069] In summary, the present invention overcomes the limitations of existing technologies by innovatively introducing MBD-DEM-FDM coupling technology. It can more accurately and efficiently simulate the complex mechanical behavior of the train-track-roadbed system, significantly improving the ability to predict the system's dynamic response. In particular, it demonstrates unique technical advantages in the analysis of the microscopic behavior and defects of the roadbed under train loads. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in related technologies, the following briefly introduces the drawings required for use in the specific embodiments or related technical descriptions. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0071] Figure 1 Schematic diagram of the numerical model of the train-ballasted track-roadbed three-dimensional coupling system established based on the existing technology, where Figure 1 (a) is a longitudinal cross-sectional view. Figure 1 (b) is a transverse cross-sectional view;

[0072] Figure 2 Schematic diagram of a three-dimensional multi-body dynamic model of a train vehicle established according to the prior art; Figure 2 (a) is a side view; Figure 2 (b) is a top view; Figure 2 (c) is a front view;

[0073] Figure 3 Flowchart of a train-ballasted track-roadbed system simulation method based on MBD-DEM-FDM coupling according to an embodiment of the present invention;

[0074] Figure 4 A schematic diagram of parameters and structure of a three-dimensional train model provided according to an embodiment of the present invention;

[0075] Figure 5 A schematic diagram of a three-dimensional train-ballasted track coupling model provided according to an embodiment of the present invention;

[0076] Figure 6 The ballast layer modeling process provided by the embodiment of the present invention, wherein Figure 6 (a) corresponds to the first three compaction processes, Figure 6 (b) After deleting the ballast on both sides, a wall is generated on the top surface of the roadbed and the ballast slopes on both sides, and the final compaction process is performed; Figure 6 (c) Process of placing sleepers corresponding to particles in the deleted sleeper area;

[0077] Figure 7 Schematic diagram of the coupling algorithm between discrete particles and the contact surface of continuous media provided according to an embodiment of the present invention; Figure 7 (a) Schematic diagram of the coupling interface position; Figure 7 (b) is a schematic diagram of the coupling process principle;

[0078] Figure 8 A diagram of a three-dimensional coupling model of sleepers, trackbeds, and roadbeds provided according to an embodiment of the present invention;

[0079] Figure 9 A flowchart of numerical calculation and analysis provided according to an embodiment of the present invention;

[0080] Figure 10 The data interaction interface and flow chart of the MBD part and the DEM-FDM part provided according to the embodiment of the present invention;

[0081] Figure 11 A comparison chart of numerical simulation results and measured data provided according to an embodiment of the present invention; Figure 11 (a) is a schematic diagram comparing the measured rail displacement with the simulation results; Figure 11 (b) is a schematic diagram comparing the measured displacement of the sleeper with the simulation results;

[0082] Figure 12 Schematic diagram of ballast-deficient working condition of the model provided in an embodiment of the present invention; Figure 12 (a) is the working condition diagram of the ballast missing in the middle of the sleeper; Figure 12 (b) is the working condition diagram of ballast shortage at rail support; Figure 12 (c) is the working condition diagram of local ballast shortage on both sides; Figure 12 (d) is the working condition diagram of large-area ballast shortage on both sides; Figure 12 (e) is the working condition diagram of complete ballast absence;

[0083] Figure 13 This is a diagram of the model application results provided according to an embodiment of the present invention; Figure 13 (a) is a schematic diagram of the contact force chain results; Figure 13 (b) is a schematic diagram of the sleeper displacement results; Figure 13 (c) is a schematic diagram of the sleeper acceleration results;

[0084] Figure 14 This is a diagram of the architecture of a train-ballasted track-roadbed system simulation system based on MBD-DEM-FDM coupling according to an embodiment of the present invention;

[0085] Figure 15 A structural diagram of an electronic device provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0086] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0087] In the description of the present invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limitations on the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0088] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood in a broad sense. For example, they may refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediate medium; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on the specific circumstances.

[0089] Example 1

[0090] See also Figure 3 This embodiment provides a train-ballasted track-roadbed system simulation method based on MBD-DEM-FDM coupling, including:

[0091] S1, establishing a train model based on a multi-body dynamics (MBD) method, including: establishing a dynamic model of the train system based on the multi-body dynamics (MBD) method, wherein the train suspension system is simplified by using springs and dampers in the dynamic model of the train system, and interaction between the train and the track is considered;

[0092] As a preferred embodiment, the S1 includes:

[0093] S11, based on MBD theory, establish rigid bodies such as the car body, bogie, and wheelset, where the car body and the two bogies are connected through the primary and secondary suspension systems, and the springs and dampers of the suspension system are simplified to linear models, such as Figure 4 Each vehicle model has 30 degrees of freedom, of which each car body and bogie has 6 degrees of freedom, which are longitudinal displacement x c , lateral displacement y c , sinking and floating (vertical displacement) z c , roll angle θ c , pitch angle φ c and yaw angle φ c Each wheelset has four degrees of freedom, namely longitudinal displacement x wi , lateral displacement y wiand vertical displacement (sinking and floating) z wi .

[0094] In this embodiment, the specific degrees of freedom are shown in Table 1, which shows the degree of freedom distribution of the train vehicle model.

[0095] Table 1

[0096]

[0097] S12, in the modeling of the suspension system, the connections between the vehicle body and the bogie, and between the bogie and the wheelset are simulated by linear springs and dampers.

[0098] In the modeling of the suspension system, the connections between the car body and the bogie, as well as between the bogie and the wheelset, are simulated using linear springs and dampers. This multi-degree-of-freedom model not only fully describes the relative motion of various components during train operation, but also considers the dynamic response characteristics of the train under different track conditions, thereby enabling subsequent track-vehicle coupled dynamics analysis. Figure 4 This is a schematic diagram of the parameters and structure of a three-dimensional train model.

[0099] S13, based on the Hamiltonian principle, starting from the total kinetic energy, total potential energy, and virtual work of the system, by constructing a generalized coordinate system, the mass matrix, stiffness matrix, damping matrix, and load matrix of the system are obtained, and finally the vibration dynamics equations of the train system are formed. The vibration dynamics equations are:

[0100]

[0101] Where: M v 、C v and K v are the mass matrix, damping matrix and stiffness matrix of the train vehicle, F v is the load vector, X v is the displacement matrix.

[0102] In this embodiment, the train has many degrees of freedom, resulting in a very complex vibration equation. Traditional force balance analysis methods are difficult and complex to directly derive its motion equations. However, analyzing its motion patterns from an energy perspective is more convenient and effective. Therefore, based on the Hamiltonian principle, starting from the system's total kinetic energy, total potential energy, and virtual work, and constructing a generalized coordinate system, the system's mass matrix, stiffness matrix, damping matrix, and load matrix are derived, ultimately forming the vibration equations for the train subsystem.

[0103] S14, establishing a three-dimensional train-track model, including: calculating the normal force between the wheel and rail based on Hertz nonlinear contact theory; simulating the wheel-rail tangential contact force based on Kalker creep theory; establishing a wheel-rail contact coupling model based on the normal force between the wheel and rail and the tangential contact force between the wheel and rail, wherein the wheel-rail contact coupling model can accurately calculate the dynamic changes of the wheel-rail contact during the train operation; continuing to comprehensively consider four different types of track irregularities, wherein the four types of track irregularities include height irregularity, directional irregularity, horizontal irregularity and gauge irregularity, including: different types of track irregularities obtained by simulation and analysis using the trigonometric series method are input into the wheel-rail contact coupling model as external excitations to obtain a first comprehensive sample of height irregularity and horizontal irregularity, and a second comprehensive sample of gauge irregularity and directional irregularity; establishing the three-dimensional train-track model based on the first comprehensive sample and the second comprehensive sample.

[0104] The power spectrum density calculation formulas for the four types of track irregularities are as follows:

[0105] (1) Uneven height:

[0106]

[0107] (2) Unsmooth direction:

[0108]

[0109] (3) Uneven level:

[0110]

[0111] (4) The power spectrum of track gauge irregularity is generally similar to the expression of horizontal irregularity, but the influence of the distance between the left and right rolling circles is not considered. Therefore, its specific expression is as follows:

[0112]

[0113] In formulas (2) to (5), the unit of formula (2), (3) and (5) is m. 2 / (rad / m), the physical meaning of formula (4) is measured by inclination angle, so the unit is 1 / (rad / m); where b is half of the distance between the left and right rolling circles, and in the embodiment of the present invention, it is taken as 0.75m based on existing research; Ω c ,Ω r ,Ω s , is the cutoff frequency; A a 、A v 、A g For the roughness coefficient, the German low-interference track power spectrum is used, and its value is shown in Table 2. Low-interference power spectrum parameter values.

[0114] Table 2

[0115]

[0116] The different types of track irregularities obtained by simulation and analysis using the trigonometric series method are used as external excitation inputs to the calculation of the overall coupled system, resulting in a combination of high and low irregularities and horizontal irregularities, as well as a comprehensive sample of gauge and directional irregularities. The final schematic diagram of the train-track three-dimensional model is shown below. Figure 5 shown.

[0117] S15, calculating the dynamic model of the train system based on the Wilson-θ integration method, including: first discretizing the vibration dynamics equations of the train system, introducing a correction factor θ to adjust the response within each time step by setting equally spaced discrete time points, and adjusting the acceleration, velocity and displacement of the next time step to reflect the correction effect of the current time step; then, gradually correcting the response of the system through an iterative process within each time step until a given convergence condition is met.

[0118] S2, establish a three-dimensional ballasted trackbed model based on the discrete element method (DEM);

[0119] As a preferred embodiment, the S2 includes:

[0120] S21, constructing a mesoscopic mechanical model of ballast particles, including: simulating contact, friction, and rolling behaviors of ballast particles based on the discrete element method (DEM), and establishing a particle stacking model as the mesoscopic mechanical model of ballast particles by setting mesoscopic parameters such as particle gradation, size, and density;

[0121] In this embodiment, the S21 includes:

[0122] (1) Define the geometric parameters of ballast particles, determine the particle size distribution, and use PFC software to generate particles;

[0123] (2) Considering the contact model between particles, the contact model between particles is set as an anti-rolling linear contact model, and boundary conditions are set to simulate the dynamic behavior between particles and other structural components.

[0124] S22, compacting the ballast particle micromechanical model to establish the three-dimensional ballasted track bed model.

[0125] In this embodiment, the compaction step S22 is as follows: Figure 6 Shown, including:

[0126] (1) In the designated area, ballast is generated three times, and after each generation, wall units are generated above the ballast particles and compacted using the servo control principle (e.g. Figure 6 (a), the compressive stress is 200kPa, and three compaction procedures are carried out. The ballast slope is 1:1.75, and the thickness of the final roadbed model is 0.55m. Then, walls are generated on the top surface of the roadbed and the ballast slopes on both sides, and the final compaction is carried out, as shown in FIG. Figure 6 As shown in (b); finally, the particles in the sleeper area are deleted and the sleepers are placed, as shown in Figure 6 (c) shown.

[0127] (2) By measuring the overall porosity of the roadbed, the ρ of the final roadbed model is calculated b About 1600kg / m 3 , meeting the requirements of the Heavy Haul Railway Design Code (TB 10625-2017). Viscoelastic artificial boundary conditions were used to reduce the reflection effect at the trackbed edge and ensure the accuracy of the numerical simulation.

[0128] S3, establishing a finite difference model of the roadbed based on the finite difference method FDM, including: considering the roadbed as a continuous medium, simulating the mechanical behavior and deformation characteristics of the roadbed under the action of train load based on the finite difference method FDM, thereby obtaining the roadbed finite difference model;

[0129] As a preferred embodiment, the S3 includes:

[0130] S31, the roadbed is regarded as a continuous medium, a roadbed grid division numerical model is established, and material properties and boundary conditions of the roadbed grid division numerical model are set;

[0131] In this embodiment, the specific location and method of setting the boundary conditions are as follows:

[0132] (1) A wall unit is established on the roadbed surface in the FDM calculation area, and the data information of velocity and force in the coupling process is transmitted through the wall unit to realize the interactive iterative coupling process of force and velocity between the DEM calculation area and the FDM calculation area.

[0133] The coupling process occurs at the contact interface between each sleeper and ballast, as well as at the contact interface between the roadbed and ballast, e.g. Figure 7 (a) The coupling mechanism is to connect the vertices of the coupling wall by the mesh nodes at the coupling interface in the FDM calculation area, and the two move synchronously with each other. The coupled triangular wall will generate the contact force (F) generated by the particle motion in the PFC calculation area. c ) and contact torque (M c). However, since the Zone element in FLAC cannot directly withstand bending moments, the concentrated force is interpreted and transferred during the coupling calculation process, each grid vertex is equivalently weighted, and the equivalent weighted vertex force is transferred to the FDM grid. At the same time, according to Newton's second law, any displacement caused by the force at the grid point will also drive the movement of the coupled wall, which further leads to corresponding changes in the position of the particles in the DEM area. These changes in the relative position between the particles and the coupling interface lead to new FDM. c and M c The specific process of Figure 7 (b) shown.

[0134] (2) The continuous iteration of the above process realizes the real-time coupling between the discrete domain and the continuous domain.

[0135] S32, the finite difference method is used to solve the numerical model of the roadbed mesh, and the mechanical behavior and deformation characteristics of the roadbed under the train load are simulated, thereby obtaining a DEM ballasted roadbed three-dimensional model including three sleepers. The model is displayed as follows Figure 8 shown.

[0136] S4, setting up a coupling medium to couple MBD-DEM-FDM and perform real-time information exchange between MBD and DEM and FDM systems;

[0137] As a preferred embodiment, the S4 includes:

[0138] S41, using the coupling relationship of track-ballast-subgrade interface to establish the coupling model between MBD-DEM and DEM-FDM;

[0139] S42, achieving real-time coupling between the train multi-body system and the discrete ballast particle system by defining a mechanical transfer relationship between the rail and the sleeper;

[0140] S43, by setting an artificial viscoelastic boundary in the discrete element numerical model, an equivalent simulation between the ballast mass and the discrete ballast particles is achieved, thereby realizing real-time information exchange between the MBD and DEM and FDM systems.

[0141] In this embodiment, the implementation of step S4 includes: first transmitting the train load to the trackbed-roadbed system through the spring damping system, and then transmitting the reaction force calculated in the trackbed-roadbed system and the dynamic response of each structural layer to the upper train model in real time, thereby realizing real-time dynamic coupling calculation of the entire coupling system, wherein the real-time dynamic coupling calculation is used to simulate the dynamic response of the train during driving. During the real-time dynamic coupling calculation process, the MBD and DEM and FDM systems will exchange information in real time to ensure that the interaction between the train and the track, trackbed, and roadbed is accurately captured. The specific flow chart is shown as follows: Figure 9 shown.

[0142] like Figure 9 As shown, the specific implementation process of this embodiment includes:

[0143] (1) The data interaction interface between the MBD part and the DEM-FDM part is established through Python program, and the motion response of the train is transmitted to the track bed and roadbed, and the corresponding calculation and judgment are performed. If the set threshold is met, the dynamic analysis of the next time step is performed. The specific judgment formula and process are as follows: Figure 10 As shown:

[0144] In order to accurately simulate the mechanical behavior of the fastener in the MBD and DEM systems, the fastener is equivalently modeled using a spring-damper system. The equivalent force on the fastener at each time step is calculated in real time. The calculation formulas for the sleeper force in each three-dimensional direction are shown in Equations (6) and (7):

[0145]

[0146]

[0147] Where: F x1 、F y1 、F z1 They represent the forces acting on the fasteners of the left rail in the x, y, and z directions respectively; F x2 、F y2 、F z2 They represent the forces acting on the fasteners of the right rail in the x, y, and z directions respectively; k x 、k y 、k z Respectively represent the spring stiffness coefficients of the fastener in the x, y, and z directions; c x 、c y 、c z Represent the damping coefficients of the fastener in the x, y, and z directions respectively.

[0148] (2) Establish the data interaction interface between the DEM part and the MBD part of the trackbed structure layer through the PFC program:

[0149] A. First, the particle aggregate is equivalent to a three-dimensional block unit body, and the equivalent axial stress inside the particle aggregate is calculated using formula (8):

[0150]

[0151] Where: σ a is the equivalent axial stress inside the particle aggregate unit; F ai is the resultant axial contact force acting on the unit boundary; Di is the diameter of the boundary unit particle; F is the axial contact pressure on a single particle unit; D is the diameter of a single particle unit.

[0152] B. Next, establish boundary conditions, including: A viscoelastic artificial boundary is achieved by arranging distributed springs and dampers on the truncated boundary. The springs are used to simulate the elastic recovery of the infinite domain, while the dampers are responsible for absorbing energy. The spring and damper forces are applied in the normal and tangential directions, respectively, to effectively simulate energy propagation and absorption under dynamic conditions in the three-dimensional model. The calculated stress equation is Equation (9):

[0153]

[0154] Where: σ n and σ s are the normal and tangential stresses respectively; C n and C s are the damping coefficients in the normal and tangential directions respectively; K n and K s are the spring stiffness in the normal and tangential directions, respectively; and are the normal and tangential velocities respectively; u n and u s are the normal and tangential displacements, respectively.

[0155] C. Discretization, including: In order to apply the viscoelastic boundary to the discrete element model, the formula needs to be discretized. By introducing the calibration coefficient β 3p , β 3s , and combined with the equivalent axial stress formula and stress equation, the force formula of each particle on the boundary condition is obtained as shown in formula (10), and the calibration coefficients are adjusted to optimize the wave absorption effect, and the optimal values ​​of these coefficients are determined by a step-by-step iterative method.

[0156]

[0157] D. Based on the above process, the forces acting on the spring-damper system between the ballast masses in the MBD system can be equated to the forces acting on the granular ballast particles in the DEM system. These forces are updated in real time and transmitted to the DEM system. Simultaneously, the DEM system updates the dynamic responses, such as particle displacement, velocity, and acceleration, in real time. The dynamic changes in the center of mass of the aggregate are calculated using the following equations (11) and (12), and the resulting dynamic responses are transmitted to the MBD system.

[0158] Center of mass displacement:

[0159] Center of mass velocity:

[0160] S5, establishing a coupling model based on MBD-DEM-FDM coupling and verifying and applying the coupling model, including: establishing a coupling model, obtaining simulation results based on the coupling model, and comparing and analyzing the simulation results with the on-site dynamic response to verify the correctness of the coupling model; establishing five ballast-deficient working conditions to calculate and obtain a particle contact force chain diagram and a sleeper displacement acceleration curve diagram to realize the application of the coupling model.

[0161] In this embodiment, the train-ballasted track-roadbed system simulation method based on MBD-DEM-FDM coupling is based on the on-site operating parameters of the heavy-duty Shuohuang Railway Line. The HXD1 locomotive has an axle load of 25t and runs at a speed of 80km / h. The MBD-DEM-FDM coupling model is established to calculate the simulation results of rail displacement and sleeper displacement, and compare them with the on-site measured dynamic response. Figure 11 As shown in the figure, it can be seen that the simulation results are in good agreement with the measured data, which verifies the correctness of the coupling method.

[0162] In addition, based on the on-site working condition parameters of the heavy-load Shuohuang Railway Line, five working conditions were established: ballast missing in the middle of the sleeper, ballast missing at the rail support, partial ballast missing on both sides, large-area ballast missing on both sides, and complete ballast missing. Figure 12 As shown in the figure, the particle contact force chain diagram and the sleeper displacement acceleration curve are calculated as shown in the figure. Figure 13 As shown, the specific application of the MBD-DEM-FDM coupling model is realized.

[0163] Example 2

[0164] like Figure 14 As shown, this embodiment provides a train-ballasted track-roadbed system simulation system based on MBD-DEM-FDM coupling, which is used to implement the method of embodiment 1, including:

[0165] The train model establishment module 101 is configured to establish a train model based on a multi-body dynamics (MBD) method, including: establishing a dynamic model of the train system based on the multi-body dynamics (MBD) method, wherein the train suspension system is simplified by using springs and dampers, and the interaction between the train and the track is considered;

[0166] The three-dimensional ballast model establishment module 102 is used to establish a three-dimensional ballast model based on the discrete element method (DEM). The module includes: simulating the contact, friction, and rolling behaviors of ballast particles based on the discrete element method (DEM); establishing a particle accumulation model by setting microscopic parameters such as particle gradation, size, and density; and compacting the particle accumulation model to establish the three-dimensional ballast model.

[0167] The subgrade finite difference model establishment module 103 is used to establish a subgrade finite difference model based on the finite difference method FDM, including: treating the subgrade as a continuous medium, simulating the mechanical behavior and deformation characteristics of the subgrade under the action of train loads based on the finite difference method FDM, thereby obtaining the subgrade finite difference model;

[0168] MBD-DEM-FDM coupling module 104 is used to set a coupling medium to couple MBD, DEM and FDM, and perform real-time information exchange between MBD and DEM and FDM systems;

[0169] The coupling model establishment and verification application module 105 is used to establish a coupling model based on MBD-DEM-FDM coupling and verify and apply the coupling model, including: establishing a coupling model, obtaining simulation results based on the coupling model, and comparing and analyzing the simulation results with the on-site dynamic response to verify the correctness of the coupling model; establishing five ballast-missing working conditions to calculate and obtain a particle contact force chain diagram and a sleeper displacement acceleration curve diagram to realize the application of the coupling model.

[0170] The present invention proposes a three-dimensional numerical simulation method based on MBD-DEM-FDM coupling in a train-ballasted track-roadbed system, overcoming the limitations of the existing technology. In particular, it achieves improvements and innovations in the following aspects:

[0171] 1. Coupling Multibody Dynamics (MBD) and Discrete Element Method (DEM): This embodiment of the present invention achieves the first real-time coupling of a multibody train dynamics model with a discrete element model of the roadbed particles. This allows for precise simulation of the microscopic mechanical behavior of ballast particles under train loads, revealing the complex mechanical effects of train load transfer. Compared to existing methods that simplify the processing of ballast particles, this invention significantly improves simulation accuracy by realistically simulating particle contact, rolling, and friction.

[0172] Technical Effect: This method can more accurately predict the dynamic impact of train loads on the track and roadbed system, and effectively reveal the mechanical mechanism of problems such as long-term track settlement and roadbed deterioration.

[0173] 2. Establishment of a 3D coupled model: By combining MBD, DEM, and FDM, a complete train-track-roadbed-subgrade coupled model is formed. This model not only analyzes the macroscopic dynamic response of the train and track, but also captures the microscopic mechanical behavior of the ballast through DEM and analyzes the deformation characteristics of the subgrade through FDM.

[0174] Technical Effect: The model can accurately simulate the macro- and micro-dynamic responses of trains under different operating conditions, greatly enhancing the expressiveness of the system's overall mechanical behavior and improving the ability to predict track and roadbed deformation and damage.

[0175] 3. Coupling Calculation Interface: This paper implements a coupling interface between the MBD system and the DEM system using Python programming, and further implements multi-level coupling with the FDM. This method enables real-time exchange of force and displacement information between subsystems, ensuring efficient calculation and stability.

[0176] Technical Effect: Through this real-time coupled calculation, the present invention can simulate the complex dynamic behavior of the train under different working conditions, including the interaction between the train, track, roadbed and roadbed, effectively reducing the need for on-site measurements.

[0177] Invention point:

[0178] 1. Establishment of MBD-DEM-FDM coupled numerical model: A three-dimensional coupled computational model based on multibody dynamics, discrete element method, and finite difference method is proposed to simulate the dynamic interaction of the train-track-roadbed-roadbed system.

[0179] 2. Real-time coupling calculation interface: The embodiment of the present invention uses Python program to achieve real-time coupling of MBD with DEM and FDM systems, and perform dynamic information exchange.

[0180] 3. Discrete element roadbed particle micromechanical model: The embodiment of the present invention aims at the micromechanical behavior of ballast particles and establishes a discrete element model that takes into account particle contact, rolling and friction, which can accurately simulate the microdynamic response of the roadbed.

[0181] 4. Equivalent treatment method of coupling interface: Through the spring damping system between the track and the roadbed, the coupling calculation of MBD and DEM, DEM and FDM is realized, and the mechanical characteristics of each layer structure are taken into account.

[0182] The present invention also provides a memory storing a plurality of instructions, wherein the instructions are used to implement the method as in the first embodiment.

[0183] like Figure 15 As shown, the present invention also provides an electronic device, including a processor 301 and a memory 302 connected to the processor 301, the memory 302 stores multiple instructions, and the instructions can be loaded and executed by the processor to enable the processor to execute the method as in embodiment 1.

[0184] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. The train-ballasted track-roadbed system simulation method based on MBD-DEM-FDM coupling is characterized by: include: S1, establishing a train model based on a multi-body dynamics (MBD) method, including: establishing a dynamic model of the train system based on the multi-body dynamics (MBD) method, wherein the train suspension system is simplified by using springs and dampers in the dynamic model of the train system, and interaction between the train and the track is considered; S2, establish a three-dimensional ballasted trackbed model based on the discrete element method (DEM); S3, establishing a finite difference model of the roadbed based on the finite difference method (FDM), including: treating the roadbed as a continuous medium, simulating the mechanical behavior and deformation characteristics of the roadbed under train loads based on the finite difference method (FDM), thereby obtaining the finite difference model of the roadbed; S4, setting a coupling medium to couple the MBD-DEM-FDM, and performing real-time information exchange between the MBD, DEM, and FDM systems; S5, establishing a coupling model based on MBD-DEM-FDM coupling and verifying and applying the coupling model, including: establishing the coupling model, obtaining simulation results based on the coupling model, and comparing and analyzing the simulation results with the on-site dynamic response to verify the correctness of the coupling model; establishing five ballast-deficient working conditions to calculate and obtain a particle contact force chain diagram and a sleeper displacement acceleration curve; in: Said S1 comprises: S11, based on MBD theory, establish the rigid body consisting of car body, bogie and wheelset; S12, in modeling the suspension system, simulating the connection between the vehicle body and the bogie, and between the bogie and the wheelset, by using linear springs and dampers; S13, based on the Hamiltonian principle, starting from the total kinetic energy, total potential energy, and virtual work of the system, by constructing a generalized coordinate system, the mass matrix, stiffness matrix, damping matrix, and load matrix of the system are obtained, and finally the vibration dynamics equations of the train system are formed. The vibration dynamics equations are: （1）； Where: M v 、C v and K v are the mass matrix, damping matrix and stiffness matrix of the train vehicle, F v is the load vector, X v is the displacement matrix; S14, establishing a train-track three-dimensional model; S15, calculating the dynamic model of the train system based on the Wilson-θ integration method, including: first, discretizing the vibration dynamics equations of the train system, introducing a correction factor θ by setting equally spaced discrete time points to adjust the response within each time step, and adjusting the acceleration, velocity, and displacement of the next time step to reflect the correction effect of the current time step; then, gradually correcting the system response through an iterative process within each time step until a given convergence condition is met; The S2 includes: S21, constructing a ballast particle mesomechanical model, including: simulating contact, friction, and rolling behaviors of ballast particles based on the discrete element method (DEM), and establishing a particle stacking model as the ballast particle mesomechanical model by setting particle gradation, size, and density mesoparameters; S22, compacting the ballast particle micromechanical model to establish the three-dimensional ballasted track bed model; The S21 includes: (1) Define the geometric parameters of ballast particles, determine the particle size distribution, and use PFC software to generate particles; (2) Considering the contact model between particles, the contact model between particles is set as an anti-rolling linear contact model, and boundary conditions are set to simulate the dynamic behavior between particles and other structural components.

2. The train-ballasted track-roadbed system simulation method based on MBD-DEM-FDM coupling according to claim 1 is characterized in that: In S11, the car body is connected to the two bogies via the primary and secondary suspension systems, and the springs and dampers of the suspension systems are simplified into linear models; The S14 includes: calculating the normal force between the wheel and rail based on Hertz nonlinear contact theory; simulating the wheel-rail tangential contact force based on Kalker creep theory; establishing a wheel-rail contact coupling model based on the normal force between the wheel and rail and the tangential contact force between the wheel and rail, and the wheel-rail contact coupling model can accurately calculate the dynamic changes of the wheel-rail contact during the train operation; continuing to comprehensively consider four different types of track irregularities, the four types of track irregularities including height irregularity, direction irregularity, horizontal irregularity and gauge irregularity, including: different types of track irregularities obtained by simulation and analysis using the trigonometric series method are input into the wheel-rail contact coupling model as external excitations to obtain a first comprehensive sample of height irregularity and horizontal irregularity, and a second comprehensive sample of gauge irregularity and direction irregularity; establishing the train-track three-dimensional model based on the first comprehensive sample and the second comprehensive sample; S15, calculating the dynamic model of the train system based on the Wilson-θ integration method, including: first discretizing the vibration dynamics equations of the train system, introducing a correction factor θ to adjust the response within each time step by setting equally spaced discrete time points, and adjusting the acceleration, velocity and displacement of the next time step to reflect the correction effect of the current time step; then, gradually correcting the response of the system through an iterative process within each time step until a given convergence condition is met.

3. The train-ballasted track-roadbed system simulation method based on MBD-DEM-FDM coupling according to claim 2 is characterized in that: The S22 includes: (1) In the designated area, ballast is generated three times. After each generation, wall units are generated above the ballast particles and compacted using the servo control principle. The compressive stress is 200 kPa. A total of three compaction procedures are performed. The ballast slope is 1:1.75, and the thickness of the final roadbed model is 0.55 m. Then, walls are generated on the top surface of the roadbed and the ballast slopes on both sides, and the final compaction is performed. Finally, the particles in the sleeper area are removed and the sleepers are placed. (2) By measuring the overall porosity of the roadbed, the ρ of the final roadbed model is calculated b About 1600kg / m 3 , meeting the requirements of the "Heavy Haul Railway Design Code" (TB 10625-2017).

4. The train-ballasted track-roadbed system simulation method based on MBD-DEM-FDM coupling according to claim 3 is characterized in that: The S3 includes: S31, the roadbed is regarded as a continuous medium, a roadbed grid division numerical model is established, and material properties and boundary conditions of the roadbed grid division numerical model are set; S32, solving the subgrade grid numerical model using a finite difference method to simulate the mechanical behavior and deformation characteristics of the subgrade under the train load, thereby obtaining the subgrade finite difference model.

5. The train-ballasted track-roadbed system simulation method based on MBD-DEM-FDM coupling according to claim 4 is characterized in that: The S4 includes: S41, using the coupling relationship of track-ballast-subgrade interface to establish the coupling model between MBD-DEM and DEM-FDM; S42, by defining the mechanical transfer relationship between rails and sleepers, the real-time coupling between the train multi-body system and the discrete ballast particle system is achieved; S43, by setting an artificial viscoelastic boundary in the discrete element numerical model, an equivalent simulation between the ballast mass and the discrete ballast particles is achieved, thereby realizing real-time information exchange between the MBD and DEM and FDM systems.

6. A train-ballasted track-roadbed system simulation system based on MBD-DEM-FDM coupling, used to implement the method according to claim 1, characterized in that: include: A train model building module (101) is used to build a train model based on a multi-body dynamics (MBD) method, comprising: building a dynamic model of a train system based on the multi-body dynamics (MBD) method, wherein the train suspension system is simplified by using springs and dampers in the dynamic model of the train system, and the interaction between the train and the track is considered; A three-dimensional ballast model establishment module (102) is used to establish a three-dimensional ballast model based on a discrete element method (DEM); the module comprises: simulating the contact, friction and rolling behavior of ballast particles based on the discrete element method (DEM), establishing a particle accumulation model by setting particle gradation, size and density microscopic parameters, and compacting the particle accumulation model to establish the three-dimensional ballast model; A roadbed finite difference model establishment module (103) is used to establish a roadbed finite difference model based on a finite difference method (FDM), comprising: treating the roadbed as a continuous medium, simulating the mechanical behavior and deformation characteristics of the roadbed under train load based on the finite difference method (FDM), and thereby obtaining the roadbed finite difference model; MBD-DEM-FDM coupling module (104), used to set a coupling medium to couple MBD-DEM-FDM and perform real-time information exchange between MBD and DEM and FDM systems; A coupling model establishment and verification application module (105) is used to establish a coupling model based on MBD-DEM-FDM coupling and verify and apply the coupling model, including: establishing a coupling model, obtaining simulation results based on the coupling model, and comparing and analyzing the simulation results with the on-site dynamic response to verify the correctness of the coupling model; establishing five ballast-missing working conditions to calculate and obtain a particle contact force chain diagram and a sleeper displacement acceleration curve diagram to realize the application of the coupling model.

7. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the memory stores a plurality of instructions, and the processor is configured to read the instructions and execute the method according to any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a plurality of instructions, and the plurality of instructions can be read by a processor to execute the method according to any one of claims 1 to 5.

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