A method for analyzing train operation safety on railway lines under earthquake conditions

Abstract

This invention discloses a method for analyzing the train operation safety of railway lines under earthquake conditions. The steps are as follows: establishing a finite element model of the track-substructure; applying seismic excitation; calculating the dynamic response under earthquake conditions using a step-by-step integration method; extracting the rail response below the wheelsets; establishing a train-track coupled subsystem using multibody dynamics software; superimposing the rail response as track irregularity with the existing track irregularity into the train-track coupled subsystem and conducting dynamic analysis; and evaluating train operation safety based on the results of the dynamic analysis of the train-track coupled subsystem. This invention decomposes the dynamic analysis of complex train-track-substructure coupled systems under earthquake conditions into dynamic analysis of the track-substructure under earthquake conditions and dynamic analysis of the train-track coupled system under the excitation of track irregularities caused by earthquakes, solving the problem of the difficulty in implementing seismic dynamic analysis of complex train-track-substructure coupled systems in engineering.

Description

Technical Field

[0001] This invention belongs to the field of track engineering technology, specifically relating to a method for analyzing the safety of train operation on railway lines under earthquake conditions. Background Technology

[0002] For more than 100 years, China's railways have gone through a difficult and tortuous development process, from nothing to something, from weak to strong. In the past ten years or so, the rapid development of my country's railway construction, especially high-speed railways, has attracted worldwide attention. By the end of 2021, my country's railway operating mileage exceeded 150,000 kilometers, of which high-speed railways exceeded 40,000 kilometers. By 2035, my country's railway plan is to build a modern high-speed railway network and improve a widely covered national railway network: (1) On the basis of the "four vertical and four horizontal" high-speed railways, some 200 km / h railways will be used to form a high-speed railway network with the "eight vertical and eight horizontal" main channels as the backbone, regional connecting lines, and intercity railways as supplements; (2) Expand the coverage of the railway network in the central and western regions, improve the network layout in the eastern region, and form a widely covered and interconnected conventional railway network.

[0003] Earthquakes are frequent, intense, shallow-focused, and widely distributed. They have caused severe damage to tracks on conventional and high-speed railway bridges, and even major accidents such as train derailments. Therefore, earthquake-induced train safety assessments are of great significance for the seismic design of the substructure and the assessment of post-earthquake track capacity.

[0004] Many scholars have conducted extensive research on train safety on different types of bridges under earthquakes. These studies typically establish complex train-track-substructure models to analyze the dynamic response of the coupled system under earthquake conditions, thereby assessing train safety. The complex train-track-substructure coupled system mainly consists of three parts: the train subsystem, the wheel-rail contact model, and the track-bridge subsystem. The vehicle model and wheel-rail contact model are usually established using multi-rigid-body dynamics, while the track-substructure model is usually established using the finite element method. Because strong excitations such as earthquakes can cause extreme situations like wheel flange contact and wheel-rail separation, a complex spatial rolling wheel-rail contact model is needed to accurately simulate wheel-rail contact behavior under earthquakes and further accurately determine train safety. However, complex spatial wheel-rail contact relationships are difficult to implement in finite element software. Furthermore, railway substructures are diverse, with varying forms and complexities, making them difficult to implement in multi-body dynamics software. These two factors determine that the dynamic analysis of the train-track-substructure coupled system under earthquakes cannot be achieved in a single software platform. Therefore, most scholars use self-programming to conduct dynamic response analysis of coupled systems, but self-programming to implement dynamic analysis of coupled systems is too complicated for engineering applications.

[0005] To reduce the complexity of dynamic analysis of train-track-substructure coupled systems, many scholars have either optimized the dynamic analysis process of the coupled system or attempted to find a direct mapping relationship between the excitation source and train operation safety to assess train operation safety. Zhang et al. used a full-process iterative method to transform the coupling between the train and the bridge at each time step into a full-process coupling, thus allowing for the separate calculation of the dynamic responses of the train subsystem and the bridge subsystem. Gong et al. used a co-simulation method to conduct dynamic analysis of the train-track subsystem and substructure in both a self-developed program and finite element software, achieving dynamic analysis of complex train-track-substructure coupled systems through data exchange between the software at each time step. These methods remain relatively complex and require consideration of the comprehensive coupling of the complex system. Liu et al. studied the correlation between various seismic motion indicators and train operation safety, pointing out that the velocity spectrum intensity and Housner intensity of seismic motion have the highest correlation with train operation safety on bridges, making them the comprehensive optimal indicators for analyzing train safety on high-speed railway bridges. Luo assumes that the track structure remains straight under earthquake conditions and that train speed has little impact on train safety during earthquakes. Based on an energy perspective, he proposes using the velocity spectrum intensity of the time history response at the top of the bridge structure as a criterion for judging train safety, and calculates the safety limits of the velocity spectrum intensity for conventional trains and Shinkansen high-speed trains under earthquake conditions. This simplified method can qualitatively assess train safety under earthquakes and is applicable to engineering practice. However, the established mapping relationship is often only applicable to specific parameters and structural systems, and cannot meet general engineering needs.

[0006] In summary, the interdisciplinary nature of these fields makes it difficult to perform dynamic analysis of complex train-track-substructure coupled systems using a single analysis software. Implementing the coupling between the train subsystem and the track-substructure subsystem in a custom-written program is overly complex. Simply establishing a mapping relationship between train safety indicators and input excitation indicators cannot accurately assess train safety under normal conditions. Therefore, current methods are not applicable in the engineering field, and new earthquake-resistant train safety assessment methods suitable for practical engineering applications are needed. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a method for analyzing the train operation safety of railway lines under earthquakes, thereby solving the problem that the dynamic analysis of the train-track-substructure coupled system under earthquakes is too complex.

[0008] The technical solution of this invention to solve the above-mentioned technical problems is: a method for analyzing the train operation safety of railway lines under earthquakes, comprising the following steps:

[0009] Step 1: In self-developed software or finite element software, establish a finite element model of the track-substructure using the finite element method. Apply seismic excitation using the mass method, equivalent load method, or high stiffness method. Calculate its dynamic response under seismic conditions using the Newmark-β or Wilson-θ stepwise integration method. Extract the rail displacement response below each wheelset based on the train speed.

[0010] Step 2: In a self-developed program or multibody dynamics software, a space vehicle model is established using multibody dynamics. A track structure model is established using the finite element method or an embedded track module. The vehicle model and the track model are coupled into a train-track coupled subsystem through the spatial rolling wheel-rail contact relationship.

[0011] Step 3: The rail displacement response obtained in Step 1 is converted from the time domain to the spatial domain according to the train speed, and is applied as a track irregularity to the train-track coupled subsystem established in Step 2, and dynamic analysis is carried out using the Newmark-β or Wilson-θ stepwise integration method.

[0012] Step 4: Based on the dynamic analysis results of the train-track coupled subsystem obtained in Step 3, evaluate the train's operational safety using standard indicators or wheel-rail geometric indicators. Extract the vertical and lateral wheel-rail forces, calculate the derailment coefficient and wheel load reduction rate, and compare them with the standard limits to determine whether the train's operation is safe. Extract the relative lateral displacement of the wheel and rail and the wheel lift, and compare them with the reference limits given in the literature to determine whether the train's operation is safe.

[0013] Furthermore, step 1 specifically includes the following steps:

[0014] Step 1.1: During the track-substructure dynamic analysis, the spatial position of each wheelset at the current time step is obtained based on the train speed and the relative distance between the train wheelsets;

[0015] Step 1.2: During the track-substructure dynamic analysis, based on the spatial position of the wheelset at the current time step, locate the rail element where each wheelset is located, obtain the corresponding track element node response, and obtain the rail response below the wheelset by performing linear interpolation or cubic spline interpolation on the element node response based on the relative position of the wheelset in the rail element.

[0016] Furthermore, step 2 specifically includes the following steps:

[0017] Step 2.1: Build a space vehicle model using multibody dynamics, or build a space vehicle model by inputting the corresponding parameters in multibody dynamics software;

[0018] Step 2.2: Establish the track structure model using the finite element method, transfer matrix method, or moving track method, or establish the track structure model by inputting relevant parameters in multibody dynamics software;

[0019] Step 2.3: Considering the geometric profiles of the wheelset and rail, establish a nonlinear spatial rolling wheel-rail contact model. Use the spatial trace method to search for the wheel-rail contact point, use the Hertz nonlinear model to calculate the wheel-rail contact normal force, use the Kalker creep theory to calculate the wheel-rail tangential creep force, and correct it using the Shen-Hedrick-Elkins theory; or input relevant parameters into multibody dynamics software to establish a spatial wheel-rail contact model.

[0020] Step 2.4: Couple the vehicle model and track model into a train-track subsystem by using the wheel-rail contact model and the coordination relationship between force and displacement.

[0021] Furthermore, step 3 specifically includes the following steps;

[0022] Step 3.1: Transform the rail response obtained in Step 1 from the time domain to the spatial domain according to the train speed, and superimpose it with the original track irregularities;

[0023] Step 3.2: In the dynamic analysis of the train-track coupled subsystem, the wheel-rail contact search at each time step considers the superimposed track irregularities, and the calculation of the wheel-rail creep force considers the rate of change of the superimposed track irregularities.

[0024] Furthermore, the multibody dynamics software used in step 2 can be SIMPACK, ADAMS, or UM.

[0025] Furthermore, in step 1, when establishing the finite element model of the track-substructure, the rails and track slabs are established using beam elements, the base plate is equivalent to the substructure, the fasteners and CA mortar layer are simulated using spring damping elements, and the substructure is simulated using corresponding elements according to the mechanical properties of each component.

[0026] Furthermore, when establishing the train-track coupling subsystem, the space vehicle model includes a car body, bogie, wheelsets, primary suspension, and secondary suspension. The car body and bogie are connected by secondary suspension, and the bogie and wheelsets are connected by primary suspension.

[0027] Furthermore, in step 2.2, the track structure model is established using the finite element method, the transfer matrix method, or the moving track method. The specific process is as follows:

[0028] Finite element method is adopted: the rails and track slabs are established using beam elements, while the fasteners and CA mortar layer are simulated using spring damping elements. All degrees of freedom of the base plate are constrained, and the dynamic equations of the track structure remain unchanged during the dynamic analysis.

[0029] The transfer matrix method is adopted: the orbital structure is periodically divided into orbital cells, the dynamic equations of various cell structures are established, the stiffness equation coefficients of each interface are calculated, the equivalent external force vector of each interface is calculated at each time step in the dynamic analysis process, the output end response is solved according to the boundary conditions, and the response of each cell is solved by ground deduction.

[0030] The moving track method is adopted: the length of the track structure is determined according to the length of the train and a buffer section of 30 m is reserved before and after. The track structure model of the corresponding length is established using the finite element method. During the dynamic analysis, when the train moves the distance of one rail element, the displacement, velocity, acceleration, and load vector degrees of freedom corresponding to the tail element of the track structure are deleted and new degrees of freedom are added at the head of the track, so as to realize the simulation of an infinitely long track structure by a finite length track structure.

[0031] The beneficial effects of this invention are as follows: Compared with the prior art, this invention uses the earthquake-induced rail response to simulate the earthquake excitation on the train, decomposing the dynamic analysis of the complex train-track-substructure coupled system under earthquake into the dynamic analysis of the track-substructure under earthquake and the dynamic analysis of the train-track coupled system under the excitation of track irregularities caused by earthquake. The relevant dynamic analyses can be carried out in finite element software, multibody dynamics software, and self-written programs, respectively, solving the problem that the seismic dynamic analysis of complex train-track-substructure coupled systems is difficult to implement in engineering. Attached Figure Description

[0032] Figure 1 This is a flowchart of the present invention;

[0033] Figure 2 This is the E1 seismic wave acceleration time history in the embodiments of the present invention;

[0034] Figure 3 This refers to the lateral displacement of the rail below the left wheel of each wheelset at a vehicle speed of 200 km / h in this embodiment of the invention.

[0035] Figure 4 This refers to the lateral displacement of the rail below the left wheel of each wheelset at a vehicle speed of 300 km / h in this embodiment of the invention.

[0036] Figure 5 This is a space vehicle model in an embodiment of the present invention;

[0037] Figure 6 This is a schematic diagram of the train-track coupling model in an embodiment of the present invention;

[0038] Figure 7 This is the lateral wheel-rail force time history at a vehicle speed of 200 km / h in this embodiment of the invention;

[0039] Figure 8 This refers to the lateral relative displacement between the wheel and rail at a vehicle speed of 200 km / h in this embodiment of the invention.

[0040] Figure 9 This is the lateral wheel-rail force time history at a vehicle speed of 300 km / h in this embodiment of the invention;

[0041] Figure 10 This refers to the lateral relative displacement between the wheel and rail at a speed of 300 km / h in this embodiment of the invention. Detailed Implementation

[0042] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are merely one embodiment of the present invention, and not all embodiments. Other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are all within the protection scope of the present invention.

[0043] Taking a 3-carriage CRH2 train crossing a 10-span simply supported beam bridge as an example, this invention analyzes the train operation safety on the bridge during an earthquake, such as... Figure 1 As shown, the present invention provides a method for analyzing the train operation safety of railway lines under earthquake conditions, comprising the following steps:

[0044] Step 1: First, establish a track-bridge model. The rails, track slabs, main beams, and piers are simulated using beam elements, while the fasteners, CA mortar layer, and supports are simulated using spring-damped elements. The base plate is equivalent to the main beam. The large mass method is used to perform seismic response calculations and analysis on the coupled track-bridge model. The ground motion is based on the El Centro earthquake record, and the maximum acceleration amplitude is adjusted to 1.5 m / s². 2 ,like Figure 2 As shown; based on the train's operating speed, the time history of rail displacement at the wheel-rail contact point is extracted, as follows. Figure 3 and Figure 4 As shown. Among them. Figure 3 This refers to the displacement of the rail under the wheels at a speed of 200 km / h. Figure 4 This refers to the displacement of the rail under the wheels at a speed of 300 km / h.

[0045] Step 2: Establish a train-track coupling subsystem through custom programming, such as... Figure 5 and Figure 6As shown, the vehicle model is established using multi-rigid-body dynamics. Each car section includes one car body, two frames, and four wheelsets. The frames and wheelsets are connected by a primary suspension, and the car body and frames are connected by a secondary suspension. Both the primary and secondary suspensions are simulated using spring-damped elements. Each car body and frame has five degrees of freedom: lateral movement, heave, roll, pitching, and yaw. Each wheelset has four degrees of freedom: lateral movement, heave, roll, and yaw. Therefore, each car section has a total of 31 degrees of freedom. The wheel-rail contact model adopts a spatial rolling wheel-rail contact model. The spatial wheel-rail contact point is searched using the trace method. The wheel-rail normal contact adopts a nonlinear Hertz contact model. The tangential creep force is calculated using Kalker linear creep theory and then corrected using Shen-Hedrick-Elkins theory. In the track structure, the rails and track slabs are simulated using beam elements, and the fasteners and CA mortar layer are simulated using spring-damped elements.

[0046] Step 3: The rail response obtained in Step 1 is superimposed on the original track irregularity and applied to the train-track coupled subsystem established in Step 2. Dynamic analysis of the train-track coupled system is carried out to obtain the lateral wheel-rail force and lateral wheel-rail offset to evaluate train operation safety.

[0047] Step 4: Figure 7 , Figure 8 The lateral wheel-rail force and the relative lateral displacement of the wheel and rail at a speed of 200 km / h are given. Figure 9 , Figure 10 The lateral wheel-rail force and relative lateral displacement at a speed of 300 km / h are given. According to the specification, the lateral wheel-rail force should not exceed 55 kN. Obviously, the lateral wheel-rail force meets the specification requirement for a speed of 200 km / h, but exceeds the specification limit for a speed of 300 km / h, and the train operation is in an unsafe state. In addition, the literature specifies a limit of 54 mm for the relative lateral displacement of the wheel and rail. Obviously, the relative lateral displacement of the wheel and rail at speeds of 200 km / h and 300 km / h does not exceed the specified limit. Therefore, from the perspective of the relative lateral displacement of the wheel and rail, the train operation is in a safe state at both speeds.

[0048] Furthermore, to verify the correctness of the earthquake-induced railway train operation safety analysis method of this invention, a dynamic response analysis of the train-track-bridge coupled system under earthquake conditions was conducted. The lateral wheel-rail force and relative wheel-rail displacement under earthquake conditions were also obtained and compared with the results of this invention. Figures 7-10 In the diagram, Conditions 1 and 3 represent the results of the method of this invention, while Conditions 2 and 4 represent the dynamic response results of the train-track-bridge coupled system. It can be seen that the responses calculated by the two methods are in good agreement, which demonstrates the correctness of the method for analyzing the train operation safety of railway lines under earthquake conditions proposed in this invention.

Claims

1. A method for analyzing train operation safety on railway lines under earthquake conditions, characterized in that, Includes the following steps: Step 1: In self-developed software or finite element software, establish a finite element model of the track-substructure using the finite element method. Apply seismic excitation using the mass method, equivalent load method, or high stiffness method. Calculate its dynamic response under seismic conditions using the Newmark-β or Wilson-θ stepwise integration method. Extract the rail displacement response below each wheelset based on the train speed. Step 2: In a self-developed program or multibody dynamics software, a space vehicle model is established using multibody dynamics. A track structure model is established using the finite element method or an embedded track module. The vehicle model and the track model are coupled into a train-track coupled subsystem through the spatial rolling wheel-rail contact relationship. Step 3: The rail displacement response obtained in Step 1 is converted from the time domain to the spatial domain according to the train speed, and is applied as a track irregularity to the train-track coupled subsystem established in Step 2, and dynamic analysis is carried out using the Newmark-β or Wilson-θ stepwise integration method. Specifically: Step 3.1: Transform the rail response obtained in Step 1 from the time domain to the spatial domain according to the train speed, and superimpose it with the original track irregularities; Step 3.2: In the dynamic analysis of the train-track coupled subsystem, the wheel-rail contact search at each time step considers the superimposed track irregularities, and the calculation of the wheel-rail creep force considers the rate of change of the superimposed track irregularities. Step 4: Based on the dynamic analysis results of the train-track coupled subsystem obtained in Step 3, evaluate the train's operational safety using standard indicators or wheel-rail geometric indicators. The specific steps are as follows: The steps for using standard indicators are as follows: extract the vertical and lateral wheel-rail forces, calculate the derailment coefficient and wheel load reduction rate, and compare them with the standard limits to determine whether the train operation is safe; The steps for using wheel-rail geometric indices are as follows: extract the relative lateral displacement of the wheel and rail and the wheel lift, and compare them with the reference limits given in the literature to determine whether the train operation is safe.

2. The method for analyzing train operation safety on railway lines under earthquake conditions as described in claim 1, characterized in that: Step 1 specifically includes the following steps: Step 1.1: During the track-substructure dynamic analysis, the spatial position of each wheelset at the current time step is obtained based on the train speed and the relative distance between the train wheelsets; Step 1.2: During the track-substructure dynamic analysis, based on the spatial position of the wheelset at the current time step, locate the rail element where each wheelset is located, obtain the corresponding track element node response, and obtain the rail response below the wheelset by performing linear interpolation or cubic spline interpolation on the element node response based on the relative position of the wheelset in the rail element.

3. The method for analyzing train operation safety on railway lines under earthquake conditions as described in claim 1, characterized in that: Step 2 specifically includes the following steps: Step 2.1: Build a space vehicle model using multibody dynamics, or build a space vehicle model by inputting the corresponding parameters in multibody dynamics software; Step 2.2: Establish the track structure model using the finite element method, transfer matrix method, or moving track method, or establish the track structure model by inputting relevant parameters in multibody dynamics software; Step 2.3: Considering the geometric profiles of the wheelset and rail, establish a nonlinear spatial rolling wheel-rail contact model. Use the spatial trace method to search for the wheel-rail contact point, use the Hertz nonlinear model to calculate the wheel-rail contact normal force, use the Kalker creep theory to calculate the wheel-rail tangential creep force, and correct it using the Shen-Hedrick-Elkins theory; or input relevant parameters into multibody dynamics software to establish a spatial wheel-rail contact model. Step 2.4: Couple the vehicle model and track model into a train-track subsystem by using the wheel-rail contact model and the coordination relationship between force and displacement.

4. The method for analyzing train operation safety on railway lines under earthquake conditions as described in claim 1, characterized in that, In step 2, the multibody dynamics software can be SIMPACK, ADAMS, or UM.

5. The method for analyzing train operation safety on railway lines under earthquake conditions as described in claim 1, characterized in that: In step 1, when establishing the finite element model of the track-substructure, the rails and track slabs are established using beam elements, the base plate is equivalent to the substructure, and the fasteners and CA mortar layer are simulated using spring damping elements. The substructure is simulated using corresponding elements according to the mechanical properties of each component.

6. The method for analyzing train operation safety on railway lines under earthquake conditions as described in claim 1, characterized in that: When establishing the train-track coupling subsystem, the space vehicle model includes a car body, bogie, wheelsets, primary suspension, and secondary suspension. The car body and bogie are connected by secondary suspension, and the bogie and wheelsets are connected by primary suspension.

7. The method for analyzing train operation safety on railway lines under earthquake conditions as described in claim 3, characterized in that: In step 2.2, the track structure model is established using the finite element method, the transfer matrix method, or the moving track method. The specific process is as follows: Finite element method is adopted: the rails and track slabs are established using beam elements, while the fasteners and CA mortar layer are simulated using spring damping elements. All degrees of freedom of the base plate are constrained, and the dynamic equations of the track structure remain unchanged during the dynamic analysis. The transfer matrix method is adopted: the orbital structure is periodically divided into orbital cells, the dynamic equations of various cell structures are established, the stiffness equation coefficients of each interface are calculated, and the equivalent external force vector of each interface is calculated at each time step during the dynamic analysis. The output response is solved according to the boundary conditions and the response of each cell is solved recursively. The moving track method is adopted: the length of the track structure is determined according to the length of the train and a buffer section of 30 m is reserved before and after. The track structure model of the corresponding length is established using the finite element method. During the dynamic analysis, when the train moves the distance of one rail element, the displacement, velocity, acceleration, and load vector degrees of freedom corresponding to the tail element of the track structure are deleted and new degrees of freedom are added at the head of the track, so as to realize the simulation of an infinitely long track structure by a finite length track structure.

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