Simulation method for calculating vehicle-track-bridge coupled dynamic response of long-span high-speed railway bridges

Abstract

The present invention relates to the field of rail transit technology, and provides a simulation method for calculating the vehicle-track-bridge coupled dynamic response of a long-span high-speed railway bridge, which comprises the following steps: step 1, establishing a finite element model of a long-span bridge; step 2, obtaining the node mileage of the main beam of the long-span bridge and the dynamic displacement of the node corresponding to the sleeper under the action of the moving load; step 3: obtaining the dynamic stiffness of the node corresponding to the sleeper of the long-span bridge; step 4: establishing a vehicle-track coupled dynamic model; step 5: coupling the equivalent dynamic stiffness of the long-span bridge to the lower part of the track subsystem with a spring element; step 6: performing vehicle-track-bridge dynamics simulation on a long-span bridge with the equivalent stiffness of the coupled bridge. When conducting a study on the vehicle-track-bridge dynamics on a high-speed railway long-span bridge, the present invention fully considers the track structure, replaces the large-scale finite element model of the long-span bridge with the equivalent stiffness of the bridge, and can quickly and efficiently complete the vehicle-track-bridge coupled dynamics simulation on the high-speed railway long-span bridge.

Description

Technical Field

[0001] The invention relates to the field of rail transit technology, and in particular to a simulation method for calculating vehicle-track-bridge coupled dynamic response of a long-span high-speed railway bridge. Background Art

[0002] When a high-speed train passes through a bridge, it is necessary to quickly and accurately analyze and evaluate the safety and comfort of the train operation. Usually, a train-track-bridge coupling dynamic model is established for simulation analysis. However, the vehicles on the long-span bridges of high-speed railways have high running speeds, large vertical deflection deformations of bridges, and complex interactions between vehicles, tracks, and bridges. The vehicle-track-bridge coupling model of long-span high-speed railway bridges based on finite elements is complex in coupling, and the length of the bridge results in a large number of units, and the existing computer computing power is difficult to meet the calculation requirements. Therefore, the development of a fast and accurate method for calculating the dynamic response of vehicles, tracks, and bridges on high-speed railway long-span bridges is of great practical significance for evaluating the driving quality of trains and the dynamic performance of tracks on bridges.

[0003] For a long time, the research on train crossing bridges, especially long-span bridges, has been dominated by scholars majoring in bridge engineering. Therefore, they mainly focus on the dynamic interaction between trains and bridges, and usually ignore the important influence of track structures. When using real-time hybrid simulation to study the vibration of the vehicle-bridge coupling system, some scholars proposed a recursive prediction optimal compensator based on optimal control and recursive least squares to reduce the time lag effect of the experimental substructure and increase the calculation accuracy and stability. In order to study the influence of vehicle-bridge interaction on bridge vibration, some scholars proposed a method to improve the bridge system to decouple the vehicle and bridge interaction problems, greatly reducing the calculation time cost. Based on the model reduction theory, some scholars proposed a new idea for vehicle-bridge coupling calculation. Some scholars proposed a novel non-iterative general method that can solve the vehicle-bridge interaction in a time-advancing manner. This method mainly uses dynamic "mortar elements" to force displacement compatibility and dynamic force balance at the system interface boundary to achieve efficient calculation of the entire system. Some scholars developed a finite element modeling method based on the moving mesh strategy based on the Lagrange-Euler method, and used this method to analyze the vehicle-bridge interaction problem affected by moving loads. Some scholars have proposed a dynamic partitioning method (DPM) that can solve vehicle-bridge interaction related problems through a set of complete second-order ordinary differential equations (DOE). This method can greatly reduce the computational cost, especially for long-span vehicle-bridge systems. The above research mainly focuses on the train-bridge coupling system, focusing on the interaction between the train and the bridge, and does not consider the track structure in detail. As an important structure connecting the train and the bridge, the track structure itself will participate in the system coupling and greatly affect the dynamic response of the train and the bridge. Therefore, it is necessary to recognize the importance of the track structure to the overall system.

[0004] For the vehicle-track-bridge coupled dynamics model of a long-span bridge, the system itself is complex and huge, the calculation time step is very small, and the track structure needs to be considered in detail. The traditional method has a high calculation cost. Some scholars choose to optimize the coupled dynamics model according to the applicable situation and have made certain progress. Some scholars have proposed an improved numerical substructure method for studying the dynamic analysis of the vehicle-track-bridge system. Some scholars use the energy variation method to formulate the motion matrix equation for the 3D train-track-bridge coupled system. Some scholars consider that the dynamic response of the bridge structure is mainly determined by the low-order mode, and use the modal superposition method to model the long-span bridge subsystem to improve the calculation efficiency of the complex model. Some scholars have proposed a time-integrated multi-time step method (MTS), which can decompose the vehicle-track-bridge coupled system into two subdomains. The train track subsystem and the bridge subsystem are calculated using fine time steps and coarse time steps respectively, which can greatly improve the calculation efficiency of the train passing through the long-span bridge. Some scholars have proposed a solution method called implicit-explicit integration multi-time step to efficiently and accurately obtain the dynamic solution of the large train-track-substructure system. Some scholars have proposed an efficient explicit time domain method (ETDM) for fast nonlinear dynamic analysis of vehicle-bridge coupling system, while taking into account the influence of nonlinear wheel-rail contact force. The ETDM method can be repeatedly used for dimension reduction iteration to solve the contact force of different random track irregularity samples, and realize the efficient Monte-Carlo simulation (MCS) of nonlinear random dynamics of vehicle-rail coupling system, with good accuracy and computational efficiency. In order to simplify the simulation of suspension bridge truss stiffening beam, some scholars, based on the dynamic characteristics analysis results of single truss stiffening beam, derived and gave simplified calculation formulas for parameters such as equivalent mass moment of inertia of Euler beam with equal cross-section corresponding to different boundary conditions based on the principle of equal parameters such as vertical bending and lateral bending. Some scholars combined ANSYS and SIMPACK software to propose two interactive methods, virtual body coupling method and equivalent flexible track method, to establish vehicle-bridge coupling model, which has high computational efficiency and good convergence rate. Some scholars proposed a three-dimensional vehicle-rail-bridge interaction model based on the assumption of rigid contact between wheel and rail. Compared with traditional methods, this model has higher computational stability, accuracy and efficiency, and the number and type of bridge units can be selected at will. Some scholars have proposed a joint simulation method for analyzing the interaction between trains, tracks and bridges under earthquakes using SIMPACK and OpenSees. This method can better combine the powerful wheel-rail contact analysis capabilities of Simpack and the complex nonlinear analysis capabilities of OpenSees. Some scholars have developed a hybrid model to analyze the dynamic interaction between trains, tracks and bridges. The model couples the train and track subsystems together to form an integrated time-dependent subsystem, which is then coupled to the bridge subsystem by forcing the compatibility of forces at the contact points between the track and the bridge. A new hybrid solution algorithm is proposed that can avoid iterative balance calculations between wheels and tracks, and significantly improve computational efficiency.

[0005] From the above research, it can be found that the current simulation of vehicle-track-bridge coupling dynamics of high-speed railway long-span bridges mainly starts from the perspectives of solution methods and coupling methods between model systems to improve the computational efficiency and stability of large and complex dynamic models. The study found that the most fundamental reason affecting the computational efficiency of vehicle-track-bridge dynamic responses on long-span bridges is the solution of the algebraic equations of the bridge substructure. Most existing studies have not considered simplifying the long-span bridge subsystem, and in order to ensure the computational efficiency and research purpose of the model, the track structure is still simplified, which greatly affects the dynamic solution of the system. Therefore, in order to ensure that the vehicle-track coupling dynamics simulation of high-speed railway long-span bridges can be completed quickly and efficiently while simulating the track structure and the dynamic support of the bridge, the present invention fully considers the characteristics of low natural frequency of long-span bridges, replaces the huge finite element model of long-span bridges with equivalent dynamic stiffness of bridges, and proposes a simulation method for quickly calculating the vehicle-track-bridge coupling dynamic response of long-span high-speed railway bridges that includes the track structure and the dynamic support of bridges. Summary of the invention

[0006] The content of the present invention is to provide a simulation method for calculating the vehicle-track-bridge coupled dynamic response of a long-span high-speed railway bridge, which can overcome the problems of large calculation models, low calculation efficiency, and overly simplified track structure models in the prior art, which are difficult to meet the problems of difficulty in coordinating the efficiency and accuracy of vehicle-track-bridge coupled dynamic simulation faced in the design and operation of long-span high-speed railway bridges at this stage.

[0007] The simulation method for calculating the vehicle-track-bridge coupled dynamic response of a long-span high-speed railway bridge according to the present invention comprises the following steps:

[0008] Step 1: Establish a finite element model of a long-span bridge;

[0009] Step 2, obtaining the node mileage of the main beam of the long-span bridge and the dynamic displacement of the node corresponding to the sleeper under the action of the moving load;

[0010] Step 3: Obtain the dynamic stiffness of the nodes corresponding to the sleepers of the long-span bridge;

[0011] Step 4: Establish vehicle-track coupling dynamics model;

[0012] Step 5: The equivalent dynamic stiffness of the long-span bridge is coupled to the lower part of the track subsystem with a spring element;

[0013] Step 6: Conduct vehicle-track-bridge dynamics simulation on a long-span bridge with coupled bridge equivalent stiffness.

[0014] Preferably, in step 1, the long-span bridge structure is simulated by using beam units and rod units, and finite element models of various structural components of the long-span bridge are constructed respectively; the various structural components of the long-span bridge are connected through the common nodes and node coupling connection relationships of the finite element software, and the establishment of the overall finite element model of the long-span bridge is completed.

[0015] Preferably, in step 2, specifically:

[0016] 2.1) The main beam nodes are encrypted, and the spacing between each node is selected to be 1 / 4 of the fastener spacing; and the modal analysis of the finite element model of the long-span bridge is performed;

[0017] 2.2) Import the required vibration modes and frequencies of the long-span bridge into the self-programming program, and calculate the displacement response of the long-span bridge under the action of moving loads;

[0018] 2.3) Then, according to the self-programming program, the node dynamic displacements corresponding to each sleeper of the main beam of the long-span bridge are extracted in turn, and the corresponding data table of the node mileage and dynamic displacement corresponding to each sleeper of the long-span bridge is obtained in combination with the relative position of each node, where the node mileage is based on the beam end of the finite element model of the long-span bridge.

[0019] Preferably, in step 2.2), specifically:

[0020] 2.2.1) According to the D'Alembert principle, the dynamic equation of a long-span bridge is established as follows:

[0021] ;

[0022] In the formula, are the mass, damping and stiffness matrices of the bridge system, are the displacement, velocity and acceleration vectors of the bridge system, is the external force vector acting on the bridge system;

[0023] 2.2.2) The main parameters of the established long-span bridge finite element model are sorted and recorded, the vibration mode and the corresponding order natural frequency required for calculation are extracted, and the canonical vibration mode coordinates are introduced. and the normalized canonical vibration mode , the displacement component use Indicates, where t represents the time variable, and x represents the mileage variable from the starting point of the beam end;

[0024] 2.2.3) The dynamic equation is transformed, decoupled and normalized to obtain the vibration equation under canonical coordinates as follows:

[0025] ;

[0026] In the formula, and The canonical vibration mode coordinates are The first and second order derivatives of and They are respectively the long-span bridge structures order damping ratio and circular frequency, is the generalized force vector in canonical coordinates;

[0027] 2.2.4) Decompose the moving load through the vibration mode to obtain the generalized force vector in the canonical coordinates. The conversion formula is as follows:

[0028] ;

[0029] Where: are the vertical, horizontal and torsional components of the external force acting on the bridge at time t, They are the vertical, horizontal and rotational vibration modes at the corresponding bridge positions respectively;

[0030] 2.2.5) Using the Newmark method, calculate and store the dynamic displacement results of each vibration mode at all time steps;

[0031] 2.2.6) Finally, according to the principle of mode superposition method, the generalized canonical coordinates corresponding to each mode are summed to obtain the node mileage and corresponding dynamic displacement results of the main beam of the long-span bridge. The formula is as follows:

[0032] ;

[0033] In the formula, represents the a-th order normal vibration mode of the long-span bridge structure, represents the coordinates of the a-th order normal vibration mode of the long-span bridge structure, and N is the total order of the selected vibration modes.

[0034] Preferably, in step 3, specifically:

[0035] 3.1) The dynamic stiffness of the nodes corresponding to each sleeper of the main beam of the long-span bridge under the unit moving load is obtained by the dynamic displacement of the nodes corresponding to each sleeper of the main beam of the long-span bridge, and the calculation is shown in the following formula:

[0036] ;

[0037] in, is the dynamic stiffness of the bridge girder; Considered as 1, it is the unit moving constant load; is the dynamic displacement of the bridge girder;

[0038] 3.2) Obtain the corresponding values ​​of the node mileage and dynamic stiffness of each sleeper at the main beam of the long-span bridge, ;in, For the corresponding Root sleeper, For the The root sleeper corresponds to the distance variable from the beam end.

[0039] Preferably, in step 4, specifically:

[0040] 4.1) The track structure is modeled using finite element software;

[0041] 4.2) The rails and lower sleepers are simulated using beam elements, and different unit types are used to establish finite element models of each component according to the characteristics of each component of the track structure;

[0042] 4.3) Connect the rails and the lower sleepers through fasteners. The specific stiffness and damping values ​​of the fasteners refer to actual data;

[0043] 4.4) Determine the specific parameters of the vehicle according to the train type given in the data, and choose to build a multi-rigid body vehicle model in the multi-body dynamics software SIMPACK platform;

[0044] 4.5) The vehicle model is established based on the Wheel / rail module of SIMPACK, and the rigid body, hinge, identification point and force element are fully utilized to determine the characteristics and connection relationship of each component of the vehicle model, and a series of dynamic control equations are formed in SIMPACK;

[0045] 4.6) The vehicle model includes 1 car body, 2 bogies, 4 wheel sets and 8 axle box moving parts. The following assumptions are made when establishing the vehicle model:

[0046] A) The springs of the primary and secondary suspension systems are linear, and the damping is viscous damping;

[0047] B) The mass and inertia moment of each component of the vehicle model are concentrated in the reference points of the vehicle body, bogie and wheelset;

[0048] C) All parts of the vehicle model are regarded as rigid bodies, and the elastic deformation of the vehicle body, bogie and wheelset is not considered;

[0049] D) Each moving part is symmetrical about the center of mass;

[0050] 4.7) The wheelset and bogie are connected through the primary suspension system, and the bogie and car body are connected through the secondary suspension system. Marking points are set at the corresponding positions of the wheelset, bogie and car body, and the marking points of each component are connected through force elements to simulate the primary and secondary suspension stiffness and damping; the axle box and wheelset are directly connected through hinges;

[0051] 4.8) The track structure model established in the finite element software is imported into the multi-body dynamics software through the interface. The dummy element method and the wheel-rail contact relationship given by the software are used to couple the track structure model and the vehicle model in the multi-body dynamics software to construct the vehicle-track coupling dynamics model.

[0052] Preferably, in step 4.8), specifically:

[0053] 4.8.1) The track structure model needs to be divided into two sub-model components, rail and sub-track structure, which are imported into the multi-body dynamics software separately;

[0054] 4.8.2) The rails and the sub-rail structure are connected by a fastener system, which is simulated by a spring-damper type force element;

[0055] 4.8.3) By setting parent identification points on the rail structure, the wheel-rail load can be distributed to the flexible body interface nodes based on the flexible body shape function, and the dynamic response can be obtained based on the dynamic behavior of the flexible body interface nodes combined with cubic spline interpolation;

[0056] 4.8.4) In the constructed multi-rigid body vehicle model, a massless virtual node, i.e., a dummy, is constructed on each wheelset component. The dummy node can move with the wheelset and participate in the wheel-rail contact analysis in real time to transmit the wheel-rail contact signal.

[0057] 4.8.5) Set sub-marking points on the dummy component, which can move with the dummy; finally, use the marking points set on the dummy and rail components to constrain, retaining only the vertical and lateral degrees of freedom, and fully simulate the transfer load and vibration behavior between the dummy and the rail.

[0058] Preferably, in step 5, specifically:

[0059] 5.1) Ensure that the track structure mileage benchmark in the constructed vehicle-track coupling model is consistent with the long-span bridge mileage benchmark, and clarify the virtual coordinates of the track structure in the long-span bridge;

[0060] 5.2) The dynamic stiffness values ​​of the nodes of the long-span bridge main beam at each sleeper corresponding to the sleeper obtained in step 3 are coupled in series with the ballast stiffness at the corresponding position through a self-programming method, and the stiffness after series coupling is regarded as the ground spring stiffness under the sleeper, thereby establishing a vehicle-track coupling dynamic model based on the dynamic stiffness of the long-span bridge main beam.

[0061] Preferably, in step 6, specifically:

[0062] 6.1) Perform pre-balancing on the vehicle subsystem. The residual acceleration after pre-balancing must be less than 0.01m / s 2 , to ensure the accuracy of vehicle subsystems and reduce the balancing time of the coupled system;

[0063] 6.2) Before calculating the model, the dynamic model sampling frequency and calculation time must be defined according to the specific working conditions to ensure that the parameters meet the calculation requirements;

[0064] 6.3) Export the .mat result file by setting the required dynamic response index in advance, so that the result data can be further processed and developed using programming software;

[0065] 6.4) Carry out dynamic calculations on the model through the offline time integration module of the multi-body dynamics software.

[0066] The beneficial effects of the present invention are as follows:

[0067] When conducting research on the dynamic response of a vehicle or track subsystem, the present invention fully considers the track structure and can quickly and efficiently complete the vehicle-track-bridge coupled dynamics simulation on a high-speed railway long-span bridge.

[0068] Compared with the traditional vehicle-track-bridge dynamics simulation model, the present invention can fully consider the track structure when conducting research on the dynamic response of the vehicle or track subsystem, and can reasonably simplify the long-span bridge structure while maintaining calculation accuracy, avoiding the need to call a large-scale bridge system model every time the working condition is calculated, reducing the simulation calculation cost, and ensuring the rapid, economical and efficient completion of the vehicle-track-bridge coupled dynamics simulation calculation on the high-speed railway long-span bridge. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 A flowchart of a simulation method for calculating the vehicle-track-bridge coupled dynamic response of a long-span high-speed railway bridge in an embodiment;

[0070] Figure 2 It is a schematic diagram of unit moving load in the embodiment;

[0071] Figure 3 It is a schematic diagram of the vehicle-track-bridge coupling dynamics model based on the dynamic stiffness of the main beam of a long-span bridge in the embodiment. DETAILED DESCRIPTION

[0072] In order to further understand the content of the present invention, the present invention is described in detail in conjunction with the accompanying drawings and embodiments. It should be understood that the embodiments are only for explaining the present invention and are not intended to limit it.

[0073] like Figure 1 As shown, this embodiment provides a simulation method for (fast) calculating the vehicle-track-bridge coupled dynamic response of a long-span high-speed railway bridge, which includes the following steps:

[0074] Step 1: Establish a finite element model of a long-span bridge;

[0075] In step 1, in order to improve the calculation efficiency, the long-span bridge structure is simulated by beam unit and rod unit, and the finite element model of each structural component of the long-span bridge is constructed respectively; the structural components of the long-span bridge are connected through the common node and node coupling connection relationship of the finite element software (ANSYS, ABAQUS), and the overall finite element model of the long-span bridge is established; and the correctness of the constructed finite element model of the long-span bridge is verified according to methods such as standard modal or measured data.

[0076] Step 2, obtaining the node mileage of the main beam of the long-span bridge and the dynamic displacement of the node corresponding to the sleeper under the action of the moving load;

[0077] 2.1) In order to improve the calculation accuracy and facilitate the subsequent data processing, the main beam nodes are encrypted, and the spacing between each node is selected as 1 / 4 of the fastener spacing; and the modal analysis of the finite element model of the long-span bridge is carried out;

[0078] 2.2) Import the required vibration modes and frequencies of the long-span bridge into the self-programming program, and calculate the displacement response of the long-span bridge under the action of moving loads;

[0079] 2.3) Then, according to the self-programming program, the node dynamic displacements corresponding to each sleeper of the main beam of the long-span bridge are extracted in turn, and the corresponding data table of the node mileage and dynamic displacement corresponding to each sleeper of the long-span bridge is obtained in combination with the relative position of each node, where the node mileage is based on the beam end of the finite element model of the long-span bridge.

[0080] In step 2.2), specifically:

[0081] 2.2.1) According to the D'Alembert principle, the dynamic equation of a long-span bridge is established as follows:

[0082] ;

[0083] In the formula, are the mass, damping and stiffness matrices of the bridge system, are the displacement, velocity and acceleration vectors of the bridge system, is the external force vector acting on the bridge system;

[0084] 2.2.2) The main parameters of the established long-span bridge finite element model are sorted and recorded, the vibration mode and the corresponding order natural frequency required for calculation are extracted, and the canonical vibration mode coordinates are introduced. and the normalized canonical vibration mode , the displacement component use Indicates, where t represents the time variable, and x represents the mileage variable from the starting point of the beam end;

[0085] 2.2.3) The dynamic equation is transformed, decoupled and normalized to obtain the vibration equation under canonical coordinates as follows:

[0086] ;

[0087] In the formula, and The canonical vibration mode coordinates are The first and second order derivatives of and They are respectively the long-span bridge structures order damping ratio and circular frequency, is the generalized force vector in canonical coordinates;

[0088] 2.2.4) Decompose the moving load through the vibration mode to obtain the generalized force vector in the canonical coordinates. The conversion formula is as follows:

[0089] ;

[0090] Where: are the vertical, horizontal and torsional components of the external force acting on the bridge at time t, They are the vertical, horizontal and rotational vibration modes at the corresponding bridge positions respectively;

[0091] 2.2.5) Using the Newmark method, calculate and store the dynamic displacement results of each vibration mode at all time steps;

[0092] 2.2.6) Finally, according to the principle of mode superposition method, the generalized canonical coordinates corresponding to each mode are summed to obtain the node mileage and corresponding dynamic displacement results of the main beam of the long-span bridge. The formula is as follows:

[0093] ;

[0094] In the formula, represents the a-th order normal vibration mode of the long-span bridge structure, represents the coordinates of the a-th order normal vibration mode of the long-span bridge structure, and N is the total order of the selected vibration modes.

[0095] Step 3: Obtain the dynamic stiffness of the nodes corresponding to the sleepers of the long-span bridge;

[0096] 3.1) The dynamic stiffness of the nodes corresponding to each sleeper of the main beam of the long-span bridge under the unit moving load is obtained by the dynamic displacement of the nodes corresponding to each sleeper of the main beam of the long-span bridge, and the calculation is shown in the following formula:

[0097] ;

[0098] in, is the dynamic stiffness of the bridge girder; Considered as 1, it is the unit moving constant load; is the dynamic displacement of the bridge girder; the schematic diagram of the unit moving load is as follows Figure 2 As shown in the figure; when the unit moving load moves to x mileage at a speed of v, the dynamic displacement of the bridge girder at the corresponding position is , the dynamic stiffness of the bridge girder at this location It can be obtained by calculation. Each discrete point in the figure represents the dynamic stiffness of the bridge main beam at different mileages. The specific calculation formula is shown in the above formula;

[0099] 3.2) Obtain the corresponding values ​​of the node mileage and dynamic stiffness of each sleeper at the main beam of the long-span bridge ;in, For the corresponding Root sleeper, For the The root sleeper corresponds to the distance variable from the beam end.

[0100] Step 4: Establish vehicle-track coupling dynamics model;

[0101] 4.1) The track structure is modeled using finite element software (ANSYS, ABAQUS);

[0102] 4.2) The rails and lower sleepers are simulated using beam elements, and different unit types are used to establish finite element models of each component according to the characteristics of each component of the track structure;

[0103] 4.3) Connect the rails and the lower sleepers through fasteners. The specific stiffness and damping values ​​of the fasteners refer to actual data;

[0104] 4.4) Determine the specific parameters of the vehicle according to the train type given in the data, and choose to build a multi-rigid body vehicle model in the multi-body dynamics software SIMPACK platform;

[0105] 4.5) The vehicle model is established based on the Wheel / rail module of SIMPACK, and the basic elements such as rigid body, joint, marker, force element, etc. are fully utilized to determine the characteristics and connection relationship of each component of the vehicle model, and a series of dynamic control equations are formed in SIMPACK;

[0106] 4.6) The vehicle model includes 1 car body, 2 bogies, 4 wheel sets and 8 axle box moving parts. In order to improve the calculation efficiency, the following assumptions are made when establishing the vehicle model:

[0107] A) The springs of the primary and secondary suspension systems are linear, and the damping is viscous damping;

[0108] B) The mass and inertia moment of each component of the vehicle model are concentrated in the reference points of the vehicle body, bogie and wheelset;

[0109] C) All parts of the vehicle model are regarded as rigid bodies, and the elastic deformation of the vehicle body, bogie and wheelset is not considered;

[0110] D) Each moving part is symmetrical about the center of mass;

[0111] 4.7) The wheelset and bogie are connected through the primary suspension system, and the bogie and car body are connected through the secondary suspension system. Markers are set at the corresponding positions of the wheelset, bogie and car body, and the markers of each component are connected through force elements to simulate the primary and secondary suspension stiffness and damping; the axle box and wheelset are directly connected through a joint;

[0112] 4.8) The track structure model established in the finite element software is imported into the multi-body dynamics software through the interface. The “dummy element method” and the wheel-rail contact relationship given by the software are used to couple the track structure model and the vehicle model in the multi-body dynamics software to construct the vehicle-track coupling dynamics model.

[0113] In step 4.8), specifically:

[0114] 4.8.1) The track structure model needs to be divided into two sub-model components: rail and sub-track structure, and imported into the multi-body dynamics software separately.

[0115] 4.8.2) The rails and the sub-rail structure are connected by a fastener system, which is simulated using spring-damper type force elements.

[0116] 4.8.3) By setting a “parent” identification point on the rail structure, the wheel-rail load can be distributed to the flexible body interface nodes based on the flexible body shape function, and the dynamic response can be obtained based on the dynamic behavior of the flexible body interface nodes combined with cubic spline interpolation.

[0117] 4.8.4) In the constructed multi-rigid body vehicle model, a massless virtual node, i.e., a dummy, is constructed on each wheelset component. The main function of the dummy is to move with the wheelset, participate in the wheel-rail contact analysis in real time, and transmit the wheel-rail contact signal.

[0118] 4.8.5) Set a "sub" identification point on the dummy component, which can move with the dummy; finally, use the identification points set on the dummy and rail components to constrain, retaining only the vertical and lateral degrees of freedom, and fully simulate the transfer load and vibration behavior between the dummy and the rail.

[0119] Step 5: The equivalent dynamic stiffness of the long-span bridge is coupled to the lower part of the track subsystem with a spring element;

[0120] 5.1) Ensure that the track structure mileage benchmark in the constructed vehicle-track coupling model is consistent with the long-span bridge mileage benchmark, and clarify the virtual coordinates of the track structure in the long-span bridge;

[0121] 5.2) The dynamic stiffness values ​​of the nodes of the long-span bridge main beam at each sleeper corresponding to the sleeper obtained in step 3 are coupled in series with the ballast stiffness at the corresponding position through a self-programming method, and the stiffness after series coupling is regarded as the ground spring stiffness under the sleeper, thereby establishing a vehicle-track coupling dynamic model based on the dynamic stiffness of the long-span bridge main beam, as shown in Figure 3 As shown, Figure 3 The model includes three parts: vehicle, track and bridge equivalent spring. The vehicle mainly includes car body, bogie, wheelset and primary and secondary suspension. The track mainly includes rails, sleepers, ballast and fastener system. They are the longitudinal and vertical degrees of freedom of the vehicle body, as well as the nodding and shaking degrees of freedom of the vehicle body. are the longitudinal and vertical degrees of freedom of the front bogie and the rear bogie respectively, They are the vertical degrees of freedom of the 1st to 4th wheel pairs, are the stiffness and damping of the secondary suspension and the primary suspension respectively. are the fastener stiffness and damping, are the mass, stiffness and damping of the ballast mass block respectively, It is the dynamic stiffness at the corresponding node mileage of the sleeper.

[0122] Step 6: Carry out vehicle-track-bridge dynamics simulation on a long-span bridge with coupled bridge equivalent stiffness;

[0123] 6.1) Perform pre-balancing on the vehicle subsystem. The residual acceleration after pre-balancing must be less than 0.01m / s 2 , to ensure the accuracy of vehicle subsystems and reduce the balancing time of the coupled system;

[0124] 6.2) Before calculating the model, it is necessary to define basic parameters such as the dynamic model sampling frequency and calculation time according to the specific working conditions to ensure that the parameters meet the calculation requirements;

[0125] 6.3) Export the .mat result file by setting the required dynamic response index in advance, so that the result data can be further processed and developed using programming software;

[0126] 6.4) Carry out dynamic calculations on the model through the offline time integration module of the multi-body dynamics software and carry out further relevant research work.

[0127] This embodiment fully considers the track structure when conducting a study on the dynamic response of a vehicle or track subsystem, and can quickly and efficiently complete the vehicle-track-bridge coupled dynamics simulation of a high-speed railway long-span bridge.

[0128] Compared with the traditional vehicle-track-bridge dynamics simulation model, this embodiment can fully consider the track structure when conducting dynamic response research on vehicle or track subsystems, and can reasonably simplify the large-span bridge structure while maintaining calculation accuracy, avoiding the need to call a large-scale bridge system model every time the working condition is calculated, reducing the simulation calculation cost, and ensuring fast, economical and efficient completion of vehicle-track-bridge coupled dynamics simulation calculations on high-speed railway large-span bridges.

Claims

1. Simulation method for calculating vehicle-track-bridge coupled dynamic response of long-span high-speed railway bridges, Features: The following steps are involved: Step 1: Establish a finite element model of a long-span bridge; Step 2, obtaining the node mileage of the main beam of the long-span bridge and the dynamic displacement of the node corresponding to the sleeper under the action of the moving load; In step 2, specifically: 2.1) The main beam nodes are encrypted, and the spacing between each node is selected to be 1 / 4 of the fastener spacing; and the modal analysis of the finite element model of the long-span bridge is performed; 2.2) Import the required vibration modes and frequencies of the long-span bridge into the self-programming program, and calculate the displacement response of the long-span bridge under the action of moving load; In step 2.2), specifically: 2.2.1) According to the D'Alembert principle, the dynamic equation of a long-span bridge is established as follows: Where M b , C b , K b are the mass, damping and stiffness matrices of the bridge system, u b , are the displacement, velocity and acceleration vectors of the bridge system, respectively, and F b is the external force vector acting on the bridge system; 2.2.2) The main parameters of the established long-span bridge finite element model are sorted and recorded, the vibration mode and the corresponding order natural frequency required for calculation are extracted, and the canonical vibration mode coordinate q is introduced. b (t) and the normalized canonical vibration mode Φ b (x), the displacement component u b Use Φ b (x)q b (t) represents, where t represents the time variable, and x represents the distance variable from the starting point of the beam end; 2.2.3) The dynamic equation is transformed, decoupled and normalized to obtain the vibration equation under canonical coordinates as follows: In the formula, and The canonical vibration mode coordinates q b The first and second derivatives of a With ω a are the a-th order damping ratio and circular frequency of the long-span bridge structure, P b is the generalized force vector in canonical coordinates; 2.2.4) The moving load is decomposed by vibration mode to obtain the generalized force vector in canonical coordinates. The conversion formula is as follows: Where: are the vertical, horizontal and torsional components of the external force acting on the bridge at time t, They are the vertical, horizontal and rotational vibration modes at the corresponding bridge positions respectively; 2.2.5) Using the Newmark method, calculate and store the dynamic displacement results of each vibration mode at all time steps; 2.2.6) Finally, according to the principle of mode superposition method, the generalized canonical coordinates corresponding to each mode are summed to obtain the node mileage and corresponding dynamic displacement results of the main beam of the long-span bridge. The formula is as follows: In the formula, Φ ba represents the a-th order normal vibration mode of the long-span bridge structure, q ba represents the coordinates of the a-th order normal vibration mode of the long-span bridge structure, and N is the total order of the selected vibration mode; 2.3) Then, according to the self-programming program, the node dynamic displacements corresponding to each sleeper of the main beam of the long-span bridge are extracted in sequence, and the corresponding data table of the node mileage and dynamic displacement corresponding to each sleeper of the long-span bridge is obtained in combination with the relative position of each node, wherein the node mileage is based on the beam end of the finite element model of the long-span bridge; Step 3: Obtain the dynamic stiffness of the nodes corresponding to the sleepers of the long-span bridge; In step 3, specifically: 3.1) The dynamic stiffness of the nodes corresponding to each sleeper of the main beam of the long-span bridge under the unit moving load is obtained by the dynamic displacement of the nodes corresponding to each sleeper of the main beam of the long-span bridge, and the calculation is shown in the following formula: K bri (x)=P / δ(x) Among them, K bri is the dynamic stiffness of the bridge main beam; P is regarded as 1, which is the unit moving constant load; δ is the dynamic displacement of the bridge main beam; 3.2) Obtain the corresponding values ​​K of the node mileage and dynamic stiffness of each sleeper at the main beam of the long-span bridge bri (x i ), where i is the corresponding sleeper, x i is the distance variable from the beam end corresponding to the i-th sleeper; Step 4: Establish vehicle-track coupling dynamics model; In step 4, specifically: 4.1) The track structure is modeled using finite element software; 4.2) The rails and lower sleepers are simulated using beam elements, and different unit types are used to establish finite element models of each component according to the characteristics of each component of the track structure; 4.3) The rails and lower sleepers are connected by fasteners. The specific stiffness and damping values ​​of the fasteners refer to actual data; 4.4) Determine the specific parameters of the vehicle according to the train type given in the data, and choose to build a multi-rigid body vehicle model in the multi-body dynamics software SIMPACK platform; 4.5) The vehicle model is established based on the Wheel / rail module of SIMPACK, and the rigid body, hinge, identification point and force element are fully utilized to determine the characteristics and connection relationship of each component of the vehicle model, and a series of dynamic control equations are formed in SIMPACK; 4.6) The vehicle model includes 1 car body, 2 bogies, 4 wheel sets and 8 axle box moving parts. The following assumptions are made when establishing the vehicle model: A) The springs of the primary and secondary suspension systems are linear, and the damping is viscous damping; B) The mass and inertia moment of each component of the vehicle model are concentrated in the reference points of the vehicle body, bogie and wheelset; C) All parts of the vehicle model are regarded as rigid bodies, and the elastic deformation of the vehicle body, bogie and wheelset is not considered; D) Each moving part is symmetrical about the center of mass; 4.7) The wheelset and bogie are connected through the primary suspension system, and the bogie and car body are connected through the secondary suspension system. Marking points are set at corresponding positions in the wheelset, bogie and car body, and the marking points of each component are connected through force elements to simulate the primary and secondary suspension stiffness and damping; the axle box and wheelset are directly connected through hinges; 4.8) The track structure model established in the finite element software is imported into the multi-body dynamics software through the interface. The dummy element method and the wheel-rail contact relationship given by the software are used to couple the track structure model and the vehicle model in the multi-body dynamics software to construct the vehicle-track coupling dynamics model; In step 4.8), specifically: 4.8.1) The track structure model needs to be divided into two sub-model components, rail and sub-track structure, which are imported into the multi-body dynamics software separately; 4.8.2) The rails and the sub-rail structure are connected by a fastener system, which is simulated by a spring-damper type force element; 4.8.3) Setting parent identification points on the rail structure can distribute the wheel-rail load to the flexible body interface nodes based on the flexible body shape function, and based on the dynamic behavior of the flexible body interface nodes, combined with cubic spline interpolation, the dynamic response can be obtained; 4.8.4) In the constructed multi-rigid body vehicle model, a massless virtual node, i.e., a dummy, is constructed on each wheelset component. The dummy node can move with the wheelset and participate in the wheel-rail contact analysis in real time to transmit the wheel-rail contact signal. 4.8.5) Set a sub-marking point on the dummy component, which can move with the dummy; finally, use the marking points set on the dummy and rail components to constrain, retaining only the vertical and lateral degrees of freedom, and fully simulate the transfer load and vibration behavior between the dummy and the rail; Step 5: The equivalent dynamic stiffness of the long-span bridge is coupled to the lower part of the track subsystem with a spring element; In step 5, specifically: 5.1) Ensure that the track structure mileage benchmark in the constructed vehicle-track coupling model is consistent with the long-span bridge mileage benchmark, and clarify the virtual coordinates of the track structure in the long-span bridge; 5.2) The dynamic stiffness values ​​of the nodes of the long-span bridge main beam at the corresponding positions of each sleeper obtained in step 3 are coupled in series with the ballast stiffness at the corresponding position through a self-programming method, and the stiffness after series coupling is regarded as the ground spring stiffness under the sleeper, thereby establishing a vehicle-track coupling dynamic model based on the dynamic stiffness of the long-span bridge main beam; Step 6: Carry out vehicle-track-bridge dynamics simulation on a long-span bridge with coupled bridge equivalent stiffness; In step 6, specifically: 6.1) Perform pre-balancing on the vehicle subsystem. The residual acceleration after pre-balancing must be less than 0.01m / s 2 , to ensure the accuracy of vehicle subsystems and reduce the balancing time of the coupled system; 6.2) Before calculating the model, the dynamic model sampling frequency and calculation time must be defined according to the specific working conditions to ensure that the parameters meet the calculation requirements; 6.3) Export the .mat result file by setting the required dynamic response index in advance, so that the result data can be further processed and developed using programming software; 6.4) Carry out dynamic calculations on the model through the offline time integration module of the multi-body dynamics software.

2. The simulation method for calculating the vehicle-track-bridge coupled dynamic response of a long-span high-speed railway bridge according to claim 1, Features: In step 1, the long-span bridge structure is simulated using beam units and rod units, and finite element models of the structural components of the long-span bridge are constructed respectively; the structural components of the long-span bridge are connected through the common nodes and node coupling connection relationships of the finite element software to complete the establishment of the overall finite element model of the long-span bridge.

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