Method for evaluating influence of beam end corner of large-span railway suspension bridge on driving performance

Abstract

The invention discloses a method for evaluating the influence of a large-span railway suspension bridge beam end corner on driving performance, and the method comprises the steps: building a three-dimensional finite element model of a large-span railway suspension bridge, coupling a suspension bridge beam end, a telescoping device and a track, and building a suspension bridge beam end-telescoping device-track coupling vibration model; the method comprises the following steps: establishing a vehicle model of a vehicle operated by a large-span railway suspension bridge, and forming a suspension bridge beam end-telescopic device-rail-train coupled vibration analysis system by taking a beam end corner or rail irregularity as external excitation; outputting a dynamic response index of the operating vehicle; dynamic response indexes of operating vehicles under different beam end corner working conditions are calculated, according to the design load of the suspension bridge, the amplitude of the beam end corner of the suspension bridge is calculated, and whether the beam end corner of the suspension bridge meets the requirement or not is evaluated. The dynamic response of the operating vehicle can be quickly obtained, and the mapping relation between the beam end corner deformation and the vehicle dynamic response index is established, so that the beam end corner rationality is more accurately evaluated according to the vehicle evaluation index.

Description

Technical Field

[0001] The present invention relates to the field of railway bridge driving analysis, and in particular to a method for evaluating the influence of the end turning angle of a long-span railway suspension bridge on driving performance. Background Art

[0002] With advances in bridge construction technology, long-span bridges are increasingly being used on railway lines. Large-span bridges have low stiffness, and under loads such as wind and temperature, they can experience significant deflection and deformation. This is especially true of the beam end rotation displacements that occur at the road-bridge transition section, posing a significant threat to the smooth and safe operation of trains. For small and medium-span bridges, the Railway Bridge and Culvert Design Code specifies beam end rotation limits. For large-span railway bridge end rotations, existing research uses the destructive pullout force of track fasteners as the indicator limit. However, in actual engineering applications, the smoothness of train operation is closely related to passenger comfort, and in severe cases, this can endanger both train operation safety and passenger life. Therefore, it is crucial to develop a new evaluation method for the impact of the end rotation of large-span railway suspension bridges on driving performance. Summary of the Invention

[0003] In response to the above-mentioned deficiencies in the prior art, the present invention provides a method for evaluating the impact of the end angle of a large-span railway suspension bridge on driving performance. A large-span suspension bridge end-expansion device-track-train coupled vibration analysis system is established, and the dynamic response of the vehicle is used as an evaluation indicator to achieve a reasonable evaluation of the beam end angle.

[0004] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: A method for evaluating the influence of the end angle of a long-span railway suspension bridge on driving performance is provided, which comprises the following steps: S1: Establish a three-dimensional finite element model of a long-span railway suspension bridge and couple the suspension bridge end, expansion joint, and track to obtain a suspension bridge end-expansion joint-track coupled vibration model. Construct the mass matrix, stiffness matrix, and damping matrix of the suspension bridge end-expansion joint-track coupled vibration model. S2: Build a vehicle model for vehicles operating on a long-span railway suspension bridge and construct its mass matrix, stiffness matrix, and damping matrix. Use beam end rotation or track irregularities as external excitations to form a coupled vibration analysis system for the suspension bridge end, expansion device, track, and train. S3: Based on the coupled vibration analysis system of the suspension bridge end-telescopic device-track-train, the position of the operating vehicle and the displacement of the suspension bridge end-telescopic device-track are initialized, and the time step is determined. The kinematic equations of the operating vehicle and the dynamic equations of the suspension bridge end-telescopic device-track are solved using the numerical integration method until convergence conditions are met, and the dynamic response indicators of the operating vehicle are output. S4: Calculate the dynamic response index of operating vehicles under different beam end rotation conditions, and obtain the mapping relationship between the dynamic response index and the beam end rotation at different vehicle speeds; calculate the amplitude of the suspension bridge end rotation angle based on the design load of the suspension bridge, and evaluate whether the beam end rotation angle of the suspension bridge meets the requirements.

[0005] Furthermore, step S1 includes: S11: Obtain the geometric, material, and boundary properties of the long-span railway suspension bridge, equate the bridge deck of the long-span railway suspension bridge to the main truss structure to form a truss structure without a bridge deck structure, and establish a three-dimensional finite element model of the long-span railway suspension bridge; S12: Based on the three-dimensional finite element model of the long-span railway suspension bridge, a suspension bridge end-extension device-track coupled vibration model is established, and the mass matrix, stiffness matrix, and damping matrix of the suspension bridge end-extension device-track coupled vibration model are constructed.

[0006] Furthermore, step S11 includes: S111: Obtain the geometric, material, and boundary properties of a long-span railway suspension bridge and establish a full-bridge model of the suspension bridge; S112: Simulates the main truss structure, towers, hangers, cable structure, and deck of a long-span railway suspension bridge. This model integrates the main truss structure, towers, hangers, cable structure, and deck into a 3D model using node sharing or degree of freedom coupling. S113: Calculate the frequency and mode shape of a long-span railway suspension bridge; S114: Remove the bridge deck unit from the three-dimensional model, discretize the bridge deck unit into a number of concentrated mass points, distribute the mass of the bridge deck to the main truss according to the area corresponding to the mass points, and adjust the stiffness parameters of the main truss structure so that the frequency and mode shape of the three-dimensional model without the bridge deck unit are consistent with the frequency and mode shape calculated in step S113; S115: Output the established three-dimensional finite element model of the long-span railway suspension bridge.

[0007] Furthermore, step S12 includes: S121: Extract several internodes near the beam ends from a 3D finite element model of a long-span railway suspension bridge. Use spring elements to simulate the constraints at the node cutoffs and use unit loads to determine the spring stiffness at the node cutoffs to construct a beam end model. Ensure that the beam end model and the 3D finite element model have the same displacement and curvature at the same location. The calibration method of the spring stiffness at the node truncation is: S1211: Apply force or moment at the node at the truncation; S1212: Extract the response values ​​of the local model near the beam end and the 3D finite element model in the same displacement or rotation direction; S1213: Adjust the stiffness of the spring at the node truncation to make the displacement and curvature of the local model consistent with that of the 3D finite element model at the truncation position; S122: Add roadbed segments before and after the beam end model to simulate the fixity of the roadbed through fixed constraints; S123: Construct a three-layer track model consisting of rails, sleepers, and ballast; S124: Based on the three-layer track model, a beam end expansion device is established between the roadbed and the bridge: S125: A suspension bridge end-extension device-track coupled vibration model is formed by constructing the beam end model, the beam end expansion device, and the three-layer track model, and the mass matrix, stiffness matrix, and damping matrix of the suspension bridge end-extension device-track coupled vibration model are constructed; specifically, the following steps are included: S1251: Enter the modal solution command in the command input area of ​​ANSYS software, then enter the command stream for extracting the mass and stiffness matrices, and export the result to a TXT file. S1252: Use MATLAB to parse the TXT format file and convert the content in the TXT format file into a sparse matrix to form a mass and stiffness matrix; S1253: Constructing a damping matrix using mass and stiffness matrices ; ; in, 、 are the overall mass and stiffness matrices of the beam end-telescopic device-track system, 、 are mass, stiffness and damping constants respectively; S1254: Obtain the mass matrix, stiffness matrix, and damping matrix of the suspension bridge end-extension device-track coupled vibration model.

[0008] Furthermore, step S2 includes: S21: Obtain the geometric and mechanical characteristics of the vehicles operating on the long-span railway suspension bridge, establish a vehicle model based on the geometric and mechanical characteristics, and construct the mass matrix, stiffness matrix, and damping matrix of the vehicle model; S22: Based on the mass matrix, stiffness matrix, and damping matrix of the suspension bridge end-telescopic device-track coupled vibration model, as well as the mass matrix, stiffness matrix, and damping matrix of the vehicle model, a suspension bridge end-telescopic device-track-train coupled vibration analysis system is formed with the beam end rotation angle or track irregularity as the external excitation.

[0009] Furthermore, step S22 includes: S221: Based on the mass matrix, stiffness matrix, and damping matrix of the vehicle model, establish the kinematic dynamics equations of the operating vehicle: ; Among them, v is the train model number in the vehicle model, 、 、 are the mass matrix, damping matrix and stiffness matrix of the train model respectively, is the load vector of the train model, 、 、 are the acceleration, velocity and displacement vectors of the train model respectively; S222: Based on the coupled vibration model of the suspension bridge end-telescopic device-track, the dynamic equations of the suspension bridge end-telescopic device-track are established: ; in, 、 、 、 are the overall mass matrix, stiffness matrix, damping matrix and node load vector of the suspension bridge end-expansion device-track coupling, b It is a suspension bridge end-telescopic device-track system. 、 、 are the acceleration, velocity and displacement vectors of the suspension bridge end-extension device-track coupling, respectively; S223: The suspension bridge end-extension device-track coupled vibration model is linked to the vehicle model through the wheel-rail relationship. The load vector of the train model and nodal load vectors Form the wheel-rail contact relationship and establish the dynamic equations of suspension bridge end-extension device-track-vehicle coupling; ; The load vector of the train model in the dynamic equation of the suspension bridge end-extension device-track-vehicle coupling include: Load in the lateral direction of the wheelset; ; in, is the lateral creep force, is the creep coefficient, 、 are the lateral speed of the wheelset and the lateral speed of the track, w is the wheelset label, r For track labels, k Number the wheelset; The interaction force between wheel and rail in the direction of heave and twist: The interaction forces between the wheel and rail in the direction of buoyancy and torsion are determined by the relative motion state between the wheel and rail in the corresponding direction. The interaction forces between the operating vehicle and the suspension bridge end-telescopic device-track include the primary suspension force, the inertia force generated by the wheelset, and the weight of the wheelset. bogies The displacement in the direction is 、 The displacement in the direction is 、 The displacement in the direction is , for any wheelset Imposed on Directional force and Directional force for: ; ; Among them, the force Indicates the forces on the suspension bridge end, expansion device and track in the torsion direction and the sinking and floating direction. is the weight of the wheelset, 、 are the stiffness and damping of the primary spring, 、 They are respectively half of the horizontal span of the primary suspension and half of the wheelbase of the operating vehicle. 、 are the wheelset moment of inertia and mass, 、 Wheelset track direction, Directional displacement, 、 Wheelset track direction, Direction speed, 、 Wheelset track direction, The acceleration in the direction 、 、 The wheelset is located at bogies direction, direction, Direction speed, is a symbolic function, the front wheel pair of the bogie of the operating vehicle Take 1, bogie rear wheel pair Take -1, z The direction is the direction of sinking and floating. The direction is the wheelset rolling direction, The direction is the wheelset nodding direction, t For the bogie, j Number the bogies; S224: A suspension bridge end-telescopic device-track-train coupled vibration model is established using the dynamic equations of the suspension bridge end-telescopic device-track-train coupling. The beam end rotation angle or track irregularity is used as the external excitation to form a suspension bridge end-telescopic device-track-train coupled vibration analysis system.

[0010] Furthermore, step S3 includes: S31: Initialize the position of the operating vehicle and the displacement of the suspension bridge end-extension device-track according to the suspension bridge end-extension device-track coupled vibration analysis system, and determine the time step; S32: Using the beam end rotation angle or track irregularity as external excitation, calculate the wheel-rail force time history of the operating vehicle wheelset at all time steps, and use the Newmark-β method to solve the operating vehicle's motion dynamics equation to obtain the operating vehicle's displacement, velocity, and acceleration, and output the operating vehicle's dynamic response indicators; specifically, it includes: S321: Load the time history curve of the track irregularity sample or the beam end rotation angle, and calculate the first-order derivative and second-order derivative of the track irregularity sample or the beam end rotation angle excitation with respect to time; S322: Calculate the position of each wheelset of the operating vehicle at the current time step, and then calculate the wheel-rail force time history caused by track irregularity or beam end rotation; S323: Use the Newmark-β method to solve the kinematic equations of the operating vehicle, obtain the displacement, velocity, and acceleration of the operating vehicle under the external excitation conditions of the beam end angle or track irregularity, and output the dynamic response indicators of the operating vehicle; S33: Apply the wheel-rail force time history to the suspension bridge end-telescopic device-track, solve the suspension bridge end-telescopic device-track dynamic equation, and obtain the displacement, velocity, and acceleration of the suspension bridge end-telescopic device-track; specifically, including: S331: Calculate the positions of all wheelsets of the operating vehicle on the track unit in each time step; S332: Convert wheel-rail forces into loads at track element nodes based on the track element shape function matrix; S333: Arrange the degrees of freedom of the suspension bridge end-telescopic device-track, load the track unit nodes according to the corresponding degrees of freedom, and form a node load vector ; S334: Use the Newmark-β method to solve the suspension bridge end-telescopic device-track dynamic equations to obtain the displacement, velocity, and acceleration of the suspension bridge end-telescopic device-track.

[0011] S34: Superimpose the displacement, velocity, and acceleration of the suspension bridge end-telescopic device-track with the beam end rotation angle or track irregularity as external excitation, and execute step S32 to calculate the new wheel-rail force time history of the operating vehicle wheelset; S35: Calculating the wheel-rail force time history error between the new wheel-rail force time history calculated in step S34 and the wheel-rail force time history calculated in step S32; If the wheel-rail force time history error is less than or equal to the wheel-rail force time history error threshold, the convergence condition is determined to be met and the dynamic response index of the operating vehicle is output; Otherwise, it is determined that the convergence condition is not met, and the process returns to step S33, reapplying the wheel-rail force time history on the suspension bridge end-telescopic device-track until the convergence condition is met, and outputting the dynamic response index of the operating vehicle.

[0012] Furthermore, step S4 includes: S41: Using a gradually increasing gradient beam end rotation angle as input, the responses of the suspension bridge end-extension device-track-train coupled vibration analysis system are calculated under different beam end rotation angle conditions. The dynamic response index of the operating vehicle under different beam end rotation angle conditions is obtained, and the mapping relationship between the dynamic response index and the beam end rotation angle at different vehicle speeds is obtained. S42: A track irregularity sample of a set length is input as an excitation source into the suspension bridge end-extension device-track-train coupled vibration analysis system to obtain the dynamic response index of the operating vehicle under the excitation source conditions. Based on the dynamic response index evaluation requirements of the operating vehicle, the influence of random irregularities is deducted to obtain the beam end rotation angle limit at different vehicle speeds. S43: Based on the three-dimensional finite element model of the suspension bridge, calculate the beam end rotation amplitude of the suspension bridge under the design load. Compare it with the beam end rotation limit to evaluate whether the beam end rotation of the suspension bridge under the design load meets the requirements.

[0013] Furthermore, step S41 includes: S411: Inputting the beam end rotation angle amplitude into the suspension bridge end-extension device-track-train coupled vibration analysis system to determine the beam end rotation angle value range that causes the dynamic response index of the operating vehicle to exceed the limit; S412: Within the range of the beam end angle value, a number of beam end angle gradient values ​​are taken according to a uniform gradient, and the dynamic response index of the operating vehicle under different beam end angle gradient value conditions is calculated. A relationship diagram between the dynamic response index and the beam end angle value is drawn to obtain a mapping relationship between the dynamic response index and the beam end angle at different vehicle speeds.

[0014] Furthermore, step S42 includes: S421: A track irregularity sample of a set length is input as an excitation source into the suspension bridge end-extension device-track-train coupled vibration analysis system to obtain the dynamic response index of the operating vehicle under the excitation source condition; S422: Performing a normality test on the dynamic response index using a normal probability graph to obtain a normal distribution of the data of the dynamic response index, and outputting a probability density function of the normal distribution; S423: Perform probability density fitting on the dynamic response index based on the non-parametric model of Gaussian kernel density estimation. The probability density function of the normal distribution is used as the kernel function of the Gaussian kernel density estimation, and the 97.5% cumulative probability distribution value is calculated. S424: According to the dynamic response index evaluation requirements of the operating vehicles and based on the 97.5% cumulative probability distribution value, the dynamic response index after deducting the track irregularity excitation is obtained, and the dynamic response index after deducting the track irregularity excitation is input into the mapping relationship between the dynamic response index and the beam end angle at different vehicle speeds to obtain the beam end angle limit at different vehicle speeds.

[0015] The beneficial effects of the present invention are: 1. This invention can significantly reduce the calculation of degrees of freedom for suspension bridges and achieve high-precision simulation. It extracts several spans at the beam ends, establishes a three-layer track model and telescopic device, and considers extending the roadbed section to reduce the error caused by the "finite length" of the track. A suspension bridge end-telescopic device-track model is constructed. The operating vehicles use multi-section formations, and on this basis, a suspension bridge end-telescopic device-train coupling model is constructed.

[0016] 2. Using the rigid gradient beam end angle and track irregularity as external excitations for the coupling model, an evaluation system for the impact of beam end angle on driving performance is formed. Solving the system based on the segregated iterative method can quickly derive the dynamic response of operating vehicles and establish a mapping relationship between beam end angle deformation and vehicle dynamic response indicators, thereby more accurately evaluating the rationality of beam end angle based on vehicle evaluation indicators. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Flowchart of the evaluation method for the impact of end turning angles on driving performance of long-span railway suspension bridges.

[0018] Figure 2 Schematic diagram of the full bridge model of a suspension bridge with a bridge deck.

[0019] Figure 3 Schematic diagram of the three-dimensional finite element model of a long-span railway suspension bridge without a bridge deck.

[0020] Figure 4 This is the finite element model diagram of the suspension bridge end-expansion device-track coupling.

[0021] Figure 5Schematic diagram of the suspension bridge end-extension device-track coupled vibration model.

[0022] Figure 6 This is a side view of a single-section train model.

[0023] Figure 7 This is the rear view of a single-section train model.

[0024] Figure 8 This is a bottom view of a single-section train model.

[0025] Figure 9 Schematic diagram of track irregularity excitation.

[0026] Figure 10 Schematic diagram of beam end rotation excitation.

[0027] Figure 11 This is a time history comparison chart of the unloading rate of the beamless end corner wheel.

[0028] Figure 12 The figure is a comparison of the vertical acceleration time history of the vehicle body at the beamless end corner.

[0029] Figure 13 This is the mapping relationship diagram between wheel weight reduction rate and vertical downward angle.

[0030] Figure 14 This is the mapping relationship diagram between the vehicle's vertical acceleration and the vertical downward angle.

[0031] Figure 15 This is the rotation angle diagram of the suspension bridge end when the wind speed is 40m / s.

[0032] Figure 16 It is the normal probability diagram of wheel load reduction rate.

[0033] Figure 17 is the normal probability diagram of vertical acceleration.

[0034] Figure 18 is the cumulative probability density distribution diagram of vertical acceleration.

[0035] Figure 19 It is the cumulative probability density distribution diagram of wheel load reduction rate. DETAILED DESCRIPTION

[0036] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0037] like Figure 1 As shown, a method for evaluating the influence of the end angle of a long-span railway suspension bridge on the driving performance includes the following steps: S1: Establish a three-dimensional finite element model of a long-span railway suspension bridge, and couple the suspension bridge end, expansion joint, and track to obtain a suspension bridge end-expansion joint-track coupled vibration model. Construct the mass matrix, stiffness matrix, and damping matrix of the suspension bridge end-expansion joint-track coupled vibration model. Step S1 specifically includes: S11: Obtain the geometric properties, material properties, and boundary properties of the long-span railway suspension bridge, equate the bridge deck of the long-span railway suspension bridge to the main truss structure to form a truss structure without a bridge deck structure, and establish a three-dimensional finite element model of the long-span railway suspension bridge. Step S11 specifically includes: S111: Acquire the geometrical properties, material properties and boundary properties of the long-span railway suspension bridge, and establish a full-bridge model of the long-span railway suspension bridge. In this embodiment, the full-bridge model of the suspension bridge is established using the APDL parameterized language of ANSYS software, such as Figure 2 As shown; S112: Use BEAM4 beam elements to simulate the main truss structure and pylons of a long-span railway suspension bridge, LINK10 cable elements to simulate the hanger and cable structure, and SHELL181 shell elements to simulate the bridge deck. Node sharing or degree of freedom coupling is used to integrate the main truss structure and pylons, hanger and cable structure, and bridge deck into a 3D model. S113: Calculate the frequency and mode shape of the long-span railway suspension bridge. In this embodiment, the calculation is performed using ANSYS software. S114: Remove the bridge deck elements in the 3D model, such as Figure 3 As shown, the bridge deck unit is discretized into a number of concentrated mass points, which are distributed according to the areas corresponding to the mass points. The bridge deck mass is distributed to the main truss, and the stiffness parameters of the main truss structure are adjusted so that the frequency and mode shape of the three-dimensional model without the bridge deck unit are consistent with the frequency and mode shape calculated in step S13; S115: Output the established 3D finite element model of the long-span railway suspension bridge, such as Figure 4 and Figure 5 As shown, Figure 4 Finite element model diagram of suspension bridge end-extension device-track coupling, Figure 5 Schematic diagram of suspension bridge end-telescopic device-track.

[0038] S12: Based on the three-dimensional finite element model of the long-span railway suspension bridge, a suspension bridge end-expansion device-track coupled vibration model is established, and the mass matrix, stiffness matrix, and damping matrix of the suspension bridge end-expansion device-track coupled vibration model are constructed. Step S12 specifically includes: S121: Extract several internodes near the beam ends from a 3D finite element model of a long-span railway suspension bridge. Use spring elements to simulate the constraints at the node cutoffs and use unit loads to determine the spring stiffness at the node cutoffs to construct a beam end model. The beam end model and the 3D finite element model have the same displacement and curvature at the same position. The spring stiffness at the node truncation is calibrated as follows: S1211: Apply force or moment at the node at the truncation; S1212: Extract the response values ​​of the local model near the beam end and the 3D finite element model in the same displacement or rotation direction; S1213: Adjust the stiffness of the spring at the node truncation to make the displacement and curvature of the local model consistent with that of the 3D finite element model at the truncation position.

[0039] S122: Add roadbed segments before and after the beam end model to simulate the fixed nature of the roadbed through fixed constraints, thus reducing the error caused by the "finite length" of the track; S123: To accurately simulate the impact of track on vehicles, a three-layer track model consisting of rails, sleepers, and ballast is constructed. This includes: S1231: The Beam4 3D elastic beam element is used to construct a rail continuum model, the sleeper and ballast structure are massed, and the Mass21 lumped mass element is used for equivalent simulation; S1232: Linear spring-damped Combine14 elements are used to simulate the rail-sleeper-ballast-roadbed and rail-sleeper-ballast-longitudinal beam. S1233: Take the stiffness and spacing values ​​of the fastener, sleeper, and ballast system to construct a three-layer track model consisting of rails, sleepers, and ballast.

[0040] S124: Based on the three-layer track model, a beam end expansion device is established between the roadbed and the bridge. In order to simulate the actual situation of the beam end in detail, a beam end expansion device is established between the roadbed and the bridge, such as Figure 5 As shown, specifically including: S1241: The longitudinal beams, movable sleepers and fixed sleepers of the telescopic device are simulated using BEAM4 beam elements; S1242: The longitudinal beam buckles and rail fasteners are simulated using the spring-damped COMBINE14 element; S1243: The longitudinal beam of the telescopic device spans the roadbed and the bridge. The longitudinal beam is connected to the fixed sleepers on the bridge via buckles. The buckles and the fixed sleepers on the roadbed can move longitudinally. The transverse connection between the longitudinal beam and the movable sleepers and the roadbed side sleepers is simulated as a fixed constraint, and linear spring constraints are used in the longitudinal and vertical directions. S125: A suspension bridge end-extension device-track coupled vibration model is formed by constructing the beam end model, the beam end expansion device, and the three-layer track model, and the mass matrix, stiffness matrix, and damping matrix of the suspension bridge end-extension device-track coupled vibration model are constructed; specifically, the following steps are included: S1251: Enter the modal solution command in the command input area of ​​the ANSYS software, then enter the command stream for extracting the mass and stiffness matrices, and export the file in TXT format. The TXT file contains the row pointers, column indices, and values ​​of non-zero elements. S1252: Use MATLAB to parse the TXT format file and convert the content in the TXT format file into a sparse matrix to form a mass and stiffness matrix; S1253: Constructing a damping matrix using mass and stiffness matrices ; ; in, 、 are the overall mass and stiffness matrices of the beam end-telescopic device-track system, 、 are mass, stiffness and damping constants respectively; S1254: Obtain the mass matrix, stiffness matrix, and damping matrix of the suspension bridge end-extension device-track coupled vibration model.

[0041] S2: Establish a vehicle model for the vehicles operating on the long-span railway suspension bridge, and construct the vehicle model's mass matrix, stiffness matrix, and damping matrix. Using the beam end rotation angle and track irregularities as external excitations, a coupled vibration analysis system for the suspension bridge end, expansion device, track, and train is formed. Step S2 specifically includes: S21: Obtain the geometric and mechanical characteristics of the vehicles operating on the long-span railway suspension bridge, establish a vehicle model based on the geometric and mechanical characteristics, and construct the mass matrix, stiffness matrix, and damping matrix of the vehicle model.

[0042] In this embodiment, a single train model is as follows Figure 6-Figure 8 As shown, it includes 1 car body, 2 bogies and 4 wheelsets. 1 bogie and two wheelsets are connected through a primary suspension device, and the bogie is connected to the car body through a secondary suspension device to form the basic model of the vehicle.

[0043] The vehicle subsystem corresponding to the vehicle model is defined as a linear system. The springs of the primary and secondary suspension devices are linear springs, and the damping is viscous damping. The body, bogie, and wheelset of the operating vehicle are regarded as rigid bodies without elastic deformation, and only their translation or rotation is considered. The dynamic behaviors of each vehicle section do not interfere with each other, and the mechanical coupling effects such as couplers and buffers are ignored. In each vehicle model, the body and the two bogies consider the five degrees of freedom of yaw, heave, roll, head shake, and nod, respectively, and the wheelset considers the degrees of freedom in the directions of yaw, heave, and roll.

[0044] The calculation parameters of the vehicle model are: train bogie wheelbase, vehicle spacing, lateral span of the primary and secondary suspensions, and the distance from the center of the vehicle body to the secondary suspension.

[0045] Obtain the mass of the car body, wheelset, and bogie, the moment of inertia in three directions, and the stiffness and damping in three directions of the primary and secondary suspension devices; sequentially construct the mass matrix, stiffness matrix, and damping matrix of the train model, and then repeatedly arrange the mass matrix, stiffness matrix, and damping matrix of the train model along the main diagonal to obtain the mass matrix, stiffness matrix, and damping matrix of the entire vehicle model.

[0046] S22: Based on the mass matrix, stiffness matrix, and damping matrix of the suspension bridge end-telescopic device-track coupled vibration model, as well as the mass matrix, stiffness matrix, and damping matrix of the vehicle model, with the beam end rotation angle and track irregularity as external excitations, together with the suspension bridge end-telescopic device-track-train coupled vibration model, a suspension bridge end-telescopic device-track-train coupled vibration analysis system is formed. Specifically, the following steps are included: S221: Based on the mass matrix, stiffness matrix, and damping matrix of the vehicle model, establish the kinematic dynamics equations of the operating vehicle: ; Among them, v is the train model number in the vehicle model, 、 、 are the mass matrix, damping matrix and stiffness matrix of the train model respectively, is the load vector of the train model, 、 、 are the acceleration, velocity and displacement vectors of the train model respectively; S222: Based on the suspension bridge end-extension device-track coupled vibration model, the suspension bridge end-extension device-track dynamic equation is established: ; in, 、 、 、 are the overall mass matrix, stiffness matrix, damping matrix and node load vector of the suspension bridge end-expansion device-track coupling, b It is a suspension bridge end-telescopic device-track system. 、 、 are the acceleration, velocity and displacement vectors of the suspension bridge end-extension device-track coupling, respectively; S223: The suspension bridge end-extension device-track coupled vibration model is linked to the vehicle model through the wheel-rail relationship. The load vector of the train model and nodal load vectors Form the wheel-rail contact relationship and establish the dynamic equations of suspension bridge end-extension device-track-vehicle coupling; ; The load vector of the train model in the dynamic equation of the suspension bridge end-extension device-track-vehicle coupling include: Load in the lateral direction of the wheelset; ; in, is the lateral creep force, is the creep coefficient, 、 are the lateral speed of the wheelset and the lateral speed of the track, w is the wheelset label, r For track labels, k Number the wheelset; Interaction forces between wheel and rail in heaving and torsional directions: The interaction forces between the wheel and rail in the heave and torsion directions can be determined by the relative motion state between the wheel and rail in the corresponding directions. The interaction forces between the operating vehicle and the suspension bridge end-extension device-track include the primary suspension force, the inertia force generated by the wheelset, and the weight of the wheelset. Defines the wheelset's bogies The displacement in the direction is 、 The displacement in the direction is 、 The displacement in the direction is , for any wheelset Imposed on Directional force and Directional force for: ; ; Among them, the force Indicates the forces on the suspension bridge end, expansion device and track in the torsion direction and the sinking and floating direction. is the weight of the wheelset, 、 are the stiffness and damping of the primary spring, 、 They are respectively half of the horizontal span of the primary suspension and half of the wheelbase of the operating vehicle. 、 are the wheelset moment of inertia and mass, 、 Wheelset track direction, Directional displacement, 、 Wheelset track direction, Direction speed, 、 Wheelset track direction, The acceleration in the direction 、 、 The wheelset is located at bogies direction, direction, Direction speed, is a symbolic function, the front wheel pair of the bogie of the operating vehicle Take 1, bogie rear wheel pair Take -1, z The direction is the direction of sinking and floating. The direction is the wheelset rolling direction, The direction is the wheelset nodding direction, t For the bogie, j Number the bogies and define the front bogie j =1, rear bogie j =2; S224: A suspension bridge end-telescopic device-track-train coupled vibration model is established using the dynamic equations of the suspension bridge end-telescopic device-track-train coupling. The beam end rotation angle and track irregularity are used as external excitations to form a suspension bridge end-telescopic device-track-train coupled vibration analysis system.

[0047] In this embodiment, the track irregularity spectrum adopts the German low-interference spectrum with a wavelength of 1-80m, and the trigonometric series method is used to simulate and generate track irregularity samples in three directions. Figure 9 shown.

[0048] The rigid beam end angle is used as input. In order to alleviate the discontinuity of the beam end angle curvature, the transition section of the road bridge described by the transition curve of the rail rigidity and the rail support rigidity is considered, such as Figure 10 The beam end rotation amplitude is calculated by the ratio of the vertical displacement at the truncation point of the beam end model to the length of the beam end model.

[0049] S3: Based on the suspension bridge end-telescopic device-track-train coupled vibration analysis system, initialize the position of the operating vehicle, the displacement of the suspension bridge end-telescopic device-track, and determine the time step; use the numerical integration method to solve the kinematic equations of the operating vehicle and the dynamic equations of the suspension bridge end-telescopic device-track until the convergence conditions are met, and output the dynamic response indicators of the operating vehicle. Specifically, it includes the following steps: S31: Initialize the position of the operating vehicle and the displacement of the suspension bridge end-extension device-track according to the suspension bridge end-extension device-track coupled vibration analysis system, and determine the time step; S32: Using the beam end rotation angle or track irregularity as external excitation, calculate the wheel-rail force time history of the operating vehicle wheelset at all time steps, and use the Newmark-β method to solve the kinematic equations of the operating vehicle to obtain the displacement, velocity and acceleration of the operating vehicle, and output the dynamic response indicators of the operating vehicle. Specifically including: S321: Load the time history curve of the track irregularity sample or the beam end rotation angle, and calculate the first-order derivative and second-order derivative of the track irregularity sample or the beam end rotation angle excitation with respect to time; S322: Calculate the position of each wheelset of the operating vehicle at the current time step, and then calculate the wheel-rail force time history caused by track irregularity or beam end rotation; S323: Use the Newmark-β method to solve the kinematic equations of the operating vehicle, obtain the displacement, velocity, and acceleration of the operating vehicle under the external excitation conditions of the beam end angle or track irregularity, and output the dynamic response indicators of the operating vehicle.

[0050] S33: Apply the wheel-rail force time history to the suspension bridge end-telescopic device-track, solve the suspension bridge end-telescopic device-track dynamic equation, and obtain the displacement, velocity, and acceleration of the suspension bridge end-telescopic device-track. Specifically including: S331: Calculate the positions of all wheelsets of the operating vehicle on the track unit in each time step; S332: Convert wheel-rail forces into loads at track element nodes based on the shape function matrix of the track beam element; S333: Arrange the degrees of freedom of the suspension bridge end-telescopic device-track, load the track unit nodes according to the corresponding degrees of freedom, and form a node load vector ; S334: Use the Newmark-β method to solve the suspension bridge end-telescopic device-track dynamic equations to obtain the displacement, velocity, and acceleration of the suspension bridge end-telescopic device-track.

[0051] S34: Superimpose the displacement, velocity, and acceleration of the suspension bridge end-telescopic device-track with the beam end rotation angle or track irregularity as external excitation, and execute step S32 to calculate the new wheel-rail force time history of the operating vehicle wheelset; S35: Calculating the wheel-rail force time history error between the new wheel-rail force time history calculated in step S34 and the wheel-rail force time history calculated in step S32; If the wheel-rail force time history error is less than or equal to the wheel-rail force time history error threshold, the convergence condition is determined to be met and the dynamic response index of the operating vehicle is output; Otherwise, it is determined that the convergence condition is not met, and the process returns to step S33, reapplying the wheel-rail force time history on the suspension bridge end-telescopic device-track until the convergence condition is met, and outputting the dynamic response index of the operating vehicle.

[0052] This embodiment takes the lower rotation angle mode of the middle beam end as an example. By inputting the lower rotation angle of the beam end into the suspension bridge end-extension device-track-train coupled vibration analysis system for analysis and extracting the time history curve of the vehicle dynamic response index, an index that is more sensitive to the beam end rotation angle can be obtained, such as Figure 11 and Figure 12 As shown in the figure, various indicators will fluctuate greatly at the corner of the beam end. The dynamic response indicators include wheel load reduction rate, vehicle body acceleration, etc.

[0053] S4: Calculate the dynamic response index of the operating vehicle under different beam end angle conditions, obtain the mapping relationship between the dynamic response index and the beam end angle at different vehicle speeds, apply track irregularity samples as excitation sources, and calculate the beam end angle limit at different vehicle speeds; calculate the suspension bridge end angle amplitude based on the design load of the suspension bridge, and evaluate whether the suspension bridge beam end angle meets the requirements. Step S4 specifically includes: S41: Using the gradually increasing gradient beam end rotation angle as input, calculate the response of the suspension bridge end-expansion device-track-train coupled vibration analysis system under different beam end rotation angle conditions, obtain the dynamic response index of the operating vehicle under different beam end rotation angle conditions, and obtain the mapping relationship between the dynamic response index and the beam end rotation angle at different vehicle speeds. Specifically, the following steps are included: S411: Inputting the beam end rotation angle amplitude into the suspension bridge end-extension device-track-train coupled vibration analysis system to determine the beam end rotation angle value range that causes the dynamic response index of the operating vehicle to exceed the limit; S412: Within the range of the beam end angle value, a number of beam end angle gradient values ​​are taken according to a uniform gradient, and the dynamic response index of the operating vehicle under different beam end angle gradient value conditions is calculated. A relationship diagram between the dynamic response index and the beam end angle value is drawn. This embodiment uses ORIGIN drawing software to draw the relationship, and obtains the mapping relationship between the dynamic response index and the beam end angle at different vehicle speeds.

[0054] S42: A track irregularity sample of a set length is input as an excitation source into the suspension bridge end-extension device-track-train coupled vibration analysis system to obtain the dynamic response index of the operating vehicle under the excitation source condition. The influence of random irregularities is deducted based on the dynamic response index evaluation requirements of the operating vehicle to obtain the beam end rotation angle limit at different vehicle speeds. The specific steps include: S421: In this embodiment, a track irregularity sample with a wavelength of 1-80 m and a length of 10 km is used as an excitation source and inputted into the suspension bridge end-extension device-track-train coupled vibration analysis system to obtain the dynamic response index of the operating vehicle under the excitation source condition; S422: Perform normality test on the dynamic response index using a normal probability graph to obtain the normal distribution of the data of the dynamic response index and output the probability density function of the normal distribution; the data points of the dynamic response index are evenly distributed near the reference line; Figure 16 and Figure 17 shown. Figure 16 The normal probability diagram of the wheel load reduction rate of this embodiment is given. Figure 17 A normal probability diagram of the vertical acceleration of this embodiment is given. The vertical acceleration and the wheel load reduction rate are both dynamic response indicators of the operating vehicle.

[0055] S423: Perform probability density fitting on the dynamic response index based on the non-parametric model of Gaussian kernel density estimation, use the probability density function of the normal distribution as the kernel function of the Gaussian kernel density estimation, and calculate the 97.5% cumulative probability distribution value; Figure 18 and Figure 19 As shown, Figure 18 The cumulative probability density distribution diagram of the vertical acceleration of this embodiment is given. Figure 19 The cumulative probability density distribution diagram of the wheel load reduction rate of this embodiment is given.

[0056] S424: According to the dynamic response index evaluation requirements of the operating vehicles and based on the 97.5% cumulative probability distribution value, the dynamic response index after deducting the track irregularity excitation is obtained, and the dynamic response index after deducting the track irregularity excitation is input into the mapping relationship between the dynamic response index and the beam end angle at different vehicle speeds to obtain the beam end angle limit at different vehicle speeds.

[0057] The dynamic response index evaluation requirements of this embodiment include: 1. The High-Speed ​​Railway Design Specifications stipulate that the vehicle body acceleration a The standards are: ; 2. The derailment coefficient is a safety indicator for determining whether a wheel has derailed. Its value is the lateral force between the wheel and rail at a certain moment. Q and vertical force P (wheel weight) ratio, that is ; The derailment coefficient standard is: ; 3. Wheel load reduction rate is a safety indicator for judging derailment due to severe wheel load reduction. Its value is the vertical load reduction of the wheels on both sides. Average static wheel weight of wheelset The larger the ratio, the greater the probability of wheel derailment.

[0058] The standards for wheel load reduction rate are: .

[0059] like Figure 13 and Figure 14 As shown, Figure 13 The mapping relationship between the beam end angle and the dynamic response index (wheel load reduction rate) is shown. At the same speed, the two are roughly linearly related. The wheel load reduction rate requirement under the existing specifications is 0.6. Considering the influence of track unevenness, the 97.5% cumulative probability distribution value of the wheel load reduction rate under track unevenness as the excitation source is calculated to be 0.1 (e.g. Figure 18 and Figure 19 As shown in the figure, the horizontal coordinate of the intersection of the red dotted line and the blue curve is 0.1), 0.1 is used as the dynamic response index error, and the 97.5% cumulative probability distribution value 0.1 under the influence of track irregularity is subtracted from the 0.6 required by the specification to obtain the dynamic response index (wheel load reduction rate) of the operating vehicle 0.5 (such as Figure 13 red horizontal dashed line), Figure 13 The horizontal coordinate of the intersection of the horizontal red dotted line and the red oblique straight line (mapping relationship) is 8.04, which is the calculated beam end angle limit at a speed of 200 km / h.

[0060] S43: Based on the three-dimensional finite element model of the suspension bridge, calculate the beam end rotation amplitude of the suspension bridge under the design load, and compare it with the beam end rotation limit to evaluate whether the beam end rotation amplitude of the suspension bridge under the design load meets the requirements. Figure 15 As shown, this embodiment uses a crosswind of 40 m / s as an example to obtain the beam end angle amplitude, including the beam end transverse angle and beam end vertical angle data. If the suspension bridge end angle amplitude exceeds the beam end angle limit, the suspension bridge beam end angle is determined to be unsatisfactory; otherwise, it is considered to be satisfactory.

Claims

1. A method for evaluating the influence of the end angle of a long-span railway suspension bridge on the driving performance, characterized in that: The following steps are involved: S1: Establish a three-dimensional finite element model of a long-span railway suspension bridge and couple the suspension bridge end, expansion joint, and track to obtain a suspension bridge end-expansion joint-track coupled vibration model. Construct the mass matrix, stiffness matrix, and damping matrix of the suspension bridge end-expansion joint-track coupled vibration model. S2: Build a vehicle model for vehicles operating on a long-span railway suspension bridge and construct its mass matrix, stiffness matrix, and damping matrix. Use beam end rotation or track irregularities as external excitations to form a coupled vibration analysis system for the suspension bridge end, expansion device, track, and train. S3: Based on the coupled vibration analysis system of the suspension bridge end-telescopic device-track-train, the position of the operating vehicle and the displacement of the suspension bridge end-telescopic device-track are initialized, and the time step is determined. The kinematic equations of the operating vehicle and the dynamic equations of the suspension bridge end-telescopic device-track are solved using the numerical integration method until convergence conditions are met, and the dynamic response indicators of the operating vehicle are output. S4: Calculate the dynamic response index of operating vehicles under different beam end rotation conditions, obtain the mapping relationship between the dynamic response index and the beam end rotation angle at different vehicle speeds, apply track irregularity samples as the excitation source, and calculate the beam end rotation angle limit at different vehicle speeds; calculate the suspension bridge end angle amplitude based on the design load of the suspension bridge, and evaluate whether the suspension bridge beam end rotation angle meets the requirements.

2. The method for evaluating the influence of the end angle of a long-span railway suspension bridge on driving performance according to claim 1 is characterized in that: The step S1 comprises: S11: Obtain the geometric, material, and boundary properties of the long-span railway suspension bridge, equate the bridge deck of the long-span railway suspension bridge to the main truss structure to form a truss structure without a bridge deck structure, and establish a three-dimensional finite element model of the long-span railway suspension bridge; S12: Based on the three-dimensional finite element model of the long-span railway suspension bridge, a suspension bridge end-extension device-track coupled vibration model is established, and the mass matrix, stiffness matrix, and damping matrix of the suspension bridge end-extension device-track coupled vibration model are constructed.

3. The method for evaluating the influence of the end angle of a long-span railway suspension bridge on driving performance according to claim 2 is characterized in that: The step S11 includes: S111: Obtain the geometric, material, and boundary properties of a long-span railway suspension bridge and establish a full-bridge model of the suspension bridge; S112: Simulates the main truss structure, towers, hangers, cable structure, and deck of a long-span railway suspension bridge. This model integrates the main truss structure, towers, hangers, cable structure, and deck into a 3D model using node sharing or degree of freedom coupling. S113: Calculate the frequency and mode shape of a long-span railway suspension bridge; S114: Remove the bridge deck unit from the three-dimensional model, discretize the bridge deck unit into a number of concentrated mass points, distribute the mass of the bridge deck to the main truss according to the area corresponding to the mass points, and adjust the stiffness parameters of the main truss structure so that the frequency and mode shape of the three-dimensional model without the bridge deck unit are consistent with the frequency and mode shape calculated in step S113; S115: Output the established three-dimensional finite element model of the long-span railway suspension bridge.

4. The method for evaluating the influence of the end angle of a long-span railway suspension bridge on driving performance according to claim 3 is characterized in that: The step S12 includes: S121: Extract several internodes near the beam ends from a 3D finite element model of a long-span railway suspension bridge. Use spring elements to simulate the constraints at the node cutoffs and use unit loads to determine the spring stiffness at the node cutoffs to construct a beam end model. Ensure that the beam end model and the 3D finite element model have the same displacement and curvature at the same location. The calibration method of the spring stiffness at the node cutoff is: S1211: Apply force or moment at the node at the truncation; S1212: Extract the response values ​​of the local model near the beam end and the 3D finite element model in the same displacement or rotation direction; S1213: Adjust the stiffness of the spring at the node truncation to make the displacement and curvature of the local model consistent with that of the 3D finite element model at the truncation position; S122: Add roadbed segments before and after the beam end model to simulate the fixity of the roadbed through fixed constraints; S123: Construct a three-layer track model consisting of rails, sleepers, and ballast; S124: Based on the three-layer track model, a beam end expansion device is established between the roadbed and the bridge: S125: A suspension bridge end-extension device-track coupled vibration model is formed by constructing the beam end model, the beam end expansion device, and the three-layer track model, and the mass matrix, stiffness matrix, and damping matrix of the suspension bridge end-extension device-track coupled vibration model are constructed; specifically, the following steps are included: S1251: Enter the modal solution command in the command input area of ​​ANSYS software, then enter the command stream for extracting the mass and stiffness matrices, and export the result to a TXT file. S1252: Use MATLAB to parse the TXT format file and convert the content in the TXT format file into a sparse matrix to form a mass and stiffness matrix; S1253: Constructing a damping matrix using mass and stiffness matrices ; ； in, 、 are the overall mass and stiffness matrices of the beam end-telescopic device-track system, 、 are mass, stiffness and damping constants respectively; S1254: Obtain the mass matrix, stiffness matrix, and damping matrix of the suspension bridge end-extension device-track coupled vibration model.

5. The method for evaluating the influence of the end angle of a long-span railway suspension bridge on driving performance according to claim 1 is characterized in that: The step S2 comprises: S21: Obtain the geometric and mechanical characteristics of the vehicles operating on the long-span railway suspension bridge, establish a vehicle model based on the geometric and mechanical characteristics, and construct the mass matrix, stiffness matrix, and damping matrix of the vehicle model; S22: Based on the mass matrix, stiffness matrix, and damping matrix of the suspension bridge end-telescopic device-track coupled vibration model, as well as the mass matrix, stiffness matrix, and damping matrix of the vehicle model, a suspension bridge end-telescopic device-track-train coupled vibration analysis system is formed with the beam end rotation angle or track irregularity as the external excitation.

6. The method for evaluating the influence of the end angle of a long-span railway suspension bridge on driving performance according to claim 5 is characterized in that: The step S22 includes: S221: Based on the mass matrix, stiffness matrix, and damping matrix of the vehicle model, establish the kinematic dynamics equations of the operating vehicle: ； Among them, v is the train model number in the vehicle model, 、 、 are the mass matrix, damping matrix and stiffness matrix of the train model respectively, is the load vector of the train model, 、 、 are the acceleration, velocity and displacement vectors of the train model respectively; S222: Based on the coupled vibration model of the suspension bridge end-telescopic device-track, the dynamic equations of the suspension bridge end-telescopic device-track are established: ； in, 、 、 、 are the overall mass matrix, stiffness matrix, damping matrix and node load vector of the suspension bridge end-expansion device-track coupling, b It is a suspension bridge end-telescopic device-track system. 、 、 are the acceleration, velocity and displacement vectors of the suspension bridge end-extension device-track coupling, respectively; S223: The suspension bridge end-extension device-track coupled vibration model is linked to the vehicle model through the wheel-rail relationship. The load vector of the train model and nodal load vectors Form the wheel-rail contact relationship and establish the dynamic equations of suspension bridge end-extension device-track-vehicle coupling; ； The load vector of the train model in the dynamic equation of the suspension bridge end-extension device-track-vehicle coupling include: Load in the lateral direction of the wheelset; ； in, is the lateral creep force, is the creep coefficient, 、 are the lateral speed of the wheelset and the lateral speed of the track, w is the wheelset label, r For track labels, k Number the wheelset; The interaction force between wheel and rail in the direction of heave and twist: The interaction forces between the wheel and rail in the direction of buoyancy and torsion are determined by the relative motion state between the wheel and rail in the corresponding direction. The interaction forces between the operating vehicle and the suspension bridge end-telescopic device-track include the primary suspension force, the inertia force generated by the wheelset, and the weight of the wheelset. bogies The displacement in the direction is 、 The displacement in the direction is 、 The displacement in the direction is , for any wheelset Imposed on Directional force and Directional force for: ； ； Among them, the force Indicates the forces on the suspension bridge end, expansion device and track in the torsion direction and the sinking and floating direction. is the weight of the wheelset, 、 are the stiffness and damping of the primary spring, 、 They are respectively half of the horizontal span of the primary suspension and half of the wheelbase of the operating vehicle. 、 are the wheelset moment of inertia and mass, 、 Wheelset track direction, Directional displacement, 、 Wheelset track direction, Direction speed, 、 Wheelset track direction, The acceleration in the direction 、 、 The wheelset is located at bogies direction, direction, Direction speed, is a symbolic function, the front wheel pair of the bogie of the operating vehicle Take 1, bogie rear wheel pair Take -1, z The direction is the direction of sinking and floating. The direction is the wheelset rolling direction, The direction is the wheelset nodding direction, t For the bogie, j Number the bogies and define the front bogie j =1, rear bogie j =2; S224: A suspension bridge end-telescopic device-track-train coupled vibration model is established using the dynamic equations of the suspension bridge end-telescopic device-track-train coupling. The beam end rotation angle or track irregularity is used as the external excitation to form a suspension bridge end-telescopic device-track-train coupled vibration analysis system.

7. The method for evaluating the influence of the end angle of a long-span railway suspension bridge on driving performance according to claim 1 is characterized in that: The step S3 comprises: S31: Initialize the position of the operating vehicle and the displacement of the suspension bridge end-extension device-track according to the suspension bridge end-extension device-track coupled vibration analysis system, and determine the time step; S32: Using the beam end rotation angle or track irregularity as external excitation, calculate the wheel-rail force time history of the operating vehicle wheelset at all time steps, and use the Newmark-β method to solve the operating vehicle's motion dynamics equation to obtain the operating vehicle's displacement, velocity, and acceleration, and output the operating vehicle's dynamic response indicators; specifically, it includes: S321: Load the time history curve of the track irregularity sample or the beam end rotation angle, and calculate the first-order derivative and second-order derivative of the track irregularity sample or the beam end rotation angle excitation with respect to time; S322: Calculate the position of each wheelset of the operating vehicle at the current time step, and then calculate the wheel-rail force time history caused by track irregularity or beam end rotation; S323: Use the Newmark-β method to solve the kinematic equations of the operating vehicle, obtain the displacement, velocity, and acceleration of the operating vehicle under the external excitation conditions of the beam end angle or track irregularity, and output the dynamic response indicators of the operating vehicle; S33: Apply the wheel-rail force time history to the suspension bridge end-telescopic device-track, solve the suspension bridge end-telescopic device-track dynamic equation, and obtain the displacement, velocity, and acceleration of the suspension bridge end-telescopic device-track; specifically, including: S331: Calculate the positions of all wheelsets of the operating vehicle on the track unit in each time step; S332: Convert wheel-rail forces into loads at track element nodes based on the track element shape function matrix; S333: Arrange the degrees of freedom of the suspension bridge end-telescopic device-track, load the track unit nodes according to the corresponding degrees of freedom, and form a node load vector ; S334: Use the Newmark-β method to solve the suspension bridge end-telescopic device-track dynamic equations to obtain the displacement, velocity, and acceleration of the suspension bridge end-telescopic device-track. S34: Superimpose the displacement, velocity, and acceleration of the suspension bridge end-telescopic device-track with the beam end rotation angle or track irregularity as external excitation, and execute step S32 to calculate the new wheel-rail force time history of the operating vehicle wheelset; S35: Calculating the wheel-rail force time history error between the new wheel-rail force time history calculated in step S34 and the wheel-rail force time history calculated in step S32; If the wheel-rail force time history error is less than or equal to the wheel-rail force time history error threshold, the convergence condition is determined to be met and the dynamic response index of the operating vehicle is output; Otherwise, it is determined that the convergence condition is not met, and the process returns to step S33, reapplying the wheel-rail force time history on the suspension bridge end-telescopic device-track until the convergence condition is met, and outputting the dynamic response index of the operating vehicle.

8. The method for evaluating the influence of the end angle of a long-span railway suspension bridge on driving performance according to claim 1 is characterized in that: The step S4 comprises: S41: Using a gradually increasing gradient beam end rotation angle as input, the responses of the suspension bridge end-extension device-track-train coupled vibration analysis system are calculated under different beam end rotation angle conditions. The dynamic response index of the operating vehicle under different beam end rotation angle conditions is obtained, and the mapping relationship between the dynamic response index and the beam end rotation angle at different vehicle speeds is obtained. S42: A track irregularity sample of a set length is input as an excitation source into the suspension bridge end-extension device-track-train coupled vibration analysis system to obtain the dynamic response index of the operating vehicle under the excitation source conditions. Based on the dynamic response index evaluation requirements of the operating vehicle, the influence of random irregularities is deducted to obtain the beam end rotation angle limit at different vehicle speeds. S43: Based on the three-dimensional finite element model of the suspension bridge, calculate the beam end rotation amplitude of the suspension bridge under the design load. Compare it with the beam end rotation limit to evaluate whether the beam end rotation of the suspension bridge under the design load meets the requirements.

9. The method for evaluating the influence of the end angle of a long-span railway suspension bridge on driving performance according to claim 8 is characterized in that: The step S41 includes: S411: Inputting the beam end rotation angle amplitude into the suspension bridge end-extension device-track-train coupled vibration analysis system to determine the beam end rotation angle value range that causes the dynamic response index of the operating vehicle to exceed the limit; S412: Within the range of the beam end angle value, a number of beam end angle gradient values ​​are taken according to a uniform gradient, and the dynamic response index of the operating vehicle under different beam end angle gradient value conditions is calculated. A relationship diagram between the dynamic response index and the beam end angle value is drawn to obtain a mapping relationship between the dynamic response index and the beam end angle at different vehicle speeds.

10. The method for evaluating the influence of the end angle of a long-span railway suspension bridge on driving performance according to claim 9 is characterized in that: The step S42 includes: S421: A track irregularity sample of a set length is input as an excitation source into the suspension bridge end-extension device-track-train coupled vibration analysis system to obtain the dynamic response index of the operating vehicle under the excitation source condition; S422: Performing a normality test on the dynamic response index using a normal probability graph to obtain a normal distribution of the data of the dynamic response index, and outputting a probability density function of the normal distribution; S423: Perform probability density fitting on the dynamic response index based on the non-parametric model of Gaussian kernel density estimation. The probability density function of the normal distribution is used as the kernel function of the Gaussian kernel density estimation, and the 97.5% cumulative probability distribution value is calculated. S424: According to the dynamic response index evaluation requirements of the operating vehicles and based on the 97.5% cumulative probability distribution value, the dynamic response index after deducting the track irregularity excitation is obtained, and the dynamic response index after deducting the track irregularity excitation is input into the mapping relationship between the dynamic response index and the beam end angle at different vehicle speeds to obtain the beam end angle limit at different vehicle speeds.

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