CN116822024A - A method for determining the most unfavorable intersection location of multi-line trains on a railway bridge - Google Patents

Abstract

The invention discloses a method for determining the most unfavorable intersection position of multi-line trains on a railway bridge, which includes the steps: S1. Conduct a vehicle-bridge coupling analysis on the bridge response when a single-line train passes the bridge and obtain the bridge dynamic alignment; S2. According to different Dynamic linear superposition of the number of train lines and different intersection positions; S3. Wavelength segmentation of the dynamic linear shape of the bridge according to the sensitive wavelength of the car body; S4. Use the midpoint chord measurement method and the midpoint chord measurement method for the dynamic linear shape of the bridge within and outside the sensitive wavelength range of the car body The curvature method is used for evaluation; S5. According to the working conditions corresponding to the chord measurement value and the curvature value, the most unfavorable intersection position of the multi-line train is obtained. This invention can quickly predict the most unfavorable positions of multi-line trains at low calculation costs, avoids the problem of low efficiency in calculating multi-intersection positions in traditional vehicle-bridge coupling analysis, and is suitable for new bridge projects when multi-line trains are running. Practical application requirements for bridge dynamic analysis.

Description

A method for determining the most unfavorable intersection location of multi-line trains on a railway bridge

Technical field

The invention relates to the field of coupled vibration of vehicle bridges, and in particular to a method for determining the most unfavorable intersection position of multi-line trains on a railway bridge.

Background technique

The calculation of the dynamic response of a train crossing a bridge has always been an important issue in the design and operation stages of the bridge. With economic development and increasing demand for transportation capacity, railway bridges have developed from the previous short-span single-line to long-span multi-line. Bridges may undergo excessive dynamic displacement under the action of multi-line high-speed trains, which will adversely affect the train's driving performance and reduce driving safety and ride comfort. Therefore, in the design stage, it is necessary to perform dynamic calculations on bridges designed with multi-line trains to ensure that the dynamic indicators of the bridge and trains meet the requirements. In the operation stage, dispatch control can be carried out according to the most unfavorable intersection position of multi-line trains to avoid this situation. .

The current analysis method for dynamic problems when trains cross bridges is mainly realized through vehicle-bridge coupled dynamic analysis, that is, establishing dynamic models for the bridge and the train respectively, and establishing motion equations through the interaction between the forces and geometry of the two. The theoretical solution is obtained, and finally the dynamic response of the bridge and vehicle is obtained. When multiple trains cross the bridge at the same time, different intersection positions will cause the bridge to show different dynamic alignments, resulting in differences in the dynamic response of the trains. Calculating only a single intersection position often ignores the most unfavorable response of the vehicle. If the vehicle-axle coupling calculation is performed for every possible intersection position, it will consume a lot of time and computing power, and is inefficient.

Therefore, proposing a method for determining the most unfavorable intersection location of multi-track trains on a railway bridge is an urgent technical problem that needs to be solved by those skilled in the art.

Contents of the invention

The purpose of this invention is to solve the problem of the numerous intersection working conditions of multi-line trains on railway bridges and the low efficiency of train-bridge coupling vibration calculation, and to guide the design and operation of bridges, and to propose the most unfavorable intersection position of multi-line trains on railway bridges. method of determination.

In order to achieve the above-mentioned object of the invention, the technical solutions adopted by the present invention are:

Provide a method for determining the most unfavorable intersection location of multiple trains on a railway bridge, including the following steps:

S1. Conduct vehicle-bridge coupling analysis on the bridge response when a single-track train crosses the bridge and obtain the bridge dynamic alignment. The bridge dynamic alignment includes the relationship between the displacement of each bridge node along the span direction and the change of the node position with time;

S2. Perform dynamic linear superposition according to the number of different train lines and different intersection locations;

S3. Wavelength segmentation of the dynamic linear shape of the bridge according to the sensitive wavelength of the vehicle body;

S4. Use the midpoint chord measurement method and the curvature method to evaluate the dynamic alignment of the bridge within and outside the sensitive wavelength range of the vehicle body;

S5. According to the working conditions corresponding to the chord measurement value and the curvature value, the most unfavorable intersection position of the multi-line train is obtained.

Further, step S1 includes the following steps:

S11: Establish bridge and train system dynamics models and their kinematic equations;

S12: Use the numerical integration method to solve the kinematic equations and obtain the dynamic alignment of the bridge when the train crosses the bridge in a single line.

Further, step S2 includes the following steps:

S21: Calculate the time difference between the train on the bridge and the train on the bridge using the train intersection position and vehicle speed;

S22: Use the dynamic linear data of the bridge where the train is running on a single line, reverse the direction along the bridge span, and include the time difference of the train on the bridge on the time axis, superimpose the displacement of the corresponding node, and obtain the time of multi-line train crossing the bridge at different intersection positions. Bridge dynamic linear data;

S23: Repeat steps S21-S22, calculate the time difference of trains on the bridge according to the intersection positions of multiple trains, and obtain the corresponding dynamic alignment of the bridge.

Further, step S3 includes the following steps:

S31: Use multiple sets of German low-interference spectrum inversion time-domain irregularity samples to excite the vehicle body and obtain the vehicle body acceleration;

S32: Use the acceleration generated by the car body under excitation to conduct spectrum analysis to obtain the wavelength frequency range that contributes the most to the car body acceleration, and correspondingly obtain the car body sensitive wavelength boundary value that contributes the most to the car body acceleration;

S33: Perform Fourier series fitting on the dynamic alignment of the bridge, and divide the dynamic alignment of the bridge into two parts using the sensitive wavelength dividing value of the car body.

Further, step S4 includes the following steps:

S41: Use the midpoint chord measurement method to analyze the bridge alignment within the sensitive wavelength range of the vehicle body, and obtain each maximum chord measurement value under the conditions of different intersection positions of the two vehicles;

S42: Use the curvature method to analyze the bridge alignment outside the sensitive wavelength range of the vehicle body, and determine the maximum curvature values of the two vehicles at different intersection positions.

The beneficial effects of the present invention are:

By obtaining the dynamic alignment of the bridge when a single-line train crosses the bridge, and using a relatively simple linear superposition method, the present invention predicts the dynamic alignment of the bridge when multi-line trains cross the bridge and realizes changes in the number of trains and intersection positions.

Based on the sensitive wavelength of the train acceleration response, this invention divides the dynamic line shape of the bridge into wavelengths and uses the midpoint chord measurement method and the curvature method for analysis respectively. The working condition corresponding to the maximum value of the chord measurement and curvature is the most unfavorable intersection position. The method is fast in calculation and has a clear process. It can accurately determine the most unfavorable intersection position without the need for large-scale structural dynamics solution, which greatly improves efficiency, thereby providing guidance for bridge design and providing a basis for dispatching after actual operation of the bridge.

Description of the drawings

Figure 1 is a schematic flow chart of a method for determining the most unfavorable intersection location of multi-line trains on a railway bridge according to the present invention;

Figure 2 is a cross-sectional view of the railway bridge main beam in the specific application scenario of the present invention;

Figure 3 is a dynamic linear diagram of the bridge when a single-line train crosses the bridge in a specific application scenario of the present invention;

Figure 4 is a dynamic linear diagram of a bridge obtained by the superposition method in a specific application scenario of the present invention where a two-track train intersects in the main span;

Figure 5 is a power spectrum diagram of body acceleration under random excitation in a specific application scenario of the present invention;

Figure 6 is a partial linear diagram of the bridge dynamic linear wavelength less than 200m in the specific application scenario of the present invention;

Figure 7 is a partial linear diagram of the dynamic linear wavelength of the bridge greater than 200m in the specific application scenario of the present invention;

Figure 8 is a schematic diagram of the principle of the midpoint chord measurement method in a specific application scenario of the present invention;

Figure 9 is a diagram showing chord measurements of parts of bridges with dynamic linear wavelengths less than 200m in specific application scenarios of the present invention;

Figure 10 is a diagram of the curvature values of the bridge dynamic linear wavelength greater than 200m in the specific application scenario of the present invention;

Figure 11 is a statistical chart of the maximum chord measurement values and curvature values of two vehicles at different intersection positions in the specific application scenario of the present invention.

Detailed ways

The specific embodiments of the present invention are described below to facilitate those skilled in the art to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the technical field, as long as various changes These changes are obvious within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions and creations utilizing the concept of the invention are protected.

S1: Carry out vehicle-bridge coupling analysis on the bridge response when a single-track train crosses the bridge and obtain the bridge dynamic alignment; the bridge dynamic alignment includes the relationship between the displacement of each bridge node along the span direction and the change of the node position with time;

S11: Establish a dynamic model of the bridge and train system, and establish kinematic equations through the interaction between the train and the bridge.

Specifically, this embodiment takes a suspension bridge with a main span of 1,000 meters as an example. The bridge span is arranged as (84+84+1092+84+84)m, and the bridge main beam section is shown in Figure 2.

The 12-degree-of-freedom space beam element is used to simulate the main beam and pier; the 6-degree-of-freedom space rod element is used to simulate the main cable and suspender, a finite element model of the bridge is established, and the mass, stiffness and damping matrix of the bridge structure are obtained. The train adopts a multi-rigid body dynamics model. A train contains 1 car body, two bogies and 4 wheel pairs. For each component, its 5 degrees of freedom are considered: lateral, vertical, side roll, nodding and shaking. Therefore Each vehicle has a total of 35 degrees of freedom. The motion equations of each system are as follows:

Kinematic equation of train subsystem:

Bridge subsystem kinematic equation:

In the formula, M _V , C _V , and K _V are the mass matrix, damping matrix, and stiffness matrix of the train subsystem respectively; M _B , C _B , and K _B are the mass matrix, damping matrix, and stiffness matrix of the bridge subsystem respectively; X _V , are the displacement, speed, and acceleration vectors of the train subsystem respectively; X _B , /> are the displacement, velocity, and acceleration vectors of the bridge subsystem respectively; F _VB is the force exerted by the train on the bridge, F _BV is the force exerted by the bridge on the train, and F _VB and F _BV are the interaction forces between the train and the bridge;

The present invention uses the numerical integration method to discretize the system in time steps. It is necessary to determine the positions of the train and the car at each time step and calculate the train-bridge interaction force.

First, according to the running speed of the train, calculate the distance traveled at each time step and determine the specific location on the bridge that this distance corresponds to. Read the track irregularity at this position and add it to the bridge deformation X _B at this position to obtain the actual position in space of this point. The calculation formula for the actual position D _Bi is as follows:

D _Bi =X _Bi + _ri

In the formula, D _Bi is the actual position of the i-th node of the bridge, X _Bi is the dynamic displacement of the i-th node of the bridge subsystem, and r _i is the unevenness value at the i-th position of the corresponding bridge node.

In this embodiment, the track irregularity uses the time domain irregularity inverted from German low-interference spectrum, and the power spectral density is as follows:

In the formula, S _v (Ω) is the power spectral density function of track irregularities; Ω is the spatial frequency respectively; A _v is the roughness constant; Ω _c and Ω _r are the cutoff frequencies;

S12: Use the numerical integration method to solve the kinematic equations and obtain the dynamic alignment of the bridge when the train crosses the bridge in a single line.

For the train-bridge interaction force, the train-bridge mutual contact force F _VB is obtained using D'Alembert's principle and based on the relative displacement of the train bridge. The calculation formula is as follows:

F _VB =k _wi ×D _B

In the formula, _kωi is the stiffness of each wheel pair of the train, D _B is the actual position of the bridge space under each wheel, F _VB is the force exerted by the train on the bridge, F _BV mutual contact force F _VB is the force exerted by the bridge on the train , F _BV and F _VB are opposite forces.

Substituting F _BV and F _VB into the right-hand side of the kinematic equations of the bridge and train, and solving them with the numerical integration method; the integral solution format of the Newmark-β method for the bridge subsystem kinematic equation is as follows:

In the formula, α and β are integration parameters, α is generally taken as 0.25, and β is generally taken as 0.5; Δt is the time integration step; n represents the nth integration step;

Displace the bridge subsystem by X _B and speed Acceleration vector/> As X _n separately, solve the bridge subsystem;

In the above formula, Express it as X _n+1 and substitute it into the dynamic equation of the bridge subsystem at time n+1:

F _(VB)n+1 is the bridge-train interaction force at time n+1.

By simplifying the dynamic equation of the bridge subsystem at time n+1, the following formula is obtained:

Solve the above equation to get X _n+1 ;

The solution formula for is as follows:

in a ₆ =Δt(1-β), a ₇ =βΔt.

The motion equations of the train system are solved using the fast display integration method;

The integral format of the fast display integration method for solving equations of motion is:

Formula in/> ψ is the integration parameter, which can generally be taken as 0.5; Δt is the time integration step; n represents the nth integration step; the train subsystem displacement, speed, and acceleration vectors X _V , Enter as X _n .

By solving each subsystem, the dynamic response of each subsystem at time n+1 is obtained.

According to the system displacement X _B of the bridge subsystem, the displacement of the bridge deck nodes at each moment is extracted, and the dynamic linear data of the bridge when the single-line train crosses the bridge is obtained:

In the formula, X _ij is the displacement value of the bridge at the i position along the span direction at time j.

In this embodiment, the train model is selected as ICE3 and the vehicle speed is 250km/h. Based on the bridge alignment calculated based on the above vehicle-bridge coupling vibration, as shown in Figure 3, the changes in bridge node displacement along the bridge span position and along the train are obtained respectively. Data on bridge crossing time changes.

S2: Dynamic linear superposition of bridges based on the number of different train lines and different intersection locations;

S21: Calculate the time difference between the train on the bridge and the train on the bridge using the train intersection position and vehicle speed;

For two or more trains to meet at different locations, first use the time of the first train to board the bridge as the base time, and calculate the delay time of each other train to board the bridge according to the following formula, that is, the train boarding time difference, the train boarding time difference Calculated as follows:

In the formula, T is the delay time required for trains on different lines; x is the coordinate of the intersection location along the bridge span direction; L is the total length of the bridge; v is the vehicle speed;

S22: Use the dynamic linear data of the bridge where the train is running on a single line, reverse the direction along the bridge span, and include the time difference of the train on the bridge on the time axis, superimpose the displacement of the corresponding node, and obtain the time of multi-line train crossing the bridge at different intersection positions. Bridge dynamic linear data.

Specifically, in this embodiment, the train runs on two lines and intersects with the working condition in the middle of the main span of the bridge. Since the bridge in this embodiment has a symmetrical structure along the span direction, the two vehicles meet in the middle of the main span, so the two vehicles should get on the bridge at the same time. First, reverse the bridge alignment along the time axis when a single line crosses the bridge, and then add it to its original shape. The dynamic alignment data of the bridge when two vehicles meet at the mid-span is as follows:

In the formula, X _1/2 is the dynamic linear data of the bridge when the two vehicles intersect at the 1/2 position of the main span. The dynamic alignment of the bridge when the two vehicles meet at the mid-span is shown in Figure 4.

When the train runs on two lines and intersects with the left bridge tower of the bridge, the time T of the last train on the bridge corresponds to the k moment in the 1 to j time series in the dynamic linear data of the bridge. Then the displacements of the corresponding nodes are superimposed to obtain the intersection of the two trains. The bridge dynamic linear data X _Tower at the position of the bridge tower. The specific bridge dynamic linear data is as follows X _Tower :

S23: Repeat steps S21-S22, calculate the time difference of trains on the bridge according to the intersection positions of multiple trains, and obtain the corresponding dynamic alignment of the bridge.

S3: Use the sensitive wavelength of the vehicle body to segment the dynamic alignment of the bridge into wavelength segments;

S31: Use multiple sets of German low-interference spectrum inversion time-domain irregularity samples to excite the vehicle body and obtain the vehicle body acceleration;

S32: Use the acceleration generated by the car body under excitation to conduct spectrum analysis to obtain the wavelength frequency range that contributes the most to the car body acceleration, and correspondingly obtain the car body sensitive wavelength boundary value that contributes the most to the car body acceleration;

S33: Perform Fourier series fitting on the dynamic line of the bridge, and divide the dynamic line of the bridge into two parts using the sensitive wavelength dividing value of the vehicle body;

In this embodiment, according to the above method, the sensitive wavelength of the vehicle model at a vehicle speed of 250km/h is about 30-200m. The vehicle body acceleration spectrum is shown in Figure 5. Since the contribution of wavelengths below 30m to vehicle body acceleration is low, the wavelength of 200m is used For the boundary, the dynamic alignment of the bridge is divided. The specific method is to first perform Fourier series fitting on the dynamic line shape of the bridge. The formula is as follows:

In the formula, a ₀ , a _n , and b _m are all constants; w ₀ is the frequency, the wavelength λ = v·w ₀ , v is the vehicle speed; x is the mileage; L is the total length of the bridge; i is the fitting series.

By expanding the bridge alignment in the form of Fourier series and segmenting the wavelength at 200m, we can obtain bridge alignment diagrams with wavelengths below 200m and above 200m, as shown in Figures 6 and 7 respectively.

Among them, the calculation formula of the vehicle body sensitive wavelength λ is as follows:

λ=v·f

In the formula, λ is the sensitive wavelength of the car body; v is the train speed; f is the natural vibration Hertz frequency of the car body; the vertical natural vibration Hertz frequency of the car body is generally about 1Hz, and there are differences between different models.

S4: Use the midpoint chord measurement method and the curvature method to analyze the dynamic linear shape of the bridge within and outside the sensitive wavelength range of the vehicle body, and obtain the chord measurement value map and curvature value map;

S41. Use the midpoint chord measurement method to analyze the bridge alignment within the sensitive wavelength range of the vehicle body, and obtain each maximum chord measurement value under the conditions of different intersection positions of the two vehicles;

Analyze bridge alignments with wavelengths below 200m through the midpoint chord measurement method;

The chord measurement amplitude of the midpoint chord measurement method is the second difference of track deformation. Its change pattern is similar to the vehicle body acceleration, which is also the second difference of track deformation. It can be used as an important indicator for evaluating track smoothness. Figure 9 shows the measurement results of bridge linear chords with wavelengths below 200m.

The midpoint chord measurement method is a widely used method for evaluating track smoothness, and its principle is shown in Figure 8. This chord measurement method requires taking a reference chord between two points in the longitudinal direction of the track, which is the line segment AC in the figure. Then the length of the line segment OB is the chord amplitude measurement value. Since the angle θ between the reference chord and the horizontal direction is generally small, the length of the line segment OB is approximately equal to the line segment OB'. In actual programming, the length of the line segment OB' can be used as the chord amplitude measurement value at the coordinate x position to improve calculations. s efficiency. The specific formula of the string measurement method is as follows:

In the formula: x represents the position coordinate; L represents the half-chord length of the reference string; v _x represents the chord amplitude measurement value at coordinate x; h _x represents the orbit deformation value at coordinate x;

S42. Use the curvature method to analyze the bridge alignment outside the sensitive wavelength range of the vehicle body, and obtain the maximum curvature values under the conditions of different intersection positions of the two vehicles;

The curvature method is used to analyze the bridge alignments with wavelengths above 200m;

Perform curvature analysis on the dynamic line shape of the bridge with a wavelength greater than 200m. According to the radius of curvature R, the centrifugal acceleration formula a=V ² /R is used to calculate the centrifugal acceleration a of the car body. Therefore, the curvature can directly reflect the centrifugal acceleration a of the car body when it passes through this position. Centrifugal acceleration, Figure 10 shows the bridge alignment and curvature results for wavelengths above 200m. The characteristics of the bridge's linear shape are judged by the midpoint chord measurement method and the curvature method respectively, and reflect the acceleration characteristics of the vehicle body when it passes through this position. Therefore, it can be determined by the specific values of the chord measurement value and the maximum value of the curvature value. predict.

S5: According to the working conditions corresponding to the chord measurement value and curvature value, the most unfavorable intersection position of the multi-line train is obtained.

In Figures 9 and 10, it can be seen that the maximum value of chord measurement is concentrated at the bridge position, while the maximum value of curvature often appears at the bridge tower and the intersection position of the two vehicles. When looking for the maximum chord measurement value and curvature value under each working condition, the results at both locations can be counted. As shown in Figure 11, three working conditions are given in which the two vehicles intersect at the middle of the main span, intersect at 1/4 of the main span, and intersect at the left bridge tower, and the chord measurement and curvature values are statistically calculated respectively. It can be seen that in this embodiment, when the two vehicles meet at the 1/4 span position of the main span, the response of the vehicles is the most unfavorable. Therefore, during the design and operation stages, this situation should be avoided; the sloping downward shadow in Figure 10 represents the dazzling measurement value, and the diamond-shaped shadow represents the curvature value.

In this method, based on the generation mechanism of the vehicle body acceleration when the train crosses the bridge, starting from the dynamic linear shape of the bridge, using wavelength segmentation technology, combined with the midpoint chord measurement method and the curvature calculation method, a fast and efficient multi-line train intersection is proposed. The most unfavorable position determination method solves the disadvantages of traditional vehicle-axle coupling calculations such as low efficiency and heavy workload.

The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, and they should be covered by within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims (5)

1. The method for determining the most unfavorable crossing position of the multi-line train on the railway bridge is characterized by comprising the following steps:

s1, carrying out crane-bridge coupling analysis on bridge response when a single-line train passes through a bridge, and obtaining a bridge dynamic line shape, wherein the bridge dynamic line shape comprises the relation between the displacement of each bridge node along the bridge span direction and the change of the position of the node along the time;

s2, carrying out dynamic linear superposition according to the number of different train lines and different intersection positions;

s3, carrying out wavelength segmentation on the dynamic line shape of the bridge according to the sensitive wavelength of the vehicle body;

s4, evaluating the dynamic line shape of the bridge within the sensitive wavelength range of the vehicle body by using a mid-point chord measurement method and a curvature method respectively;

s5, obtaining the most unfavorable crossing position of the multi-line train according to the working condition of the chord measured value and the curvature value.

2. The method for determining the most unfavorable crossing location of a multi-line train on a railroad bridge according to claim 1, wherein step S1 comprises the steps of:

s11: establishing a dynamic model and a kinematic equation of a bridge and train system;

s12: and solving a kinematic equation by using a numerical integration method to obtain the dynamic line shape of the bridge when the train passes by the bridge in a single line.

3. The method for determining the most unfavorable crossing location of a multi-line train on a railroad bridge according to claim 1, wherein step S2 comprises the steps of:

s21: calculating the train bridging time difference of the train bridging by utilizing the train intersection position and the train speed;

s22: the bridge dynamic line data of the single line operation of the train are utilized, the bridge dynamic line data are reversed along the bridge span direction, the bridge time difference on the train is counted on a time axis, and the displacement of corresponding nodes is overlapped to obtain the bridge dynamic line data when the multi-line train passes through the bridge at different intersection positions;

s23: and repeating the steps S21-S22, respectively calculating the bridge-up time difference of the trains according to the intersection positions of the trains, and obtaining the corresponding dynamic line shape of the bridge.

4. The method for determining the most unfavorable crossing location of a multi-line train on a railroad bridge according to claim 1, wherein step S3 comprises the steps of:

s31: exciting the vehicle body by using a plurality of groups of time domain irregularity samples inverted by the German low interference spectrum to obtain the vehicle body acceleration;

s32: the acceleration of the vehicle body generated under excitation is utilized for carrying out spectrum analysis, so as to obtain a wavelength frequency range with the maximum contribution to the acceleration of the vehicle body, and correspondingly obtain a vehicle body sensitive wavelength demarcation value with the maximum contribution to the acceleration of the vehicle body;

s33: and carrying out Fourier series fitting on the bridge dynamic line shape, and dividing the bridge dynamic line shape into two parts by utilizing the sensitive wavelength demarcation value of the vehicle body.

5. The method for determining the most unfavorable crossing location of a multi-line train on a railroad bridge according to claim 1, wherein step S4 comprises the steps of:

s41: analyzing the bridge line shape in the sensitive wavelength range of the vehicle body by using a mid-point chord measurement method to obtain each maximum chord measurement value under the working conditions of different intersection positions of the double vehicles;

s42: and analyzing the bridge line shape outside the sensitive wavelength range of the vehicle body by using a curvature method, wherein the maximum curvature values of the double vehicles are under different intersection position working conditions.