CN116822024A - Method for determining least favored crossing position of multi-line train on railway bridge - Google Patents
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Abstract
The invention discloses a method for determining the least favored crossing position of a multi-line train on a railway bridge, which comprises the following steps: s1, carrying out driving-bridge coupling analysis on bridge response when a single-line train passes through a bridge, and obtaining dynamic line shape of the bridge; 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. The method can rapidly predict the most unfavorable position of the multi-line train with lower calculation cost, avoids the problem of low calculation efficiency for the multi-meeting position in the traditional train-bridge coupling analysis, and is suitable for the practical application requirement of bridge power analysis during the operation of the multi-line train in the novel bridge engineering.
Description
Technical Field
The invention relates to the field of coupling vibration of a vehicle bridge, in particular to a method for determining the least favored crossing position of a multi-line train on a railway bridge.
Background
The power response calculation problem during the bridge crossing of a train is always an important problem in the bridge design and operation stage. With the economic development and the increase of the traffic demand, the railway bridge is developed from the past short-span single line to the large-span multi-line. The bridge can generate excessive dynamic displacement under the action of the multi-line high-speed train, so that the running performance of the train is adversely affected, and the running safety and riding comfort are reduced. Therefore, in the design stage, power calculation is required to be performed on the bridge designed with the multi-line train, so that the power indexes of the bridge and the train meet the requirements, and in the operation stage, scheduling control can be performed according to the least favored crossing position of the multi-line train, so that the situation is avoided.
The existing analysis method for the power problem when the train passes through the bridge is mainly realized through train-bridge coupling power analysis, namely, a dynamic model is respectively established for the bridge and the train, a motion equation is established through the interaction relation between the forces and the geometry of the bridge and the train, a theoretical solution is obtained, and finally, the power response of the bridge and the vehicle is obtained. When a train passes through the bridge in multiple lines, different crossing positions can enable the bridge to present different dynamic lines, and the difference of dynamic responses of the train is caused. Calculating only a single intersection location tends to ignore the vehicle's most adverse response, and if a vehicle-bridge coupling calculation is performed for each possible intersection location, a significant amount of time and effort is consumed, which is inefficient.
Therefore, the method for determining the most unfavorable crossing position of the multi-line train on the railway bridge is provided, and is a technical problem to be solved urgently by the person skilled in the art.
Disclosure of Invention
The invention aims to solve the problems of multiple multi-line train crossing conditions on a railway bridge and low calculation efficiency of train-bridge coupling vibration, and to guide the design and operation of a bridge, and provides a method for determining the most unfavorable crossing position of a multi-line train on the railway bridge.
In order to achieve the aim of the invention, the invention adopts the following technical scheme:
the method for determining the most unfavorable crossing position of the multi-line train on the railway bridge comprises 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.
Further, the step S1 includes the following steps:
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.
Further, the step S2 includes the following steps:
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.
Further, the step S3 includes the following steps:
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.
Further, the step S4 includes the following steps:
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.
The beneficial effects of the invention are as follows:
according to the method, the dynamic line shape of the bridge of the single-line train passing through the bridge is obtained, and the dynamic line shape of the bridge of the multi-line train passing through the bridge is predicted by a simpler line shape superposition method, so that the number of trains and the change of intersection positions are realized.
The method has the advantages that based on the sensitive wavelength of train acceleration response, the wavelength division is carried out on the dynamic line shape of the bridge, the mid-point chord measurement method and the curvature method are respectively adopted for analysis, the working condition corresponding to the maximum value of the chord measurement and the curvature is the most unfavorable intersection position, the calculation is quick, the process is clear, the most unfavorable intersection position can be accurately judged without carrying out large-scale structural dynamics solution, the efficiency is greatly improved, the guidance is provided for the bridge design, and the scheduling basis is provided for the actual operation of the bridge.
Drawings
FIG. 1 is a flow chart of a method for determining the most adverse crossing location of a multi-line train on a railroad bridge according to the present invention;
FIG. 2 is a cross-sectional view of a girder of a railway bridge in a specific application scenario of the present invention;
FIG. 3 is a dynamic line diagram of a bridge when a single line train passes the bridge in a specific application scenario of the invention;
FIG. 4 is a dynamic line graph of a bridge where two trains meet in a main span obtained by a superposition method in a specific application scene of the invention;
FIG. 5 is a graph of vehicle acceleration power under random excitation in a specific application scenario of the present invention;
FIG. 6 is a graph of a portion of a bridge dynamic line wavelength less than 200m in a specific application scenario of the present invention;
FIG. 7 is a graph of a portion of a dynamic linear wavelength of a bridge greater than 200m in a specific application scenario of the present invention;
FIG. 8 is a schematic diagram of mid-chord measurement principle in a specific application scenario of the present invention;
FIG. 9 is a graph of measured chord values of a portion of the bridge with a dynamic linear wavelength of less than 200m in a specific application scenario of the present invention;
FIG. 10 is a graph of a portion of a curvature value of a bridge dynamic linear wavelength greater than 200m in a specific application scenario of the present invention;
FIG. 11 is a graph showing the maximum value statistics of chord measurements and curvature values under different intersection position conditions of a double vehicle in a specific application scene of the present invention.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and all the inventions which make use of the inventive concept are protected by the spirit and scope of the present invention as defined and defined in the appended claims to those skilled in the art.
S1: performing driving-bridge coupling analysis on bridge response when a single-line train passes through a bridge, and obtaining dynamic line shape of the bridge; the dynamic line shape of the bridge 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;
s11: and establishing a dynamic model of the bridge and the train system, and establishing a kinematic equation through the interaction relationship between the train and the bridge.
Specifically, in this embodiment, a suspension bridge with a main span in kilometer level is taken as an example, the bridge spans are arranged as (84+84+1092+84+84) m, and the section of the main beam of the bridge is shown in fig. 2.
Simulating a main girder and a bridge pier by using a space beam unit with 12 degrees of freedom; and simulating the main cable and the suspender by using a space rod unit with 6 degrees of freedom, and establishing a bridge finite element model to obtain a mass, rigidity and damping matrix of the bridge structure. The train adopts a multi-rigid-body dynamic model, and one train comprises 1 train body, two bogies and 4 wheel pairs, and 5 degrees of freedom of transverse, vertical, side rolling, nodding and head shaking of each component are considered, so that each train has 35 degrees of freedom. The equations of motion of the systems are as follows:
train subsystem kinematics equation:
bridge subsystem kinematics equation:
wherein M is V 、C V 、K V The mass matrix, the damping matrix and the rigidity matrix of the train subsystem are respectively adopted; m is M B 、C B 、K B The mass matrix, the damping matrix and the rigidity matrix of the bridge subsystem are respectively adopted; x is X V 、The displacement, the speed and the acceleration vectors of the train subsystem are respectively; x is X B 、/>The displacement, the speed and the acceleration vectors of the bridge subsystem are respectively; f (F) V-B For acting force of train on bridge, F B-V For acting force of bridge to train, F V-B 、F B-V Is the interaction force between the train and the bridge;
the invention adopts a numerical integration method to carry out time step dispersion on the system, and the positions of the train and the automobile at each time step are required to be determined and the interaction force of the train and the bridge is calculated.
First, according to the running speed of the train, the distance of each time step is calculated and the specific position on the bridge corresponding to the distance is determined. Reading the track irregularity at the position and deforming X with the bridge at the position B Adding to obtain the space actual position of the point, the actual position D Bi The calculation formula of (2) is as follows:
D Bi ＝X Bi +r i
wherein D is Bi X is the actual position of the ith node of the bridge Bi Dynamic displacement, r, of the ith node of the bridge subsystem respectively i Is the irregularity value at the position corresponding to the bridge node i.
In this embodiment, the track irregularity adopts the time domain irregularity of the german low-interference spectrum inversion, and the power spectrum density is as follows:
wherein S is v (Ω) is a track height irregularity power spectral density function; omega is the spatial frequency respectively; a is that v Is a roughness constant; omega shape c 、Ω r Is the cut-off frequency;
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.
For the train-bridge interaction force, the Dalangbeil principle is utilized, and the train-bridge interaction force F is obtained according to the relative displacement of the train bridge V-B Calculation ofThe formula is as follows:
F V-B ＝k wi ×D B
wherein k is ωi For the rigidity of each wheel set of the train, D B For each wheel lower bridge space actual position F V-B For acting force of train on bridge, F B-V Force of mutual contact F V-B For acting force of bridge to train, F B-V And F is equal to V-B Is the opposite force.
Will F B-V And F V-B Substituting the numerical integration method into the right end of a bridge and train kinematics equation, and solving the numerical integration method; the Newmark-beta method integral solving format of the bridge subsystem motion equation is as follows:
wherein alpha and beta are integral parameters, alpha is generally 0.25, beta is generally 0.5; Δt is the time integration step; n is the number n of integration steps;
displacement X of bridge subsystem B Speed and velocity ofAcceleration vector->Respectively and individually as X n Solving a bridge subsystem;
will be of the above formulaBy X n+1 Expressed and substituted into the dynamics equation of the bridge subsystem at time n+1:
F (V-B)n+1 and the bridge-train interaction force is n+1.
The bridge subsystem dynamics equation at the moment n+1 is simplified, and the following formula is obtained:
solving the above to obtain X n+1 ；
The solution formula of (2) is as follows:
wherein the method comprises the steps ofa 6 ＝Δt(1-β)，a 7 ＝βΔt。
Solving a motion equation of the train system by adopting a quick display integration method;
the integration format of the fast display integration method for solving the motion equation is as follows:
in->Psi is an integral parameter, which is generally taken to be 0.5; Δt is the time integration step; n is the number n of integration steps; vector X of displacement, speed and acceleration of train subsystem V 、Is brought as X n 。
And solving each subsystem to obtain the power response of each subsystem at the time of n+1.
Based on system displacement X of bridge subsystem B Extracting the displacement of the bridge deck node at each moment to obtain bridge dynamic linear data when a single-line train passes the bridge:
wherein X is ij The displacement value of the bridge at the moment j along the span direction i is the displacement value of the bridge.
In this embodiment, the train model is selected to be ICE3, the speed of the train is 250km/h, and the bridge line shape obtained by calculating according to the train-bridge coupling vibration is shown in fig. 3, so as to obtain the data of the bridge node displacement along the bridge span position change and along the train bridge crossing time change.
S2: according to the number of different train lines and different crossing positions, carrying out dynamic linear superposition on the bridge;
s21: calculating the train bridging time difference of the train bridging by utilizing the train intersection position and the train speed;
for two or more trains meeting at different positions, firstly taking the time of the first train to get on the bridge as the reference time, calculating the delay time of the bridge on other trains according to the following formula, namely the bridge on the bridge time difference, and the bridge on the bridge time difference calculation formula is as follows:
wherein T is the time of delay required by different trains; x is the coordinate of the intersection position along the bridging direction; l is the whole bridge length; v is the vehicle speed;
s22: and utilizing bridge dynamic line data of single-line running of the train to reverse along the bridge span direction, and counting the bridge on-train time difference on a time axis, and superposing the displacement of corresponding nodes to obtain the bridge dynamic line data when the multi-line train passes the bridge at different intersection positions.
Specifically, in this embodiment, the train runs in double lines and intersects the working condition of the bridge main span. Because the bridge is symmetrical along the span direction in the embodiment, the double vehicles meet in the main span, so the double vehicles should get on the bridge at the same time. Firstly, the bridge line shape is reversed along the direction of a time axis when a single line passes through a bridge, and then the bridge line shape is added with the original line shape, and the dynamic line shape data of the bridge when a double vehicle meets the midspan is as follows:
wherein X is 1/2 The dynamic linear data of the bridge when the double vehicles meet at the 1/2 position of the main span. The dynamic alignment of the bridge when the double vehicles meet at midspan is shown in fig. 4.
When the trains run in double lines and meet the left bridge tower of the bridge, the rear on-bridge train time T corresponds to k time in a 1-j time sequence in the dynamic linear data of the bridge, and the displacements of the corresponding nodes are overlapped to obtain the dynamic linear data X of the bridge when the double trains meet the position of the bridge tower Tower Specific bridge dynamic line shape data is as follows X Tower ：
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.
S3: the dynamic line shape of the bridge is segmented by utilizing the sensitive wavelength of the vehicle body;
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: performing Fourier series fitting on the bridge dynamic line shape, and dividing the bridge dynamic line shape into two parts by utilizing a vehicle sensitive wavelength demarcation value;
in this embodiment, the sensitive wavelength of the vehicle model is about 30-200m at the vehicle speed of 250km/h according to the method, and the vehicle acceleration frequency spectrum is shown in fig. 5, and since the wavelength below 30m contributes little to the vehicle acceleration, the dynamic line shape of the bridge is divided by using the wavelength of 200m as a boundary. The specific method comprises the steps of firstly carrying out Fourier series fitting on the dynamic line shape of the bridge, wherein the formula is as follows:
wherein a is 0 、a n 、b m Are all constants; w (w) 0 Wavelength λ=v·w for frequency 0 V is the vehicle speed; x is mileage; l is the whole bridge length; i is the number of fitting steps.
By segmenting the bridge line shape in the form of an expansion of fourier series and the wavelength of 200m as a boundary, bridge line graphs of wavelengths of 200m or less and wavelengths of 200m or more can be obtained as shown in fig. 6 and 7, respectively.
The calculation formula of the vehicle body sensitive wavelength lambda is as follows:
λ＝v·f
wherein lambda is the sensitive wavelength of the vehicle body; v is the train speed; f is the self-vibration Hertz frequency of the vehicle body; the vertical natural vibration frequency of the vehicle body is generally about 1Hz, and the vehicle body has differences among different vehicle types.
S4: analyzing the dynamic line shape of the bridge in the sensitive wavelength range of the vehicle body by using a mid-point chord measurement method and a curvature method to obtain a chord measurement value graph and a curvature value graph;
s41, analyzing the bridge line shape in the sensitive wavelength range of the vehicle body by using a midpoint chord measurement method to obtain each maximum chord measurement value under the working conditions of different intersection positions of the double vehicles;
analyzing the bridge line shape with the wavelength below 200m by a mid-point chord measurement method;
the chord measurement value of the midpoint chord measurement method is a secondary difference of track deformation, and the change rule of the chord measurement value has similarity with the vehicle body acceleration which is the secondary difference of track deformation, so that the chord measurement value can be used as an important index for evaluating the track smoothness. FIG. 9 shows bridge linear chord measurements below 200m wavelength.
The mid-point chord measurement method is a widely used rail smoothness assessment method, and the principle of the mid-point chord measurement method is shown in fig. 8. The chord measurement method needs to take a reference chord between two points in the longitudinal direction of the track, namely a line segment AC in the figure, and the length of the line segment OB is the chord measurement value. Because the included angle theta between the reference string and the horizontal direction is generally smaller, the length of the line segment OB is approximately equal to the length of the line segment OB ', and the length of the line segment OB' can be taken as the string measurement value of the coordinate x position in actual programming so as to improve the calculation efficiency. The specific formula of the chord measurement method is as follows:
wherein: x represents a position coordinate; l represents the half chord length of the reference chord; v x Representing the chord measurement value at coordinate x; h is a x Representing the track deformation value at coordinate x;
s42, analyzing the bridge line shape outside the sensitive wavelength range of the vehicle body by using a curvature method to obtain each maximum curvature value under the working conditions of different intersection positions of the double vehicles;
analyzing the bridge line shape with the wavelength of more than 200m by a curvature method;
curvature analysis is carried out on bridge dynamic lines with the wavelength larger than 200m, and a centrifugal acceleration formula a=V is adopted according to the curvature radius R 2 and/R is calculated to obtain the centrifugal acceleration a of the vehicle body, so that the curvature can directly reflect the centrifugal acceleration generated when the vehicle body passes through the position, and the bridge line shape and curvature results with the wavelength of more than 200m are shown in figure 10. The bridge linear characteristics are respectively judged by a mid-point chord measurement method and a curvature method, and the acceleration characteristics of the vehicle body passing through the position are reflected, so that the specific numerical values of the chord measurement value and the maximum value of the curvature value can be predicted.
S5: and obtaining the least favorable intersection position of the multi-line train according to the working condition of the chord measured value and the curvature value.
In fig. 9 and 10, it is possible to obtain that the chordwise maximum is concentrated at the bridge location, whereas the maximum of curvature tends to occur at the pylon and at the intersection of the two vehicles. When searching the maximum value of the chord measurement value and the maximum value of the curvature value under each working condition, the results at the two positions can be counted. As shown in FIG. 11, 3 working conditions of double-vehicle crossing in the main span, crossing in 1/4 span and crossing in the left bridge tower are given, and chord measurement and curvature values of the working conditions are counted respectively. It can be seen that in this embodiment, the vehicles are correspondingly most disadvantageous when the double vehicle is intersected at the main span 1/4 span position. Therefore, in the design and operation stage, the occurrence of the situation should be avoided; the diagonal down-shading in fig. 10 represents the glare values, and the diamond-shaped shading represents the curvature values.
According to the method, a wavelength segmentation technology is utilized from the dynamic line shape of a bridge through a vehicle body acceleration generation mechanism when a train passes through the bridge, and a mid-point chord measurement method and a curvature calculation method are combined, so that a rapid and efficient method for determining the most unfavorable position of a multi-line train intersection is provided, and the defects of low efficiency and high workload of traditional vehicle-bridge coupling calculation are overcome.
The foregoing is merely illustrative of the present invention, and the present invention is not limited thereto, and any person skilled in the art will readily appreciate variations or alternatives within the scope of the present invention. Therefore, the protection scope of the invention is 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.
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