A calculation method of bridge longitudinal section synthetic slope based on dynamic load action

Abstract

The application relates to a calculation method of a bridge longitudinal section synthetic slope based on dynamic load action, comprising the following steps: S1, obtaining the total time step number of a train passing through a bridge and the wheel pair position of the train at each time step; S2, simulating the dynamic loading process of the train driving on the bridge based on vehicle-bridge coupling dynamic time history analysis to obtain the bridge longitudinal section linear data at all time steps; S3, fitting the bridge linear function within the train length range of the bridge at a certain time step; S4, determining the slope corresponding to the axle load mass borne by the wheel pair at the wheel pair position on the bridge according to the wheel pair position of the train on the bridge at the time step and the bridge linear function; S5, calculating the synthetic slope according to the axle load mass borne by the locomotive wheel pair and the freight car wheel pair, the slope corresponding to the axle load mass borne by the wheel pair at the wheel pair position on the bridge at the time step; repeating S3 to S5 to obtain the dynamic synthetic slope. The calculation method provided by the application tracks the bridge longitudinal section linear based on the dynamic load of the train to calculate the slope, and the result is more in line with the actual situation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bridge longitudinal section design, and particularly relates to a calculation method of bridge longitudinal section synthetic gradient based on dynamic load action. BACKGROUND

[0002] In the operation and maintenance process of railway bridge lines, deformation will inevitably occur under the conditions of temperature, train load, wind load, etc. With the increase in the number of train marshalling, the train load is continuously improved. In the preliminary design of the bridge, in order to adapt to the running of heavy axle load and long heavy load trains and ensure the safety and stability of the heavy load train operation, it is necessary to consider whether the maximum gradient value of the longitudinal section alignment of the heavy load train passing through the bridge meets the specification requirements. The maximum gradient of the heavy load train line is the maximum gradient value of the continuous uphill stage of the locomotive when the heavy load train is pulled by the locomotive at a constant speed.

[0003] In the related art, such as the locomotive algorithm based on the heavy load train with the traction locomotive, only the corresponding gradient of the locomotive located at the head position in the continuous uphill stage is considered, and the alignment at the moment of the maximum deflection is selected from a series of bridge longitudinal section alignments as the alignment when the maximum gradient is calculated, or the slope of the line connecting the coordinate points at both ends of the bridge is taken as the gradient. However, for the bridge line, the bridge longitudinal section does not have a relatively long longitudinal section like the railway line, and generally the herringbone slope is considered to be arranged. Therefore, when the train passes through the bridge, the train body may cross multiple gradient stages within the total length of the train, and it is impossible for the train to be completely in the continuous uphill stage.

[0004] The above-mentioned locomotive algorithm calculates the maximum value of the static alignment slope, and compares the maximum value of the slope with the specification limit, but the maximum value of the slope may not be consistent with the actual position of the locomotive. At the same time, considering that the bridge alignment changes at any time with the change of the loading position of the train, it is unreasonable to calculate the gradient under the train traction quality based on a certain specific alignment, and there may be a situation that the maximum gradient value is not reached by the train. Therefore, the calculation result of the above-mentioned locomotive algorithm is conservative, the gradient limit value is large, and the precision is low, which cannot be used as the representative value of the bridge gradient calculation, and does not conform to the actual situation. SUMMARY

[0005] The present application provides a calculation method of bridge longitudinal section synthetic gradient based on dynamic load action, which solves the technical problems of the overly conservative calculation result, the large gradient limit value and the low precision in the calculation of the gradient by the locomotive algorithm in the related art.

[0006] The present application provides a calculation method of bridge longitudinal section synthetic gradient based on dynamic load action, which solves the technical problems of the overly conservative calculation result, the large gradient limit value and the low precision in the calculation of the gradient by the locomotive algorithm in the related art.

[0007] Step S1, obtaining the total time step of the train passing through the bridge and the wheel position of the train at each time step;

[0008] Step S2, simulating the dynamic loading process of the train driving on the bridge based on the coupled dynamic time-history analysis of the train and the bridge to obtain the longitudinal profile data of the bridge at all time steps;

[0009] Step S3, fitting the bridge profile function within the train length on the bridge at a time step;

[0010] Step S4, determining the slope corresponding to the axle load of the wheelset at the wheelset position on the bridge according to the wheelset position of the train on the bridge at the time step and the bridge profile function;

[0011] Step S5, calculating the synthetic slope of the train driving on the bridge at the time step according to the axle load of the locomotive wheelset and the axle load of the wagon wheelset, and the slope corresponding to the axle load of the wheelset at the wheelset position on the bridge at the time step;

[0012] Repeating steps S3 to S5 to obtain the dynamic synthetic slope of the train driving on the bridge within the time course, and taking the maximum value of the synthetic slope as the maximum slope within the time course of the train driving on the bridge.

[0013] In an embodiment, the step S4, calculating the synthetic slope of the train driving on the bridge at the time step according to the axle load of the locomotive wheelset and the axle load of the wagon wheelset, and the slope corresponding to the axle load of the wheelset at the wheelset position on the bridge at the time step,

[0014] The calculation formula is: ;

[0015] Wherein, is the synthetic slope; is the axle load of the locomotive wheelset; is the axle load of the wagon wheelset; is the slope corresponding to the axle load of the wheelset at the wheelset position; is the total number of wheelsets of the train formation.

[0016] In an embodiment, the step S1, obtaining the total number of time steps of the train driving on the bridge and the wheelset position of the train at each time step, comprises:

[0017] Step S11, obtaining the train speed and the bridge length to obtain the total number of time steps of the train driving on the bridge;

[0018] Step S12, determining the train length and the total number of wheelsets according to the formation of the train to obtain the bridge position corresponding to each wheelset of the train at each time step as the wheelset position.

[0019] In an embodiment, the step S2 simulates the dynamic loading process of the train driving on the bridge based on the coupled dynamic analysis of the vehicle and the bridge to obtain the bridge longitudinal profile data at all time steps, comprising:

[0020] The step S21 establishes a finite element model of the bridge, and obtains a coordinate matrix of the bridge nodes and the time history position of the wheelset force at different time steps;

[0021] The step S22 determines the bridge element length coordinates corresponding to the time history position of the wheelset force from the coordinate matrix of the bridge nodes based on the time history position of the wheelset force at a single time step;

[0022] The step S23 sets an interpolation function to distribute the force acting on the bridge element length to the adjacent bridge nodes;

[0023] The step S24 stores the wheelset force corresponding to each of the bridge nodes at each time step;

[0024] The step S25 loads the wheelset force to the bridge nodes at the time position of the train in the finite element model of the bridge;

[0025] The steps S22 to S25 are repeated to simulate the wheelset force loading process of the train from driving on the bridge to driving off the bridge at all time steps, and the bridge longitudinal profile data at all time steps is obtained.

[0026] In an embodiment, the time history position of the wheelset force in the step S21 is determined by the wheelbase of the train, the distance between the bogies of the train and the marshalling.

[0027] In an embodiment, the step S3 fits the bridge profile function within the length range of the train driving on the bridge at a time step, comprising:

[0028] The step S31 determines the equivalent head position and the equivalent tail position according to the position of the wheelset of the train driving on the bridge at a time step;

[0029] The step S32 intercepts the bridge longitudinal profile data within the length range of the train driving on the bridge at the time step according to the equivalent head position and the equivalent tail position;

[0030] The step S34 performs curve fitting on the bridge longitudinal profile data to obtain the bridge profile function within the length range of the train driving on the bridge at the time step.

[0031] In an embodiment, the step S31 determines the equivalent head position and the equivalent tail position according to the position of the wheelset of the train driving on the bridge at a time step, comprising:

[0032] The positions of each wheel pair of the train at different time steps form a multi-dimensional matrix, and the last wheel pair coordinate of the train at different time steps is obtained.

[0033] The last wheel pair coordinate of the train at a certain time step is compared with the first beam end coordinate of the bridge.

[0034] If the last wheel pair coordinate of the train at a certain time step is less than the first beam end coordinate of the bridge, the first beam end coordinate of the bridge is taken as the equivalent tail position, and the first wheel pair coordinate of the train is taken as the equivalent head position.

[0035] If the last wheel pair coordinate of the train at a certain time step is not less than the first beam end coordinate of the bridge, the last wheel pair coordinate of the train is taken as the equivalent tail position, and the first wheel pair coordinate is taken as the equivalent head position.

[0036] In an embodiment, the step S3 of fitting the bridge alignment function within the train length range on the bridge at a certain time step further comprises: a step S33 of interpolating and encrypting the bridge alignment data.

[0037] In an embodiment, the step S33 of interpolating and encrypting the bridge alignment data comprises any one of a cubic spline interpolation method, a least square method, a Lagrange polynomial interpolation method, and a Hermite polynomial interpolation method.

[0038] In an embodiment, the step S4 of determining the slope corresponding to the axle load borne by the wheel pair at the wheel pair position on the bridge according to the wheel pair position of the train on the bridge at the time step and the bridge alignment function comprises:

[0039] A step S41 of performing a first derivative on the bridge alignment function to obtain a slope expression.

[0040] A step S42 of calculating the bridge alignment slope value corresponding to each wheel pair according to the wheel pair position of the train on the bridge at the time step and the slope expression, as the slope corresponding to the axle load borne by the wheel pair at the wheel pair position on the bridge.

[0041] The technical scheme provided by the embodiments of the present application has the following beneficial effects:

[0042] The application provides a calculation method of bridge longitudinal section synthetic gradient based on dynamic load effect, simulates the whole train running process through vehicle-bridge coupling dynamic time-history analysis, considers the dynamic influence of train load on bridge longitudinal section alignment when driving on the bridge, such as wheel-rail interaction, bridge vibration and other dynamic effects, and is more in line with actual working conditions than static load assumption. Secondly, processing is performed in time step and wheelset position dual dimensions, instantaneous train load distribution change can be captured, bridge longitudinal section alignment is tracked based on dynamic load effect, and gradient maximum value is more accurately calculated. Finally, the influence of axle load mass borne by different wheelsets of the train on the gradient is considered, train calculation mass and traction mass are shared to wheelsets of the locomotive and the freight car, average gradient of the train when passing through the bridge is calculated as the synthetic gradient through the conversion relationship between the axle load mass borne by the wheelset and the gradient, contribution weight of different axle loads to the synthetic gradient is reflected, and the calculation result is more in line with the actual stress state of the train and will not be conservative. BRIEF DESCRIPTION OF DRAWINGS

[0043] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiment description. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort.

[0044] Figure 1 It is a schematic diagram of train geometric configuration in an embodiment of the present application.

[0045] Figure 2 It is a schematic diagram of train loading in an embodiment of the present application. DETAILED DESCRIPTION

[0046] In order to make the personnel in the technical field better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described in the following with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without any creative effort are within the scope of protection of the present application.

[0047] The embodiment of the present application provides a calculation method of bridge longitudinal section synthetic gradient based on dynamic load effect, which can solve the technical problems of too conservative calculation result, large gradient limit value and low precision in the related art when the locomotive algorithm calculates the gradient.

[0048] The embodiment provides a calculation method of bridge longitudinal section synthetic gradient based on dynamic load effect, which includes the following steps:

[0049] Step S1, obtaining the total time step of the train passing the bridge and the wheel pair position of the train at each time step;

[0050] Step S2, simulating the dynamic loading process of the train driving on the bridge based on the vehicle-bridge coupling dynamic time history analysis to obtain the longitudinal profile linear data of the bridge at all time steps;

[0051] Step S3, fitting the bridge linear function within the train length range on the bridge at a certain time step;

[0052] Step S4, determining the slope corresponding to the axle load mass borne by the wheel pair at the wheel pair position on the bridge according to the wheel pair position of the train on the bridge at the time step and the bridge linear function;

[0053] Step S5, calculating the synthetic slope of the train passing the bridge at the time step according to the axle load mass borne by the locomotive wheel pair and the axle load mass borne by the wagon wheel pair, the slope corresponding to the axle load mass borne by the wheel pair at the wheel pair position on the bridge at the time step;

[0054] Repeating steps S3 to S5 to obtain the dynamic synthetic slope in the train passing the bridge time history, and taking the maximum value of the synthetic slope as the maximum slope in the train passing the bridge time history.

[0055] The embodiment provides a calculation method of the synthetic slope of the bridge longitudinal profile based on dynamic load action, simulates the whole train driving process through vehicle-bridge coupling dynamic time history analysis, considers the dynamic influence of the train load on the bridge longitudinal profile on the bridge, such as wheel-rail interaction, bridge vibration and other dynamic effects, and is more in line with the actual working condition than the static load assumption. Secondly, the processing is performed in the time step and the wheel pair position dimensions, the instantaneous train load distribution change can be captured, the bridge longitudinal profile is tracked based on the dynamic load action, and the maximum slope is more accurately calculated; finally, the influence of the axle load mass borne by different wheel pairs of the train on the slope is considered, the train calculation mass and the traction mass are shared to the wheel pairs of the locomotive and the wagon, the average slope of the train passing the bridge is calculated as the synthetic slope through the conversion relationship between the axle load mass borne by the wheel pair and the slope, the contribution weight of different axle loads to the synthetic slope is embodied, and the calculation result is more in line with the actual stress state of the train and is not conservative.

[0056] The following will be described in detail.

[0057] As shown in Figure 1 and Figure 2 , wherein, Figure 1 is a schematic diagram of the train geometric structure in the embodiment of the application. Figure 2 is a schematic diagram of the train loading in the embodiment of the application.

[0058] Figure 1 , wherein, m cThe train body mass; m b The train bogie mass; m t The wheelset mass; the axle load is the weight of the train acting on the rail through each wheelset, so the wheelset bears the axle load mass ( m c +2* m b +4* m t ) / 4; l 1 and l 2 are the distances of the primary suspension and the secondary suspension, used to determine the coordinates of the wheelset in the time step; the primary suspension, also known as the main suspension, is arranged between the locomotive bogie frame and the axle box, and mainly plays the role of transmitting the force between the axle box and the wheelset and positioning. The secondary suspension, also known as the secondary suspension, is arranged between the vehicle body frame and the bogie frame, and mainly plays the role of connecting the suspension between the frame and the vehicle body, and has a certain limiting effect on the lateral rotation of the vehicle body. Figure 2 In the above-mentioned embodiment, taking a long and heavy load train with 1 locomotive and 38 freight cars as an example, the train is loaded on the bridge and travels at a constant speed, the wheelset positions are indicated by arrows, and the axle loads are indicated by numbers. Due to the action of the heavy load train, the longitudinal profile of the bridge will produce a large slope. The train advances at different times to change the longitudinal profile of the bridge, and the slope also changes over time.

[0059] In an embodiment, the step S1 of obtaining the total time step number of the train passing through the bridge and the wheelset position of the train in each time step comprises:

[0060] The step S11 of obtaining the train speed and the bridge length to obtain the total time step number of the train passing through the bridge.

[0061] The step S12 of determining the train length and the total number of wheelsets according to the marshalling of the train to obtain the bridge position corresponding to each wheelset of the train in each time step as the wheelset position.

[0062] Specifically, the train length and the total number of wheelsets of the train can be determined through the marshalling of the train, and the bridge position corresponding to each wheelset of the train in each time step can be calculated according to the geometric structure of the train as the wheelset position, which can also be used as the wheelset coordinates; the wheelset position can be in the form of a matrix.

[0063] Through the above-mentioned scheme, the wheelset position of the train in each time step is determined, which serves as the basis for subsequent segmented fitting of the bridge profile function to obtain the slope corresponding to each wheelset position.

[0064] The vehicle-bridge coupled dynamic time-history analysis is a numerical simulation method for studying the interaction between train and bridge structure under dynamic load. The vehicle-bridge coupling refers to regarding the train and the bridge as a whole system, considering the dynamic interaction between the two (such as wheel-rail contact force, vibration transmission, etc.), and loading the train axle load at different bridge nodes at different time steps. The time-history analysis refers to calculating the response (displacement, velocity, acceleration, internal force, etc.) of the system in the time history through the step-by-step integration method. The wheel pair force is the dynamic contact force between the vehicle wheel pair and the bridge track, including vertical force, lateral force and longitudinal force (such as braking / traction force). The time-history position includes spatial position and time position, the spatial position is the coordinate of the wheel pair on the bridge (such as the longitudinal distance from the end point of the bridge), and the time position is the value of the force-time history of the wheel pair at the simulation time. That is, the time-history position of the wheel pair refers to the spatial position of the train wheel (such as the train wheel) at the simulation time and the corresponding contact force state.

[0065] In an embodiment, step S2 simulates the dynamic loading process of the train running on the bridge based on the vehicle-bridge coupled dynamic time-history analysis to obtain the bridge longitudinal section alignment data at all time steps, including:

[0066] Step S21 establishes a bridge finite element model, obtains the coordinate matrix of the bridge nodes, and the time-history position of each wheel pair force at different time steps;

[0067] Step S22 determines the bridge element length coordinates corresponding to the time-history position of each wheel pair force from the coordinate matrix of the bridge nodes based on the time-history position of each wheel pair force at a single time step;

[0068] Step S23 sets an interpolation function to distribute the force acting on the bridge element length to the adjacent bridge nodes;

[0069] Step S24 stores the wheel pair force corresponding to each bridge node at each time step;

[0070] Step S25 loads the wheel pair force on the bridge nodes at the time position of the train in the bridge finite element model;

[0071] Repeat steps S22 to S25 to simulate the wheel pair force loading process of the train from the bridge to the bridge at all time steps, and obtain the bridge longitudinal section alignment data at all time steps.

[0072] By the above scheme, the dynamic loading process of the vehicle on the bridge is simulated, and the full-time transient response analysis is performed. Specifically, the dynamic distributed train load is accurately matched to the bridge element length coordinate by time step discretization and wheelset position mapping, avoiding local stress distortion; the interpolation function is used to distribute the wheelset force to the adjacent nodes, which conforms to the principles of finite element mechanics, and ensures the continuity and balance of load transfer; the wheelset force corresponding to each bridge node at each time step is stored, which can trace back the load distribution state at any time, and provides complete input for dynamic response analysis.

[0073] In an embodiment, in step S21, the time history position of each wheelset force is determined by the train wheelbase, the train bogie distance and the marshalling.

[0074] In an embodiment, step S3, fitting the bridge alignment function within the train length range on the bridge at a certain time step includes:

[0075] Step S31, determining the equivalent head position and the equivalent tail position according to the position of the train wheelset on the bridge at a certain time step.

[0076] According to the position of different wheelsets at a certain time step, the train length on the bridge is determined, and the wheelset on the bridge indicates that the part of the train body is also on the bridge. Specifically, it includes:

[0077] Step S311, the position of each wheelset on the bridge at different time steps forms a multi-dimensional matrix, and the coordinates of the last wheelset of the train at different time steps are obtained;

[0078] Step S312, comparing the coordinates of the last wheelset of the train at a certain time step with the coordinates of the first beam end of the bridge;

[0079] Step S313, if the coordinates of the last wheelset of the train at a certain time step are less than the coordinates of the first beam end of the bridge, then the coordinates of the first beam end of the bridge are taken as the equivalent tail position, and the coordinates of the first wheelset of the train are taken as the equivalent head position;

[0080] Step S314, if the coordinates of the last wheelset of the train at a certain time step are not less than the coordinates of the first beam end of the bridge, then the coordinates of the last wheelset of the train are taken as the equivalent tail position, and the coordinates of the first wheelset are taken as the equivalent head position.

[0081] Step S32, according to the equivalent head position and the tail position, the bridge longitudinal section alignment data within the train length range on the bridge at the time step is intercepted.

[0082] Step S34, curve fitting is performed on the bridge longitudinal section alignment data to obtain the bridge alignment function within the train length range on the bridge at the time step.

[0083] Since the bridge alignment varies within the train's range at different time steps, the above scheme allows for piecewise fitting of the bridge alignment function within the train's length range at a given time step, which is closer to the actual situation and ensures the smoothness and stability of the alignment.

[0084] In one embodiment, step S3, fitting the bridge alignment function within the train length range at a certain time step, further includes step S33, performing interpolation and encryption processing on the bridge longitudinal profile alignment data.

[0085] The above scheme can improve the integrity and continuity of data by supplementing the values ​​between known bridge data points, thereby making the data denser, the line smoother, and the trend more obvious.

[0086] In one embodiment, step S33, interpolating and encrypting the longitudinal profile data of the bridge, includes any one of cubic spline interpolation, least squares interpolation, Lagrange polynomial interpolation, and Hermite polynomial interpolation.

[0087] Specifically, a further optimization method is used to densify the data points on the longitudinal profile of the bridge using cubic spline interpolation. The interpolation curve generated by cubic spline interpolation gradually approximates the actual curve as the interval between interpolation points decreases. In addition, this interpolation curve has the characteristics of good shape preservation and smoothness.

[0088] In one embodiment, step S34, when performing curve fitting on the longitudinal profile data of the bridge, uses dynamic fitting.

[0089] In one embodiment, dynamic fitting includes:

[0090] The objective function to be fitted is n Polynomial of degree;

[0091] The optimal polynomial degree is evaluated based on the longitudinal profile data of the bridge, and then a fit is performed.

[0092] Specifically, the objective function for fitting the bridge alignment is generally as follows: n Polynomials of degree: If the order of the objective function is... n Setting the order too low may lead to underfitting, meaning the fitted function will fail to capture the complexity and characteristics of the bridge's alignment. This manifests as the fitted curve not accurately tracking the trend of the data points, resulting in a larger prediction error. If the order of the objective function is too low... n Setting the value too high may lead to overfitting.

[0093] The above scheme evaluates the optimal polynomial degree based on the longitudinal profile data of the bridge and performs dynamic fitting to obtain a suitable order of the objective function.

[0094] In an embodiment, step S4, the gradient corresponding to the axle load borne by the wheelset at the wheelset position on the bridge is determined according to the wheelset position of the train on the bridge at the time step and the bridge alignment function.

[0095] Step S41, the bridge alignment function is differentiated once to obtain a slope expression.

[0096] Step S42, the bridge alignment slope value corresponding to each wheelset is calculated according to the wheelset position of the train on the bridge at the time step and the slope expression, as the gradient corresponding to the axle load borne by the wheelset at the wheelset position on the bridge.

[0097] In an embodiment, step S5, the composite gradient of the train when passing through the bridge at the time step is calculated according to the axle load borne by the locomotive wheelset and the axle load borne by the freight car wheelset, the gradient corresponding to the axle load borne by the wheelset at the wheelset position on the bridge at the time step,

[0098] The calculation formula is: ;

[0099] Wherein, is the composite gradient; is the axle load borne by the locomotive wheelset; is the axle load borne by the freight car wheelset; is the gradient corresponding to the axle load borne by the wheelset at the wheelset position; is the total number of wheelsets in the train formation.

[0100] In the related art, the locomotive algorithm is used to calculate the gradient, and the specific content is: according to TB 10098-2017 “Railway Line Design Specification”, the maximum gradient of the single locomotive traction heavy-haul train on the railway line is the gradient of the single locomotive traction heavy-haul train running at the locomotive calculation speed on the continuous uphill, and the calculation formula is:

[0101] ;

[0102] In the formula, is the locomotive calculation mass; is the design proposed traction mass standard; is the locomotive traction coefficient, which is 0.9; is the maximum traction mass of the train; , is the unit basic resistance of the locomotive and the freight car; this formula is suitable for the relationship obtained by the single locomotive traction heavy-haul train on the continuous uphill.

[0103] The application finds that the gradient is a dimensionless constant of the train traction mass, that is, the gradient value is obtained by conversion between the train wheel pair masses. Therefore, considering the influence of the axle load mass borne by different wheel pairs of the train on the gradient, the train calculation mass and the traction mass are shared to the wheel pairs of the locomotive and the freight car, the average gradient of the train passing through the bridge is calculated through the axle load mass borne by the wheel pairs, as the synthetic gradient, the calculation result further conforms to the actual situation, is not conservative, and the precision is also correspondingly improved.

[0104] Through the above scheme, after the synthetic gradient at a certain time step is obtained from the perspective of the whole vehicle marshalling, the dynamic synthetic gradient of the train passing through the bridge time history is obtained through repeated steps S3-S5 according to different cycles of train advancing position.

[0105] A specific embodiment is provided below for illustration.

[0106] Taking a large-span bridge scheme as an engineering background, the embodiment provides a calculation method of the bridge longitudinal section synthetic gradient based on dynamic load action, which comprises the following steps:

[0107] Step S1, obtaining the total time step number of the train passing through the bridge and the wheel pair position of the train at each time step.

[0108] Specifically, the bridge length is 1280 meters, a long and heavy load train is composed of 1 locomotive and 38 freight cars, the axle load of the locomotive is 23t, and the axle load of the freight car is 22.625t. The train advancing speed is set to 120km / h, and each time interval is 0.02s, so the train advancing distance at each time step is 0.667 meters. From the first wheel pair of the locomotive on the bridge to the last wheel pair of the freight car off the bridge, the total train mileage is 1784.27 meters, and the total time step number is about 2677 steps. According to the geometric structure of the train, the number of wheel pairs is 156.

[0109] Step S2, simulating the dynamic loading process of the train driving on the bridge based on the vehicle-bridge coupled dynamic time history analysis to obtain the bridge longitudinal section alignment data at all time steps.

[0110] Specifically, a bridge finite element model is established, and there are 297 track nodes of the main beam. The dynamic loading process of the train driving on the bridge is simulated based on the vehicle-bridge coupled dynamic time history analysis, the total train time step is 2677 steps, that is, there are 2677 time history positions of the wheel pair force, and a total of 2677 bridge longitudinal section alignment data are obtained.

[0111] Step S3, fitting the bridge alignment function in the train length range on the bridge at a certain time step.

[0112] Specifically, the positions of the 156 wheelsets at each time step are recorded as xx, with a dimension of 2677x156. According to the positions of the train wheelsets on the bridge at a certain time step, the equivalent train head position and the equivalent train tail position are determined, the bridge longitudinal profile data within the train length range L_nihe of the train on the bridge at the time step is intercepted, and the intercepted bridge longitudinal profile data is interpolated and encrypted by a cubic spline interpolation method. The bridge profile function within the train length range on the bridge at the time step is dynamically fitted.

[0113] Step S4, determining the gradient corresponding to the axle load borne by the wheelset at the wheelset position on the bridge according to the wheelset position on the bridge and the bridge profile function at the time step.

[0114] Specifically, the bridge profile function is derived once, and the slope expression is obtained; the wheelset position (i.e. the wheelset coordinates) of the train on the bridge at the time step is substituted into the slope expression to calculate the bridge profile slope value corresponding to each wheelset, as the gradient corresponding to the axle load borne by the wheelset at the wheelset position on the bridge.

[0115] Step S5, calculating the synthetic gradient of the train when passing through the bridge at the time step according to the axle load borne by the locomotive wheelset and the axle load borne by the freight car wheelset, and the gradient corresponding to the axle load borne by the wheelset at the wheelset position on the bridge at the time step.

[0116] The calculation formula is: .

[0117] Steps S3 to S5 are repeated to obtain the dynamic synthetic gradient of the train within the train passing time range, and the maximum value of the synthetic gradient is taken as the maximum gradient within the train passing time range (i.e. within the time range from the start of the train passing through the bridge to the end of the train passing through the bridge). The maximum value is compared with the specification limit value. Compared with the locomotive algorithm result in the related art, the calculation result provided by the present application is smaller and closer to the actual situation, and also meets the specification requirements.

[0118] It should be noted that the above-mentioned sequence numbers of the embodiments of the present application are only for description, and do not represent the advantages and disadvantages of the embodiments. The terms "include" and "have" in the specification and claims of the present application and in the above-mentioned drawings are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device including a series of steps or units is not limited to the listed steps or units, but can optionally include steps or units not listed, or can optionally include other steps or units inherent to the process, method, product or device. The terms "first", "second" and "third" and the like descriptions are used to distinguish different objects, and do not represent the order or limit the types of "first", "second" and "third".

[0119] In the description of the embodiments of the present application, "exemplary", "for example", "e.g." or "for instance" are used on the basis that a person of ordinary skill in the art will be able to draw more general principles from the embodiments disclosed herein, and not to imply or restrict the disclosure to a specific embodiment or implementation. Any embodiment or design scheme described as "exemplary", "for example", or "for instance" in the embodiments of the present application should not be interpreted as being more preferred or advantageous than other embodiments or design schemes. Rather, the use of "exemplary", "for example", or "for instance" is intended to present relevant concepts in a concrete manner.

[0120] In the description of the embodiments of the present application, unless otherwise specified, " / " means or, for example, A / B can mean A or B; "and / or" in the text only describes the relationship of the associated objects, which means that there can be three relationships, for example, A and / or B, which can represent the three cases of A alone, A and B together, and B alone. In addition, in the description of the embodiments of the present application, "multiple" means two or more than two.

[0121] In some of the processes described in the embodiments of the present application, a plurality of operations or steps are included in a specific order, but it should be understood that these operations or steps can be executed or in parallel without the order in which they appear in the embodiments of the present application, and the serial number of the operation is only used to distinguish different operations, and the serial number itself does not represent any execution order. In addition, these processes can include more or fewer operations, and these operations or steps can be executed in sequence or in parallel, and these operations or steps can be combined.

[0122] The above is only the preferred embodiment of the present application, and does not limit the patent scope of the present application, and any equivalent structure or equivalent process transformation using the content of the specification and drawings of the present application, or directly or indirectly applied to other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A method for calculating the resultant slope of the longitudinal section of a bridge based on the dynamic load action, characterized in that, It comprises the following steps: Step S1, obtaining the total time step number of the train crossing the bridge and the wheelset position of the train at each time step; Step S2, simulating the dynamic loading process of the train driving on the bridge based on the vehicle-bridge coupling dynamic time history analysis to obtain the bridge longitudinal profile linear data at all time steps; Step S3, fitting the bridge linear function within the train length range on the bridge at a certain time step; Step S4, determining the slope corresponding to the axle load mass borne by the wheelset at the wheelset position on the bridge according to the wheelset position of the train on the bridge at the time step and the bridge linear function; Step S5, calculating the synthetic slope of the train crossing the bridge at the time step according to the axle load mass borne by the locomotive wheelset and the axle load mass borne by the car wheelset, the slope corresponding to the axle load mass borne by the wheelset at the wheelset position on the bridge at the time step; Repeating steps S3 to S5 to obtain the dynamic synthetic slope of the train crossing the bridge within the time history to take the maximum synthetic slope as the maximum slope within the train crossing the bridge time history; In the step S2, the bridge longitudinal profile linear data at all time steps is obtained by simulating the dynamic loading process of the train driving on the bridge based on the vehicle-bridge coupling dynamic time history analysis, which comprises: Step S21, establishing a bridge finite element model to obtain the coordinate matrix of the bridge nodes and the time history position of each wheelset force at different time steps; Step S22, determining the bridge element length coordinates corresponding to the time history position of each wheelset force from the coordinate matrix of the bridge nodes based on the time history position of each wheelset force at a single time step; Step S23, setting an interpolation function to distribute the force acting on the bridge element length to the adjacent bridge nodes; Step S24, storing the wheelset force corresponding to each bridge node at each time step; Step S25, loading the wheelset force at the time position of the train on the bridge node in the bridge finite element model; Repeating steps S22 to S25 to simulate the wheelset force loading process of the train from the bridge to the bridge at all time steps to obtain the bridge longitudinal profile linear data at all time steps.

2. The method of claim 1, wherein the dynamic load-based calculation of the synthetic grade of the bridge longitudinal profile is based on the following equation: ###0001### where: L = length of the bridge; and P = dynamic load. In the step S4, the synthetic slope of the train crossing the bridge at the time step is calculated according to the axle load mass borne by the locomotive wheelset and the axle load mass borne by the car wheelset, and the slope corresponding to the axle load mass borne by the wheelset at the wheelset position on the bridge at the time step, which comprises: The calculation formula is: ; wherein, is the synthetic grade; is the axle load mass borne by the locomotive wheelset; is the axle load mass borne by the wagon wheelset; is the grade corresponding to the axle load borne by the wheelset at the wheelset position; is the total number of wheelsets of the train consist.

3. The method of claim 1, wherein the dynamic load-based calculation of the synthetic grade of the bridge longitudinal profile is based on a dynamic load effect of the bridge. The step S1, obtaining the total time step number of the train crossing the bridge and the wheelset position of the train at each time step, comprises: Step S11, obtaining the train speed and bridge length to obtain the total time step number of the train crossing the bridge; Step S12, determining the train length and total wheelset number according to the train marshalling to obtain the bridge position corresponding to each wheelset of the train at each time step as the wheelset position.

4. The method of claim 1, wherein the dynamic load-based calculation of the synthetic grade of the bridge longitudinal profile is based on a dynamic load effect. In step S21, the time history position of each wheelset force is determined by the train wheelbase, the train bogie distance and the marshalling.

5. The method of claim 1, wherein the dynamic load-based calculation of the synthetic grade of the bridge longitudinal profile is characterized by, The step S3, fitting the bridge linear function within the train length range on the bridge at a certain time step, comprises: Step S31, determining the equivalent head position and the equivalent tail position according to the position of the train wheelset on the bridge at a certain time step; Step S32, intercepting the bridge longitudinal profile data within the train length range on the bridge at the time step according to the equivalent head position and the equivalent tail position; Step S34, curve fitting the bridge longitudinal profile data to obtain the bridge profile function within the train length range on the bridge at the time step.

6. The method for calculating the synthetic grade of the longitudinal profile of a bridge based on dynamic load action according to claim 5, characterized in that, The step S31 of determining the equivalent head position and the equivalent tail position according to the position of the train wheelset on the bridge at a time step comprises: forming a multi-dimensional matrix of the position of each wheelset on the bridge at different time steps to obtain the coordinates of the last wheelset of the train at different time steps; comparing the coordinates of the last wheelset of the train at a time step with the coordinates of the first beam end of the bridge; if the coordinates of the last wheelset of the train at a time step are less than the coordinates of the first beam end of the bridge, taking the coordinates of the first beam end of the bridge as the equivalent tail position and the coordinates of the first wheelset of the train as the equivalent head position; if the coordinates of the last wheelset of the train at a time step are not less than the coordinates of the first beam end of the bridge, taking the coordinates of the last wheelset of the train as the equivalent tail position and the coordinates of the first wheelset as the equivalent head position.

7. The method of claim 5, wherein the dynamic load-based calculation of the synthetic grade of the bridge longitudinal profile is based on the following equation: ###0001### where: G = the synthetic grade of the bridge longitudinal profile; L = the length of the bridge; and P = the dynamic load. The step S3 of fitting the bridge profile function within the train length range on the bridge at a time step further comprises: step S33, interpolating and encrypting the bridge longitudinal profile data.

8. The method for calculating the synthetic grade of the longitudinal profile of a bridge based on dynamic load action according to claim 7, characterized in that, The step S33 of interpolating and encrypting the bridge longitudinal profile data comprises any one of cubic spline interpolation method, least square method, Lagrange polynomial interpolation method and Hermite polynomial interpolation method.

9. The method of claim 1, wherein the dynamic load-based calculation of the synthetic grade of the bridge longitudinal profile is based on a dynamic load effect. The step S4 of determining the slope corresponding to the axle load of the wheelset on the bridge at the position of the wheelset on the bridge at the time step according to the position of the wheelset on the bridge and the bridge profile function comprises: Step S41, taking the derivative of the bridge profile function to obtain a slope expression; Step S42, calculating the bridge profile slope value corresponding to each wheelset according to the position of the wheelset on the bridge at the time step and the slope expression, as the slope corresponding to the axle load of the wheelset on the bridge at the position of the wheelset on the bridge.

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