Longitudinal force and longitudinal displacement analysis method for long and large ramp seamless track under train braking

Abstract

The invention discloses a method for analyzing longitudinal force and longitudinal displacement of a long and large ramp continuously welded track under train braking, which comprises the following steps of: establishing an analysis / finite element model of the long and large ramp ballast track continuously welded track, taking initial ballast bed longitudinal resistance as an input parameter, and calculating to obtain initial distribution of longitudinal force and longitudinal displacement of a continuously welded track steel rail; meanwhile, the maximum value of longitudinal displacement of the continuously welded rail is obtained; and establishing a discrete element model of the long and large ramp ballast track seamless track, taking the maximum value of the initial distribution of the longitudinal displacement of the seamless track steel rail as an input condition, carrying out cyclic loading of the long and large ramp ballast track under the loading condition through a longitudinal displacement-longitudinal resistance dual-control method, extracting the longitudinal resistance of a track bed under the non-loading condition, and calculating the maximum value of the longitudinal displacement of the long and large ramp ballast track. And importing the data into the established analysis / finite element model to obtain updated distribution of longitudinal force and longitudinal displacement of the continuously welded rail. According to the method, the evolution characteristics of the longitudinal resistance of the long and large ramp ballast track seamless track ballast bed can be reasonably reflected.

Description

Technical Field

[0001] The present invention belongs to the technical field of railway engineering and rail transportation, and particularly relates to a method for analyzing the longitudinal force and longitudinal displacement of a seamless track on a long slope under train braking. Background Art

[0002] Due to factors such as geographical conditions and capital investment, railway lines often face the problem of long and steep slopes during construction. Compared to flat slopes, on long and steep slopes, when a train brakes, the CWR rails are subjected to the combined effects of the train's braking force and the slope component of the train's weight. This causes the CWR rails to creep to varying degrees along the longitudinal direction of the line. This can cause changes in the locked rail temperature during long-term operation, hindering the long-term maintenance of the CWR track's geometric state parameters and driving stability. For CWR lines with ballasted tracks on long and steep slopes, the longitudinal resistance of the trackbed is the key parameter that determines the distribution of the longitudinal force and longitudinal displacement of the CWR rails under train braking. Currently, the change in the longitudinal resistance of the trackbed is mainly characterized by a bilinear model with fixed values. In reality, under repeated braking of a train, the loose ballast particles in the ballasted trackbed are constantly squeezed and displaced, and the longitudinal restraint they provide to the sleepers is also constantly changing. However, research on the impact of repeated braking on the trackbed's longitudinal resistance is currently insufficient.

[0003] Therefore, for ballasted seamless tracks on long and steep slopes, it is urgent to propose a method that can reasonably reflect the evolution characteristics of the longitudinal resistance of the roadbed under repeated braking of trains, and then realize the updated calculation of the longitudinal force and longitudinal displacement distribution of the rails on ballasted seamless tracks on long and steep slopes under repeated braking of trains, so as to provide theoretical support for the maintenance and repair of ballasted seamless tracks on long and steep slopes. Summary of the Invention

[0004] In view of this, the present invention provides a method for analyzing the longitudinal force and longitudinal displacement of a seamless track on a long and steep slope under train braking. Aiming at the distribution characteristics of the longitudinal force and longitudinal displacement of the seamless track rails on a ballasted track on a long and steep slope under repeated braking of a train, a method combining analytical method / finite element method and discrete element method is used to analyze the evolution characteristics of the longitudinal resistance of the roadbed on a ballasted track on a long and steep slope under repeated braking of a train, obtain an updated value of the longitudinal resistance of the roadbed, and then calculate the updated distribution of the longitudinal force and longitudinal displacement of the seamless track rails, which is helpful to provide theoretical support for the maintenance and repair of the seamless track on a ballasted track on a long and steep slope.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] In a first aspect, the present invention provides a method for analyzing the longitudinal force and longitudinal displacement of a seamless track on a long slope under train braking, the method mainly comprising the following steps:

[0007] Step 1: Obtain the longitudinal resistance curve of the roadbed of the long and steep ballasted track seamless line;

[0008] Step 2: Build an analytical / finite element model of the CWR ballasted track on a long slope based on the analytical / finite element method. Input the longitudinal resistance curve of the roadbed obtained in step 1, calculate the longitudinal force and longitudinal displacement distribution of the CWR rail under train braking, and record the maximum longitudinal displacement of the CWR rail.

[0009] Step 3: Based on the discrete element method, a discrete element model of the long slope ballasted track seamless line is established. Combined with the longitudinal resistance curve of the roadbed in step 1, the parameter calibration and verification of the discrete element model are carried out.

[0010] Step 4: Based on the discrete element model of the long and steep slope ballasted track seamless track established in Step 3, calculations are carried out. The maximum displacement of the seamless track rail calculated in Step 2 is used as the loading control value, and the longitudinal resistance of the sleeper is used as the unloading control value. Cyclic loading of the long and steep slope ballasted track under loaded conditions is carried out using the longitudinal displacement-longitudinal resistance dual control method.

[0011] Step 5: Obtain the longitudinal resistance curve of the roadbed under no-load conditions after a certain number of cyclic loading cycles. Use this curve as the input parameter for the analytical / finite element model of the CWR ballasted track on long and steep slopes in Step 2. Calculate the updated distribution of the longitudinal force and longitudinal displacement of the CWR rail.

[0012] Furthermore, in step 1, when obtaining the longitudinal resistance curve of the roadbed, considering that the longitudinal displacement of the seamless line rail is small under single braking, the linear variation coefficient of the longitudinal resistance of the roadbed when the longitudinal displacement of the sleeper does not exceed 2 mm under vehicle load and no-load conditions is used.

[0013] Furthermore, in step 2, the longitudinal force and longitudinal displacement distribution of the seamless line rail under the braking action of the train are calculated, and the calculation formulas are:

[0014]

[0015] Where P(x) represents the longitudinal force, u(x) represents the longitudinal displacement, μ is the wheel-rail adhesion coefficient, α is the line slope value, Q i is the vertical force between the wheel and rail at the i-th wheel, x i is the position coordinate of the i-th wheel; k is the coefficient of variation of the longitudinal resistance of the roadbed, E is the elastic modulus of the rail, F is the cross-sectional area of ​​the rail, and N is the number of wheels.

[0016] Furthermore, in step 3, when establishing a discrete element model of a long and steep ballasted track seamless line based on the discrete element method, irregular particle units are used for the ballast, and a block splicing method is used to achieve rapid balancing of the discrete element model.

[0017] Furthermore, in step 4, the established discrete element model of the long and steep ballasted track seamless line is used to carry out longitudinal cyclic loading analysis under loaded conditions. Within a bogie load range, the sleeper's contribution to the wheel load under a single wheel load is analyzed using a Gaussian function fitting, and the fitting equation for the sharing ratio is:

[0018]

[0019] Where p is the sharing ratio, d is the distance between the sleeper and the wheel load;

[0020] For the case where one bogie corresponds to two wheel loads, the load sharing at different sleepers is the superposition of the two wheel loads.

[0021] In a second aspect, an embodiment of the present invention further provides an electronic device comprising a processor and a memory, wherein the memory stores machine executable instructions that can be executed by the processor, and the processor executes the machine executable instructions to implement the above-mentioned method for analyzing the longitudinal force and longitudinal displacement of a seamless line on a long slope under train braking.

[0022] As can be seen from the above technical solutions, the present invention discloses a method for analyzing the longitudinal force and longitudinal displacement of a seamless track on a long and steep slope under train braking, which has at least the following beneficial effects compared to the prior art:

[0023] The present invention adopts analytical method / finite element method to establish analytical / finite element model of seamless track of ballasted track on long and steep slope, takes the obtained initial longitudinal resistance of the roadbed as input parameter, calculates the initial distribution of longitudinal force and longitudinal displacement of seamless track rail, and obtains the maximum value of longitudinal displacement of seamless track rail at the same time; establishes discrete element model of seamless track of ballasted track on long and steep slope based on discrete element method, takes the maximum value of initial distribution of longitudinal displacement of seamless track rail as input condition, carries out cyclic loading of ballasted track on long and steep slope under loaded condition through longitudinal displacement-longitudinal resistance dual control method; after completing a certain number of cyclic loading times, extracts longitudinal resistance of seamless track roadbed of ballasted track on long and steep slope under no-load condition, imports it into the established analytical / finite element model of seamless track of ballasted track on long and steep slope, and obtains updated distribution of longitudinal force and longitudinal displacement of seamless track rail. The method proposed in the present invention can reasonably reflect the evolution characteristics of the longitudinal resistance of the roadbed of the ballasted track seamless line on a long and steep slope under the repeated braking of the train, facilitate the updating of the longitudinal resistance of the roadbed, and then calculate the updated distribution of the longitudinal force and longitudinal displacement of the rails of the ballasted track seamless line on a long and steep slope, providing a new idea and theoretical basis for studying the longitudinal force and displacement distribution of the ballasted track seamless line on a long and steep slope under repeated braking.

[0024] Other features and advantages of the present invention will be described in the following description, and in part will become apparent from the description, or will be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures particularly pointed out in the written description and the accompanying drawings.

[0025] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, a brief introduction will be given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0027] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0028] Figure 1 A flow chart of a method for analyzing the longitudinal force and longitudinal displacement of a seamless track on a long slope under train braking is provided in an embodiment of the present invention.

[0029] Figure 2 Schematic diagram of the initial distribution of rail longitudinal force and longitudinal displacement provided by an embodiment of the present invention.

[0030] Figure 3 Schematic diagram of the discrete element model of a long-slope ballasted track seamless line provided in an embodiment of the present invention.

[0031] Figure 4 A schematic diagram of load sharing provided by an embodiment of the present invention.

[0032] Figure 5 Schematic diagram of updated distribution of rail longitudinal force and longitudinal displacement provided by an embodiment of the present invention.

[0033] Figure 6 A schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0035] In describing the present invention, it should be noted that some processes described in this specification and accompanying drawings include multiple operations that appear in a specific order. However, it should be understood that these operations may be performed in a different order than the order in which they appear, or may be performed in parallel. Furthermore, the use of various sequence numbers is for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0036] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0037] See also Figure 1 As shown, an embodiment of the present invention provides a method for analyzing the longitudinal force and longitudinal displacement of a seamless track on a long slope under train braking, which specifically includes the following steps:

[0038] (1) Obtain the longitudinal resistance variation curve of the ballast track seamless track on long and steep slopes through on-site measurement or technical data;

[0039] (2) Based on the analytical method / finite element method, a CWR model of the ballasted track on a long and steep slope (analytical / finite element model) is established. The longitudinal resistance curve of the roadbed obtained in (1) is input to calculate the longitudinal force and longitudinal displacement distribution of the CWR rail under the action of train braking, and the maximum longitudinal displacement of the CWR rail is recorded.

[0040] (3) Based on the discrete element method, a seamless track model of long and steep ballasted track (discrete element model) is established, and the parameter calibration and verification of the discrete element model are carried out in combination with the longitudinal resistance curve of the trackbed in (1);

[0041] (4) Based on the discrete element model of the long slope ballasted track seamless line established in (3), the calculation is carried out, the maximum displacement value of the seamless line rail calculated in (2) is used as the loading control value, and the longitudinal resistance value of the sleeper is used as the unloading control value. The cyclic loading of the long slope ballasted track under loaded conditions is carried out by the longitudinal displacement-longitudinal resistance dual control method;

[0042] (5) Obtain the longitudinal resistance curve of the roadbed under no-load conditions after a certain number of loading times, which is used as the input parameter of the analytical / finite element model in (2) to calculate the updated distribution of the longitudinal force and longitudinal displacement of the seamless line rail.

[0043] The present invention adopts the analytical method / finite element method to establish a seamless track model of a ballasted track on a long and steep slope, takes the obtained initial longitudinal resistance of the roadbed as an input parameter, calculates the initial distribution of the longitudinal force and longitudinal displacement of the seamless track rail, and simultaneously obtains the maximum value of the longitudinal displacement of the seamless track rail; based on the discrete element method, a discrete element model of a seamless track of a ballasted track on a long and steep slope is established, takes the maximum value of the initial distribution of the longitudinal displacement of the seamless track rail as an input condition, and carries out cyclic loading of the ballasted track on a long and steep slope under loaded conditions through the method of longitudinal displacement-longitudinal resistance dual control; after completing a certain number of cyclic loading times, the longitudinal resistance of the seamless track roadbed of the ballasted track on a long and steep slope under no-load conditions is extracted, and is imported into the established analytical / finite element model of the seamless track of the ballasted track on a long and steep slope to obtain the updated distribution of the longitudinal force and longitudinal displacement of the seamless track rail.

[0044] The method proposed in the present invention can reasonably reflect the evolution characteristics of the longitudinal resistance of the roadbed of a ballasted track seamless line on a long and steep slope under repeated braking of a train, realize the update of the longitudinal resistance of the roadbed, and then calculate the updated distribution of the longitudinal force and longitudinal displacement of the rails of the ballasted track seamless line on a long and steep slope, providing a new idea for studying the longitudinal force and displacement distribution of the ballasted track seamless line on a long and steep slope under repeated braking.

[0045] The analysis method proposed in the present invention is further introduced in detail below through an example of the analysis method of the longitudinal force and longitudinal displacement of a seamless track on a long slope under train braking.

[0046] 1. Selection of calculation parameters:

[0047] For long and steep ballasted track seamless lines, 60kg / m rails are used, and the rail cross-sectional area is 7745mm 2 The rail elastic modulus is 210GPa. The sleepers are type IIIc concrete sleepers, and the ballasted trackbed uses special graded ballast. The longitudinal resistance of the trackbed is determined according to the requirements of TB10015-2012 "Railway Seamless Line Design Specifications". In this example calculation, the linear variation coefficient of the longitudinal resistance of the trackbed is used when the longitudinal displacement of the sleeper does not exceed 2mm under vehicle load and no-load conditions, and its value is 7.5N / (mm 2· The high-speed train uses the CRH380A 8-carriage EMU, with an axle load of 15t, a wheelbase of 2.5m, and 32 wheels. The wheel-rail adhesion coefficient is 0.164. The line slope is 24‰.

[0048] 2. Initial distribution of longitudinal force and longitudinal displacement of rails on ballasted track with long and steep slopes:

[0049] In the present invention, the analytical method / finite element method can be used to establish the seamless track model of the ballasted track on a long slope. When the analytical method is used to establish the seamless track model of the ballasted track on a long slope, it is necessary to establish and solve the longitudinal force differential equation of the rail micro-segment, and further consider the superposition effect of the EMU group wheel braking, so as to obtain the calculation expression of the longitudinal force and longitudinal displacement of the seamless track rail; when the finite element method is used to establish the seamless track model of the ballasted track on a long slope, the rail can be simulated by beam units. Considering that the longitudinal displacement value of the seamless track under single braking is small, the simulation of the longitudinal resistance of the roadbed can be simulated by simplified linear spring units. In this example, the analytical method is preferably used to carry out calculation analysis, and the calculation method of the longitudinal force P(x) and longitudinal displacement u(x) at different positions of the seamless track rail under the braking of the EMU train is obtained as shown in formulas (1)-(2).

[0050]

[0051] Where: μ is the wheel-rail adhesion coefficient, α is the line slope value; Q i is the vertical force between the wheel and rail at the i-th wheel, x i is the position coordinate of the i-th wheel; k is the coefficient of variation of the longitudinal resistance of the roadbed, E is the elastic modulus of the rail, F is the cross-sectional area of ​​the rail, and N is the number of wheels.

[0052] The longitudinal force and longitudinal displacement distribution in the rail of the ballasted track seamless line on a long slope under train braking are calculated by equations (1) and (2). The results are as follows: Figure 2 As shown, the longitudinal displacement of the rail is displayed according to the absolute value of the calculated result.

[0053] 3. Updated distribution of rail longitudinal force and longitudinal displacement on ballasted track seamless lines with long slopes:

[0054] In this example, a discrete element model for a seamless track with ballasted track on a long slope was established using irregular particle elements and a block splicing method to achieve rapid equilibrium of the discrete element model. Before using the discrete element model for calculations, microscopic parameter calibration and model validation were performed, combining the longitudinal resistance of the trackbed used in the initial calculation of the longitudinal force and displacement distribution of the rails on a seamless track with ballasted track on a long slope. This example employed a two-dimensional discrete element model, and during microscopic parameter calibration, the longitudinal resistance of the trackbed was adjusted to half its actual value.

[0055] Using the established discrete element model of a long and steep ballasted track seamless line, a longitudinal cyclic loading analysis was conducted under loaded conditions. Within a bogie load range, the sleeper's contribution to the wheel load under a single wheel load was analyzed using a Gaussian function fit. The fitting equation for the contribution ratio, p, is shown in Equation (3). For the case where one bogie corresponds to two wheel loads, the load contribution at different sleepers is the sum of the two wheel loads.

[0056]

[0057] Where d is the distance between the sleeper and the wheel load.

[0058] The discrete element model established in this example and the sharing of vertical wheel load by different sleepers within a bogie range are shown as follows: Figure 3 and Figure 4 shown.

[0059] By importing the maximum value of the longitudinal displacement of the rail in the initial distribution of the longitudinal displacement of the long slope ballasted track seamless line into the discrete element model, the double-controlled cyclic loading of the sleeper longitudinal displacement and the sleeper longitudinal resistance is carried out. In this example, the number of cyclic loading is 10. After the cyclic loading is completed, Figure 4 The coefficient of variation of the longitudinal resistance of the roadbed for sleepers ① to 9 under no-load conditions is shown in Table 1. Its value is obtained by converting the corresponding longitudinal resistance of the roadbed when the sleeper moves 2 mm.

[0060] Table 1 Longitudinal resistance of the roadbed at different sleepers after cyclic loading

[0061]

[0062] The average value of the longitudinal resistance coefficient of the roadbed at the 9 sleepers in Table 1 is 5.96N / (mm 2 .rail), using this value as the updated input condition, the established long slope ballasted track seamless line analytical model is used to calculate the updated seamless line rail longitudinal force and longitudinal displacement. The results are as follows Figure 5 As shown. Figure 2 and Figure 5 It can be seen that for a ballasted track seamless line with a slope of 24‰, the longitudinal resistance of the ballasted track bed decreases after the train repeatedly brakes 10 times compared to before repeated loading. When calculating the longitudinal force and longitudinal displacement of the seamless line rail under train braking, the peak value of the rail braking force increases by about 9.3%, and the peak value of the rail longitudinal displacement increases by about 24.3%.

[0063] From the description of the above embodiments, those skilled in the art can know that: the present invention provides a method for analyzing the longitudinal force and longitudinal displacement of a seamless track on a long slope under train braking, in which: the initial longitudinal resistance change characteristics of the roadbed of the ballasted track seamless track on a long slope are obtained, the analytical / finite element model of the ballasted track seamless track on a long slope is imported, the initial distribution of the longitudinal force and longitudinal displacement of the seamless track rails is obtained, and the maximum longitudinal displacement of the seamless track rails is obtained at the same time; the maximum longitudinal displacement of the seamless track rails is used as the input condition, and cyclic loading of the longitudinal resistance-longitudinal displacement dual control is carried out under load conditions based on the discrete element model of the ballasted track seamless track on a long slope, and the updated longitudinal resistance of the roadbed under no-load conditions is extracted after a certain number of loading times; the obtained updated longitudinal resistance of the roadbed is imported into the analytical / finite element model of the ballasted track seamless track on a long slope, and the updated distribution of the longitudinal force and longitudinal displacement of the seamless track rails is calculated. This study analyzes the significant impact of repeated train braking on the roadbed resistance of CWR rails on long and steep slopes. By combining analytical methods with the finite element method and the discrete element method, this study investigates the updated distribution characteristics of the longitudinal force and displacement of CWR rails under repeated train braking. This method rationally reflects the evolution of the longitudinal resistance of the roadbed under repeated train braking on ballasted track on long and steep slopes, providing a theoretical basis for studying the distribution characteristics of the longitudinal force and displacement of CWR rails under repeated train braking on long and steep slopes.

[0064] Further, refer to Figure 6 As shown, an embodiment of the present invention also provides an electronic device that can execute the above method. The electronic device may include a processor 10, a memory 11, a communication bus 12 and a communication interface 13, and may also include a computer program stored in the memory 11 and run on the processor 10.

[0065] In some embodiments, the processor 10 may be composed of an integrated circuit, such as a single packaged integrated circuit, or a plurality of packaged integrated circuits with the same or different functions, including one or more central processing units (CPUs), microprocessors, digital processing chips, graphics processors, and a combination of various control chips. The processor 10 is the control core (Control Unit) of the electronic device, connecting the various components of the entire electronic device using various interfaces and circuits, and executing or executing programs or modules stored in the memory 11 and calling data stored in the memory 11 to perform various functions of the electronic device and process data.

[0066] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, electronic devices, or computer program products, etc. Therefore, the present invention may take the form of an entirely software embodiment, an entirely hardware embodiment, or an embodiment combining software and hardware aspects.

[0067] It should be noted that the word "comprising" does not exclude the presence of elements or steps not listed in a claim. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The invention can be implemented by means of hardware comprising several distinct elements, and by means of a suitably programmed computer.

[0068] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0069] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for analyzing the longitudinal force and longitudinal displacement of a seamless track on a long and steep slope under train braking, characterized in that: The method comprises the following steps: Step 1: Obtain the longitudinal resistance curve of the roadbed of the long and steep ballasted track seamless line; Step 2: Build an analytical / finite element model of the CWR ballasted track on a long slope based on the analytical / finite element method. Input the longitudinal resistance curve of the roadbed, calculate the longitudinal force and longitudinal displacement distribution of the CWR rail under train braking, and record the maximum longitudinal displacement of the CWR rail. Step 3: Based on the discrete element method, a discrete element model of the long slope ballasted track seamless line is established, and the parameters of the discrete element model are calibrated and verified in combination with the longitudinal resistance curve of the track bed; Step 4: Calculations were performed based on the discrete element model of the CWR ballasted track on a long slope. The maximum displacement of the CWR rail was used as the loading control value, and the longitudinal resistance of the sleeper was used as the unloading control value. Cyclic loading of the ballasted track on a long slope under loaded conditions was performed using a dual-control method of longitudinal displacement and longitudinal resistance. Step 5: Obtain the longitudinal resistance curve of the roadbed under no-load conditions after a certain number of cyclic loading cycles. Use this curve as the input parameter for the analytical / finite element model of the CWR ballasted track on long and steep slopes. Calculate the updated distribution of the longitudinal force and longitudinal displacement of the CWR rail.

2. The method for analyzing longitudinal force and longitudinal displacement of a seamless track on a long and steep slope under train braking according to claim 1 is characterized in that: In step 1, when obtaining the longitudinal resistance curve of the roadbed, the linear variation coefficient of the longitudinal resistance of the roadbed when the longitudinal displacement of the sleeper does not exceed 2 mm under vehicle load and no-load conditions is used.

3. The method for analyzing longitudinal force and longitudinal displacement of a seamless track on a long and steep slope under train braking according to claim 1 is characterized in that: In step 2, the analytical method is used to calculate the longitudinal force and longitudinal displacement distribution of the seamless line rail under the action of train braking. The calculation formulas are: Where P(x) represents the longitudinal force, u(x) represents the longitudinal displacement, μ is the wheel-rail adhesion coefficient, α is the line slope value, Q i is the vertical force between wheel and rail at the i-th wheel, x i is the position coordinate of the i-th wheel; k is the coefficient of variation of the longitudinal resistance of the roadbed, E is the elastic modulus of the rail, F is the cross-sectional area of ​​the rail, and N is the number of wheels.

4. The method for analyzing longitudinal force and longitudinal displacement of a seamless track on a long and steep slope under train braking according to claim 1 is characterized in that: In step 3, when establishing a discrete element model of a long and steep ballasted track seamless line based on the discrete element method, irregular particle units are used for the ballast, and a block splicing method is used to achieve rapid balancing of the discrete element model.

5. The method for analyzing longitudinal force and longitudinal displacement of a seamless track on a long and steep slope under train braking according to claim 1 is characterized in that: In step 4, the established discrete element model of the long and steep ballasted track seamless line is used to carry out longitudinal cyclic loading analysis under loaded conditions. Within a bogie load range, the sleeper's contribution to the wheel load under a single wheel load is analyzed using a Gaussian function fitting analysis. The fitting equation for the sharing ratio is: Where p is the sharing ratio, d is the distance between the sleeper and the wheel load; For the case where one bogie corresponds to two wheel loads, the load sharing at different sleepers is the superposition of the two wheel loads.

6. An electronic device, characterized in that: It includes a processor and a memory, the memory stores machine-executable instructions that can be executed by the processor, and the processor executes the machine-executable instructions to implement a method for analyzing the longitudinal force and longitudinal displacement of a seamless track on a long and steep slope under train braking as described in any one of claims 1 to 5.

Images