Method and device for calculating equivalent elastic curve of railway catenary anchor section joint and medium

Abstract

The application discloses a railway catenary anchor section joint equivalent elastic curve calculation method and device and a medium, and relates to the technical field of electrified railway catenary. The application adopts an absolute node coordinate method to construct an initial configuration model of an anchor section joint. A virtual lifting structure is arranged below a low-position contact wire, the anchor section joint is divided into multiple displacement steps, and a rated lifting force is applied in multiple stages. For each stage of load, the relative position of the virtual lifting structure and the contact wire is determined according to the nominal contact state of the node, the effective contact stiffness is obtained, the structure basic stiffness is synchronously calculated, and then the system total stiffness matrix is obtained, the incremental balance equation is constructed, the vertical displacement is solved through the nested iteration method, and the equivalent elasticity is calculated. After all nodes and displacement steps are traversed, the anchor section joint equivalent elastic curve is generated. In this way, the accuracy and stability of the elastic calculation under the double-contact wire working condition are improved, and the performance evaluation of the pantograph-catenary system can be effectively supported.

Description

Technical Field

[0001] This application relates to the field of electrified railway catenary technology, specifically to a method, device, and medium for calculating the equivalent elastic curve of the anchor section joint of a railway catenary. Background Technology

[0002] The anchor joint of the railway catenary is the core structure for realizing the mechanical connection and electrical transition between adjacent anchor sections. Its elastic distribution characteristics are a key control factor determining the pantograph-catenary contact state, current collection quality, and operational safety when the pantograph passes at high speed. The equivalent elasticity of the anchor joint is defined as the ratio of the rated vertical lifting force at the calculated section to the maximum vertical lifting amount of the two contact wires of the working and non-working supports under the action of the rated vertical lifting force (200N). The elastic non-uniformity of the anchor section joint region is one of the core indicators for evaluating the dynamic performance of the pantograph-catenary system. Establishing an accurate method for calculating the equivalent elastic curve is of great significance for optimizing the design of the anchor section joint, improving the current collection quality of the pantograph-catenary system, and ensuring the safety of high-speed operation. However, traditional research on the elasticity of the catenary mainly focuses on the analysis and optimization of the elastic characteristics of the standard cross-conventional section, neglecting the study of the equivalent elasticity of the two contact lines at the anchor section joint. Conventional single-line elastic calculation methods cannot accurately characterize the equivalent elastic distribution law of the anchor section joint. When analyzing the static characteristics of the catenary after optimizing the catenary configuration, only the changes in elastic performance of the conventional section are considered, ignoring the analysis of the equivalent elasticity of the two contact lines at the anchor section joint. Summary of the Invention

[0003] The purpose of this application is to provide a method, device, and medium for calculating the equivalent elastic curve of the joint of the anchor section of railway catenary, so as to solve the problem that traditional methods are difficult to accurately obtain the equivalent elastic distribution curve of the joint of the anchor section of railway catenary.

[0004] To achieve the above objectives, the first aspect of this application provides a method for calculating the equivalent elastic curve of a railway catenary anchor section joint, comprising: An initial configuration model of the anchor joint of the railway catenary is constructed using the absolute node coordinate method. The initial configuration model includes two catenary systems. The contact wire, catenary wire, and elastic suspension cable in both systems are discretized using beam elements, while the dropper and positioner are discretized using cable elements. A virtual lifting structure is set up below the low-level contact line, the anchor joint is divided into multiple displacement steps, the rated lifting force is applied in multiple stages, and the displacement steps and loads are calculated one by one. For each load level, the nominal contact state of each computing node is determined based on the relative position of the virtual lifting structure and the two contact lines, and the effective contact stiffness of each computing node is determined. The effective contact stiffness of the lower contact line is always active, while the effective contact stiffness of the higher contact line is selectively activated or deactivated according to the contact state. The structural foundation stiffness is recalculated synchronously based on the effective contact stiffness, the total stiffness matrix of the system is updated, and the corresponding incremental equilibrium equation is constructed. The vertical displacement of each calculation node is obtained by solving the incremental equilibrium equation through a nested iterative algorithm, and the equivalent elasticity corresponding to each calculation node is calculated. By traversing all calculation nodes and displacement steps, and based on the equivalent elastic data of each calculation node, an equivalent elastic curve characterizing the elastic distribution properties of the anchor joint is generated.

[0005] The second aspect of this application provides a device for calculating the equivalent elastic curve of a railway catenary anchor section joint, comprising: The construction module is used to construct the initial configuration model of the anchor joint of the railway catenary using the absolute node coordinate method. The initial configuration model includes two catenary systems. The contact wire, catenary wire and elastic suspension cable in the two systems are discretized using beam elements, and the dropper and positioner are discretized using cable elements. The grading module is used to set up a virtual lifting structure below the low-level contact line, divide the anchor joint into multiple displacement steps, apply the rated lifting force in multiple levels, and calculate the displacement step and load level by level. The determination module is used to determine the nominal contact state of each computing node and the effective contact stiffness of each computing node based on the relative position of the virtual lifting structure and the two contact lines for each load level. The effective contact stiffness of the lower contact line is always active, while the effective contact stiffness of the higher contact line is selectively activated or deactivated according to the contact state. The calculation module is used to synchronously recalculate the structural foundation stiffness in conjunction with the effective contact stiffness, update the total stiffness matrix of the system, construct the corresponding incremental equilibrium equation, solve the incremental equilibrium equation through a nested iterative algorithm to obtain the vertical displacement of each calculation node, and calculate the equivalent elasticity corresponding to each calculation node. The generation module is used to traverse all calculation nodes and displacement steps, and generate equivalent elastic curves that characterize the elastic distribution characteristics of the anchor joint based on the equivalent elastic data of each calculation node.

[0006] A third aspect of this application provides a computer-readable storage medium storing a program that can be loaded by a processor and executed by the above-described method for calculating the equivalent elastic curve of the joint of the railway catenary anchor section.

[0007] The beneficial effects of this application are: This application first employs the absolute nodal coordinate method to construct an initial configuration model of the anchor joint containing two contact wire systems. Then, a virtual lifting structure is set up, dividing the anchor joint into multiple displacement steps and rated lifting forces into multiple levels, calculating each displacement step and load level sequentially. This overcomes the limitations of traditional single-contact-line modeling, restoring the true structure of the anchor joint. Under each load level, the nominal contact state of each calculation node is determined based on the relative position of the virtual lifting structure and the two contact wires, determining the effective contact stiffness. Simultaneously, the structural foundation stiffness is recalculated, updating the system's total stiffness matrix, thus solving the problems of fixed stiffness and low calculation accuracy in traditional methods. Then, based on the updated system total stiffness matrix, an incremental equilibrium equation is constructed. The equivalent elasticity is calculated by nested iterations to solve the vertical displacement of the nodes, ensuring stable convergence and reducing calculation errors. Finally, all displacement steps and calculation nodes are traversed, and the equivalent elasticity data is integrated to generate the equivalent elasticity curve of the anchor joint, filling the gap in traditional methods that cannot quantify the elastic distribution of the anchor joint.

[0008] Other features and advantages of this application will be described in detail in the following detailed description section. Attached Figure Description

[0009] Figure 1 This is a flowchart illustrating a method for calculating the equivalent elastic curve of a railway catenary anchor section joint, as provided in this embodiment of the application. Figure 2 This is a schematic XZ plane diagram of the initial configuration of a railway catenary provided in an embodiment of this application; Figure 3 This is a diagram showing the calculation results of the equivalent elastic curve of a railway catenary anchor section joint provided in the embodiments of this application; Figure 4 This is a comparison diagram of the equivalent elastic curves of the anchor section joint under tension conditions of 25 sets of contact wires and catenary cables provided in the embodiments of this application; Figure 5 This is a magnified comparison diagram of the equivalent elastic curves of the anchor section joint under tension conditions of 25 sets of contact wires and catenary cables provided in the embodiments of this application; Figure 6 This is a comparison diagram of the equivalent elastic curves of the anchor section joints at five different ridge heights provided in the embodiments of this application; Figure 7 This is a magnified comparison of the equivalent elastic curves of the anchor section joints at five different ridge heights provided in the embodiments of this application; Figure 8 This is a schematic diagram of the structure of a railway catenary anchor section joint equivalent elastic curve calculation device provided in the embodiments of this application. Detailed Implementation

[0010] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0011] In the description of this application, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the stated features. In the description of this application, "a plurality of" means two or more, unless otherwise explicitly specified. Details are set forth in the following description for illustrative purposes. It should be understood that those skilled in the art will recognize that this application can be implemented without using these specific details. In other instances, well-known structures and processes will not be described in detail to avoid unnecessarily obscuring the description of this application. Therefore, this application is not intended to be limited to the embodiments shown, but rather to be consistent with the broadest scope of the principles and features disclosed herein.

[0012] The purpose of this application is to propose a method for calculating the equivalent elastic curve of the anchor section joint in a railway catenary. This method establishes an initial catenary configuration model, an effective contact stiffness determination model for the contact wire, and an incremental catenary lifting balance model. After obtaining the initial catenary configuration, a triple-nested iterative incremental solution architecture is used to calculate the equivalent elastic curve of the anchor section joint, while also being compatible with the elasticity calculation of conventional sections of the catenary. This method can reflect the changing characteristics of the elastic curve of the anchor section joint along the longitudinal direction of the track, and can simultaneously consider the influence of the tension conditions of the contact wire and the catenary cable, as well as the geometric characteristics of the joint, on the elastic curve at the anchor section joint.

[0013] Figure 1 This is a flowchart illustrating a method for calculating the equivalent elastic curve of a railway catenary anchor section joint, as provided in an embodiment of this application. Figure 1 As shown, the method may include steps 101-105, which will be described in detail below.

[0014] Step 101: Construct the initial configuration model of the anchor joint of the railway catenary using the absolute node coordinate method.

[0015] Absolute Nodal Coordinate Formulation (ANCF) is a finite element modeling method suitable for structures with large deformations. It uses nodal displacement and gradient as degrees of freedom and can accurately describe the geometry and mechanical deformation of the overhead contact system. ANCF is used to establish the initial configuration model of the railway overhead contact system anchor joint. The initial configuration model can include two overhead contact system systems. The contact wire, catenary, and elastic suspension cables in both systems are discretized as ANCF beam elements, while the droppers and positioners are discretized as ANCF cable elements. Attachments such as clamps and fixtures are represented as concentrated masses attached to the conductor. The element stiffness matrix is ​​derived from the element strain energy. Based on the tangent stiffness matrix, iterative solutions are used to obtain the nodal degrees of freedom and the strain-free length of the elements, ultimately determining the initial geometric configuration of the overhead contact system anchor joint, providing an accurate structural foundation for subsequent mechanical calculations.

[0016] Step 102: Set up a virtual lifting structure below the low-level contact line, divide the anchor joint into multiple displacement steps, apply the rated lifting force in multiple levels, and calculate the displacement step and load level by level.

[0017] The virtual lifting structure is a virtual component located below the low-position contact line, used to simulate the pantograph lifting the contact line with rated force, thus enabling the determination of the contact state of the two contact lines. The low-position contact line is the contact line with a lower initial vertical height. A virtual lifting structure is set up below the low-position contact line to simulate the vertical lifting effect of the pantograph. Then, the anchor joint is divided into multiple calculation displacement steps along the longitudinal direction of the line, discretized into several calculation positions with a fixed step size. For each displacement step, the rated vertical lifting force is divided into multi-level linear load sub-steps, and the lifting load is applied in a progressively increasing manner from 0, forming a triple nested calculation framework of "position traversal - load grading - sub-step iteration".

[0018] Step 103: For each load level, based on the relative position of the virtual lifting structure and the two contact lines, determine the nominal contact state of each calculation node and the effective contact stiffness of each calculation node.

[0019] The nominal contact state refers to determining whether a node is in a lifted contact state by calculating the relative positional relationship between the virtual lifting structure and the contact line node during the lifting process of the virtual lifting structure. It serves as the basis for dynamically enabling / disabling the effective contact stiffness. The effective contact stiffness is dynamically determined based on the node contact state; only the contacted nodes participate in the force calculation, while the stiffness of uncontacted nodes is 0. For example, the effective contact stiffness of each node can be determined based on the sign of the contact force. The effective contact stiffness of the lower-level contact line is always active, while the effective contact stiffness of the higher-level contact line is selectively activated or deactivated based on the contact state. For example, the stiffness is set to 0 when not in contact, thus truly reflecting the force participation state of the two contact lines.

[0020] Step 104: Simultaneously recalculate the structural foundation stiffness by combining the effective contact stiffness, update the total stiffness matrix of the system, and construct the corresponding incremental equilibrium equation. Solve the incremental equilibrium equation through a nested iterative algorithm to obtain the vertical displacement of each calculation node, and calculate the equivalent elasticity corresponding to each calculation node.

[0021] The structural foundation stiffness matrix is ​​formed by superimposing the material stiffnesses of elements such as the contact wire, catenary, droppers, and positioners, and is recalculated as the node positions are updated. The overall system stiffness matrix is ​​obtained by superimposing the augmented foundation stiffness matrix with the contact stiffness matrix of the same dimension, and is used to construct the incremental equilibrium equations. For example, the self-weight of the contact wire and the additional concentrated mass are equivalent to external loads on the nodes. The contact stiffness matrix is ​​assembled based on the current effective contact stiffness, and the structural foundation stiffness matrix is ​​recalculated based on the updated node positions, thus obtaining the updated overall system stiffness matrix.

[0022] Then, an initial equivalent nodal force is introduced to eliminate the influence of initial internal forces. The equilibrium equation for the contact network lift increment is constructed by combining the lifting load, system internal forces, and total stiffness. The Newton-Raphson iterative method is used to solve the equation within each substep, obtaining the vertical displacement increment of the nodes and updating the node coordinates and structural configuration, completing one round of iterative calculation. After all load substeps of the current displacement step converge, the vertical lift of the two contact lines at that location is extracted. The equivalent elastic value of the current node is obtained by dividing the rated lifting force by the larger of the two contact line lifts. The equivalent elasticity is the ratio of the rated vertical lifting force to the larger of the two contact line lifts at that location, used to quantify the local stiffness of the contact network.

[0023] Step 105: Traverse all calculation nodes and displacement steps, and generate an equivalent elastic curve characterizing the elastic distribution characteristics of the anchor joint based on the equivalent elastic data of each calculation node.

[0024] The equivalent elastic curve is the equivalent elastic distribution curve along the track direction of the anchor joint, which can intuitively reflect key characteristics such as abrupt changes in joint elasticity and uneven stiffness. By traversing all displacement steps and calculation nodes, the equivalent elastic data of each node are summarized sequentially along the longitudinal direction of the track, and a complete equivalent elastic curve of the anchor joint is generated through fitting, which can intuitively characterize the elastic distribution and stiffness variation law of the joint region.

[0025] This application first employs the absolute node coordinate method to construct an initial configuration model of the anchor joint containing two contact wire systems. Then, a virtual lifting structure is set up, dividing the anchor joint into multiple displacement steps and rated lifting forces into multiple levels, calculating each displacement step and load level sequentially. This overcomes the limitations of traditional single-contact-line modeling, restoring the true structure of the anchor joint. Under each load level, the nominal contact state of each calculation node is determined based on the relative position of the virtual lifting structure and the two contact lines, determining the effective contact stiffness. Simultaneously, the structural foundation stiffness is recalculated, updating the system's total stiffness matrix, thus solving the problems of fixed stiffness and low calculation accuracy in traditional methods. Then, an incremental equilibrium equation is constructed based on the updated system total stiffness matrix. The equivalent elasticity is calculated by nested iterations to solve the vertical displacement of the nodes, ensuring stable convergence and reducing calculation errors. Finally, all displacement steps and calculation nodes are traversed, integrating the equivalent elasticity data to generate the equivalent elasticity curve of the anchor joint, filling the gap in traditional methods that cannot quantify the elastic distribution of the anchor joint.

[0026] In step 101, the contact wire, catenary, and elastic suspension cable can be constructed as beam elements using the absolute nodal coordinate method, the droppers and positioners can be constructed as cable elements using the absolute nodal coordinate method, and the clamps and fixtures at the connection points can be treated as concentrated masses attached to the conductor. This completes the overall finite element discretization of the railway contact network and establishes the initial structure of the railway contact network.

[0027] For each beam or cable element, first define a nodal degree-of-freedom vector containing displacement and gradient, then establish the global position vector of the beam or cable element based on the shape function matrix. Taking a beam element as an example, for a beam element with two nodes... and For ANCF beam elements, the nodal degree-of-freedom vector containing displacement and gradient is defined as: (1) in, It is the nodal degree of freedom vector of the ANCF beam element. , , It is a node Three-dimensional coordinates in the global coordinate system , , It is a node Three-dimensional coordinates in the global coordinate system These are local coordinates along the beam, ranging from 0 to the length of the undeformed element. , , It is a node At this point, global coordinates relative to local coordinates The partial derivatives (i.e., the position gradient) are used to describe the tangent direction and bending deformation of the beam. Similarly, , , It is a node The gradient at that location. Therefore, the global position vector. It can be represented as: (2) in, It is the classical shape function matrix used in the finite element method.

[0028] Then, the total strain energy is calculated based on the axial deformation and bending deformation of the beam element, and the element stiffness matrix is ​​derived based on the total strain energy.

[0029] The strain energy can be calculated as follows: (3) in, It is the total strain energy of the ANCF beam element. It is the elastic modulus of the material. It is the cross-sectional area of ​​the beam element section. It is the moment of inertia of the beam element section. The axial strain of the beam element reflects the degree of bending deformation of the element. Let be the curvature of the beam element, reflecting the degree of bending deformation of the element, which can be expressed as: (4) (5) in, The first-order partial derivative of the global position vector with respect to the local coordinates represents the tangent vector along the axis of the beam element. For the shape function matrix, Construct axial geometric relations by taking the first-order partial derivatives of the shape function matrix with respect to local coordinates. The second-order partial derivative of the global position vector with respect to the local coordinates represents the curvature vector of the beam element axis. For the magnitude operation of a vector, scalarize the curvature value.

[0030] Generalized elastic force The internal force geometry corresponding to the nodal degrees of freedom can be defined as: (6) in, It is the total strain energy Corresponding node degree of freedom vector The partial derivative of elastic force is the definition of elastic force. The element stiffness matrix is ​​derived from the derivative of strain energy with respect to degrees of freedom, establishing a linear relationship between element internal forces and displacements. Therefore, the element stiffness matrix related to the absolute coordinates can be obtained. The global position vector of the index cell is established in the same way.

[0031] Next, the basic stiffness matrix is ​​assembled from the element stiffness matrix, and iterative calculations are performed based on the tangent stiffness matrix to obtain the incremental node degree of freedom vector and the incremental strain-free length, thus solving for the initial geometric configuration of the railway catenary anchor section joint.

[0032] Most studies prefer to use the tangent stiffness matrix, which can iteratively calculate the incremental nodal degree-of-freedom vectors during form-finding and dynamic simulation. and incremental strain-free length Tangent stiffness matrix Stiffness matrix related to load Equation (6) can be used to and Differentiation yields: (7) in, This is the generalized force increment, used for the external force increment in the equilibrium equation. The partial derivative of the elastic force with respect to the degrees of freedom is the tangent stiffness matrix. It is used to linearize the solution of the degree of freedom increment. This is the partial derivative of the elastic force with respect to the unstrained length, i.e., the load-dependent stiffness matrix. It is used to handle load terms that vary with length.

[0033] Equation (7) can be used to calculate the incremental degree of freedom vector and the strain-free length to obtain the initial geometric configuration of the contact wire.

[0034] In step 102, considering the pull-out value of the railway catenary, it is assumed that there is a rated vertical lifting force (200N) under the railway catenary, which is applied to the virtual lifting structure. The height of the contact line with the lower initial vertical height is used as a unified reference vertical height to establish a contact state judgment benchmark. Using the lower contact line as a unified reference height eliminates the judgment error caused by the initial height difference between the two contact lines, solves the problem that traditional methods cannot simultaneously determine the contact state of the two contact lines, and can truly reflect the force participation state of the two contact lines at the anchor section joint.

[0035] By employing the penalty function method, the nominal contact force of each computational node is calculated based on the uplift of the virtual lifting structure, the current vertical coordinates of the nodes, and a unified reference vertical height. This allows the contact stiffness to change in real time with the node position and uplift, rather than using a fixed stiffness, significantly improving the accuracy of nonlinear solutions and reducing the computational bias of traditional fixed stiffness models.

[0036] In one example, the nominal contact force can satisfy the following formula: (8) in, For the first The nominal contact force at the nodes of each beam element. For nominal contact stiffness, The lifting amount of the virtual lifting structure. This represents the node's current vertical coordinate. The unified reference vertical height for the two contact lines at the current node location.

[0037] Then, based on the sign of the nominal contact force, the effective contact stiffness of the corresponding computed node is activated or deactivated. In one example, when the nominal contact force is positive, the node is in contact, and the node's effective contact stiffness is activated. When the nominal contact force is negative, the node is in non-contact, and the node's effective contact stiffness is deactivated.

[0038] The effective contact stiffness can satisfy the following formula: (9) in, For the first Effective contact stiffness of individual beam element nodes.

[0039] By determining the positive and negative values ​​of nominal contact force and switching the effective contact stiffness, a dynamic switching simulation of the high-position contact wire never making contact is achieved. This solves the problem that traditional methods cannot simulate the participation of the high-position contact wire in force, and more closely resembles the actual working condition of the pantograph being raised at the anchor section joint. The output dynamic effective contact stiffness is a key input for subsequent assembly of the contact stiffness matrix and updating of the system's overall stiffness matrix, providing accurate and reliable basic data for the construction and solution of subsequent incremental equilibrium equations, ensuring the accuracy and stability of the entire elasticity calculation process.

[0040] In step 103, for the overhead contact system with rated vertical lifting force (200N), a triple nested iterative loop structure of "overlapping contact position - progressive loading of load substeps - nonlinear iteration within substeps" is constructed, and the nonlinear finite element incremental iteration method (Newton-Raphson method) is used to establish an incremental balance model for overhead contact lifting.

[0041] Specifically, the self-weight of the overhead contact system and the additional concentrated mass are equivalent to nodal external loads, forming a self-weight external load vector. Self-weight external load vector It can be represented as: (10) in, This represents the total number of elements in the finite element model of the railway catenary. The nodal degree-of-freedom vector of the beam element Length, The nodal degree-of-freedom vector of the beam element The shape function matrix, The vector of gravitational acceleration. , The nodal degree-of-freedom vector of the beam element The linear density (mass per unit length) along the length direction is a constant for contact wires and catenary cables, but for droppers, the concentrated mass at both ends must be considered. The amount of additional concentrated mass (such as the concentrated mass of the dropper, the mass of the positioner, etc.). To concentrate quality The shape function matrix at the location is used to effectively distribute the gravitational force of that mass to adjacent element nodes. To concentrate quality The gravity vector.

[0042] After each load level and each iteration of node position updates, the structural foundation stiffness matrix is ​​recalculated and updated. Based on the currently re-determined effective contact stiffness of each calculated node, a contact stiffness matrix is ​​assembled.

[0043] The structural stiffness matrix of the overhead contact system is formed by superimposing the material stiffness matrices of all elements of the contact system according to their nodal degrees of freedom indices, and can be expressed as: (11) in, For the structural foundation stiffness matrix, , , , , , These are collections of contact wire units, catenary units, dropper units, positioner units, elastic sling units, and elastic sling connection units. , , , , , These are the material stiffness matrices for the contact wire unit, the catenary unit, the dropper unit, the positioner unit, the elastic sling unit, and the elastic sling connection unit, respectively.

[0044] Then, the updated structural foundation stiffness matrix is ​​augmented and superimposed with the contact stiffness matrix of the same dimension to form the total system stiffness matrix in the current iteration step.

[0045] Overall Stiffness Matrix of the System The augmented structural foundation stiffness matrix and the contact stiffness matrix of the same dimension We obtain the following by superimposing the corresponding degrees of freedom: (12) Multiply the updated total system stiffness matrix by the current system position vector to obtain the system internal force vector.

[0046] Internal forces of the overhead contact system From the system's overall stiffness matrix and the current system position vector Multiplying them together gives: (13) An initial equivalent nodal force vector is introduced to eliminate the internal forces at the initial height, and the rated vertical lifting force is used as the lifting load.

[0047] Initial equivalent nodal force vector of the overhead contact system It is used to eliminate the system internal forces introduced by the "initial height," which is determined by the initial height of the overhead contact line and the contact stiffness, and is expressed as: (14) in, This is the initial reference height. The total number of nodes. It is a matrix of shape functions.

[0048] Based on the initial equivalent nodal force vector, self-weight external load vector, lifting load, system internal force vector, and the system total stiffness matrix of the current iteration step, the catenary lifting increment balance equation is constructed.

[0049] The incremental balance equations satisfy the following formula: (15) in, This is the displacement increment vector of the contact wire. This is the initial equivalent nodal force vector. For loading factor, To increase the load, The external load vector is the self-weight. Let the internal force vector of the system be... This is the overall stiffness matrix of the system.

[0050] In step 104, the calculation interval for the anchor joint can be defined first, and multiple calculation positions can be obtained by discretizing with a fixed step size. Equivalent elasticity calculations are then performed for each position. The calculation interval for the anchor joint is a specially defined area covering the transition region between the working and non-working support contact lines, specifically designed to accurately reflect the elasticity distribution characteristics of the joint. It includes key structural locations such as contact line intersections, positioning points, and dropper placement points. A fixed step size is used to divide the calculation interval into a series of calculation points at uniform intervals, ensuring that the equivalent elasticity data is continuous and smooth along the line, facilitating the formation of elasticity curves suitable for engineering evaluation. Specifically, firstly, a calculation interval containing the key transition region of the anchor joint is defined along the direction of the contact network line. This interval is then discretized longitudinally along the line with a uniform fixed step size, resulting in a series of independent calculation positions distributed along the line. Equivalent elasticity solutions are then performed sequentially for each calculation position.

[0051] For each calculation location, the rated lift force is divided into several linear load substeps and applied progressively. The linear load substeps divide the rated lift force into multiple small-amplitude loads in a linear proportion and apply them progressively to improve the iterative stability of highly nonlinear problems such as large deformation and double contact line switching. Within each load substep, a nonlinear iterative method is used to solve the incremental equilibrium equations. After each iteration to obtain the displacement increment and update the node positions, the structural foundation stiffness matrix is ​​recalculated and the effective contact stiffness is re-determined. Convergence is judged based on the displacement increment convergence condition. The nonlinear iteration is based on the Newton-Raphson method, an iterative solution method that gradually reduces the unbalanced force and approaches the equilibrium state by continuously updating the displacement, structural stiffness, and contact stiffness. This method is suitable for the mechanical analysis of large deformation of contact wires.

[0052] During the nonlinear iteration process, the infinite norm of the displacement increment is calculated in real time and compared with a convergence threshold. The displacement increment is the change in nodal displacement obtained in each iteration, used to update nodal positions and determine the convergence status of the iteration. The infinite norm of the displacement increment is the maximum absolute value of all nodal displacement increments in the current iteration step, used to determine whether the iteration has reached the required computational accuracy. The convergence threshold is a pre-set accuracy limit for the displacement increment. When the infinite norm of the displacement increment is less than this threshold, the current load substep is considered to have met the accuracy requirements. For example, the convergence threshold may include a threshold for the number of consecutive non-convergence iterations. The number of consecutive non-convergence iterations is the maximum allowed number of consecutive non-convergence iterations set by the threshold, used to trigger the fault tolerance mechanism of automatically refining the load steps. If the current load substep iteration does not converge and has not reached the threshold for the number of consecutive non-convergence iterations, the iteration continues. If the number of consecutive non-convergence iterations reaches the set threshold, the number of load substeps corresponding to the lifting force is automatically doubled and the iteration solution and stiffness update calculation are re-executed. Here, the set threshold represents the threshold at which to stop further iteration. The load substep doubling function automatically doubles the number of load segments when the iteration is difficult to converge, reducing the single-step load increase and significantly improving the solution success rate under complex working conditions.

[0053] After all load substeps at the current calculation position converge, the vertical uplift of the two contact lines at that position is extracted, and the equivalent elasticity is calculated. The vertical uplift is the magnitude of the vertical displacement of the contact line node relative to its initial position under the rated uplift force. The equivalent elasticity is the ratio of the rated vertical uplift force to the larger of the vertical uplift values ​​of the two contact lines at the corresponding position, used to characterize the local stiffness of the contact network. After traversing all calculation positions, the equivalent elasticity curve of the anchor joint is output. The equivalent elasticity curve is a curve showing the change in equivalent elasticity distributed along the anchor joint line direction, which can intuitively reflect the abrupt changes in joint stiffness and the non-uniformity of elasticity.

[0054] This application employs a triple-nested structure of "position traversal - load grading - sub-step iteration," coupled with an automatic load sub-step doubling mechanism, effectively addressing the convergence problem under strongly nonlinear conditions. Each iteration recalculates the foundation structure stiffness and re-determines the effective contact stiffness, accurately reflecting the changes in structural stiffness and contact state under large deformations, achieving a calculation accuracy far exceeding traditional fixed stiffness methods. Using the infinite norm of displacement increment as the convergence criterion ensures a unified and clearly quantified standard, guaranteeing reliable calculation results across the entire range. The uplift of the two contact lines is extracted at each position, and the larger value is used to calculate the equivalent elasticity, precisely matching the actual uplift force pattern of the pantograph. Discrete calculations along the line at fixed step lengths generate smooth and continuous equivalent elasticity curves, fully reflecting the elastic distribution of the anchor joints and providing direct data support for pantograph-catenary design and evaluation.

[0055] In step 105, after completing the nonlinear iterative solution and convergence judgment for all calculation locations, all calculation nodes and displacement steps can be traversed. After confirming that the iterative solution for each calculation location has converged, the vertical uplift of the two contact lines at each calculation node is extracted. For example, all discrete calculation nodes and displacement steps are uniformly traversed to confirm that the incremental equilibrium equation solution, structural foundation stiffness update, and effective contact stiffness judgment for each calculation location all meet the convergence conditions.

[0056] Then, according to the definition of equivalent elasticity of the anchor joint, the equivalent elasticity value of the current calculation node is obtained by dividing the rated vertical lifting force by the larger of the vertical lifting amounts of the two contact lines at the corresponding node. Next, the equivalent elasticity values ​​of all discrete calculation nodes are summarized sequentially along the anchor joint line direction, and the equivalent elasticity values ​​of each calculation node are fitted to generate an equivalent elasticity curve characterizing the elasticity distribution of the anchor joint. The discrete calculation nodes are a set of points uniformly divided along the longitudinal direction of the anchor joint at fixed step lengths, used for point-by-point calculation of equivalent elasticity, ensuring continuous distribution of the elasticity curve, uniform point locations, and comparable results.

[0057] The larger of the two contact wire lift values ​​is used for calculation, which conforms to the actual working condition where the pantograph simultaneously lifts both contact wires and only interacts with the contact wire with the higher lift. Through full node traversal and data fitting, a continuous, smooth, and directly applicable equivalent elastic curve can be obtained for engineering evaluation. It clearly reflects the elastic abrupt changes and stiffness variation trends in the joint region, providing accurate basis for catenary optimization design and pantograph-catenary current collection quality assessment. Results are output only after all iterations converge, ensuring the accuracy and reliability of the curve data, which can be directly used for design, construction, and testing evaluation.

[0058] In one specific embodiment, the catenary lifting increment balance model is solved by numerical solution method, and the overall iterative solution algorithm is as follows.

[0059] (1) Obtain the initial configuration of the contact network through relevant contact network data and the initial configuration model of the contact network, and determine the initial geometric configuration of the contact network and the core calculation parameters such as materials and boundaries.

[0060] (2) Determine the total number of degrees of freedom of the system and the solution subspace of the degrees of freedom, and pre-calculate the external load vector of the structure's self-weight and the stiffness matrix of the foundation structure.

[0061] (3) Define the calculation interval of the anchor section joint, discrete the position of the contact network with a fixed step length, and initialize the initial value of the number of divisions of the rated lifting force. .

[0062] (4) Reset the structural configuration and the displacement vector of the contact wire for the current contact wire position.

[0063] (5) Locate the effective contact unit nodes of the two contact lines and take the minimum initial height of the two contact lines as the unified reference contact height.

[0064] (6) Assuming there is a virtual lifting structure under the low-level contact wire, and applying a rated vertical lifting force (200N) to lift the contact wire, the rated lifting force is divided into... A linear load substep.

[0065] (7) Initialize the non-convergence determination counter.

[0066] (8) Apply a corresponding proportional lifting load. Based on the current configuration and considering the pull-out value of the contact wire, use the penalty function method to calculate the contact force on the contact wire at the current node. Determine the effective contact stiffness of the node by the sign of the contact force.

[0067] (9) Calculate the structural foundation stiffness matrix, update the total system stiffness matrix, calculate the internal force vector and equivalent nodal force of the contact network system, and assemble the unbalanced force vector of the system by combining the external load and the lifting load.

[0068] (10) Solve the incremental equilibrium equation in the free degree of freedom subspace to obtain the displacement increment and update the nodal displacement and structural geometry synchronously.

[0069] (11) Calculate the infinite norm of the displacement increment. If the convergence threshold is met, proceed to step (12); otherwise, proceed to step (13).

[0070] (12) The current load substep has not reached the total number of parts. Then increment the sub-step number by 1 and return to step (7). The total number of portions has been reached. If the solution converges at the current position, extract the lifting amount of the two contact lines, and obtain the equivalent elasticity at the position by dividing the rated vertical lifting force (200N) by the larger lifting amount of the two contact lines, then proceed to step (14).

[0071] (13) If the number of consecutive non-convergences does not reach the threshold, update the counter and return to step (8). If the threshold is reached, divide the lifting force into portions. Double the result and return to step (4).

[0072] (14) If not all positions are solved, proceed to the next contact wire position and return to step (3). If all positions are solved, output the equivalent elastic curve of the anchor joint and end the solution.

[0073] (15) Modify the tension conditions of the contact wire and the catenary cable and the geometric characteristics of the joint in sequence, recalculate the equivalent elastic curves under various conditions, and analyze the influence of the contact wire parameters on the equivalent elasticity of the anchor joint.

[0074] This application differs from previous calculation methods that could only calculate the elasticity of conventional sections. It establishes an initial catenary configuration model, an effective contact stiffness determination model for the contact wire, and a catenary lifting increment balance model. It presents a complete modeling process, from catenary configuration to catenary lifting increment calculation, ultimately achieving balance between the catenary system and the rated vertical lifting force (200N). A triple-nested iterative incremental solution method is also provided. This enables the equivalent elasticity calculation of anchor joints in high-speed railway catenary systems, reflecting the changing characteristics of the anchor joint's elasticity curve along the longitudinal direction of the track, while considering the influence of the contact wire and catenary tension conditions, as well as the joint's geometric characteristics, on the elasticity curve at the anchor joint.

[0075] The following example illustrates the calculation of the equivalent elastic curve of the joint of the railway catenary anchor section based on the above-mentioned overall iterative solution algorithm.

[0076] First, ANCF beam elements for the contact wire, catenary, and elastic suspenders, and ANCF cable elements for the droppers and positioners are constructed based on ANCF. The clamps and fixtures at the connection points are considered as concentrated masses attached to the conductor, establishing the initial configuration model of the contact network. Then, considering the contact network pull-out value, a virtual beam is assumed to exist under the contact network, and a rated vertical lifting force (200N) is applied to the virtual beam to lift the contact wire. A penalty function method is used to construct a model for determining the effective contact stiffness of the contact wire. Finally, a nonlinear finite element incremental iteration method is used to establish an incremental balance model for the contact network lift.

[0077] Subsequently, following steps (1) to (14), the triple nested iterative loop solution method is used to solve the catenary lifting incremental balance model. Figure 2 This is a schematic XZ-plane diagram of the initial configuration of a railway catenary provided in this embodiment. The horizontal axis (X-axis) is the distance along the longitudinal direction of the line (unit: meters), ranging from approximately 500 m to 1500 m, covering the complete anchor joint and standard catenary section. The left front catenary and right rear catenary are conventional catenary sections, including components such as catenary wires, droppers, elastic suspension cables, positioners, and contact wires, exhibiting a uniform span sag curve shape. The red box in the middle represents the anchor joint, where the two contact wires intersect and transition; the intersection point marked in the figure is the core transition position of the joint. The vertical axis (Z-axis) represents the initial height of the catenary structure (unit: meters), ranging from approximately 5.3 to 8, reflecting the initial height of each component of the catenary system (contact wire, catenary wires, droppers, etc.). The conventional catenary sections remain basically parallel, while near the intersection point (1015 m) of the two contact wires at the anchor joint, the contact wire height undergoes a significant abrupt change, visually reflecting the geometric changes and stress distribution characteristics of the anchor joint, providing a basic geometric basis for equivalent elasticity calculation.

[0078] Figure 3 This is a calculation result diagram of the equivalent elastic curve of a railway catenary anchor section joint provided in the embodiments of this application. This curve is the equivalent elastic curve of the catenary under a static lifting force of 200N. Figures 4-7 Under the same conditions, the overall shape exhibits a "peak in the middle and stable on both sides": a significant elastic peak (close to 9200 N / m) appears in the joint transition area, indicating the highest stiffness and the smallest contact wire lift when the pantograph is raised; while the elastic values ​​in the normal sections on both sides are stable at about 2000-3000 N / m, representing the stiffness level of the normal contact wire section. This curve intuitively reflects the elastic abrupt change characteristics of the anchor section joint area, providing a quantitative basis for pantograph-catenary current collection quality assessment and structural optimization.

[0079] Finally, following step (15), modify the parameters of the contact wire, set 25 sets of contact wire and catenary tension conditions (see Table 1) and 5 sets of ridge height conditions (see Table 2), and calculate the equivalent elastic curve of the anchor joint under each condition. Figure 4This is a comparison diagram of the equivalent elastic curves of the anchor section joint under tension conditions of 25 sets of contact wires and catenary cables provided in the embodiments of this application. Figure 5 This is a magnified comparison diagram of the equivalent elastic curves of the anchor section joint under tension conditions of 25 sets of contact wires and catenary cables provided in the embodiments of this application. Figure 5 Enlarged Figure 4 The equivalent elastic curve at the intersection of the joint contact lines in the middle anchor section. Figure 4 and Figure 5 A comparison of equivalent elasticity under different tension combinations. Figure 4 The wide viewing angle showcases different contact line tensions. ) and tension of the load-bearing cable ( The equivalent elastic distribution curve of the entire anchor joint under the combined tension is shown. In the joint transition zone (approximately 1015 m), a distinct peak appears in the equivalent elasticity, with the peak value varying with the tension combination; the elasticity in the conventional section remains stable at approximately 2000-4000 N / m. It can be seen that the tension of the contact wire and the catenary directly affects the peak elasticity in the joint region. Higher tension results in a greater peak elasticity (i.e., higher stiffness and greater resistance to lifting). Figure 5 To enlarge the peak image, Figure 4 A magnified view of the peak position, focusing on the 1010-1020 m range. The curve exhibits a symmetrical triangular peak, with the apex at 1015 m, representing the stiffest point of the joint. The curves for different tension combinations show a "layered" distribution: the purple / green high-tension curves are at the top (maximum elasticity), and the blue low-tension curves are at the bottom (minimum elasticity). This intuitively demonstrates the "regulating effect of tension parameters on the elastic distribution of the anchor joint," providing a direct basis for subsequent tension optimization design.

[0080] Figure 6 This is a comparison diagram of the equivalent elastic curves of the anchor joints at five different ridge heights provided in the embodiments of this application. Figure 7 This is a magnified comparison of the equivalent elastic curves of the anchor joints at five different ridge heights provided in the embodiments of this application. Figure 7 Enlarged Figure 6 The equivalent elastic curve at the intersection of the joint contact lines in the middle anchor section. Figure 6 and Figure 7 Comparison of equivalent elasticity under different elevation differences. Figure 6For a wide viewing angle, the equivalent elastic distribution curves of the anchor joint are shown under different initial contact line height differences. 75mm, 65mm, 50mm, 35mm, and 20mm represent the height difference (in millimeters) between the intersection of the two contact lines and the contact line height of the conventional section. It can be seen that the peak position is consistent (approximately 10¹⁵ m), all appearing at the intersection of the two contact lines, but the peak elasticity differs under different height differences. The peak elasticity is highest at a height difference of 75mm (yellow line), and lowest at a height difference of 20mm (green line). Therefore, the ridge height of the anchor joint significantly affects the elasticity level of the joint area; the greater the height difference, the higher the peak elasticity (higher stiffness). Figure 7 For is Figure 6 A magnified view of the peak location focuses on the 1014.9-1015.1m range. The differences in peak height at different ridge heights are clearly magnified: the peak value for a 75mm height difference is approximately 9136 N / m, and the peak value for a 20mm height difference is approximately 9089 N / m, a difference of approximately 47 N / m. The width and symmetry of the curves also vary slightly, reflecting the subtle influence of ridge height on the elastic distribution pattern. This demonstrates that "ridge height is a key geometric parameter affecting the elasticity of the anchor joint," providing a quantitative reference for controlling the ridge height of the contact wire.

[0081] These four figures clearly show that the equivalent elasticity calculated using the method of this application embodiment exhibits a significant increasing trend in the anchor joint section, and the magnitude of this change is affected by the contact line tension. With tension of the load-bearing cable The impact is significant: the larger the values ​​of both, the steeper the equivalent elasticity curve and the larger the peak value; the smaller the values, the flatter the curve and the smaller the peak value. Meanwhile, the ridge height also has a certain impact: the larger the ridge height, the smaller the range of abrupt changes in equivalent elasticity, but the slightly larger the peak value; conversely, the smaller the ridge height, the larger the range of abrupt changes in equivalent elasticity, and the slightly smaller the peak value.

[0082] Table 1

[0083] Table 2

[0084] This application establishes an initial catenary configuration model, an effective contact stiffness determination model for the contact wire, and a catenary lifting increment balance model, and proposes a method for calculating the equivalent elastic curve of the anchor joint of the high-speed railway catenary. Compared with traditional methods, this application can calculate the equivalent elasticity of the anchor joint of the high-speed railway catenary, while also being compatible with the elasticity calculation of conventional sections of the catenary. It can reflect the variation characteristics of the elastic curve of the anchor joint along the longitudinal direction of the line, and can simultaneously consider the influence of the tension conditions of the contact wire and the catenary cable, as well as the geometric characteristics of the joint, on the elastic curve at the anchor joint. This improves the calculation of the equivalent elasticity of the anchor joint, realizes the universality of calculating the elasticity of conventional sections of the catenary and the anchor joint across all scenarios, and can provide new quantitative indicators and accurate theoretical support for subsequent static characteristic analysis of the catenary.

[0085] Figure 8 This is a schematic diagram of the structure of a railway catenary anchor section joint equivalent elastic curve calculation device provided in an embodiment of this application. Figure 8 As shown, the equivalent elastic curve calculation device 800 for the anchor section joint of the railway catenary may include a construction module 801, a classification module 802, a judgment module 803, a calculation module 804, and a generation module 805.

[0086] The construction module 801 is used to construct the initial configuration model of the anchor section joint of the railway catenary using the absolute node coordinate method. The initial configuration model includes two catenary systems. The contact wire, catenary wire and elastic suspension cable in the two systems are discretized using beam elements, and the dropper and positioner are discretized using cable elements.

[0087] The grading module 802 is used to set up a virtual lifting structure below the low-level contact line, divide the anchor joint into multiple displacement steps, apply the rated lifting force in multiple levels, and calculate the displacement step and load level by level.

[0088] The determination module 803 is used to determine the nominal contact state of each calculation node for each load level based on the relative position of the virtual lifting structure and the two contact lines, and to determine the effective contact stiffness of each calculation node. The effective contact stiffness of the lower contact line is always active, while the effective contact stiffness of the higher contact line is selectively activated or deactivated according to the contact state.

[0089] The calculation module 804 is used to synchronously recalculate the structural foundation stiffness in conjunction with the effective contact stiffness, update the total stiffness matrix of the system, and construct the corresponding incremental equilibrium equation. The vertical displacement of each calculation node is obtained by solving the incremental equilibrium equation through a nested iterative algorithm, and the equivalent elasticity corresponding to each calculation node is calculated.

[0090] The generation module 805 is used to traverse all calculation nodes and displacement steps, and generate equivalent elastic curves that characterize the elastic distribution characteristics of the anchor joint based on the equivalent elastic data of each calculation node.

[0091] Among them, the construction module 801, the grading module 802, the judgment module 803, the calculation module 804 and the generation module 805 can be used to execute steps 101-105 in the embodiment corresponding to the above calculation of the equivalent elastic curve of the anchor section joint of the railway catenary. For the specific implementation of these modules and more details, please refer to the corresponding method section, which will not be elaborated here.

[0092] This application also provides a computer-readable storage medium storing a program that can be loaded and executed by a processor using any of the methods for calculating the equivalent elastic curve of a railway catenary anchor section joint in this application.

[0093] Those skilled in the art will understand that all or part of the functions of the various methods in the above embodiments can be implemented by hardware or by computer programs. When all or part of the functions in the above embodiments are implemented by computer programs, the program can be stored in a computer-readable storage medium, which may include: read-only memory, random access memory, disk, optical disk, hard disk, etc., and the program is executed by a computer to achieve the above functions. For example, the program can be stored in the memory of a device, and when the program in the memory is executed by the processor, all or part of the above functions can be achieved. In addition, when all or part of the functions in the above embodiments are implemented by computer programs, the program can also be stored in a server, another computer, disk, optical disk, flash drive, or external hard drive, etc., and can be downloaded or copied to the memory of a local device, or the system of the local device can be updated. When the program in the memory is executed by the processor, all or part of the functions in the above embodiments can be achieved.

[0094] The above examples illustrate this application only to aid understanding and are not intended to limit its scope. Those skilled in the art to which this application pertains can make various simple deductions, modifications, or substitutions based on the ideas presented.

Claims

1. A method for calculating the equivalent elastic curve of a railway catenary anchor section joint, characterized in that, include: An initial configuration model of the anchor joint of the railway catenary is constructed using the absolute node coordinate method. The initial configuration model includes two catenary systems. The contact wire, catenary wire, and elastic suspension cable in both systems are discretized using beam elements, while the dropper and positioner are discretized using cable elements. A virtual lifting structure is set up below the low-level contact line, the anchor joint is divided into multiple displacement steps, the rated lifting force is applied in multiple stages, and the displacement steps and loads are calculated one by one. For each load level, the nominal contact state of each computing node is determined based on the relative position of the virtual lifting structure and the two contact lines, and the effective contact stiffness of each computing node is determined. The effective contact stiffness of the lower contact line is always active, while the effective contact stiffness of the higher contact line is selectively activated or deactivated according to the contact state. The structural foundation stiffness is recalculated synchronously based on the effective contact stiffness, the total stiffness matrix of the system is updated, and the corresponding incremental equilibrium equation is constructed. The vertical displacement of each calculation node is obtained by solving the incremental equilibrium equation through a nested iterative algorithm, and the equivalent elasticity corresponding to each calculation node is calculated. By traversing all calculation nodes and displacement steps, and based on the equivalent elastic data of each calculation node, an equivalent elastic curve characterizing the elastic distribution properties of the anchor joint is generated.

2. The method for calculating the equivalent elastic curve of the anchor section joint of the railway catenary according to claim 1, characterized in that, The initial configuration model of the anchor section joint of the railway catenary constructed using the absolute nodal coordinate method includes: The contact wire, the catenary, and the elastic suspension cable are each constructed as beam elements using the absolute node coordinate method. The dropper and the positioner are each constructed as cable elements using the absolute node coordinate method. The clamps and fixtures at the connection points are used as concentrated masses attached to the conductor to establish the initial structure of the railway contact network. For each beam element or cable element, a nodal degree-of-freedom vector containing displacement and gradient is defined, and a global position vector of the beam element or cable element is established based on the shape function matrix. The total strain energy is calculated based on the axial and bending deformations of the beam element or the cable element, and the element stiffness matrix is ​​derived based on the total strain energy. The basic stiffness matrix is ​​assembled from the unit stiffness matrix, and iterative calculations are performed based on the tangent stiffness matrix to obtain the incremental node degree of freedom vector and the incremental strain-free length, thereby solving for the initial geometric configuration of the railway catenary anchor section joint.

3. The method for calculating the equivalent elastic curve of the joint of the railway catenary anchor section according to claim 1, characterized in that, For each load level, the nominal contact state of each computational node is determined based on the relative position of the virtual lifting structure and the two contact lines, including: The height of the contact line with the lower initial vertical height among the two contact lines is used as a unified reference vertical height; The penalty function method is used to calculate the nominal contact force of each calculation node based on the lifting amount of the virtual lifting structure, the current vertical coordinate of the node, and the unified reference vertical height. Based on the sign of the nominal contact force, activate or deactivate the effective contact stiffness of the corresponding computation node; The nominal contact force satisfies the following formula: ； in, For the first The nominal contact force at the nodes of each beam element. For nominal contact stiffness, The lifting amount of the virtual lifting structure. This represents the node's current vertical coordinate. The unified reference vertical height for the two contact lines at the current node location.

4. The method for calculating the equivalent elastic curve of the anchor section joint of the railway catenary according to claim 3, characterized in that, The step of activating or deactivating the effective contact stiffness of the corresponding computation node based on the sign of the nominal contact force includes: When the nominal contact force is positive, the effective contact stiffness of the node is activated; When the nominal contact force is negative, the effective contact stiffness of the node is turned off. The effective contact stiffness satisfies the following formula: ； in, For the first Effective contact stiffness of individual beam element nodes.

5. The method for calculating the equivalent elastic curve of the joint of the railway catenary anchor section according to claim 1, characterized in that, The process of simultaneously recalculating the structural foundation stiffness based on the effective contact stiffness, updating the system's total stiffness matrix, and constructing the corresponding incremental equilibrium equations includes: The self-weight of the overhead contact system and the additional concentrated mass are equivalent to the external loads of the nodes, forming a self-weight external load vector; After each load level and each iteration of updating the node positions, the structural foundation stiffness matrix is ​​recalculated and updated. Based on the effective contact stiffness of each calculation node that has been reassessed, a contact stiffness matrix is ​​assembled. The updated structural basic stiffness matrix is ​​augmented and superimposed with the contact stiffness matrix of the same dimension to form the total system stiffness matrix in the current iteration step; Multiply the updated total system stiffness matrix by the current system position vector to obtain the system internal force vector; An initial equivalent nodal force vector is introduced to eliminate the initial height internal forces, and the rated vertical lifting force is used as the lifting load. Based on the initial equivalent nodal force vector, self-weight external load vector, lifting load, system internal force vector, and the system total stiffness matrix of the current iteration step, the catenary lifting increment equilibrium equation is constructed. The incremental balance equation satisfies the following formula: ； in, This is the displacement increment vector of the contact line. This is the initial equivalent nodal force vector. For loading factor, To increase the load, The external load vector is the self-weight. Let the internal force vector of the system be... This is the overall stiffness matrix of the system.

6. The method for calculating the equivalent elastic curve of the joint of the railway catenary anchor section according to claim 1, characterized in that, The process of solving the incremental equilibrium equation using a nested iterative algorithm to obtain the vertical displacement of each computational node and calculating the equivalent elasticity corresponding to each computational node includes: The calculation interval of the anchor joint is defined and multiple calculation positions are obtained by discretizing with a fixed step size; For each calculation location, the rated lifting force is divided into several linear load substeps and applied step by step; In each load substep, the incremental equilibrium equation is solved using a nonlinear iterative method. After each iteration, the displacement increment is obtained and the node position is updated, the structural foundation stiffness matrix is ​​recalculated and the effective contact stiffness is re-determined. The convergence condition of the displacement increment is used to determine whether the equation has converged. After all load substeps at the current calculation position have converged, the vertical uplift of the two contact lines at that position is extracted and the equivalent elasticity is calculated. After traversing all calculated positions, the equivalent elastic curve of the anchor joint is output.

7. The method for calculating the equivalent elastic curve of the joint of the railway catenary anchor section according to claim 6, characterized in that, The method of solving the incremental balance equation using a nonlinear iterative approach within each load substep also includes: During the iteration process, the infinite norm of the displacement increment is calculated in real time and compared with the convergence threshold; If the current load substep iteration does not converge and has not reached the threshold for the number of consecutive non-convergences, then continue iterating; If the number of consecutive non-convergences reaches a set threshold, the load substeps corresponding to the lifting force will be automatically doubled and the iterative solution and stiffness update calculation will be re-executed.

8. The method for calculating the equivalent elastic curve of the joint of the railway catenary anchor section according to claim 1, characterized in that, The process involves traversing all computation nodes and displacement steps, and generating an equivalent elastic curve characterizing the elastic distribution properties of the anchor joint based on the equivalent elastic data of each computation node. This includes: After traversing all calculation nodes and displacement steps and confirming that the iterative solution at each calculation position has converged, the vertical uplift of the two contact lines at each calculation node is extracted. The equivalent elastic value of the current calculation node is obtained by dividing the rated vertical lifting force by the larger of the vertical lifting amounts of the two contact lines at the corresponding node. The equivalent elastic values ​​of all discrete calculation nodes are summarized sequentially along the anchor joint line direction. The equivalent elastic values ​​of each calculation node are then fitted to generate an equivalent elastic curve that characterizes the elastic distribution of the anchor joint.

9. A device for calculating the equivalent elastic curve of a railway catenary anchor section joint, characterized in that, include: The construction module is used to construct the initial configuration model of the anchor joint of the railway catenary using the absolute node coordinate method. The initial configuration model includes two catenary systems. The contact wire, catenary wire and elastic suspension cable in the two systems are discretized using beam elements, and the dropper and positioner are discretized using cable elements. The grading module is used to set up a virtual lifting structure below the low-level contact line, divide the anchor joint into multiple displacement steps, apply the rated lifting force in multiple levels, and calculate the displacement step and load level by level. The determination module is used to determine the nominal contact state of each computing node and the effective contact stiffness of each computing node based on the relative position of the virtual lifting structure and the two contact lines for each load level. The effective contact stiffness of the lower contact line is always active, while the effective contact stiffness of the higher contact line is selectively activated or deactivated according to the contact state. The calculation module is used to synchronously recalculate the structural foundation stiffness in conjunction with the effective contact stiffness, update the total stiffness matrix of the system, construct the corresponding incremental equilibrium equation, solve the incremental equilibrium equation through a nested iterative algorithm to obtain the vertical displacement of each calculation node, and calculate the equivalent elasticity corresponding to each calculation node. The generation module is used to traverse all calculation nodes and displacement steps, and generate equivalent elastic curves that characterize the elastic distribution characteristics of the anchor joint based on the equivalent elastic data of each calculation node.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a program that can be loaded by a processor and executed as described in any one of claims 1 to 8, the method for calculating the equivalent elastic curve of the joint of the railway catenary anchor section.

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