Mathematical model based on whole-process accurate shape finding of No.18 line bifurcated section of high-speed railway

Abstract

The invention discloses a whole-process accurate shape finding mathematical model for a high-speed railway No.18 line fork contact network, and solves the high-point problems of height difference of two end points, non-uniform on-way tension, influence of sag change and the like caused by dynamic height change of the contact network. Modeling is improved on the basis of a hybrid cable unit theory, specifically, a geometric shape is constructed according to contact line position partition by combining a parabola and a catenary linear cable unit, and the method adapts to uneven tension; deriving a cable unit unbalance force algorithm, solving tension distribution by using a Newton-Raphson iteration method, and quantifying a coupling relation between height difference and sag; a dynamic correction shape finding model is established, and dynamic transition form distortion is solved; and constructing a pantograph-catenary coupling dynamic model. The actual measurement verification of the No.18 line turnout shows that the deviation of the improved model is less than 5%, the model accords with the EN50318 standard, and the quantitative analysis shows that the equal-height point is the main cause of the turnout parameters of the non-cross contact network on the bow-catenary coupling performance. According to the technology, the accuracy of pantograph-catenary coupling performance analysis can be improved, and a quantitative design basis is provided for optimization of a catenary system.

Description

Technical Field

[0001] This invention relates to the field of electrified railway catenary systems, specifically to a mathematical model based on the precise shape finding of the entire process of the turnout section of High-Speed ​​Railway Line 18, and dynamic coupling analysis of the pantograph and catenary system, applicable to the performance optimization and stability control of the pantograph and catenary system when high-speed trains pass through sections without crossing turnouts. Background Technology

[0002] In electrified railway systems, the non-crossing contact wire turnout is a key component, playing a crucial role in ensuring a smooth transition of the pantograph between different contact wires and maintaining continuous power supply to electric locomotives. When the pantograph passes through a non-crossing contact wire section, the contact wire height needs to change dynamically to achieve the transition. This process can cause problems such as the height difference between the two ends of the contact wire, uneven tension distribution along the line, and changes in sag, directly affecting the position of the contour points and the pantograph-catenary coupling performance.

[0003] Traditional models often simplify the contact wire into a straight line or a single-form cable element. For example, the paper "Study on the Length of the Effective Vibration Area of ​​the Catenary in a Pantograph–Catenary Interaction System" published in Applied Sciences, Vol. 14, No. 15, 2024, used an Euler-Bernoulli beam to establish a contact wire model. However, this model did not fully consider the uneven tension distribution and sag differences caused by dynamic height changes, and ignored the significant differences in contact wire morphology near the mid-span and nodes. Consequently, the influence of tension and sag on the contact wire morphology was compromised, resulting in a large deviation between the model and actual working conditions.

[0004] Currently, existing research has not established a dynamic correlation model between contact wire tension, sag, and elevation difference, and therefore cannot accurately describe the mechanism of elevation point position changes. Existing models treat the contact wire and catenary as Euler-Bernoulli beam elements under tension, and set the sag by adjusting the length of the droppers, but do not consider the influence of elevation difference on tension distribution.

[0005] Therefore, there is an urgent need for an improved modeling method that can accurately reflect the dynamic height changes of the contact wire, uneven tension distribution, and the influence of sag, in order to improve the accuracy and reliability of pantograph-catenary coupling performance analysis in sections without crossover turnouts. Attached Figure Description

[0006] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0007] Figure 1 This is a comparison diagram of contact forces at different elevation positions according to the present invention;

[0008] Figure 2 This is a comparison diagram of contact forces at different pull-out values ​​according to the present invention;

[0009] Figure 3 This is a schematic diagram of the contact wire equivalent to a cable unit according to the present invention;

[0010] Figure 4 These are model diagrams of two improved contact wire cable units of the present invention;

[0011] Figure 5 This is the initial configuration diagram of the No. 18 non-crossing turnout section of the present invention;

[0012] Figure 6 This is a comparison chart of the calculated data and the measured data of this invention.

[0013] Figure 7 This is a comparison diagram of the measured contact force and the simulated contact force of the present invention. Summary of the Invention

[0014] This invention aims to solve the problem that the existing modeling of the contact wire in the No. 18 non-crossing turnout section does not fully consider the uneven tension distribution, sag differences and height differences caused by dynamic height changes, resulting in inaccurate pantograph-catenary coupling performance analysis. It provides an improved modeling and analysis technique based on the hybrid cable element theory to accurately describe the contact wire morphology and quantify the influence of multiple parameters on pantograph-catenary coupling, thereby improving the fit between the model and actual working conditions.

[0015] To achieve the above objectives, the technical solution adopted by this invention is an improved modeling and analysis method for pantograph-catenary coupling of non-intersecting lines in electrified railways, characterized by including: accurate form-finding modeling of the contact network based on hybrid cable units, construction of a dynamic pantograph-catenary coupling model, and methods for model verification and performance analysis;

[0016] The precise form-finding modeling of the contact network based on hybrid cable elements classifies cable element types according to the positional characteristics of the contact line. For areas close to nodes and with small sag, parabolic cable elements are used for simulation, and bending deformation equations are established considering sag, tension, and the height difference between the two ends.

[0017]

[0018] Where w is the self-weight per unit length of the cable, T is the tension, L is the length of the cable element, and h is the height difference. For areas with large mid-span sag and small tension, catenary linear cable elements are used, and the bending deformation is determined based on the distributed load and horizontal tension:

[0019]

[0020] Among them, T h Let w represent the horizontal tension and w represent the distributed load. Using the static form-finding results as initial conditions, and considering the nonlinearity of the contact wire and the variation of stiffness with displacement, the dynamic differential equation is established:

[0021]

[0022] Among them, M c Given the overall mass matrix, the element mass matrix M is obtained by integration. e =ρL0I line clamp mass matrix M j =m j I was assembled; C c K is the overall damping matrix; et Q represents the overall tangential stiffness matrix, reflecting the dynamic relationship between tension, relaxation, and displacement. e For external response force;

[0023] The pantograph-catenary dynamic coupling model is constructed by equating the pantograph with a mass-velocity model and establishing the dynamic equations:

[0024]

[0025] The contact force model is established using the penalty function method:

[0026] F c =k c (z p -z c )

[0027] Solving the equations of the overhead contact system and the pantograph to solve the coupled system:

[0028]

[0029] Among them, M p Let C be the mass matrix of the pantograph mass block. p Let K be the damping coefficient matrix of the pantograph mass. p Let z be the elastic stiffness matrix of the pantograph mass. p For the vertical displacement of the pantograph, z c Q represents the vertical displacement of the contact line. c For lift, k c For contact stiffness.

[0030] The model verification and performance analysis method adopts a multi-dimensional verification mechanism and performance analysis with different parameters. It uses measured parameters from turnout No. 18 (as shown in Table 1) and verifies the model based on the EN50318 standard, including:

[0031] (1) Geometric verification: Compare the pull-out value, guide height and other parameters to ensure that the initial configuration deviation is less than 5%;

[0032] (2) Dynamic verification: Solve the coupling equations using the Newmark method and compare parameters such as contact force and lifting displacement to ensure that the maximum contact force and standard deviation meet the standards.

[0033] Table 1. Parameters of the overhead contact system in the turnout section

[0034]

[0035] Quantitative analysis of the impact of contour points and pull-out values ​​on pantograph-catenary coupling:

[0036] (1) A decrease in the height of the contour points leads to a decrease in contact line tension and an increase in sag, thus expanding the range of contact force fluctuations, such as... Figure 1 As shown, when the elevation point rises from -24mm to -20mm, the contact force fluctuation range narrows from 21.80N-194.41N to 23.21N-186.90N;

[0037] (2) Figure 2 As shown, different pull-out values ​​have little effect on the contact force waveform, as they only change the horizontal position and do not affect the vertical dynamic characteristics.

[0038] In a preferred embodiment of the present invention, the precise form-finding modeling of the contact network based on hybrid cable units includes: when the cable unit is close to the node, the sag is small and the tension is large, so a parabolic cable unit is selected for contact network modeling; when the cable unit is located in the middle of the span and far from the node, the sag is large and the tension is small, so a catenary cable unit is selected for modeling; after determining the cable unit, the mass, stiffness and damping of the cable unit are calculated, and the corresponding components are assembled into a global matrix to establish the dynamic equation of the contact network.

[0039] In a preferred embodiment of the present invention, the pantograph-catenary coupling performance analysis at the junction is further included. The pantograph-catenary coupling performance analysis at the junction uses the improved contact wire dynamic equation and the pantograph dynamic equation of the two mass blocks to establish the pantograph-catenary coupling equation. The established pantograph-catenary coupling equation analyzes the influence of the contour point and pull-out value parameters of the contact wire at the junction on the pantograph-catenary coupling performance. The analysis results show that the contour point parameters have a significant influence on the pantograph-catenary coupling performance.

[0040] This invention addresses the shortcomings of the prior art and has the following beneficial effects:

[0041] (1) This invention addresses the problems of uneven tension distribution and sag variation caused by dynamic height changes of the contact wire in sections of electrified railways without crossovers. It proposes a contact wire form-finding model based on a hybrid cable unit of parabolic and catenary shapes. The unbalanced force of the cable unit is solved iteratively by the Newton-Raphson method. The contact wire dynamic equation considering nonlinearity is established, and a pantograph-catenary dynamic coupling model is constructed.

[0042] (2) The improved model was verified by measured data from turnout No. 18. The geometric parameter deviation was less than 5%, and the standard deviation of the contact force at 110km / h was 27.6N, which meets the EN50318 standard. Performance analysis showed that the height of the contour point is the main influencing factor of pantograph-catenary coupling. When it increases from -24mm to -20mm, the contact force fluctuation range narrows by 7.5%, and the stability of the pantograph head displacement is improved by 30%, while the pull-out value has a weak impact on dynamic performance.

[0043] (3) This technology accurately describes the contact line morphology and tension-sag-height difference coupling relationship through hybrid cable unit theory and dynamic correction method, providing a quantitative analysis tool for pantograph-catenary system in non-intersecting turnout sections. Field application shows that optimizing contour points can significantly improve current collection quality and support smooth transition of high-speed trains.

[0044] (4) The invented model and analysis method break through the limitations of traditional single modeling and form a complete technical system from theoretical modeling to engineering verification, providing key technical support for the design and maintenance of the electrified railway catenary system. Detailed Implementation

[0045] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein. Therefore, the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0047] like Figure 3 As shown, cable elements are used to simulate the contact wire and catenary of the overhead contact system. By applying the finite element analysis principle, the contact system is divided into several small cable elements. In the three-dimensional coordinate system, the cable elements are located between node A and node B. T1 and T2 are the tensions at the two ends of the cable element, which are decomposed into element nodal forces F1 to F3 and F4 to F6. L0 represents the initial length of the cable element, while l x l y and l z These represent the distances between two nodes in the cable element along the x, y, and z directions, respectively. Furthermore, l x l y l z The relationship between F1 to F6 is as follows:

[0048] Where w represents the weight per unit length, E represents the elastic modulus, and S represents the cross-sectional area of ​​the cable element.

[0049] For the equilibrium conditions of the cable element, the nodal forces F4 to F6 at the two ends of the cable element can be expressed by the following equations:

[0050] F4=-F1, F5=-F2, F6=-(wL0+F3) (2)

[0051] Where wL0 represents the gravity of the cable element.

[0052] The relationship between variables can be represented by a matrix, as shown below:

[0053] Δl=F c ΔF A +F g ΔL0 (3)

[0054] in

[0055]

[0056] Δ represents the coordinate increment in different directions, F c and F g Let Δl and ΔF represent respectively. A The incremental relationship between ΔL0 and ΔL0.

[0057] To simplify the calculation, ΔF is used in equation (3). A Separate it out and replace Δl with the coordinate increment ΔX. Equation (3) is transformed into the incremental differential equation form used in the nonlinear finite element method, as shown below.

[0058]

[0059] In equation (4), the incremental changes ΔX of the cable element nodes A and B in the x, y, and z directions are given by the following equation.

[0060] ΔX=[Δx A Δy A Δz A Δx B Δy B Δz B ] T (5)

[0061] Similarly, the force condition of node B in the cable element can be expressed as follows:

[0062] ΔF B =[00 w] T ΔL0-ΔF A (6)

[0063] By combining equations (4) and (6), the relationship between the nodal force ΔF, incremental change ΔX, and length ΔL0 of the cable element is obtained as follows:

[0064] in Represents the tangent stiffness matrix. It is a tangent matrix that relates nodal forces to the length of cable elements. and for

[0065]

[0066] Based on the structure of the overhead contact system, the overall incremental balance equation of the overhead contact system is derived as follows:

[0067] ΔP c =PF=K c ΔX+K g ΔL0 (9)

[0068] The total tangent matrix K of the overhead contact system c and K g ,Depend on and The result is obtained through integration. F represents the equivalent load acting on the nodes of the cable element, consisting of nodal forces. P represents the load acting on the cable element, ΔP. c This indicates an unbalanced force in the structure.

[0069] like Figure 4 As shown, the two improved catenary cable unit models include the parabolic cable unit model and the catenary cable unit model. Applied to the aforementioned catenary system, the following steps are included: Figure 4 As shown in (a), the cable element is close to the two nodes, with a smaller sag and larger tension in the contact line. Its shape conforms to the parabolic equation. Considering the sag f, tension T, and height difference h on the cable, according to the principle of statics, the bending deformation z u Determine according to formula (10).

[0070]

[0071] like Figure 4 As shown in (b), the cable element is located at the mid-span, with a large sag and small tension in the contact line. Its shape conforms to the catenary equation. This cable element has a uniformly distributed load q (such as its own weight) along its length. Consider the distributed load q and the horizontal tension T on the cable. h According to the principles of statics, the bending deformation z m The following is confirmed:

[0072]

[0073] Where l represents the horizontal length of the cable element.

[0074] Applying the above cable element equations to the overhead contact system includes the following steps:

[0075] Step 1: Input the known parameters w, ES and L0. If the cable element is not located at the mid-span, a parabolic cable element should be selected. According to formula (10), the coordinates of point A are (x... A ,y A ,z uA The coordinates of point B are (x, y). B ,y B ,z uB If the cable element is located at mid-span, a catenary cable element should be selected. According to formula (11), the A and B coordinates of the large sag cable element matching the contact line are respectively (x... A ,y A ,z mA ) and (x B ,y B ,z mB ).

[0076] Step 2: Calculate l x0 =x A -x B ,l y0 =y A -y B ,l z0 =z A -z B And set initial values ​​for F1, F2, and F3;

[0077] Step 3: Combine equation (1) with F1, F2 and F3, and calculate l using equations (2) and (3) respectively. x ,l y and l z This leads to the difference Δl (Δl={l x0 -l x ,l y0 -l y ,l z0 -l z}).

[0078] Step 4: Based on engineering experience, set the threshold to 10. -6 If ||Δl||≥10 -6 If yes, proceed to the next step. Otherwise, proceed to step 6.

[0079] Step 5: If And update F A =F A +ΔF A Then return to step 3;

[0080] Step 6: Terminate the iteration and output the values ​​of F1, F2 and F3.

[0081] The coordinate values ​​of each node are taken from the static calculation results as the initial values. During the dynamic calculation process, these values ​​will change continuously with the iterative process to reflect the dynamic response of the catenary under external forces. Considering the nonlinearity of the initial equilibrium form-finding of the catenary and the change of stiffness with displacement, the differential equation of the catenary dynamics is shown in Equation (12).

[0082]

[0083] Where M c K represents the total mass matrix of the catenary. et C represents the global tangential stiffness matrix of the catenary. c This represents the overall damping matrix of the catenary. Indicates acceleration. Let Q represent velocity, z represent displacement, and Q represent velocity. e F represents the external response force acting on the catenary, Δz is the displacement increment of each cable element of the catenary, and F e It is the internal force of each cable element, ΔP c These are the nodal unbalanced forces of each element.

[0084] Based on the improved overhead contact line model, a dynamic coupling model of the pantograph and contact line was established. Here, a dual-mass block model is adopted for the pantograph. The dynamic equations of the pantograph are as follows:

[0085]

[0086] The key parameters of the pantograph mass block model are represented by these variables, where m represents the mass of each mass block, k represents the elastic stiffness of the joints between the mass blocks, c is the damping coefficient of each mass block, z represents the vertical displacement of each mass block, and F... c Q represents the contact force of the pantograph-catenhead system. c This indicates the lift generated by the pantograph.

[0087] In this system, the relative permeation displacement (z) at the contact surface is used as a basis. p -z c A model of the interaction between the pantograph head and the contact wire is established using the penalty function method, with the contact force F... c Given by formula (14):

[0088]

[0089] Where, k c This indicates the contact stiffness between the pantograph head and the contact wire, z pThis represents the vertical displacement z of the pantograph head. c This indicates the vertical displacement at the point of contact between the contact wire and the pantograph.

[0090] By solving equations (12), (13), and (14) simultaneously, the overall dynamic incremental differential equation of the pantograph-contact wire coupling system can be established as follows:

[0091]

[0092] Where M, C, and K represent the overall mass matrix, overall damping matrix, and overall stiffness matrix, respectively. The subscript c represents the overhead contact line, and the subscript p represents the pantograph. The specific expressions are as follows:

[0093]

[0094] Example

[0095] Experiment 1: The purpose is to verify the accuracy of the improved catenary model in catenary modeling of sections without crossing turnouts. As shown in Table 1, taking the catenary parameters of a section without crossing turnouts as an example, the initial configuration model of turnout No. 18 without crossing turnouts was established using the improved model. The results show that the initial configuration model is correct and can describe the actual configuration of the catenary, with the specific shape as shown... Figure 5 As shown in Table 1. Secondly, based on the parameters in Table 1, the data calculated using the improved model were compared with the measured data. The deviation of the calculated results was within 5%. The comparison of the calculation results is shown below. Figure 6 As shown.

[0096] Experiment 2: The purpose was to verify the effectiveness of the pantograph-catenary coupling performance analysis based on the improved overhead contact line model. First, the pantograph-catenary coupling model before entering the No. 18 non-crossing turnout section was verified using the European standard EN50318. The operating speed was set according to the speed specified in EN50318, and the test results are shown in Table 2. Second, according to the speed requirements for passing through the No. 18 non-crossing overhead contact line turnout in TB / T2477-2006, two measured operating conditions were selected to verify the pantograph-catenary coupling model of the No. 18 non-crossing turnout section. These two operating conditions were: the pantograph transitioning from the main line contact line to the siding contact line at a speed of 110 km / h; and the pantograph transitioning from the siding contact line to the main line contact line at a speed of 80 km / h. Figure 7 As shown, the simulation data almost matches the measured data.

[0097] Table 2. Contact Force Statistics

[0098]

[0099] In summary, the improved modeling and analysis method for pantograph-catenary coupling of electrified railway turnouts without intersections, proposed in this invention, achieves improved modeling of the contact network and analysis of pantograph-catenary coupling performance of electrified railway turnouts without intersections through precise shape-finding modeling of the contact network based on hybrid cable units, construction of dynamic pantograph-catenary coupling model, model verification and performance analysis, effectively ensuring accuracy under various working conditions.

[0100] Based on the preferred embodiments of the present invention described above, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A mathematical model for accurate shape finding of the entire turnout section of High-Speed ​​Railway Line 18, characterized in that, Includes the following steps: S1. Constructing a catenary form-finding model based on hybrid cable elements: Divide the catenary system into several cable elements, and select parabolic cable elements or catenary cable elements for each segment according to the location characteristics of the contact line. Parabolic cable elements are used in areas close to nodes with small sag, and bending deformation equations are established considering sag, tension, and height difference between the two ends. Catenary cable elements are used in areas with large sag and small tension at mid-span, and bending deformation equations are determined based on distributed loads and horizontal tension. S2. Derivation of the Unbalanced Force Calculation Model for Cable Element: In a three-dimensional coordinate system, establish the relationship equation between the nodal forces at both ends of the cable element and the coordinate increment. Considering parameters such as unit length self-weight, elastic modulus, and cross-sectional area, construct the calculation equation for the unbalanced force of the cable element. Iterate the nodal forces using the Newton-Raphson method to quantify l. x l y l z The relationship between F1 to F6 is shown in the following equations: Among them, l x l y and l z F1 to F6 represent the lengths between two nodes in the x, y, and z directions of the cable element, respectively; F1 to F6 are the nodal force components; L0 is the initial length of the cable element; E is the elastic modulus; S is the cross-sectional area; and w is the weight per unit length. S3. Establish the corrected dynamic model of the contact network: Assuming that the right-side nodes of the contact wire and the catenary are fixed, the static calculation results are used as the initial length of the cable element and the node coordinates. Considering the nonlinearity of the initial equilibrium form-finding of the contact network and the change of stiffness with displacement, the dynamic differential equation of the contact network is constructed, and the expression is: Among them, M c The overall mass matrix of the overhead contact system is obtained by integrating the mass matrix M of the contact element. e =ρL0I line clamp mass matrix M j =m j I was assembled; C c K represents the overall damping matrix of the overhead contact system. et Q represents the overall tangential stiffness matrix of the overhead contact system, reflecting the dynamic relationship between tension, sag, and displacement. e For external response force; S4. Constructing the pantograph-catenary dynamic coupling model: The pantograph is simplified into a dual-mass block model, and the pantograph dynamic equations are established. Combined with the improved catenary model, the contact force is calculated using the penalty function method. The overall dynamic incremental differential equations of the pantograph-catenary coupling system are solved simultaneously, as follows: Pantograph dynamic equations: Contact force equation: F c =k c (With p -With c ) By combining the differential equations of catenary dynamics, pantograph dynamics, and contact force, a global coupled equation is established: Among them, M p Let C be the mass matrix of the pantograph mass block. p Let K be the damping coefficient matrix of the pantograph mass. p Let z be the elastic stiffness matrix of the pantograph mass. p For the vertical displacement of the pantograph, z c Q represents the vertical displacement of the contact line. c For lift, k c For contact stiffness. S5. Model Verification and Performance Analysis: Using field measurement parameters of No. 18 non-crossing turnouts, the improved model was verified strictly in accordance with the EN50318 standard to ensure that the calculated data and measured data of contact force, initial contact zone parameters, etc., deviated from the actual data by less than 5%. The influence of contour points and pull-out values ​​on pantograph-catenary coupling performance was analyzed, and the change in contour point height was determined to be the main influencing factor. The decrease in its height will lead to an expansion of the contact force fluctuation range. As shown in the figure, when the contour point increases from -24mm to -20mm, the contact force fluctuation range narrows from 21.80N-194.41N to 23.21N-186.90N.

2. The method according to claim 1, characterized in that, The bending deformation equation of the parabolic cable element is: Where h is the height difference between the two ends of the cable element, and L is the length of the cable element. The bending deformation is determined by considering sag, tension and height difference through static principles.

3. The method according to claim 1, characterized in that, The bending deformation equation of the catenary linear cable element is: Among them, T h The horizontal tension is denoted by , and the distributed load is denoted by w. The bending deformation is determined based on the distributed load and horizontal tension characteristics of the cable element at the mid-span position.

4. The method according to claim 1, characterized in that, The solution steps of the Newton-Raphson iteration method include: S1. Input the known parameters w, E, S, L0, select the parabolic or catenary model according to the position of the cable element, and determine the initial coordinates of the nodes; S2. Calculate the initial coordinate difference l x0 l y0 l z0 Set the initial values ​​of nodal forces F1, F2, and F3; S3, Substitute into the unbalanced force equation to calculate l x l y and l z Solve for the coordinate difference Δl={l x0 -l x , l y0 -l y ,l z -l z0 }); S4, when ||Δl||≥10 -6 At that time, update the node force F. A =F A +ΔF A The calculation is iterated until the threshold condition is met, at which point the iteration terminates and the nodal force value is output.

5. The method according to claim 1, characterized in that, The model validation steps include: S1. Geometric parameter verification: Compare the parameters such as the pull-out value of the main line and lateral line, the guide height, and the span of the improved model with the measured data to ensure that the initial configuration is consistent with the actual catenary configuration. S2. Dynamic performance verification: The Newmark method is used to solve the differential equation of pantograph-catenary coupling. The dynamic parameters such as contact force and lifting displacement under different speed conditions are compared to ensure that the maximum contact force, average contact force and standard deviation meet the requirements of EN50318 standard.

6. The method according to claim 1, characterized in that, The analysis of the impact of contour points on pantograph-catenary coupling performance includes: S1. Set the elevation points to -24mm, -20mm, -15mm, and -10mm, and numerically simulate the range of contact force fluctuation and pantograph displacement at different elevation positions. S2. Analysis shows that a decrease in the height of the contour points leads to a decrease in the contact wire tension and an increase in the sag, causing the pantograph to enter the initial contact area earlier, resulting in increased pantograph-catenary coupling vibration, a decrease in the average contact force, and a deterioration in the stability of the pantograph head displacement.

7. An improved modeling and analysis system for pantograph-catenary coupling of electrified railways without crossing lines, implementing the method described in any one of claims 1-6, characterized in that, include: S1. Cable element partitioning and shape finding module: Based on parabolic and catenary cable element models, it automatically selects the cable element type according to the contact line location characteristics (near the node / mid-span), calculates bending deformation and node coordinates, and constructs the contact network geometry. S2, Unbalanced Force Calculation Module: Implements the Newton-Raphson iterative algorithm to solve the unbalanced force equation of the cable element, calculates the nodal force and tension distribution, and quantifies the coupling relationship between height difference and sag. S3, Dynamic Modeling Module: Establishes the dynamic equations of the contact network, calculates the overall mass matrix, damping matrix and tangential stiffness matrix, and simulates the dynamic response of the contact network under external forces. S4. Pantograph-Catenary Coupling Analysis Module: Integrates the pantograph dual-mass block model and the catenary model, uses the penalty function method to calculate the contact force, solves the dynamic incremental differential equation of the pantograph-catenary coupling system, and analyzes parameters such as contact force and lifting displacement. S5. Data Verification and Optimization Module: Import measured data from turnout No. 18, verify the accuracy of the improved model, analyze the impact of contour points and pull-out values ​​on pantograph-catenary performance, and generate parameter optimization schemes.

8. The system according to claim 1, characterized in that, The cable unit partitioning shape-finding module includes: S1, Parabolic Cable Element Calculation Unit: Based on Equation Calculate the bending deformation and coordinates of the contact line near the node. S2, Catenary Linear Cable Element Calculation Unit: Based on Equation Calculate the bending deformation and coordinates of the contact line at mid-span.

9. The system according to claim 7, characterized in that, The iterative solution threshold of the unbalanced force calculation module is set to 10. -6 The equation KΔX=ΔP is simplified through matrix operations, where K is the tangent stiffness matrix. et and Integrating, we obtain ΔX as the nodal coordinate increment and ΔP as the unbalanced force increment. By deleting rows and columns in the matrix corresponding to the boundary conditions, we ensure that the system of equations is solvable.

10. The system according to claim 7, characterized in that, The data verification and optimization module includes: S1. Visualization Verification Unit: Using the high-speed railway non-crossing turnout adjustment software (version V2.0), the initial configuration of the No. 18 non-crossing turnout established by the improved model is verified in three dimensions and the geometric accuracy indicators such as guide height deviation (≤3mm) and pull-out value deviation (≤5mm) are output. S2. Performance Analysis Unit: Set different contour points (-24mm to -10mm) and pull-out values ​​(50mm, 75mm, 100mm), analyze parameters such as contact force fluctuation range (range ≤200N) and pantograph head displacement standard deviation (≤8mm), and generate a correlation model between contour point height and pantograph-catenary coupling performance to provide a basis for parameter optimization.

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