Curve track wheel-rail interaction simulation method based on double-coordinate system collaborative modeling

Abstract

The invention discloses a curve track wheel-rail interaction simulation method based on double-coordinate system collaborative modeling. The method comprises the steps that a train model is established according to train physical parameters; generating an orbit model according to the curve orbit control points and the orbit physical parameters; a moving coordinate system and a fixed coordinate system are used for establishing a kinematics equation of the train model and the track model, the moving coordinate system is used for describing vehicle motion, the fixed coordinate system is used for describing track motion, and the kinematics equation under the double coordinate systems is established through the kinematics mapping relation between the moving coordinate system and the fixed coordinate system; the contour lines of the wheels and the track are extracted, a contact coordinate system is established under the moving coordinate system based on the geometric contact condition of the contour lines, and the wheel-rail contact force in the kinematics equation and the train response under the curve track are solved under the contact coordinate system; and drawing the obtained train response and wheel-rail contact force into a curve, and analyzing a calculation result. Efficient simulation of complex working conditions such as a curve track can be achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of dynamics analysis, and in particular to a curved track wheel-rail interaction simulation method based on dual coordinate system collaborative modeling. Background Art

[0002] The dynamic analysis of wheel-rail interaction is a complex problem in the engineering field. Its strong nonlinearity and high computational time-consuming characteristics have long restricted the simulation accuracy and efficiency. Existing research methods are mainly divided into two categories: substructure method and integration method. The substructure method regards the vehicle and track as independent subsystems and realizes coupling through external forces. Although explicit integration and predictive correction algorithms have been developed, it is necessary to frequently deal with deformation coordination and force balance between subsystems, and it relies on multi-platform data exchange, resulting in cumbersome calculation processes; the integration method adopts a unified modeling framework, treats the wheel-rail contact force as an internal force, and realizes the coupling of geometric relationship and mechanical response through dedicated contact units. Although it avoids the problem of substructure coordination, the existing models are mostly limited to uniform linear motion conditions, and it is difficult to accurately simulate nonlinear behaviors such as multi-point contact and wheel rim collision in complex scenarios such as curved tracks. Both methods have significant limitations in adaptability to non-uniform motion. Traditional models often require the preset ideal track geometry, resulting in insufficient engineering practicality. Although recent studies have attempted to combine multi-body dynamics and finite element methods to construct a three-dimensional contact model and introduced Hertz contact theory and Polach creep formula to improve calculation accuracy, they still face challenges such as insufficient universality of kinematic description and low calculation efficiency under complex working conditions.

[0003] The invention patent with patent announcement number CN 117078812 B discloses a three-dimensional animation simulation method, storage medium and device for rail transit trains. The method includes: obtaining a rail transit line vector map based on the point, line and surface data of the rail transit line, and measuring the geographical location of each subway station and the position between stations; passing the rail transit line vector map into the Map class of the map engine for WebGIS developers, and giving initial coordinates and map containers, constructing a rail transit digital twin map, and constructing a rail transit train operation scene; in the rail transit train operation scene, performing rail transit train simulation linear animation according to the real-time speed of the rail transit train on the track, the geographical location of each subway station, and the position between stations; initializing the physical world in the rail transit train operation scene; simulating and calculating the initialized world, and synchronously updating it to the rail transit train simulation linear animation.

[0004] The invention patent with patent announcement number CN 118192301 B discloses a wheel-rail anti-skid and anti-spin adhesion control simulation method considering the drive system, including the following steps: first, a heavy-duty train longitudinal dynamics model considering the locomotive drive system is established through a first simulation platform; second, a wheel-rail anti-skid and anti-spin adhesion control model is established through a second simulation platform; then, the heavy-duty train longitudinal dynamics model of the first simulation platform and the wheel-rail anti-skid and anti-spin adhesion control model of the second simulation platform are jointly simulated, and data are exchanged at a set time node. When the data is exchanged, the adhesion control process is completed. The present invention can accurately consider the influence of the drive system on the wheel-rail adhesion control, and complete the adhesion control process through real-time joint simulation of dynamics and adhesion control.

[0005] Traditional wheel-rail interaction simulation methods need to frequently deal with the deformation coordination and force balance between moving parts (vehicles) and fixed parts (tracks / bridges) in the dynamic analysis of train-track systems, which makes the calculation process cumbersome and easy to introduce errors. At the same time, it relies on multi-platform collaboration (such as commercial software SIMPACK, ABAQUS, etc.) and data exchange requirements, which increases the implementation cost and flexibility limitations. Therefore, it is urgent to develop a curved track wheel-rail interaction simulation method based on dual coordinate system collaborative modeling. Summary of the invention

[0006] In view of this, the purpose of the present invention is to propose a curved track wheel-rail interaction simulation method based on dual coordinate system collaborative modeling, which describes vehicle motion through a mobile coordinate system and characterizes track constraints through a fixed coordinate system, separates the dynamic responses of moving parts and fixed parts through dual coordinate systems, supports curved track dynamic contact modeling, constructs a new wheel-rail contact unit to uniformly process contact geometry and mechanical responses, and can be applied to both uniform linear motion conditions and curved track motion conditions. In addition, full-process modeling is realized based on an open source finite element platform (such as OpenSees), which reduces dependence on commercial software, improves the portability and cost-effectiveness of the method, and realizes efficient simulation of complex conditions such as curved tracks.

[0007] In order to achieve the above technical objectives, the technical solution adopted by the present invention is: A method for simulating wheel-rail interaction on a curved track based on collaborative modeling of dual coordinate systems comprises the following steps: Step 1, establishing a train model according to the physical parameters of the train; generating curved track control points according to the curved track control point generation program, and then generating a track model according to the curved track control points and the track physical parameters; Step 2: Use a dual coordinate system based on a mobile coordinate system and a fixed coordinate system to establish the kinematic equations of the train model and the track model, where the mobile coordinate system is used to describe the vehicle motion, and the fixed coordinate system is used to describe the track motion, and the kinematic equations of the train model and the track model in the dual coordinate system are jointly established through the kinematic mapping relationship between the mobile coordinate system and the fixed coordinate system; Step 3: According to the model information corresponding to the train model and the track model, the contour lines of the wheels and the tracks are extracted, and a contact coordinate system is established in the moving coordinate system based on the geometric contact of the contour lines. The wheel-rail contact force in the kinematic equation and the train response on the curved track are solved in the contact coordinate system. Step 4: Plot the obtained train response and wheel-rail contact force into a curve, and analyze the calculation results.

[0008] Furthermore, the step 1 specifically includes: Step 11: determine the train physical parameters and track physical parameters corresponding to the train and track to be calculated, wherein the train physical parameters include the train model, and the track physical parameters include the track model, curve track style, and curve function type; Step 12: Establish a train model based on actual calculation examples and train physical parameters; Step 13, write a curve track control point generation program in Matlab, and make a user input interface and an image generation interface; Step 14: Input the geometric parameters corresponding to the track on the user input interface, generate a program drawing and generate the curve track control points according to the curve track control point generation program; Step 15: Establish a track model based on the actual calculation example, the curved track control points and the track physical parameters, and display it on the image generation interface; Step 16: Save the model information corresponding to the train model and track model into the target folder.

[0009] Furthermore, the curve track control point generation program includes the following modules: Parametric input module: supports users to input track straight segment length, transition curve length, circular curve length, circular curve radius, track gauge and node spacing; Control point generation module: Based on the transition curve and arc integration algorithm, the coordinates of the track centerline control points are automatically calculated, and the coordinates of the inner and outer track control points are generated through the normal offset algorithm; Dynamic visualization module: real-time rendering of the track 3D model, supporting simultaneous display and partial zoom of the center line, inner rail and outer rail.

[0010] Furthermore, the mathematical expressions of the transition curve and the circular curve are as follows: A transition curve is a curve whose curvature changes linearly with the arc length. It is used to connect straight line segments and circular curve segments. Its curvature is defined as: (1) in, The arc length The curvature of R is the radius of the target circle, L s is the total length of the transition curve; The expression of the transition curve is expressed in the form of a parametric equation using the Fresnel integral form: (2) in, and They represent the arc length of the control point of the transition curve. Where x and y coordinate, is the tangent angle, is the integral independent variable; in the arc length Tangent angle at satisfy: (3) in, A is the parameter of the transition curve, which characterizes the rate of change of curvature; In actual programming, Taylor expansion or numerical integration is used to approximate the relaxation curve: (4) The parametric equation of the circular curve is expressed as: (5) in, and They represent the arc length of the circular curve control point Where x and y coordinate; According to track gauge and curvature direction, the inner rail control point coordinates and the outer rail control point coordinates are the normal offsets of the track centerline control point coordinates, specifically expressed as: (6) in, Indicates the coordinates of the inner track control points, represents the coordinates of the outer track control points, represents the coordinates of the track centerline control point, Represents the centerline unit normal vector and points to the center side of the circular curve.

[0011] Furthermore, the step 2 specifically includes: Step 21, the vehicle model is regarded as a moving part in a moving coordinate system, and the track model is regarded as a stationary part in a fixed coordinate system; Step 22: Construct a dual coordinate system collaborative system based on the mobile coordinate system and the fixed coordinate system, establish the kinematic equation in the fixed coordinate system, discretize the kinematic equation in the fixed coordinate system and combine it with the displacement, velocity, and acceleration mapping relationship in the mobile coordinate system to form a unified correction force term, and establish the kinematic equations of each part of the train model and the track model in the mobile coordinate system and the fixed coordinate system.

[0012] Furthermore, the step 22 specifically includes: Step 221: According to the D'Alembert principle, the basic formula of the kinematic equations of the train model and the track model in a fixed coordinate system is: (7) Among them, M represents the mass matrix of the train model and the track model, C represents the damping matrix, represents the internal force matrix of the train model and the track model, represents the relative displacement of the contact point between the train wheel and the track, F represents the external load matrix, and They represent the second and first derivatives of the displacement u in the fixed coordinate system, i.e., acceleration and velocity; Step 222: Use the Newmark-beta method to discretize equation (7): (8) in, n and n +1 represents the current time step and the next time step in the discrete solution process. represents the discrete time step, and They represent the parameters of the Newmark-beta method, and their values ​​are , ; Rewrite formula (7) as: (9) (10) in, is the unbalanced force of the kinematic equation. The solution obtained by setting it to zero is the displacement response of the system at the current moment. represents the external load term; Step 223, the displacement, velocity and acceleration in the mobile coordinate system have the following mapping relationships with the displacement, velocity and acceleration in the fixed coordinate system: (11) (12) (13) Among them, u, and They represent displacement, velocity and acceleration in a fixed coordinate system respectively; , and They represent the displacement, velocity and acceleration of the object in the moving coordinate system respectively; , and They represent the displacement, velocity and acceleration of the mobile coordinate system itself as reference parameters; Step 224: Discretize formulas (11)-(13) and substitute them into (8) to obtain: (14) According to (15) in, i and i +1 indicates the current iteration step and the next iteration step in the solution process; as well as (16) get: (17) Substituting formula (17) into formulas (9)-(10), we obtain: (18) in: (19) because This term is only related to external damping and has nothing to do with internal damping. This term is related to the external load term Forming a correction force term under a curved track , realizing the unification of the form of the kinematic equations in the mobile coordinate system and the fixed coordinate system, thereby achieving the simultaneous kinematic equations.

[0013] Furthermore, the step 3 specifically includes: Step 31: according to the model information corresponding to the train model and the track model, use dense point linear fitting to fit the contours of the wheel and the track; Step 32: Establish a contact coordinate system in the moving coordinate system based on the geometric contact of the contour line, wherein the contact coordinate system x Axis direction and moving coordinate system xThe contact coordinate system is defined according to the embedding point of the wheel and the track. y Axis direction; through the contact coordinate system x Axis and y The cross product of the axes gives the contact coordinate system z Axis direction; Step 33: Use the Newton-Raphson implicit iteration method to calculate the n The first step under the time i The displacement of the iteration step; Step 34, determine whether it has converged, if not, proceed to step 35; if yes, continue to check whether all time steps are completed, if yes, record the response of each time step; if not, proceed to the next time step and return to step 33; Step 35: Use the Newmark-beta method to calculate the n The first step under the time i The speed of the iteration step; Step 36: Use the nonlinear Hertz formula to calculate the wheel-rail normal contact force, and use the Polach formula to calculate the wheel-rail tangential contact force; Step 37, converting the wheel-rail normal contact force and the wheel-rail tangential contact force to obtain the wheel-rail coupling unit internal force; Step 38: Update the kinematic equation according to the internal force of the wheel-rail coupling unit; Step 39, enter the next iteration step and return to step 33.

[0014] Furthermore, in step 36, the nonlinear Hertz formula is used to calculate the wheel-rail normal contact force, which specifically includes: Maximum embedding depth based on wheel and rail contours , and the nonlinear Hertz formula is used to calculate the wheel-rail normal contact force; The wheel-rail normal contact force is obtained by the following formula: (20) in, represents the wheel-rail normal contact force, K It represents the wheel-rail normal contact force coefficient, which is related to the curvature and elastic modulus of the wheel-rail. 1.5 represents the power value.

[0015] Furthermore, the wheel-rail tangential contact force is calculated using the Polach formula in step 36, which specifically includes: The wheel-rail creep rate is defined as a physical quantity related to the relative speed between the wheel and the rail. The wheel-rail creep rate is calculated as follows: (twenty one) in, expressx The translation creep rate in the direction, express y The translation creep rate in the direction, Indicates winding z Rotational creep rate for axial rotation, and The wheel contact point and the track contact point are respectively x and y The relative speed difference in direction, Indicates that the wheel contact point and the track contact point are around z The relative speed difference in the direction of shaft rotation, Indicates the travel speed; The Polach formula describes the relationship between the wheel-rail tangential contact force and the creep rate. The Polach formula is expressed as: (twenty two) in, Representation and and The associated corrected translational creep rate, F tr and F ys denote the modified tangential force and the tangential force generated by pure spin, respectively. and Respectively x The wheel-rail tangential contact force in the direction y The wheel-rail tangential contact force in the direction.

[0016] Furthermore, the step 3 of solving the wheel-rail contact force and the train response on the curved track in the kinematic equation in the contact coordinate system specifically includes: Write a program to calculate the wheel-rail contact force in the open source finite element platform OpenSees, including the nonlinear Hertz formula for calculating the wheel-rail normal contact force and the Polach formula for calculating the wheel-rail tangential contact force. The open source finite element platform OpenSees also comes with the Newton-Raphson implicit iteration method and the Newmark-beta method. In the open source finite element platform OpenSees, the wheel-rail contact force in the kinematic equations and the train response on the curved track are calculated and solved using the Newton-Raphson implicit iteration method, Newmark-beta method, nonlinear Hertz formula and Polach formula.

[0017] By adopting the above technical solution, the present invention has the following beneficial effects compared with the prior art: 1. Dual-coordinate decoupling modeling: Using the mobile-fixed dual-coordinate collaborative architecture, the vehicle dynamic response and track constraints are separated, avoiding the complexity of frequent coordination of mobile and fixed components in traditional methods, improving the calculation efficiency, and can be extended to curved track dynamic contact modeling.

[0018] 2. Full-process open source integration: Based on open source platforms such as OpenSees, the unified solution of wheel-rail contact unit and mechanical response is realized, eliminating the dependence on commercial software such as SIMPACK and ABAQUS, avoiding cross-platform interaction, enhancing the portability of the method, and improving computational efficiency.

[0019] 3. Universal simulation of complex working conditions: Construct a new wheel-rail contact unit (contact coordinate system) that is compatible with scenes such as uniform-speed straight lines, curved tracks and wheel rim collisions, accurately depicts the nonlinear behavior of multi-point contacts, and has strong engineering applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0021] Figure 1 It is an execution flow chart of a curved track wheel-rail interaction simulation method based on dual coordinate system collaborative modeling provided by an embodiment of the present invention.

[0022] Figure 2 It is a flow chart of the pre-processing step provided by an embodiment of the present invention.

[0023] Figure 3 It is a flow chart of the finite element analysis process provided by an embodiment of the present invention.

[0024] Figure 4 It is a schematic diagram of a wheelset and a curved track provided in an embodiment of the present invention.

[0025] Figure 5 This is a GUI interface diagram of a curve track control point generation program provided by an embodiment of the present invention.

[0026] Figure 6 It is a wheel-rail cross section and wheel-rail profile diagram provided by an embodiment of the present invention.

[0027] Figure 7 This is a diagram of the lateral force and lateral displacement of a wheelset at a speed of 10 m / s provided by an embodiment of the present invention.

[0028] Figure 8This is a diagram of the lateral force and lateral displacement of a wheelset at a speed of 15 m / s provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0029] The present invention will be further described in detail below in conjunction with the accompanying drawings and examples. It is particularly noted that the following examples are only used to illustrate the present invention, but are not intended to limit the scope of the present invention. Similarly, the following examples are only partial embodiments of the present invention rather than all embodiments, and all other embodiments obtained by those of ordinary skill in the art without creative work are within the scope of protection of the present invention.

[0030] See also Figure 1-Figure 8 A method for simulating wheel-rail interaction of a curved track based on dual coordinate system collaborative modeling of the present invention comprises the following steps: Step 1, establishing a train model according to the physical parameters of the train; generating curved track control points according to the curved track control point generation program, and then generating a track model according to the curved track control points and the track physical parameters; In this embodiment, the step 1 specifically includes: Step 11: determine the train physical parameters and track physical parameters corresponding to the train and track to be calculated, wherein the train physical parameters include the train model, and the track physical parameters include the track model, curve track style, and curve function type; Step 12: Establish a train model based on actual calculation examples and train physical parameters; Step 13: Write a curve track control point generation program in Matlab (Matrix Laboratory, a high-performance numerical calculation and visualization software widely used in engineering, science, mathematics, finance and other fields), and create a user input interface and an image generation interface; Step 14: Input the geometric parameters corresponding to the track on the user input interface, generate a program drawing and generate the curve track control points according to the curve track control point generation program; Step 15: Establish a track model based on the actual calculation example, the curved track control points and the track physical parameters, and display it on the image generation interface; Step 16: Save the model information corresponding to the train model and track model into the target folder.

[0031] Preferably, the curve track control point generation program includes the following modules: Parametric input module: supports users to input track straight segment length, transition curve length, circular curve length, circular curve radius, track gauge and node spacing; Control point generation module: Based on the transition curve and arc integration algorithm, the coordinates of the track centerline control points are automatically calculated, and the coordinates of the inner and outer track control points are generated through the normal offset algorithm; Dynamic visualization module: real-time rendering of the track 3D model, supporting simultaneous display and partial zoom of the center line, inner rail and outer rail.

[0032] In the pre-processing stage, a curved track control point generation program was developed based on Matlab to achieve accurate parametric modeling of transition curves (clotic curves) in curved tracks, ensure the continuity and smoothness of the curvature gradients between straight segments, transition curve segments and circular curve segments, eliminate geometric mutations in traditional manual modeling, and provide high-fidelity track geometry input for wheel-rail dynamic contact simulation.

[0033] By integrating track geometry parameter input, control point algorithm generation and 3D visualization functions, the automatic output of high-precision track centerline and inner and outer rail coordinates can be achieved. This part can be divided into three modules: parameterized input module, control point generation module and dynamic visualization module. Among them, the parameterized input module: supports users to input the core parameters of track straight segment length (L1, L2), transition curve length (Ls1, Ls2), circular curve length (Lc), circular curve radius (R), track gauge (D) and node spacing (ds), with built-in data verification and exception handling mechanism to check the input parameter range to ensure the accuracy of the input parameters. Control point generation module: based on the transition curve (circle) and circular arc integral algorithm, the track centerline coordinates are automatically calculated, and the inner and outer rail control points are generated through the normal offset algorithm to ensure the smooth transition between the transition curve and the circular curve. Dynamic visualization module: uses the Matlab graphics engine to render the track 3D model in real time, supports the synchronous display and local zoom of the centerline, inner rail and outer rail, and provides a node coordinate export interface.

[0034] Preferably, the mathematical expressions of the transition curve and the circular curve (core algorithm for generating control points) are as follows: A transition curve is a curve whose curvature changes linearly with the arc length. It is used to connect straight line segments and circular curve segments to ensure a smooth transition of curvature. Its curvature is defined as: (1) in, The arc length The curvature of R is the radius of the target circle, L s is the total length of the transition curve; The expression of the transition curve is expressed in the form of a parametric equation using the Fresnel integral form: (2) in, and They represent the arc length of the control point of the transition curve. Where x and y coordinate, is the tangent angle, is the integral independent variable; in the arc length Tangent angle at satisfy: (3) in, A is the parameter of the transition curve, which characterizes the rate of change of curvature; In actual programming, Taylor expansion or numerical integration (such as Simpson's method) is used to approximate the relaxation curve: (4) The parametric equation of the circular curve is expressed as: (5) in, and They represent the arc length of the circular curve control point Where x and y coordinate; According to track gauge and curvature direction, the inner rail control point coordinates and the outer rail control point coordinates are the normal offsets of the track centerline control point coordinates, specifically expressed as: (6) in, Indicates the coordinates of the inner track control points, represents the coordinates of the outer track control points, represents the coordinates of the track centerline control point, Represents the centerline unit normal vector and points to the center side of the circular curve.

[0035] According to the above formula, a curve track control point growth program is written in Matlab, and the following is generated: Figure 5 The GUI interface (Graphical User Interface) shown in the figure is divided into left and right columns. The left side is the parameter input area and the right side is the track visualization area, which supports real-time interactive operations. The left panel contains the track geometry parameter input box, the generate button and the parameter description label. The right panel dynamically displays the track centerline, the curves of the inner and outer rails, and supports zooming, panning and partial zooming.

[0036] Step 2: Use a dual coordinate system based on a mobile coordinate system and a fixed coordinate system to establish the kinematic equations of the train model and the track model, where the mobile coordinate system is used to describe the vehicle motion, and the fixed coordinate system is used to describe the track motion, and the kinematic equations of the train model and the track model in the dual coordinate system are jointly established through the kinematic mapping relationship between the mobile coordinate system and the fixed coordinate system; During the modeling stage, a collaborative modeling system of mobile coordinate system and fixed coordinate system is constructed. The mobile coordinate system describes the vehicle motion, and the fixed coordinate system represents the track geometric constraints. The kinematic mapping relationship is used to realize the simultaneous solution of the vehicle-track subsystem motion equations in the two coordinate systems, avoiding deformation coordination and multi-platform data exchange in the substructure method.

[0037] In this embodiment, step 2 specifically includes: Step 21, the vehicle model is regarded as a moving part in a moving coordinate system, and the track model is regarded as a stationary part in a fixed coordinate system; Step 22: Based on the mobile coordinate system and the fixed coordinate system, a dual coordinate system coordination system is constructed, and the kinematic equations in the fixed coordinate system are established. The kinematic equations in the fixed coordinate system are discretized and combined with the displacement, velocity, and acceleration mapping relationship in the mobile coordinate system to form a unified correction force term, and the kinematic equations of the train model and the track model in the mobile coordinate system and the fixed coordinate system are established. By establishing the kinematic mapping relationship between the mobile coordinate system and the fixed coordinate system, the kinematic equations are derived and combined, and the applicability of this method is extended from a simplified uniform linear motion scenario to a curved track simulation.

[0038] Preferably, the step 22 specifically includes: Step 221: According to the D'Alembert principle, the basic formula of the kinematic equations of the train model and the track model in a fixed coordinate system is: (7) Among them, M represents the mass matrix of the train model and the track model, C represents the damping matrix, represents the internal force matrix of the train model and the track model, represents the relative displacement of the contact point between the train wheel and the track, F represents the external load matrix, and They represent the second and first derivatives of the displacement u in the fixed coordinate system, i.e., acceleration and velocity; Step 222: Since the wheel-rail interaction involves strong nonlinearity, the Newmark-beta method (the Newmark-β method is a numerical integration method for solving structural dynamics equations) is usually used to discretize equation (7): (8) in,n and n +1 represents the current time step and the next time step in the discrete solution process. represents the discrete time step, and They represent the parameters of the Newmark-beta method, and their values ​​are , ; Rewrite formula (7) as: (9) (10) in, is the unbalanced force of the kinematic equation. The solution obtained by setting it to zero is the displacement response of the system at the current moment. represents the external load term; It has no specific meaning and is substituted in formula (9) to prevent formula (10) from being too long.

[0039] Step 223, the displacement, velocity and acceleration in the mobile coordinate system have the following mapping relationships with the displacement, velocity and acceleration in the fixed coordinate system: (11) (12) (13) Among them, u, and They represent displacement, velocity and acceleration in a fixed coordinate system respectively; , and They represent the displacement, velocity and acceleration of the object in the moving coordinate system respectively; , and They represent the displacement, velocity and acceleration of the mobile coordinate system itself, respectively, as reference parameters; Step 224: Discretize formulas (11)-(13) and substitute them into (8) to obtain: (14) According to (15) in, i and i +1 indicates the current iteration step and the next iteration step in the solution process; as well as (16) get: (17) Substituting formula (17) into formulas (9)-(10), we obtain: (18) in: (19) because This term is only related to external damping and has nothing to do with internal damping. This term is related to the external load term Forming a correction force term under a curved track , realizing the unification of the form of the kinematic equations in the mobile coordinate system and the fixed coordinate system, so that the system response can be obtained by solving the simultaneous kinematic equations, realizing the unified modeling of trains and tracks, and avoiding the repeated iteration problem in the substructure method.

[0040] Step 3: According to the model information corresponding to the train model and the track model, the contour lines of the wheels and the tracks are extracted, and a contact coordinate system is established in the moving coordinate system based on the geometric contact of the contour lines. The wheel-rail contact force in the kinematic equation and the train response on the curved track are solved in the contact coordinate system. During the solution stage, a three-dimensional wheel-rail contact unit was designed under the finite element framework, that is, a contact coordinate system was established; and the Newton-Raphson implicit iteration method (Newton-Raphson method), Newmark-beta method (Newmark-β method is a numerical integration method for solving structural dynamics equations), nonlinear Hertz formula and Polach (a theoretical model for calculating wheel-rail longitudinal creep force, widely used in railway vehicle dynamics analysis) formula were integrated into the open source finite element platform OpenSees (Open System for Earthquake Engineering Simulation, an open source earthquake engineering simulation software framework, mainly used for nonlinear analysis of structures and geological engineering), and the contact coordinate system was directly embedded in the dual coordinate system solution process to support simulation of complex working conditions such as multi-point contact and wheel flange collision under curved tracks.

[0041] The present invention adopts the Newton-Raphson implicit iteration method to synchronously iterate the joint motion equation of the mobile / fixed system response discretized by the Newmark-beta method, and combines the smooth track data generated by pre-processing to significantly improve the convergence speed of nonlinear contact problems.

[0042] In this embodiment, step 3 specifically includes: Step 31: The open source finite element platform OpenSees retrieves the model information from the target folder, and uses dense point linear fitting to fit the contours of the wheel and track according to the model information corresponding to the train model and the track model, and obtains the following: Figure 6 The schematic diagram shown; Step 32: Establish a contact coordinate system in the moving coordinate system based on the geometric contact of the contour line, and the contact coordinate system is used to calculate the wheel-rail contact force; wherein the contact coordinate system x Axis direction and moving coordinate system x The axis direction is consistent; according to the embedding point of the wheel and the track ( P i , P i+1 , assuming no deformation) defines the contact coordinate system y Axis direction; through the contact coordinate system x Axis and y The contact coordinate system is obtained by taking the cross product of the axes (the cross product is a concept in vector algebra that describes the vectors of two vectors perpendicular to the plane in which they are located in three-dimensional space) z Axis direction; Step 33: Use the Newton-Raphson implicit iteration method to calculate the n The first step under the time i The displacement of the iteration step; n and i is a positive integer, and n and i The maximum value is given by the user. n When the maximum value is reached, the program calculation is completed; when the iteration step i When it is less than the given maximum value and the program converges, it proceeds to the next iteration step. i If the given maximum value is reached but convergence has not yet occurred, the program fails to converge and the calculation ends. The user needs to perform a convergence check and modify related parameters.

[0043] Step 34, determine whether it has converged, if not, proceed to step 35; if yes, continue to check whether all time steps are completed, if yes, record the response of each time step; if not, proceed to the next time step and return to step 33; Step 35: Use the Newmark-beta method to calculate the n The first step under the time i The speed of the iteration step; Step 36: Use the nonlinear Hertz formula to calculate the wheel-rail normal contact force, and use the Polach formula to calculate the wheel-rail tangential contact force; Step 37, converting the wheel-rail normal contact force and the wheel-rail tangential contact force to obtain the wheel-rail coupling unit internal force; Step 38: Update the kinematic equation according to the internal force of the wheel-rail coupling unit; Step 39, enter the next iteration step and return to step 33.

[0044] Preferably, in step 36, the nonlinear Hertz formula is used to calculate the wheel-rail normal contact force, which specifically includes: The wheel-rail normal contact force is related to the maximum embedding depth of the wheel-rail contour line. The calculation of the wheel-rail contact force will be briefly introduced below. The present invention uses a nonlinear Hertz method to calculate the wheel-rail normal contact force. This method assumes that the wheel and the track are rigid bodies that do not deform but have virtual mutual penetration. Use dense points to linearly fit the wheel and track contour lines to find the maximum embedding depth of the two. . Maximum embedding depth based on wheel and rail contours , and the nonlinear Hertz formula is used to calculate the wheel-rail normal contact force; The wheel-rail normal contact force is obtained by the following formula: (20) in, represents the wheel-rail normal contact force, K It represents the wheel-rail normal contact force coefficient, which is related to the curvature and elastic modulus of the wheel-rail. 1.5 represents the power value.

[0045] Furthermore, the wheel-rail tangential contact force is calculated using the Polach formula in step 36, which specifically includes: The Polach formula can more accurately describe the relationship between the wheel-rail tangential contact force (longitudinal and lateral) and the wheel-rail creep rate by introducing the friction saturation effect and simplified assumptions of the contact spot stress distribution. This method considers that the wheel-rail tangential contact force is closely related to the wheel-rail creep rate, and defines the wheel-rail creep rate as a physical quantity related to the relative speed between the wheel and the track. The wheel-rail creep rate is calculated as follows: (twenty one) in, express x The translation creep rate in the direction, express y The translation creep rate in the direction, Indicates winding z Rotational creep rate for axial rotation, and The wheel contact point and the track contact point are respectively x and y The relative speed difference in direction, Indicates that the wheel contact point and the track contact point are around z The relative speed difference in the direction of shaft rotation, Indicates the travel speed; The Polach formula describes the relationship between the wheel-rail tangential contact force and the creep rate. The Polach formula is expressed as: (twenty two) in, Representation and and The associated corrected translational creep rate, F tr and F ys denote the modified tangential force and the tangential force generated by pure spin, respectively. and Respectively x The wheel-rail tangential contact force in the direction y The wheel-rail tangential contact force in the direction.

[0046] Preferably, solving the wheel-rail contact force and train response on the curved track in the kinematic equation in the contact coordinate system in step 3 specifically includes: Write a program to calculate the wheel-rail contact force in the open source finite element platform OpenSees, including the nonlinear Hertz formula for calculating the wheel-rail normal contact force and the Polach formula for calculating the wheel-rail tangential contact force. The open source finite element platform OpenSees also comes with the Newton-Raphson implicit iteration method and the Newmark-beta method. In the open source finite element platform OpenSees, the wheel-rail contact force in the kinematic equations and the train response on the curved track are calculated and solved using the Newton-Raphson implicit iteration method, Newmark-beta method, nonlinear Hertz formula and Polach formula.

[0047] Step 4: Plot the obtained train response and wheel-rail contact force into a curve, and analyze the calculation results.

[0048] The present invention obtains the response of a single wheel set passing through a curved track example after calculation. The curved track is composed of a straight line segment, a 50-meter-long transition curve segment and a 50-meter-long circular curve segment, and the curve radius is 200 meters. The corresponding curved track control points are generated by the Matlab curved track control point generation program, and the corresponding tcl file is generated and put into the corresponding folder for OpenSees to call. The wheel adopts the ML95 model and the track adopts the UIC50 model.

[0049] like Figure 7The figure shows the lateral force and lateral displacement of the wheelset moving forward at a speed of 10 m / s. It can be seen that the wheelset deflects slightly under the action of centrifugal force, but generally still moves in a serpentine manner along the center line.

[0050] like Figure 8 The figure shows the lateral force and lateral displacement of the wheelset moving at a speed of 15 m / s. It can be seen that the wheelset has a serious deflection under the action of centrifugal force, resulting in continuous contact between the wheel flange and the track. At the same time, the continuous contact between the wheel flange and the track also causes a sudden change in the lateral force.

[0051] The above descriptions are only some embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any equivalent device or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for simulating wheel-rail interaction on a curved track based on collaborative modeling of dual coordinate systems, characterized in that: The steps include: Step 1, establishing a train model according to the physical parameters of the train; generating curved track control points according to the curved track control point generation program, and then generating a track model according to the curved track control points and the track physical parameters; Step 2: Use a dual coordinate system based on a mobile coordinate system and a fixed coordinate system to establish the kinematic equations of the train model and the track model, where the mobile coordinate system is used to describe the vehicle motion, and the fixed coordinate system is used to describe the track motion, and the kinematic equations of the train model and the track model in the dual coordinate system are jointly established through the kinematic mapping relationship between the mobile coordinate system and the fixed coordinate system; Step 3: According to the model information corresponding to the train model and the track model, the contour lines of the wheels and the tracks are extracted, and a contact coordinate system is established in the moving coordinate system based on the geometric contact of the contour lines. The wheel-rail contact force in the kinematic equation and the train response on the curved track are solved in the contact coordinate system. Step 4: Plot the obtained train response and wheel-rail contact force into a curve, and analyze the calculation results.

2. The method for simulating wheel-rail interaction on a curved track based on dual coordinate system collaborative modeling according to claim 1, characterized in that: The step 1 specifically includes: Step 11: determine the train physical parameters and track physical parameters corresponding to the train and track to be calculated, wherein the train physical parameters include the train model, and the track physical parameters include the track model, curve track style, and curve function type; Step 12: Establish a train model based on actual calculation examples and train physical parameters; Step 13, write a curve track control point generation program in Matlab, and make a user input interface and an image generation interface; Step 14: Input the geometric parameters corresponding to the track on the user input interface, generate a program drawing and generate the curve track control points according to the curve track control point generation program; Step 15: Establish a track model based on the actual calculation example, the curved track control points and the track physical parameters, and display it on the image generation interface; Step 16: Save the model information corresponding to the train model and track model into the target folder.

3. The method for simulating wheel-rail interaction of curved track based on dual coordinate system collaborative modeling according to claim 1, characterized in that: The curve track control point generation program includes the following modules: Parametric input module: supports users to input track straight segment length, transition curve length, circular curve length, circular curve radius, track gauge and node spacing; Control point generation module: Based on the transition curve and arc integration algorithm, the coordinates of the track centerline control points are automatically calculated, and the coordinates of the inner and outer track control points are generated through the normal offset algorithm; Dynamic visualization module: real-time rendering of the track 3D model, supporting simultaneous display and partial zoom of the center line, inner rail and outer rail.

4. The method for simulating wheel-rail interaction of curved track based on dual coordinate system collaborative modeling according to claim 3, characterized in that: The mathematical expressions of the transition curve and the circular curve are as follows: A transition curve is a curve whose curvature changes linearly with the arc length. It is used to connect straight line segments and circular curve segments. Its curvature is defined as: (1) in, The arc length The curvature of R is the radius of the target circle, L s is the total length of the transition curve; The expression of the transition curve is expressed in the form of a parametric equation using the Fresnel integral form: (2) in, and They represent the arc length of the control point of the transition curve. Where x and y coordinate, is the tangent angle, is the integral independent variable; in the arc length Tangent angle at satisfy: (3) in, A is the parameter of the transition curve, which characterizes the rate of change of curvature; In actual programming, Taylor expansion or numerical integration is used to approximate the relaxation curve: (4) The parametric equation of the circular curve is expressed as: (5) in, and They represent the arc length of the circular curve control point Where x and y coordinate; According to track gauge and curvature direction, the inner rail control point coordinates and the outer rail control point coordinates are the normal offsets of the track centerline control point coordinates, specifically expressed as: (6) in, Indicates the coordinates of the inner track control points, represents the coordinates of the outer track control points, Indicates the coordinates of the track centerline control point, Represents the centerline unit normal vector and points to the center side of the circular curve.

5. The method for simulating wheel-rail interaction on a curved track based on dual coordinate system collaborative modeling according to claim 1, characterized in that: The step 2 specifically includes: Step 21, the vehicle model is regarded as a moving part in a moving coordinate system, and the track model is regarded as a stationary part in a fixed coordinate system; Step 22: Construct a dual coordinate system collaborative system based on the mobile coordinate system and the fixed coordinate system, establish the kinematic equation in the fixed coordinate system, discretize the kinematic equation in the fixed coordinate system and combine it with the displacement, velocity, and acceleration mapping relationship in the mobile coordinate system to form a unified correction force term, and establish the kinematic equations of each part of the train model and the track model in the mobile coordinate system and the fixed coordinate system.

6. The method for simulating wheel-rail interaction on a curved track based on dual coordinate system collaborative modeling as claimed in claim 5, characterized in that: The step 22 specifically includes: Step 221: According to the D'Alembert principle, the basic formula of the kinematic equations of the train model and the track model in a fixed coordinate system is: (7) Among them, M represents the mass matrix of the train model and the track model, C represents the damping matrix, represents the internal force matrix of the train model and the track model, represents the relative displacement of the contact point between the train wheel and the track, F represents the external load matrix, and They represent the second and first derivatives of the displacement u in the fixed coordinate system, i.e., acceleration and velocity; Step 222: Use the Newmark-beta method to discretize equation (7): (8) in, n and n +1 represents the current time step and the next time step in the discrete solution process. represents the discrete time step, and They represent the parameters of the Newmark-beta method, and their values ​​are , ; Rewrite formula (7) as: (9) (10) in, is the unbalanced force of the kinematic equation. The solution obtained by setting it to zero is the displacement response of the system at the current moment. represents the external load term; Step 223, the displacement, velocity and acceleration in the mobile coordinate system have the following mapping relationships with the displacement, velocity and acceleration in the fixed coordinate system: (11) (12) (13) Among them, u, and They represent displacement, velocity and acceleration in a fixed coordinate system respectively; , and They represent the displacement, velocity and acceleration of the object in the moving coordinate system respectively; , and They represent the displacement, velocity and acceleration of the mobile coordinate system itself as reference parameters; Step 224: Discretize formulas (11)-(13) and substitute them into (8) to obtain: (14) According to (15) in, i and i +1 indicates the current iteration step and the next iteration step in the solution process; as well as (16) get: (17) Substituting formula (17) into formulas (9)-(10), we obtain: (18) in: (19) because This term is only related to external damping and has nothing to do with internal damping. This term is related to the external load term Forming a correction force term under a curved track , realizing the unification of the form of the kinematic equations in the mobile coordinate system and the fixed coordinate system, thereby achieving the simultaneous kinematic equations.

7. The method for simulating wheel-rail interaction on a curved track based on dual coordinate system collaborative modeling according to claim 1, characterized in that: The step 3 specifically includes: Step 31: according to the model information corresponding to the train model and the track model, use dense point linear fitting to fit the contours of the wheel and the track; Step 32: Establish a contact coordinate system in the moving coordinate system based on the geometric contact of the contour line, wherein the contact coordinate system x Axis direction and moving coordinate system x The contact coordinate system is defined according to the embedding point of the wheel and the track. y Axis direction; through the contact coordinate system x Axis and y The cross product of the axes gives the contact coordinate system z Axis direction; Step 33: Use the Newton-Raphson implicit iteration method to calculate the n The first step under the time i The displacement of the iteration step; Step 34, determine whether it has converged, if not, proceed to step 35; if yes, continue to check whether all time steps are completed, if yes, record the response of each time step; if not, proceed to the next time step and return to step 33; Step 35: Use the Newmark-beta method to calculate the n The first step under the time i The speed of the iteration step; Step 36: Use the nonlinear Hertz formula to calculate the wheel-rail normal contact force, and use the Polach formula to calculate the wheel-rail tangential contact force; Step 37, converting the wheel-rail normal contact force and the wheel-rail tangential contact force to obtain the wheel-rail coupling unit internal force; Step 38: Update the kinematic equation according to the internal force of the wheel-rail coupling unit; Step 39, enter the next iteration step and return to step 33.

8. The method for simulating wheel-rail interaction on a curved track based on dual coordinate system collaborative modeling as claimed in claim 7, characterized in that: In step 36, the nonlinear Hertz formula is used to calculate the wheel-rail normal contact force, which specifically includes: Maximum embedding depth based on wheel and rail contours , and the nonlinear Hertz formula is used to calculate the wheel-rail normal contact force; The wheel-rail normal contact force is obtained by the following formula: (20) in, represents the wheel-rail normal contact force, K It represents the wheel-rail normal contact force coefficient, which is related to the curvature and elastic modulus of the wheel-rail. 1.5 represents the power value.

9. The method for simulating wheel-rail interaction on a curved track based on dual coordinate system collaborative modeling according to claim 7, characterized in that: In step 36, the wheel-rail tangential contact force is calculated using the Polach formula, which specifically includes: The wheel-rail creep rate is defined as a physical quantity related to the relative speed between the wheel and the rail. The wheel-rail creep rate is calculated as follows: （21） in, express x The translation creep rate in the direction, express y The translation creep rate in the direction, Indicates winding z Rotational creep rate for axial rotation, and The wheel contact point and the track contact point are respectively x and y The relative speed difference in direction, Indicates that the wheel contact point and the track contact point are around z The relative speed difference in the direction of shaft rotation, Indicates the travel speed; The Polach formula describes the relationship between the wheel-rail tangential contact force and the creep rate. The Polach formula is expressed as: （22） in, Representation and and The associated corrected translational creep rate, F tr and F ys denote the modified tangential force and the tangential force generated by pure spin, respectively. and Respectively x The wheel-rail tangential contact force in the direction y The wheel-rail tangential contact force in the direction.

10. The method for simulating wheel-rail interaction of curved track based on dual coordinate system collaborative modeling according to claim 1, characterized in that: The step 3 of solving the wheel-rail contact force and the train response on the curved track in the kinematic equation in the contact coordinate system specifically includes: Write a program to calculate the wheel-rail contact force in the open source finite element platform OpenSees, including the nonlinear Hertz formula for calculating the wheel-rail normal contact force and the Polach formula for calculating the wheel-rail tangential contact force. The open source finite element platform OpenSees also comes with the Newton-Raphson implicit iteration method and the Newmark-beta method. In the open source finite element platform OpenSees, the wheel-rail contact force in the kinematic equations and the train response on the curved track are calculated and solved using the Newton-Raphson implicit iteration method, Newmark-beta method, nonlinear Hertz formula and Polach formula.

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