Method for analyzing damage of hidden parts of track structure after train derailment caused by earthquake

Abstract

The invention provides a method for analyzing the damage of a hidden part of a track structure after train derailment caused by an earthquake, and relates to the field of dynamic response analysis of track structures. The method comprises the following steps: establishing a track substructure model, sequentially establishing track substructures such as a steel rail, a fastener system, a track plate, a filling layer and a base plate from top to bottom, and introducing cohesion unit simulation between structural layers, according to the earthquake load simulation, earthquake waves are transmitted to the structural non-supporting point freedom degree through the structural supporting point freedom degree, and then the whole vehicle system is influenced. According to the method, the accuracy and the calculation efficiency of dynamic response analysis of a track structure under the earthquake action are remarkably improved by introducing an improved nonlinear elastic theory and a multi-point non-Hertz contact model and combining a modal superposition method and a multi-scale analysis method in consideration of a vehicle-track complex collision contact behavior after derailment.

Description

Technical Field

[0001] The present invention relates to the technical field of track structure dynamic response analysis, and in particular to a method for analyzing damage to hidden components of a track structure after a train derailment caused by an earthquake. Background Art

[0002] my country's railway operating mileage has exceeded 150,000 kilometers, of which over 40,000 kilometers are high-speed railways. Ensuring the safe operation of high-speed trains has become a major concern for high-speed railway operations. However, earthquake-induced train derailments are common, and the impact of train collisions and extreme earthquake loads after derailment causes significant damage to the track structure. Regarding engineering, the track structure is a multi-layered system, with interlayer restraints achieved through bonding and the provision of restraint bosses. These structures are concealed structures. The effects of the coupled earthquake-train collision load on the residual deformation and damage of interlayer bonding and the sub-slab restraint structure are difficult to detect through on-site inspections. Therefore, it is necessary to propose a refined simulation analysis method for the stress damage characteristics of concealed track structure components under earthquake-train collision loads.

[0003] Traditional track structure dynamic response analysis methods typically establish solid units for each substructure, including the rail, fastener system, track slab, infill layer, and base plate. These substructures are connected through binding, with a fully constrained connection between the base plate and the track foundation. The wheel-rail contact of the vehicle system is often simulated using the Hertz contact method. While these analysis methods offer a certain degree of accuracy and comprehensiveness, they often assume elasticity or full constraint when dealing with interlayer contact. Seismic action can cause significant damage to the track interlayer structure. Furthermore, after a wheel breaks free from the rail, the wheel-rail rolling contact relationship disappears, leading to uncertainty in the collision contact relationship between vehicle components (such as wheels, brake discs, and gearboxes) and track components (such as rails, fasteners, track slabs, and track protection structures). Traditional simplified interlayer models and Hertz contact simulation methods cannot fully reflect the real-world situation. Summary of the Invention

[0004] The present invention aims to provide a method for analyzing damage to hidden components of track structures after train derailment caused by an earthquake, so as to solve the above problems.

[0005] The technical solution of the present invention is: a method for analyzing damage to hidden components of a track structure after a train derailment caused by an earthquake, comprising:

[0006] S1. Build the track substructure model, including the rails, fastener system, track plate, filling layer, and base plate from top to bottom.

[0007] S2. Construct the rail mechanics equation and use the mass matrix, damping matrix and stiffness matrix to represent the wheel-rail equivalent load and fastener equivalent load on the rail;

[0008] S3. Use the Boolean matrix to select the nodes where the track structure connects to the rails, so that the degrees of freedom of the rails and the ballastless track structure are consistent;

[0009] S4. Establish a ballastless track structure model in a physical coordinate system, and represent the external loads on the ballastless track structure and the interaction forces of adjacent track structures through mass matrix, damping matrix, and stiffness matrix;

[0010] S5. Use the modal superposition method to effectively reduce the model calculation cost by retaining the modal order of the ballastless track structure;

[0011] S6. The critical wheel-rail contact relationship of derailment uses non-Hertz contact theory, studies the multi-point contact relationship of wheel and rail under complex earthquake loads based on virtual penetration, and uses the KikPiotrowski algorithm to analyze the normal contact model;

[0012] S7, derailment criticality Kalker's FASTSIM algorithm is used to solve the wheel-rail tangential adhesion-creep state, and the creep force and slip velocity in the adhesion and creep zones within the wheel-rail contact patch are obtained;

[0013] S8, based on the K-DOPs hierarchical tree bounding box collision detection method, identifying the collision and contact relationship between vehicle components and track components after derailment;

[0014] S9. Based on the idea of ​​profile discretization, the collision contact elements and contact forces between the vehicle substructure and the track substructure after the train derailment are solved;

[0015] S10. Establish a 35-degree-of-freedom vehicle system dynamics model including the vehicle body, bogie, and wheelset, perform force analysis on each component using the D'Alembert principle, and establish the vehicle system motion differential equation;

[0016] S11. In the vehicle system dynamics model, the mass matrix, damping matrix, and stiffness matrix of each vehicle component are substituted and combined with the nonlinear wheel-rail contact force vector to establish the differential equations of motion of each component of the vehicle system;

[0017] S12. Earthquake load simulation uses an improved earthquake load simulation method, which improves the accuracy of earthquake load simulation by adding actual data and introducing a combination of time domain analysis and frequency domain analysis;

[0018] S13, earthquake load simulation uses earthquake waves to transmit through the structural support point freedom degree to the structural non-support point freedom degree, and then affect the entire vehicle system;

[0019] S14. Combine the improved earthquake load simulation results with the track substructure model to perform dynamic response analysis of the track structure under earthquake action.

[0020] Preferably, in S1, each substructure of the rail, track plate, filling layer, and base plate is simulated by solid elements, the rail and ballastless track are connected by fasteners, and the fasteners are simulated by nonlinear springs; the interlayer of the ballastless track multi-layer structure system (including the track plate, filling layer, and base plate) adopts an improved cohesive force model under the seismic load mode, and the interlayer damage initiation factor (F D ) can be expressed as:

[0021]

[0022] In the formula, <> is the Macaulay symbol, indicating that the crack initiation criterion calculation is performed only when the normal nominal stress is non-negative, which ensures that no damage will occur in the normal direction of the interlayer interface in the pure compression state; t n , t s , t t They represent the normal and longitudinal and transverse tangential stresses transmitted by earthquake waves through structural support points to interlayer non-structural support points, respectively. They represent the nominal peak stresses of the multi-layer track structure under the tensile and shear tests respectively;

[0023] When the wheel impact load increases to F after the earthquake and derailment D = 1, the damage factor D begins to develop and enters the softening and descending stage of the bilinear cohesive force model. The damage factor D can be defined as:

[0024]

[0025] Where, It represents the maximum effective displacement of the non-structural support point between floors under the action of earthquake load, is the effective displacement of the inter-layer non-structural support point corresponding to the earthquake load reaching the damage initiation stage, The displacement of the non-structural support points between layers corresponding to the complete damage of the track layers caused by an earthquake;

[0026] The mechanical properties of the rails, fastening systems and track plates described in S1 are simulated using homogeneous materials.

[0027] Preferably, in S2,

[0028] In the rail structure model, the rail mechanical equation can be expressed as:

[0029]

[0030]

[0031] In formula (1), M rr 、C rr , K rr are the mass matrix, damping matrix and stiffness matrix of the rail respectively; is the acceleration of the rail, is the speed of the rail, q r is the displacement of the rail; Q wr Indicates the wheel-rail equivalent load on the rail; Q rs is the equivalent load of the fasteners on the rail;

[0032] In formula (2), Nf is the number of fasteners in the model; q s is the displacement freedom of the ballastless track structure; q r is the rail displacement freedom; K rf,i and C rf,i are the stiffness and damping matrices of the interaction between rail and track plate at a single fastener; Hehe are the accelerations of the rail and track plate at a single fastener respectively;

[0033] In order to facilitate the subsequent establishment of a large vehicle-track system dynamics model, it is necessary to transform formula (2) and use the Boolean matrix to select the nodes connecting the track structure and the rails to achieve the same degree of freedom of the rails and ballastless track structures.

[0034]

[0035] In formula (3), B sr It is a Boolean matrix, that is, a 0-1 matrix, in which the elements are either 0 or 1; K rs 、C rs are the stiffness and damping matrices of the interaction between the rail and the track plate, respectively. Substituting formula (1) into formula (3) and then shifting the unknown variables such as rail structure displacement and velocity, the finite element dynamic equation of the rail can be obtained as follows:

[0036]

[0037] The rail mechanical equations in S2 are solved by finite element analysis.

[0038] Preferably, in S3,

[0039] The formula used is as follows:

[0040]

[0041] Among them, K rs is the stiffness matrix of the fastener, C rs is the damping matrix of the fastener, B r 、B s is a Boolean matrix, q s is the displacement of the ballastless track structure;

[0042] The selected nodes of the Boolean matrix in S3 are determined according to the connection points between the track structure and the rails.

[0043] Preferably, in S4, the ballastless track structure model,

[0044] The control equation of the ballastless track structure in the physical coordinate system can be expressed as:

[0045]

[0046]

[0047] In formula (5), M ss 、C ss , K ss are the mass matrix, damping matrix and stiffness matrix of the ballastless track structure respectively; is the acceleration of the ballastless track structure, is the speed of the ballastless track structure, u s is the displacement of the ballastless track structure; Q sr is the external load on the ballastless track structure; Q ss It represents the interaction force between adjacent ballastless track structures. If the ballastless track is a unit structure, the parameter value is zero.

[0048] In formula (6), Nf is the number of fasteners in the model; q r,i is the rail displacement; u s,i is the displacement of the ballastless track structure at the fastener;

[0049] By reasonably retaining the modal order m of the ballastless track structure, the model calculation cost can be effectively reduced. After using the modal superposition method, the ballastless track dynamic model is greatly reduced from the real degrees of freedom to the generalized degrees of freedom m in the modal space.

[0050]

[0051] In formula (7), the modal matrix The dimension of is (s×m), which is the broadband modal set of ballastless track bed. s is the displacement of the s-order degree of freedom; q m is the displacement of the mth degree of freedom after order reduction;

[0052] According to the orthogonal conditions of the modal superposition method, formula (5) can be decoupled and expressed as follows:

[0053]

[0054] In formula (8), is the generalized mass matrix of the ballastless track structure; is the generalized damping matrix of the ballastless track structure; is the generalized stiffness matrix of the ballastless track structure; and Represents the generalized load on the ballastless track structure;

[0055] Different generalized matrices can be expressed as:

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063] To facilitate the construction of the vehicle-track system dynamic equation, the ballastless track dynamic equation is described as Equation (11);

[0064] Where diag[] is the method for extracting diagonal elements;

[0065] The dynamic response of the support points and non-support points of the ballastless track multi-layer structure under seismic load is expressed as:

[0066]

[0067] Among them, the subscripts S and b are the non-support point and support point of the structure respectively. u are the acceleration, velocity and displacement of the support point, respectively, and F is the load at the support point;

[0068] The direct method is used to input the earthquake wave displacement, acceleration, and velocity response into the support points of the lower foundation structure, and the displacement response of the non-support points of the inter-story structure is solved through earthquake load transfer:

[0069]

[0070] The constitutive relation of the improved cohesion model under seismic load mode can be expressed as:

[0071]

[0072] Where K n,s,t is the interlayer interface stiffness in the absence of damage, u n,s,t is the relative displacement of non-structural support points between stories under earthquake loads. The damage factor D can be introduced into the inter-story stiffness matrix as a stiffness reduction factor.

[0073] The interaction forces between adjacent ballastless track structures described in S4 are represented by constraint conditions.

[0074] Preferably, in S5,

[0075] The modal superposition method is expressed as:

[0076]

[0077] According to the orthogonal conditions of the modal superposition method, the decoupling expression is:

[0078]

[0079] Among them, Φ i is the modal shape function, q i is the modal coordinate, M mm is the generalized mass matrix, C mm is the generalized damping matrix, K mm is the generalized stiffness matrix, is the modal acceleration, is the modal velocity, q m is the modal displacement, Q sf is a generalized representation of external loads, Q sm is a generalized representation of the interaction force between adjacent structures;

[0080] The modal superposition method described in S5 uses orthogonal conditions for decoupling.

[0081] Preferably, in S6,

[0082] The virtual penetration function is:

[0083]

[0084] Where δ is the wheel-rail penetration after force is applied, and f(y) is the wheel-rail surface function;

[0085] The Kik-Piotrowski algorithm described in S6 assumes that the wheel-rail profile and the amount of wheel-rail intrusion after loading jointly determine the shape of the wheel-rail contact patch.

[0086] Preferably, in S7,

[0087] The solution is expressed as:

[0088] ΔS(x,y)=S(x,y)-LΔP t (x,y)

[0089] Where S(x, y) is the true sliding velocity, L is the Kalker flexibility coefficient, ΔP t (x, y) is the tangential force in the contact patch grid;

[0090] The FASTSIM algorithm described in S7 solves the wheel-rail tangential contact based on the finite difference method.

[0091] Preferably, in S6 and S7,

[0092] Before the train derailed, the nonlinear elastic theory was used to simulate the track structure, and the wheel-rail contact force was calculated as follows:

[0093]

[0094] Among them, E * is the equivalent elastic modulus, ν is Poisson's ratio, R is the radius of curvature, and δ is the compression amount;

[0095] The relationship between the virtual penetration and wheel-rail deformation of the wheel-rail normal contact model is expressed as:

[0096]

[0097] Where N is the normal force of wheel-rail contact, R is the radius of curvature, E is the elastic modulus, and ν is the Poisson's ratio;

[0098] The calculation formula of wheel-rail tangential contact force is:

[0099]

[0100] Among them, F t is the tangential contact force, μ is the friction coefficient, N is the normal force, v r is the relative sliding velocity, v s is the sliding speed threshold;

[0101] In S8, the vehicle components after derailment include wheels, brake discs, and gearboxes, and the track components include rails, fasteners, track plates, and track protection structures. Based on the idea of ​​outline discretization, the appearance of the vehicle and track system substructures is discretized into a large number of triangles. If two substructures of the vehicle track system collide after the vehicle derails, the triangles of the structural appearance will intersect. The intersection relationship between all wheel polygonal surfaces and ballastless track plate polygonal surfaces is detected. If the minimum distance is less than a certain capture distance (the empirical value is 10 -20 m) attaching the corresponding line to the intersection polygon and repeating the calculation to obtain its endpoints, and finally determining the spatial polygon where the vehicle component and the track component intersect;

[0102] In S10, the vehicle system motion differential equation is:

[0103]

[0104] Where [M] is the train mass matrix, [C] is the damping matrix, and [K] is the stiffness matrix. is the acceleration vector of the train component, is the velocity vector of the train component, X is the displacement vector of the train component, F wr is the nonlinear wheel-rail contact force vector.

[0105] Preferably, in S9, after the train derails, the normal force expression of the collision contact unit between the vehicle component and the track component is,

[0106]

[0107] Where, F dk Damping force part, F ck is the elastic part of the contact normal force, and its expression is:

[0108] F ck =k l ·A k ·u nk

[0109] Among them, the derailed vehicle components include wheels, brake discs, and gearboxes, and the track components include rails, fasteners, track plates, and track protection structures;

[0110] The viscous damping force is affected by the viscous damping coefficient and the normal component. The expression of the viscous damping force component is:

[0111]

[0112] Where d l is the damping coefficient of the surface elastic layer, v k is the rigid body relative velocity vector,

[0113] v k To express is for

[0114]

[0115] Where, are the relative linear velocity vector and angular velocity vector of the master and slave surfaces respectively;

[0116] The tangential force of the contact element depends on the tangential relative velocity and the normal force.

[0117] The expression of tangential force is:

[0118]

[0119] Where v ε is the sliding friction speed limit, v tk is the tangential relative velocity, and the expression of the tangential relative velocity is:

[0120] v tk =|v k-v nk ·n k |

[0121] The total force vector F of the contact element k From the normal component F nk Along its normal vector n k The projection and tangential force F tk The sum of the projections along the tangential velocity direction is expressed as:

[0122]

[0123] Finally, the forces of all contact elements are added together to obtain the total force of the contact patch between the wheel and the ballastless track slab.

[0124]

[0125] Where k is the number of contact elements within the finite polygon of contact between vehicle components and track components. Vehicle components include wheels, brake discs, gearboxes, car bodies, and axles. Track components include rails, fasteners, track plates, and track protection structures.

[0126] The establishment of the vehicle system dynamics model described in S9 includes the degrees of freedom in five directions: lateral, vertical, roll, nod, and shake.

[0127] The beneficial effects of the present invention are:

[0128] By introducing an improved nonlinear elastic theory and a multi-point non-Hertz contact model, combined with the modal superposition method and multi-scale analysis methods, the accuracy and computational efficiency of the dynamic response analysis of track structures under seismic action are significantly improved. Compared with traditional methods, this solution reduces model simplifications and assumptions, and can more accurately simulate the shape and stress distribution of the wheel-rail contact patch. By optimizing the seismic load simulation method, it effectively captures the dynamic response details of the track structure under long-term, large-scale earthquakes, addressing the shortcomings of traditional methods in simulation accuracy and computational cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0129] Figure 1 A schematic flow chart of a method for analyzing damage to hidden components of a track structure after an earthquake-induced train derailment is provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0130] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. The embodiments of the present invention are not limited thereto.

[0131] Example 1

[0132] A method for analyzing damage to hidden components of track structures after a train derailment caused by an earthquake, comprising:

[0133] S1. Build the track substructure model, including the rails, fastener system, track plate, filling layer, and base plate from top to bottom.

[0134] In S1, the rails, track slabs, filling layers, and base plates are all simulated using solid elements. The rails and ballastless track are connected by fasteners, which are simulated by nonlinear springs. The interlayers of the ballastless track multi-layer structure (including track slabs, filling layers, and base plates) adopt the improved cohesive force model under the seismic load mode. The interlayer damage initiation factor (F D ) can be expressed as:

[0135]

[0136] In the formula, <> is the Macaulay symbol, indicating that the crack initiation criterion calculation is performed only when the normal nominal stress is non-negative, which ensures that no damage will occur in the normal direction of the interlayer interface in the pure compression state; t n , t s , t t They represent the normal and longitudinal and transverse tangential stresses transmitted by earthquake waves through structural support points to interlayer non-structural support points, respectively. They represent the nominal peak stresses of the multi-layer track structure under the tensile and shear tests respectively;

[0137] When the wheel impact load increases to F after the earthquake and derailment D = 1, the damage factor D begins to develop and enters the softening and descending stage of the bilinear cohesive force model. The damage factor D can be defined as:

[0138]

[0139] Where, It represents the maximum effective displacement of the non-structural support point between floors under the action of earthquake load, is the effective displacement of the inter-layer non-structural support point corresponding to the earthquake load reaching the damage initiation stage, The displacement of the non-structural support points between layers corresponding to the complete damage of the track layers caused by an earthquake;

[0140] The mechanical properties of the rails, fastening systems and track plates described in S1 are simulated using homogeneous materials.

[0141] S2. Construct the rail mechanics equation and use the mass matrix, damping matrix and stiffness matrix to represent the wheel-rail equivalent load and fastener equivalent load on the rail;

[0142] In S2,

[0143] In the rail structure model, the rail mechanical equation can be expressed as:

[0144]

[0145]

[0146] In formula (1), M rr 、C rr , K rr are the mass matrix, damping matrix and stiffness matrix of the rail respectively; is the acceleration of the rail, is the speed of the rail, q r is the displacement of the rail; Q wr Indicates the wheel-rail equivalent load on the rail; Q rs is the equivalent load of the fasteners on the rail;

[0147] In formula (2), Nf is the number of fasteners in the model; q s is the displacement freedom of the ballastless track structure; q r is the rail displacement freedom; K rf,i and C rf,i are the stiffness and damping matrices of the interaction between rail and track plate at a single fastener; Hehe are the accelerations of the rail and track plate at a single fastener respectively;

[0148] In order to facilitate the subsequent establishment of a large vehicle-track system dynamics model, it is necessary to transform formula (2) and use the Boolean matrix to select the nodes connecting the track structure and the rails to achieve the same degree of freedom of the rails and ballastless track structures.

[0149]

[0150] In formula (3), B sr It is a Boolean matrix, that is, a 0-1 matrix, in which the elements are either 0 or 1; K rs 、C rs are the stiffness and damping matrices of the interaction between the rail and the track plate, respectively. Substituting formula (1) into formula (3) and then shifting the unknown variables such as rail structure displacement and velocity, the finite element dynamic equation of the rail can be obtained as follows:

[0151]

[0152] The rail mechanical equations in S2 are solved by finite element analysis.

[0153] S3. Use the Boolean matrix to select the nodes where the track structure connects to the rails, so that the degrees of freedom of the rails and the ballastless track structure are consistent;

[0154] In S3,

[0155] The formula used is as follows:

[0156]

[0157] Among them, K rs is the stiffness matrix of the fastener, C rs is the damping matrix of the fastener, B r 、B s is a Boolean matrix, q s is the displacement of the ballastless track structure;

[0158] The selected nodes of the Boolean matrix in S3 are determined according to the connection points between the track structure and the rails.

[0159] S4. Establish a ballastless track structure model in a physical coordinate system, and represent the external loads on the ballastless track structure and the interaction forces of adjacent track structures through mass matrix, damping matrix, and stiffness matrix;

[0160] In S4, the ballastless track structure model,

[0161] The control equation of the ballastless track structure in the physical coordinate system can be expressed as:

[0162]

[0163]

[0164] In formula (5), M ss 、C ss , K ss are the mass matrix, damping matrix and stiffness matrix of the ballastless track structure respectively; is the acceleration of the ballastless track structure, is the speed of the ballastless track structure, u s is the displacement of the ballastless track structure; Q sr is the external load on the ballastless track structure; Q ss It represents the interaction force between adjacent ballastless track structures. If the ballastless track is a unit structure, the parameter value is zero.

[0165] In formula (6), Nf is the number of fasteners in the model; q r,i is the rail displacement; u s,i is the displacement of the ballastless track structure at the fastener;

[0166] By reasonably retaining the modal order m of the ballastless track structure, the model calculation cost can be effectively reduced. After using the modal superposition method, the ballastless track dynamic model is greatly reduced from the real degrees of freedom to the generalized degrees of freedom m in the modal space.

[0167]

[0168] In formula (7), the modal matrix The dimension of is (s×m), which is the broadband modal set of ballastless track bed. s is the displacement of the s-order degree of freedom; q m is the displacement of the mth degree of freedom after order reduction;

[0169] According to the orthogonal conditions of the modal superposition method, formula (5) can be decoupled and expressed as follows:

[0170]

[0171] In formula (8), is the generalized mass matrix of the ballastless track structure; is the generalized damping matrix of the ballastless track structure; is the generalized stiffness matrix of the ballastless track structure; and Represents the generalized load on the ballastless track structure;

[0172] Different generalized matrices can be expressed as:

[0173]

[0174]

[0175]

[0176]

[0177]

[0178]

[0179]

[0180]

[0181] To facilitate the construction of the vehicle-track system dynamic equation, the ballastless track dynamic equation is described as Equation (11);

[0182] Where diag[] is the method for extracting diagonal elements;

[0183] The dynamic response of the support points and non-support points of the ballastless track multi-layer structure under seismic load is expressed as:

[0184]

[0185] Among them, the subscripts S and b are the non-support point and support point of the structure respectively. u are the acceleration, velocity and displacement of the support point, respectively, and F is the load at the support point;

[0186] The direct method is used to input the earthquake wave displacement, acceleration, and velocity response into the support points of the lower foundation structure, and the displacement response of the non-support points of the inter-story structure is solved through earthquake load transfer:

[0187]

[0188] The constitutive relation of the improved cohesion model under seismic load mode can be expressed as:

[0189]

[0190] Where K n,s,t is the interlayer interface stiffness in the absence of damage, u n,s,t is the relative displacement of non-structural support points between stories under earthquake loads. The damage factor D can be introduced into the inter-story stiffness matrix as a stiffness reduction factor.

[0191] The interaction forces between adjacent ballastless track structures described in S4 are represented by constraint conditions.

[0192] S5. Use the modal superposition method to effectively reduce the model calculation cost by retaining the modal order of the ballastless track structure;

[0193] In S5,

[0194] The modal superposition method is expressed as:

[0195]

[0196] According to the orthogonal conditions of the modal superposition method, the decoupling expression is:

[0197]

[0198] Among them, Φ i is the modal shape function, q i is the modal coordinate, M mm is the generalized mass matrix, C mm is the generalized damping matrix, K mm is the generalized stiffness matrix, is the modal acceleration, is the modal velocity, q m is the modal displacement, Q sf is a generalized representation of external loads, Q sm is a generalized representation of the interaction force between adjacent structures;

[0199] The modal superposition method described in S5 uses orthogonal conditions for decoupling.

[0200] S6. The critical wheel-rail contact relationship of derailment uses non-Hertz contact theory, studies the multi-point contact relationship of wheel and rail under complex earthquake loads based on virtual penetration, and uses the KikPiotrowski algorithm to analyze the normal contact model;

[0201] In S6,

[0202] The virtual penetration function is:

[0203]

[0204] Where δ is the wheel-rail penetration after force is applied, and f(y) is the wheel-rail surface function;

[0205] The Kik-Piotrowski algorithm described in S6 assumes that the wheel-rail profile and the amount of wheel-rail intrusion after loading jointly determine the shape of the wheel-rail contact patch.

[0206] S7, derailment criticality Kalker's FASTSIM algorithm is used to solve the wheel-rail tangential adhesion-creep state, and the creep force and slip velocity in the adhesion and creep zones within the wheel-rail contact patch are obtained;

[0207] In S7,

[0208] The solution is expressed as:

[0209] ΔS(x, y) = S(x, y) - LΔP t (x, y)

[0210] Where S(x, y) is the true sliding velocity, L is the Kalker flexibility coefficient, ΔP t (x, y) is the tangential force in the contact patch grid;

[0211] The FASTSIM algorithm described in S7 solves the wheel-rail tangential contact based on the finite difference method.

[0212] In S6 and S7,

[0213] Before the train derailed, the nonlinear elastic theory was used to simulate the track structure, and the wheel-rail contact force was calculated as follows:

[0214]

[0215] Among them, E * is the equivalent elastic modulus, ν is Poisson's ratio, R is the radius of curvature, and δ is the compression amount;

[0216] The relationship between the virtual penetration and wheel-rail deformation of the wheel-rail normal contact model is expressed as:

[0217]

[0218] Where N is the normal force of wheel-rail contact, R is the radius of curvature, E is the elastic modulus, and v is the Poisson's ratio;

[0219] The calculation formula of wheel-rail tangential contact force is:

[0220]

[0221] Among them, F t is the tangential contact force, μ is the friction coefficient, N is the normal force, v r is the relative sliding velocity, v s is the sliding speed threshold.

[0222] S8, based on the K-DOPs hierarchical tree bounding box collision detection method, identifying the collision and contact relationship between vehicle components and track components after derailment;

[0223] In S8, the vehicle components after derailment include wheels, brake discs, and gearboxes, and the track components include rails, fasteners, track plates, and track protection structures. Based on the idea of ​​outline discretization, the appearance of the vehicle and track system substructures is discretized into a large number of triangles. If two substructures of the vehicle track system collide after the vehicle derails, the triangles of the structural appearance will intersect. The intersection relationship between all wheel polygonal surfaces and ballastless track plate polygonal surfaces is detected. If the minimum distance is less than a certain capture distance (the empirical value is 10 -20 m) attaching the corresponding line to the intersection polygon and repeating the calculation to obtain its endpoints, and finally determining the spatial polygon where the vehicle component and the track component intersect;

[0224] S9. Based on the idea of ​​profile discretization, the collision contact elements and contact forces between the vehicle substructure and the track substructure after the train derailment are solved;

[0225] In S9, after the train derails, the normal force expression of the collision contact unit between the vehicle components and the track components is:

[0226]

[0227] Where, F dk Damping force part, F ck is the elastic part of the contact normal force, and its expression is:

[0228] F ck =k l ·A k ·u nk

[0229] Among them, the derailed vehicle components include wheels, brake discs, and gearboxes, and the track components include rails, fasteners, track plates, and track protection structures;

[0230] The viscous damping force is affected by the viscous damping coefficient and the normal component. The expression of the viscous damping force component is:

[0231]

[0232] Where d l is the damping coefficient of the surface elastic layer, v k is the rigid body relative velocity vector,

[0233] v k To express is for

[0234]

[0235] Where, are the relative linear velocity vector and angular velocity vector of the master and slave surfaces respectively;

[0236] The tangential force of the contact element depends on the tangential relative velocity and the normal force.

[0237] The expression of tangential force is:

[0238]

[0239] Where v ε is the sliding friction speed limit, v tk is the tangential relative velocity, and the expression of the tangential relative velocity is:

[0240] v tk =|v k -v nk ·n k |

[0241] The total force vector F of the contact element k From the normal component F nk Along its normal vector n k The projection and tangential force F tk The sum of the projections along the tangential velocity direction is expressed as:

[0242]

[0243] Finally, the forces of all contact elements are added together to obtain the total force of the contact patch between the wheel and the ballastless track slab.

[0244]

[0245] Where k is the number of contact elements within the finite polygon of contact between vehicle components and track components. Vehicle components include wheels, brake discs, gearboxes, car bodies, and axles. Track components include rails, fasteners, track plates, and track protection structures.

[0246] The establishment of the vehicle system dynamics model described in S9 includes the degrees of freedom in five directions: lateral, vertical, roll, nod, and shake.

[0247] S10. Establish a 35-degree-of-freedom vehicle system dynamics model including the vehicle body, bogie, and wheelset, perform force analysis on each component using the D'Alembert principle, and establish the vehicle system motion differential equation;

[0248] In S10, the vehicle system motion differential equation is:

[0249]

[0250] Where [M] is the train mass matrix, [C] is the damping matrix, and [K] is the stiffness matrix. is the acceleration vector of the train component, is the velocity vector of the train component, X is the displacement vector of the train component, F wr is the nonlinear wheel-rail contact force vector;

[0251] The solution of the differential equation of motion described in S10 is performed by the D'Alembert principle.

[0252] S11. In the vehicle system dynamics model, the mass matrix, damping matrix, and stiffness matrix of each vehicle component are substituted and combined with the nonlinear wheel-rail contact force vector to establish the differential equations of motion of each component of the vehicle system;

[0253] The earthquake load simulation method described in S11 includes a combination of time domain analysis and frequency domain analysis.

[0254] S12. Earthquake load simulation uses an improved earthquake load simulation method, which improves the accuracy of earthquake load simulation by adding actual data and introducing a combination of time domain analysis and frequency domain analysis;

[0255] S13, earthquake load simulation uses earthquake waves to transmit through the structural support point freedom degree to the structural non-support point freedom degree, and then affect the entire vehicle system;

[0256] When the earthquake load simulation results described in S13 are combined with the track substructure model, multiple simulation methods are used for comparative verification.

[0257] S14. Combine the improved earthquake load simulation results with the track substructure model to perform dynamic response analysis of the track structure under earthquake action.

[0258] Description in this application:

[0259] In S1, solid element is a model type in the finite element modeling method: shell, solid, etc.

[0260] In S3, nodes at the connection must meet displacement coordination conditions; otherwise, force transfer errors or numerical convergence may occur. The Boolean matrix screens key nodes to ensure that the number and type of degrees of freedom match, thus avoiding incompatible degree of freedom issues.

[0261] The constitutive relationship of the improved cohesion model under the seismic load mode is a professional term, and its simple explanation is that it represents the relationship between deformation and force.

[0262] In S10, a vehicle consists of 7 substructures: 1 body, 2 bogies, 4 wheelsets, each substructure has 5 degrees of freedom, for a total of 35 degrees of freedom.

[0263] Obviously, those skilled in the art may make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalents, this application is intended to include these modifications and variations.

Claims

1. A method for analyzing damage to hidden components of track structures after train derailment caused by an earthquake, characterized in that: include: S1. Build the track substructure model, including the rails, fastener system, track plate, filling layer, and base plate from top to bottom. S2. Construct the rail mechanics equation and use the mass matrix, damping matrix and stiffness matrix to represent the wheel-rail equivalent load and fastener equivalent load on the rail; S3. Use the Boolean matrix to select the nodes where the track structure connects to the rails, so that the degrees of freedom of the rails and the ballastless track structure are consistent; S4. Establish a ballastless track structure model in a physical coordinate system, and represent the external loads on the ballastless track structure and the interaction forces of adjacent track structures through mass matrix, damping matrix, and stiffness matrix; S5. Use the modal superposition method to effectively reduce the model calculation cost by retaining the modal order of the ballastless track structure; S6. The critical wheel-rail contact relationship of derailment uses non-Hertz contact theory, studies the multi-point contact relationship of wheel and rail under complex earthquake loads based on virtual penetration, and uses the KikPiotrowski algorithm to analyze the normal contact model; S7, derailment criticality Kalker's FASTSIM algorithm is used to solve the wheel-rail tangential adhesion-creep state, and the creep force and slip velocity in the adhesion and creep zones within the wheel-rail contact patch are obtained; S8, based on the K-DOPs hierarchical tree bounding box collision detection method, identifying the collision and contact relationship between vehicle components and track components after derailment; S9. Based on the idea of ​​profile discretization, the collision contact elements and contact forces between the vehicle substructure and the track substructure after the train derailment are solved; S10. Establish a 35-degree-of-freedom vehicle system dynamics model including the vehicle body, bogie, and wheelset, perform force analysis on each component using the D'Alembert principle, and establish the vehicle system motion differential equation; S11. In the vehicle system dynamics model, the mass matrix, damping matrix, and stiffness matrix of each vehicle component are substituted and combined with the nonlinear wheel-rail contact force vector to establish the differential equations of motion of each component of the vehicle system; S12. Earthquake load simulation uses an improved earthquake load simulation method, which improves the accuracy of earthquake load simulation by adding actual data and introducing a combination of time domain analysis and frequency domain analysis; S13, earthquake load simulation uses earthquake waves to transmit through the structural support point freedom degree to the structural non-support point freedom degree, and then affect the entire vehicle system; S14. Combine the improved earthquake load simulation results with the track substructure model to perform dynamic response analysis of the track structure under earthquake action.

2. The method for analyzing damage to hidden components of a track structure after an earthquake-induced train derailment according to claim 1 is characterized in that: In S1, the rails, track slabs, filling layers, and base plates are all simulated using solid elements. The rails and ballastless track are connected by fasteners, which are simulated by nonlinear springs. The interlayers of the ballastless track multi-layer structure (including track slabs, filling layers, and base plates) adopt the improved cohesive force model under the seismic load mode. The interlayer damage initiation factor (F D ) can be expressed as: In the formula, <> is the Macaulay symbol, indicating that the crack initiation criterion calculation is performed only when the normal nominal stress is non-negative, which ensures that no damage will occur in the normal direction of the interlayer interface in the pure compression state; t n , t s , t t They represent the normal and longitudinal and transverse tangential stresses transmitted by earthquake waves through structural support points to interlayer non-structural support points, respectively. They represent the nominal peak stresses of the multi-layer track structure under the tensile and shear tests respectively; When the wheel impact load increases to F after the earthquake and derailment D = 1, the damage factor D begins to develop and enters the softening and descending stage of the bilinear cohesive force model. The damage factor D can be defined as: Where, It represents the maximum effective displacement of the non-structural support point between floors under the action of earthquake load, is the effective displacement of the inter-layer non-structural support point corresponding to the earthquake load reaching the damage initiation stage, The displacement of the non-structural support points between layers corresponding to the complete damage of the track layers caused by an earthquake; The mechanical properties of the rails, fastening systems and track plates described in S1 are simulated using homogeneous materials.

3. The method for analyzing damage to hidden components of a track structure after an earthquake-induced train derailment according to claim 1 is characterized in that: In S2, In the rail structure model, the rail mechanical equation can be expressed as: In formula (1), M rr 、C rr , K rr are the mass matrix, damping matrix and stiffness matrix of the rail respectively; is the acceleration of the rail, is the speed of the rail, q r is the displacement of the rail; Q wr Indicates the wheel-rail equivalent load on the rail; Q rs is the equivalent load of the fasteners on the rail; In formula (2), Nf is the number of fasteners in the model; q s is the displacement freedom of the ballastless track structure; q r is the rail displacement freedom; K rf,i and C rf,i are the stiffness and damping matrices of the interaction between rail and track plate at a single fastener; Hehe are the accelerations of the rail and track plate at a single fastener respectively; In order to facilitate the subsequent establishment of a large vehicle-track system dynamics model, it is necessary to transform formula (2) and use the Boolean matrix to select the nodes connecting the track structure and the rails to achieve the same degree of freedom of the rails and ballastless track structures. In formula (3), B sr It is a Boolean matrix, that is, a 0-1 matrix, in which the elements are either 0 or 1; K rs 、C rs are the stiffness and damping matrices of the interaction between the rail and the track plate, respectively. Further, by substituting formula (1) into formula (3) and then shifting the unknown variables such as the rail structure displacement and velocity, the finite element dynamic equation of the rail can be obtained as follows: The rail mechanical equations in S2 are solved by finite element analysis.

4. The method for analyzing damage to hidden components of a track structure after an earthquake-induced train derailment according to claim 1 is characterized in that: In S3, The formula used is as follows: Among them, K rs is the stiffness matrix of the fastener, C rs is the damping matrix of the fastener, B r 、B s is a Boolean matrix, q s is the displacement of the ballastless track structure; The selected nodes of the Boolean matrix in S3 are determined according to the connection points between the track structure and the rails.

5. The method for analyzing damage to hidden components of a track structure after an earthquake-induced train derailment according to claim 1 is characterized in that: In S4, the ballastless track structure model, The control equation of the ballastless track structure in the physical coordinate system can be expressed as: In formula (5), M ss 、C ss , K ss are the mass matrix, damping matrix and stiffness matrix of the ballastless track structure respectively; is the acceleration of the ballastless track structure, is the speed of the ballastless track structure, u s is the displacement of the ballastless track structure; Q sr is the external load on the ballastless track structure; Q ss It represents the interaction force between adjacent ballastless track structures. If the ballastless track is a unit structure, the parameter value is zero. In formula (6), Nf is the number of fasteners in the model; q r,i is the rail displacement; u s,i is the displacement of the ballastless track structure at the fastener; By reasonably retaining the modal order m of the ballastless track structure, the model calculation cost can be effectively reduced. After using the modal superposition method, the ballastless track dynamic model is greatly reduced from the real degrees of freedom to the generalized degrees of freedom m in the modal space. In formula (7), the modal matrix The dimension is (s×m), which is the broadband modal set of ballastless track bed; u s is the displacement of the s-order degree of freedom; q m is the displacement of the mth degree of freedom after order reduction; According to the orthogonal conditions of the modal superposition method, formula (5) can be decoupled and expressed as follows: In formula (8), is the generalized mass matrix of the ballastless track structure; is the generalized damping matrix of the ballastless track structure; is the generalized stiffness matrix of the ballastless track structure; and Represents the generalized load on the ballastless track structure; Different generalized matrices can be expressed as: To facilitate the construction of the vehicle-track system dynamic equation, the ballastless track dynamic equation is described as Equation (11); Where diag[] is the method for extracting diagonal elements; The dynamic response of the support points and non-support points of the ballastless track multi-layer structure under seismic load is expressed as: Among them, the subscripts S and b are the non-support point and support point of the structure respectively. u are the acceleration, velocity and displacement of the support point, respectively, and F is the load at the support point; The direct method is used to input the earthquake wave displacement, acceleration, and velocity response into the support points of the lower foundation structure, and the displacement response of the non-support points of the inter-story structure is solved through earthquake load transfer: The constitutive relation of the improved cohesion model under seismic load mode can be expressed as: Where K n,s,t is the interlayer interface stiffness in the absence of damage, u n,s,t is the relative displacement of non-structural support points between stories under earthquake loads. The damage factor D can be introduced into the inter-story stiffness matrix as a stiffness reduction factor. The interaction forces between adjacent ballastless track structures described in S4 are represented by constraint conditions.

6. The method for analyzing damage to hidden components of track structure after train derailment caused by an earthquake according to claim 1, characterized in that: In S5, The modal superposition method is expressed as: According to the orthogonal conditions of the modal superposition method, the decoupling expression is: Among them, Φ i is the modal shape function, q i is the modal coordinate, M mm is the generalized mass matrix, C mm is the generalized damping matrix, K mm is the generalized stiffness matrix, is the modal acceleration, is the modal velocity, q m is the modal displacement, Q sf is a generalized representation of external loads, Q sm is a generalized representation of the interaction force between adjacent structures; The modal superposition method described in S5 uses orthogonal conditions for decoupling.

7. The method for analyzing damage to hidden components of track structure after train derailment caused by an earthquake according to claim 1, characterized in that: In S6, The virtual penetration function is: Where δ is the wheel-rail penetration after force is applied, and f(y) is the wheel-rail surface function; The Kik-Piotrowski algorithm described in S6 assumes that the wheel-rail profile and the amount of wheel-rail intrusion after loading jointly determine the shape of the wheel-rail contact patch.

8. The method for analyzing damage to hidden components of track structure after train derailment caused by an earthquake according to claim 1, characterized in that: In S7, The solution is expressed as: ΔS(x,y)=S(x,y)-LΔP t (x,y) Where S(x,y) is the true sliding velocity, L is the Kalker flexibility coefficient, ΔP t (x,y) is the tangential force in the contact patch mesh; The FASTSIM algorithm described in S7 solves the wheel-rail tangential contact based on the finite difference method.

9. The method for analyzing damage to hidden components of track structure after train derailment caused by an earthquake according to claim 1, characterized in that: In S6 and S7, Before the train derailed, the nonlinear elastic theory was used to simulate the track structure, and the wheel-rail contact force was calculated as follows: Among them, E * is the equivalent elastic modulus, v is Poisson's ratio, R is the radius of curvature, and δ is the compression amount; The relationship between the virtual penetration and wheel-rail deformation of the wheel-rail normal contact model is expressed as: Where N is the normal force of wheel-rail contact, R is the radius of curvature, E is the elastic modulus, and v is the Poisson's ratio; The calculation formula of wheel-rail tangential contact force is: Among them, F t is the tangential contact force, μ is the friction coefficient, N is the normal force, v r is the relative sliding velocity, v s is the sliding speed threshold; In S8, the vehicle components after derailment include wheels, brake discs, and gearboxes, and the track components include rails, fasteners, track plates, and track protection structures. Based on the idea of ​​outline discretization, the appearance of the vehicle and track system substructures is discretized into a large number of triangles. If two substructures of the vehicle track system collide after the vehicle derails, the triangles of the structural appearance will intersect. The intersection relationship between all wheel polygonal surfaces and ballastless track plate polygonal surfaces is detected. If the minimum distance is less than a certain capture distance (the empirical value is 10 -20 m) attaching the corresponding line to the intersection polygon and repeating the calculation to obtain its endpoints, and finally determining the spatial polygon where the vehicle component and the track component intersect; In S10, the vehicle system motion differential equation is: Where [M] is the train mass matrix, [C] is the damping matrix, and [K] is the stiffness matrix. is the acceleration vector of the train component, is the velocity vector of the train component, X is the displacement vector of the train component, F wr is the nonlinear wheel-rail contact force vector.

10. The method for analyzing damage to hidden components of track structure after train derailment caused by earthquake according to claim 1, characterized in that: In S9, after the train derails, the normal force expression of the collision contact unit between the vehicle components and the track components is: Where, F dk Damping force part, F ck is the elastic part of the contact normal force, and its expression is: F ck =k l ·A k ·u nk Among them, the derailed vehicle components include wheels, brake discs, and gearboxes, and the track components include rails, fasteners, track plates, and track protection structures; The viscous damping force is affected by the viscous damping coefficient and the normal component. The expression of the viscous damping force component is: Where d l is the damping coefficient of the surface elastic layer, v k is the rigid body relative velocity vector, v k To express is for Where, are the relative linear velocity vector and angular velocity vector of the master and slave surfaces respectively; The tangential force of the contact element depends on the tangential relative velocity and the normal force. The expression of tangential force is: Where v ε is the sliding friction speed limit, v tk is the tangential relative velocity, and the expression of the tangential relative velocity is: v tk =|v k -v nk ·n k | The total force vector F of the contact element k From the normal component F nk Along its normal vector n k The projection and tangential force F tk The sum of the projections along the tangential velocity direction is expressed as: Finally, the forces of all contact elements are added together to obtain the total force of the contact patch between the wheel and the ballastless track slab. Where k is the number of contact elements within the finite polygon of contact between vehicle components and track components. Vehicle components include wheels, brake discs, gearboxes, car bodies, and axles. Track components include rails, fasteners, track plates, and track protection structures. The establishment of the vehicle system dynamics model described in S9 includes the degrees of freedom in five directions: lateral, vertical, roll, nod, and shake.

Images