Reverse research method for three-dimensional mechanical curve of metro coupler based on pose parameters under impact working condition

Abstract

The invention discloses a subway coupler three-dimensional mechanical curve research reverse method based on pose parameters under an impact working condition, and relates to the technical field of train collision tests. The invention puts forward a construction method of a reverse finite element model for transverse and vertical deflection of a coupler under the impact working condition and an optimization reverse method based on a pose parameter under the impact working condition, and puts forward a reverse research thought for a mechanical curve of the coupler under the impact working condition by carrying out research on reverse calculation of a coupler force curve based on the pose parameter under the impact working condition. On the basis, a segmented reverse solving method and a reverse solving model based on a time sequence are provided, reverse solving of the coupler force curve of the coupler under the fixed working condition and the bias working condition is achieved, and the influence of coupler bias on the train collision behavior is analyzed on the basis of the research.

Description

Technical Field

[0001] The invention relates to the technical field of train collision tests, and in particular to an inverse method for studying three-dimensional mechanical curves of subway car hooks based on posture parameters under impact conditions. Background Art

[0002] As the operating speed of trains continues to increase, it has brought great convenience to people, but also brought potential safety hazards. Once a rail train accident occurs, it often causes serious economic losses and casualties. Unlike collision problems in other fields, since the train is composed of multiple carriages, its entire collision behavior is complex and changeable, often accompanied by zigzag derailment, vertical arching, lateral folding and overturning, etc. These collision behaviors often further cause squeezing and stacking between carriages, seriously endangering the lives of drivers and passengers. As a key component of train force transmission, the coupler buffer device is subjected to longitudinal, lateral and vertical forces during the collision process, which has a significant impact on the collision behavior of the train.

[0003] During a train collision, the three-dimensional forces generated by the deflection of the coupler during the collision have a significant impact on the train collision posture. Previous studies have shown that the large horizontal deflection angle and lateral pressure-bearing deflection behavior of the coupler during the collision are important causes of wheel-rail lateral displacement and derailment. At the same time, the vertical component of the compression force on the coupler due to the deflection of the coupler is the main reason for the damage to the components such as the hook tail frame and the base frame of the EMU coupler buffer device.

[0004] In order to obtain the mechanical properties of the coupler buffer device in all directions under collision conditions, experimental testing is the most effective means. For the test of the mechanical properties of the coupler in high-speed collision, a joint analysis is often performed through the force measuring wall of the train collision test bench and high-speed photography. However, this method cannot directly measure the coupler force under complex conditions, such as the measurement of the coupler force in a train line collision, and there is currently little research on the vertical and lateral curves of the coupler during the collision process.

[0005] Therefore, the present invention needs to design an inverse method for studying the three-dimensional mechanical curve of the subway hook based on the posture parameters under impact conditions to solve the above-mentioned problems. Summary of the invention

[0006] The purpose of the present invention is to provide an inverse method for studying the three-dimensional mechanical curve of a subway hook based on posture parameters under impact conditions in order to solve the above problems, thereby solving the problems mentioned in the background technology.

[0007] In order to solve the above problems, the present invention provides a technical solution:

[0008] A method for studying and inverting the three-dimensional mechanical curve of a subway car hook based on posture parameters under impact conditions is provided. The method comprises the following steps:

[0009] S1. Based on the research ideas of inverse analysis of the mechanical curve of the coupler under impact conditions and the current research status of scholars at home and abroad, a method for constructing a finite element model for inverse analysis of the lateral and vertical deflection of the coupler under impact conditions and an optimization inverse analysis method based on posture parameters under impact conditions are proposed;

[0010] S2. Taking the subway train coupler buffer device as the research object, the working principle of each part of the subway train coupler is analyzed, and the subway train coupler is divided into rigid parts, energy absorption parts and rotating parts to build the reverse model of the subway coupler under impact conditions. The subway single-side coupler impact test is carried out, and the test coupler curve is compared with the simulation coupler curve to verify the accuracy of the reverse model of the subway coupler under impact conditions;

[0011] S3. Taking the single-side coupler as the research object, without considering the coupler rotation, a segmented inverse method of the coupler characteristic curve based on time series is proposed, and the inverse results are compared with the test results. Then, the subway coupler offset collision impact test is carried out, and the fitting of the coupler rotation parameters is introduced into the segmented inverse method to realize the inverse of the three-dimensional force and three-dimensional motion posture of the coupler under the impact condition;

[0012] S4. Construct a finite element model of the collision between two subway trains, analyze and compare the effects of different rotation parameters on the body posture, and input the coupler rotation input curve and coupler mechanical curve obtained by inverse analysis of the test to analyze the collision posture of the two subway trains under different coupler offset states.

[0013] As a preferred technical solution, step S1 includes the following specific steps:

[0014] S101. Study the inverse method of the mechanical curve of the coupler, and build the corresponding inverse model and method of the coupler according to the mechanical characteristics and motion characteristics of the subway coupler itself;

[0015] S102. A method for constructing a finite element model for inverse calculation of the lateral and vertical deflection of a coupler is formed. According to the movement characteristics of the coupler, the movement of the coupler can be divided into three parts, namely, axial compression, vertical swing and lateral swing. A finite element model is constructed which reflects the compression energy absorption characteristics of the coupler in the axial direction and the lateral and vertical swing characteristics of the coupler in the vertical and lateral directions. Simulating the movement characteristics of the coupler by using beam units can not only shorten the calculation time, but also better reflect the movement of the coupler.

[0016] As a preferred technical solution, step S101 includes the following specific steps:

[0017] When the train is running normally, the coupler buffer device is responsible for transmitting traction and braking force. When a collision occurs, the coupler buffer device first compresses and absorbs energy. After the coupler has finished working, the main energy absorption structure, anti-climbing device and car body work in turn to absorb the collision energy.

[0018] The load, test simulation model and structural deformation response are represented in the form of input and output respectively. The known dynamic load can be solved through the known vibration system to achieve the solution of the result response. Conversely, the solution of the load can be obtained through the inverse inversion of the result response.

[0019] After realizing the process from load to response, the load parameters are set as variables, and these node responses are fitted with the experimental test responses through the optimization algorithm. After the node responses are fitted, the corresponding load variables are output. If the fitting effect is not good, the load variables are changed to continue fitting.

[0020] As a preferred technical solution, step S102 includes the following specific steps:

[0021] The direct relationship between the coupler force curve and displacement curve is established through the Beam unit model in LS-DYNA;

[0022] The calculation of the mechanical characteristics of complex structures is achieved by defining several nonlinear springs to represent the mechanical characteristics of the structure in certain directions.

[0023] As a preferred technical solution, step S2 includes the following specific steps:

[0024] S201. After the construction of the reverse model of the coupler under the impact condition is realized, the subsequent optimization reverse method is studied. The optimization algorithm embedded in Hyperworks supports users to write optimization programs in Compose. Users register the optimization program in the software program library and call the program through the program name.

[0025] S201, predicting a solution curve by using a proxy model method, wherein the proxy model includes a polynomial response surface model, a Kriging model, and a radial basis neural network model.

[0026] As a preferred technical solution, step S3 includes the following specific steps:

[0027] S301, performing overall inverse calculation of the coupler axial force of the posture response;

[0028] S302, performing a segmented inverse analysis of the time series of the coupler axial force curve;

[0029] S303, conducting a subway car coupler offset collision impact test;

[0030] S304. Perform inverse analysis on the subway car coupler force curve under offset collision.

[0031] As a preferred technical solution, step S301 includes the following specific steps:

[0032] For the inverse calculation of the coupler axial force, the overall inverse calculation was first performed, and the minimum fitting of the axial displacement area difference was taken as the optimization goal. The overall optimization of the coupler overall force value variable was performed 100, 200, 500, and 1000 times respectively. With the increase of the number of iterations, the average value of the force value error at each time point gradually decreased from 4.41% to 4.15%, and the maximum displacement deviation also gradually decreased, but there was no obvious change pattern in the maximum force value error.

[0033] The results show that as the displacement surface difference decreases, the axial force obtained by inverse calculation is closer and closer to the test, which verifies the convergence relationship between the displacement area difference and the inverse calculation accuracy. At the same time, the results also show that the increase in the number of iterations does not significantly improve the situation where the force value at some time points on the inverse curve deviates seriously from the test, which may be caused by too few variable values.

[0034] The step S302 includes the following specific steps:

[0035] In order to improve the accuracy of curve inversion and reduce the exponential increase in the difficulty of optimization due to the increase in variables, a method for inversion of the coupler axial force based on time series is proposed. For the test results of a single-sided coupler with one side of the coupler fixed, the buffer curve and the crush tube curve are input to increase the number of variables in sections, and the test coupler displacement-time curve is gradually fitted in sections. Finally, the inversion of the coupler axial force is achieved when the buffer is divided into 5 sections and the crush tube is divided into 3 sections.

[0036] The inverse results show that compared with the overall inverse, the maximum error of the inverse force value at each time point is reduced from 57.4% to 14.38%, a decrease of 43.02%; the average error of the inverse at each time point is reduced from 4.15% to 1.52%, a decrease of 2.63%, which shows that the segmented method is feasible for the inverse of the axial force of the coupler under impact conditions;

[0037] The step S303 includes the following specific steps:

[0038] In order to inversely determine the coupler force under offset working conditions, an offset collision impact test of subway couplers was carried out. In addition to analyzing the force-time, force-displacement and displacement-time curves of the coupler axial direction, the lateral swing displacement and vertical swing displacement of the coupler were extracted at four cross-sectional positions of the coupler under the top and left perspectives based on top and left high-speed photography.

[0039] The step S304 includes the following specific steps:

[0040] While inversely calculating the coupler axial force based on the time series, the coupler vertical swing and lateral swing parameters are introduced to simultaneously fit the lateral and vertical swing of the coupler in the collision. In the selection of the optimal solution for multi-objective optimization, the solution with the smallest axial displacement area difference is selected as the optimal solution for each segment iteration. According to the test data, the coupler force under the offset collision is inversely calculated. The maximum force error of the inverse curve is 12.98% compared with the test force curve, and the average force error is 3.22%. The lateral and vertical swing of the coupler are successfully fitted, and the input parameters of the coupler buffers on both sides, the coupler crush tube input parameters, the coupler lateral swing parameters, and the coupler vertical swing parameters are obtained.

[0041] As a preferred technical solution, step S4 includes the following specific steps:

[0042] S401, constructing a finite element model of two subway vehicle collisions and understanding offset conditions;

[0043] S402, observing the influence of different coupler rotation parameters on the vehicle body posture;

[0044] S403, analyzing the movement behavior of the coupler in the coupler offset state;

[0045] S404, analyzing the movement behavior of the vehicle body under the coupler offset state;

[0046] S405. Analyze the risk of train derailment when the coupler is offset.

[0047] As a preferred technical solution, step S401 includes the following specific steps:

[0048] The presence or absence of torque within the angle limit will affect the vertical movement of the vehicle axis and the amplitude of the vehicle's front and rear tilt angle;

[0049] The vertical motion amplitude of the center of mass is larger when there is torque than when there is no torque in the angle limit, while the opposite is true for the front and rear tilt angles of the vehicle body;

[0050] The step S402 includes the following specific steps:

[0051] Vertical offset and lateral offset have a great influence on the vertical and lateral swing of the coupler;

[0052] Vertical offset has the greatest impact on vertical swing and little impact on lateral swing. Similarly, lateral offset has the greatest impact on lateral swing.

[0053] As a preferred technical solution, step S403 includes the following specific steps:

[0054] During the collision, the first drop in the center of mass of the impact vehicle A is greater than that of the stationary vehicle B, and as the lateral offset and vertical offset increase, the vertical movement of the center of mass of the vehicle body increases;

[0055] The increase of vertical offset and lateral offset will increase the front-to-back tilt angle of vehicle B during the collision, and the front-to-back tilt speed of vehicle B is significantly greater than that of vehicle A under the same working conditions. The increase of lateral offset will significantly increase the rotation amplitude of vehicle A and vehicle B, but will have no significant effect on the front-to-back tilt angle of vehicle A.

[0056] The step S405 includes the following specific steps:

[0057] As the vertical offset and lateral offset increase, the risk of wheel derailment will increase, and the closer to the rear end of the train, the greater the lifting amount. The wheelset lifting of the impact-side train will be more severe than that of the stationary-side train. Under the vertical offset condition of the coupler, the wheel lifting is higher than that under the lateral offset condition. However, under the lateral offset condition, the left and right movement of the wheelset may be aggravated, increasing the risk of slipping off the track.

[0058] The beneficial effects of the present invention are as follows: the present invention conducts research on the inverse search of the coupler force curve based on posture parameters under impact conditions, proposes a research idea for the inverse search of the coupler mechanical curve under impact conditions, and on this basis proposes a segmented inverse search method and inverse search model based on time series, thereby realizing the inverse search of the coupler force curve under fixed conditions and offset conditions, and based on the above research, analyzes the influence of coupler offset on train collision behavior. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] For ease of explanation, the present invention is described in detail with reference to the following specific implementations and the accompanying drawings.

[0060] Figure 1 It is a flowchart of a method for inversely seeking a three-dimensional mechanical curve of a subway hook based on posture parameters under an impact condition provided by an embodiment of the present invention;

[0061] Figure 2 It is a flow chart of a method for studying the inverse of the three-dimensional mechanical curve of a subway hook based on posture parameters under an impact condition provided by an embodiment of the present invention;

[0062] Figure 3 It is a schematic diagram of the installation position and function of the coupler of the inverse method for studying the three-dimensional mechanical curve of the subway coupler based on the posture parameters under the impact condition provided by the embodiment of the present invention;

[0063] Figure 4 It is a description diagram of the load inversion problem of the inversion method for studying the three-dimensional mechanical curve of a subway hook based on posture parameters under impact conditions provided by an embodiment of the present invention;

[0064] Figure 5It is a deformation sequence diagram of a coupler offset collision test according to an inverse method for studying three-dimensional mechanical curves of a subway coupler based on posture parameters under impact conditions provided by an embodiment of the present invention;

[0065] Figure 6 It is a coupler offset collision force-time curve of a three-dimensional mechanical curve study inverse method of a subway coupler based on posture parameters under impact conditions provided by an embodiment of the present invention;

[0066] Figure 7 It is a schematic diagram of a finite element model for reverse analysis of a three-dimensional mechanical curve of a subway coupler under an impact condition provided by an embodiment of the present invention;

[0067] Figure 8 It is a schematic diagram of a collision condition of a method for studying the inverse of a three-dimensional mechanical curve of a subway hook based on posture parameters under an impact condition provided by an embodiment of the present invention;

[0068] Fig. 9 It is a schematic diagram illustrating the numbering of a car body bogie wheel pair according to an inverse method for studying a three-dimensional mechanical curve of a subway car coupler based on posture parameters under an impact condition provided by an embodiment of the present invention;

[0069] Fig.10 It is a schematic diagram of the positive direction of the vehicle body movement of the inverse method for studying the three-dimensional mechanical curve of a subway hook based on posture parameters under an impact condition provided by an embodiment of the present invention;

[0070] Fig.11 It is a schematic diagram of a conventional input method of coupler rotation parameters for a method for studying the inverse method of three-dimensional mechanical curves of a subway coupler based on posture parameters under impact conditions provided by an embodiment of the present invention;

[0071] Fig.12 It is a schematic diagram of the wheel lifting action sequence of an A-4 wheelset under a vertical offset of 50 mm according to the inverse method for studying the three-dimensional mechanical curve of a subway coupler based on posture parameters under an impact condition provided by an embodiment of the present invention;

[0072] Fig.13 It is a finite element model diagram of a coupler according to an inverse method for studying three-dimensional mechanical curves of a subway coupler based on posture parameters under impact conditions provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0073] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application will be further described in detail below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present application.

[0074] The embodiment provided in this application is an embodiment of a method for analyzing the correlation between driving behavior factors and driving risks based on big data.

[0075] like Figure 1-Figure 13 As shown, the specific implementation of the present invention adopts the following technical solutions:

[0076] The embodiment of the present invention provides a method for studying and inverting the three-dimensional mechanical curve of a subway car hook based on posture parameters under an impact condition, and the method comprises the following steps:

[0077] S1. Based on the research ideas of inverse analysis of the mechanical curve of the coupler under impact conditions and the current research status of scholars at home and abroad, a method for constructing a finite element model for inverse analysis of the lateral and vertical deflection of the coupler under impact conditions and an optimization inverse analysis method based on posture parameters under impact conditions are proposed;

[0078] The step S1 comprises the following specific steps:

[0079] S101. Study the inverse method of the mechanical curve of the coupler, and build the corresponding inverse model and method of the coupler according to the mechanical characteristics and motion characteristics of the subway coupler itself;

[0080] The step S101 includes the following specific steps:

[0081] The installation position and working process of the coupler buffer device are shown in the attached Figure 3 When the train is running normally, the coupler buffer device is responsible for transmitting traction and braking force. When a collision occurs, the coupler buffer device first compresses and absorbs energy. After the coupler has finished working, the main energy absorption structure, anti-climber and car body work in turn to absorb the collision energy. In addition to the axial compression action, the coupler buffer device can also swing to a certain extent in the axial and vertical directions.

[0082] If the load, test simulation model and structural deformation response are expressed as input and output respectively, then Figure 4 To express this problem, if the dynamic load is known, the result response can be solved through the known vibration system. Conversely, the load solution can be obtained by inverse inversion of the result response.

[0083] After the process from load to response is realized, the load parameters are set as variables, so that different node responses will be obtained under different loads. These node responses are fitted with the experimental test responses through the optimization algorithm. After the node responses are fitted, the corresponding load variables are output. If the fitting effect is not good, the load variables are changed to continue fitting.

[0084] S102, forming a method for constructing a finite element model for inverse calculation of the lateral and vertical deflection of a coupler. According to the movement characteristics of the coupler, the movement of the coupler can be divided into three parts, namely, axial compression, vertical swing and lateral swing. A finite element model is constructed that reflects the compression energy absorption characteristics of the coupler in the axial direction and the lateral and vertical swing characteristics of the coupler in the vertical and lateral directions. Simulating the movement characteristics of the coupler by using beam units can not only shorten the calculation time, but also better reflect the movement of the coupler.

[0085] The step S102 includes the following specific steps:

[0086] The direct relationship between the coupler force curve and displacement curve is established through the Beam unit model in LS-DYNA;

[0087] Beam elements, with their accuracy and fast computing power, have become the key to improving the efficiency of finite element models. Traditionally, beam elements are mainly divided into two types: Euler-Bernoulli beams and Timoshenko beams. When the ratio of the cross-sectional size to the length of the beam is less than 1 / 15, the Euler-Bernoulli beam can be used, but it cannot handle shear forces. During the calculation process, the Euler-Bernoulli beam assumes that the shear surface always remains at the neutral layer and determines the stress distribution on the beam by linear interpolation. In contrast, the Timoshenko beam can handle shear stress and is suitable for situations where the cross-sectional size and length are relatively large. All beam elements are set according to their cross-sectional shape and material parameters. Since the cross-sectional geometric parameters are directly called for calculation, the beam element is faster than the finite element mesh model, which requires continuous calculation of the node stiffness matrix;

[0088] Belytschko Beam is a commonly used beam element in LS-DYNA. The axial force calculation formula is:

[0089]

[0090] Among them, the axial stiffness of the beam element is K a =AE / l0, A is the cross-sectional area of ​​the beam element, E is the elastic modulus of the beam element, l0 is the original length of the beam element, and δ is the axial deformation;

[0091] The bending moment calculation formula of the Belytschko Beam element is:

[0092]

[0093] The bending constant in the formula is obtained by the following formula:

[0094]

[0095]

[0096] The torque calculation formula of the Belytschko Beam unit is:

[0097]

[0098] in:

[0099]

[0100] Since collision problems in the field of rail vehicles often involve large-scale and nonlinear deformation of structures, the beam unit used for static and modal analysis in the past cannot solve the above problems. To solve the above problems, discrete beam units are proposed. It calculates the mechanical characteristics of complex structures by defining a number of nonlinear springs to express the mechanical characteristics of the structure in certain directions. There are many types of discrete beam units available in LS-DYNA. Among them, MAT119 can specify the mechanical curves on the six degrees of freedom of the beam unit as needed, and can define the loading and unloading curves in each direction separately. If material failure simulation is required, relevant failure parameters can also be defined;

[0101] The calculation formula of the discrete beam element force is:

[0102]

[0103] in, It is the force in the local coordinate system, generally the unit axial force.

[0104] The force component of the discrete element in the global coordinate system is obtained by the cosine of the element direction:

[0105]

[0106] Where:

[0107]

[0108] Where (x, y, z) is the position of the unit node in the global coordinate system;

[0109] For nonlinear discrete beam elements defined using force-displacement curves or force-velocity curves, the element force can be calculated using the following formula:

[0110]

[0111] Among them, the coefficient K is the total change in the length of the unit, and the slope of the force-displacement curve or force-velocity curve corresponding to Δl;

[0112] The discrete beam element model provides a flexible modeling method, that is, it can be used without defining cross-sectional properties, and can also be set to be massless. According to the needs of the simulation, the mass matrix can also be defined. When the discrete beam has rotational freedom in any direction, a non-zero mass moment must be specified. This model can accurately describe the tensile, compressive or bending mechanical properties in all directions, which is consistent with the mechanical behavior of the rail vehicle energy absorption structure during the impact process. Therefore, in theory, it is completely feasible to use the discrete beam element model to simplify the finite element mesh model of the energy absorption structure;

[0113] The beam unit can show different mechanical behaviors from the spring when compressed. The distance from the end point of the unloading curve to the origin represents the final deformation of the beam unit. The area enclosed by the loading and unloading curves and the displacement represents the energy absorbed by the beam unit in this direction. This loading / unloading curve definition method is similar to the force-displacement curve characteristics of the energy absorbing tube. However, in the crashworthiness problem, the beam unit model simulating the energy absorbing structure usually does not define the mechanical properties of the tensile stage.

[0114] The discrete beam element model is an effective tool for simulating the mechanical properties of complex structures in nonlinear large deformation problems. Since its definition parameters only include mechanical characteristic curves, there are limitations in the input of geometric parameters. The beam element is defined by the cross-sectional shape and therefore has a real geometric structure. Since the discrete beam element does not have a directly corresponding geometric parameter, its geometric structure can be any structure that satisfies its defined mechanical characteristics.

[0115] In summary, the present invention intends to use discrete beam elements to establish an equivalent model of the coupler energy absorption structure to simulate the axial energy absorption characteristics of the coupler under impact conditions;

[0116] Under impact conditions, the coupler will produce lateral and vertical movements during the collision process due to the different initial collision postures of the hook heads on both sides. The lateral and vertical swings of the coupler during the movement process can be understood as the process in which the coupler body rotates around the coupler base with the coupler base as the rotation center. This process can be realized by the ball joint unit in LS-DYNA.

[0117] In the LS-DYNA Material Manual, the complex motion relationship between two objects can be realized through hinge elements;

[0118] The hinge element in LS-DYNA is implemented by the penalty method, by defining the constraint equation:

[0119] C(x i ,x i )=0 (2-17)

[0120] And the Lagrangian penalty coefficient -1 / 2kC 2(x i , x j ) is added to the coefficients to obtain the nodal forces at nodes i and j:

[0121]

[0122] However, the forces acting on the nodes must be converted into forces acting on the rigid body. The forces and moments of the nodes around the center of mass can be expressed as follows:

[0123] F i x =f i (2-19)

[0124]

[0125] The penalty stiffness k is chosen so that it does not control the stable time step. For the central difference method, the stable time step Δt is limited by the following condition:

[0126]

[0127] where Ω is the highest frequency in the system. The six vibration frequencies associated with each rigid body are determined by solving their e-value problems assuming k = 1. For an object with m constraint equations, the linearized equation for the translational degree of freedom is:

[0128]

[0129] For the frequency Where M is the mass of the rigid body, θ is the rotation amount, and the corresponding rotation equation is:

[0130]

[0131] Where J is the inertia tensor and K is the stiffness matrix of the moment contribution from the penalty constraint. The stiffness matrix is ​​the moment contribution through the constraint and can be approximated as:

[0132] F x =-kr i ×(θ×r i ) (2-24)

[0133] r i =x i -X cm (2-25)

[0134] and through

[0135]

[0136] Can get

[0137]

[0138] The rotation frequency Ω 2 The equation is det|K-Ω 2 The root of J|=0, the maximum frequency on all rigid bodies with k=1 is defined as Ωmax, and the time step scale factor TSSF is introduced, the equation of k is:

[0139]

[0140] Joint constraints are defined based on the displacement of each node. No matter whether the node belongs to the solid element of the structural element or not, only its translational degrees of freedom are used in the constraint equation;

[0141] For a spherical joint, three constraint equations are required to define the spherical joint for nodes i and j:

[0142] x 1i -x 1j =0,x 2i -x 2j =0,x 3i -x 3j =0 (2-29)

[0143] The revolute joint requires five constraints, defined by two revolute joints, for a total of six constraint equations. Redundancy in the joint constraint equations is not important due to the use of penalty formulations. The cylindrical joint is defined by taking the revolute joint and eliminating the penalty forces along the directions defined by the two cylindrical joints. In a similar way, the planar joint is defined by eliminating the penalty forces perpendicular to the two spherical joints.

[0144] A translation joint is a cylindrical joint that allows sliding along its axis but not rotation. An extra pair of nodes is required outside the axis to provide additional constraints. The only effective force between the extra nodes acts in a direction perpendicular to the plane defined by the three pairs of nodes. The universal angle is defined by four nodes. Let the nodes on one entity be i and k, and the nodes on the other entity be j and l. The two nodes i and j are used to define the spherical joint of the first three constraint equations. The fourth constraint equation is:

[0145] C(x i ,x j ,x k ,x l )=(x k -x i )·(x i -x j )=0 (2-30).

[0146] S2. Taking the subway train coupler buffer device as the research object, the working principle of each part of the subway train coupler is analyzed, and the subway train coupler is divided into rigid parts, energy absorption parts and rotating parts to build the reverse model of the subway coupler under impact conditions. The subway single-side coupler impact test is carried out, and the test coupler curve is compared with the simulation coupler curve to verify the accuracy of the reverse model of the subway coupler under impact conditions;

[0147] The step S2 comprises the following specific steps:

[0148] S201. After the construction of the reverse model of the coupler under the impact condition is realized, the subsequent optimization reverse method is studied. The optimization algorithm embedded in Hyperworks supports users to write optimization programs in Compose. Users register the optimization program in the software program library and call the program through the program name.

[0149] S201, using a surrogate model method to predict the solution curve, there are three main methods for building a surrogate model: a polynomial response surface model, a Kriging model, and a radial basis neural network model;

[0150] As a preferred technical solution, after realizing the construction of the inverse model of the coupler under impact conditions, it is necessary to further study the subsequent optimization inverse method. Hyperworks not only has built-in common optimization algorithms, but also supports users to write optimization programs in Compose. Users register the optimization program in the software library and can call the program by the program name. When solving the optimization task of discrete variables, a variety of strategies can be adopted. For example, the adaptive response surface method ARSM dynamically adjusts the response surface model by analyzing the relationship between parameter changes and objective functions to more effectively identify key parameters. This method can converge quickly, but is sometimes limited by local optimal solutions. In order to overcome this challenge, the global response surface search method GRSM extends ARSM by considering a wider gradient interval to avoid falling into the local optimal solution too early. In addition, the genetic algorithm GA, as a heuristic search method, explores in the solution space by simulating natural selection and genetic mechanisms, and is suitable for complex and multi-peak optimization problems;

[0151] In addition to using the built-in optimization algorithm in Hyperstudy, you can also use the proxy model method to predict the solution curve. At present, there are three main proxy model construction methods commonly used in the field of engineering optimization: polynomial response surface model, Kriging model and radial basis neural network model.

[0152] (1) Polynomial response surface model

[0153] The polynomial response surface model (PRS) is a method for exploring the relationship between design variables and responses based on experimental design results. Its model construction is simple, the calculation requirements are small, and the relationship between variables and responses can be expressed through clear mathematical formulas, which makes PRS particularly suitable for dealing with problems with low complexity and low nonlinearity.

[0154] The commonly used polynomial response surface model is generally a quadratic polynomial model. For m-dimensional variables x = [x1,…,x m ] T , whose response is y=[y1,…,y m ] T , then the quadratic polynomial response surface model between variable x and response y can be expressed as

[0155]

[0156] In the formula, α0, α i , α ii and α ij The coefficients to be determined are arranged in order to form a vector α, and α is obtained by the least squares method using the information of n sample points, as shown below.

[0157] a=(X T X) -1 X T Y (2-32)

[0158] (2) Kriging model

[0159] The Kriging model (KRI) is an interpolation technique based on statistical theory. It determines the distance range of the point to be interpolated that is affected by the known sample points by analyzing the spatial attributes of the known sample points, and uses the relevant sample points to obtain an unbiased estimate of the point to be interpolated.

[0160] The typical Kriging model is divided into two parts: linear regression and random distribution, as shown below:

[0161]

[0162] Where y(x) represents the response value; β = [β1 β2 … β p ] T is a column vector of regression model coefficients; f(x)=[f1(x) f2(x) … f p (x)] T is the polynomial function of the sample point x, z(x) is a function that follows the normal distribution N(0,σ 2 ) represents a random model of the local deviation from the approximate model;

[0163] (3) Radial Basis Function Neural Network Model

[0164] The radial basis function neural network is a specific type of artificial neural network. This network is mainly composed of three layers and has the characteristics of fast learning speed, excellent approximation performance and generalization ability. Compared with other types of neural networks, the structure of the RBF neural network is relatively simple. It can be used for function approximation and pattern classification tasks. The RBF neural network converges quickly because it is a local approximation network. For each input, the weights on the network only need to be adjusted locally, which makes the learning speed relatively fast.

[0165] For n-dimensional input variables [x1 x2 … x n ] T , whose response value is [y1 y2 … y n ] T , if the number of sample points is m, for any input variable x, the corresponding output response y can be expressed as:

[0166]

[0167] Where, Φ=[φ1 φ2 … φ n ] T is the radial basis function of the input variable; ω=[ω1 ω2 … ω n ] T is the weighting coefficient of the radial basis function; φ=φ(||xx i ||) represents any input variable x to a known sample point x i The Euclidean distance of

[0168] In summary, there are many related optimization methods, but for the input of the axial beam unit mechanical curve in the coupler inverse model under impact conditions constructed in this paper, it is very likely that multiple nodes are input together, and it is easy to fall into the local optimum during the optimization process. Therefore, in order to reduce the risk of falling into the local optimum and improve the optimization effect, the GRSM method is selected as the optimization method.

[0169] S3. Taking the single-side coupler as the research object, without considering the coupler rotation, a segmented inverse method of the coupler characteristic curve based on time series is proposed, and the inverse results are compared with the test results. Then, the subway coupler offset collision impact test is carried out, and the fitting of the coupler rotation parameters is introduced into the segmented inverse method to realize the inverse of the three-dimensional force and three-dimensional motion posture of the coupler under the impact condition;

[0170] The step S3 comprises the following specific steps:

[0171] S301. Perform overall inverse calculation of the coupler axial force of the posture response: First, the overall inverse calculation of the coupler axial force is performed, and the minimum fitting of the axial displacement area difference is taken as the optimization target. The overall optimization of the coupler overall force value variable is performed 100, 200, 500, and 1000 times respectively. With the increase of the number of iterations, the average value of the force value error at each time point gradually decreases from 4.41% to 4.15%, and the maximum displacement deviation also gradually decreases, but there is no obvious change pattern of the maximum force value error;

[0172] The results show that as the displacement surface difference decreases, the axial force obtained by inverse calculation is closer and closer to the test, which verifies the convergence relationship between the displacement area difference and the inverse calculation accuracy. At the same time, the results also show that the increase in the number of iterations does not significantly improve the situation where the force value at some time points on the inverse curve deviates seriously from the test, which may be caused by too few variable values.

[0173] (1) Basic model settings

[0174] Since only the coupler force curve is considered for inverse analysis, and the action of the circular tubes on both sides in the test occurs after the coupler fails, in order to reduce the calculation time, the finite element model under the coupler impact condition is simplified, the protective devices on both sides and the coupler base box are removed, and the coupler axial force inverse model is obtained. Since the hook head on one side of the coupler is completely fixed on the rigid wall in this test, there is no large lateral vertical swing. Therefore, only the axial crushing force of the coupler is inversely analyzed in this test. In the construction of the model, the trolley is established using a hexahedral solid mesh and assigned a rigid material MAT_RIGID. The contact between the wheel and the rail is defined by AUTOMATIC_SURFACE_TO_SURFACE. The speed and mass settings are the same as the test results, and the trolley mass is loaded to the center of mass position.

[0175] (2) Variable settings

[0176] Based on the previous article, a total of 7 characteristic values ​​of the coupler crush tube and rubber buffer force-displacement curves are set as variables, and their variation range is ±10% of the design parameters;

[0177] In the displacement curve of the crushed tube, the first variable has not only the change in force value, but also the change in displacement. This is to restore as much as possible the slope of the gradual increase in stiffness when the crushed tube begins to crush;

[0178] (3) Setting optimization goals

[0179] In the coupler impact test, the displacement, velocity and acceleration time curves of the coupler can be directly obtained through high-speed photography. However, since the velocity and acceleration curves are actually obtained by derivation of the displacement time curve, there will be some distortion compared with the real velocity and acceleration data in this process. Therefore, in this paper, the force curve is mainly obtained by optimizing the iteration by fitting the displacement time curve. In order to reduce the occurrence of local optimal solutions, the GRSM global optimization algorithm is selected. In order to fit the two displacement time curves, a function named curve_difference is defined in the program. After inputting the displacement time curves of the two curves, the function will calculate the shape area difference of the two curves and output it. Therefore, the optimization goal is to minimize the shape difference between the displacement time curve of the coupler test and the axial displacement time curve of the coupler simulation. The axial displacement is represented by "Z", which is expressed mathematically as follows:

[0180] Min{curve_difference(z)} (4-1)

[0181] Secondly, in order to obtain the compression displacement curve of the coupler, the data of 5 points are read at the coupler head and coupler base in the model respectively, and the data of the measurement points on the same side are averaged and then subtracted to obtain the compression displacement curve of the coupler;

[0182] Through the GRSM global optimization algorithm, the initial variables were iterated 100, 300, 500, and 1000 times, and the corresponding optimal solutions were the 85th, 195th, 423rd, and 855th times, respectively. The collision interface axial force of the optimal solution simulation model obtained by iteration was compared with the experimental test force curve. After 100 iterations, the optimal solution that met the response setting was the 85th time. The trend of the overall force value has begun to approach the test curve, but there is still a large deviation before 0.1s and after 0.8s. The maximum force value error at each time point is 53.1%, and the average force value error at each time point is 4.41%. The displacement error gradually increases in a wave shape, and the maximum displacement error is 0.581mm.

[0183] Table 1 The results of 100 rounds of overall inverse optimization for the optimal solution

[0184]

[0185] After 200 iterations, the optimal solution that meets the response setting is the 195th iteration. It can be seen that the overall force value trend has begun to approach the test curve, but there are still large errors before 0.1s and after 0.8s. The relative error of the force value is slightly increased compared with 100 iterations, and its maximum value is 54.3%. The average error of the force value is 4.28%. The displacement error gradually increases in a wave shape, and its maximum error is reduced compared with 100 iterations, and its deviation is 0.461mm.

[0186] Table 2 The results of 200 rounds of overall inverse optimization for the optimal solution

[0187]

[0188] After 500 iterations, the optimal solution that meets the response setting is the 423rd iteration. It can be seen that the overall force trend has begun to approach the test curve, but there is still a large deviation before 0.1s and after 0.8s. The relative error of the force value is reduced compared with 200 iterations, and its maximum value is 52.6%. The average error of the force value is 4.21%. The displacement error increases in a wave shape, then decreases, and then increases again. Its maximum error is reduced compared with 200 iterations, and its maximum error is 0.196mm.

[0189] Table 3 500 times of overall inverse optimization results for the optimal solution

[0190]

[0191] After 1000 iterations, it can be seen that the overall force trend has begun to approach the test curve, but there are still large deviations before 0.1s and after 0.8s. The deviation of the force-time curve in the middle section is small. The relative error of the force value increases compared with 500 iterations, and its maximum value is 57.4%. The average error of the force value is 4.15%. The displacement error increases in a wave shape, then decreases, and then increases. Its maximum error is slightly reduced compared with 500 iterations, and its error is 0.149mm.

[0192] Table 4 1000 times of overall inverse optimization results for the optimal solution

[0193]

[0194] As the number of iterations increases, the simulation displacement curve gradually approaches the test curve. The displacement area difference decreases fastest in the first 100 iterations. After more than 500 iterations, the displacement area difference decreases very slowly.

[0195] Table 5 Iteration results analysis

[0196]

[0197] It can be seen from Table 5 that with the increase of the number of iterations, the average force error gradually decreases from 4.41% to 4.15%, and the maximum displacement deviation also gradually decreases, but the maximum force error does not have an obvious change pattern. From the above data, it can be obtained that the size of the displacement curve area difference in the model and the accuracy of the inverse force value are in a convergent relationship, that is, with the decrease of the displacement area difference, the inverse force curve gradually approaches the test force curve. Combined with the relative error diagram of the force-time curve of each iteration result, it is found that the time points at which the maximum error of the inverse force value occurs are almost at the same time node. Therefore, with the increase of the number of iterations, the maximum force error does not decrease significantly, which may be due to too few eigenvalue variables of the initial force curve.

[0198] It can be seen from the force curve comparison that even after 1000 iterations, there is still a large deviation between the first 0.1s and the last 0.8s of the force curve, and the effect of reducing this deviation by increasing the number of iterations is not ideal. This may be due to the lack of variables on the initial curve, which makes it impossible to fit better. If you want to increase the variable points on the curve, it will bring a problem. However, as the variables increase, the number of optimizations will increase exponentially. In order to increase the number of variable points and reduce the number of optimizations, this paper intends to divide the entire inverse process into segments according to the time series and add variable points to each segment to solve this problem.

[0199] S302, perform segmented inverse analysis of the time series of the coupler axial force curve: In order to improve the curve inverse accuracy and reduce the exponential increase in the difficulty of optimization due to the increase in variables, a method for inverse analysis of the coupler axial force based on the time series is proposed. For the test results of a single-sided coupler with one side of the coupler fixed, the buffer curve and the crush tube curve are input respectively to increase the number of variables in segments, and segmented and step-by-step fitting is performed according to the test coupler displacement-time curve. Finally, the inverse analysis of the coupler axial force is achieved when the buffer is divided into 5 segments and the crush tube is divided into 3 segments.

[0200] The inverse results show that compared with the overall inverse, the maximum error of the inverse force value at each time point is reduced from 57.4% to 14.38%, a decrease of 43.02%; the average error of the inverse at each time point is reduced from 4.15% to 1.52%, a decrease of 2.63%, which shows that the inverse method of the axial force of the coupler under the impact condition is feasible by the segmented method;

[0201] When the subway coupler studied in the present invention takes effect, the buffer takes effect first, and then the crush pipe takes effect. Therefore, the buffer and the crush pipe can be reversed in sequence. This study is only for the buffer coupler type that is insensitive to speed changes. Compared with the whole curve, the segmented curve can effectively increase the inverse variable points while reducing the number of inverse iterations. However, compared with the whole curve, errors may occur at the segment connection. This error will cause the next curve to shift, resulting in larger errors in subsequent curves and distortion of the inverse result of the whole curve.

[0202] In order to reduce the possible errors at the segment connection points, it is proposed to use the connection points of each segment solution as the initial points for the next segment solution, and then iterate the solution at the connection points to reduce the errors at the connection points.

[0203] Two curves are used to inverse the force-time curve before 0.2s. Three variable points are set for each curve. The first curve has only two variable points because of the existence of time 0. The data point at time 0.1s is the intersection of the two curves. After the first curve is solved, the variable point at 0.1s is brought into the second curve for solution, and so on until the whole curve is solved.

[0204] In order to improve the inverse accuracy of the coupler force curve, the segmented method is used to iteratively solve the impact curve of the buffer in the front half of the coupler and the impact curve of the crush tube. According to the main parameters of the test coupler, the compression stroke of the buffer is 55mm, and the end point of the stroke corresponds to the time point of the test test at around 0.013s. Therefore, the first 0.013s of the curve is iteratively inverted. Three variable points are set for each curve segment, and the displacement step length between each point is the same. The GRSM algorithm is used for optimization and iteration 100 times for each segment.

[0205] In order to determine the optimal number of segmentation of the front coupler buffer impact curve, the above method was used to perform segmented iterative solutions for 2, 3, 4 and 5 segment curves respectively;

[0206] Table 6 Buffer impact curve second segment inverse optimization results

[0207]

[0208] After solving the force curve of the buffer part through two segmented iterations, the maximum relative error of the force value is 18.91%, and the corresponding time point is 0.009s. The average error of the force value during this period is 9.23%. The maximum displacement error is 0.948mm, and the corresponding time point is 0.002s. The average displacement error during this period is 0.256mm.

[0209] Table 7 Buffer impact curve three-step reverse optimization results

[0210]

[0211] After solving the force curve of the buffer part through three segmented iterations, the maximum relative error of the force value is 18.75%, and the corresponding time point is 0.001s. The average error of the force value during this period is 8.76%. The maximum displacement error is 0.949mm, and the corresponding time point is 0.002s. The average displacement error during this period is 0.236mm.

[0212] Table 8 Buffer impact curve 4-step reverse optimization results

[0213]

[0214] After solving the force curve of the buffer part through four segmented iterations, the maximum relative error of the force value is 14.56%, and the corresponding time point is 0.003s. The average force error during this period is 7.47%. The maximum displacement deviation is 0.942mm, and the corresponding time point is 0.002s. The average displacement deviation during this period is 0.229mm.

[0215] Table 9 Buffer impact curve 4-step reverse optimization results

[0216]

[0217]

[0218] After solving the force curve of the buffer part through five segmented iterations, the maximum relative error of the force value is 14.38%, and the corresponding time point is 0.003s. The average force error during this period is 6.69%. The maximum displacement deviation is 0.751mm, and the corresponding time point is 0.002s. The average displacement error during this period is 0.222mm.

[0219] With the increase of segmentation times, the test curve and the inverse curve, except for the fourth time, gradually approach the inverse curve in trend. From the value of the force-time curve, with the increase of segmentation times, the maximum force deviation and relative force error gradually decrease, and the average force error of all curves is less than 10%;

[0220] As the number of segmentation increases, it can be seen that the area difference of the displacement curve is getting smaller and smaller, but the magnitude of the reduction is getting smaller and smaller. This may be caused by the cumulative superposition of errors at each connection point as the number of segmentation increases. Although iterations have been repeated at the connection points, this cannot eliminate the errors. It also shows that the more segments a segment is, the better. As the number of segmentation increases, the errors will accumulate more and more, making the displacement area difference fitting effect smaller and smaller.

[0221] Table 10 Average relative error of inverse force in each section before 0.013s

[0222]

[0223] It can be seen from Table 10 that with the increase of the number of segmentation times, the maximum deviation of the inverse force value, the average value of the inverse force error, the maximum displacement error and the average displacement error of the buffer curve gradually decrease. The maximum error of the inverse force value decreases from 18.91% to 14.38%, a decrease of 4.53%; the average value of the inverse force error decreases from 9.23% to 6.69%, a decrease of 2.54%; the maximum displacement error decreases from 0.948mm to 0.751mm, a decrease of 0.197mm; the average displacement error decreases from 0.256mm to 0.222mm, a decrease of 0.034mm;

[0224] After the buffer impact curve was inverted for 5 times, the maximum deviation of the inverse force value was reduced to 14.38%. Compared with the maximum deviation of the overall inverse of 57.4%, the accuracy of the inverse curve was improved by 43.02%.

[0225] Compared with the inverse solution of the entire curve, the force obtained by segmented iteration is obviously closer to the test curve, which shows that this method is feasible;

[0226] According to the results of the buffer impact curve fitting in the previous article, the crush pipe impact curve is fitted on this basis, and the last variable point of the buffer curve is also brought into the solution of the crush pipe curve; in order to determine the optimal number of segmented iterative solutions for the crush pipe, the curves are inversely solved in 1, 2 and 3 segments, with 3 variable points set in each segment, and the displacement step length between each variable point is the same. The GRSM algorithm is used for 100 iterations;

[0227] Table 11 Result table of 1-step reverse optimization of the impact curve of the collapsed pipe

[0228]

[0229] After solving the buffer curve and solving the force curve of the crushed pipe part through 100 iterations, the maximum relative error of the force value is 16.55%, and the corresponding time point is 0.088s. The average force error during this period is 4.21%. The maximum displacement error is 0.951mm, and the corresponding time point is 0.002s. The average displacement error during this period is 0.046mm.

[0230] Table 12 Results of 2-step reverse optimization of the impact curve of the collapsed pipe

[0231]

[0232] On the basis of solving the buffer curve, after solving the force curve of the crushed pipe part through two segmented iterations, the maximum relative error of the force value is 15.51%, and the corresponding time point is 0.088s. The average force value error during this period is 2.73%. The maximum displacement deviation is 0.949mm, and the corresponding time point is 0.002s. The average displacement deviation during this period is 0.032mm.

[0233] Table 13 Results of three-step reverse optimization of the impact curve of the crushed pipe

[0234]

[0235] On the basis of solving the buffer curve, after solving the force curve of the crushed pipe part through three segmented iterations, the maximum relative error of the force value is 15.43%, and the corresponding time point is 0.085s. The average force value error during this period is 1.52%. The maximum displacement deviation is 0.581mm, and the corresponding time point is 0.002s. The average displacement deviation during this period is 0.025mm.

[0236] As the number of segmentation increases, it can be seen that the inverse force curve from no segmentation to 3 segmentation becomes more and more stable and closer to the test curve, and the deviation of the platform force is also gradually decreasing;

[0237] The displacement area difference decreases significantly with the increase of segmentation times, among which the reduction from segment 1 to segment 2 is the largest, and the reduction from segment 2 to segment 3 is significantly reduced. The segmented inverse results of the impact curve of the collapsed pipe are sorted out to obtain Table 14;

[0238] Table 14 Segmental inverse results of the impact curve of the collapsed pipe

[0239]

[0240] It can be seen from the table that with the increase of the number of segmentation of the impact curve of the collapsed pipe, the maximum error of the inverse force value, the average error of the inverse force value, the maximum displacement error and the average displacement error gradually decrease, among which the maximum error of the inverse force value decreases from 16.55% to 15.43%, a decrease of 1.12%; the average error of the inverse force value decreases from 4.21% to 1.52%, a decrease of 2.69%; the maximum displacement error decreases from 0.951mm to 0.581mm, a decrease of 0.37mm; the average displacement error decreases from 0.046mm to 0.032mm, a decrease of 0.021mm;

[0241] Compared with the optimal solution of 1000 iterations of overall inverse, the maximum error of the inverse force value was reduced from 57.4% to 15.43%, a decrease of 41.97%; the average error of the inverse force value was reduced from 4.15% to 1.52%, a decrease of 2.63%. Compared with the overall inverse method, the segmented inverse of the axial force curve based on the time series uses fewer iterations and obtains a more accurate coupler axial force curve, which further verifies that the segmented method is reliable and feasible for inverse coupler curves.

[0242] S303, conducting an offset collision impact test of a subway coupler: In order to realize the inverse calculation of the coupler force under the offset working condition, an offset collision impact test of a subway coupler was carried out. In addition to analyzing the force-time, force-displacement and displacement-time curves of the coupler axial direction, the lateral swing displacement and vertical swing displacement of the coupler were extracted at four cross-sectional positions of the coupler under the top and left perspectives based on top and left high-speed photography;

[0243] Basic parameters of subway car coupler offset collision impact test:

[0244] In actual train collision scenarios, there are often lateral horizontal displacement differences and vertical height differences between the couplers on both sides. In order to meet actual engineering needs and explore the reverse calculation of the mechanical characteristic curve of the coupler under the condition of coupler offset, a coupler offset collision impact test was carried out. The impact side coupler was installed 40mm higher than the impacted side coupler, and the coupler height difference was set according to the collision scenario specified in the European standard EN15227.

[0245] Before the test, the opposite side hook and auxiliary energy absorbing tooling are installed on the force measuring panel, and the impact side hook and protective tooling and counterweight are installed on the test trolley. At the beginning of the test, the test trolley is driven by an air cannon and drives the impact side hook and protective tooling towards the rigid wall at a certain speed. The protective device and auxiliary energy absorbing tooling take effect after the energy absorption of the hook is completed. Their function is to absorb the remaining collision energy to ensure the safety of the test.

[0246] The relevant test equipment mainly includes a trolley and counterweight, 2 high-speed cameras, 3 sets of 5 force sensors, 1 velocimeter, and 2 acceleration sensors. The basic information of the relevant test instruments and the main technical parameters of the test are shown in the following table;

[0247] Table 15 Main technical parameters of coupler offset collision impact test

[0248]

[0249] Table 16 Main technical parameters of relevant test instruments

[0250]

[0251] Before the test, the installation of various components was completed according to the test requirements. In order to show the relevant test details for easy understanding, various perspectives of the test site were sorted out;

[0252] Analysis of subway car coupler offset collision impact test results:

[0253] (1) Collision deformation analysis

[0254] In this test, two high-speed cameras were used to shoot the process of the specimen hitting the rigid wall from the left and top perspectives respectively. The deformation sequence diagrams of the left and top perspectives of the coupler during the collision were analyzed and explained. Each perspective captured the collision start time, coupler contact time, coupler hook time, compression time, coupler compression stroke maximum time, and collision end time, as shown in the attached figure. Figure 5 ;

[0255] It can be observed from the images taken by high-speed photography that during the coupling process, the hook heads on both sides slide up and down to complete the coupling action, and then the coupler buffers and crush tubes on both sides are compressed synchronously. When the crush tubes on both sides are compressed to a certain extent, the compression speed of the left crush tube is obviously faster than that of the right crush tube, until the left crush tube reaches the maximum stroke. After that, the right crush tube continues to compress until it reaches the maximum stroke, triggering the right coupler shear bolt, causing the coupler to fail and fall off. From then on, the entire coupler energy absorption process ends, and the remaining kinetic energy is continuously absorbed by the auxiliary energy absorption tooling on both sides.

[0256] (2) Collision axial displacement analysis

[0257] According to the collision sequence images of the specimen recorded by the high-speed camera, a series of identification points are selected in the image using the motion image sequence analysis software. The moment when the coupler starts the collision action in the high-speed photography is used as the initial moment, and the marking points selected on the trolley are used to analyze the displacement changes of the specimen and the trolley during the collision. The final displacement-time curve in this article is drawn based on the difference between the identification points selected on the trolley without relative motion, and 3 times are taken at the same position for analysis, and the average value is taken to eliminate the system error;

[0258] The displacement of the specimen gradually increased with time. At 0.125s, the bolts of the test coupler were completely sheared off and reached the maximum stroke. At this time, the total displacement was 620.32mm, of which the compression displacement of the left coupler was 305.47mm and the compression displacement of the right coupler was 314.85mm.

[0259] (3) Collision vertical displacement analysis

[0260] In order to obtain the lateral motion posture data of the coupler, three points were taken on four cross sections of the couplers on both sides, and the average value was taken to analyze the vertical motion of the coupler;

[0261] The collision sequence images of the specimens recorded by the high-speed camera were analyzed by using the motion image sequence analysis software. The moment when the coupler started to collide in the high-speed photography was taken as the initial moment, and the vertical displacement curve of the coupler was obtained.

[0262] (4) Collision lateral displacement analysis

[0263] In order to obtain the lateral motion posture data of the coupler, three points were taken on four cross sections of the couplers on both sides, and the average value was taken to analyze the vertical motion of the coupler;

[0264] The collision sequence images of the specimens recorded by the high-speed camera were analyzed by using the motion image sequence analysis software. The moment when the coupler started to collide in the high-speed photography was taken as the initial moment, and the vertical displacement curve of the coupler was obtained.

[0265] (5) Collision force analysis

[0266] During the test, three 200t force sensors were used to measure the collision absorption capacity of the coupler buffer. The force-time data on the three force sensors were superimposed to obtain the coupler offset collision force-time curve, as shown in the attached figure. Figure 6 ;

[0267] The collision process lasted for 0.125s, which was consistent with the results of high-speed photography analysis. The coupler buffers on both sides were compressed before 0.024s, and the coupler crushing tubes on both sides were in stable compression from 0.024 to 0.110s, with a stable deformation force value of 1228.73kN. The shear bolt shear movement interval was from 0.110 to 0.125s, with a peak force of 1437.32kN.

[0268] (6) Collision energy analysis

[0269] In this section, the collision energy absorbed by the coupler during the collision process is mainly investigated. The collision force-time curve and displacement-time curve are synthesized to obtain the collision force-displacement curve. By integrating the force-displacement curve, the energy absorbed by the coupler in this collision test can be obtained. The energy absorbed by the coupler in this collision test is 659.75 kJ.

[0270] S304. Inverse analysis of subway coupler force curve under offset collision: While inversely analyzing the coupler axial force based on the time series, the coupler vertical swing and lateral swing parameters are introduced to simultaneously fit the lateral and vertical swing of the coupler in the collision. In the selection of the optimal solution for multi-objective optimization, the solution with the smallest axial displacement area difference is selected as the optimal solution for each segment iteration. Based on the test data, the coupler force under offset collision is inversely analyzed. The maximum force value error of the inverse curve compared with the test force curve is 12.98%, and the average force value error is 3.22%. The lateral and vertical swing of the coupler are successfully fitted, and the input parameters of the coupler buffers on both sides, the coupler crush tube input parameters, the coupler lateral swing parameters, and the coupler vertical swing parameters are obtained;

[0271] Iterative parameter settings of the subway coupler force inverse model:

[0272] (1) Inverse model setting for coupler offset collision

[0273] Since the auxiliary energy absorption devices on both sides take action after the coupler has finished its action, in order to reduce the reverse calculation time, the reverse model of the coupler offset collision was simplified based on the test site conditions. The auxiliary energy absorption devices and protective tooling on both sides were removed, and the finite element reverse model of the coupler under the corresponding working conditions was constructed, as shown in the attached figure. Figure 7 As shown;

[0274] The left side is the opposite side coupler, and the right side is the impact side coupler. According to the test conditions, a 40mm vertical height difference is set at the coupler head, where the impact side coupler is 40mm higher than the opposite side coupler. According to the on-site counterweight conditions, a mass of 32.36t and a speed of 25km / h are assigned to the center of mass of the trolley. The contact algorithm CONTACT_AUTOMATIC_SUFACE_TO_SUFACE is set at the coupler heads on both sides and between the wheels and rails of the trolley. The relevant parameters of the coupler model are established according to Chapter 3 of the article.

[0275] (2) Inverse iterative variable setting

[0276] In the collision of couplers, in addition to the axial compression deformation, the couplers will also produce lateral and vertical swings. In order to inversely fit this action, vertical and lateral rotation parameters are introduced on the basis of segmented fitting of axial displacement, that is, the lateral and vertical displacements in the collision of couplers are fitted simultaneously by changing the torque corresponding to different vertical and lateral torsion angles. In the finite element model of couplers, the lateral and vertical movements of couplers are controlled by lateral torsion BEAM and vertical torsion BEAM in combination with ball joint units.

[0277] Since the lateral and vertical swing angles of the coupler in the test did not reach the designed swing threshold and the swing amplitude was not large, the vertical and lateral rotation angle-torque input curves of the coupler were equivalent to a stiffness curve when setting the variables. Therefore, the torque exceeding the test test was equivalent to the slope of the previous curve, and the vertical and lateral rotation parameters of the coupler were changed by changing the size of the corresponding torque at the maximum rotation angle.

[0278] Since the same type of coupler is used in the test, the initial input parameters of the coupler model are the same. Since two variables, the maximum lateral torque and vertical torque at the swing angle limit, are newly added in each segmented iteration, the number of iterations is increased to 300 times, and the optimization algorithm adopts GRSM.

[0279] (3) Setting optimization objectives and selecting the optimal solution

[0280] On the basis of the previous article, the experimental displacement-time curve has been used to realize the inverse calculation of the axial force of the coupler. For the offset collision condition of the coupler, in order to fit the axial force of the coupler in the collision while fitting the vertical and lateral swing posture of the coupler, the response points are marked on the simulation model for the same four vertical and lateral cross-sectional positions in the test, and the lateral swing and vertical swing posture of the coupler are fitted while fitting the axial force. The curve fitting function is curve_difference, which fits the shape area difference of the two curves. Z, H and C are used to represent the axial, lateral and vertical displacement fitting of the coupler, respectively. The multi-objective optimization is expressed mathematically as follows:

[0281]

[0282] In the process of segmented iteration, the selection of the optimal solution for each iteration is involved. For the coupler buffer device, the focus is on its axial mechanical characteristics, followed by its vertical and lateral swing characteristics. Therefore, in the selection of the optimal solution, the solution of the axial displacement fitting closest to the experimental test is taken as the optimal solution for the iterative inverse in this paper.

[0283] Based on the previous article, the segmented inverse method of the coupler force curve has been determined. First, the impact curve of the coupler buffer is inversely calculated, and the axial force of the collision interface obtained by inverse calculation is compared with the test force measurement result; after five segmented iterative solutions;

[0284] The overall deviation between the test force curve and the inverse force curve is not large, among which the maximum deviation of the force value is 8.56%. The average error of the force value during this period is 4.64%. The displacement curve fits well, among which the maximum deviations of the displacement of the couplers on both sides are 0.097mm and -0.127mm. On this basis, the segmented iteration of the crushed tube part is continued, and the inverse result of the axial force of the coupler offset collision is obtained;

[0285] The overall deviation between the test force curve and the inverse force curve is not large, among which the maximum error of the force value is 12.98%, and the average error of the force value during this period is 3.22%. The displacement curve is well fitted, among which the maximum deviation of the displacement is 0.144mm, and the input curves of the buffer and the crush tube after iteration are obtained;

[0286] The vertical displacement of the coupler in the time period of 0s-0.09s before the shear bolt of the coupler test is sheared is taken as the target curve. After segmented optimization iteration together with the axial force, the vertical displacement posture of the coupler that best fits the test test is obtained.

[0287] Under the collision condition with a vertical height difference of 40mm between the couplers, the coupler head swings slightly up and down after being connected. At section 1, the test displacement has the same trend as the inverse displacement, but the corresponding displacement peaks and troughs have some deviations. The maximum displacement deviation of the two curves at the same time is 1.26mm. At the hook head on the impacted side of section 2, the curve change trend is the same as the displacement change trend of the bottom end of the buffer on the same side, and the maximum displacement deviation at the same time is 3.12mm. At the hook head on the impact side of section 3, the test displacement and the inverse displacement are in good agreement in the first two troughs, and there are some deviations between the two curves in the last two troughs, and the maximum difference in displacement at the same time is 2.41mm. At section 4, the inverse displacement curve is ahead of the test curve, and its trough value is slightly larger than the test, and the maximum difference in displacement at the same time is 0.96mm. The absolute value of the torque at the angle limit of the left coupler is 15.6kN·m, and the absolute value of the torque at the angle limit of the right coupler is 14.1kN·m. The vertical force during the collision process was obtained by reading the vertical force of the coupling collision section of the iterative model. The vertical force showed an overall upward trend. The average vertical force during the whole process was 110.78 kN, and the maximum vertical force was 155.32 kN.

[0288] The lateral displacement of the coupler in the time period of 0s-0.09s before the shear bolt of the coupler test is cut off is taken as the target curve. After the segmented optimization iteration together with the axial force, the lateral displacement posture of the coupler that best fits the test test is obtained;

[0289] Under the collision condition with a vertical height difference of 40mm between the hooks, the hooks on both sides of the hooks are slightly misaligned after the hooks are connected. At section 1, the test displacement and the reverse displacement have the same trend, but there is a large deviation at 0.5s, and the maximum displacement deviation is 0.06mm. At the hook head on the impacted side of section 2, the test and reverse displacements are well matched before 0.2s, and then the displacement deviation increases first, then decreases, and then increases. The maximum deviation of displacement at the same time is 0.19mm. At the hook head on the impacted side of section 3, the test displacement and reverse displacement are well matched before 0.3s. The maximum deviation of the displacement at the same time is 0.12mm. At section 4, the overall trend of the test curve is consistent with the inverse curve. The maximum deviation of the displacement at the same time is 0.05mm. The absolute value of the torque at the angle limit is 1.26kN·m, and the absolute value of the torque at the angle limit of the right coupler is 1.61kN·m. The lateral force during the collision process is obtained by reading the lateral force of the coupler collision section of the iterative model. The lateral force shows an overall upward trend. The average lateral force of the whole process is 3.66kN, and the maximum lateral force is 5.51kN.

[0290] S4. Construct a finite element model of two subway train collisions, analyze and compare the effects of different rotation parameters on the body posture, and input the coupler rotation input curve and coupler mechanical curve obtained by inverse analysis of the test, and analyze the collision posture of the two subway trains under different coupler offset states;

[0291] The step S4 comprises the following specific steps:

[0292] S401, constructing a finite element model of a collision between two subway vehicles and understanding the offset working condition: the presence or absence of torque within the angle limit will affect the vertical movement of the center of mass of the vehicle body and the amplitude of the front and rear tilt angle of the vehicle body;

[0293] The vertical motion amplitude of the center of mass is larger when there is torque than when there is no torque in the angle limit, while the opposite is true for the front and rear tilt angles of the vehicle body;

[0294] Construction of the finite element model of two subway car collisions:

[0295] Taking a certain type of subway train head car as the research object, the body model and bogie model of the subway train head car were established. Since in the subsequent analysis and research, only the collision characteristics of the coupler and the train posture during the coupler action were studied, and the possible body collision was not studied, the body part was established with rigid material MAT20.

[0296] In the train collision simulation, since the bogie is difficult to deform, in order to reduce the calculation time, the bogie is established using shell units and given MAT20 rigid material. In order to simulate the motion characteristics of the bogie, nonlinear discrete beam units are used to simulate the primary and secondary suspensions of the bogie. The bogie traction rod shaft and the bogie base are constrained by a rotating hinge, and the contact CONTACT_SURFACE_TO_SURFACE is set for the parts that move relative to each other during the bogie collision process.

[0297] A simplified finite element model of the coupler was constructed, and a finite element model of the subway train head car collision was established, in which the coupler base and the car body were connected using CONSTRAINED_RIGID_BODIES, the contact CONTACT_SURFACE_TO_SURFACE was set between the bogie and the wheel-rail, and the wheel-rail friction coefficient was set to 0.10;

[0298] In order to study the collision posture of two subway trains under the coupler offset condition, the coupler parameters obtained by inverse analysis of the coupler offset collision test were selected as the input of the coupler curve.

[0299] In the setting of the collision condition, the collision speed is set to 25km / h, and the total mass of the car body is the mass in normal working state plus the mass of 50% of the seated passengers, which is 45.2t. In order to explore the influence of different initial postures on the collision process, two working conditions are designed: Working condition 1 is that the coupler of the impact car A is higher than the passive car B by hmm, and the h values ​​are 0mm, 20mm, 40mm and 50mm respectively; Working condition 2 is that the coupler of the impact car A is laterally offset by qmm compared with the passive car B, and the q values ​​are 0mm, 20mm, 40mm and 50mm respectively. The schematic diagram of the working condition is shown in the attached figure. Figure 8 As shown;

[0300] In order to facilitate the description of the car body, coupler and bogie in the following text, the objects involved in the model are numbered and explained. The impact side train is defined as car A, the stationary car is defined as car B, and the bogies in the initial state of the collision are numbered as shown in the attached figure. Fig. 9 As shown;

[0301] Taking the impact train A as an example, A represents the car body, the first number represents the position of the wheelset, from the front to the rear, they are wheelset 1, wheelset 2, wheelset 3 and wheelset 4, and the last L and R represent the left and right wheels. For example, "B-4-L" represents the left wheel of the 4th wheelset of the impacted train.

[0302] In order to facilitate the description of the vertical motion of the center of mass of the vehicle body, the lateral motion of the center of mass, the front and rear tilting motion of the vehicle body, and the front and rear rotation motion of the vehicle body during the collision, the following Fig.10 The positive direction of the relative motion is defined in;

[0303] For vertical movement of the center of mass, the positive direction is along the positive Z axis; for horizontal movement of the center of mass, the positive direction is along the positive Y axis; for the front and rear tilt angle of the vehicle body, the center of the vehicle body is the rotation center, the downward rotation of the vehicle head is negative, and the upward rotation is positive; for the rotation angle of the vehicle body, the clockwise direction around the z axis is the positive direction;

[0304] S402, observe the influence of different coupler rotation parameters on the vehicle body posture: vertical offset and lateral offset have a great influence on the vertical and lateral swing of the coupler;

[0305] The vertical offset has the greatest impact on the vertical swing, but has little impact on the lateral swing. The lateral offset also has the greatest impact on the lateral swing.

[0306] The mechanical properties of the coupler have a significant impact on the collision behavior of the train. Therefore, in order to simulate the mechanical properties of the real coupler, in addition to defining the axial mechanical parameters of the coupler, the vertical and lateral rotation parameters of the coupler must also be defined. In the study of train collision posture, the input method for the rotation parameters of the lead car coupler is usually in the following form, as shown in the attached figure. Fig.11 As shown;

[0307] The physical meaning of this input method is that the coupler can rotate freely within the angle limit, and cannot continue to rotate when the angle limit is reached. However, in fact, since the lead car coupler has an automatic centering function, using this input method may not be able to simulate the real coupler mechanical characteristics;

[0308] Based on the previous research, the corresponding coupler rotation parameter curves have been obtained. In order to explore the influence of the two input methods on the train collision posture, based on the 40mm vertical height difference of the coupler in the two train collision models in the previous text, the two coupler rotation parameter input methods are used for calculation respectively when other parameters remain unchanged. The movement of the impact vehicle A during the collision process is analyzed and compared. Fig.11 The input of the coupler rotation parameters is defined as no torque within the angle limit;

[0309] For the vertical movement of the center of mass of the vehicle and the front-to-back tilt angle of the vehicle, the overall movement trends are the same when using the two input methods. The presence or absence of torque within the angle limit will affect the vertical movement of the center of mass of the vehicle and the amplitude of the front-to-back tilt angle of the vehicle. The vertical movement amplitude of the center of mass is larger when there is torque in the angle limit than when there is no torque. For the front-to-back tilt angle of the vehicle, the opposite is true. When there is torque within the angle limit, the front-to-back tilt angle of the vehicle will decrease compared to the case without torque. For the lateral movement of the center of mass of the vehicle and the front-to-back rotation angle of the vehicle, when using the two input methods, the trends in the first half of the entire movement process are the same, while there are large differences in the second half.

[0310] Different input methods of coupler rotation parameters have a certain influence on the vehicle body motion posture. Since the corresponding vertical and lateral rotation parameters have been obtained by inverse calculation of the vertical and lateral motion posture of the coupler in the previous article, the rotation parameters obtained by inverse calculation will be used to study and analyze the vehicle body posture in the subsequent research.

[0311] S403, analyzing the movement behavior of the coupler under the coupler offset state: during the collision process, the first drop in the center of mass of the impact vehicle A is greater than that of the stationary vehicle B, and as the lateral offset and vertical offset increase, the vertical movement of the center of mass of the vehicle body increases;

[0312] The increase in vertical offset and lateral offset will increase the front-to-back tilt angle of Car B during the collision, and under the same working conditions, the front-to-back tilt speed of Car B is significantly greater than that of Car A. The increase in lateral offset will significantly increase the rotation amplitude of Car A and Car B, but will have no significant effect on the front-to-back tilt angle of Car A.

[0313] During a train collision, the coupler will not only experience axial compression, but also vertical and lateral swings. Next, based on the collision finite element model of two subway vehicles and the input parameters of the coupler model, the different offset working conditions set in the previous article were calculated. The axial motion behavior of the coupler during the collision under different working conditions and the vertical and lateral swing behaviors of the coupler were analyzed and compared through the simulation results.

[0314] When there is a vertical height difference, the action process of the coupler buffer device is similar. The final deformation diagram of the coupler during the collision shows that the final lateral and vertical deflections of the coupler gradually increase with the increase of the initial lateral and vertical offsets;

[0315] With the increase of vertical offset, the vertical rotation angle of the coupler gradually increases, and the vertical swing curve is wavy in shape, first decreasing and then increasing. When the vertical offset of the coupler is 50 mm, the maximum vertical rotation angle of the coupler is -1.08°. The increase of vertical offset has no obvious effect on the lateral rotation of the coupler. Before 0.11 s, the trends of the lateral rotation angles of the coupler under different vertical offsets are roughly the same, and the maximum lateral deflection angle is 0.176°.

[0316] With the increase of vertical offset, the vertical rotation angle of the coupler gradually increases, and the vertical swing curve is wavy in shape, first decreasing and then increasing. When the vertical offset of the coupler is 50 mm, the maximum vertical rotation angle of the coupler is -1.08°. The increase of vertical offset has no obvious effect on the lateral rotation of the coupler. Before 0.11 s, the trends of the lateral rotation angles of the coupler under different vertical offsets are roughly the same, and the maximum lateral deflection angle is 0.176°.

[0317] With the increase of lateral offset, the lateral deflection angle of the coupler gradually increases, and the maximum lateral deflection angle is 0.948° when the offset is 50mm; however, the increase of lateral offset has little effect on the vertical rotation of the coupler during the collision, and the overall curve is wavy, first decreasing, then increasing, then decreasing, and then increasing;

[0318] 0-0.16s is taken as the compression energy absorption stage of the coupler, and the average value of the vertical deflection and the lateral deflection in this period is taken to obtain the average rotation angle of the coupler under the influence of the vertical deflection and the lateral deflection;

[0319] With the increase of vertical and lateral offsets, the average values ​​of the coupler angles increased. The vertical offset had a greater impact on the vertical angle of the coupler. When the height difference was 50 mm, the average vertical angle of the coupler had reached -0.802°, with a significant increase. However, it had a smaller impact on the head shaking angle, with a slightly smaller increase. When the vertical height difference was 50 mm, the average lateral angle of the coupler was 0.047°, which was only 0.008° higher than that without offset. On the contrary, the lateral offset had a greater impact on the average lateral angle of the coupler. When the lateral offset was 50 mm, the average lateral angle of the coupler had reached 0.842°, but the head shaking angle was only -0.116°.

[0320] S404, analyzing the movement behavior of the vehicle body under the coupler offset state;

[0321] During a train collision, the center of mass of the train body often moves vertically and laterally, accompanied by the forward and backward tilt and rotation of the train body. Next, the vertical displacement of the center of mass of the train body, the horizontal displacement of the center of mass of the train body, the forward and backward tilt angle of the train body, and the rotation angle of the train body under different offset conditions are analyzed;

[0322] The vertical and lateral motions of the center of mass of cars A and B under different collision conditions were extracted, and the motion of the center of mass under different offsets was obtained;

[0323] Under vertical offset, the vertical motion behaviors of the center of mass of car A and car B are very similar in the first 0.05s, both moving downward, but the downward motion of the center of mass of car A is larger. As the offset increases, the maximum vertical displacement of the center of mass of car A and car B increases to a certain extent.

[0324] For the horizontal movement of the center of mass, there is no obvious regularity in the horizontal movement of the center of mass of car A, but for car B, before 0.13s, as the offset increases, the horizontal displacement movement amplitude of the center of mass of car B increases significantly;

[0325] Under lateral offset, for the vertical movement of the center of mass, the increase of lateral offset has no obvious effect on the movement of the center of mass of vehicle A, but it will increase the movement amplitude of the center of mass of vehicle B. Similarly, before 0.05s, the downward movement amplitude of the center of mass of vehicle A is significantly greater than that of vehicle B.

[0326] For the horizontal motion of the center of mass, the increase of the lateral offset will affect the amplitude of the motion of the center of mass of vehicle A, but will not have much impact on its motion law. For vehicle B, as the lateral offset increases, the horizontal displacement of the center of mass increases significantly before 0.1 s;

[0327] Combining the above two working conditions, it can be found that during the collision, the first drop in the center of mass of the impact vehicle is greater than that of the stationary vehicle, and with the increase of the lateral offset and vertical offset, the vertical and horizontal motions of the center of mass of the vehicle body in the first 0.1sB will increase;

[0328] The rotation of the vehicle body under different collision conditions was extracted and the rotation of the vehicle body under different conditions was obtained.

[0329] Under vertical offset, for the front and rear tilt angles of the vehicle body, as the vertical offset increases, the tilt amplitudes of both vehicle A and vehicle B gradually increase. Under the same working conditions, the tilt amplitude of vehicle B is greater than that of vehicle A, and the tilt speed of vehicle B in the collision is significantly greater than that of vehicle A.

[0330] For the front-to-back rotation angle of vehicle A, there is no obvious rule. For vehicle B, compared with the condition without vertical offset, the increase of vertical offset increases the front-to-back rotation angle of vehicle B.

[0331] Under lateral offset, as the lateral offset increases, the front and rear tilt angle of car A does not change significantly, while the tilt amplitude of car B increases significantly. In addition, during the collision, the tilt speed of car B is significantly greater than that of car A.

[0332] As for the rotation angle of the vehicle body, with the increase of the lateral offset, the rotation amplitude of the vehicle body of vehicle A increases significantly, and gradually increases with the increase of the offset. For vehicle B, the increase of the lateral offset will also increase the front and rear rotation angle of the vehicle body at the same time during the collision process, making the time to reach the maximum rotation angle of the vehicle body earlier;

[0333] Combining the body rotation under the above two working conditions, it can be found that the increase in vertical offset and lateral force will increase the front and rear tilt angle of the body of car B during the collision, and the front and rear tilt speed of car B is significantly greater than that of car A under the same working condition. The increase in lateral offset will significantly increase the rotation amplitude of the body of car A and car B, but has no obvious effect on the front and rear tilt angle of car A.

[0334] S405. Analysis of the risk of train derailment under the condition of coupler offset: With the increase of vertical offset and lateral offset, the risk of wheel derailment will increase, and the closer to the rear end of the train, the greater the lifting amount. The lifting of the wheelset on the impact side is more severe than that on the stationary side. Under the condition of vertical coupler offset, the wheel lifting is higher than that under the condition of lateral offset. However, under the condition of lateral offset, the left and right movement of the wheelset may be aggravated, increasing the risk of sliding off the track.

[0335] When a train collides, the wheels are often lifted, and excessive wheelset lift increases the risk of wheelset derailment. Next, the lift amount of the wheels under different working conditions is extracted through simulation results, and the impact of different offset working conditions on wheel lift is analyzed and compared;

[0336] When a train derails, it is often accompanied by a significant lift of the wheelset. In the evaluation of train derailment behavior, the wheel lift is used as an evaluation indicator for evaluating train derailment behavior. According to the simulation results, the maximum lift of the 8 wheels on the left and right sides of the two trains in the collision under the vertical offset condition is extracted, and the maximum lift of each wheelset under different offset conditions is plotted.

[0337] The wheels on both sides first rise and then fall, and at 0.12s, the left and right wheels rise significantly, and the lowest part of the left wheel rim is significantly higher than the track height. At this time, the coupler is in the stage of crushing tube compression;

[0338] Next, the wheelset lift under lateral offset conditions is analyzed. Based on the simulation results, the maximum lift values ​​of the eight wheels on the left and right sides of the two trains in the collision under vertical offset conditions are extracted, and the maximum lift values ​​of each wheelset under different offset conditions are plotted, as shown in the attached figure. Fig.12 As shown;

[0339] The wheel lifting sequence shows that the left wheelset has the largest lifting amount at 0.12s, which is significantly higher than the track height, and the wheelset shows obvious signs of leftward movement compared to the initial situation, which may be caused by the lateral offset of the coupler. Compared with the vertical 50mm height difference, the lateral 50mm offset has a slightly smaller effect on the wheelset lifting, and the left wheel lifts more than the right wheel lifts, but the lateral offset of the coupler may aggravate the left-right movement of the wheelset, thereby increasing the risk of one wheel slipping off the track.

[0340] Specifically: This invention focuses on the inverse analysis of the coupler force curve based on the posture parameters under the impact condition, proposes a research idea for the inverse analysis of the coupler mechanical curve under the impact condition, and proposes a segmented inverse analysis method and inverse analysis model based on the time series on this basis, which realizes the inverse analysis of the coupler force curve under the fixed condition and the offset condition, and analyzes the influence of the coupler offset on the train collision behavior based on the above research. The main research work is as follows:

[0341] (1) A method for inverse analysis of the mechanical curve of the coupler under impact conditions was proposed. Based on the research ideas of inverse analysis of the mechanical curve of the coupler under impact conditions and the current research status of scholars at home and abroad, a method for constructing a finite element model for inverse analysis of the lateral and vertical deflection of the coupler under impact conditions and an optimization inverse analysis method based on posture parameters under impact conditions were proposed;

[0342] (2) The finite element inverse model of the subway coupler under impact conditions was constructed and verified. Taking the subway coupler as the research object, the finite element inverse model of the subway coupler was constructed according to its structure and working principle. The subway single-side coupler impact test was carried out, and the coupler mechanical curve and coupler posture response were obtained. The deformation posture and simulation results obtained by simulation were compared with the test, and the accuracy of the finite element inverse model of the subway coupler under impact conditions was verified.

[0343] (3) A segmented inverse method for the mechanical characteristic curve of the coupler based on time series was proposed, and the inverse of the coupler force curve under fixed and offset conditions of the subway coupler was realized. Taking the impact test results of the subway single-sided coupler as the inverse target, a single-sided subway coupler inverse model was constructed, and the coupler force was iteratively inverted as a whole. The limitations of using the overall inverse curve in the absence of offset, namely the insufficient number of variables, were studied. On this basis, it was proposed to segment the coupler buffer and crush tube curves to increase the number of variables to solve the coupler axial force. Finally, the coupler axial force was successfully solved when the buffer curve was divided into 5 segments and the crush tube curve was divided into 3 segments. In order to realize the inverse analysis of the mechanical characteristics and spatial posture of the coupler under the offset collision of the coupler, an offset collision impact test of the subway coupler was carried out, and the coupler mechanical curve, axial motion curve, lateral swing curve and vertical swing curve were obtained by analysis. According to the corresponding working conditions of the test, the inverse model of the offset collision of the subway coupler was constructed, and on the basis of the segmented inverse analysis of the coupler force based on the time series, the vertical swing parameters and lateral swing parameters of the coupler were introduced. When the axial force was inversely analyzed, the vertical and lateral motions of the coupler were fitted at the same time, and the vertical and lateral rotation parameters of the coupler and the corresponding vertical and lateral force-time curves were obtained, and the inverse analysis of the coupler force under the offset working condition was successfully realized.

[0344] (4) Based on the inverse model and results of the subway coupler offset collision under impact conditions, a collision model of two subway trains was constructed, and the influence of different coupler rotation parameters on the body posture was studied. Based on the coupler parameters obtained through the coupler offset collision test, the influence of different coupler offsets on the train collision behavior was studied. Two collision conditions were set, namely, the lateral and vertical offsets of the coupler were 0mm, 20mm, 40mm and 50mm respectively, and the coupler collision characteristics and train derailment behavior were analyzed. The results show that: with the increase of the lateral and vertical offsets of the coupler, the lateral and vertical swing amplitudes of the coupler in the collision gradually increase, but the magnitude of the coupler force in the collision has basically no obvious change. For the body movement behavior, the first drop in the center of mass of the stationary vehicle during the collision is greater than the impact. The impact car, and with the increase of lateral offset and vertical offset, the vertical movement of the center of mass of the car body will increase. The increase of vertical offset and lateral offset will increase the front and rear tilt angle of the body of car B during the collision, and the front and rear tilt speed of car B is significantly greater than that of car A under the same working conditions. The increase of lateral offset will significantly increase the rotation amplitude of the body of car A and car B, but has no obvious effect on the front and rear tilt angle of the body of car A. The lifting amount of the wheelset is used as the evaluation index of train derailment analysis. It is found that the overall lifting of the wheelset of the impact side train in the collision is greater than that of the stationary car, and the wheelset with the largest lifting on both trains is the No. 4 wheelset close to the rear of the train. Under the same offset, the vertical offset will make the wheelset lift higher, and the lateral offset will intensify the left and right movement of the wheelset, thereby increasing the risk of the wheelset slipping off the track.

[0345] Those of ordinary skill in the art will appreciate that the modules and method steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0346] The above are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. The inverse method of the three-dimensional mechanical curve of the subway car hook based on the posture parameters under the impact condition is characterized by: The research inverse method comprises the following steps: S1. According to the research idea of ​​inverse analysis of the mechanical curve of the coupler under impact conditions, a method for constructing a finite element model for inverse analysis of the lateral and vertical deflection of the coupler under impact conditions and an optimization inverse analysis method based on posture parameters under impact conditions are proposed; S2. Taking the subway train coupler buffer device as the research object, the working principles of the various components of the subway train coupler are analyzed, and the subway train coupler is divided into a rigid component, an energy-absorbing component and a rotating component to build a reverse model of the subway coupler under impact conditions. A subway unilateral coupler impact test is carried out to verify the accuracy of the reverse model of the subway coupler under impact conditions. S3. Taking the single-side coupler as the research object, without considering the coupler rotation, a segmented inverse method of the coupler characteristic curve based on time series is proposed, and the inverse results are compared with the test results. The fitting of the coupler rotation parameters is introduced into the segmented inverse method to realize the inverse of the three-dimensional force and three-dimensional motion posture of the coupler under impact conditions; S4. Construct a finite element model of the collision between two subway trains, analyze and compare the effects of different rotation parameters on the body posture, and input the coupler rotation input curve and coupler mechanical curve obtained by inverse analysis of the test to analyze the collision posture of the two subway trains under different coupler offset states.

2. The inverse method for studying the three-dimensional mechanical curve of a subway car hook based on posture parameters under impact conditions according to claim 1 is characterized by: The step S1 comprises the following specific steps: S101. Study the inverse method of the mechanical curve of the coupler, and build the corresponding inverse model and method of the coupler according to the mechanical characteristics and motion characteristics of the subway coupler itself; S102. A method for constructing an inverse finite element model of the lateral and vertical deflection of the coupler is formed. According to the movement characteristics of the coupler, the movement of the coupler can be divided into three parts, namely, axial compression, vertical swing and lateral swing. A finite element model is constructed which reflects the compression energy absorption characteristics of the coupler in the axial direction and the lateral and vertical swing characteristics of the coupler in the vertical and lateral directions.

3. The inverse method for studying the three-dimensional mechanical curve of a subway car hook based on posture parameters under impact conditions according to claim 2 is characterized by: The step S101 includes the following specific steps: When the train is running normally, the coupler buffer device is responsible for transmitting traction and braking force. When a collision occurs, the coupler buffer device first compresses and absorbs energy. After the coupler has finished working, the main energy absorption structure, anti-climbing device and car body work in turn to absorb the collision energy. The load, test simulation model and structural deformation response are represented in the form of input and output respectively. The known dynamic load can be solved through the known vibration system to achieve the solution of the result response. Conversely, the solution of the load can be obtained through the inverse inversion of the result response. After realizing the process from load to response, the load parameters are set as variables, and these node responses are fitted with the experimental test responses through the optimization algorithm. After the node responses are fitted, the corresponding load variables are output. If the fitting effect is not good, the load variables are changed to continue fitting.

4. The inverse method for studying the three-dimensional mechanical curve of a subway car hook based on posture parameters under impact conditions according to claim 2 is characterized by: The step S102 includes the following specific steps: The direct relationship between the coupler force curve and displacement curve is established through the Beam unit model in LS-DYNA; The calculation of the mechanical characteristics of complex structures is achieved by defining several nonlinear springs to represent the mechanical characteristics of the structure in certain directions.

5. The inverse method for studying the three-dimensional mechanical curve of a subway car hook based on posture parameters under impact conditions according to claim 1 is characterized by: The step S2 comprises the following specific steps: S201. After the construction of the reverse model of the coupler under the impact condition is realized, the subsequent optimization reverse method is studied. The optimization algorithm embedded in Hyperworks supports users to write optimization programs in Compose. Users register the optimization program in the software program library and call the program through the program name. S201, predicting a solution curve by using a proxy model method, wherein the proxy model includes a polynomial response surface model, a Kriging model, and a radial basis neural network model.

6. The inverse method for studying the three-dimensional mechanical curve of a subway car hook based on posture parameters under impact conditions according to claim 1 is characterized by: The step S3 comprises the following specific steps: S301, performing overall inverse calculation of the coupler axial force of the posture response; S302, performing a segmented inverse analysis of the time series of the coupler axial force curve; S303, conducting a subway car coupler offset collision impact test; S304. Perform inverse analysis on the subway car coupler force curve under offset collision.

7. The inverse method for studying the three-dimensional mechanical curve of a subway car hook based on posture parameters under impact conditions according to claim 6 is characterized by: The step S301 includes the following specific steps: For the inverse calculation of the coupler axial force, the overall inverse calculation was first performed, and the minimum fitting of the axial displacement area difference was taken as the optimization goal. The overall optimization of the coupler overall force value variable was performed 100, 200, 500, and 1000 times respectively. With the increase of the number of iterations, the average value of the force value error at each time point gradually decreased from 4.41% to 4.15%, and the maximum displacement deviation also gradually decreased, but there was no obvious change pattern in the maximum force value error. The results show that as the displacement surface difference decreases, the axial force obtained by inverse calculation is closer and closer to the test, which verifies the convergence relationship between the displacement area difference and the inverse calculation accuracy. At the same time, the results also show that the increase in the number of iterations does not significantly improve the situation where the force value at some time points on the inverse curve deviates seriously from the test, which may be caused by too few variable values. The step S302 includes the following specific steps: In order to improve the accuracy of curve inversion and reduce the exponential increase in the difficulty of optimization due to the increase in variables, a method for inversion of the coupler axial force based on time series is proposed. For the test results of a single-sided coupler with one side of the coupler fixed, the buffer curve and the crush tube curve are input to increase the number of variables in sections, and the test coupler displacement-time curve is gradually fitted in sections. Finally, the inversion of the coupler axial force is achieved when the buffer is divided into 5 sections and the crush tube is divided into 3 sections. The inverse results show that compared with the overall inverse, the maximum error of the inverse force value at each time point is reduced from 57.4% to 14.38%, a decrease of 43.02%; the average error of the inverse at each time point is reduced from 4.15% to 1.52%, a decrease of 2.63%, which shows that the segmented method is feasible for the inverse of the axial force of the coupler under impact conditions; The step S303 includes the following specific steps: In order to inversely determine the coupler force under offset working conditions, an offset collision impact test of subway couplers was carried out. In addition to analyzing the force-time, force-displacement and displacement-time curves of the coupler axial direction, the lateral swing displacement and vertical swing displacement of the coupler were extracted at four cross-sectional positions of the coupler under the top and left perspectives based on top and left high-speed photography. The step S304 includes the following specific steps: While inversely calculating the coupler axial force based on the time series, the coupler vertical swing and lateral swing parameters are introduced to simultaneously fit the lateral and vertical swing of the coupler in the collision. In the selection of the optimal solution for multi-objective optimization, the solution with the smallest axial displacement area difference is selected as the optimal solution for each segmented iteration. According to the test data, the coupler force under offset collision is inversely calculated. Compared with the test force curve, the maximum force value error of the inverse curve is 12.98%, and the average force value error is 3.22%. The lateral and vertical swing of the coupler are successfully fitted, and the input parameters of the coupler buffers on both sides, the coupler crush tube input parameters, the coupler lateral swing parameters and the coupler vertical swing parameters are obtained.

8. The inverse method for studying the three-dimensional mechanical curve of a subway car hook based on posture parameters under impact conditions according to claim 1 is characterized by: The step S4 comprises the following specific steps: S401, constructing a finite element model of two subway vehicle collisions and understanding offset conditions; S402, observing the influence of different coupler rotation parameters on the vehicle body posture; S403, analyzing the movement behavior of the coupler in the coupler offset state; S404, analyzing the movement behavior of the vehicle body under the coupler offset state; S405. Analyze the risk of train derailment when the coupler is offset.

9. The inverse method for studying the three-dimensional mechanical curve of a subway car hook based on posture parameters under impact conditions according to claim 8 is characterized by: The step S401 includes the following specific steps: The presence or absence of torque within the angle limit will affect the vertical movement of the vehicle axis and the amplitude of the vehicle's front and rear tilt angle; The vertical motion amplitude of the center of mass is larger when there is torque than when there is no torque in the angle limit, while the opposite is true for the front and rear tilt angles of the vehicle body; The step S402 includes the following specific steps: Vertical offset and lateral offset have a great influence on the vertical and lateral swing of the coupler; Vertical offset has the greatest impact on vertical swing and little impact on lateral swing. Similarly, lateral offset has the greatest impact on lateral swing.

10. The inverse method for studying the three-dimensional mechanical curve of a subway car hook based on posture parameters under impact conditions according to claim 8, characterized in that: The step S403 includes the following specific steps: During the collision, the first drop in the center of mass of the impact vehicle A is greater than that of the stationary vehicle B, and as the lateral offset and vertical offset increase, the vertical movement of the center of mass of the vehicle body increases; The increase of vertical offset and lateral offset will increase the front-to-back tilt angle of vehicle B during the collision, and the front-to-back tilt speed of vehicle B is significantly greater than that of vehicle A under the same working conditions. The increase of lateral offset will significantly increase the rotation amplitude of vehicle A and vehicle B, but will have no significant effect on the front-to-back tilt angle of vehicle A. The step S405 includes the following specific steps: As the vertical offset and lateral offset increase, the risk of wheel derailment will increase, and the closer to the rear end of the train, the greater the lifting amount. The wheelset lifting of the impact-side train will be more severe than that of the stationary-side train. Under the vertical offset condition of the coupler, the wheel lifting is higher than that under the lateral offset condition. However, under the lateral offset condition, the left and right movement of the wheelset may be aggravated, increasing the risk of slipping off the track.

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