Inverse solution method for three-dimensional mechanical curve research of subway coupler based on pose parameters under impact conditions

Abstract

The present invention discloses an inverse solution method for the three-dimensional mechanical curve of a subway coupler based on pose parameters under impact conditions, which relates to the technical field of train collision tests. It includes the research idea of inverse solution of the coupler mechanical curve under impact conditions, and combines the research status of domestic and foreign scholars to propose a construction method for the finite element model of the transverse vertical yaw inverse solution of the coupler under impact conditions and an optimized inverse solution method based on pose parameters under impact conditions. The present invention conducts research around the inverse solution of the coupler force curve based on pose parameters under impact conditions, proposes a research idea for the inverse solution of the coupler mechanical curve under impact conditions, and on this basis, proposes a segmented inverse solution method and an inverse solution model based on time series, realizes the inverse solution of the coupler force curve under fixed conditions and offset conditions of the coupler, and analyzes the influence of coupler offset on train collision behavior based on the above research.

Description

Technical Field

[0001] The present invention relates to the technical field of train collision tests, and specifically to an inverse solution method for studying the three-dimensional mechanical curves of subway couplers based on pose parameters under impact conditions. Background Technique

[0002] With the continuous increase in the operating speed of trains, while bringing great convenience to people, it also brings potential safety hazards. That is, once a rail train traffic accident occurs, it often causes serious economic losses and casualties to people. Different from collision problems in other fields, since a train consists of multiple carriages, its entire collision behavior is complex and variable, often accompanied by "zigzag" derailment, vertical arching, lateral buckling, and overturning. These collision behaviors often further trigger the extrusion and stacking between carriages, seriously endangering the lives and safety of passengers and crew. The coupler buffer device, as a key component for transmitting forces in a train, the longitudinal, lateral, and vertical forces it receives during a collision have a significant impact on the collision behavior of the train.

[0003] During a train collision, the three-directional forces generated due to the deflection of the coupler during the collision process have a significant impact on the collision attitude of the train. Existing research has shown that a large horizontal deflection angle of the coupler and lateral bearing deflection behavior during a collision are important reasons for wheel-rail lateral displacement and derailment. At the same time, the vertical component of the compression force borne by the coupler due to the deflection of the coupler is the main reason for the damage to components such as the coupler yoke and underframe of the coupler buffer device of multiple unit trains.

[0004] In order to obtain the mechanical characteristics of the coupler buffer device in all directions under collision conditions, taking experimental tests is the most effective means. For the test of the mechanical characteristics of high-speed collision couplers, it is often jointly analyzed through the force-measuring wall and high-speed photography of a train collision test bench. 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 currently, there is 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 solution method for studying the three-dimensional mechanical curves of subway couplers based on pose 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 solution method for studying the three-dimensional mechanical curves of subway couplers based on pose parameters under impact conditions to solve the problems mentioned in the background technique.

[0007] To solve the above problems, the present invention provides a technical solution:

[0008] An inverse solution method for studying the three-dimensional mechanical curves of subway couplers based on pose parameters under impact conditions, the research inverse solution method includes the following steps:

[0009] S1. According to the research idea of inverse solution of the coupler mechanical curve under impact conditions, combined with the research status of domestic and foreign scholars, a construction method of the finite element model for inverse solution of the transverse and vertical yaw of the coupler under impact conditions and an optimization inverse solution method based on pose parameters under impact conditions are proposed;

[0010] S2. Taking the coupler buffer device of the subway train as the research object, analyzing the working principles of each component of the subway train coupler, dividing the subway train coupler into rigid components, energy-absorbing components and rotating components to build an inverse solution model of the subway coupler under impact conditions. Conduct a unilateral coupler impact test on the subway, and compare the test coupler curve with the simulation coupler curve to verify the accuracy of the inverse solution model of the subway coupler under impact conditions;

[0011] S3. Taking the unilateral coupler as the research object, without considering the rotation of the coupler, a method for piecewise inverse solution of the coupler characteristic curve based on time series is proposed, and the inverse solution result is compared with the test result. Then, a subway coupler offset collision impact test is carried out, and the fitting of the coupler rotation parameter is introduced into the piecewise inverse solution method to realize the inverse solution of the three-direction force and three-dimensional motion posture of the coupler under impact conditions;

[0012] S4. Build a finite element model of the collision of two subway trains, analyze and compare the influence of different rotation parameters on the vehicle body posture, and input the coupler rotation input curve and the coupler mechanical curve obtained by experimental inverse solution to analyze the collision postures of two subway trains in different offset states of the coupler.

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

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

[0015] S102. Form a construction method of the finite element model for inverse solution of the transverse and vertical yaw of the coupler. According to the motion characteristics of the coupler, the coupler motion can be divided into three parts, namely axial compression, vertical swing and horizontal swing. Build a finite element model that reflects the compression energy absorption characteristics of the coupler axially and the lateral and vertical swing characteristics of the coupler vertically and horizontally. Using the beam element to simulate the motion characteristics of the coupler can not only shorten the calculation time, but also better reflect the motion of the coupler.

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

[0017] When the train is running normally, the coupler buffer device is responsible for transmitting the traction force and braking force. When a collision occurs, the coupler buffer device takes the lead in compressing and absorbing energy to play a role. After the coupler acts, the main energy-absorbing structure, anti-climbing device and vehicle body act in turn to absorb the collision energy;

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

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

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

[0021] Establish a direct relationship between the coupler force curve and the displacement curve through the Beam element model in LS-DYNA;

[0022] Define several nonlinear springs to represent the mechanical characteristics of the structure in certain directions to realize the calculation of the mechanical characteristics of complex structures.

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

[0024] S201. After constructing the coupler inverse solution model under the impact condition, conduct research on subsequent optimization inverse solution methods. Support users to write optimization programs in Compose through the optimization algorithm embedded in Hyperworks. Users register the optimization programs in the software program library and call the programs by the program name;

[0025] S201. Use the method of surrogate model to predict and solve the curve. The surrogate model includes polynomial response surface model, Kriging model, and radial basis neural network model.

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

[0027] S301. Conduct the overall inverse solution of the coupler axial force for the pose response;

[0028] S302. Conduct the segmented inverse solution analysis of the coupler axial force curve for the time series;

[0029] S303. Conduct the offset collision impact test for the subway coupler;

[0030] S304. Conduct the inverse solution analysis of the subway coupler force curve under offset collision.

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

[0032] For the inverse calculation of the coupler axial force, first, an overall inverse calculation was carried out. Taking the minimum fitting of the axial displacement area difference as the optimization goal, the overall force value variables of the coupler were optimized 100, 200, 500, and 1000 times respectively. As the number of iterations increased, the average value of the force error at each time point gradually decreased, from 4.41% to 4.15%. The maximum deviation of the displacement also gradually decreased, but there was no obvious change rule for the maximum force error;

[0033] The results show that as the displacement area difference decreases, the inverse calculated axial force is getting closer and closer to the test, verifying 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 calculation curve deviates severely from the test, which may be due to too few variable values;

[0034] Step S302 includes the following specific steps:

[0035] In order to improve the curve inverse calculation accuracy and reduce the exponential increase in the optimization difficulty due to the increase in variables, a method for inverse calculation of the coupler axial force based on time series was 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 were respectively input to increase the number of variables in segments, and were gradually fitted in segments according to the test coupler displacement-time curve. Finally, when the buffer was divided into 5 segments and the crush tube was divided into 3 segments, the inverse calculation of the coupler axial force was realized;

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

[0037] Step S303 includes the following specific steps:

[0038] In order to realize the inverse calculation of the coupler force under the offset condition, a subway coupler offset collision impact test was carried out. In addition to analyzing the force-time, force-displacement, and displacement-time curves of the coupler in the axial direction, according to the high-speed photography at the top and left sides, the lateral swing displacement and vertical swing displacement of the coupler were extracted at 4 cross-section positions of the coupler from the top and left perspectives;

[0039] Step S304 includes the following specific steps:

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

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

[0042] S401. Construct a finite element model of the collision of two subway vehicles and understand the offset condition;

[0043] S402. Observe the influence of different coupler rotation parameters on the body attitude;

[0044] S403. Analyze the movement behavior of the coupler in the offset state;

[0045] S404. Analyze the movement behavior of the vehicle body in the offset state of the coupler;

[0046] S405. Analyze the derailment risk of the train in the offset state of the coupler.

[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 body axis and the amplitude of the front-back tilt angle of the vehicle body;

[0049] The vertical movement amplitude of the center of mass is greater when there is torque within the angle limit than when there is no torque, while for the front-back tilt angle of the vehicle body, it is exactly the opposite;

[0050] 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] The vertical offset has the greatest influence on the vertical swing and very little influence on the lateral swing. Similarly, the lateral offset also has the greatest influence on the lateral swing.

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

[0054] During the collision process, the first drop amplitude of the center of mass of the impacting vehicle A is greater than that of the stationary vehicle B, and with the increase of the lateral offset and vertical offset, the vertical movement of the center of mass of the vehicle body will increase;

[0055] The increase of both the vertical offset and the lateral direction will cause the front and rear tilting angles of the vehicle body of vehicle B during the collision process to increase, and under the same working conditions, the front and rear tilting speeds of vehicle B are significantly greater than those of vehicle A. The increase of the lateral offset will cause the rotation amplitudes of the vehicle bodies of vehicle A and vehicle B to increase significantly, but it has no obvious effect on the front and rear tilting angles of the vehicle body of vehicle A;

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

[0057] With the increase of the vertical offset and the lateral offset, the derailment risk of the wheels will increase, and the lifting amount is larger closer to the tail end of the train. The wheel set lifting situation of the impacting side train is more intense than that of the stationary side train. Under the vertical offset condition of the coupler, the wheel lifting situation is higher than that under the lateral offset condition, but under the lateral offset condition, it may exacerbate the left - right movement of the wheel set and increase the risk of slipping off the track.

[0058] The beneficial effects of the present invention are as follows: The present invention focuses on the inverse solution of the coupler force curve based on pose parameters under impact conditions, proposes a research idea for the inverse solution of the coupler mechanical curve under impact conditions, and on this basis, proposes a segmented inverse solution method and an inverse solution model based on time series, realizes the inverse solution of the coupler force curve under fixed conditions and offset conditions of the coupler, and analyzes the influence of coupler offset on the collision behavior of the train based on the above research. Brief Description of the Drawings

[0059] For ease of explanation, the present invention is described in detail by the following specific embodiments and accompanying drawings.

[0060] Figure 1 It is a flow chart of the inverse solution method for the three - dimensional mechanical curve of the subway coupler based on pose parameters under impact conditions provided by the embodiment of the present invention;

[0061] Figure 2 It is a schematic flow diagram of the inverse solution method for the three - dimensional mechanical curve of the subway coupler based on pose parameters under impact conditions provided by the embodiment of the present invention;

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

[0063] Figure 4 It is a description diagram of the load inverse solution problem in the inverse solution method for the three - dimensional mechanical curve of the subway coupler based on pose parameters under impact conditions provided by the embodiment of the present invention;

[0064] Figure 5It is the deformation sequence diagram of the coupler offset collision test in the reverse solution method for the three-dimensional mechanical curve research of subway couplers based on pose parameters under impact conditions provided by the embodiments of the present invention;

[0065] Figure 6 It is the coupler offset collision force-time curve in the reverse solution method for the three-dimensional mechanical curve research of subway couplers based on pose parameters under impact conditions provided by the embodiments of the present invention;

[0066] Figure 7 It is the schematic diagram of the reverse solution finite element model of the coupler offset collision in the reverse solution method for the three-dimensional mechanical curve research of subway couplers based on pose parameters under impact conditions provided by the embodiments of the present invention;

[0067] Figure 8 It is the schematic diagram of the collision condition in the reverse solution method for the three-dimensional mechanical curve research of subway couplers based on pose parameters under impact conditions provided by the embodiments of the present invention;

[0068] Figure 9 It is the schematic diagram of the description of the car body bogie wheel set numbers in the reverse solution method for the three-dimensional mechanical curve research of subway couplers based on pose parameters under impact conditions provided by the embodiments of the present invention;

[0069] Figure 10 It is the schematic diagram of the positive direction of the car body movement in the reverse solution method for the three-dimensional mechanical curve research of subway couplers based on pose parameters under impact conditions provided by the embodiments of the present invention;

[0070] Figure 11 It is the schematic diagram of the previous coupler rotation parameter input method in the reverse solution method for the three-dimensional mechanical curve research of subway couplers based on pose parameters under impact conditions provided by the embodiments of the present invention;

[0071] Figure 12 It is the schematic diagram of the wheel lifting action sequence of the A-4 wheel set under a vertical offset of 50 mm in the reverse solution method for the three-dimensional mechanical curve research of subway couplers based on pose parameters under impact conditions provided by the embodiments of the present invention;

[0072] Figure 13 It is the finite element model diagram of the coupler in the reverse solution method for the three-dimensional mechanical curve research of subway couplers based on pose parameters under impact conditions provided by the embodiments of the present invention. Detailed implementation manners

[0073] In order to make the objectives, 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 a part of the embodiments of the present application, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts shall fall within the protection scope of the present application.

[0074] For the embodiments provided in this application, that is, embodiments of a method for analyzing the correlation between driving behavior factors and driving risks based on big data.

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

[0076] The present invention provides an inverse research method for the three-dimensional mechanical curve of a subway coupler based on pose parameters under impact conditions. The inverse research method includes the following steps:

[0077] S1. According to the inverse research idea of the coupler mechanical curve under impact conditions and combining the research status of domestic and foreign scholars, propose a construction method for the finite element model of the coupler transverse vertical yaw inverse under impact conditions and an optimized inverse method based on pose parameters under impact conditions;

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

[0079] S101. Study the inverse research idea of the coupler mechanical curve, and construct a corresponding coupler inverse model and inverse method according to the mechanical characteristics and motion characteristics of the subway coupler;

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

[0081] The installation position and action process of the coupler buffer device are shown in the appendix Figure 3 . When the train is running normally, the coupler buffer device is responsible for transmitting traction and braking forces. When a collision occurs, the coupler buffer device takes the lead in compressing and absorbing energy and acts. After the coupler acts, the main energy-absorbing structure, anti-climbing device, and car body act in sequence to absorb collision energy. In addition to the axial compression action, the coupler buffer device can also swing to a certain extent axially and vertically;

[0082] Represent the load, test simulation model, and structural deformation response in the form of input and output respectively, then this problem can be described by Figure 4 . Given the dynamic load, the result response can be solved through the known vibration system. Conversely, the load can also be solved by inverse inversion of the result response;

[0083] After realizing the process from load to response, set the load parameter as a variable. In this way, different node responses will be obtained under different load actions. Fit these node responses with the test measurement responses through an optimization algorithm. After the node responses are well fitted, output the corresponding load variable. If the fitting effect is not good, change the load variable and continue fitting;

[0084] S102. Establish a method for constructing a finite element model by inverse calculation of the transverse pendulum deviation of the coupler. According to the movement characteristics of the coupler, the coupler movement can be divided into three parts, namely axial compression, vertical swing, and lateral swing. A finite element model is constructed to reflect the coupler compression energy absorption characteristics axially and the coupler lateral and vertical swing characteristics vertically and laterally. Using beam elements to simulate the movement characteristics of the coupler 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] Establish a direct relationship between the coupler force curve and the displacement curve through the Beam element 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 of the beam to its length is less than 1 / 15, Euler-Bernoulli beams can be used, but they cannot handle shear forces. During the calculation, Euler-Bernoulli beams assume that the shear plane always remains at the neutral layer and determine the stress distribution on the beam through linear interpolation. In contrast, Timoshenko beams can handle shear stresses and are suitable for cases with a relatively large ratio of cross-sectional size to length. All Beam elements are set with properties according to their cross-sectional shapes and material parameters. Due to directly calling cross-sectional geometric parameters for calculation, Beam elements are faster than finite element mesh models, which need to continuously calculate the nodal stiffness matrix;

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

[0089]

[0090] where 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 element is as follows:

[0097]

[0098] Where:

[0099]

[0100] Since collision problems in the field of rail vehicles often involve large-scale and non-linear deformations of structures, the Beam elements used for static and modal analysis in the past cannot solve the above problems. To solve the above problems, discrete beam elements are proposed. It calculates the mechanical characteristics of complex structures by defining several non-linear springs to represent the mechanical characteristics of the structure in certain directions. There are many types of discrete beam elements available in LS-DYNA. Among them, MAT119 can specify the mechanical curves on the 6 degrees of freedom of the beam element according to needs, and can separately define the loading and unloading curves in each direction. If material failure needs to be simulated, relevant failure parameters can also be defined;

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

[0102]

[0103] Where, is the force in the local coordinate system, generally the axial force of the element.

[0104] The component forces of the discrete element in the global coordinate system are obtained from the cosines of the element directions:

[0105]

[0106] In the formula:

[0107]

[0108] Where, (x, y, z) are the positions of the element nodes in the global coordinate system;

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

[0110]

[0111] Where, the coefficient K is the total change in the length of the element, 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 can be used without defining cross-sectional properties and can also be set to be massless. According to the needs of the simulation, a mass matrix can also be defined. When the discrete beam has rotational degrees of 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 energy-absorbing structure of the rail vehicle during the impact process. Therefore, theoretically, it is completely feasible to use the discrete beam element model to simplify the finite element mesh model of the energy-absorbing structure;

[0113] The Beam element can exhibit different mechanical behaviors from a spring during compression. The distance from the end point of the unloading curve to the origin represents the final deformation of the Beam element. The area enclosed by the loading and unloading curves and the displacement represents the energy absorbed by the Beam element in this direction. This method of defining the loading / unloading curve is similar to the force-displacement curve characteristics of the energy-absorbing tube. However, in crashworthiness problems, the Beam element model for simulating the energy-absorbing structure usually does not define the mechanical properties in the tensile stage;

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

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

[0116] Under impact conditions, due to the different initial attitudes of the two coupler heads during the collision, the coupler will have lateral and vertical movements. Regarding the lateral and vertical swings of the coupler during the movement process, it can be understood as a process in which the coupler body rotates around the coupler base as the rotation center. This process can be achieved by using the spherical hinge element in LS-DYNA;

[0117] In the LS-DYNA material manual, the complex motion relationship between two objects can be achieved through the hinge element;

[0118] The hinge element in LS-DYNA is achieved 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 coefficient to obtain the nodal forces at nodes i and j:

[0121]

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

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

[0124]

[0125] By choosing the magnitude of the penalty stiffness k such that it does not control the stable time step. For the central difference method, the stable time step Δt is restricted 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 eigenvalue problems assuming k = 1. For an object with m constraint equations, the linearized equation for the translational degrees of freedom is:

[0128]

[0129] For the frequency that is where M is the mass of the rigid body and θ is the angular momentum. The corresponding rotational equation is:

[0130]

[0131] where J is the inertia tensor and K is the stiffness matrix from the moment contribution of the penalty constraint. The stiffness matrix can be approximated by the moment contribution of the constraint 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] It can be obtained that

[0137]

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

[0139]

[0140] The joint constraints are defined based on the displacements of each node. Whether the node belongs to the solid element of the structural unit or not, only its translational degrees of freedom are used in the constraint equations;

[0141] For a spherical hinge, 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 rotational joint requires five constraints and is defined by two rotational joints, with a total of six constraint equations. Since the penalty formula is used, the redundancy in the joint constraint equations is not important. The cylindrical joint is defined by adopting a rotational joint and eliminating the penalty force along the direction defined by the two cylindrical joints. In a similar way, the planar joint is defined by eliminating the penalty force perpendicular to the two spherical joints;

[0144] The translational joint is a cylindrical joint that allows sliding along its axis but not rotation. A pair of additional nodes are required outside the axis to provide additional constraints. The only effective force between the additional nodes acts in the direction perpendicular to the plane defined by the three pairs of nodes. The gimbal angle is defined by four nodes. Let the nodes on one solid be i and k, and the nodes on the other solid be j and l. Among them, two nodes i and j are used to define the spherical joint for 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 coupler buffer device of the subway train as the research object, analyze the working principles of each component of the subway train coupler, and divide the subway train coupler into rigid components, energy-absorbing components, and rotary components to establish the inverse model of the subway coupler under impact conditions. Conduct the impact test on the single-sided coupler of the subway, and compare the test coupler curve with the simulation coupler curve to verify the accuracy of the inverse model of the subway coupler under impact conditions;

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

[0148] S201. After realizing the construction of the inverse model of the coupler under impact conditions, conduct research on the subsequent optimized inverse method. The optimization algorithm embedded in Hyperworks supports users to write optimization programs in Compose. Users register the optimization programs in the software program library and call the programs through the program name;

[0149] S201. Use the method of surrogate model to predict and solve the curve. There are mainly three methods for constructing the surrogate model: polynomial response surface model, Kriging model, and 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 conduct research on the subsequent optimized inverse method. Hyperworks not only embeds common optimization algorithms, but also supports users to write optimization programs in Compose. Users register the optimization programs in the software program library and can call the programs through the program name. When solving the optimization task of discrete variables, multiple strategies can be adopted. For example, the adaptive response surface method ARSM analyzes the correlation between parameter changes and the objective function, and dynamically adjusts the response surface model to more effectively identify key parameters. This method can converge quickly, but sometimes it is limited by local optimal solutions. To overcome this challenge, the global response surface search method GRSM extends ARSM by considering a wider gradient interval to avoid falling into local optimal solutions prematurely. 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 applicable to complex and multimodal optimization problems;

[0151] In addition to using the optimization algorithms built into Hyperstudy, the method of surrogate model can also be used to predict and solve the curve. Currently, there are mainly three methods for constructing the surrogate model 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 the results of experimental design. Its model construction is simple, the computational requirements are small, and the relationship between variables and responses can be expressed by clear mathematical formulas, which makes PRS particularly suitable for dealing with problems with low complexity and low non-linearity;

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

[0155]

[0156] In the formula, α0, α i , α ii and α ij are undetermined coefficients. Arrange the undetermined coefficients in order to form a vector α, and use the information of n sample points to find α by the least squares method as follows.

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

[0158] (2) Kriging model

[0159] The Kriging model (Kriging model, abbreviated as KRI) is an interpolation technique based on statistical theory. It analyzes the spatial attributes of known sample points, determines the distance range in which the value of the point to be interpolated is affected by the known sample points, and uses relevant sample points to obtain an unbiased estimated value of the point to be interpolated;

[0160] A typical Kriging model is divided into two parts: linear regression and random distribution, as follows:

[0161]

[0162] In the formula, y(x) represents the response value; β = [β1 β2 … β p T is a column vector composed of regression model coefficients; f(x) = [f1(x) f2(x) … f p (x)] T is a polynomial function of the sample point x, and z(x) is a random model that follows the normal distribution N(0, σ 2 ), representing the local deviation of 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 mainly consists of three layers and has characteristics such as 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 convergence speed of the RBF neural network is relatively fast because it is a local approximation network. For each input, only local adjustments are required for the weights on the network, resulting in a relatively fast learning speed.

[0165] For the n-dimensional input variables [x1 x2 … x n T , whose response values are [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(||x - x i ||) represents the Euclidean distance from any input variable x to the known sample point x i .

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

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

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

[0171] ​​​​S301. Overall inverse calculation of the coupler axial force for pose response: For the inverse calculation of the coupler axial force, an overall inverse calculation was first carried out, taking the minimum fitting of the axial displacement area difference as the optimization goal. The overall force value variables of the coupler were optimized 100, 200, 500, and 1000 times respectively. As the number of iterations increased, the average value of the force error at each time point gradually decreased, from 4.41% to 4.15%. The maximum displacement deviation also gradually decreased, but there was no obvious change rule for the maximum force error;

[0172] The results show that as the displacement surface difference decreases, the axial force obtained by inverse calculation is getting closer and closer to the test, verifying 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 values at some time points on the inverse calculation curve deviate severely from the test, which may be due to too few variable values;

[0173] (1) Basic model settings

[0174] Since only the inverse calculation of the coupler force curve is considered, and the actions of the two side circular tubes in the test occur after the coupler fails, in order to reduce the calculation time, the finite element model under the coupler impact condition was simplified. The two side protective devices and the coupler base box were removed to obtain the coupler axial force inverse calculation model. Since one hook head of the coupler was completely fixed on the rigid wall in this test, there was not much lateral and vertical swing. Therefore, only the axial crushing force of the coupler was inversely calculated in this test. In the construction of the model, the trolley was established using hexahedral solid meshes and given a rigid material MAT_RIGID. The contact between the wheel and rail was defined by AUTOMATIC_SURFACE_TO_SURFACE. The settings of speed and mass were the same as the test results, and the trolley mass was loaded to the centroid position;

[0175] (2) Variable settings

[0176] On the basis of the above, seven characteristic values of the force-displacement curves of the coupler crushing tube and the rubber buffer were set as variables, and their variation ranges were ±10% of the design parameters;

[0177] In the displacement curve of the crushing tube, the first variable has not only a change in the force value but also a change in displacement. This is to restore as much as possible the slope of the gradually increasing stiffness process when the crushing tube just starts to crush;

[0178] (3) Setting of the optimization goal

[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 differentiating the displacement time curve, there will be some distortion compared with the true velocity and acceleration data in this process. Therefore, in this paper, the force curve is optimized and iteratively obtained mainly by fitting the displacement time curve. To reduce the occurrence of local optimal solutions, the GRSM global optimization algorithm is selected. To fit two displacement time curves, a function named curve_difference is defined in the program. After inputting the displacement time curves of the two curves, this function will calculate the shape area difference between the two curves and output it. Therefore, the optimization objective is to minimize the shape difference between the coupler test displacement time curve and the coupler simulation axial displacement time curve. Represent the axial displacement with "Z", and it can be expressed mathematically as follows:

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

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

[0182] Through the GRSM global optimization algorithm, the initial variables are iterated 100, 300, 500, and 1000 times respectively, and the corresponding optimal solutions are the 85th, 195th, 423rd, and 855th times respectively. The axial force at the collision interface of the optimal solution simulation model obtained by iteration is compared and analyzed with the test force curve. After 100 iterations, the optimal solution that meets the response setting is the 85th time. The overall force value trend has begun to approach the test curve, but there are still large deviations before 0.1 s and after 0.8 s. Among them, 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 wavy shape, and the maximum displacement error is 0.581 mm;

[0183] Table 1 Results table of the optimal solution of the overall inverse solution optimization for 100 times

[0184]

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

[0186] Table 2 Results Table of the Optimal Solution for 200 - time Overall Inverse Seeking and Optimization

[0187]

[0188] After 500 iterations, the optimal solution that meets the response setting is the 423rd time. It can be seen that the trend of the overall force value has started to approach the test curve, but there are still large deviations before 0.1 s and after 0.8 s. The relative error of the force value has decreased compared with 200 iterations, with a maximum value of 52.6%, and the average error of the force value is 4.21%. The displacement error shows a wavy pattern, first increasing, then decreasing, and then increasing again. Its maximum error has decreased compared with 200 iterations, and the maximum error is 0.196 mm.

[0189] Table 3 Results Table of the Optimal Solution for 500 - time Overall Inverse Seeking and Optimization

[0190]

[0191] After 1000 iterations, it can be seen that the trend of the overall force value has started to approach the test curve, but there are still large deviations before 0.1 s and after 0.8 s, and the deviation of the force - time curve in the middle section is smaller. The relative error of the force value has increased compared with 500 iterations, with a maximum value of 57.4%, and the average error of the force value is 4.15%. The displacement error shows a wavy pattern, first increasing, then decreasing, and then increasing again. Its maximum error has slightly decreased compared with 500 iterations, and the error is 0.149 mm.

[0192] Table 4 Results Table of the Optimal Solution for 1000 - time Overall Inverse Seeking and Optimization

[0193]

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

[0195] Table 5 Analysis of Iteration Results

[0196]

[0197] As can be seen from Table 5, as the number of iterations increases, the average error of the force value gradually decreases, from 4.41% to 4.15%, and the maximum deviation of the displacement also gradually decreases. However, there is no obvious change rule for the maximum error of the force value. From the above data, it can be obtained that there is a convergent relationship between the size of the area difference of the displacement curve in the model and the accuracy of the inverse force value, that is, as the area difference of the displacement decreases, the inverse force curve gradually approaches the test force curve. Combining the relative error diagram of the force-time curve of each iteration result analysis, it is found that the time points where the maximum error of the inverse force value appears are almost at the same time node. Therefore, as the number of iterations increases, the maximum error of the force value does not decrease significantly. It may be that there are too few characteristic value variables in the initial force curve;

[0198] In the comparison of the force curves, it can be seen that even after 1000 iterations, there are still large deviations between the first 0.1 s and after 0.8 s 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 insufficient variables on the initial curve, so that it cannot be better further fitted. If you want to increase the variable points on the curve, there will be a problem, but the result of increasing the variables is that the number of optimization times will increase exponentially. In order to increase the variable points and reduce the number of optimization times, this paper intends to solve this problem by segmenting the entire inverse process according to the time series and adding variable points on each segment;

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

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

[0201] When the subway coupler studied in the present invention functions, first the buffer functions, and after the buffer functions, the crush tube functions. Therefore, the buffer and the crush tube can be segmented and inversely solved in sequence. This study only focuses on the buffer coupler type that is not sensitive to speed changes. Compared with the entire curve, the segmented curve can effectively increase the inverse solution variable points while reducing the inverse solution iteration times. However, compared with the entire curve, errors may occur at the segmented connection points. Such errors will cause the next segment of the curve to shift, resulting in an increasing error in the subsequent curve and the distortion of the inverse solution result of the entire curve;

[0202] In order to reduce the possible errors at the segmented connection points, the connection points solved in each segment are proposed to be used as the initial points for the solution of the next segment, and the connection points are iteratively solved again to reduce the errors at the connection points;

[0203] Two segments of curves are used to inversely solve the force-time curve before 0.2 s. Three variable points are set for each segment. Since there is a 0 moment in the first segment of the curve, there are only two variable points. The data point at 0.1 s is the intersection point of the two segments of curves. After the solution of the first segment of the curve is completed, the variable point at 0.1 s is brought into the solution of the second segment of the curve, and so on until the solution of the entire curve is completed;

[0204] In order to improve the inverse solution accuracy of the coupler force curve, the method of segmentation is used to iteratively solve the buffer impact curve and the crush tube impact curve of the front half of the coupler. According to the main parameters of the test coupler, the buffer compression stroke is 55 mm, and the time point corresponding to the end of its stroke is near 0.013 s in the test. Therefore, the first 0.013 s of the curve is iteratively inversely solved. Three variable points are set for each segment of the curve, and the displacement step length between each point is the same. Each segment uses the GRSM algorithm to optimize and iterate 100 times;

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

[0206] Table 6 Optimization result table of the 2-time segmented inverse solution of the buffer impact curve

[0207]

[0208] After solving the force curve of the buffer part through 2-time segmented iteration, the maximum relative error of the force value is 18.91%, and the corresponding time point is at 0.009 s. The average error of the force value during this period is 9.23%. The maximum displacement error is 0.948 mm, and the corresponding time point is at 0.002 s. The average displacement error during this period is 0.256 mm;

[0209] Table 7 Optimization result table of the 3-time segmented inverse solution of the buffer impact curve

[0210]

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

[0212] Table 8 Results of the 4 - sub - segment inverse solution and optimization of the buffer impact curve

[0213]

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

[0215] Table 9 Results of the 4 - sub - segment inverse solution and optimization of the buffer impact curve

[0216]

[0217]

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

[0219] As the number of sub - segments increases, except for the fourth curve, the test curves and the inverse - solved curves gradually approach the inverse - solved curve in trend. From the numerical values of the force - time curves, as the number of sub - segments increases, the maximum value of the force deviation and the relative error of the force value gradually decrease, and the average value of the force error of all curves is less than 10%;

[0220] As the number of sub - segments increases, it can be seen that the area difference of the displacement curves becomes smaller and smaller, but the decreasing amplitude becomes smaller and smaller. This may be due to the cumulative superposition of errors at each connection point as the number of sub - segments increases. Although repeated iteration has been performed at the connection points, this cannot eliminate the errors. At the same time, it also shows that the more sub - segments are not necessarily better. As the number of sub - segments increases, more and more errors will accumulate, making the improvement of the fitting effect of the displacement area difference smaller and smaller;

[0221] Average relative error of the inverse force of each segment in the first 0.013 s of Table 10

[0222]

[0223] As can be seen from Table 10, with the increase of the number of segments, 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 all 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 value error decreases from 9.23% to 6.69%, a decrease of 2.54%; the maximum displacement error decreases from 0.948 mm to 0.751 mm, a decrease of 0.197 mm; the average displacement error decreases from 0.256 mm to 0.222 mm, a decrease of 0.034 mm;

[0224] After 5 times of segmental inverse solution of the buffer impact curve, the maximum deviation of the inverse force value decreases to 14.38%. Compared with the overall maximum inverse deviation of 57.4%, the accuracy of the inverse curve is improved by 43.02%;

[0225] Compared with the inverse solution of the whole curve, the force obtained by the segmented iterative solution is significantly closer to the test curve, indicating that this method is feasible;

[0226] According to the results of the buffer impact curve fitting in the previous text, on this basis, the impact curve of the crush tube is fitted, and the last variable point of the buffer curve is also brought into the solution of the crush tube curve; in order to determine the optimal number of segmental iterative solutions of the crush tube, the inverse solutions are carried out for the curves divided into 1 segment, 2 segments and 3 segments respectively. Each segment is set with 3 variable points, and the displacement step length between variable points is the same. The number of iterative optimizations using the GRSM algorithm is 100 times;

[0227] Table 11 Optimization result table of the first segment inverse solution of the crush tube impact curve

[0228]

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

[0230] Table 12 Optimization result table of the second segment inverse solution of the crush tube impact curve

[0231]

[0232] Based on the solution of the buffer curve, after solving the force curve of the crushing tube part through two-stage piecewise iteration, the maximum relative error of the force value is 15.51%, and the corresponding time point is at 0.088 s. The average value of the force value error during this period is 2.73%, the maximum displacement deviation is 0.949 mm, and the corresponding time point is at 0.002 s. The average displacement deviation during this period is 0.032 mm;

[0233] Table 13 Results of the three-stage piecewise inverse solution and optimization of the impact curve of the crushing tube

[0234]

[0235] Based on the solution of the buffer curve, after solving the force curve of the crushing tube part through three-stage piecewise iteration, the maximum relative error of the force value is 15.43%, and the corresponding time point is at 0.085 s. The average value of the force value error during this period is 1.52%, the maximum displacement deviation is 0.581 mm, and the corresponding time point is at 0.002 s. The average displacement deviation during this period is 0.025 mm;

[0236] As the number of segmentation increases, it can be seen that the force curve obtained by inverse solution from non-segmentation to three-stage segmentation becomes smoother and closer to the test curve, and the deviation of the platform force also gradually decreases;

[0237] The difference in displacement area decreases significantly as the number of segmentation increases. Among them, the reduction amplitude from one segment to two segments is the largest, and the reduction amplitude from two segments to three segments decreases significantly. The inverse solution results of the impact curve of the crushing tube are sorted out to obtain Table 14;

[0238] Table 14 Results of the piecewise inverse solution of the impact curve of the crushing tube

[0239]

[0240] As can be seen from the table, as the number of segmentation of the impact curve of the crushing tube increases, the maximum error of the inverse solution force value, the average value of the inverse solution force value error, the maximum displacement error, and the average displacement error all gradually decrease. Among them, the maximum error of the inverse solution force value decreases from 16.55% to 15.43%, a decrease of 1.12%; the average value of the inverse solution force value error decreases from 4.21% to 1.52%, a decrease of 2.69%; the maximum displacement error decreases from 0.951 mm to 0.581 mm, a decrease of 0.37 mm; the average displacement error decreases from 0.046 mm to 0.032 mm, a decrease of 0.021 mm;

[0241] Compared with the optimal solution obtained by the overall inverse solution after 1000 iterations, the maximum error of the inverse force value decreased from 57.4% to 15.43%, a reduction of 41.97%; the average value of the inverse force value error decreased from 4.15% to 1.52%, a reduction of 2.63%. Compared with the overall inverse solution method, the segmented inverse solution of the axial force curve based on the time series uses fewer iterations and obtains a more accurate coupler axial force curve, further verifying that it is reliable and feasible to use the segmented method to inverse the coupler curve;

[0242] S303. Conduct the offset collision impact test of the subway coupler: In order to realize the inverse solution of the coupler force under the offset condition, the offset collision impact test of the subway coupler was carried out. In addition to analyzing the force-time, force-displacement, and displacement-time curves of the coupler in the axial direction, according to the high-speed photography at the top and left sides, the lateral swing displacement and vertical swing displacement of the coupler were extracted at 4 cross-section positions of the coupler from the top and left perspectives;

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

[0244] In the actual train collision scenario, there are often lateral horizontal displacement differences and vertical height differences between the two couplers. In order to explore the inverse solution of the mechanical characteristic curve of the coupler under the condition of coupler offset close to the actual engineering needs, the coupler offset collision impact test was carried out. Among them, the installation position of the impact-side coupler is 40 mm higher than that of the impacted-side coupler, and the setting of the coupler height difference refers to the collision scenario specified in the European standard EN15227;

[0245] Before the test, the opposite coupler and the auxiliary energy-absorbing tooling were installed on the force-measuring panel, and the impact-side coupler, the protective tooling, and the counterweight were installed on the test trolley. When the test started, the test trolley was driven by an air cannon and drove the impact-side coupler and the protective tooling towards the rigid wall at a certain speed. Among them, the protective device and the auxiliary energy-absorbing tooling came into play after the coupler energy-absorbing effect was completed, and their function was to absorb the remaining collision energy to ensure the safety of the test;

[0246] The relevant test equipment mainly includes the trolley and the counterweight block, 2 high-speed cameras, 3 sets of force-measuring sensors in total of 5, 1 speedometer, 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 the offset collision impact test of the coupler

[0248]

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

[0250]

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

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

[0253] (1) Analysis of collision deformation

[0254] In this test, two high-speed photography devices were used to photograph the process of the specimen hitting the rigid wall from the left-side view and the top-down view respectively. The deformation sequence diagrams of the coupler from the left-side view and the top view during the collision process were analyzed and explained. For each view, the moments of the start of the collision, the contact of the coupler, the engagement of the coupler, the compression, the moment when the compression stroke of the coupler is the largest, and the end of the collision were intercepted, as shown in the appendix Figure 5 ;

[0255] It can be observed from the images taken by the high-speed photography that during the coupling process, the two hook heads slide up and down relative to each other to complete the coupler coupling action. Subsequently, the buffer and crush tube of the two couplers are compressed synchronously. When the two crush tubes are compressed to a certain extent, the compression speed of the left crush tube is significantly faster than that of the right crush tube until the left crush tube reaches its maximum stroke. After that, the right crush tube continues to be compressed until it reaches its maximum stroke and triggers the shear bolt of the right coupler, causing the coupler to fail and fall off. Thus, the entire energy absorption process of the coupler ends, and the remaining kinetic energy is continuously absorbed by the auxiliary energy absorption tools on both sides;

[0256] (2) Analysis of collision axial displacement

[0257] According to the sequence images of the specimen collision recorded by the high-speed camera, a series of marker points were selected in the images using motion image sequence analysis software. The moment when the coupler starts the collision action in the high-speed photography was used as the initial moment, and the marked points selected on the trolley were used to analyze the displacement changes of the specimen and the trolley during the impact process. The final displacement-time curve in this article was plotted based on the difference between the marker points selected without relative movement on the trolley, and the analysis was carried out 3 times at the same position and the average value was taken to eliminate the systematic error;

[0258] The displacement of the specimen gradually increases with time. At 0.125 s, the bolt of the test coupler is completely sheared and reaches the maximum stroke. At this time, the total displacement is 620.32 mm, of which the compression displacement of the left coupler is 305.47 mm and the compression displacement of the right coupler is 314.85 mm;

[0259] (3) Analysis of collision vertical displacement

[0260] In order to obtain the lateral movement attitude data of the coupler, 3 points were taken on each of the four cross-sections of the two couplers, and the average value was taken to analyze the vertical movement of the coupler;

[0261] The sequential images of the specimen collision recorded by a high-speed camera are analyzed using motion image sequence analysis software. Taking the moment when the coupler starts to collide in the high-speed photography as the initial moment, the vertical displacement curve of the coupler is obtained.

[0262] (4) Lateral displacement analysis during collision

[0263] To obtain the lateral motion attitude data of the coupler, 3 points are taken on each of the four sections of the two-side couplers, and the average value is taken to analyze the vertical motion of the coupler.

[0264] The sequential images of the specimen collision recorded by a high-speed camera are analyzed using motion image sequence analysis software. Taking the moment when the coupler starts to collide in the high-speed photography as the initial moment, the vertical displacement curve of the coupler is obtained.

[0265] (5) Collision force analysis

[0266] During the test, a sensor composed of 3 200t force sensors is used to measure the collision energy absorption value of the coupler buffer. The force-time data on the 3 force sensors are superimposed to obtain the force-time curve of the coupler offset collision, as shown in the appendix Figure 6 ;

[0267] The collision process lasts for 0.125 s, which is consistent with the high-speed photography analysis result. Before 0.024 s, the two-side coupler buffers are compressed. From 0.024 s to 0.110 s is the stable compression interval of the two-side coupler crush tubes, and its stable deformation force value is 1228.73 kN; from 0.110 s to 0.125 s is the shear motion interval of the shear bolts, and its peak force is 1437.32 kN;

[0268] (6) Collision energy analysis

[0269] In this subsection, the collision energy absorbed by the coupler during the collision is mainly investigated. The obtained 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. Conduct the inverse analysis of the subway coupler force curve under offset collision: While performing the inverse calculation of the coupler axial force based on the time series, introduce the vertical and lateral swing parameters of the coupler to simultaneously fit the lateral and vertical swing conditions of the coupler during the collision. When selecting the optimal solution for multi-objective optimization, select the solution with the smallest axial displacement area difference as the optimal solution for each segmented iteration. According to the test data, the coupler force under offset collision was inversely calculated. The maximum error between the inverse calculation curve and the test force curve was 12.98%, and the average error of the force value was 3.22%. Moreover, the lateral and vertical swing conditions of the coupler were successfully fitted, and the input parameters of the coupler buffers on both sides, the input parameters of the coupler crush tubes, the lateral swing parameters of the coupler, and the vertical swing parameters of the coupler were obtained;

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

[0272] (1) Settings for the inverse model of coupler offset collision

[0273] Since the two-sided auxiliary energy absorption devices act after the coupler action, when constructing the inverse model of coupler offset collision, in order to reduce the inverse calculation time, it was simplified on the basis of the test site working conditions, removing the two-sided auxiliary energy absorption devices and protective tooling, and constructing a finite element inverse model of the coupler for the corresponding working conditions, as shown in the appendix; Figure 7 as shown;

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

[0275] (2) Settings for inverse iteration variables

[0276] During the coupler collision, in addition to the axial compression deformation, the coupler will also produce lateral and vertical swings. In order to inversely calculate and fit this movement, on the basis of segmentally fitting the axial displacement, vertical and lateral rotation parameters are introduced, that is, by changing the torque magnitudes corresponding to different vertical and lateral torsion angles to simultaneously fit the lateral and vertical displacements of the coupler during the collision. In the coupler finite element model, controlling the lateral and vertical movements of the coupler is achieved through the cooperation of the lateral torsion BEAM and the vertical torsion BEAM with the spherical hinge unit;

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

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

[0279] (3) Setting of optimization objectives and selection of optimal solutions

[0280] On the basis of the foregoing, the inverse solution of the coupler axial force has been realized using the test displacement-time curve. For the coupler offset collision condition, in order to fit the vertical and lateral swing postures of the coupler while fitting the coupler axial force during the collision, response points were marked at the same four vertical and lateral cross-section positions on the simulation model as in the test. While fitting the axial force, the lateral and vertical swing postures of the coupler were also fitted. The curve fitting function is curve_difference, that is, the difference in the shape area of the two fitted curves. Using Z, H, and C to represent the displacement fitting conditions of the coupler in the axial, lateral, and vertical directions respectively, the multi-objective optimization is expressed mathematically as follows:

[0281]

[0282] During the process of segmented iteration, the problem of selecting the optimal solution for each iteration will be involved. For the coupler buffer device, its axial mechanical properties are concerned, and then its vertical and lateral swing properties. Therefore, in the selection of the optimal solution, the solution with the axial displacement fitting closest to the test measurement is taken as the optimal solution for the iterative inverse solution in this paper.

[0283] On the basis of the foregoing, the method for segmented inverse solution of the coupler force curve has been determined. First, the impact curve of the coupler buffer is inversely solved, and the axial force at the collision interface obtained by the inverse solution is compared with the test force measurement result; and then it is solved through 5-segment iteration.

[0284] The overall deviation between the test force curve and the inverse solution force curve is not large. The maximum deviation of the force value is 8.56%, and the average error of the force value during this period is 4.64%. The displacement curve is well fitted. The maximum deviations of the displacements of the two side couplers are 0.097mm and -0.127mm respectively. On this basis, the segmented iteration of the crush tube part is continued to obtain the inverse solution result of the axial force of the coupler offset collision.

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

[0286] Taking the vertical displacement of the coupler in the time period of 0 s - 0.09 s before the shear bolt of the coupler test is cut as the target curve, after segmented optimization iteration together with the axial force, the optimal vertical displacement attitude of the coupler that fits the test is obtained;

[0287] Under the collision condition with a vertical height difference of 40 mm of the coupler, the coupler head swings slightly up and down after coupling. At section 1, the trends of the test displacement and the inverse displacement are the same, but there are some deviations in the corresponding displacement peaks and valleys. The maximum displacement deviation between the two curves at the same time is 1.26 mm. At the coupler head on the impacted side of section 2, the curve change trend is the same as that of the displacement at the bottom of the buffer on the same side. The maximum displacement deviation at the same time is 3.12 mm. At the coupler head on the impacted side of section 3, the test displacement and the inverse displacement fit well in the first two valleys, and there are some deviations in the last two valleys. The maximum difference in displacement at the same time is 2.41 mm. At section 4, the inverse displacement curve shows a situation ahead of the test curve, and its valley value is slightly larger than that of the test. The maximum difference in displacement at the same time is 0.96 mm. The absolute value of the torque at the left coupler angle limit is 15.6 kN·m, and the absolute value of the torque at the right coupler angle limit is 14.1 kN·m. By reading the vertical force of the coupler collision section from the iterated model, the vertical force during the collision process is obtained. The vertical force as a whole shows an upward trend. The average vertical force during the whole process is 110.78 kN, and the maximum vertical force is 155.32 kN;

[0288] Taking the lateral displacement of the coupler in the time period of 0 s - 0.09 s before the shear bolt of the coupler test is cut as the target curve, after segmented optimization iteration together with the axial force, the optimal lateral displacement attitude of the coupler that fits the test is obtained;

[0289] Under the collision condition with a vertical height difference of 40 mm between couplers, after coupling, the coupler heads on both sides of the coupler undergo a small displacement. At section 1, the trends of the test displacement and the reverse-engineered displacement are the same, but there is a large deviation at 0.5 s, and the maximum displacement deviation is 0.06 mm. At the coupler head on the impacted side of section 2, the test and reverse-engineered displacements match well before 0.2 s. After that, the displacement deviation first increases, then decreases, and then increases again, and the maximum displacement deviation at the same time is 0.19 mm. At the coupler head on the impacted side of section 3, the test displacement and the reverse-engineered displacement match well before 0.3 s, and the maximum displacement deviation at the same time is 0.12 mm. At section 4, the overall trends of the test curve and the reverse-engineered curve are consistent, and the maximum displacement deviation at the same time is 0.05 mm. The absolute value of the torque at the angle limit is 1.26 kN·m, and the absolute value of the torque at the angle limit of the right coupler is 1.61 kN·m. By reading the lateral force of the coupler collision section from the iterated model, the lateral force during the collision process is obtained. The lateral force as a whole shows an upward trend, and the average lateral force during the whole process is 3.66 kN, and the maximum lateral force is 5.51 kN.

[0290] S4. Construct a finite element model of the collision of two subway trains, analyze and compare the influence of different rotation parameters on the body attitude, and input the coupler rotation input curve and the coupler mechanical curve obtained by test reverse engineering to analyze the collision attitude of two subway trains in different offset states;

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

[0292] S401. Construct a finite element model of the collision of two subway vehicles and understand the offset condition: The presence or absence of torque within the angle limit will affect the vertical movement of the vehicle's center of mass and the amplitude of the vehicle's front and rear tilt angles;

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

[0294] Construction of a finite element model of the collision of two subway vehicles:

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

[0296] In train collision simulation, since it is difficult for the bogie to deform, in order to reduce the calculation time, the bogie is modeled using shell elements and assigned the rigid material MAT20. To simulate the motion characteristics of the bogie, non-linear discrete beam elements are used to simulate the primary and secondary suspensions of the bogie. A rotational hinge is used to establish the constraint between the bogie drawbar rotating shaft and the bogie base, and CONTACT_SURFACE_TO_SURFACE contacts are set for the components that move relative to each other during the bogie collision process.

[0297] A simplified finite element model of the coupler is constructed, and a finite element model of the collision of the leading car of the subway train is established. Among them, CONSTRAINED_RIGID_BODIES are used to connect the coupler base and the car body, CONTACT_SURFACE_TO_SURFACE contacts are set between the bogie and the wheel-rail, and the wheel-rail friction coefficient is set to 0.10.

[0298] To study the collision attitude of two subway trains under the condition of coupler offset, the coupler parameters obtained by inverse calculation of the coupler offset collision test are selected for the input of the coupler curve.

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

[0300] To facilitate the description of the car body, coupler, and bogie in the following text, the objects involved in the model are numbered and described. The impacting train is defined as car A, and the stationary car is defined as car B. The numbers of each bogie in the initial collision state are as shown in the appendix. Figure 9 as shown;

[0301] Taking the impacting train car A as an example, A represents the car body, the first number represents the position of the wheel set, and the wheel sets are successively wheel set 1, wheel set 2, wheel set 3, and wheel set 4 from the front of the car to the rear. The final L and R represent the left wheel and the right wheel. Taking "B-4-L" as an example, it represents the left wheel of the 4th wheel set of the impacted train.

[0302] To facilitate the description of the vertical movement of the car body centroid, the lateral movement of the centroid, the front-back tilt movement of the car body, and the front-back rotation movement behavior during the collision process, the positive directions of the relevant movements are defined in the appendix. Figure 10 as shown;

[0303] For the vertical movement of the centroid, the positive direction is along the positive Z-axis; for the horizontal movement of the centroid, the positive direction is along the positive Y-axis; for the front-back tilt angle of the car body, with the center of the car body as the rotation center, the downward rotation of the front of the car is negative, and the upward rotation is positive; for the rotation angle of the car body, the positive direction is clockwise around the z-axis;

[0304] S402. Observe the influence of different coupler rotation parameters on the car body attitude: The vertical offset and the lateral offset have a great influence on the vertical and lateral swing of the coupler;

[0305] The vertical offset has the greatest influence on the vertical swing and little influence on the lateral swing. Similarly, the lateral offset also has the greatest influence on the lateral swing;

[0306] The mechanical properties of the coupler have a significant influence 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, it is also necessary to define the vertical and lateral rotation parameters of the coupler. In the study of the train collision attitude, the input method of the coupler rotation parameters of the leading car is mostly in the following form, as shown in the appendix Figure 11 as follows;

[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 reaching the angle limit. However, in fact, due to the automatic centering function of the leading car coupler, using this input method may not necessarily be able to simulate the real mechanical characteristics of the coupler;

[0308] On the basis of 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 attitude, on the basis of the coupler vertical 40mm height difference working condition in the previous two-section train collision model, with other parameters unchanged, these two coupler rotation parameter input methods are used for calculation respectively, and the movement of the car body of car A during the impact in the collision process is analyzed and compared. The definition of the coupler rotation parameter input adopted in the appendix Figure 11 is that there is no torque within the angle limit;

[0309] For the vertical movement of the car body centroid and the front-back tilt angle of the car body, the overall movement trends are the same under the two input methods. The presence or absence of torque within the angle limit will affect the amplitude of the vertical movement of the car body centroid and the front-back tilt angle of the car body. Among them, when there is torque within the angle limit, the amplitude of the vertical movement of the centroid is larger than that without torque. For the front-back tilt angle of the car body, it is exactly the opposite. When there is torque within the angle limit, the front-back tilt angle of the car body will decrease compared with the case without torque. For the lateral movement of the car body centroid and the front-back rotation angle of the car body, under these two input methods, the trends in the first half of the whole movement process are the same, while there are significant differences in the second half;

[0310] The input methods of different coupler rotation parameters have a certain impact on the vehicle body's motion attitude. Since the corresponding vertical and lateral rotation parameters have been obtained by inverse-solving the vertical and lateral motion attitudes of the coupler based on the previous research, the inverse-solved rotation parameters will be used to study and analyze the vehicle body attitude in the subsequent research;

[0311] S403. Analysis of the coupler's motion behavior in the offset state: During the collision process, the first downward amplitude of the impact on the center of mass of vehicle A is greater than that of stationary vehicle B, and with the increase of the lateral offset and vertical offset, the vertical motion of the vehicle body's center of mass will increase;

[0312] The increase of the vertical offset and lateral direction will cause the front and rear tilt angles of vehicle B's body to increase during the collision process, and the front and rear tilt speeds of vehicle B are significantly greater than those of vehicle A under the same working conditions. The increase of the lateral offset will cause the rotation amplitudes of vehicle A's body and vehicle B's body to increase significantly, but it has no obvious impact on the front and rear tilt angles of vehicle A's body;

[0313] During the train collision process, in addition to axial compression, the coupler will also be accompanied by vertical and lateral swings. Next, based on the input parameters of the finite element model of the collision of two subway vehicles and the coupler model, the different offset working conditions set above are calculated, and the axial motion behavior of the coupler and the vertical and lateral swing behaviors of the coupler during the collision process under different working conditions are 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 process shows that with the increase of the initial lateral and vertical offsets, the final lateral and vertical deflections of the coupler gradually increase;

[0315] With the increase of the vertical offset, the vertical rotation angle of the coupler gradually increases, and the overall vertical swing curve is wavy, first decreasing and then increasing. When the vertical offset of the coupler is 50mm, the maximum vertical rotation angle of the coupler is -1.08°. The increase of the vertical offset has no obvious impact on the lateral rotation of the coupler. Before 0.11s, the lateral rotation angle trends 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 the vertical offset, the vertical rotation angle of the coupler gradually increases, and the overall vertical swing curve is wavy, first decreasing and then increasing. When the vertical offset of the coupler is 50mm, the maximum vertical rotation angle of the coupler is -1.08°. The increase of the vertical offset has no obvious impact on the lateral rotation of the coupler. Before 0.11s, the lateral rotation angle trends 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 the lateral offset, the lateral deflection angle of the coupler gradually increases, and the maximum lateral deflection angle of 0.948° appears at an offset of 50 mm. However, the increase of the lateral offset has little effect on the vertical rotation of the coupler during the collision process, and the overall curve shows a wavy shape, first decreasing, then increasing, then decreasing, and then increasing.

[0318] Taking 0 - 0.16 s as the coupler compression energy absorption stage, the average rotation angle of the coupler under the influence of vertical deflection and lateral offset is obtained by taking the average value of the vertical deflection and lateral deflection during this time period.

[0319] With the increase of the vertical and lateral offsets, the average rotation angle of the coupler increases. Among them, the vertical offset has a greater impact on the vertical rotation angle of the coupler. When the height difference is 50 mm, the vertical average rotation angle of the coupler has reached -0.802°, and the increase amplitude is obvious. However, it has a smaller impact on the yaw angle, and the increase amplitude is slightly less. When the vertical height difference is 50 mm, the lateral average rotation angle of the coupler is 0.047°, which is only 0.008° higher than that without offset. On the contrary, the lateral offset has a greater impact on the lateral average rotation angle of the coupler. When the lateral offset is 50 mm, the lateral average rotation angle of the coupler has reached 0.842°, but the pitch angle is only -0.116°.

[0320] S404. Analysis of the vehicle body movement behavior under the coupler offset state;

[0321] During the collision of the train, the center of mass of the vehicle body often has vertical and lateral movements, accompanied by the front - rear tilt and rotation of the vehicle body. Next, the vertical displacement of the center of mass of the vehicle body, the horizontal displacement of the center of mass of the vehicle body, the front - rear tilt angle of the vehicle body, and the rotation angle of the vehicle body under different offset conditions are analyzed.

[0322] The vertical and lateral movements of the center of mass of cars A and B under different collision conditions are extracted to obtain the movement of the center of mass under different offsets.

[0323] Under the vertical offset, the vertical movement behaviors of the centers of mass of cars A and B are very similar before 0.05 s, both moving downward, but the amplitude of the downward movement of the center of mass of car A is greater. With the increase of the offset, the maximum vertical displacements of the centers of mass of cars A and B both increase to a certain extent.

[0324] Regarding the horizontal movement of the center of mass, there is no obvious pattern in the horizontal movement of the center of mass of car A. However, for car B before 0.13 s, with the increase of the offset, the amplitude of the horizontal displacement movement of the center of mass of car B increases significantly.

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

[0326] For the horizontal movement of the centroid, an increase in the lateral offset will affect the amplitude of the centroid movement of Vehicle A, but will not have much impact on its movement law. For Vehicle B, as the lateral offset increases, the horizontal displacement of the centroid before 0.1 s increases significantly;

[0327] Combining the above two working conditions, it can be found that during the collision process, the first decline amplitude of the centroid of the impacting vehicle is greater than that of the stationary vehicle, and with the increase of the lateral offset and vertical offset, both will increase the vertical and horizontal movements of the centroid of Vehicle B's body in the first 0.1 s;

[0328] For different collision working conditions in the simulation, the rotation conditions of the vehicle body were extracted, and the rotation conditions of the vehicle body under different working conditions were obtained;

[0329] Under the 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. Among them, 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 during the collision is significantly greater than that of Vehicle A;

[0330] For the front and rear rotation angles of the vehicle body, for the front and rear rotation angles of Vehicle A, there is no obvious rule. For Vehicle B, compared with the working condition without vertical offset, the increase in vertical offset makes the front and rear rotation angles of Vehicle B's body increase;

[0331] Under the lateral offset, for the front and rear tilt angles of the vehicle body, as the lateral offset increases, the front and rear tilt angles of Vehicle A do not change significantly, the tilt amplitude of Vehicle B's body increases significantly, and during the collision process, the tilt speed of Vehicle B's body is significantly greater than that of Vehicle A;

[0332] For the rotation angle of the vehicle body, as the lateral offset increases, the rotation amplitude of Vehicle A's body increases significantly and gradually increases with the increase of the offset. For Vehicle B, the increase in lateral offset will also increase the front and rear rotation angles 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 advance;

[0333] Combining the rotation conditions of the vehicle body under the above two working conditions, it can be found that the increase in vertical offset and lateral will both increase the front and rear tilt angles of Vehicle B's body during the collision process, and under the same working conditions, the front and rear tilt speeds of Vehicle B are significantly greater than those of Vehicle A. The increase in lateral offset will significantly increase the rotation amplitudes of Vehicle A's body and Vehicle B's body, but has no obvious effect on the front and rear tilt angles of Vehicle A's body;

[0334] S405. Analysis of the derailment risk of the train in the coupler offset state: As the vertical offset and lateral offset increase, the derailment risk of the wheels will increase. Moreover, the lifting amount is greater closer to the end of the train. The wheel set lifting of the impact side train is more intense than that of the stationary side train. Under the vertical offset condition of the coupler, the wheel lifting situation is higher than that under the lateral offset condition. However, under the lateral offset condition, it may exacerbate the left-right movement of the wheel set and increase the risk of slipping off the track.

[0335] When a train collides, there is often a lifting of the wheel set, and excessive wheel set lifting will increase the risk of wheel set derailment. Next, the lifting amounts of the wheels under different working conditions are extracted from the simulation results to analyze and compare the influence of different offset conditions on wheel lifting.

[0336] When a train derails, there is often a large lift of the wheel set. In the judgment of the train derailment behavior, the wheel lifting amount is used as an evaluation index for the train derailment behavior. According to the simulation results, the maximum values of the wheel lifting amounts of the 8 wheels on the left and right sides of the two trains during the collision under the vertical offset condition are extracted, and the maximum lifting conditions of each wheel set under different offset conditions are obtained by plotting.

[0337] The movements of the wheels on both sides first lift and then fall, and there is a large lift of the left and right wheels at 0.12 s. The lowest point of the left wheel flange is significantly higher than the track height. At this time, the coupler is in the compression stage of the crush tube.

[0338] Next, the wheel set lifting situation under the lateral offset condition is analyzed. According to the simulation results, the maximum values of the wheel lifting amounts of the 8 wheels on the left and right sides of the two trains during the collision under the vertical offset condition are extracted, and the maximum lifting conditions of each wheel set under different offset conditions are obtained by plotting, as shown in the appendix Figure 12 as follows;

[0339] From the wheel lifting action sequence, it can be seen that the lifting amount of the left wheel set is the largest at 0.12 s, which is significantly higher than the track height, and there is an obvious left shift sign of this wheel set compared with the initial situation. This may be caused by the lateral offset of the coupler. And compared with the vertical height difference of 50 mm, the influence of the lateral offset of 50 mm on the wheel set lifting is slightly smaller. The lifting of the left wheel is greater than that of the right wheel, but the lateral offset of the coupler may exacerbate the left-right movement of the wheel set, thereby increasing the risk of one side of the wheel slipping off the track.

[0340] Specifically, the present invention focuses on the inverse solution of the coupler force curve based on pose parameters under impact conditions, proposes a research idea for the inverse solution of the coupler mechanical curve under impact conditions, and on this basis, proposes a segmented inverse solution method and an inverse solution model based on time series, realizes the inverse solution of the coupler force curve under fixed conditions and offset conditions of the coupler, and analyzes the influence of 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 solution of the coupler mechanical curve under impact conditions is proposed. According to the research idea of inverse solution of the coupler mechanical curve under impact conditions and combining the research status of domestic and foreign scholars, a construction method for the finite element model of inverse solution of coupler transverse vertical yaw under impact conditions and an optimized inverse solution method based on pose parameters under impact conditions are proposed;

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

[0343] (3) A segmented inverse solution method for the coupler mechanical characteristic curve based on time series is proposed, and the inverse solution of the coupler force curve under fixed and offset conditions of the subway coupler is realized. Taking the impact test results of the subway single-sided coupler as the inverse solution target, the inverse solution model of the subway single-sided coupler is constructed, and the coupler force is iteratively inversely solved as a whole. The limitation of using the overall inverse solution curve without offset is studied, that is, the number of variables is insufficient. On this basis, the curves of the coupler buffer and the crush tube are segmented to increase the number of variables to solve the axial force of the coupler. Finally, when the buffer curve is divided into 5 segments and the crush tube curve is divided into 3 segments, the axial force of the coupler is successfully solved. In order to realize the inverse solution of the mechanical characteristics and spatial attitude of the coupler under offset collision, the impact test of the subway coupler offset collision is carried out, and the coupler mechanical curve, axial motion curve, lateral swing curve and vertical swing curve are analyzed and obtained. According to the corresponding test conditions, the inverse solution model of the subway coupler offset collision is constructed, and on the basis of the segmented inverse solution of the coupler force based on time series, the vertical swing parameter and lateral swing parameter of the coupler are introduced, and the vertical and lateral motions of the coupler are simultaneously fitted when inversely solving the axial force, and the vertical and lateral rotation parameters of the coupler and the corresponding vertical and lateral force-time curves are obtained, and the inverse solution of the coupler force under offset conditions is successfully realized;

[0344] (4) Based on the subway coupler offset collision inverse model and inverse results under impact conditions, a collision model of two subway trains was constructed to study the influence of different coupler rotation parameters on the car body attitude. Based on the coupler parameters obtained by inverse calculation through the coupler offset head-on collision test, the influence of different coupler offsets on the train collision behavior was studied. Two collision conditions were set, that is, the coupler was offset 0mm, 20mm, 40mm, and 50mm horizontally and vertically respectively, and the coupler collision characteristics and train derailment behavior were analyzed. The results show that: with the increase of the horizontal and vertical offsets of the coupler, the horizontal and vertical swing amplitudes of the coupler during the collision gradually increase, but the magnitude of the coupler force during the collision basically has no obvious change. For the movement behavior of the car body, the first drop amplitude of the center of mass of the stationary car during the collision is greater than that of the impact car, and with the increase of the horizontal and vertical offsets, the vertical movement of the car body center of mass will increase. The increase of the vertical offset and the horizontal offset will increase the front and rear tilt angles of the car body of car B during the collision, and the front and rear tilt speeds of car B are significantly greater than those of car A under the same conditions. The increase of the horizontal offset will significantly increase the rotation amplitudes of the car bodies of car A and car B, but has no obvious influence on the front and rear tilt angles of the car body of car A. Taking the wheel set lift amount as the evaluation index for train derailment analysis, it is found that the overall lift of the wheel sets on the impact side of the train during the collision is greater than that of the stationary car, and the wheel set with the largest lift for both trains is the No. 4 wheel set near the rear of the car body. Under the same offset, the vertical offset will make the wheel set lift higher, and the horizontal offset will exacerbate the left-right movement of the wheel set, thereby increasing the risk of the wheel set slipping off the track.

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

[0346] The above is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A reverse solution method for the three-dimensional mechanical curve of a subway coupler based on pose parameters under impact conditions, characterized in that The described research reverse engineering method includes the following steps: S1. According to the reverse engineering research idea of the coupler mechanical curve under impact conditions, propose a method for constructing a finite element model for reverse seeking the transverse and vertical yaw of the coupler under impact conditions and an optimization reverse seeking method based on pose parameters under impact conditions; S2. Take the coupler buffer device of the subway train as the research object, analyze the working principles of each component of the subway train coupler, divide the subway train coupler into rigid components, energy-absorbing components and rotating components to build a reverse seeking model of the subway coupler under impact conditions, and conduct a subway single-sided coupler impact test to verify the accuracy of the reverse seeking model of the subway coupler under impact conditions; S3. Take the single-sided coupler as the research object. Without considering the rotation of the coupler, propose a method for segmental reverse seeking of the coupler characteristic curve based on time series, compare the reverse seeking results with the test results, and introduce the fitting of the coupler rotation parameters in the segmental reverse seeking method to realize the reverse seeking of the three-directional force and three-dimensional motion posture of the coupler under impact conditions; S4. Build a finite element model of the collision of two subway trains, analyze and compare the influence of different rotation parameters on the vehicle body posture, and input the coupler rotation input curve and coupler mechanical curve obtained by experimental reverse seeking to analyze the collision postures of two subway trains in different offset states of the coupler.

2. The inverse solution method for the three-dimensional mechanical curve of the subway coupler based on pose parameters under impact conditions according to claim 1, characterized in that: The step S1 includes the following specific steps: S101. Conduct research on the reverse engineering idea of the coupler mechanical curve, and construct a corresponding coupler reverse seeking model and reverse seeking method according to the mechanical characteristics and motion characteristics of the subway coupler itself; S102. Form a method for constructing a finite element model for reverse seeking the transverse and vertical yaw of the coupler. According to the motion characteristics of the coupler, divide the coupler motion into three parts, namely axial compression, vertical swing and lateral swing, and construct a finite element model that reflects the compression and energy absorption characteristics of the coupler axially and the lateral and vertical swing characteristics of the coupler vertically and laterally.

3. The three-dimensional mechanical curve research reverse seeking method of the subway coupler based on pose parameters under impact conditions according to claim 2, characterized in that: The step S101 includes the following specific steps: When the train is running normally, the coupler buffer device is responsible for transmitting traction force and braking force. When a collision occurs, the coupler buffer device takes the lead in compressing and absorbing energy and takes effect. After the coupler acts, the main energy-absorbing structure, anti-climbing device and vehicle body act in turn to absorb collision energy; Represent the load, test simulation model and structural deformation response in the form of input and output respectively. Given the dynamic load through the known vibration system, the solution of the result response can be realized. On the contrary, the load can be solved by inverse inversion through the result response; After realizing the process from load to response, set the load parameters as variables, fit these node responses with the test responses through an optimization algorithm, output the corresponding load variables after the node responses are fitted well, and change the load variables to continue fitting if the fitting effect is not good.

4. The inverse solution method for the three-dimensional mechanical curve of the subway coupler based on pose parameters under impact conditions according to claim 2, characterized in that: The step S102 includes the following specific steps: Establish a direct relationship between the coupler force curve and the displacement curve through the Beam element model in LS-DYNA; Realize the calculation of the mechanical characteristics of complex structures by defining non-linear springs to represent the mechanical characteristics of the structures.

5. The inverse solution method for the three-dimensional mechanical curve of the subway coupler based on pose parameters under impact conditions according to claim 1, characterized in that: The step S2 includes the following specific steps: After the construction of the coupler inverse solution model under impact conditions in S201, the subsequent optimization of the inverse solution method was studied. Through the optimization algorithm embedded in Hyperworks, users can write optimization programs in Compose, register the optimization programs in the software program library, and call the programs by the program name. S201. The method of using a surrogate model to predict and solve the curve, and the surrogate model is one of a polynomial response surface model, a Kriging model, and a radial basis neural network model.

6. The inverse solution method for studying the three-dimensional mechanical curve of the subway coupler based on pose parameters under impact conditions according to claim 1, characterized in that: The step S3 includes the following specific steps: S301. Conduct the overall inverse solution of the coupler axial force for pose response. S302. Conduct the segmented inverse solution analysis of the coupler axial force curve for time series. S303. Conduct the offset collision impact test of the subway coupler. S304. Conduct the inverse solution analysis of the subway coupler force curve under offset collision.

7. The inverse solution method for the three-dimensional mechanical curve of the subway coupler based on pose parameters under impact conditions according to claim 6, wherein: The step S301 includes: For the inverse solution of the coupler axial force, first conduct the overall inverse solution, taking the minimum fitting of the axial displacement area difference as the optimization goal, and conduct 100, 200, 500, and 1000 times of overall optimization for the coupler overall force value variables respectively. As the number of iterations increases, the average value of the force value error at each time point gradually decreases, and the maximum deviation of the displacement also gradually decreases, but the maximum error of the force value does not have an obvious change rule. The step S302 includes: In order to improve the curve inverse solution accuracy and reduce the exponential increase in the optimization difficulty due to the increase in variables, an inverse solution method 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 segmented respectively to increase the number of variables, and segmented step-by-step fitting is carried out according to the test coupler displacement-time curve. Finally, under the condition of dividing the buffer into 5 segments and the crush tube into 3 segments, the inverse solution of the coupler axial force is realized. The step S303 includes: In order to realize the inverse solution of the coupler force under offset conditions, an offset collision impact test of the subway coupler was carried out. In addition to analyzing the force-time, force-displacement, and displacement-time curves of the coupler in the axial direction, according to the top and left high-speed photography, the lateral swing displacement and vertical swing displacement of the coupler were extracted at 4 cross-section positions of the coupler from the top and left perspectives. The step S304 includes: While conducting the inverse solution of the coupler axial force based on time series, introduce the vertical swing and lateral swing parameters of the coupler to simultaneously fit the lateral and vertical swing conditions of the coupler during the collision. In the selection of the optimal solution for multi-objective optimization, select the solution with the minimum axial displacement area difference as the optimal solution for each segmented iteration; according to the test data, conduct the inverse solution of the coupler force under offset collision, and fit the lateral and vertical swing conditions of the coupler to obtain the input parameters of the buffer of both sides of the coupler, the input parameters of the coupler crush tube, the lateral swing parameters of the coupler, and the vertical swing parameters of the coupler.

8. The inverse solution method for the three-dimensional mechanical curve of the subway coupler based on pose parameters under impact conditions according to claim 1, characterized in that: The step S4 includes the following specific steps: S401. Construct the finite element model of the collision of two subway vehicles and understand the offset conditions. S402. Observe the influence of different coupler rotation parameters on the vehicle body attitude. S403. Analyze the movement behavior of the coupler in the coupler offset state; S404. Analyze the movement behavior of the car body in the coupler offset state; S405. Analyze the derailment risk of the train in the coupler offset state.

9. The inverse solution method for the three-dimensional mechanical curve research of the subway coupler based on pose parameters under impact conditions according to claim 8, characterized in that: The step S401 includes: The presence or absence of torque within the angle limit will affect the vertical movement of the car body axis and the amplitude of the front and rear tilt angles of the car body; When there is torque within the angle limit, the vertical movement amplitude of the center of mass is greater than when there is no torque, while for the front and rear tilt angles of the car body, it is exactly the opposite.

10. The inverse solution method for the three-dimensional mechanical curve research of the subway coupler based on pose parameters under impact conditions according to claim 8, characterized in that: The step S405 includes: The increase in vertical offset and lateral offset will both increase the derailment risk of the wheels, and the lift amount is greater the closer to the end of the train. The wheel set lift of the impact side train is more severe than that of the stationary side train. Under the vertical offset condition of the coupler, the wheel lift situation is higher than that under the lateral offset condition, but under the lateral offset condition, it will exacerbate the left and right movement of the wheel set and increase the risk of slipping off the track.

Images