An Efficient Prediction Method for the Fatigue Life of Elastic Rail Clips in High-Speed Railways

Abstract

The present invention belongs to the technical field of railway engineering, and provides an efficient prediction method for the fatigue life of the elastic clip of high-speed railway fasteners, including: based on the natural frequencies obtained from the prestressed modal analysis of the solid element finite element model, the linear constraint stiffness of the elastic clip beam element model is optimized by using the particle swarm algorithm, and the static equivalent stress of the elastic clip beam element model, as well as the natural frequencies, vibration modes and modal equivalent stresses of different frequency orders in the prestressed modal analysis are derived, and the dynamic equation of the elastic clip in the installed state is established based on the modal superposition method; applying the vehicle-track spatial coupling dynamic model, generating the three-dimensional dynamic responses of the rail and the track slab corresponding to the contact position of the elastic clip, and using this as the excitation input into the elastic clip dynamic model, calculating the dynamic responses such as the vibration acceleration and equivalent dynamic stress of the elastic clip; based on the fatigue cumulative damage theory, calculating the fatigue life at different positions of the elastic clip, and judging the dangerous area and the most dangerous point where the elastic clip is prone to high-frequency fatigue fracture.

Description

Technical Field

[0001] The present invention relates to the technical field of railway engineering, and particularly relates to an efficient prediction method for the fatigue life of the elastic clip of high-speed railway fasteners. Background Art

[0002] The operating environment and line conditions of the Chinese high-speed railway network are complex and variable, and a series of damage and deterioration problems have occurred in the track structure components during long-term operation. Among them, the rail fastener is an essential key component of the track structure, which plays the role of fixing the rail, providing elastic support, and maintaining the stability and smoothness of the track. Under the action of high-frequency excitations such as rail corrugation and wheel polygon, the high-frequency fatigue fracture of the elastic clip of high-speed rail fasteners occurs frequently. The fracture of the elastic clip will weaken the three-way restraint of the fastener system on the rail, thus triggering a series of adverse consequences such as rail creep, extrusion of the rubber pad under the rail, and deterioration of the track geometry, intensifying the dynamic interaction between the wheel and the rail, reducing the riding comfort, and even threatening the train operation safety. Especially in recent years, with the active exploration and practice of higher operating speeds for high-speed railways, the high-frequency excitation frequency band has been continuously broadened, making the elastic clip of the fastener that was originally outside the resonance frequency band also face the risk of fatigue fracture.

[0003] Existing research mainly relies on commercial finite element software to establish a fine three-dimensional solid finite element model of the fastener system, and uses the analysis method of transient dynamics to study the dynamic response and fatigue life of the elastic clip under the action of wheel-rail excitation. The modeling process is cumbersome, the model degrees of freedom are large, the solution efficiency is very low, and the traditional vehicle-track spatial coupling dynamics model does not consider the participation of the elastic clip in vibration. Summary of the Invention

[0004] The purpose of the present invention is to provide an efficient prediction method for the fatigue life of the elastic clip of high-speed railway fasteners, obtain the dynamic response of the elastic clip under different driving conditions and the dangerous areas prone to high-frequency fatigue fracture, provide a scientific reference for the damage detection, operation and maintenance, and optimal design of the elastic clip of the fastener, and thus ensure the long-term safe and stable operation of the railway.

[0005] To solve its technical problems, the present invention adopts the following technical solutions:

[0006] An efficient prediction method for the fatigue life of the elastic clip of high-speed railway fasteners includes the following steps:

[0007] According to the basic parameters of the central axis of the elastic clip and the parametric equations of each central axis segment, establish the parametric mathematical equation of the elastic clip;

[0008] According to the parametric mathematical equation of the elastic clip and the pre-tightening force of the fastener bolt, establish the finite element model of the elastic clip solid element and the finite element model of the elastic clip beam element under the standard installation state respectively, and conduct prestressed modal analysis;

[0009] Construct a fitness function that describes the frequency difference between the finite element model of the elastic clip solid element and the finite element model of the elastic clip beam element. Taking the linear spring constraint stiffness of the finite element model of the elastic clip beam element as the design optimization object and minimizing the fitness function as the goal, optimize the finite element model of the elastic clip beam element based on the particle swarm optimization algorithm to obtain the optimal value of the constraint stiffness of the finite element model of the elastic clip beam element;

[0010] According to the optimized finite element model of the elastic clip beam element, derive the static equivalent stress under the standard installation state of the elastic clip, as well as the natural frequencies, vibration modes, and modal equivalent stresses of different frequency orders in the prestressed modal analysis, and establish a dynamic model of the elastic clip based on the modal superposition method;

[0011] Apply the vehicle-track spatial coupling dynamic model to generate the three-dimensional dynamic responses of the rail and the track slab corresponding to the contact position of the elastic clip under the action of short-wave irregularities, and use this as the excitation input into the dynamic model of the elastic clip to calculate the dynamic response of the elastic clip;

[0012] Based on the fatigue cumulative damage theory, calculate the fatigue life at different positions of the elastic clip according to the equivalent dynamic stress time history curve of the elastic clip nodes obtained from the dynamic response of the elastic clip;

[0013] Calculate the fatigue life distribution of different nodes of the elastic clip, and determine the dangerous area and the most dangerous point where the elastic clip is prone to high-frequency fatigue fracture.

[0014] As a further optimization, the components of the finite element model of the elastic clip solid element under the standard installation state include the elastic clip, flat washer, insulating gauge block, and gauge retaining plate. A surface-to-surface contact relationship is established between adjacent components, the tangential algorithm of the contact surface is set as the penalty function, and the normal direction is set as "hard contact", that is, the components do not penetrate each other;

[0015] The material properties of the elastic clip and the flat washer adopt the bilinear hardening elastoplastic model;

[0016] The boundary conditions are set as full constraints on the bottom surfaces of the insulating gauge block and the gauge retaining plate, the longitudinal and transverse displacements are constrained on the inner ring surface when the flat washer is pressed down, and the vertical displacement of the flat washer is constrained after installation;

[0017] The standard installation state of the elastic clip is to apply a pre-tightening force downward through the bolt so that the front end of the middle limb of the fastener elastic clip just contacts the insulating gauge block. The expression of the relationship between the bolt pre-tightening force and the tightening torque is:

[0018] ,

[0019] In the formula, T is the tightening torque, K is the tightening torque coefficient, F is the bolt pre-tightening force, dis the nominal diameter of the bolt.

[0020] As a further optimization, in the finite element model of the elastic clip beam unit in the standard installation state, longitudinal, transverse, and vertical linear springs are set as constraint conditions at the actual contact positions between the elastic clip and the rail or track slab to simulate the contact behavior between the elastic clip and adjacent components, and a downward displacement constraint is applied to the actual contact position between the middle limb of the elastic clip and the flat washer to simulate the prestressed installation state of the elastic clip.

[0021] As a further optimization, before the fitness function that describes the frequency difference between the finite element model of the elastic clip solid unit and the finite element model of the elastic clip beam unit, it also includes: taking the natural frequency calculated by the common finite element model of the elastic clip solid unit as the benchmark.

[0022] As a further optimization, taking the linear spring constraint stiffness of the finite element model of the elastic clip beam unit as the design optimization object and minimizing the fitness function as the goal, the finite element model of the elastic clip beam unit is optimized based on the particle swarm optimization algorithm, including the following steps:

[0023] Write a particle swarm optimization algorithm program using MATLAB software;

[0024] Based on the co-simulation of MATLAB and ANSYS software, MATLAB initializes the constraint stiffness and starts ANSYS APDL;

[0025] ANSYS reads the constraint stiffness and calculates the modal frequency;

[0026] MATLAB extracts the first N m order modal frequencies calculated by ANSYS and calculates the fitness value function value. The calculation formula of the fitness value function is:

[0027] ,

[0028] In the formula, represents the infinity norm, is the first-order modal frequency calculated by the finite element model of the elastic clip beam unit, is the second-order modal frequency calculated by the finite element model of the elastic clip beam unit, is the nth-order modal frequency calculated by the finite element model of the elastic clip beam unit, is the first-order modal frequency calculated by the finite element model of the elastic clip solid unit, is the second-order modal frequency calculated by the finite element model of the elastic clip solid unit, is the nth-order modal frequency calculated by the finite element model of the elastic clip solid unit, N m is the modal truncation number of the elastic clip, λ and denotes the frequency difference weighting coefficient;

[0029] When the number of iterations of the particle swarm reaches the preset maximum number of iterations, the calculation stops.

[0030] As a further optimization, the dynamic model of the elastic clip is established based on the mode superposition method. Among them, the expression of the vibration equation of the n th order of the elastic clip in the modal coordinate system is:

[0031] ,

[0032] In the formula, are the displacement, velocity and acceleration responses of the elastic clip in the modal coordinate, is the damping ratio, is the n th natural frequency, n 0 is the number of force-bearing nodes of the elastic clip, are the modal displacements of the n th order vibration mode of the elastic clip in the longitudinal, transverse and vertical directions, is the position coordinate of the i th force-bearing point of the elastic clip, are the longitudinal, transverse and vertical loads of the i th force-bearing point of the elastic clip.

[0033] As a further optimization, at the contact position between the elastic clip and the rail, the calculation formulas for the longitudinal, transverse and vertical loads of the i th force-bearing point are:

[0034] ,

[0035] In the formula, are the longitudinal, transverse and vertical displacements of the rail, are the angular displacement around the centroid of the rail z axis, y axis, x axis, are the longitudinal, transverse and vertical contact stiffnesses at the contact position between the elastic clip and the rail, are the abscissa and ordinate of the contact point between the elastic clip and the rail in the rail coordinate system;

[0036] At the contact position between the elastic clip and the track slab, the calculation formulas for the longitudinal, transverse and vertical loads of the i th force-bearing point are:

[0037] ,

[0038] In the formula, are the longitudinal, transverse and vertical displacements of the track slab, They are the longitudinal, transverse, and vertical contact stiffnesses at the contact position between the elastic clip and the track slab, is the thickness of the track slab.

[0039] As a further optimization, the dynamic responses of the elastic clip include vibration displacement, velocity, and acceleration, and their calculation formulas are:

[0040] ,

[0041] In the formula, is the modal displacement in the longitudinal, transverse, and vertical directions at the n th mode and the j th node of the elastic clip, are the vibration displacements in the longitudinal, transverse, and vertical directions at the j th node of the elastic clip in the Cartesian coordinate system, are the vibration velocities in the longitudinal, transverse, and vertical directions at the j th node of the elastic clip in the Cartesian coordinate system, are the vibration accelerations in the longitudinal, transverse, and vertical directions at the j th node of the elastic clip in the Cartesian coordinate system.

[0042] As a further optimization, the dynamic response of the elastic clip also includes the equivalent dynamic stress time history curve, and its calculation formula is:

[0043] ,

[0044] In the formula, is the static equivalent stress of the elastic clip in the installed state, is the modal equivalent stress of the n th mode of the elastic clip obtained from the prestressed modal analysis.

[0045] As a further optimization, calculating the fatigue life at different positions of the elastic clip includes the following steps:

[0046] According to the stress time history curve obtained by calculating in the dynamic response of the elastic clip when a bogie passes through, use the rain flow counting method to find out the fatigue stress cycle amplitude, stress cycle mean value, and stress cycle times of the elastic clip;

[0047] Use the Goodman method to correct the influence of the mean stress, and the calculation formula for the stress amplitude of the k th stress cycle after correction is:

[0048] ,

[0049] In the formula, is the stress amplitude before correction, is the stress mean value, is the tensile strength of the elastic clip material;

[0050] The cumulative damage of each symmetric cyclic load is linearly superimposed using the Palmgren-Miner linear cumulative damage criterion to obtain the cumulative damage value, and its reciprocal is finally taken to obtain the fatigue life. The calculation formula for the fatigue life of the elastic clip is as follows:

[0051] ,

[0052] In the formula, n is the number of stress cycles, L is the fatigue life of the elastic clip.

[0053] The beneficial effects of the present invention are as follows: Through the above-mentioned efficient prediction method for the fatigue life of the elastic clip of high-speed railway fasteners, the present invention establishes a beam element elastic clip dynamics model based on the particle swarm optimization algorithm and the mode superposition theory, applies the vehicle-track spatial coupling dynamics model to generate the three-dimensional dynamic responses of the rail and the track slab at the contact position between the elastic clip and the track, and uses these as the input excitation of the elastic clip dynamics model. Finally, based on the fatigue cumulative damage theory, the efficient prediction of the fatigue life of the elastic clip is realized. At the same time, since the elastic clip beam element dynamics model established in the present invention uses linear springs to replace the nonlinear contact relationships of the components of the solid model, and the degrees of freedom are greatly reduced, the fatigue life of the elastic clip can be efficiently predicted, and the dynamic responses of the elastic clip under different driving conditions and the dangerous areas prone to high-frequency fatigue fracture can be obtained, providing a scientific reference for the damage detection, operation and maintenance, and optimization design of the fastener elastic clip, which is of great significance for ensuring the long-term safe and stable operation of the railway. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a flow chart of an efficient prediction method for the fatigue life of the elastic clip of high-speed railway fasteners in an embodiment of the present invention;

[0055] Figure 2 is a schematic diagram of the finite element model of the solid unit of the fastener elastic clip in an embodiment of the present invention;

[0056] Figure 3 is a schematic diagram of the finite element model of the elastic clip beam element in an embodiment of the present invention;

[0057] Figure 4 is a flow chart of the particle swarm optimization algorithm in an embodiment of the present invention;

[0058] Figure 5 is a convergence curve graph of the fitness function value in the particle swarm optimization algorithm in an embodiment of the present invention;

[0059] Figure 6 is a schematic diagram of the convergence analysis of the elastic clip dynamic response in an embodiment of the present invention;

[0060] Figure 7Schematic diagram of the vertical acceleration time history response at the highest point of the side limb of the clip in the embodiment of the present invention;

[0061] Figure 8 Schematic diagram of the equivalent stress time history curve at the dangerous point of the clip in the embodiment of the present invention;

[0062] Figure 9 Histogram of stress rain flow counting of the clip in the embodiment of the present invention;

[0063] Figure 10 Schematic diagram of the position distribution of the selected nodes of the clip in the embodiment of the present invention;

[0064] Figure 11 Schematic diagram of the fatigue life at different nodes of the clip in the embodiment of the present invention. Detailed implementation manners

[0065] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Generally, the components of the embodiments of the present invention described and illustrated herein can be arranged and designed in various different configurations. Embodiment

[0066] This embodiment provides an efficient prediction method for the fatigue life of the clip of high-speed railway fasteners. The flowchart is shown in Figure 1 , and the method includes the following steps:

[0067] S1. Establish a parametric mathematical equation of the clip according to the basic parameters of the central axis of the clip and the parametric equations of each central axis segment.

[0068] Among them, taking the W1 type clip commonly used in high-speed railways as the research object, a parametric mathematical equation of the central axis of the clip is constructed according to the structural parameters of the two-dimensional plane expansion diagram and the front view of its central axis.

[0069] S2. Establish a finite element model of the clip solid element and a finite element model of the clip beam element under the standard installation state respectively according to the parametric mathematical equation of the clip and the pre-tightening force of the fastener bolt, and perform prestressed modal analysis.

[0070] Among them, the finite element model of the clip solid element is as shown in Figure 2As shown, the number of elements and nodes are 21528 and 97262 respectively. The whole model includes elastic clips, flat washers, insulating gauge blocks, and gauge baffles. A surface-to-surface contact relationship is established between adjacent components. The tangential algorithm of the contact surface is set as the penalty function, and the normal direction is set as "hard contact", that is, the components do not penetrate each other. The material properties of the elastic clip material 60Si2MnA and the flat washer material Q235-A both adopt the bilinear strengthening elastoplastic model. The boundary conditions are set as follows: the bottom surfaces of the insulating gauge blocks and gauge baffles are fully constrained. When the flat washer is pressed down, the longitudinal and transverse displacements of the inner ring surface are constrained, and the vertical displacement of the flat washer is constrained after installation. The standard installation state of the elastic clip is to apply a pre-tightening force downward through the bolt so that the front end of the middle limb of the fastener elastic clip just contacts the insulating gauge block. The expression of the relationship between the bolt pre-tightening force and the tightening torque is:

[0071] ,

[0072] In the formula, T is the tightening torque, and the theoretical tightening torque of the W1 type elastic clip is about 140 - 180 N·m; K is the tightening torque coefficient, which is taken as 0.2 under the conditions of surface oxidation and lubrication; F is the bolt pre-tightening force; d is the nominal diameter of the bolt, which is taken as 25 mm;

[0073] The calculated value range of the bolt pre-tightening force is 28 - 36 kN. A reasonable bolt pre-tightening force is selected and applied to the flat washer so that the front end of the middle limb of the elastic clip just contacts the insulating gauge block.

[0074] The finite element model of the elastic clip beam element is as Figure 3 shown. The number of elements and nodes are 296 and 593 respectively. At the actual contact positions of the elastic clip with the rail and the track slab, longitudinal, transverse, and vertical linear springs are set as constraint conditions to simulate the contact behavior between the elastic clip and adjacent components. A downward displacement constraint is applied to the actual contact position between the middle limb of the elastic clip and the flat washer to simulate the installation state of the elastic clip.

[0075] S3. Based on the natural frequency calculated by the commonly used finite element model of the elastic clip solid element at present, a fitness function describing the frequency difference between the finite element model of the elastic clip solid element and the finite element model of the elastic clip beam element is constructed. Taking the linear spring constraint stiffness of the finite element model of the elastic clip beam element as the design optimization object and minimizing the fitness function as the goal, the finite element model of the elastic clip beam element is optimized based on the particle swarm optimization algorithm to obtain the optimal value of the constraint stiffness of the finite element model of the elastic clip beam element.

[0076] Among them, taking the linear spring constraint stiffness of the finite element model of the elastic clip beam element as the design optimization object and minimizing the fitness function as the goal, optimizing the finite element model of the elastic clip beam element based on the particle swarm optimization algorithm includes the following steps:

[0077] Write a particle swarm optimization algorithm program using MATLAB software;

[0078] Based on the co - simulation of MATLAB and ANSYS software, MATLAB initializes the constraint stiffness and starts ANSYS APDL;

[0079] ANSYS reads the constraint stiffness and calculates the modal frequencies;

[0080] MATLAB extracts the first N m order modal frequencies calculated by ANSYS and calculates the fitness function value. The calculation formula of the fitness function is:

[0081] ,

[0082] In the formula, represents the infinity norm, is the first - order modal frequency calculated by the finite - element model of the elastic strip beam element, is the second - order modal frequency calculated by the finite - element model of the elastic strip beam element, is the n - th order modal frequency calculated by the finite - element model of the elastic strip beam element, is the first - order modal frequency calculated by the finite - element model of the elastic strip solid element, is the second - order modal frequency calculated by the finite - element model of the elastic strip solid element, is the n - th order modal frequency calculated by the finite - element model of the elastic strip solid element, N m is the modal truncation number of the elastic strip, λ and represent the frequency difference weighting coefficients;

[0083] When the iteration times of the particle swarm reach the preset maximum iteration times, the calculation stops.

[0084] Figure 4 is the flow chart of the particle swarm optimization algorithm. The particles in the figure represent the constraint stiffness of the finite - element model of the elastic strip beam element; Figure 5 is the convergence curve of the fitness function value in the particle swarm optimization algorithm. It can be seen that after 200 iterations, the frequency difference between the beam model and the solid model can meet the accuracy requirements;

[0085] Table 1 shows the first 5 order frequency results after the constraint stiffness optimization of the elastic strip beam element model. It can be seen that after the iteration of the particle swarm optimization algorithm, the frequency errors between the first 5 order modal frequencies of the elastic strip beam element model and the frequencies calculated by the solid model are all less than 5%. Moreover, the degrees of freedom and modeling difficulty of the beam model are much smaller than those of the solid model. Therefore, by optimizing the constraint stiffness of the elastic strip beam element model through the particle swarm optimization algorithm, the calculation efficiency can be greatly improved while ensuring the accuracy.

[0086] Table 1. Modal Frequency Optimization Results of the Constraint Stiffness of the Elastic Strip Beam Element Model

[0087] ,

[0088] S4. According to the optimized finite element model of the elastic strip beam element, the static equivalent stress in the standard installation state of the elastic strip is derived, as well as the natural frequencies, vibration modes and modal equivalent stresses of different frequency orders in the prestressed modal analysis. And a dynamic model of the elastic strip is established based on the modal superposition method.

[0089] For the dynamic model of the elastic strip established based on the modal superposition method, the expression of the vibration equation of the elastic strip in the modal coordinate system at the n -th order is as follows:

[0090] ,

[0091] In the formula, are the displacement, velocity and acceleration responses of the elastic strip in the modal coordinate system respectively, is the damping ratio, is the n -th order natural frequency, n 0 is the number of force-bearing nodes of the elastic strip, are the modal displacements of the n -th order vibration mode of the elastic strip in the longitudinal, transverse and vertical directions respectively, is the position coordinate of the i -th force-bearing point of the elastic strip, are the longitudinal, transverse and vertical loads of the i -th force-bearing point of the elastic strip respectively.

[0092] At the contact position between the elastic strip and the rail, the calculation formulas for the longitudinal, transverse and vertical loads of the i -th force-bearing point are as follows:

[0093] ,

[0094] In the formula, are the longitudinal, transverse and vertical displacements of the rail respectively, are the angular displacement around the centroid of the rail z axis, y axis, x axis respectively. are the longitudinal, transverse, and vertical contact stiffnesses at the contact position between the elastic clip and the rail, are the abscissa and ordinate of the contact point between the elastic clip and the rail in the rail coordinate system;

[0095] At the contact position between the elastic clip and the track slab, the i calculation formulas for the longitudinal, transverse, and vertical loads of the

[0096] ,

[0097] wherein, are the longitudinal, transverse, and vertical displacements of the track slab, are the longitudinal, transverse, and vertical contact stiffnesses at the contact position between the elastic clip and the track slab, is the thickness of the track slab.

[0098] S5. Apply the vehicle-track spatial coupling dynamics model to generate the three-dimensional dynamic responses of the rail and the track slab corresponding to the contact position of the elastic clip under short-wave irregularities, and use this as the excitation input to the dynamics model of the elastic clip to calculate the dynamic response of the elastic clip.

[0099] The dynamic response of the elastic clip includes vibration displacement, velocity, and acceleration, and its calculation formulas are:

[0100] ,

[0101] wherein, is the longitudinal, transverse, and vertical modal displacements at the n th node of the j th order vibration mode of the elastic clip, are the longitudinal, transverse, and vertical vibration displacements at the j th node of the elastic clip in the Cartesian coordinate system, are the longitudinal, transverse, and vertical vibration velocities at the j th node of the elastic clip in the Cartesian coordinate system, are the longitudinal, transverse, and vertical vibration accelerations at the j th node of the elastic clip in the Cartesian coordinate system.

[0102] The dynamic response of the elastic clip also includes the equivalent dynamic stress time history curve, and its calculation formula is:

[0103] ,

[0104] wherein, is the static equivalent stress of the elastic clip in the installed state, is the modal equivalent stress of the n th order mode of the elastic clip obtained by prestressed modal analysis.

[0105] Figure 6 It is a schematic diagram for the convergence analysis of the dynamic response of the elastic clip. The calculation condition is the peak value of the vertical acceleration of the elastic clip and the mean stress corresponding to the maximum stress amplitude when the high-speed vehicle passes at 300 km / h under the excitation of the measured wheel polygon. As can be seen from the figure, when the modal order of the elastic clip N m exceeds 2, the response tends to be stable, which proves that the modal superposition using the constraint mode in the installed state of the elastic clip has good convergence.

[0106] Figure 7 It is a schematic diagram of the time history response of the vertical acceleration at the highest point of the side limb of the elastic clip. As can be seen from the figure, under the excitation of the wheel polygon, the vibration response of the elastic clip is intense, and the peak value of the vertical acceleration reaches 320g.

[0107] Figure 8 It is a schematic diagram of the stress time history curve at the dangerous point of the elastic clip. The dangerous point at the inner side of the heel end of the elastic clip observed on site is selected, and its stress time history curve is calculated. The calculation results of the elastic clip using solid elements and beam elements are compared in the figure, and the two curves almost coincide, which proves that the beam element ensures the calculation accuracy while improving the calculation efficiency.

[0108] S6. Based on the fatigue cumulative damage theory, according to the equivalent dynamic stress time history curve of the elastic clip nodes obtained from the dynamic response of the elastic clip, calculate the fatigue life at different positions of the elastic clip.

[0109] The calculation of the fatigue life at different positions of the elastic clip includes the following steps:

[0110] According to the stress time history curve of the elastic clip when a bogie passes calculated in step S5, use the rain-flow counting method to obtain the fatigue stress cycle amplitude, stress cycle mean value, and stress cycle times of the elastic clip;

[0111] Figure 9 It is a histogram of the rain-flow counting of the elastic clip stress. As can be seen from the figure, through the rain-flow counting of the stress time history curve, a series of stress amplitudes and stress mean values with known cycle times can be obtained;

[0112] Use the Goodman method to correct the influence of the mean stress, and the formula for the stress amplitude of the k th stress cycle after correction is:

[0113] ,

[0114] In the formula, is the stress amplitude before correction, is the stress mean value, is the tensile strength of the elastic clip material;

[0115] Using the Palmgren-Miner linear cumulative damage criterion, the cumulative damage of each symmetric cyclic load is linearly superimposed to obtain the cumulative damage value, and the reciprocal of it is finally taken to obtain the fatigue life. The calculation formula for the fatigue life of the elastic clip is as follows:

[0116] ,

[0117] In the formula, n is the number of stress cycles, L is the fatigue life of the elastic clip.

[0118] According to the stress time history curve of the dangerous point of the elastic clip, the fatigue life of the dangerous point of the elastic clip is calculated. Table 2 shows the fatigue life of the dangerous point of the elastic clip. It can be seen that under the excitation of wheel polygon, the fatigue life of the dangerous point of the elastic clip is already lower than the design requirement of 5 million times.

[0119] S7. Calculate the fatigue life distribution of different nodes of the elastic clip, and judge the dangerous area and the most dangerous point where the elastic clip is prone to high-frequency fatigue fracture, so as to provide guidance for the maintenance of the elastic clip of high-speed rail fasteners.

[0120] Among them, Figure 10 is the schematic diagram of the position distribution of the selected nodes of the elastic clip. According to the structural symmetry, a total of 20 nodes of half of the elastic clip structure are selected to calculate the fatigue life; Figure 11 is the schematic diagram of the fatigue life distribution at different nodes of the elastic clip. It can be seen from the figure that the dangerous area of the elastic clip is located at the heel end, and the fatigue life of the most dangerous point is 3.37 million times, which is lower than the design requirement of 5 million times, indicating that under the excitation of wheel polygon, fatigue fracture is likely to occur here, which is basically consistent with the fracture area of the elastic clip observed on site.

[0121] The above is only the preferred embodiment of the present invention and is not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. An efficient prediction method for the fatigue life of elastic fasteners for high-speed railways, characterized in that, It includes the following steps: Establish a parametric mathematical equation of the elastic clip according to the basic parameters of the central axis of the elastic clip and the parametric equations of each central axis segment; Establish a finite element model of the elastic clip solid element and a finite element model of the elastic clip beam element under the standard installation state respectively according to the parametric mathematical equation of the elastic clip and the pre-tightening force of the fastener bolt, and conduct prestressed modal analysis; Construct a fitness function describing the frequency difference between the finite element model of the elastic clip solid element and the finite element model of the elastic clip beam element, take the linear spring constraint stiffness of the finite element model of the elastic clip beam element as the design optimization object, take minimizing the fitness function as the goal, and optimize the finite element model of the elastic clip beam element based on the particle swarm optimization algorithm to obtain the optimal value of the constraint stiffness of the finite element model of the elastic clip beam element; According to the optimized finite element model of the elastic clip beam element, derive the static equivalent stress of the elastic clip under the standard installation state, as well as the natural frequencies, vibration modes and modal equivalent stresses of different frequency orders in the prestressed modal analysis, and establish a dynamic model of the elastic clip based on the modal superposition method; Apply the vehicle-track spatial coupling dynamic model to generate the three-dimensional dynamic responses of the rail and the track slab corresponding to the contact position of the elastic clip under the action of short-wave irregularities, and use this as the excitation input into the dynamic model of the elastic clip to calculate the dynamic response of the elastic clip; Based on the fatigue cumulative damage theory, calculate the fatigue life at different positions of the elastic clip according to the equivalent dynamic stress time history curve of the elastic clip node obtained from the dynamic response of the elastic clip; Calculate the fatigue life distribution of different nodes of the elastic clip, and judge the dangerous area and the most dangerous point where the elastic clip is prone to high-frequency fatigue fracture; 2. The high-speed railway fastener clip fatigue life efficient prediction method according to claim 1, characterized in that The components of the finite element model of the elastic clip solid element under the standard installation state include the elastic clip, flat washer, insulating gauge block and gauge retaining plate. A surface-to-surface contact relationship is established between adjacent components, the tangential algorithm of the contact surface is set as the penalty function, and the normal direction is set as "hard contact", that is, the components do not penetrate each other; The material properties of the elastic clip and the flat washer adopt a bilinear hardening elastoplastic model; The boundary conditions are set as full constraints on the bottom surfaces of the insulating gauge block and the gauge retaining plate, the longitudinal and transverse displacements of the inner ring surface are constrained when the flat washer is pressed down, and the vertical displacement of the flat washer is constrained after installation; The standard installation state of the elastic clip is to apply a pre-tightening force downward through the bolt so that the front end of the middle limb of the fastener elastic clip just contacts the insulating gauge block. The expression of the relationship between the bolt pre-tightening force and the tightening torque is: ， In the formula, T is the tightening torque, K is the tightening torque coefficient, F is the bolt preload, d is the nominal diameter of the bolt.

3. An efficient prediction method for the fatigue life of the elastic clip of high-speed railway fasteners according to claim 2, characterized in that, For the finite element model of the elastic clip beam element under the standard installation state, longitudinal, transverse and vertical linear springs are set as constraint conditions at the actual contact positions of the elastic clip and the rail or the track slab to simulate the contact behavior between the elastic clip and adjacent components, and a downward displacement constraint is applied to the actual contact position of the middle limb of the elastic clip and the flat washer to simulate the prestressed installation state of the elastic clip; 4. An efficient prediction method for the fatigue life of the elastic clip of high-speed railway fasteners according to claim 1, characterized in that Before constructing the fitness function describing the frequency difference between the finite element model of the elastic clip solid element and the finite element model of the elastic clip beam element, it also includes: taking the natural frequency calculated by the common finite element model of the elastic clip solid element as the benchmark.

5. The high-efficiency prediction method for the fatigue life of the elastic clip of a high-speed railway fastener according to claim 1, characterized in that Taking the linear spring constraint stiffness of the elastic strip beam element finite element model as the design optimization object and minimizing the fitness function as the goal, the elastic strip beam element finite element model is optimized based on the particle swarm optimization algorithm, including the following steps: Write a particle swarm optimization algorithm program using MATLAB software; Based on the co-simulation of MATLAB and ANSYS software, initialize the constraint stiffness in MATLAB and start ANSYS APDL; ANSYS reads the constraint stiffness and calculates the modal frequency; MATLAB extracts the first N m order modal frequency obtained from ANSYS calculation, calculates the fitness value function value, and the calculation formula of the fitness value function is: ， In the formula, represents the infinity norm, is the first-order modal frequency calculated from the finite element model of the clip beam element, is the second-order modal frequency calculated from the finite element model of the clip beam element, is the nth-order modal frequency calculated from the finite element model of the clip beam element, is the first-order modal frequency calculated from the finite element model of the clip solid element, is the second-order modal frequency calculated from the finite element model of the clip solid element, is the nth-order modal frequency calculated from the finite element model of the clip solid element, N m is the clip modal truncation number, λ and represent the frequency difference weighting coefficients; When the iteration times of the particle swarm reach the preset maximum iteration times, the calculation is stopped.

6. An efficient prediction method for the fatigue life of the elastic clip of a high-speed railway fastener according to claim 1, characterized in that, The dynamic model of the elastic clip is established based on the modal superposition method. Among them, the expression of the vibration equation of the n -th order of the elastic clip in the modal coordinate system is as follows: ， In the formula, are the displacement, velocity, and acceleration responses of the clip in the modal coordinates, is the damping ratio, is the n th natural frequency, n 0 is the number of force-bearing nodes of the clip, are the modal displacements of the n th vibration mode of the clip in the longitudinal, transverse, and vertical directions, is the position coordinate of the i th force-bearing point of the clip, are the longitudinal, transverse, and vertical loads of the i th force-bearing point of the clip.

7. An efficient prediction method for the fatigue life of the elastic rail clip of high-speed railway fasteners according to claim 6, characterized in that At the contact position between the elastic clip and the rail, the calculation formulas for the longitudinal, transverse, and vertical loads at the i th force application point are as follows: ， In the formula, are the longitudinal, transverse and vertical displacements of the rail respectively, are the angular displacement about the z axis, y axis, x axis of the rail centroid respectively, are the longitudinal, transverse and vertical contact stiffnesses at the contact position between the elastic clip and the rail respectively, are the abscissa and ordinate of the contact point between the elastic clip and the rail in the rail coordinate system respectively; At the contact position between the elastic clip and the track slab, the calculation formulas for the longitudinal, transverse, and vertical loads of the i th stress point are as follows: ， Wherein, are respectively the longitudinal, transverse, and vertical displacements of the track slab, are respectively the longitudinal, transverse, and vertical contact stiffnesses at the contact position between the elastic clip and the track slab, is the thickness of the track slab.

8. An efficient prediction method for the fatigue life of the elastic clip of high-speed railway fasteners according to claim 1, characterized in that The dynamic responses of the elastic strip include vibration displacement, velocity and acceleration, and their calculation formulas are: ， In the formula, is the longitudinal, transverse and vertical modal displacements at the n -th node of the j -th order vibration mode of the elastic strip, are the longitudinal, transverse and vertical vibration displacements at the j -th node of the elastic strip in the Cartesian coordinate system, are the longitudinal, transverse and vertical vibration velocities at the j -th node of the elastic strip in the Cartesian coordinate system, are the longitudinal, transverse and vertical vibration accelerations at the j -th node of the elastic strip in the Cartesian coordinate system.

9. An efficient prediction method for the fatigue life of the elastic clip of high-speed railway fasteners according to claim 8, characterized in that, The dynamic response of the elastic strip also includes the equivalent dynamic stress time history curve, and its calculation formula is: ， In the formula, is the static equivalent stress of the elastic strip in the installed state, is the modal equivalent stress of the n th order mode of the elastic strip obtained by prestressed modal analysis.

10. An efficient prediction method for the fatigue life of the elastic clip of high-speed railway fasteners according to claim 1, characterized in that, Calculating the fatigue life at different positions of the elastic strip includes the following steps: According to the stress time history curve obtained by calculating the dynamic response of the elastic strip when a bogie passes through, use the rain flow counting method to find out the fatigue stress cycle amplitude, stress cycle mean value and stress cycle times of the elastic strip; The influence of the mean stress is corrected using the Goodman method, and the stress amplitude calculation formula for the k th stress cycle after correction is as follows: ， Wherein, is the stress amplitude before correction, is the stress mean value, is the tensile strength of the elastic strip material; Use the Palmgren-Miner linear cumulative damage criterion to linearly superimpose the cumulative damage of each symmetric cyclic load to obtain the cumulative damage value, and take its reciprocal to finally obtain the fatigue life. The calculation formula of the elastic strip fatigue life is: ， In the formula, n is the number of stress cycles, L is the fatigue life of the elastic strip.

Images