Method for efficiently predicting fatigue life of high-speed railway fastener elastic strip

Abstract

The invention belongs to the technical field of railway engineering, and provides a high-speed railway fastener elastic strip fatigue life efficient prediction method, which comprises the following steps of: optimizing linear constraint stiffness of an elastic strip beam unit model by adopting a particle swarm optimization algorithm on the basis of inherent frequency obtained by pre-stress modal analysis of an entity unit finite element model; exporting static equivalent stress of the elastic strip beam unit model and inherent frequency, vibration mode and modal equivalent stress of different frequency orders in prestress modal analysis, and establishing an elastic strip kinetic equation in a mounting state based on a modal superposition method; applying the vehicle-track space coupling dynamic model to generate a steel rail and track plate three-dimensional dynamic response corresponding to the contact position of the elastic strip, inputting the three-dimensional dynamic response as excitation into the elastic strip dynamic model, and calculating to obtain dynamic responses such as vibration acceleration and equivalent dynamic stress of the elastic strip; and calculating the fatigue life of the elastic strip at different positions based on a fatigue cumulative damage theory, and judging the dangerous area and the most dangerous point where the elastic strip is easy to generate high-frequency fatigue fracture.

Description

Technical Field

[0001] The invention relates to the technical field of railway engineering, and in particular to a method for efficiently predicting fatigue life of spring bars of high-speed railway fasteners. Background Art

[0002] The operating environment and line conditions of China's high-speed railway network are complex and changeable, and a series of damage and degradation problems have occurred in the track structure components during long-term operation. Among them, rail fasteners are essential key components of the track structure, which play a role in fixing the rails, providing elastic support, and maintaining the stability and smoothness of the track. Under the high-frequency excitation of rail corrugation and wheel polygons, high-frequency fatigue fracture of high-speed rail fastener spring bars frequently occurs. The fracture of spring bars will weaken the three-way constraint of the fastener system on the rails, thereby causing a series of adverse consequences such as rail creep, rubber pads under the rails, and track geometry degradation, aggravating the dynamic interaction between wheels and rails, reducing ride comfort, and even threatening driving safety. In particular, with the active exploration and practice of high-speed railways for higher operating speeds in recent years, the high-frequency excitation frequency band has been continuously broadened, making the fastener spring bars that were 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 sophisticated three-dimensional solid finite element model of the fastener system, and uses transient dynamics analysis methods to study the dynamic response of the spring clip under wheel-rail excitation and its fatigue life. The modeling process is cumbersome, the model has a large degree of freedom, and the solution efficiency is very low. In addition, the traditional vehicle-track spatial coupling dynamics model does not consider the parametric vibration of the spring clip. Summary of the invention

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

[0005] The present invention solves the technical problem and adopts the following technical solution: An efficient prediction method for fatigue life of high-speed railway fastener spring clips comprises the following steps: According to the basic parameters of the center axis of the spring clip and the parametric equations of each center axis segment, the parametric mathematical equation of the spring clip is established; According to the parametric mathematical equation of the spring clip and the preload of the fastener bolt, the spring clip solid unit finite element model and the spring clip beam unit finite element model under the standard installation state are established, and the prestressed modal analysis is carried out; The fitness function describing the frequency difference between the finite element model of the spring bar solid unit and the finite element model of the spring bar beam unit is constructed, and the linear spring constraint stiffness of the finite element model of the spring bar beam unit is taken as the design optimization object. With the minimization of the fitness function as the goal, the finite element model of the spring bar beam unit is optimized based on the particle swarm optimization algorithm, and the optimal value of the constraint stiffness of the finite element model of the spring bar beam unit is obtained. According to the optimized finite element model of the spring bar beam unit, the static equivalent stress of the spring bar under the standard installation state, as well as the natural frequency, vibration mode and modal equivalent stress of different frequency orders in the prestressed modal analysis are derived, and the dynamic model of the spring bar is established based on the modal superposition method; The vehicle-track spatial coupling dynamics model is used to generate the three-dimensional dynamic response of the rail and track plate corresponding to the contact position of the spring clip under the action of short-wave irregularities, and this is used as the excitation input into the dynamic model of the spring clip to calculate the dynamic response of the spring clip. Based on the fatigue cumulative damage theory, the fatigue life of the spring clip at different positions is calculated according to the equivalent dynamic stress time history curve of the spring clip node obtained from the dynamic response of the spring clip. The fatigue life distribution of different nodes of the spring clip is calculated, and the dangerous area and the most dangerous point where the spring clip is prone to high-frequency fatigue fracture are determined.

[0006] As a further optimization, the components of the spring bar entity unit finite element model in the standard installation state include spring bars, flat washers, insulating gauge blocks and gauge baffles, and a surface-to-surface contact relationship is established between adjacent components. The tangent algorithm of the contact surface is set as a penalty function, and the normal is set to "hard contact", that is, the components do not penetrate each other; The material properties of the spring bar and flat washer adopt the bilinear enhanced elastic-plastic model; The boundary conditions are set as follows: the bottom surface of the insulating gauge block and the gauge baffle is fully constrained, the inner ring surface constrains the longitudinal and lateral displacement 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 spring clip is to apply a preload downward through the bolts so that the front end of the middle limb of the spring clip of the fastener is in contact with the insulating gauge block. The relationship between the bolt preload and the tightening torque is expressed as: , 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.

[0007] As a further optimization, the finite element model of the spring bar beam unit in the standard installation state sets longitudinal, transverse and vertical linear springs as constraints at the actual contact position between the spring bar and the rail or track plate to simulate the contact behavior between the spring bar and adjacent components, and imposes a downward displacement constraint on the actual contact position between the middle limb of the spring bar and the flat washer to simulate the prestressed installation state of the spring bar.

[0008] As a further optimization, before constructing the fitness function describing the frequency difference between the spring bar entity unit finite element model and the spring bar beam unit finite element model, it also includes: taking the natural frequency calculated by the commonly used spring bar entity unit finite element model as a reference.

[0009] As a further optimization, the linear spring constraint stiffness of the finite element model of the spring bar beam unit is taken as the design optimization object, and the finite element model of the spring bar beam unit is optimized based on the particle swarm optimization algorithm with the minimization of the fitness function as the goal, including the following steps: Use MATLAB software to write particle swarm optimization algorithm program; Based on the joint simulation of MATLAB and ANSYS software, MATLAB initializes the constraint stiffness and starts ANSYS APDL; ANSYS reads the constraint stiffness and calculates the modal frequency; MATLAB extracts the front N m The fitness value function value is calculated based on the modal frequency. The fitness value function calculation formula is: , In the formula, represents the infinite norm, is the first-order modal frequency calculated by the finite element model of the spring bar beam unit, is the second-order modal frequency calculated by the finite element model of the spring bar beam unit, is the nth modal frequency calculated by the finite element model of the spring bar beam unit, is the first-order modal frequency calculated by the finite element model of the spring bar entity unit, is the second-order modal frequency calculated by the finite element model of the spring bar entity unit, is the nth modal frequency calculated by the finite element model of the spring bar entity unit, N m is the modal cutoff number of the spring bar, λ and represents the frequency difference weighting coefficient; When the number of particle swarm iterations reaches the preset maximum number of iterations, the calculation stops.

[0010] As a further optimization, the dynamic model of the spring bar is established based on the modal superposition method, wherein the spring bar in the modal coordinate system n The expression of the first-order vibration equation is: , In the formula, are the displacement, velocity and acceleration responses of the spring bar in modal coordinates, is the damping ratio, For the n The natural frequency, n 0 is the number of nodes of the elastic bar, They are respectively n The modal displacement of the order vibration mode in the longitudinal, transverse and vertical directions, For the spring i The position coordinates of the force points, They are respectively i Longitudinal, transverse and vertical loads at each load point.

[0011] As a further optimization, at the contact point between the spring bar and the rail, i The calculation formula for the longitudinal, transverse and vertical loads of each force point is: , In the formula, are the longitudinal, transverse and vertical displacements of the rail respectively, The centroid of the rail z axis, y axis, x Angular displacement of the shaft, are the longitudinal, transverse and vertical contact stiffness at the contact position between the spring bar and the rail, are the horizontal and vertical coordinates of the contact point between the spring bar and the rail in the rail coordinate system respectively; At the contact point between the spring bar and the track plate, i The calculation formula for the longitudinal, transverse and vertical loads of each force point is: , In the formula, are the longitudinal, transverse and vertical displacements of the track slab, are the longitudinal, transverse and vertical contact stiffness at the contact position between the spring bar and the track plate, is the thickness of the track slab.

[0012] As a further optimization, the dynamic response of the spring bar includes vibration displacement, velocity and acceleration, and the calculation formula is: , In the formula, For the spring n The first order vibrationj The modal displacements in the longitudinal, transverse and vertical directions at each node are: They are respectively the first j The vibration displacement in the longitudinal, transverse and vertical directions at each node, They are respectively the first j The vibration speed in the longitudinal, transverse and vertical directions at each node, They are respectively the first j The vibration acceleration in the longitudinal, lateral and vertical directions at each node.

[0013] As a further optimization, the dynamic response of the elastic bar also includes an equivalent dynamic stress time history curve, and its calculation formula is: , In the formula, is the static equivalent stress of the spring bar in the installed state, The spring bars obtained by prestressed modal analysis n Modal equivalent stress of the order mode.

[0014] As a further optimization, the calculation of fatigue life of the spring clip at different positions includes the following steps: According to the stress time history curve of a bogie passing through the spring clip calculated from the dynamic response of the spring clip, the fatigue stress cycle amplitude, stress cycle mean and stress cycle number of the spring clip are calculated using the rain flow counting method; The Goodman method is used to correct the influence of the mean stress and obtain the corrected k The calculation formula for the stress amplitude of a stress cycle is: , In the formula, is the stress amplitude before correction, is the mean stress value, is the tensile strength of the spring bar material; The Palmgren-Miner linear cumulative damage criterion is used to linearly superimpose the cumulative damage of each symmetrical cyclic load to obtain the cumulative damage value, and the reciprocal is taken to finally obtain the fatigue life. The calculation formula for the fatigue life of the spring clip is: , In the formula, n is the number of stress cycles, L is the fatigue life of the spring bar.

[0015] The beneficial effects of the present invention are as follows: through the above-mentioned method for efficiently predicting the fatigue life of a high-speed railway fastener spring clip, the present invention establishes a beam unit spring clip dynamics model based on a particle swarm algorithm and modal superposition theory, applies a vehicle-track space coupling dynamics model to generate a three-dimensional dynamic response of the rail and the track plate at the contact position between the spring clip and the track, and uses this as the input excitation of the spring clip dynamics model, and finally realizes efficient prediction of the fatigue life of the spring clip based on the fatigue cumulative damage theory. At the same time, since the spring clip beam unit dynamics model established in the present invention uses a linear spring to replace the nonlinear contact relationship of each component of the solid model, and the degree of freedom is greatly reduced, it is possible to efficiently predict the fatigue life of the spring clip, obtain the spring clip dynamics response under different driving conditions and the dangerous area prone to high-frequency fatigue fracture, provide a scientific reference for damage detection, operation maintenance and optimization design of the fastener spring clip, and is of great significance to ensuring the long-term safe and stable operation of the railway. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a flow chart of a method for efficiently predicting fatigue life of spring bars of high-speed railway fasteners in an embodiment of the present invention; Figure 2 Schematic diagram of a finite element model of a fastener spring bar entity unit in an embodiment of the present invention; Figure 3 It is a schematic diagram of a finite element model of a spring bar beam unit in an embodiment of the present invention; Figure 4 It is a flow chart of the particle swarm optimization algorithm in an embodiment of the present invention; Figure 5 It is a convergence curve diagram of the fitness function value in the particle swarm optimization algorithm in an embodiment of the present invention; Figure 6 Schematic diagram of convergence analysis of spring bar dynamic response in an embodiment of the present invention; Figure 7 It is a schematic diagram of vertical acceleration time history response of the highest point of the spring clip side limb in an embodiment of the present invention; Figure 8 It is a schematic diagram of the equivalent stress time history curve of the dangerous point of the spring clip in the embodiment of the present invention; Fig. 9 A histogram of spring bar stress rain flow counts in an embodiment of the present invention; Fig.10 A schematic diagram of the position distribution of the nodes selected by the spring bar in an embodiment of the present invention; Fig.11 Schematic diagram of fatigue life at different nodes of the spring bar in an embodiment of the present invention. DETAILED DESCRIPTION

[0017] In order to make the purpose, 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 in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations. Example

[0018] This embodiment provides an efficient prediction method for fatigue life of high-speed railway fastener spring bars, and its flow chart is shown in Figure 1 , wherein the method comprises the following steps: S1. According to the basic parameters of the center axis of the spring bar and the parametric equations of each center axis segment, a parametric mathematical equation of the spring bar is established.

[0019] Among them, the W1 type fastener spring clip commonly used in high-speed railways is taken as the research object, and the parametric mathematical equation of the central axis of the spring clip is constructed based on the structural parameters of the two-dimensional plane unfolding diagram and the front view of its central axis.

[0020] S2. According to the parametric mathematical equation of the spring clip and the preload force of the fastener bolt, the spring clip solid unit finite element model and the spring clip beam unit finite element model under the standard installation state are established respectively, and the prestressed modal analysis is carried out.

[0021] Among them, the finite element model of the fastener spring bar entity unit is as follows Figure 2 As shown in the figure, the number of units and nodes are 21528 and 97262 respectively. The whole model includes spring bars, flat washers, insulating gauge blocks and gauge baffles. Surface-to-surface contact relationships are established between adjacent components. The tangent algorithm of the contact surface is set as a penalty function, and the normal is set as "hard contact", that is, the components do not penetrate each other. The material properties of the spring bar material 60Si2MnA and the flat washer material Q235-A are both based on the bilinear enhanced elastic-plastic model. The boundary conditions are set to fully constrain the bottom surface of the insulating gauge block and the gauge baffle. When the flat washer is pressed down, the inner ring surface constrains the longitudinal and lateral displacements, and the vertical displacement of the flat washer is constrained after installation. The standard installation state of the spring bar is to apply a preload downward through the bolt so that the front end of the middle limb of the fastener spring bar is in contact with the insulating gauge block. The expression of the relationship between the bolt preload and the tightening torque is: , In the formula, T The theoretical tightening torque of the W1 spring clip is about 140-180 N·m. K is the tightening torque coefficient, which is taken as 0.2 under the condition of surface oxidation and lubrication; F is the bolt preload; d is the nominal diameter of the bolt, take 25mm; The calculated value range of the bolt preload is 28 to 36 kN. A reasonable bolt preload is selected and applied to the flat washer to make the front end of the middle limb of the spring clip just contact with the insulating gauge block.

[0022] The finite element model of the spring beam unit is as follows Figure 3 As shown in the figure, the number of units and nodes are 296 and 593 respectively. Longitudinal, transverse and vertical linear springs are set as constraints at the actual contact positions between the spring clip and the rail and track plate to simulate the contact behavior between the spring clip and adjacent components. A downward displacement constraint is imposed on the actual contact position between the middle limb of the spring clip and the flat washer to simulate the installation state of the spring clip.

[0023] S3. Based on the natural frequency calculated by the commonly used elastic bar entity unit finite element model, a fitness function describing the frequency difference between the elastic bar entity unit finite element model and the elastic bar beam unit finite element model is constructed. The linear spring constraint stiffness of the elastic bar beam unit finite element model is taken as the design optimization object. With the minimization of the fitness function as the goal, the elastic bar beam unit finite element model is optimized based on the particle swarm optimization algorithm to obtain the optimal value of the constraint stiffness of the elastic bar beam unit finite element model.

[0024] The method of optimizing the finite element model of the spring bar beam unit based on the particle swarm optimization algorithm with the linear spring constraint stiffness of the spring bar beam unit finite element model as the design optimization object and minimizing the fitness function as the goal includes the following steps: Use MATLAB software to write particle swarm optimization algorithm program; Based on the joint simulation of MATLAB and ANSYS software, MATLAB initializes the constraint stiffness and starts ANSYS APDL; ANSYS reads the constraint stiffness and calculates the modal frequency; MATLAB extracts the front N m The fitness value function value is calculated based on the modal frequency. The fitness value function calculation formula is: , In the formula, represents the infinite norm, is the first-order modal frequency calculated by the finite element model of the spring bar beam unit, is the second-order modal frequency calculated by the finite element model of the spring bar beam unit, is the nth modal frequency calculated by the finite element model of the spring bar beam unit, is the first-order modal frequency calculated by the finite element model of the spring bar entity unit, is the second-order modal frequency calculated by the finite element model of the spring bar entity unit, is the nth modal frequency calculated by the finite element model of the spring bar entity unit, N m is the modal cutoff number of the spring bar, λ and represents the frequency difference weighting coefficient; When the number of particle swarm iterations reaches the preset maximum number of iterations, the calculation stops.

[0025] Figure 4 This is the flow chart of particle swarm optimization algorithm. The particles in the figure represent the constraint stiffness of the finite element model of the spring bar beam unit. Figure 5 This 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; Table 1 shows the first five frequency results after the constraint stiffness of the spring bar beam unit model is optimized. It can be seen that after iterations of the particle swarm optimization algorithm, the frequency errors of the first five modal frequencies of the spring bar beam unit model and the calculated frequency of the solid model are less than 5%, and the degree 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 spring bar beam unit model through the particle swarm optimization algorithm, the calculation efficiency can be greatly improved while ensuring the accuracy.

[0026] Table 1. Modal frequency optimization results of constraint stiffness of elastic beam element model , S4. Based on the optimized finite element model of the spring bar beam unit, the static equivalent stress of the spring bar under the standard installation state, as well as the natural frequency, vibration mode and modal equivalent stress of different frequency orders in the prestressed modal analysis are derived, and the dynamic model of the spring bar is established based on the modal superposition method.

[0027] The dynamic model of the spring bar is established based on the modal superposition method, wherein the spring bar in the modal coordinate system n The expression of the first-order vibration equation is: , In the formula, are the displacement, velocity and acceleration responses of the spring bar in modal coordinates, is the damping ratio, For the n The natural frequency, n 0 is the number of nodes of the elastic bar, They are respectively n The modal displacement of the order vibration mode in the longitudinal, transverse and vertical directions, For the spring i The position coordinates of the force points, They are respectively iLongitudinal, transverse and vertical loads at each load point.

[0028] At the contact point between the spring bar and the rail, i The calculation formula for the longitudinal, transverse and vertical loads of each force point is: , In the formula, are the longitudinal, transverse and vertical displacements of the rail respectively, The centroid of the rail z axis, y axis, x Angular displacement of the shaft, are the longitudinal, transverse and vertical contact stiffness at the contact position between the spring bar and the rail, are the horizontal and vertical coordinates of the contact point between the spring bar and the rail in the rail coordinate system respectively; At the contact point between the spring bar and the track plate, i The calculation formula for the longitudinal, transverse and vertical loads of each force point is: , In the formula, are the longitudinal, transverse and vertical displacements of the track slab, are the longitudinal, transverse and vertical contact stiffness at the contact position between the spring bar and the track plate, is the thickness of the track slab.

[0029] S5. Apply the vehicle-track spatial coupling dynamics model to generate the three-dimensional dynamic response of the rail and track plate corresponding to the contact position of the spring clip under the action of short-wave irregularities, and use this as the excitation input to the dynamic model of the spring clip to calculate the dynamic response of the spring clip.

[0030] The dynamic response of the spring bar includes vibration displacement, velocity and acceleration, and the calculation formula is: , In the formula, For the spring n The first order vibration j The modal displacements in the longitudinal, transverse and vertical directions at each node are: They are respectively the first j The vibration displacement in the longitudinal, transverse and vertical directions at each node, They are respectively the first j The vibration speed in the longitudinal, transverse and vertical directions at each node, They are respectively the first j The vibration acceleration in the longitudinal, lateral and vertical directions at each node.

[0031] The dynamic response of the elastic bar also includes an equivalent dynamic stress time history curve, and its calculation formula is: , In the formula, is the static equivalent stress of the spring bar in the installed state, The spring bars obtained by prestressed modal analysis n Modal equivalent stress of the order mode.

[0032] Figure 6 The schematic diagram of the convergence analysis of the dynamic response of the spring bar is shown in Figure 1. The calculation condition is the peak value of the vertical acceleration of the spring bar and the mean stress corresponding to the maximum stress amplitude when a high-speed vehicle passes at 300 km / h under the measured wheel polygon excitation condition. It can be seen from the figure that when the modal order of the spring bar is N m When the order exceeds 2, the response tends to be stable, which proves that the modal superposition using the constrained mode under the spring clip installation state has good convergence.

[0033] Figure 7 It is a schematic diagram of the vertical acceleration time-history response of the highest point of the spring bar side limb. It can be seen from the figure that under the wheel polygon excitation, the spring bar vibrates violently and the vertical acceleration peak reaches 320g.

[0034] Figure 8 The figure is a schematic diagram of the stress-time curve of the dangerous point of the spring clip. The dangerous point on the inner side of the spring clip heel end observed on site is selected, and its stress-time curve is calculated. The figure compares the calculation results of the spring clip using solid elements and beam elements. The two curves are almost identical, proving that the beam element can improve the calculation efficiency while ensuring the calculation accuracy.

[0035] S6. Based on the fatigue cumulative damage theory, the fatigue life of the spring clip at different positions is calculated according to the equivalent dynamic stress time history curve of the spring clip node obtained from the dynamic response of the spring clip.

[0036] The method of calculating the fatigue life of the spring clip at different positions comprises the following steps: According to the spring clip stress time history curve when a bogie passes calculated in step S5, the fatigue stress cycle amplitude, stress cycle mean and stress cycle number of the spring clip are calculated using the rain flow counting method; Fig. 9 It is the histogram of rain flow counting of elastic bar stress. It can be seen from the figure that by counting the rain flow of the stress time history curve, a series of stress amplitudes and stress means with known number of cycles can be obtained; The Goodman method is used to correct the influence of the mean stress and obtain the corrected k The calculation formula for the stress amplitude of a stress cycle is: , In the formula, is the stress amplitude before correction, is the mean stress value, is the tensile strength of the spring bar material; The Palmgren-Miner linear cumulative damage criterion is used to linearly superimpose the cumulative damage of each symmetrical cyclic load to obtain the cumulative damage value, and the reciprocal is taken to finally obtain the fatigue life. The calculation formula for the fatigue life of the spring clip is: , In the formula, n is the number of stress cycles, L is the fatigue life of the spring bar.

[0037] According to the stress-time curve of the spring clip danger point, the fatigue life of the spring clip danger point is calculated. Table 2 shows the fatigue life of the spring clip danger point. It can be seen that under the wheel polygon excitation, the fatigue life of the spring clip danger point is lower than the design requirement of 5 million times.

[0038] S7. Calculate the fatigue life distribution of different nodes of the spring clip, and determine the dangerous area and the most dangerous point where the spring clip is prone to high-frequency fatigue fracture, providing guidance for the maintenance of high-speed rail fastener spring clips.

[0039] in, Fig.10 The schematic diagram of the position distribution of the nodes selected for the spring clip. According to the structural symmetry, a total of 20 nodes of half of the spring clip structure were selected to calculate the fatigue life; Fig.11 The figure is a schematic diagram of the fatigue life distribution at different nodes of the spring clip. It can be seen from the figure that the dangerous area of ​​the spring 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. This shows that under the polygonal excitation of the wheel, fatigue fracture is prone to occur here, which is basically consistent with the spring clip fracture area observed on site.

[0040] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. An efficient prediction method for fatigue life of high-speed railway fastener spring bars, characterized in that: The steps include: According to the basic parameters of the center axis of the spring clip and the parametric equations of each center axis segment, the parametric mathematical equation of the spring clip is established; According to the parametric mathematical equation of the spring clip and the preload of the fastener bolt, the spring clip solid unit finite element model and the spring clip beam unit finite element model under the standard installation state are established, and the prestressed modal analysis is carried out; The fitness function describing the frequency difference between the finite element model of the spring bar solid unit and the finite element model of the spring bar beam unit is constructed, and the linear spring constraint stiffness of the finite element model of the spring bar beam unit is taken as the design optimization object. With the minimization of the fitness function as the goal, the finite element model of the spring bar beam unit is optimized based on the particle swarm optimization algorithm, and the optimal value of the constraint stiffness of the finite element model of the spring bar beam unit is obtained. According to the optimized finite element model of the spring bar beam unit, the static equivalent stress of the spring bar under the standard installation state, as well as the natural frequency, vibration mode and modal equivalent stress of different frequency orders in the prestressed modal analysis are derived, and the dynamic model of the spring bar is established based on the modal superposition method; The vehicle-track spatial coupling dynamics model is used to generate the three-dimensional dynamic response of the rail and track plate corresponding to the contact position of the spring clip under the action of short-wave irregularities, and this is used as the excitation input into the dynamic model of the spring clip to calculate the dynamic response of the spring clip. Based on the fatigue cumulative damage theory, the fatigue life of the spring clip at different positions is calculated according to the equivalent dynamic stress time history curve of the spring clip node obtained from the dynamic response of the spring clip. The fatigue life distribution of different nodes of the spring clip is calculated, and the dangerous area and the most dangerous point where the spring clip is prone to high-frequency fatigue fracture are determined.

2. The method for efficiently predicting fatigue life of spring bars of high-speed railway fasteners according to claim 1 is characterized in that: The components of the spring clip entity unit finite element model in the standard installation state include spring clips, flat washers, insulating gauge blocks and gauge baffles. A surface-to-surface contact relationship is established between adjacent components, the tangent algorithm of the contact surface is set as a penalty function, and the normal is set to "hard contact", that is, the components do not penetrate each other; The material properties of the spring bar and flat washer adopt the bilinear enhanced elastic-plastic model; The boundary conditions are set as follows: the bottom surface of the insulating gauge block and the gauge baffle is fully constrained, the inner ring surface constrains the longitudinal and lateral displacement 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 spring clip is to apply a preload downward through the bolts so that the front end of the middle limb of the spring clip of the fastener is in contact with the insulating gauge block. The relationship between the bolt preload and the tightening torque is expressed as: ， 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. The method for efficiently predicting fatigue life of spring bars of high-speed railway fasteners according to claim 2 is characterized in that: The finite element model of the spring bar beam unit in the standard installation state sets longitudinal, transverse and vertical linear springs as constraint conditions at the actual contact position between the spring bar and the rail or track plate to simulate the contact behavior between the spring bar and adjacent components, and applies a downward displacement constraint to the actual contact position between the middle limb of the spring bar and the flat washer to simulate the prestressed installation state of the spring bar.

4. The method for efficiently predicting fatigue life of spring bars of high-speed railway fasteners according to claim 1 is characterized in that: Before constructing the fitness function describing the frequency difference between the spring bar entity unit finite element model and the spring bar beam unit finite element model, the method further includes: taking the natural frequency calculated by the commonly used spring bar entity unit finite element model as a reference.

5. The method for efficiently predicting fatigue life of spring bars of high-speed railway fasteners according to claim 1 is characterized in that: The method takes the linear spring constraint stiffness of the spring bar beam unit finite element model as the design optimization object, takes minimizing the fitness function as the goal, and optimizes the spring bar beam unit finite element model based on the particle swarm optimization algorithm, including the following steps: Use MATLAB software to write particle swarm optimization algorithm program; Based on the joint simulation of MATLAB and ANSYS software, MATLAB initializes the constraint stiffness and starts ANSYS APDL; ANSYS reads the constraint stiffness and calculates the modal frequency; MATLAB extracts the front N m The fitness value function value is calculated based on the modal frequency. The fitness value function calculation formula is: ， In the formula, represents the infinite norm, is the first-order modal frequency calculated by the finite element model of the spring bar beam unit, is the second-order modal frequency calculated by the finite element model of the spring bar beam unit, is the nth modal frequency calculated by the finite element model of the spring bar beam unit, is the first-order modal frequency calculated by the finite element model of the spring bar entity unit, is the second-order modal frequency calculated by the finite element model of the spring bar entity unit, is the nth modal frequency calculated by the finite element model of the spring bar entity unit, N m is the modal cutoff number of the spring bar, λ and represents the frequency difference weighting coefficient; When the number of particle swarm iterations reaches the preset maximum number of iterations, the calculation stops.

6. The method for efficiently predicting fatigue life of spring bars of high-speed railway fasteners according to claim 1 is characterized in that: The dynamic model of the spring bar is established based on the modal superposition method, wherein the spring bar in the modal coordinate system n The expression of the first-order vibration equation is: ， In the formula, are the displacement, velocity and acceleration responses of the spring bar in modal coordinates, is the damping ratio, For the n The natural frequency, n 0 is the number of nodes of the elastic bar, They are respectively n The modal displacement of the order vibration mode in the longitudinal, transverse and vertical directions, For the spring i The position coordinates of the force points, They are respectively i Longitudinal, transverse and vertical loads at each load point.

7. The method for efficiently predicting fatigue life of spring bars of high-speed railway fasteners according to claim 6 is characterized in that: At the contact point between the spring bar and the rail, i The calculation formula for the longitudinal, transverse and vertical loads of each force point is: ， In the formula, are the longitudinal, transverse and vertical displacements of the rail respectively, The centroid of the rail z axis, y axis, x Angular displacement of the shaft, are the longitudinal, transverse and vertical contact stiffness at the contact position between the spring bar and the rail, are the horizontal and vertical coordinates of the contact point between the spring bar and the rail in the rail coordinate system respectively; At the contact point between the spring bar and the track plate, i The calculation formula for the longitudinal, transverse and vertical loads of each force point is: ， In the formula, are the longitudinal, transverse and vertical displacements of the track slab, are the longitudinal, transverse and vertical contact stiffness at the contact position between the spring bar and the track plate, is the thickness of the track slab.

8. The method for efficiently predicting fatigue life of spring bars of high-speed railway fasteners according to claim 1 is characterized in that: The dynamic response of the spring bar includes vibration displacement, velocity and acceleration, and the calculation formula is: ， In the formula, For the spring n The first order vibration j The modal displacements in the longitudinal, transverse and vertical directions at each node are: They are respectively the first j The vibration displacement in the longitudinal, transverse and vertical directions at each node, They are respectively the first j The vibration speed in the longitudinal, transverse and vertical directions at each node, They are respectively the first j The vibration acceleration in the longitudinal, lateral and vertical directions at each node.

9. The method for efficiently predicting fatigue life of spring bars of high-speed railway fasteners according to claim 8 is characterized in that: The dynamic response of the elastic bar also includes an equivalent dynamic stress time history curve, and its calculation formula is: ， In the formula, is the static equivalent stress of the spring bar in the installed state, The spring bars obtained by prestressed modal analysis n Modal equivalent stress of the order mode.

10. The high-efficiency prediction method for fatigue life of high-speed railway fastener spring bars according to claim 1, characterized in that: The method of calculating the fatigue life of the spring clip at different positions comprises the following steps: According to the stress time history curve of a bogie passing through the spring clip calculated from the dynamic response of the spring clip, the fatigue stress cycle amplitude, stress cycle mean and stress cycle number of the spring clip are calculated using the rain flow counting method; The Goodman method is used to correct the influence of the mean stress and obtain the corrected k The calculation formula for the stress amplitude of a stress cycle is: ， In the formula, is the stress amplitude before correction, is the mean stress value, is the tensile strength of the spring bar material; The Palmgren-Miner linear cumulative damage criterion is used to linearly superimpose the cumulative damage of each symmetrical cyclic load to obtain the cumulative damage value, and the reciprocal is taken to finally obtain the fatigue life. The calculation formula for the fatigue life of the spring clip is: ， In the formula, n is the number of stress cycles, L is the fatigue life of the spring bar.

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