Design method of high-frequency vibration absorption fastener for inhibiting local bending mode vibration of steel rail

Abstract

The invention discloses a high-frequency vibration absorption fastener design method for restraining local bending mode vibration of a steel rail. The method comprises the following steps that a finite element analysis model of the steel rail is established according to the set length and steel rail parameters, a rail model under the harmonic excitation condition is established, and a relational expression met by the overall rigidity and damping of a double-layer fastener model is established; constructing a kinetic equation of vertical movement of the iron base plate; constructing a target optimization function for designing the track fastener system based on the error; and constructing a cost model of the fastener in the production process, optimizing cost control of fastener design, outputting the quality of the iron base plate, the rigidity of the upper layer structure and the rigidity of the lower layer structure under the optimal cost control, and designing the fastener system. According to the method, high-feasibility solutions are provided for relieving local bending modal vibration of the steel rail, high-order polygons of wheels and corrugation of the steel rail.

Description

Technical Field

[0001] The present invention relates to the field of rail fastener design, and in particular to a method for designing a high-frequency vibration-absorbing fastener for suppressing local bending modal vibration of a rail. Background Art

[0002] Since the idea that local third-order rail bending modes can cause high-order (primarily 18th-23rd-order) polygonization of high-speed train wheels was proposed in 2017, many researchers have attempted to establish a relationship between these local rail bending modes, wheel polygonization, and the polygonal wheel passing frequency. Because most reported studies fail to consider the multi-component assembly characteristics of the fastening system, the phenomenon of local rail bending modes cannot be accurately replicated through theoretical models, hindering the exploration of solutions to the wheel polygonization problem. Research has shown a near 1:1 mapping between the local rail bending mode frequencies and the polygonal wheel passing frequencies, indirectly demonstrating that local rail bending modes are one of the causes of wheel polygonization. The iron plate of the fastening system acts as a dynamic vibration absorber in the vehicle-track coupling system, and the matching relationship between the iron plate mass and the upper / lower plate stiffness significantly influences the local rail bending modes. Therefore, a high-frequency vibration-absorbing fastener design method to suppress the vibration of local rail bending modes is urgently needed. Summary of the Invention

[0003] In view of the above-mentioned deficiencies in the prior art, the present invention provides a design method for a high-frequency vibration-absorbing fastener for suppressing local bending modal vibration of rails. The design parameters of the rail fastener system are optimized based on a new vibration absorber principle.

[0004] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: A method for designing a high-frequency vibration-absorbing fastener for suppressing local bending modal vibration of a rail is provided, comprising the following steps: S1: Establish a finite element analysis model of the rail according to the set length and rail parameters, and construct the rail with an amplitude of F The track model under the condition of harmonic excitation is established, and based on the structural characteristics of the fastener system on the rail, the relationship between the overall stiffness and damping of the double-layer fastener model is established; S2: Based on the overall stiffness relationship of the double-layer fastener model, the natural vibration frequency of the iron plate on the fastener system is calculated, and the dynamic equation of the vertical motion of the iron plate is constructed; S3: Based on the designed local bending modal frequency of the rail, the allowable error between the designed local bending modal frequency and the natural vibration frequency of the iron plate is calculated. Based on the error, the target optimization function for designing the track fastener system is constructed, and the data sets of the iron plate mass, superstructure stiffness, and substructure stiffness that meet the constraints are output; S4: Construct a cost model for fasteners during production. Utilize the output data sets of the iron pad mass, superstructure stiffness, and substructure stiffness to optimize the cost control of the fastener design. Output the iron pad mass, superstructure stiffness, and substructure stiffness under optimal cost control to design the fastener system.

[0005] Furthermore, step S1 includes: S11: Establish a finite element analysis model of the rail based on the set length and rail parameters, and define the rail as a continuous Timoshenko beam model with full constraints at both ends. F Orbital model under harmonic excitation conditions; ; in, 、 For rails in position x Place, time t The vertical deformation displacement and vertical deflection of the section, A is the cross-sectional area of ​​the rail, is the rail material density, is the vertical shear coefficient, G is the shear modulus of the rail material, is the Dirac function, e is a natural constant, i is a unit imaginary number, is the angular velocity of the harmonic excitation, is the moment of inertia of the rail in the vertical direction, E is the elastic modulus of the rail material; S12: Based on the structural characteristics of the rail fastener system, the fastener system is simplified into a double-layer fastener model, and the relationship between the overall stiffness and damping of the double-layer fastener model is established; ; in, is the stiffness of the superstructure, is the overall stiffness, is the stiffness of the lower structure, is the resistance of the superstructure, is the overall damping, The damping of the lower structure.

[0006] Furthermore, the upper structure represents the upper rubber pad and elastic bar of the fastener on the rail, and the upper rubber pad and elastic bar provide stiffness and damping for the upper rubber plate. The lower structure represents the lower rubber pad, and the lower rubber pad provides stiffness and damping for the lower rubber plate. The pad between the upper rubber pad and the lower rubber pad serves as a vibration absorber.

[0007] Furthermore, step S2 includes: S21: Based on the overall stiffness relationship of the double-layer fastener model, the mass of the iron plate on the fastener system is calculated as m The natural vibration frequency ; ; S22: Track model and natural vibration frequency based on rails The dynamic equation of the vertical motion of the iron plate is constructed based on the relationship between the overall stiffness and damping of the double-layer fastener model; ; in, is the vertical deformation displacement of the fastener on the rail Vertical displacement under the conditions.

[0008] Furthermore, step S3 includes: S31: Local bending modal frequencies according to rail design , the local bending mode frequency and natural vibration frequency Mapping and calculation of local bending mode frequencies and natural vibration frequency The allowable error between ; S32: Error-based Quality of iron plates used to construct and design rail fastening systems m , superstructure stiffness , lower structure stiffness The objective optimization function ; ; Objective optimization function The constraints are: ; in, m 0 is the maximum mass of the iron plate based on cost control, is the design range of superstructure stiffness, is the lower structure stiffness Design scope; S33: Using the objective optimization function Output the mass of all iron plates that meet the constraints m , superstructure stiffness and substructure stiffness Dataset , dataset The quality of the iron plate m , superstructure stiffness and substructure stiffness Take a positive integer.

[0009] Furthermore, step S4 includes: S41: Construct a cost model for fasteners during production and construct a cost-controlled fastener design optimization objective function based on the cost model. ; ; in, is the cost function of the superstructure stiffness, is the cost function of the lower structure stiffness, i is the production process number of the superstructure, u is the production process number of the lower structure, For the upper structure i The cost of a production process, For the lower structure u The cost of a production process, I is the number of production processes for the superstructure, U is the number of production processes in the lower structure, a is the unit mass cost of the iron plate; S42: Using the optimization objective function Output iron plate quality under optimal cost control , superstructure stiffness and substructure stiffness , based on the quality of the iron plate , superstructure stiffness and substructure stiffness Design fastening systems.

[0010] The present invention utilizes a novel vibration absorber principle to optimize the fastener system's design parameters, including the iron backing plate mass, upper and lower rubber plate stiffness, to align the absorber frequency with the local bending mode frequency, thereby suppressing local bending mode vibration and wheel polygonization. This provides a highly feasible solution for alleviating rail local bending mode vibration, high-order wheel polygonization, and rail corrugation. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 Flowchart of the design method for high-frequency vibration-absorbing fasteners to suppress local bending modal vibrations of rails.

[0012] Figure 2 Simplified topology diagram of the fastener system of model W300-1.

[0013] Figure 3 Simplified topology diagram of the fastener system of the WJ-8 model.

[0014] Figure 4 Simplified topology diagram of the fastener system of the WJ-7 model.

[0015] Figure 5 The acceleration sweep diagram of the wheel / fastener under unilateral excitation conditions.

[0016] Figure 6 The acceleration sweep diagram of the wheel / fastener under double-sided excitation conditions. DETAILED DESCRIPTION

[0017] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0018] like Figure 1 As shown, a method for designing a high-frequency vibration-absorbing fastener for suppressing local bending modal vibration of a rail includes the following steps: S1: Establish a finite element analysis model of the rail according to the set length and rail parameters, and construct the rail with an amplitude of F The track model under the harmonic excitation condition is proposed, and based on the structural characteristics of the fastener system on the rail, the relationship between the overall stiffness and damping of the double-layer fastener model is established.

[0019] This example uses 60 kg / m rail parameters to establish a finite element analysis (FEM) model. The rail is considered a continuous Timoshenko beam with full constraints at both ends. The shear and rotational inertia effects of the beam cross-section are exploited to accurately analyze the rail's vertical bending and vibration behavior. To avoid the impact of excessively short rails on high-frequency wheel-rail vibration modes, the rail model is designed to be 80 sleeper spans long. The element type selected for the FEM model is B32, with a basic element length of 5 mm.

[0020] Step S1 specifically includes: S11: Establish a finite element analysis model of the rail based on the set length and rail parameters, and define the rail as a continuous Timoshenko beam model with full constraints at both ends. F Orbital model under harmonic excitation conditions; ; in, 、 For rails in position x Place, time t Vertical deformation displacement, vertical deflection of the section, A is the cross-sectional area of ​​the rail, is the rail material density, is the vertical shear coefficient, G is the shear modulus of the rail material, is the Dirac function, e is a natural constant, i is a unit imaginary number, is the angular velocity of the harmonic excitation, is the moment of inertia of the rail in the vertical direction, E is the elastic modulus of the rail material; When building traditional track models, the fastener system is simplified to a single-layer fastener model. This model has a simple structure, high computational efficiency, and can better simulate low-frequency wheel-rail response. However, real high-speed railway fasteners are generally a combination of "double-layer elastic pads + one layer of sandwich iron pads", such as Figure 2-Figure 4 In the W300-1, WJ-8 and WJ-7 fastener systems shown, the iron pad (and its associated vibrating parts) have a non-negligible mass, the upper rubber pad and elastic bars provide stiffness and damping to the upper rubber pad, and the lower rubber pad provides stiffness and damping to the lower rubber pad.

[0021] S12: Based on the structural characteristics of the rail fastener system, the fastener system is simplified into a double-layer fastener model, and the relationship between the overall stiffness and damping of the double-layer fastener model is established; ; in, is the stiffness of the superstructure, is the overall stiffness, is the stiffness of the lower structure, is the resistance of the superstructure, is the overall damping, The damping of the lower structure.

[0022] In this embodiment, the upper structure represents the upper rubber pad and spring bar of the rail fastener, which provide stiffness and damping for the upper rubber pad. The lower structure represents the lower rubber pad, which can provide stiffness and damping for the lower rubber pad. The real high-speed railway fastener is generally a combination structure of "double-layer elastic pad + one layer of sandwich iron pad", such as Figure 2 As shown in the figure, the iron plate (and its attached vibrating parts) have non-negligible mass, and the iron plate can be regarded as a vibration absorber.

[0023] S2: Based on the overall stiffness relationship of the double-layer fastener model, calculate the natural vibration frequency of the iron plate on the fastener system and construct the dynamic equation of the vertical motion of the iron plate. Step S2 specifically includes: S21: Based on the overall stiffness relationship of the double-layer fastener model, the mass of the iron plate on the fastener system is calculated as m The natural vibration frequency ; ; S22: Track model and natural vibration frequency based on rails The dynamic equation of the vertical motion of the iron plate is constructed based on the relationship between the overall stiffness and damping of the double-layer fastener model; ; in, is the vertical deformation displacement of the fastener on the rail Vertical displacement under the conditions.

[0024] S3: Based on the designed local bending modal frequency of the rail, the allowable error between the designed local bending modal frequency and the natural vibration frequency of the iron plate is calculated. Based on the error, the target optimization function for designing the track fastener system is constructed, and the data set of the iron plate mass, superstructure stiffness, and substructure stiffness that meet the constraints is output.

[0025] Based on the principle of high-frequency vibration-absorbing fasteners: optimize the design parameters of the fastener system, including the mass of the iron pad, the stiffness of the upper rubber plate, the stiffness of the lower rubber plate, etc., so that the vibration absorber frequency is close to the local bending mode frequency to suppress local bending mode vibration.

[0026] Step S3 specifically includes: S31: Local bending modal frequencies according to rail design , the local bending mode frequency and natural vibration frequency Mapping and calculation of local bending mode frequencies and natural vibration frequency The allowable error between ; S32: Error-based Quality of iron plates used to construct and design rail fastening systems m , superstructure stiffness , lower structure stiffness The objective optimization function ; ; Objective optimization function The constraints are: ; in, m 0 is the maximum mass of the iron plate based on cost control, is the design range of superstructure stiffness, is the lower structure stiffness Design scope; The setting standard of the total stiffness range of the fastener in this embodiment is: High-speed railways (stiffness range: 30-60 MN / m) require stability: High train speeds (≥250 km / h) require high stiffness to maintain track smoothness and reduce dynamic deformation. Low-frequency vibration suppression: High stiffness reduces the risk of track structure resonance and prevents fatigue failure of rails and fasteners due to high-frequency vibration. Gauge maintenance: Resisting the lateral forces of high-speed trains prevents track gauge widening.

[0027] Urban rail transit (stiffness range: 20-40 MN / m): Vibration and noise reduction: Low-stiffness fasteners (such as rubber pads) can absorb medium- and high-frequency vibrations, reducing noise pollution to surrounding buildings. Curved section adaptability: Small-radius curves require higher elasticity to compensate for lateral rail displacement. Lightweight design: Low train axle weights (typically ≤16 tons) eliminate the need for excessive vertical support.

[0028] In this embodiment, the total stiffness of the fastener is selected to be in the range of 20-60 MN / m based on comprehensive considerations.

[0029] The elastic backing material (rubber, polyurethane, EVA, etc.) directly affects stiffness. For example, rubber backings have a wide range of stiffness (20–80 kN / mm), while rigid nylon backings can reach over 100 kN / mm. The fastener structure (e.g., spring clips, e-type fasteners) influences the stiffness distribution: spring clips have low vertical stiffness but high lateral stiffness.

[0030] In this embodiment, the stiffness range of the upper and lower layers is considered to be 20-1000 MN / m.

[0031] S33: Using the objective optimization function Output the mass of all iron plates that meet the constraints m , superstructure stiffness and substructure stiffness Dataset , dataset The quality of the iron plate m , superstructure stiffness and substructure stiffness Take a positive integer.

[0032] S4: Construct a cost model for the fastener during production. Utilize the output data sets of the iron plate mass, upper structure stiffness, and lower structure stiffness to optimize the cost control of the fastener design. Output the iron plate mass, upper structure stiffness, and lower structure stiffness under optimal cost control to design the fastener system. Step S4 specifically includes: S41: Construct a cost model for fasteners during production and construct a cost-controlled fastener design optimization objective function based on the cost model. ; ; in, is the cost function of the superstructure stiffness, is the cost function of the lower structure stiffness, i is the production process number of the superstructure, u is the production process number of the lower structure, For the upper structure i The cost of a production process, For the lower structure u The cost of a production process, I is the number of production processes for the superstructure, U is the number of production processes in the lower structure, a is the unit mass cost of the iron plate; S42: Using the optimization objective function Output iron plate quality under optimal cost control , superstructure stiffness and substructure stiffness , based on the quality of the iron plate , superstructure stiffness and substructure stiffness Design fastening systems.

[0033] This embodiment maintains the overall stiffness of the WJ-8 model fastener system ( = 31.8 MN / m) remains unchanged, a set of optimization parameters ( m = 8 kg, = 63.6 MN / m, = 63.6 MN / m), design a natural vibration frequency Vibration-absorbing fastening system at approximately 627 Hz.

[0034] This embodiment selects three schemes, and compares the second and third schemes with the technical solution of the present invention. The purpose is to reduce the vibration peak near 600Hz. The specific schemes and simulation results are as follows: Solution 1, based on the principle of high-frequency vibration absorbing fasteners: optimize the design parameters of the fastener system, including the mass of the iron pad, the stiffness of the upper rubber plate, the stiffness of the lower rubber plate, etc., so that the vibration absorber frequency is close to the local bending mode frequency to suppress the local bending mode vibration. By comparing the original WJ-8 model fastener parameters ( m = 6.8 kg, = 350 MN / m, =35 MN / m) and the corresponding results are compared, such as Figure 5 and Figure 6As shown, the modal response is significantly suppressed. However, it should be noted that this approach may induce other high-frequency vibration issues, such as more intense vibrations above 800 Hz. To further address this issue, this paper proposes a differentiated fastener layout based on the uneven frequency distribution across the entire line. This involves installing different fasteners (with different matching parameters) in different sections of the line to disrupt the local bending modal frequencies of the entire line, thereby disrupting the development of the wheel polygon.

[0035] Solution 2: From the perspective of increasing the stiffness of the upper / lower rubber plate: Different fasteners have different parameter matching, and the specific stiffness that needs to be increased needs to be based on the actual situation. Taking the WJ-8 model fastener system as an example, the choice of increasing the stiffness of the lower rubber plate is (increased from 35 MN / m to 140 MN / m), the final result is as follows Figure 5 and Figure 6 It should be noted that increasing the stiffness of the lower rubber sheet can lead to an increase in the overall stiffness of the fastener, which may affect the fatigue strength of the fastener system and the load transfer relationship of the high-speed railway system.

[0036] Solution 3, from the perspective of fastener damping: increasing damping can alleviate local bending mode vibration. A set of damping parameters selected in this embodiment (from = 35 kN·s / m& =3.5 kN·s / m Increase to =140 kN·s / m& =14 kN·s / m), Figure 5 and Figure 6 As shown in Figure 2, it can be seen that the local bending modal response is significantly reduced. However, it should be noted that the true dynamic damping under high-frequency excitation is difficult to accurately control.

[0037] like Figure 6 As shown, for the three schemes implemented in this paper, increasing stiffness and increasing damping are common parameter adjustment schemes, which are used here to compare with Scheme 1. From the results, it can be seen that the high-frequency vibration absorbing fastener parameters we selected are better than the fastener parameter schemes of increasing stiffness four times and increasing damping four times. However, in actual application, the latter two schemes have their shortcomings or are difficult to implement, so the parameters of Scheme 1 are more recommended.

[0038] Based on a novel vibration absorber principle, this invention optimizes the design parameters of the fastener system, including the mass of the iron backing plate and the stiffness of the upper and lower rubber plates. This approach aligns the absorber frequency with the local bending mode frequency, thereby suppressing local bending mode vibration and wheel polygonization. This invention provides a highly feasible solution for alleviating local bending mode vibration, high-order wheel polygonization, and rail corrugation.

Claims

1. A method for designing a high-frequency vibration-absorbing fastener for suppressing local bending modal vibration of a rail, characterized in that: The following steps are involved: S1: Establish a finite element analysis model of the rail according to the set length and rail parameters, and construct the rail with an amplitude of F The track model under the condition of harmonic excitation is established, and based on the structural characteristics of the fastener system on the rail, the relationship between the overall stiffness and damping of the double-layer fastener model is established; S2: Based on the overall stiffness relationship of the double-layer fastener model, the natural vibration frequency of the iron plate on the fastener system is calculated, and the dynamic equation of the vertical motion of the iron plate is constructed; S3: Based on the designed local bending modal frequency of the rail, the allowable error between the designed local bending modal frequency and the natural vibration frequency of the iron plate is calculated. Based on the error, the target optimization function for designing the track fastener system is constructed, and the data sets of the iron plate mass, superstructure stiffness, and substructure stiffness that meet the constraints are output; S4: Construct a cost model for fasteners during production. Utilize the output data sets of the iron pad mass, superstructure stiffness, and substructure stiffness to optimize the cost control of the fastener design. Output the iron pad mass, superstructure stiffness, and substructure stiffness under optimal cost control to design the fastener system.

2. The method for designing a high-frequency vibration-absorbing fastener for suppressing local bending modal vibration of a rail according to claim 1, characterized in that: The step S1 comprises: S11: Establish a finite element analysis model of the rail based on the set length and rail parameters, and define the rail as a continuous Timoshenko beam model with full constraints at both ends. F Orbital model under harmonic excitation conditions; ； in, 、 For rails in position x Place, time t The vertical deformation displacement and vertical deflection of the section, A is the cross-sectional area of ​​the rail, is the rail material density, is the vertical shear coefficient, G is the shear modulus of the rail material, is the Dirac function, e is a natural constant, i is a unit imaginary number, is the angular velocity of the harmonic excitation, is the moment of inertia of the rail in the vertical direction, E is the elastic modulus of the rail material; S12: Based on the structural characteristics of the rail fastener system, the fastener system is simplified into a double-layer fastener model, and the relationship between the overall stiffness and damping of the double-layer fastener model is established; ； in, is the stiffness of the superstructure, is the overall stiffness, is the stiffness of the lower structure, is the resistance of the superstructure, is the overall damping, The damping of the lower structure.

3. The method for designing a high-frequency vibration-absorbing fastener for suppressing local bending modal vibration of a rail according to claim 2, characterized in that: The upper structure represents the upper rubber pad and elastic strip of the rail fastener, which provide stiffness and damping for the upper rubber pad. The lower structure represents the lower rubber pad, which provides stiffness and damping for the lower rubber pad. The pad between the upper and lower rubber pads serves as a vibration absorber.

4. The method for designing a high-frequency vibration-absorbing fastener for suppressing local bending modal vibration of a rail according to claim 2, characterized in that: The step S2 comprises: S21: Based on the overall stiffness relationship of the double-layer fastener model, the mass of the iron plate on the fastener system is calculated as m The natural vibration frequency ; ； S22: Track model and natural vibration frequency based on rails The dynamic equation of the vertical motion of the iron plate is constructed based on the relationship between the overall stiffness and damping of the double-layer fastener model; ； in, is the vertical deformation displacement of the fastener on the rail Vertical displacement under the conditions.

5. The method for designing a high-frequency vibration-absorbing fastener for suppressing local bending modal vibration of a rail according to claim 4, characterized in that: The step S3 comprises: S31: Local bending modal frequencies according to rail design , the local bending mode frequency and natural vibration frequency Mapping and calculation of local bending mode frequencies and natural vibration frequency The allowable error between ; S32: Error-based Quality of iron plates used to construct and design rail fastening systems m , superstructure stiffness , lower structure stiffness The objective optimization function ; ； Objective optimization function The constraints are: ； in, m 0 is the maximum mass of the iron plate based on cost control, is the design range of superstructure stiffness, is the lower structure stiffness Design scope; S33: Using the objective optimization function Output the mass of all iron plates that meet the constraints m , superstructure stiffness and substructure stiffness Dataset , dataset The quality of the iron plate m , superstructure stiffness and substructure stiffness Take a positive integer.

6. The method for designing a high-frequency vibration-absorbing fastener for suppressing local bending modal vibration of a rail according to claim 5, characterized in that: The step S4 comprises: S41: Construct a cost model for fasteners during production and construct a cost-controlled fastener design optimization objective function based on the cost model. ; ； in, is the cost function of the superstructure stiffness, is the cost function of the lower structure stiffness, i is the production process number of the superstructure, u is the production process number of the lower structure, For the upper structure i The cost of a production process, For the lower structure u The cost of a production process, I is the number of production processes for the superstructure, U is the number of production processes of the lower structure, a is the unit mass cost of the iron plate; S42: Using the optimization objective function Output iron plate quality under optimal cost control , superstructure stiffness and substructure stiffness , based on the quality of the iron plate , superstructure stiffness and substructure stiffness Design fastening systems.

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