Midspan support damper and analysis method thereof

Abstract

The invention discloses a midspan supporting damper which comprises rubber damping materials arranged on the two sides of a track, the rubber damping material on one side is arranged at one end of a first rigid support through a nylon clamping jaw, and the other end of the first rigid support is connected with a second rigid support. The rubber damping material on the other side is arranged on the second rigid support through a nylon clamping jaw. The invention further discloses an analysis method of the midspan support damper. According to the method, a midspan support damper is taken as a research object, a wheel track vibration sound radiation model considering the novel steel rail damper is established, and the influence of the geometric dimension and material parameters of a damping material on vibration and noise reduction performance is discussed.

Description

Technical Field

[0001] The invention relates to the technical field of wheel-rail vibration noise, in particular to a mid-span support damper and an analysis method thereof. Background Art

[0002] With the increase in subway lines and mileage, the density of the line network has gradually increased, and it has become increasingly difficult for subway lines to avoid some environmental noise sensitive points. At the same time, with the improvement of the quality of life requirements, the complaints of residents along the line about subway noise have increased day by day. A large number of subway noise-related studies have shown that within the speed range of subway trains, rail vibration noise dominates the wheel-rail noise. Therefore, reducing rail noise is considered to be an effective way to reduce wheel-rail noise. Extensive research on vibration reduction and noise reduction of track structures has been carried out at home and abroad.

[0003] Rail damping directly affects the track attenuation rate and the sound radiation of the track structure. Improving the rail damping coefficient through damping measures is one of the effective ways to reduce the rail sound radiation. Parker and Weber conducted field tests and proved that damped rails can reduce railway noise by 1.5dB. Rail dampers can also suppress the formation of short-pitch corrugation on rails by suppressing Pinned-Pinned resonance.

[0004] Croft et al. established a time-step analysis model and showed that installing a damper can reduce the wheel-rail interaction force. Xiao et al. studied the influence of rail vibration damper design parameters on track structure dynamics. Zhao et al. found that after installing the damper, the Pinned-Pinned vibration frequency shifted to low frequency. Yang Xinwen et al. established a vibration-acoustic radiation model to study the vibration and noise reduction performance of the dynamic vibration absorber installed at the bottom of the rail. Li et al. proposed a shear-type multi-band tuned rail damper (MTRD), which has good vibration and noise reduction performance in its main working frequency band of 200Hz-800Hz. In the actual line measurement, the overall sound pressure level was reduced by 5.9dB(A). However, the rail vibration caused by the wheel-rail interaction force usually involves multiple main frequencies or wide frequency bands. Most of the current research focuses on the control effect of the rail damper on a single vibration frequency or narrow frequency band, and its influence on the change of track dynamic characteristics. In recent years, there have also been related studies on vibration and noise reduction of embedded tracks. Although this type of track has very outstanding vibration and noise reduction effects, the installation process of this type of track is more complicated than that of rail dampers. Summary of the invention

[0005] In order to solve the problems existing in the prior art, the purpose of the present invention is to provide a mid-span support damper and an analysis method thereof. The present invention takes the mid-span support damper as the research object, establishes a wheel-rail vibration and acoustic radiation model considering the new rail damper, and discusses the influence of the damper's geometric dimensions and its material parameters on the vibration and noise reduction performance.

[0006] To achieve the above-mentioned purpose, the technical solution adopted by the present invention is: a mid-span support damper, including rubber damping materials arranged on both sides of the track, wherein the rubber damping material on one side is arranged on one end of a first rigid bracket through a nylon claw, the other end of the first rigid bracket is connected to a second rigid bracket, and the rubber damping material on the other side is arranged on the second rigid bracket through a nylon claw.

[0007] As a further improvement of the present invention, the first rigid bracket and the second rigid bracket are connected by bolts.

[0008] As a further improvement of the present invention, the first rigid bracket is fixed on the track plate.

[0009] As a further improvement of the present invention, a rubber pad is provided between the first rigid bracket and the bottom of the track.

[0010] The present invention also provides a method for analyzing the mid-span support damper as described above, comprising the following steps:

[0011] Step 1: Establish a wheel-track vibration sound radiation model based on the finite element-boundary element method;

[0012] Step 2: Verify the wheel-rail vibration and acoustic radiation model from the perspective of vibration and noise;

[0013] Step 3: Use the verified wheel-track vibration and acoustic radiation model to analyze the vibration and noise reduction effect of the mid-span support damper and the acoustic sensitivity of the damper parameters.

[0014] As a further improvement of the present invention, the step 1 is specifically as follows:

[0015] Firstly, a wheel-rail vibration model is established, wherein the wheel-rail vibration model includes a track vibration model and a wheel vibration model;

[0016] Then, the wheel-rail interaction model is established: the wheel-rail interaction leads to elastic deformation. According to Hertz theory, the contact area is regarded as an ellipse with a size of (2a, 2b); in the contact area, the roughness with a shorter wavelength compared with the rolling direction 2a will weaken the excitation of the wheel-rail vibration, that is, the contact filtering effect; the mathematical expression of the wheel-rail contact filtering function is as follows

[0017]

[0018] Where J1(x) is the first-order cylindrical Bessel function, b is the contact spot radius, k is the roughness wave number, and a is the correlation coefficient of the roughness within the width of the contact area;

[0019] The Hertz linear contact theory is used to simplify the simulation of the vertical contact stiffness of the wheel and rail, as follows:

[0020]

[0021] Where E is the elastic modulus, ν is Poisson's ratio, P is the static load of a single wheel, and R e is the effective wheel-rail contact radius, R w is the wheel radius, R r is the radius of curvature of the rail top surface, ξ is a dimensionless constant related to the contact radius;

[0022] The contact spring connects the wheel model and the track model in the contact area, and the roughness is used as an excitation to form a wheel-rail coupling model. Using the wheel-rail coupling model, the wheel-rail force is obtained by the following formula:

[0023]

[0024] Where r is the combined roughness of the wheel-rail surface, α c is the wheel-rail contact admittance, α r is the rail admittance, α w is the wheel admittance; where α C =1 / k H , k H is the wheel-rail contact stiffness;

[0025] Finally, the wheel-rail sound radiation model is established: the steady-state sound pressure p at any point (x, y, z) in the spatial sound field is determined by the second-order Helmholtz equation:

[0026]

[0027] Where k = ω / c = 2πf / c is the wave number, c is the speed of sound, ω is the angular frequency, and f is the frequency;

[0028] According to the characteristics of wheel-rail noise, the direct boundary element method is used to solve the external sound field problem at any point in the three-dimensional sound field. The sound pressure satisfies:

[0029]

[0030] Where G(R) is the Green's function, (x, y, z) is any point in the sound field, (x′, y′, z′) is any point on the boundary surface;

[0031] The normal vibration velocity and surface acoustic pressure of the boundary surface are determined, and based on the boundary conditions, the acoustic boundary element model of the rail and wheel is established using the acoustic boundary element theory.

[0032] As a further improvement of the present invention, in the wheel-rail sound radiation model, the normal vibration velocity is used as the boundary condition, and the radiated sound power is calculated by the direct boundary element method; and the grid normals of the boundary element models of the rail and the wheel are all pointed to the outside of the structure, and the grid size needs to be less than 1 / 6 of the shortest calculated wavelength; in order to prevent sound leakage from the hub hole, the hub hole is blocked by an additional unit.

[0033] As a further improvement of the present invention, the step 3 specifically includes:

[0034] The influence of the mid-span support damper on the vibration characteristics of the rail at different damper lengths is analyzed. A vertical downward unit harmonic force is applied to the rail at the mid-span, and a harmonic response analysis is performed. The noise reduction performance of the mid-span support damper at different elastic moduli and damping ratios is analyzed. A linear model is used, and the track vibration is obtained and the acoustic characteristics are calculated through harmonic response analysis.

[0035] The beneficial effects of the present invention are:

[0036] The noise reduction effect of the designed rail damper is significantly correlated with the length of the damper. The longer the damper length, the more prominent the noise reduction effect, up to 3.9dB(A). BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 Schematic diagram of the mid-span support damper structure in an embodiment of the present invention;

[0038] Figure 2 is a calculation flow chart of the wheel-rail vibration noise prediction model in an embodiment of the present invention;

[0039] Figure 3 is a finite element model diagram of a track in an embodiment of the present invention;

[0040] Figure 4 A diagram of a wheel model in an embodiment of the present invention;

[0041] Figure 5 Schematic diagram of wheel displacement admittance in an embodiment of the present invention;

[0042] Figure 6 Schematic diagram of a wheel-rail coupling model in an embodiment of the present invention;

[0043] Figure 7 Schematic diagram of the combined roughness of the wheel and rail in an embodiment of the present invention;

[0044] Figure 8 Schematic diagram of rolling friction between wheel and rail in an embodiment of the present invention;

[0045] Fig. 9 Schematic diagram of an acoustic boundary element model of a rail and a wheel in an embodiment of the present invention;

[0046] Fig.10 This is a diagram of a hammer impact test in an embodiment of the present invention;

[0047] Fig.11 This is a wheel-rail noise test diagram in an embodiment of the present invention;

[0048] Fig.12 It is a comparison diagram of the simulation and test results of the rail vertical admittance wheel-rail noise in an embodiment of the present invention;

[0049] Fig.13 This is a comparison diagram of the simulation and test results of wheel-rail noise at a speed of 50 km / h in an embodiment of the present invention;

[0050] Fig.14 Schematic diagram of the structure of different damper lengths in an embodiment of the present invention;

[0051] Fig.15 A displacement admittance comparison diagram of a track with mid-span support dampers of different damper lengths installed in an embodiment of the present invention and a reference track;

[0052] Fig.16 Schematic diagram of the effect of mid-span support dampers with different damper lengths on the total radiated noise reduction of the wheel-rail in an embodiment of the present invention;

[0053] Fig.17 Schematic diagram of the effect of different damper lengths on the total noise reduction of wheel-rail sound radiation in an embodiment of the present invention;

[0054] Fig.18 Schematic diagram of the effect of different elastic moduli of rubber on the total radiated noise reduction of wheel and rail in an embodiment of the present invention;

[0055] Fig.19 Schematic diagram of the influence of different elastic moduli of rubber on the total value of wheel-rail sound radiation in an embodiment of the present invention;

[0056] Fig. 20 This is a comparison chart of the total radiation noise reduction of the wheel-rail with different damping ratios of rubber in the embodiment of the present invention;

[0057] Fig.21 It is a schematic diagram of the total noise reduction of wheel-rail sound radiation under different rubber damping ratios in an embodiment of the present invention;

[0058] Fig. 22 A displacement admittance comparison diagram of two tracks in an embodiment of the present invention;

[0059] Fig.23Schematic diagram of the effect of the mid-span support damper on the total wheel-rail radiation in an embodiment of the present invention. DETAILED DESCRIPTION

[0060] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0061] Example

[0062] 1. New mid-span support damper:

[0063] Figure 1 The schematic diagram of the novel mid-span support damper structure designed in this embodiment is shown. The damper includes a rubber damper 1, a nylon claw 2, a rubber pad 3 and a first rigid bracket 4. Installed between adjacent sleepers of the ballastless track, the first rigid bracket 4 is fixed to the track plate and connected to the second rigid bracket 5 by bolts to stabilize other structures and connect to the track 6 and the track plate. Specific material characteristic parameters are detailed in Table 1.

[0064] Table 1 Material characteristic parameters of mid-span support damper

[0065]

[0066] This new mid-span support damper improves the longitudinal discontinuity of conventional track structures and significantly enhances the vibration and noise reduction performance of the track system. From the installation position, it is similar to reducing the distance between fasteners, effectively improving the stability of the track system, and can achieve continuous support for the track structure when the coverage length is maximum. In terms of structural design, the mid-span support damper has a large contact area with the rail in the lateral and vertical directions, making full use of the viscoelastic deformation characteristics of the rubber damping material to dissipate energy, thereby effectively suppressing vibration noise.

[0067] 2. Wheel-rail vibration acoustic radiation model:

[0068] Based on the wheel-rail noise, the parameters of the new mid-span support damper are designed. In this embodiment, a wheel-rail vibration noise prediction model is established. The calculation process is as follows: Figure 2 The track, mid-span support damper and wheel are all modeled with three-dimensional finite element models, and the direct boundary element model is used for acoustic radiation simulation. The noise excitation mode of the wheel-rail system is selected based on the equivalent force excitation input model caused by the roughness of the wheel-rail surface.

[0069] 2.1 Wheel-rail vibration model:

[0070] 2.1.1. Track vibration model:

[0071] Since the track structure has lateral symmetry and the vibration of the ballast plate and its lower structure is small, the impact on the propagation of sound waves is relatively limited. Therefore, in this embodiment, only one rail is solid modeled. In the model, the rail uses UI C60 rail, which is simulated by SOLID185 solid unit, and the fastener system is modeled by linear spring damping unit.

[0072] In the three-dimensional finite element model established in ANSYS software (such as Figure 3 As shown), the elastic modulus of the rail is 2.1×10 11 Pa, density 7850kg / m 3 , Poisson's ratio 0.3, damping ratio 0.1%, vertical stiffness of fastener system 15×10 6 N / m, damping 1×10 4 N*s / m. The track fastener spacing is 0.63m, and the track is connected in a common node manner, with a total of 52,290 units and 76,369 nodes. The bottom of the track structure, that is, the vibration reduction fastener, is fully constrained, and a unit harmonic force is applied vertically downward at the wheel-rail contact position.

[0073] 2.1.2 Wheel vibration model:

[0074] When the vibration is transmitted to the superstructure, due to the vibration isolation effect of a series of steel springs, when the frequency is higher than 20Hz, the bogie is decoupled from the wheelset, so that the wheelset can be regarded as a free state. Therefore, in the high-frequency vibration analysis of the wheel system, the influence of the spring superstructure vibration can be ignored, and only the wheel model is retained. The model is established with a wheel diameter of 0.84m and an elastic modulus of 2.1×10 11 Pa, density 7850kg / m 3 , Poisson's ratio 0.3, damping ratio 0.1%, the model contains 9240 units and 46080 nodes, and fixed constraints are applied on the contact surface between the wheel hub and the axle, such as Figure 4 shown.

[0075] After the modal analysis is performed using the wheel vibration model, the harmonic response analysis is performed. A radial unit harmonic force is applied to the nominal contact point of the wheel tread, and the singularity of the dynamic compliance of the excitation point is considered. The radial and axial displacement responses of the excitation point can be calculated. For details, see Figure 5 .

[0076] Depend on Figure 5It can be seen that the radial vibration displacement at the wheel tread position is greater than the axial vibration displacement, which is due to the influence of radial load excitation on the wheel tread. In terms of radial response, the main vibration peaks appear at 2960.4Hz, 3461Hz, and 3759.5Hz, corresponding to radial modes such as (r, 3), (r, 0), and (r, 4); in terms of axial response, the main vibration peaks are located at 233.87Hz, 321.99Hz, 454.47Hz, 2556.1Hz, and 3219.9Hz, corresponding to axial modes such as (0, 1), (0, 0), (0, 2), (1, 1), and (1, 2).

[0077] 2.2 Wheel-rail interaction model:

[0078] The roughness of the wheel-rail surface is one of the main causes of wheel-rail rolling noise. When the wheel rolls on the rail, the roughness of the wheel-rail contact surface arouses the relative movement between the wheel and rail and the elastic vibration of the wheel and rail itself. This elastic vibration will radiate to the surrounding air, thus generating noise.

[0079] 2.2.1. Contact filtering:

[0080] In actual operation, the wheel-rail interaction leads to elastic deformation. According to Hertz theory, the contact area can be regarded as an ellipse with a size of (2a, 2b). In this contact area, the roughness with a shorter wavelength compared to the rolling direction 2a will weaken the excitation of the wheel-rail vibration, which is the contact filtering effect. The mathematical expression of the wheel-rail contact filter function is shown in (1):

[0081]

[0082] Where J1(x) is the first-order cylindrical Bessel function, b is the contact spot radius, k is the roughness wave number, and α is the correlation coefficient of the roughness within the width of the contact area.

[0083] 2.2.2 Contact stiffness:

[0084] The wheel-rail contact model of this embodiment is only applicable to the case where the vehicle runs smoothly on a straight track. This model mainly considers the interaction between the wheel and the rail in the vertical direction, and uses the Hertz linear contact theory to simplify the simulation of the vertical contact stiffness of the wheel and the rail, as shown in equations (2)-(4),

[0085]

[0086] Where E is the elastic modulus, ν is Poisson's ratio, P is the static load of a single wheel, and R e is the effective wheel-rail contact radius, R w is the wheel radius, R ris the radius of curvature of the rail top surface, and ξ is a dimensionless constant related to the contact radius.

[0087] The contact spring connects the wheel model and the track model in the contact area, and the roughness is used as an excitation to form a wheel-track coupling model, such as Figure 6 shown.

[0088] The running speed of urban rail trains is generally 40 to 120 km / h. In this embodiment, 120 km / h is selected for calculation. The wheel radius is 0.42 m and the single wheel load is 4.5×10 3 kg. After considering the contact filtering effect between the wheel and rail, the combined roughness of the wheel and rail is Figure 7 shown.

[0089] Using the above wheel-rail coupling model, the wheel-rail force can be obtained by equation (5):

[0090]

[0091] Where r is the combined roughness of the wheel-rail surface, α c is the wheel-rail contact admittance, α r is the rail admittance, α w is the wheel admittance. Among them, α C =1 / k H , k H is the wheel-rail contact stiffness. Wheel-rail contact stiffness k H 1.09×10 -9 N / m 2 , wheel-rail contact admittance α C 9.74×10 -10 m / N.

[0092] Depend on Figure 8 It can be seen that the interaction force between the wheel and the rail reaches a maximum value of 267N at 460Hz, and the fluctuation is mainly concentrated in the medium and high frequency bands. The first valley value appears at 1020Hz, which may be related to the Pinned-Pinned vibration mode of the track at this frequency.

[0093] 2.3 Wheel-rail sound radiation model:

[0094] The steady-state sound pressure p at any point (x, y, z) in the spatial sound field is determined by the second-order Helmholtz equation:

[0095]

[0096] In the formula, k=ω / c=2πf / c is the wave number, c is the speed of sound, ω is the angular frequency, and f is the frequency. The solution can be obtained as long as the boundary conditions are determined.

[0097] According to the characteristics of wheel-rail noise, the direct boundary element method is used. For the external sound field problem at any point in the three-dimensional sound field, the sound pressure satisfies equation (7).

[0098]

[0099] Where G(R) is the Green's function, (x, y, z) is an arbitrary point in the sound field, and (x′, y′, z′) is an arbitrary point on the boundary surface.

[0100] To solve equation (7), we first need to determine the normal vibration velocity and surface acoustic pressure of the boundary surface. Then, based on these boundary conditions, the acoustic boundary element model of the rail and wheel is established using the acoustic boundary element theory. In the model, the normal vibration velocity is used as the boundary condition, and the radiated sound power is calculated using the direct boundary element method. To ensure the accuracy of the acoustic analysis, the mesh normals of the boundary element models of the rail and wheel point to the outside of the structure, and the mesh size must be less than 1 / 6 of the shortest calculation wavelength. To prevent sound leakage from the hub hole, an additional unit is used to block the hub hole, such as Fig. 9 shown.

[0101] The vibration response of the wheel is input into the acoustic boundary element model as the boundary condition, and the radiated sound power is calculated using the Virtual.Lab acoustic boundary element software to obtain the sound power level. The air density is ρ = 1.21 kg / m 3 , the speed of sound in air c = 344m / s. The calculation frequency range is 20~5000Hz, and the step length is 20Hz.

[0102] 2.4 Model Validation

[0103] To verify the accuracy of the wheel-rail vibration noise model, a force hammer test and wheel-rail noise test were conducted on a ballastless track line of a subway in Singapore. The track adopts UIC60 rail and the track fastener spacing is 0.7 meters. Fig.10 As shown in Figure 1, an acceleration sensor is installed just above the fastener, and a force hammer is used to vertically strike the sensor to obtain the frequency response function of the rail. Fig.11 As shown in Figure 1, an acoustic sensor is installed next to the wheel at the axle box position. Calculations are performed based on the above modeling method and compared with the measured results to verify the accuracy of the wheel-rail vibration noise model. Fig.12 , 13 The comparison charts of simulation and test results of rail vertical admittance and wheel-rail noise at a speed of 50km / h are given respectively.

[0104] Depend on Fig.12It can be seen that the measured data of the displacement admittance of the track model has the same trend as the simulation results, and the amplitude is basically consistent. The measured results have a peak at a frequency of 240Hz, corresponding to the first-order resonance mode of the rail, corresponding to the overall sinking and floating of the rail on the fastener, and the result of the field test is 243Hz. It can be judged that the track model established in this embodiment according to the above modeling method can also more accurately reflect the vibration characteristics of the rail.

[0105] according to Fig.13 It can be seen that the high-frequency band of the sound energy level of the wheel-rail noise model is dominant, and the simulation results are in good agreement with the measured data in the frequency range of 500-5000Hz. However, in the low-frequency part, the measured data is obviously higher, and the difference between the two increases significantly as the frequency decreases. This difference is mainly due to the influence of acoustic boundaries such as the ground and the vehicle body floor during the wheel-rail noise test.

[0106] In summary, the wheel-rail vibration noise prediction model established according to the method adopted in this embodiment can relatively accurately reflect the characteristics of the significant frequency bands of subway wheel-rail vibration noise.

[0107] 3. Characteristics analysis of mid-span support damper:

[0108] Based on the wheel-rail vibration noise prediction model established above, a mid-span support damper structure is added to the track model to study the performance of the damper on noise reduction under different geometric dimensions and material parameters of the rail mid-span support damper. The sound radiation of the track structure is closely related to the system damping and attenuation rate. Improving the two can effectively reduce the total radiated noise of the wheel and rail.

[0109] 3.1. Influence of damper length:

[0110] The damper lengths of the mid-span support damper are 0.3m, 0.4m, 0.5m, and 0.63m (damper length 0.63m) for parameter investigation. Fig.14 Shown

[0111] In order to study the influence of mid-span support damper on the vibration characteristics of rail at different damper lengths, a vertical downward unit harmonic force is applied to the rail in the mid-span, and the harmonic response analysis is carried out. Fig.15 The displacement admittance comparison of the track with mid-span support dampers of different damper lengths installed and the reference track is shown.

[0112] Depend on Fig.15It can be seen that after installing the mid-span support damper, the vibration reduction effect is significant at the first-order resonance frequency and the Pinned-Pinned resonance frequency (1020Hz), the vibration is slightly increased in the frequency range of 0-1100Hz, and a stable vibration reduction effect is shown in the frequency range of 1100-5000Hz. Among them, the first-order resonance frequency increases to around 120Hz. This is because the addition of the mid-span support damper increases the vertical support stiffness of the track system, and the increase is greater than the influence of the parametric mass. The Pinned-Pinned resonance frequency remains at 1020Hz because the sleeper spacing has not changed. When the coating is 0.3m, the vibration amplitude of the Pinned-Pinned resonance frequency increases from 2.92×10 -9 m is reduced to 1.68×10 -9 m, a 42% reduction. The change in damper length within 0.3-0.63m is mainly reflected in vertical stiffness and damping. The impact on vibration is concentrated in the lower frequency band, with the most significant impact on the first-order resonance frequency and limited impact above 1100Hz. The vibration reduction effect is most significant when the damper length is 0.63m, but there is no obvious advantage compared with other working conditions.

[0113] Fig.16 The effect of mid-span support dampers with different damper lengths on the total wheel-rail radiation noise reduction is shown. The right coordinate axis corresponds to the wheel-rail radiation sound power level of the reference rail, and the left coordinate axis corresponds to the total wheel-rail radiation noise reduction of the rail. Fig.17 The effect of different damper lengths on the total noise reduction of wheel-rail sound radiation is shown.

[0114] according to Fig.16 According to the data, the effective working frequency band of the mid-span support damper is mainly concentrated in the range of 400Hz-2500Hz, and it has a significant noise reduction effect in this frequency band. As the length of the damper increases, the noise reduction working frequency band of the damper hardly shifts. The stronger the noise amplification in the low frequency band below 400Hz, the more significant the noise reduction performance in its main working frequency band. All working conditions reached the maximum noise reduction at 1000Hz, which were 3.6dB(A), 4.6dB(A), 5.4dB(A), and 6.4dB(A) respectively.

[0115] Fig.17 It is shown that within the frequency range of 0-5000Hz, as the damper length increases, the overall noise reduction effect of the mid-span support damper continues to improve, corresponding to its vibration reduction characteristics. When the damper length is 0.63m, the effect is most significant, and the noise reduction of the total wheel-rail sound radiation value reaches 3.9dB(A), which is reduced by about 2.5 times. This is because the increased damper length not only helps to improve the vibration reduction performance, but also effectively isolates and attenuates the sound energy.

[0116] 3.2. Influence of rubber material properties:

[0117] Due to its excellent damping performance, rubber is widely used in engineering fields such as vibration reduction and noise reduction. Rubber structural parts will deform repeatedly at a certain deformation amplitude and frequency, and lose vibration energy through their viscoelastic deformation.

[0118] Under the condition of a damper length of 0.4m, the noise reduction performance of the mid-span support damper under different elastic moduli and damping ratios was studied, considering the material properties and actual application requirements. Due to the small deformation characteristics of rubber, a linear model was used, and the track vibration and acoustic characteristics were obtained through harmonic response analysis. Fig.18 This is the effect of different elastic modulus of rubber on the total radiated noise reduction of wheel-rail.

[0119] according to Fig.18 According to the data analysis, when the elastic modulus of rubber varies in the range of 0.5-2.5MPa, the main noise reduction frequency band of the mid-span support damper does not shift significantly. In the full frequency band of 0-5000Hz, the noise reduction performance of the damper is positively correlated with the elastic modulus. All working conditions achieved the optimal noise reduction effect at 1000Hz. When the elastic modulus was 2MPa and 2.5MPa, the noise reduction reached 5.0dB(A) and 5.5dB(A) respectively. At 315Hz, the elastic modulus has little effect on the noise reduction effect of the damper. In the frequency band below this frequency, the effect of the elastic modulus is different from the length of the damper. An increase in the elastic modulus increases the noise, but the overall trend is that the larger the elastic modulus, the better the acoustic performance.

[0120] Fig.19 The influence of different elastic modulus of rubber on the total value of wheel-rail sound radiation is shown. When the elastic modulus is 2MPa and 2.5MPa, the total value of wheel-rail sound radiation is 100.3dB(A), and the noise reduction reaches a maximum value of 2.8dB(A).

[0121] Fig. 20The comparison of the total radiated noise reduction of the wheel-rail with different damping ratios of rubber is shown. When the rubber damping ratio varies in the range of 0.05-0.5, there is almost no obvious effect on the noise reduction frequency band of the damper. However, with the increase of the damping ratio in the full frequency band of 0-5000Hz, the noise reduction ability of the damper is enhanced. When the damping ratio is greater than 0.2, the noise reduction effect is best at 1000Hz, and the noise reduction reaches 5.5dB(A) when the damping ratio is 0.5; when the damping ratio is less than 0.2, the noise reduction effect is best at 630Hz, and the noise reduction is about 4.6dB(A). The effect of the damping ratio on the noise reduction performance is most significant at the frequency of 315Hz. When the damping ratio increases from 0.05 to 0.5, the noise reduction increases by 5.4dB(A), and increases by 1.7dB(A) at 1000Hz. In the frequency bands below 100Hz, at 630Hz, and above 2000Hz, the damping ratio has limited effect on improving the noise reduction effect.

[0122] Fig.21 The comparison of the noise reduction of the total wheel-rail sound radiation under different rubber damping ratios is shown. When the damping ratio is 0.3, the total wheel-rail sound radiation is 100.3dB(A), and the noise reduction reaches the maximum value of 2.8dB(A).

[0123] 3.3. Comprehensive design suggestions and effect analysis of dampers:

[0124] According to the parameter survey results, within the specified range, the change in damper length has a significantly greater impact on the noise reduction performance of the damper than the influence of the rubber material parameters. Considering the material properties and practical applications, the key design parameters of the mid-span support damper are recommended to be: damper length 0.63m type (damper length 0.63m), elastic modulus 2MPa, and damping ratio 0.3.

[0125] A new type of continuously supported high damping track model (called new track) with mid-span support dampers designed according to the above parameters was established, and its vibration reduction and noise reduction performance was compared with that of ordinary tracks. Fig. 22 is the displacement admittance comparison diagram of the two tracks, Fig.23 This is the effect of the mid-span support damper on the total wheel-rail radiation.

[0126] according to Fig. 22 The data show that the vibration of the new track in the frequency range of 1180-5000Hz is lower than that of the reference track. Among them, the first-order resonance frequency shifts from 100Hz to 160Hz, and the amplitude is 1.38×10 -8 m, which is reduced by 66.1%; while the amplitude at the Pinned-Pinned resonance frequency is 1.35×10 -9 m, a decrease of 65.6%.

[0127] according to Fig.23The results show that in the frequency band of 400-5000Hz, the total wheel-rail radiated sound power level of the new track is lower than that of the reference track. In particular, at 2000Hz, the noise reduction reaches 5.9dB(A); at 800Hz, it is 7.0dB(A); at 1000Hz, the noise reduction effect is the best, reaching 7.4dB(A). Combining the data of the full frequency band 0-5000Hz, the total wheel-rail sound radiation of the new track is 99.1dB(A), while that of the reference track is 103.1dB(A). The noise reduction of the mid-span support damper reaches 4dB(A), about 2.5 times, with significant effect.

[0128] This example takes the vibration-damping track as the research object, establishes a wheel-track vibration and acoustic radiation model based on the finite element-boundary element method, and systematically analyzes the influence of the mid-span support damper on the track vibration and acoustic radiation. The following conclusions are drawn through simulation:

[0129] (1) The mid-span support damper significantly reduces noise in the frequency range of 400Hz-2500Hz, rather than focusing on a specific frequency. This operating frequency band is stable, less sensitive to changes in damper length and rubber parameters, and has strong engineering applicability.

[0130] (2) The noise reduction effect of the damper is positively correlated with its damper length. Increasing the damper length significantly improves the noise reduction effect. The best effect is achieved when the damper length is 0.63m, with a maximum of 3.9dB(A).

[0131] (3) For the damper with a damper length of 0.4m, the elastic modulus and damping ratio of the rubber have limited influence on its noise reduction effect. When the elastic modulus is 2.5Mpa, the noise reduction is the largest at 1000Hz, reaching 5.5dB(A); with the increase of the damping ratio (0.05-0.5), the noise reduction effect is most significant at 0.5, also reaching 5.5dB(A) at 1000Hz. However, the influence of both on the total value of wheel-rail sound radiation does not exceed 0.5dB(A), and the influence is limited.

[0132] (4) The damper of the comprehensive design can effectively reduce the total value of wheel-rail sound radiation by 4 dB(A). The noise reduction effect is strongest at a frequency of 1000 Hz, reaching 7.4 dB(A), which has a significant noise reduction effect.

[0133] The above-mentioned embodiments only express the specific implementation of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A mid-span support damper, characterized in that: It includes rubber damping materials arranged on both sides of the track, wherein the rubber damping material on one side is arranged on one end of a first rigid bracket through a nylon claw, the other end of the first rigid bracket is connected to a second rigid bracket, and the rubber damping material on the other side is arranged on the second rigid bracket through a nylon claw.

2. The mid-span support damper according to claim 1, characterized in that: The first rigid bracket and the second rigid bracket are connected by bolts.

3. The mid-span support damper according to claim 1, characterized in that: The first rigid bracket is fixed on the track plate.

4. The mid-span support damper according to claim 1, characterized in that: A rubber pad is provided between the first rigid bracket and the bottom of the track.

5. An analysis method for a mid-span support damper according to any one of claims 1 to 4, characterized in that: The following steps are involved: Step 1: Establish a wheel-track vibration sound radiation model based on the finite element-boundary element method; Step 2: Verify the wheel-rail vibration and acoustic radiation model from the perspective of vibration and noise; Step 3: Use the verified wheel-track vibration and acoustic radiation model to analyze the vibration and noise reduction effect of the mid-span support damper and the acoustic sensitivity of the damper parameters.

6. The analysis method of the mid-span support damper according to claim 5, characterized in that: The step 1 is specifically as follows: Firstly, a wheel-rail vibration model is established, wherein the wheel-rail vibration model includes a track vibration model and a wheel vibration model; Then, the wheel-rail interaction model is established: the wheel-rail interaction leads to elastic deformation. According to Hertz theory, the contact area is regarded as an ellipse with a size of (2a, 2b); in the contact area, the roughness with a shorter wavelength compared with the rolling direction 2a will weaken the excitation of the wheel-rail vibration, that is, the contact filtering effect; the mathematical expression of the wheel-rail contact filtering function is as follows Where J1(x) is the first-order cylindrical Bessel function, b is the contact spot radius, k is the roughness wave number, and a is the correlation coefficient of the roughness within the width of the contact area; The Hertz linear contact theory is used to simplify the simulation of the vertical contact stiffness of the wheel and rail, as follows: Where E is the elastic modulus, ν is Poisson's ratio, P is the static load of a single wheel, and R e is the effective wheel-rail contact radius, R w is the wheel radius, R r is the radius of curvature of the rail top surface, ξ is a dimensionless constant related to the contact radius; The contact spring connects the wheel model and the track model in the contact area, and the roughness is used as an excitation to form a wheel-rail coupling model. Using the wheel-rail coupling model, the wheel-rail force is obtained by the following formula: Where r is the combined roughness of the wheel-rail surface, α c is the wheel-rail contact admittance, α r is the rail admittance, α w is the wheel admittance; where α C =1 / k H , k H is the wheel-rail contact stiffness; Finally, the wheel-rail sound radiation model is established: the steady-state sound pressure p at any point (x, y, z) in the spatial sound field is determined by the second-order Helmholtz equation: Where k = ω / c = 2πf / c is the wave number, c is the speed of sound, ω is the angular frequency, and f is the frequency; According to the characteristics of wheel-rail noise, the direct boundary element method is used to solve the external sound field problem at any point in the three-dimensional sound field. The sound pressure satisfies: Where G(R) is the Green's function, (x, y, z) is any point in the sound field, (x′, y′, z′) is any point on the boundary surface; The normal vibration velocity and surface acoustic pressure of the boundary surface are determined, and based on the boundary conditions, the acoustic boundary element model of the rail and wheel is established using the acoustic boundary element theory.

7. The analysis method of the mid-span support damper according to claim 6, characterized in that: In the wheel-rail acoustic radiation model, the normal vibration velocity is used as the boundary condition, and the radiated sound power is calculated using the direct boundary element method. The mesh normals of the boundary element models of the rail and wheel point to the outside of the structure, and the mesh size must be less than 1 / 6 of the shortest calculated wavelength. In order to prevent sound leakage from the hub hole, the hub hole is blocked by an additional unit.

8. The analysis method of the mid-span support damper according to claim 7, characterized in that: The step 3 specifically includes: The influence of the mid-span support damper on the vibration characteristics of the rail at different damper lengths is analyzed. A vertical downward unit harmonic force is applied to the rail at the mid-span, and a harmonic response analysis is performed. The noise reduction performance of the mid-span support damper at different elastic moduli and damping ratios is analyzed. A linear model is used, and the track vibration is obtained and the acoustic characteristics are calculated through harmonic response analysis.

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