Comparative analysis of rail pad lateral dynamic performance in metro systems

Bai Y., He Z., Qu S., Li B., Yun J., Li P., Zhai W.

Zheng Z., Hu J., Qian Y., Xu J., Hou M.

Qu S., Ding W., Dong L., Zhu J., Zhu S., Yang Y., Zhai W.

Chiral phononic crystals (CPCs) offer an advanced approach to vibration isolation by exploiting inertial amplification, establishing broad band gaps at low frequencies and outperforming conventional phononic designs. This study pioneers a CPC-inspired railway track that significantly enhances low-frequency vibration isolation through an orthogonal polarization coupling mechanism of the chiral subunit cell. Mechanical modeling and simulations have validated the causes of the enhanced performance and the tunability of crucial physical parameters across characteristic dimensions. Incorporating this structure within a coupled vehicle-floating slab track (FST)-tunnel system facilitates a comparative analysis against conventional steel spring FSTs. The CPC-inspired track system demonstrates enhanced isolation, significantly reducing vibrations within the 200 Hz range for both slab and tunnel structures, achieving a maximum insertion loss of 7.19 dB for the slab and 5.69 dB for the tunnel. Further evaluation of rail and slab displacements, alongside the wheel load reduction rate, underscores the operational safety of trains with the CPC-inspired system implemented. This pioneering exploration of CPC-inspired structures showcases the potential to significantly advance vibration control in urban rail infrastructure, providing a foundational reference for future research.

Bai Y., He Z., Bao N., Li P.

In this paper, a novel mesh-type rail pad with second-order stiffness (MTRPSOS) is proposed, which is comprised of a mesh-type rail pad (MTRP) and multiple filled blocks. By adjusting the height of the filled blocks, the stiffness curves of the MTRPSOS exhibit pronounced second-order stiffness (SOS) characteristics. A finite element (FE) model of the MTRPSOS and a dynamic model were established to investigate the SOS characteristics and their impact on various dynamic indices. The FE calculations reveal that both static and dynamic stiffness of the MTRPSOS increase as the height of the filled blocks decreases. Moreover, as the height of the filled blocks increases, stress distribution becomes more uniform. The dynamic calculations demonstrate that the SOS characteristics of the MTRPSOS significantly affect various dynamic indices. As the SOS of the MTRPSOS decreases, rail displacement correspondingly increases, while vibration acceleration, wheel-rail forces, fastener reaction forces, and derailment coefficient all decrease. This indicates that the MTRPSOS offers superior vibration reduction under the SOS conditions compared to the first-order stiffness conditions. Additionally, a comparative study was conducted to assess the vibration reduction effect of the MTRPSOS in contrast to traditional rail pad, and the results show that the MTRPSOS consistently exhibits lower vibration levels under the same operating conditions, underscoring its superior capacity for vibration reduction.

Niu Z., Gao L., Liu L., Qin J.

Alsharo A., Douier K., Hussein M.F., Renno J.

Bai Y., He Z., Bao N., Wang H., Zhang P.

The dynamic stiffness (DS) curve of the rail pad (RP) is related to its damping performance. In a vibration period under the action of a sinusoidal load, the energy consumed by the damping force of the RP is equal to the energy generated by the applied load. The theoretical derivation found that the DS curve area of the RP is proportional to its damping ratio (DR) and loading frequency, and the accuracy of the theoretical derivation is verified by establishing a finite element model of the fastening system. The finite element calculation (FEC) found that the larger the loading frequency, the larger the DS curve area of the RP. The larger Young’s modulus of the RPs, the smaller the area of its DS curve. The prismatic rail pad (PRP) and mesh-type high damping rail pad (MTHDRP) are respectively assembled in the fastening system, and the static/dynamic stiffness (S/DS) curves of the two RPs are compared through the FEC, it is concluded that the MTHDRP has lower S/DS, and its linearity of the SS curve is better, indicating that the MTHDRP has better stability and stiffness retention. Meanwhile, the area of the DS curve of the MTHDRP is significantly larger than that of the GRP, indicating that it has better damping performance. The S/DS tests of the two RPs verified the accuracy of the FEC. Finally, taking the elasticity of the damping block (DB), the height of the DB, and the meshes numbers as the research variables, the law of their influence on the S/DS and DR of the MTHDRP is studied. It is concluded that by increasing the elasticity of the DB, the S/DS of the MTHDRP will increase, and the DR will decrease. The S/DS and DR of the MTHDRP will increase with the increase of the height of the DB. As the meshes numbers increase, both the S/DS and DR of the MTHDRP will decrease.

Zhang J., Zhu Z., Zhu X., Meng Y., Chu W.

Shield tunnels are susceptible to large uneven settlements owing to their low longitudinal stiffnesses, which can lead to structural defects and unfavorable wheel–rail interactions. These conditions may even worsen if uneven settlement occurs in curved track sections with small radii. Therefore, the running safety and riding comfort of metro trains should be considered when dealing with curved tunnel sections with differential settlements. In this study, a train–curved-track–tunnel dynamic interaction model was established to evaluate the influence of uneven settlement and a small curve radius on the running safety and riding comfort of a metro train under different curve radii, vehicle speeds, and settlement ranges and amplitudes. Considering initial random irregularities with respect to the longitudinal level and alignment, the dynamic responses of the vehicle were determined, including the wheel–rail forces, accelerations of the vehicle, wheel load reduction rate, derailment coefficient, and stability index. In addition, the characteristics of uneven settlement when the vehicle responses reached peak values were illustrated. The results revealed that the wheel–rail lateral and vertical forces increased significantly with an increase in velocity. The wheel load reduction rate, derailment coefficient, and lateral comfort were negatively correlated with the curve radius, whereas vertical comfort was not very sensitive to changes in the curve radius. Additionally, the outer wheel exhibited a greater load reduction than the inner wheel, thus leading to a greater likelihood of derailment. More attention should therefore be directed toward the settlement wavelengths and amplitudes at which the wheel load reduction rate, derailment coefficient, and vertical and lateral riding comfort indexes achieve their maximum values.

He Z., Bai Y., Su C., Bao N., Wang H., Yun J., Wang Y.

Bai Y., He Z., Su C., Bao N., Wang H., Shi G., Wang Y., Yun J., Wang Z.

• The novel filled damping block mesh-type rail pad (FDBMTRP) for a heavy haul railway fastening system is proposed for the first time. • The FDBMTRP has better structural characteristics and damping performance compared with the existing rail pads. • The FDBMTRP can effectively reduce the vibration of the track structure and can improve vehicle running stability. Currently, the commonly used rail pads for heavy haul railways are grooved rubber rail pads (GRRP) and prismatic thermoplastic polyester elastomer (TPEE) rail pads (PTRP). However, the rail pad of the traditional structure has an obvious stress concentration when compressed and limited damping performance, which severely limits the service life of the rail pad. This study proposes a novel filled damping block mesh-type rail pad (NFDBMTRP) suitable for heavy haul railways. The rail pad has better damping performance than that of the traditional rail pad under the same stiffness condition. When the rail pad is under pressure, its hexagonal mesh structure can ensure that the stress distribution of the rail pad is uniform. Meanwhile, the damping block filled in the hexagonal mesh cavity can absorb part of the energy so that the overall stress level of the NFDBMTRP is small, which is beneficial for prolonging the service life of the rail pad. On the basis of the vehicle–track coupled dynamics theory, the C 80 truck–track coupled dynamics calculation model was established, and a field test of the heavy haul railway was conducted. The time and frequency domain signals of the rail and sleeper acceleration obtained from the test were compared with those from the simulation to verify the accuracy of the dynamics model calculations. Under the same stiffness (70 kN/mm), the dynamic response differences in the four rail pads were compared and studied. The dynamic calculation results showed that the NFDBMTRP not only has smaller acceleration than that of the other three rail pads on the rail, sleeper, and car body but also has the smallest wheel–rail vertical force and derailment coefficient. This implies that improving the damping of the rail pad is beneficial for improving the safety and stability of train operation and has a certain protective effect on the under–track structure. To sum up, the NFDBMTRP has better structural properties and vibration damping performance compared with the traditional rail pad, and has broad application prospects in the heavy haul railway fastening system.

Zhang X., Thompson D., Ryue J., Jeong H., Squicciarini G.

Zhai Z., Zhu S., Yuan X., He Z., Cai C.

Nonlinear dynamic behavior of a new mesh-type rail pad on the vehicle-slab track coupled system is investigated considering the influences of frequency and amplitude dependence in extremely cold environment. The frequency dependence of the new mesh-type rail pad is modeled by a fractional derivative viscoelastic element while a frictional component considers the amplitude dependence. Laboratory tests are performed to investigate the frequency and amplitude dependent performance of the rail pad and to determine key model parameters. Temperature factor and Mooney-Rivlin strain energy density are also introduced to simulate the mechanical properties of the rubber material of rail pad in low temperature environments. Further, the proposed nonlinear model for the rail pad is implemented in a coupled vehicle-slab track dynamics model to investigate the complicated nonlinear effects of the rail pad due to the dependence of the temperature, amplitude and frequency. The analysis indicates that the dynamic stiffness and damping of the mesh-type rail pads increase with the frequency increases. The proposed model for the mesh-type rail pad enables a more accurate dynamic simulation of vehicle-slab track system in extremely cold environment than the traditional Kelvin-Voigt model which overestimates the wheel rail force, rail vibration acceleration and other indicators at 3.15 Hz–40 Hz and 250 Hz–500 Hz, while underestimates these indicators at 50 Hz–125 Hz.

Castillo-Mingorance J.M., Sol-Sánchez M., Mattinzioli T., Moreno-Navarro F., Rubio-ámez M.C.

• Rail eco-pads made from recycled polymers were designed. • Waste plastics and end-of-life tyres were combined to modify pad stiffness. • The influence of pad geometry on its stiffness was determined. • The carbon footprint of the designs was determined. • Recycled high density polyethylene-based pads were found to be the most durable. • The net and gross carbon footprints of the pads were explored. This article focuses on the study and design of rail pads from recycled plastics for their application in railway tracks, aiming to reduce environmental impacts produced from virgin materials. For this purpose, sustainable rail pads were designed and manufactured using two separate locally recycled plastics: high-density polyethylene from plastic boxes, and from a combination of polypropylene and low-density polyethylene from reclaimed geomembranes. A high-performance polymeric industrial resin was also used as a reference material. These separate plastics were also combined with different quantities and sizes of recycled crumb rubber from end-of-life tires. The results of this paper analyse the influence of pad composition and geometry on the mechanical performance of the pads, while also assessing the durability and environmental benefits of the most optimal solutions. Results found that the pads from high-density polyethylene presented values of static stiffness around 800 kN/mm while the low-density polyethylene led to values close to 150 kN/mm, where the reference industrial binder outputted intermediate values. In addition, the combination of different quantities and sizes of crumb rubber resulted in a range of viable solutions, in some cases reducing stiffness more than 50%. Additionally, both recycled plastics offered a reduced carbon footprint compared to conventional pads, although this did decrease with increasing amounts of crumb rubber. Nonetheless, it was found that the softer solutions led to higher plastic deformations during fatigue tests, reducing the durability in comparison to the pads made from high-density polyethylene.

Qu S., Yang J., Zhu S., Zhai W., Kouroussis G.

• A hybrid prediction method is put forward for predicting train-induced vibrations. • Train-induced vibrations under different conditions can be high-effectively calculated. • Vibration effect on the sensitive equipment in a far-field building is evaluated. • Mitigation measure is adopted to achieve vibration attenuation in concerned frequency ranges. The prediction of train-induced vibration on far-field buildings is a challenging issue in the transportation environment communities. In this work, a hybrid prediction method is put forward utilizing the idea of substructure analysis, which can high-effectively calculate the train-induced vibration under different operation conditions. Based on vehicle-track coupled dynamics theory, wavenumber finite element theory (2.5D FEM) and Green’s function method, this method could comprehensively analyze vibration characteristics of the source, propagation path and sensitive target/vibration receiver by appropriately considering the boundary conditions between each part. The proposed model possesses the advantages of 2.5D FEM in calculation efficiency and could consider the dynamic interaction between vehicle and track system more elaborately. In addition, the vibration response under different operation conditions can be high-efficiently obtained by updating the track supporting forces without repeatedly solving the Green’s functions of the system. On this basis, this work predicts the vibration impact of subway train operation on the sensitive equipment in a far-field large-scale building, and uses the generic vibration criteria for sensitive equipment to evaluate the vibration responses. Further, to mitigate the impact of train-induced vibration, floating slab track is adopted to achieve the vibration attenuation in the concerned frequency. Results show that the train-induced vibration on the monolithic bed track exceeds the limit specified in the standard in some frequency bands. The use of floating slab track can effectively reduce the vibration response of the building and ensure the routine use of sensitive equipment.

Kedia N.K., Kumar A., Singh Y.

This paper focuses on the effect of short and long wavelength track irregularities and rail pads on train induced vibration and noise using a train-track interaction model. An Indian rail vehicle is modelled as a spring-mass-damper system, and a ballasted track structure is modelled as an infinite rail resting on the viscoelastic foundation. Long-wavelength track irregularity is obtained from measured field data; however, short-wavelength track irregularity is generated using Sato track spectrum. It is observed that vibration and noise levels are not only higher for short-wavelength compared to long-wavelength but also exceed the limits imposed by the Indian Railway standards. Thus, track properties are modified by varying stiffness and damping of rail pads to reduce vibration and noise levels. The stiffer pads reduced vibration level in the range of 7dB–24dB and noise level in the range of 8dBA–14dBA; hence, stiffer pads are recommended for the ballasted track. Moreover, track properties for short-wavelength also keep vibration and noise levels within the permissible limit for long-wavelength. Thus, modification of track properties based on only short-wavelength irregularity is required.