Fastener Stiffness Research Articles

Use of probabilistic fastener velcro as a friction-induced vibration damping treatment

Probabilistic fasteners are biologically inspired clamping devices that are interlocked by stems on each surface. Due to dynamic characteristics of fastening mechanism, friction inevitably occurs between stems in a vibrating environment. The use of the probabilistic fastener as a vibration reduction component were investigated with advantages from friction-induced damping in this study. The dynamic stiffness and loss factor of the probabilistic fastener were derived from the vibration interaction with a mechanical structure. This allowed determination of energy dissipation due to the friction in hook and loop from the wave propagation analysis. As the vibration amplitude increased, the loss factor of the fastener gradually increased because the friction between multiple stems increased. With the probabilistic fastener application, the vibration generation and transmission were reduced compared to the bolted joint due to the inherent frictional contacts. With this unique advantage, the probabilistic fastener has potential applications when large damping is required with additional benefit on the reduced weight.

Development of a model for stochastic analysis of vehicle–track interaction considering spatial variability of track parameters

In this work, a model for achieving stochastic analysis of vehicle–track interaction systems is proposed based on random field realization of track parameters and the finite element coupling of rigid-elastic bodies. Aiming at the clarification of the spatial variability and correlation of track parameters on the influence of vehicle–track dynamic performance, a general scheme based on Karhunen–Loève Expansion and cyclic calculation method is developed to realize a multi-dimensional random field that holds an arbitrary marginal distribution function and correlation structure, and to consider the inhomogeneity of system parameters along the longitudinal direction efficiently. Furthermore, the validation of the random field expansion against the vehicle–track system is implemented, and the dynamic effects of random track parameters are investigated through two special issues. Numerical results show that the spatial correlation of fastener stiffness affects the extreme response, especially the low-frequency component of rail displacement. The spatial dependence of the filling layer has little influence on the dynamic behavior of the vehicle subsystem, but it obviously changes the extreme stress and strain of the filling layer. Ignoring the spatial correlation of random variables might underestimate the performance of the track system.

An Analytical Solution for the Geometry of High-Speed Railway CRTS Ⅲ Slab Ballastless Track

To study the mapping relationship between girder deformation and rail deformation for the CRTS Ⅲ slab ballastless track (SBT) multi-span simply supported bridge, this study derived a simplified analytical solution, and the corresponding ANSYS finite element model (AFEM) was established. Compared with the fine analytical model (FAM) and the AFEM, the calculation results of the three models under the conditions of pier settlement and girder vertical fault were compared, which verified the universal properties of the simplified analytical model (SAM). Based on the verified SAM, the influence of pier settlement, fastener stiffness, girder span, and girder vertical fault on rail deformation was studied. The results show that the rail deformation is approximately proportional to pier settlement and girder vertical fault. With the increase in fastener stiffness, the fastener internal force increases, the rail mapping deformation increases, and the length of the rail mapping deformation area decreases. With the increase in girder span, the rail deformation curve becomes smooth, the length of the rail mapping deformation area becomes longer, and the fastener internal force is significantly reduced.

Influence of rail weld irregularity on dynamic stress of bogie frame based on vehicle-track rigid-flexible coupled model

To examine the effects of rail weld irregularity on the dynamic stress of the bogie frame, a numerical model which considers the bogie frame flexibility is established. Field measurements were conducted to validate the reliability of the proposed model and the bogie frame’s modal vibration including the bending deformation of cross beams at 50 Hz can be observed. A comparison between the flexible bogie frame model and the traditional multi-body dynamics model is conducted to investigate the influences of the bogie frame’s flexibility on wheel-rail interactions. Then the numerical model of the rail weld joint is proposed to study the P2 resonance performance and the dynamic stress patterns of the bogie frame. A comparison of influences with different rail weld irregularities and parameter studies are conducted. Then the effects of fastener stiffness on P2 resonance frequencies are discussed. The results show that it is necessary to consider the bogie frame’s flexibility in simulations which will aggravate the wheel-rail vibrations. The short wavelengths in combination with a certain speed could induce the bogie frame’s modal vibration and large track supporting stiffness will threaten the running safety of the vehicle which may also contribute to the formation of wheel out-of-roundness. Besides, the limit values of the rail weld irregularities are discussed to provide a reference for rail surface grinding from different aspects.

Quantification of longitudinal fastener stiffness and the effect on fastening system loading demand

Over the past 20 years, there have been at least 10 derailments due to spike fastener fatigue failures in North America. These fatigue failures have been considered a moderate to severe challenge that require manual walking inspections that are both time and labor intensive. These fatigue failures have been found to result from spike overloading due to lateral and longitudinal loads. To date, there has been limited quantification of the vertical, lateral, and longitudinal fastener forces in track. This paper quantifies the effect of fastener type on fastener load to account for various track types and locations. Laboratory experimentation was performed to quantify the stiffness of multiple fastening systems and this data was input into a previously validated analytical model to quantify the effect of stiffness on fastener loading. Additional laboratory experimentation was performed to quantify the relationships between both fastening system type and vertical loading and spike strain. While the laboratory data indicate a significant variance in stiffness between fastening systems, the model results indicate that the load transferred to the fastening system is less sensitive. However, spike strain data indicate the load path was affected by fastener type and vertical load. The characterization of longitudinal stiffness of multiple fastening systems and the relationship to spike load as presented can be used to advance track mechanistic-empirical design and improve rail neutral temperature prediction and track buckling models.

Numerical study on high-frequency effect of rail corrugation on subway-induced environmental vibrations.

Rail corrugation is a common phenomenon in railway engineering, but its high-frequency effects on environmental vibrations are neglected in most previous research. Therefore, a hybrid numerical method was proposed in this paper to analyze subway-induced ground vibrations, especially in the high-frequency range caused by rail corrugation. The analysis model composed of a three-dimensional (3D) load generation subsystem and a two-dimensional (2D) wave propagation subsystem was established based on the vehicle-track coupling method and finite element method, and validated by the measured data. Then the high-frequency effects under different tunnel depths and rail fasteners were further studied. The results show that high-frequency vibrations propagate radially from the tunnel wall to the surrounding soil and transmit to the ground by the dominant path under different tunnel depths. The increase of tunnel depths could result in more serious high-frequency effects in the vibration amplification region. When the depth changes from 17 to 29 m, the 250 Hz ground vibration at around 30 m away from the track increases by 5.6 dB. Besides, it was found that in the commonly used range, the reduction of fastener stiffness can effectively eliminate high-frequency ground vibrations, while there is a significant nonlinear relationship between fastener damping and high-frequency vibration. The findings of this paper could provide references for parameter design in subway construction and rail corrugation remediation, and help create better living environments.

Formation mechanism of short-pitch rail corrugation on metro tangent tracks with resilient fasteners

A type of short-pitch rail corrugation on tracks with resilient fasteners called ‘Vanguard’ fasteners is widely found on different metro lines in China. Field measurements and numerical calculations are used to investigate the cause of the corrugation formation. The corrugation with wavelengths of 30–60 mm occurs on both the curved and straight tracks through field measurements. Corrugation passing frequencies are in the range of 340–700 Hz. The frequencies of pinned-pinned resonance, the P2 resonance and the wheelset torsional resonance are far away from the corrugation passing frequencies. The investigated results show the vertical dynamic characteristic of the track is the main factor for occurrence of the short-pitch rail corrugation. The short-pitch rail corrugation arises by a wavelength-fixing mechanism of rail vertical bouncing on the resilient fasteners. The corrugation wavelength mainly is related to the vertical stiffness of the rail fasteners. Rail corrugation with wavelengths of 25–63 mm easily occurs on tracks with resilient fasteners with the vertical stiffness of less than 20 MN/m.

Study of Problems Related to Laying Ballastless Track in the Turnout of Ballasted Track at High-Speed Railway Stations

Due to the complex dynamic interactions of the vehicle-track system in the turnout of high-speed railway stations on a ballasted track, the geometric position of the line changes rapidly. In order to improve the stability of the line, the ballasted track in the turnout area of the stations can be replaced by a ballastless track. Based on the engineering background of laying ballastless track in the turnout area of Zhonglan’s high-speed railway station, this paper studies the subgrade reinforcement scheme, subgrade settlement prediction, and ballasted-ballastless track transition section setting. The result shows that, in order to meet the requirements of laying ballastless track in the turnout area, a reinforcement scheme of subgrade impact rolling, surcharge preloading, and closed water isolation on the subgrade surface is proposed. Based on the commonness and individuality of the grey Verhulst, hyperbola, and Deng Yinger prediction model, this paper optimizes the combination of the three models. The sum of squares of the minimum errors of the combined model is used as the objective function to solve the optimal weighting coefficient, and in this way the combined prediction model is constructed. Through the prediction comparison, we found that the accuracy of the three-model combination prediction model is better than any single- or two-model combination, and its adaptability and reliability are stronger and more reliable. This dynamic analysis model of vehicle tracks was established to carry out the dynamic response analysis under the conditions of fastener stiffness grading transition and ballast glue grading curing ballast bed transition. The results show that the dynamic response indexes under the two transition modes meet the requirements for the smooth running of trains. Due to the convenience of fastener stiffness transition construction and easier replacement, this measure is recommended.

Effect of dynamic stiffness of fasteners on vibration and acoustic radiation of a ballastless track

A new model for a single wheel rolling over a metro ballastless track is developed. It is used to carry out the analysis on the effect of dynamic characteristics of fastener on the vibration and noise radiation of the wheel and the track in the vertical direction, under the excitation of the wheel/rail uneven surfaces in detail. In this analysis, a rail is modeled as a Timoshenko beam resting on discrete rubber booted short sleepers, and the sleepers are connected with the slab through linear springs and damping units, the slab is modeled by using the FE method, the fastener is characterized by using the Poynting-Thomson model which takes into account that the stiffness and dumping of the fasteners vary with vibration frequency in their service. The dynamic characteristics of the fastener include the variation of its stiffness and damping with frequency. The analysis considers that the fastener dynamic stiffness increases with the excitation frequency while its damping decreases. The vibration and acoustic radiation of the wheel/track is, to varying degree, affected by the dynamic property of the fastener. The vibration and acoustic radiation of the sleeper and the slab is greatly affected by the dynamic property of the fastener. But the effect of the total noise level of the wheel and the track by the dynamic property of the fastener is not so large because the wheel and rail noise is dominant in the whole analyzed system. These conclusions have certain reference values for the study of the vibration and noise reduction measures of the wheel and track coupled system using the fastening characteristic.

Influences of friction self-excited vibration characteristics of various types of high-speed trains on rail corrugations in braking sections

To study the typical rail corrugation in braking sections at large slope downhills of Chinese high-speed railways, finite element models of wheelset-rail-brake systems of various high-speed trains are established in the present paper. Then, the complex eigenvalue analysis method is used to study friction self-excited vibration characteristics of wheelset-rail-brake systems in braking sections at large slope downhills. Finally, the influences of friction coefficient of the braking subsystem and vertical fastener stiffness of the wheelset-rail subsystem are analyzed. Results show that the friction self-excited vibration of the entire system induced by the stick–slip friction coupling effect of the wheelset-rail subsystem and the rolling-slip friction coupling effect of the braking subsystem is the dominant cause of rail corrugation. Then, the brake combination of the wheel disc and axle disc is more likely to cause the friction self-excited vibration of the wheelset-rail-brake system than the single braking mode. Parametric analyses show that with the increase of the friction coefficient of the braking subsystem, the self-excited vibration of the entire system increases, which means that the possibility of rail corrugation increases. Furthermore, with the increase of the vertical fastener stiffness of the wheelset-rail subsystem, the self-exicted vibration of the entire system first decreases and then gradually increases. When the vertical fastener stiffness is 30 MN/m, rail corrugations can be suppressed to a certain extent.

Analytical Nonlinear Modeling of Rail and Fastener Longitudinal Response

Comparatively little attention has been given to the quantification of fastener demands, especially in the longitudinal direction. Research quantifying fastener demands is justified by the more than 250 FRA reportable derailments on mainlines and sidings in the United States caused by “defective or missing spikes or rail fasteners” over the last 20 years. Failed fasteners are rarely caused by loads acting from a single direction (vertical, lateral, or longitudinal); they occur from a combination of these loads. A literature review identified that though multiple models have been developed for analyzing track, they were not designed to quantify fastener demands, especially those in the longitudinal direction, and some make assumptions that could be improved on based on more recent research into the mechanics of fastening system behavior. This paper advances the mechanistic–empirical (M-E) track analysis and design approach through the development, validation, and application of a 3D nonlinear parametric track model that quantifies longitudinal fastener demands. Key research findings include: bilinear approximations, in combination with considering the interaction between vertical loads and slip, were necessary to accurately quantify fastener forces; ballast and fastener stiffness had a direct logarithmic relationship on fastener load; and for well-supported sleepers, changes in component resistance to slip produced minimal changes in fastener demands because the vertical applied load increased the required load to produce slip. Going forward, this validated model could be used to quantify fastener and track demands for additional loading and operational scenarios to further optimize component design for improved track safety and reliability.

Parametric Study of Track Support Structure to Minimize the Occurrence Possibility of Rail Corrugation

Changing the track support structure is an effective method to suppress or eliminate rail corrugation in practical engineering. Rail corrugation on small-radius curves with booted short sleepers is the main research object in the present paper. A relevant finite element model of the wheelset-track system supported by booted short sleepers is built combined with the dynamic analysis of the vehicle-track system. The effects of various parameters of booted short sleeper structure on the wheel–rail friction-induced vibration are investigated by complex eigenvalue analysis. Considering the interaction of multiple parameters in the booted short sleeper structure, the multi-parameter fitting equation forecasting the possibility of rail corrugation is obtained using the least squares algorithm. Results show that wheel–rail friction-induced oscillation is a contributing factor in the formation of rail corrugation. Controlling wheel–rail friction-induced oscillation with a frequency of about 300 Hz is beneficial to suppress the possibility of rail corrugation in sections with booted short sleepers. Lower fastener stiffness or greater vertical fastener damping make it less likely that rail corrugation will occur. Rail corrugation is not generated when the vertical stiffness of the fastener is controlled below 20 MN/m in the booted short sleeper.

Dynamic simulation of HTS maglev vehicle/track coupled based on discrete elastic support track model

High-Temperature Superconducting (HTS) Maglev has the potential to run at high speed with the advantages of stability. As a kind of track transportation vehicle, the performance of vehicle-track coupled vibration will affect the comfort and safety of vehicle operation. In this paper, the track structure is analysed and designed based on the dynamic response of vehicle-track coupling. The model of long pillow embedded ballastless track is used to simulate the discrete permanent magnet track supported by the fastener and elastic rubber pad under the fastener. Through the calculation of the coupling system of HTS maglev train, the vehicle dynamic performance under different fastener stiffness, different fastener distance and different speed is obtained. The dynamic performance of the vehicle is quantitatively evaluated by the maximum acceleration of the car body, fluctuation of suspension gap and the running stability of the vehicle. The vibration responses of vehicles and tracks under different working conditions are discussed, and reasonable design suggestions are given.

Features of the influence of intermediate rail fastenings on the operational durability of rails

Heat-strengthened rails of the R65 type are the main type of rails used on the railway network of Russian Railways. Reducing the number of cropped and acutely defective rails is possible due to the rational use of the design features of intermediate rail fasteners and their current content.The article presents study results of the stiffness influence of intermediate fasteners on the operational durability of rails. The general statistics of the use of various types of intermediate rail fastenings on the network of Russian railways is considered. The main results of previously published studies on the effect of the stiffness of intermediate rail fasteners on the accumulation of contact fatigue damage in rails are briefly presented.Calculations of the accumulation of contact-fatigue damages in rails, carried out by the authors, are based on the data on the vertical and horizontal transverse stiffness of intermediate rail fastenings obtained from the results of bench tests. Calculations of the accumulation of contact-fatigue damage were carried out using the “Universal Mechanism” software package. In the process of modeling, four types of intermediate rail fasteners were considered: ARS-4, ZhBR-65Sh, ZhBR-65PShM and W-30. Calculation results were obtained for a curve with a radius of 650 m on a continuous welded track section.

Improved indirect measurement of the dynamic stiffness of a rail fastener and its dependence on load and frequency

The dynamic stiffness of rail fasteners has a significant effect on the noise radiated by the rails as well as the vibration transmitted to the underlying structures, such as bridges, tunnels or track at grade. This study investigates the load- and frequency-dependence of a WJ-2A fastener which is commonly used in urban rail transit systems in China. This is a two-stage fastener with a rail pad and a baseplate pad separated by a steel plate. Results are obtained using the indirect measurement method in the frequency range 30 to 1000 Hz. The dynamic stiffness of the individual components is investigated as well as that of the whole fastener system and the combined stiffness of the components is verified by comparison with the whole fastener system. A numerical model of the test rig is used to provide understanding of various artefacts that are observed in the measurements and corrections are proposed to minimise their effects on the measured results. These allow for the differences between the response at the measurement positions and at the ideal positions at the interfaces between the fastener system and the rig. The stiffness magnitude of the rail pad, baseplate pad, and whole fastener system increases strongly with increasing static preload and increases weakly with increasing frequency; it is important to take these effects into account in prediction models for noise and vibration. The damping loss factors are not strongly dependent on preload or frequency. To describe the frequency-dependence, a fractional derivative Kelvin-Voigt (FDKV) model is introduced and is fitted to the dynamic stiffness with the help of a genetic algorithm method. The dynamic stiffness of the whole fastener system is influenced by both the rail pad and the lower baseplate pad. It is important to take account of both of them, as well as the internal resonance of the baseplate assembly which appears at around 1 kHz.

Testing research on frequency-dependent characteristics of dynamic stiffness and damping for high-speed railway fastener

In this paper, the Vossloh W300 fastener currently used in China's high-speed railway is taken as the research object. Combined with the requirements of ISO 10846 series standards and the knowledge of the author, to the best of the authors knowledge, the first high-frequency dynamic stiffness test system for elastic elements of rail fastener has been successfully developed and built. By taking the influence of preloading into consideration, the vertical and lateral dynamic frequency-dependent stiffness and loss factor of high-speed railway W300 fastener at 5~1250 Hz were obtained through the 1:1 test model coupling test method for the first time. Referring to the prediction method of high-speed railway wheel-rail vibration and noise, and factoring in the high-speed rotating, the infinite length of plate track structure and high-speed movement of sound source to wheels, the Kelvin - Voigt simulation sub-model of fastening system was added to predict and analyze the difference between the total sound pressure levels of the wheel and rail that is relative to the standard point under the constant stiffness and frequency-dependent stiffness of fastener. The results indicate that the frequency-dependent characteristics of fastener stiffness have significant impact on the spectrum of wheel-rail interaction forces, total sound pressure levels of rail and wheel-rail. The total sound pressure level of the wheel-rail relative to standard point, which factors in the frequency-dependent stiffness of fastener was approximately reduced 2.6 dB, that is, the frequency-dependent stiffness of fastener can rectify the overestimation of wheel-rail sound pressure level by stiffness coefficient.

Analysis of parameters on the wheel–rail P2 force of subways

An experiment of falling wheels was performed in this study along with full-field tests, for a type of subway train on four subway lines. The results confirmed that 40–80 Hz vibration signals on the ground and train are caused by the wheel–rail P2 force. Vehicle–track-coupled dynamics models were created where the single-layer elastic support model, double-layer elastic support model and floating slab track model were considered. The results were validated by available experimental data and three types of theoretical models: Jenkins, Winkler and double-beam model. This shows that the amplitude of the P2 force increases with larger suspended rail joint angle, higher train speed, heavy unsuspended mass and stronger fastener stiffness. Besides, both fastener damping and the vertical stiffness of primary suspension enabled control of the amplitude of the P2 force in a limited interval. Supporting stiffness of track and unsprung mass played a key role in the frequency of the P2 force. However, the vertical stiffness of the primary suspension had a reduced effect on the frequency of P2 force as compared with the supporting stiffness. Thus, for an effective change to the supporting stiffness, the fastener stiffness could be changed accordingly.

Influence of core stiffness on the behavior of tall timber buildings subjected to wind loads

This study analyzes the feasibility of the use of cross-laminated timber (CLT) as a load-bearing structural element in a 40-story building based on Chinese design requirements. The proposed design of the high-rise concrete—CLT building utilizes the core—outrigger system. Concrete is used for the central core and outriggers, and CLT is used for the rest of the structure of the building. Finite element models with different types of connections were developed using SAP2000 to analyze the lateral behavior of the building under wind action. The finite element models with rigid connections deduce the wind load distributions on individual structural elements, which determine the total number and the stiffness of fasteners of the CLT panels. Accordingly, spring links with equivalent stiffness that simulate the mechanical fasteners were employed in SAP2000. The results indicate that CLT increases the lateral flexibility of the building. A closed concrete core was substituted by two half cores to measure the requirement of the maximum lateral deflection. However, the acceleration at the building top still exceeded the limitation prescribed in Chinese Code JGJ 3–2010 owing to the lightweight of CLT and decreased stiffness of the hybrid building. To restrict this top acceleration within the limit, further approaches to increase the stiffness in the weak direction of the building are required. Methods such as the modification of the floor layout, increase in the thickness of walls, and addition of extra damping capacity should be considered and verified in the future.

Reliability-based assessment of high-speed railway subgrade defect

In this paper, a dynamic response mapping model of the wheel-rail system is established by using the support vector regression (SVR) method, and the hierarchical safety thresholds of the subgrade void are proposed based on the reliability theory. Firstly, the vehicle-track coupling dynamic model considering the subgrade void is constructed. Secondly, the subgrade void area, the subgrade compaction index K30 and the fastener stiffness are selected as random variables, and the mapping model between these three random parameters and the dynamic response of the wheel-rail system is built by using the orthogonal test and the SVR. The sensitivity analysis is carried out by the range analysis method. Finally, the hierarchical safety thresholds for the subgrade void are proposed. The results show that the subgrade void has the most significant influence on the carbody vertical acceleration, the rail vertical displacement, the vertical displacement and the slab tensile stress. From the range analysis, the subgrade void area has the largest effect on the dynamic response of the wheel-rail system, followed by the fastener stiffness and the subgrade compaction index K30. The recommended safety thresholds for the subgrade void of level I, II and III are 4.01m2, 6.81m2 and 9.79m2, respectively.

Effect of Lap Length and Stiffness of Peel-Stop Fasteners in Single Lap Joints

Strength tests on single lap joints with one adhesive (AV138/HV998) and one adhesive layer thickness (0.5 mm), three peel stoppers (brass bolt, nylon bolt and steel pin), and four lap lengths (12.5 mm, 25 mm, 40 mm and 100 mm) were conducted to investigate the effects of varying the lap length and stiffness of the peel-stop fasteners. Joint failure stress decreased, but failure force increased with lap length. Furthermore, joint failure stress was higher with the peel stopper. The effect of the brass-bolt peel stoppers was significant, whereas the effects of the nylon bolts and steel pins were smaller than that of the brass bolts. This indicates that the axial clamp strength and stiffness of the peel stopper are important factors in the shear strength of the lap. In addition, the effect of the stopper was negligible for the 12.5 mm lap. The reason is that the shear strength in the case of the 12.5 mm lap was large and thus the effect of the peel stopper was comparatively small. Moreover, the strength of the 100 mm lap reached the adherent material’s strength.