A model of the development of rail-head acoustic roughness on tangent track has been formulated. The model consists of a two-dimensional time domain wheel-rail interaction force calculation, with the normal force used as the input to a two-dimensional rolling contact and wear model. The possibility of multiple wear mechanisms arising from stress concentrations is considered by using a wear coefficient that can vary with the conditions
at each point in the contact. The contact model is based on a variational technique, taking account of non-Hertzian and transient effects. A novel feature of the rolling contact model
is the introduction of a velocity-dependent friction coefficient. In rolling contact this leads to a high frequency stick-slip oscillation in the slip zone at the trailing edge. Roughness development depends on the dynamics of the track. Roughness growth
has often been linked to the pinned-pinned frequency and other resonances of the coupled track and vehicle system. Here the effect of different vehicle and track parameters on track
dynamics, wear and roughness development has been examined. Rail dampers are studied as they change the dynamic response of the track. Results are presented in the form of roughness growth rate functions both for individual vehicle types and for mixed traffic. The model parameters match those at a site used for measurements of roughness
development taken by Deutsche Bahn AG as part of the EU project Silence. The study shows that it is important to include non-Hertzian effects when studying roughness with wavelengths shorter than 100 mm. With a non-Hertzian contact model, no
mechanism has been found for consistently increasing roughness levels. The model predicts that roughness wavelengths shorter than the contact length will wear away. Rail
dampers are shown to reduce the pinned-pinned frequency and smooth the peaks and troughs in the track receptance. Rail dampers also reduce the dynamic wheel-rail
interaction forces, especially around the pinned-pinned resonance, and shift the force spectrum to lower frequencies or longer wavelengths. However, rail dampers are not
predicted to affect roughness growth rates significantly

Croft, Briony Elizabeth

English

Southampton (e-Prints Soton)

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When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given e.g.AUTHOR (year of submission) "Full thesis title", University of Southampton, name of the University School or Department, PhD Thesis, paginationhttp://eprints.soton.ac.uk   UNIVERSITY OF SOUTHAMPTON  FACULTY OF ENGINEERING, SCIENCE AND MATHEMATICS  Institute of Sound and Vibration Research         The Development of Rail-head Acoustic Roughness  by  Briony Elizabeth Croft      Thesis for the degree of Doctor of Philosophy  October 2009  UNIVERSITY OF SOUTHAMPTON  ABSTRACT FACULTY OF ENGINEERING, SCIENCE AND MATHEMATICS INSTITUTE OF SOUND AND VIBRATION RESEARCH  Doctor of Philosophy THE DEVELOPMENT OF RAIL-HEAD ACOUSTIC ROUGHNESS by Briony Elizabeth Croft  A model of the development of rail-head acoustic roughness on tangent track has been formulated. The model consists of a two-dimensional time domain wheel-rail interaction force calculation, with the normal force used as the input to a two-dimensional rolling contact and wear model. The possibility of multiple wear mechanisms arising from stress concentrations is considered by using a wear coefficient that can vary with the conditions at each point in the contact. The contact model is based on a variational technique, taking account of non-Hertzian and transient effects. A novel feature of the rolling contact model is the introduction of a velocity-dependent friction coefficient. In rolling contact this leads to a high frequency stick-slip oscillation in the slip zone at the trailing edge.  Roughness development depends on the dynamics of the track. Roughness growth has often been linked to the pinned-pinned frequency and other resonances of the coupled track and vehicle system. Here the effect of different vehicle and track parameters on track dynamics, wear and roughness development has been examined. Rail dampers are studied as they change the dynamic response of the track. Results are presented in the form of roughness growth rate functions both for individual vehicle types and for mixed traffic. The model parameters match those at a site used for measurements of roughness development taken by Deutsche Bahn AG as part of the EU project Silence. The study shows that it is important to include non-Hertzian effects when studying roughness with wavelengths shorter than 100 mm. With a non-Hertzian contact model, no mechanism has been found for consistently increasing roughness levels. The model predicts that roughness wavelengths shorter than the contact length will wear away. Rail dampers are shown to reduce the pinned-pinned frequency and smooth the peaks and troughs in the track receptance. Rail dampers also reduce the dynamic wheel-rail interaction forces, especially around the pinned-pinned resonance, and shift the force spectrum to lower frequencies or longer wavelengths. However, rail dampers are not predicted to affect roughness growth rates significantly.  40 Corrugation growth has also been linked to standing waves in the track between the successive wheels of a bogie [Igeland, 1996]. The bogie wheelbase was found to be an important parameter and, if the wheelbase is equal to an integer number of sleeper spacings, can lead to amplification of pinned-pinned resonance effects. Separate work by Manabe [2000] using an analytical model without discrete rail supports also determined that standing waves between multiple wheels are a possible wavelength fixing mechanism for corrugation. This mechanism may explain why observed corrugation wavelengths do not always vary linearly with vehicle speed.  Igeland and Ilias [1997] compared corrugation development predictions developed using different wheel-rail interaction models, achieving similar results from both models. They found that non-linear and linear models give different predictions for roughness growth. Ilias [1999] linked stiffer rail pads with higher corrugation growth, and also noted that parametric excitation of the system is important for corrugation growth.  In an attempt to explain the lack of velocity dependence of corrugation wavelengths observed in practice, Müller [1999, 2000] investigated short pitch corrugation using a linear model. He found that, as well as the pinned-pinned resonance, other resonances and anti-resonances can dominate the development of the rail profile. The dominant wavelength that arises where there are multiple resonances is determined by a contact mechanical filtering function that limits corrugation growth to a particular wavelength band.  J.B. Nielsen* [1999] neglected the dynamics of the track and vehicle, reducing the system to a cylinder rolling over a periodically varying surface. The development of corrugation then becomes purely a contact mechanics problem, treated using an analytical model including some non-Hertzian effects arising from the surface corrugation. J.B. Nielsen’s model predicts a minimum wavelength at which corrugation will occur, corresponding to the filtering effect of the size of the contact patch. A characteristic wavelength at which corrugation is more likely to develop was also identified, determined by the magnitude of the creep and the length of the contact. This is a constant wavelength effect, not a constant frequency effect like the pinned-pinned resonance. For wheel-rail contact the characteristic                                                  * N.B. in general, references to ‘Nielsen’ mean ‘J.C.O. Nielsen’  122 The effect of different track and vehicle parameters on the dynamic interaction force between a wheel or wheels and the rail has been investigated. It is important to divide the rail into at least eight elements in each sleeper bay. If the rail pads are relatively soft it is important to include more than one wheel in the model, as the wheels are coupled by the track and can interact to give a different interaction force spectrum to that if a single wheel is considered. Including more than one wheel is less important if the track has stiff rail pads or rail dampers, since the track decay rate is higher, at higher frequencies, leading to less interaction between the wheels in the model. However, for uniformity, four wheels are included in the interaction force model as standard.  The roughness of the rail is the single parameter that has the most effect on the interaction force spectrum. Differences are also seen between different vehicle types passing over the same track and rail roughness profile, as a result of their different speeds and static loads. The stiffness of the rail pads also has a significant effect on the interaction force between wheels and rail. Variations in the wheel spacing and unsprung mass of the wheel have less effect on the force.  Adding rail dampers to the track shifts the pinned-pinned frequency of the track and consequently shifts the peak in the force spectrum corresponding to this resonance to longer wavelengths.  241 The roughness growth rate has therefore been examined for two different track forms, one with relatively soft rail pads of 200 MN/m stiffness and the other with relatively stiff rail pads of 800 MN/m stiffness. The addition of rail dampers to the track has also been included in both the modelling work and the measurements. Three different vehicle types (listed in Table 4.1) are considered as representatives of the type of traffic operating at the Gersthofen site. The approximate proportions of wheel passages due to each vehicle type is known, and has been used to estimate a ‘mixed traffic’ roughness growth rate from the model results.   When calculating the interaction force between the wheel and rail for track with soft rail pads, it is important to include more than one wheel in the vehicle model since the track decay rate is low and allows interaction between successive wheels coupled by the rail. However, when using a non-Hertzian contact model to predict the wear of the rail and the roughness growth rates, similar results were obtained from a model with a single wheel and a model with four wheels. Including multiple wheels therefore does not significantly affect the predicted roughness growth rates.   Roughness growth rate results have been compared from three different versions of the model. If a Hertzian contact model is used, roughness is predicted to grow significantly in the one-third octave wavelength bands between 12.5 mm and 40 mm. Outside this range, roughness is predicted to grow slightly at shorter wavelengths and decrease slightly or remain stable at longer wavelengths. However, if a non-Hertzian contact model is used, the results are very different. Roughness is then predicted to decrease in all wavelength bands, particularly at wavelengths shorter than 25 mm. The inclusion of a velocity-dependent coefficient of friction causes some variation in the wear of each particular case, and in some cases at some wavelengths roughness growth is positive. When roughness growth rates are averaged over many initial rail profiles however there is very little difference in the predicted results compared with when a constant coefficient of friction is used with the non-Hertzian contact model.  The non-Hertzian contact models, therefore, do not support any tendency of the rails to become rougher over time. In fact, the model predicts that, as long as only longitudinal forces and creep are significant, tangent track with an initially low level of broadband roughness should become smoother under the passage of many wheels. This also assumes  242 that the wheels are smooth, since the combined roughness of the wheels and rails provides the excitation of the system.  Roughness measurements over two years at the Gersthofen test site do not show any significant or consistent tendency of the rails to become rougher over time at any wavelength. There is some evidence to suggest that rails may become smoother over time, as predicted by the model. However, the differences observed over the two-year period are not large enough in most wavelength bands to give confidence that they are not an artefact of normal measurement variance.  Neither the modelled nor the measured roughness growth rates indicate that the installation of the rail dampers will have a significant effect on the development of broadband acoustic roughness over time, either positive or negative. Also, the roughness growth rate results presented in this chapter do not suggest that roughness should develop differently on track with different rail pad stiffnesses.   The roughness development predicted by a non-Hertzian contact model is generally independent of the rail pad stiffness, the wheel spacing, the pinned-pinned resonance and the addition of rail dampers. It is therefore largely independent of the track dynamics (the effect of vehicle speed on roughness growth rates has not been explicitly examined, although different vehicle types have different speeds). So, although the wheel-rail interaction force is highly dependent on the dynamics of the track and vehicle system, it appears that the resulting roughness growth rate is not.  247  Future work on roughness development and corrugation should consider that if Hertzian contact is assumed, any change in the wheel-rail interaction forces leads to a change in the predicted wear. The Hertzian assumption therefore results in an exaggerated relationship between the resonances of the track and vehicle system and the wear of the rail.   The measurements taken by Deutsche Bahn AG as part of the Silence project are valuable because there are very few documented cases of roughness measurements being repeated at the same location over several years. Even over two years, the roughness at the site has not changed enough to be sure that the observed decreases in roughness are not due to measurement variability. These measurements should be continued. It is commonly accepted that broadband roughness on tangent track does increase, but roughness growth is not necessarily linear with time. Smooth track (possibly in conjunction with smooth wheels) may remain in good condition over many years, while track with initially high roughness levels may worsen more rapidly. At the Gersthofen test site initial roughness levels were uniformly low so it has not been possible to investigate differences in roughness development caused by the initial level. It would be useful to prove that roughness development is not linear, and to identify the relationship between initial or existing roughness level and roughness development.  More measurements of roughness development over time are required to validate the roughness growth model and to understand the mechanisms of roughness growth. A useful long term experiment would be to take roughness measurements at six-monthly intervals over many years at locations with initially low roughness levels. It would also be useful to compare measurements from track with predominantly disc-braked vehicles, with roughness levels on track where the traffic is mostly tread braked. This would assess whether higher wheel roughness leads to higher roughness growth on the rails, possibly as a result of plastic deformation. Other factors that might be monitored in addition to the roughness itself include traffic axle loads, lateral forces and/or wheelset alignment, and traction and braking forces. However, these would be more difficult (and perhaps impossible) to collect on the time scales of roughness development.  In terms of short-pitch corrugation research, the absence of any mechanism for corrugation formation found here suggests that the search for causes of corrugation should concentrate on lateral effects. Corrugation is more common on curves than on tangent track, where  248 lateral dynamics are more important. Discrete longitudinal effects such as rail joints or wheel-rail defects could also be investigated further as possible initiators of corrugation. In addition, metallurgical factors that have not been considered in this work could be important, including hardness and variations or defects in the crystalline structure of the rail steel.   In the rolling contact analysis used here, the rail and the wheel have been treated as half-spaces. Track and wheel dynamic effects have been included by means of their effect on the normal wheel-rail interaction forces. The stick-slip effect identified with the velocity-dependent friction law is a very high-frequency phenomenon. It has a wavelength of the order of 1.2 mm in steady rolling, which corresponds to about 25 kHz at typical train speeds. It could conceivably interact with resonances of the track or wheel system. Further investigation is needed including the track and wheel dynamics in the rolling contact analysis to examine if the stick-slip oscillation might lock into another resonance of the system.  

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The development of rail-head acoustic roughness

The development of rail-head acoustic roughness

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