Stuart L. Grassie

Modelling of Railway Track and Vehicle/Track Interaction at High Frequencies

Abstract A review is presented of dynamic modelling of railway track and of the interaction of vehicle and track at frequencies which are sufficiently high for the tracks dynamic behaviour to be significant. Since noise is one of the most important consequences of wheel/rail interaction at high frequencies, the maximum frequency of interest is about 5kHz: the limit of human hearing. The topic is reviewed both historically and in particular with reference to the application of modelling to the solution of practical problems. Good models of the rail, the sleeper and the wheelset are now available for the whole frequency range of interest. However, it is at present impossible to predict either the dynamic behaviour of the railpad and ballast or their long term behaviour. This is regarded as the most promising area for future research.

Rail Corrugation: Characteristics, Causes, and Treatments

Rail corrugation is a phenomenon of great diversity but appears now to be substantially understood. This review proposes some differences in classification of the phenomenon to take account of work undertaken since a widely cited review was published by Grassie and Kalousek in 1993, it attempts to fill holes in an overall understanding of the problem, and answers questions that remained open in 1993 and several that have arisen since. All types of corrugation that have been documented to date are essentially constant-frequency phenomena. By treating the vehicle—track system in its entirety, treatments are proposed that impinge upon track and vehicle design as well as upon the wheel—rail interface where corrugation appears. There is no neat solution to rail corrugation, but it can be treated comprehensively and in many cases also prevented by using products that are already commercially available. Since the frequency of common wavelength-fixing mechanisms varies roughly in the range 50—1200 Hz, trains travelling at different speeds can produce corrugation of substantially similar wavelength by different mechanisms in different locations. Although historical data can no longer be checked, this is the most likely explanation of the belief that rail corrugation was a substantially constant-wavelength phenomenon.

Measurement of railhead longitudinal profiles: a comparison of different techniques

The underlying principles are considered plus attractions and limitations on the practical application of three different types of longitudinal rail profile measuring equipment which can be used in a vehicle. Axlebox accelerometer systems are a good compromise for obtaining statistical profile data at line speeds. Other accelerometer-based systems are the best means of obtaining data at a few metres per second but are corrupted by extraneous vibration. Both these and chord-based systems are compromises in most practical circumstances where there is significant extraneous vibration.

RAIL CORRUGATION ON NORTH AMERICAN TRANSIT SYSTEMS

Abstract This paper describes work which has greatly improved our understanding of the processes by which rail corrugation typically develops on North American Transit systems. Several types of corrugation were identified from observations and measurements in the field. A new mechanism for corrugation formation is proposed for the most common type of corrugation observed, and a mathematical model has accordingly been developed which combines both low frequency and high frequency behaviour of the vehicle/track system. The mathematical model itself, plus results from it and from measurements are discussed here. Novel recommendations for corrugation mitigation are made.

Short wavelength rail corrugation: field trials and measuring technology

Abstract Two field trials were set up during the period 1974–1984 to help understand the mechanism of formation of short pitch rail corrugation on British railways. These required the development of novel measuring equipment: a trolley profilometer and a straight edge device with microcomputer-based recording equipment. Regular monitoring was undertaken of test sections of main-line track. It was found that this type of corrugation arises from a mechanism of differential wear, in which corrugation troughs wear barely 10% more than the peaks. Grinding significantly reduces the roughness on new rail, so that even after 3 months of traffic the spectrum of roughness on new unground rail is greater than that on ground rail by a factor of 10. There is a corresponding delay in the formation of corrugation. Transverse marks arising from the grinding operation and with a pitch of 25–30 mm were worn away under traffic. Wheelslip of up to 15% was measured on a locomotive in service, which is sufficient to give the temperatures required for transformation of a thin layer of the rail surface to martensite. No explanation was found for the corrugations periodicity.

Models of Railway Track and Vehicle/Track Interaction at High Frequencies: Results of Benchmark Test

SUMMARY Results have been compared of eight contributions to a benchmark test which was written for programs developed to examine the high frequency dynamic interaction of railway vehicles and the track. Participants were requested to consider a vehicle passing over uniform, sinusoidal corrugation, and to calculate the vertical rail acceleration and various forces and bending moments in rail and sleeper. From the results for the wide variety of time and frequency domain models which were used it is concluded that substantially identical results can be obtained from both types of model in the majority of conditions considered in the test. There is a greater variation in results between the 5 frequency domain models used in these submissions than between the 2 high frequency time domain models.

Traction and curving behaviour of a railway bogie

In conventional railway systems, vehicles exert traction and must also negotiate curves. The creep forces between a bogie and the track are shown here for a wide range of curve radii (300–1800 m), a wide range of applied traction (traction ratios of 0, 0.14 and 0.28) and for bogies of widely different yaw stiffness, which is the factor that most affects a bogie’s curving performance. Traction destroys the steering performance of any bogie, increasing the lateral displacement of the critical leading wheelset and also its angle of attack, thereby increasing the tendency for ‘squeal’ noise. The resultant wheel/rail creep forces also typically increase and change orientation significantly. There is a significant difference in creep force across both wheelsets, with slip occurring first at the leading wheel on the high rail. For modest levels of applied traction, low yaw stiffness improves curving performance. However, low yaw stiffness becomes ever less beneficial as traction increases. Indeed, at levels of applied traction typical of modern locomotives, a bogie and the wheelsets within it behave essentially as a rigid bogie, regardless of the yaw stiffness.

A CONTRIBUTION TO DYNAMIC DESIGN OF RAILWAY TRACK

SUMMARY A linear technique based on Fourier Transforms is presented to calculate the dynamic response of railway track and vehicles to non-sinusoidal irregularities on the running surfaces of wheel and rail. The model has been validated tentatively by comparison of calculation with data measured in a field experiment with a variety of irregular wheels and types of track. Calculation underestimates the difference in sleeper bending moment and overestimates the difference in contact force arising from the use of stiff and resilient railpads. An example is given in which the model is used to help in design of track by indicating the relative importance of different damage mechanisms.

Dynamic Models of the Track and Their Uses

Mathematical models developed for the track’s response to dynamic excitation in the frequency range 5Hz–5kHz are reviewed, particularly with regard to their use in practice. Experimental data strongly suggest that for vertical excitation the most significant deficiency of a model of a beam on a uniform, continuous support is that it does not satisfactorily represent behaviour at the so-called “pinned-pinned” resonance. The severity of this deficiency has yet to be quantified satisfactorily. The errors incurred in neglecting loss of contact are also relatively poorly explored. A variety of measurements in track indicate that typical ballast stiffnesses are in the range 30–80MN/m per railseat; the stiffnesses of 5mm and 10mm elastomeric railpads are typically about 250MN/m and 100MN/m respectively. To model the lateral response satisfactorily it is necessary to respresent both bending and torsion of the rail at lower frequencies, and bending of the web for frequencies of about 1500Hz or more. Track longitudinally behaves as a strong viscous dashpot in parallel with an elastic spring.

Traction, curving and surface damage of rails, Part 2: Rail damage

The tangential forces on a rail resulting from a combination of traction and curving are considered. These forces are a significant component of both wear and shakedown. These two simple mechanisms can be used to understand most types of damage that occur on both rails and wheels.