Klaus Knothe

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.

Review on rail corrugation studies

In Japan, rail corrugations had not been so serious formerly, but it began to be prevailing in recent years. In order to prevent the generation of rail corrugation, many studies have been reported in the world since the end of 19th century, but theories on them have not explained the formation mechanism perfectly and no perfect countermeasures have been established so far. Thus, the studies on corrugation are getting more important, because generation of corrugation shows a tendency to increase due to the speed-up of trains, to the introduction of new vehicles, etc. In such a situation, three authors review the studies on them in the past and those carried out now in the world and more precisely in Japan. The review is on bibliographies, attempts in the 1970s, classification of rail corrugation, short-pitch corrugation and studies in Japan in recent years.

An extended linear model for the prediction of short pitch corrugation

Abstract According to Grassie and Kalousek (S.L. Grassie and J. Kalousek, Proc. Inst. Mech. Eng., Part F, 207 (1993) 57–68) for most of the corrugation problems causes and treatments are known. Only roaring rails or short pitch corrugation still are unsolved problems. This paper presents an advanced linear model for the prediction of short pitch corrugation. It bases on the idea of a feedback between structural dynamics and wear. Since the last presentation in 1990 (K. Hempelmann, F. Hiss, K. Knothe and B. Ripke, Wear , 44 (1991) 179–195), the model of the contact mechanics has been improved. The calculation of global corrugation growth rates provides an easier and better understanding of the results. Two main mechanisms of the corrugation formation have been identified. The contact mechanics provide a filter (contact filter) which suppresses the growth of very short wavelength corrugation. Stiff loci in the vertical structural dynamics, mainly of the track, cause high contact forces and lead finally to corrugation. Some results of parameter studies are presented, others and their influence on the formation of corrugation are summarized.

Determination of temperatures for sliding contact with applications for wheel-rail systems

Contact temperatures and temperature fields of components in relative sliding motion can be analyzed by Laplace transforms and the method of Greens functions. For the case of constant and ellipsoidal pressure distribution the temperatures obtained agree with the results of earlier work. The solution technique can also be used to solve arbitrary pressure distributions, which, coupled with the general normal contact problem, leads to extended solutions. The case of loadings with fluctuations due to surface roughness and indents are investigated. It can be shown that each kind of fluctuation causes a rise of the maximum contact temperature. All applications are for wheel-rail systems. The results are discussed.

A comparison of analytical and numerical methods for the calculation of temperatures in wheel/rail contact

Abstract The maximum surface temperature during rolling contact of railway wheels with sliding friction can be estimated using Blok’s flash temperature formula. For a more detailed investigation, semi-analytical and numerical methods are available. A survey of various methods is given and an efficient approach is proposed for Hertzian contact. The actual contact temperature is confined to a very thin surface layer. Due to continuous frictional heating, the bulk temperature of the wheel increases with time. For the long-term behaviour of the wheel temperature, not only the convection at the free wheel surfaces but also the heat conduction from the wheel into the colder rail has to be considered. Practical consequences of the theoretical results are discussed.

Advanced Contact Mechanics–Road and Rail

The development of contact theories and numerical formula for various applications is a field which expands rapidly. This publication focuses on the rolling contact problem both for tire-road and wheel-rail contact. For the tire-road application a central problem is the modeling of the composite structure of the tire under internal pressure and axle load. One actual contact problem is the rolling on soft soil, which is discussed as the main application. In the wheel-rail case the contact area is much smaller and much more emphasis has been laid on the treatment of material changes, wear and creep phenomena. These approaches are discussed in detail as well as a more recent finite element formulation following the arbitrary Lagrange-Eulerian concept. Ideas about damage mechanisms finish the article.

Normal and tangential contact problem of surfaces with measured roughness

Experimental results show, that measured creepforce-creep-curves differ in some characteristical points from the analytical one first found by Carter [Proc. R. Soc., Ser. A 112 (1926) 151]. In correspondence to those experiments, the results from calculations with a deterministic two-dimensional contact model prove, that for the rail/wheel contact the initial slope of that curve depends on the characteristics of the effective micro-roughness on the running band, even when dry conditions are considered. Due to the different definition of the real area of contact in the here presented deterministic approach the results look contradictory to the ones from a Greenwood/Tripp-like model [Trans. ASME, Ser. E, J. Appl. Mech. 34 (1967) 153]. Beside the standard roughness parameters of the roughness heights the highest spatial frequencies contained in the roughness pattern have a strong influence on the gradient of the linear region of the creepforce-creep-curve.

The formation of wear patterns on rail tread

Short wavelength corrugations of railway tracks are described by a linear model of transient dynamics and a wear feedback loop. The description is based on the Fourier decomposition of the profile irregularities. The presented results show that corrugations are a direct consequence of the resonance peaks of the dynamical components, e.g. the pinned-pinned mode of the track, and depend strongly on the initial profile irregularities.

Simulation of High Frequency Vehicle-Track Interactions

SUMMARY An effective time domain method for simulating the vertical vehicle-track interactions for low and high frequencies is presented. To be able to investigate the effects of local defects of the track (eg voided sleepers) on contact forces and loads and long-term deterioration of track components, a discrete track model based on finite elements is necessary. The track model developed is extremely accurate and is able to consider irregularities and nonlinearities in the track structure. The number of sleepers to be considered is chosen so that the infinite extension of the track can be dealt with approximately. For excitation due to short wavelengths like short pitch corrugation or wheel flats, nonlinear contact mechanics has to be considered. The time-step integration algorithm is based on a modal decomposition of linear substructures and is therefore absolutely stable. The method includes the effects of moving masses and is valid for train speeds up to 500 m/s. The capacity of the algorithm is demon...

Short wavelength rail corrugation and non-steady-state contact mechanics

J. J. Kalker has been the first to consider non-steady-state or transient contact mechanics. Based on Kalker the second author developed a linear contact model for the non-steady-state rolling contact of a wheel running over slightly corrugated rails. The theoretical investigations are concentrated on linear, non-steady-state contact mechanics superimposed to a nonlinear reference state. The reference state is given by the running behaviour of a wheelset due to traction, curving or hunting. For the linear, non-steady-state analysis Kalkers theory has to be modified to predict wear rates in dependency of the corrugation wavelengths. As a result corrugations are only amplified in the range between 2 and 10 cm. Therefore, non-steady-state contact mechanics and wear are responsible for a wavelength fixing mechanism. Structural mechanics of the rail indicate that wavelength in this range is predominantly amplified.