A History of Railway Vehicle Dynamics

I. INTRODUCTION

The railway train running along a track is one of the most complicated dynamical systems in engineering. Many bodies comprise the system and so it has many degrees of freedom. The bodies that make up the vehicle can be connected in various ways and a moving interface connects the vehicle with the track. This interface involves the complex geometry of the wheel tread and the rail head and nonconservative frictional forces generated by relative motion in the contact area.

The technology of this complex system rests on a long history. In the late 18th and early 19th century, development concentrated on the prime mover and the possibility of traction using adhesion. Strength of materials presented a major problem. Even though speeds were low, dynamic loads applied to the track were of concern and so the earliest vehicles used elements of suspension adopted from horse carriage practice. Above all, the problem of guidance was resolved by the almost universal adoption of the flanged wheel in the early 19th century, the result of empirical development, and dependent on engineering intuition.

Operation of the early vehicles led to verbal descriptions of their dynamic behaviour, such as Stephenson’s description of the  kinematic oscillation, discussed below. Later  in  the  19th century  the  first  simple  mathematical  models  of  the  action  of  the  coned  wheelset  were introduced  by  Redtenbacher  and  Klingel,  but  they  had  virtually  no  impact  on  engineering practice. Actually, the balancing of the reciprocating masses of the steam locomotive assumed much greater importance.

A catastrophic bridge failure led to the first analytical model in 1849 of the interaction between vehicle and flexible track.

The growing size of the steam locomotive increased the problem of the forces generated in negotiating curves, and in 1883 Mackenzie gave the first essentially correct description of curving. This became the basis of a standard calculation carried out in design offices throughout the era of the steam locomotive.

As train speeds increased, problems of ride quality, particularly in the lateral direction, became more important. The introduction of the electric locomotive at the end of the 19th century involved Carter, a mathematical electrical engineer, in the problem, with the result that a realistic model of the forces acting between wheel and rail was proposed and the first calculations of lateral stability carried out.

Generally, empirical engineering development was able to keep abreast of the requirements of ride quality and safety until the middle of the 20th century. Then, increasing speeds of trains and the greater potential risks arising from instability stimulated a more scientific approach to vehicle dynamics. Realistic calculations, supported by experiment, on which design decisions were based were achieved in the 1960s and as the power of the digital computer increased so did the scope of engineering calculations, leading to today’s powerful modelling tools.

This chapter tells the story of this conceptual and analytical development. It concentrates on the most basic problems associated with stability, response to track geometry, and behaviour in curves of the railway vehicle and most attention is given to the formative stage in which an understanding was gained. Progress in the last 20 years is only sketchily discussed, as the salient points are considered later in the relevant chapters. Moreover, many important aspects such as track dynamics, noise  generation,  and  other  high  frequency (in  this  context,  above  about  15 Hz) phenomena are excluded.

II. CONING  AND THE KINEMATIC OSCILLATION

The conventional railway wheelset, which consists of two wheels mounted on a common axle, has a long history1 and evolved empirically. In the early days of the railways, speeds were low, and the objectives were the reduction of rolling resistance (so that the useful load that could be hauled by horses could be multiplied) and solving problems of strength and wear.

The flanged wheel running on a rail existed as early as the 17th century. The position of the flanges was on the inside, outside, or even on both sides of the wheels, and was still being debated in the 1820s. Wheels were normally fixed to the axle, although freely rotating wheels were sometimes used in order to reduce friction in curves. To start with, the play allowed between wheel flange and rail was minimal.

Coning was introduced partly to reduce the rubbing of the flange on the rail, and partly to ease the motion of the vehicle around curves. It is not known when coning of the wheel tread was first introduced. It would be natural to provide a smooth curve uniting the flange with the wheel tread, and wear of the tread would contribute to this. Moreover, once wheels were made of cast iron, taper was normal foundry practice. In the early 1830s the flangeway clearance was opened up to reduce the lateral forces between wheel and rail so that, typically, in current practice about 7 to 10 mm of lateral displacement is allowed before flange contact.