Simon Iwnicki (Editor)_ Maksym Spiryagin (Editor)_ Colin Cole (Editor)_ Tim McSweeney (Editor) - Handbook of Railway Vehicle Dynamics, Second Edition-CRC Press (2019)

A History of Railway Vehicle Dynamics
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(a)
(b)
FIGURE 2.7 Normal and lateral tangential forces acting on wheelset in (a) central position and (b) laterally
displaced position, illustrating the gravitational stiffness effect. (From Iwnicki, S. (Ed.), Handbook of Railway
Vehicle Dynamics, CRC Press, Boca Raton, FL, 2006. With permission.)
largely dictated by the proposed duty of the vehicle. But Matsudaira recognised that the designer
could vary both the way in which wheelsets were connected and the corresponding stiffness properties,
and this pointed the way to future progress.
One of the members of Levi’s ORE committee was A. D. de Pater, who considered the hunting
problem and formulated it as a non-linear problem [96,97]. Even though severe assumptions were
made, interesting theoretical results emerged. In 1964, one of de Pater’s students, P. van Bommel,
published non-linear calculations [98] for a two-axle vehicle using worn wheel and rail profiles and
the creep force-creepage laws proposed by Levi and Chartet. However, the practical relevance of
the results was limited because lateral and longitudinal suspension flexibility was not considered.
2.11 THE COMPLETE SOLUTION OF THE HUNTING PROBLEM
In the early 1960s, British Railways, like Japanese National Railways, faced an increasing incidence
of derailments of short wheelbase two-axle wagons as freight train speeds increased. After
some false starts [9], and the failure to solve the problem by empirical means, a team was formed
at Derby to undertake research into railway vehicle dynamics. Based on Carter’s work and quickly
understanding the significance of Matsudaira’s 1960 paper, it was possible to extend the analysis of
stability by introducing a new feature, lateral suspension damping, and by reintroducing the ‘gravitational
stiffness’ effect, which de Possel and Boutefoy had already used in [95]. The model used
had seven degrees of freedom, lateral displacement and yaw of the wheelsets and car body and roll
of the car body. As a result, it was shown that, with a careful choice of lateral suspension damping
and the lateral and longitudinal stiffnesses, it was possible to eliminate the low-speed body instability
(a strongly contributory factor in wagon derailments) so that the vehicle operating speed was
only limited by the wheelset instability. In this work, the application of analytical and both analogue
and digital computer techniques marched hand in hand with experimental work on models.
Comprehensive details of the behaviour of a simple elastically restrained wheelset were derived.
As the equations of motion are not symmetric and the system is non-conservative, the wheelset is
able to convert energy from the forward motion to the energy of the lateral motion [99]. Moreover,
the representation and analysis of the wheelset were introduced as a feedback system.
On the full-scale experimental side, measurements of critical speeds and mode shapes, associated
with the hunting limit-cycle of a range of vehicles, were made by King [100] and by Pooley [101].
The most striking validation of the theory came from a series of full-scale experiments with two
kinds of standard two-axle vehicles, Gilchrist et al. [74]. As the linear critical speeds of these
vehicles were low, it was possible to measure the fully developed hunting limit cycle. Quite apart
from the highly non-linear suspension characteristics, which were realistically modelled, two major
limitations of linear theory were faced. These were creep saturation and wheel-rail geometry. Creep
saturation was modelled by a two-part characteristic, Kalker’s linear values being taken for the
linear part and the creep forces being limited by sliding friction. The wheel-rail geometry was