ABSTRACT
Matsudaira was the first to investigate the dynamic stability of the two-axle vehicle, using Carter’s theory of creep, and incorporating both the lateral and longitudinal flexibilities between wheelsets and the car body [3]. Subsequently, it was shown in [4] that inclusion of appropriate amounts of suspension damping, neither too small or too large, resulted in regions of clear stability up to relatively high speeds. Moreover, a realistic theory, taking into account the nonlinear flexibility between the wheelsets and the car body or bogie frame, and the forces acting between vehicle and track, yielded results which are consistent with experiment [1.11]. The theory shows that there are two ways of exploiting the suspension stiffnesses in the design of two-axle railway vehicles for stable running at speed. The first is to use a relatively flexible suspension, in which the flexibility parameter ∆ = f 2λl/kbksr0defined in Section 4.3 is large, with appropriately chosen parameters − this approach is suitable for two-axle vehicles with relatively long wheelbase. The second approach is to use a suspension which has large lateral and yaw stiffness in which the flexibility parameter ∆ is small, − this is appropriate to a short wheelbase vehicle such as a bogie. These concepts were demonstrated in the laboratory on a roller rig [4] and by track tests with a specially designed full-scale variable parameter test vehicle HSFV1[23]. Further experimental and theoretical experience has led to the development of suspensions for two-axle freight and passenger vehicles capable of running at similar speeds to bogie vehicles, such as the widely used Class 143 and 144 passenger vehicles on British Railways. The improvement of curving performance whilst still providing the yaw restraint necessary for stable running can be achieved by frequency sensitive yaw restraint between the wheelsets and car body using a relaxation or yaw damper, as first proposed by Hobbs [5]. The yaw damper provides little restraint at low frequencies so that the wheelsets are able to take up an approximately radial position, but at high frequencies the restraint is sufficient to stabilise the vehicle. The advent of reliable dampers suitable for use in the primary suspension, in the 1970s, made it possible to apply this concept to freight vehicles [6] and articulated passenger vehicles as discussed in Chapter 8. As mentioned in Section 4.2 for conventional bogies in which there are primary longitudinal and lateral springs connecting the wheelsets to a frame there is a limit to the overall shear stiffness which can be provided in relation to the bending stiffness and therefore the stability/curving trade-off in which the bending stiffness must be minimised is constrained. This limitation is removed if the wheelsets are connected directly by diagonal elastic elements or cross-bracing, or interconnections which are structurally equivalent. Such an arrangement is termed a self-steering bogie. Superficially, this arrangement is similar to systems of articulation between axles by means of rigid linkages which have a long history in railway engineering. The first application of cross-bracing appears to have been on the vehicles of the LinzBudweiser Pferdebahn (1827), to be seen in the Vienna Museum of Technology. In the 1970s the self-steering bogie was successfully developed and put into service, notably by Scheffel [7]. The essential feature of cross-bracing in modern practice is that it is elastic. Self-steering bogies are common in current practice and have been applied to locomotives (with benefits to the maximum exploitation of adhesion), passenger vehicles and freight vehicles [8]. It should be noted that inter-
wheelset connections can be provided by means other than springs and dampers. In [9] the equivalent of cross-bracing is provided by means of a passive hydrostatic circuit which has a number of potential design advantages.
