ABSTRACT
Though early railway passenger and freight vehicles were generally symmetric, locomotives early adopted an unsymmetric configuration in order to maximise the axle-load on driving wheels and make use of the available adhesion. Additional smaller wheelsets were soon provided to improve the steadiness of running. It has already been mentioned, in Chapter 6, how the introduction of the leading swivelling bogie improved both stability and curving behaviour, and it was a matter of experience that the running behaviour of these unsymmetric configurations was strongly dependent on the direction of motion [1]. A later example of an unsymmetric vehicle design, used in trams, is provided by “maximum traction trucks” devised in the 1890’s and in which the driving wheels were followed or preceded by pony wheels which had a diameter about two-thirds of the driving wheels [2]. In this case each bogie was unsymmetric but the complete vehicle was usually symmetric. The classic work on the stability of unsymmetric railway vehicles is by Carter [3] which was directed toward the configurations then current in railway practice. Carter applied Routh's stability theory, not only to electric bogie locomotives, then exhibiting many problems of instability, but also to a variety of steam locomotives. In his mathematical models, a bogie consists of two wheelsets rigidly mounted in a frame, and locomotives comprise wheelsets rigidly mounted in one or more frames. Following Carter’s first paper of 1916 the theory was elaborated in a chapter of his 1922 book [4]. Carter’s next paper [5] gave a comprehensive analysis of stability within the assumptions mentioned above. As he was concerned with locomotives the emphasis of his analyses was on the lack of fore-and-aft symmetry characteristic of the configurations he was dealing with, and he derived both specific results and design criteria. Carter's work expressed, in scientific terms, what railway engineers had learnt by hard experience, that stability at speed required rigid-framed locomotives be unsymmetric and uni-directional. His analysis of the 0-6-0 locomotive found that such locomotives were unstable at all speeds if completely symmetric and he comments that this class of locomotive is “much used in working freight trains; but is not employed for high speed running on account of the proclivities indicated in the previous discussion.” Carter analysed the 4-6-0 locomotive both in forward and reverse motion and found that in forward motion beyond a sufficiently high speed or sufficiently stiff
bogie centring spring (laterally connecting the bogie to the locomotive body) oscillatory instability occurs, but as the mass of the bogie is small compared with the main mass of the locomotive, the resulting oscillation was unlikely to be dangerous at ordinary speeds. Carter’s stability diagrams, the first of their kind in the railway field, are shown in Figure 9.1(a) and 9.1(b). In reverse motion, Figure 9.1(b), Carter found that beyond a certain value of the centring spring stiffness buckling of the wheelbase occurred which would tend to cause derailment at the leading wheelset. As this wheelset is incorporated in the main frame of the locomotive, the lateral force acting between wheel and rail would be proportional to the mass of the main frame and would be correspondingly large, and potentially dangerous. This was the explanation of a number of derailments at speed of tank engines such as the derailment of the Lincoln to Tamworth mail train at Swinderby on 6 June 1928, as discussed in his final paper [6].
