A mathematical model of train continuous motion uphill

The determination problem of adhesion coefficient of locomotives' wheels with rails is described in this paper. The use of methods of mathematical statistics and theory of probability provides wider possibilities for determining the most acceptable (suitable) value of the adhesion coefficient. The random factors influencing on this value are analysed. The use of the adhesion coefficient values based on reliable research results could help maintain uninterrupted (continuous) traffic of heavy freight trains and increase not only the carrying capacity, but also the volume of the transported goods. The paper considers a mathematical model of steady traffic of heavy freight trains pulled by upgraded locomotives of the series 2M62M on railway line with a gradient. The research results show that the actual values of the adhesion coefficient and the total resistance are distributed according to the normal distribution law. A mode of locomotive motion largely depends on the relationship between the total train's running resistance and locomotive tractive force. Finally, basic conclusions are given.