Stability of the rectilinear motion of a railway Wheelset

A railway wheelset rolling on rails without slip is studied with consideration of the creep hypothesis. The wheelset is represented by two cones having a common base; the rails are represented by two circular cylinders with parallel axes. The kinematic characteristics of undisturbed rolling for the wheelset are determined when its center of mass moves along a straight line; these characteristics are also determined in the case of disturbed motion when the mass center of the wheelset moves along a sinusoidal trajectory. For these modes of motion, the constraint reactions are found with an accuracy up to the second order of smallness with respect to the values of disturbed variables. When the absolutely rigid point contact is replaced by the elastic contact, the creep hypothesis is used, the method of averaging with respect to the fast variables is applied, and a critical velocity above which the rectilinear rolling becomes unstable is determined on the basis of the averaged equations.