On the action of a locomotive driving wheel

In the appendix to a paper read before the Institution of Civil Engineers, dealing generally with the subject of the 'Electric Locomotive,' the author discussed the running qualities of locomotives from the point of view of dynamics. He based the discussion on the forces set up between wheel and rail, and these forces he referred to the creepage of the surfaces in contact due to elastic deformation of the material in the neighbourhood of the contact, defining "creepage" traversed. He later introduced two quantities,f andf ', which represented respectively the tractive force per unit creepage, longitudinally and transversly, to the rail. The quantitiesf andf ', which were assumed constant in any particular problem, were not determined at the time, and the present paper is primarily an attempt to compute the first of them. The area of contact between wheel and rail varies with the statr of wear of the parts. For a new rail the longitudinal dimension of the contact is in general greater than the transverse dimension; but, as the rail flattens with use, the contact area approximates in shape to a uniform strip transverse to the rail. The final state is assumed herein, the wheel and rail being conceived as cylinders having their generating lines parallel. The problem proposed is accordingly a two-dimensional one. Instead of assuming the problem to be that of a cylinder rolling on a plane, however, we implicitly assume it to be that of two cylinders of like material and of equal and opposite radii, pressed together and rolling on one another, one being subject to a torque and the other to an equal counter-torque. Under this assumption, any state of stress or strain in one member, due to tangential tractive forces only, is matched by an equal reversed state in the other, and the distribution of pressure between the members is unaffected by the traction, since the radial displacements of the surfaces in contact are complementary. We may note also that any conclusion deduced for a driving wheel is true, with reversal of stresses and strains, for a wheel undergoing braking.