This paper presents analytical considerations which are important to design a rail head for reducing rail damage due to heavy axle loads. There are two important parameters of design of rail crown: (1) the wheel tread rail crown contact stress and (2) the contact tilt angle called the β angle. Contact should not be allowed to move out of the rail crown. Analysis of lateral oscillations of new and worn wheel sets shows that they do not impose an engineering constraint on the choice of rail crown radius. Rail rolling on curves due to lateral creepage forces is however of great importance in rail loading and stresses. The point of contact location is significantly affected by such roll. For the two commonly used rails, 132 RE and 136 RE, this roll results in the contact moving to the part of the rail head with radius of 1 1/4 in. Such movement of the contact also develops rapidly when hollowed worn wheels roll on flattened worn rails. It is pointed out that this condition results in forces higher than the wheel load and stresses more than twice the value developed when the contact is within the rail crown and that this is most likely responsible for many of the rail failure problems including cracking, shelling, and fractures. A design analysis of rail crown including Hertzian contact and rail twist considerations shows that none of the three current rails analyzed satisfy the criteria developed for good rail head design. A suitable ellipitical crown should prove better. Finally a systems approach to rail wheel interaction with a number of design recommendations is given.

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