This paper presents a theoretical/design analysis of wheel-rail contact stresses and geometries for U.S. freight cars of 70, 95, 100, and 125 ton freight capacities operating on various crown rails. After discussing various types of rail stresses, it is pointed out that the contact stresses are the major factor and the only parameter that enables a designer to improve or optimize the rail life and performance. In order to determine the most suitable diameters for the heavier cars, an engineering lower bound analysis of the contact has been completed. It uses in a two-dimensional Hertzian analysis, the field information of well worn-out wheel and rail contacts which are almost rectangular and of 1 in. width. The lower engineering bound values of maximum normal contact stresses for the 100 and 125 ton cars using wheels of diameters from 33 to 42 in. are given. This stress for the current 100 ton car with 36 in. diameter wheels is 98.35 ksi. To approach this value for the 125 ton car it is necessary to use 42 in. diameter wheels which is strongly recommended for the U.S. railroads. A Hertz theory based analysis of the contact stresses with varying wheel diameter, tread profile radius and rail crown radius for the 70, 95, 100, and 125 ton cars has been presented. Using the field information that the difference in radii of curvature of worn wheel and rail is approximately 5 in., choice of radii of rail and wheel profile curvatures is made so that the design radii difference is always 5 in. or more. Wheel diameter and wheel profile radius ranges used for this analysis were 33 to 44 in. and 15 to 35 in., respectively. The rail crown radius range was 10 to 30 in. It was concluded that a rail crown radius of 15 to 20 in. and wheel tread profile radius of 22 to 30 in. are good initial ranges for further analysis of design.

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