The geometric description is a fundamental step in the formulation of the equations that govern the mechanics of railroad vehicle systems. Both the differential geometry theory of curves and theory of surfaces are required in order to be able to formulate the wheel and rail kinematic and force equations. In this chapter, a finite element approach, called the absolute nodal coordinate formulation, is used to define the rail geometry. The definition of the unit normal vector to the wheel and rail surfaces at the point of contact is necessary in order to be able to determine the direction of the normal contact force. The chapter introduces the first and second fundamental forms of surfaces. These fundamental forms allow measuring distances and defining surface curvatures. The coefficients of the surface fundamental forms are used to define the principal curvatures and principal directions that enter into the formulation of wheel/rail interaction forces.
Differential Geometry
2021-04-05
38 pages
Article/Chapter (Book)
Electronic Resource
English
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