Abstract
A moving axle finite element (FE) was developed to study the contact between a wheel and curved rail, where the FE can simulate multi-point contact with sticking, sliding, and separation modes. The possible contact region is inputted as a number of nodes along the wheel and rail surfaces, while the wheel nodes are simulated as cubic-splines. The rail node to wheel cubic-splines contact method is then used to find the normal and shear forces, where the normal and tangential stiffness values obtained from the three-dimensional (3D) FE analysis for an actual wheel and rail are used to model the force–displacement relationship. A simple theoretical solution for curved railways was used to validate the proposed FE in 3D analyses. The results show that good agreement with the theoretical and FE solutions for the contact normal force, shear force, wheel sliding, and wheel separation under various train speeds, curve radius, cant angles, and friction coefficients. This FE can be used in combination with other elements to simulate a train traveling on a curved track system, in which only the standard Newton–Raphson and Newmark’s methods are required in the FE main program.
Highlights
Illustration of Coordinate SystemsThe X-Y-Z is the global coordinate system, which can be set to the first straight line segment, where X can be the rail direction, Z can be the vertical direction, and Y = Z × X
Rail dynamics analysis of trains traveling at high speed on a curved or straight bridge, and they used the finite element method (FEM) to model vehicle and bridge subsystems coupled by contact forces [2]
Zeng et al established a vehicle–rail model, where the paper focuses on the effects of frequent earthquakes on a vehicle on horizontally curved railways [3]
Summary
The X-Y-Z is the global coordinate system, which can be set to the first straight line segment, where X can be the rail direction, Z can be the vertical direction, and Y = Z × X. The x-y-z is the local coordinate system for a curved segment, where z is the tangent direction of the plane curve, y is the vertical direction, and x = y × z (toward the center of the curve). For a rail vector of the x-y-z coordinate, and {vXYZ } is a vector of the X-Y-Z coordinate. For a rail with a cant angle θ, we define the wheel coordinate system as 1-2-3, where. 3 where axis 3 is with a cant angle θ, moving we define the moving wheel coordinate system as axis.
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