Spatial-Dynamics Formulation of the L/V Ratio. Technical Report # MBS2022-5-UIC

Nadal’s L/V limit, which is based on quasi-static planar analysis, was used to develop derailment criteria; where L and V are, respectively, lateral and vertical forces acting on railroad wheel flange. This paper describes new spatial L/V dynamic formulation based on the assumptions of Nadal’s limit. The spatial analysis, which leads to simple L/V ratio that demonstrates limitations of the planar analysis, employs non-generalized coordinates and is independent of the bank angle that defines the track super-elevation. The single-degree-of-freedom wheel-climb model developed accounts for curving behavior, track super-elevation, and centrifugal and Coriolis inertia forces; and can be used to develop an inverse problem to study different wheel climb patterns. It is demonstrated that the wheel absolute acceleration is not in general zero for zero climb acceleration as in the planar analysis, and the lateral force L and vertical force V depend on quadratic-velocity inertia forces. The condition of zero absolute acceleration and non-zero climb acceleration is defined. It is shown that the spatial L/V limit can approach four if the direction of the friction force is properly accounted for, highlighting the need for accurate measurement of the components of the relative velocity at the wheel/rail contact point to have proper interpretation and use of the wheel-climb criteria. The proposed approach can be used to develop real-time onboard-computer positive-train-control (PTC) algorithms that define wheel-climb pattern using online measurements. Such PTC algorithms can contribute to avoiding derailments caused by wheel climb during curve negotiations.