Frenet force analysis in performance evaluation of railroad vehicle systems

A data-driven science approach, based on integrating nonlinear multibody system (MBS) formulations and new geometric concepts, is used in this paper to compare the performance of two widely used railroad bogies: the three-piece bogie and the Y25 bogie. MBS algorithms are used to solve the bogie nonlinear differential/algebraic equations (DAEs) to determine the bogie motion trajectories. To have a better understanding of the bogie dynamic behavior, a distinction is made between the geometry of actual motion trajectories (AMT) and the track geometry. The AMT curves are described using the motion-dependent Frenet-Euler angles, referred to as Frenet bank, curvature, and vertical development angles, which differ from their counterparts used in the description of the track geometry. In particular, the Frenet bank angle defines the super-elevation of the AMT curve osculating plane, referred to as the motion plane, distinguishing this Frenet super-elevation from the fixed-in-time track super-elevation. The paper explains the difference between the lateral track plane force balance used in practice to determine the balance speed and the Frenet force balance which is based on recorded motion trajectories. Computer simulations of bogies travelling on a track, consisting of tangent, spiral, and curve sections are performed with particular attention given to the deviations of the AMT curves from the track centerline. The results obtained in this study demonstrate the dependence of the AMT curve geometry on the wheelset forward motion, highlighting the limitations of tests performed using roller test rigs which do not allow longitudinal wheelset motion.