Performance Study of the Three-Piece and Y25 Bogies Using Frenet Geometric Analysis

In this thesis, a data-driven science DDS) approach, based on integrating nonlinear multibody system (MBS) formulations and new geometric concepts, is used to compare the performance of two widely used railroad bogies: the three-piece bogie, widely used in North America and other parts of the world, and the European Y25 bogie. Despite their popularity, such a comparative study, based on a MBS approach, is lacking in the literature. MBS algorithms are used to automatically construct and numerically solve the bogie nonlinear differential/algebraic equations (DAEs) to determine the bogie motion trajectories. To have a better understanding of the bogie dynamic behavior, new criteria are used in the comparative study performed in this investigation. To this end, a distinction is made between 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 superelevation of the AMT curve osculating plane, referred to as the motion plane, which changes with time as the vehicle moves, distinguished from the fixed-in-time track super-elevation. This thesis 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 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. Because all bogie performance criteria cannot be addressed in one study, this investigation is focused on recording centrifugal inertia forces of the two bogie types without making judgement on their overall performance. The contents of this thesis are based on the paper “Frenet Performance Evaluation of Railroad Vehicle Systems”, accepted for publication by the journal Acta Mechanica (Bettamin et al, 2021).