Effect of forward kinematics on the motion-trajectory oscillations and inertia forces

Abstract

In vehicle-motion scenarios, non-negligible centrifugal-force component that cannot be balanced by the gravity force may develop, leading to increase in wheel-contact forces. This inertia-force component, which depends on vehicle forward velocity and oscillation amplitude, can arise when the vehicle negotiates straight road or railroad track. An approach based on the Frenet geometry and recorded motion trajectory (RMT) is introduced in this investigation to examine forward-kinematics effect on the motion geometry and inertia forces and to obtain general expression of the ratio between the amplitudes of the centrifugal and gravity forces. While the two three-dimensional vectors of applied and constraint forces define Frenet osculating plane of mass-center trajectories; for non-centroidal points, the osculating plane is defined by two vectors; the resultant of the applied and constraint forces and an inertia-force vector that depends on the angular velocity and angular acceleration. The concepts of instantaneous motion plane (IMP) and instantaneous zero-force axis (IZFA) are used to convert three-dimensional Cartesian forces into two-dimensional Frenet forces, based on the Frenet-Newton equations. Because contact forces can be formulated using two fundamentally different approaches; constraint contact formulation (CCF) and elastic contact formulation (ECF), the effect of the contact formulation on the IMP and IZFA orientation is examined. The results obtained, using railroad suspended wheelset example, demonstrate the following: (1) limitations of roller rigs that do not properly account for forward-velocity effect on the inertia forces; (2) difference between IMP and intermediate wheelset plane defined by wheelset lateral axis and global vertical axis; (3) non-negligible inertia centrifugal-force component in the absence of physical curvature; and (4) need to distinguish between physical and motion geometries; the latter is one that directly enters into the definition of the inertia forces. Trajectories with oscillation frequency independent of the oscillation amplitude for a given forward velocity are also identified.