Large Angle of Attack Wheel Climb

Abstract

It is shown in this paper that wheel climb can be initiated as the result of kinematic conditions that can be described using algebraic equations that do not depend explicitly on time. These algebraic kinematic conditions can lead to instantaneous wheel climb that is independent of the motion history. The analysis presented in this paper shows that if the contact is maintained at the wheel perimeter, a single kinematic constraint equation, expressed in terms of the wheel generalized coordinates, is obtained. This algebraic constraint equation clearly shows that a decrease in the lateral distance between the center of mass of the wheel and the rail, which can be the result of application of a lateral force, leads to an instantaneous wheel climb in the case of a constant angle of attack. It is shown that the ratio between the lateral and vertical reaction forces at the contact point is governed by a well-defined algebraic equation, and such a ratio does not depend on the applied forces. This ratio is given by dy/(dz sin2 α), where dy and dz are, respectively, the lateral and vertical distances of the wheel center from the contact point, and α is the angle of attack. In order to develop the governing dynamic equations, the kinematic constraint equations are used to derive a velocity transformation matrix that defines the relationship between the wheel velocities and the derivatives of the degrees of freedom. This velocity transformation matrix is used to obtain the independent wheel equations of motion which are solved numerically to determine the wheel motion in response to different lateral and friction forces. The results obtained show that wheel climb can be initiated with small lateral force, and an increase in the lateral force is not necessary for climb initiation. In order to shed light on the L/V ratio commonly used in wheel climb derailment criteria, the relationship between the external lateral force acting on the wheel and the reaction lateral force at the contact point is developed in this investigation. It is also shown that in the case of a tangent track and zero roll angle; the wheel longitudinal motion is completely decoupled from the vertical and yaw displacements. Therefore, the use of the distance to climb in tangent track wheel climb criteria needs to be reexamined.