Rolling Condition and Gyroscopic Moments in Curve Negotiations

In vehicle system dynamics, the effect of the gyroscopic moments can be significant during curve negotiations. The absolute angular velocity of the body can be expressed as the sum of two vectors; one vector is due to the curvature of the curve, while the second vector is due to the rate of change of the angles that define the orientation of the body with respect to a coordinate system that follows the body motion. In this paper, the configuration of the body in the global coordinate system is defined using the trajectory coordinates in order to examine the effect of the gyroscopic moments in the case of curve negotiations. These coordinates consist of arc length, two relative translations, and three relative angles. The relative translations and relative angles are defined with respect to a trajectory coordinate system that follows the motion of the body on the curve. It is shown that when the yaw and roll angles relative to the trajectory coordinate system are constrained and the motion is predominantly rolling, the effect of the gyroscopic moment on the motion becomes negligible and, in the case of pure rolling and zero yaw and roll angles, the generalized gyroscopic moment associated with the system degrees of freedom becomes identically zero. The analysis presented in this investigation sheds light on the danger of using derailment criteria that are not obtained using laws of motion and, therefore, such criteria should not be used in judging the stability of railroad vehicle systems. Furthermore, the analysis presented in this paper shows that the roll moment, which can have a significant effect on the wheel/rail contact forces, depends on the forward velocity in the case of curve negotiations. For this reason, roller rigs that do not allow for the wheelset forward velocity cannot capture these moment components and, therefore, should not be used in the analysis of curve negotiations. A model of a suspended railroad wheelset is used in this investigation to study the gyroscopic effect during curve negotiations.