Geometry and differentiability requirements in multibody railroad vehicle dynamic formulations |
| |
Authors: | Cheta Rathod Ahmed A Shabana |
| |
Institution: | (1) Department of Mechanical Engineering, University of Illinois at Chicago, 842 West Taylor Street, Chicago, IL 60607, USA |
| |
Abstract: | The dynamic equations of multibody railroad vehicle systems can be formulated using different sets of generalized coordinates;
examples of these sets of coordinates are the absolute Cartesian and trajectory coordinates. The absolute coordinate based formulations do not require introducing an intermediate track coordinate system since all the absolute coordinates are defined in the global system. On the other hand, when the trajectory coordinates are
used, a track coordinate system that follows the motion of a body in the railroad vehicle system is introduced. This track
coordinate system is defined by the track geometry and the distance traveled by the body along the track centerline. The configuration
of the body with respect to the track coordinate system is defined using five coordinates; two translations and three Euler
angles. In this paper, the formulations based on the absolute and trajectory coordinates are compared. It is shown that these
two sets of coordinates require different degrees of differentiability and smoothness. When an elastic contact formulation
is used to study the wheel/rail dynamic interaction, there are significant differences in the order of the derivatives required
in both formulations. In fact, as demonstrated in this study, in the absence of a contact constraint formulation, higher order
derivatives with respect to geometric parameters are still required when the equations are formulated using the trajectory
coordinates. The formulation of the constraints used in the analysis of the wheel/rail contact is discussed and it is shown
that when the absolute coordinates are used, only third order derivatives need to be evaluated. The relationship between the
track frame used in railroad vehicle dynamics and the Frenet frame used in the theory of curves to describe the curve geometry
is also discussed in this paper. Based on the analysis presented in this paper, the advantages and drawbacks of a hybrid method
which employs both the absolute and trajectory coordinates and planar contact conditions in order to reduce the number of
contact constraints and relax the differentiability requirements are discussed. In this method, the absolute coordinates are
used to formulate the equations of motion of the railroad vehicle system. The absolute coordinate solution can be used to
determine the trajectory coordinates and their time derivatives. Using the trajectory coordinates, the motion of the body
in the vehicle with respect to the track coordinate system can be predicted and used in the formulation of the planar contact
model. |
| |
Keywords: | Railroad vehicles Multibody dynamics Planar and three-dimensional contact Trajectory coordinates Absolute coordinates |
本文献已被 SpringerLink 等数据库收录! |
|