Geometric coupling in the wheel/rail contact formulations: a comparative study

摘要

The wheel/rail contact conditions can be formulated using three- or two-dimensional theories. In the three-dimensional theory, four geometric parameters that describe the wheel and rail surfaces are introduced. The contact conditions, which are formulated in terms of these four surface parameters, are used to predict online the location of the points of contact between the wheels and rails. In the two-dimensional theory, which is used in most specialized railroad vehicle computer algorithms, the contact conditions are formulated in terms of only two geometric parameters that describe the wheel and rail profiles. These contact conditions are defined by a projection on a wheel plane that intersects the rail surface, thereby defining a curve on which the contact point lies. In this study, the planar and spatial contact conditions are implemented in a general multi-body system algorithm that can be used in the computer-aided analysis of railroad vehicle systems. This computer algorithm is used to compare between the results obtained using the planar and spatial contact conditions. The comparative study presented in this paper will be focused on two important specific issues related to the non-linear dynamics of railroad vehicles; the first is the prediction of the critical speed, while the second is the accuracy of predicting the location of the contact point using the two-dimensional theory. A two-dimensional formulation predetermines the contact plane and then searches for the contact points in that plane, while in the three-dimensional contact model all the surface parameters (coordinates of the contact points) are solved for simultaneously. In the contact formulations used in this paper, the kinematic and dynamic equations are expressed in terms of a mixed set of generalized and non-generalized coordinates. The non-generalized coordinates, which represent the surface parameters of the wheel and the rail, are used in the formulation of the kinematic and dynamic equations and also used to define geometric vectors such as the normal and tangent vectors as well as their derivatives at arbitrary points on the wheel and rail surfaces. The contact points are predicted online during the dynamic simulation by solving a set of non-linear algebraic equations instead of using look-up tables. A full vehicle model is used to obtain the numerical results in this comparative study. The results obtained based on the particular vehicle model used in this investigation show that the accuracy of predicting the vehicle critical speed is not affected when the simpler planar contact conditions are used. On the other hand, the comparison shows that there are differences between the dynamic force results obtained using the two methods due to small differences in the prediction of the locations of the contact points.