The lateral stability of railroad vehicles travelling on tangent tracks is one of the important problems that has been the subject of extensive research since the nineteenth century. Early detailed studies of this problem in the twentieth century are the work of Carter and Rocard on the stability of locomotives. The linear theory for the lateral stability analysis has been extensively used in the past and can give good results under certain operating conditions. In this paper, the results obtained using a linear stability analysis are compared with the results obtained using a general nonlinear multibody methodology. In the linear stability analysis, the sources of the instability are investigated using Liapunov’s linear theory and the eigenvalue analysis for a simple wheelset model on a tangent track. The effects of the stiffness of the primary and secondary suspensions on the stability results are investigated. The results obtained for the simple model using the linear approach are compared with the results obtained using a new nonlinear multibody based constrained wheel/rail contact formulation. This comparative numerical study can be used to validate the use of the constrained wheel/rail contact formulation in the study of lateral stability. Similar studies can be used in the future to define the limitations of the linear theory under general operating conditions.

There are three basic finite element formulations, which are used in multibody dynamics. These are the floating frame reference approach, the incremental method and the large rotation vector approach. In the floating frame of reference and incremental formulations, the slopes are assumed small in order to define infinitesimal rotations that can be treated and transformed as vectors. This description, however, limits the use of some important elements such as beams and plates in a wide range of large displacement applications. As demonstrated in some recent publications, if infinitesimal rotations are used as nodal coordinates, the use of the finite element incremental formulation in the large reference displacement analysis does not lead to exact modeling of the rigid body inertia when the structures rotate as rigid bodies. In this paper, a new and simple finite element procedure that employs the mathematical definition of the slope and uses it to define the element coordinates instead of the infinitesimal and finite rotations is developed for large rotation and deformation problems. By using this description and by defining the element coordinates in the global system, not only the need for performing coordinate transformation is avoided, but also a simple expression for the inertia forces is obtained. Furthermore, the resulting mass matrix is constant and it is the same matrix that appears in linear structural dynamics. It is demonstrated in this paper, that this coordinate description leads to exact modeling of the rigid body inertia when the structure rotate as rigid bodies. Nonetheless, the stiffness matrix becomes nonlinear function of time even in the case of small displacements. The method presented in this paper differs from previous large rotation vector formulations in the sense that the inertia forces, the kinetic energy, and the strain energy are not expressed in terms of any orientation coordinates, and therefore, the method does not require interpolation of finite rotations. While the use of the formulation is demonstrated using a simple planar beam element, the generalization of the method to other element types and to the three dimensional case is straightforward. Using the finite element procedure presented in this paper, beams and plates can be treated as isoparametric elements.

In this investigation, a method for the finite rotation and large deformation analysis of plates is presented. The method, which is based on the absolute nodal coordinate formulation, leads to a plate element capable of representing exact rigid body motion. In this method, continuity conditions on all the displacement gradients are imposed. Therefore, non-smoothness of the plate mid-surface at the nodal points is avoided. By developing such a plate element, a constant mass matrix is obtained, and as a consequence, the centrifugal and Coriolis forces are equal to zero. Generalization of the formulation to the case of shell elements is discussed. Numerical results are presented in order to demonstrate the use of the proposed method in the large rotation and deformation analysis of plates and shells.

In this investigation, computational multibody systems (MBS) algorithms are used to develop detailed railroad vehicle models for the prediction of the wear resulting from the pantograph/catenary dynamic interaction. The catenary wear is predicted for different motion scenarios that include constant-speed curve negotiation, and acceleration and deceleration on a tangent (straight) track. The effect of the vehicle vibration in these different motion scenarios on the contact force is further used to study the wear rates of the contact wire. The wear model used in this investigation accounts for the electrical and the mechanical effects. The nonlinear finite element (FE) absolute nodal coordinate formulation (ANCF), which is suitable for implementation in MBS algorithms, is used to model the flexible catenary system, thereby eliminating the need for using incremental rotation procedures and co-simulation techniques. The pantograph/catenary elastic contact formulation employed in this study allows for separation between the pantograph pan-head and the contact wire, and accounts for the effect of friction due to the sliding between the pantograph pan-head and the catenary cable. The approach proposed in this investigation can be used to evaluate the electrical contact resistance, contribution of the arcing resulting from the pan-head/catenary separation, mechanical and electrical wear contributions, and effect of the pantograph mechanism uplift force on the wear rate.

In existing freight-train braking systems, braking is applied on individual cars sequentially at the speed of the air pressure. In the case of long trains that consist of hundreds of rail cars, there is a time delay that results in large and impulsive compressive and tensile coupler forces. These coupler forces compromise the train safe operation and stability, make train handling difficult, cause track damage, raise significantly the maintenance cost, and increase the stopping distances which can lead to serious accidents. The objective of this investigation is to investigate the effect of the brake-delay time on the train longitudinal dynamics (LTD) coupler forces by integrating for the first time detailed three-dimensional coupler and air-brake force models. A spatial non-linear coupler model that takes into account the geometric nonlinearities is employed in order to allow for capturing arbitrary three-dimensional rail-car motion and coupler kinematic degrees of freedom that cannot be captured using existing simpler models. This coupler model is integrated with a detailed air brake model that consists of the locomotive automatic brake valve, air brake pipe, and car control unit (CCU) in order to evaluate conventional air brake force models that account for the air-flow effect in long train pipes as well as the effect of leakage and branch pipe flows. The coupling between the air brake, locomotive automatic brake valve, car control units, and train equations is established and used in the nonlinear LTD simulations, which are performed using the computer software ATTIF ( A nalysis of T rain/ T rack I nteraction F orces). Different LTD braking scenarios are considered and the effect of brake signal time delay on the coupler forces is examined. The results obtained in this study demonstrate the importance of applying all brake forces simultaneously in order to ensure train stability and safety.

Commonly-used sloshing models are either unable to capture changes in the continuous distribution of the fluid free surface, or are not suited for the integration with high fidelity computational multibody system (MBS) algorithms. The objective of this investigation is to address this deficiency by developing a new continuum-based liquid sloshing approach that accounts for the effect of complex fluid and tank geometry and can be systematically integrated with MBS algorithms in order to allow for studying complex motion scenarios. A unified geometry/analysis mesh is used from the outset to examine the effect of liquid sloshing on railroad and highway vehicle dynamics during various maneuvers including braking and curve negotiation [1,2]. Using a non-modal approach, the geometry of the tank and fluid is accurately defined, a continuum-based fluid constitutive model is developed, and a fluid-tank contact algorithm using the penalty approach is employed. In order to examine the effect of liquid sloshing on vehicle dynamics during curve negotiation, a general and precise definition of the outward inertia force is defined, which for flexible bodies does not take the simple form used in rigid body dynamics. During maneuvers, the liquid may experience large displacements and significant changes in shape that can be captured effectively using absolute nodal coordinate formulation (ANCF) finite elements. For rail systems, the liquid sloshing model is integrated with a three-dimensional MBS vehicle algorithm, in which the three-dimensional wheel/rail contact force formulation is used to account for the longitudinal, lateral, and spin creep forces that influence vehicle stability. The effects of fluid sloshing on vehicle dynamics in the case of a tank partially filled with liquid are studied and compared with the equivalent rigid body model in braking and curve negotiation. The results obtained in the study of the rail vehicle model show that liquid sloshing can exacerbate the unbalance effects when the rail vehicle negotiates a curve at a velocity higher than the balance speed, and can significantly increase coupler forces during braking. Analysis of the highway vehicle model shows that the liquid sloshing changes the contact forces between the tires and the ground — increasing the forces on certain wheels and decreasing the forces on other wheels — which in cases of extreme sloshing, can negatively impact the vehicle stability by increasing the possibility of wheel lift and vehicle rollover.