In this paper, a new continuum-based pantograph/catenary model based on the absolute nodal coordinate formulation (ANCF) is proposed and used to develop an effective method to control the contact force which arises from the pantograph/catenary interaction. In the proposed new model, only one ANCF gradient vector is used in the formulation of the pantograph/catenary contact conditions, thereby allowing for using the proposed approach for both fully parameterized and gradient-deficient ANCF finite elements. The proposed contact formulation can also be considered as a more general sliding joint formulation that allows for the use of the more efficient gradient-deficient ANCF finite elements in modeling very flexible cables. A three-dimensional multibody system (MBS) model of a pantograph mounted on a train is developed using a nonlinear augmented MBS formulation. In order to take into account the catenary large deformation, ANCF finite elements are used. The contact between the pantograph and the catenary system is ensured using a sliding joint constraint whereas the contact between the rail vehicle wheels and the train track is modelled using an elastic contact formulation. In addition to the use of the new MBS approach to model the pantograph/catenary interaction, the contact force between the pantograph and the catenary is computed using a simpler lumped parameter model which describes the pan-head and the plunger subsystem dynamics. In order to reduce the standard deviation of the contact force without affecting its mean value, a control actuator is used between the pan-head and the plunger. To this end, three types of control laws for the control action are designed to improve the contact quality both in the transient phase and in the steady state phase of the pantograph/catenary interaction. The first control law proposed features a feedback structure whereas the second and the third control strategies employ a feedback plus feed-forward architecture. In order to demonstrate the effectiveness of the proposed method, the results of a set of numerical simulations with and without the controllers are presented.

The development of new and complex vehicle models using the absolute nodal coordinate formulation (ANCF) and multibody systems (MBS) algorithms is discussed in this paper. It is shown how a continuum-based finite element (FE) leaf spring and tire assembly can be developed at a preprocessing stage and integrated with MBS algorithms, allowing for the elimination of dependent variables before the start of the dynamic simulations. Leaf springs, which are important elements in the suspension system of large vehicles, are discretized using ANCF FEs and are integrated with ANCF tire meshes to develop new models with significant details. To this end, the concept of the ANCF reference node (ANCF-RN) is used in order to systematically assemble the vehicle model using linear algebraic constraint equations that can be applied at a preprocessing stage. These algebraic constraint equations define new FE connectivity conditions that include the leaf spring shackle/chassis assembly, tire flexible tread/rigid rim assembly, tire/axle assembly, and revolute joints between different vehicle components. The approach presented in this paper allows for using both gradient deficient and fully parameterized ANCF FEs to develop the new models. In order to develop accurate leaf spring models, the prestress of the leaves and the contact forces between leaves are taken into consideration in the ANCF models developed in this investigation. Numerical results are presented in order to demonstrate the use of the computational framework described in this paper to build continuum-based leaf spring/tire assembly that can be integrated with complex vehicle models. The results of this paper also demonstrate the feasibility of developing a CAD (computer-aided design)/analysis system in which the geometry and analysis mesh of a complete vehicle can be developed in one step, thereby avoiding the incompatibility and costly process of using different codes in the flexible MBS analysis.

In this paper, a new continuum-based pantograph/catenary model based on the absolute nodal coordinate formulation (ANCF) is proposed and used to develop an effective method to control the contact force which arises from the pantograph/catenary interaction. In the proposed new model, only one ANCF gradient vector is used in the formulation of the pantograph/catenary contact conditions, thereby allowing for using the proposed approach for both fully parameterized and gradient deficient ANCF finite elements. A three-dimensional multibody system (MBS) model of a pantograph mounted on a train is developed using a nonlinear augmented MBS formulation. In order to take into account the catenary large deformation, ANCF finite elements are used. The contact between the pantograph and the catenary system is ensured using a sliding joint constraint whereas the contact between the rail vehicle wheels and the train track is modelled using an elastic contact formulation. In addition to the use of the new MBS approach to model the pantograph/catenary interaction, the contact force between the pantograph and the catenary is computed using a simpler lumped parameter model which describes the pan-head and the plunger subsystem dynamics. In order to reduce the standard deviation of the contact force without affecting its mean value, a control actuator is used between the pan-head and the plunger. To this end, three types of control laws for the control action are designed to improve the contact quality both in the transient phase and in the steady state phase of the pantograph/catenary interaction. The first control law proposed features a feedback structure whereas the second and the third control strategies employ a feedback plus feed-forward architecture. In order to demonstrate the effectiveness of the proposed method, the results of a set of numerical simulations with and without the controllers are presented.

The parabolic leaf spring is widely used in modern vehicle suspension systems because it has many desirable features, such as weak interleaf friction and light weight. In this paper, the parabolic leaf spring is analyzed using automatic geometric data acquisition (AGDA) and the finite element (FE) absolute nodal coordinate formulation (ANCF). In order to account for manufacturing considerations in developing the virtual models, the relaxed uniform cubic B-Spline is used to represent the leaf spring profile curves and geometry. Three-dimensional scanning techniques based on structured light and multiple images are explored in this study to automatically extract the leaf spring complex geometric data. A new procedure is proposed to develop the ANCF/FE mesh from the physical object. Both double-leaf uniform-thickness and double-leaf parabolic spring models are developed and analyzed using different ANCF elements. Using ANCF geometry, piecewise linearly tapered parabolic leaf spring models are constructed, accounting for the leaf pre-stress. The interleaf contact is enforced using a penalty approach and a smoothed Coulomb friction model. It is shown that the fully-parameterized low-order beam and plate elements suffer from locking problems, while the thin plate element can lead to less accurate results. The use of the new strain-split method (SSM) as a locking alleviation technique is also examined in this investigation. It is shown that while the current SSM implementation can be effective in solving the locking problem in the case of symmetric bending-dominant loading, it may not produce accurate results in the case of torsional loading. The comparative study performed demonstrates that the higher order ANCF beam element is more suitable for developing the leaf spring models compared to other ANCF elements considered in this investigation. The numerical results obtained show that the friction effect in parabolic leaf springs is much weaker than that in the leaf spring with uniform-thickness.

The convergence characteristics of three geometrically-accurate spatial finite elements (FE) are examined in this study using an eigenvalue analysis. The spatial beam, plate, and solid elements considered in this investigation are suited for both structural and multibody system (MBS) applications. These spatial elements are based on geometry derived from the kinematic description of the absolute nodal coordinate formulation (ANCF). In order to allow for an accurate reference-configuration geometry description, the element shape functions are formulated using constant geometry coefficients defined using the position-vector gradients in the reference configuration. The change in the position-vector gradients is used to define a velocity transformation matrix that leads to constant element inertia and stiffness matrices in the case of infinitesimal rotations. In contrast to conventional structural finite elements, the elements considered in this study can be used to describe the initial geometry with the same degree of accuracy as B-spline and NURBS (Non-Uniform Rational B-Spline) representations, widely used in the computer-aided design (CAD). An eigenvalue analysis is performed to evaluate the element convergence characteristics in the case of different geometries, including straight, tapered, and curved configurations. The frequencies obtained are compared with those obtained using a commercial FE software and analytical solutions. The stiffness matrix is obtained using both the general continuum mechanics approach and the newly proposed strain split method (SSM) in order to investigate its effectiveness as a locking alleviation technique.