This paper describes and compares the use and limitations of two constraint-based formulations for the wheel-rail contact simulation in multibody dynamics; (1) the use of contact lookup tables and (2) the Knife-edge Equivalent Contact constraint method (KEC-method). Both formulations are presented and an accurate procedure to interpolate within the data in the lookup table is also described. Since the wheel-rail constraint contact approach finds difficulties at simultaneous tread and flange contact scenarios, the lookup table method is implemented with a penetration-based elastic contact model for the flange, turning the method into a hybrid (constant in the tread and elastic in the flange) approach. To deal with the 2-point contact scenario in the KEC-method, a regularisation of the tread-flange transition allows the use of the constraint approach in the tread and also in the flange. To show the applicability and limitations of both methods, they are studied and compared with special emphasis in the calculation of normal and tangential contact forces. Numerical results are based on the simulation of a two-wheeled bogie vehicle in different case studies that consider irregular tracks and two wheel-rail profiles combination: profiles that do not show two-point wheel-rail contacts and profiles that do show two-point wheel-rail contacts. Although results show a good agreement between both approaches, the use of the KEC-method is more extensive since it allows to reproduce the wheel-climbing scenario that cannot be simulated with the lookup table method with the hybrid contact approach. It is concluded that simulations with this later method may not be in the safe side.

This paper introduces a procedure in the field of computational contact mechanics to analyze contact dynamics of beams undergoing large overall motion with large deformations and in self-contact situations. The presented contact procedure consists of a contact search algorithm which is employed with two approaches to impose contact constraint. The contact search task aims to detect the contact events and to identify the contact point candidates that is accomplished using an algorithm based on intersection of the oriented bounding boxes (OBBs). To impose the contact constraint, an approach based on the complementarity problem (CP) is introduced in the context of beam-to-beam contact. The other approach to enforce the contact constraint in this work is the penalty method, which is often used in the finite element and multibody literature. The latter contact force model is compared against the frictionless variant of the complementarity problem approach, linear complementarity problem approach (LCP). In the considered approaches, the absolute nodal coordinate formulation (ANCF) is used as an underlying finite element method for modeling beam-like structures in multibody applications, in particular. The employed penalty method makes use of an internal iteration scheme based on the Newton solver to fulfill the criteria for minimal penetration. Numerical examples in the case of flexible beams demonstrate the applicability of the introduced approach in a situation where a variety of contact types occur. It was found that the employed contact detection method is sufficiently accurate when paired with the studied contact constraint imposition models in simulation of the contact dynamics problems. It is further shown that the optimization-based complementarity problem approach is computationally more economical than the classical penalty method in the case of studied 2D-problems.

Contact description plays an important role in modeling of applications involving flexible multibody dynamics. Example of such applications include contact between a belt and pulley, crash-worthiness analysis in aerospace and automotive engineering. Approaches such as the linear complementarity problem (LCP), nonlinear complementarity problem (NCP) and penalty method have been proposed for contact detection and imposition of contact constraints. Contact description within multibody dynamics, however, continues to be a challenging topic, particularly in the case of flexible bodies. This paper describes and compares the use of two contact descriptions in the framework of flexible multibody dynamics; (1) the use of nonlinear cone complementarity approach (CCP) and (2) the penalty method. Both contact models are presented together with a master-slave detection algorithm. The modified form of node-to-node approach presented facilitates creation of pseudo-nodes where gap function can be calculated. This reduces the cumbersome effort of contact search. Since large deformations can be an important phenomenon in flexible multibody applications, beam elements based on the absolute nodal coordinate formulation (ANCF) are implemented in this study. To make a comparison of two approaches, the damping component is included in the penalty method by using the continuous contact model introduced by Hunt and Crossley. Numerical results are based on the simulation of ANCF beam contact with rigid ground, rigid body with an arbitrary shape and pendulum contact. Although kinematic results show a good agreement between both approaches when the coefficient of restitution is zero, the unphysical interpenetration appears in the penalty method. Nonlinear minimization problem solved by CCP approach helps to prevent the penetration during contact event. Furthermore, the proposed contact detection algorithm is proved to be capable of being used for multiple contact between beam and arbitrary shape rigid body; different contact types, such as side-by-side and corner-by-side, can be performed without prediction.

The multibody system dynamics approach allows describing equations of motion for a dynamic system in a straightforward manner. This approach can be applied to a wide variety of applications that consist of interconnected components which may be rigid or deformable. Even though there are a number of applications in multibody dynamics, the contact description within multibody dynamics still remains challenging. A user of the multibody approach may face the problem of thousands or millions of contacts between particles and bodies. The objective of this article is to demonstrate a computationally straightforward approach for a planar case with multiple contacts. To this end, this article introduces a planar approach based on the cone complementarity problem and applies it to a practical problem of granular chains.

The numerical and computation aspects of the Knife-edge Equivalent Contact (KEC) constraint and lookup table (LUT) methods are compared in this paper. The LUT method implementation uses a penetration-based elastic contact model for the flange and a constraint-based formulation at the wheel tread. For the KEC method, where an infinitely narrow rail contacts an equivalent wheel, regularization of the tread-flange transition is adopted to simultaneously account for tread and flange contacts using constraints. A comparison between the two methods is carried out using well-known numerical integrators to show the applicability and limitations of both methods.Two fixed-step-size integrators, the explicit Runge–Kutta (RK4) and the predictor–corrector Adam–Bashforth–Moulton (ABM) methods, and two variable-step-size Matlab built-in function integrators, the explicit $ode45$ o d e 45 and implicit $ode15s$ o d e 15 s , were applied to get the numerical solutions to the dynamic problems and study the relative numerical performance of the two contact description methods. To complete the railway vehicle model, both contact methods were implemented for the multibody model of a benchmark railway vehicle (the Manchester wagon 1). Numerical results were obtained for different railway tracks with and without irregularities. Profiles of the S1002 wheel and LB-140-Area rail, which demonstrate the two-point contact phenomenon, were considered. Both methods were implemented in Matlab and validated against commercial simulation software. The kinematic results for both approaches show good agreement, but the KEC method was up to 20% more efficient than the LUT method regardless of integrator used.