Co-Simulation of Multibody Systems With Contact Using Reduced Interface Models

Abstract

Co-simulation techniques enable the coupling of physically diverse subsystems in an efficient and modular way. Communication between subsystems takes place at discrete-time instants and is limited to a given set of coupling variables, while the internals of each subsystem remain undisclosed and are generally not accessible to the rest of the simulation environment. In noniterative co-simulation schemes, commonly used in real-time applications, this may lead to the instability of the numerical integration. The stability of the integration in these cases can be enhanced using interface models, i.e., reduced representations of one or more subsystems that provide physically meaningful input values to the other subsystems between communication points. This work describes such an interface model that can be used to represent nonsmooth mechanical systems subjected to unilateral contact and friction. The dynamics of the system is initially formulated as a mixed linear complementarity problem (MLCP), from which the effective mass and force terms of the interface model are derived. These terms account for contact detachment and stick–slip transitions, and can also include constraint regularization in case of redundancy in the system. The performance of the proposed model is shown in several challenging examples of noniterative multirate co-simulation schemes of a mechanical system with hydraulic components, which feature faster dynamics than the multibody subsystem. Using an interface model improves simulation stability and allows for larger integration step-sizes, thus resulting in a more efficient simulation.

Explicit smooth/nonsmooth cosimulation using kinematic constraints

“…This approach is commonly used in the cosimulation of discrete element methods (DEM) or nonsmooth methods [12,13] and multibody dynamics (MBD) [4,9,14,15]. Apart from connecting subsystems through contact forces, in some studies, smooth and nonsmooth subsystems are linked by ideal kinematic constraints, for example, mechanical systems mounting particle dampers [16] and nonsmooth systems coupled with other physical modules [17]. In these cases, although contact forces can still be employed as coupling variables, an alternative choice is to decompose the overall system at the kinematic constraints and to send reaction forces/moments to other subsystems.…”

“…For coupled smooth/nonsmooth systems with kinematic constraints, if an explicit forcedisplacement cosimulation scheme [7] is employed in addition to the risk of losing stability, then another problem that may occur is the inconsistency of kinematic constraints between the monolithic DAEs and the nonsmooth methods. In fact, in nonsmooth timestepping methods [17,28,[30][31][32], kinematic constraint equations are usually formulated at the velocity level for consistency with the nonsmooth dynamic equations at the impulsemomentum level, whereas in monolithic DAEs and cosimulation, constraint equations are expected to be satisfied at position, velocity, and acceleration levels at the synchronization time [21,22]. This inconsistency cannot be eliminated when subsolvers are expected to remain opaque, as is a common practice when cosimulating between existing well-established solvers, and although just alternatively coupling positions or velocities would be an option, the stability of the cosimulation scheme would be poor in general cases.…”

A tight coupling scheme for smooth/non-smooth multibody co-simulation of a particle damper

“…In the above mentioned implicit/semi-implicit schemes, the sub-solvers are characterized as simulation blocks with inputs and outputs, and all integrators need to be reinitialized and repeated at each time step. Peiret et al [31] proposed reduced interface models (RIMs) for multi-physics systems, and applied RIMs to the loose co-simulation scheme of non-smooth multibody systems with hydraulic components [40]. Using RIMs, the influence of the extrapolation methods and integrators in each subsystem were also studied for two mechanical-hydraulic systems, which indicates that the accuracy of the co-simulation can be improved by an appropriate selection of the integration schemes [41].…”

Efficiency comparison of various friction models of a hydraulic cylinder in the framework of multibody system dynamics

“…In the framework of multibody system dynamics [35,46], a large number of studies have been presented that demonstrate coupling of multibody systems and hydraulic actuators [22,40]. Coupling has been carried out using either monolithic [48,49] or cosimulation approaches [44,47]. There are even studies using a monolithic approach that demonstrate this coupling for real-time applications, such as [6] and [31].…”