Combining performance and numerical stability is a key issue in co-simulation. The Transmission Line Modeling method uses physically motivated communication delays to ensure numerical stability for stiff connections. However, using a fixed communication delay may limit performance for some models. This paper proposes Steady-State Identifcation for enabling variable communication delays. Three algorithms for online Steady-State Identification are evaluated in three different co-simulation models. All algorithms are able to identify steady-state and can thereby determine when communication delays can be allowed to increase without compromising accuracy and stability. The results show a reduction in number of the solver derivative evaluations by roughly 40-60% depending on the model. The proposed method additionally supports connections with asymmetric communication delays, which allows each sub-model to independently control the delay of its input variables. Models supporting delay-size control can thereby be connected to those that do not so that the step length of each individual sub-model is maximized. Controlling the delay-size in sub-models also makes the method independent of the master co-simulation algorithm. 

Modeling and simulation are important tools for efficient product development. There is a growing need for collaboration, interdisciplinary simulation, and re-usability of simulation models. This usually requires simulation tools to be coupled together for co-simulation. However, the usefulness of co-simulation is often limited by poor performance and numerical instability. Achieving stability is especially hard for stiff mechanical couplings. A suitable method is to use transmission line modeling (TLM), which separates submodels using physically motivated time delays. The most established standard for tool coupling today is the Functional Mock-up Interface (FMI). Two example models in one dimension and three dimensions are used to demonstrate how the next version of FMI for co-simulation can be used in conjunction with TLM. The stability properties of TLM are also proven by numerical analysis. Results show that numerical stability can be ensured without compromising on performance. With the current FMI standard, this requires tailor-made models and custom solutions for the interpolation of input variables. Without using custom solutions, variables must be exchanged using sampled communication and extrapolation. In this case, stability properties can be improved by reducing communication step size. However, it is shown that stability cannot be achieved even when using unacceptably small communication steps. This motivates the need for the next version of FMI to include an intermediate update mode, where variables can be interchanged in between communication points. It is suggested that the FMI standard should be extended with optional callback functions for providing intermediate output variables and requesting intermediate input variables.

OpenModelica is a unique large-scale integrated open-source Modelica- and FMI-based modeling, simulation, optimization, model-based analysis and development environment. Moreover, the OpenModelica environment provides a number of facilities such as debugging; optimization; visualization and 3D animation; web-based model editing and simulation; scripting from Modelica, Python, Julia, and Matlab; efficient simulation and co-simulation of FMI-based models; compilation for embedded systems; Modelica-UML integration; requirement verification; and generation of parallel code for multi-core architectures. The environment is based on the equation-based object-oriented Modelica language and currently uses the MetaModelica extended version of Modelica for its model compiler implementation. This overview paper gives an up-to-date description of the capabilities of the system, short overviews of used open source symbolic and numeric algorithms with pointers to published literature, tool integration aspects, some lessons learned, and the main vision behind its development.

Numerical stability is a key aspect in co-simulation of physical systems. Decoupling a system into independent sub-models will introduce time delays on interface variables. By utilizing physical time delays for decoupling, affecting the numerical stability can be avoided. This requires interpolation, to allow solvers to request input variables for the time slot where they are needed. The FMI for co-simulation standard does not support fine-grained interpolation using interpolation tables. Here, various modifications to the FMI standard are suggested for improved handling of interpolation. Mechanical and thermodynamic models are used to demonstrate the need for interpolation, as well as to provide an industrial context. It is shown that the suggested improvements are able to stabilize the otherwise unstable connections.

In systems engineering and object-oriented design, encapsulation is a key concept to handle complexity. Interfaces are defined for the external interaction of a component, whereas internal details are hidden. Complex systems such as cars or airplanes consist of many components, which, in turn, consist of many components – hierarchically, through many levels. Therefore composition is built into modelling languages such as Modelica. External interfaces must be defined for external interaction, whereas internal components cannot be accessed if they are not available through these interfaces.

However, in 3D mechanical systems modelling and design, it is natural to be able to connect components whose surfaces are externally available. For example, the motor belonging to a car can be externally accessible in the 3D view, even though it can be regarded as an internal component of the car.

In this paper we compare two modelling approaches, one is Modelica used for systems engineering as well as modelling of multi-body systems and the other one is BEAST which is a specialised multi-body systems tool with good support for contact modelling. The current Modelica approach requires strict interfaces with encapsulation of internal components, whereas BEAST allows connections to internal components which are visible in a 3D view, which is often natural from the 3D mechanical systems point of view. For 3D mechanical systems, Modelica might be too strict, whereas BEAST might be too forgiving. Two different solutions are presented and discussed (in the form of possible Modelica extensions) to combine the advantages of both approaches.

This paper describes a rotor-dynamics application, a grinding spindle arrangement, that contains several non-linear components, e.g., two ball bearings supporting the spindles shaft and a control system determining the rotation of the shaft. To be able to study the different parts in detail they should be modelled in specialised simulation tools, i.e., model  control systems in Simulink and multibody systems in MSC.ADAMS.However, to understand the system as a whole it is necessary to investigate all parts simultaneously. This is especially true for transient (dynamic) simulation models with several interdependent parts. One solution for a more complete and accurate system analysis is to couple different simulation models into one coherent simulation, also called a co-simulation. This also allows the reuse of existing simulation models and preserves the investment in these models.

The grinding spindle arrangement has successfully been modelled and simulated using a general framework for co-simulation and  metamodelling. Four simulation models have been connected by means of a meta-model, that contains an MSC.ADAMS spindle model, two BEAST  ball bearings fixing the shaft in the housing, and a Simulink driver that controls the rotation of the shaft. Rotor-dynamics effects, such as, grinding-wheel vibrations and stiffness are presented to verify the results of the simulation.

A general approach for modelling of mechanical system co-simulations is presented that is built upon the previously defined general framework for TLM co-simulations and co-simulation meta-modelling.

Co-simulation is one technique for coupling different simulators into one coherent simulation. Existing co-simulation applications are often capable of interconnecting two specific simulators where a unique interface between these tools is defined. However, a more general solution is needed to make co-simulation modelling applicable for a wider range of tools. Any such solution must also be numerically stable and easy to use to be applicable by a larger group of people.

In this work the concept of meta-modelling is applied to mechanical co-simulation. Several tool-specific simulation models can be integrated and connected by means of a meta-model, where the meta-model  defines the physical interconnections of these models.

A general meta-modelling process is described that represents the basis for this work. A meta-modelling language (MML) has been defined to support the modelling process and store the meta-model structure. Besides elements for physical interconnections, etc., the language also defines graphical elements that can be used for meta-model  visualisation. All proposed solutions are general and simulation tool independent.

A fully functional modelling environment has been created to make meta-modelling applicable. The modelling environment supports easy encapsulation and integration of simulation tool-specific models. Each simulation tool implements a single, well defined co-simulation interface. All interfaces implement a numerically stable method for force/moment interaction. The presented environment features a graphical user  interface for co-simulation modelling with support for three dimensional  visual representation of the co-simulation model including all its components.

Modeling and simulation often require different tools for specialized purposes, which increase the motivation to use co-simulation. Since physical models often are describing enterprises¿ primary know-how, there is a need for a sound approach to securely perform modeling and simulation. This paper discusses different possibilities from a security perspective, with focus on secure distributed co-simulation over wide area networks (WANs), using transmission line modeling (TLM). An approach is outlined and performance is evaluated both in a simulated WAN environment, and for a real encrypted co-simulation between Sweden and Australia. It is concluded that several parameters affect the total simulation time, where especially the network delay (latency) has a significant impact.

A framework for meta-modelling with Transmission Line (TLM) joints is presented. The framework is intended to support transient simulations of mechanical systems using co-simulation of different tools. The expressive power of the Modelica language is used to describe the meta-model in an easy to understand, object oriented way. A ModelicaXML based translator is used to convert Modelica code to an XML document which is accepted as input by the co-simulation engine. The framework prototype for SKF’s BEAST and MSC.ADAMS is presented here. It is designed to be general, so that support for other simulation tools can be easily added. The main focus is on modelling of co-simulation Meta-Models taking advantage of Modelicas graphical and object-oriented modelling capabilities.