TLM) and Functional Mock-Up Interface (FMI
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Modeling, Identification and Control, Vol. 39, No. 3, 2018, pp. 179{190, ISSN 1890{1328 Composite modelling in 3-D mechanics utilizing Transmission Line Modelling (TLM) and Functional Mock-up Interface (FMI) Dag Fritzson 1 Robert Braun 2 Jan Hartford 1 1AB SKF, SE-415 50 G¨oteborg, Sweden. E-mail: [email protected] 2Link¨opingUniversity, SE-581 83 Link¨oping,Sweden. E-mail: [email protected] Abstract Composite modelling and simulation is a solution to utilize investments in models and tools, use the right tool for the right task, increase the accuracy by means of more accurate modelled boundary conditions, switch between levels in model complexity for a specific sub-system, and facilitate co-operation in orga- nizations. With the new Functional Mock-up Interface (FMI) standardization, efforts are increasing to make this happen. SKF BEAST is an advanced dynamic simulation tool for rolling bearings and other mechanical systems with contacts. The tool incorporates a framework for composite modelling and co- simulation, i.e., a Master Simulation Tool (MST). It uses Transmission Line Modelling (TLM) to ensure robust numerical behaviour of the complete composite system model and supports the Functional Mock-up Interface (FMI) for model import, including both model exchange and co-simulation. In this paper, the tools and the techniques for composite modelling are discussed in further detail and application examples are given. Keywords: Master Simulation Tool (MST), Functional Mockup Interface (FMI), Transmission Line Modelling (TLM), co-simulation, composite modelling, BEAST 1 Introduction simulate larger systems, and to analyze how different subsystems interact with each other. The need for composite modelling/simulation or co- It can be desirable to switch between models of dif- simulation arises from several different aspects. ferent complexity, and thus computation cost, for a First of all, different simulation tools are popular specific sub-system. within different organizations. Some tools may also be commonly used within certain technical disciplines or Finally, it can also improve accuracy of the results by engineering sectors. It is not uncommon that a specific allowing more realistic boundary conditions by means simulation tool becomes a de facto standard within a of simulating a larger system. This is especially suit- specific field, and there is a large investment in exist- able for simulation of rolling bearings, where realistic ing models and trained staff. Connecting different tools loading and motion are of great importance. with each other can facilitate cooperation between or- Tool coupling is often time consuming and requires ganizations and departments. highly specialized knowledge. For this reason, it is of- Another reason for connecting multiple simulation ten avoided and used only when absolutely necessary. tools is that different tools may be suitable for different Hence, it is important to minimize the workload and parts of the model. Co-simulation makes it possible to knowledge requirements in order to maximize the ben- doi:10.4173/mic.2018.3.4 c 2018 Norwegian Society of Automatic Control Modeling, Identification and Control efits. This requires a minimalistic coupling interface in this paper, this approach relies on rollback mecha- and an intuitive user interface. nisms. FMUs must be able to save and restore states Continuous-time simulation puts high demands on to previous communication points. This is often not numerical robustness. If numerical stability cannot be possible, due to limitations in the tools from where the guaranteed, simulation results cannot be trusted. The FMUs are exported. co-simulation framework must be able to simulate nu- A method for solver coupling using a predictor- merically stiff models without stability problems, or corrector method and relaxation techniques was pre- manual tuning of model parameters or solver settings. sented in (Schweizer et al., 2016). In this way, stable There is an evolving standard, Functional Mock-up co-simulation could be achieved for higher-order ex- Interface (FMI) (Functional Mock-up Interface (FMI)), trapolation of coupling variables. However, the correc- for encapsulation of models/tools. It specifies low-level tor step requires the FMUs to support solver rollback interfaces for connecting simulation tools. It does not to previous states. cover the system specific issues, i.e., master simulation The Transmission Line Modelling (TLM) method tool, or composite model building/editing. In order to enables numerically stable couplings using fixed-size provide maximum connectivity it is important to sup- communication delays (Johns and O'Brien, 1980; Aus- port FMI, while still providing easy-to-use composite lander, 1968). Co-simulation using FMI and TLM with modelling and also ensure simulation accuracy. synchronous communication has been investigated for Thus the main challenges in composite modelling Modelica (Modelica and the Modelica Association) and simulation are: models (Braun and Krus, 2013) and for connections between Hopsan (Hopsan project) and ADAMS (MSC • robust and numerical stable simulation, Adams; Braun et al., 2015). These experiments con- • parallel simulation of the complete composite firmed the feasibility of the concept, but does not pro- model, vide a general platform for FMI co-simulation. • support of FMI, 2.1 Discussion of related work • modelling on appropriate abstraction level, e.g., encapsulating low level details of FMI, and Roughly, there are two subgroups of master simulation tools. One that focuses mostly on the modelling, com- • easy-to-use tool for building composite models. putation, and communication aspects. The issues of numerical stability are not adressed, and left for the In the following sections the composite modelling user to solve. tool and the underlying technology is discussed. The other group tries to handle tightly coupled mod- Examples of industrial use-cases and demonstrators els as well. They typically rely on the FMI function- are given. They motivate the research and prove that ality for rejecting steps and supply of Jacobians. A it works in real applications. drawback is that the external simulation tools must support rejecting steps, which is not always the case. The same can be said for Jacobians, which also can be 2 Related work { FMI/TLM costly to compute. Several researchers have investigated master algo- Unlike these methods, the work in this paper is fo- rithms for co-simulation using FMI. cused on decoupling at the modeling level using TLM. A basic master algorithm was proposed by (Bas- Hence, time delays are inserted directly into the model tian et al., 2011). Master algorithms based on High- equations and no numerical decoupling algorithms are Level Architecture (HLA) have also been investigated required. (Elsheikh et al., 2013; Awais et al., 2013; Neema et al., The asynchronous transmission line modelling tech- 2014). All these implementations provides successful nique is employed to simulate the composite model in results for their respective test models. However, nei- a completely robust and parallel way. ther of them attempts to address the issues of numeri- FMI is supported by treating it just as an additional cal stability. generic simulation tool type. A wrapper is used to In (Schierz et al., 2012), a master algorithm for FMI encapsulate and translate to the low level details of using communication step size control was presented. the FMI model interface. Error estimation was used to adapt the communica- To provide easy to use tool support to build com- tion step, which provided significant improvements to posite models, a proven 3-D model editor is extended stability and performance. Unlike the work presented to support FMI external models and mixed models. 180 Fritzson et.al., \Composite modelling in 3-D mechanics utilizing TLM and FMI" 3 Composite model editor and For external models in FMI 2.0 (Functional Mock- master simulation tool up Interface (FMI)) format, both variants of FMI, i.e., model exchange and co-simulation, are sup- A co-simulation model is here denoted composite ported since December 2016. model, which consists of several interconnected external Alternatives based on XML or Modelica have been in- models, simulated independently in external tools. vestigated, but a small dedicated language was pre- To study and predict dynamic phenomena, one needs ferred in the end (Siemers, 2010). to use a dynamic simulation tool. One such tool is Among the ties, there is a 3-D mechanical bi- BEAST (Fritzson et al., 2014), which is a 3-D multi- directional TLM connector type. Thus, a single high body simulation tool specialized in detailed contact level connector type encapsulates 24 scalar variables calculations, making it a very efficient tool for rolling describing the motion and the loading in the tie. bearings and other machine elements where contacts A model with only external models is defined as a are important. \pure" composite model, whereas a model with both The tool simultaneously solves the dynamics of the internal components and external models is defined as multi-body system, the structural deformations, the a \mixed" model. thermal balance, and the local lubricated contact con- User defined parameters can be defined at different ditions. The tool is used for optimizing the product levels in the system model, and also as expressions of design, for evaluating performance under various appli- other parameters. The parameter look-up follows the cation conditions, and for advanced