Geometrical Theory for Mechatronic Design Ontology

COMPUTER-AIDED DESIGN & APPLICATIONS, 2017 VOL. 14, NO. 5, 595–609 http://dx.doi.org/10.1080/16864360.2017.1280270

Use of technologically and topologically related surfaces (TTRS) geometrical theory for mechatronic design ontology

Régis Plateaux 1, Olivia Penas 1, Romain Barbedienne 1, Peter Hehenberger 2, Jean-Yves Choley 1 and Aude Warniez 1

1SUPMECA, Laboratoire Quartz (EA 7393), Saint Ouen, France; 2Johannes Kepler University Linz, Austria

ABSTRACT KEYWORDS This paper presents the MBSE challenges related to the conceptual design of mechatronic systems Ontology; semantic and especially the need to ensure geometrical knowledge consistency. To tackle this issue, we pro- modeling; mechatronic pose to define an ontology based on the TTRS (Technologically and Topologically Related Surfaces) design; geometrical geometrical modeling. We implement it in the Protégé environment and validate it through the modeling modeling process of an Electric Power Train, including many additional geometrical issues related to mechatronic system design, such as physical integration and the related compactness metric and the thermal modeling for multi-physical couplings. Geometrical knowledge consistency has been ensured through a model transformation between SysML and FreeCAD, using Python.

1. Introduction and Topologically Related Surfaces) geometrical modeling theory into a mechatronic ontology is presented, in Today, very few research studies on conceptual design order to ensure geometrical data consistency during the have focused on the integration and importance of conceptual design stage. Finally, it is implemented in an geometrical knowledge consistency management when Electric Power Train case study. selecting promising solution concepts related to their component 3D positioning and physical behavioral constraints. As geometrical data can be multiple and vari- 2. Context ous, they indeed depend on the model they are used in. 2.1. Geometrical consistency needed for When considering mechatronic systems design, geome- mechatronic conceptual design try challenges mainly relate to their high physical integration, be it to increase their compactness (that needs This section describes why ensuring geometry consis- to be evaluated through metrics), or to take into account tency is important for mechatronic conceptual design. multi-physical couplings due to the proximity of com- The design of mechatronic systems is particularly ponents. The definition of a suitable ontology including complex because of their high functional integration, the geometrical point of view is then required in order to multi-domain and multi-physical aspects, and other cor- ensure the geometrical data consistency in such a com- responding couplings [11][17]. Indeed, such systems plexmechatronicsystemdesignthankstoaModel-Based are characterized by the synergic interactions between System Engineering (MBSE) approach. Indeed, semantic their components from different technological domains, knowledge-based engineering can efficiently support an as they integrate mechanics, electronics, automation automatic consistent products design. In order to meet and information technologies. These interactions enable these objectives, it is then necessary to describe the geo- mechatronic systems to achieve more functionalities (due metrical properties of the mechatronic system as of the to couplings) than the sum of the functionalities of early design stage to select a suitable concept, but also to their components considered independently. Individual ensure their consistency from the requirements specifica- parts also incorporate more functions in an increas- tion phase to the verification phase (with the traceability ingly highly-integrated package (“cross-functional inte- of the selected geometrical concept 3D architecture). In gration”) [1], which results in an increasing number of this paper, the integration of the TTRS (Technologically components to be integrated in a compact volume, in

CONTACT Régis Plateaux [email protected]

© 2017 CAD Solutions, LLC, http://www.cadanda.com 596 R. PLATEAUX ET AL. which various physical fields interact and create multi- architectures, in order to evaluate their performance physical couplings [11]. For example, Pérez-Grande & al. relating to the considered MoP [13]. show that compactness is a current optimization crite- Finally, it is also necessary to trace whether initial rion for an aircraft environmental control system [27], (geometrical and physical) requirements are fulfilled by and Ooshima & al. underline the issue of multi-physical the various potential 3D designed architectures. interactions for the optimization of the size of a system Toaddress these challenges, we have proposed a MBSE [24]. As the physical integration of mechatronic systems approach to build a seamless process during the concep- is one major issue of their design, it requires to be con- tual design phase for a consistent transmission of the 3D sidered as one of the criteria of the decision-making geometrical data Fig. 1 [7]. The corresponding platform process, to select the convenient system architecture. The implementation has to guarantee that all representations definition of such physical integration metrics (based of the system - in the System model for the specifications, on these criteria) requires to know, from the concep- in multi-disciplinary modeling for physic behavioral sim- tual design stage, the simplified geometry and relative ulation or in 3D environment for 3D architecting - will be positioning of components [33]. Additionally, the high consistent. integration of mechatronic systems leads to an increas- Finally, the implementation of such an approach pre- ing number of desired and undesired interactions among viously requires a geometry knowledge formalization to the components. Undesired interactions are the distur- describe features, such as the structure and the behav- bances (mainly due to multi-physical couplings between ior of such complex systems, in a clear and consistent components) that can affect the behavior of the entire way. The topological (graph-based) representation of the system. However, due to the lack of 3D data in the early system could then be useful to define the hierarchical design stage, the multi-physical behavior of mechatronic structure of components and their interconnection laws, systems is not usually studied before the detailed design be it geometrical or physical, but it is not sufficient to phase, and its modeling is thus based on time consuming define the corresponding semantic. In fact, according to finite elements methods. However, assessing the 3D spa- the semantic complexity of mechatronic design, even dic- tial architectures, under multi-physical constraints, from tionaries, thesauri and taxonomies are not enough to theconceptualdesignphasewilldefinitelydecreasethe express, formalize and structure all the knowledge enti- risk of the late expensive changes occurring during fur- ties described in such a semantic environment. Thus, ther design phases, and consequently reduce the global an ontology modeling, based on a geometrical theory design time [5]. adapted to conceptual design, will ease the definitions of To meet this challenge and support the design of these complex concepts and relationships required for mecha- complex mechatronic systems, it is necessary to take into tronic design. It will help to automatically describe a account the components geometry and positioning as coherent knowledge-based engineering design process of soon as possible, as of the conceptual design stage, by mechatronic products, by providing powerful means of proposinganapproachtoevaluatethe3Darchitecture analysis (of problems, of their causes, of their solutions), under geometrical and physical constraints. to support knowledge sharing and reuse, and also plan- Therefore, system architects first need to easily supply ning, coordination and control of the complex product the same geometry specifications to all domain techni- design process activities. cal teams. These can be either geometrical requirements of the system and its components or some geometrical 2.2. TTRS modeling constraints of relative positions between them. Then, designers have to analyze and compare them, The Technologically and Topologically Related Surfaces prior to selecting the optimal one, by usually perform- (TTRS) theory represents and classifies surfaces [10]. ing some preliminary physical behavior simulations. Still Classes of TTRS refer to the symmetry-based classifica- as the simplest assessment of any physical behavior relies tion of surfaces and relate to their kinematic invariance. on the orientation and distance between the compo- Then, any surface or association of the real surfaces of nents or even on some dimensional data [32], designers an object is related to a kinematic invariance class named usually need to consider geometry as soon as possible TTRS class. There are 7 classes of TTRS classified accord- in the design life cycle (notably during the conceptual ing to their increasing degrees of freedom (DOF). These design phase) in order to evaluate physical interactions. classesare:spherical,planar,cylindrical,helical,revolute, For example, in the case of Measures of Performances prismatic, and complex. For example, the revolute class (MoP), some geometrical relationships like physical laws characterizes all invariant to rotation forms such as a cir- including shape factors, are usually required for pre- cle, a torus or cone. Adding one degree of freedom, we liminary behavioral simulations of physical alternative can obtain another surface class, such as the cylindrical. COMPUTER-AIDED DESIGN & APPLICATIONS 597

Figure 1. Overview of the global approach [4].

Table 1. (a) Deﬁnition of TTRS and MRGE and (b) their relative TTRS constraints.

Foreachclass,itispossibletoassociateoneMinimal classes are associations of sphere, cylindrical and planar Reference Geometric Element (MRGE) (Fig. 2)thatisthe classes. Then, when restricting TTRS classes to only these minimal combination of the following simpler geomet- three TTRS classes, only 13 constraints between their ric objects, named Reduced Geometric Elements (RGE): MRGEs are enough for their positioning and orientation plane, line and point, since only these three geomet- (Tab. 1). rical entities are necessary to describe the previous 7 Additionally, TTRS can also manage constraints classes. For example, the cone belongs to the revolute between different parts of an assembly in order to class.Wemayresumeitwithapointandastraightline. define the kinematic joint between these parts, notably This reduced geometrical representation facilitates object for tolerancing considerations. They are then called positioning in the Euclidian space. Pseudo-TTRS [9] and the constraints between the MRGE Finally, as TTRSs define an algebraic group structure, of the parts are the same as in the TTRS theory. TTRS modeling also manages the composition of other The TTRS theory presents many advantages meeting TTRS and their relative positioning [31]. An example is thepreviousdescribedneeds,sinceitincludesboththe when building a component based on a cone and a cylin- modeling of components and their positioning (when der, while considering the coincidence between their considering their surfaces) that is required be it to symmetry axis (D1 = D2), the reclassed TTRS results in specify geometrical requirements, to spatially position a revolute TTRS, whose MRGE is point and line. components in a 3D environment, and finally support Moreover, when analyzing each MRGE, we can find the corresponding geometrical information necessary for that the MRGE of identity, revolute, prismatic and helical physical simulation. Another advantage of this theory 598 R. PLATEAUX ET AL.

Figure 2. MRGE generation for TTRS modeling. is that GPS (Global Product Specifications) standards Other studies have focused on the semantically [18][19] are based on it. These standards are already based description of the information and product data implemented into many CAD software like CATIA V5, exchange during the conceptual mechatronic design pro- allowing users to formalize positioning constraints with cess. Hehenberger & al. were particularly interested in the the same “logics”. Finally, this approach allows to create useofanontologyasameansofinconsistenciesdetec- all kinds of geometry, be it simple or complex, so that it tion and tracking during the design changes, notably for suits any geometry whatever its initial complexity level. the design/process planning integration [16]. Finally, it is particularly appropriate for the concep- Considering existing ontologies for the 3D model- tual design stage, since conceptual design requires a ing, few studies have specifically addressed the geom- simpleandquickmeanstohaveanoverviewofthe etry knowledge mentioned earlier. They have mainly spatial distribution of simplified components of a given dealt with the semantic representation of 3D contents architecture,tosupportthechoiceofthebestconcept [3][28]. Other authors describe some spatial ontologies, (that fulfills system model requirements). Therefore, the regarding space for geographical interests [8]. Further- abstraction level of TTRS theory is very useful, since more, Liang & al. propose a port ontology for conceptual most of components geometries can be simplified in a design that includes “form attributes” classes related to simple geometry having a kinematic invariance sym- the geometry. They associate a CAD feature to a “form metry. Besides, the kinematic invariance is very useful feature” including a “form attribute” linked to its loca- in a 3D environment to recommend the displacement tion, in order to make possible the specification of a direction to follow to meet some geometrical or physical partial geometry definition (points, curves and surfaces) requirements. [22]. They address geometry and transfer flows (energy, material, signal) compatibility, without describing how to deal with some geometrical and interactive physical constraints that may also be quantified. 2.3. Ontologies related works Finally, none of the previous studies has dealt with As an ontology defines a common vocabulary for an ontology integrating the geometrical knowledge from those who need to share information in a domain, the the early phases of the conceptual design, and its specific usage of ontologies and corresponding expert system challenges related to the assessment of 3D multi-physical software is a major issue for the mechatronic design integration of mechatronic systems. process. Welp & al. propose a semantic web service platform 3. Our approach for a knowledge-based design of mechatronic systems [34], by integrating the design environment and using TheaimofourapproachistoconsidertheTTRSthe- software agents, since ontologies also include machine- ory as the support of the geometrical knowledge within interpretable definitions of basic concepts in specific the mechatronic ontology, in order to notably ensure its domains and relations between them. They use the consistency during the conceptual design stage. semantic web technology to intelligently deal with web contents [35] and they define three knowledge levels: 3.1. Definition process of the mechatronic design the ontology layer, the metadata layer and the informa- ontology tion layer. Their mechatronic ontology is based, on one hand, on four basic elements (actuator, sensors, infor- The fundamental objective when defining an ontology is mation processing and mechanical basic system) and integrating knowledge of numerous information sources on the other hand on two basic forms of interfaces and various viewpoints. Indeed, beneficial interactions (energy-dominated interfaces and signal dominated between mechatronics domains are actively pursued in interfaces). order to boost the performance of new products, even COMPUTER-AIDED DESIGN & APPLICATIONS 599 if leading to an increasing complexity of their design account some geometrical constraints or other physical [26]. Conceptual stage starts from the specification of behavior requirements. Besides, a mechatronic system requirements and aims at providing a support to decide structure has a component-dominated topology, since a on the feasibility of a given system architecture, before mechatronic system can be decomposed into some sys- proceeding to its detailed design [23]. Conceptual phase tems and then into modules. A mechatronic system con- modeling elements may be represented as a graph-like cept is related to an environment which can also be a structure [29]. A typical topological representation of mechatronicsystem(e.g.robots).Finally,theFunction- the design of such a system could be represented by the Behavior-Structure modeling of a system allows to cover Fig. 3. different views of complex systems [15]. When considering the 4-layer metamodeling architecture of MDA (Model Driven Architecture) [12], the metamodeling defines an ontology of concepts for a domain,aswellasthevocabularyandgrammaticalrules of a modeling language. A domain ontology formally describes concepts, relationships among concepts and constraints which are used in the metamodel and model definition. Thus, the ontology is the content theory that specifies the concepts and their relations used in a specific knowledge. To facilitate the understanding of the developed ontology, Fig. 4 presents our view of the ontology-related notions. Figure 3. Topological representation of system design [6,29]. Moreover, when designing a mechatronic system, designers implicitly apply their aggregated knowledge This figure shows the interdependency links of mod- to the new concept, without being aware of what elingdata,accordingtotheviewaddressed. other designers will consider as design rules, functional Indeed, during the conceptual design, it is usual to requirements, etc. Then it is also important to formal- define rough and simple dimensioning models by an ize the integration of the already existing ontologies. This appropriate reduction of more complex systems. The integration can be made at different levels: by combining first impact is then to consider simple geometry of two existing ontologies (mapping or inter-ontology map- components, which permits to evaluate, through metrics, ping), or even by inserting content from an ontology to different 3D spatial architectures alternatives, taking into another [20][21].

Figure 4. Ontology and related notions. 600 R. PLATEAUX ET AL.

Figure 5. Mechatronic Design Ontology Deﬁnition.

The developed ontology contains the basic mecha- defined by one or more constraints. These positioning tronic systems knowledge for the conceptual design constraints, derived from Tab. 1,aredefinedbetweenthe phase. The concepts and their relationships describe then MRGE of the two TTRS considered. The 3D parameters, the relevant knowledge of mechatronic design, as previ- requestedfortherepresentationofthemechatronicentity ously presented. This knowledge needs to be structured volume in a 3D Euclidean space, are defined by the posi- according to a semantic representation. For example, tion and the orientation of each RGE contained in the we define a mechatronic design ontology with ten con- MRGE of the considered TTRS. cepts and thirteen different relationships, as described on Fig. 5. 3.3. Ontology-based geometrical consistency implemented in SAMOS 3.2. TTRS theory integration In this section, we explain how the implementation of the Ourapproachisthatthepreviousgeometricalmodeling previous ontology in software tools allows to ensure the is supported by the TTRS theory. Fig. 6 presents the cor- consistency of geometry knowledge, for 3D architecting responding TTRS-based geometrical modeling ontology. and physical behavior simulation, under geometrical and The mechatronic entity, which can be made of other physical constraints, of mechatronic system during the mechatronic modules (sub-systems), is composed of one conceptual design. TTRS (corresponding to its whole surface), which can Conceptual design of mechatronic systems is a deci- itself comprise some TTRS (some elementary infinite sive phase when the simulation teams have an inter- surfaces) (Fig. 7). Finite surface has its own resulting est in quickly pre-validating spatial architectures from TTRS. the physical architecture proposed by the system archi- A mechatronic entity has finite dimensions defined by tects. Indeed, they need to evaluate the physical behav- some dimensional parameters. ior resulting from the high integrated 3D architecture Whatever the considered level, each TTRS relates on of mechatronic systems. Still, this step could be very one kinematic invariance of a “TTRS Class”: kinematic difficult, since they have no dedicated means and tools invariance is represented through a 6-dimensional vec- to manage geometry consistency all along the prelimi- tor (3 for each translation invariance and 3 for each nary design phase. In order to help them to efficiently rotational invariance). Each TTRS class defines its corre- achieve this task, the theoretical formalization of our sponding MRGE (Minimal Reference Geometrical Ele- approach (through the developed ontology) will provide ments). The relative position of TTRS to another is a consistent integration of the geometry knowledge all COMPUTER-AIDED DESIGN & APPLICATIONS 601

Figure 6. TTRS-based geometrical modeling ontology.

along the conceptual design. The corresponding model Systems Engineering (INCOSE) to support MBSE and transformation platform, named SAMOS (Spatial Archi- has been defined by an OMG (Object Management tecture based on Multi-physics and Organization of Group) specification since 2006. A common approach to Systems),thenensuresaseamlessgeometricalconsis- formalize an ontology in a system modeling language is tency and traceability from the requirements to the fur- to propose some UML profiles or SysML extensions. A ther design stages [4]. Besides, as the simplest assess- profile in the UML provides a generic extension mech- ment of any physical behavior requires prior knowledge anism to customize UML models for particular domains of the components position, investigating the geometry- and platforms. Accordingly, our prior developments have related physical interactions during the conceptual consisted in enriching the system model with geometrical design phase will avoid selecting a 3D physical archi- and physical data and their corresponding constraints, tecture with unmanageable unwanted multi-physical by providing two SysML extensions based on the TTRS behaviors. theory: GERTRUDe (Geometrical Extension Related to As a MBSE process needs an abstraction of the system, TTRS Reference for a Unified Design) for geometri- we have investigated on how to use it to create a consistent cal aspects [6] and TheReSE: Thermics Related SysML linkbetweenthegeometricaldataoftheabstractionlevel Extension, for thermal modeling.[5]. The data model of ofthesystemmodelandthegraphicalviewofa3Dsketch these extensions, based on the developed ontology, is required to better perform the conceptual design of the presented in Fig. 8. system, and notably the preliminary physical behavior ThesecondpartoftheSAMOSplatform,isbasedon modeling. a 3D environment that is more adapted to the simula- The SysML (Systems Modeling Language) language tion teams’ tasks. Indeed, they need to test different 3D has been chosen, as we require a language which architectures of components by quickly simulating their allows specifying all requirements and system architec- corresponding physical behavior, in order to pre-validate tures,whateverthedisciplineortechnicalteam.This those which meet the requirements issued from the sys- language was initiated by the International Council on tem modeling, while dealing with simplified geometry of 602 R. PLATEAUX ET AL.

Figure 7. TTRS decomposition levels.

components and some hypotheses to simplify for exam- OMG standard is the Meta Object Facility or MOF. The ple thermal behavior by analytical equations. Then these proposed approach is described on Fig. 9. simulation results, corresponding to a specific 3D geom- Thechosentoolsfortheexperimentationofour etry architecture of components, need to be traced back approach are Artisan studio 7.4 [2]forSysMLmodeling in the system model. and FreeCAD [14] for CAD modeling. The interface used Firstly, from the geometrical point of view, this model for the transformation platform has been implemented transformation has to ensure that the creation of a new inthePythonlanguage.Thedetaileddescriptionofthe geometry in the SysML model automatically generates model transformation process will be presented in [7]. thesameactioninthecorrespondingCADmodel,and Considering the physical behavior modeling and sim- vice versa, without any additional development. Model ulation, we are working on the thermal modeling: with transformation operators often work at the M2 meta- the prior development of the TheReSE extension [5], model level, by manipulating instances of metamodel and by taking into account the impact of the developed constructs (from GERTRUDe and a CAD tool meta- TTRS-based ontology on the formalization of thermal models). A metamodel (M2) is a model that defines behavior equations (for conduction, convection and radi- the language which is used in a model (M1) of the ation) [7]. To model interacting components through real world (M0). A metamodel (M2) conforms to a lan- which the physical flow passes between two compo- guage whose abstract syntax is represented by a reflex- nents, TheReSE proposes a stereotyped block called ive (that conforms to itself) metametamodel (M3). The “Media”.MediaisacomponentwithallitsTTRS-based COMPUTER-AIDED DESIGN & APPLICATIONS 603

Figure 8. GeRTRUDe and TheReSE data models, based on the developed ontology.

Figure 9. Geometrical Knowledge Model Transformation Approach. 604 R. PLATEAUX ET AL.

Figure 10. Geometrical knowledge consistency ensured by the TTRS-based ontology.

geometrical properties (concrete geometry, emitting and 4. Case study application: Electric Power Train receiving thermal geometry) and the parameters required 4.1. Case study description to be managed by thermal equations during simulation. Be it geometrical constraints equations or thermal equa- To illustrate this approach, and to see how ontology can tions, they are managed by Modelica modeling which help to ensure the geometrical consistency of a mecha- is also interfaced by Python. Indeed TTRS constraints, tronic system design, we choose the scenario of the 3D based on the TTRS-based ontology have already been architecture of an Electric Power Train (EPT) for bus implemented in the Modelica language [25][30]. vehicles, mounted on a chassis. Regarding the geometri- Fig. 10 presents the various modeling types occur- cal specifications about the minimal volume, two archi- ring in the conceptual design stage (respectively based tectures have been considered: on the SysML and Modelica languages and FreeCAD tool) and how the use of the TTRS-based ontology allows • Thefirstarchitectureconsistsofonegearedmotor,one to keep the geometry knowledge consistency, notably inverter, one electronics control unit and one differen- through successive model transformations. Indeed, from tial gear. a meta-model viewpoint, the various respective modeling • The second one differs from the first one by two domains are based on the developed ontology as a refer- motors and two inverters (one by wheel), but it does ence, since this can be considered as an “upper/generic not need the differential gear any longer. ontology”forthegeometricalpointofview.Thiswill ensure the meeting of the geometrical specifications and For this example, we took dimensions and mass of corresponding data traceability, and then facilitate the existing C.O.S.T.S. (as mentioned in Tab. 2). The cor- verification automation. responding dimensions of the simplified geometry have

Table 2. Architecture evaluation results. COMPUTER-AIDED DESIGN & APPLICATIONS 605

Figure 11. Case study based on the ontology developed with the PROTÉGÉ environment. been based on the higher dimensions related to the con- with the HermiT1.3.8.3 reasoner. The reasoner classifies sidered spatial directions. and assesses classes and object properties (Fig. 12).

4.2. Case study ontology modeling 4.3. Ontology-based scenario validation The developed ontology and its application to the case Geometrical consistency is ensured by the model trans- study have been implemented with the Protégé environ- formation between these various level modeling, made ment (Fig. 11). possible by the implementation of the following devel- An inference engine embedded in the Protégé soft- opments: TTRS-based ontology in the SysML meta- ware proposes some reasoning processes. The consis- model through GeRTRUDe and TheReSE developments, tency of the developed ontology model has been checked the integration of the TTRS constraints in Modelica 606 R. PLATEAUX ET AL.

Figure 12. Result of consistency checking of the case study within Protégé using HermiT 1.3.8.3.

Figure 13. Alternative EPT spatial architectures in SysML with GeRTRUDE. and the use of OpenModelica Python language to sup- Then, 3D modeling (Fig. 14) is automatically gen- port physical behavior modeling, and the TTRS finite erated in the FreeCAD environment thanks to the volumes and constraints libraries in FreeCAD for the developed SAMOS platform (Fig. 15), based on model 3D modeling. transformations [4], which implements the developed These different modeling steps are presented with the ontology. EPT case study example. After performing the geometrical metric defining the On the Fig. 13,botharchitecturesarespecifiedbythe compactness of each architecture [33], as the second System Architect in the SysML modeling, thanks to the architecture presents the slighter weighted compactness developed GERTRUDe SysML extension [6]. Compo- metric (Tab. 2), we choose it to carry out the thermal nents represented by blocks are stereotyped with “Com- modeling. ponent”: each block is associated with a simplified geom- For this thermal behavior modeling, performed etry and its corresponding dimensions can be specified thanks to the developed TheReSE SysML extension [5] in the predefined unit. The geared motors and differential (based also on this ontology) and then Modelica, we have been approximated by cylinders, and inverters, elec- need four additional components: a fan and three pipes tronic control unit and chassis have been approximated to complete the 3D architecture, in order to simulate by rectangle parallelepipeds. the thermal behavior based on the defined 3D geometri- The relative positioning (position and orientation) of cal architecture. These components can be added either components can also be specified by the TTRS con- in FreeCAD by 3D designers and then traced back in straints, between their respective Minimal Reference the SysML model or they can be directly defined in the Geometrical Element (MRGE). In our example, we spec- SysML environment by System Architects (Fig. 16 on the ify some contact and coaxiality constraints between the left). Then the Modelica modeling can be processed and architecture components. Finally, the geometrical metric simulated, after having defined thermal requirements, to calculate the compactcness of the system is also defined thermal properties of components and thermal simula- by a constraint block. tion conditions, in the SAMOS implemented platform. COMPUTER-AIDED DESIGN & APPLICATIONS 607

Figure 14. Generated 3D modeling of the diﬀerent architectures.

Figure 15. HMI development in FreeCAD for the implementation of the SAMOS approach.

Figure 16. Thermal constraints and modeling of the architecture 1 in SysML (left) and Modelica (right) environments.

The developed geometrical knowledge ontology for 5. Conclusions mechatronic systems design based on the TTRS theory has been implemented in the data models of the After presenting the TTRS theory and describing mecha- GERTRUDe and TheReSE SysML extensions. It allows to tronics design complex challenges, we have proposed a specify the simplified geometry and relative positioning geometricalontology,basedonthistheory,tobeincluded constraints of the components of both EPT architectures in a mechatronic design ontology. This approach allows and to trace the final 3D architecture resulting from the to automatically ensure the consistency of geometri- thermal modeling in Modelica, back to the System model. cal knowledge all along the conceptual design stage, The evolving geometrical knowledge during this con- from the specifications to the verification (traceability), ceptual design phase has been kept consistent, since the in accordance with MBSE approaches. This ontology corresponding model transformation processes (between has been validated through the effective development SysML, Modelica and FreeCAD models) have been car- of model transformation processes between the differ- ried out between geometrical data models based on the ent modeling using geometrical data. Moreover, it has same (TTRS-based) ontology. been applied to a scenario of the architecture choice of an 608 R. PLATEAUX ET AL.

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