Template-based Geometric Transformations of a Functionally …4)_2014_436-449.pdf · 2018. 10. 10. · 436 Template-based Geometric Transformations of a Functionally Enriched DMU

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Template-based Geometric Transformations of a Functionally Enriched DMU intoFE Assembly Models

Flavien Boussuge1,2, Ahmad Shahwan2, Jean-Claude Léon2, Stefanie Hahmann2, Gilles Foucault2 and Lionel Fine1

1EADS – Innovation Works, [email protected], [email protected] University/INRIA, [email protected], [email protected],

[email protected], [email protected]

ABSTRACT

Pre-processing of CAD models derived from Digital Mock-Ups (DMUs) into finite element (FE) mod-els is usually completed after many tedious tasks of model preparation and shape transformations.It is highly valuable for simulation engineers to automate time-consuming sequences of assemblypreparation processes. Here, it is proposed to use an enriched DMU with geometric interfaces betweencomponents (contacts and interferences) and functional properties. Then, the key concept of template-based transformation can connect to assembly functions to locate consistent sets of components inthe DMU. Subsequently, sets of shape transformations feed the template content to adapt componentsto FE requirements. To precisely monitor the friction areas and the mesh around bolts, the templatecreates sub-domains into their tightened components and preserves the consistency of geometricinterfaces for the mesh generation purposes. From a user-selected assembly function, the method isable to robustly identify, locate and transform groups of components while preserving the consistencyof the assembly needed for FE models. To enlarge the scope of the template in the assembly functiontaxonomy, it is shown how the concept of dependent function enforces the geometric and functionalconsistency of the transformed assembly. To demonstrate the proposed approach, a business orientedprototype processes bolted junctions of aeronautical structures.

Keywords: assembly, DMU, CAD – CAE integration, functional information.

1. NOTATIONS - ACRONYMS

General purpose acronyms:BC: boundary condition;DMU: digital mock-up;FE: finite elements;FEA: finite element analysis(es);KBE: Knowledge-based engineering;PDP: product development process;OWL: web ontology language;RDF: resource description framework;STEP: Standard for the Exchange of Product modeldata;

Acronyms specific to the paper:CI: conventional interface; CIG: conventional interfacegraph;CC: compatibility conditions between T and ST ;FD: functional designation of a component;FI: functional interface;

IC: set of components such that each of its compo-nents has all its FIs in T;PC: set of components such that each of its compo-nents has some of its FIs in T;TCI: taxonomy of conventional interfaces;TFD: taxonomy of functional designations of compo-nents;TFI: taxonomy of functional interfaces;TFN: taxonomy of functions;SME: reference state expressing static mechanicalequilibrium of a component;SLC: reference state expressing a static load cycleinside an assembly;ST : shape transformation incorporated in a template,hence ST (T);ST 1: removal of a threaded link; ST 2: cylindricalsub domain around a screw shaft to localize fric-tion effects; ST 3: removal of the locking nut of abolted junction; ST 4: screw head transformations;

Computer-Aided Design & Applications, 11(4), 2014, 436–449, http://dx.doi.org/10.1080/16864360.2014.881187c© 2014 CAD Solutions, LLC, http://www.cadanda.com

mailto:[email protected], [email protected]

mailto:[email protected], [email protected], [email protected], [email protected]

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ST 5: preserve the cylindrical loose fit between screwand plates to set up contact friction BCs;T: function-based template performing shape trans-formations;TI: union of all components belonging to IC.

2. INTRODUCTION

To speed up a PDP, aeronautical, automotive andother companies face increasing needs in setting upFE simulations of large sub-structures of their prod-ucts. The challenge is to study not only standalonecomponents but to simulate the structural behavior oflarge assembly structures containing up to thousandsof components [9]. DMUs are widely used duringa PDP as the virtual geometric product reference.This model contains detailed 3D representation ofthe whole product structure available for simulationengineers. To prepare large sub-structure models forsimulation (such as wings or aircraft fuselage section);the DMU offers a complete geometric input model.However, speeding up the simulation model genera-tion strongly relies on the time required to performthe geometric transformations needed to adapt theDMU to FE requirements.

Currently, time and human resources involved inpre-processing CAD models derived from DMUs intoFE models prevent engineers from setting up struc-tural analyses. Very tedious tasks are required toprocess the large amount of DMU components andthe connections between them. The shape transfor-mations required for each assembly component, andinteractively performed by engineers, can cover defea-turing [16,37], idealization [5,6], domain decomposi-tion [30,32] as well as the definition of contact areas.Even on repetitive configurations such as junctions,similar geometric transformations must be repeatedon all the components and interfaces of all the assem-bly junctions. Aeronautical structures are particularlycomplex to transform due to their many independentconnectors such as bolts or rivets (see Fig. 1). Eventhough CAE software possess specific operators forbolted junctions, pre-stressed configurations, . . . , tospeed up FEA pre-processing, the user must already

have available a DMU incorporated all the desired geo-metric transformations. Automated domain decom-position, geometric simplifications, selection of targetcomponents are examples of processes still inter-active and error prone that a user must performtediously. Within the available resources and timescale planned in an industrial PDP, the analyst istherefore limited to simulate small models ratherthan complete assembly structures.

Compared to standalone components, the aboveobservations highlight the prominence of geometricinterfaces processing when preparing an assemblymodel for FEA. Their mechanical behavior and thenew shape transformations they convey are specificfeatures of assemblies [9]. As described in [36], com-ponent’s geometric interfaces are the basis of compo-nent’s functional designation. Effectively, to speed upthe transformation of a DMU into a FE model, the engi-neer would process the components in accordanceto their mechanical effect in the assembly, i.e. theirfunction. Consequently, the relationship between FEsimulation hypotheses, component’s functions andcomponent’s interfaces appears as a key issue toimprove the efficiency of DMU transformation forFEA. Indeed, setting up a FEA aims at studying themechanical behavior of an assembly. Function, behav-ior and shape share strong connections, as studiedby Gero [18,19] and Albers [1,2] among others, hencethe aforementioned example of the FE preparationprocess contributing to the representation of boltedconnections in an aeronautical assembly.

In this paper, we propose an approach to reducethe FE model preparation time to adapt CAD assemblymodels derived from DMUs, into FE assembly models.Based on the analysis of DMU transformation require-ments for FE assembly model preparation [9], themethod uses an enriched DMU as input. It is obtainedfrom previous developments and contains explicitgeometric interfaces between components (contactsand interferences) as well as their functional designa-tions. This last step is achieved using a qualitative rea-soning process. From this enriched model, it is shownthat further enrichment is needed to reach a levelof product functions where simulation objectives canbe used to specify new geometric operators that canbe robustly applied to automate components’ and

Fig. 1: Examples of aeronautical DMUs with a variety of bolted junctions.


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interfaces’ shape transformations during an assem-bly preparation process for FEA. If close to KBE,this scheme is nonetheless more generic and morerobust than KBE approaches because functional des-ignations and functions are generic concepts. KBEaims at structuring engineering knowledge and pro-cessing it with symbolic representations [14,27] usinglanguage based approaches. Here, the focus is ona robust connection between geometric models andsymbolic representations featuring functions.

To prove the validity of our approach and themethodology proposed in [4–9], this paper presentsa template-based operator dedicated to automateshape transformations of bolted junctions. Using thefunctional information and geometric interfaces, theoperator applies a user-defined template to simplifybolts and sets control sub-domains around themin their associated tightened components to enablethe description of the friction phenomenon betweenthese components. This template is used to preciselymonitor the meshing process while preserving theconsistency of contacts and adapting the assemblymodel to simulation objectives.

The rest of the paper is organized as fol-lows. In Section 2, we review the CAD-CAE inte-gration research for FE assembly models. Section 3reviews the method to enrich the DMU with geo-metric interfaces between components and functionaldesignations of components. New requirements areintroduced to connect functional designations withfunctions. Section 4, describes the concept oftemplate-based transformation operator and illus-trates it with a template-based operator of boltedJunctions transformation. Finally, the paper presentsthe result of this operator on an industrial aeronauti-cal use-case and section 5 exemplifies an extension ofthe template definition with idealization transforma-tions.

3. RELATED WORK

Assembly models have been studied throughout thedevelopment of solid modeling concepts. Essentially,assembly models have been proposed for design andmanufacture applications [31–34] with recent applica-tions to collaborative design. With the development offeatures, approaches set assemblies as componentsrelated to each other through geometric constraints[40]. These approaches share a common denominatorwhere assemblies are described as geometric modelsprogressively enriched with technological and then,functional data [15]. However, the closer the func-tional information, the higher is the requirement toobtain external information to CAD environments andthe greater is the need of user’s interactions duringa design process. Though these additional informa-tions are mandatory in a design process, it does notseem efficient to incorporate them into a prepara-tion process for FE simulation when time reduction

is critical to insert simulations into a PDP. If theseinformations were available at the level of FE simula-tion, a dedicated approach could be set up to processthem but companies are currently not able to setup a digital representation of these data that is con-nected to the DMUs they produce with CAD systems.Within this framework, Roy and Bharadwaj [33] set upa design approach to connect functions to 3D geom-etry using a Part Function Model (PFM). There, theyaddress the relationships between function, behaviorand geometry of a part in a top-down manner fromfunction to geometry to obtain parts from functionalspecifications. The PFM described requires up to lowlevel functions that connect part boundary faces tofunction since the behavior model builds up on inter-faces between parts, i.e. contact surfaces to positionparts with respect to each other. At the level of com-plex assemblies with hundreds to thousands of parts,adding the amount of complementary data definingsuch a behavioral model becomes too tedious. Recentapproaches [25] reduce the description of junctionsbetween components to global parameters describingbolted and riveted connections without referring tothe individual surfaces of each bolt or rivet. This fitswell with a design process but simulation objectivesmay require a detailed representation of interfaceswhen the purpose is to assess the stress field distri-bution in a bolted connection with tens or hundredsof bolts.

Developments of ontology-based approaches takeadvantage of new capabilities to structure conceptsand to connect them with component models [26,31]or at the level of 3D geometry entities [7–20]. Someof these approaches have been applied to assem-blies [7,23,31] and can take advantage of reasonersto set up inference rules to ensure the consistencyof the assembly description or extract informationthat is not readily available in the dataset describingan assembly. In [23,31], there is no direct connectionbetween the ontology content and the 3D model ofcomponents. Here, ontologies support a design pro-cess where the engineer gets consistent informationin a collaborative context but the ontology does notconnect to boundary entities of component geometricmodels. Barbeau et al. [7] cover a larger descriptionof a product with an ontological description incor-porating the geometry and structure levels as avail-able through STEP APIs [21,22], up to the functionaldescription that can be inserted through ontologicalrepresentation of the Core Product Model (CPM) [17].The authors showed that not all concepts of STEPcould be rigorously expressed using OWL standard[29] leading to limitations in detecting inconsisten-cies. If CPM is able to relate component functions toform features, the content of the CPM reflects thedesigners’ choices to determine the level of productfeatures inserted in this model and its level of connec-tion with each component’s geometry. Consequently,there is no guarantee that functional information canbe available downward to the level of B-Rep entities


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of each component. Reasoning capabilities associ-ated with ontologies are set up to browse the wholeassembly ontology but they are not applied to derivenew functional information or reinforce the connec-tion between function and geometry in an assemblymodel. Consequently, we can observe that assemblyprocessing is often addressed in a design contextof top-down approach from primary product func-tion point of view and there is no low level robustconnection between components’ geometry and lowlevel functions. Additionally, the reasoning capabil-ities of ontology-based approaches are exploited tobrowse existing assembly data and derive data notreadily available. These reasoning processes do notextend further than relative positioning constraintsbetween components. KBE approaches [14,27] formal-ize engineering knowledge to automate some designtasks. KBE concepts take advantage of artificial intel-ligence techniques and strongly rely on language-based approaches. As such, they follow top-downapproaches based on enterprise ‘best practices’ andaddress preliminary design stages rather than embod-iment or detailed design ones, which is the productgeometric description addressed here with DMUs.This is hardly applicable to other companies and evenmore to other products. Still, if KBE approaches incor-porate connections with geometric models, geometryis perceived as attribute of higher level conceptslike components, which does not bring new structureto the geometric models of components. Recently,Shahwan et al. [36] inserted a qualitative reasoningprocess that can relate geometric interfaces up tothe functional designation of components, thus cre-ating a robust and automated connection between3D geometric entities and functional designations ofcomponents. It is a bottom-up approach that fits toour current requirements.

Research in CAD-CAE integration has mainlyfocused on the use of global geometric transforma-tions of standalone CAD components [37]. Few con-tributions addressed the automation of assembly pre-processing. Automatic simplifications of assemblyfor collaborative environment as the multi-resolutionapproach of Kim [24] or surface simplification ofAndujar [3] transform assembly components inde-pendently of each other. This is not sufficient topre-process FE assembly models because mechanicaljoints and interfaces tightening the different com-ponents must be part of their pre-processing. Com-mercial software proposes to automatically detectgeometric interfaces between assembly components.However, their algorithms use a global proximity tol-erance to find face pairs of components and theydon’t produce explicitly the geometric model of theircontact area. In the assembly simplification methodof Russ et al. [35], the authors propose to set compo-nents dependencies to remove groups of componentshaving no influence on a simulation or to replacethem by defeatured equivalent ones. However, theparent/child relationships created from constraint

placement of components do not guarantee to obtainthe entire neighborhood of a component becausethese constraints are not necessarily related to thecomponents’ geometric interfaces. In addition, DMUsdon’t contain components’ location constraints whenassemblies are complex, as occurring in the auto-motive and aeronautic industries, to ease designmodifications during a PDP. Moreover, part namingidentification used in this approach is not sufficientbecause it locates only individual components con-tained in the assembly without establishing relationswith their adjacent components and their associategeometric model, i.e. replacing a bolted junction byan idealized fastener implies simplifying its nut, itsscrew as well as the hole connected to them in thetightened components. To provide mesh domainsconnectivity, Lou [28] and Choudria [10] proposesto identify and re-mesh contact interfaces. Quadros[30] establishes sizing functions to control assemblymeshes. However, these methods are used directlyon already meshed models, which addresses specificPDP configurations where CAD models are not readilyavailable. Clark [11] detects interfaces in CAD assem-blies to create non-manifold models before meshgeneration but does not consider the interactionsbetween interfaces and components’ shapes trans-formation processes. In [9], we underline that if acomponent is simplified or idealized, its shape trans-formation has an influence on the transformationof its neighbors, e.g. a component idealized as apunctual mass impacts its neighboring componentinterfaces.

Indeed, to adapt an assembly to FEA require-ments, geometric transformations derive from sim-ulation objectives and components’ functions areneeded to geometrically transform groups of com-ponents. It is also critical to structure the geometricmodels of components so that their shape trans-formations can preserve the DMU consistency [9].We propose an approach where a DMU is enrichedwith geometric interfaces between its components,i.e. contacts and interferences, and functional proper-ties. From this enriched model, simulation objectivescan be used to specify geometric operators that canbe robustly applied to automate components andinterfaces shape transformations during an assemblypreparation process.

4. DMU ENRICHMENT WITH FUNCTIONALINFORMATION

4.1. From a Component Geometry to itsFunctional Designation

The principle of DMU functional enrichment can besummarized with the process flow shown on Fig. 2.Its detailed description can be found in [36]. Thefocus is placed on this approach because, to theauthors’ knowledge, Shahwan’s approach can auto-matically produce a functionally enriched DMU from


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Fig. 2: Process flow to enrich a DMU with functional designations of components and their associated structuredgeometric models.

a pure geometric input model, which is the reliableinput data addressed here.

Fig. 2 starts from the STEP [21,22] representationof an assembly model with the extraction of geomet-ric interfaces between components. Two categories ofinterfaces are addressed: contacts (surface and lineones) and interferences. The latter originates fromthe conventional representations of components, e.g.a screw is represented with a threaded part definedas a cylinder whose diameter equals the outer diam-eter of the thread and its nut is represented with athreaded part defined as a cylinder whose diameterequals an inner diameter of the thread; this producesa geometric interference between these components.At this stage, each component boundary gets mod-ified to incorporate the imprints of its neighboringcomponents through contacts and interferences. Thegeometric interfaces feed instances of ‘conventionalinterfaces’ (CI) classes structured into a taxonomy,TCI, that binds geometric and symbolic data, e.g.planar contact, spherical partial contact, cylindricalinterference, . . . Simultaneously, CIs and assemblycomponents are organized into a CI graph: CIG(C, I)where the components C are nodes and CIs I are arcs.

Then, instances of functional interfaces (FIs) arederived from CI ones, possibly with multiple instancesof FIs originated from a single instance of CI, e.g.a cylindrical contact can become either a cylindri-cal loose fit or cylindrical tight fit but a planarcontact becomes only a planar support. Instancesof FIs fit also into a taxonomy TFI. Now, the dual-ity between geometry and interaction forces is usedto derive mechanical parameters, i.e. screws (result-ing force, resulting moment), from each instanceof FI. These parameters are expressed qualitativelyand feed symbolic behaviors of the assembly inorder to take advantage of the shape, behavior, func-tion relationship [1,2,18,19]. Assembly behaviors are

characterized by reference states and aim at reducinga single FI instance per CI instance. Here, two refer-ence states are of interest: the mechanical equilibriumreference state, SME, and the static load cycle one,SLC. SME expresses the fact that each component musthold tight when the assembly has no mechanical inter-action with its environment, i.e. each component cansatisfy the static equilibrium equations. SLC expressesthe fact that any threaded link between any two com-ponents of an assembly must generate close loops offorces, i.e. force cycles so that the corresponding com-ponents stay at static equilibrium. Fig. 3 illustratesthis concept with a bolted junction and a force cyclein magenta.

Force cycles symbolically express the effect of athreaded link throughout an assembly, which endsup with the identification of sub graphs of the CIGdefining the effect of each threaded link.

Now, a matching process takes place based ona taxonomy of functional designations of compo-nents, TFD. A functional designation of a componentis an unambiguous denomination that functionallydistinguishes one class of components from another.It relates the geometric model of a component, itsFIs and FIs of its functionally related components,e.g. those contained in a load cycle, to its denom-ination. The functional designation of a componentbinds the 3D model of a component and FIs to asymbolic representation of its functions. Regardingscrews, examples of functional designations are: capscrew, locked cap screw, set screw, stop screw, . . .The matching process is set up using inferences pro-cessed by a reasoner, FACT++, that can be connectedto OWL or RDF [29] descriptions of the instancesof FIs attached to a given component. The infer-ences characterize the necessary properties of FIsthat a component must satisfy to belong to a givenfunctional designation.


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Internal Force Generator

Internal Force Cycle

Eliminated InterpretationA

Design Constraint

#3

#1

#0

#2

#4

#5

Planar Contact

Planar Support

#0

Planar Contact

Planar Support

Planar Contact

Planar Support

Cylindric Contact

Loose Shaft/Bushing LinkTight Shaft/Bushing Link

#1

Cylindric Contact


Conic Contact

Conical Support

#2

Cylindric Contact


#3

#4

Planar Contact

Planar Support

#5Cylindric Interference

Thread LinkSpline Link

Cylindric Interference

Thread LinkSpline Link

Fig. 3: Example of force cycle, as subset of the CIG, initiated by a threaded link.

Planar Support

Planar SupportPlanar Support

Threaded Link

Cap-screw

Initial Geometry Functional Interfaces Functional Designation

Head

TightenedComponents

Thread Shaft

Fig. 4: Structuring the model of a component with functional properties after analyzing its geometricinteractions and assigning it a functional designation, here a ‘cap screw’.

As a result, components models as well as theirgeometric model get structured, i.e. their 3D modelcontain imprints of their FIs and geometric relation-ships with FIs of functionally related components; FIscontain the lowest symbolic information describingthe elementary functions of a component and eachfunctional designation expresses uniquely the neces-sary relations between these elementary functions.Fig. 4 illustrates this result with a cap screw.

4.2. From Components’ Functional Designationsto Functions

Though the bottom-up approach summarized in theprevious section provide assembly components witha structured model incorporating functional informa-tion that is independent of their dimensions, theirfunctional designation does not appear as an appro-priate entry point to derive shape transformationoperators as required for FE analyses. Indeed, to setup FE assembly models, an engineer looks for boltedjunctions that he, resp. she, wants to transform toexpress friction phenomena, pre-stressed state in thescrew, . . . Consequently, the functional level neededis not the functional designation, which is bound to asingle component, it is the function itself to addressthe corresponding set of components and their FIs.

To this end, it is mandatory to refer to functions.This is achieved with a taxonomy of functions, TFN,

that can produce a functional structure of an assem-bly (see Fig. 5). Blue items define the sub-path in TFNhierarchy that characterizes bolted junctions.

Assembly

Disassemblable

Obstacle

Bolted adjusted

Screw + nut

Blocked nut

Adherence Dependent function

Dependent function

Bolted

Fig. 5: Subset of TFN, defining a functional structureof an assembly.

Each instance of a class in TFN contains a set ofcomponents identified by their functional designa-tion, i.e. it contains their structured geometric mod-els and FIs. The generation of these instances takesadvantage of the functional designations of compo-nents, e.g. adjusted cap screw in the present case, andthe load cycles attached to them and derived fromSLC. This generation is achieved with inferences onfunctional designations and properties of load cycles.To this end, it is mandatory to distinguish statically


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determined configurations from statically undeter-mined ones. These details are not described here topreserve the paper consistency and concentrate onthe exploitation of these functional informations.

As a result of the use of TFN, a component of aDMU can be automatically identified when it falls intothe category of cap screws, nuts, locking nuts thatare required to define bolted junctions. This meansthat their B-Rep model incorporates their geometricinterfaces with neighboring components. The graphof interfaces identifies the components a bolted junc-tion contains, the components are assigned functionaldesignations that intrinsically identifies cap screws,nuts, locking nuts, . . . , and connects them with andassembly instance in TFN.

It is now the purpose of the next section to takeadvantage of this information to set up the template-based transformations.

5. TEMPLATE-BASED TRANSFORMATIONS FOR FEMODELS

As a result, the DMU is now geometrically structured,components are linked by their geometric interfaces,and groups of components can be accurately identi-fied and located in the DMU using their function andgeometric structure, e.g. ‘adjusted bolted junctionswith screw+nut’ (see Fig. 5). Now, the geometric trans-formations needed to adapt the DMU to FEA objec-tives are strengthened because screws, nuts, lockingnuts can be robustly identified, groups of tightenedcomponents are also available through the load cyclesattached to cap screws.

Two possible accesses are proposed to define afunction-based template T related to an assemblyfunction:

• A component C through a user-defined selec-tion: from it and its FD, a datastructure givesaccess to the functions it contributes to. Afterselecting C, the user selects the function ofinterest among the available functions attachedto C in TFN and compatible with T. Other compo-nents are recovered through the selected func-tion this component participates to,

• The function itself in TFN that can lead to the setof components needed to define this functionand all the instances of this function existing inthe targeted assembly.

These accesses can be subjected to constraints thatcan help identifying the proper set of instances.Constraints aim at filtering out instances when atemplate T is defined from a function to reduce aset of instances to the user’s needs, e.g. assemblyfunction with bolts ‘constrained with’ 2 tighteningplates ‘component_i’ and ‘component_j’. Constraintsaim at extending a set of instances when a templateis defined from a component, i.e. a single function

instance recovered, and needs to be extended, e.g.assembly function with bolts ‘constrained with’ sametightened components and screw head FI of type ‘pla-nar support’ or ‘conical fit’. The overall pipeline toprocess a functionally enriched DMU with T is givenin Fig. 6.

5.1. Function-based Template and CompatibilityConditions of Transformations

The previous paragraph has sketched how componentfunctions can be used to identify sets of compo-nents in an assembly. Indeed, this identification isbased on classes appearing in TFN. Here, the pur-pose is to define more precisely how the templatecan be related to TFN and what constraints are seton shape transformations to preserve the geometricconsistency of the components and assembly. Shapetransformations are application-dependent and thepresent context is structural mechanics and FEA todefine a range of possible transformations.

The simplest relationship between a template Tand TFN is to relate T to a leaf of TFN. In this case,T covers instances defining sets of components thatcontain a variable number of components. T is alsodimension independent since it covers any size ofcomponent, i.e. it is a parameterized entity. Shapetransformations on T are designated as ST and thetemplate devoted to an application becomes ST (T).Now, reducing the scope to disassemblable assemblyfunctions and more specifically bolted junctions, oneleaf of TFN can be used to define more precisely Tand ST (T). Conforming to Fig. 5, let us restrict firstto the leaf ‘screw+nut’ of TFN. Then, T contains thefollowing FIs: one threaded link, two or more pla-nar supports (one between nut and plate and at leastone between two plates), either one planar support orone conical fit between the screw head and a plate,as many cylindrical loose fits as plates between thescrew and plates because the class of junctions is oftype adjusted. The shape transformations ST (T) of Tset up to process bolted junctions can be summarizedas (see Fig. 6):

• ST 1: merging screw and nut (see section 5.1) ;• ST 2: localization of friction effects with a sub

domain around a screw (see section 5.1) ;• ST 3: removal of locking nut if it exists (see

section 5.2) ;• ST 4: screw head transformation for mesh gener-

ation purposes (see section 5.3) ;• ST 5: cylindrical loose fit around the screw shaft

to support the contact condition with tightenedplates (see section 5.4).

Each of these transformations will be detailedthroughout the following sections.


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Fig. 6: Principle of the template-based shape transformations. The exponent of a component C, if it exists,identifies the functional designation of C.

(a) (b) (c) (d) (e)

Fig. 7: Compatibility conditions (CC) of shape transformations ST applied to T.

Now, the purpose is to define ST so that ST (T)exists and preserves the consistency of the compo-nents and the assembly. This defines compatibilityconditions, CC, between T and ST that are conceptu-ally close to attachment constraints of form featureson an object [39] (see Fig. 6). CC apply to ST and areintroduced briefly here. Given the set of componentscontained in T, this set can be subdivided into twodisjoint subsets as follows:

• IC is the set of components such that each ofits components has all its FIs in T, e.g. thescrew belongs to IC. Consequently, componentsbelonging to IC are entirely in T (see the greenrectangle in Fig. 6) ;

• PC is the set of components such that each of itscomponents has some of its FIs in T, e.g. a platebelongs to PC. Components belonging to PC arepartially in T (see the red rectangle in Fig. 6).

IC can be used to define a 3D sub domain of T, TIdefined as the union of all components belonging toIC. Now, if a transformation ST takes place in IC andgeometrically lies inside TI, ST (T) is valid because itcannot create interferences with other components ofthe assembly, i.e. CC are satisfied.

Let us consider some of these transformationsto illustrate some CC. As an objective of FEA, thepurpose of the assembly model is to analyze thestress distribution between plates and their interac-tions with bolts. To this end, the stress distributionaround the threaded link between a screw and a nutis not relevant. Therefore, one shape transformation,ST 1 is the removal of the threaded link to merge thescrew and the nut (see Fig. 7c). ST 1 is always compat-ible since the screw and the nut belong to IC, hencethe CC are always valid.

Now, considering another transformation, ST 2, isthe localization of friction effects between platesaround the screw shaft and the representation of thestress distribution nearby the screw shaft. This ismodeled with a circular area centered on the screwaxis and a cylindrical sub domain around the screwshaft (see Fig. 7d). Indeed, ST 2, is a domain decom-position [12,13] taking place in the plates belongingto T. Because the plates belong to PC, CC are nottrivial. However, ST 2, takes place inside the platesso they cannot interfere with other components,rather they can interfere with the boundary of theplates or they can interfere between them when sev-eral screws are close to each other on the sameplate (see Fig. 8). In this case, CC can be simply


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Interference

No interference

User MeshingTolerance

Ø Subdomains =User Ratio XØScrew

Fig. 8: Checking the compatibility of ST (T) with respect to the surrounding geometry of T.

expressed, in a first place, as a non-interferenceconstraint.

Other shape transformations will be listed whendescribing one example template in section 5.4.

5.2. Shape Transformations and FunctionDependency

The previous section has connected T to TFN in thesimplest way possible, i.e. using a leaf that character-izes a single function. The purpose of this section isto analyze into which extent T can connect to classesof TFN that perform several functions in the assembly.

In a first place, let us review shortly some conceptsof functional analysis [38]. There, it is often referredto several categories of functions that are related toa design process, i.e. external, internal, auxiliary, etc.However, this does not convey consistency conditionsamong these functions, especially from a geometricpoint of view. Here, the current content of TFN refersto internal functions, i.e. functions strictly performedby components of the assembly. The ‘screw+nut’ func-tion, as part of bolted junctions, is one of them.Bolted junctions can contain other functions. Let usconsider the locking function, i.e. the bolt is lockedto avoid any loss of tension in the screw when thecomponents are subjected to vibrations. The lock-ing process can take place either on the screw or onthe nut. For the purpose of the analysis, we considerhere a locking process on the nut, using a lockingnut (see Fig. 10a). In functional analysis, this functionis designated as auxiliary function but this conceptdoes not characterize geometric properties of thesefunctions.

From a geometric point of view, it can be observedthat FIs of the screw, nut and locking nut are locatedin 3D such that the FI (planar support) between thenut and locking nut cannot exist if the nut does nottighten the plates. Consequently, the locking functioncannot exist if the tightening function does not exist.Rather than using the designation of auxiliary func-tion, which is geometrically imprecise, it is referredto dependent function.

The concept of dependent functions is insertedin TFN at different levels of TFN to attach the

corresponding functions when they exist (see Fig. 5).Based on the concept of dependent function, it is pos-sible to extend the connection rule between T andTFN. Rather than connections at the leaf level, higherlevel classes can be connected to T if the dependentfunctions are taken into account in the CC of shapetransformations ST so that ST (T) exists and preservesthe consistency of the assembly. As an illustration,let us consider T connected to ‘Bolted adjusted’ (seeFig. 5). Now, ST can cover the class of bolted junc-tions with locking nut. Let ST 3, be the transformationthat removes the locking nut of a bolted junction,which meets also the FEA objectives mentioned ear-lier. Because ST 3 applies to a dependent functionof ‘screw+nut’, the CC are always satisfied and theresulting model has a consistent layout of FIs, i.e.the removal of the locking nut cannot create newinterfaces in the assembly (see Fig. 6 and 7b). Con-sequently, T can be effectively connected to ‘Boltedadjusted’, which is a generalization of T.

5.3. Template Generation

T is generated on the basis of the componentsinvolved in its associated function in TFN. T incorpo-rates the objectives of the FEA to specify ST . Here, STcovers all the transformations described previously,i.e. ST 1, ST 2, ST 3. Fig. 7 and 8 illustrates the keyelements of these shape transformations.

Other shape transformations, ST 4, can be definedto cover screw head transformations and extend therange of screws to flat head ones. However, this mayinvolve geometric transformations where the volumeof a screw head gets larger. In this case, ST 4 takesplace in PC and the compatibility conditions are notintrinsic to T (see Fig. 6). Consequently, it is manda-tory to perform an interface/interference checkingwith the other components of the assembly to makesure that the transformation is valid (see Fig. 7e).

Then, the set of shape transformations structuresthe dialog with the user to allow him, resp. her,to select some of these transformations. However,the user settings are applied to instances wheneverpossible, i.e. when the instance belongs to a classwhere the shape transformations are applicable.


445

(a) (b)

Fig. 9: (a) Multi-scale simulation with domain decomposition around bolted junctions (b) Load transfers atcritical holes (courtesy of ROMMA project [4]).

Fig. 10: Template based transformation ST (T) of a bolted junction into simple mesh model with friction andcontact areas definition around screw and nut.

5.4. Example of Template-based Operator ofBolted Junctions Transformation

During the PDP of an aeronautical company, simula-tion engineers perform specific FEAs on assembly substructures such as the aircraft junction between wingsand fuselage. Based on pre-existing physical testingperformed by ROMMA project partners, this structurecan be subjected to tensile and compressive forces toanalyze:

• The distribution of the load transfer among thebolted junctions;

• The admissible extreme loads throughout thisstructure.

From the physical testing and preliminary numeri-cal models, the following simulation objectives havebeen set up that initiate the requirements for theproposed template-based transformations.

To adapt the FE model to these simulation objec-tives while representing the physical behavior ofthe structure, an efficient domain decompositionapproach [12,13] uses a coarse mesh far enoughfrom the bolted junctions and a specific sub domainaround each bolted junction with friction and preloadphenomena (see Fig. 9a, b). The objective is not to gen-erate a detailed stress distribution everywhere in thisassembly but to observe the load distribution areasamong bolts using the mechanical models set in thesub domains. The objective of this section is to vali-date the template-based approach based on a demon-strator that transforms automatically the bolts into

simplified sub domains ready for meshing with fric-tion area definition while preserving the consistencyof the assembly. The template features are alignedwith the needs for setting up a simulation model ableto exhibit some of the physical phenomena observedduring testing and expressed in the above simulationsresults.

5.4.1. Operator description

Having enriched the assembly with functional infor-mation, the template interface lets the user select anode of TFN that is compatible with T. In this exam-ple, the function to select is: ‘assembly with Boltedjunction’ (see Fig. 11). Now, several ST are either preset or user accessible. ST 3 is user accessible and sethere to remove the dependent function ‘locking withlocking nut’ because the simulation objective does notfocus on dynamic effects. Then, ST 5 is pre set in T topreserve the cylindrical loose fit between screw andplates to set up contact friction BCs without inter-penetration over these FIs. ST 1 is also pre set aswell as ST 4. The latter is performed on the FI (pla-nar support) between the screw head/nut and theplates to obtain a meshing process independent ofnut and screw head shapes. Now, T can cover anybolted junction to merge screw, nut and locking-nutinto a single domain, reduce the screw and nut shapesto a simple shape of revolution while preservingthe consistency of its interfaces. To precisely moni-tor the stress distribution around bolts and frictionbetween plates, ST 2 is user-selected. It a simplifiedmodel of the Rotscher’s cone [8] (see Fig. 10) that


446

(b) (d)

(c) (e)

(a)

Fig. 11: User interface for transformation of ‘assembly Bolted Junctions’ (a), filtering bolts based on diameters(b) or screw type (c), template-based transformations with (d) or without (e) sub domains.

enables generating a simple mesh pattern aroundbolts.

Based on T, ST (T) is fairly generic and parameter-ized to intelligently select and transform bolts, i.e. it isindependent of the number and thicknesses of plates,of the screw diameter, the length and head type (cylin-drical (see Fig. 10a) versus flat ones) in addition to thelocation of each bolt.

Here, ST (T) contains ST 2, a generation of subdomains taking into account the physical effectsof the Rotscher’s cone. This geometric transforma-tion could interact with plate boundaries to changethe shape of these sub domains and influence themesh generation process. Presently, templates arestandalone entities and are not taking into accountthese effects left for future developments. At present,the user can adjust the sub domain to avoid theseinteractions (see Fig. 11a).

5.4.2. Implementation and results

The developed prototype is based on OpenCascadeand Python scripting language. The DMU is importedas STEP assembly models, the geometric interfacesbetween components are represented as independenttrimmed CAD faces with identifiers of the initial facepairs of the FI. The assembly functional descriptionis imported as a text file from the specific applica-tion performing the functional enrichment describedin [36] and linked to the assembly model by compo-nents’ identifiers.

Fig. 11a shows the user interface of the proto-type. When selecting the ‘assembly with Bolted Junc-tion’ function, the user has a direct access to thelist of bolted junctions in the assembly. To allowthe user filtering his selection, DMU parameters areextracted from the FD of components, e.g. the screwand nut type, the number of tightened components,or from geometry processing based on FDs, e.g. screw

diameter. Using these parameters, the user is ableto select bolted junctions with diameter between 10and 16 mm (see Fig. 11b) or bolted junctions withscrew and locking nut (see Fig. 11c), etc. The usercan monitor the Rotscher’s cone dimension with aFEA parameter called ‘sub domain ratio’ that repre-sents the ratio between the screw nominal diameterand the sub-domain diameter (see Fig. 11d and e).Then, the user-defined ‘meshing tolerance’ is usedduring the verification phase to check the compat-ibility conditions, CC, between instances and theirsurrounding geometry (see Fig. 6 and 8).

Fig. 12 shows two results of the template-basedtransformations on aircraft structures:

(1) A junction between the wing and the fuse-lage. The assembly contains 45 bolted junc-tions with 3 different diameters and 2 differentscrew heads;

(2) An engine pylon. The assembly contains over250 bolted junctions with identical screws andnuts.

The final CAD assembly (see Fig. 11b) with sim-plified bolted junctions has been exported to a CAEsoftware, i.e. Abaqus. STEP files transfer the geo-metric model and associated xml files describes theinterfaces between components to trigger meshingstrategies with friction area definition.

Comparing with the process pipeline used withexisting industrial software, the figures are as follows.The model preparation from CAD software to Abaqussimulation model takes 5 days of interactive workfor aircraft structure 1 mentioned above. Using thepipeline performing the functional enrichment of theDMU and the proposed template-based shape trans-formations, to directly produce the meshable modelin Abaqus and perform the mesh in Abaqus, theoverall time is reduced to one hour. The adequacy


447

(a) (b) (c)

Fig. 12: (a) CAD model with functional designations and geometric interfaces, (b) model after applying ST (T) onbolts, (c) mesh assembly model with friction area definition.

of this model conforms to the preliminary numeri-cal models set up in ROMMA project and extendingthis conformity to testing results is ongoing sincethe template enables easy adjustments of the meshmodel. Regarding the aircraft structure 2, there is noreference evaluation of its model preparation timefrom CAD to mesh generation because it is consid-ered as too complex to fit into the industrial productdevelopment process. However, it is possible to esti-mate the time reduction since the interactive timecan be linearly scaled according with the numberof bolted junction. This ends up with 25 days ofinteractive work compared to 1.5 hour with the pro-posed approach where the time is mostly devoted tothe mesh generation phase rather than the template-based transformations, which stay automated.

Though the automation is very high, the template-based approach leaves the user with meaningfulparameters enabling him/her to adapt the shapetransformations to subsets of bolted junctions whenFE is required models.

6. CONCLUSIONS

In this work, a template-based method empowers theuse of DMUs enriched with geometric interfaces andfunctional information, to automate CAD assemblypre-processing and generate a FE-friendly equivalenceof this assembly. Because the template is directlyconnected to assembly functions, its instances con-tain a group of components consistently involvedin the same assembly function. When selecting aspecific function, the user has a direct access tothe associated components, their structured modelas well as their FIs. It has been shown also that

the template can cover a rather large range of con-figurations since it is parameterized with respectto components’ dimensions, components’ number,components’ shapes and finally, component func-tion with the concept of dependent function. Usingthe template-based transformations, the user canrobustly and efficiently define the geometric trans-formations according to his/her FEA objectives andmeshing constraints. Thus, new components’ shapesadapted to CAE software requirements are producedwhile the consistency of the assembly model is pre-served. The template can be instantiated over thewhole assembly to transform quickly repetitive con-figurations such as bolted junctions which werehighly time consuming with interactive processing.Finally, a demonstrator has been presented to provethe efficiency of the template-based transformationapproach and its valuable contribution to a PDP. Thetemplate-based approach show how shape transfor-mations highly benefit from functional informationand strengthen these transformations in the contextof complex models like assemblies where many com-ponents interact with each other. Bolted junctionsof two industrial use-cases have been automaticallytransformed into simplified macro elements with sub-domains generation. The resulting model producesa seamless generation of FE models conforming tothe simulation objectives while taking into accountmeshing constraints.

ACKNOWLEDGMENT

This work is carried out as part of the ROMMA(RObust Mechanical Models for Assemblies) project[4] under the reference ANR-09-COSI-012. The authorsare very grateful for the financial support from theAgence Nationale de la Recherche (ANR).


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