Processing Geometric Models of Assemblies to Structure and Enrich them with Functional Information


Supervised by

Jean-Claude LEON


August 29, 2014

In the frame of

ROMMA Project

Robust Mechanical Models for Assemblies


What is a DMU?

and robust
relation between
CAD Models and function.
Iyer et al. '05

What is a structural simulation?

  • Objective: assess the load distribution over the bolted junctions under prescribed external loads.
  • Preparation: 5 man-days.
  • Computation: 15'.
How to reduce simulation preparation time?

Simulation model differ from CAD models

  • Certain hypotheses are made to produce simulation models.
    • Shape transformations are needed.
  • Simulation objectives and hypotheses refer to specific functional subsets of components.

CAD models need to be enriched with functional knowledge and restructured accordingly.


Enrich DMUs with functional knowledge required by geometric transformation for FEA preprocessing, taking into account current industrial practices and conventions.

Bottom-up approach


      Function, form and behavior

      Function is the semantics of a design.
      Gero '90
      • Relationship between function and structure, i.e. form* Gero '90, Umeda '09, Qian '96, Albers '06.
      Example of form-behavior-structure (FBS) model applied to a buzzer Qian & Gero '96.
      • Methods to apply this relationship in design suggest behavior to make the connection.
      • Function Behavior Form
      * In the domain of mechanical engineering.

      of the bottom-up approach

      • Industrial conventions
      • Real shape
        Digital shape
      • Restructuring of the CAD model
      • LevelEnrichmentRestructuring
        Funct. interface Comp. interface Geometric
        Funct. unit Component None
        Funct. module Comp. group Organizational

        Form at the outset

        • Function stems from interactions between components De Kleer '98, Albers '02.
        • For mechanical components, functionality happens at the geometric interface level.
        • Top-down methods built on functional interaction to boost geometric design Roy & Bharadwaj '02, Kim '04.
        Relationship between form and function at the interface level Roy & Bharadwaj' 02
        To capture functionality, geometric interactions need to be analysed first.
        Conventional Rep. of a threaded link

        Conventional Interface

        A CI is a conceptual entity that represents an interaction between two components in an assembly.
        • Identified by the geometric interaction of components in a DMU.
        • Augmented with semantics such as physical and functional properties.

        CI types

        • Contact; curve or surface
        • Interference; shared volume
        • Clearance. play distance
        Threaded link: a functional interaction (source ASM)

        Functional Interfaces

        An FI is an interaction between two neighboring mechanical components that fulfills, or contributes to the fulfillment of a function.
        • Functionally explains an CI.
        • One CI many FIs!
        • Functional interfaces are represented through canonical surfaces.
        Only geometric interactions between canonical surfaces are of significant interest.

        Simple, yet efficient geometric interaction detection

        • Generation of a unique geometric representation:
          • Maximal edges and surfaces.
        • Three-level filtering:
          1. Bounding boxes;
          2. Geometric attributes comparison;
          3. Boolean operators.
        • Efforts in the frame of ROMMA project. Jourdes et al. '14

        Assembly Graph Structure

        • CIs connect components together.
        • A graph whose
          • nodes are the components;
          • edges are the CIs.
        • Overrides DMU tree-structure.

        Conventional Interface Graph

        A graph that represents geometric interactions between components in a DMU.
        First step toward DMU restructuring.


        • Centrifugal pump with 43 components.
        • Geo. Analysis time
          Bool. Op. ≈ 8'!
          3-level filtering ≈ 0.15''.
        • 100-edge CIG:
          • 87 contacts;
          • 13 interferences.
        Cross section in the DMU of a centrifugal pump.


        • Root joint with 148 components.
        • Geo. Analysis time
          3-level filtering < 0.2''.
        • 512-edge CIG:
          • 396 contacts;
          • 116 interferences.
        DMU of an aircraft root joint.

        Form meets function

        • Objective link form to function. Gero '90, Qian '96
        • Problem
          more than one possible interpretation. Roy '02
        • Need to incorporate context.
        Threaded Link Cylindric Interference Spline Link

        Spline link

        Functional interpretations

        • Hierarchical representation of interfaces (taxonomies).
        • Each CI is associated multiple FIs acc. a dictionary.
        Geometric and functional knowledge structuring at the interface level.

        Relevant structure

        Form Function
        module Group
        ? Geometry
        unit Component
        interface CI
        FIs Geometry

          Behavior as a broker

          • Can behavior Gero '90, Umeda '09, Qian '96, Albers'06 be used to mend the nexus from form to function?
            Stand point
            Threaded Link valid valid
            Spline Link valid invalid
          • Objective use a qualitative behavioral representation to deduce functional knowledge.
          • Reference states define behavioral validity.
            • Elimination of FI that violate a given behavior.

          Reference States

          • Hypotheses
            • Rigid bodies;
            • Energy-conservative systems;
            • Only mechanical interactions.
          $\iint\limits_{\partial C} \vec{f_1} \; dS + \iint\limits_{\partial C} \vec{f_2} \; dS = \vec{0}$

          Product at rest

          Components of a product hold in place. Ref. State I
          • Mechanical equilibrium:
            • $\sum \vec{f} = \vec{0}, \; \sum \vec{m} = \vec{0}$.
          $$\sum\limits_{i \in \mathcal{I}(C)} \mathsf{W}_{i} = \sum \{ \vec{f}_{i} | \vec{m}_{i} \} = \{ \vec{0} | \vec{0} \}$$
          • Casting a physical dimension on mere geometry.
          • External forces and moments on a rigid body:
            • can be represented using a wrench screw Poinsot 1861;
            • can only go through CIs of component C: $\mathcal{I}(C)$.

          Qualitative physical representation

          • Force and moment values are not available in a DMU!
          • Need for qualitative representation:
            • values: real intervals.
              Not Null$\odot$$]-\infty, 0[ \: \cup \: ]0, +\infty[$
              Null$\oslash$$[0, 0]$
              Strictly Positive$\oplus$$]0, +\infty[$
              Strictly Negative$\ominus$$]-\infty, 0[$
              Arbitrary$\otimes$$]-\infty, +\infty[$
            • and operations: interval arithmetics.
              $$ \begin{array}{l@{}l@{}l} K + L &= \{z | \exists (x, y) \in K \times L, z = x + y &\} \\ K \cdot L &= \{z | \exists (x, y) \in K \times L, z = x \cdot y &\} \end{array} $$

          Elimination of statically-invalid FIs

          • Iterate CIG nodes until there's no more FIs to eliminate.
          • Heuristically pick node C.
          $\left\{ \begin{array}{c|c} \otimes & \otimes \\ \otimes & \otimes \\ \odot & \oslash \end{array} \right\} $
          Threaded Link
          $\left\{ \begin{array}{c|c} \oslash & \otimes \\ \oslash & \otimes \\ \ominus & \oslash \end{array} \right\} $
          Planar Support
          $\left\{ \begin{array}{c|c} \otimes & \otimes \\ \otimes & \otimes \\ \otimes & \otimes \end{array} \right\} $
          $\left\{ \begin{array}{c|c} \otimes & \otimes \\ \otimes & \otimes \\ \oslash & \otimes \end{array} \right\} $
          Spline Link
          $\left\{ \begin{array}{c|c} \oslash & \otimes \\ \oslash & \otimes \\ \ominus & \oslash \end{array} \right\} $
          Planar Support
          $\left\{ \begin{array}{c|c} \oslash & \otimes \\ \oslash & \otimes \\ \ominus & \oslash \end{array} \right\} $
          $\odot$Not Null
          $\oplus$Strictly Positive
          $\ominus$Strictly Negative
          • Nothing more to do at node C, close it.
          • Pick next component...
          First level of behavioral filtering at the interface level.
          Eliminate FIs that produce static invalidity.

          Reference States

          • R.S. I is unable to uniquely determine the FI of a given CI.
            • more than one statically-valid solution.
          $\iint\limits_{\partial C} \vec{f_1} \; dS + \iint\limits_{\partial C} \vec{f_2} \; dS = \vec{0}$

          Static Determinacy

          Statically indeterminate structures must be functionally justified. Ref. State II
          • The solution for static equilibrium equations is unique*.
          • Static indeterminacy is minimized.
          • Unless necessary, or functionally justified, indeterminate static solutions are rejected.
            • Reduce the number of FIs to one per CI.
          * Given one force or moment value.
          Further behavioral filtering at the interface level.
          Eliminate FIs that produce unnecessary static indeterminacy.
          Functional groups labeled as bolted junctions.

          Functional Group

          A set of components that together deliver a coherent function or set of functions.
          • Each functional group is given a label (functional cluster).
          • Bolted junction is an example of a functional cluster.
          Loads cycle goes into a bolted junctions.

          Force Propagation

          Loads generated by an internal load generator propagate through a cycle in a functional product. Ref. State III
          • A threaded link is a load generator.

          Internal load cycles

          Force propagation graphs
        • One per direction.
        • Subgraphs of CIG.
          • FIs producing static indeterminacy are eliminated.
          • A load cycle with a threaded link reveals a bolted junctions.

          Qualitative behavioral analysis led to:
          • Reduction of interpretations to one FI per CI.
          • Functional knowledge at the component group level.

          Functional knowledge

          Form Function
          module Group
          ? One FC Geometry & Behavior
          unit Component
          interface CI
          FIs One FI Geometry & Behavior

            Functional unit

            • Thanks to R.S. functional knowledge is available at component interface and component group levels.
            • Objective Use this knowledge to functionally classify components.
            Cap-screw as an FD.

            Functional Designation

            An FD is a denomination that functionally identifies a class of a component.
            • Relates the functionality to geometry through FIs and to assembly through FCs.
            • Observations
              • Function of a component is related to functions of its interfaces and functional groups.
              • Vast and dynamic diversity of component function.
            FDs are organized in a taxonomy that can be domain-specific.
            • FDs need to be represented formally, and reasoned upon with dynamic rules.
            • How to represent functional knowledge?
            • How to process functional knowledge?

            Functional knowledge representation

            Knowledge-based engineering (KBE)

            • Engineering-oriented expert systems, bottom-up approaches Chapman '01, La Rocca '07, Emberey '07.
            • KBE adds up to CAD systems, without changing them.
              • CAD models remain unchanged!
            • Procedural programming. Native representation.
              • Poor semantic formalism!


            • Formal semantics based on the Semantic Web paradigm.
            • Borrowed into assembly knowledge representation Rahmani '12, Kitamura '03 and reasoning Kim '06.
              • No significant application in functional reasoning, yet!

            Functional knowledge reasoning

            • A cap-screw is a component that has a threaded link and a planar support, and that participates to a bolted junction*.
            • In First Order Logic (FOL): Undecidable!
            • $$ \begin{array}{llll} Capscrew \leftarrow & Component(x) && \land \\ & ThreadedLink(i) &\land \; forms(x, i) & \land \\ & PlanarSupport(j) &\land \; forms(x, j) & \land \\ & BoltedJoint(b) &\land \; participatesTo(x, b) & \end{array} $$
            • In Description Logic (DL): Decidable.
            • $$ \begin{array}{>{\sf}l>{\sf}l>{\sf}l} \sf Capscrew \sqsupseteq & \sf Component & \sqcap \\ & \exists \sf forms.ThreadedLink & \sqcap \\ & \exists \sf forms.PlanarSupport & \sqcap \\ & \exists \sf participatesTo.BoltedJoint & \sqcap \end{array} $$
            • OWL DL is an ontology language that supports DL reasoning.
            • DL-reasoning engines with well-established algorithmic behavior (Pellet, FaCT++, Racer, ect.).
            * Simplified from the real rule in use to identify cap-screws.

            Captured knowledge

            • The romma ontology to capture domain knowledge.
            • Model knowledge is instantiated against romma concepts and instances are assigned to their respective geometric entities.
            Model Knowledge
            Domain Knowledge

            Ontological reasoning

            • Ontology romma is submitted to DL reasoner.
            • CIG is translated into DL fact, which are posted to reasoner.
            DIG protocol
            Geometric and behavioral module
            DIG protocol
            Components are functionally enriched down to the interface level, and geometrically restructured accordingly.


            Total time: 16.54 sec
            Intel© Core™2 Duo CPU P8600 @ 2.40GHz
            4GB memory

            Successful detection of 6 different FDs on an example of a centrifugal pump.


            Total time: 20.68 sec
            Intel© Core™2 Duo CPU P8600 @ 2.40GHz
            4GB memory

            Successful detection of cap-screws, nuts, and locking nuts on an industrial example of root joint.

            Complete connection

            Form Function
            module Group
            One FC Geometry & Behavior
            unit Component
            ? One FD Expert Rules
            interface CI
            One FI Geometry & Behavior

            Template-based preprocessing of DMU for FEA purposes.

            • Highly automated geometric pre-processing method, feeds on functional information of the DMU Boussuge et al. '14.
            • Templates are matched to functional groups (bolted junction).
            • Elements of templates are mapped to components (cap-screw, nut, locking nut).
            • Sub-domains are defined based on FIs.
            Reduction of preparation time
            from 5 man-days to 1 hour!


              • Geometric restructuring of components.
                • CIs: components bear imprints of functional zones.
                • FIs: functionality stems at the interface level.
              • Structural re-organization of the DMU.
                • CIG: capturing functional interaction between components in a graph structure.
                • FCs: grouping functionally related components in sub-graphs.
              • Use behavior to unambiguously bind form to function.
                • RSs: qualitative behavioral assessment of function.
              • Apply rule-based inference to connect the dots.
                • FDs: match functional patterns to restructured components.


              • Other applications rather that FEA:
                • Virtual and augmented reality.
                • Assembly/Disassembly planning.
              • Future work direction:
                • Take into account symmetry and repetitive geometries.
                • Implement and introduce new reference states, such as kinematic chains.
                • Extend existing ontology by defining new FDs and their rules.

              Thank you.