A graph-based method and a software tool for interactive tolerance specification

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Procedia CIRP 00 (2017) 000–000 Procedia CIRP 75 (2018) 173–178 www.elsevier.com/locate/procedia

15th CIRP CAT CAT 2018 2018 15th CIRP CIRP Conference Conference on on Computer Computer Aided Aided Tolerancing Tolerancing –– CIRP

CIRP Design Conference, Nantes, France A graph-based method and aa software tool A28th graph-based method May and2018, software tool for tolerance specification fortointeractive interactive tolerance specification A new methodology analyze the functional and physical architecture of aa b a Stanislao Patalano Ferdinando Vitolo ,, Salvatore Gerbino ,, Antonio Lanzotti existing products foraa,, an assembly oriented product Stanislao Patalano Ferdinando Vitolo Salvatore Gerbinobfamily Antonioidentification Lanzottia,, a a

Fraunhofer Italy Fraunhofer JL JL IDEAS IDEAS -- Dept. Dept. of of Industrial Industrial Engineering, Engineering, University University of of Naples Naples Federico Federico II, II, P.le P.le Tecchio, Tecchio, 80 80 -- 80125 80125 Naples Naples –– Italy

Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat

DiBT DiBT Dep't Dep't -- Engineering Engineering Division, Division, Univ. Univ. of of Molise, Molise, Campobasso, Campobasso, Via Via De De Sanctis Sanctis snc snc -- 86100 86100 Campobasso Campobasso (CB) (CB) -- Italy Italy École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France ** Corresponding author. Tel.: +39-081-7682457; fax: +39-081-7682470. E-mail address: [email protected] Corresponding author. Tel.: +39-081-7682457; fax: +39-081-7682470. E-mail address: [email protected] b b

* Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected]

Abstract Abstract The method and and aa preliminary preliminary software software tool: tool: Abstract The paper paper deals deals with with the the problem problem of of tolerance tolerance specification specification and, and, in in particular, particular, proposes proposes aa graph-based graph-based method (i) (i) to to accomplish accomplish the the tolerance tolerance specification specification for for aa mechanical mechanical assembly; assembly; (ii) (ii) to to verify verify the the consistency consistency of of the the specification specification and, and, (iii) (iii) to to allow allow the the of relationships among and of assembly. The method adopts Reference Elements Intracing today’s environment, the trend towards more variety customization is unbroken. Due toGeometric this development, need of tracing ofbusiness relationships among parts parts and features features of the theproduct assembly. Theand method adopts Minimum Minimum Reference Geometric Elementsthe(MRGE), (MRGE), directed (di-graphs) and of algorithms to the problems of that during an interactive tolerance agile and graphs reconfigurable production systems emerged to cope with various product families. To design directed graphs (di-graphs) and aa set set of dedicated dedicated algorithms to tackle tackle the products problemsand of consistency consistency that occur occur duringand an optimize interactiveproduction tolerance specification activity. Finally, an application illustrates the proposed method and its actual implementation. systems as well as to choose the optimal product matches, product analysis methods are needed. Indeed, most of the known methods aim to specification activity. Finally, an application illustrates the proposed method and its actual implementation. © Authors. Published by B.V. analyze product or one product family on the physical level. Different product families, however, may differ largely in terms of the number and © 2018 2018aThe The Authors. Published by Elsevier Elsevier B.V. © 2018 The Authors. Published by B.V. Committee of the 15th CIRP Conference on Computer Aided Tolerancing - CIRP CAT 2018. Peer-review under responsibility of Elsevier the Scientific nature of components. This fact impedes an efficient comparison and choice of appropriate product family combinations for theCAT production Peer-review underresponsibility responsibility theScientific Scientific Committee of the CIRP Conference on Computer Tolerancing CIRP Peer-review under ofofthe Committee of the 15th15th CIRP Conference on Computer AidedAided Tolerancing - CIRP-CAT 2018. 2018. system. A new methodology is proposed to analyze existing products in view of their functional and physical architecture. The aim is to cluster Keywords: tolerance specification; GD&T; Datum; Datum; graph theory; MRGE; these products in new assembly oriented productgraph families forMRGE; the optimization of existing assembly lines and the creation of future reconfigurable Keywords: tolerance specification; GD&T; theory; .. assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified, and a functional analysis is performed. Moreover, a hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the similarity between product families by providing design support to both, production system planners and product designers. An illustrative 1. essentially aims define: (i) 1. Introduction Introduction specification activity essentially aims to toof steering define: columns (i) datum datum example of a nail-clipper is used to explain the proposed methodology. Anspecification industrial case activity study on two product families of references at part and assembly level; (ii) tolerance thyssenkrupp Presta France is then carried out to give a first industrial evaluation of theat proposed approach. references part and assembly level; (ii) tolerance type type and and Product development is by ranges © 2017 The Authors. Published by Elseviercomposed B.V. Product development is essentially essentially composed by three three main main ranges for for each each geometric geometric feature feature involved, involved, in in order order to to assure assure phases: design, manufacturing and control. The first one a set of assembly functional requirements. A traditional Peer-review under responsibility of theand scientific committee of the one 28th CIRP Design Conferencefunctional 2018. phases: design, manufacturing control. The first a set of assembly requirements. A traditional and and

develops aa “virtual” unchanged develops “virtual” product, product, the the manufacturing manufacturing phase phase releases releases unchanged challenge challenge is is to to coherently coherently assign assign tolerance tolerance type type and and and range, including datum references frame for the set a real product affected by inevitable dimensional and range, including datum references frame for the set of of parts parts geometrical variations, while control control phase phase assures assures the the composing geometrical variations, while composing an an assembly, assembly, as as aa whole. whole. Geometric Geometric Dimensioning Dimensioning verification of acceptable variations and, therefore, guarantees and Tolerancing (GD&T) standards, verification of acceptable variations and, therefore, guarantees and Tolerancing (GD&T) standards, like like ANSI-ASME ANSI-ASME or or the fulfillment fulfillment of of product product functional functional requirements requirements (FRs). (FRs). ISO-GPS Standards [4-6], provide aa wide range of symbols the ISO-GPS Standards [4-6], provide wide range of symbols 1. Introduction of the product range and characteristics manufactured and/or Tolerances are are the the link link between between these these three three phases phases and and and to do tolerance specification for each geometric Tolerances and rules rules in tothis do system. tolerance specification formain eachchallenge geometric assembled In this context, the in tolerancing is a mandatory step to assure functional feature. However, international standards are part-centric and tolerancing is a mandatory step to assure functional feature. However, international standards are part-centric and Due to the fast development in the domain of modelling and analysis is now not only to cope with single requirements. not therefore, standards lack on requirements. not assembly-centric; assembly-centric; therefore, lack rules rules on communication and an ongoing trend of digitization and products, a limited product range or standards existing product families, Tolerancing is usually divided into several specializations: assembly-centric specifications and these are essentially relied Tolerancing is usually divided into several specializations: assembly-centric specifications and these are essentially relied digitalization, manufacturing enterprises are facing important but also to be able to analyze and to compare products to define tolerance specification specification [1]; [1]; tolerance tolerance modeling modeling and analysis analysis to skills. CAT commercial software, such tolerance to designers’ designers’ skills. Specific Specific commercial software, such challenges in today’s market environments: a and continuing new product families. It can beCAT observed that classical existing [2]; tolerance verification; each specialization has detailed as VisMockup® or 3DCS and 3D CAD systems, provide [2]; tolerance verification; each specialization has detailed as VisMockup® or 3DCS and 3D CAD systems, provide tendency towards reduction of product development times and product families are regrouped in function of clients or features. goals actually, shows pillars and, at the useful for tolerance specification, annotation and goals and, and,product actually, shows significant significant pillars the same same However, useful tools tools for oriented toleranceproduct specification, annotation and shortened lifecycles. In addition, there and, is anatincreasing assembly families are hardly to find. time, limitations and challenges. The present paper deals with analysis but a tolerance consistency tool is still not time, limitations and challenges. The present paper deals with analysis but a tolerance consistency tool is still not demand of customization, being at the same time in a global On the product family level, products differ mainly in two the tolerance specification task. implemented. Therefore, a senior designer could easily assign the tolerance specification task. implemented. Therefore, a senior designer could easily assign competition with competitors all over the world. This trend, main characteristics: (i) the number of components and (ii) the Tolerance specification is activity in product tolerances, assuring assuring coherence coherence at at part part level. level. On the Tolerance specification is aa strategic strategic tolerances, Onelectronical). the contrary, contrary, which is inducing the development fromactivity macro into product micro type of components (e.g. mechanical, electrical, development and, even more, in assembly design where (s)he has no software tools to assure the global consistency of development and, even more, in assembly design where (s)he has no software tools to assure the global consistency of markets, results in diminished lot sizes due to augmenting Classical methodologies considering mainly single products multiple inter-part relations are involved [3]. Tolerance specification as well as the explicit tracking of relationships multiplevarieties inter-part relations toare involved production) [3]. Tolerance specification as well existing as the explicit of analyze relationships product (high-volume low-volume [1]. or solitary, already producttracking families the To cope with this augmenting variety as well as to be able to product structure on a physical level (components level) which identify possible optimization potentials in the existing causes difficulties regarding an efficient definition and 2212-8271 2212-8271 © © 2018 2018 The The Authors. Authors. Published Published by by Elsevier Elsevier B.V. B.V. production system, it is important to have a precise knowledge comparison of different product families. Addressing this Peer-review under responsibility of the Scientific Committee of the 15th CIRP Conference on Aided -- CIRP CAT Peer-review under responsibility of the Scientific Committee of the 15th CIRP Conference on Computer Computer Aided Tolerancing Tolerancing CIRP CAT 2018. 2018. Keywords: method; identification a real Assembly; product Design affected by Family inevitable dimensional

2212-8271©©2017 2018The The Authors. Published by Elsevier 2212-8271 Authors. Published by Elsevier B.V. B.V. Peer-review under responsibility of scientific the Scientific Committee of the 15th CIRPConference Conference on Computer Aided Tolerancing - CIRP CAT 2018. Peer-review under responsibility of the committee of the 28th CIRP Design 2018. 10.1016/j.procir.2018.04.077

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between functional features and tolerance specifications, at assembly level. Several contributes are known in literature about the problem of tolerance specification and, in particular, the consistency, the traceability at assembly level and the use of graph representations. Ballu et al. [7] uses the axiomatic design framework to accomplish a functional method for the managing of features, parameters and tolerances. In particular, they present a tool that uses a skeleton of the assembly to enhance the design of variants. No details are presented to assure consistency of tolerance specification. In [8] authors deal with the consistent tolerancing of a single part and deepen a set of detailed positioning tables and related links between contact surfaces. The wide study gives rise to a VBA implementation, but it does not tackle the problems related to the traceability of tolerance specification within the assembly context. In [9] an innovative product model is presented; the model allows the formalization of tolerancing expertise and enhances the traceability of the geometric conditions throughout the design steps. The work does not take into account the geometrical specifications on 3D CAD models and the possibility to accomplish a CAT analysis. Giordano et al. [10] propose a very useful tool for tolerance representation of mechanical assembly: the hyper-graphs. They define three graph levels: assembly graph (highest level) where nodes represent the parts and arcs represent the joints; contact graph where nodes represent functional features (contact faces implied in joint) and arcs represent the relations between functional features; tolerancing graph (part level) where nodes can represent toleranced features or geometrical or dimensional tolerance and arcs represent the links between two of them. Hyper-graph is the complete tolerancing graph. Although hyper-graph provides a clearer tolerances representation it is difficult to automatically build the graph. A successive and exhaustive dissertation to accomplish the graphical representation of mechanical assemblies with specifications is presented in [11]; there, the authors formalize an extension of the graphs used to represent joints and links of a mechanism by adding functional requirements, surfaces for tolerancing, situation features and, finally, specifications between surfaces. They voluntarily do not tackle the problem of identifying the key objects or specification as their final goal is the complete graph representation. The present paper proposes a graph-based method to enhance interactive tolerance specification and to automatically generate the tolerances graph relations, allowing consistency analysis of mechanical assemblies as well as the tracing of relationships among parts and features of the assembly. Starting from the Minimum Reference Geometric Element (MRGE), belonging to Technologically and Topologically Related Surface (TTRS) model, and using graph theory, the approach proposed in [12] is here used to perform the consistency analysis of a tolerance specification set. The method detects errors when tolerance specification does not fulfil the geometrical rules and carries out a consistency analysis, at assembly level, through the use of directed graphs (di-graphs) and a set of dedicated algorithms.

2. Method overview During the design phase, dimensional and geometrical tolerances have to be in a fully, correctly and consistency way defined. Furthermore, such a definition of the tolerance set has to be verified during all intermediate product development stages. The proposed method intends to manage and record consistent tolerance set by simplifying the exploration and verification. The MRGE description of the features and a digraph representation of the geometric relations, based on hyper-graph definition, are here used to assure the three key conditions for a consistent tolerance specification. 2.1. MRGE The MRGE of a TTRS is the minimum set of points, lines or planes necessary and sufficient to define the reference frame corresponding to the invariant sub-group of that TTRS [13]. The MRGE remains invariant for the displacement it is defining. For each elementary surface, it is possible to associate an MRGE. Moreover, the MRGE describe the degrees of invariance associated to a surface or TTRS. For instance, the line or axis of a cylindrical surface can only be translated along or rotated about itself and it leaves four degrees of invariance: two in translation and two in rotation. However, in the present work the focus is limited to axes, planes and cylinders. 2.2. Directed-graph Part and assembly relations can be represented by a digraph [14-15] which consists of nodes and arcs. The first ones (as in hyper-graph [10]) represent the toleranced or functional features while arcs represent the geometrical or topological relations among them (Fig.1).

Fig. 1. Di-graph representation for a three-part assembly.

2.3. Consistency A tolerance specification is assumed consistent when it is coherent, complete and non-redundant. Therefore, the consistency is obtained by the three following conditions:



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• Coherency: a specification is coherent if it is logically connected; the coherency is accomplished through syntax and semantic controls on tolerance specification; • Completeness: the tolerance process is complete when it specifies geometric variations that assure the assembly functional requirements. It must include all geometric features and parameters to describe the functionalities of a product [16]. • Non-redundancy: a specification is non-redundant when the extraction of information for each tolerance specification exists and no overlapped information is defined. 3. Tolerance specification method The proposed method is composed by four main activities: Feature parametrization – it is based on MRGE. Each feature is defined by a triad and characterized by a specific set of data. For example, an axis is parametrized by a point (defining the orientation belonging to the axis, a versor ; a plane is – parallel to the axis) and a frame belonging to the plane, a versor parametrized by a point (defining the orientation – normal to the plane) and a ; a cylinder is parametrized by an axis plus a frame radius. Datum definition – it sets the datum reference frame (DRF). DRF can be defined as the way to position the part in the assembly, therefore it should be based on the assembly sequence and the relations among parts. Based on [11], DRF is defined by using a combination of Datum Features which are theoretically exact geometries such as point, line and plane. The mathematical representation of DRFs consists in a frame of three orthogonal vectors and a point which defines the origin of the frame.

Consistency analysis algorithm is based on graph theory, too. Data are structured by means of: (i) adjacency matrix (A), (ii) incidence matrix (I), and, (iii) list of edges (L). The element of the adjacency matrix are characterized by three values: 0 if no connection exists between node and ; 1 if an edge exists from to ; -1 if an edge exists from j to . Using the above data structure and synergic operation of graph algorithms, a consistency algorithm (flowchart depicted in Fig.3) has developed. It consists of three checks: • Coherence: algorithms based on assignations and dependencies rules (as table1) driven each specification in terms of syntax and semantic correctness (no errors occur). All dependency relations are mapped as in Tab.1. Each specification needs an entity and tolerance type selection which corresponds to a specific mapping table uses to check the assignation coherence at part level. For example, the method does not allow to specify a flatness for an axis because the Tab.1 has value 0 in the corresponding cell. Besides, an algorithm checks that no isolated features exist at part level (all features are connected). For each part, the method provides an adjacency matrix which manages the features relations. The isolated feature algorithm detects that for each raw and each column of the matrix a non-zero element at least exists. • Completeness: it is analyzed through the graphs; an algorithm, named requirement isolated, detects that no isolated FRs exist and all created nodes are connected at least to one chain. The operating flow is similar to isolated feature algorithm, but requirements isolated algorithm concurrently operates both at part level and assembly level. Requirement definition generates an augmented incidence matrix composed by all defined requirements and all features of the assembly. A node not connected in the graph means that it does not add useful information to the analysis.

Tolerance specification – it aims to assign tolerance type and range. Specifications are array based and selectively chosen. Tab. I shows a Boolean representation of the relations between tolerance and feature.

straightness

flatness

circularity

cylindricity

parallelism

perpendicularity

angularity

position

symmetry

concentricity

circular runout

total runout

Tab. 1. Boolean representation of the allowable relations between tolerance and feature.

Axis Plane

1 1

0 1

0 0

1 0

1 1

1 1

1 1

1 0

1 1

1 0

1 1

1 0

Graph based relations – tolerance specification is made first at part level and then at assembly level. Data are recorded and managed using graph theory. Parts can be classified in: ○ Datum part – a part which has no target part; ○ Target part – a part whose feature are used to constrain another part; ○ Object part – a part assembled by means of a feature belonging to a target part.

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Fig. 2. Software tool structure

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Fig. 3. Flowchart of the consistency algorithm

• Non-redundancy: it is evaluated through the loop detection within the graph generated for the tolerance specification set. The loop detection algorithm operates, at assembly level, on the augmented incidence matrix. The algorithm, starting from each assembly features, generates a vector which represents the sequence of nodes. A belonging check runs for each new vector node, if the node already belongs to the vector a loop is detected. 4. Tolerance specification software tool A graphical user interface (GUI), developed in MatLAB® environment, was accomplished in order to enable the interactive tolerance specification and automatic consistency analysis. Fig. 2 shows the logical structure of the developed tool. The main window named “Consistency tool” (see Fig.4) is divided in three fields: the control tree (left side) where all imported parts, defined requirements and features are shown; the 3D view where the active part is visualized; editing panels on the right side where features can be created and assembly or tolerance tool can be run. Assembly is imported into software, parts by parts, using STL file format. Feature recognition is operated by users through the “entity save” panel. For example, a feature plane is defined by the selection of three points enhanced by a object snap function. The operations are driven by a snap grid.

Fig. 4. Main window of the software tool

4.1. Tolerance toolbox Tolerance toolbox (Fig.5) allows to define datum reference frame and tolerance for each part. Tolerance specification is done in the following way: (i) select feature in the “Datum Panel” and, eventually, specify if it is a datum; (ii) assign tolerance in “Tolerances” panel. To improve interactive tolerance specification, a feature identification algorithm was implemented. The algorithm identifies the associated elements and enables only the associable tolerances. To avoid inconsistent specification, a reference dependencies algorithm was implemented. It checks redundancy for each tolerance assignment and it allows recording assignment without redundancy. The Toolbox stores all information and retrieve data for each feature. When it is necessary to qualify references elements through the application of appropriate tolerances of shape, position or orientation, both geometrical and semantic control are performed. Finally, it is possible to plot the part-graph composed by the datum reference frame with its tolerance specification and all functional features connected to the references by geometrical tolerances.

Fig. 5. Tolerance toolbox window



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4.2. Assembly toolbox Assembly toolbox allows to define the relations between two parts. Selecting functional feature respectively for targetpart and object-part a mating can be specify. Besides, for each mating part the assembly-graph can be plot. A set of searching algorithms [17] was implemented to interactively explore and verify the assembly tolerance specification: shortest path algorithm; ordered paths algorithm; ordered and constraint paths algorithm; shortest path to a source node algorithm; shortest path to source nodes algorithm.

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Slider-crank assembly is imported into software, parts by parts, using STL file format. A datum reference frame was defined and a tolerance specification set was done for each functional surface by using “Tolerance Tool”. For example, Fig.8 shows the equivalent tolerance specification carried out by the tool. Fig.9 shows the part tolerancing graph, i.e. the relations among all crankshaft features. It represents the tolerance dataset of the crankshaft. Analogue tolerance specification was carried out for each component obtaining the following dataset: datum reference frame; tolerance specification set; part adjacency matrix. Inter-part relations were defined by using assembly tool generating the assembly adjacency matrix which corresponds to assign joints between features of the parts. The obtained assembly-graph is depicted in Fig.10.

Fig. 6. Assembly toolbox window

5. Slider-crank assembly A slider-crank assembly is analyzed to test the developed software tool. The assembly is composed by: a crankshaft; a bushing; a piston rod; a piston and a pin. The exploded view of the assembly is shown in Fig. 7.

Fig. 8. Crankshaft tolerance scheme

Fig. 9. Crankshaft part tolerancing graph

6. Conclusions

Fig. 7. Slider-crank assembly: 1) crankshaft; 2) bushing; 3) piston rod; 4) piston; 5) pin.

The present paper presents a graph-based method to manage and record tolerance specification set. Besides, a software tool, development in MatLAB® environment, to interactively assign tolerance specifications and to enabling both consistency analysis and automatic tolerance graph

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Fig. 10. Assembly graph of the slider-crank assembly

generation is presented. The proposed method is applied to a crank slider mechanism. Further integrations are needed for the automatic feature recognition in order to simplify the importing step of assembly. Acknowledgements The present work was developed performing the activities of the project “Cervia - Certification and Verification of Innovative and Advanced methods”. Authors acknowledge Mr. Daniele Gemei and Mr. Domenico Stanzione for their support in the GUI implementation, during their master degree theses at IDEAS Lab. References [1] Hong YS, Chang TC. A comprehensive review of tolerancing research. Journal of production research 2002; 40: 2425-2459. [2] Franciosa P, Gerbino S, Patalano S. Variational modeling and assembly constraints in tolerance analysis of rigid part assemblies: planar and cylindrical features. The International Journal of Advanced Manufacturing Technology 2010; 49.1: 239-251. [3] Franciosa P, Gerbino S. A CAD-based Methodology for Motion and Constraint Analysis According to Screw Theory. In: ASME International Mechanical Engineering Congress and Exposition; 2009. p. 287-296. [4] ASME Y14.5 – 2009 (Revision of ASME Y14.5M-1994(R2004)) – Dimensioning and Tolerancing - Engineering Drawing and Related Documentation Practices [5] ISO 1101:2017. [6] ISO 5459:2011 [7] Ballu A, Falgarone H, Chevassus N, Mathieu L. A new Design Method based on Functions and Tolerance Specifications for Product Modelling. CIRP Annals-Manufacturing Technology 2006; 55.1: 139-142.

[8] Anselmetti B, Chavanne R, Yang J-X, Anwer N. Quick GPS: A new CAT system for single-part tolerancing, Computer-Aided Design 2010; 42: 768–780. [9] Dufaure J, Teissandier D. A tolerancing framework to support geometric specifications traceability. International Journal of Advanced Manufacturing Technology 2008; 36: 894–907. [10] Giordano M, Pairel E, Hernandez P. Complex mechanical structure tolerancing by means of hyper-graphs. Models for computer aided tolerancing in design and manufacturing 2007; 105-114. [11] Ballu A, Luc Mathieu L, Legoff O. Representation of Mechanical Assemblies and Specifications by Graphs. Geometric Tolerancing of Products 2010; 87-110. [12] Franciosa P, Patalano S, Riviere A. 3D tolerance specification: an approach for the analysis of the global consistency based on graphs. International journal of interactive design and manufacturing 2010; 4: 110. [13] Clément A, Rivière A, Serré P, Valade C. The TTRSs: 13 constraints for dimensioning and tolerancing. Geometric design tolerancing: theories, standard and application 1998; 122-131. [14] Patalano S, Vitolo F, Lanzotti A. A graph-based software tool for the CAD modeling of mechanical assemblies. In: International Conference on Computer Graphics Theory and Applications; 2013. p. 60-69. [15] Franciosa P., Gerbino S., Lanzotti A, Patalano S. Automatic evaluation of variational parameters for tolerance analysis of rigid parts based on graphs, International Journal of Interactive Design and Manufacturing (IJIDeM) 2013; 7.4: 239-248. [16] Ballu A., Mathieu L. A model for a coherent and complete tolerancing process. Models for Computer Aided Tolerancing in Design and Manufacturing 2007; 35-44. [17] Patalano S, Vitolo F, Lanzotti A. A digital pattern approach to 3D CAD modelling of automotive car door assembly by using directed graphs. Graph-based modelling in engineering. Springer International Publishing 2017; 175-185.