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A functional approach for the formalization of the fixture design processR. Huntera, J. Riosb,*, J.M. Pereza, A. VizanaaDepartment of Mechanical and Manufacturing Engineering, Escuela Tecnica Superior de Ingenieros Industriales, Universidad Politecnica de Madrid,Jose Gutierrez Abascal, 2, 28006 Madrid, SpainbCurrently in Enterprise Integration (Bldg 53), Cranfield University, Cranfield, MK43 0AL, UKReceived 14 January 2005; accepted 14 April 2005Available online 26 August 2005AbstractThe design of machining fixtures is a highly complex process that relies on designer experience and his/her implicit knowledge to achievea good design. In order to facilitate its automation by the development of a knowledge-based application, the explicit definition of the fixturedesign process and the knowledge involved is a prior and a fundamental task to undertake. Additionally, a fundamental and well-knownengineering principle shouldbe considered: the functional requirements and their associated constraints should be the first input toany designprocess. Considering these two main ideas, this paper presents the development undertaken to facilitate the automation of the fixture designprocess based on a functional approach.In this context, the MOKA methodology has been used to elicit fixtures knowledge. IDEF0 and UML have been used to represent thefixture design process. A methodology based on the function concept and aiming to formalize such design process is proposed. Fixturefunctional requirements have beendefined and formalized. Functional fixtures elements havebeen used tocreate a functionaldesign solution,the link of these elements with the functional requirements and with typical commercial fixture components has been defined via tables andrules mapping. And finally, a prototype knowledge-based application has been developed in order to make an initial validation of theproposed methodology.q 2005 Elsevier Ltd. All rights reserved.Keywords: Fixture design process; Fixture knowledge modelling, Fixture functional requirements1. IntroductionThe main objective of any design theory is to provide asuitable framework and methodology for the definition ofa sequence of activities that conform the design process of aproduct or system 1. In general, all of them identifyrequirements as the starting point in the design process. Infact, the engineering discipline dealing with product designcan be defined as the one that considers scientific andengineering knowledge to create product definitions anddesign solutions based on ideas and concepts derived fromrequirements and constraints 24.For this research, a relevant issue when consideringrequirements, taking this as a general concept, is to makeexplicit the meaning of two main terms: FunctionalRequirement (FR) and Constraint (C). A functionalrequirement, as it stated by different authors, representswhat the product has to or must do independently of anypossible solution, 2,4. A FR is a kind of requirement, andconsidering some basic principles widely recognized in thefield of Requirements Engineering, we could add it is aunique and unambiguous statement in natural language of asingle functionality, written in a way that it can be ranked,traced, measured, verified, and validated. A constraintcan be defined as a restriction that in general affects somekind of requirement, and it limits the range of possiblesolutions while satisfying the requirements. So, a constraintshould be always linked to a requirement, and its purpose isto narrow the design outcome to acceptable solutions.Considering the Theory of Axiomatic Design 4,functional requirements should be defined in the functionaldomain, which brings on the scene the issue of how to defineand represent the functionality of a product. The way used torepresent it will affect the reasoning process of the designer,and in that sense, the mapping between the functionalInternational Journal of Machine Tools & Manufacture 46 (2006) 683697/locate/ijmactool0890-6955/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.ijmachtools.2005.04.018*Corresponding author. Tel.: C44 1234 754936; fax.: C44 1234750852.E-mail address: j.rioscranfield.ac.uk (J. Rios).and the physical domains, being the later the one where thedesign solutions are developed. Several authors haveinvestigated the concept of functionality and functionalrepresentation 2,58. Their design approach provides aview based on the Function-Behaviour-Structure frame-work, where function is defined using structure andbehaviour 6. The objective is to fill the gap that allowsa designer to progress from FRs to physical designsolutions. The approach is that product functions areachieved by means of its structure, which seems to lead toan iterative causal approach, where solutions are soughtuntil the selected structure causes the intended functionality.The approach adopted in the research presented in this paperis based on the definition of Fixture Functional Components(FFC), which can satisfy the fixture functionality, and on themapping between such FFC and fixture commercialelements.An advanced approach to the definition of requirementsand functions comes from the creation of ontologies. Theontological approach pursues the definition of the meaningof terms making use of some kind of logic, and the definitionof axioms to enable automatic deduction and reasoning 9.The ontological approach has got a higher relevance sincethe representation of knowledge is considered the key factorin whatever engineering process, and it has been recognizedas a way to facilitate the integration of engineeringapplications 10, to describe functional design knowledge7, and to define requirements 11. Considering a puristapproach, if an ontology does not include axioms to enablereasoning then it could be considered more like aninformation model, and in this sense, this is the approachdeveloped in the work presented in this paper.When considering the methodologies developed for thedesign of fixtures, it can be stated that in general they arerational and propose a series of steps to follow. For example,the methodologies proposed by Scallan and Henriksen 12,13, make use of this approach to describe in general termsthe information needed in each stage of the fixture designprocess. Basically, the importance of modelling in detailsuch information, which mainly is related to fixturerequirements, fixture functionality, fixture components,manufacturing resources, manufacturing processes, anddesign rules; resides on the possibility to automate thedesign process through the development of a knowledge-based application or system. It is relevant to mention thatseveral authors have already aimed to develop knowledge-based applications for fixture design, none of them based ona functional approach, some of the most recently publishedworks can be found in the Refs. 1419.Inthefollowingsections,thispaperpresentsamethodology to formalize the design process of machin-ingfixturesbasedontheengineeringconceptsoffunctional requirements and fixture functions 20. Theformalization of the functional requirements is achievedthrough the application of a structured way of specifica-tion via natural language. Additionally, IDEF0, MOKAmethodology, and UML diagrams are used to capture,represent and formalize knowledge, being the ultimategoal to facilitate the automation of the fixture designprocess.The IDEF0 method is used to create an activity model ofthe fixture design process, allowing the identification of theinformation used in each one of the different tasks itcomprises. UML has been used to complement the IDEF0model by representing the interaction between the activitiesof the process. The MOKA methodology together withUML, are used to capture and represent knowledge involvedin the fixture design process. Finally, to validate theproposed methodology, partial results obtained from thedevelopment of a prototype knowledge-based applicationare presented.2. Analysis of machining fixtures requirementsIn Section 1, two terms have been defined: functionalrequirement and constraint. Requirements have alwaysexisted, the way in which they are expressed, and howthey are integrated in the product design process, are aspectsthat are addressed from different disciplines, for example:product design engineering and requirements engineeringamong others. In general, Requirements Engineering refersto the discipline dealing with the capture, formalization,representation, analysis, management and verification ofrequirements fulfilment. However, all these aspects need tobe integrated in the product design process, and require-ments should lead to the definition of the possible productdesign solutions, which in general demands an integratedview of the requirements issue. It is important to keep inmind that the development of such discipline is stronglyrelated to Software Engineering and Systems Engineering,and in fact much of the research related to requirementscome from authors from these engineering areas 2123.When considering the analysis of requirements, prob-ably, the first aspect to think about is how the requirementsare represented or declared. As it has been previouslymentioned, the way of expressing requirements definitivelyaffects their interpretation and the creation of a designsolution. In this sense, it is widely accepted, that the use ofnatural language is the most common way of expressingrequirements and in consequence, their writing becomes animportant issue. The anatomy proposed by Alexander et al.24 to write requirements in a semi-structured way is usedas basis to declare the functional requirements andconstraints of fixtures 20.In machining, work holding is a key aspect, and fixturesare the elements responsible to satisfy this general goal. Intheir design process, the starting point is the definition of themachining fixtures functional requirements and constraints.Usually, a fixture solution is made of one or several physicalelements, as a whole the designed fixture solution mustsatisfy all the FRs and the associated Cs. Centring, locating,R. Hunter et al. / International Journal of Machine Tools & Manufacture 46 (2006) 683697684orientating, clamping, and supporting, can be considered thefunctional requirements of fixtures, what a fixture must doindependently of any particular solution. In terms ofconstraints, what limits the range of possible solutions,there are many factors to be considered, mainly dealingwith: shape and dimensions of the part to be machined,tolerances, sequence of operations, machining strategies,cutting forces, number of set-ups, set-up times, volume ofmaterial to be removed, batch size, production rate, machinemorphology, machine capacity, cost, etc. At the end, thesolution can be characterized by its: simplicity, rigidity,accuracy, reliability, and economy.2.1. Functional requirementsFrom the literature review 2527, and from theinterview with designers of machining fixtures 28, it canbe concluded that basic functional requirements that anyfixture solution must satisfy are related to: centring,locating, orientating, clamping, and supporting.However, the way that designers deal with these FRs isfar from being independent of the solution they areconsidering, and in general the FRs are not explicit butimplicit in the design process. Chakrabarti et al. 29 pointout some of the problems that appear in relation torequirements during the design process, for examplerequirements during conceptual and embodiment designsresult mainly from analysis of proposed designs, which infact it is in contradiction with the basic principle, presentedby different authors, of functional definition prior to anydesign solution identification. Adopting the ideas ofToyotas Set-based Concurrent Engineering 30 andAxiomatic Design Theory 4, it seems logical to statethat the FRs should be clearly identified and defined prior toselecting any possible design solution and as the designprogresses the different constraints linked to the FRs shouldbe refined to narrow the set of possible solutions.Chakrabarti et al. 29 also conclude that in order forrequirements to be adequately fulfilled by the final design,they must be identified, understood, remembered and used.Thisconclusion is not new, and in this sense, it demonstrateshow actual and relevant this issue is. It also reinforces acouple of ideas widely recognized in engineering design,one is the need to capture, formalize and documentknowledge, and the second is to make use of it in thedevelopment of Knowledge-Based Engineering (KBE)applications that could help the designers to carry outtheir job and make use in an automatic way of as muchscientific knowledge as possible 31. In this particular caseapplied to the design of machining fixtures.When addressing the development of a KBE application,there are two different sorts of FRs that need to be identifiedand documented. One kind is the functional requirements ofthe application itself; in this case a KBE application forthe design of machining fixtures; and the second one is thefunctional requirements of the components subject of theapplication; in this case machining fixtures. An example ofthe former ones for an application developed in collabor-ation with an industrial partner is presented by Rios et al.28. For this kind of FRs specification, UML seems to beFig. 1. MOKA Entity form for fixture FRs.R. Hunter et al. / International Journal of Machine Tools & Manufacture 46 (2006) 683697685a good methodology: activity, component, and use casediagrams help to specify and give a view of the system.However, when getting into the logical view where classand interaction diagrams have to be defined, it is needed tohave a complete understanding of the object of theapplication: machining fixtures. With this objective, andconsidering that the design of machining fixtures based onfunctional requirements would be the aim of a KBEapplication, the capture and documentation of the machin-ing fixtures FRs is part of the subject of the work developed20, and it is commented next.In this context, the approach adopted was to use part ofthe tools provided by the MOKA methodology 31, thenamed: Illustrations, Constraints, Activities, Rules andEntities forms, to elicit knowledge about machiningfixtures as a first step in the formalization of the FRs andCs. Based on these forms, it is possible to represent themain components linked with the fixture design process:non-functional requirements, functional requirements,constraints, design rules, fixture functional elements,fixture commercial components, etc. 20. Figs. 1 and 2present an example of application to the definition offixture FRs and Cs.After this first phase, the requirements capture iscompleted with the formalization of the functionalrequirements syntax. At this point, it is important toremember that the declaration of a FR is a sentence writtenin a way that allows the FR to be measured, verified, andvalidated. The structure proposed is based on Alexandersanatomy 24, and it has similarities with the functionrepresentation presented by Takeda et al. 6, where it isstated that a function is a combination of a function body(verb), an objective entity (on which the function occurs onor to), and functional modifiers (adverb). The structureproposed in this research is made up of four maincomponents: action, object, resource, and qualifiers(Fig. 3). And unlike with the Takeda approach, all themodal adverbs (i.e.: firmly, precisely, in general allInside the working area of the table:X = 200 mmY = 400 mmZ = 400 mmTolerance for all the dimensions: 1 mmObjectResourcePart A in vertical ma chining center DM T50 ActionQualifierSupport Fig. 3. Functional requirement structure.MOKA ICARE: ENTITYNameReferenceEntity TypeFunctionBehaviourContext, Information,ValidityDescriptionManagementAuthorDateVersionStatusConstraints Functional Requirements for the FixtureConstraints Functional Requirements (CFR)StructureDefine constrains to Functional Requirements for the fixtureNot ApplicableDefine constraints that support the functional requirementsThe constraints will be structured thinking on the functional requirements structureWith this target it has been defined a group of constraints associated with eachfunctional requirement of the fixture, such as:OrientationSupportLocateClampMachiningResourcesRenato Hunter03-07-041.0In progressFig. 2. MOKA Entity form for fixture Cs.R. Hunter et al. / International Journal of Machine Tools & Manufacture 46 (2006) 683697686the adverbs ending with the suffix y) are not considered as amodifier, since they do not have a quantitative value, and inconsequence they cannot be measured neither validated.The Action component is expressed by an active verb thatrefers to the function of the fixture. As named previously,these functions are: centre, position, orientate, clamp, andsupport. A noun expresses the Object component, and refersto the physical object on which the action is performed. Inthe first level of fixture FRs definition, Object will be thepart to be machined. A noun expresses the Resourcecomponent, and it refers to where the action will beperformed. In the first level of fixture FRs definition,part_requirementscost_requirementsprocess_requirementsorientation_requirements-identificacion : char-nombre : char-descripcion : char-accion : char-que : char-recurso : char-calificador : chardocumentation_requirementFixture_requirementslocate_requirementssupport_requirementsclamp_requirements-Requirements1-Documentation1.*accesibility_requirements-Process1.*-Part1formal_representation_requirements-identificador : char-nombre : char-descripcion : char-accion : char-que : char-recurso : char-calificador : charfunctional_requirements-identificador : char-nombre : char-descripcion : char-accion : char-que : char-recurso : char-cualificador : charno_functional_requirements-identificador : char-nombre : char-descripcion : char-accion : char-que : char-recurso : char-calificador : charstructure_requirementscentre_requirementsmachine_tool_requirementsmachining_feature_requirements-Part1-feature1.*-Process1-Feature1.*-Identificator: char-name: char-description: char-action: char-object: char-resource: char-qualifier: char-Identificator: char-name: char-description: char-action: char-object: char-resource: char-qualifier: char-Identificator: char-name: char-description: char-action: char-object: char-resource: char-qualifier: char-Identificator: char-name: char-description: char-action: char-object: char-resource: char-qualifier: charFig. 4. UML model of the fixture functional requirements.Table 1Instances of fixture FRsActionObjectQualifiersQualifier typeOrientatePartIn the machine tool (M0)(Resource)Respect to the coordinated system of thepart (M1)(How)On the orientation part activity (M2)(When/Where)Modifier (M0)Respect to system axis of machine toolModifier (M0)In a vertical milling machineModifier (M1)Respect to the tool pathConstraintsMachine tool type (Vertical or horizontalmill)Work area: lengths in X, Y, ZSupportPartIn machine tool (M0)(Resource)On static equilibrium (M1)(How)On the support part activity (M2)(When/Where)Modifier (M0)In a vertical milling machineModifier (M1)When the sum of forces is equal to zeroModifier (M2.1)Vertical degree of freedom of the partModifier (M2.2)When the orient activity propose a resultConstraintsWork area: lengths in X, Y, Z Shape andsize of the base plateR. Hunter et al. / International Journal of Machine Tools & Manufacture 46 (2006) 683697687Resource will be the machine tool on which the machiningis performed. A quantitative adjective group or noun groupexpresses a Qualifier for the action. The Qualifierscomponents refer to limits of the FRs, and allowrepresenting the constraints (Cs) associated with them.Each quantitative qualifier must have at least a nominalnumerical value, a unit of measure, and a tolerance. Each FRmust have at least one quantitative qualifier. Considering theprevious concept of constraints refinement to narrow the setof possible solutions, the specification of the qualifiers maynot have numerical values when they are initially defined,but in the final stage, when the constraints have to beconsidered to select a candidate solution the numericalvalues need to be declared. The proposed structure of thefixture FR was then modelled in UML (Fig. 4).The class functional_requirements has as attributes thefour components previously defined: Action, Object,Resource and Qualifier. Considering an Object Orientedimplementation, each instance of the class will have aunique identifier that allows tracing that particular FR. Withthis capability, it is possible to modify and update any of theattributes of such FR at any time during the design process.As an example, instances of fixture FRs for orientating andsupporting are represented in the Table 1.3. Proposed methodology for the formalizationof the fixtures design processThe methodology proposed in this research for thefixtures design process is based on five main design phases(numbered 15), named: Functional Requirements develop-ment (FR), definition of Fixture design Functions (FF),Functional Design fixture solution (FD), Detailed Designfixture solution (DD) and Fixture final design solutionValidation (FV). These stages aims to define a process withcontinuous feedback, which allows developing the fixturedesign in a systematic, structured and concurrent way(Fig. 5).Phase 1: The first phase, development of functionalrequirements (FR), comprises the capture of the knowledgeneeded to perform the design process formachining fixtures.It has two main tasks, first filling in the MOKA forms, andsecond formalization of the functional requirementsaccording to the structure defined in Section 2.Phase 2: The secondphase, definition offixture functions(FF), is aimed to complete a set of high level softwarefunction templates that implemented in a knowledge-basedapplication allows to generate fixture solutions which arecompliant with the functional requirements defined in theprevious phase. The fixture functions have been definedgraphically using a method based on the IDEF0 modelling.The representation notation permits to embody graphicallythe attributes and operations needed for the implementationof a function. Fig. 6 shows an example. The proposedrepresentation is a high-level function definition; it isindependent of the knowledge representation to be used inthe implementation, and it does not require from the fixturedesigner a deep knowledge of any software modellingtechnique.Thedefinitionofthesefixturefunctionsisafirststepinthemodelling needed for a KBE application development. Forexample, considering stability as one of the main constraintsaffecting the fixture FRs, any fixture functional solutionshould satisfy this constraint. To achieve that, it would benecessary to define a fixture function (FF) for stabilityFig. 5. Fixture design process methodology.R. Hunter et al. / International Journal of Machine Tools & Manufacture 46 (2006) 683697688evaluation, and this function could be called from the fixturefunction clamp (clamp_FF) presented as example in theFig.6.From ahighlevelperspective,thestability_FF wouldneed as input: part information (i.e.: material mechanicalproperties, shape, dimensions and tolerances), machiningprocess information (i.e.: machining operations, machiningstrategies, volumes to remove, cutting parameters, cuttingtool parameters), and fixture functional element information(i.e.: function, constraints, rules, containing volume, pointand vector of application). Part of this information will havetobeusedtodetermine somederived parameterslikecuttingand allowed clamping forces. Making use of such infor-mation together with an analysis model, for example the oneproposed by Liao et al. 32, and optimization methods, forexample the one proposed by Pelinescu et al. 33, suchstability_FF could be developed and implemented. Thecomplexity in the detailed specification of such stability_FFis extremely high, and demands its own research by itself32,34,35, but the definition of a high level function whereall the information needed for its development could berepresented,isoneoftheobjectivesoftheresearchpresentedin this paper.Phase 3: The third phase, functional design (FD), isaimed to create a set of functional solutions for the fixturedesign. A functional solution is independent of anyparticular commercial fixture component, and it is rep-resented by means of a set of fixture functional elements. Afixture functional element satisfies at least one of thefunctions identified as inherent to a fixture, i.e.: centre,position, orientate, clamp, and support. These elements arerepresented by means of graphical symbols, also calledfunctional symbols, which apart from the functionality alsorepresent some qualifiers that affect them. Such fixturefunctional symbols are based on the technological elementsdefined in the AFNOR standard NF E 04-013 - 1985 36.Fig. 7 presents their structure, which comprises: kind ofPart machining:operationsstrategiescutting parameterscutting tool parametersvolume to removeFixture functional elements:functionconstraintsrulescontaining volumeOptimization methodAnalysis modelConstraints:DeformationStabilityInterferenceFunction Clamp(clamp_FF)F4Part orientationPart support:support pointssupport vectorssupport surfacesPart location:locating pointslocating vectorslocating surfacesPart information:mechanical propertiesfriction coefficientraw material shape and dimensionspart shape and dimensionstolerancesDetermine cutting forcesDetermine clamping surfaceDetermine clamping pointsDetermine clamping orientationDetermine clamping forcesDetermine clamping elementsFig. 6. High-level function template representation.Fig. 7. Structure of the AFNOR fixture technological elements.R. Hunter et al. / International Journal of Machine Tools & Manufacture 46 (2006) 683697689technology, state of the part surface, function of thetechnological element, and the kind of contact betweenthe part surface and the fixture element.In order to progress from the functional design to thedetailed one, which is the next phase, it has been defined amapping table between functional symbols and commercialfixture elements 20, Table 2 represents an example.For the creation of the possible functional solutions a setof input information, analysis models, optimization func-tions, and rules has to be included in the software functionspreviously defined in the second phase. Basically, the inputsdefined are: Part information: material mechanical properties, shapeand dimensions of the part to be machined, and theassociated tolerances. Functional element information: functions, associatedrestrictions, orientation, containing volume, contactparameters, and location point. Part manufacturing process: sequence of operations, andfor each operation: machining strategy, cutting para-meters, cutting tool, and volume to remove. Production estimation of: number of set-ups, set-uptimes, batch size, production rate, and target cost. Resource information: machine morphology, andmachine capacity.Functional design brings benefits to design environmentswhere the solution is mainly driven by the satisfaction ofquantitative functions, as opposite to environments wheresubjective aspects like aesthetics has a major relevance. Inparticular, in the fixture design environment, the advantageof creating a functional solution derives from not using afull library of commercial fixture elements but a reducednumber of basic functional elements, which can betransformed into the former ones in a second designphase. And this is particularly relevant when some kind ofartificial intelligence technique is going to be applied in theimplementation phase, since many of these techniques arebased on the initial generation of a complete design spacewhere the possible solutions are contained, if the designspace can be reduced then the determination of the solutionscan be done more efficiently. And with the functional designapproach the design space is divided in two subsets, onesubset dealing with the functional solution and other dealingwith the physical one.Phase 4: The fourth phase, detailed design (DD)comprises the creation of detailed solutions from afunctional one. To undertake this phase the mapping tablespreviously mentioned and the corresponding interpretationrules have to be used. To mention as well, that the fixturesoftware functions apply in a similar way, but with adifferent input, which basically is the geometry (containingvolume) associated with the fixture element, this isparticularly relevant for the interference checking. How-ever, in this case the space of possible solutions is reducedby the fact that only those commercial elements that can bemapped to the functional ones can be used, and that a pointof application and an orientation vector for the elements tobe used are data as well. A detailed solution contains thefinal fixture commercial elements to be used in themachining of the part and their set-up.Finally, the fifth phase, validation of the design (FV), isaimed to make a final evaluation and validation of thefunctional requirements and their associated constraintsdefinedinthefirstphase.However,itisimportanttomentionthat in addition to a final validation, the functional approach,with the separation of the design spaces in two parts, allowsimplementing the validation in two prior stages. First in thefunctional design phase, so the possible functional designsolutions fulfil the imposed requirements, and second in thedetailed design phase. This can be made by means of theoptimization method that can be included in the FixtureFunction(FF),asitwaspreviouslymentionedinthePhase3.Based on this methodology, a detailed definition of thefixture functional design process is presented in the nextsection.4. Fixture functional design process modelAs it was mentioned in the introduction, the functionalapproach to design has drawn the attention of severalresearchers 2,5,6,7,8. However, as it is pointed out byTable 2Relation between AFNOR elements and fixture commercial componentsFixture functionFunctional representationCommercial elements selected typeClamp function*Type technology: Clamp(Attribute)Type technologySurface ClassType FunctionType contact surface*Surface class: Machined*Type technology*Type contact surface: Punctual*Surface class*Type function: Machining Fixture*Type contact surface*Type functionR. Hunter et al. / International Journal of Machine Tools & Manufacture 46 (2006) 683697690Kitamura 7, in general, the functional knowledge is leftimplicit, there are not clear definitions of the functionalconcepts, and the generic functions proposed in theliterature are too generic to be used by designers. In thissense, the ontological approach is an interesting contri-bution to formalize the functional design knowledge. Theapproach adopted in this research deals with the definitionof what would be the first step in a fixture ontologydevelopment, which is the modelling of the fixtureinformation.The functional approach to fixture design, based on aninformation model definition, has some characteristics thatcan be deduced from the facts presented in the previoussections, that is: a reduced number offunctions that a fixturehas to perform, the possibility of formalizing the FRsspecification with quantitative qualifiers, and the reductionof the design space by using functional elements. However,prior to the definition of any fixture information model, it isnecessary to define the fixture design process and theinformation flow along it.Following is the activity model developed in thisresearch to represent the fixture design process. Themodel is represented using the IDEF0 technique andUML, and it allows identifying the knowledge unitsneeded during such process, and the interaction amongthe activities. The development of this model is based onthe findings from the literature review, and on thefindings from a development conducted in collaborationwith an industrial partner 28. Some authors have alsoused modelling techniques to represent the process andpart of the information related to the fixture designprocess 37,38, but without taking a functional approachto it.Starting with the input knowledge units related to partgeometry,manufacturingprocessplan,machiningresources, and following the IDEF0 methodology, the firststep is to create a context diagram or highest-level diagram,of the fixture design process. The knowledge units thatconstitute the final output to the process are the fixturedetailed design, and the fixture assembly plan. The resourceknowledge units are the machine-tool unit and the modularfixture elements one.The IDEF0 methodology is based on the definition of ahierarchical break down of activities, each of them isdefined by an active verb, together with a set of inputs toand outputs from each activity, resources needed for itscompletion, and elements can be used as control in itsundertaking. Following are the main diagrams developedduring the research.From the root diagram, the first level diagram is created.As it presented in the Fig. 8, it comprises the activitiesdealing with the analysis and definition of the three maininformation units defined: part geometrical information,manufacturing process plan, and fixture design plan. It isrelevant to mention, that the performance of these activitiesis highly concurrent and iterative.Activity A1: The fixture designer analyse the partgeometrical features, shape and dimensions, tolerances,C2M2FixtureDesignerO1Fixture Assemby PlanC4Principles of Fixture DesignC3Manufacturing ConditionsO3FixtureDesignANALYSEFEATURES OF THE PARTANALYSE MACHINING PROCESSDETAIL FIXTURE DESIGN PLANPart FeaturesMachining operations and tool pathDesign RulesI3Part Information:GeometryI1Defined Phaseand SubphasesC1and SubphaseM1ManufacturingResourcesI2Machining OperationsA1A2A3P.3P.4P.5State of resourcesDefined PhaseFig. 8. Node A0: design machining fixture.R. Hunter et al. / International Journal of Machine Tools & Manufacture 46 (2006) 683697691and surface finish. The output is the set of part technologicalfeatures to be considered in the fixture design process.Activity A2: The fixture designer analyse the partmanufacturing process plan, machining operations, volumesto remove, cutting tool, cutting conditions, machiningstrategy, and machine tool morphology. The output is anunderstanding of the correspondence between the parttechnological features and the machining operations.Activity A3: Using the outputs from the two otheractivities, plus the production information, the designerdefines the functional requirements and the constraints ofthe fixture. After that, he starts with the identification ofpossible functional solutions to fulfil such requirements.Each of these solutions has to be evaluated in order toguarantee that the requirements are satisfied. The followingstage is to define for each functional solution the feasibledetailed ones, those including commercial fixture elements.The second level of break down is presented in threedifferent diagrams, Fig. 9 for the A1 node, Fig. 10 for the A2node, and Fig. 11 for the A3 node.The activity A1 has been divided into four sub activities(Fig. 9). The activity A11 creates a list of geometricinformation defining the volumes to machine. The activityA12 deals with the dimensional, tolerances and surfacefinish analysis. The Activity A13 defines the starting rawmaterial, in case that the part is not shaped in a primarymanufacturing process. And finally, the Activity A14focuses on the definition of the technological features ofthe machining to be performed on the part. It comprisesthe input of the results from the previous three activitiesand it creates a list of machining features with theirassociated dimensions and tolerances.The activity A2 has been divided into three sub activities(Fig. 10). The activity A21 deals with the productioninformation, and the analysis of the machine tool to be used,for example: machining working space dimensions, speedspindle rates, feed rates, and table dimensions. The activityA22 focus on the analysis of the machining operations,possible operation sequences, identification of possibleorientations for the part. Finally, the activity A23 combinesthe output of the Activity A14, machining features, with theoutput of the activity A22, machining process analysis, todefine a set of machining subphases, set of operationsperformed with the same cutting tool, with all theinformation needed for their execution.The activity A3, elaborate detailed fixture design plan,has been broken down into four sub activities, all of themrelated to the methodology proposed in the Section 3,Fig. 11 shows the diagram. The activity A31 comprisesthe definition of the fixture requirements and constraintsaccording to description previously presented in theSection 2.1. The activity A32 requires the use of a setof predefined fixture functions (FF), presented in themethodology section. The final objective would be toimplement these functions in a knowledge-based appli-cation, so the functional design solution would fulfil therequirements defined. In this case, a first level objectivewas addressed in this research, to make these functionsand the information needed for their development explicit,in a way that any fixture designer could understand themC1M1FixtureDesignerANALYSE GEOMETRY TO MACHINING ANALYSE DIMENSIONS AND TOLERANCES OF THE PART DEFINE PART MATERIALDEFINE TECHNOLOGICAL FEATURES OF THE PARTTolerance Analysis CriterionsConstraints TolerancesMaterial of thePartI1Part Information:GeometryO1PartGeometricFeatures of the A11A12A13A14 FeaturesDesign RulesFig. 9. Node A1: analyse part characteristics.R. Hunter et al. / International Journal of Machine Tools & Manufacture 46 (2006) 683697692and decide which actions to undertake to get a functionalsolution. Additionally, the description proposed for the FFmakes them independent of any deployment environment,and any programmer could use them as a starting point todevelop such fixture design knowledge-based application.Making use of the FFs, the activity A33 focus onthe definition of the fixture functional design, which isrepresented using the functional elements based on theAFNOR standard presented in the Section 3 36. Finally,the activity A34 deals with the fixture detailed design.Making use of the fixture functional design, functionalelements-commercialelementsmappingtables,O2Machining operations and tool pathsM1FixtureDesignerC4Manufacturing ConditionsC3State of resourcesO1Fixture Assemply PlanANALYSE MACHINING PHASE AND SUBPHASESANALYSE MACHINING OPERATIONSANALYSE MACHINETOOLOperations ListTolerances ConstraintsI4Part Information:GeometryM2ManufacturingResourcesI2Machining OperationsC2Defined Phaseand SubphasesI3Defined Phaseand SubphasesI1Part FeaturesC1Part FeaturesMachine-ToolConditionsA21A22A23Fig. 10. Node A2: analyse machining process.C1Machining operations and tool pathsM1FixtureDesignerC3Principles of Fixture DesignO1Fixture Assemby PlanO3FixtureDesignI1Machining operations and tool pathsC2Manufacturing ConditionsDEVELOPFIXTURE REQUIREMENTSDEVELOP FIXTURE FUNCTION ELABORATE FUNCTIONAL DESIGNELABORATE DETAILED DESIGNRepresentationFormatFunctional RepresentationFixture RequirementsFixture FunctionsFunctionalFixture DesignFunctionalElementsProgrammerModification of RequirementsFixture ModificationsI2Part Information:GeometryM2ManufacturingResourcesA33A34A32A31Fig. 11. Node A3: detail fixture design plan.R. Hunter et al. / International Journal of Machine Tools & Manufacture 46 (2006) 683697693and the corresponding FFs, the final fixture design can beobtained.The diagrams presented so far need a complementaryview to show the temporal interaction among the high levelactivities that constitute the fixture design process. TheUML sequence diagram presented in the Fig. 12 providesthis view.5. Information model, instantiation, and methodologyvalidationFollowing the modelling of the fixture design process,the identified knowledge units: fixture requirements, fixturefunctions, part definition, machining operations, functionaldesign rules, detail design rules, fixture resources, andfixture validation, have been modelled in an object-orientedstructure, and UML has been used for its representation20. For some of these knowledge units, specifically forpart definition and machining operations, prior develop-ments have been used 39,40.Following is an example to show a partial instantiation ofsuch model, and the results obtained from a prototypeknowledge-based application, which has been developed ina commercial CAD/CAM system to validate the method-ology proposed in this research 20.As starting point, the Table 3 presents initial geometricand machining data used as input to initiate the fixturedesign process for a particular part to be machined in a CNCvertical milling machine.Following the methodology proposed in the Section 3,the process starts with the analysis of the part geometricalinformation and machining plan. As a consequence, thefixture functional requirements have to be defined. Theseactivities are part of the phase 1 (FR). Then the fixturefunctions have to be defined and represented (phase 2) (FF).Fig. 13 depicts a sample of these two design phases.Specifically, Fig. 13a presents an instance of the functionalrequirement support, with the attributes: action (support),object (part), resource (vertical milling machine), andqualifier (machining subphase 10, Table 3). Keeping thestructure proposed in the section 2.1. These attributes areused as input in the fixture function support_FF, the linesgoing from the Fig. 13a to the Fig. 13b represent the link.functional requirementsfixture functionsfunctionaldesigndetailed designvalidate design1: 3: establish value2: define functions8: validate design4: validate design5: check design7: establish correspondence13: Verification functional requirements6: establish value14: approve design Fig. 12. Fixture design sequence diagram.Table 3Geometric and machining part dataInformationFeature for fixture design processInitial shape geometryMachining operations listMachining subphase 10:Pocket_milling :24 mmPocket_milling :26 mmPocket_milling :30 mmDrilling :8 mm (2 Holes)Counterboring :36 mm, 5 mmCounterboring :40 mm, 8 mmMachining subphase 20:Manufacturing resourcesVertical milling machineModular fixture elementsFinal shape geometryR. Hunter et al. / International Journal of Machine Tools & Manufacture 46 (2006) 683697694The Fig. 13b represents the function support_FF usingUML, and its instantiation in CCC is presented in theFig. 13c.The functional design phase (FD) makes use of the FFsdefined in the previous phase, which directly correspondto the functional requirements (FRs): support_FF,clamp_FF,centre_FF,orientate_FF,position_FF,together with a set of design rules. In Fig. 14c, it isshown the raw material part, in Fig. 14b the volumes ofmaterial to be removed, and in Fig. 14a, the correspond-ing attributes for the support function. In the example, therules defined have relation with the determination of:surfaceandpointofsupport,kind,locationandorientation of the functional element (Fig. 14d). TheFig. 14e represents a result of the application of thefunctions and the associated rules.Finally, the detailed design phase (DD) should determinethe commercial standard fixture elements to use inthe machining of the part. To achieve this objective, themapping tables between functional elements and thecommercial fixture elements have to be used. Followingwith the example, according to the mapping presented in theTable 2, the Fig. 15 represents a detailed solution to thefunctional one presented in the Fig. 14. -machining_geometry : void = Subphase_10 information -initial_geometry : void = Case1.CATPart resource - machine_type : char = Vertical_milling resource - support_element : char = AFNOR_support constrains -machining_operation : char = Subphase_10 constrains -tool_path : charsupport_function_part+determine_support_surface() : void+determine_support_point() : void- identificator : char = iFunction_support_1- name : char = Function_support_1 information -machining_geometry : void = Subphase_10 information -initial_geometry : void = Case1.CATPart resource - machine_type : char = Vertical_milling resource - support_element : char = AFNOR_support constrains -machining_operation : char = Subphase_10 constrains -tool_path : charsupport_function_part- identificator : char = iRequerement_support - name : char = Requirement_support - description : char - action : char = support - what : char = Part Case1. CATPart - resource : char = vertical milling - qualifier : char = subphase machining 10 support_requirement - identificator : char = iRequerement_support - name : char = Requirement_support - description : char - action : char = support - object char = Part Case1. CATPart - resource : char = vertical milling - qualifier : char = subphase machining 10 support_requirement #include support_function_part.h“support_function_part: support_function_part (): Function_fixture (), m_identificator(iFunction_support _1), m_name(Function_support _1), m_machining_geometry(Subphase 10), m_initial_geometry(Case _1. CATPart ), m_machine_type(Vertical_milling ), m_support_element(support_element_AFNOR ) Information Group Functional Requirement Information Group Fixture FunctionsInstantiationFunctions C+ (a) (b)(c)Fig. 13. Functional requirements interpretation and fixture functions.Fig. 14. Functional design solution example.Fig. 15. Detailed design solution example.R. Hunter et al. / International Journal of Machine Tools & Manufacture 46 (2006) 6836976956. ConclusionsAn integrated approach to the design process ofmachining fixtures has been adopted in this research.The basic aim was to formalize a methodology tofacilitate the automation of such design process. Basedon the findings and conclusions obtained from theliterature review and the interaction with fixture designers,some principles were considered to guide the research.Following are these principles and how they were takeninto consideration: The starting step is the definition of the fixturefunctional requirements. This principle led to theformalization of such requirements, based on someapproaches from Requirements Engineering, and to thefunctional representation of fixture design solutions,based on the standard AFNOR NF E 04-013 - 1985.This approach allows validating the design solutionsagainst the specified requirements. There is a need to capture and formalize machiningfixture knowledge. This principle led to the use of anestablished methodology, in this case MOKA, and tothe ontology, and information modelling approachfinally adopted. UML was used for its representation. There is a need to define and represent the machiningfixture design process. This principle led to itsdefinition and representation using IDEF0 and UML. There is a need to define software fixture functions,whose objective is to create solutions that fulfil thefixture functional requirements. And the definition hasto be independent of any implementation system. Thisprinciple led to the study of some of the solutionsalready done in this area, in particular optimizationworks, and to the conclusion that only a high leveldescription of such functions, where the informationand the basic rules needed for their implementationwere specified, was possible to address. The analysisof the MOKA modelling language was also analyzed,however the high level of complexity of the fixturefunctions, demands a further investigation in order todefine how to break them down into lower levels ofdetail while keeping the representation independent ofthe implementation level.From the research conducted, it can be concluded that theformalization of the fixture design process based onfunctional requirements allows developing a more inte-grated approach to the problem offixtures design. The basicsteps, and fundamental input to any implementation aimingto automate such process, start with the Fixture DesignProcess, and continue with the definition of the FixtureKnowledge Units: fixture requirements, fixture functions,part definition, machining operations, functional designrules, detail design rules, fixture resources, and fixturevalidation. To validate the methodology, and based onthe developed models, a prototype knowledge-basedapplication has been implemented in a commercialCAD/CAM system (CATIA V5).References1 N. Cross, Engineering Design Methods: Strategies and Tactics forProduct Design, Second ed., Wiley, New York, 1994.2 G. Pahl, W. Beitz, Engineering design A Systematic Approach,Second ed., Springer, London, 1996.3 D. Ullman, T. Dietterich, L. Stauffer, A model of the mechanicaldesign process based on empirical data, Artificial Intelligence inEngineering Design and Manufacturing (1988) 3352.4 N.P. Suh, Axiomatic Design: Advances and Applications, OxfordUniversity Press, Oxford, 2001.5 B. Chandrasekaran, J.R. Josephson. Representing function as effect.Proceedings of the Fifth International Workshop on Advances inFunctional Modeling of Complex Technical Systems (1997) 316.6 H. Takeda, M. Yoshioka, T. Tomiyama, Y. Shim