Feature-based design for heterogeneous objects - Mechanical ...

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1264X. Qian, D. Dutta / Computer-Aided Design 36 (2004) 1263–1278Fig. 1. Schematic structure of an FGM interface within a prosthesis.hydroxyapatite (HAp). Ti has good mechanical toughnessand HAp has good biocompatibility. Simple combination ofTi and HAp would cause bio-incompatibility and weakenedstrength due to their material property differences. Suchmaterial property differences are resolved in heterogeneousobjects by using a mixture of Ti and HAp with varyingproportions. The sharp interface between the Ti and HAp iseliminated due to a graded zone of Ti/HAp. The bendingstrength of the resulting material is similar to a human bone.As evidenced in this example, many applications basedon the concept of functionally gradient materials can bedeveloped to exploit multiple desirable material propertiesfrom different materials. In order to obtain mass applicationsof such heterogeneous objects, efficient and effectivedesign methodologies for heterogeneous objects are crucial.Existing design methodologies are highly sophisticated, butthey are inefficient and even infeasible for handlingheterogeneous objects. These methodologies are primarilydeveloped for the production of homogeneous objects ofwhich there is only one homogeneous material. Theintroduction of material variation throughout the objectsadds a new dimension to the problem.The state-of-the-art research on heterogeneous objectmodeling has been primarily focusing on representationschemes for heterogeneous objects. Currently, there is onlylimited means available to obtain heterogeneous objectmodel. They are ineffective for heterogeneous object designin that these heterogeneous object models do not explicitlycapture design intent and they do not support iterativedesign processes.To address these issues, in this research we propose theuse of features to facilitate the design of heteorgeneousobjects. In the example of the prosthesis design, the choicesof materials (Ti and HAp) and the graded interface are basedon a designer’s experience and these choices have specificphysical reasons. Ti has good mechanical strength. HAp is astrorage form of Calcium and Phosporus in the bone and ithas good bio-compatibility. We provide a design tool thatallows designers to design such heterogeneous objects witha high level design component—features. Under thisframework, a designer can incorporate the design intuitioninto the design process. Instead of specifying materialcomposition for each spatial location within the object, theusers can choose a feature (a graded interface in thisexample) and the desired material properties at the desiredlocations when designing the object.The remainder of this paper is organized as follows. InSection 2, we present a review of the existing researchrelating to the design of heterogeneous objects. In Section 3,a general methodology—feature based design (FBD) forheterogeneous objects—is presented. Sections 4 and 5present two enabling component techniques for a featurebased design method, material heterogeneity modelingwithin each material feature and constructive featureoperations for combining material features. Section 6presents the implementation and examples of the featurebased design methodology, including the feature baseddesign process for the prosthesis design. Finally, Section 7summarizes this paper.2. Literature reviewMany representation schemes have been developed torepresent solids. Manifold solids and R-sets were firstproposed to represent solid model [8,25]. Radial-edge datastructure is another data structure for modeling nonmanifoldsolid [32]. For conventional feature modeling,the usage of non-manifold structure was first proposed byPratt [19]. Selected Geometric Complex (SGC) is a nonregularizednon-homogeneous point set represented throughenumeration as union of mutually disjoint connected opencells [26]. Constructive Non-Regularized Geometry(CNRG) was also proposed to support dimensionallynon-homogeneous, non-closed point sets with internalstructures [27]. Middleditch et al. presented mathematics
X. Qian, D. Dutta / Computer-Aided Design 36 (2004) 1263–1278 1265and formal specification for the mixed dimensional cellulargeometric modeling [16].Current research on heterogeneous objects has led tomany representation schemes for heterogeneous objectmodeling. Kumar and Dutta proposed R-m sets be usedfor representing heterogeneous objects [12]. Jackson et al.proposed another modeling approach based on subdividingthe solid model into sub-regions and associating theanalytical composition blending function with each region[10,11]. Park et al. presented a volumetric texturingapproach for modeling heterogeneous objects [17]. Biswaset al. proposed a distance field based approach forheterogeneous object modeling, in which the space isparametrized by distance to the geometry boundaries [4].Huang and Fadel employed a Bezier basis function foroptimizing material heterogeneity in flywheel [9]. Dutta[29] and Tan [30] presented constructive approaches forheterogeneous object modeling. Kumar and Dutta presenteda trivial fiber-bundle based model to represent severalattributes of an object along with the geometry [13]. Paskoet al. used a functional representation (Frep) to constructivelymodel object geometry and properties of arbitrarynature [18].Even though existing representation schemes for heterogeneousobjects provide means to represent heterogeneousobjects, they do not necessarily support the heterogeneousobject design process. The current methods for specifyingmaterial composition face a trade-off between the modelcoverage and operation convenience [23]. These methodsonly provide a low level description of geometry andmaterial composition within the objects. The characteristicsof material variation are not explicitly captured. Theresulting material properties are often not available fordesigners. These methods do not provide effective tools fordesigners to create and edit the heterogeneous object model.In the domain of homogeneous objects, featuremethodologies have been extensively researched to facilitatetheir design and fabrication. Features were initiallyproposed to automate the link between design and NC pathgeneration [7]. Since then, feature techniques have beenwidely and successfully used in CAD/CAM systems.Feature-based design expedites the design process andfeature recognition facilitates the fabrication processplanning. A feature-based product model also simplifiesthe assembly, inspection planning, and other downstreamapplications [28].In order to facilitate the design and fabrication ofheterogeneous objects, Qian and Dutta proposed the usageof feature methodologies for the design and layeredmanufacturing of heterogeneous objects [20,21]. Thispaper will present some of the results. Liu et al. alsopresented their feature based design approach to achievelocal control of material properties, in which they usedthe Laplace equation to create material compositionblending [14].3. Feature based design for heterogeneous objectsIn this section, we examine the relationships betweenform features and material features in heterogeneousobjects. We synthesize form features and material featuresand we propose a constructive feature based design methodfor heterogeneous objects.3.1. FeaturesFeature techniques, traditionally, have only been focusingon the geometry, i.e. form features. Because of thenature of material variation in heterogeneous objects, weshall examine features not only in terms of the geometry butalso in terms of the material composition in a part.In order to mathematically represent the features, we firstdefine some notations. A part, PðG; MÞ; is defined as aproduct space, where G is the geometry and M is thematerial space.3.1.1. Form featureForm feature is a specific geometric shape, which carriesengineering significance, such as a hole and a slot. A formfeature can be either a volume feature or a surface feature. Inthis paper, we focus on volume features.As with homogeneous objects, a form feature inheterogeneous objects is a specific shape within a partregardless of the material composition variation. In order todistinguish form features from material features, we notetwo necessary conditions to the definitions of form features.First, the shape of the volume must correspond to somespecific engineering meaning. For example, form featuressuch as a hole or a groove, have specific geometric shapesand engineering significance. Second, such a shape shouldcontribute to the formation of the boundary of the final partgeometry. That is to say, during the part creation process,the evolving part geometries should be different before andafter the introduction of the form features. We note the partgeometry as G i before the form feature FF iþ1 is introducedto the part. Then the second necessary condition for formfeatures can be represented as: FF iþ1 2 G i – B: This willbe further explained in Section 3.1.3.For example, in Fig. 2, the heterogeneous object hasthree form features: a block, a hole, and a boss. They eachrepresent a particular geometric shape. If we disregard thematerial variation in the object, these three form featurescreate the final geometry of the object. In the two FGMregions, FGM1 is a form feature while FGM2 is not. FGM2does not satisfy the second condition of form feature, i.e.FGM2, as a shape, does not contribute to the boundary offinal part geometry.3.1.2. Material featureBefore we present the definition of material features, wefirst examine material variation in heterogeneous objects.
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