w CAD/CAM wz 15«3y 2010 6 pp. 243-252 p x» y w k *, s*, Ÿ*, y**, x***, **** A Simplification Method for -based Solid Models Tae-geun Son*, Dong-Pyoung Sheen*, Dae-Kwang Myung*, Cheolho Ryu**, Sang Hun Lee*** and Kunwoo Lee**** ABSTRACT This paper describes a new practical simplification method for feature-based solid models. In this approach, a solid model created using feature modeling operations is first simplified by the suppression of detailed features, and then, if necessary, the model is converted to a surface model to facilitate its modification. Finally, the simplified surface model is delivered to analysis packages. The algorithm was implemented based on CATIA V.5 and applied to mid-surface generation of plastic parts for structural analysis to prove the validity and usefulness. Key words : Solid Model, Simplification,, CAD-CAE Integration 1. 3 CAD l t y š, p, p x (feature)» l š. w, wœ, ƒ t w w t w l (digital mock-up(dmu)) w z t j, ƒ y t w sƒ, œ s w t» jš wš [1,2]. w, t w v e t v w ƒ ƒwš. CAE l w w t ³ ƒš. CAE ƒ w w (finite element analysis). *w z, w w» wœœw ** z, wœ w w l *** z, w œw - nš : 2010. 03. 16 - : 2010. 04. 22 - : 2010. 04. 23 t x w (mesh) š w w g l w. ful w k w w ƒ š ù w y j y w ù ù ƒ q ù v xk k w [3-5]. p, v p t x œ ù w w Ì yw l g w ww wš. w y w v w p x w v w. w y CAE wš t w w» w CAD l y w g v v w. y j»,, p x ù w v w p x k w w. p x w p 243
244 k, s, Ÿ, y, x, x (feature recognition), p x y(feature conversion) mw, p x ¾ w w ƒ w w. w y œw w v ƒ. CAD y j» w l ƒ w. Gregory CAD form feature w w w p x k w w w ƒ l w [6], Lee Fourier y w x w [7]. Sheffer w CAD y j j l (clustering method) w š šw [8], Li v q(filleting) w (level of detail(lod))» d l wš p x ww w [9]. Bianconi p x ql w LOD w v ƒ p x w p x w [10], Zhu y j» w v ü w š w [11]. Koo smooth-out w w p x ü t l w ƒ w [12]. Chong w k y w [13], Lee w w B-rep w» w p x w ù y j l w, l w w w CAD x l y w w k [14]. wr, w y œw» w w t» p x» w (feature-based multi-resolution modeling)» [15]. wù x w w y p x CAD œw», ful v» (polygon-based) w» ƒ Õ,, { p x y. CAD y g w z y w» w FEM œ w w, p» x [16,17], ƒ v mk ƒ. w p w CAD t k w p x» y š Table 1. Research on feature-based multiresolution modeling No 1 2 3 4 5 Method Delta Volume Approach Cellular- Topology Based Approach Integrated B-rep Approach Maximal Volume Approach Data Structure Solid Cellular Solid Selective Nonmanifold Volume Approach Object Design Design Recognized Cellular Recognized Design LOD Criterion Simplification Method Boolean Volume of Operations on Subtractive Delta Volumes Volume of Subtractive Area of Volume of Subtractive Volume of Selection of Volumes Wrap-around, Smooth-out, and Thinning Operations Selection of Volumes and Boolean Operations Selection of Topological Entities Storage Computation Time Small Large Small Large Large Long Short Medium Medium Short Advantage(+)/Disadvantage( ) Ref. (+) Implemented on a commercial CAD system ( ) Applicable to only subtractive [22] features ( ) Slow for generation of LOD models (+) Improvement of speed to generate LOD models ( ) Applicable to only subtractive features [16] (+) Improvement of speed by not using Boolean operations [12] ( ) No clear criteria on LOD and inconsistent simplification process (+) Providing LOD models independent from part modeling process ( ) Applicable to only subtractive [21] features ( ) Recognized features are not design features. (+) Rapid extraction of LOD models (+) Applicable to not only subtractive features but also additive features. [15] ( ) Non-unique intermediate LOD models depending on feature rearrangement procedure.
p x» y w 245 [4,12,15,16,18]. ¾ p x» w t w ü Table 1 ùkù. ù ¾ p x q» w ù w ù wš w k w w. ù p x w ƒ x CAD l w wš w x š w š. w y w w ù CAD l xw w w. w w w» w CAD l ƒ w y wš xwš w. ƒ p x w wš, y q ƒ w y r w w» œw kw. w p x w ƒ š y qw y ƒ w v w». w, w y œw» w š y ƒ w w. w š CATIA V.5 xwš v p t w w y w z w. 2. p x mw w p x j» wš l ùƒ p x» w».» tx w p x swwš w w p x w w ý [4,12]. ù CAD l p x - ƒ w w w f k CAD l p x ã w. CAD l w w v w. w x» k (Historybased Selective Boolean Operation: HS-Boolean operations)» w» y e w w w. y e l w w» w p x w p x v w p x (suppression) j w t xw w [19], p w w œ w.» p x w p x y y j z p x w wù v w y y g w. w w» CAD l w» w xw. p x mw w w w., x» r w. p x F ùküš, F» i p x i x e e, F j x k j p x e i e, š F j» i x k j ew p x š w. š p x z Z š w. p x w w(+) w( ) ùküš, P p x» (primitive) ùkü š w.» i ù z x j e x» k i ˆ P t w w (1) ù i j ký [19]. ( 1) x» k : i i ˆ j P (1) j 1 i» Z j P i k( l) = ϕ( j, l)γ( ik, ( l) )P l (2)», i i i = Z j = j Z j ϕ( ij, ) l = 0 1 if i j = 0 otherwise 1 if i< j γ( ij, ) = 0 otherwise
246 k, s, Ÿ, y, x, š k( l) x l p x» e ùkü. x» k y e w ã ƒ. ƒ LOD w p x x» k k tx. LOD x» k y e ã w x LOD. x» k w p x z (1) p x w γ = 0 ƒ., w ƒ LOD Z j i = P i k. ùkü txw [19]. m j = 0 ˆ j kj ( )P j m = ˆ kj ( ) P k)j (, 0 m n (3) j = 0, x p x» CAD l w LOD» w p x p v w p x w w» w. w, w š w LOD w p x k. p x z k x LOD LOD w p x z j w ù w, p x w LOD w» w l» w ww. Fig. 1 Table 2 w w ƒ. p x LOD q» F 0 F 3 F 2 F 4 F 1. ƒ LOD x» k. ã x» k (1) ü yw., LOD = 2 w 0 +ˆ 0 3 3 2 2 0 0 2 0 P ˆ 1P +ˆ 2P +ˆ 0 P +ˆ 2 3 3 = 1P ˆ 2P = P 0 + P 2 P 3 ùký. Table 2 ƒ LOD w x» k w š. Fig. 1. An example model with five features [19]. Table 2. LOD models of the example model: (a) using the history-based selective Boolean (HS-Boolean) operations, (b) using the equivalent ordinary Boolean operations of the HS-Boolean operations
p x» y w 247 3. y CATIAù Unigraphics CAD l» v» œwš, v y ƒ w. w p x w w w k ù y w y y p x w tx w p x x p x w ƒ w ƒ w. w w x p x» w w, ƒ v ƒ ƒ w v» w w { z. Fig. 2 v w p x w š, v y k z, v» w p x w kw. w, z ww» w ƒ» w. Fig. 2. Overall procedure for simplification of a featurebased solid model. 4. p x y. (Step 1) p x k : p x» CAD l p x p (feature tree)ƒ w p x k, q l, reference, š swwš. p x p zw p x w s l p. (Step 2) p x k: p x w p w w w. p x p x, Ì, v q l k., j», w. w» w q» p x w w, w w y wš w q» û w w. p x w v p x t w. (Step 3) k p x š y: k ƒ p x wš q w p x ƒ w w. p x B ƒ A, p x A B w š, w m - (parent-child). p x A ƒ p x B w» p x Aƒ l. w w» w š (isolation operation) ww - g w ww. (Step 4) p x : p x š p x w p x w w. w p p x w l w vw. y ƒò p x w š w wš l ƒ w ƒ w. w z wwš CAD z we w öe ƒ. w y w p x w
248 k, s, Ÿ, y, x, s»wš w w l z w w, l xw. Fig. 3. Removal of detailed features in the solid modeling mode: (a) a detailed solid model, (b) the resulting solid model after removal of detailed features. Fig. 3 w w y ww š. v p t w v w p x k. ù p x» w p x CAD lü p x p ùkù w x. w ù w p x m p x» ü l œ p x x ew x š ý, w p x p x k w p x ww w w p x ƒ w. w ƒ p x š q w w. p x w Hypermesh [20] ü Hypermesh» w ƒ Fig. 4 ùkù. Fig. 4(a) (b) p x w š Hypermesh ü š, Fig. 4(c) (d) p x w Hypermesh ü k. z ƒ òw y w. 5. v y v y j ƒ w v k z, wù w v Fig. 4. Effect of solid simplification for mid-surface generation, which is conducted on the preprocessor of Hypermesh: (a) an original detailed solid model, (b) a mid-surface model generated directly from the original solid model, (c) a simplified solid model, (d) a mid-surface model generated from the simplified solid model. Fig. 5. Effect of conversion of a solid model into a surface model for mid-surface generation, which is conducted on the preprocessor of Hypermesh: (a) an original detailed solid model, (b) a mid-surface model generated directly from the original solid model, (c) a surface model converted from the solid model, (d) a mid-surface model generated from the converted surface model.
p x» y w 249 k., ƒ w w p x id k. v p x ƒ ƒ w w., w p x w w ƒ. v y k Hypermesh» CAE l ý w. Fig. 5 ƒ ù. Fig. 5(a) (b) CATIA Hypermesh ü š, Fig. 5(c) (d) v y k z CATIA Hypermesh ü k. z ƒ òw y w. w x w Hypermesh š v j e ƒ w». CAD l v w ƒ ƒ yw e ƒ. 6. v p x y v v w w 1 CAD l œw v» w ww. y ww w» w Tiny Surface Management, Face Group Deletion, š Healing Surface» ƒ r» w. 6.1 Tiny Surface Management»» v w w w w» w y w» w g z ƒ. w k w id p œw», p w w kw», y y g», å». w» w y w z Fig. 6. The tiny surface management function: (a) the graphic user interface, (b) an example for searching for tiny surfaces, (c) the result of removal of the tiny surfaces. ww. Fig. 6» w lr ƒ ùk ù. 6.2 Face Group»» v, p w,,» p x w w wù ƒ ƒ w w. v ƒƒ w k wù. ù v y k p x w» v p x k ƒ w. Fig. 7 ƒ. Fig. 7(a) wù p x š, Fig. 7(b) ƒ kw w ù l wù p x w 10 k š. Fig. 8 v p x w kw w š.
250 k, s, Ÿ, y, x, Fig. 7. Searching for a face group of a feature: (a) a feature in a solid model, (b) a face group of the feature in a surface model converted from the solid model. Fig. 10. The filling function: (a) a gap created by removing surfaces, (b) the result of filling. Fig. 8. Deleting a group of faces: (a) selecting surfaces to be deleted, (b) deleting the selected surfaces. 6.3 Healing Surface» v w p x w ù p ƒ w. w p l œw»» w še š š w. w Fig. 9. The stitching function: (a) a hole created by removing a fillet surface, (b) the result of stitching in which two new planes are created. w w» w Fig. 9 Fig. 10 ùkù Stitching Filling Healing Surface» w. Stitching» v w w p» w w k z š» v w p w e. Filling» w p» ƒ š w ƒ w sš v w š ƒ ƒ w kw x. 6.4 p x» w k y k z, v y g ƒ y j e w w w. Fig. 11(a) ù kù v p t y k Fig. 11(b) ùkù, w w xw w Hypermesh» w k ƒ Fig. 11(c) ùkù. Fig. 11. A case study of solid simplification: (a) a solid model for a plastic part, (b) a simplified model of the solid model, (c) a mid-surface model generated from the simplified model.
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