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1 w CAD/CAM wz 15«3y pp 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 : : : 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

2 244 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 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.

3 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

4 246 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 P ˆ 1P +ˆ 2P +ˆ 0 P +ˆ = 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

5 p x» y w 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

6 248 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.

7 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.

8 250 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.

9 p x» y w p x» CAD l y j w w. ƒ š p x w y w y wš, ƒ ù rw v yw w w., p x w p x p x x w v ƒ v yw l œw v» w p w v» w w w. l v p t w xw w y j x z. ù x l x» w l y jš» ƒ k v ƒ. w, l» CAD swwš p x w y j w š. w p x w p x y w w», w t p x y w ƒ š. w p x p x» sw k p x ù p x w w w v ƒ wx w x w w w. š x 1. Lin, E., Minis, I., Nau, D. S. and Regli, W. C., Virtual Manufacturing, CIM/virtual.html, March 25, Sun, G., A Digital Mock-up Visualization System Capable of Processing Giga-scale CAD Models, Computer-Aided Design, Vol. 39, No. 2, pp , Armstrong, C. G., Modelling Requirements for Finite-element Analysis, Computer-Aided Design, Vol. 26, No. 7, pp , Lee, S. H., A CAD-CAE Integration Approach Using -based Multi-resolution and Multiabstraction Modelling Techniques, Computer Aided Design, Vol. 37, No. 9, pp , Sheen, D.-P., Son, T.-G., Myung, D.-K., Ryu, C., Lee, S. H., Lee, K. and Yeo, T. J., Transformation of a Thin-walled Solid Model into a Surface Model via Solid Deflation, Computer-Aided Design, (In Press) 6. Gregory, B. L. and Shephard, M. S., The Generation of Airframe Finite Element Models Using an Expert System, Engineering with Computers, Vol. 2, pp , Lee, Y. G. and Lee, K., Geometric Detail Suppression by the Fourier Transformation, Computer- Aided Design, Vol. 30, pp , Sheffer, A., Model Simplification for Meshing Using Face Clustering, Computer-Aided Design, Vol. 33, pp , Li, B. and Liu, J., Detail Recognition and Decomposition in Solid Model, Computer-Aided Design, Vol. 34, pp , Bianconi, F. and Di Stefano, P., An Intermediate Level Representation Scheme for Secondary s Recognition and B-rep Model Simplification, Proceedings of the Shape Modeling International, pp , Zhu, H. and Menq, C. H., B-rep Model Simplification by Automatic Fillet/round Suppressing for Efficient Automatic Recognition, Computer-Aided Design, Vol. 34, No. 2, pp , Koo, S. and Lee, K., Wrap-around Operation to Make Multi-resolution Model of Part and Assembly, Computers & Graphics, Vol. 26, No. 5, pp , Chong, C. S., Kumar, A. S. and Lee, K. H., Automatic Solid Decomposition and Reduction for Nonmanifold Geometric Model Generation, Computer- Aided Design, Vol. 36, No. 13, pp , Lee, K. Y., Armstrong, C. G., Price, M. A. and Lamont, J. H., A Small Suppression/Unsuppression System for Preparing B-Rep Models for Analysis, Proceedings of the 2005 ACM Symposium on Solid and Physical Modeling, pp , Lee, S. H., -based Multiresolution Modeling of Solids, ACM Transactions on Graphics, Vol. 24, No. 4, pp , Lee, J. Y., Lee, J.-H., Kim, H. and Kim, H. S., A Cellular Topology-based Approach to Generating Progressive Solid Models from -centric Models, Computer-Aided Design, Vol. 36, No. 3, pp.

10 252 k, s, Ÿ, y, x, , Wu, D., Dhargava, S. and Sarma, R., Solid Model Streaming as the Basis for a Distributed Design Environment, Proceedings of the 2000 ASME Design Engineering Technical Conferences & Computers and Information in Engineering Conference, 26th Design Automation Conference, Baltimore, Maryland, DETC2000/DAC-14250, September 10-13, Kim, S., Lee, K., Hong, T., Kim, M., Jung, M. and Song, Y., An Integrated Approach to Realize Multiresolution of B-rep Model, Proceedings of the 2005 ACM Symposium on Solid and Physical Modeling, pp , Lee, S. H. and Lee, K., Concurrent Multiresolution Modeling of -based CAD Models with Part Design, Computer-Aided Design, (Submitted) 20. Hypermesh, y, w w ƒœ t y, w CAD/CAMwz, 12«, 2y, pp , x, ½k,, p x y w B-rep w x, w CAD/CAMw z, 7«, 2y, pp , k 2006 w» wœœw w 2006 ~x w» wœœ w mw : CAD, Human-centered Design, -based modeling, Medical Device, Medical Imaging s 2004 w» wœœw w 2008 w» wœœw 2009 ~x w» wœœw : CAD, -based modelling, Musculoskeletal Human Model, Multibody dynamics Ÿ 2007 w» wœœw w 2009 w» wœœw 2009 ~x : CAD/CAM, Human-centered Design, 3D Graphics, Parallel Computing y 1996 w w œw w 1998 w w œw 2002 w w œw ~ w œw ~ U.S. Naval Postgraduate School z ~ w w œw BK21 q ~ x wœ w w l : œw, Digital Shipbuilding, š x, Ship CAD/CAM x 1986 w» w w 1988 w» w 1993 w» w 1993 ~1995 g» 1996 š» 1996 ~x w : CAD/CAM, Human-centered Design, Human-Vehicle lnteraction, 3D Geometric Modeling, Die and Mold CAD 1978 w» œw w 1981 M.I.T» œw 1984 M.I.T» œw 1984 ~1986 Univ. of Illinois at Urbana-Champaign 1992 ~1993 M.I.T» œw 1986 ~x w œ w» wœœw : CAD, Assembly Modeling, Multi-resolution Modeling, Rapid Prototyping, Medical device, Human Modeling & Analysis