Recognition of machining features for cast then machined parts

COMPUTER-AIDED DESIGN Computer-Aided Design 34 (2002) 71±87

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Recognition of machining features for cast then machined parts Y.S. Kim*, E. Wang School of Mechanical Engineering, Sungkyunkwan University, 300 Chunchun-Dong, Jangan-Gu, Suwon 440-746, South Korea Received 3 August 1999; revised 30 November 2000; accepted 4 December 2000

Abstract Mechanical parts are typically manufactured using multiple manufacturing processes. Primary processes such as casting realize the primary shape of the part, while secondary processes such as machining generate more detailed shape of the part. This paper presents a feature recognition method to support machining process planning for cast-then-machined parts. From the part model including the speci®cation of machined faces, we generate the starting workpiece for machining, which represents the casting output in suf®cient detail to support machining process planning. The starting workpiece is generated by identifying faces to be made by casting followed by machining, then offsetting the part through these faces by a uniform machining thickness to obtain cast faces, and combining the halfspaces induced by machined faces and the halfspaces induced by their bounding cast faces to enclose removal volumes. Machining features are then recognized from the removal volumes using a volume decomposition method called Alternating Sum of Volumes with Partitioning. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: Cast then machined part; Machining feature recognition; Computer-aided process planning

1. Introduction Typically the manufacture of a mechanical part is composed of various manufacturing processes. Primary processes such as casting realize the primary shape of the part. Then secondary processes such as machining generate more detailed shape of the part. Previous research in machining feature recognition has generally considered the case where parts are created entirely by machining operations starting from stock material [6,10,12,13,18]. However, many real-world parts are constructed with machining operations applied to workpieces created by casting or welding. When a new part design is introduced, how much of the part geometry will be created by machining and how much by other manufacturing processes such as welding or casting should be determined. For machining process planning, the removal volume is determined from the delta volume obtained by subtracting the part volume from the stock or starting workpiece. Thus, the machining features and the process plans are dependent on the starting workpiece. When considering high level process planning, the determination of such starting workpiece itself is a crucial step where automated geometric reasoning support is needed to make overall manufacturing * Corresponding author. Tel.: 182-31-290-7452; fax: 182-31-290-5849. E-mail address: [email protected] (Y.S. Kim).

process effective. Also, the capability to generate different starting workpieces is desirable so that it could be combined with other casting design criteria. Feature recognition for multiple manufacturing processes has not yet been properly attempted. Boothroyd et al. [1] describes a method to select materials and manufacturing processes at high level, but the scope is limited with very simple component parts. Herrmann et al. [3] studied high level process planning consideration in the context of virtual enterprises, including the comparison of different manufacturing partners, for ¯at mechanical and electromechanical parts again with very simple geometry. Both previous works assumed a very simple geometry processing capability would be enough to handle such parts. Nor did they address the issue of alternative part shape decomposition across the high level processes. Wang and Kim [16] describes a feature recognition method using convex decomposition that recognizes form features from intrinsic part geometry, which provides local and global geometric relations that could support multiple manufacturing processes. An example is given in Wang and Kim [16] where features are combined with the base block to obtain a casting shape with simple machining features. This capability has not been pursued in detail yet. A few other previous research works may deserve remark as they have some relevance to this paper. Dong and Wozny [2] generate volumetric features from surface features by

0010-4485/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0010- 448 5( 01) 00058- 6

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extending neighboring faces of the part. Their method considers only feature recognition for simple part geometry, and cannot be readily used for parts to be made by multiple manufacturing processes, such as casting followed by machining. Xu and Hinduja [19] combine feature recognition with incremental updating of the workpiece to recognize rough machining features from intermediate states of the workpiece. But they assume the blank, or starting workpiece, is provided as input in addition to the part. Nor does their method preserve the geometric relations between recognized features, which is critical to support machining process planning activities. The method presented in this paper addresses the level of part complexity as encountered in typical mechanical parts with non-simple primary shapes and many interacting features. To date, no feature recognition system has addressed parts to be made by multiple manufacturing processes at such a complexity level. The remainder of this paper is organized as follows. Section 2 reviews the hybrid feature recognition method using a face pattern based approach and volumetric decomposition method that we have previously developed [17], and its application to machined parts. It then gives an overview of the method to apply it to cast-then-machined parts. Section 3 describes the method to generate the starting workpiece for machining from the ®nished part model and the speci®cation of the machined faces. Section 4 describes the application of our volume decomposition feature recognition method to obtain the volumetric machining features from the part model and the starting workpiece. In Section 5, we apply our method to an example cast-then-machined part. Concluding remarks are presented in Section 6. 2. Hybrid machining feature recognition We have previously implemented a hybrid machining feature recognition method as part of the feature-based automatic process planning system (FAPPS) for machining process planning [17]. Our hybrid feature recognition method is composed of (1) a face pattern based approach that ef®ciently recognizes non-interacting features, and (2) a volumetric decomposition method to recognize interacting features. 2.1. Face pattern based feature recognition Early approaches to feature recognition involved searching the part model for prede®ned patterns of faces, edges, and other information [4]. This approach is ef®cient when features do not interact. In FAPPS, we de®ne a taxonomy of atomic machining features such as pockets, holes, slots, and steps that are frequently machined in real-world parts. Each atomic machining feature is represented as a face pattern consisting of a base face surrounded by one or more rings of side faces [7]. By comparing the faces of the part model to every face pattern, we can quickly recognize non-interacting features. These are then ®ltered out of the

part model by constructing the feature volumes and unioning them with the part model. The result of this step is the set of non-interacting volumetric machining features, and the ®ltered part model which still has interacting machining features. 2.2. Feature recognition using ASVP decomposition To the ®ltered part model, we apply the feature recognition method using alternating sum of volumes with partitioning (ASVP) decomposition [5]. ASVP is a convex volume decomposition using convex hull, set difference, and cutting operations [8,9]. It organizes the boundary faces of a part in an outside-in hierarchy, while associating volumetric components with these faces. Faces are distinguished as original when they ®rst appear in the decomposition hierarchy representing faces of the original part, otherwise as ®ctitious. By systematically combining components according to the hierarchical structure of the decomposition and the face dependency information obtained during ASVP decomposition, the ASVP decomposition is converted into the form feature decomposition (FFD) [6]. For machining applications, we apply positiveto-negative conversion [14,15] to convert the FFD into a Negative Feature Decomposition (NFD) consisting of a positive base component and negative removal volumes. These negative removal volumes are classi®ed as machining features according to their face classi®cations as original or ®ctitious, and the atomic machining feature de®nitions [17]. This method has demonstrated a robust capability to recognize interacting features in practical machined parts [16]. Furthermore, it supports design re®nement in a product development scenario through the incremental updating of the ASVP decomposition in response to the designer's modi®cations to the input part [11]. The result of the feature recognition method using ASVP Decomposition is the NFD of the interacting volumetric features. Next, face dependency information is updated to obtain face dependencies between these interacting volumetric features and the non-interacting volumetric features recognized by the face pattern based feature recognition method of Section 2.1. The non-interacting volumetric features are then inserted into the NFD according to the face dependency information, resulting in an NFD that contains all recognized volumetric machining features. Face dependency information is then used to generate geometry-based machining precedence relations between recognized features [17] and other geometric information to support machining process planning. The output of the hybrid feature recognition method consists of (1) the combined NFD containing all volumetric machining features and (2) the machining precedence relations. 2.3. Feature recognition for cast-then-machined parts We now consider the application of our machining feature

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Fig. 1. Starting workpiece generation and machining feature recognition for cast-then-machined parts.

recognition method to the domain of cast-then-machined parts. First, we distinguish machining features into two types. Surface machining features. Surface machining features are features having small thickness and constant crosssection, created by surface machining operations. They typically correspond to a single machined face in the ®nished part. As such machined faces are to be realized by casting followed by machining, they are called cast-then-machined faces. The identi®cation of cast-then-machined faces in the ®nished part is a primary step in generating the surface features and the starting workpiece for machining. Volumetric machining features. Volumetric machining features are created by machining operations entering through the cast faces of the starting workpiece or machined faces exposed by previous machining operations. Each volumetric machining feature typically corresponds to two or more machined faces. Volumetric features may interact with each other, which can cause their machined faces to be split, merged, deleted, or otherwise modi®ed. When volumetric machining features do not interact, we may de®ne each atomic feature type as a pattern of machined faces, and recognize instances of the features by searching the part model for these face patterns, which is the face pattern based recognition method of Section 2.1. But because features in real parts may interact, the face pattern based approach alone cannot recognize all instances of the features. Thus, we apply the ASVP decomposition feature

recognition method of Section 2.2, which recognizes features as interrelations between original faces of the input part corresponding to the machined faces [7,17]. We now present an overview of the method to generate the starting workpiece and to recognize machining features from the starting workpiece and the ®nished part model. The overall ¯ow of information in our algorithm is shown in Fig. 1, including: (a) the input data; (b) major steps of the algorithm; and (c) the output data generated by each step. The input to our method consists of the following information, as summarized in Fig. 1(a). 1. 2. 3. 4.

Solid model of the ®nished part P. Tolerance and/or surface ®nish speci®cation. User speci®cation of the machining thickness. (Optional) User speci®cation of cast-then-machined faces.

Tolerance and/or surface ®nish speci®cations have been added to the faces of the part in the solid model by the user. The method to generate the starting workpiece automatically determines which machined faces are to be realized by casting followed by surface machining, based on edge convexity information. The user may make special speci®cation to certain machined faces so that the faces are realized by casting followed by surface machining, not by volumetric machining. These speci®cations are used to modify the generation of the starting workpiece.

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The machining thickness, or casting outline thickness, represents the amount of material to be removed by surface machining operations for surface features. The default thickness of 3±5 mm is usually suf®cient for small and medium-sized cast parts. We can now give an overview of starting workpiece generation and machining feature recognition for cast-then-machined parts, as summarized in Fig. 1(b) and (c). 2.4. Algorithm overview 1. Apply face pattern based feature recognition to identify simple (non-interacting) volumetric machining features in the ®nished part P (Section 3.1). As each non-interacting volumetric feature Vsi …P† is recognized, its volume is unioned with the part model P, which ®lters the feature from the part model. The result of this step is the ®ltered part Filtered(P) and the set of simple volumetric features Vs(P), as shown in Fig. 1(c). 2. Identify cast-then-machined faces in the ®ltered part model, based on edge convexity information and user speci®cation (Section 3.2). Lift each of these cast-then-machined faces outward by the machining thickness to obtain offset volumes Voi …P†. Add the set of offset volumes Vo(P) to the ®ltered part. The result of this step is the offset part Offset(P) and the set of offset volumes Vo(P). The face resulting from lifting is also regarded as a cast face. Group the remaining machined faces into connected sets through their common incident edges. Each maximally connected set of machined faces corresponds to a general depression comprised of interacting volumetric features and bounded by a set of cast faces. 3. For each general depression of Offset(P) found in Step 2, obtain a depression volume by intersecting the halfspace induced by the set of machined faces and the halfspace induced by the set of bounding cast faces (Sections 3.2± 3.4). Union these depression volumes with Offset(P). This obtains the starting workpiece for machining Workpiece(P), which corresponds roughly to the casting output. 4. Grow the offset volumes Vo(P) within the boundary of Workpiece(P) to obtain the surface machining features Vg(P) (Section 3.5). 5. Obtain the set of machining removal volumes Dm(P) from Workpiece(P), Filtered(P), and the surface machining features Vg(P) (Section 4). 6. Apply feature recognition using ASVP decomposition to the machining removal volumes Dm(P) (Section 4). Grow recognized volumetric features to their effective feature volumes. The result of this step is the Negative Feature Decomposition NFD(P) containing all recognized machining features. We now describe each of these steps in detail.

3. Generation of starting workpiece for machining In typical machining process planning activities for castthen-machined parts, the ®nished part is provided, but the casting output is not provided. In this section, we describe how we generate the starting workpiece for machining, which corresponds roughly to the casting output. In this work, we do not intend to generate the exact casting output. We generate instead a representation of the casting output that is good enough to be used as a starting workpiece for the purpose of machining process planning. That is, we extract all machining features with proper geometric detail to be used to identify machining operations, machining volumes, and machining conditions. Section 3.1 describes the application of face pattern based feature recognition to ®lter out non-interacting volumetric machining features. Section 3.2 presents a simple case of the algorithm to obtain the starting workpiece from the ®ltered part. Section 3.3 extends the algorithm to handle general cases. Section 3.4 describes the further enhancement of the algorithm to incorporate the user's speci®cation of cast-then-machined faces. Section 3.5 describes how the offset volumes are grown to obtain surface machining features. We illustrate the simple case of the algorithm using example part G, shown in Fig. 2(a). Part G is a grip tool handle, which is a real part of a machining center. It contains several simple machining features such as steps, holes, and slots, with some feature interactions. Machined faces are denoted by plain face labels in Fig. 2(a), while cast faces have italic labels, or are unlabeled. Labels in parentheses indicate hidden faces. 3.1. Generating the ®ltered part We ®rst apply the face pattern based feature recognition method of Section 2.1 to the ®nished part P. This ef®ciently obtains the set of non-interacting volumetric machining features Vs(P). We obtain the ®ltered part Filtered(P) as Filtered…P† ˆ P

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Fig. 2. Grip tool handle G.

approach. We ®rst present the algorithm that handles simple cases, such as Filtered(G). Step 1: Identify cast-then-machined faces in the ®ltered part. We consider any face that has a tolerance or surface ®nish speci®cation to be a machined face. All other faces are treated as cast faces. Machined faces are further identi®ed as cast-then-machined faces by considering their edge convexity. In the simple case, every machined face all of whose incident edges are convex is automatically identi®ed as a cast-then-machined face. Such faces comprise portions of the extremal boundary of the part, and hence would be used in determining the starting workpiece. For example part Filtered(G), top faces 17, 18, and 19 and bottom face 20 are identi®ed as cast-then-machined faces, as shown in Fig. 2(c). Step 2: Lift the cast-then-machined faces to generate offset volumes. Every cast-then-machined face f is lifted along its outward normal direction by the machining thickness. This operation can be viewed as offsetting the ®ltered part through face f. We refer to the volume created by lifting face f of Filtered(P) as offset volume Vof …P†, and the set of all offset volumes as Vo(P). The offset part Offset(P) is obtained as Offset(P) ˆ Filtered(P)

faces are cast faces that do not appear in the ®nished part P. The cast faces that do occur in the ®nished part P, which are the cast faces that were unaffected by machining operations, are called original cast faces of P. After this step, all remaining machined faces of Offset(P) are created by volumetric machining operations. Applying this step to Filtered(G) results in Offset(G) with four offset volumes Vo17 , Vo18 , Vo19 , and Vo20 , as shown in Fig. 2(d). The lifted cast faces of these offset volumes are now denoted 17c, 18c, 19c, and 20c. Step 3: Construct maximally connected sets of machined faces through common incident edges. Volumetric machining operations remove volume from the cast part, and as a result, general depressions are created in the ®nished part consisting of one or more interacting volumetric machining features. In the simple case, these general depressions are characterized by containing machined faces that have one or more concave incident edges. Such faces are referred to as volumetric-machined faces. Thus, we may identify general depressions of the part by taking the transitive closure of adjacency among volumetric-machined faces through their common incident edges. By this process, machined faces are grouped into connected face sets, separated by cast faces. Because the transitive closure of machined faces does not propagate across cast faces, each machined face set Fi is bounded by a set of cast faces Gi, which may include lifted cast faces. Gi is obtained as the set of

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cast faces that are adjacent to any machined face of Fi. The result of this step is the set of machined face sets Fi and their bounding cast face sets Gi, where every pair of Fi and Gi represents one general depression of Offset(P). The result of applying this step to Offset(G) is shown in Fig. 2(e). Four maximally connected sets of machined faces are found. F1 ˆ {1,2} is bounded by the set of cast faces G1 ˆ {17c,21,22,23}, F2 ˆ {3,4,5,6,7,8,9} is bounded by G2 ˆ {17c,18c,24,25}, F3 ˆ {10,11,12,13,14} is bounded by G3 ˆ {18c,19c,24,26,27}, and F4 ˆ {15,16} is bounded by G4 ˆ {20c,24}. Step 4: Intersect the halfspaces induced by sets of bounding cast faces and the halfspaces induced by corresponding sets of machined faces to enclose depression volumes. For each bounding cast face set Gi corresponding to a general depression of Offset(P), the halfspaces induced by each cast face of Gi are combined into a halfspace H(Gi) representing the set of bounding cast faces. Two halfspaces are combined by taking their intersection if they interact along a convex incident edge, and by taking their union if they interact along a concave incident edge. If the bounding surfaces of the two halfspaces do not intersect, the halfspaces are combined by taking their union if they are disjoint, otherwise by taking their intersection. Thus, the combined halfspace may be represented as a disjunct of conjuncts, where each conjunct is the intersection of one or more halfspaces as described above, and all conjuncts are unioned to obtain the combined halfspace. The halfspaces induced by each face of machined face set Fi corresponding to Gi are also combined into a halfspace H(Fi) bounding a depression volume and representing the set of machined faces. Note that the halfspace on the material side is taken from the bounding cast faces, while the halfspace on the non-material side is taken from the machined faces. By intersecting the two halfspaces H(Fi) and H(Gi), the depression volume Di(P) is obtained representing the general depression corresponding to Fi and Gi: Di …P† ˆ H…Fi † >p H…Gi †. We then consider the depression volume Di(P) corresponding to the machined face set Fi to be created by applying surface and volumetric machining operations locally to the volume enclosed by the bounding cast faces Gi. For machined face set F1 of Offset(G) in Fig. 2(e), halfspace H…F1 …G†† obtained from machined faces 1 and 2 and halfspace H…G1 …G†† obtained from cast faces 17c, 21, 22, and 23 are intersected to obtain depression volume D1(G), shown in Fig. 2(f). This step is repeated for all sets of machined faces

Fig. 3. Extending adjacent offset volumes to connect lifted cast faces.

Fi, obtaining the set D(P) of all depression volumes. The result of this step is the extended part Extended(P), which is obtained as Extended(P) ˆ Offset…P†

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Fig. 4. Part S.

3.3. Generating the starting workpiece for machining: algorithm for the general case The simple case of the algorithm given in the previous section has assumed that a machined face can be regarded as cast-then-machined if all of its incident edges are convex, and as volumetric-machined if any of its incident edges are concave. This assumption holds when cast-then-machined faces are extremal with respect to the set of volumetricmachined faces. However, a machined face with convex incident edges only may be the top face of a local protrusion feature that is contained within a larger depression. Such faces should also be regarded as volumetric-machined faces.

In Part S, shown in Fig. 4(a), all incident edges of C-shaped machined face 4 are convex, but face 4 is not extremal with respect to machined face 1. The set of simple features Vs(S) consisting of four hole features is obtained by the face pattern based feature recognition method, as shown in Fig. 4(b), resulting in Filtered(S) in Fig. 4(c). First, the simple case of the algorithm is applied to Filtered(S). In Step 1, face 4, front face 13, left face 14, top face 16, and bottom face 17, the faces with convex incident edges only, are identi®ed as cast-then-machined faces. In Step 2, these faces are lifted to obtain offset volumes Vo4 , Vo13 , Vo14 , Vo16 , and Vo17 , resulting in Offset(S) shown in Fig. 4(d). In Step 3, maximally connected sets of machined faces

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are generated, resulting in F1 ˆ {1,2,3} bounded by G1 ˆ {4c,14c,15,16c} and F2 ˆ {5,6,7,8,9,10,11,12} bounded by G2 ˆ {4c,13c,14c,15}. Applying Step 4 to machined face set F1 results in H(G1) ˆ h(4c) > h(14c) > h(15) > h(16c), where h(4c) denotes the halfspace induced by face 4c. Note that the bounding planes of h(4c) and h(16c) are parallel, and h(4c) is enclosed within h(16c). Therefore, h(4c) > h(16c) ˆ h(4c), and H(G1) reduces to h(4c) > h(14c) > h(15). Volumetric-machined face 1 is not properly enclosed within halfspace h(4c) of H(G1), as shown in Fig. 4(d). This indicates that face 4, which was automatically identi®ed as a cast-then-machined face, is not extremal with respect to the set of volumetric-machined faces, but is instead part of the same depression that also includes face 1. Hence, face 4 should be realized using volumetric machining operations. Thus, it is to be reclassi®ed as a volumetric-machined face. To handle this case, we extend Step 4 of the algorithm given in Section 3.2 by adding a veri®cation procedure at the beginning of Step 4 to test whether every lifted cast properly encloses its machined face set. The revised Step 4, including this veri®cation procedure, is as follows. Step 4

For every machined face set Fj and bounding cast face set Gj representing a general depression of Offset(P): Step 4(a) If Gj contains no lifted cast faces, then Gj passes the veri®cation procedure. Return to Step 4 to test Fj11 and Gj11. Step 4(b) Combine the halfspaces induced by each cast face of Gj to obtain the combined halfspace H(Gj) representing the set of bounding cast faces. The method to combine halfspaces has been described in Step 4 of Section 3.2. Step 4(c) For every machined face f of Fj, test whether f is properly enclosed within H(Gj). Case 1: If f is properly enclosed in H(Gj), then f passes this test. If all f of Fj are properly enclosed in H(Gj), then H(Gj) passes the test, and we return to Step 4 to test Fj11 and Gj11. Case 2: If f is not enclosed within H(Gj), then H(Gj) does not properly enclose the general depression that includes f. Test whether f is enclosed within each halfspace h of H(Gj) to ®nd those halfspaces H(Gc) that do not properly enclose f. Identify the lifted cast faces gc of Gj from which these halfspaces were induced. These lifted cast faces do not properly enclose a depression volume. Hence, they should not be created as cast-then-machined faces. For such lifted cast face gc of Gj, the corresponding face g of the part is reclassi®ed as volumetricmachined. Offset volume Vog corresponding to g is removed from Offset(P): Offset 0 (P) ˆ Offset(P)2 pVog. Machined face g is combined

with all machined face sets Fk that have lifted cast face gc in their bounding cast face sets Gk, corresponding to all depressions adjacent to g. This obtains a single machined face set F 0 representing the combined depression: F 0 ˆ h(13) > h(14c) > h(15) which properly encloses all machined faces of F2, so G2 passes the veri®cation procedure. G1 induces halfspace H(G1) ˆ h(4c) > h(14c) > h(15), as described above. In Step 4(c)(2), it is found that halfspace h(4c) of H(G1) that was induced by lifted cast face 4c does not properly enclose machined face 1. Offset volume Vo4 is removed from Offset(S), resulting in Offset 0 (S) shown in Fig. 4(e). The new machined face set is F 0 ˆ F1 < {4} < F2 ˆ {1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12} It is bounded by G 0 ˆ {13c,14c,15,16c}. The veri®cation procedure is now applied to F 0 . Since G 0 contains lifted cast faces 13c, 14c, and 16c, it proceeds to Step 4(b). G 0 induces the halfspace H(G 0 ) ˆ h(13c) > h(14c) > h(15) > h(16c), which encloses all of the machined faces of F 0 . So G 0 passes the veri®cation procedure. Proceeding with Step 4 and 5 of Section 3.2, the starting workpiece Workpiece(S) is obtained, as shown in Fig. 4(f). This veri®cation procedure detects any candidate castthen-machined faces that would generate improper depression volumes. Such candidate faces are changed to volumetric-machined faces, and their adjacent machined face sets are merged. In this way, local protrusion features contained within larger depressions are detected and properly merged into their surrounding depressions. Note that when a part is made by machining, its globally interacting shape is to be generated by machining. Thus, machining feature recognition should address both global and local geometric relations. When a part is cast to make the primary shape and then machined to make features, the features to be recognized for machining are local in nature, by the design of the part and by the nature of the manufacturing

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Fig. 5. Example part S 0 with cast-then-machined face speci®cation.

processes. For typical cast-then-machined parts, combining the halfspaces induced by machined faces and bounding cast faces in the manner described in Sections 3.2 and Sections 3.3 would generate proper depression volumes for the remaining machining features. Thus, our method can handle typical realworld complex cast-then-machined parts. 3.4. Generating the starting workpiece for machining: using user speci®cation of cast-then-machined faces The general algorithm of starting workpiece generation described in Section 3.3 automatically determines whether a machined face is cast-then-machined or volumetricmachined, based on local and global geometry of the part. To provide the user with some control over the shape of the starting workpiece, the user may explicitly specify a machined face to be cast-then-machined. Part S 0 , shown in Fig. 5(a), is the same as Part S but with user speci®cation that face 1 is a cast-then-machined face. Offset(S 0 ), shown in Fig. 5(b), differs from Offset(S) in Fig. 4(d) by the addition of offset volume Vo1 . Machined face set F1 0 ˆ {2,3} is bounded by G1 0 ˆ {1c,4c,14c,15}. The veri®cation procedure of Section 3.3 is now applied. The combined halfspace H…G1 0 † ˆ ‰h…1c † > h…14c † > h…15†Š < ‰h…4c † > h…14c † > h…15†Š is generated, and it is found that H…G1 0 † properly encloses machined faces 2 and 3 of Offset(S 0 ). Therefore, the veri®cation procedure ends successfully, and the starting workpiece Workpiece(S 0 ) is generated as shown in Fig. 5(c). Note however that the user speci®cation of cast-thenmachined faces may not necessarily be valid. For example,

if faces 1 and 3 of Part S 0 in Fig. 5(a) were both speci®ed as cast-then-machined faces, then machined face 2 would have no adjacent machined faces, so it would comprise a maximally connected set of machined faces by itself. It would then be bounded by lifted cast faces 1c, 3c, and 14c, and original cast face 15. This bounding cast face set would induce the halfspace ‰h…1c † > h…14c † > h…15†Š < ‰h…3c † > h…14c † > h…15†Š, which does not enclose face 2. The speci®cation of both faces 1 and 3 as cast-then-machined faces is therefore invalid, and must be revised. Thus, the user speci®cations of cast-then-machined faces are to be evaluated by cast-then-machined face validity checking. Any speci®cations that are found to result in unbounded machined face sets are ¯agged and informed to the user for revision. The user may remove these speci®cations, or add additional speci®cations to ensure proper enclosure of all machined faces. Continuing the example for Part S 0 from the preceding paragraph, either the speci®cation of face 3 could be removed, or an additional speci®cation of face 2 as cast-then-machined could be added. Note that by identifying the machined faces that do not pass the veri®cation procedure for lifted cast faces, our method could generate suggestions to the user to specify these faces as cast-then-machined faces in order to make a more effective (that is, smaller) starting workpiece. 3.5. Generating the surface machining features The previous sections have described how the starting workpiece is generated from the offset volumes Vo(P) obtained by lifting cast-then-machined faces, then

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combining the halfspaces induced by machined and cast faces to enclose depressions of the offset part. Next, the offset volumes Vo(P) are grown through ®ctitious faces within the boundary of the starting workpiece to obtain the set of surface machining features Vg(P). Surface machining features Vg(P) may be viewed as special cases of depression volumes that have constant depth equal to the machining thickness. They can be obtained as the intersection between halfspaces induced by their machined faces and lifted cast faces and other cast faces of the part, similar to the manner in which depression volumes are enclosed in Step 4 of the algorithm to generate the starting workpiece. Note that this growing step can result in non-convex surface machining features. Additionally, two or more offset volumes could be merged into one surface machining feature. Furthermore, this growing step introduces volumetric intersection between adjacent surface machining features. For surface machining features whose lifted cast faces interact along a convex incident edge, as shown for Vo1 0 and Vo2 0 in Fig. 3(b), we consider the volumetric intersection to be insigni®cant for machining process planning. However, when two lifted cast faces interact along a concave incident edge, neither of the surface features could be machined in its entirety before the other one, due to volumetric interference when attempting to machine the intersection volume. Consequently, for every such pair of surface machining features, one of the surface features must be speci®ed to be machined ®rst, and its volume is modi®ed by subtracting the intersection volume. Such interactions along concave incident edges thus impose a partial ordering on the machining sequence for the set of surface machining features. The user may interactively specify this partial ordering, whereupon the surface machining features' volumes are updated to re¯ect the speci®ed sequence. In Section 3, we have now presented the algorithm to obtain the starting workpiece for machining from the part model and the speci®cation of machined and cast-thenmachined faces. Cast-then-machined faces are identi®ed and lifted to obtain offset volumes. By combining the halfspaces induced from machined faces and bounding cast faces, depression volumes are enclosed. These are added to the offset part to obtain the starting workpiece. Offset volumes are then grown to obtain surface machining features. The result of this step as described in Section 3 is (1) the starting workpiece Workpiece(P), (2) the set of surface machining features Vg(P), and (3) the set of simple, non-interacting volumetric machining volumes Vs(P) obtained through face pattern based feature recognition. 4. Machining feature recognition for cast-then-machined parts In the previous section, we have described the algorithm to generate the starting workpiece. In this section, we

describe how volumetric machining features are recognized from the starting workpiece. The machining feature recognition method we have previously developed for FAPPS utilizes a hybrid approach, combining the face pattern based recognition method for non-interacting atomic features and the volumetric decomposition method using ASVP Decomposition for interacting atomic features. Applying this method to the domain of castthen-machined parts has required that these two recognition methods be interwoven with the new method to generate the starting workpiece for machining, as summarized in Fig. 1(b). The machining feature recognition method is as follows. Step 1: Apply face pattern based feature recognition to the ®nished part P to obtain the simple machining features Vs(P). This has been described in Section 3.1. Step 2: Generate Workpiece(P), the starting workpiece for machining, and the surface machining features Vg(P). This has been described in Sections 3.2±3.5. Step 3: Obtain the volumetric machining removal volume Dm(P). The delta volume D(P), representing the entire volume to be removed from the starting workpiece, is obtained as D(P) ˆ Workpiece(P)2p Filtered(P). This delta volume D(P) includes the surface machining features Vg(P). These surface features are to be made by surface machining operations, so they need not be considered as volumetric machining features. Thus, we obtain the volumetric machining removal volume as Dm…P† ˆ D…P† 2p Vg …P† ˆ Workpiece…P† 2 pFiltered…P† 2p Vg …P†: This is the portion of the delta volume that is to be decomposed into volumetric machining features. It will consist of one or more removal volumes Dmi(P), each of which will be decomposed separately. Step 4: Apply feature recognition using ASVP decomposition to each machining removal volume Dmi(P). The feature recognition method using ASVP has been brie¯y described in Section 2.2. By this step, each Dmi(P) is decomposed into a Negative Feature Decomposition of a set of volumetric features Vi(P). Recognized features are classi®ed as atomic machining features according to their face classi®cations as original or ®ctitious. Step 5: Grow each volumetric feature Vij …P† to its effective feature volume Vej …P†. Note that the volumetric machining features Vi(P) recognized by ASVP Decomposition for cast-then-machined parts are dependent on the starting workpiece Workpiece(P), which is the casting output. Each recognized feature Vij …P† is grown through ®ctitious faces to an effective feature volume Vej …P† that preserves the atomic machining feature classi®cation and does not interfere with the ®nished part P.

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Fig. 6. Machining feature recognition results for part S and part S 0 .

While the recognized feature Vij …P† represents the required removal volume that must be removed as a result of machining operations, its effective feature volume Vej …P† preserves its fundamental characteristics for machining process planning. If Vej …P† interferes with part P, then the recognized feature Vij …P† is used without growing. The result of applying this step to each Negative Feature Decomposition obtained in Step 4 is a Negative Feature Decomposition NFD(Dmi(P)) containing effective feature volumes Ve(P). Step 6: Combine the NFDs NFD(Dmi(P)) obtained in Step 5 with the simple volumetric machining features Vs(P) obtained in Step 1 to obtain NFD(P): NFD…P† ˆ
Fig. 6(b). Dm(S) is decomposed into two Step features and a Slot feature that interact with each other, and an Open Pocket feature, shown in Fig. 6(c). In addition, Vs(S) consisting of four Hole features recognized by the face pattern based feature recognition method, shown in Fig. 4(b), are also included as volumetric machining features for Part S in Fig. 6(c). The machining removal volume Dm(S 0 ) for Part S 0 of Fig. 5, which re¯ects user speci®cation of a face to be cast-then-machined, is shown in Fig. 6(d). Dm(S 0 ) is decomposed into a Step feature, an Open Pocket feature, and a Slot feature. These three features, plus Vs(S 0 ) consisting of four Hole features, comprise the volumetric machining features for Part S 0 , shown in Fig. 6(e). The volumetric machining features recognized from Grip Tool Handle G of Fig. 2 are shown in Fig. 7. Face pattern based feature recognition has obtained 3 Hole features and a Cylindrical Slot, as shown previously in Fig. 2(b) and again in Fig. 7. Four maximally connected sets of machined faces F1, F2, F3, and F4, shown in Fig. 2(e), result in machining removal volumes, and ASVP decomposition is applied to these. F1 consists of two original faces, as indicated by the shaded marks in Fig. 7. Hence, its depression volume D1(G), shown in Fig. 2(f), is classi®ed as a step atomic machining feature, and it is grown to the effective Step feature volume shown in Fig. 7. F3 is decomposed into Virtual Open Pocket 1 and a slot atomic machining feature having 3 original faces, which is grown to the Slot 2 effective feature volume. F2 is decomposed into

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Fig. 7. Volumetric machining features for grip tool handle G (after growing).

Fig. 8. Adjuster base A.

Slot 1 and an Open Pocket feature, while F4 is recognized as Virtual Open Pocket 2, as shown in Fig. 7. 5. Results obtained for an example cast-then-machined part Now we present an example that involves complex cases of combining the machined faces and bounding cast faces to obtain the starting workpiece. Adjuster Base A is shown in Fig. 8, where all machined faces of interacting features, and their bounding cast faces, are labeled, and also in Fig. 9(a). Eleven non-interacting volumetric features are recognized by face pattern based feature recognition, as shown in Fig. 9(b), resulting in Filtered(A) in Fig. 9(c). First, we consider the case where the starting workpiece is generated automatically, without user speci®cation of castthen-machined faces. Top faces 1, 2, and 3, left face 4, and bottom face 5 marked in Fig. 8 are automatically identi®ed as cast-then-machined faces. These faces are lifted to obtain the initial state of OffsetB(A), as shown in Fig. 10(a), where the B

subscript indicates that no user speci®ed cast-then-machined face exists. Two machined face sets are obtained. Face set F1 consists of machined faces 15, 16, 17, 18, and the set P of twelve machined faces corresponding to the interacting pocket and slot features. F1 is bounded by G1 ˆ {1c,4c} < C1, where C1 denotes a set of original cast faces as shown in Fig. 8. Face set FB2 ˆ {6,7,8,9,10,11,12,13,14} is bounded by GB2 ˆ {1c,2c,3c} < C2. The veri®cation procedure for lifted cast faces described in Section 3.3 is now applied. For machined face set F1, the combined halfspace H(G1) obtained from lifted cast faces 1c and 4c and the set of original cast faces C1 properly encloses all machined faces of F1, so G1 passes the veri®cation procedure. For machined face set FB2, we ®rst generate the combined halfspace H(GB2) ˆ h(1c) > h(2c) > h(3c) > H(C2). Note that h(3c) is enclosed within halfspace h(2c), and both h(3c) and h(2c) are enclosed within halfspace h(1c). Thus, we have h(1c) > h(2c) > h(3c) ˆ h(3c), and therefore H(GB2) ˆ h(3c) > H(C2). Machined faces 6, 7, 10, 11, 12, and 14 are not properly enclosed within h(3c) of H(GB2). Therefore, face 3 is reclassi®ed as a volumetric-machined face, and offset volume Vo3 is removed from OffsetB(A). As face 3 is not adjacent to any other general depressions, FB2 0 ˆ FB2 . However, face 3 is adjacent to original cast faces labeled C2 0 , so GB2 0 ˆ {1c ; 2c } < C2 < C2 0 . The veri®cation procedure is next applied to GB2 0 . The combined halfspace H…GB2 0 † ˆ h…1c † > h…2c † > H…C2 † > H…C2 0 † is generated, which reduces to H…GB2 0 † ˆ h…2c † > H…C2 † > H…C2 0 †. Now machined faces 6, 10, 11, and 12 are not properly enclosed within h(2c) of H…GB2 0 †. Thus, face 2 is also reclassi®ed as a volumetricmachined face, and offset volume Vo2 is removed, resulting in FB2 00 ˆ FB2 and GB2 00 ˆ {1c } < C2 < C2 0 < C2 00 . H…GB2 00 † generated from GB2 00 properly encloses all

Fig. 9. Filtering simple machining features from adjuster base A.

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Fig. 10. Starting workpiece for adjuster base A, with no additional speci®cation of cast-then-machined surfaces.

machined faces of FB2, so the veri®cation procedure ends successfully. The ®nal state of OffsetB(A) obtained as a result of the veri®cation procedure is shown in Fig. 10(b). Applying halfspace combination and offset volume extension (Steps 4 and 5 of Section 3.2) results in WorkpieceB(A), shown in Fig. 10(c). The three remaining offset volumes Vo1 , Vo4 , and Vo5 are grown as described in Section 3.5 to obtain 1 surface machining features VBg , Vg4 , and Vg5 , respectively, as shown in Fig. 10(d). For clarity, these surface machining features are drawn in an exploded view. Now suppose that the user evaluates WorkpieceB(A) and decides that a smaller starting workpiece is preferred. The user provides cast-then-machined speci®cations for faces 6 and 7. These speci®cations are determined to be valid as described in Section 3.4. Cast-then-machined faces 1 through 7 are lifted to obtain 7 offset volumes, resulting in Offset(A) shown in Fig. 11(a). Machined face set F1 is the same as in the previous case where no user speci®ed cast-then-machined face existed,

but F2 ˆ {8,9,10,11,12,13,14} is now bounded by G2 ˆ {1c ; 2c ; 3c ; 6c ; 7c } < C2 : The veri®cation procedure for lifted cast faces is now applied. F1 is properly enclosed by H(G1), as in the previous case. Bounding cast face set G2 induces the combined halfspace H…G2 † ˆ ‰h…1c † > h…6c † > H…C2 †Š < ‰h…2c † > h…7c † > H…C2 †Š

<‰h…3c † > H…C2 †Š All faces of machined face set F2 are properly enclosed within H(G2). Therefore, all lifted cast faces pass the veri®cation procedure. Halfspace combination is applied to Offset(A), resulting in Workpiece(A), shown in Fig. 11(b). The offset volumes Vo(A) are grown to obtain the surface machining features Vg(A), shown in Fig. 11(c). Note that while offset volume Vo6 is convex, its surface machining feature Vg6 is non-convex due to its interactions with Vg2 and Vg7 along concave incident edges.

Fig. 11. Starting workpiece for adjuster base A, with no additional speci®cation of faces 6 and 7 as cast-then-machined surfaces.

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Fig. 12. Decomposing removal volume Dm1(A) into volumetric machining features.

Fig. 13. Decomposing removal volume Dm2(A) into volumetric machining features.

The machining removal volume Dm(A) is obtained as shown in Fig. 11(d), consisting of two disjoint removal volumes Dm1(A) and Dm2(A). Removal volume Dm1(A), shown in Fig. 12(a), is decomposed into machining features using the ASVP decomposition feature recognition method. By applying combination operations to convert ASVP decomposition into form feature decomposition [5], and positive to negative conversion [14], the negative feature decomposition NFD(Dm1(A)) is obtained as shown in Fig. 12(b), consisting of Steps 1 and 2, Pocket 3, and Slot 4. Steps 1 and 2 have two original faces each, as indicated by the shaded marks, so they have been classi®ed as step atomic machining features. They are grown to the effective feature volumes shown in Fig. 12(b), as described in Step 5 of Section 4. Pocket 3 and Slot 4 are classi®ed as a Pocket and a Slot feature, respectively, and they are already equal to their effective volumes. Applying ASVP decomposition and combination operations to machining removal volume Dm2(A) in Fig. 13(a) results in the form feature decomposition (FFD) shown in Fig. 13(b). As noted in Step 5 of Section 4, the shape of the features in the FFD is dependent on the shape of the starting workpiece. Furthermore, the generation of the starting workpiece as the combination of halfspaces can result in a non-convex starting workpiece. This could, in turn, create certain geometry in the machining removal volumes that require cutting operations during ASVP Decomposition.

Consequently, a single machining feature in the removal volume could appear as two or more features in the FFD as a result of cutting operations. In the FFD of Dm2(A), negative features B1, B2, and B3 have been separated from each other by cutting operations. Negative features B1 and B4 are classi®ed as Corner Pocket 5 and Slot 7, respectively, as shown in Fig. 13(c). Negative components B2 and B3 may be joined along the cutting plane corresponding to the shaded ®ctitious face of B3. This obtains a non-convex feature shown in Fig. 13(c) that has three original faces as indicated by the shaded marks. This feature is then classi®ed as Slot 6, and is grown to the effective feature volume shown in Fig. 13(c). Such joining operations are applied in order to lessen the in¯uence that the workpiece shape may have on the set of recognized features. The effective feature volumes Ve(A) obtained from the machining removal volume Dm(A) are shown in Fig. 14. In addition to these volumetric features that are intrinsic to the geometry of Adjuster Base A, we generate alternative feature representations to support ¯exible machining process planning activities. Note that Corner Pocket 5 and Slot 6 share the same base face and are both accessible from the vertical downward direction. They can be aggregated to obtain Virtual Open Pocket 8 [14], as shown in Fig. 15. Slot 6 has been grown upwards to the same height as Corner Pocket 5 to obtain this aggregate feature.

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Fig. 14. Effective features volumes Ve(A).

As Adjuster Base A has many interacting features, we illustrate automatically generated geometry-based machining precedence relations between surface and volumetric machining features, using the method described in [17]. By exploiting the face dependency relations obtained between features during ASVP decomposition feature recognition, as well as the atomic machining feature de®nitions, we generate the geometry-based machining precedence relations as follows. Whenever a ®ctitious face f of feature F has a face dependency relation to an original face g of feature G, the precedence relation G ! F is generated, indicating that G should be machined before F. The machining precedence relations for Adjuster Base A are shown in Fig. 16. Note that the top face of Pocket 3 is ®ctitious, and has face dependency to the bottom face of Step 1, which is original, resulting in the precedence relation Step 1 ! Pocket 3. Similarly, face dependency from the front face of Step 2, which is ®ctitious, to the back face of Step 1, which is original, results in the precedence relation Step 1 ! Step 2. The remaining precedence relations are generated in a similar manner. The dotted double-headed arrows between surface machining features Vg2 , Vg3 , Vg6 , and Vg7 in Fig. 16 indicate that these surface machining features interact along concave incident edges, as described in Section 3.5. Therefore, either precedence relation between such pairs of surface machining features is possible, as indicated by the double-headed arrow. Every dotted arrow would be converted into an unambiguous precedence relation by selecting one of its two surface features to be machined ®rst. The volume of the selected surface feature is then updated. Such speci®cation of the sequence in which to machine interacting surface features

could be provided interactively by the user. The recognized machining features and machining precedence relations are then provided to downstream modules in FAPPS, where they support machining process planning activities. 6. Summary We have presented a novel method to recognize machining features for cast-then-machined parts. By reasoning about the ®nished part geometry and the speci®cation of faces as cast or machined, we identify cast-then-machined faces, lift them to obtain offset volumes, and combine the halfspaces induced by connected sets of machined faces and their bounding cast faces to enclose depression volumes, which results in the starting workpiece for machining. The starting workpiece is a representation of the casting shape that is good enough to support machining feature recognition and machining process planning. Offset volumes are grown within the boundary of the starting workpiece to obtain surface machining features, and the machining removal volume is obtained from the starting

Fig. 15. Virtual open pocket 8, obtained by aggregating corner pocket 5 and slot 6.

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Fig. 16. Geometry-based machining precedence relations for surface and volumetric machining features of adjuster base A.

workpiece, the surface machining features, and the part model. We then apply our established feature recognition method using volume decomposition to decompose the machining removal volume into volumetric machining features, and to generate machining precedence relations between features to support machining process planning activities. This method can handle typical real-world complex cast-then-machined parts. The ®nal output produced by this method re¯ects the multiple processes used to manufacture the ®nished part, including the starting workpiece representing the casting shape, surface features that are made by surface machining operations, and volumetric machining features. Also, the system provides the utility in generating multiple casting shapes. The system can evaluate the user speci®cations of cast-then-machined faces, and provide suggestions to the user identifying faces that should be speci®ed as castthen-machined to obtain a more effective starting workpiece of the part. This utility of generating multiple starting workpieces could be combined with any other casting design

criteria to make the overall manufacturing process more effective.

Acknowledgements The work reported in this paper has been supported by the Korea Institute of Science and Technology (KIST). References [1] Boothroyd G, Dewhurst P, Knight W. Selection of materials and processes for component parts. NSF Design and Manufacturing Grantees Conference, Atlanta, January 1992. [2] Dong X, Wozny M. A method for generating volumetric features from surface features. Proceedings of Symposium on Solid Modeling Foundations and CAD/CAM Applications, Austin, June 1991. p. 185± 94. [3] Herrmann J, Lam G, Minis I. Manufacturability analysis using highlevel process planning. Proceedings of ASME Design for Manufacture Conference, Irvine, August 1996.

Y.S. Kim, E. Wang / Computer-Aided Design 34 (2002) 71±87 [4] Joshi S, Chang TC. Graph-based heuristics for recognition of machined features from a 3D solid model. Computer-Aided Design 1988;20(2):58±66. [5] Kim YS. Recognition of form features using convex decomposition. Computer-Aided Design 1992;24(9):461±76. [6] Kim YS. Volumetric feature recognition using convex decomposition. In: Shah J, Nau DS, MaÈntylaÈ M, editors. Advances in feature based manufacturing, Amsterdam: Elsevier, 1994. p. 39±63 Chapter 3. [7] Kim YS, Wang E. Automatic recognition of machining features and precedence relations. Proceedings of Korean Society of Precision Engineering Annual Conference, Chungjoo, May 1998. [8] Kim YS, Wilde DJ. A convergent convex decomposition of polyhedral objects. ASME Journal of Mechanical Design 1992;114(3):468± 76. [9] Kim YS, Wilde DJ. A convex decomposition using convex hulls and local cause of its non-convergence. ASME Journal of Mechanical Design 1992;114(3):459±67. [10] Little G, Clark DER, Corney JR, Tuttle JR. Delta-volume decomposition for multi-sided components. Computer-Aided Design 1998;30(9):695±705. [11] Pariente F, Kim YS. Incremental and localized update of convex decomposition used for form feature recognition. Computer-Aided Design 1996;28(8):589±602. [12] Regli WC, Gupta SK, Nau DS. Extracting alternative machining features: an algorithmic approach. Research in Engineering Design 1995;7(3):173±92. [13] Shah JJ, Shen Y, Shirur A. Determination of machining volumes from extensible sets of design features. In: Shah JJ, Nau DS, MaÈntylaÈ M, editors. Advances in feature based manufacturing, Amsterdam: Elsevier, 1994. p. 129±57 Chapter 7. [14] Waco D, Kim YS. Geometric reasoning for machining features using convex decomposition. Computer-Aided Design 1994;26(6): 477±89. [15] Waco D, Kim YS. Handling interacting positive components in machining feature reasoning using convex decomposition. Advances in Engineering Software 1994;20(2/3):107±19. [16] Wang E, Kim YS. Form feature recognition using convex decomposition: Results presented at the 1997 ASME CIE Feature Panel Session. Computer-Aided Design 1998;30(13):983±9. [17] Wang E, Kim YS, Lee CS, Rho HM. Feature-based machining precedence reasoning and sequence planning. Proceedings of ASME Computers in Engineering Conference, Atlanta, September 1998.

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[18] Vandenbrande JH, Requicha A. Geometric computation for the recognition of spatially interacting machining features. In: Shah JJ, Nau DS, MaÈntylaÈ M, editors. Advances in feature based manufacturing, Amsterdam: Elsevier, 1994. p. 83±106 Chapter 5. [19] Xu X, Hinduja S. Recognition of rough machining features in 21/2D components. Computer-Aided Design 1998;30(7):503±16.

Yong Se Kim is an Associate Professor of Mechanical Engineering at Sungkyunkwan University (SKKU), where he directs the CAD Laboratory. He joined SKKU in 2000. From 1997 to 2000, he was an Associate Professor at the University of Wisconsin± Milwaukee. From 1990 to 1997, he was an Assistant Professor at the University of Illinois at Urbana±Champaign. He received his PhD in Mechanical Engineering from the Design Division of Stanford University in 1990. Professor Kim's research interests include computer-integrated design and manufacturing, process planning, product development and visual reasoning. Professor Kim is a past chair of the Computers and Information in Engineering (CIE) Division of the American Society of Mechanical Engineers (ASME), and is a member of the Executive Committee of ASME CIE division. He is also a member of the Advisory Board of ASME Journal of Computing and Information Science in Engineering. Professor Kim is a Director of International Relations of the Society of CAD/CAM Engineers in Korea.

Eric Wang is a Visiting Researcher at the CAD Laboratory at Sungkyunkwan University and also at the CAD/CAM Research Center of the Korea Institute of Science and Technology (KIST), and is a PhD candidate in the Computer Science Department of the University of Illinois at Urbana±Champaign. Mr Wang's research interests include feature-based computer-aided process planning, assembly planning and geometric reasoning.