An oriented feature extraction and recognition approach for concave-convex mixed interacting features in cast-then-machined parts

Abstract

Feature recognition is an important technology of computer-aided design/computer-aided engineering/computer-aided process planning/computer-aided manufacturing integration in cast-then-machined part manufacturing. Graph-based approach is one of the most popular feature recognition methods; however, it cannot still solve concave-convex mixed interacting feature recognition problem, which is a common problem in feature recognition of cast-then-machined parts. In this study, an oriented feature extraction and recognition approach is proposed for concave-convex mixed interacting features. The method first extracts predefined features directionally according to the rules generated from attributed adjacency graphs–based feature library and peels off them from part model layer by layer. Sub-features in an interacting feature are associated via hints and organized as a feature tree. The time cost is reduced to less than $O (n^{2})$ by eliminating subgraph isomorphism and matching operations. Oriented feature extraction and recognition approach recognizes non-freeform-surface features directionally regardless of the part structure. Hence, its application scope can be extended to multiple kinds of non-freeform-surface parts by customizing. Based on our findings, implementations on prismatic, plate, fork, axlebox, linkage, and cast-then-machined parts prove that the proposed approach is applicable on non-freeform-surface parts and effectively recognize concave-convex mixed interacting feature in various mechanical parts.

Keywords

Feature recognition concave-convex mixed interacting feature cast-then-machined part graph-based rules hints mechanical part

Introduction

Feature recognition is to extract and recognize form features of a three-dimensional (3D) computer-aided design (CAD) part model. The feature recognition results are helpful to product designing,^1–3 process planning,^4–10 and numerical control (NC) programming.^11–17 Thus, it is regarded as the premier technic for the integrated representation of product lifecycle data.¹⁸ With the popularization of digital manufacturing and intelligent manufacturing, feature recognition has been implemented in manufacturing reuse¹⁹ and NC machining¹³ of aircraft structural parts, automatic process planning of mold components⁴ and V-bending,⁸ and construction of 3D working procedure model.⁹

Feature recognition is also a primary method required to extract the features need to be machined after casting in spacecraft structure part manufacturing. The cabin structure in spacecraft (refer to Figure 1) is a cast-then-machined part with more than 120 features which belongs to over 10 categories. The machining features include isolated concave features, isolated convex features, and interacting features. Most of the interacting features are concave-concave interacting features (A in Figure 1) and concave-convex interacting features (B, C, D in Figure 1).

Figure 1.

3D design model of spacecraft cabin structures: (a) The model of Prt₁ and (b) The model of Prt₂.

Note that the concave features and convex features in cast-then-machined parts are manufactured in different ways. Concave features like holes, cavities, and grooves are derived from removing materials, while the convex features such as bosses are first casted with a machining allowance and then machined. Thus, the concave and convex features should be recognized separately. Moreover, if a feature is interacted with another, the manufacturing process can be various, which means the interacting relationship is also important information. Therefore, the coexistence of hundreds of concave and convex mixed features and the various interacting relationship among them, which have never been studied, make feature recognition of cabin structure much more difficult. This article focuses on solving this critical problem in feature recognition.

The novelty of this work is reflected in the following three aspects: first, a novel oriented feature extraction and recognition approach (OFERA) is proposed for concave-convex mixed interacting features; second, rules are used to search and recognize features instead of subgraph isomorphism and matching operations, so that the time cost is dropped sharply; third, the proposed approach can be applied on a wide range of mechanical parts.

Literature review

Existing feature recognition methods developed by numerous researchers are mainly divided into four categories, namely, the volumetric decomposition,^20–23 graph-based,^24–38 hint-based,^39–43 and artificial neural network (ANN) approaches.^44–46 By considering the massiveness and diversity of feature and variety of feature interacting ways in cabin structures, volumetric decomposition method is not applicable for its huge amount of volume segmentation operations and time costing. Hint-based technique is in trouble to observe enough useful hints. ANN method is not yet applicable on interacting feature recognition problems. Graph-based approach is considered the only feasible method for cabin structures. Because of the correspondence between boundary representation (B-rep) data structures and graph structures, the graph-based approach is the most popular feature recognition method. It successfully benefits from the well-developed mathematics of graph theory, but its performance is still need to be promoted.

The original graph-based approach proposed by Joshi and Chang²⁴ deletes the surface whose incident edges are all convex, and disconnects the surfaces sharing a common convex edge, so that subgraphs containing only concave edges are obtained. The feature type is finally identified via graph matching. A great deal of studies on interacting feature recognition have been inspired soon afterward. Joshi and Chang²⁴ recognized two kinds of interacting features by heuristics. However, their graph isomorphism results were incorrect for features with convex edges. Following researchers combined graph-based approach with other approaches. Kashyap and colleagues^25,26 introduced virtual links, but they could not get all necessary virtual links effectively. Gao and Shah²⁷ generated minimal condition subgraphs (MCSGs) with fixed procedures and used them as hints. Although their method was open to new features without code changing, MCSG generation was easily interfered by redundant convex edges in sophisticated models. Rahmani and Arezoo⁴¹ also used graph-based hints and proposed volume generation algorithms for 2.5D and 3D interacting features. Sunil et al.²⁹ presented a new graph and rule-based approach, which successfully recognized variable feature interactions.

Take note that almost all the existing graph-based algorithms segment part graph into subgraphs first, but the fixed subgraph segmenting codes do not suit all parts, especially the parts that contain convex features and concave-connected non-machining surface. On the other hand, features interacting may produce convex edges, which interfere acquiring predefined feature through graph decomposing. In addition, some of the casted surfaces, which are also connected by concave edges, may be misjudged as a feature needs processing.

In this work, a novel hybrid (graph + rule + hint)-based efficient feature recognition methodology is proposed, which is named OFERA. OFERA use rules rather than graph isomorphism to directly extract predefined concave and convex features regardless of other structures. As a result, the concave and convex features can be successfully recognized and do not interfere with each other, and the time complexity is dropped to less than $O (n^{2})$ .

Basic concepts and notations

In this section, some basic concepts are defined, which are mentioned in recognition of concave, convex, and interacting features. First, notations used in this study are listed in Table 1.

Table 1.

Notations and description.

Notations	Description
$Lib$	The standard feature library
$Prt$	The part model
$f_{j}$	The jth feature in a part model
$T (f_{j})$	Topology matrix of $f_{j}$
$G (f_{j})$	Geometry matrix of $f_{j}$
$O (f_{j})$	Outer adjacency matrix of $f_{j}$
$R (f_{j})$	Special relationship matrix of $f_{j}$
$HAAM (f_{j})$	The HAAM model of $f_{j}$
$Fnum (f_{j})$	Feature surface number of $f_{j}$
$F_{i}$	The ith surface in a feature
$ASnum (F_{i})$	Adjacent surfaces number of surface $F_{i}$
$ASnu m_{cave} (F_{i})$	Concave adjacent surfaces number of surface $F_{i}$
$ASnu m_{vex} (F_{i})$	Convex adjacent surfaces number of surface $F_{i}$
$τ (f_{j} / e_{k})$	The type of surface $f_{j}$ or edge $e_{k}$
$Ω (F_{i})$	The type of surface $F_{i}$
$CYL$	Cylinder surface
$e_{k}$	The kth edge in a feature
$γ (e_{k})$	The concavity and convexity of edge $e_{k}$ $γ (e_{k}) = cave$ means $e_{k}$ is a concave edge $γ (e_{k}) = vex$ means $e_{k}$ is a convex edge

HAAM: hierarchical attributed adjacency matrices.

The basic concepts are presented as below:

Feature surface: if a surface $F_{a} \in f_{b}$ , then surface is a feature surface of $f_{b}$ and remarked as $F_{a} f_{b}$ .

Outer adjacent surface: if a surface $F_{a} \notin f_{c}, \exists e_{d} \in F_{a} \cap F_{b}, F_{b} \in f_{c}$ , then surface $F_{a}$ is an outer adjacent surface of $f_{c}$ and denoted as $F_{a}$ ⋈ $f_{c}$ .

Top surface: if $\forall e_{k} = F_{i}, γ (e_{k}) = vex$ , then $F_{i}$ is a top surface.

Bottom surface: if $\forall e_{k} = F_{i}, γ (e_{k}) = cave$ , then $F_{i}$ is a bottom surface.

Side surface: if $F_{a}$ is a top surface or bottom surface, then $\forall F_{i} \cap F_{a} \neq \emptyset$ is a side surface.

Primary and secondary sub-feature: the sub-feature which is first extracted in a pair of sub-features of an interacting feature is the secondary sub-feature, and the other one is the primary sub-feature.

Associating edge: if $e_{k} \in f_{x} \cap f_{y}$ , then $e_{k}$ is the associating edge of $f_{x}$ and $f_{y}$ .

Merged surface: if $F_{i} \in f_{x} \cap f_{y}$ , then $F_{i}$ is the merged surface of $f_{x}$ and $f_{y}$ .

Start surface: the distinctive surface in $f_{j}$ need to be located before searching other feature surfaces of $f_{j}$ .

Left surface: for a surface $F_{i}$ , if $\exists F_{a}, F_{b}, F_{c} \in f_{j}, γ (F_{a} \cap F) = γ (F_{b} \cap F_{i}) = γ (F_{a} \cap F_{c})$ , then $F_{i}$ is a left surface of $f_{j}$ .

Methodology overview

The proposed methodology architecture is presented in Figure 2. First, a graph-based virtual feature library $Lib$ needs to be developed. An improved hierarchical attributed adjacency matrices (HAAM) model³⁷ is used to define the features.

Figure 2.

Methodology architecture.

Different from traditional graph-based method, adjacent attributes of surfaces provided by graph-based feature library are used to customize rules for recognizing predefined features, so that no subgraph decomposing and matching operations are needed. At the same time, feature interaction hints like merged surfaces and left surfaces are also found during execution of feature surface searching rule. Standard feature recognition and hints finding operations are implemented by OFERA till no features are recognized. Finally, the recognized features related by hints are assembled as interacting features and organized as a feature tree to be the output.

Feature library

In the library, features are mainly divided into standard features and interacting features first as previous researchers^24,27,29 did. They are expressed in feature library using improved HAAM model.

Feature representation method

The HAAM model improved from the previous work³⁷ is adopted to depict the information of 3D model

HAAM (f_{j}) = (T (f_{j}), G (f_{j}), O (f_{j}), R (f_{j}))

(1)

Topology matrix $T$ is to express adjacency relationships between feature surfaces. Geometry matrix $G$ is proposed to further clarify the geometric information about the feature surfaces, such as their surface types, included angles, and other relative position attributes. Special relationship matrix $R$ is proposed to indicate special surfaces and edges in the feature. However, these information are not abundant enough to distinguish the features such as (i), (k), and (l) shown in Table 3, which are different in the adjacency attributes between their feature and outer adjacent surfaces. Therefore, outer adjacent matrix $O$ is introduced in HAAM model to store the associations among feature surfaces and outer adjacent surfaces of a feature in corresponding cells, like outer adjacent surface types, common edge types of feature surfaces and outer adjacent surfaces, and relative position relationships among outer adjacent surfaces.

Analysis of standard features

Standard features consist of convex features and concave features, which are sorted by the adjacent attribute among their feature surfaces. Some typical convex and concave features are demonstrated in Tables 2 and 3, respectively.

Table 2.

Typical convex features and their attributes.

Independent convex features
Example	(a)	(b)	(c)	(d)	(e)
Example
Distinctive surface, $F_{D}$
Top surface
Other feature surface, $F_{i}$	$γ (F_{i} \cap F_{D}) = vex$
Semi-independent convex features
Example	(f)	(g)	(h)	(i)	(j)
Example
Distinctive character	$\forall F_{a}$ ⊿ $\forall F_{a} f_{j}, e_{k} \in F_{a} \cap f_{j}, γ (e_{k}) = cave$ $F_{b}, F_{c} \in f_{j}, \forall e_{l} \in F_{b} \cap F_{c}, γ (e_{l}) = vex$

Table 3.

Typical concave features and their attributes.

Through hole-containing features
Example	(a)	(b)	(c)
Example
Distinctive surface, $F_{D}$
Distinctive surface, $F_{D}$	$F_{b}, F_{D} \in f_{a}, Ω (F_{b}) = Ω (F_{D}) = CYL$ $\forall e_{k} = F_{b} \cap F_{D}, γ (e_{k}) = cave$ $\forall F_{c} \cap F_{D} \neq \emptyset, F_{c}$ ⊿ $f_{a}, γ (F_{c} \cap F_{D}) = vex$
Other feature surface, $F_{i}$	$if F_{i} \cap F_{D} \neq \emptyset, γ (F_{i} \cap F_{D}) = cave$ $Ω (F_{i}) = CYL$
Bottom surface-containing features
Example	(d)	(e)	(f)	(g)	(h)
Example
Distinctive surface, $F_{D}$
Distinctive surface, $F_{D}$	Bottom surface
Other feature surface, $F_{i}$	$if F_{i} \cap F_{D} \neq \emptyset, γ (F_{i} \cap F_{D}) = cave$
Open concave features
Example	Side-open			Bottom-open
	(i)	(j)	(k)	(l)	(m)

Distinctive character	$\forall F_{i}$ ⊿ $f_{j}, \exists F_{x} \in f_{j}, F_{x} \cap F_{i} \neq \emptyset$ $\exists F_{y} \in f_{j}, F_{y} \cap F_{i} = \emptyset$			$\exists F_{a}, F_{b}$ ⊿ $f_{j}, \forall F_{i} \in f_{j}$ $F_{i} \cap F_{a} \neq \emptyset \land F_{i} \cap F_{b} \neq \emptyset$

An independent convex feature is the convex feature which has a top surface, as illustrated in Table 2(a)–(e). The top surface can be used to locate an independent convex feature. A semi-independent convex feature is the convex feature generated by leaning an independent convex feature on other solid surfaces, as shown in Table 2(f)–(j). Semi-independent convex features have no distinctive surface like the top surface in independent feature.

A through hole-containing feature is the concave feature that includes a through hole, such as through hole itself, through counterbore, and through stepped hole presented in Table 3(a)–(c). The distinctive surface of a through hole-containing feature is either of the cylinder surface in a through hole. A bottom surface-containing feature is the concave feature $f_{a} ∋ F_{b}$ , that $F_{b}$ is a bottom surface, as can be seen in Table 3(d)–(h). Similar to the top surface in an independent convex feature, the bottom surface in a bottom surface-containing feature is the distinctive surface. Open concave feature is the concave feature that can be formed as a bottom surface-containing feature with an added surface, as shown in Table 3(i)–(m). The extraction of open concave features and semi-independent features are easily mixed up, because for either an open concave feature or a semi-independent feature $f_{a}$ , $\forall F_{i} \in f_{a}, \exists F_{x} \cap F_{i} = e_{b}, γ (e_{b}) = vex, \exists F_{y} \cap F_{i} = e_{c}, γ (e_{c}) = cave$ . Hence, they should be differentiated by other topology information. Their distinctive characteristics are illustrated in Tables 2 and 3.

Analysis of interacting features

The interacting features are sorted into four categories in accordance with the topology changes after interaction. Four interacting feature types are, namely, edge-associated, surface-merging, edge-missing, and surface-split interacting features. Assume that $f_{z} = f_{x} \cup f_{y}$ , $f_{x} \cap f_{y} \neq \emptyset$ , and $f'_{x}, f'_{y}$ are the original standard features corresponding to $f_{x}, f_{y}$ , respectively: if $f_{x}$ is the primary sub-feature and $f_{y}$ is the secondary sub-feature, ${e_{k} | e_{k} \in f_{x}} \ {e_{k} | e_{k} \in f_{x}^{'}} ¹ {e_{k} | e_{k} \in f_{x} \cap f_{y}}$ , then $f_{z}$ is an edge-associated interacting feature; if ${F_{i} | F_{i} \in f_{x} \cap f_{y}} \neq \emptyset$ , then $f_{z}$ is a surface-merged interacting feature; if $\exists e'_{d} \in f'_{x}$ , $\exists e_{d} \in f_{x}$ that corresponding to $e'_{d}$ , then $f_{z}$ is an edge-missing interacting feature; if $\exists F'_{d} \in f'_{x}$ , ${F_{d 1}, F_{d 2}, \dots, F_{di}} \in f_{x}, i \geq 2$ that $F_{d 1} \cup F_{d 2} \cup \dots \cup F_{di} \subset F'_{d}$ , then $f_{z}$ is a surface-split interacting feature. The corresponding feature topology changes can also be seen in Table 4. It is worth mentioning that these four interacting feature classes have no direct correspondence with the interaction classifications defined in previous researches.^24,27,29

Table 4.

Four different kinds of interactions and the corresponding topology changes.

	Edge-associated interacting feature	Surface-merging interacting feature	Edge-missing interacting feature	Surface-split interacting feature
Example
Sub-feature
Associating edge
Number of incident edges is increased?	Yes	Yes	Yes	Yes
Merged surface	None
Contain merged surfaces?	No	Yes	Maybe	Maybe
Missed edge	None	None		None
Adjacent relationship is changed?	No	No	Yes	Yes
Split surface	None	None	None
Number of surface is increased?	No	No	No	Yes

Analysis of edge-associated interacting features

As Table 5 presents, in an edge-associated interacting feature $f_{z} = f_{x} \cup f_{y}$ , $f_{x} \cap f_{y} = {e_{1}, e_{2}, \dots, e_{k}}$ , $T (f_{x}) = T (f'_{x})$ , $T (f_{y}) = T (f'_{y})$ . Suppose that $f_{x}$ is the primary sub-feature, and $f_{y}$ is the secondary sub-feature, each of them can be either concave feature or convex feature. $f_{x}$ and $f_{y}$ can be easily distinguished from $f_{z}$ , because $f_{x} \ (f_{x} \cap f_{y}) = f'_{x}$ , while $f_{y} = f'_{y}$ . As a result, $f_{y}$ can be extracted via regular standard feature recognition operations. For primary sub-features, because $T (f_{x}) = T (f'_{x})$ , they can also be identified after removing $f_{y}$ and all edges $e_{k} \in f_{y}$ from $Prt$ . When all sub-features of an edge-associated interacting feature are extracted, they are related by the associating edges ${e_{1}, e_{2}, \dots, e_{k}} = f_{x} \cap f_{y}$ to form the edge-associated interacting feature.

Table 5.

Typical edge-associated interacting features and their attributes.

	(a)	(b)	(c)	(d)
Edge-associated interacting feature
Sub-feature
Associating edge

Analysis of surface-merging interacting features

In a surface-merging interacting feature $f_{z} = f_{x} \cup f_{y}$ , $f_{x} \cap f_{y} = {F_{1}, F_{2}, \dots, F_{i}}$ , $T (f_{x}) = T (f'_{x}), T (f'_{y}) = T (f'_{y})$ , but suppose $F'_{i}$ is the original surface of merged surface $F_{i} \in f_{x} \cap f_{y}$ before merging, $\exists e_{k} ϵ F_{i}, e_{k} \notin F'_{i}$ (refer to Table 6). Because of surface merging, if merged surface $F_{M}$ is removed with the first extracted sub-feature $f_{y}$ , then the remaining sub-feature $f_{x}$ is different with $f'_{x}$ in standard feature library. So $F_{M}$ should be reserved till extracting the last sub-feature containing it. Merged surface $F_{M}$ is also used as a hint to assemble the sub-features sharing it as an interacting feature.

Table 6.

Typical surface-merging interacting features and their attributes.

	(a)	(b)	(c)	(d)
Surface-merging interacting feature
Sub-feature
Associating edge
Merged surface

Analysis of edge-missing interacting features

At least one sub-feature of edge-missing interacting features lose edges after interaction, as illustrated in Table 7. In an edge-missing interacting feature $f_{z} = f_{x} \cup f_{y}$ , if $f_{x}$ is the primary sub-feature, then $Fnum (f_{x}) = Fnum (f'_{x}), Fnum (f_{y}) = Fnum (f'_{y})$ , but $T (f_{x}) \neq T (f'_{x})$ , because losing an edge $e_{a} = F_{b} \cap F_{c}$ means disconnecting the adjacency between $F_{b}$ and $F_{c}$ . As a result, either $F_{b}$ or $F_{c}$ cannot be searched during regular standard feature recognition. If $f_{x}$ is a concave feature, $F_{b}$ is the left surface, $\exists F_{d}, F_{e} \in f_{x}, γ (F_{d} \cap F_{b}) = γ (F_{e} \cap F_{b}) = cave$ . Similarly, if $f_{x}$ is a convex feature, $\exists F_{d}, F_{e} \in f_{x}, γ (F_{d} \cap F_{b}) = γ (F_{e} \cap F_{b}) = vex$ . Therefore, to pick up the left surface, whether the extracted surfaces have an unsearched common adjacent surface should be checked.

Table 7.

Typical edge-missing interacting features and their attributes.

	(a)	(c)
Edge-missing interacting feature
Sub-feature
Associating edge
Merged surface	None	None
Missed edge

Analysis of surface-split interacting features

Table 8 presents that in surface-split interacting features, $Fnum (f_{x})$ of the split sub-feature is increased due to surface splitting caused by feature interaction. Also $T (f_{x}) \neq T (f'_{x})$ , which makes the type of split sub-feature hard to be identified. Note that two major ways of surface splitting are side-surface splitting and top/bottom-surface splitting. In the second case, one of the split surfaces becomes left surface in feature extracting. Usually, the sub-feature that splits the primary sub-feature is the secondary sub-feature. Thus, after secondary sub-features are extracted, the split side surfaces and top/bottom surfaces are not much different from the original one in respect of adjacent relationship with other feature surfaces. As a result, the role of the left surface can be confirmed, so that original standard feature of the split sub-feature can be restored.

Table 8.

Typical surface-split interacting features and their attributes.

	(a)	(b)	(c)
Surface-split interacting feature
Sub-feature
Associating edge
Merged surface		None	None
Missed edge	None	None	None
Split surface

OFERA

Overall process of OFERA

The overall process of OFERA is demonstrated in Figure 3. Due to feature interaction, OFERA has $t$ rounds of standard feature recognition $(OFER A_{std})$ till $S_{t} = \emptyset$ . $OFER A_{std}$ also judges whether a standard feature is interacted with others by finding interaction hints. Interacting feature recognition $(OFER A_{intr})$ includes all rounds of $OFER A_{std}$ and an operation that linking sub-features of an interacting feature by hints. Finally, a feature tree is built in line with the interaction relations.

Figure 3.

Schematic flow of OFERA: (a) main process of OFERA and (b) standard feature recognition and hints finding operations.

According to Figure 3, if $n$ is the number of surfaces in $Prt$ , $n'$ is the total surface number of all extracted features, s is the max feature surface number of each feature, and $λ$ is the max outer adjacent surface number of each features, then the total cycle time of OFERA is $tn [(s - 1) + λ n']$ . Thus, the time complexity of OFERA is $O (nn') < O (n^{2})$ .

Standard feature extraction and recognition $(OFER A_{std})$

$OFER A_{std}$ is designed with three stages according to the analysis of the graph-based information of standard features from $Lib$ . The three stages are determining start surface (ST), searching feature surface (FS), and confirming feature type (FT). In each stage, rules are used to extract and recognize the predefined standard features. These rules are customized for each feature $f_{j}$ according to $T (f_{j})$ , $G (f_{j})$ , $O (f_{j})$ , and $R (f_{j})$ . In practice, the part structure is various and the rules may be modified particularly. So only some of them are listed in Tables 9 –11.

Table 9.

Start surface determining (ST) rules.

No.	Quantity of adjacent surfaces		Surface type
No.	Concave	Convex	Surface type
ST1	1	–	Cylinder
ST2	≥2	0	Planar/Cylinder/Conical
ST3	0	≥2	Planar/Cylinder
ST4	2	>0	Planar/Cylinder

Table 10.

Feature surface searching (FS) rules.

No.	Adjacency with input surfaces	Lower bound of adjacent surfaces		Surface type
No.	Adjacency with input surfaces	Concave	Convex	Surface type
FS1	Concave	1	2	Cylinder
FS2	Convex	2	2	Planar
FS3	Convex	1	2	Conical
FS4	Concave	2	1	Cylinder
FS5	Concave	2	2	Planar/Cylinder
FS5	Concave	3	1	Planar/Cylinder
FS6	Concave	2	0	Conical
FS7	Convex	2	2	Planar/Cylinder
FS7	Convex	1	3	Planar/Cylinder
FS8	Convex	[1,2]	[1,3]	Planar/Cylinder

Table 11.

Feature type confirming (FT) rules.

No.	Feature surface quantity	Geometry matrix		Outer adjacency relationship
No.	Feature surface quantity	Feature surface type	Quantity	Outer adjacent surfaces quantity	Adjacent feature surfaces quantity
FT1	3	Cylinder	2	–
FT2	4	Planar	4	–
FT3	5	Planar	5	–
FT4	5	Planar	3	–
FT4	5	Cylinder	2	–
FT5	6	Planar	6	–
FT6	9	Planar	9	–
FT7	3	Planar	3	3	2
FT8	3	Planar	3	1	2
FT8	3	Planar	3	1	2
FT9	3	Planar	3	2	3
FT10	4	Planar	4	2	4
FT11	4	Planar	2	2	4
FT11	4	Cylinder	2	2	4
FT12	2	Planar	1	–	–
FT12	2	Cylinder	1
FT13	3	Planar	3	1	2
FT13	3	Planar	3	1	2
FT14	3	Planar	3	2	3
FT15	4	Planar	3	2	3
FT16	4	Planar	3	2	3
FT16	4	Cylinder	1	2	3

The rules are applied orderly in accordance with the route map demonstrated in Figure 4. The ST rules are designed to locate the distinctive surface of each kind of features (see Figure 5(b))

Start Surface (F_{1}, F_{2}, \dots) = {OFERA}_{std}^{(ST)} (STx)

(2)

where $STx$ is a start surface determining rule. After this, in Figure 5(c)–(e), FS rules are used to find the feature surfaces based on their relationships with a start surface $F_{i}$ , as below

Feature Surface (F_{1}, F_{2}, \dots) = {OFERA}_{std}^{(FS)} (F_{i}, FSx)

(3)

where FSx is a feature surface searching rule. Because of the similarity of feature structures, some features share ST rules and first few steps of FS. If no surface is gotten in a FS step or no FS step is following, $OFER A_{std}$ stops FS and output $FeatureSurface (F_{1}, F_{2}, \dots)$ . Note that some feature types can be identified directly after completing FS. However, most of feature types are confirmed by particular FT rules, as shown in equation (4)

Feature Type (f_{j}) = {OFERA}_{std}^{(FT)} (f_{i}, FTx)

(4)

where $FTx$ is a feature type confirming rule. Current recognizable standard features are output at the end of $OFER A_{std}$

Standard Feature (f_{1}, f_{2}, \dots) = OFER A_{std} (Prt)

(5)

Figure 4.

Route map of $OFER A_{std}$ . (a) Route of recognizing through hole-containing features. (b) Route of recognizing bottom surface-containing features. (c) Route of recognizing independent convex features. (d) Route of recognizing open concave features and semi-independent convex features.

Figure 5.

Example of implementing $OFER A_{std}$ . (a) The original model. (b) Locating the start surface. (c), (d), and (e) Searching feature surfaces.

Interacting feature extraction and recognition $(OFER A_{intr})$

$OFER A_{intr}$ comprises several rounds of $OFER A_{std}$

OFER A_{intr} = {OFERA}_{intr}^{(1)} \cup {OFERA}_{intr}^{(2)} \cup \dots

(6)

where ${OFERA}_{intr}^{(t)} = OFER A_{std}$ . Common edges, merged surfaces, and the left common neighbor surfaces are important objects in $OFER A_{intr}$ . These hints are obtained during $OFER A_{std}$ . Figure 3(b) illustrates that when $F_{i}$ is searched, $ASnum (F_{i})$ is counted. Figure 6 shows the whole process of $OFER A_{intr}$ on four kinds of interacting features. If the $ASnu m_{cave} (F_{i})$ or $ASnu m_{vex} (F_{i})$ are more than defined in FS rules, then the surface is marked as a merged surface, like surface $F_{M}$ in Figure 6(b2) and (b4)

Merged Surface (F_{M 1}, F_{M 2}, \dots) = {OFERA}_{std}^{(Hint)} (F_{i}, FSx)

(7)

where $Merged Surface (F_{M 1}, F_{M 2}, \dots) \subset Feature Surface (F_{1}, F_{2}, \dots)$ is derived from equation (3). $F_{M}$ is also reserved to the next round of feature extraction and recognition. Every time the FS is ended, $OFER A_{intr}$ checks whether there is any left surface till none can be found (refer to Figure 6(d5) and (d6))

L e f t S u r f a c e (F_{L 1}, F_{L 2}, \dots) = O F E R A_{s t d}^{(H i n t)} (F e a t u r e S u r f a c e (F_{1}, F_{2}, \dots))

(8)

Figure 6.

Extraction and recognition of (a) an edge-associated, (b) a surface-merging, (c) an edge-missing, and (d) a surface-split interacting feature.

Left surfaces are added into the just extracted feature.

All rounds of feature recognition results about part $Prt$ are output sequentially in feature sets $S_{1}, S_{2}, \dots$

S_{t} = {f_{1}, f_{2}, \dots} = {OFERA}_{intr}^{(t)} (Prt)

(9)

Sub-features of the same interacting feature are related by common edges, merged surfaces, and left surfaces as demonstrated in Figure 7(d)

I n t e r a c t i n g F e a t u r e (f_{I 1}, f_{I 2}, \dots) = O F E R A_{i n t r} (H i n t s, S_{1}, S_{2}, \dots)

(10)

Figure 7.

Sketch map of feature tree organization: (a) the original model, (b) locating start surface, (c) searching feature surfaces, (d) feature recognition results, and (e) feature tree.

The primary and secondary sub-features in each pair of associated sub-features are easy to be differentiated according to round order.

The last step of OFERA is to organize all recognized features as a feature tree. As shown in Figure 7, isolated features (like $f_{5}$ ) and sub-features with no primary sub-feature (such as $f_{8}, f_{7}$ ) are added as the root nodes of the tree. If a root node feature has any secondary sub-features, then these secondary sub-features are inserted as its child root (like $f_{6}, f_{3}$ to $f_{8}$ ). Hence, the feature tree describes the structure of a part conceptually.

Case studies

The proposed approach is realized using VC++ programming language to redevelop Pro/Engineering API (Application Programming Interface). B-rep information needed in OFERA are extracted from CAD model by API objects. To highlight the applications of OFERA, example models are adopted from National Design Repository (NIST) and practical cabin structure models; on the other hand, several of the traditional approaches are reproduced as part of this work.

Illustrative case study 1

In order to verify the versatility on parts of basic types, some typical prismatic, plate, fork, axlebox, linkage, shaft, and cast-then-machined parts are selected from NIST. The test results in Figure 8 show that most of the features to be machined are recognized by applying OFERA successfully, regardless of the types of parts. Note that (g1) demonstrates one of the derived adjacent surface sets by applying traditional graph-based method.^{24–27,29,41,47} The highlighted surface are grouped as a concavely connected surface set by disconnecting convex edges. However, none of these surface groups is to be machined in one operation after casting. In comparison, the holes and bosses are identified by OFERA in (g2) and (g3). This case study demonstrates that OFERA can be widely used in feature recognition of mechanical parts and performs better than the traditional graph-based method.

Figure 8.

Test results of (a) prismatic, (b) plate, (c) fork, (d) axlebox, (e) linkage, (f) shaft, and (g) cast-then-machined parts.

Illustrative case study 2

The proposed method is compared with the feature recognition algorithm presented in the literature,^27,29 which is shown in Figure 9. The convex feature 23 in Figure 9(a) was segmented into several surface features in the literature.²⁷ Furthermore, the feature relationships, which are presented as a feature tree in Figure 9(a), were not identified in the literature.²⁷Figure 9(b) illustrates that, together with other 18 features, feature 13 is also recognized, which was not extracted in the literature.²⁹ Therefore, the proposed methodology is proved to have better performance on the cases solved by previous graph-based approaches.

Figure 9.

Recognition results of part model used in (a) test 2 of literature¹⁸ and (b) case study 2 of literature.²⁰

Illustrative case study 3

Figure 10(a)–(d) presents the results of implementing OFERA on a real cabin structure. Figure 10(a) shows all isolated standard features, and four large-scale interacting features are highlighted in Figure 10(b). A typical edge-associated interacting feature in the cabin structure is demonstrated in Figure 10(c). The interacting feature in Figure 10(d) contains both edge-associated and surface-splitting interacting features.

Figure 10.

Test results of cabin structure A and B. The recognized (a) isolated standard features, (b) large-scale interacting features, (c) two concave-convex mixed interacting features, (d) another two concave-convex mixed interacting features in cabin structure A. The recognized (e) isolated standard features, (f) edge-associated interacting features, (g) surface-merging interacting feature, (h) concave-convex mixed interacting feature, and (i) another concave-convex mixed interacting feature in cabin structure B.

Application effects of OFERA on another cabin structure part are demonstrated in Figure 10(e)–(i). The recognized isolated features are highlighted in Figure 10(e). Two kinds of recurring edge-associated interacting features are marked in Figure 10(f). A surface-merging interacting feature is recognized in Figure 10(g). Figure 10(h) and (i) demonstrates two concave-convex mixed interacting features. In Figure 10(h), four round bosses with a blind hole are on the bottom surface of a four-side cavity. A chamfered boss and a stepped hole are integrated as the edge-associated interacting feature in Figure 10(i).

Both of two real cabin structure parts have plenty of concave and convex features. The mass of concave-convex mixed interacting structures makes it difficult to obtain accurate results for subgraph isomorphism. Therefore, only few of isolated concave features can be recognized by traditional graph-based method.^{24–27,29,41,47} Instead, OFERA first locates the distinctive surface of each concave and convex standard features by start surface determining rules. Then, it searches other feature surfaces to complete a feature. Hence, it automatically ignores the surfaces on other structures of the model, which do not fit the judgment conditions of corresponding rules. As a result, OFERA is more effective in extracting concave and convex standard features, and concave-convex mixed interacting feature from complicated part models.

Conclusion

In this work, a novel oriented feature extraction and recognition approach for concave-convex mixed interacting features in cast-then-machined parts was successfully presented as known OFERA. Its time cost was under $O (n^{2})$ . OFERA was verified to be effective in recognizing concave-convex mixed interacting features, which were not considered by previous graph-based methods.

Basically, the proposed approach is an extensible methodology framework of feature recognition. Moreover, this design can be customized for specific parts and features by modifying conditions in rules. Based on this point, there is great potential for employing the proposed approach to recognize features in other parts with plenty of features interacted in different ways, such as structure parts of aircraft, automobile engines, calibrating dies, and plastic injection molds.

It should be mentioned that the source code of the proposed methodology framework is not fixed because of its extendibility while adding new predefined features. In addition, features containing freeform surfaces were not under consideration. In the future work, how to automatically construct the 3D process model and generate NC program using the feature recognition results will be studied.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the First Batch of Guidelines of “13th Five-Year” Pre-research on Common Information System Equipment for the Whole Army (No. 41423010101).

ORCID iD

Haichao Wang

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An oriented feature extraction and recognition approach for concave-convex mixed interacting features in cast-then-machined parts

Abstract

Keywords

Introduction

Literature review

Basic concepts and notations

Methodology overview

Feature library

Feature representation method

Analysis of standard features

Analysis of interacting features

Analysis of edge-associated interacting features

Analysis of surface-merging interacting features

Analysis of edge-missing interacting features

Analysis of surface-split interacting features

OFERA

Overall process of OFERA

Standard feature extraction and recognition ( OFER A std )

Interacting feature extraction and recognition ( OFER A intr )

Case studies

Illustrative case study 1

Illustrative case study 2

Illustrative case study 3

Conclusion

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References

Standard feature extraction and recognition $(OFER A_{std})$

Interacting feature extraction and recognition $(OFER A_{intr})$