maximally convex volumes

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1 appears in Computer-Aided Design, 31(2), pp , CUSTOM-CUT: A Customizable Feature Recognizer Daniel M. Gaines gainesdm@vuse.vanderbilt.edu Computer Science Department Vanderbilt University Caroline C. Hayes hayes@me.umn.edu Department of Mechanical and Industrial Engineering University of Minnesota Keywords: Feature Recognition, Process Planning, CAD/CAM Abstract The tools and processes available in a given shop greatly inuence the way in which manufacturers view a part and the way in which they decompose it into machinable volumes, or features. Likewise, a feature recognizer should be able to produce a dierent feature decomposition when dierent tools are available. Additionally, it should be easy for a user to add new tool descriptions to the system in order to maintain and customize the feature recognizer. We address this challenge in two parts. First, we present an extensible representation which allows users to easily add their own custom tool descriptions to a feature recognizer's knowledge base. Second, we present CUSTOM-CUT, a tool-based, resource-adaptive feature recognizer. CUSTOM- CUT accepts the user-dened cutting tools as input and automatically identies the areas of the part that can be cut using the custom tools. We call CUSTOM-CUT resource-adaptive because the features it identies will be dierent if it is given dierent cutting tools. The advantages of this is that it is easier for the user to maintain and customize and provides greater assurance that the features identies are actually machinable with the given set of equipment. 1 Introduction The tools and processes available in a given shop greatly inuence the way in which manufacturers view a part and the way in which they decompose it into machinable volumes, or features. For example, Figure 1 shows how adding a new tool shape adds additional ways of breaking the part down into machinable volumes. In order to eectively support a human or computer-based process planner, a feature recognizer must be able to identify the shapes tools such as this one can create. Furthermore, it must be easy for the user, who may not be a programmer, to update the feature 1

2 recognizer's knowledge base with new equipment descriptions. Therefore, the goal of this paper is to design a feature recognizer that: 1. Allows users to specify their own, possibly special purpose tools. 2. Shows them the impact that adding those tools will have on the feature decomposition. 3. Shows them the impact that adding those tools will have on the manufacturing methods that can be used in the process plan. maximally convex volumes V1 V2 V (a) part (b) features found by various feature recognizers (c) an additional feature interpretation needed when new tool is added Figure 1: Various ways of decomposing a part into features. The challenge in achieving these goals is that the machining equipment interacts in complex ways to create a wide variety of shapes. Previous approaches attempting to catalog these shapes in a set of feature classes have resulted in systems that can be dicult to maintain, restricted in the range of parts handled and have diculty identifying features when they intersect. Signicant progress has been made by recent trace-based feature recognizers (Han and Requicha, 1995; Gupta et al., 1994) in overcoming the ambiguities created when features intersect. Volume-decomposition 2

3 approaches (Shah et al., 1994; Kim, 1994) can recognize a broader range of feature types across domains, however, system maintenance still remains a problem. We address the maintenance goal in several parts. First, we present an extensible tool representation which allows users to easily add their own custom rotational tool descriptions to a feature recognizer's knowledge base. Second, we present a knowledge acquisition tool, TOOL-EDITOR, that provides a convenient interface for designing new cutting tools. Third, we present CUSTOM-CUT, a tool-based resource-adaptive feature recognizer that can identify the regions in the part that can be cut with each user-dened tool. We call it tool-based feature recognizer (rather than trace-based or volume decomposition-based) because its method uses manufacturing process and resource information to identify areas of the part that can be created with combinations of the process resources. We say that it is resource-adaptive because the features it identies will change when the user supplies it with dierent 3-axis manufacturing resources descriptions (i.e. dierent tool shapes or motions). 1.1 MEDIATOR CUSTOM-CUT is a component of the MEDIATOR feature recognition system. We describe MEDIATOR mainly to put CUSTOM-CUT and TOOL-EDITOR in context. One of MEDIATOR's interesting properties is that it combines feature recognition tasks with process planning tasks to the benet of both processes. Thus, as the manufacturing resources change, so do the features that MEDIATOR recognizes. Additional subsystems in MEDIATOR, which are outside the scope of this paper, are CUT-IT, which nds features for standard tooling and CLAMP-IT, which assesses the clamping feasibility for each tool approach direction proposed. MEDIATOR is organized into four types of components: blackboards, which MEDIATOR uses to store and share information, processing agents, that perform the reasoning, knowledge bases that 3

4 contain knowledge about the machining equipment and a knowledge acquisition tool that helps users enter and update information in the cutting tools knowledge base. The heavy lines in Figure 2 indicate components of MEDIATOR that will be the focus of this paper. MEDIATOR's inputs are CAD models of the part and stock. Its outputs are a the features found in the part and a set of candidate machining methods for each feature. Each machining method species the cutting tool, tool approach direction, machine tool motion requirements and clamping conguration that can be used to create a feature. stock part low-level Problem Description CAD model MEDIATOR Blackboards: Processing agents: Knowledge bases: Knowledge Aqusition Tools: Goals Operators Operators features tool methods fixture methods Information bus INITIALIZE-IT Initialization CUT-IT Cuttability analysis Custom-CUT Cuttability analysis CLAMP-IT Clampability analysis Standard Cutting Tool Shapes User-Defined Cutting Tool Shapes Machine Tool Motions Fixture Knowledge d 1 θ θ d d 3 θ 3 r 1 θ 4 r2 θ 5 d 4 Tool Editor COORDINATOR Setup planning Figure 2: MEDIATOR architecture Blackboards MEDIATOR uses four blackboards to pass shared information among the reasoning agents and to gather information about the features: features, tool methods and xture methods. Agents can read 4

5 or write to any of these blackboards. Each feature on the features blackboard contains one or more links to methods in the tool methods blackboard. Each cutting tool method describes the cutting tool's shape, orientation and machine tool motion requirements that can be used to create the feature. Finally, the xture methods blackboard contains one or more xturing congurations for each tool approach that may be considered. CUSTOM-CUT writes only to the rst two blackboards Processing Agents MEDIATOR consists of four processing agents: The INITIALIZER generates the delta volume from the part and stock and identies faces that require machining, CUT-IT and CUSTOM-CUT identify faces and volumes in the part that can be machined with the given cutting and machine tool resources and CLAMP-IT generates clamping congurations for each tool approach direction. CUSTOM-CUT's task is very similar to CUT-IT's. The dierence is that CUT-IT allows users to select from a set of standard rotation cutting tools (such as at endmills and ball endmills) and identies the features for that particular combination of tools, while CUSTOM-CUT allows users to describe their own custom-designed cutting tools and identies the areas of the part that can be cut using the custom tools. Currently, the user decides whether to run CUSTOM-CUT or CUT-IT on a given part. In future versions, we may rst apply CUT-IT, and then use CUSTOM-CUT to work on any areas of the part that CUT-IT could not handle. 1.2 Knowledge Bases Each agent accesses accompanying knowledge bases that describe properties of the machining equipment it reasons about. The Standard Cutting Tool Shapes knowledge base provides CUT-IT with information about the shape of standard cutting tools. The User-Dened Cutting Tool Shapes 5

6 knowledge base contains geometric models of user-dened cutting tools for use by CUSTOM-CUT. This knowledge base provides the user with more exibility than the Standard Cutting Tool Shapes allowing the user to design more complicated cutting tool shapes. The representation used for this knowledge base will be described in the Section 3.2. The Machine Tool Motions knowledge base also serves the CUSTOM-CUT agent by providing information about the motion capabilities of the available machine tool. The motion capabilities of machine tools is represented in CUSTOM-CUT using vectors and arcs, as shown in Figure 3. This gure represents the motion capabilities of a 3-axis machine tool. The single dotted line segment denotes the tool spindle in the \home position." Each vector represents a degree of freedom, i.e. a direction in which the tool spindle can move from the home position. Finally, the Fixture knowledge base provides CLAMP-IT with information about the xturing devices. 3-Axis Mill z y x Key tool spindle translational motion Figure 3: Representation of 3-axis machine tool motions. 6

7 CUSTOM-CUT's inputs are a set of cutting tool and machine tool descriptions and the delta volume of the part (the dierence between the stock and part). CUSTOM-CUT uses this information to generate methods for machining individual faces in the delta volume. As the methods are generated, CUSTOM-CUT builds features by identifying the set of faces that can be machined with each method. The output of CUSTOM-CUT is a set of features representing shapes in the part that can be cut with each of the custom tools in the database, and a set of machining methods for creating each feature. Each machining method states the type of cutting tool to use, the orientation of the cutting tool, the volume of material that will be removed from the part by this method and the machine tool motions that will be required. 2 Related Work We coarsely divide feature recognition approaches into three groups. 1) manufacturing-feature approaches use a library of feature shapes to characterize the shapes that a given set of manufacturing processes can produce in a part. 2) Volume decomposition techniques decompose parts into primitive volumes, later a post-processor can be used to map these general features to specic manufacturing features so they can be used by process planners in a specic domain. Finally, 3) tool-based reasoning from properties of the manufacturing equipment. Manufacturing-feature approaches: A manufacturing feature library is a set of manufacturing features, each of which represents a class of shapes, such as slots, holes and pockets, which characterize the types of shapes that can be produced with a given manufacturing process. Feature extractors (Joshi and Chang, 1988; Vandenbrande and Requicha, 1993; Jong and Fuchs, 1994; Han and Requicha, 1995) search the part's geometry for instances of features in the library to determine if the part can be produced. This makes it easy to support downstream reasoning, such as setup 7

8 planning and tool path planning, because the features are well dened and methods for producing them, and therefore the interactions among the features are known in advance. A disadvantage of manufacturing-feature approaches is that they compile in knowledge about many types of equipment, such as the cutting tools, machines and xtures. The problem is that when a tool or machine is added or removed from the machine shop, it often changes the types of shapes that can be made in that machine shop, or the way a part should be decomposed into features. One can update the feature class descriptions to reect these changes but it is often dicult to infer what changes should be made. It can also be dicult to verify that the feature library completely covers the set of shapes that the equipment can produce. While it is possible to add new features classes to the library to account for missed shapes, as (Shirur and Shah, 1996) points out, it is not convenient. Volume decomposition approaches: The intent of volume decomposition based approaches is to avoid the restrictions imposed by a pre-dened feature class library. Several techniques, such as half-space partitioning (Shah et al., 1994; Sakurai, 1994) and convex decomposition (Woo, 1982; Kim, 1994), have been developed for decomposing a part into primitive volumes. The primitive volumes are dierent from the feature volumes described above as they do not necessarily correspond to shapes that a process can produce. Instead, they have some basic property, such as convexity. Unlike feature classes, these volumes are not explicitly linked to manufacturing processes at the time they are identied. However, to be used by a process planner, these volumes must be mapped to the manufacturing processes which can create them. Some example of mapping processes include (Shah et al., 1994; Shirur and Shah, 1996; Gaines et al., 1995). Thus, the domain specic work is not avoided by these systems, rather it is pushed further downstream into the post-processor. Furthermore, the domain independence of these methods prevents the use of domain specic knowledge to help guide the decomposition of the part into appropriate volumes. Tool-Based approaches: Tool-based approaches use knowledge about the available equipment 8

9 and processes to identify the features in a part. Examples of tool-based approaches include (Gaines et al., 1996; Stage et al., 1997; Laxmiprasad and Sarma, 1997; Lee, 1997). Like volume decomposition methods, tool-based methods avoid the restrictions derived from using pre-dened manufacturing-feature classes. However, rather than using a purely geometric process to decompose a part, like volume decomposition methods, tool-based methods use properties of the tools and processes to direct the construction of features. A distinction that marks this class of approaches is that as they generate features, they simultaneously identify methods for creating the features. For example, instead of using a pocket feature to represent a shape the equipment can create, a tool-based approach represents the shapes of the tools and the degrees of freedom of a machine tool and uses \rst principles" reasoning to identify which portions of the part can be created with the processes. There have been a number of \hybrid" approaches which combine aspects of the tool-based technique. For example, (Gupta et al., 1994) combines trace-based and tool-based reasoning while (Shirur and Shah, 1996; Gaines et al., 1995) merge volume-decomposition and tool-based. The approaches mentioned above are all restricted to reasoning about standard sets of cutting tools. Adding additional tool shapes requires re-programming. CUSTOM-CUT's advances are twofold: 1) It allows users to easily enter custom-designed tool shapes using TOOL-EDITOR, and 2) it can identify the features in the part that the user-dened tools can cut, without requiring re-programming of the system. 3 An Example of Representing Cutting Tools with TOOL-EDITOR Often, when making large batches of parts in a long production run, machinists design custom cutting tools to reduce the number of operations required to machine a part. Therefore, it is 9

10 advantageous for a system to allow users to dene their own custom cutting tools and to identify the regions in the part these tools can create. This example will show how users can add their cutting tool descriptions to the CUSTOM-CUT feature recognizer using TOOL-EDITOR and how CUSTOM-CUT nds the shapes these tools can create. Figure 4: A custom tool (adapted from (Sandvik Coromat, 1995)). 3.1 TOOL-EDITOR: A Knowledge Acquisition Tool TOOL-EDITOR is a knowledge acquisition tool that allows users to customize CUSTOM-CUT to t their own needs by describing their own custom designed tools. Figure 5 shows a screen capture of the TOOL-EDITOR user interface. The left side shows the user's two dimensional sketch of a custom tool's vertical prole. The right side contains a three dimensional rendering of the tool. The dialog boxes at the top allow the user to edit the prole and add constraints on its dimensions. 3.2 User-Dened Cutting Tool Shapes Knowledge Base TOOL-EDITOR stores each of the user-dened cutting tools in MEDIATOR's User-Dened Cutting Tool Shapes knowledge base. We developed a new representation for storing these custom-designed tools by extending the National Institute of Standards and Technology's (NIST) requirement specication for modeling manufacturing resources (Jurrens et al., 1995). It was necessary to extend the NIST representation to allow users to add their own cutting tool designs. This section will describe the 10

11 Figure 5: TOOL-EDITOR. representation, showing how TOOL-EDITOR represents the cutting tool in Figure 4. Each entry in the User-Dened Cutting Tool Shapes knowledge base represents a class of tools. Each tool class describes the general geometry shared by all tools in the class. The class also describes the constraints on the minimum and maximum dimensions of tools. The geometry of each cutting tool class is represented using several two-dimensional cross-sections called proles, one vertical and one or more horizontal proles. Each prole consists of segments and segment joints. Figure 6 shows how the custom tool from Figure 4 is represented in CUSTOM-CUT. The gure includes a three-dimensional rendering of the tool shape and the two-dimensional parametric 11

12 representation of the tool's vertical prole and two of its horizontal proles. Below the gure the constraints on the segments and segment joints in the tool's vertical prole are listed in counterclockwise order. Vertical Proles: Vertical proles represent the shape of one cross-section of the tool and are composed of segments and segment joints. Segments: Segments represent the geometry of surfaces in the tool and can be either a line segment or an arc segment. Segment Constraints: Each segment has a number of constraints attached to it that describe the range of dimensions which specic tools in a class may have. A constraint includes a parameter and a range. A line segment has a single constraint on the length of the line. For example, the constraint on line segment d 6 in Figure 6 indicates that all tools in this class are at least 0.25" long for this dimension and no longer than 2.00". An arc segment includes a constraint on each of these parameters. As an example, r 1, r 2 are the major and minor axes for one arc segment in the vertical prole of Figure 6. 6 is the constraint on that arc segments length. Segment Joints: Adjacent prole segments are connected by segment joints. The segment joints carry a constraint on the angle at which the two segments meet. For example, 8 in Figure 6 constraints the line segment d 6 to meet its adjacent line segment, d 7 at 90. Segment Labels: Each segment in the prole is labeled by the user as \cutting" or \noncutting." Once the user is done entering a tool description, CUSTOM-CUT makes an additional label on each segment in the tool's vertical prole as being free or xed. The function of free and xed labels is to allow CUSTOM-CUT to make a rst pass guess at whether or not a given surface on the tool can be used to cut a surface larger than itself in the part. The tool surfaces that can cut surfaces longer than themselves are labeled as \free" (as shown in Figure 7 (a)). The tool surfaces, such as d 6, that cannot cut surfaces longer than themselves are labeled as \xed." Otherwise, they 12

13 Tool vertical Tool Prole horizontal d 1 r r 3 4 Component Type θ2 d 2 d 3 θ 3 d 4 θ4 d 5 θ 1 θ 5 θ 7 d 6 θ 8 d 7 θ 6 r 1 Tool Constraints (in counter-clockwise order) Component Type Parameter Values line segment d 1 2:00 00 d 1 9:00 00 segment joint 1 1 = 270 line segment d 2 1:50 00 d 2 4:00 00 segment joint 2 2 = 90 line segment d 3 0: d 3 2:00 00 segment joint 3 90 < 3 < 180 line segment d 4 0:25 00 d 4 1:0 00 segment joint 4 90 < 4 < 180 line segment d 5 0:25 00 d 5 1:0 00 segment joint 5 5 = 180 arc segment 6 6 = 90 arc segment r 1 0: r 1 1:0 00 arc segment r 2 0: r 2 1:0 00 segment joint 7 7 = 180 line segment d 6 0:25 00 d 6 2:0 00 segment joint 8 8 = 90 line segment d 7 0:25 00 d 7 4:00 00 Key Constraints Parameter Type line segment d - length of line r 1 - radius of major axis arc segment r 2 - radius of minor axis - angle of arc segment joint - angle of joint r 2 θ 9 r r 5 6 Segment Symbol cutting non-cutting cutting non-cutting Figure 6: Example tool and prole P (adapted from (Sandvik Coromat, 1995)). θ 10 13

14 are labeled as \xed." Figure 7 (b) shows how if one tries to use tool surface d 6 to cut face 1, which is longer than d 6, then tool surface d 5 will cut o the top of face 1 as the tool moves downward. d 3 tool tool d 5 d 6 d 7 part part (a) free segments (b) a xed segment cannot cut larger surfaces Figure 7: Some tool surfaces can machine surfaces that are larger than they are. Figure 8 shows how CUSTOM-CUT computes the free and xed labels for each segment. Each line segment is extended at both endpoints. If the extension intersects the tool, then the segment is labeled \xed." Otherwise, it is labeled \free." A similar test is performed for arc segments. An arc segment is free if it is convex, and lines extended along the tangents of the arc endpoints do not intersect the tool. These labelings will be used when CUSTOM-CUT matches tool proles with surfaces in the part to see if cutting surfaces in the tool can machine larger surfaces in the part. It is important to note that, while the free and xed labels tell CUSTOM-CUT if a tool surface might be able to machine a larger surface, they do not guarantee that it will be able to machine the surface. CUSTOM-CUT must also determine if the machine tool can provide the machine tool motion required to move the tool along that surface. 14

15 d 7 d 6 d 4 free fixed fixed Figure 8: Free/xed labelings for prole line segments. Horizontal Proles: Each cutting segment in a vertical prole includes a pointer to a horizontal prole. These horizontal proles represent the horizontal cross-section of the tool at the midpoint of each segment. The representation used for horizontal proles is identical to that used for vertical proles. For rotating tools, like those used in milling, each horizontal prole is a single circular arc segment. Two horizontal proles are shown for the tool in Figure 6. An extension to the NIST tool representation. CUSTOM-CUT's representation for cutting tools is an extension to the National Institute of Standards and Technology's (NIST) requirement specication for modeling manufacturing resources (Jurrens et al., 1995). NIST's representation includes generic tool classes such as endmill, dovetail mill and angle mill, but does not explicitly describe those tool shapes geometrically. The user can select from these classes but cannot dene their own custom tool shapes. Because the shape information is only implicitly represented in the NIST tool class names, it does not lend itself well to the detailed and explicit geometric reasoning that CUSTOM-CUT performs. CUSTOM-CUT extends the NIST representation by describing the geometry of the tools explicitly and allowing users to design their own tool classes. 15

16 4 Recognizing Features with CUSTOM-CUT In this section, we will show what CUSTOM-CUT will do with the tool entered by the user in Figure 6 when applied to the part shown in Figure 9. We will begin by showing the inputs to CUSTOM-CUT which are created by MEDIATOR's INITIALIZER agent. face f f21 z f16 f12 f6 f1 f17 f18 f13 f14 f15 f2 f3 f9 f11 f7 f8 y f20 x f19 part stock Figure 9: An example part and stock. INITIALIZER. MEDIATOR's rst agent identies which faces in the part require machining. These surfaces are identied by subtracting the part from the stock to obtain the delta volume. Each face that belongs to both the delta volume and the part is a face that requires machining. Figure 10 shows the results of the initialization for the example part. The shaded faces will require machining. In the remainder of this example, we will show how CUSTOM-CUT works on face f, the bottom face of the complex pocket in Figure CUSTOM-CUT Architecture Algorithm 1 contains an overview of the CUSTOM-CUT algorithm. The rst agent, Match Cutting Tools identies directions from which the tool can approach each face in the part, the faces it 16

17 * stock part delta volume faces to be machined Figure 10: Initialization. will come into contact with at each of these directions and the machine tool motions that will be required to machine those faces. The second agent, Match Machine Tools determines if the machine tool is capable of providing the motion requirements needed. The motivation for this method is similar in spirit to trace-based approaches for manufacturing feature-class recognition (Han and Requicha, 1995; Gaines et al., 1995). That is, the part geometry can be used to provide clues for the machining operations the can be used to create it. Tracebased feature-class recognition works by relating part geometry to the geometry of feature classes. In contrast, CUSTOM-CUT works by relating part geometry to the geometry of the cutting tools. When a cutting tool passes through a part, it leaves a trace of its geometry in the part faces it leaves behind. Therefore, we can work backward from these faces to identify the geometry of the cutting tools which may be capable of leaving those same faces. To do this, we need a way of comparing the part geometry with the cutting tool representations described in the previous section. Because the cutting tools are represented as 2-dimensional cross-sections, if we take similar cross-sections from the part model, we can easily compare the shape of the part with the cutting tool proles. The slices we take of the part will provide clues for the possible orientations of the cutting tools. The tools will be aligned such that segments in the cutting tool align with segments in the part slices. The shape of the cutting tool can then be compared with the shape of the part by matching 17

18 Algorithm 1: CUSTOM-CUT. CUSTOM-CUT(Part, Volume, Cutting Tool Shape, Machine Tool Motions) foreach face to be machined, f, in Volume, and each cutting tool, t Match Cutting Tools Agent: Identify Shape Slices of gets a set of slices (one slice for each face in the part adjacent to f). Find Tool Alignments nds the candidate set of alignments from which tool t can approach face f foreach alignment, a Match Vertical Prole determines at which alignments tool t matches the shape of the part. For each alignment that matches, three results are produced: i a feature (set of faces that will be machined with this operation) ii constraints on the size of t iii requirements for machine tool motion posted to tool motion requirements blackboard Match Horizontal Proles compares the horizontal cross section of the tool t. foreach feature found by Match Shapes Match Machine Tools Agent: Match Motions nds machine tool motions for each tool motion requirement for this feature. corresponding segments in the tool prole and part slice since, if this tool were used to machine the part, these are the faces it would leave behind. Finally, if the tool shape matches, constraints on its dimensions can be gathered from the part slices to ensure that the tool will create the faces of the appropriate size. Because slices are used to determine candidate approach directions and compare tool geometry to part geometry, care must be taken so that slices are taken in positions that will lead to \interesting" approach directions for the tools. The method we use is to take slices with respect to the faces that are adjacent to the face we wish to machine. The idea is that, since the tool geometry must match the geometry of these faces, we want are slices to contain information about these faces. However, this method is only a heuristic and may miss important information. For example, 18

19 not all possible approach directions will be contained in a nite number of part slices. Consider for example that the side of a at endmill can machine a planar face from an innite number of directions. Not all of these directions will be useful, however, because xturing considerations must also be considered. The use of adjacent faces is motivated by the notion that these adjacent faces may provide clamping surfaces, and thus, will lead to useful approach directions. 4.2 Match Cutting Tools Agent Match Cutting Tools identies which cutting tool classes can create the face and what tool approach directions may be used. The agent does this using three subsystems: Identify Shape Slices of generates a set of two-dimensional cross-sections, called slices, of the delta volume, Find Tool Alignments uses these slices to identify possible directions from which the tool can machine the face, and Match Shapes compares the geometry of the cutting tools with the geometry of the slices at each approach direction Identify Shape Slices of The rst task is to determine the directions from which the cutting tool can machine a given face, such as face f in Figure 9. The choice of approach directions is constrained by the shape of the cutting tool and the way face f interacts with its adjacent faces. To identify possible approach directions, CUSTOM-CUT compares the shape of the cutting tools with the shape of the part by generating two-dimensional cross-sections of the delta volume, called slices. A slice is generated for each of the 6 faces that are adjacent to f in this part. The adjacent faces are f 1 through f 5 and f 19 (shown in Figure 9). Figure 11 illustrates the slice generation process for the slice through face f 1. Their common edge, e 1, is used to dene a cutting plane for the slice. The slice passes through the midpoint of e 1 19

20 and is oriented so that it is perpendicular to the edge at its midpoint. The choice of the edge's midpoint is somewhat arbitrary. The slices could have just as easily been taken at the endpoints, or any other point along the edge. In fact, the algorithm can be easily modied to take slices at a number of points along the edge. This would provide more information about the shape of the part but would signicantly increase the computational expense of the algorithm. face f 1 cutting plane commone edge e 1 midpoint f 2 f 3 face f f 4 f 1 f f 5 (a) part (b) close up of slot slice s cutting plane 1 material to remove material remaining (c) slice s 1 in the part (d) slice s 1 Figure 11: Example of slice creation. 20

21 Figure 12 shows the set of unique slices for f. The slices for f 1 and f 5 are identical, as are the slices for f 3 and f 19. Therefore, only four unique slices are generated. Each segment in the slice is labeled with the part surface that it represents. Match Cutting Tools Agent part and 4 unique slices s2 s s 3 1 s 4 face f Identify Shape Slices a) slice s1 slice s 2 slice s 3 slice s 4 face f face f face f face f c) alignment a d) alignment a b) alignment 2 s1 3s1e) a1s alignment a f) alignment a 1 s 4 s1 5 g) alignment a 1 1s h) alignment a 3 4 s3 Find Tool Alignments face f Figure 12: Some example of possible alignments of the prole for face f Find Tool Alignments The slices from the previous step are used to identify a set of candidate approach directions from which the cutting tool may be able to machine face f. CUSTOM-CUT must also identify which cutting surfaces in the tool will be in contact with face f for each approach direction. The tool approach direction and cutting surface which contacts face f together are called an alignment. The alignment identication process is as follows. First, the segment shape (line or arc) of face f in each slice is noted. For example, in slices s 1 - s 4 (Figure 12) face f appears as a line segment. This is necessarily the case since face f 1 is planar. However, non-planar faces, such as cylindrical faces, may appear as arc segments in some slices and line segments in others. Given a slice and a cutting tool, alignments are identied by nding each segment in the tool's 21

22 vertical prole with the same shape (line or arc) as face f in that slice. Alignments are made by aligning each of these segments with face f. Figure 12 (b)-(f) shows some of the alignments for the example cutting tool found for slice s 1. In each one, a dierent linear cutting surface from the tool is aligned with face f. Note that, although a s1 1 and a s1 4 have the same approach direction, they are dierent alignments because they align dierent tool segments with face f. The labels for the alignments in the gure denote the slices used to generate the alignments. For example, alignment a s1 2 (Figure 12 (c)) is the second alignment for slice s 1. Some of these alignments will eventually be identied as invalid. Alignment a s1 3, for example, is invalid because the end portion of the tool will cut too deeply into the part. This problem will be detected by later stages in the algorithm. Combining redundant alignments. In some cases, two dierent slices may produce some of the same alignments. For example, Figure 12 shows that alignment a s1 5 is generated by all of the slices. Two alignments are considered the same if they align the same tool segment with face f and have the same approach direction. Redundant alignments are simply shown as having multiple parents Match Shapes At this point, CUSTOM-CUT has identied a set of alignments that the cutting tool may be able to use to machine face f. However, the tool will come into contact with other faces in the part. Match Shapes eliminates any alignments where the tool does not match each of the alignments parent slices. Additionally, for each valid alignment, Match Shapes identies: 1) the set of faces that can be machined along with face f and 2) the constraints that these faces impose on the tool's dimensions. Match Shapes rst matches the vertical prole of the tool and then each of the horizontal proles. 22

23 Match Vertical Prole. Given an alignment, this step matches the tool with the part faces in each of the parent slices. This comparison will determine if 1) the geometry of each cutting segment in the tool matches the geometry of the part segment contacted in the slice and 2) the segments in the tool locally avoid collision with the part. Those alignments that do not satisfy these conditions are eliminated. For the groupings that do satisfy the conditions, there are three results: 1) constraints will be placed on the dimensions of the vertical prole, 2) tool motion requirements may be written to the motion requirements blackboard and 3) contiguous part faces which can be made in the same cutting operation with face f will be placed on the features blackboard. Figure 13 shows the matching process for slice s 3, one of alignment a s1 5's parents in Figure 12. The algorithm does a \walk" around both the tool and the slice, starting at face f in the slice and the corresponding tool segment, segment d 7. The algorithm walks outwards from this pair of segments in both clockwise and counter-clockwise directions, matching segments and segments joints of the tool and slice as it goes. slice s <= d7 <= 6 d 7 d <= d7 <= 2 end end start face f = 6.0" face f 3 = 2.0" a) part and slice b) matching process c) tool profile Figure 13: Matching the vertical prole of the tool against slice s 3. A tool segment matches a slice segment if it passes each of the following two checks. 1) 23

24 The segment shape check is passed if the tool segment's type (line or arc) is the same as the slice segment's type. For example, segment d 7 and slice segment f are both line segments, so this check is passed. 2) The segment dimension check is passed if: a) the tool segment is free, or b) the tool segment is xed (See Section 3.2) and the dimensions of the slice segment are within the range dened by the tool segment's constraints. For case a), if the tool segment is shorter than the slice segment, a motion requirement is written to the motion requirements blackboard. For example, if a 2" diameter endmill is to cut a 4" wide slot, then the endmill must move in the horizontal direction. For case b), if these are line segments, a constraint is added to the tool segment stating that its length must equal the slice segment length. If they are arc segments, constraints are added to the tool segment stating that the major and minor axes and the arc length must equal the corresponding dimensions from the slice segment. If both of these checks are passed, the face represented by the slice segment is added to a set of faces which can be machined with this cutting tool at this tool alignment. Returning to the example, face f is 6:0 00 long in this slice but d 7 is constrained to be no longer than 4:0 00 (See constraints in Figure 6). However, d 7 is free, therefore the motion requirement shown in Figure 14 is written to the motion requirements blackboard and the check is passed. The joints on the left side of the tool segment and slice segment are not checked because the slice segment joint connects to a face that does not belong to the part. A tool segment joint matches a slice segment joint if it passes each of the following two checks. 1) The segment joint shape check is passed if the tool segment joint has a) the same convexity, (i.e. convex or concave), as the tool segment joint and b) the same blending type (i.e. smooth or sharp) 1 as the tool segment joint. 2) The segment joint dimension check is passed if the angle of the slice segment joint is within the range dened by the tool segment joint's constraints. If both 1 More precisely, the tool segment joint and tool segment joint are required to have the same g1 continuity. 24

25 motion requirement z y x Figure 14: Tool motion requirement found for example part. checks are passed, a new constraint is added to the tool segment joint stating that the joint must equal the angle of the slice segment joint. The walk around the tool and slice terminates with success when any of these three conditions are satised: 1) there are no more segments in the tool or slice to match, 2) the next slice segment represents a face that does not belong to the part or 3) the next tool segment joint is convex and the slice segment joint is concave. The walk terminates with failure when any of these two conditions occur: 1) a tool segment does not match the corresponding slice segment or 2) a tool segment joint does not match the corresponding slice segment joint. Any time a failure occurs, the alignment is eliminated. For our example, the walk ended in success. The dark lines in Figure 13 show the tool and slice segments that were matched. The dark segments in the slice represent the surfaces that can be cut in the same operation with face f. The combined set of faces that are matched by all parent slices are shown in Figure 15 in gray. These represent the set of faces that can all be machined at the same time as face f. They are tentatively grouped as a feature. Note that the tool will not be able to completely machine the entire area of face f 11. During the processing of other faces, CUSTOM-CUT will nd an operation 25

26 for machining the rest of this face. Figure 16 shows the updated set of constraints for the tool in this example. tool approach direction face f11 face f Figure 15: A feature: shaded faces can all be cut with the example tool from this approach direction. Constraints Component Type Parameter Values line segment d 4 d 4 = 0:5 00 line segment d 5 d 5 = 0:25 00 arc segment r 1 r 1 = 0:5 00 arc segment r 2 r 2 = 0:5 00 arc segment 4 4 = 90 line segment d 6 d 6 = 2:0 00 line segment d 7 0:25 00 d 7 4:0 00 Figure 16: New constraints on the tool class: the tool selected for the operation must fall within these ranges. Match Horizontal Proles. This step compares the shapes of the horizontal cross-sections of the tool with the group of faces found during Match Vertical Prole. For each pair of adjacent faces in the group, if their common edge is not perpendicular to the approach direction, a horizontal 26

27 slice is created which cuts through the midpoint of this common edge with a plane perpendicular to the approach direction. The horizontal prole associated with the tool segment that matched these faces during Match Vertical Prole is compared with this newly created slice. As an example, Figure 17 shows the slice created for faces f 1 and f 2. Because tool segment d 6 matched these faces in slices s 1 and s 2, respectively, the horizontal tool segment for segment d 6 is used in the match. edge slice horizontal tool profile Figure 17: Example horizontal slice. 4.3 Match Machine Tools Agent In the previous step, requirements for machine tool motions were identied. The next step is to decide if the machine tool can actually provide these motions Match Motions First, the machine tool is oriented according to the cutting tool alignment. Next, each of the motion requirements is compared with the motion capabilities of the machine tool to see if the machine tool is capable of moving the tool in that direction. This is done by checking if the required motion is a linear combination of the machine tool vectors. The motion required for the example tool to machine face f are shown in Figure 18. The machine tool is capable of producing all the motions, 27

28 so the feature in Figure 15 is posted on the features blackboard and alignment a s1 5 is posted on the tool methods blackboard as a possible method for creating the feature. Figure 18 shows the 3-axis motions that are found for the motion requirements posted during the Match Cutting Tools stage. 3-Axis Mill Figure 18: Matching tool motion requirements. A removal volume is generated by sweeping the prole of the cutting tool along a path around the face that is being machined, in this case it is face f. To avoid self-intersections, the algorithm checks to see if a path edge is \open" or \closed." A path edge is \open" if it is not on a part face, or, it is on a part face and the normal of the face at the intersection is parallel with the tool approach direction. A path edge is \closed" if it is not \open". If the path edge is \open" the tool prole is not used to create the sweep along that path edge. Instead, a linear edge is created with the same height of the tool's wire body. 4.4 Summary of Results for Example Figure 19 (a) shows the feature and method found for machining face f. CUSTOM-CUT runs on each face requiring machining in the part, nding methods for machining each face and the corresponding 28

29 cutting method cutting method feature 1 feature 2 face f face f 11 (a) feature 1 (b) feature 2 Figure 19: Features and cutting methods found for example part. features. Most of these features are subsets of the feature in Figure 19 (a), except Figure 19 (b) which shows a feature and method for machining face f Example 2 This example shows how using a custom cutting tool can reduce the number of setups required to machine the part. Suppose we ask CUT-IT to make the part shown in Figure 20 (a), a modied robot elbow housing. Recall that CUT-IT (Section 1.1.2) uses only standard cutting tools such as at endmills, ball endmills. Figure 20 (b) shows the set of 23 features found by CUT-IT. Given these resources, CUT-IT recognizes the slot on the left as being composed of two features. Note that the complex shape of the slot makes it necessary to use two operations to create each slot: the at endmill creates the planar surfaces, while a ball endmill creates the cylindrical surface. 29

30 slot (a) elbow part slot features and methods flat endmill ball endmill (b) features Figure 20: Features found for the elbow part using only standard tools. These features are passed to COORDINATOR, a setup planner (Faheem, 1998), which generated the 5 setup plan in Figure 23 (a). A separate setup is required to machine each slot (setups 1 and 2). Since no other operations in the part require putting the part in this orientation, it adds two additional setups to the plan to machine these slots. If the creation of the slots could be combined with some other setup then these setups could be avoided, and the plan shortened. Towards this end, the machinist/process planner designs the custom tool shown in Figure 21, and enters it into CUSTOM-CUT's library through TOOL-EDITOR. CUSTOM-CUT nds an additional 30

31 interpretation of the slots as a single feature each which can be made by the method shown in Figure 22. This method allows both of the slots to be cut from the same tool approach direction as the holes and circular pockets on the top side of the part. Figure 23 (b) shows the new plan generated by COORDINATOR. No extra setups are required for the slots. Thus, the addition of the custom tool allowed two cutting operations and two setups to be eliminated. Tool Vertical Profile Figure 21: A custom tool. 6 Limitations and Future Work The current version of CUSTOM-CUT has a number of limitations. The limitations include the approximation of the three dimensional solid with two dimensional slices, assumptions made about the tool shapes and machine tools, and restrictions in expressing machine tools. First, some constraints on the tool dimension and accessibility may be lost if the slices fall at inappropriate places in the part. If a slice does not happen to cut through the most narrow part of the passage of a complex pocket, then the proper constraint on the tool will not be found. This could lead CUSTOM-CUT to believe that a given cutting tool could machine the pocket even though 31

32 tool approach direction vise Figure 22: Alternative method for creating the slots with a custom tool. the tool is too wide. A possible solution may be to design specic algorithm for nding the most narrow passage, for example, see (Regli, 1995) for such an algorithm. The second limitation is that CUSTOM-CUT makes assumptions about the shapes of the cutting tools. CUSTOM-CUT assumes that the horizontal proles of cutting tools is a single circular arc. This restricts the set of tools CUSTOM-CUT can handle. For example, y cutters, which have an annular cross-section, and ram EDM bits, which have irregular cross-sections, are currently beyond the scope of CUSTOM-CUT. A y cutter can be eectively approximated with a single circular arc. This assumption is done for reasons of eciency and CUSTOM-CUT could be extended by modications to the Match Horizontal Proles, making it more similar to Match Vertical Prole. 32

33 initial stock setup 1 setup 2 setup 3 setup 4 setup 5 final part (a) plan using standard tools initial stock setup 1 setup 2 setup 3 final part (b) plan using custom tool and standard tools Figure 23: Two plans for machining the elbow part. The third limitation is that CUSTOM-CUT does not currently reason about the motion capabilities of machine tool's such as a lathe. CUSTOM-CUT's representation allows for complicated machine tool descriptions, but as of yet, the system has only been tested on 3-axis machine tools. Future work will include applying the technique to turning and mill-turning domains. 7 Conclusions This paper has described a representation for cutting tools that extends NIST's representation to allow users to dene their own custom tool designs and allow explicit reasoning about the tool geometry, TOOL-EDITOR, a knowledge acquisition tool which uses this tool representation to allow users to enter custom-designed tool descriptions, and CUSTOM-CUT, a feature recognizer that takes these tool descriptions and automatically identies the shapes the tools can create and the manufacturing operations used to create these shapes. 33

34 Together, TOOL-EDITOR and CUSTOM-CUT increase the maintainability and customizability of feature recognition and process planning. Benets of this approach are that it provides a convenient way for the user (who may not be a programming expert) to update the manufacturing knowledgebase without reprogramming the system. Additionally, it adds exibility to existing work in feature extraction by allowing the system to reason about the user's own complex custom-designed rotational tools, not just standard shapes. This exibility makes it possible for specic shops to tailor feature extraction software to meet their specic needs and resources, without programming knowledge. This work brings deeper reasoning about the requirements and capabilities of manufacturing equipment into feature recognition. With the increased integration of equipment knowledge, the feature recognizer is more robust, maintainable and able to provide downstream applications, such as setup-planning, with information suited to the particular capabilities and requirements of the available equipment. 8 Acknowledgments This work was funded by the Department of Energy 1996 Predoctoral Integrated Manufacturing Fellowship and was performed while the primary author was at the University of Illinois at Urbana- Champaign. 34