Machining algebra for mapping volumes to machining operations for developing extensible generative CAPP

Machining algebra for mapping volumes to machining operations for developing extensible generative CAPP

Shirur, Arvind


This paper presents geometric models for representing machining operations. The characteristic shapes produced by machining operations are represented in a uniform (canonical form. The canonical representation is an algebraic expression that encodes the geometric shapes that can be produced by a process as a set of volumes resulting from two types of toolworkpiece interactions. Each interaction is characterized by a type of sweep operator. The directors of these sweep operations are derived from cutting and feed motion directions. The profiles used in the sweeps are defined in terms of geometric entities and constraints based on tool geometry and tool-workpiece interaction. Most conventional machining processes can be represented using the proposed model (process-to-volume mapping). Inverse operators are also defined for mapping volumes to processes; the inverse operators can be used in selecting potential machining processes for removing given volumes. Thus, representation of machining knowledge is process-based not feature-based, which overcomes the problem of dealing with new feature shapes that are not predefined in the process selector. The formulation allows users to add new processes to the system without any changes to the code.

Keywords: CAPP, CAD, Generative Process Planning, Feature Mapping, Machining

2. Background

2.1 Introduction

The ultimate goal of this project is to develop a set of computational techniques to integrate CAD (computer-aided design) systems with CAPP (computer-aided process planning) systems without the need for human intervention. The major components of this study are as follows:

(i) Automatic bar stock selection for parts from

user-defined stock inventory.’

(ii) Volume decomposition based on half-space partitioning for machining feature

(iii) Machining algebra to map convex volumes to feasible machining operations based on nominal shape only.’

(iv) Mapping of dimensions and tolerances (D&T) from design features to machining features using DTF graphs based on entity degrees of freedom.5

(v) Incorporating D&T information in machining algebra for process selection.

(vi) Developing metrics for evaluating process plans and plan optimization.

This paper describes only the results of projects (iii) and (v).

2.2 Scope

Given a set of volumes to be removed (machining volumes) from a workpiece by machining, the problem is to determine a set of feasible machining processes that could do the job. Such volumes are usually obtained by decomposing the Boolean difference of the workpiece (bar stock, forging, casting) and the finished part. The machining volumes are usually convex; if they are nonconvex, a preprocessor is needed to decompose them into a set of volumes that are individually convex. Many volume decomposition techniques have been reported in the literature; an overview is given in section 2.4. This paper focuses on the next step after decomposition of removal volumes into convex machining volumes, that is, finding candidate machining operations that can produce each decomposed volume.

The scope of the project is limited to volumes bounded by “regular” surfaces, such as planar, cylindrical, conical, and spherical surfaces. Sculptured surfaces are not considered at this time, although the methodology could be extended with some modifications. The workpiece/part can contain sculptured surfaces, though, as long as they are not required to be machined; that is, these surfaces are assumed to be acceptable as produced by casting, forging, extrusion, and so on. Tool and workpiece motion can be either linear or rotational or a combination of the two; in the last case, the motion is decomposed into linear and rotational components.

It should be kept in mind that this paper looks at only a subset of problems related to process selection; the focus in this paper is on the selection of feasible processes based on nominal shape, size, and tolerances only. Process parameters (feeds, speeds), tool parameters (rake angles, etc.), cost, sequence optimization, and D&T mapping are not discussed in this paper, although they are part of the larger project; these topics are discussed elsewhere.5,6

2.3 Solution Strategy

One popular approach used in generative process planning for selecting machining processes is to find and classify portions of the part’s geometry into generic categories, such as through-holes, rectangular pockets, and so on; then hard-coded production (if-then) rules are used to select machining operations for each feature. Rules are typically written in the form: “If feature is of type X, of dimensions x1

2.4 Volume Decomposition

Volume-based feature recognition techniques are popular for recognizing machining features in generative process planning and some other applications. Several generic strategies have been proposed, such as: convex hull decomposition, orthogonal sectioning, and delta volume decomposition.^sup *7^ The end result of all of these are sets of volumes that need to be removed by machining. The objective of this

study is to develop a general-purpose methodology for matching volumes to machining processes, regardless of the particular method used for volume decomposition. Volume decomposition itself is not the subject of this paper, but the following overview is provided to understand the context.

All volume decomposition methods involve four major phases:2’l2

1. Determine volume to be removed (machined out) as the raw stock minus the finished part.

2. Partition each material removal volume into simpler subvolumes or cells.

3. Combine selected adjacent cells into potential “machining” features.

4. Match machining features to predefined stereotypical shapes, such as pockets, slots, and so on.

In step 2 a unique volume decomposition results, while step 3 generally produces many alternative sets of machining features. This reflects the fact that there usually are many alternative ways of machining a part. If the predefined features used in Step 4 are a priori associated with feasible machining processes that can produce them, then the final result is that it is known how each machining feature found can be made. This paper proposes an alternative to the hard-coding of rules for process selection by skipping step 4. Nevertheless, the method is compatible with most decomposition schemes that can be used for performing steps 1-3.

Convex hull decomposition follows a different strategy to produce a set of candidate machining volumes (features). The part is first subtracted from its convex hull, and the process is repeated until each volume is equal to its own convex hull, decomposing the part into an alternating sum of volumes.’3-IS A convex hull of an object is the minimal convex volume that can completely enclose the object. Delta volume decomposition is used to decompose machining volumes into units corresponding to distinct machining operations using various partitioning strategies.2,3,8-12 Regardless of the particular decomposition method, the result is the same: one or more alternative sets of machining volumes that then need to be matched to machining operations.

3. Literature Review

Process selection can basically be done by two approaches popularly known as variant and generative. In variant process planning, a classification scheme is used to associate standard process plans with part families. The part family code for the part for which a plan is sought is first determined; then the standard plan for that family is retrieved. The standard plan is then customized to the part at hand. In generative process planning, the computer system attempts to synthesize the process plan directly. For machined parts, the typical approach is to consider the part as a collection of machining features and do the planning on a feature-by-feature basis.

In the past, “if-then” production rules were the most commonly used techniques to code manufacturing knowledge in generative systems. The studies based on this method are too numerous to cite. In recent years, it has been recognized that the knowledge encoded in these rules is shallow (see section 2.3). Alternative ways are now being sought for capturing manufacturing knowledge in more fundamental terms. This paper only reviews these alternative systems, as they are the only ones relevant to the subject of this paper.

Vandenbrande and Requicha developed a method based on partial feature information called “feature hints.”12 Feature hints correspond to the minimum trace of a machining feature left behind as a result of feature interactions. The largest possible nonintrusive machining volume is then generated by extending the volume corresponding to the hint in a number of directions. The portions of the feature that are disconnected due to feature interactions are thus reconnected. Features are also segmented into optional and required portions to explicitly represent the interaction with other features. The algorithm does not define a formal method of choosing the feature elements as hints. The number of feature elements that can be considered as feature hints can be very large. Secondly, the feature hints result not only from the shape of elementary machining volumes but also from the possible ways of accumulating these elementary volumes.

Gupta et al.16 considered all the part surfaces that needed to be created and identified manufacturing feature instances capable of creating those surfaces. Further, they maximized the identified feature, that is, enlarged the feature, similar to “extending” of features used by Vandenbrande and Requicha,12 such that the feature volume did not intersect the part. The method can handle a variety of holes and pocket features with accessibility constraints on the features. Gupta et al.” represented machining features as a triple phi = (rem (phi), acc (phi), class (phi)), which are, respectively, removal volume, accessibility volume, and instance of some generic class of features, phi. They have defined a fixed finite set of features, Phi = {phi1, phi2, …} from which their system attempts to synthesize a given part. To perform a machining operation, a tool volume is swept linearly along a trajectory in a way that there is no interference with noncutting surfaces of the workpiece. This allows their method to handle linear swept features, such as slots, holes, pockets, and so on. The approach in this paper handles both linear and rotational sweeping and does not require a fixed finite set of features. Sakurai9 developed a volume decomposition method by using face extensions. All the faces of the object were extended to intersect with each other, from which edges were The volumes found from combining the cells are matched with the topological and geometric characteristics of a set of predefined features.

Common to all methods discussed so far in this section is that they require a set of predefined machining features. Even though one can add new features to these programs, the disadvantage is the continual burden of updating, and finding out that new features have to be added only after the program fails on a part that contains them.

Hsiao investigated the feasibility of creating a meta knowledge base to generate possible process plans for both predefined and undocumented features” (predefined features are defined as those design features that are known to the process selection program, while undocumented features are design features that the process selection program does not have knowledge of). In Hsiao’s knowledge base, a machining process was represented by its elementary machining volume, the limitations of tool motions, and size/tolerance limitations. The techniques described in this paper are an extension of the meta knowledge base idea proposed by Hsiao. The method in the present paper is more general and based on a uniform formal representation of machining processes that is suitable for use in geometric modeling.

4. Characterizing Machining Operations

A geometric model that is capable of representing most common machining processes in a uniform way was developed. Given the nature of the cutting tool-workpiece interaction characteristic of a machining process, the model can be used to represent the process in the form of an algebraic expression. Evaluation of the algebraic expression with specified parameters gives the machining volume, that is, the shape of the volume that will be removed by the process. This procedure will be called mapping from processes to volumes; however, for the problem of determining feasible machining processes for volumes produced by decomposition of removal volumes, the inverse of this mapping procedure must be executed. This will be called inverse mapping (from volumes to feasible processes). Use of this model in process selection does not require one to predefine the set of features for which process selection is to be made, since the model is process-based not feature-based. Thus, this method overcomes the limitations of shallow “if-then” rules commonly used for process selection, which require the comparison of machining volumes to predefined features. The following sections describe the machining process model in the following order: set operators, mapping machining processes to volumes, inverse operators, and inverse mapping of volumes to machining processes.

Metal cutting by any operation can be described as the successive removal of some characteristic shape, labeled an elementary machining volume, M^sub E^. Successive passes of the tool on the workpiece are equivalent to the growth of this volume in each of the feed directions. The machining (delta) volume, M^sub T^, is the resultant volume removed by one machining operation. The total removal volume, M^sub R^, is the material removed by all operations combined, that is, the union of all M^sub T^ for the part. It also corresponds to the Boolean difference between the raw stock and the part. To cut the material, the tool must spatially interfere with the workpiece and there must be a relative movement between the tool and the workpiece. In addition, of course, the material and structural conditions must be met for fracture of the workpiece layers to take place. This paper is only concerned with the geometric conditions, however. The geometry and constraints of machining operations can be represented by swept volumes, where the generator is the tool-workpiece interference and the director is the tool-workpiece relative motion. The tool-workpiece interaction can be divided into two basic types: the primary one causes the cutting action and the secondary ones correspond to feed.

4.6 Characterization of Machining Processes

The capabilities of machining processes that need to be considered in matching processes to volumetric shapes they can remove are as follows:

(i) Nominal shape that the process can produce based on kinematic freedom of the tool with respect to the workpiece.

(ii) Range of dimensions, tolerances, surface finish, etc.

(iii) Local tool access.

(iv) Global tool access.

(v) Minimization of tool changes and setups; fixturing requirements.

(vi) Material removal rate.

(vii) Relative cost.

(viii) Materials that can be processed.

This paper deals only with (i), (ii), and (iii); work on other topics is still in progress.

Most machining processes are capable of removing volumes having a variety of shapes. In the featurebased approach, each of the several shapes can be associated with a possible machining operation. The disadvantages of this were discussed previously in this paper. In the process-based approach, the capabilities of the process are represented in a way that they can be matched to shapes, regardless of whether the shape is predefined (pre-known to the system) or not. Most machining processes can be represented by Eq. (4b); they differ only in the values to the different operands in the machining expression. The way to differentiate between the processes is to look at the following:

(i) Constraints on the geometry of the generator profile P.

(ii) Constraints on the bi-vector Ve representing the cutting motion.

(iii) Constraints on the bi-vectors V1, V2 representing the feed motions.

(iv) Constraints on the relationships between operands.

The relationship between the variables P, V^sub e^, P^sub e^, v^sub 1^, P^sub 1^, v^sub 2^, P^sub 2^ are specific properties of the machining processes. For example, in a drilling operation, the vector v^sub e^, must be parallel to one straight edge of the profile P, and p^sub e^, must lie on the straight line along this edge. Previously, Figure 3 showed how these quantities are related to each other for two common machining processes. Each machining process has a different range of possible dimensions of the profile P. For example, there is a limit on the diameter of the drilling tool that may be used.

Constraints may be specified on composing geometric entities of a profile, on either position, orientation, size, or other attributes of the entities. Profile constraints are defined for each machining process using a generic syntax from Ali,la as follows:



constraint_name: name of the constraint, such as “parallel,” “perpendicular,” etc.

entity_1_type: type of the first entity, such as `point,” “edge,” etc.

entity-1: string that the calling application uses to identify the first entity, for example, “ve,’ “x_axis,” etc.

entity_2_type: type of the second entity.

entity_2: string used by calling application to identify the second entity.

relation-type: this is a word that can be either “=” or “”.

value: this is a decimal number specifying the value of the constraint.

Several common profile shapes have been predefined for convenience, but these definitions can be modified or extended using the above syntax. The mechanism for this is discussed in section 5.

4.7 Dimension and Tolerance Considerations in Operation Selection

Dimensions and tolerances (D&T) specified on parts are of the following two types:

1. Intrinsic. These define dimensions and variations of or between geometric entities that are all contained within a single machinable (delta) volume. The width of a slot, parallelism of opposite faces of the slot, roundness of a hole, flatness of a surface, etc., are examples of the intrinsic D&T.

2. Extrinsic. These define D&T of a machining volume with respect to other volumes or the stock. Examples of extrinsic D&T are position/orientation of a hole with respect to another hole or datum system on the part, perpendicularity of a hole axis with respect to the face on which the hole is drilled, and the location of a slot.

The above are D&T aspects of the part to be manufactured or of the machining volumes. In the process-based approach, the D&T capabilities of each process must be captured in addition to the shape capabilities encoded in the machining algebra. As described in section 4.6, one of the process characteristics is the set of constraints on the generator profile P. This profile definition contains not only the shape but also the size ranges that reflect the size capability of the process. For example, in the drilling process, a profile of the type shown in Figure 7a is used. The profile has three edges, el, e2, e3, where el \ e3 and el is at some angle to e2. The size of the hole that this drilling process will produce is represented by adding a distance constraint between the two edges, el and e3. The representation of this constraint in the syntax described in the last section is as follows:

(Distance) (line) (el) (line) (e3) (>) (min. dia.)

(Distance) (line) (el) (line) (e3) (

where min./max. dia. are actual numerical values that represent the maximum and minimum sizes of holes that the drilling process can produce. Similarly, the drill point angle range can be specified by a set of angle constraints between e 1 and e2.

Extrinsic D&T considers the relationships of the volumes with respect to their local datum. The relationship may be positional or orientational. For establishing the relationship, the removal volume is first resolved into its representative entity. For example, the axis of a hole is the resolved entity for the hole. Similarly, the midplane of a slot is the resolved entity for the slot. Having done this, the positional and orientational capabilities of processes are represented as constraint sets between this resolved entity and its datum entity. For example, in the drilling process above, the resolved entity of the hole generated by the drill is Ve (refer to Figure 7b). Its relationship with the reference entity R on the part is expressed in the process definition with the following constraint:

(Distance) (direction) (Ve) (axis) (R) (=) ( +/-0.05 * dim_value)

This constraint implies that the variation in the distance between the reference and the resolved entity can be maintained to a tolerance band of about 0.1 * dimension value by the drilling process. The dimension value is populated in runtime for each dimension. If the part dimension scheme calls for closer tolerance, then this process will not guarantee that tolerance.

Similar constraint sets are included for form/finish capabilities also. Thereby, it can be determined whether a process is feasible or not for producing the desired shape, size, location, and orientation within the specified dimensions and tolerances.

5. Implementation

A prototype system for mapping convex machining volumes to machining processes has been implemented using C++, ACIS geometric modeling kernel, and Motif XWindow based tools for the user interface. The design part is created using design features in an in-house modeler, the Arizona State University Features Testbed, which is based on ACIS.19 The convex volumes are produced by a decomposition system, which subtracts the part volume from the workpiece (bar stock) volume to get the total removal volume M^sub R^. M^sub R^ is then decomposed into minimal convex volumes, various combinations of which are concatenated into maximal convex volumes that are potential machining features (set of M^sub T^). The decomposer also determines the RDoF and TDoF of each M^sub T^. Details can be found in Shen and Shah,2 Shen,3 and Shah and Rogers.19 The input to the machining volume mapping system can come from any system that produces convex machining volume sets, such as Gupta et al.,16 Sakurai,9 Kim,14 and so on.

5.1 Implementation of Inverse Operators

Inverse mapping makes use of inverse operators (*^sup -1^ and .^sup -1^). The sweep operator (*) and dot operator () were not needed for the implementation.

Inverse Sweep Operator (*^sup -1^)

Two types of bi-vectors are considered: translational and rotational. In both cases, the inverse sweep operation involves splicing the volume using a plane to get a section profile. In the case of a translational bi-vector, the sectioning plane is perpendicular to the direction vector of the bi-vector. For the rotational bi-vector, the sectioning plane is along the axis of the rotation; that is, the plane contains the axis of rotation. In either case, the result is a wireobject that represents the section. From this wireobject, a profile representation may be obtained. Figures 8 and 9 illustrate examples of inverse sweep (*^sup -1^) operations for translational and rotational bivectors, respectively. The resulting profile in the case of a rotational volume (Figure 9) is split into two along the axis, and only one half is considered. Most solid modelers provide the functionality of sectioning solid models to get profiles.

From Figure 8 it is seen that the profile may be obtained by a slicing operation; however, for successful inverse operation, the length of the translational sweep bi-vector needs to be found. This length must be equal to the dimension of the machining volume along its translational direction. In the specific case when the closing surfaces at the two ends of the translational volume are both normal to the translational direction, the translational distance may be found as the distance between the two planar surfaces at the ends. In a general situation, it is necessary to find the dimension of any 3-D object along an arbitrary direction, U. One of the available alternatives is to use the bounding box functionality available in most solid modelers. Using this functionality, it is possible to determine the minimum bounding box that can completely enclose the solid model of the object (see Figure 10). The edges of the bounding box are parallel to the xyz directions. The following steps (illustrated in Figure 10) may be used to find the linear dimension of a 3-D object along a certain direction:

1. Orient the object and the direction U along the xaxis.

2. Find the bounding box of the object in its new position.

3. Get the dimension of the bounding box along the x-axis.

4. Return the object back to its original position and orientation.

The dimension of the bounding box along the x-axis obtained in step 3 gives the dimension of the object along the direction U.

Inverse Dot Operator (*^sup -1^)

Figure 11 shows a 2-D geometric entity, E, and a translational bi-vector, V^sub 1^. The inverse dot operation produces the entity G. Determining the geometric entity G from E and V^sub 1^ involves the following steps:

1. Identify all the straight edges (e2 and e5) that are parallel to the bi-vector V1.

2. If no edges are found, or if any of these edges are smaller in length than the length of the bi-vector V1, then the inverse dot operation is not possible.

3. The straight edges found in step 1 are reduced in length by an amount equal to the length of the bi-vector V1. The result is the entity G.

The above algorithm works equally well for rotational bi-vectors. However, in the case of rotational bi-vectors, circular edges with centers lying along the axis of the bi-vector are selected instead of straight edges; and instead of distances, angles are considered. It is important to note that the inverse dot operation on an object is possible only for some selected bi-vectors.

Figure 12 shows an example in which a 3-D entity E is inverse dot operated using a translational bivector V1. The result is the geometric entity G1. The following steps are used to determine the entity G1:

1. Identify all planar faces that have normals perpendicular to the bi-vector V1 (f1, f3) and all cylindrical faces that have axes along the direction of V1 (f2, f4).

2. If no such faces are found or if the faces do not form a set of adjacent faces with adjacency along straight edges parallel to VI, then the inverse dot operation is not possible. Also, the lengths of these straight edges must be greater than the length of the translational bi-vector VI.

3. For each of the planar and circular faces found in step 1, perform inverse dot operations using the bi-vector VI according to the method specified for dot operation on 2-D objects.

As described in the case of 2-D inverse dot operation, the above method works equally well for rotational bi-vectors; however, in this case, instead of planar faces, the faces that are identified in step 1 are either cylindrical or toroidal in geometry with axes along the specified bi-vector. The adjacency among these faces is along circular edges instead of straight edges. The algorithm for inverse dot operation for 2-D entities is used to get the result G.

5.2 Creating a Machining Processes Library

All of the process definitions are kept in a process database library, which is extensible so that the user can add new machining processes and update the machining process library. It should be pointed out that the need to add new machining processes is far less frequent than the need to add new features; thus, it is much more practical to maintain the processbased system rather than the feature-based system. In any case, the addition of a new process definition does not require any changes to the program code because the processes are defined by populating essentially an object-oriented database. The generic class mc_process encapsulates the constraints on the attributes of the profile, constraints on the motion of the M^sub E^, the type of interference, and certain other parameters of the machining process, as shown in Table 1.

Several properties in mc_processes, such as Constraints_on_ME, Constraints_on_vp, and Profile require the specification of geometric relations between composing geometric entities of a profile, on either position, orientation, size, or other attributes of the entities. Profile constraints are defined for each machining process using a generic syntax from Ali,18 which is not discussed here. Several common geometries have been predefined and stored in a library of profile_shapes. Table 2 shows one example of process definition (plunge milling) in terms of the generic properties defined in Table 1.

5.3 Determination of Machining Processes

The given machining volume is first represented in the form of the machining expression by inverse mapping, that is, extracting a generator profile and a generating bi-vector. The path of the bi-vector is determined by the direction of “full” RDoF or TDoF of the volume. There could be multiple possible sets of profile and bi-vectors for any given volume; each possible set corresponds to an alternate machining viewpoint. Each of the algebraic representations obtained in the inverse mapping step are checked for satisfaction of the constraints associated with a machining process to determine the machining feasibility by that process.

The D/T capabilities of the machining processes are represented as constraints on:

(1) Profile: For example, in the “angle” profile type (used in drilling), for the min. dia. capability, the following constraint is used.

(Distance) (line) (el) (line) (e2) (>) (“min. dia.”)

(2) Feed/depth vectors: As an example, in the process definition file (.prc files) of plunge milling, the constraints on the positional/orientational capabilities are represented with the following constraints:

ConstraintSet: on_Location_of_EMV (Distance) (direction) (Ve) (axis) (R) (=) (dimension value) (+/- 0.1 *dim_value)

ConstraintSet: on_Orientation_of_EMV (Angle) (direction) (Ve) (axis) (R) (=) (nominal angle) (+/- 0.05* angle value)

The constraints are defined in the mc.process object in the initialization program. In effect, these are the D&T capabilities of the process in addition to the existing shape capabilities.

6. Conclusions

The geometric model of machining operations provides a general methodology for capturing machining characteristics of different processes. One application is finding alternative process plans for a given part. A process selection system has been implemented to demonstrate the feasibility of this approach. The system accepts a sequence of machining volumes as input and produces a list of feasible machining operations. The system utilizes an extensible set of machining processes represented using the declarative approach. The system can handle complex variations of machining features, such as holes, pockets, slots, steps, and so on. The input/output of the system for two test parts is shown in Figures 13 and 14. Figure 13 shows a part (a) and its removal volume (b) if made from a rectangular stock. There are two kinds of machining features found by the system: a profile cut around the boss, and the holes, both shown in (c). The system finds the profile cut could be manufactured by plunge end milling but not by broaching, shaping, etc. Figure 13d shows two alternatives produced by the system for the profile cut. The profile and cutting and feed directions are displayed (color coded, unfortunately). Two machining alternatives for the holes are shown in (e). Figure 14 shows the results for a more complex part, the swivel bracket shown in (a). The removal volumes can be interpreted in many alternative ways.2,3 For each feature set interpretation, the inverse mapper determines feasible machining processes for each volume in the set. Figures 14c through 14g show one or more feasible processes found for each volume in the interpretation shown in (b).

It should be pointed out that the system is a preprocessor for CAPP; it does not consider setups, fixturing, tolerances, or sequence optimization. It simply creates a manufacturing view of the product. The rest of the decisions are left to CAPP.

The inverse mapping method can operate on convex volumes produced by any decomposition scheme. The inverse mapping system produces multiple alternatives but makes no attempt at ranking them or sorting through them; it is designed for use by a higher level (smart) CAPP system, which can add heuristics for evaluating the plans. As is, the mapper does not contain any heuristics; it is based on geometry and the nature of tool-workpiece interaction.

At each phase in the design-to-manufacturing mapping process, there are many alternative solutions. Many alternative stock shapes can be used to machine a part, the same removal volume can be decomposed into different sets of machining features, each feature can be produced by several alternative processes, or the same set of features can usually be sequenced in several alternative ways. Choices made at each level affect subsequent options available. For example, a given volume decomposition may not result in the optimal set of processes. As stated before, the mapping modules themselves do not make any recommendation. There is currently ongoing work on an integrated CAPP system synthesized from all the modules shown in Figure 15. This system includes a “Plan Evaluation & Refinement System” in which the first set of 10 alternatives is evaluated and compared based on three sets of metrics at the process, sequence, and feature levels. Evaluation criteria include machining time, setup time, accuracy, repeatability, and so on.2 The results provide a direction for further search, setting up a hill-climbing algorithm.21 Depending on the evaluation results, the plan may need to be refined at the process level (feedback to Inverse Mapper), sequence level (feedback to ReComposer), feature/volume level (feedback to Decomposer), as shown in Figure 15. Additional feedback loops may include changing the bar stock or even asking the designer to make changes to improve manufacturability.

The method is limited currently to swept volumes usually produced in a three-axis machining center. Rotational volumes may have cylindrical, conical, and circular plane faces. Translational volumes may only have cylindrical and planar faces. Future work will include non-swept volumes and other types of faces.


The authors gratefully acknowledge the financial support received from the National Science Foundation (grants DDM-9114696 and DMI9522971). An earlier version of this paper was presented at the 1996 ASME Design for Manufacturing Conference.

* The naming of these techniques is not standard in the literature.


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14. Y.S. Kim, “Recognition of Form Features Using Convex Decomposition,” Computer-Aided Design (v24, n9, 1992). 15. Y Kim, “Volumetric Feature Recognition Using Convex Decomposition,” in Advances in Feature Based Manufacturing, J. Shah, M. Mantyla, and D. Nau, eds. (Amsterdam: Elsevier, 1994). 16. S.K. Gupta, T.R. Kramer, D.S. Nau, WC. Regli, and G. Zhang, `Building MRSEV Models for CAM Applications,” Technical Report 9384 (Univ. of Maryland, Institute of Systems Research, 1993). 17. D. Hsiao, “Feature Mapping and Manufacturability Evaluation with an Open Set Feature Modeler,” PhD thesis (Tempe, AZ: Dept. of Mechanical Eng., Arizona State Univ., 1991). 18. A. Ali, “Declarative Approach for Form Feature Modeling,” MS thesis (Tempe, AZ: Dept. of Mechanical Eng., Arizona State Univ. 1994). 19. J. Shah and M. Rogers, “Rapid Prototyping of Feature Applications,” in Advances in Feature Based Manufacturing, J. Shah, M. Mantyla, and D. Nau, eds. (Amsterdam: Elsevier, 1994).

20. K. Hirode, “Automatic Evaluation and Interactive Refinement of Machining Process Plans,” MS thesis (Tempe, AZ: Dept. of Mechanical Eng., Arizona State Univ., 1996).

21. X. Li, S. Kambhampathi, K. Hirode, and J. Shah, “Process Planner’s Assistant: An Interactive and Iterative Approach to Automating Process planning,” ASME Design Eng. Technical Conf., DFM track (Sacramento, CA: Sept. 1997).

Arvind Shirur, Jami J. Shah, and Kartheek Hirode, Arizona State University, Tempe, Arizona

Authors’ Biographies

Arvind Shirur is an R&D engineer at 3D/EYE in Atlanta. He obtained his MS in mechanical engineering at Arizona State University in 1994 and his BSME from Manglore University (India) in 1990. He is member of ASME. His interests are in design, computational geometry, and CAPP.

Jami J. Shah is a professor of mechanical and aerospace engineering at Arizona State University, where he has been on the faculty since 1984. He holds a PhD in mechanical engineering from Ohio State University. He is also director of the Design Automation Lab, which conducts research in CAD, parametric and feature-based modeling, manufacturing process planning, product data management, and STEP data exchange standards.

Kartheek Hirode is an application engineer with Ford Motor Co. (Dearborn, MI). He obtained his MS in mechanical engineering from Arizona State University in 1996. His interests are in CAD/CAM and machining process planning.

Copyright Society of Manufacturing Engineers 1998

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