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1 Copyright ? 2004 by ASME Proceedings of DETC ‘04 ASME 2004 Design Engineering Technical Conferences and Computers and Information in Engineering Conference September 28 – October 2, 2004, Salt Lake City, Utah USA DETC2004-57689 CAFIXD: A CASE-BASED REASONING FIXTURE DESIGN METHOD. FRAMEWORK AND INDEXING MECHANISMS Iain M. Boyle Kevin Rong * Computer Aided Manufacturing Laboratory, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609-2280 David C. Brown Department of Computer Science, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609-2280 ABSTRACT Fixtures accurately locate and secure a part during machining operations such that the part can be manufactured to design specifications. To reduce design costs associated with fixturing, various computer-aided fixture design (CAFD) methods have been developed through the years to assist the fixture designer. One approach is to use a case-based reasoning (CBR) method where relevant design experience is retrieved from a design library, and adapted to provide a new fixture design solution. Indexing design cases is a critical issue in any CBR approach, and CBR systems can suffer from an inability to distinguish between cases if indexing is inadequate. This paper presents a CAFD methodology, entitled CAFixD, that adopts a rigorous approach to defining indexing attributes in which axiomatic design functional requirement decomposition is adopted. Thus, a design requirement is decomposed in terms of functional requirements, physical solutions are retrieved and adapted for each individual requirement, and the design is then re-constituted to form a complete fixture design. Furthermore, adaptability is used as the basis by which designs are retrieved in place of the normal attribute similarity approach, which can sometimes return a case that is difficult or impossible to fix. This paper presents the CAFixD framework and operation, and discusses in detail the indexing mechanisms used. Keywords: case-based reasoning, retrieval-by-adaptability, axiomatic design, fixture design * email rong@wpi.edu, phone 508-831-6020, fax 508-831-6412 1. INTRODUCTION A key concern to a manufacturing company is the ability to manufacture high quality products in as short a time as possible. Quick release of a product into the market place, ahead of any competitors, is crucial to securing a higher percentage of the market place. Fixtures play an important role within many manufacturing processes. They accurately locate and secure a workpiece during machining such that the part can be manufactured to design specifications. Thus fixtures have a direct effect upon machining quality, productivity, and the cost of products. A typical fixture unit is illustrated in Figure 1. The workpiece rests on locators that accurately locate the workpiece, and clamps are used to hold the workpiece securely in this position during machining. The typical structure of a fixture consists of a base-plate, to which the clamping and locating units are attached. Locating and clamping units consist of a supporting unit plus either a locator or clamp. Fixtures may contain different numbers and types of clamping and locating units, but units generally always follow this same basic format. Figure 1: A typical modular fixture The costs associated with the design and manufacture of fixtures are sizeable, accounting for some 10 – 20% of the total cost of a manufacturing system [Bi ? Retrieval – where cases that have all or some of the required features are identified; ? Selection – the retrieved cases are evaluated and then ranked in order of similarity. Adaptation recognizes the differences between the selected design and the new problem for which a design solution is sought. Once the necessary changes are identified, they are then made. With regard to indexing cases, inseparability is an important issue [McSherry (2002)]. Inseparability occurs when a CBR system is unable to distinguish between two cases: i.e., two cases can have the same values for all attributes, but it is unlikely that both cases will be equally suited to the current design requirement. Inseparability is caused by either having too few indexing attributes or by selecting a poor choice of attributes: i.e., the attributes and/or their values are common to all or many designs and do not distinguish between designs. The indexing approach adopted by many has been to define attributes associated with the design problem. For example Kumar (1995) indexed design cases using attributes that described the workpiece for which a fixture was to be designed, such as machining features, inter-feature relationships, surface information, machining direction and so on. However, there are few guidelines on choosing appropriate indexes, and the norm is for the designer to determine appropriate indexes using his/her experience. Thus, there is a need to develop a formal methodology for determining case indexes that clarify the design requirement. Many CBR systems base case recall upon attribute similarity: i.e., a nearest neighbor approach using standard weighting techniques [Chang et al (2000), Varma ? To use this fuller understanding of the design requirement to generate complete fixture designs that fully detail the physical structure of the locating/clamping units; ? To address the inseparability issue within CBR by developing a formal method for determining the indexing attributes of a design case; ? To develop a retrieval method that is both computationally feasible and has a well-defined control mechanism to restrict control of the search space, and that has the greatest probability of returning a satisfactory design solution; ? To develop a method that can effectively measure adaptability and gauge the effect of potential design decisions. In order to achieve these objectives: ? The concept of design requirement decomposition is used in which a complete list of functional requirements of the fixture design problem is produced. This accomplishes two goals: one, the functional requirements can be used as a thorough indexing mechanism for design cases thus alleviating the problem of inseparability; two, the thoroughness of this requirement decomposition technique allows the designer to fully define the total operational requirements of a fixture and subsequently use this comprehensive specification to drive and guide the design process; ? Emphasis is given to adaptability-based retrieval to help ensure that a satisfactory design solution is achieved. However, similarity-based retrieval is still used to vet possible design solutions and help constrain the search to prevent control problems arising during navigation of the solution space; ? A data structure entitled the “second layer of the design matrix” is proposed as a means of identifying the possible adaptations required to fix a design and of gauging the effect of potential design decisions when evaluating designs in terms of their adaptability. 3.2 The CAFixD methodology Overall, the CAFixD methodology (Figure 2) decomposes the design problem into a series of smaller problems, searches the case base for a solution to each individual problem, and then reconstitutes the individual solutions to form one complete solution. The approach is similar to that adopted by a human designer, who would initially generate a conceptual design solution, and subsequently fill in the details of that solution during a detailed design stage. Thus, CAFixD has two design case libraries. One contains conceptual design solutions and is used during the conceptual design stage, and the second contains detailed designs of individual fixture units and supports the detailed design stage. During retrieval, emphasis is given to evaluating the adaptability of design cases. Figure 2: The CAFixD methodology Initially, a series of design rules select the appropriate conceptual design from case library 1. Workpiece and machining information are then processed to generate a list of functional requirements (FRs) and constraints that the design must satisfy. Utility analysis (Thurston 1991) is then used to guide the decision making process during retrieval from case library 2. Utility analysis is similar to standard linear weighting but is considered a more expressive and accurate method of capturing a designer’s preferences as it allows the designer to state non-linear preferences. Similar to weighting approaches, the output is a figure of merit or utility (U) that represents the relative desirability of a design alternative of several attributes. Thus in CAFixD, for each FR and constraint the designer must record his/her preferences in the form of a utility curve, similar to that presented in Figure 3. These graphs illustrate the utility 4 Copyright ? 2004 by ASME of a given attribute based upon its value, thus in Figure 3 a weight of 6 lbs is of considerably greater utility than that of 16 lbs. The method by which these curves are generated is outwith the scope of this paper, but interested readers are directed to Boyle et al (2003) for a description of the process. Using the utility curves and the FR/constraint list, candidate fixture units are retrieved on the basis of functional similarity. Case base 2 contains previous design cases that are indexed by their FRs. The top ranked cases are then re-evaluated in terms of their adaptability. Specifically, cases are re-evaluated in terms of the design decisions that will have to be made in order to meet the new design situation, and the effect of these changes upon the overall worth of the design is then used as the basis for retrieving the most suitable case. The case that requires the most favorable modifications i.e. the modifications that result in the design of highest utility is then proposed as the most suitable case for modification. The modifications are subsequently executed and the design tested to ensure the FRs are met. The design is also evaluated for possible addition to the case library. Figure 3: A utility curve 3.2.1 Indexing design cases Axiomatic design decomposition principles are used to determine the indexing of both design cases and their solutions, as illustrated in Figure 4. Axiomatic design decomposition [Suh (2001)] involves the processing of information across four domains. Mapping occurs between the customer domain, the functional domain, the physical domain, and the process domain. The needs of the customer are listed as customer attributes (CAs) in the customer domain and are subsequently formulated into a set of functional requirements (FRs). A design solution is then created through mapping between the FRs and the design parameters (DPs), which exist in the physical domain. These DPs are mapped into the process variables (PVs). A fundamental aspect of the mapping process is the idea of decomposition. The design process progresses from a higher, abstract level down to a more detailed level. This results in the formation of design hierarchies in the FR, DP, and PV domains. In fixture design the customer attributes are the workpiece information and machining information. This maps onto a list of FRs that explicitly state the functions that the fixture design must perform. These FRs relate to all desired fixture operational requirements. In addition, constraints may also be included here e.g. fixture cost. The FRs map onto DPs, which are the individual fixture units used to achieve the FRs. The PVs in turn are base design parameters (for example the thickness of a locator) used to achieve the DPs. The significant difference between this and standard CBR approaches is that the functions of the sought design solution are explicitly stated. Normal CBR approaches map directly from the CAs directly onto the DPs. Figure 4: Axiomatic domains applied to fixture design 3.2.2 The Design Case Libraries The high-level design of the case library is presented in Figure 5. The case base consists of two libraries. Case library 1 is related to fixture planning. It stores conceptual fixture designs largely in terms of their locating principles. The second case base holds the individual units that constitute the fixture design. Examples include locator support units or clamp types. The approach adopted is to navigate through case library 1 to retrieve a conceptual design, before proceeding to the second case library to retrieve appropriate fixture units. Thus, the output from case library 1 constrains the search through case library 2 as only units that can be used in the retrieved locating principle are considered as potential solutions. Figure 5: The Design Case Base 3.2.2.1 Case Library 1 The structure of case library 1 is presented in Figure 6. It contains cases that are conceptual in nature i.e. they contain information relating to locating principles in terms of locating methods and locating point distributions. There are 3 basic locating methods: plane, pin-hole, and external profile locating. For each method, there are subsequent decompositions and refinements of the root locating method. For example, plane locating (3-2-1) has seven variations (Figure 7). The third variation is locating with six individual points of location where three locators provide primary location, two provide secondary location, and one provides tertiary location. The primary points all act in the same direction but can act on different planar surfaces, as can be the case with the secondary locating points. CAs FRs DPs PVs maps workpiece CAD model machining information Functions that fixture must perform: -includes accuracy, stability, ergonomic requirements, and constraints Individual units – locating/clamping units, base plates, locators, clamps Base design parameters: e.g. thickness, height, surface finish consists of Design case base Case library 1: Conceptual design solutions Case library 2: Individual unit design solutions decomposes into constrains search through utility curve utility fixture weight, lbs 5 Copyright ? 2004 by ASME Figure 6: Case Library 1 - Conceptual Design Solutions Figure 7: Decomposition of 3-2-1 Locating Solutions Once the conceptual design has been found in case library 1, the search for a design solution can proceed to the second case library, where appropriate individual fixture units can be retrieved for modification. To each leaf of case library 1 are attached skeleton FR sets. 3.2.2.2 FR decomposition Skeleton FR sets can be generated for each of the design cases in case library 1. A partial decomposition of the format of a design requirement for a simple 3-2-1 locating scheme is presented in Figure 8. FRs are grouped into three main categories. One group deals with the locating accuracy requirements, the second with the stability requirements of the fixture, and the third deals with ergonomic issues related to fixturing. The first two groups are the simplest to handle in terms of automating their generation. The locating principle determines the number of units in the fixture design. As there are six units associated with variation 3 of 3-2-1 locating, there are therefore 6 FRs relating to the accuracy of the locating units (FR 1.2 ), 6 FRs relating to the clamping forces required to hold the workpiece against the locators (FR 2.1.1 ), and 12 FRs relating to the stiffness of the 6 locating and 6 clamping units (FR 2.1.2 ). A tolerance analysis of the workpiece is performed to determine the performance values of the locating accuracy FRs. Similarly, a simple force analysis of the machining forces allows the performance values for the stability FRs to be defined. The significant problem is related to the third group of FRs, which are related to ergonomic considerations. These FRs include design requirements such as chip shedding, error proofing, workpiece surface protection at the locator/workpiece interface, and assisting tool positioning during machining. These need to be user specified and are created interactively with the designer. Figure 8: A partial FR decomposition 3.2.2.3 Case Library 2 The second case base contains information relating to individual fixture units i.e. information relating to an individual clamping or locating unit, and where it can be used. Figure 9 presents a partial breakdown of the case library, which contains locating units, clamping units, locator types, and fixture base types that can be combined to create a complete fixture for a workpiece. Figure 9: The Decomposition of Case Library 2 Each step down the hierarchy represents a refinement of the unit design. For example, locators can be split up into two types – horizontal locators and vertical locators depending upon the direction of support they provide. Horizontal locators can be subsequently decomposed into two possible types, designated as HL01 (a requirement for step over locating units) Fixture designs 3-2-1 Plane locating Clamping model Locating model Pin-hole locating External profile locating Short pin V-pad Round pin Var 1 3-2-1 Var 2 3-2-1 Var 7 3-2-1 .. … V-block Vertical model Horizontal model Var 1 sp Var 2 sp Var 3 sp Var 1 rp Var 2 rp Var 1 vp Var 2 vp Var 2 vb Var 1 vb Var 1 vc Var 2 vc Var 2 hc Var 1 hc Fixture units Locating units Clamping units Locator types Horizontal locating units HL0 Step-over locating units HL01 Var 1, HL011 Design cases Simple side locating units HL02 Var 2, HL012 Design cases Var 1, HL021 Var 2, HL022 Design cases Design cases Vertical locating units VL0 Fixture base units Vertical clamps VC0 Horizontal Clamps HC0 Simple clamps HC01 Step-over clamps HC02 Open surface clamps VC01 Var 1, VC011 Var 2, HC012 Var 1, HC011 Design cases Design cases Design cases FR 1 – Locate workpiece to required accuracy FR 1.1 – Locate the workpiece FR 1.1.1 – Provide location directions – 6 FRs FR 1.1.2 – Provide contact between locator and workpiece – 6 FRs FR 1.2 – Control accuracy of locations FR 1.2.1 – Locate workpiece to required drawing tolerances – 6 FRs FR 2 – Support workpiece against machining forces experienced during machining FR 2.1 – Hold workpiece in situ during machining – 6 FRs FR 2.2 – Support workpiece during machining – 12 FRs FR 3 – Ergonomic requirements FR 3.1 – Prevent damage at the fixture workpiece interface FR 3.2 – Channel coolant flow during machining FR 3.3 – Ease the loading/unloading of the workpiece into/from the fixture FR 3.4 – Assist tool positioning during machining FR 3.5 – Error proof the fixture Constraints: C 1 – fixture cost C 2 – fixture weight C 3 – workpiece loading time C 4 – workpiece unloading time C 5 – fixture assembly time 6 Copyright ? 2004 by ASME and HL02 (a requirement for simple locating units). HL01 represents the situation where there is another face existing below and which extends beyond the locating face, and HL02 the situation where there is a face above or no face above the locating plane. Each of these locating situations require different types of locating units. For example, HL01 requires the use of L-shaped locating units, whereas HL02 allows tower side locating units or also possibly L-shaped locator units to be used as illustrated in Figure 10. To each leaf of the case base are attached previous instances of locating and clamping units together with the functional requirements that the unit is used to achieve. Also linked are the relevant PVs. Figure 10: The Two Types of Horizontal Locators 3.2.2.4 Indexing Design Cases – An Example In this section, a fixture design for a caliper will be used to illustrate how cases are stored in the case library. Figure 11 illustrates the caliper workpiece and its corresponding fixture design. Figure 12 details the locating points. Figure 11: The fixture for a