[Psychology] Mechanical Assemblies Phần 5 pptx

212 8 THE DATUM FLOW CHAIN FIGURE 8-1. The Stapler, Its Liaison Diagram (left), and Two Key Characteristics (right). Several irrelevant liaisons have been colored gray because they play no role in positioning parts to deliver either KC. FIGURE 8-2. The KCs of the Stapler Shown Separately with the Liaisons That Deliver Them. Irrelevant liaisons are not shown. the process for creating it and thus only indirectly defines the assembly. We will also define two types of assembly joints, called mates and contacts: Mates pass dimensional constraint from part to part, while contacts merely provide support, reinforcement, or partial constraint along axes that do not involve delivery of a KC. Some joints act as mates along some degrees of freedom and as contacts along others. Symbols for each of these types of joints will be introduced. We will then present the scope of the DFC in assembly planning using several examples. Finally, we will see that the DFC contains all the information needed to carry out a variation analysis of the KC it delivers. This fact links the scheme by which the parts are located in space to the sources of variation in their locations. To visualize the ideas to be presented in this chapter, we again turn to the desktop stapler. In this chapter, we will learn how to characterize the liaisons of an assembly as delivery chains for key characteristics. This is illustrated in Figure 8-1, where some of the liaisons are shown in gray to denote that they play no role in KC delivery. It is further emphasized in Figure 8-2, where each KC chain is shown separately and the irrelevant liaisons are omitted altogether. The stapler also illustrates the difference between mates and contacts. The difference is illustrated in Figure 8-3. All these concepts will be made concrete in this chapter and related to their underlying mathematical representations introduced in earlier chapters. FIGURE 8-3. Illustrating the Difference Between a Mate and a Contact. The mate provides constraint for the staples by establishing their position relative to the end of the carrier. The pusher and staples share a contact, which reinforces or stabilizes the stapler-carrier mate. In the vocabulary of Chap- ter 4, the staples are properly constrained along the axis of the carrier. Note that the contact is colored gray, indicating that it does not participate in KC delivery. B.C. SUMMARY OF THE METHOD FOR DESIGNING ASSEMBLIES 213 8.B. HISTORY AND RELATED WORK Assemblies have been modeled systematically by [Lee and Gossard], [Sodhi and Turner], [Srikanth and Turner], and [Roy et al.] and others. Such methods are intended to capture relative part location and function, and they en- able linkage of design to functional analysis methods like kinematics, dynamics, and, in some cases, tolerances. Al- most all of them need detailed descriptions of parts to start with, in order to apply their techniques. [Gui and Mantyla] applies a function-oriented structure model to visualize assemblies and represents them in varying levels of detail. In this book, we have not attempted to model assemblies functionally. Our work begins at the point where the functional requirements have been established and there is at least a concept sketch. Top-down design of assemblies emphasizes the shift in focus from managing design of individual parts to managing the design of the entire assembly in terms of mechanical "interfaces" between parts. We saw in Chapter 4 that [Smith] proposes eliminating or at least minimiz- ing critical interfaces, rather than part-count reduction, in the structural assembly of aircraft as a means of reduc- ing costs. He emphasizes that, at every location in the assembly structure, there should only be one controlling element that defines location, and everything else should be designed to "drape to fit." In our terms, the controlling element is a mate and the joints that drape to fit are contacts. [Muske] describes the application of dimensional management techniques on 747 fuselage sections. He describes a top-down design methodology to systematically translate key characteristics to critical features on parts and then to choose consistent assembly and fabrication methods. These and other papers by practitioners indicate that several of the ideas to be presented here are already in use in some form but that there is a need for a theoretical foundation for top-down design of assemblies. Academic researchers have generated portions of this foundation. [Shah and Rogers] proposes an attributed graph model to interactively allocate tolerances, perform tolerance analysis, and validate dimensioning and tolerancing schemes at the part level. This model defines chains of dimensional relationships between different features on a part and can be used to detect over- and underdimen- sioning (analogous to over- and underconstraint) of parts. [Wang and Ozsoy] provides a method for automatically generating tolerance chains based on assembly features in one dimensional assemblies. [Shalon et al.] shows how to analyze complex assemblies, including detecting incon- sistent tolerancing datums, by adding coordinate frames to assembly features and propagating the tolerances by means of 4 x 4 matrices. [Zhang and Porchet] presents the oriented functional relationship graph, which is similar to the DFC, including the idea of a root node, prop- agation of location, checking of constraints, and prop- agation of tolerances. A similar approach is reported in [Tsai and Cutkosky] and [Soderberg and Johannes- son]. The DFC is an extension of these ideas, empha- sizing the concept of designing assemblies by designing the DFC first, then defining the interfaces between parts at an abstract level, and finally providing detailed part geometry. CAD today bountifully supports design of individual parts. It thus tends to encourage premature definition of part geometry, allowing designers to skip systematic con- sideration of part-part relationships. Most textbooks on engineering design also concentrate on design of machine elements (i.e., parts) rather than assemblies. Current CAD systems provide only rudimentary assembly modeling capabilities once part geometry exists, but these capabilities basically simulate an assembly draw- ing. Most often the dimensional relations that are explic- itly defined to build an assembly model in CAD are those most convenient to construct the CAD model and are not necessarily the ones that need to be controlled for proper functioning of the assembly. What is missing is a way to represent and display the designer's strategy for locating the parts with respect to each other, which amounts to the underlying structure of dimensional references and mutual constraint between parts. The DFC is intended to capture this logic and to give designers a way to think clearly about that logic and how to implement it. 8.C. SUMMARY OF THE METHOD FOR DESIGNING ASSEMBLIES Ideally, the design of a complex assembly starts by a general description of the top-level requirements in the form of KCs for the whole assembly. These requirements are then systematically formalized and flowed down to subassemblies and finally down to individual parts. The assembly designer's task is to create a plan for delivering 214 8 THE DATUM FLOW CHAIN each KC. To do this, he or she defines a DFC for each KC, showing how the parts in each DFC will be given their desired nominal locations in space. This is equivalent to properly constraining each part. During these early stages of design, the designer has to do the following: Systematically relate the identified KCs to important datums on subassemblies, parts, and fixtures at the various assembly levels from parts to subassemblies to the final assembly. Design consistent dimensional and tolerance relationships or locating schemes among elements of the assembly so as to deliver these KC relationships. Identify assembly procedures that best deliver the KCs repeatedly without driving the costs too high. These major elements of the assembly design process are implemented by establishing three basic kinds of information about an assembly: "Location responsibility": Which parts or fixtures locate which other parts. Constraint: Which degrees of freedom of a part are constrained by which surfaces on which features on which other parts or fixtures, including checking for inappropriate over- or underconstraint. Variation: How much uncertainty there is in the location of each of the parts relative to some base part or fixture which represents the reference dimension. The design process comprises two steps: nominal design and variation design. The nominal design phase creates the constraint structure described above, by using the concepts in Chapter 4, and assuming that the parts and their features are rigid and have nominal size, shape, and location. The variation design phase comprises making the DFC robust against variations away from nominal dimensions, plus checking each DFC using traditional tolerance analysis, as described in Chapters 5 and 6, to determine if each KC can be delivered. A KC, as described in Chap- ter 2, is said to be "delivered" when the required geometric relationship is achieved within some specified tolerance an acceptable percent of the time. The DFC provides a way to define a competent nominal assembly. Nominal means that the assembly has all its dimensions at their ideal values and that there is no variation. Competent means that the assembly is capable of properly constraining all its parts, that all its KCs have been identified, and that a way to deliver each KC has been provided. We will see below that these elements of "competency" are all related to each other and that they are really different ways of saying the same thing. Furthermore, they can be addressed using the nominal dimensions. Once we are sure that the nominal design is competent, we can examine it for its vulnerability to variation. Portions of this step are included in conventional tolerance analysis, but it will become clear that we mean much more than that. The method is capable of describing assemblies that are built simply by joining parts as well as those that are built using fixtures. In either case, the participating elements (parts and fixtures) are linked by the DFC and its underlying constraint scheme. A typical assembly sequence builds the DFC beginning at its root or datum reference and working its way out to the KCs. Sequences that "build the DFC" are a very small subset of the feasible sequences found by methods described in Chapter 7. When DFCs are found to be deficient during the design process, it often emerges that a different assembly sequence is associated with an alternate DFC design. This fact links assembly sequence analysis to assembly design, variation buildup, and assembly process planning. The method also provides guidance in the surprisingly common situation in which there are more KCs than the degrees of freedom of the assembly can deliver indepen- dently. This situation is called KC conflict. We will see that KC conflict can be detected using the methods of constraint evaluation presented in Chapter 4. In this method, parts 3 are merely frameworks that hold assembly features, while assembly features are the links that establish the desired state of constraint among adjacent parts, leading to the achievement of the assembly- level geometric relationships. The DFC is an abstract version of this framework, providing a kind of skeleton for the assembly. The mathematical foundation of the method is the 4 x 4 transform and Screw Theory, which are used to describe the three-dimensional locations of parts and features, to determine the degrees of freedom constrained by individual features, and to check for proper constraint when parts are joined by sets of features. These elements of the method were presented in Chapters 3 and 4. 3 Here, we mean parts considered only from the point of view of their membership in the assembly, not as, for example, carriers of load or liquids, barriers against heat flow, and so on. These factors comprise significant requirements on parts that must be considered as part of their design. 8.D. DEFINITION OF A DFC 215 An important conclusion from this method is that most of the information required to support it can be stored as text. Very little detailed geometry is needed, and its use is isolated to a few steps in the process and a few places on the parts. This is important because it reflects the fact that the most important steps in designing an assembly comprise establishing connectivity and constraint, not defining geometry. This, in turn, is important because it provides a route to representing assembly information more abstractly, richly, and compactly than is permitted by geometry alone. This, in turn, provides a language and other constructs for capturing this information as a natu- ral part of the design process, avoiding the need to dis- cover it by analyzing geometry, as many CAD systems do today. A corollary is that the method describes steps that de- mand the careful definition of a data and decision record that constitutes declaration of the consistent design intent for the assembly. This record can be used to judge the ad- equacy of the design as well as to manage its realization up and down the supply chain and debug that realization on the factory floor and in the field. 8.D. DEFINITION OF A DFC 8.D.1. The DFC Is a Graph of Constraint Relationships A datum flow chain is a directed acyclic graphical representation of an assembly with nodes representing the parts and arcs representing mates between them. "Directed" means that there are arrows on the arcs. "Acyclic" means that there are no cycles in the graph; that is, there are no paths in the graph that follow the arrows and return to the start of the path. Loops or cycles in a DFC would mean that a part locates itself once the entire cycle is traversed, and hence are not permitted. Every node represents a part or a fixture, and every arc transfers dimensional constraint along one or more degrees of freedom from the node at the tail to that at the head. Each arc has an associated 4x4 transformation matrix that represents mathemati- cally where the part at the head of the arc is located with respect to the part at the tail of the arc. A DFC has only one root node that has no arcs directed toward it, which represents the item from which the locating scheme begins. This could be either a carefully chosen base part or a fixture. A DFC can be a single chain of nodes or it can branch and converge. For example, if two assembled parts together constrain a third part, the DFC branches in order to enter each of the first two parts and converges again on the third part. Figure 8-4 shows a simple liaison diagram and associated DFC. In this DFC, part A is the root. It completely locates parts B and C. Parts A and C together locate part D. A thought question at the end of the chapter asks the reader to define some assembly features that are able to accomplish this locating scheme. FIGURE 8-4. A Simple Liaison Diagram and Datum Flow Chain. The liaison diagram (left) shows which parts are connected to each other. The DFC (right) shows how they are connected and constrained. Each arc is labeled with the degrees of freedom it constrains or the names of those degrees of freedom in any convenient coordinate system. This DFC is intended to deliver a KC between parts A and D. The KC is indicated by the double line next to the arrow. No information is given regarding which degrees of freedom are of interest in this KC. Every arc in a DFC is labeled to show which degrees of freedom it constrains, which depends on the type of mating conditions it represents. The sum of the unique degrees of freedom constrained by all the incoming 4 arcs to a node in a DFC should be equal to six (less if there are some kinematic properties in the assembly or designed mating conditions such as bearings or slip joints which can ac- commodate some amount of predetermined motion; more if locked-in stress is necessary such as in preloaded bearings). This is equivalent to saying that each part should be properly constrained, except for cases where over- or underconstraint is necessary for a desired function. 4 Arcs that are "incoming" to a node are defined as arcs whose arrows point toward the node. 216 8 THE DATUM FLOW CHAIN A DFC is similar in many ways to an electric circuit diagram. A circuit diagram defines a connection structure or network that has many properties of its own, independent of the resistors, capacitors, and other individual circuit elements. It has a unique ground or reference voltage. Many operating characteristics of the circuit can be calculated from its graphical properties, such as spanning trees and independent loops. Both the nominal operating behavior and the sensitivity to component variations can be calculated from the circuit. We will see that many of these properties of electric circuits are shared by DFCs, including their ability to set the agenda for design and analysis. 8.D.2. Nominal Design and Variation Design The DFC represents the designer's intent concerning how the parts will obtain their locations in space in all six degrees of freedom. Each KC will have its own DFC, and thus each DFC is responsible for delivering its KC. If the parts are perfect, then the KC will be delivered perfectly. If they are not, then a variation analysis like those in Chap- ter 6 must be undertaken. Variation in parts passes from part to part along the DFC and accumulates to determine the variation in the KC. Thus the DFC acts as a tolerance chain that guides the designer in finding all the variations that contribute to each KC. It is not necessary to perform a separate analysis to find the tolerance chain in order to carry out the variation analysis of a KC. 8.D.3. Assumptions for the DFC Method The following assumptions are made to model the assembly process using a DFC: 1. All parts in the assembly are assumed rigid. Hence each part is completely located once its position and orientation in three dimensional space are determined. 2. Each assembly operation completely locates the part being assembled with respect to previously assembled parts or an assembly fixture. Only after the part is completely located is it fastened to the remaining parts in the assembly. Assumption 1 states that each part is considered to be fully constrained once three translations and three rota- tions are established. If an assembly, such as a preloaded pair of ball bearings, must contain locked-in stress in order to deliver its KCs, the parts should still be sensibly constrained and located kinematically first, and then a plan should be included for imposing the overconstraint in the desired way, starting from the unstressed state. If flexible parts are included in an assembly, they should be assumed rigid first, and a sensible locating plan should be designed for them on that basis. Modifications to this plan may be necessary to support them against sagging under gravity or other effects of flexibility that might cause some of their features to deviate from their desired locations in the assembly. Assumption 2 is included in order to rationalize the assembly process and to make incomplete DFCs make sense. An incomplete DFC represents a partially completed assembly. If the parts in a partially completed assembly are not completely constrained by each other or by fixtures, it is not reasonable to expect that they will be in a proper condition for receipt of subsequent parts, in-process measurements, transport, or other actions that may require an incomplete assembly to be dimension- ally coherent and robust. This assumption enables us to critique alternate assembly sequences, as explained in Section 8.K. 8.D.4. The Role of Assembly Features in a DFC The DFC comprises design intent for the purpose of locating the parts but it does not say how the parts will be located. Providing location means providing constraint. We know from the foregoing chapters that assembly features are the vehicles we use to apply constraint between parts. Thus the next step after defining the DFC is to choose features to provide the constraint. Once features have been declared, we can calculate the nominal locations of all the parts by chaining their 4x4 transforms together, and we can check for over- or underconstraint, using methods that are by now familiar. In order to be precise about our locating scheme, however, we need to distinguish two kinds of feature joints: mates and contacts. These are the subject of the next section. 8.E. MATES AND CONTACTS 217 8.E. MATES AND CONTACTS A typical part in an assembly has multiple joints with other parts in the assembly. Not all of these joints transfer lo- cational and dimensional constraint, and it is essential to distinguish the ones that do from the ones that are redun- dant location-wise and merely provide support or strength. We define the joints that establish constraint and dimensional relationships between parts as mates, while joints that merely support and fasten the part once it is located are called contacts. Hence mates are directly associated with the KCs for the assembly because they define the resulting spatial assembly relationships and dimensions. The DFC therefore defines a chain of mates between the parts. If we recall that the liaison diagram includes all the joints between the parts, then it is clear that the DFC is a subset of the liaison diagram. The process of assembly is not just of fastening parts together but should be thought of as a process that first defines the location of parts using the mates and then reinforces their location, if necessary, using contacts. 8.E.1. Examples of DFCs This section uses some simple examples to illustrate how to draw a DFC starting from the KC(s). The first example is assembly of an automobile wheel to an axle. The second is assembly of three simple sheet metal parts. Both examples illustrate the difference between mates and contacts. 8.E.1.a. Wheel and Axle Consider Figure 8-5, a simplified automobile axle and wheel. The axle hub includes a rim plus four studs. The wheel contains a round opening in the center, plus four holes, larger than the studs, centered around this opening. When the wheel is mounted to the hub, the opening fits snugly over the rim and the studs protrude through the holes, ready for the nuts to be installed. The designer's goal for this design is to achieve dy- namic balance and a smooth ride. The KCs he has chosen to achieve this goal are as follows: Make the wheel concentric with the axle shaft's axis. Make the plane of the wheel perpendicular to this axis. To deliver these KCs, the designer has chosen two features on the axle, the face of the hub and the rim. The hub face must be perpendicular to the axle's axis and the rim must be concentric with this axis. Similarly, he has chosen two features on the wheel, namely, the plane of the wheel and the opening in the center. The plane must be in the coordinate frame in which the wheel's inertia matrix is diagonal, and the opening must be centered on this frame. 5 In our terms, the hub face and rim constitute mate features, as do the wheel plane and opening. The studs and their holes constitute contacts. They play no role in achieving the KCs. They merely keep the wheel from falling off. Of course, this is important and we could have called it a KC, but achieving it does not depend on how the parts involved are geometrically located. The important constraint relationships between the axle and wheel are completely determined by the mate features already defined. A DFC for the wheel and hub is shown in Figure 8-6. It represents mates as graph arcs with arrows on them as well as a number indicating how many degrees of freedom are located by the mate. Contacts are shown as dashed lines. All the important features are defined, and their roles in establishing constraint relationships and KCs are shown. 5 Small errors in the wheel features are inevitable due to the unpre- dictability of the mass distribution of the rubber tire. These are re- moved by dynamically balancing the wheel using small lead weights. FIGURE 8-5. A Wheel and Axle Illustrating the Difference Between Mates and Contacts. The dimensional and constraint relationships between the wheel and axle are established by the mate between the wheel's opening and the axle's rim, as well as by the mate between the planar face of the wheel and the planar face of the hub. All other interfaces between these parts provide no constraint and are contacts. 218 8 THE DATUM FLOW CHAIN FIGURE 8-6. DFC and KCs for the Wheel and Axle in Fig- ure 8-5. Top: The simplest representation of the DFC for this assembly consists of two nodes representing the parts, a set of parallel lines representing a KG, and one arrow with the number 5 on it, indicating that the axle has a mate with the wheel that defines 5 of its degrees of freedom. Bottom: A little more detail (adapted from [Zhang and Porchet]) reveals that the KG can be decomposed into two separate KCs and that different features on the parts are involved in delivering them. The features on the axle and wheel are related in different ways. The hub and rim on the axle each have mates with the opening and plane on the wheel, respectively. Together, these features define 5 of the wheel's six degrees of freedom and all the KCs. The joint between the studs and holes is a dashed line, indicating that it is a contact. When the nuts are tightened onto the studs, the sixth degree of freedom is fastened, but its exact value is not of interest to us. There is no KC on this dimension. The studs fit easily into oversize holes, and any orientation of the wheel within the stud-hole clear- ance is acceptable. Note that one of these datum features is the axle's centerline. This is not a piece of geometry itself. Calling it a feature is, however, perfectly consistent with GD&T. Figure 8-7 expands the DFC for the assembly to show all the necessary features on each part and their relative location requirements. The symbolic blobs in Figure 8-6 representing the two parts, with their four black dots representing the important features, have been expanded to show the perpendicularity and concentricity relationships between the features. Also shown is a possible simplified statement of these requirements for the axle using the symbols of GD&T as discussed in Chapter 5. Figure 8-5, Figure 8-6, and Figure 8-7 present together a simple example of definition of assembly requirements, their capture as KCs, the definition of DFCs to deliver these KCs, the identification of feature-to-feature relationships between the parts that create the necessary mates, and finally definition of the resulting requirements on mutual feature relationships inside one of the parts of this assembly. It FIGURE 8-7. DFC with Features and Their Required Mu- tual Locations Inside the Parts. Above is an expanded view of the assembly in symbolic form. It shows all the interpart relationships between features. These features play essential roles in delivering the axle-wheel assembly's KCs. Below is a possible simplified rendition of a GD&T specification for real- izing the necessary feature-to-feature relationships inside one of the parts. The interpart relationships express the requirements that the hub must be perpendicular to the axle shaft's centerline and that the rim must be located with respect to the centerline, both within some tolerances. The circle on which the studs lie must also be located with respect to the shaft centerline, but a larger tolerance is allowed. The root of the DFC in the axle's centerline is also the A datum for the axle. should be clear from these figures that the DFC represents a continuous chain not only between parts but inside them as well. The only difference between the arcs of a DFC between parts and the arcs inside a part is that only mate relationships exist inside parts. Contact relationships exist only between parts. An alternate design for joining these parts is commonly used. It dispenses with the rim and its mating opening and uses five studs and holes instead. The nuts have generous chamfers on them where they engage chamfered holes in the wheel. A thought question at the end of the chapter asks the reader to compare this alternate design with the one described here. 8.E. MATES AND CONTACTS 219 TABLE 8-1. Distinguishing Mates and Contacts Full six dof constrained No dof constrained Some dof constrained along a KC Yes No Yes along KC directions No Yes Yes along non-KC directions Square peg in square hole Nuts attaching wheel to axle hub Rim on axle hub; slip joint in sheet metal FIGURE 8-8. An Assembly with a Mate and a Contact. The KC is the overall length L of the assembly. In the direction of the KC, the A-B joint provides location and constraint, but the B-C joint does not. It simply joins B and C and will do so as long as overlap dimension b is large enough. 8.E.1.b. Sheet Metal Parts Figure 8-8 above shows three simplified sheet metal automobile body parts. Between them they have two joints, namely, one butt joint called a mate and one slip joint called a contact. 6 The KC is the overall length L of the assembly. The slip joint can be adjusted in the direction oftheKC. If we consider this to be a full three-dimensional assembly, then it is obviously underconstrained, and neither of the joints would then be called a mate. However, if we consider the KC, which specifies one dimension only, then we could argue that the joint between A and B is a mate because it constrains the part-to-part relationship in a direction that contributes to delivery of the KC. Similarly, we could argue that the joint between B and C is a contact because it does not provide such constraint. However, the B-C joint clearly does provide constraint in the direction normal to the planes of the parts. Why then call it a contact? The reason is that there is no KC specified in that direction to which this joint makes a contribution. This leads us to a rule, namely that every assembly must be properly constrained (up to the limit where function may require some unconstrained degrees of freedom) but not every joint that provides constraint in some direction(s) 6 Butt joints and slip joints were introduced in Chapter 6. In the auto industry, the butt joints are called coach joints. has to be a mate. Underconstrained assemblies need help to achieve proper constraint beyond what the joints them- selves can provide. As we will see below, fixtures are usu- ally used to provide the missing constraint. Typically, the parts will have joints with the fixtures at these points and the DFC will pass through these part-fixture joints, caus- ing us to call them mates. Table 8-1 combines these definitions. Later in this chapter we will use the name "hybrid mate-contact" to refer to joints that provide incomplete constraint and which act as mates along the directions they constrain. In terms of the definitions used in Chapter 4, joints that provide full six degree of freedom (dof) constraint play the role of "loca- tors" while joints that provide no constraint play the role of "effectors." 8.E.2. Formal Definition of Mate and Contact Generalizing on Table 8-1, we can categorize all joints between parts as shown in Figure 8-9. This figure makes use of the concepts of wrench space and twist space introduced in Chapter 4. It permits us to examine a joint systematically, surface contact by surface contact, to determine the function of each surface contact in the assembly. The categorization in Figure 8-9 can be applied to joints or to fundamental surface-to-surface contacts as discussed in Chapter 4. For example, Figure 8-10 reviews the cylinder-plane contact and shows its twist space and wrench space. Constraint and variation occur only along the directions in the wrench space. 8.E.3. Discussion Explicit identification and definition of the mates in an assembly is an integral part of assembly design and is a prerequisite to assembly process planning and variation analysis. The choice of which joints will be mates and which ones will be contacts is made by the designer at the conceptual design stage. Example Contact? Mate? Function 220 8 THE DATUM FLOW CHAIN FIGURE 8-9. Categories of Joints Between Parts. Some joints are mates while others are contacts. Within each mate is a twist space and a wrench space. Constraint behavior characteristic of a mate occurs in its wrench space. Adjustment behavior (typically associated with contacts) can occur in its twist space. Joints where this occurs are called hybrid mate-contacts. FIGURE 8-10. Twist Space (a) and Wrench Space (b) for the Cylinder-Plane Surface Contact. 8.F. TYPE 1 AND TYPE 2 ASSEMBLIES EXAMPLE 221 When defining the DFC, the designer must define ex- plicitly the surfaces or reference axes on mating features which are intended to carry dimensional constraint to the mating part. This approach makes it unnecessary, even counterproductive, to construct algorithms that "identify" tolerance chains or loops, since the DFC equips the designer to define them purposefully as a main objective of assembly design. On the other hand, defining the DFC and its implementing features prepares the designer to carry out the steps of GD&T or some other systematic tolerancing scheme for each part, as illustrated by the example in Figure 8-5 through Figure 8-7. We turn next to the distinction between two types of assemblies, called Type 1 and Type 2. The DFCs for these, and the strategies used to achieve their KCs, are quite different. 8.R TYPE 1 AND TYPE 2 ASSEMBLIES EXAMPLE To clarify our approach to designing assemblies, we need to distinguish between two kinds of assemblies, which we call Type 1 and Type 2. Type 1 assemblies are constrained completely by feature relations between their parts. Type 2 assemblies are underconstrained by their features and need fixtures or measurements to add the missing constraint. We will illustrate the difference with an example from the automobile industry. Figure 8-11 shows a simplified car floor pan. 7 This assembly consists of three stamped sheet metal parts. The KC is the overall width of the car, which is nominally of dimension L. The design shown in the figure consists of parts with flanges that are spot-welded together to form butt or coach joints. On the right in Figure 8-11 is the liaison diagram for this assembly, showing the KC as a double line joining parts A and C. Parts A and C contain the features that must be a distance L apart in order to deliver the KC. The way this assembly has been designed, each part locates the adjacent part in the left-right direction by means of a flange, a short piece of metal that is intended to be perpendicular to the plane of the part. This flange is formed by stamping the part from flat stock. The flanges are typically spot welded together. As discussed in Chapter 6, when such a part is stamped, there is some uncertainty in the bend radii at each end. The result of this is that the overall width of the part from flange to flange is uncertain. Figure 8-12 shows a DFC for this assembly. Because each part locates the adjacent part, we say that it has a mate with that part. We indicate this with arrows between the parts in the DFC. Figure 8-12 can be read to say: "Part A locates part B and part B locates part C. The KC is a geometric relationship between part A and part C." Note 7 This example was provided by Robert Bonner and James D'Arkangelo of Ford Motor Company. that we can trace a chain of mates from one end of the KC to the other. Note, too, that the flange joints completely constrain the adjacent parts along this chain. On this basis, we say that this assembly is a Type 1. The direction of the chain, as well as the designation of part A as the root, is arbitrary. A feasible assembly sequence for this assembly is 1. Mate parts A and B; 2. Mate parts B and C. All of the foregoing, together with the DFC, comprise the documentation of the design intent for this simple assembly. Figure 8-13 shows an alternate design for this assembly. It differs from that shown in Figure 8-11 in that there is a contact between part B and part C. The designer has proposed this design because he predicts that the sizes of the parts measured between the flanges will not be accu- rate enough to ensure delivery of the KC. He knows that only the overall width L matters, so he has shown parts B and C joined by a slip joint. This joint can be adjusted so that width L will be achieved. However, this design differs fundamentally from the original. A candidate DFC appears in Figure 8-14. This DFC does not contain a chain of mates from one end of the KC to the other. In fact, we can see that part B and part C do not constrain each other in the direction of the KC. These two facts tell us that this is a Type 2 assembly and that we need a fixture or measurement to provide the missing constraint. Figure 8-15 shows a candidate fixture designed to re- move the under-constraint from this assembly, while Fig- ure 8-16 shows the DFC that applies to the assembly when this fixture is used. A number of points are worth noticing. First, it is now possible to trace a chain of mates through the DFC from one end of the KC to the other, although this [...]... inside the bore 8.1 EXAMPLE TYPE 2 ASSEMBLIES 2 35 FIGURE 8-41 Two Possible DFCs for the Throttle Body Left: The DFC for the design shown in Figure 8-38 Right: An alternate design All the KCs regarding how the disk fits to the bore without sticking are condensed into one KC symbol 8.I EXAMPLE TYPE 2 ASSEMBLIES In this section we will look at some Type 2 assemblies These assemblies cannot be built merely... to identify each feature in the chain for each direction and the internal surfaces of each feature that affect the chain Figure 8 -50 and Figure 8 -51 do this for the GM process Figure 8 -50 shows that all directions of the appearance KC are delivered in the same way Figure 8 -51 shows that the weather seal KC is delivered differently in the different directions Each hybrid joint is shown as a mate for the... simplified version of this process is shown in Figure 8 -55 It creates a full 360° fuselage tube, ready to be joined to another one Typical individual sections of large aircraft are about 40 feet long and 12 to 24 feet in diameter Figure 8 -56 shows the DFC for controlling the diameter and circumference, including contributions by suppliers Figure 8 -57 shows the joining process for two of these tubes Typical... circumference KCs are shown in Figure 8 -56 Figure 8 -57 shows all the KCs that are sought during final body join It is easy to see that there are more than can be individually adjusted or given independent tolerances, inasmuch as the two sections are practically rigid The most important KC is structural, requiring minimum edge 8.1 EXAMPLE TYPE 2 ASSEMBLIES 241 FIGURE 8 -53 Chains for Determining Constraint... reexamined and revised 8.M A DESIGN PROCEDURE FOR ASSEMBLIES 2 45 8.L DFCs, TOLERANCES, AND CONSTRAINT We learned in Chapter 4 that assemblies could be properly constrained or overconstrained We showed that we could tell the difference using only nominal dimensions and did not need to consider tolerances The distinction between properly and overconstrained assemblies is crucial for understanding the role... bevels and holes are visible in Figure 8-22 and details of their construction are shown in Figure 8- 25 The bevels can also be seen in Figure 8-26 8.H.2 Automobile Transmission Automobile transmissions are complex assemblies comprising a die-cast case, a number of planetary gear sets, shafts, and subassemblies called clutches The general "Recall that the features inside a rigid part are always properly... important is the relation between the motor (sun) gear and the planetary gears 8.H EXAMPLE TYPE 1 ASSEMBLIES 233 FIGURE 8- 35 Comparison of Two Assembly Processes for the Pump Impeller Left: The original process Right: The improved process FIGURE 8-36 DFCs for the Two Assembly Processes Shown in Figure 8- 35 Top: DFC for the original process, drawn to describe the assembly of the impeller to the shaft... on the assembly process Equivalently, we can say that different Type 2 assemblies are in fact different assembly processes, with different fixtures, different assembly sequences, and different final variation in the assembly, even though they assemble the same parts Type 1 assemblies may thus be called part-driven, while Type 2 assemblies are called assembly processdriven 8.G KC CONFLICT AND ITS RELATION... keel and a straight passenger floor and deliver all the seat track KCs The fuselage body would be straight, and all major circumferences would 242 8 THE DATUM FLOW CHAIN FIGURE 8 -55 Aircraft Fuselage Assembly The individual subassemblies are assembled from the bottom of the aircraft to the top Fixtures are in gray A photograph of a typical fixture appears in Chapter 19, which is on the CD-ROM packaged... aircraft manufacturer, each of the subassemblies shown is outsourced, except for the passenger floor FIGURE 8 -56 DFCs for Aircraft Body Section Assembly to Achieve Diameter and Circumference KCs Three companies are involved in this complex DFC The figure greatly oversimplifies the situation but captures the essence The assembly comprises several skin panel subassemblies made by assembling skins to . 2 ASSEMBLIES EXAMPLE To clarify our approach to designing assemblies, we need to distinguish between two kinds of assemblies, which we call Type 1 and Type 2. Type 1 assemblies . model assemblies functionally. Our work begins at the point where the functional requirements have been established and there is at least a concept sketch. Top-down design of assemblies. tolerance chains based on assembly features in one dimensional assemblies. [Shalon et al.] shows how to analyze complex assemblies, including detecting incon- sistent tolerancing datums,

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