[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 intro￾duced. We will then present the scope of the DFC in as￾sembly planning using several examples.

Finally, we will see that the DFC contains all the in￾formation 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 chap￾ter, we again turn to the desktop stapler. In this chapter,

we will learn how to characterize the liaisons of an as￾sembly 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 li￾aisons are omitted altogether. The stapler also illustrates

the difference between mates and contacts. The differ￾ence is illustrated in Figure 8-3. All these concepts will be

made concrete in this chapter and related to their under￾lying 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 as￾semblies 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 func￾tional 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 man￾aging the design of the entire assembly in terms of me￾chanical "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 con￾tacts. [Muske] describes the application of dimensional

management techniques on 747 fuselage sections. He de￾scribes 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 toler￾ancing 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 sim￾ilar 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 as￾sembly 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 rela￾tionships 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 in￾formation about an assembly:

"Location responsibility": Which parts or fixtures lo￾cate 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 lo￾cation of each of the parts relative to some base part

or fixture which represents the reference dimension.

The design process comprises two steps: nominal de￾sign and variation design. The nominal design phase cre￾ates 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 dimen￾sions, 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 di￾mensions 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 identi￾fied, 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 differ￾ent 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 exam￾ine 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 un￾derlying 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, parts3

are merely frameworks that hold

assembly features, while assembly features are the links

that establish the desired state of constraint among adja￾cent 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 indi￾vidual 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 as￾sembly 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 repre￾sentation 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

4 x 4 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 be￾gins. 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 associ￾ated 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 con￾nected to each other. The DFC (right) shows how they are

connected and constrained. Each arc is labeled with the de￾grees 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 infor￾mation 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 incoming4

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 bear￾ings). 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, indepen￾dent of the resistors, capacitors, and other individual cir￾cuit elements. It has a unique ground or reference voltage.

Many operating characteristics of the circuit can be cal￾culated 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 de￾grees 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 assem￾bly 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 assem￾bled 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 con￾strained 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 com￾pleted assembly. If the parts in a partially completed as￾sembly 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 locat￾ing the parts but it does not say how the parts will be lo￾cated. 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 fea￾tures to provide the constraint. Once features have been

declared, we can calculate the nominal locations of all the

parts by chaining their 4x 4 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, how￾ever, we need to distinguish two kinds of feature joints:

mates and contacts. These are the subject of the next

section.