A Framework for Component Layout and Geometry
Design of Mechanical Systems:
Configuration Network and its Viewing Control
Kikuo Fujita and Shinsuke Akagi
Department of Mechanical Engineering
for Industrial Machinery and Systems,
Osaka University
Suita, Osaka
JAPAN
Abstract
A Framework of computational design method and model
is proposed for layout and geometry design of complicated
mechanical systems, which is named “configuration network
and its viewing control ”. In the method, a design object
is represented with a set of declarative relationships among
various elements of a system, that is, configurations, which
is gradually extended from schematic structure to exact
layout and geometry through design process. Since a
whole of such configurations forms a too complicated
network to compute all together, how to view subparts
is controlled based on levels of granularity and width
of scope range. Such a configuration network is made
to grow and refined through embodying geometry and
layout corresponding to a focused subpart with a numerical
optimization procedure. The framework has also an ability
to flexibly integrate with engineering analysis. Moreover,
a design system is implemented with an object-oriented
programming technique, and it is applied to a design
problem of air conditioner units in order to show the validity
and effectiveness of the framework.
design automation systems since early days, and their
ability are much improved by feature-based modeling
and so on (Krause and Jansen, 1990) in operationality and
representation ability. However, they are still not enough
for the aforementioned layout design coordinated with
geometry design, especially for their inventive or generative
aspects, because they intend to precisely represent static
state of geometry and they are not linked with design process
contexts.
As for computer applications to layout problems,
successful approaches have been developed in the fields of
VLSI design (Shechen and Sangiovanni-Vincentelli, 1985;
Shahookar and Mazumer, 1990), and also in the field of
architectural design (Flemming et al., 1986), by introducing
optimization techniques such as simulated annealing and
genetic algorithms, or expert systems technique. One of
the reasons why those approaches are so successful are that
each geometry of individual elements is quite simple even if
the number of elements is enormously large, that respective
problem elements are almost unique on their granularity, and
that objectives can be clearly defined. As compared with
these situations, the layout problems of mechanical systems
are still so difficult because of their complicated properties.
In this paper, we propose a framework for layout
design coordinated with geometry design, which is named
“configuration network and its viewing control ”, based
on a discussion on the complexity and computability of
mechanical systems design. In the framework, a design
object is represented with a set of declarative relationships
among various elements of a system, i.e., configurations,
which is gradually extended from schematic structure to
exact layout and geometry through design process. Since
a whole network of configurations is too complicated to
compute all together, how to view subparts is controlled
based on levels of granularity and width of scope range, and
it is made to grow and refined through embodying geometry
and layout with a numerical optimization procedure. Based
on this framework, we implement an experimental CAD
system with an object-oriented programming technique, and
it is applied to a design problem of air-conditioner units.
1
Introduction
A mechanical system is designed so as to realize some
functions, and it has schematic structure as a system
which consists of a number of components. Component
layout and their geometry design are an essential part of
design process of a mechanical system, because position
and geometry of components have a great influence on
their behavior, performance, cost and so on.
Such
design problems are recognized as a very complicated
search problem, since respective components are located
somewhere in a package, each geometry of them includes
multi-level geometric representations such as configurationlevel primitives, additional-level features and so on, and
such multiple levels have different effects on a variety of
functional disciplines.
The geometric modeling techniques have been a
most important element of computer-aided design and
1
2.1
Complexity of layout and geometry design
The difficulty of layout and geometry design problems
mentioned in the Introduction is recognized to be related
to ‘complexity ’ on representation and computation of a
design object (McCarthy and Hayes, 1969; Dennett, 1984;
Hashida and Matsubara, 1994). In order to overcome such
limitations, the meta control on how to model a design object
within the limited ability is necessary for complicated design
problems, especially in the mechanical engineering field.
The criteria for such complexity of layout and geometry
design are summarized as follows:
Wide
Narrow
Complexity and Computation in Mechanical Design
Problems
Viewing Scope for
Design Object
2
Upper Limit of
Computation
Design
Process
Rough
Fine
Viewing Level on Granularity
Fig. 1
(1) Granularity · · · System structure, layout and geometry of a mechanical systems have hierarchical structure from rough levels to fine levels. These levels are
called “granularity,” which was originally discussed by
Hobbs (Hobbs, 1985) in the field of artificial intelligence. In the design process of a complicated system,
we should manage which granularity is taken under a
consideration and how to switch among them.
(2) Scope range · · · Concerning the above granularity, in
a rough level of granularity the whole of a design object
could be dealt with all together, but in a fine level of
granularity information related to a design object would
be tremendously large and only small limited part of
a design object could be dealt with. Therefore, we
should manage the width of “scope range ” against the
levels of granularity. In layout design problems, global
layout can be dealt with in rough grain, and exact layout
and precise geometry of individual components can be
determined in fine grain.
(3) Open property · · · As for how respective system
components are developed into actual geometry, what
kinds of geometry will be used cannot be predicted,
and it is dependent on how design process be proceeded
in individual cases. Even if every possibilities on
geometry could be listed, all of them could not
be computed.
Consequently, the formulation of
layout problem has essentially “open ” property from
a viewpoint of search space.
Complexity and computability in design
problem
2.2
Computable approach for mechanical design
problems
As discussed in the above, in order to efficiently and
rationally determine layout and geometry of a complicated
object, we should manage the various aspects on the
complexity of mechanical design within the computational
capability.
Figure 1 illustrates such necessity on the management
for the complexity. In the figure, a design computation is
executed with each view by switching levels of granularity
and width of scope range. In design process, such design
view is gradually shifting from rough grain and wide scope
to fine grain and narrow scope, because main layout and
geometry with rough granularity restrict subsidiary layout
and geometry with fine granularity. That is, first rough
layout and geometry are fixed, and then fine layout and
geometry is arranged within restrictions by rough one.
In addition to gradually shifting views, preceded layout
and geometry are refined through feedback information
from succeeded layout and geometry. Such refinements
generate some alternatives, and comparison among them
are indispensable in order to find a more globally suitable
design, because the complicated design problems are
much combinatorial and many evaluation items should be
compromised.
As for the open property of design objects, it means that
all of possible design solutions cannot be searched and that
it is natively impossible. Therefore, fundamental contents
related to main functions should be designed with a global
scope, and subsidiary contents related to auxiliary functions
should be arranged with a local scope. Since these result
is dependent on design contexts, how design process is
organized and in which scope range respective contents are
dealt with are essentially important, and reasonable metacontext should be suitably organized in advance of design.
From viewpoints on granularity and scope range, a
complicated system is generally related to a variety of
engineering disciplines, which are, for example, functional
behavior, cost, manufactuability, ease of maintenance,
etc.
Among them, rough layout and geometry are
dominant for some items, and fine layout and precise
geometry are important for other items. Moreover, each
discipline includes several analysis models corresponding to
granularity levels of a hierarchical object and steps of design
process. Therefore, a scope range should be also provided
based on kinds of disciplines and levels of granularity.
Concurrent engineering is one of present major research
directions in the design engineering field (Haug, 1992;
Kusiak, 1993).
Life cycle issues, design for X (X
= Manufacturing, Maintenance, Assembly, Disassembly,
Recycling, etc.), and information models for them are
widely discussed and studied, since present situation
concerning engineering design requires total integration
with all aspects of those engineering disciplines. Our
standpoint against those researches is that such integrations
requires a resolution of the underlying complexity of
mechanical engineering design problems.
2.3 Configurations versus layout and geometry
In order to realize the design method and model based
on the standpoints discussed in the above subsections,
various object representation under respective views should
be linked together from schematic structure to fine geometry
through rough arrangement. For this purpose, we introduce
the following hybrid representation of a design object:
Configuration · · · A set of object components and
relationships among them, constructive geometric
primitives of such objects and spatial and topological
relationships among them, etc., which are defined
with declarative clauses within and between respective
levels. So-called schematic structure is recognized as
most rough-level representation of configurations in the
2
Scope
Range
Scope Range
Alternatives
Cofiguration Network
Schematic Structure
Rough
Best
Granularity
Fine
Layout &
Geometry
Viewing
Viewing Control
Control
Viewing
Control
2D Full View
Focusing
3D Partial
View
Expansion
Partial Views
Wide
Active
Active
View
Active
View
Active
ActiveView
View
View
Fine
Refinement
Refinement
Refinement
Refinement
Refinement
Contradictory
Rough
Expansion
Narrow
Better
Scope
ScopeRange
Range
Scope
Range
Scope
Scope
Range
Range
Granularity
.
..
Other Views
..
: Expansion
Translation
Embodying
Mathematical
Embodiment
Model
Layout & Numerical - Design
Variables
- Constraints
Geometry Optimization
- Objective Functions
Algorithm
: View
: Contradictory
Fig. 3 Active view as a combination of configurations
Engineering
Analysis
execute some operations within a limitation of computation
ability or related to an engineering discipline. In the
lower part, actual layout and geometry are embodied from
mathematical model generated under a focused view by
a numerical optimization algorithm, or some engineering
evaluations are executed with analysis models translated
from embodied layout and geometry. The result gotten in
the lower part are referred as feedback information in order
to refine configurations generated in the upper parts.
A view means here a viewpoint under a certain level of
granularity and a corresponding scope range, which is used
for focusing on a subpart of configurations.
Fig. 2 Configuration network and its viewing control
layout and geometry design problems. For examples,
‘A is located in front of B with some interval.’ 1
Layout and geometry · · · Positions and dimensions of
primitives and related features, which are represented
with numerical values. When determining those
dimensions, they are constrained by spatial conditions
corresponding to the configurations within a focused
view, and they can be fixed with a suitable numerical
optimization algorithm. For examples, ‘A is located
380 mm in front of B.’
The concept that topological and sizing representations are
separated is also found in a layout design approach of power
plants (Fujita et al., 1994) and a nesting method by a genetic
algorithm (Fujita et al., 1993).
3.2 Layout and geometry under configurations
Actual layout and geometry represented with numerical
values of dimensions, etc. are determined under restrictions
deduced from configurations.
Since configurations are declarative clauses on spatial
conditions among components, they can be translated into
constraints and objective functions including positional and
dimensional variables of components in a sense of numerical
optimization techniques. Once constraints and objective
functions are introduced, a feasible region is defined within
a numerically continuous search space by constraints, and a
suitable layout and geometry is determined under a guidance
with objectives by a numerical optimization procedure.
Conversely, these objectives and constraints are regarded
as the artificial potential functions which are heuristically
introduced in order to embody configurations. As for
contents of constraints and objectives, ‘minimization of a
package size’, ‘minimization of pipe length’, etc. are used
in the case of air conditioner unit design which will be
mentioned later.
3
Configuration Network and its Viewing Control
The contexts of a design object can be effectively
categorized into topological parts and numerical parts with
afore-mentioned ‘configuration ’ and ‘layout and geometry.’
The former part forms a network graph composed of a set of
declarative items and clauses. In this paper, such a graph is
called a ‘configuration network.’ Under such a configuration
network, layout and geometry design is recognized as a
process defining configurations step by step through their
refinement based on feedback information from embodied
layout and geometry and switching among alternatives.
In this section, we describe how to expand and manage
these configurations and embody actual layout and geometry
from configurations.
3.3
Management of configurations and multiple contexts
On a configuration network shown in Fig. 2, views
are switched from one to another during design process.
Configurations under respective views are expanded,
combined and refined. Such multiple contexts should be
managed for multiple scope ranges, granularity levels and
alternatives generated through refinement. This mechanism
is named ‘viewing control ’ in this paper.
Figure 3 shows the mechanism for managing such
multiple contexts on a configuration network.
The
mechanism has three axes respectively related to scope
range, granularity and alternatives. If alternatives are
omitted from Fig. 3, it corresponds to the upper part of
3.1 Configuration network
Figure 2 shows conceptual outline of our framework.
In the upper part of the figure, schematic structure of a
design object and followed configurations are represented
as a network graph, in which they are expanded from a
rough level to a fine level. In the middle part, various
partial configuration subnetworks are focused on in order to
1 ‘Configuration ’ natively means conceptual and topological structure of
the whole of a design object, which typically well corresponds to so-called
rough sketches. But, in this paper, the term, a configuration, is used to
indicate a primitive item for representing such a structure.
3
superclass
Fig. 2, where configurations are gradually expanded and
views are organized. Each design operation mentioned in
the above is applied to an active view, which is shown with
a curved line segment with arrows at both ends in Fig. 3. An
active view means here a view which is presently used for
focusing. For example, an expansion operation is done by
focusing configurations under a active view and replacing
them with more detailed configurations. This causes a shift
of the active view from a rough level to a fine level of
granularity. A refinement operation is done by focusing
configurations under a active view and replacing some of
them with alternative configurations within a granularity
level. This generates alternatives which includes a pair
of contradictory sets of configurations. Such alternatives
should be managed as well as granularity and scope range
related to hierarchy of a configuration network, because
they should be compared with each other in order to find
a more suitable design solution from global viewpoints
and to compromise plural objectives. This means that
switching mechanism between alternatives is required and
that internally contradicted views should be automatically
avoided.
The viewing mechanism would be accomplished by controlling visibility and invisibility of respective configurations
under a view, implementation of which is shown in the next
section. It is expected that a mechanism holding multiple alternatives provides designers flexibility on iteratively
searching more suitable configurations.
world
system
externalconf.
object
geometry
optimization
subclass
initial-world
rough-layout-world
expanded-configuration-world
external-configuration-world
virtual-element
package
actual-element
component
element
element-with-ports
pipe
element-with-geometry
pipeelement
port
actual-port
virtual-port
within
settled-on-bottom
in-upper-part
maintenace-space
up-down
rough-restriction
left-right
spatial-relation
front-back
set-of-3D-solid-primitives
3D-solid 3D-solidbox
column segment
primitive tube bend
2D-region-primitive
region
3D-point
circle
port-entity
3D-vector
3D-eular
3D-direction
x
2D-point
2D-vector
ψ
y
2D-direction point
z
θ
geometricφ
angle eular
variable
variable
direction
u
externalv
dimension
variable
w
objective
expression constraint
equality
inequality
Fig. 4 Class hierarchy on configuration network
is built with CLIM (Common Lisp Interface Manager) under
the X window system. A solid modeler, DESIGNBASE2 , is
also integrated for precise 3-dimensional geometric modeling. The whole system is integrated on an engineering workstation, Sun SPARC Station.
3.4 Integration with engineering analysis
In the design process of mechanical systems, engineering
analysis is indispensable to evaluate design results. It
includes various engineering disciplines, and various
analysis models from the rough to the precise are also
required corresponding to granularity levels in design
process. For example, vibration analysis of pipe systems can
be executed in several granularity levels from with skeleton
beam models to with FEM models and for various parts of
pipe systems.
The configuration network proposing here holds design
process contexts, and it keeps individual object models in
respective granularity levels. This will provide the ability
focusing subparts of a design object related to each analysis
model, which will be flexible and effective for the abovementioned requirements related to a variety of engineering
analysis.
4.2 Object-orientation for configuration network
Figure 4 shows class hierarchy used in the implementation
of the configuration network. The roles of respective typical
classes are summarized as follows:
world · · · Class used for managing and maintaining
multiple views. Respective subclasses corresponds to
different granularity levels.
system · · · Class for representing schematic structure of
a design object and how they are decomposed into
sub components and primitives through expansion
operations.
element · · · Class for representing entities of a
design object. An instance object of this class
represents only an entity without information
related to exact geometry.
port · · · Class for representing relationships among
entities of a design object, that is, where and
how they are connected or contacted each other.
Instances of this class are owned by element
instances.
In actual, individual elements of a mechanical system
are connected with each other via mechanical pairs or
piping ports. The above two classes are used in order
to represent such connections.
external-conf. · · · Class for representing external configurations. “External configurations ” mean here
some configurations defined among components,
while “internal configurations ” are represented within
schematic structure by using above elements and ports.
Therefore, they are expressly defined with instance ob-
4
Object-Oriented Implementation of Configuration
Network
In this section, we show how the framework discussed in
the above sections is implemented on a computer system.
4.1 Outline of implementation
Configuration network is composed of system components, configurations and relationships among them, which
can be represented as a network graph. In our implementation, the network graph is implemented with
an object-oriented programming technique (Booch, 1991;
Akagi and Fujita, 1990; Akagi and Fujita, 1989).
CLOS
(Common Lisp Object System), an object-oriented system
on COMMON LISP (Steel Jr, 1990), is used as a practical programming language, because of its object-orientation, symbolic manipulation functions, automated garbage collection
mechanism, etc. Moreover, the C programming language
is cooperated with it in order to efficiently execute numerical optimization calculations. The graphical user interface
2 DESIGNBASE
4
is a trademark of Ricoh Company Ltd.
Geometric
Configurations
Primitives
System Elements External & Features
Components, Ports Configurations 3D
2D
compressor
radius 2
Region-of
port 5
column 1
p-segment 1 Geometry-of
p-e 1
port 2
port 6
port 7 Geometry-of
p-e 5
pipe 1
p-bend 2
Expand
p-e 6
accumlator
bottom 4
: Objects (Instances)
Fig. 5
obj. 2
Depend-on
x3
const. 4
y3
pos. 5
dir. 6
u6
within 2
const. 2
const. 3
w4
pos. 3
Region-of
port 9
z 1
Depend-on
v4
dir. 4
x5
rectangle 2
p-segment 5
y1
u4
segment 2
port 8
port 3
port 4
pos. 1
obj. 1
const. 1
Formulation
circle 1
x1
angle 8
length 9
: Relations
z 5
z 3
Expression
y5
v6
w6
Depend-on ψ
8
θ8
φ8
: Associations
const. 5
Values
bottom 3
length a
const. 6
const. 7
Numerical Optimization Algorithm
Translate
within 1
port 1
invisible under a view and how to combine and distinct
objects among views. As practically shown in Fig. 5,
a configuration network is composed of a lot of instance
objects and relationships among them. Such objects are
registered in a name server, which is actually a hash table
in CLOS, so as that they be referred with their names.
The referability of each object in a certain view is
managed with instances of world classes, each of which
corresponds to a view, by using bit vectors in the following
way: Each world is indexed with an integer number, and
each object holds a bit vector in its slot. If the bit value of
an object at the position indexed for a world is on, the object
is visible within the world. Otherwise, it is invisible. The
referability of other objects via associations and relations
is also managed in the following way: If both of instance
objects concerning such a relationship are visible, respective
objects are referable via such a relationship. Otherwise,
they are not referable each other.
For examples of
these mechanisms, sets of expanded instance objects under
different views are exclusive, and they can be distinguished
each other via ‘expand ’ associations.
These mechanisms provide us native means for controlling multiple contexts.
Mathematical Model
Variables :
Constraints &
Positions, Directions
Objectives
& Dimensions
const. 8
Translate
obj. 3
: Pointer
: Message
4.4
Embodying layout and geometry with numerical
optimization
In the configuration network, configurations are embodied
into exact layout and geometry, by solving an optimization
problem formulated with the restrictions caused by
configurations, in the following way (Fujita et al., 1994):
First, instance objects representing numerical constraints
and objective functions are generated based on a focused
part of a configuration network under a view. Second,
the equations held in slots of those instance objects are
arranged in order to efficiently execute an optimization
calculation by means of symbolic algebra, and a subprogram
corresponding to the arranged optimization model is
automatically coded in the C language.
Third, an
optimization calculation is executed by linking it with
a subroutine of an optimization algorithm, where QuasiNewton method is used in the application. Finally, the values
of attributes fixed with the optimization calculation are
stored in respective instance objects. Consequently, exact
layout and geometry corresponding to the configurations are
embodied.
Object-oriented representation of configuration network
jects under this class. Subclasses correspond to more
specific external configurations.
geometry · · · Class for representing geometry of elements. This is classified into subclasses for 3dimensional or 2-dimensional definite geometric primitives and subclasses for subsidiary information for
defining those units such as points, dimensions, directions and angles. Instances of the former hold instances
of the latter as pointer in their slots.
optimization · · · Class for representing mathematical
relations among instance objects of the above classes.
variable · · · Class for representing variables. Most
instance objects of this class are held in
slots of instance objects representing geometric
information. Each instance holds its value, status,
etc. in its slots.
expression · · · Class for representing mathematical
equations corresponding to internal and external
configurations. This is categorized into equalities,
inequalities and objective functions.
Figure 5 shows an example of representation of a
configuration network under these classes. In the figure,
many instance objects are defined and they are connected
with each other through ‘associations’, ‘relations’ and
‘pointers in slots’. Associations and relations are our
customized extension to CLOS for representing relationships
between a pair of instance objects. The former are used for
representing directional relationships, and the latter are used
for representing non-directional relationships. For examples
of these relationships, ‘expand ’ associations are used for
representing the relationships from instance objects in a high
grain to instance objects in a low grain.
5
Application to Air Conditioner Unit Design
In this section, we show an application of the
configuration network and its viewing control to the layout
design problem of air conditioner units.
5.1
Characteristics and context of air conditioner unit
design
In the design problem of air conditioner units, several
components such as compressors, an accumulator, an
receiver, etc. should be arranged and pipes should be also
routed among them, so as to minimize the total length of
pipes, to satisfy conditions relating to ease of assembly and
maintenance, to reduce vibration of pipes and so forth. The
layout problem is complicated because they are arranged
in free 3-dimensional space and multiple disciplines are
concerned, though the number of components are relatively
small. Its characteristics and context are summarized from
the viewpoints of complexity as follows:
• Design process is decomposed into ‘rough layout
of components,’ ‘determination of configurations of
4.3 Management of multiple contexts
As shown in Fig. 2 and Fig. 3, a configuration network
includes multiple contexts. The viewing control mechanism
is required concerning how to make objects visible or
5
( 1 ) : Schematic Structure
filter
Pipe Subsystem (OUT-STD)
Compressor
pipe
pipe
Filter
Check
Valve
pipe
1/2 B
Oil Separator
Filter
Pipe Subsystem (OUT-STD)
solenoid expansion valve
heat exhanging pipe
4-directional
1B
valve
1/2 B
1B
y
x
closing
valve
Oil Separator
Check
Valve
Compressor
(STD)
5/8 B
check valve
5/8 B
1 1/4 B
(INV)
9/8 B
filter
compressor
7/8 B
(STD)
package
Fig. 7 Schematic diagram of an air conditioner unit
positions, dimensions and directions. Finally, the values
of those variables are determined, and then layout and
geometry are fixed as ‘solids.’
How to represent these models in CLOS with objectorientation was represented with the classes shown in
Fig. 4, and an example of instance network was shown
in Fig. 5. In such a modeling method, what kinds of
external configurations are used is deeply related to contents
and meta-context of an individual application. In the case
of air conditioner unit design, spatial relations between
elements and a package, rough restriction of components
based on rough layout, relatively spatial relationships among
components, etc. are represented as external configurations.
Pipe Subsystem
(OUT-STD)
Oil Separator
z
1B
oil separator
compressor
Filter
Other
Components
1B
accumlator
( 4 ) : Solids
Pipe Subsystem (IN)
Switch Box
heat
exchanger
7/8 B
( 3 ) : Skelton with Features
Pipe Subsystem
(OUT-STD)
fan
1/2 B
1B
Oil Separator
Check Valve
Compressor
( 2 ) : Pipe Sequence Codes
filter
1/2 B
receiver
Fig. 6 Configurations versus layout and geometry
individual pipe systems’ and ‘embodiment of exact
shapes of those pipe systems.’ Granularity can be
introduced based on these levels.
• Among various issues, rough layout of components are
dominant for a whole part, and respective piping routes
are important in individual detail parts. Therefore,
scope ranges can be introduced based on these
distinction in cooperation with granularity.
• The following frames can be introduced for search
space of a layout problem in order to properly limit
possibility of alternatives into a computable level.
. Geometry of each main component can be roughly
represented as a simple solid primitive or a set
of ones. They are arranged in a quasi twodimensional way with a certain reference plane.
. A pipe system is modeled as a sequence composed
of pipe segments and pipe bends, i.e., ‘pipe
sequence codes.’ A pipe route is primarily
represented with skeleton by ignoring radius of
pipes and bends in a pipe sequence.
The
operations determining such a route are also done
by referring the above reference plane in a 2.5
dimensional space.
5.3 An example of component layout and pipe routing
In the following, we show how to practically execute
various layout operations step by step, and illustrate an
example result corresponding to respective operations.
(1) Schematic structure of an air conditioner unit
Before layout and geometry design, schematic structure
is given as a design condition. Figure 7 shows an example
of schematic structure of air conditioner units. In the figure,
several main components are connected with pipes and some
auxiliary components are inserted within respective pipes.
(2) Rough layout of components
First of all, main components are arranged in the
2-dimensional space.
When arranging, the following
conditions are considered: (1) All components are arranged
in a package with a better balance. (2) A pair of components
which are directly connected with a pipe is located in
close to each other, because the distance between them is
dominant for exact length of the pipe. (3) Some estimated
space for piping is required around respective components.
And, (4) critical space concerning ease of assembly and
maintenance for several components and pipes is kept in this
level, because it is difficult to arrange such contents in the
succeeded fine levels without afore-consideration.
In the application shown here, the margin space is
introduced by virtually enlarging the size of respective
components for a balance and piping space. Maximization
of such spaces and minimization of the distances between
component pairs connected with pipes are taken as objective
functions. Other conditions are also formulated as inequality
constraints. Since this mathematical problem includes
conflicted objectives, several solutions are generated so as
to minimize the pipe length under some fixed sizes of
margin space, and a superior one is selected by referring
how layout violates other conditions. These alternatives for
5.2 Object modeling and configuration elements
The concept for object modeling in this application is
illustrated in Fig. 6. In the figure, layout and geometry
of a pipe subsystem are determined from the upper part
to the bottom part as follows: First, schematic structure
is given as a design specification, which is composed of
components and connections among them through pipes.
Second, the ‘pipe sequence codes ’ of pipe elements which
is composed of segments and bends is determined based on
port directions of individual components, etc. Third, a pipe
is represented as a ‘skeleton ’ in three dimensional space,
and solid templates are defined with feature variables on
6
Fig. 8 Rough layout of components
several margin sizes form multiple contexts and they are
simultaneously held with the world instances.
Figure 8 shows an example of rough layout for the
schematic diagram shown in Fig. 7. In the figure, dotted
lines show margin spaces for individual components and
thick lines indicate which pairs are connected with pipes. In
addition, rectangular areas in the front of two compressors
are virtual spaces remained for assembly, etc. The positions
determined in this way are referred as desired positions in
the next pipe routing step.
(3) Full layout with pipe routing
In the next step, pipes are routed step by step and the
final positions of components are determined through the
following steps:
1. Determining pipe sequence codes for a pipe · · · First,
the internal configuration of a pipe, that is, pipe
sequence codes which was mentioned with Fig. 6,
is assumed based on port directions of components.
While several alternatives are deducted, a candidate
which is composed of less elements is selected, because
shorter pipe length is expected.
2. Embodying pipe geometry · · · The pipe sequence is
skeletonized and expanded into solid primitives, i.e.,
segments and bends. Their positions and dimensions
are fixed by a numerical optimization procedure under
the configurations. Objectives are here to minimize
total pipe length and to minimize deviation from the
positions determined in rough layout of components.
As a result, the pipe layout and geometry are embodied.
3. Verifying and refining configurations related to a pipe
· · · In some cases, the embodied layout and geometry
violates the criteria which are not considered in the predefined configurations. The designed result is evaluated
through engineering analysis. If some problems are
found, the configurations are refined by replacing a part
of pipe sequence codes or adding additional external
configurations.
4. Embodying, verifying and refining for combined sets of
pipes · · · Configurations related to layout and geometry
determined for individual pipes are gradually combined
into. They are embodied into layout and geometry,
verified and refined iteratively in the same way as the
cases of individual ones.
Among these procedures, since determination of configurations on individual pipes are essentially so complicated, first
a small part of configurations are fixed, and then such subparts are combined into a whole step by step. These combinations and refinements cause a variety of alternatives,
Fig. 9 Partial layout of a pipe system
Fig. 10 Whole layout of components and pipes
which are held with the mechanisms with world instances.
This enables for designers to easily compare candidates with
each other and to flexibly organize a design process.
Figure 9 shows a layout result of a pipe subsystem
between an oil separator and a compressor, where a valve
and a filter are also inserted in it. In the figure, the positions
of two components are restricted with the result of rough
layout shown in Fig. 8. Figure 10 shows a final layout result
of the whole part. This result follows partial layout results
including a layout shown in Fig. 9.
(4) Integration with vibration analysis
An example of integration with rough vibration analysis
is demonstrated here in Fig. 11, while various engineering
disciplines are related to the layout design problem of air
conditioner units. Vibration analysis with a rough but light
model can be executed by using transfer matrix method
(Seto et al., 1988), in which a pipe system is modeled as a
skeleton. This model well corresponds to pipe sequence
codes. Therefore, the analysis model can be easily integrated
with object models concerning the configuration network,
and analysis can be executed in a proper level of granularity
7
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Fig. 11 Vibration analysis of a pipe system
within the prescribed context of design process.
6
Concluding Remarks
In this paper, we proposed a framework for layout and
geometry design of mechanical systems, which is named
“configuration network and its viewing control ”. The
framework was experimentally implemented, and it was
applied to a design problem of air conditioner units in
order to demonstrate its concept and to ascertain its validity.
The fundamental concept beyond the framework is that the
information and contents are natively too much to deal
with in a whole, and that a well-structured meta-context for
design process should be prescribed. For this direction, this
paper provides a framework which has abilities for holding
hierarchical and multiple contexts in a cooperated fashion
and for interpreting declarative configurations into exact
layout and geometry step by step.
This study has been still applied to an example of
limited problems. We are planning to more generalize the
framework and to apply it to several mechanical systems in
other fields.
Acknowledgment
We thank Noriyasu Hirokawa, Masato Fuwa and Hiroyuki Tada
of Osaka University for their programming efforts for experimental
implementation of the framework for air conditioner unit design. We
also thank Yoshiyuki Uemura, Nobuhiro Kusumoto and Touro Hirano of
Daikin Industries, Ltd. for their helpful instruction on the practical design
problem of air-conditioner units. Moreover, we are appreciative of the
support provided by The Ministry of Education, Science and Culture of
Japan through Grant-in-Aid for General Scientific Research 06452169.
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8