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IMPROVING ENGINEERING SYSTEM DESIGN THROUGH
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IMPROVING ENGINEERING SYSTEM DESIGN THROUGH
SCIENTIFIC VISUALIZATION METHODS

By

Gayle Ellen Ermer

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Mechanical Engineering
1994

ABSTRACT

IMPROVING ENGINEERING SYSTEM DESIGN THROUGH
SCIENTIFIC VISUALIZATION METHODS
By

Gayle Ellen Ermer

One of the greatest challenges for designers of complex engineering systems is to
interpret simulation data. Numerical results need to be presented in a way which is
meaningful and encourages understanding Of the simulated system behavior. Scientific
visualization (SV) is an emerging discipline in which methods are developed for clear

presentation of data to scientists and engineers.

This thesis presents a significantly improved design environment for engineering
systems which has been developed and implemented using the concepts of SV . The
design environment is based on the Bond Graph (30) as a modeling representation. The
36 captures the interconnectedness of the system components and Shows power
pathways as energy is transferred within the system. Animation of Simulation results
directly on the BG and the correspondence between the bond graph model and the
physical system are both exploited to aid the designer in comprehending the system’s

behavior.

The research was conducted in two phases for each of which pilot environments
were designed. In phase one a two-dimensional animation tool for simulation of variable
values on the 86 was developed (BGVis-2D). A complex railcar airbrake switching

system was modeled and simulated to illustrate the benefits of the visualization. A

second example was developed to show the application Of the new visualization tool in a
somewhat abstract model space, namely modal analysis . In phase two a tool to represent
805 as 3-D objects was developed using the PHIGS graphics standard (BGVis-3D). A
bounce-pitch-roll model of a car body and suspensions was implemented in the 3-D

environment and its simulated behavior when encountering a pothole was investigated.

Dedication

To my husband, Eric.

iv

ACKNOWLEDGEMENTS

I would like to sincerely thank my major professor, Dr. Ronald Rosenberg, for his
support, guidance, and encouragement throughout my PhD. program. Not only was his
knowledge invaluable for my research, but I learned many things about teaching from

him as well.

I also express my appreciation to the members of my thesis committee: Drs.
Clark Radcliffe, Erik Goodman, and Richard Hall gren. Their suggestions and comments

were very valuable.

My gratitude also extends to ASME for providing me a graduate teaching
fellowship and to the Zonta organization for awarding me the Amelia Earhart Fellowship.
These scholarships were very precious to me, not only financially, but in the

encouragement they gave me to continue pursuing this degree.

Finally, special thanks go to my parents, Robert and Carol Essenburg, and the rest
of my family for always encouraging me to use my talents and for instilling in me the

values that made this accomplishment possible.

 

TABLE OF CONTENTS

List of Tables ...................................... viii

List of Figures ..................................... ix

Nomenclature ..................................... xii

Chapter 1 - Introduction ................................ 1

1.1 Problem Definition ............................. 1

1.1.1 Importance of Improving the Efficiency of System Design . . . 1

1.1.2 The Role of Insight and Interpretation of Results ........ 2

1.1.3 The Role of Visualization in the Modeling Process ....... 5

1.2 Research Objectives ............................ 11

1.3 Description of Thesis Organization .................... 14

Chapter 2 - Bond Graphs and Scientific Visualization ................ 16
2.1 Using Bond Graphs as a Tool for System Analysis and Design ..... 16-

2.1.1 Modeling of Engineering Systems ............... 16

2.1.2 Bond Graph Modeling Methodology .............. 19

2.1.3 Computer Support for Simulation ................ 23

2.2 Scientific Visualization .......................... 24

2.2.1 Description of the Field ..................... 24

2.2.2 Current Tools and Research Areas ............... 27

Chapter 3 - A Two-Dimensional Bond Graph Visualization Environment ..... 30

3.1 Environment Specifications ....................... 30

3.2 Design of the Two-Dimensional Visualization Environment ...... 31

3.2.1 Features Selected for Implementation ............. 31

vi

3.2.2 Platform Selected for Implementation ............. 38

3.2.3 User's Guide ................... , ....... 40
Chapter 4 - A Three-Dimensional Bond Graph Visualization Environment ..... 45
4.1 Environment Specifications ....................... 45
4.2 Design of the Three-Dimensional Visualization Environment ...... 46
4.2.1 Features Selected for Implementation ............. 46
4.2.2 Platform Selected for Implementation ............. 48
4.2.3 Description of the PHIGS Graphics Standard ......... 49
4.2.4 User's Guide ........................... 53
Chapter 5 - Visualization Examples Using BGVis-2D ................ 57
5.1 Automobile Modeling Example ..................... 57
5.2 Railcar Airbrake Switching System Example .............. 79
5.3 Modal Analysis Example ........................ 110
Chapter 6 - Visualization Example Using BGVis-3D ................ 116
Chapter 7 - Conclusions ............................... 122
7.1 Summary of Contributions ....................... 122

7.1.1 Two-Dimensional Visualization ................ 122 -
7.1.2 Three-Dimensional Visualization ............... 123
7.2 Areas for Further Research ....................... 124
Appendix A - A Brief Introduction to Bond Graph Modeling ........... 128
Appendix B - Program Documentation and Code ................. 139
8.1 Two-Dimensional Environment ..................... 139
8.2 Three-Dimensional Environment .................... 203
Appendix C - Example Model Files ......................... 254
References ...................................... 271

vii

LIST OF TABLES

Table 1. Standard Bond Graph Elements ..................... 22
Table 2. Car Body and Suspension Model Equations and Parameters ...... 65
Table 3. Response Data from Pothole Simulation ................ 67
Table 4. Eigenvalues/vectors of Mechanical Three DOF System ........ 112
Table A-1. Variables in Various Energy Domains ................ 129
Table A-2. Standard Bond Graph Elements ................... 130
Table A-3. Block Diagram Elements ....................... 130

Table A-4 Causality Possibilities for Bond Graph Elements ........... 13S

viii

Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.
Figure 8.
Figure 9.
Figure 10.
Figure 11.
Figure 12.
Figure 13.
Figure 14.
Figure 15.
Figure 16.
Figure 17.
Figure 18.
Figure 19.
figure 20.
Figure 21.
figure 22.

LIST OF FIGURES

A Design Process Description ..................... 4
An Engineering Simulation Activity Diagram ............. 5
Interpretation of Results Diagram ............... . . . . 1 1
Scientific Visualization and the Design Process ............ 27
Dynamic Display Key to Widths and Colors .............. 36
ENPORT Postprocessor Module Control Window ........... 40
Dynamic Display Module Control Window .............. 41
PI-IIGS Modeling Transformation Pipeline ............... 52
3-D Postprocessor Control Window .................. 53
The 3-D Postprocessor Display Window ............... 56
Vehicle System Illustration .................. . . . . 58
Schematic of Car Chassis Unit and Suspensions with Seat ...... 59
Macro Bond Graph of BPR Model .................. 60
2-D Bond Graph Representation of Seat Unit ............. 61
2-D Bond Graph Representation of Rigid Chassis Unit ........ 62
Detail of Single Suspension Assembly ................ 63
Two-Dimensional Bond Graph of Car Model ............. 64
Mathematical Model of Pothole Source of Flow ........... 66
Response Data from Pothole Simulation ............... 68
Power Variable Response for BPR Model (Time = 0.050) ...... 70
Power Variable Response for BPR Model (Time = 0.110) ...... 71
Power Variable Response for BPR Model (Time = 0.115) ...... 72

ix

Figure 23. Power Variable Response for BPR Model (Time = 0.135) ...... 73
Figure 24. Power Variable Response for BPR Model (Time = 0.300) ...... 74
Figure 25. Power Variable Response for BPR Model (Time = 0.305) ...... 75
Figure 26. Power Variable Response for BPR Model (Time = 0.325) ...... 76
Figure 27. Glyph Display of Energy Response for BPR Model (Time = 0.135) . 77
Figure 28. Time Plot of Displacement Obtained by Selecting Q88 ....... 78
Figure 29. Schematic of the Airbrake Control Valve Switch ........... 80
Figure 30. Top Level Bond Graph Decomposition ................ 81
Figure 31. Bond Graph Decomposition of DB- 10 Module ............ 82
Figure 32. Schematic of the Service Accelerated Release Valve (2) ....... 83
Figure 33. Bond Graph of the Service Accelerated Release Valve ........ 84
Figure 34. Power Variable Display for Check Valve (Time = 0.5) ....... 87
Figure 35. Power and Effort Variable Display for Check Valve (Time = 0.76) . 88
Figure 36. Flow Variable Display for Check Valve (Time = 0.21) ........ 89
Figure 37. Flow Variable Display for Check Valve (Time = 0.6) ........ 90
Figure 38. Bond Graph of the Main Piston System and Reservoirs ........ 92
Figure 39. Power Response for Air Brake Model Charging Mode (Time = 18.9) 94
Figure 40. Power Response for Air Brake Model Charging Mode (Time = 31.8) 95
Figure 41. Power Response for Air Brake Model Charging Mode (Time = 49.8) 96
Figure 42. Power Response for Air Brake Model Charging Mode (Time = 58.2) 97

Figure 43.
Figure 44.
Figure 45.
Figure 46.

Power Response for Air Brake Model Braking Mode (Time = 12.9) . 99

Power Response for Air Brake Model Braking Mode (Time = 14.1) . 100
Power Response for Air Brake Model Braking Mode (Time = 19.95) 101
Flow Response for Air Brake Model Recharging Mode (Time = 2.85) 103

Figure 47. Flow Response for Air Brake Model Recharging Mode (Time = 5.4) 104
Figure 48. Flow Response for Air Brake Model Recharging Mode (Time = 9.45) 105
Figure 49. Flow Response for Air Brake Model Recharging Mode (Time = 14.4) 106

X

Figure 50.
Figure 51.
Figure 52.
Figure 53.
Figure 54.
Figure 55.
Figure 56.
Figure 57.
Figure 58.
Figure 59.
Figure 60.

Figure 61.

Power Response for Air Brake Model Release Mode (Time = 2.25)
Power Response for Air Brake Model Release Mode (Time = 4.2)
Schematic of Mechanical Three DOF System .............
Bond Graph of Mechanical Three DOF System ............
Flow Variable Display Showing First Mode Shape ..........
Displacement Variable Display Showing Second Mode Shape . . . .
Displacement Variable Display Showing Third Mode Shape

3-D Bond Graph Representation of Car and Suspensions Model

3-D Dynamic Display Of Response to Pothole Input (Time = 0.112) .
3-D Dynamic Display of Response to Pothole Input (Time = 0.115) .
3-D Dynamic Display of Response to Pothole Input (Time = 0.300) .
3-D Dynamic Display of Response to Pothole Input (Time = 0.305) .

Figure A-1. Mechanical Translation Example ..................

Figure A-2.
Figure A-3.
Figure A-4.
Figure A-S.
Figure A-6.
Figure A-7.

Electrical Example ..........................
Hydraulic Circuit Example ......................
Schematic of Radar Pedestal Control System ............
Section (Macro) Bond Graph as Illustration of Decomposition . . .
Bond Graph of the Radar Pedestal System . ............

Response to a Step Input .......................

xi

. 108

109
110
111
113
114
115
117

138

NOMENCLATURE

cg - Center of Gravity

e - Voltage
E - Effort
F - Flow
F - Force

i - Current

P - Momentum
P - Power

Q - Displacement
t — time

V — Velocity

w - Rotational velocity

ABBREVIATIONS

AR - Auxiliary Reservoir
BC - Brake Cylinder

BG - Bond Graph

BP - Brake Pipe

CV - Check Valve

ER - Emergency Reservoir

SV - Scientific Visualization

xii

 
 

Chapter 1

Introduction

1.1 Problem Definition

1.1.1 Importance of Improving the Efficiency of System Design

Today's competitive global markets put a great deal of pressure on engineers to
efficiently design, manufacture, and maintain engineering systems. It is no longer sufficient
to produce systems which are adequate. In the future, engineers must be concerned with
achieving the "best” design to meet specifications by improving device performance and
eliminating undesirable behaviors. They must produce new products in the shortest
possible amount of time in order to stay competitive. They also need to know how much
variation in the designed system's behavior can be tolerated to determine manufacturing

constraints.

The design process is intended to produce an optimum solution to a problem
through iteration (Arora, 1989). This is becoming an increasingly difficult task as
engineering systems become larger in scale and span many different engineering
disciplines. Automobiles and aircraft are important examples of complex systems which
require detailed prediction and assessment of system function to generate improvements in
Performance and reductions in undesired behaviors such as noise. Studying system

behaVior by modeling the system with experimental physical prototypes is a time

consuming and expensive method for design enhancement. Some systems, such as the

2
proposed National Aerospace Plane designed to fly at speeds up to Mach 25, may be

impossible to study to any great extent in this way.

Therefore, it is necessary to improve the practice of design by making it easier to
predict and comprehend the behavior of engineering systems. Mathematical modeling and
simulation of physical systems is one of the most cost effective methods for analysis and
prediction of system behavior, especially for systems of very large scale. The trends of the
future require mathematical modeling and simulation which promote learning and
understanding about system behavior to allow engineers and designers to make changes
which improve a system. This dissertation describes research to improve engineering
system design through the development Of tools that improve the efficiency and

effectiveness of the design process.

1.1.2 The Role of Insight and Interpretation Of Results

Considerable thought has been given to the subject of what components should be
included in a design methodology and the order in which they should be executed. Some
current views of the process of designing will be briefly described in order to set the Stage
for a system design progression which shows clearly some areas where improvements

would be welcome.

In his book The Principles of Design, Suh specifies a design method which begins
with the identification of "function requirements" from a given societal need. A product is
created and its behavior is compared to the functional requirements. The product is then

modified iteratively until the functional requirements are satisfied (Suh, 1990). Medland
prOposac a computer-based design process which consists Of three main phases: concept,

analysis, and scheming. These processes are interconnected and information can flow

3
between any pair of them (Medland, 1986). Shoup defines a more precise six-step process

Of design which includes: recognition of need, creating a design, preparing a model, testing
and evaluating the model, improving the design, and communicating the design. These
activities form a control loop of sorts where the design is improved until it passes the testing
and evaluation stage (Shoup, et a1, 1987). Manufacturability is also a key element in the
design of systems, and recently much attention has been given to how this concept should
be integrated into the design process (Gadh and Prinz, 1991). These models of design
synthesis, along with others in the literature, can be helpful in identifying where
improvements to this process are needed. In order to provide a common framework within
which the improvements to the design process described in this thesis can be detailed, a

description of design practice has been developed which is specific to lumped parameter

system design.

Figure 1 presents a general design process description which involves several
information objects. This particular diagram is only one view of the process of system
design selected from the many which have been proposed, but it covers the main features of
this activity as described by others, and it gives a basis for the figures and discussion which
follow. The aim of an engineering design process is to fill a given societal need either by
inventing a physical system to solve some problem, or by improving the performance of a
given System. In this context, the designer's model is the mental picture the designer has of
the Strueture and behavior of the physical object which constitutes the engineering system.
In the Case where the design is only conceptual, the internal model is the designer's
perception of the components and behavior of the resulting design. The designer's model is
the“ inherently hard to identify or control, since it exists only in the mind of the designer.
The activity of design involves relating several concrete inf orrnation objects to the
desi guer’ 3 model in order to provide knowledge about potential system improvement and

Opt“ .
lm‘Zation. One information Object is the specified behavior for the system to be

4
designed, which may be numerical or qualitative. Although the relationship between

specified behavior and modeling is very important, the examination of this aspect of design
is not the focus of this research. Another information object is the measured behavior. This
would consist of any experimental lab testing which reveals information about the behavior
of the system. Obviously if the design is only in the conceptual stage, there may not be data
of this type available. The remaining information state is the simulated behavior of the
system. This is information which can be obtained from mathematical modeling and
analysis. This research is concerned with the shaded area of the diagram, which has been
labeled analysis activity. The focus is on the interaction between the reference model in the
engineer's mind and the knowledge which (an be gained through the activities of modeling

and simulation. It is the improvement of the relation of these two information objects that is

Valuable in leading to optimization of the design.

 

 

 

 

 

 

 

 

Figure l. A Design Process Description.

a;

3

1.1.3 The Role of Visualization in the Modeling Process

Figure 2 shows a more detailed Simulation activity diagram which focuses on the
analysis portion of Figure 1. This particular process outline is based on the use of system
or bond graphs as a structured modeling technique. The nodes in the diagram are model
information states, while the connectors represent transfonnations of information from one
state to another. Paths between the nodes other than the ones actually drawn in the diagram

exist, but were omitted for clarity. A brief description of each of the Steps in Figure 2

follows. Some of the current computer tools available to support these stages are also

mentioned.

 

l

 

 

(6) Visual Display 0?

 

 

 

 

Behavior
13 2-3
5-6
(5) Numerical Characterization 1-4 (3) System Graph Model
of Behavior

 

 

V 34

(4) Equation Model

4-5

 

FIgure 2. An Engineering Simulation Activity Diagram

6

Designer's Model (node I ). The first step in physical system analysis is to mentally

identify the particular system under consideration. This mental model is primarily visual
and has been described as "the mind's eye, the locus of our images of remembered reality
and imagined contrivance" (Ferguson, 1992). Building this model includes identifying the
boundaries of the system and important system variables, as well as comprehending and
visualizing the basic relationships among system components. All characteristics of the
system significantly affecting the behavior must be included in the designer's reference
model; otherwise the results of the model simulation will not be accurate. In physical

systems of realistic complexity, some relatively unimportant characteristics may have to be

neglected in order to make the problem manageable.

Schematic model (node 2). The next Step typically involves making further
assumptions about system characteristics and sketching the Operational ones on paper or on
a computer screen in a form which is commonly understood. This process is associated
wi th path 1-2 in Figure 2. The schematic model is an idealization of the physical system
Which includes all important aspects of system behavior to be considered, and it is usually
domain specific. For example, mechanics has its own symbols for commonly used items
such as springs, masses, dampers, and the connections between them, while electrical
engineering has developed a standard set Of circuit diagramming techniques. At this point

the Schematic model is an iconic one (Suckling, 1978). That is, it represents the physical
SyStem components and interconnectedness in a Spatial way without holding to actual
dimensions, but clearly the schematic corresponds to the topology of the actual system. For
some simple design problems it may be possible to form an equation model directly from
kno“(ledge of the physical system, following a path from 1 to 4, but this is not usually
pra“meal for complex systems. The problem with Obtaining an equation model from
schernatic information, following a path from 2 to 4, arises because different parts of a large

m - .
“1 tldisciplinary system are expressed in domain-specific modes, Wthh leaves no easy

‘

.7

method for a consistent translation to the form of a mathematical model which will allow
simulation. Hence the use of bond graph methods becomes desirable for multidomain

engineering systems.

Software applications do exist which facilitate the transition from domain Specific
schematic models to mathematical models directly. Circuit modelers such as PSPICE
(PSPICE User Manual, 1989), mechanical multibody systems analyzers such as ADA MS
(ADAMS User’s Manual, 1989), finite element solvers such as ANSYS (ANSYS User's
Manual, 1993), and hydraulic software packages like PipeFlo (Shearing, 1992) all fall into
this category. For example, using ADAMS it is possible to create 3-D solid models of rigid
bodies and their connectors with a graphical editor, and then to animate the mathematically
simulated motions of the system on a computer monitor. Such a display is very helpful in
giving the designer a feel for how the design will move under different conditions. These
types of software are of great benefit in designing their respective single-discipline systems,
but they are not sufficient for use when integrating several disciplines into one system

design.

System Graph Model (node 3). In order to put all the pans of the system model in a
unified form, a system graph model can be constructed, as in path 2-3. System or bond
graph modeling is a standardized modeling approach which deals with energy transfer
between model components (Karnopp, Margolis, and Rosenberg, 1990). It sets up a
framework into which systems from most domains of engineering can be translated.
Information in the form of control signal and block diagram elements can also be included,
in which case the bond graph becomes a system graph. A system graph is a topological
model, presenting the components of a system and their connections with no regard as to
their actual geometry or spatial placement. The advantage of developing a system bond

graph is that a complete operational mathematical model of the system behavior can easily

8
be obtained, and computer support is available for this task. However, the disadvantage of

formulating the model in bond graph form is that the apparent correspondence between the
model and the physical system is weaker than it is with a schematic. A two-dimensional
system graph representation requires visualization effort on the part of the designer when he

or she is considering the behavior of a three—dimensional physical system.

Computer software exists which can aid the engineer in creating and manipulating
bond graph models as well as in deriving equation models and in calculating numerical
solutions. One particular program is ENPORT, which has been designed to implement
bond graph modeling techniques (Rosenberg, 1993). The bond graph elements and
structure can be input by using a two-dimensional graphical editor. Another bond graph
modeling environment is CAMAS (Broenink, 1990). CAMAS is an interactive computer
language developed to implement bond graphs. The graphical editing capabilities also

permit bond graph development represented in two dimensions.

Equation Model (node 4). A mathematical equation model contains all relevant
quantitative information about a system in question. The equation model allows prediction
of the responses of an engineering system to various conditions without implementing them
physically. For lumped parameter systems, the mathematical models generally consist of
sets of ordinary differential equations. However, for many designers, there is very little
conceptual correspondence between a three-dimensional physical system and a set of
equations. The abstractness of this type of model is what generates the need for
intermediate modeling techniques like schematics and bond graphs. It is also very difficult
to compose the large sets of equations required to describe complex systems without a
structured graphical model. Equations can be generated automatically from system graph
models (path 3-4) using ENPORT or from discipline-specific schematics using programs
like PSPICE.

Numerical Characterization of Behavior (node 5). At this point the model building
task is complete. Given the equation model, computers can be used to perform the
simulation (path 4-5), usually by solving the mathematical equations iteratively, since most
practical problems do not have closed-form solutions. Various algorithms exist which are
capable of performing this task. As real-world systems design is becoming increasingly
complex, continuing increases in computational speed and memory size allow for more and

more data to be generated related to a system under analysis.

Many computer programs exist for general numerical solution of equations. These
facilitate the creation and solution of equation models obtained from physical systems or
schematics and can be identified as direct equation or block-diagram type programs.
Examples of these are the MATRIX-x software environment (MATRIX-x User’s Guide,
1990), and MATI-IEMATICA, a powerful mathematical symbolic equation solver (Wolfram,
1991). These programs provide two and three dimensional output, but variables are not
necessarily directly related to the physical system. Difficulty in using these programs is
also encountered when the systems to be analyzed are very large involving many
mathematical equations. Programming in this case can be extremely complicated. Many
single-discipline modeling programs such as PSPICE have their own solvers based on
commonly used algorithms. ENPORT and CAMAS also have their own built-in equation

solvers.

Visual Display of Behavior ( node 6). A critical part of the simulation process is to
take the resulting response data from a numerical simulation and interpret it in a meaningful
way so that the physical system itself can be better understood (path 6-1). This involves
both quantitative analysis of simulation results and qualitative analysis leading to

understanding of global system function. The important features of the system response

10
need to be highlighted. A designer who understands how a system behaves will be

equipped to make the right changes to improve the design. Rosenblum and Brown call this
process "realization" (Rosenblum and Brown, 1992). Appropriate displays of system

response can greatly improve the interpretation of results process.

Figure 3 shows some of the possible ways to relate visualization to model
information states in order to apply simulation results to the designer's conceptual model.
The designer visualizes system response in terms of (2), (3), or (4) depending upon which
model building strategy was used. If the system is single-domain and has an accepted
iconic representation (e. g. rigid bodies or electronic circuits), then the most useful display is
the link between (6) and (2); this is denoted (A) in Figure 2. This type of display has been
implemented in many domain-specific computer programs. For example, ADAMS shows
motions of rigid bodies; PSPICE displays currents related to electric circuit diagrams.
Linking the results directly to the equations (C) would allow plotting of variables versus
time or cross-plotting of variables, one versus another. Often, however, the degree of

abstractness of an equation model makes visualization difficult.

Path (B) can be followed to link simulation results data with the system graph in a
display which could Show system variables (e.g. powers, energies, forces, currents) directly
related to the system graph. By linking results data directly to the system graph in a
computer environment, the engineer can take advantage of the structure provided by the
bond graph model to understand the overall meaning of the results data. It is this
visualization process that is enhanced by the work described here. The usefulness of a
coherent design package based on the bond graph modeling technique which aids in all
steps of the design process, especially the interpretation step, is becoming clear.

ll

(1) Designer's Model

   
   
 

 

 

 

 

(2) Schematic Model

 

66) Visual Display oh
Behavior

 

 

 

(3) System Graph ModeD

(5) Numerical Characterization
of Behavior

 

 

 

((4) Equation 14on

Figure 3. Interpretation of Results Diagram

1.2 Research Objectives

The principal objective of this research was to create and implement a Si gnif icantly
improved design environment for engineering systems based on the use of bond graph
methods as a structured modeling technique. A common practice in the context of dynamic
system analysis is to build a system graph model, to choose a set Of parameters for defining
the constitutive equations of each of the elements of the model, to run a numerical
simulation of the model for given initial conditions, and finally to compare the output results
to the expected or required behavior. In this way an engineer can determine if the model is
behaving properly (model verification). Once the model is verified, the engineer can
experiment with changing parameters to improve the system performance compared to the
design requirements for the output response. The types of questions asked by the designer
after a simulation might be: Which subcomponents of the model are most important in

determining overall system behavior? Which components use very little power and might

12
be eliminated to reduce the computational order of the model? Which parts of a mechanical

model move the largest distances over the course of a dynamic response? Which voltages
in the electrical part of a model fluctuate the most and do they remain within required levels?
DO the power levels of all the elements stay within reasonable limits for the chosen
parameters and initial conditions? A major goal of this research was to design an
environment which makes the interpretation of dynamic system response easier for

designers and makes answering these types of questions as straightforward as possible.

This objective was met in two separate stages, for each of which prototype softwares
were implemented. The first stage concentrates on improving the interpretation of
simulation results by providing a power-related animation directly tied to the 2-D system
graph. Current 2-D bond graph computer models were enhanced to provide time-varying
power information on the system graph. Computer animation is a natural way of visualizing
time-varying results obtained from a simulation. The animation shows global patterns of
behavior as well as focusing on individual quantitative details Upon demand. Energy
transfer and/or other variable value information being indicated by color and line-width
variation or glyph-type symbology as an animation in time was explored. The line-width
variation technique has previously been implemented in ENPORT to display time-averaged
power variables on the system graph (Rosenberg and Zhou, 1988). This approach was
extended to dynamic display of time-varying quantities on the system graph, thus providing
an energy and information-based animation of the system behavior. Various scaling
options are made available to the user to provide for selection of a scaling which most
clearly Shows the dynamics of the energy propagation in the system. A method was
developed for representing the changing direction of each energy flow. Other display codes
were also used which involve changes in glyph drawings to reflect the energy change in a
node with time. Once these concepts were studied in a 2-D environment, they were applied

to the next phase.

13

The second stage involved building a pilot environment for using three-dimensional
system graphs. Three-dimensional visualization is necessary because better correspondence
between topological system graph models and actual physical systems or schematics will
help the designer apply his or her physical intuition to a model in a more meaningful way.
A topological model in general is helpful because it conveys the relationships between
variables in the system, but it lacks a direct relationship to the spatial characteristics Of the
system. An engineer can conceptualize about a physical system because it can be pictured
visually in space, but at the point where a two-dimensional bond graph model is constructed,
direct correspondence to the physical system is lost to a large degree. In this work, a
system graph was allowed to be more than a topological model alone. A graphical
environment was developed in which system graph display can correspond directly to the
geometric imagery of the physical problem. The concept can be thought of as 'true
geometry' in the sense that a three-dimensional system graph can be a scaled representation
of a physical system with its elements fixed to the spatial positions of the matching elements
of the physical system. Capability for dynamic rotation Of the display was provided in
order to achieve an actual three-dimensional effect (Hays, 1992). The user is also allowed
to manipulate the model as a geometric object in the computer environment. The result is
better visualization of the power flow pathways captured in the three-dimensional structure

of the bond graph.

The principles of the emerging field of scientific visualization as expressed by some
of its proponents (T ufte, 1983 and 1990, Cox, 1990) were used to make the visualization of
each stage clear and easily understandable. In the past, traditional methods have been
successful in providing knowledge of system behavior to designers, but the production of
ever larger, more complex, and interdependent systems require substantially improved

design methods like the ones described here, in order to promote comprehension and

14

learning. This work makes a significant contribution to the area of complex system design
by providing a new tool for engineers which complements existing tools. Since the nature
of the project is closely tied to computers and their ability to produce color graphics and
animation, color printouts and photographs are included in this thesis wherever possible,
and a videotape of the example systems as implemented in the pilot 2-D and 3-D computer
environments is available upon request from the author directly or through the Mechanical

Engineering Department of Michigan State University.

1.3 Description of Thesis Organization

This thesis consists of the sections described in this paragraph. The current chapter
contains an introduction to the problem and motivation for the research as well as the order
or Presentation of further contents. Chapter 2 contains background information relevant to
the problem, in particular a short description of bond graphs and a discussion of scientific
visualization principles and practice. Chapter 3 includes a complete description of the two
dimensional visualization environment created in answer to the problem statement. Chapter
4 Covers the extension of bond graphs to a three-dimensional representation and
visualization of results in the three-dimensional environment. Chapter 5 illustrates the use
of the designed environment for solving some problems of practical scale, namely an air-
brake switching system and a car and suspension model. It also contains a discussion of
how the designed environments can be used in educational situations. Finally, Chapter 6
p’eSents a summary of what was accomplished and some ideas for future development.
Appendices are included which contain more details on certain topics related to this thesis.
Appendix A includes a more comprehensive explanation of bond graph modeling for
readers who are not familiar with the techniques. More details on the Structure and coding

or the visualization software implementations are shown in Appendix B. The complete

description of the Air-brake Switch bond graph model and its equations. as well as the

15
ENPORT model files for both the car and suspensions example and the air-brake switching

system, are included in Appendix C. This document concludes with a list of references of

particular use in carrying out this research.

Chapter 2

Bond Graphs and Scientific Visualization

2.1 Using Bond Graphs as a Tool for System Analysis and Design

2.1.1 Modeling of Engineering Systems

In the introductory chapter of this thesis the importance of modeling in the process
of designing a physical system was emphasized. Models exist in many different forms, but
in all cases their purpose is to convey to an engineer as much information about the
System's behavior as possible, and to provide the information in such a way that the
underlying concepts behind the behavior are clear and insight into the problem is gained.
An engineer cannot design a system without a reasonable conception of the way the system

oPetates and the influence that parameters have on the behavior.

Certainly it is possible to learn a great deal about a system's behavior by building
and running tests on the system itself. Usually this is not a practical way to approach
d‘Sign and it is not the most efficient. Once a system has been built, it is very expensive to
make the changes in the design that might be necessary in order for it to meet performance
critearia. Optimization in this situation is very difficult. Scaled models of systems, which
Presumably represent the behavior of a larger system but on a smaller scale, can also be
use51.111 in yielding insight about the system. Unfortunately, these types of models (wind
tunnel mockups, for example) incur some of the same disadvantages as full-scale
Pmtorypes. They are still very expensive and time-consuming to build and are hard to

modify once they have been built.

16

17

In order to learn about system behavior without building physical prototypes it is

very useful to construct mathematical models of systems. This practice is often called

“virtual prototyping” (Puttre, 1992), Since the idea is to identif y the behavior of a system

within a computer environment in order to replace or supplement what can be learned about

system behavior from the construction of physical prototypes. These virtual prototypes or

models capture the physical behavior of the system in their structure and can be simulated to

provide information about the system's response to different inputs and changes in system
characteristics. The mathematical models used to represent lumped parameter systems
typically occur as sets of ordinary differential equations. Parameters in the equations can
easily be changed to reflect design modifications, and unnecessary hardware costs are
avoided. Solving the equations numerically for given initial conditions and parameters over
a certain time period provides a prediction of the actual response of the system, and if the
Virtual prototype accurately captures the important aspects of the behavior of the system, it
can then be used to see the effect of changes in the parameters or conditions under which

the system is operated. In this way the design of the system can be improved and

Optimized.

Unfortunately, obtaining a set Of mathematical equations for a system of realistic
complexity is not a very straightforward task and can be prone to error. The large number
or Variables and parameters involved, along with the complex relations between those
Variables, make the problem difficult to approach. To make the transformation from
Physical system to equations easier, various types Of graphical modeling systems are used.
Gmphical modeling can be seen as a “bridge between the mathematics of differential
e(Nations and the physics of engineering systems” (Rosenberg and Kamopp, 1983).
GraPhical models are easier to understand in terms of the connectivity of the various parts

of the system model than are the equations. Graphical models are more closely related to

18
the geometry of the original system. They are appropriate for managing the information in

large-scale systems in a hierarchical way. In general, the more removed an engineering
model representation is from the geometric form of the physical system, the harder it is for

an engineer to understand it intuitively.

Different types of graphical modeling are involved in the process of going from a
physical system to a set of mathematical equations. One type is the schematic diagram.
Schematic diagrams help to capture the attributes of a system in order to make equation
derivation easier, but quite often schematic diagrams are not precise enough in the definition
of variables to make the process of equation formulation exact and unique. For instance, in
mechanical schematics, often certain assumptions are not made clear in their structure, such
as whether friction applies to a given motion or not, or whether heat losses from a
Component are important and should be considered. It is also difficult to connect schematic
models which have been constructed in different engineering disciplines, Since the notations
are quite different in each. For example, in mechanical schematics certain symbols are
commonly used to represent masses, springs, and dampers. In electrical schematics certain
SYmbOIS represent resistors and other electrical circuit elements. However, the connections
bflween these two different schematic domains are not well defined in either terms. Another
common graphical modeling system is the block diagram. Block diagrams clearly indicate
the existence of functional relationships among variables in the system, but the structure of
the graph does not take into account the physics of the problem in a direct way unless the
entire system is signal-based. Block diagrams are closer to mathematical equation models
in that they Show variables directly as the connectors and represent functional relationships

by the nodes (i.e. blocks).

Bond Graphing is a very useful modeling technique which can be used to avoid

Some of the problems associated with both schematic diagram models and block diagram

.-~

if? 3

71¢ "‘ "
“t."

 

'l‘l

tr‘

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4

'rt.
.54“ I

 

 

19

models. Bond Graphs are topological in form and therefore provide a close relationship
between the physical device and the model, while still providing a clear representation of
functional relationships in the model which can be translated directly into mathematical
terms. Bond graphs are especially valuable in cases where the system to be considered
spans more than one energy domain because they can represent energy transduction in a

graphically consistent manner. A brief description of bond graph modeling methodology

is included in the next section.
2.1.2 Bond Graph Modeling Methodology

Bond graphing is a Structured modeling technique used to represent multi-domain
SYStems as a series of components linked by power bonds. The systems best modeled by
b0nd graphs are lumped parameter systems which can be mathematically modeled as sets of
Ordinary differential equations. Bond graphs provide a basis for detailed physical modeling
0f engineering systems in preparation for simulating their behavior. The graphs capture the
flow paths for energy within a system in a way which agrees with the underlying physical
laws of the components (Karnopp, et a1, 1990). Some examples of bond graph models can
be seen in chapter 5, where the visualization examples are described. Additional examples

appear in a brief introduction to using bond graphs for system modeling included in

Appendix A.

Bond graphs support hierarchical decomposition of large-scale systems by dividing
them into subcomponents and connections at different levels. Each of the connections
represents an energy transfer, or power, at that connection. The power is the product of a
Pair of variables, denoted effort and flow. If consistent units are used, power units can be

equated across different engineering domains (e. g. watts). Energy measured consistently

can then be seen to flow through the connectors from one domain to the other. This is one

20
feature that makes bond graphs useful for modeling multi-domain systems. It keeps the

bond graph much closer to the physics of the system than a block diagram, which does not

track energy flow directly.

An additional characteristic of bond graphs is that they are highly organized in the
representation of information in the model. The bond graph modeling process can be
followed in a very structured way, which makes model building clearer and less prone to
error and confusion. Bond graphs are also very precise statements of which model effects
are included. They make clear all of the assumptions made in the modeling process at the

energy level. They do not indicate the functional details of the effects.

At the lowest levels of a bond graph decomposition of a system, a relatively small set
0f bond graph elements can represent the physical behaviors present in a remarkably broad
set of components and effects. Bond graph techniques recognize the similarity of physical
behaviors across different energy domains and use this energetic similarity to produce
Concise, unified models. For example, in electric circuits a linear resistor behaves as a
device which drains power (P) from the circuit at a rate equal to the current (i) in the resistor
multiplied by the voltage (e) in the resistor (P = i*e); correspondingly in a mechanical
SyStem a viscous damper also dissipates power from the system and does so at a rate of the
Velocity (V) multiplied by the force (F) in the damper (P = V*F). The constitutive
ecIllations for these two effects are the same and bond graphs take advantage of that fact to
Produce coherent models. Although this example demonstrates linear relationships between

var‘iables, non-linear effects can readily be represented by bond graphs also. The process
of using bond graphs to model a system often enhances the modeler's knowledge of the

System and can also yield insight into the system’s behavior, even before simulation has

been performed.

21
The set of standard bond graph elements includes several element or node types.

These are shown in Table 1. Source elements supply energy to the system. Passive
elements describe observed types of physical behaviors, such as the dissipative effect
mentioned above. Two—port elements support the modeling of energy transformation from
one domain to another. Junction elements serve to connect these elements together in a way
which is consistent with the physical laws governing the behavior of the component. Each
element has its own constitutive equations which describe the behavior of that element.
These equations can be either linear or non-linear. Once a complete bond graph of a system
is constructed using these elements, causality can be added to graphically indicate which
variables are inputs and which are outputs within the system. Bond graphs can also be
combined with block diagram elements and Si gnals to allow for the study of different types
or control structures and their effect on system behavior. A bond graph that integrates

Control signals through block diagrams with bonds is called a System Graph.

System graphs support the direct formulation of a set of state Space equations from
the model. State space equations are a useful form for doing system analysis or control
design. At this point the equations can be numerically solved and simulations can be run
for various test conditions. A critical part of the system analysis process is to take the
Faulting response data from the numerical simulation and interpret it in a meaningful way.
Advantage Should be taken of the structure provided by a bond graph model in the display
of the numerical results of a simulation, since the bond graph already has a special

c0lTespondence to the physical system in the designer’s mind.

 

22

Table 1. Standard Bond Graph Elements.

 

 

 

 

 

 

 

 

 

 

 

Element Element Bond Graph Constitutive equations
Type Name Symbol General Form Linear Form
B
Sources Source of SE ——>‘ E = f (time) E = Constant
Effort F
Source of SF __E_;. F = 1“ (time) F = Constant
Flow F
Passive - 4f__ - _ a:
One—Ports Resrstance R F E — f (F) E — R F
, E E=f(Q) E=l/C*Q
Capacnance C ‘7— F = dQ/dt F = dQ/dt
. E V=f(P) V=l/L*P
Inertia I ‘———F E = dP/dt E = dP/dt
1“” 1'1 El E2 E1 = n * E2
O'PO Transformer -——‘ T ——-‘
transducers F1 {-2 F1 = l/n * F‘2
E1 E1 = r * F2
_.3 ____.x
q; Gyrator Fl GY F2 F1 = I“. 3 E2
E1 E3 _. ..
Junction One-Junction —-‘ 1———‘ F1 ’ F1 " F3
elements F1 E2 LE2 F3 E1-E2-E3 = 0
El [-3
Zero-Junction —F—3 07—3 E1 = E. = E3
‘ ELK! ‘ F1-F2-F3=O

 

 

2.1-3 Computer Support for Simulation

Computer support for the activities of modeling and simulation is necessary to
enable practical design work. The typical activities involved in simulating system response
are selecting appropriate parameters for all of the constitutive equations of the bond graph

model, then solving for the dynamic response for some selected initial conditions. The
purpose of the simulation at first might be to see if the model performance matches the
expected performance. This is the model verification stage. Once the model has been
shown to behave properly, it can be used to test the system performance's sensitivity to
changes in parameters. The response can be optimized according to some performance
criteria. A variety of output data types can be used to generate information about the
model's behavior, such as time-history data, linearization and eigenvalue data, steady-state

Values, and sensitivity of these values to system parameter changes.

Several valuable services are provided by computer simulation to make the process
or design iteration and optimization more efficient. The first is that computers can be used
to remove the tedium of deriving the actual ordinary differential equations sets, and to make
coIlStr'uction and modification of models easier. Mistakes can also be avoided which might
Occur in equation derivation due to the complexity of the problem. With good computer
SnPport, the user can concentrate on modeling and design decisions, since the computer can
hilndle the updating of equations as changes are made. Second, computers are useful in
numerically solving the mathematical model, since most problems of practical size do not
have closed form solutions. Third, one of the most important functions of the computer in
System modeling and simulation is in the capability it provides for display and examination
of results data. Computers allow the user to explore the data, looking at in from different

perspectives so as to gain insight into the system behavior.

24

Bond graph models lend themselves to algorithmic derivation of the system
equations. Therefore computer support for bond graph modeling can be provided and
system behavior can be simulated effectively at the detailed numerical level. For example,
the ENPORT software accepts bond graphs and block diagrams as components in an
integrated modeling environment (Rosenberg, 1993). ENPORT makes construction and

modification of system graphs a straightforward graphical process, as well as supporting the
equation derivation and solution processes. ENPORT can also be used to display the
results data in X-Y plots of variables versus time. Display of time-averaged power variables
is directly on the bond graph as color and line-width variation of the bond structure (Zhou,
1988). This may not be adequate if transient phenomena are considered, which is quite
often the case in complex system design. It is also possible to pass the equations from
ENPORT in symbolic form to other software that can interpret the equations; this is another

level of manipulation that can lead to insight
2.2 Scientific Visualization
2.2. 1 Description of the Field

Scientific visualization, also referred to as data visualization, is emerging as a means
t0 help answer the need for clearer ways of presenting response data to designers. As ever
mOre powerful computers and measuring instruments generate ever more data, we face a
need for more effective ways to interpret and use that data. One definition of scientific
visUalization is "using computer-generated graphics to help us understand and visually
Clarif y the relationships inherent in data" (Rosenblum and Brown, 1992). Another is that
scientific visualization "uses computer generated images to help scientists extract knowledge
and understanding from experimental or simulated data" (Nielsen, 1993). A National

Science Foundation report was recently published which encouraged engineers and

 

25

scientists to develop new visualization methods to promote both research and education
(McCormick, DeFanti and Brown, 1987). NSF also recently awarded $14.6 million to
establish the National Science and Technology Center for Computer Graphics and
Scientific Visualization, illustrating just how much importance is placed on progress in this
area. The research reported upon here is an attempt to meet this challenge in the specific

area of dynamic engineering systems design.

Scientific visualization addresses the problem of data interpretation by combining
several different computer-related disciplines. Scientific visualization depends on computer
expertise relating to graphics and information processing, as well as on expertise related to
the different scientific domains in which visualization is used. There is also an artistic
component that involves aesthetics, and a biological component involving theories of human

perception.

How humans perceive things and what is meant by understanding are issues that are
not entirely defined at this time. The field of human perception attempts to explore these
iSsues by observation and experimentation. This field relates directly to scientific
Visualization because knowing how humans relate to data and the physical world around
“mm is a prerequisite to creating the most effective design and simulation environments.
Like a computer, a human undergoes a specific process used to internalize information.
Unlike a computer, this process is somewhat hard to identify. If some aspects of this
Process are examined, information can be organized in such a way as to take the best

advantage of human information processing capabilities.

It has been shown that data which are organized in a structured fashion are
understood and remembered better that data presented in an unorganized manner (Haber

and Wilkinson, 1982). It has also been shown that humans are capable of comprehending

26

more complex concepts visually than through words and numbers alone (Haber and
Wilkinson, 1982). The visual system provides a way to organize even non-pictorial data in
a geometric structure. Various studies have shown that the natural way for people to relate
to data is pictorially. Visual data is remembered better than words or numbers (Standing,
Conezio, and Haber, 1970), and our visual systems automatically attempt to interpret fiat

pictures as if they are real geometries in three dimensions.

Another facet of human perception is that humans tend to remember and relate to
data better when they have control over their manipulation of the data. This is why user-
driven interactive visualization is a goal to be striven for. There are also certain ways of
presenting data which distort the human perceptual process and can be used to trick the
user. Although there is no motivation to distort data in an engineering modeling problem,
Since the goal is accurate understanding of system behavior, care must still be taken to avoid
unintentionally presenting data in a way which might be misinterpreted. Obviously, a good

design and simulation environment should avoid any possibility cf confusion.

For engineering modeling and simulation, scientific visualization provides a way to
make interesting features of the simulated behavior stand out rather than be obscured by
numerical data. The challenge of applying the concepts of scientific visualization in a
design context is to create computer-aided visualization environments which help engineers
‘0 comprehend the physical significance of their simulation models' behavior. The idea of
Visualization can also be applied in engineering education, where visual thinking and mental
in'lagery need to be stressed in order to promote better understanding of engineering

fnnclamentals.

Scientific visualization concepts can be used to support better understanding of

b0nd graph model analysis by providing two types of capabilities. These are illustrated in

27
Fr gure 4 where the connection between the designer's model, the bond graph model, and the

visual display of model behavior is highlighted. The first capability involves presentation of
data obtained from simulations by relating the response directly to the bond graph structure
(Path Y). The second capability increases the correspondence between the bond graph
model and the designer's models, and therefore the physical system, by associating the bond

graph with the system geometry in three dimensions (Path X).
2.2.2 Current Tools and Research Areas

The field of scientific visualization is used in many different scientific domains and
in a variety of ways. Applications are found in disciplines as diverse as medicine,
meteorology, engineering, architecture, computer programming, physics, chemistry,
statistics, and mathematics. These applications range from the simple display of two-

dimensional scatter plots to complex‘three—dimensional mappings of data to geometry.

< (l) Designer's Model >
X
Y

 

 

(6) Visual Display of
Behavior

((2) Schematic ModeD

 

 

 

((3) System Graph Model)

(5) Numerical Characterization
of Behavior

 

 

((4) Equation Model

 

Figure 4. Scientific Visualization and the Design Process.

28

One of the major areas of current development in scientific visualization is the
display of continuous or sampled data in two or three dimensions. This visualization
process involves a series of transformations which provide a mapping between raw data and
certain graphical element attributes. Some examples of programs which support the
display of general distributed data values are: l) PV-Wave (Schmalzel, 1992), which
includes 2-D line and scatter plots, 3-D contour and surface plots, as well as table and
animation data views; 2) Data Visualizer by Wavefront Technologies (Brittain, 1990),
which can handle distributed fully structured as well as unstructured data; 3) AVS, a
commercial module-based visualization system (Upson, 1989); 4) Visage, which supports
distributed visualization (IEEE Visualization, 1992); and 5) the equation solvers like
MATHEMATICA and ANSYS previously mentioned. Such programs require the user to
decide on a visualization method and to direct how the raw data will be displayed. It was
decided that these stand-alone general visualization softwares were not sufficient for the
required bond graph design environment although they are complementary. The structure
supplied by the bond graph model should be exploited for understanding as fully as

possible.

Another area which is being extensively studied is distributed system visualization
known as scenic or quasi-scenic rendering (Becker and Cleveland, 1991). The goal of this
type of visualization is to map information obtained from experiments or simulations onto
their associated distributed geometric surfaces or volumes. This covers areas such as
volume visualization of medical data (Fuchs, et a], 1989) and computational fluid dynamics
(Giles and Haimes, 1990). Similar techniques are being applied to stresses and strains in

engineering mechanics (Haber, 1990).

Although distributed parameter systems, which in a modeling context involve the

Solution of partial differential equations, have been and are being extensively explored by

29

scientific visualization techniques, less has been done in the area of spatially lumped or
finite dimensional systems, which involve the solution of time dependent ordinary
differential equations. Imaging methods are needed in this area to provide as much detailed
information to designers as possible within a global context that corresponds well to the

graphical model and the physical problem.

For this research an area of application for scientific visualization principles has
been identified which has not been explored up to this time, namely the application to bond
graph modeling and display of simulation data. The structure of this type of visualization is
lumped, rather than distributed over a volume, since the positions of nodes and connectors
have been defined, and the goal is to use this structure to do modeling that relates to
physical systems and to display data in a meaningful way. The display can be thought of as
a problem of high-dimensional data, since 3 physical dimensions (x, y, z) are dealt with as
well as time and the values of the variables of interest. The topic of display of high
dimensional data has not been an area of a lot of research, perhaps because it is so complex.
The research that has been done includes the use of iconic representations like Chemof f
faces (Chemof f , 1973), and some work which is concerned with showing a dependent
variable which is a function of many independent variables (Beshers and Feiner. 1992 and
Mihalisin, et a1, 1991). The bond graph output display problem is somewhat different in
that it is necessary to show the values of many dependent variables (associated with the
powers on all the connectors of the bond graph) as a function of time in the context of their

position in the bond graph model.

Chapter 3
A Two-Dimensional Bond Graph Visualization

Environment (BGVis-ZD)

3.1 Environment Specifications

The goal of this visualization environment is to relate the response data calculated
by a solution of the system equations obtained from the bond graph model to the structure
of the bond graph model. The response is usually determined by a numerical solution of
the equations, but could be obtained from a closed-form solution in the case of linear
systems. Since the designer presumably understands how the bond graph model relates
to the actual physical system under study, this will organize the output data in a way that
is highly consistent with the designer’s understanding of the physical system. Since bond
graphs are designed to capture power paths within a system, some useful quantities to
display will be the power and energy values. What is needed is a way to display the
instantaneous value of a variable type for each of the bonds in a system graph as an

animation in time.

The common method for displaying results from a bond graph model simulation
consists of plotting one or a small number of variable values versus time on a two-
dimensional screen or hardcopy. Output from block diagram or direct mathematical
equation model solutions are displayed in this same way, indicating that the structure of
the bond graph itself is not being utilized in any way to aid in the organization and
Presentation of the output data. This approach also requires that the user choose the

Variables of importance for display. This implies some prior knowledge or expectation of

30

31

which elements in the system need to be checked, which may not always be obvious.
Displaying a larger number of variables in an organized fashion would allow the
significant aspects of the global system behavior to become clear. Then relevant

variables can be identified and plotted if the user requires more detailed information.

One existing possibility of taking advantage of the bond graph structure for
displaying data is the option of displaying time-averaged variables in a static display as
line width and color variation on the bond graph (Zhou, 1988). This type of presentation
is very helpful in separating sections of the graph which demonstrate high versus low
averages of variables, which might lead to model reduction, but it is not necessarily
adequate for dealing with the interpretation of transient system response. The Zhou
method of average value presentation can be used as a base to extend the display of

variable values to a dynamic animation in time.

The visualization environment should be smoothly integrated as part of a data
post-processor into a bond graph model building and solving environment. As much
control of the display as possible should be given to the user to allow him or her to
interact with the data in ways that are most meaningful. The user interface should, of

course, be clear and easy to understand and manipulate.

3.2 Design of the Two-Dimensional Visualization Environment

3.2.1 Features Selected for Implementation

The variable types chosen for potential display on the bond graph are the power

variables, effort and flow, as well as the power variable itself, and also the energy

variables displacement and momentum, as well as the energy variable itself. Effort (E)

32

and flow (F) variables for each bond over every time stage in the time range of solution
are obtained from the simulation and stored in the results file. Power (P) variables for
each bond are calculated in the dynamic display postprocessor by multiplying the effort
and flow on each bond for each time stage. The momentum (P) and displacement (Q)
variables are not stored as a result of the simulation, except for those that are state
variables. In order to calculate all of the P and Q variable values over the solution time
range, the fact that effort and momentum and flow and displacement are related by the
integral relationships P -fE dr+ Po, and Q -der+Qo , respectively, was used. A
trapezoidal integration routine was implemented to calculate the momentum variable
from the effort variables for each time step, and the same procedure was used to calculate
the displacement variable from the flow variables for each time step. The following

equation defines the trapezoidal integration.

Ema. Pg-[x(.0).2x(r,).2x(.2).....2.(.,,_ l).,.(i,,)]

For the integrations, all of the initial values for displacements and momentums were
taken to be zero. Instantaneous energy variables were determined by integrating the

product cf the flow and effort on each bond for each time step.

Once the variable values over all the bonds for the time range of interest are
available, each variable type is checked for global maximum and minimum values, and
magnitude ranges are determined. This allows each variable type to be scaled
consistently over all bonds. Three types of scaling options are available: linear,
logarithmic and absolute logarithmic. The logarithmic scaling options normally are
useful when values of a variable type extend over several orders of magnitude.
Logarithmic scaling can only be used if all variable values for the variable type to be
displayed are greater than zero. The dynamic display checks for this condition, and prints

an error if an attempt is made to scale negative or zero-valued data logarithmically.

33

Absolute logarithmic scaling uses only the absolute magnitudes of the values, where the
negative sign on the value is indicated by the arrow direction or color change. Thus the
problem of negative numbers is avoided. Zero values are set to the minimum magnitude

value for the variable type to avoid the error associated with taking the logarithm of zero.

Bond Coding. The two primary modes for time varying display of bond related
variables are line width variation of each bond and color variation of each bond. This
method can be thought of as "flow" display, as opposed to ”level" display which is
described under the heading of Node Coding. Line width variation and color variation
methods can be used independently, allowing two different variable types to be displayed
at once, or they can represent the same variable type, thus providing reinforcing display

variations for the same variable type.

Ten levels of difference variation are provided for the line width modulating
feature. The choice of this number was affected by the geometry of which the display
device is capable. A maximum line width was determined by the relationship of bonds to
nodes in the presentation of the graph, while the minimum line width was determined by
the minimum line width allowed in the line drawing routine. After some
experimentation, it was determined that ten gradations of line width between the
maximum and the minimum provide the user with variation sufficient to detect
meaningful differences in variable values. Negative values for a given variable are
indicated by a shift in the arrow placement on the bond for linear and absolute
logarithmic scaling methods. This is an especially natural way to think about power
flow, since by definition power flow on a bond is positive in the direction of the half

arrow.

34

Ten levels of color variation are also provided. This number could be increased
for more detailed data display since human perception of color variation is more sensitive
than perception of geometry differences. When line width and color are used to show the
same variable type, only one set of colors, shaded from purple to red, is used, since the
arrow directions indicate negative results. When color and line width are used to
represent separate variables, two sets of color are used, the same as above for positive
values, and a set shaded from green to blue for negative values. The two distinct color
sets allow the negative versus positive data to show up very clearly. Another possibility
is to use the VBGYOR (rainbow) spectrum to show value level change, but it is not clear
that this color set is always intuitive for people in comprehending the corresponding
levels, and the position of a zero-valued level is not obvious. For each time stage of the
animation, the bonds are redrawn with the appropriate width corresponding to the
variable value type selected for line-width and the appropriate color corresponding to the

variable type selected for color.

Node Coding. During a results display the nodes of the graph are drawn once in
the colors originally defined by the model builder relating to energy domain: white for
general, blue for mechanical, green for electrical, purple for hydraulic, and so on, as

defined in the ENPORT model building module (Rosenberg, 1992).

A secondary visualization tool that is supplied in the BGVis-2D tool, associated
with nodes or ”levels" rather than bonds or ”flows”, is a glyph symbol located at each C, I
and R node in the graph. This method can be used by itself or in combination with the
previously described ”flow" type display. A glyph is a geometric symbol that represents
information at a given position. The glyph is based on a thermometer motif and shows
the amount of energy stored or dissipated in that element at a given time. The energy

increase or decrease is shown by an increase or decrease of the line height in the

35
thermometer-style glyph. The glyph technique might also be extended to include display

of other variable types that can be viewed as ”levels", such as displacement.

The net energy transfer to any node in a bond graph can be determined by
integrating the instantaneous power values on each of the bonds connected to that node
and summing the results. The C and I elements are known as energy storage elements
because the amount of energy stored in the element can be determined from the net
energy transfer plus the addition of any initial energy already stored in the node. The
user is allowed to supply a numerical value for the initial energy stored in each C and 1
element. The amount of energy dissipated in an R element is determined directly from
the net energy transfer. The glyph display at these nodes can be useful for the designer
trying to understand where energy is being accumulated and released throughout the

system globally during a simulation.

Signal Coding. Signals are not included in the dynamic display of power, energy,
effort, flow, momentum, or displacement variables, since the power flow along a signal is
by definition equal to zero, and because there is no consistent way to indicate to which
variable type the information carried by a signal belongs. If bond graph builders were
encouraged to label signal values with the first letter of the label corresponding to the
variable type (E, F, P, or Q), then a method might be set up to include the apprOpriate
signals when a given variable type is displayed. At this point, signal variable values can
be displayed independently from bond variables by choosing to display a ”signal"

variable type.

A key is provided to indicate the correspondence between line widths and colors
and numerical value levels. An example of the key is shown in Figure 5. Each line width

is drawn in the first column, and the range of numerical values it represents is indicated

36

above and below it. In the second column, each color is demonstrated, both negative and
positive, and the numerical values corresponding to that color are printed. In the case
where no variable is chosen to be displayed with line width variation, the line widths are
drawn without numerical labels. Similarly if no variable is chosen for color variation, the
colors are still shown, but are also unlabeled. The key is updated whenever new variable
types are chosen for display as either line width or color variation. At the bottom of the
key, the value of the time for which the data is currently being displayed is shown. This
value is updated whenever the time step displayed is changed.

 

 

 

 

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Figure 5. Dynamic Display Key to Widths and Colors.

37
Time Plots. The graphical variation methods described above are intended to be

qualitative in nature, dealing with relationships between the values of variables at
different locations within the entire bond graph. At some point it may become useful to
zoom in on variable values associated with a particular bond. This function has been
provided by allowing the user to select a bond in the dynamic display, whereupon the
user is allowed to choose one of the bond variables for display in a plot as a function of
time. An even more precise display might focus on choosing a particular point in time
from the time plot for a particular variable and obtaining numerical values for variables in
table form. This function has not yet been implemented in the dynamic display
environment, but a similar result can be obtained by using the "table” function provided
outside of the dynamic display environment. Time plots of several chosen variables
related to different bonds in the graph can also still be constructed by using the facility

provided in the original ENPORT postprocessor.

Animation Control. A user may desire to display the results of a simulation over
the entire time frame used in the solution of the differential equations or over some subset
of that time. The choice of time subsets for the simulation data is provided by the
ENPORT postprocessor. The determination of ranges for each variable type is performed

over this chosen time frame.

The user also requires a way to control the rate at which the animation is
presented. Time controls are provided for this task. Several options have been
implemented. The user is allowed to run the display from the current time to a later time
specified by the user at a constant speed (seconds per frame) that is input by the user.
During this constant speed animation, no user input is allowed. In order to account for a
user who might not want to proceed through the animation at a fixed rate, single time step

functions are provided. These functions allow users to proceed with the animation at

38

their own pace by selecting a button to move forward or backward one step. A function
is also provided to allow users to quickly go to a specified time stage without having to

step through all the intermediate stages.

View Control. A user of the BGVis-2D environment might also wish to display
only a portion of a bond graph model if the model is so large that the display will be
cluttered. The ability to pan through the graph in both the x and y directions is provided
by scrollbars attached to the graph viewing window. It is also possible to zoom in to or

out from a graph view.

3.2.2 Platform Selected for Implementation

The bond graph modeling program ENPORT was chosen as the vehicle for
implementation of the environment characteristics described above. ENPORT was
described in the previous chapter as a software environment which accepts bond graphs
and block diagrams as components in an integrated modeling environment, makes
construction and modification of system graphs a straightforward graphical process, and
supports the equation derivation and solution processes. ENPORT was chosen because it
is a well-documented and verified software program, and because the software code was
available in a convenient setting for modification and addition of visualization

functionality.

ENPORT is currently available in three different formats. An earlier version is
written in FORTRAN and runs on mainframe computers which run the VMS operating
system. At the time this research took place, the VMS operating system was being
gradually phased out. The most common currently distributed version of ENPORT is

written in FORTRAN and runs on MS-DOS based personal computers. An experimental

39

version of ENPORT is implemented in a UNIX environment and is programmed in the C
computer language, taking advantage of the X Window System user interface. The
UNIX version of ENPORT was chosen for the addition of the new display technologies
of this research for several reasons. The mouse-driven X Windows format provided
better user interface characteristics when compared to the other versions, which are more
menwdriven. What is more important, the higher processing requirements of the
graphics display anticipated, especially for the 3-D capability, required the power of a
workstation. It is planned that the display enhancements generated by this research will
eventually be carried over into the PC environment, especially since 486 and Pentium

processors are becoming more widely used by engineers.

The implementation of this research was performed on a Sun Spare-10
workstation running the UNIX operating system. The ENPORT version used was the 1.0
8 version running under UNIX. All additional code was written in the C computer
language, and the Xt Intrinsics functions, along with the Athena widget set, were used to
support the user interface functions (Nye and O'Reilly, 1990). Documentation and the
computer code generated in the course of the project are included in Appendix B of this
report. The enhancements to the bond graph modeling environment were added as part of

a postprocessor module of ENPORT.

Examples of how the BGVis-ZD environment described in this chapter is actually
used for visualization purposes are described in chapter 5. The figures provided in that
chapter provide a rough idea of a process that is inherently dynamic and interactive.
There is a videotape available from the author directly or from the Mechanical
Engineering Department at Michigan State University which provides a clearer indication

of how the designed bond graph visualization environment actually performs.

3.2.3 User's Guide

The following section can be used as a reference for running the software
implementation of the BGVis-2D tool. Each of the available functions is described in the
order in which it would most likely be performed. Pictures of the user interfaces are

included.

Starting the Postprocessor. The ENPORT program's postprocessor window is
started by typing the name of the postprocessor program, which is "BGVis-ZD". This
interface can be used to load in simulation results files, provide 2-D plots of selected
variables versus time, specify time intervals of interest, and start the animation module.
A picture of the control window is shown in Figure 6 for reference. Exiting the ENPORT

postprocessor can be executed by clicking on the "Exit" button at the appropriate time.

 

Figure 6. ENPORT Postprocessor Module Control Window.

i5

is;

 

41
Loading an Output File. Clicking on the "Load" button will bring up the

directory structure window which will allow the user to select an ENPORT simulation
output file (suffix .SZP) previously generated by the ENPORT solver module. Clicking

on the file name will then cause that file to be loaded into the postprocessor.

Selecting a Time Interval. The default time limits shown in the initial and final
time boxes are taken as the beginning and ending times of the simulation (see Figure 6).
If some subset of that time interval is desired for study, new time limits can be entered

into the boxes by simply typing them in using the keyboard.

 

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Figure 7. Dynamic Display Module Control Window.

42
Entering the Dynamic Display Module. Clicking on the button labeled ”Dynamic

Display" will initialize the Dynamic Display Dialog. A picture of this control window is

shown in Figure 7 for reference.

Loading the model file. Clicking the "Load" button at the top of the menu area at
the far left will bring up the same file selection window as in the postprocessor. This
window can be used to select the ENPORT model file (suffix .ENP) to be loaded. This
file contains the system graph as constructed in the ENPORT model build module. The
system graph will then be drawn in the animation viewport, scaled so that the model fits
in the window. Determination of output variable ranges occurs at the time of model f ile

loading.

Using the Animation Viewport. The large window in the dynamic display dialog
is the canvas on which the system graph is drawn. There are two functions included
related to controlling the appearance of the graph. The first allows the user to shrink or
increase the size of the model by clicking the "Zoom” button at the bottom left of the
dialog. Doing so will bring up a window into which a chosen scale factor can by typed
via the keyboard. The second involves using the scrollbars at the bottom and to the right

of the window to pan through the model.

Choosing variables for display. The choice for which of the seven variable types
(power, effort, fiow, energy, momentum, displacement, signal, none) to display for line
width and which one to display for color are made by mouse selection from pull-down
menus provided at the top of the dynamic display control window (see Figure 7).
Clicking and holding in the box to the right of the menu label will cause the pulldown
menu to pop up, and the mouse can be dragged down and released on the appropriate

variable option. The user can choose whether or not to display the glyphs during an

43

animation by using the “Show glyphs?" pulldown menu also at the top of the dynamic

display window.

Choosing a Scaling Method. The program allows three choices for scaling of
variables: linear, logarithmic, and absolute logarithmic. The choice of which to use is
governed by the pull-down menu obtained when the button next to the "Scaling Choice"
label is clicked and dragged down to the appropriate choice and then released. If negative
values of the chosen variables are present when logarithmic scaling is chosen, an error

message will be shown.

Controlling the Animation. The controls for running the dynamic display are
included in the box at the top right of the dynamic display dialog labeled ”Animation
Control Menu” (See Figure 7). When the "Animate" button is chosen, the dynamic
display is drawn for each time increment from the current time to the time specified by
the user at a speed (seconds per frame) that is input by the user. The fastest rate available
is 1 second per frame and the user can choose any multiple of that as the approximate rate
of display by typing into a popup window. During the time this animation is being
performed, the display updates automatically, and no interference by the user is allowed.
in order to account for a user who might want to control the animation by moving one
frame at a time, “Step forward” and “Step backward" functions are provided. These
functions allow the animation to proceed either forward or backward by one time
increment when the button is clicked. If the current timestage is the lower time limit, and
”Step backward” is chosen, no action is taken. Similarly, it the current timestage is the
upper limit, no action is taken. A “Go to timestagez” function is also provided to allow
the animation to be redrawn at the specified time stage without having to step through all
the intermediate stages. Clicking on this button will pop up a box into which the desired

time value can be entered by the user.

Interpreting the Data Key. The smaller viewport window on the right is provided
to show the numerical scale values of the displayed variables that correspond to each
color and line width possibility. The current time stage value is also displayed at the

bottom of this window.

Obtaining a Time Plot for a Bond. If a detailed plot of a variable associated with
a single bond is desired, it can be obtained by clicking on the bonds name in the
animation viewport. The user is allowed to specify which variable type will be displayed
(power, effort, flow, energy, momentum, displacement, signal). This pops up the plot
window, with the selected variable for that bond displayed as a function of time. Time
plots of several variables can be displayed by returning to the ENPORT postprocessor

control window and using the "Plot” button.

Leaving the Dynamic Display Module. Click on the ”Exit" button in the menu
area at the far left to close the window and exit the dynamic display module. This will
return the user to the postprocessor where a different results f ile can be located, or the

program can be exited.

Chapter 4
A Three-Dimensional Bond Graph Visualization
Environment (BGVis-SD)

4.1 Environment Specifications

As was shown in the previous chapter, there are definite advantages to be gained
from relating the response data from a simulation directly to the bond graph. These
advantages are extended with the ability to display bond graphs in a three-dimensional
environment and to manipulate them as 3-D geometric objects. The basic goal of the
three-dimensional bond graph modeling environment is to make the viewing of power
pathways or other variable values easier and to make interpretation of the model behavior
clearer. An example of this type of thinking in the area of chemistry/physics is the
visualization of complex molecular structures. This type of visualization is generally
conducted for the purpose of interpretation of molecular behavior (Mof fat, 1991). In a
similar manner, more insight into a bond graph model can be gained if the designer can
interact with it in such a way that it can be visualized in three dimensions and the viewing
process can be under the modeler's control. The BGVis-3D environment allows for
viewing of the 3-D graph from different angles and from a range of distances. The user is
able to position the graph in the way that makes its structure and behavior the most clear.
The same specifications related to controlling the data presentation in the animation that

were presented for the 2-D situation also apply here.

The intention of the environment is also to allow the user to display a bond graph

model which corresponds closely, allowing for scale, with the three-dimensional

45

46
geometry of the physical system being designed. Bond graphs are usually described as a

topological modeling type, meaning that the connectivity of the graph does not generally
relate to the geometry of the physical object. This can be an advantage, since the
subcomponents of the bond graph model can be moved in whatever way seems suitable
without changing the character of the model, as long as the correct connectivity is
maintained. The disadvantage of a topological model is that it does not encourage
visualization of the geometry of the physical system in the modeling process. The ability
to use a three-dimensional geometric bond graph gives the model a well-defined spatial
relationship to the physical object, allowing the designer to understand the model
behavior in light of the actual geometry of the system. The environment allows for
animation of variable types on the bonds in much the same way as for the 2-D
environment, but the results can be even more clearly related to the physical system in the

3-D environment.

4.2 Design of the Three-Dimensional Visualization Environment

4.2.1 Features Selected for Implementation

The bond graph is displayed in the 3-D environment with spheres as nodes and
cylindrical solids with cone-shaped arrows as bonds. Although standard bond graph
convention calls for a half-arrow to indicate bond direction, full arrows are used in the
BGVis-3D display. The primary reason for this choice is that any arrow that does not
extend out in all directions from the cylindrical bond might not be seen if the graph is
viewed from a particular orientation. To avoid any ambiguity in interpretation of
connector type, signals are displayed as rectangular solids, distinguishing them from
cylindrically shaped bonds. Bond graph nodes are drawn as spheres, while block diagram

elements are drawn as rectangular solids. The nodes are drawn in colors corresponding

47

to their power domains, while the connectors have changing colors depending on the

variable values being shown.

The model is presented in a perspective projection, and lighting and shading
parameters are specified to make the 3-D geometry look as real as possible. Direct trade-
offs need to be made between quality of the display surfaces and the timely performance
of display updating. After much experimentation, it was decided to maintain a
reasonable display quality despite long draw times, based on the assumption that the
performance problem could be reduced in the future with the use of a workstation with

greater processing power.

Manipulation of the 3-D model is provided by valuators on the screen. A valuator
consists of a box with a sliding handle whose position can be controlled by dragging the
handle with the mouse. The position of the handle corresponds to a particular value of a
viewing parameter. One valuator controls the size of the f ield of view, providing for a
zooming in/out function. The others control the angular position about the x, y, and z
axes of the model in the workstation by changing the view position in the x, y, and 2

directions.

The same variable types are available for display as in the 2-D environment
(power, effort, flow, energy, momentum, displacement, signal). Data loading, calculation
of momentum and displacement values, and scaling functions are also the same. The
variation method provided for showing values is color change on each bond. Bond width
was not used as a variation technique, since 3-D perspective drawing of the graph causes
parts of the model that are further away to be shown smaller than parts of the model at the
front. Changing bond widths to represent information would cause erroneous

conclusions due to the perspective effect. Ten levels of color are provided based on a

48
VBGYOR (rainbow) type spectrum with violet as the low value and red as the high.

Reference bond directions are reversed in the display to show negative variable values.

Functionsfor controlling the animation with respect to time are provided which
are similar in nature to those of the 2-D environment. Animation at a constant speed and
step-type functions are provided within the 3—D framework by choosing buttons in a
selector window. Each time the animation is updated the nodes are redrawn in the neutral
color, while the bonds are redrawn in the appropriate colors corresponding to the chosen

variable value. A key is also provided to index colors with numerical value levels.

Currently the BGVis-3D environment can be used for display of 3-D bond graph
representations and not for graphical construction of the models. Two-dimensional
model files can be changed to three-dimensional model f iles by using a text editor and
manually typing in z coordinate values. It is anticipated that a three-dimensional model
builder could be constructed using techniques directly corresponding to the current
ENPORT two-dimensional model builder. Since the intent of this project was to show
the value of enhanced simulation results display, it was decided to leave 3-D model

building capabilities to a future time.
4.2.2 Platform Selected for Implementation

The implementation of this research was also performed on a Sun Spare-10
workstation running the UNIX operating system. The 3-D display post-processor is
implemented as a stand-alone module that can access ENPORT (1.0 8 version) library
routines necessary for f ile reading and any other necessary utilities. Three-dimensional
models can be loaded from ENPORT model files which have been modified to include a

third coordinate. To support this modification, the basic data structure defined in

49
ENPORT to store node and connector data was altered. This also led to modifications to

the file reading/writing routines. Documentation and the computer code generated in the
course of this phase of the research can be found in Appendix B. An example illustrating

the utility of the 3-D display environment can be found in Chapter 5.

In order to build a 3D modeling environment with the characteristics described
above, it was necessary to either find or build programming software capable of
performing the 3-D graphics tasks. The fact that developing computer graphics code for
allowing 3-D display of ball and stick type structure is very time consuming and the
desire to make portable code led to the use of a graphics standard to support the modeling
effort. The PHIGS graphics standard (Kasper and Ams, 1993) was used to supply the
capability for controlling and drawing 3-D geometries, including lighting and shading

effects. A description of PHIGS can be found in the next section.

4.2.3 Description of the PHIGS Graphics Standard

A computer graphics standard is a set of computer graphics subroutines which has
been established as a basis for performing computer graphics operations. It has generally
been designed to be as portable as possible, allowing the applications using the standard
to be used on different computer systems and to be useful in a broad range of graphics
application domains. The standard is also designed to be independent of computer

programming language used.

Several different graphics standards have come into existence since the late
1960’s, when development of standards was begun. Among the first was the Graphical
Kernel System (GKS), which was specified to address 2-D display of computer graphics.
GKS was also later used to support 3-D display, and GKS-3D was published in 1988

50
(Int’l Standard, GKS-3D, 1988). Another standard was developed and presented around

the same time which supports both the modeling and viewing functions of computer
graphics. That standard is called the Programmer’s Hierarchical Interactive Graphics
System (PHIGS), and this was the standard chosen for use in creating the 3-D bond graph
display environment (Int’l Standard, PHIGS, 1988). PHIGS is described as “a set of
functions for computer graphics programming in environments requiring rapid
modification of graphical data that describes geometrically related objects” (Arnold and
Duce, 1990). The 3-D bond graph environment falls under this category of applications
and thus the PHIGS standard was considered useful for developing the software. An
addition to the original standard called PHIGS PLUS was also defined later to provide
higher level capabilities for lighting and shading calculations (Int’l Standard, PHIGS
PLUS, 1992). This standard is also used in this work along with PHIGS. Some of the
basic characteristics of PHIGS and how it is used in designing graphics applications will

be described here.

Since PHIGS is defined independently of programming language, it was
necessary to use the standard-specified C binding for PHIGS, which defines how the
functionality of PHIGS is tied to the C programming language. All programming done in

the course of designing the 3-D bond graph environment was written in C.

An important feature of PHIGS, and one on which the standard is based, is the
concept of a workstation. PHIGS uses this term to mean “an abstract collection of
hardware and software with graphics capabilities” (Kasper and Ams, 1993). A particular
workstation is implemented by connections to physical output and input devices. There
are some functions of PHIGS which are workstation-independent, i.e. designed to be
portable between all hardware systems, and some functions which are workstation-

dependent.

51

The functionality of PHIGS allows for creation of device-independent graphical
models by defining graphical data units called structures. These structures consist of
hierarchically arranged element primitives or building blocks along with their attributes.
The structures are stored and can be accessed by their application-specified names.
Editing of these structures after initial creation is also allowed. Once the graphical model
has been constructed, PHIGS provides routines defining the viewing parameters for the

model. Finally, the model is posted to a workstation for display.

In the course of graphics modeling and viewing, it is necessary for the model to
go through a pipeline of coordinate transformations. A diagram of the PHIGS supported
modeling transformation pipeline is shown in Figure 8. The initial model is described in
a modeling coordinate system, which can be chosen for convenience in constructing
individual pieces of a model. A world coordinate system is defined which allows
individual pieces to be assembled into a larger model. Thus model subcomponents can
be constructed in a local coordinate system and then be scaled, rotated, and translated be

before placement in the global modeling space.

52
3-D Elements

J Modeling Coordinates

 

(Composite Modeling TransformatioD

 

World Coordinates

 

(View Orientation Transformation)

 

 

View Reference Coordinates

 

(View Mapping Transformation)

 

Normalized Projection Coordinates

C Workstation Transformation l

Device Coordinates

 

Display

Figure 8. PHIGS Modeling Transformation Pipeline.

A view reference coordinate system can be chosen to select the direction from
which the model will be viewed. The model in view reference coordinates is then
normalized in preparation for display on a particular workstation. The final
transformation takes place changing normalized projection coordinates to device
coordinates, which are the actual coordinates used to display the model on a particular
graphical output device. PHIGS provides routines which support all of the functions
described in a way which ensures that the user does not have to deal explicitly with the
mathematics, primarily matrix identification and multiplication, involved in the
transformations. It thus provides three-dimensional graphical processing capabilities at a

relatively high level which can easily be integrated into an application.

53
4.2.4 User's Guide

The following section can be used as reference for running the 3-D dynamic
display environment. Each of the functions available is described under the appropriate

heading.

Starting the 3-D Display Module. The 3-D Display Postprocessor can be loaded
by typing the name "enport3D". This window provides the functions of loading of model
and data files, specifying the time range of the display, selecting the scaling type and
variable to display, and opening the PHIGS display window. A picture of the 3-D
postprocessor control window is shown in Figure 9. Exiting the 3-D postprocessor can be

executed by clicking on the "Quit" button.

 

Wt/I/mmwot-firefl-

Figure 9. 3-D Postprocessor Control Window.

54
Loading an Output File. Clicking on the "Load Data” button will bring up the

directory structure window which will allow the user to select an ENPORT simulation
output file (suffix .S2P) previously generated by the ENPORT solver module. Clicking

on the f ile name will then cause that file to be loaded into the 3-D postprocessor.

Loading a Model File. Bond graph model data can be loaded into the application
using the "Load Model” button in the same way as for the data file. The selection
window can be used to select the z-modified ENPORT model file (suffix .ENP) to be
loaded. This file contains the system graph as constructed by the ENPORT model build
module, but modified to include a third coordinate (z) for all of the model elements.

Determination of all output variable ranges occurs at this time.

Selecting a Time Interval. The default time limits shown in the initial and final
time boxes are taken as the beginning and ending times of the simulation (see Figure 9).
If some subset of that time interval is desired for study, new time limits can be entered

into the boxes by simply typing them in using the keyboard.

Choosing variables for display. The choice for which of the seven variable types
(power, effort, flow, energy, momentum, displacement, signal, none) to display for color
variation on the 3-D model are made by mouse selection from a pull-down menu
provided near the bottom of the control window (see Figure 9). Clicking and holding in
the box to the right of the menu label will cause the pull down menu to pop up, and the

mouse can be dragged down and released on the appropriate variable option.

Choosing a Scaling Method. The program allows three choices for scaling of
variables: linear, logarithmic, and absolute logarithmic. The choice of which to use is

governed by the pull-down menu obtained when the button next to the "Scaling Type"

55
label is clicked and dragged down to the appropriate choice and then released. If negative

values of the chosen variables are present when logarithmic scaling is chosen, an error

message will be shown.

Entering the 3-D PHIGS Display Module. The model can be displayed by
choosing the “ToPhigs” option once the model and data files have been loaded. A
PHIGS workstation is opened, and the bond graph is displayed there in three dimensions.
The workstation in this case is an X window. A picture of the 3-D display control
window is shown in Figure 10 for reference. The graph is displayed with spheres as
nodes and rectangular solids with arrows as connectors. The model is presented in a
perspective projection and lighting and shading parameters are specified to make the 3-D

geometry look as real as possible.

Manipulation of the 3-D Model. Manipulation of the 3-D model is provided by
valuators on the screen. Four valuators are present. One controls the size of the field of
view, providing for a zooming in and out function. The other three control angular
position of the model in the workstation — one each providing rotation about the x, y, and
z axes respectively. Each of these valuators can be worked by dragging the button to

different positions along the track.

Controlling the Animation. The controls for running the 3-D animation are
included in a selector window popped up along with the valuators by the PHIGS
workstation. The same buttons are provided as in the 2-D environment See section 3.2.3

for details of how they work.

56

Interpreting the Data Key. A smaller workstation is provided to show the
numerical scale values of the displayed variables that correspond to each displayed color.

The current time stage value is also displayed at the bottom of this window.

Leaving the 3-D Dynamic Display Module. Click on the "Exit“ button in the
selector menu area at the far left to close the window and exit the dynamic display control

window. The entire program can be exited from the higher level window.

'K.““-!"- g ..,.. ',
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Figure 10. The 3-D Postprocessor Display Window.

Chapter 5
Visualization Examples Using BGVis-ZD

5.1 Automobile Modeling Example

In the field of automotive engineering one of the critical tasks is to design
automobile suspensions for good performance, for example to provide reasonable settling
times and limited motions for the car chassis and passenger due to a displacement
disturbance from a rough road. As an example to demonstrate the capabilities of the two-
dimensional bond graph visualization tool (BGVis-2D), the three-dimensional vehicle
illustrated in Figure 11 was chosen for study. This particular example was chosen for
two reasons. First, because the vehicle is a real life engineering system design problem.
Second, because the system is straightforward enough for exPerienced engineers to form
a conception of how the system will perform under different inputs. The purpose of the
BGVis-2D environment is to provide insight into the behavior of an engineering system.
The benefits of using BGVis-2D are clearly demonstrated by comparing the visualized

response against the expected response.

A schematic diagram of the car chassis unit and suspensions with seat/passenger
is shown in Figure 12. The schematic model functions as follows. The car chassis unit is
treated as a rigid body which is allowed to translate (bounce), in the vertical direction (2
axis), and rotate about the Y (pitch) axis and the X (roll) axis. For simplicity the angular
motions are assumed to be small. An independent mechanical suspension system is
attached at each comer of this rigid body. The comers thus experience different vertical

(Z-axis) displacements depending on the position and orientation of the chassis. The

57

58
suspensions consist of a spring and damper connected in parallel to the axle. A wheel is

mounted to each axle and maintains contact with the ground. The input to the system is a
vertical velocity applied to each wheel induced by the car traveling over a specified
ground profile at a constant linear speed in the horizontal direction (X axis). A
seat/driver are included in the model, connected through a compliance and damping
effect to a point in the front half of the chassis. One of the primary responses of interest
is the position of the seat/passenger in the car, which is allowed to vary in the Z (vertical)
direction. The following section will consider a three degree-of-freedom
bounce/pitch/roll (BPR) model of the vehicle dynamics. A two-dimensional bond graph
representation will be used. A three-dimensional bond graph representation of the BPR

model is described in chapter 7.

 

Figure 11. Vehicle System Illustration.

59

Y q (Pitch)

   

Seat and pmsenger

 

Figure 12. Schematic of Car Chassis Unit and Suspensions with Seat.

Bond Graph Model Description. The BPR model of the vehicle can be thought of
as consisting of several major sections, or macros, which are connected by power bonds.
Figure 13 shows the macro bond graph of the BPR car model. The seat unit is connected
to the rigid chassis unit by a rigid connection labeled CS on the graph. Each of the
suspensions is connected to a comer of the car via a rigid connection. RF stands for the
right front comer, LF for left front, and RR and LR for the right and left rear comers,
respectively. Each of the suspensions also maintains contact with the ground. Viewing
the model as a macro bond graph representation is very useful if overall system response
is of concern, rather than individual responses occurring within each subcomponent. A

macro construction feature is currently not available in the workstation version of

60
ENPORT, but it is intended as an addition to the functionality of the program in the near

future. Adding macro viewing capability to the BGVis-2D tool would assist in assessing

the behavior of systems, especially in very complex systems with large numbers of

bonds.

 

[ )
1C3

 

 

 

C Rigid Chassis Unit
.1 .4 ..
Suspension Suspension Suspension Suspension
Unit 1 Unit 2 Unit 3 Unit 4
RFG1 1 RRG1 LRG

LFG

Figure 13. Macro Bond Graph of BPR Model.

For the purpose of simulating the behavior of the BPR model, each of the macros
was expanded in detail using basic bond graph elements. The bond graph representations
of the seat unit, rigid chassis unit, and suspension unit will each be shown and explained.
The 2-D bond graph representation of the seat unit is shown in Figure 14. Node 126
represents the vertical motion of the seat unit. The SE6 node includes the input force on

the seat due to gravity and the 1M6 node includes the inertia effect of the seat unit mass.

61

RD and CK are the dissipation and compliance effects of the coupling between the seat

and the point on the rigid body chassis to which it is attached.

SE6 -—>- 125—4- 1M6

/

OZ—> 1D

\

CS CK

Figure 14. 2-D Bond Graph Representation of Seat Unit

The rigid chassis unit bond graph model is shown in Figure 15. The TF nodes
and their connectors represent the geometric constraints satisfied by the rigid body. The
1W junction represents the translational motion of the rigid body chassis in the Z
direction, while IP is the roll motion (about the X axis), and IQ is the pitch motion
(about the Y axis). The 0218 junction serves to calculate the position of the point on the
rigid chassis to which the seat unit is attached. 0217, 0211, 0215, and 0213 each
determine the position of a corner of the rigid chassis to which a suspension is attached.
All velocities and forces are considered positive in the downward direction. All
rotational quantities are taken positive in the directions indicated on the schematic of

Figure 12.

62

TF8 TF7

\‘m \
“:17 \ <~ TF1 1v TF13
7 TF17Y {» TFISY l /rF13Y

 

/

0217 Ole 0215 0213

A A ml ml

Figure 15. 2-D Bond Graph Representation of Rigid Chassis Unit.

A detailed schematic of one of the independent suspension, axle, and wheel
systems which attaches to a comer of the chassis is shown in Figure 16 along with the
corresponding bond graph. The stiffness and damping of each suspension are represented
in this model with mechanical elements (CSI and RS1), but for an industrial application
the suspension unit could be modeled as an electronic active suspension containing
electrical and hydraulic components as well as mechanical elements. With bond
connections between the suspension elements at different corners of the car, non-
independent suspensions like roll bars also could be modeled and analyzed. The axles
and wheels are modeled in this example with inertia (1W1), resistance (RWI), and
compliance (CW1) effects. The schematic shows the coordinate systems used to

construct the bond graph.

63

Attached to car body at comer r
; Vcar 1217

RS 1
Suspension \
/

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

axle Maxie
Vaxle
l SEWl /
RWl
Wheel ‘\ 1W1 v- 01
_ CW /
d l RFG
groun } Vground
(a) Schematic Diagram (b) Word Bond Graph

Figure 16. Detail of Single Suspension Assembly

A two-dimensional bond graph of the entire three degree-of—freedom BPR
vehicle model is shown in Figure 17. This model is formed by joining the sections
described previously, connected as they were in the macro bond graph of Figure 13. One
simplification was made in the full model, which eliminated the 12 node of the seat unit.
Each vertical branch in the full BPR model bond graph represents a suspension and wheel
series. Branch 1 is the f ront/ri ght suspension, branch 2 is the f ront/lef t, while branches 3
and 4 are the rear/right and rear/left respectively (corresponding to the schematic in
Figure 12). The ground connections are represented by source of flow nodes. A vertical

velocity is imposed on the wheel which is induced by the interaction of the forward

64
horizontal velocity (assumed to be constant) and the shape of the ground position profile

that each wheel experiences. More details on the velocity input modeling can be found in

the next section. Table 2 contains a summary of the equations used for this model along

with their parameter values.

 

S56 —" 126——. N6
l m

seat unit IOZIN

 

 

 

 

 

\
i
I
5/
z! _.

 

 

 

 

 

   

> 4
TF” . TFllY 11:15}. TF13 11:13} 1
WHY I
ngrd 2 / .
chassis / i
g m. 0217 02411 0.2115 0213
RS] 1317 R82\ 1311 12F RS3 1213 RS4
117‘017 111l—-011 015-5115 013-3113 CS4
CS” . 1 s 1 l ,. \z. \‘
cs2
- 1W1 1W2 [W4
1216 l/ 1210 1214\ Mac8 1le ...—>
sgw/ sr—zwz SEW3 \SEW4
112w RW3 RW4
' /1wr‘-RW012\1W21—02
CW1 C“r2 CW3 CVV4 :
1 5121 s14:

Figure 17. Two-Dimensional Bond Graph of Car Model.

65
Table 2. Car Body and Suspension Model Equations and Parameters

C unctton
e W a

.— II II
II

1
t

("H
nllll

r-o
l

33

I
t
I
I

"He-o
"1111
0".

F00"
II II

H
II
pus

II 11
BB

 

System Response and Assessment. The bond graph model of the car body and
suspensions was subjected to an input consisting of an encounter with a relatively large
pothole in the road. The pothole was modeled as a function following a sinusoidal
profile. The vertical velocity induced by this function was determined and applied to the
right front tire at the time the pothole was encountered. The same velocity function is
experienced by the rear tire, but after a time delay which is dependent on the horizontal
velocity of the automobile (for this example, approximately 35 mph). Figure 18
illustrates the mathematical modeling of the bump input. The ENPORT model file and

function definitions for this example are included in Appendix C, along with the initial

conditions used for the simulation.

 

 

 

 

 

 

0'150 0.1 0.2 03 0.4 0.5

_ 0.6
x distance (m)

Pothole Profile: 2 = ~0.075*cos((10/3)*Pl*x) +0.075
for 0 < 2 < 0.6

Vx = 13.42 m/s
V2 2 dz/dt = dz/dx * dx/dt = dzjdx * Vx
t: x/Vx

 

 

 

 

 

'1’0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045
time (5)

Vertical Flow Source: V2 : (3.355)*PI*sin((10/3)*PI*13.42*t)
Time delay for back wheel: t = length of car/Vx = (2.5 m) / (13.42 m/s) = 0.19 s

Figure 18. Mathematical Model of Pothole Source of Flow.

67

Table 3 shows a tabulation of the response values for the suspension spring

deflections of the system (Q42, Q45, Q48, Q51) to the pothole input over a time range of

0.5 second. This response was obtained by setting the initial values for the displacements

to their equilibrium values (see Appendix C) and solving for the response using the

Runge-Kutta integration routine in ENPORT. It is obvious that this presentation of

response as a table of data is difficult to interpret in terms of the geometry of the model.

Figure 19 shows a time plot of the variables mentioned above, along with the position of

the seat and passenger with respect to the chassis (Q86) for the same 0.5 second time

period. It also takes considerable effort to relate this presentation of variable values back

to the bond graph and the schematic, and to visualize their meaning.

TIME

+0.00000E+OO
+2.00000E-02
+4.00000E—02
+6.00000E-02
+8.00000E¢02
+1.00000E-Ol
+1.20000E-Ol
+1.4000OE-Ol
+1.6000OE-01
+1.800003-Ol
+1.999908-Ol
+2.19990E-Ol
+2.3999OE-Ol
+2.5999OE-Ol
+2.79990E-01
+2.9999OE-Ol
+3.20000E-Ol
+3.4000OE-Ol
+3.6000OE-Ol
+3.800lOE-Ol
+4.00010E-01
+4.20010E-01
+4.40020E-01
+4.60020E-01
+4.80020E-Ol
+5.0003OE-Ol

Table 3. Response Data from Pothole Simulation.

.32700E-02
.327OOE-O2
.327003-02
.327008-02
.327OOE-02
.32700E-02
.83600E-02
.18300E-02
.06320E-Ol
.15300E-02
.49200E-02
.O8lOOE-02
.73500E-02
.503OOE-02
.424OOE-02
.286OOE-02
.23800E-02
.086008-02
.29300E-02
.843003-02
.936008-02
.520008-02
.484008-02
.354008-02
.222003-02
.180003-02

.75100E-02
.7SlOOE-02
.75100E-02
.75100E-02
.751003-02
.75100E-02
.6S3OOE-02
.63000E-02
.llSOOE—OZ
.96200E-02
.BOlOOE-OZ
.329OOE-02
.37000E—02
.33800E-02
.SOSOOE-OZ
.534OOE-02
.79700E-02
.953008-02
.OSlOOE-OZ
.239008-02
.319003-02
.l6800E-02
.42800E-02
.49500E-02
.SSSOOE-OZ
.673005-02

.95000E-02
.94900E-02
.95000E-02
.95000E-02
.950003-02
.950003-02
.424008-02
.52400E-02
.99100E-02
.lOZOOE-OZ
.l69OOE-02
.48000E-02
.293003-02
.24500E-02
.OSSOOE-OZ
.24SOOE-02
.826OOE-02
.1834OE-Ol
.651003-02
.98400E-02
.253003-02
.329003-02
.Ol7OOE-02
.91200E-02
.85800E—02
.77300E-02

.37200E-02
.372003-02
.372003-02
.37200E-02
.372003-02
.37200E-02
.498003-02
.29700E-02
.58100E-02
.122003-02
.34800E-02
.7SlOOE—02
.90300E-02
.09600E-02
.lZZOOE-OZ
.238OOE-02
.70lOOE-02
.624003-02
.30800E-02
.O4SOOE-02
.44lOOE-02
.O4900E-02
.93SOOE-02
.O64OOE-02
.199003-02
.26lOOE-02

 

ErgonI/u_sr.o-oeta 11:11:54 09/13/94
§ " ' 1{ ' ‘ .

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w

 

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' g . I . 4 v . -
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' ., (.1 l
: . ,

     

 

 

 

 

 

 

 

 

Figure 19. Response Data from Pothole Simulation

Response Using the BGVis-ZD Tool. Several figures are shown to illustrate the
assessment of response of the BPR vehicle model to the pothole using the enhanced bond
graph display environment The variable type selected for line width display in these
figures is power. The first (Figure 20) shows the car at its equilibrium position before the
bump is encountered. Since at this equilibrium point the parts of the vehicle are not
undergoing any vertical velocity, powers are all equal to zero and all of the bonds are
drawn at their minimum width. Figure 21 shows the response of the system at the time
just after the front/right tire has encountered the pothole. Power can be seen to be
flowing up branch 1 (right/front) into the CW1 element as the tire responds to the
downward velocity. In Figure 22, power flows further up the suspension branch to be

dissipated by the suspension's viscous damping (RSI). F1 gure 23 shows that the power

69
input to the model by the pothole is nearly damped out by this damping effect at a later

time stage. In Figures 24 through 26, responses are shown at a time after the rear/right
tire has encountered the pothole. The response follows the same pattern as occurred in
Figures 21 through 23, but now power can be seen to be transmitted up branch 3. The
line width variation technique lends itself well to the visualization of ”flow” type

quantities within the system.

In addition, Figure 27 shows a display of energy variable values using the "level"
indicators at a time soon after the front tire encountering the pothole. The glyph symbols
next to the R, C, and 1 elements indicate that at this particular moment in the course of the
animation energy is stored kinetically in the I element for the wheel/axle (1W1), while a
small amount of energy has been dissipated in the suspension (RSI). Eventually, the
majority of the energy input to the system by the pothole is clamped out through the
action of the R elements in suspensions 1 and 3. The "flow" and "level" type indicators
could also be used together to enhance the engineer's understanding of how the system

functions.

For the purpose of checking exactly how much relative displacement is
experienced by the seat unit during the simulation, bond 88 was selected with the mouse,
and the time plot of displacement shown in Figure 28 was obtained. The time plot shows
a small change in the absolute position of the seat unit mass during the course of the
simulation for the chosen model parameter values. It can be concluded that although less
than one tenth of the maximum power transmitted to the wheel ever reaches the car
chassis and passenger (as shown by Figures 20 through 26), there is still a small amount
of deflection experienced by the passenger. These visualization techniques give a
qualitative idea of how the vehicle reacts to a pothole in the road, which would allow

tuning of the suspensions to further isolate the road surface from the passenger motion.

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71

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79
5.2 Rallcar Air Brake Switching System Example

The DB-6O Control Valve is part of a power braking system used to stop railway
train cars. The braking system consists of pressurized air brakes which provide friction to
the wheels of each car to decrease its speed, a brake pipe containing pressurized air which
extends from the engine to all of the cars, and the DB-6O control valve which directs air
to the air brakes from storage reservoirs as necessary depending on the engineer’s control
of brake pipe pressure. The storage tanks are also included in the system, and the switch

controls air flow to these reservoirs for charging and recharging of the system as well.

The DB-60 is a combination of hydraulic and mechanical components. Figure 29
presents the schematic diagram of the railcar airbrake control valve given in the DB-6O
Control Valve Instruction Manual ME—21 (New York Air Brake, 1991). The manual
consists of thirteen three-page-wide color plates and twenty-eight pages of explanatory
text all for the purpose of educating an engineer about how the system functions. The air
brake control valve was chosen as an example for this research because it is a complex,
industrial level modeling problem involving moving mechanical parts and pneumatic
circuitry, and therefore illustrates the necessity and effectiveness of better visualization.
The BGVis-ZD tool is of great value in supporting the construction and verification of a
working model of the air brake system. A model which has been validated against actual

test results would be a very useful tool for testing proposed design improvements.

Model Description. The construction of a bond graph model for a system as
complex as the control valve is not an easy task. The approach taken was to
hierarchically decompose the overall system into successively smaller and more detailed
subcomponents and their connections. The key activity involved in this modeling

decomposition is the identification of the ports (input/outputs) of the system as a whole

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Figure 29. Schematic of the Air Brake Control Valve Switch.

81

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 30. Top Level Bond Graph Decomposition.

and of each individual sub-system. The result of the first step of identifying the input and
output ports from the environment to the DB-60 device being modeled is shown in Figure
30. This figure also shows the breakdown of the main device into subdevices called
the DB-lO Service Portion, DB-20 Emergency Portion, and DB-30 Pipe Bracket
modules. This example focuses on the 03-10 module. The reticulation of the DB-lO
module into seven subcomponents, following the numbering convention established in
the Instruction Manual, is shown in Figure 31. The pneumatic ports from the
environment to the DB-lO unit are the Brake Pipe (connector BPl), the Emergency
Reservoir (connector ERl), the Auxiliary Reservoir (connector (ARI), the Brake
Cylinder (connector BCl), and the Retainer (RETl). Connectors RP and E? are ports to
the atmosphere and RVH is a mechanical port. The figure shows sub-devices numbered

82
0 through 6 and their interconnections. Due to the complexity of the system, only those

subdevices necessary to the functioning of the different modes of operation under study

in this example were modeled. These are described in the following paragraphs.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 31. Bond Graph Decomposition of DB-lO Module.

Modes of operation. The DB-lO module is designed to perform many different
functions depending on brake pipe (BP) pressure and pressure levels in the storage
reservoirs. Several have been identified for modeling. When the storage reservoirs are
empty, an increase in BP pressure causes charging of the auxiliary reservoir (AR) and
emergency reservoir (ER) from the BP. Charging involves primarily the Service Main
Piston System (1) (see Figure 29). In a standard braking procedure, a decrease in BP
pressure causes air from the AR to be directed to the brake cylinder (BC) to stop the train.
Standard braking also primarily involves the Service Main Piston. After braking is
completed, BC air is exhausted to end brake application, and ER air may be fed into the

83

B? to support recharge of the system. Recharging occurs with assistance from the
Service Accelerated Release Valve (2) as well as the Main Piston. At any time, a manual
lever can be used to exhaust the AR and ER to the atmosphere. Manual release involves
the Release Valve (6) in combination with the Main Piston. These subdevices of the
model were modeled appropriately and correctly connected to each other. Equations
were set up for each of the elements using reasonably estimated parameters. With the
parameters set, simulations of the different modes of behavior of the device were
completed. Before presenting the entire system model, a modeling and simulation
exercise involving the Service Accelerated Release Valve (2) will first be described. The
behavior of this subsystem is also visualized before moving on to the full Air Brake

Valve System model.

Check Valve Modeling. To verify the concepts involved in creating bond graph
models of pneumatic/mechanical devices. especially modeling of check valve (CV)
behavior, a bond graph model of the Service Accelerated Release Valve (2) only was
created. A detailed schematic of the subcomponent is shown in Figure 32. The bond
graph model for this device is shown in Figure 33. The device consists of a Back Flow
Check Valve (2-1) and a diaphragm actuated valve (2-2) which together control flow

from the emergency reservoir to the brake pipe.

 

 

Figure 32. Schematic of the Service Accelerated Release Valve (2).

 

 

 

 

 

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The CV is modeled as a mass which is allowed to translate in the X direction
(1X21). Forces on this mass which affect its motion are l) the force due to the spring
(Csp21); 2) a force due to the stop when it is encountered by the mass (Cst21); 3) a force
due to viscous friction (R21); 4) an inertia force (121); (5) and a force due to the differing
pressures on each side of the mass (through bond ZlSEl ). When the displacement of the
CV is positive, and the pressure difference over the CV is positive, there will be flow
through the valve (from SEER to 0comp) which can be calculated by a non-linear
relationship depending on the values of the pressure difference and the valve opening
dimension. This equation is implemented by the Rx21 node. The diaphragm actuated
valve works in the same manner, where flow from 0comp to SEBP is only allowed if the

pressure difference over the diaphragm overcomes the spring force causing the valve to

85
open. Therefore, in order for flow to occur from the ER through to the BP, the AR

pressure must be lower than the BP (to open the diaphragm actuated valve), and the BP
pressure must be lower than the ER pressure (to open the check valve). This sub-
component thus provides ER air to the BP for recharging when the AR pressure is low,

for example after a standard braking application.

A simulation of the Service Accelerated Release Valve has been performed to
verify the basic behavior of the model. Parameters were estimated to achieve reasonable
results. Details of the parameters and equations used for the bond graph elements shown

in Figure 33 can be found in Appendix C.

Verification of the expected functioning of the component can be easily seen by
using the BGVis-2D display of the power variable type on the bond graph using line
width variation. Figures 34 and 35 show two different time stages during the course of
the animation. In Figure 34, at time = 0.5 it can be clearly seen that no power transfer is
occurring in the device (minimum line widths for all bonds), since the AR pressure is
low, but BP and ER pressures are equal. Figure 35 is used to illustrate the use of color as
well as line width variation by the BGVis-2D tool. In Figure 35, at time = 0.76, the AR
pressure is still low, and the BP pressure has experienced a smaller decrease. Color
variation on the bonds shows pressure on bond ER12 is greater than pressure on bond
BP2122 which is greater than pressure on bond AR2122. The line widths show that there
is power flow through the valve (large widths for bonds all along the path from SEBP to
SEER). The arrow directions indicate the direction of flow. Thus the model behaves as
intended. In addition, Figures 36 and 37 show the flow variable type displayed with line
width. At time t = 0.21 seconds, the AR pressure is decreasing, causing the diaphragm to
move. This velocity is shown by the large line widths connected to the 1x22 node in

Figure 36. At time t = 0.6 seconds (Figure 37), the BP pressure is decreasing. This

86

causes the check valve to move into the open position (larger bond widths on the 1x21
node), while the diaphragm (1x22) moves back somewhat toward its initial position since
the pressure difference between AR and BP has decreased. Arrow direction changes on
the bonds connected to node 1x22 show the occurrence of negative flow. The
visualization provides a qualitative analysis of what is going on in the device without

having to select individual bond values for display of time plots.

     

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91

Main Piston Modeling. With regard to the overall air brake control valve
modeling task, the objective was to model the modes of behavior of the device described
previously using ENPORT. The modes of operation that were simulated and visualized
in this example were: 1) initial charging of the auxiliary and emergency reservoirs, 2)
standard braking where air from the auxiliary reservoir is directed to the brake cylinder,
3) secondary recharging where brake cylinder pressure is released and air from the
emergency reservoir is directed to the brake pipe, and 4) manual release of auxiliary and
emergency reservoir pressure. A bond graph of the parts of the Main Piston System (1),
Service Accelerated Release Valve (2), and the Manual Release Valve (6), which are
involved in the modes of operation of the device described previously is shown in Figure
38. This bond graph models the ER and the AR each as a C type storage element (car
and eer). The 3? pressure is the input to the system (sebp). The velocity of the
diaphragm of the main piston is represented as node hr. The forces on the node include a
spring, seat, viscous damping, and inertia as in the previous check valve example. Also
included is a force generated when the diaphragm comes in Contact with the ER charging
valve stem (1x3), a force generated when the diaphragm comes in contact with the AR
charging valve stem (1x2), and a force generated in the opposite direction when the
diaphragm comes in contact with the BC inlet valve (1x5). The hydraulic flow rate
through these valves is determined from the valve opening dimension in elements rx, rx2
and rx5 respectively. The pressure difference across the diaphragm is calculated at node
ltf and the force on the diaphragm is determined by multiplying the pressure difference
by the diaphragm area at the tf node. The 0bp node is the pressure above the diaphragm,
while the Oar node is the pressure below the diaphragm. These areas are connected
through several valve and choke pathways to the reservoirs and input pressures. The ER
Charging Check Valve is part of the Main Piston sub-assembly and is included with node
1x4 and associated nodes as shown in the box on the graph. The Service Accelerated

Release Valve is included at the top of the bond graph with appropriate connections to

92
reservoirs and inputs. The Manual Release sub-component is modeled by the lrel

junction. A mechanical force can be input to this element via the serel node, and the
position of the release valve controls the volume flow rate through the rxar and rxer

elements.

 

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93

Made 1: Initial Charging of the Reservoirs. The results of the simulations of the
four modes were visualized using the BGVis-2D tool in order to show how the tool helps
in making the behavior of the system easier to comprehend. The first mode is initial
charging of the AR and ER from the BP. Charging of the system is accomplished by a
linear increase in BP pressure supplied as an input. When the BP pressure is increased, it
is expected that the pressure in the storage reservoirs will also experience an increase in
pressure due to flow of air from the BP through the main piston system. Figures 39
through 42 show this response. Power is shown as a variable type using line width. At
time = 0, there is no flow, and all initial pressures are set to zero. Initial displacements
for all of the mechanical valves are set to their equilibrium values (see Appendix C). In
Figure 39, the pressure in the BP has increased, which causes flow to start through the
main piston, which causes the pressure in the AR to increase. Figure 40 shows the
system at a later time where the BP pressure has become high enough to start flow into
the ER. Figure 41 shows the response as the BP pressure nears its maximum. Air is still
flowing into both tanks and power is higher due to the higher pressures and flow rates
involved. Figure 42 shows the response after the brake pipe has reached its maximum
pressure level, and is now remaining steady. Since there is less pressure difference across
the diaphragm, flow into the reservoirs decreases. Eventually all pressures are equal, so
all check valves are closed and no more How in the sub-assembly occurs. The manual

calls this situation charging lap position.

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Brake Model Charging Mode (Time = 58.2).

1!"

Power Response for A

Figure 4".

98

Standard braking. The main piston system is also involved in sending air from
the AR to the BC when the BP pressure is decreased, if AR and ER pressures are high.
This mode is known as standard braking and is shown in Figures 43 through 45. The
system starts out in a fully charged state (charging lap position) with the initial conditions
for nodes car and cer set to a high value (see Appendix C for values). Power is shown as
the variable type using line width once again. In Figure 43, the pressure in the BP has
decreased, which causes the main diaphragm to shif t in the opposite direction from when
charging, opening the BC inlet valve. Power can be seen to be flowing into node cbc and
also some power is lost to the BP as AR pressure tries to equalize with BP pressure.
Figure 44 shows the system when BP pressure has stabilized at a lower value. The AR is
still losing energy to the BP. Figure 45 shows flow decreasing to the point where the

system will once again be in lap position, but at a lower overall pressure.

   

 

 

 

        

 

 

 

 

 

 

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Figure 44. Power Response for Air Brake Model Braking Mode (Time = 14.1).

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Figure 45. Power Response for Air Brake Model Braking Mode (Time = 19.95).

102
Recharging. After a standard braking application, when the system is in service

lap position, an increase in BP pressure should cause release of BC pressure to the
atmosphere to end the braking action. Also, the AR should be recharged from the B? to
ready the system for the next braking action. The Service Accelerated Release Valve
contributes to this recharging initially by sending ER air into the BP for AR recharging.
Figures 46 through 49 show accelerated recharge with the flow variable shown as line
width variation. In Figure 46, the pressure in the BP (sebp) is starting to increase, which
causes flow from cbc to seatm. In this figure the wider line widths around the 1x21 node
also indicate that the check valve of the Service Accelerated Release Valve is moving to a
new position to allow flow through the valve. Figure 47 shows the system at a later time
when the flow out of the BC has increased and a small amount of flow can be seen to
occur from ER to BP through the Service Accelerated Release Valve. Figure 48 shows
the response as the BP pressure continues to increase. The BC is still emptying while air
is starting to flow from the BP to recharge the AR. Finally, Figure 49 shows the response
after the BP has steadied out at its maximum pressure level. Small amounts of flow are

still occurring. Soon the system returns to lap position.

103

 

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104

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105

 

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Figure 48. Flow Response for Air Brake Model Recharging Mode (Time = 9.45).

106

 

 

 

 

 

 

 

     

 

 

  
    

 

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Figure 49. Flow Response for Air Brake Model Recharging Mode (Time = 14.4).

107

Manual release. From any lap position the option should always be available to
manually release the pressure from the AR and the ER. When AR pressure decreases this
will also cause release of the BC, assuming that BP pressure remains fixed. Figure 50
shows this occurrence. The power variable is displayed with line width variation. The
force input serel is increased by a set amount to cause the manual release valve to move
up from its valve seat, creating a flow path from ER and AR to atmosphere. It can be
seen on the graph that power is high along the paths from car and cer to seatm. Nearly
all of this power is dissipated in the flow resistances (rxar and rxer). The power is low
on the bonds connected to Oat because the atmospheric pressure is a very small value
compared to AR and ER pressures. A small flow also occurs along the path from cbc to
seatm. In Figure 51, AR and ER pressures have decreased to the point that flow into the
system from 8? starts to occur. If the system were held in this position with the manual
release valve held open, pressures would all stabilize to that of the BP, and a constant

flow would occur from 8? out to atmosphere.

108

 

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109

 

 

 

 

   

   

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110

 

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Figure 52. Schematic of Mechanical Three DOF System.

5.3 Modal Analysis Example

In addition to applying visualization techniques to industrial scale systems design
problems, there is also usefulness in extending the concepts to educational problems, in
order to aid students in their understanding of basic phenomena. One of these
educational applications of visualization is modal analysis in vibrating systems.
Mathematical models of systems with several degrees of freedom can be used to
determine system natural frequencies and mode shapes. The mode shape is a description
of how a system vibrates when it is operated at or near one of its natural frequencies. The
BGVis-ZD tool can be useful in helping students to "picture" the different mode shapes of

a system and understand the actual time response better.

An example three degree of freedom (DOF) mechanical system used to illustrate
how the dynamic display can show mode shapes is shown in Figure 52. In this system
three masses are connected together with linear springs. Each mass is allowed to

translate in the x direction. The system is connected to a base, which can be used as a

111

source of motion for the system, but for this example which will involve natural
vibrations, the base is fixed in place. A bond graph of this system is shown in Figure 53.
Each 1 element along with the corresponding I element represents the velocity of a mass.
The C elements model the springs between each mass. All of the elements are linear,
with the masses of the bodies 1, 2, and 3 equal to 1 kg, 2 kg, and 2 kg, respectively. The
C element stiffnesses are 1 Wm for C1, 1 N/m for C2, and 2 Wm for C3. The bond
graph is set up to conform to the geometry of the actual system, to aid in the
visualization. The model file including the equations for this example can be found in

Appendix C.

1x1-—A 11

CIT—01
1x2—> 12

C2'<——— 02

1X3—-—\13
C3<——O3

1Y<—-—SF

Figure 53. Bond Graph of Mechanical Three DOF System.

ENPORT was used to determine the three unique eigenvalues (natural
frequencies) and eigenvectors (mode shapes) of the mechanical three DOF system. The
eigenvalue and eigenvector values calculated are shown in Table 4. When an eigenvector
is used as the initial condition for a simulation of the natural response, the system
experiences the natural mode of vibration corresponding to that eigenvector. Simulations
of the time response for the three different modes of this system were completed and the

results were visualized using the BGVis-2D display environment.

l 12
Table 4. Eigenvalues/vectors of Mechanical Three DOF System.

genvector

 

Figure 54 shows the response of the flow variable type displayed at a time when
the flows are near their maximum. Since the response is sinusoidal, the displacements of
the masses are also sinusoidal functions with the same frequency and amplitudes all
scaled by the natural frequency. The line widths on bonds 1, 2, and 3 illustrate the first
mode shape for the system. During the course of the time response the overall values rise
and fall, but the relationship between the displacements of masses 1, 2, and 3 stays the
same. Mass 1 experiences the greatest displacement, with mass 2 experiencing a
somewhat less displacement in the same direction, and mass 3 has the least displacement
also in the same direction. Watching the levels of the glyph symbols allows the student
to track how energy is shifted between kinetic energy (I elements) and stored energy in
the springs (C elements) during the course of the animation. Figure 55 shows the second
mode shape. In this mode masses 2 and 3 move together, but with the displacement of
mass 2 at about half the value of mass 3, while mass 1 moves in the opposite direction
with a displacement value near that of mass 3. Figure 56 shows the third mode shape. In
this mode masses 1 and 3 experience equal displacements in the same direction, while the
displacement of mass 2 is equal and opposite. The advantage of using the dynamic

display would be even greater for systems with more degrees of freedom and for systems
involving energy domains other than mechanical translation where mode shapes are not

as easily visualizable (e. g. electrical).

113

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114

    

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115

 

 

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Figure S6. Displacement Variable Display Showing Third Mode Shape.

Chapter 6
Visualization Example Using BGVis-BD

The three degree-of-freedom BPR car and suspensions bond graph model
representation was extended to three dimensions using the three-dimensional bond graph
display environment (BGVis-3D). The 3-D bond graph representation of the BPR model
is shown in Figure 57. The 3-D representation can be seen to have the same connectivity
as the 2-D version, but clearly the 3-D representation corresponds more closely to the
geometry of the schematic (refer to Figure 12). The suspension branches and the
rotation/translation axes are much easier to associate with their corresponding locations in
the schematic, so much so that it may no longer be necessary to keep the schematic

nearby for constant reference.

Figures 58 through 61 show the same power response obtained from the model of
chapter 5 with a pothole input visualized in the 3-D environment. Color variation is used
to show the power values on the bonds. Figure 58 shows the expansion stage of the
right/front branch at the beginning of the pothole. Figure 59 shows a later time stage
when energy is being damped out of the front branch after the front tire has passed the
pothole. Figure 60 shows the effect of the rear tire encountering the pothole and Figure
61 shows the damping out of this energy in branch 3. Combining the response data with
a 3—D representation of the bond graph model lessens the amount of work required by the
modeler to visualize the response with respect to the schematic and therefore the physical

system itself.

116

117

 

Figure 57. 3-D Bond Graph Representation of Car and Suspensrons Model.

118

 

Figure 58. 3-D Dynamic Display of Response to Pothole Input (Time = 0.112).

ll9

 

Figure 59. 3-D Dynamic Display of Response to Pothole Input (Time = 0.115).

 

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120

 

Figure 60. 3-D Dynamic Display of Response to Pothole Input (Time = 0.300).

121

 

Figure 61. 3-D Dynamic Display of Response to Pothole Input (Time = 0.305).

Chapter 7

Conclusions

7.1 Summary of Contributions

The research work completed has made a significant contribution to the use of
bond graphs in modeling and design of large-scale systems. The principal research
objective of designing and implementing an improved design environment for
engineering systems based on the use of bond graph methods as a structured modeling
technique, which makes the interpretation of dynamic system response easier for

designers, has been achieved.

7.1. 1 Two-Dimensional Visualization

The BGVis-2D environment provides the dynamic link between model response
data and bond graph structure which is necessary to take advantage of the knowledge of
the system that the bond graph supplies to the engineer. This link between simulation
data and bond graph model makes the visualization of response more meaningful. This is
especially useful in the process of gaining insight about model behavior. The
environment is also very valuable in assisting in the task of explaining complicated
system behavior to those who are not familiar with an existing system model. The
visualization provides a way to communicate how the system is behaving in a basically

qualitative way.

122

123

The primary functions implemented in the BGVis-2D display environment were:
1) loading of bond graph model files into the data post-processor; 2) integration of
effort and flow variables with respect to time to obtain the net energy variables explicitly;
3) three different scaling options for data; 4) bond color and width variation for a
display of bond graph variables including power as if they were flowing on the graph; 5)
glyph display for a level-type display of associated energy values in the energy storing
and dissipating elements of the bond graph; 6) time controls necessary to control the
display of the animation at the user's discretion. Two practical engineering system
examples, an automobile in bounce-pitch-roll mode and a railcar airbrake switching

system, were developed to illustrate the use of the BGVis-2D tool.

7.1.2 Three-Dimensional Visualization

The BGVis-3D environment provides a stronger link between the bond graph and
the physical system by allowing display of three-dimensional representations of bond
graphs. Matching key points in the bond graph and physical schematic further enhances
the link between the physical system and the model behavior. The computer graphics
standard PHIGS was used to implement the functions of the graphical display. A method
for translating bond graphs into three-dimensional objects using spheres for nodes and

cylinders with arrows for bonds was established.

The primary functions implemented in the BGVis-3D display environment, in
addition to some of those mentioned above in the 2-D environment description, were: 1)
loading of 3-D bond graph model files and data files into the environment; 2) control of
the viewing parameters, including changing the angle of view and the distance from

which the 3-D bond graph is viewed 3) color variation to show values of bond graph

124

variables including power and energy on the graph. The automobile example was

extended to three dimensions to show the capabilities of the BGVis-3D environment.

7 .2 Areas for Further Research

Several areas have been identified as possibilities for future research. An overall
goal of future research might be working toward what has been called ”interactive
quantitative visualization” or "computational steering" (Peskin, et al, 1991). The basic
idea behind these concepts is to graphically link the model with results during
computation so the designer can make decisions about the quality of the model as the
computation progresses. The suggested future research areas are grouped into two
categories, the first relating primarily to the BGVis-ZD environment, the second to the

BGVis-3D environment.

Regarding the two-dimensional bond graph visualization, the following areas

warrant further attention.

1. The integration of macro-modeling capabilities and library storage of sub-
components with the new display capabilities would be welcome. In this way large
systems could be expressed in bond graph form without having to see all the individual
details of each subcomponent. Elements in close geometric proximity could be grouped

to make the power animation clearer.

2. Additional scaling options for variables could be implemented to show
behavior in the clearest way possible. Scaling of variables by energy domain might be
helpful to distinguish between variable levels which vary greatly over the different

energy domains. Power and energy can be directly equated across the domains if

125

appropriate units are used, but individual variables have their own units in each domain.
For example, considering the behavior of the airbrake switching system, the efforts in the
hydraulic sections are numerically large, while the forces on the mechanical parts are
very small in comparison. If all the efforts are scaled together, the relative values of
forces on different mechanical components is obscured. If the mechanical efforts could
be scaled independently of the hydraulic efforts, better relative comparisons could be

made.

3. The capability for including multibonds in the graph should be added to the
ENPORT modeling software. A multibond is a concise way to represent a natural
grouping of single bonds (Breedveld, 1985). Although multibonds do not necessarily aid
in helping bond graphs to correspond to natural geometry at a detailed level, they can

sometimes be of great help in simplifying graphs at the macro level.

4. It would be desirable to show in the animation not only information related to
each specific instant in time, but to include some time history information as well. In this
way still prints or photographs of different time stages would show power data related to
several previous and following time stages, allowing for better interpretation of dynamic

response without having to view an entire animation sequence.

5. It would be useful to transfer the functions of the 2-D environment described
in this thesis from the UNIX version of ENPORT to the more widely disseminated PC-
DOS version. More powerful PC's such as Pentium and Power-PC based machines make
the animation realizable in the PC environment and would therefore make it available to

many more engineers to aid in their system design work.

126

6. The files used to store the simulation results data are often very large due to
the fact that all efforts and flows for all bonds over all time stages is stored along with the
state variables. A certain amount of this information is redundant due to bond graph
constraints. For example, all of the efforts on bonds connected to the same zero-junction
are constrained to be equal. It might be useful to establish a format for output data files
which compresses the files by eliminating all redundant information. Reconstruction of

the data could be performed in the visualization postprocessor.

In addition to the 2-D list, the following suggestions for future research apply for

the three-dimensional bond graph visualization.

1. Since the goal of this research was to show the effectiveness of display of
simulated behavior data on a 3-D bond graph representation, the activity of 3-D bond
graph construction was ignored. In the future it would be useful to develop a 3-D model

builder along the lines of the current 2-D model builder

2. To further enhance the correspondence of 3-D bond graph representations to
physical systems or schematics it would be useful to develop the concept of anchor points
in the bond graph. These points would be specifically intended to refer directly to
specified locations in the system. The ability to place and manipulate these anchor point
elements would allow the engineer to scale the model with the physical system, as in a

CAD drawing environment.

3. In the interest of providing as much information to a designer as possible in a
given display, it would be useful to develop an animation of the physical motions of the
mechanically translating bodies in the system using bond graph element anchor points in

the bond graph display environment. Multibody dynamic mechanical system modelers

127
like ADAMS already use this technique with rigid body models to enhance interpretation

of simulation results, and adding this type of display to bond graph models would also be

useful.

APPENDICES

Appendix A
A Brief Introduction to Bond Graph Modeling

A.1 Bond Graph Variables and Node Types

In Chapter 2 of this report, the purpose of bond graph modeling was stated and a
general description of bond/system graphs was given. The purpose of this appendix is to

provide a few more details about system graphs and the way they are constructed.

A bond graph is a graphical representation of the physical behavior of a system
leading to an explicit mathematical model involving system variables. A bond represents
a power transfer connection which appears at a port, or place where energy is transferred
to or from a device. The structure of a bond graph takes advantage of the fact that
physical variables in many engineering domains appear as related pairs whose product is
power. These power variables are denoted as effort and flow. Related to the power
variables, two other types of variables are identified which are of use in determining
energies. These are called momentum and displacement. Depending upon which
energy domain the power transfer occurs in, the generic variables effort, flow,
momentum, and displacement can be assigned to different physical quantities. Table A-1

lists the variable names and units for several common engineering energy domains.

A given system can be separated into subcomponents connected at their ports to
other subcomponents via bonds. This decomposition can be done at various levels, until
at the most precise level, physical behaviors of a subcomponent can be described with a

relatively small set of bond graph elements (node types) and their associated constitutive

128

129
equations. The set of standard bond graph modeling elements was shown in Table 2 of

Chapter 2 and is repeated here as Table A-2. These elements can be used to describe

behaviors found in most engineering system domains.

Bond graphs can also be augmented by the addition of block diagram elements
and signals. In this way information flow as well as energy flow can be accounted for
and control systems can be modeled along with the actual system under study. Signals
are different from bonds, since signals by definition carry no power, only information.

Signals are represented graphically by using a double arrow rather than the single arrow

used on a bond. Some examples of block diagram elements are shown in Figure A-3.

Table A-1. Variables in Various Energy Domains.

 

 

 

 

 

 

 

 

 

 

 

 

 

Variable General Mechanical Mechanical Electrical Hydraulic
Translation Rotation
Effort e(t) F, force T. torque e, voltage P, pressure
(Newton) (Newton*meter) flolt) (Pascal)
Flow f(t) V, velocity w. angular V61. i, current Q, volume flow rate
(meter/second) (radian/second) (Amiere) (meter3/seeond)
Momen- P 'f e d P, momentum H. angular mom. 2. flux link. Pp. integral of press.
tum (Newton*second) (Newton*m*sec) QVcber) (Pascal *second)
Displaee- ‘1 'If m X, distance 9. angle q, charge V, volume
merit (meter) (radian) (Coulomb) (meter 3)
Power P(t)=e(t)f(t) 130V (t) (W arr) t(t)w(l) (W at!) e(t)i(t) (W att P(t)Q(t) (Watt)
Energy E(p)= ff dp fV dP . kinetic [(1) dB , kinetic f. c9. , I Q de . kinetic
(Joule) (Joule) (Joule) magnetic (J) (Joule)
E(q)= f c dq f F d.\' , potential frde , potential fe dq . f P dV' , potential
(Joule) (Joule) (Joule) electric (J) (Joule)

 

 

Table A-2. Standard Bond Graph Elements.

130

 

 

 

 

 

 

 

 

 

 

 

Element Element Bond Graph Constitutive equations
Type Name Symbol General Form Linear Form
E
Sources Source of SE —A E = f (time) E = Constant
Effort F
Source of SF _E_> F = 1' (time) F = Constant
Flow F
Passive - 4_E_ - _ a:
One-P Resrstance R F E - f (F) E - R F
. E E=f(Q) E=l/C*Q
Capacrtance C ‘—F— p = dQ/dt F = dQ/dt
. E V=f(P) V=1/L*P
Inertia I 4?— E = dP/dt E = dP/dt
Two-port L _.3 El = n * 132
transducers Transformer Ft TI: F2 F1 = l/n * F2
El [‘2 El = r * F2
__\
Gyrator Fl GY —F2—3 F1 ___ l/r * £2
£1 £3 _ _
Junction One-Junction -—\ l——\ H - F1 - F3
elements Fl F3 EI-EZ-EB = O
[-2 Ln
El E3
Zero-Junction ‘ 0 \ 131 = 132 = B
F' 3 LP, *3 Fl-F2-F3 = o

 

 

Table A-3. Block Diagram Elements.

 

Element Name

Symbol

Constitutive equation

 

 

Signal Source W Y = f (time)
Signal Sink No output equation
Gain v = K * u
Integrator U Y Y = Udt
Function U . Y = NU)
Transfer Function U Y Y = T(s) * U

 

 

Summer

Distri butor

 

 

 

 

Y=U1+U2+U3

Y1: U. Y2 = U. Y3 = L'

 

 

 

131
A.2 Standard Procedures for Modeling

Because bond graphs have been developed with the goal of allowing structured
heirarchical decomposition of a system, straightforward methods can be used to translate
schematic diagrams into bond graph models. The methods differ depending on the
energy domain being modeled, and several of these methods for handling common
domains will be detailed in the following sections, along with simple examples. The
general steps for obtaining a bond graph from a schematic are: 1) establish a coordinate
system and unique system variables for the system to be modeled; 2) follow the
appropriate procedure to obtain bond graph model with appropriate signs on bonds; and
3) define causality to establish input/output relationships within model in order to prepare
for algorithmic equation derivation. This section outlines the establishment of coordinate
systems and modeling procedures for mechanical, electrical, and hydraulic systems.

Causality considerations will be discussed in a later section.

Mechanical Translation and Rotation. The procedure for obtaining a bond graph
model of a mechanical translational system consists of the following steps. First, identify
all unique velocities in the system (flows) and choose the positive directions for each
velocity and its associated force (effort). The positive power direction occurs when both
of the previous quantities are positive. Next, establish a l-junction for each unique
velocity. Attach necessary inertia elements to their appropriate l-junctions, along with
sources of force or velocity. Finally, connect in compliance and damping effects with O-

junctions in between the appropriate l-junctions.

Figure A-l shows a simple mechanical system schematic and its bond graph
representation. The l-junction indicates that a common velocity (V) exists for several

different effects, and that the forces generated by these effects on the mass must add up to

132
zero. The effects suggested by the schematic are the input force on the body (Se), the

compliance effect of the spring (C), the resistance effect of the damper (R), and the force
due to the inertia of the body (I). Mechanical rotational systems follow the same
procedure, but linear velocities are replaced by angular velocities (flows) and forces are

replaced by torques (efforts).

 

 

 

x (V,a)
F(t)
Se
IV
C/ 1V \ I
R

Figure A-I. Mechanical Translation Example.

Electrical Networks. There are two different ways to approach electrical model
building. The first is to use I-junctions (common current) for electrical elements in series
and O-junctions (common voltage) for electrical elements in parallel, and construct the
entire model by observation. Another procedure, called the circuit-construction method.
is more straightforward. The procedure starts with establishing positive directions for
currents in the circuit. Next, all unique voltages are identified, and a O-junction is
established for each unique voltage. All other circuit elements are connected into this

structure with l-junctions between appropriate voltages. It is finally necessary to choose

133

one voltage as ground, eliminate that O-junction, and simplify the graph as much as

possible.

A simple circuit example is shown in Figure A-2. The l-junction represents the
common current (i) in the circuit, with all the voltage drops around the loop adding to
zero. The effects indicated in the schematic are the voltage source (Se), the electrical

resistor (R), the electrical capacitor (C), and the electrical inductance (I).

 

 

Se

 

 

\
/ ,

Figure A-2. Electrical Example.

Hydraulic Circuits. Bond graph models can also be used to represent
hydraulic/pneumatic circuits. The procedure used is similar to that for electrical circuits,

but currents are replaced by volume flow rates (flows) and voltages are replaced by

134

pressures (efforts). First, the positive directions for volume flow rates (Q's) should be
established. Next, O-junctions should be used to represent each unique pressure in the
system. Storage (C) elements can be placed on their appropriate O-junctions, and all
other hydraulic elements can be added in with l-junctions connected between the

appropriate 0- junctions.

Figure A-3 shows a hydraulic pump system example. The pump itself transforms
mechanical power (t, w) to hydraulic power (P, Q). There are two unique pressures in the

system: the inlet pressure (03), and the outlet pressure (Ob). The l-junction determines
the difference between the two pressures and relates that value to the mechanical input

through the transformer (TF).

Pb, Q

 

Pa, Q
Ob
Pb
_t__x TF__s. 1 Q
‘9 (lzT)
Pa
0a

Figure A-3. Hydraulic Circuit Example.

I35
A.3 Causality Assignment

Once a system bond graph has been constructed, it is necessary to establish a
system of input and output relationships in order to make the composition of the
constitutive equations of the elements into a set of system differential equations more
direct. Applying causality provides a structured way to develop system differential
equations. A causal stroke on each bond is used to indicate in which direction the flow is
the input, and therefore in which direction the effort is an output. With the causal stroke

placed on the left for the following elements

 

A l \ B
it can be inferred that the flow variable is the input to element B, and conversely, the
effort is the output from element B. From the point of view of element A, effort is the
input, and flow is the output. Different element types have different restrictions placed
upon where the causal strokes can be placed. Table A-4 lists the available causalities for

each element type.

Table A-4. Causality Possibilites for Bond Graph Elements.

 

Source Elements SC—‘l SIP—-
Passive Elements I ——"I Integral causality

c I——— Integral causality

R l-—— R ——I
Two-port Elements —-l TF —'1 F'— TFl'-——
——4 GY l— l—- GY ———-|

Junction Elements T i

——-lo——-I t 1}

 

 

 

 

 

 

 

 

 

 

 

136
A.4 Multi-Domain Example

In order to show the methodology of bond graph modeling for multi-domain
systems, an example is presented here. Each part of the system in a given domain is
modeled using the previously mentioned methods. The connections between domains are
provided by transformers or modulated source elements. The example system is the
Radar Pedestal Position Control System shown in Figure A-4. The system consists of a
radar pedestal which supports a radar dish which is allowed to rotate about the z-axis. In
order for the radar to track objects accurately, it is necessary to carefully control the
position of the pedestal by means of a motor supplying a torque and angular velocity
through a shaft and gearing system. A partial decomposition of the system into

subcomponents is shown in Figure A-S.

A complete system graph is shown in Figure A-6. In the complete system graph
element names ending in E are part of the electrical circuit driving the motor.
Specifically, IE and RE are the inductance and resistance of the motor circuit
respectively. Element names ending in M are part of the mechanical part of the system,
including a shaft with compliance and gearing system for speed reduction. Specifically,
1M and RM are the inertia and damping in the motor, CS is the shaft compliance, TF
represents the speed reducing gears, IP is the load inertia, and RP is the bearing friction
of the load. The block diagram elements provide the control action to be applied to the
circuit controlling the motor speed. The variable w is the angular speed of the pedestal,
and theta is the position of the pedestal, calculated by integrating the speed signal.
Causality is also shown on the diagram. The system's equations have been derived using
the computer program ENPORT, and the response of this system to a step increase is

shown in Figure A-7.

 

 

 

 

 

 

Command Signal
(reference value)

Figure A-4. Schematic of the Radar Pedestal Control System.

Control
Action

Electrical Motor Motor and Gear Speed Pedestal
C i— —- ~-

Figure A-S. Section (macro) bond graph as illustration of hierarchical decomposition.

 

 

 

 

 

 

 

 

 

138

 

 

 

 

 

  

 

 

llllllll ...?!
such-.58... IVIIUOI

l 'I”

 

 

Figure A-6. Bond Graph of the Radar Pedestal System.

 

 

6.40

3.20 4.80

TUESZALE

I.

 

 

 

 

 

 

LEE“)! “EM —'2 ""‘E.S3

xtlE

Figure A-7. Response to a Step Input.

Appendix B

Program Code
8.] Two-Dimensional Environment
The software developed for this application is stored in a file called dyndis.c. It is
necessary to compile this along with the ENPORT library routines stored in Iibenp.a and

the file mainpp.c which contains the main program. What follows is a listing of the C

language code used to implement the 2-D visualization environment (BGVis—2D).

139

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8.2 Three-Dimensional Environment

The software developed for this application is stored in a file called enport3d.c.
It is necessary to compile this along with the ENPORT library routines stored in Iibenp.a
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file used to implement the BGVis-3D environment.

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Appendix C
ENPORT Model Files

The following pages contain the ENPORT model files that were generated to
model and simulate each of the examples described in chapters 5 and 6. Stored in these
files are all of the positions of nodes and connectors in the system graph along with the
constitutive equation functions and parameters for each node. The last file in the series is

a modified 3-D file which contains 2 locations for nodes, as well as x and y values.

255

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