Date

 

This is to certify that the
thesis entitled

Simulation of Engineering Systems
Using MACRO Bond Graph Models

presented by

James Eugene Devlin

has been accepted towards fulfillment
of the requirements for

Masters degree in Science

 

 

   

 

Major professor

8/ 9/ 78

 

0-7639

 

 

Simulation of Engineering Systems
Using MACRO Bond Graph Models

by

James Eugene Devlin

A Thesis

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

Master of Science

Department of Mechanical Engineering

ABSTRACT

SIMULATION OF ENGINEERING SYSTEMS
USING MACRO BOND GRAPH MODELS

By

James Eugene Devlin

Modern engineering systems typically incorporate a number of
energy types: mechanical, electrical, hydraulic, pneumatic, and thermal
powers, to name some common ones. For such systems a unified struc-
tural representation is made possible by the use of bond graphs. A
particular problem of interest arises when most of the system's
components can be represented by lumped-parameter models but there
are some transmission elements to be considered, such as shafts or
lines.

A modeling and simulation technique has been developed to assist
in the design of such systems. The key new concept involves the
representation of a micro-element of the transmission component in
bond graph form and the automated expansion of such micro-elements
into a macro-element compatible with the rest of the system model.

The designer concentrates on choosing a suitable type of macro-
element, insight for which choice can be obtained from causal con-
siderations at the system level, and on selecting an appropriate
assemblage of such parts to obtain satisfactory accuracy at reasonable
cost. Transmission elements such as stepped and tapered shafts can

be approached this way.

ACKNOWLEDGEMENTS

I particularly wish to express my gratitude to my major professor,
Dr. Ronald C. Rosenberg, who as teacher and friend has been a constant
source of inspiration and encouragement.

I am grateful for the opportunity to share with him and my other
friends associated with the Department of Mechanical Engineering,

the exasperation and exhilaration of this and other work.

ii

To Bill, Gloria, Kathy and Sue, who gave purpose to this work.

iii

Contents

Chapter I. The Problem
1.1 Introduction
l.2 Objectives and Organization

l.3 Literature Review

Chapter II. The MACRO Approach
2.1 Introduction
2.2 Motor-Pump Example
2.3 Auto Drive Train Example
2.4 Implementation in ENPORT—S

Chapter III. The MICRO Option
3.1 Introduction
3.2 SHAFT Example and Implementation in ENPORT-S

Chapter IV. Conclusions and Recommendations
4.1 Conclusions

4.2 Recommendations
References

Appendices
A. User's Guide to REPLACE
8. Glossary of REPLACE
C. Listings of Programs

1v

Page

0010101

14

28
28
28

33
33
33

36

Figure

Figure

Figure

Figure

Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure

Figure
Figure
Figure
Figure
Figure

to 00 \l 05 01
o o o o o

11.
12.
13.
14.
15.
16.

17.
18.
19.
20.
21.

LIST OF FIGURES

Electric Motor and Pump System

(a) Electric Motor
(b) Macro Bond Graph

(a) Hydraulic Pump
(b) Macro Bond Graph

(a) Fluid Line
(b) Macro Bond Graph

Motor Pump System

Model for Electric Motor
Replacement Model for Macro MOTOR
Replacement Model for Macro PUMP
Replacement Model for Macro FLDLIN
Bond Graph for Vehicle Drive Train
Input/Output of the GRAPH Function
Replacement Model for Macro ENGINE
Replacement Model for Macro CLUTCH
Replacement Model for Macro TRANS
Forward Causal Environment of Macro SHAFT

(a) Replacement Model for Macro SHAFT Option l
(b) Bond Graph for Macro SHAFT Option 1
(c) Replacement Model for Macro SHAFT Option 2

Page
16

16
16

16

17
17

17
17
18
18
18
19
20
20
20
21
21

21
21
21

(d) Bond Graph for Macro SHAFT Option 2 (Pi network)21

Replacement Model for Macro VEHCLE
Replacement Model for Macros RNHEL and LNHEL
Replacement Model for Macro DIFF

Aft Causal Environment of Macro SHAFT

Input to GRAPH Function, Motor Pump Example

V

22
22
22
23
24

Figure
Figure
Figure
Figure

Figure

Figure
Figure

Figure
Figure
Figure

Figure
Figure
Figure
Figure

22.
23.
24.
25.
26.

27.
28.

29.
30.
31.

32.
33.

35.

Output of GRAPH Function, Motor Pump Example
Input to REPLACE Function, Motor Pump Example
Output of REPLACE Function, Motor Pump Example
Complete Motor Pump System

Input to REPLACE Function, Auto Drive Train
Example

Complete Auto Drive Train System

Output of REPLACE Function, Auto Drive Train
Example

Micro Shaft
Abridged Auto Drive Train System

(a) Input
(b) Output of GRAPH Function, Micro Example

Input to the REPLACE Function, Micro Example
Output of REPLACE Function, Micro Example
Complete SHAFT System

Illustration of Geometric Reticulation for a Plate

vi

24
24
25
25

26
26

27
3O
3O
30

3O
31
32
35

LIST OF TABLES

Table 1. Listing of subroutine READBG.
Table 2. Listing of subroutine REPLACE.
Table 3. Listing of subroutine MICROR.

vii

Chapter 1
The Problem

1.1 Introduction

In recent years, interest in design and simulation of engineering
systems has increased greatly. This increase has been supported by the
growing availability and popularity of the digital computer and is
evidenced by the number of generalized simulation programs described in
the literature. Increasing sophistication of device and component design
leads to more complex device models, which when assembled yield systems
which are larger in scale and more complex than ever before. The difficulty
in managing the system design process is evident. This study outlines an

approach that will aid in the design and simulation of such systems.

1.2 Objectives and Organization

When studying a particular system one typically thinks in terms of
major components and their interfaces with each other. Our purpose is
the development of software that will allow the engineer to analyze the
system at this level first, and then allow him to define these major
components in detail, for further study, in an automated manner. When
a major component is described in terms of the standard set of bond
graph elements, a macro model results.* A relocatable MACRO is a multi-
port model defined by the engineer as an independent graph entity. It
may be used several times in different places in the system model,

thereby saving time for focusing attention on the more subtle aspects

 

*The standard set of bond graph elements include (Se’ Sf. C. I, R, TF,

GY, l, O) and is defined and applied in the standard bond graph references
(1.2).

of the problem. In this spirit a user-definable element has been
developed to enhance the ENPORT-S program, which is a successor to
ENPORT-4 (3). The main features of a MACRO element are usually ob-
tained from an understanding of engineering models for such devices
as dc motors, pumps, gear boxes, and so on. A detailed discussion of
MACRO usage and replacement is offered in Chapter 2.

Another type of modeling problem arises in connection with the
geometry of’some devices. For example if we wish to include in a system
model the influence of a power-transmission component,* it is not obvious
a priori to what level of detail the transmission line dynamics should
be specified. For elementary models the MACRO approach would suffice.
However, models with a high degree of repetitiveness are commonly used.
To aid the engineer in modeling such devices in a highly automated
fashion, a MICRO modeling capability has been developed as part of the
ENPORT-S computer program. Implementation requires the specification
of the unit MICRO model (i.e., that portion of the transmission element
that is repeated) and a number indicating the number of repetitions or
lumps of the MICRO model to be cascaded. Detailed discussion of MICRO
replacement is found in Chapter 3.

With the use of macro elements the system designer gains insight
at two levels. First, when the bond graph containing macro elements
is processed, the resulting reduction of the complexity of the component
models is highly desirable. Also, at the macro modeling level the user
gains valuable understanding about the causal implications supplied by
the macro's environment. This information will aid the user in formulating

the best arrangement of the basic components to accomplish the macro's

*A power transmission element such as a drive shaft, hydraulic line, or
electric conductor which carries power from one place to another.

purpose. The suitability of a particular macro element can only be
judged finally in the basis of its effect on the entire system. Secondly,
for the component designer, who is interested in modeling the subtle
effects in the design of a single device, the REPLACE operation will

allow her/him macro redefinitions without altering the basic system
structure. This crucial step requires skill and insight on the part of
the designer since all models of components, however complex, will

always yield only an approximateion to the performance of the physical

device.

1.3 Literature Review

For these readers not familiar with bond graphs and bond graph
computer analysis, informative references are "System Dynamics" by
Karnopp and Rosenberg [1], and "Introduction to Bond Graph and Their
Applications" by Thoma [4]. For computer analysis "A User's Guide to
ENPORT-4" by R.C. Rosenberg [3], and "Simulation of Engineering Systems
Containing Lumped Components and Transmission Elements" by R.C. Rosenberg
and J.E. Devlin [5] are informative. A convenient survey of bond
graph publications is "Bond Graph Bibliography for 1961-1976" by
Gebben [2].

It should be noted that there are a number of related engineering
simulation programs in the literature, including “SCEPTRE” by Bowers
and Sedore [6], "Digital Computer Simulation of Complex Hydraulic
Systems" by Smith [7], "IMP (Integrated Mechanisms Programs)" by Sheth
and Wiker [8], and the MADUSA program, which is based on bond graph
theory [9]. The need for inexpensive interactive simulation of nonlinear

bond graphs is satisfied by THTSIM, developed by Kraan and Keerman at

Twente University of Technology and adapted to bond graphs by
Van Dixhoorn [10]. Some offer a macro capability and some accept bond

graphs, but ENPORT-S is the only existing program that does both.

Chapter 2
The MACRO Approach

2.1 Introduction

The purpose of this chapter is to demonstrate, by way of example,
the use of macro elements in the ENPORT-S computer program. In an
effort to exemplify the highlights of the existing program as well as
illustrate areas of possible future development two examples have been
selected. The development of each macro element will be discussed

first for both examples, followed by a discussion of their implementation.

2.2 Motor-Pump_Example

First consider the electric motor in tandem with a hydraulic pump
shown in Figure 1. As shown in Figure 2(a), the electric motor has two
electrical ports (field and armature) and a mechanical port (shaft). A
macro bond graph model is given hiFigure 2(b), from which the following

relations are taken

m=fifiWJrfl Lana
va . ¢]2(vf,1a,r) 2.2.1(b)
”sonwpun) LLHQ

The pump draws fluid from a reservoir, moves it through the pump, and
forces it down a long flexible line. Macro PUMP has three ports shown
in Figure 3(a); namely, two hydraulic ports (fluid-in and fluid-out)

and one mechanical port (shaft). The following is one possible set of

input-output relations taken from the macro bond graph model shown in

Figure 3(b).

t = ¢21(P1,P2,w) 2.2.2(a)
02 = °22(P1’P2’“) 2.2.2(b)
Q] 3 ¢23<P19P29w1 2.2.2(C)

The macro element FLDLIN, which will be used to model the long
flexible fluid line, has two hydraulic ports as illustrated in Figures 4(a)
and 4(b). Once again one possible set of input-output relations for

macro FLDLIN is

P3 = ¢(QZ,Q3) 2.2.3(a)

P2 8 o(Qz,Q3) 2.2.3(b)

These macro models may be bonded together at appropriate ports to
form the core of our desired system model. Notice in Figure 5 that
the electrical motor has been bonded to the hydraulic pump at their
common port, shaft. Also, the hydraulic power leaving the pump is
applied to the fluid line (FLDLIN) at its appropriate port. A 1-port
R elements (Rr) has been used to model the resistance the pump realizes
when pumping from a reservoir. The other dissipative effect shown is
the resistance felt when pumping through a filter (Rf). The two sources
of effort physically model the same thing, that being the pressure of the
atmosphere.

Observe that each power port has been factored into a pair of
product variables, a flow and an effort (e.g., voltage-current, torque-
angular velocity, pressure-flow rate). And that, so far, we have dis-
cussed three types of energy exchange; electrical, rotary-mechanical and
hydraulic, all represented compatibly. This compatibility of several
energy domains - mechanical, electrical, thermal, hydraulic and other
energy flows, as well as signal flows - is a very powerful feature of the
bond graph approach. Signal flows, or activated bonds, have one-way
influences, which is to say, they have no power flow associated with them.
An example of an activated bond occurs in modeling the field of an electric
motor, discussed later.

The next step in this example is formulating replacement models for
the macro elements in terms of standard bond graph elements. First con-
sider the electric motor. A motor model has been developed, and will
serve as a starting place here [11]. As seen in Figure 6 a modulated
gyrator has been used to show the conversion of electrical armature-port
power into rotary-mechanical power. This conversion process is modulated
by a field signal, in particular the field current. Notice the full
arrow on the field bond, indicating an activated bond. There are three
principal dissipation effects; these are the armature resistance (Ra)’
the field resistance (Rf), and the resistance due to mechanical rota-
tion (Rm). The intertial motor dynamics are important because of start-
up transient behavior. These additional energy effects are the armature
and field inductances (Ia and If, respectively) and the mass of the motor
and other revolving parts (1m). Notice the ideal conversion is still at
the core of the model, but the external ports now interface through re-.
sistive losses and dynamic energy effects. We now have a model which can

be used to predict the conversion, loss, and dynamic behavior of the macro

device. Figure 7 illustrates a special case that can be derived easily
from this model. If a constant armature current is applied the core of
the model will behave like a linear gyrator (GY). In this case, the
mechanical output is controllable by the field-port directly, and a
control-type motor results. An activated gyrator model is a good
description of the basic motor conversion effect. Notice that a voltage
source (Se) has been bonded at the field port to drive the field. Note
that the electric motor acts as a speed source.

Next consider the replacement model for macro PUMP. Recall that
macro PUMP is a three port; shaft power in, fluid power in, and fluid
power out. The replacement bond graph is shown in Figure 8.

The dynamic and dissipation effects are not included in this model.
Because it would be rigidly attached to the rotating mass of the electric
motor, the rotary inertia associated with element I7 in Figure 7 may
be taken to include the rotating mass of the pump and the resistive
effect R8 may likewise be taken to include that effect of the pump.

This is a simple model for a positive displacement type pump.

Notice that the causal condition imposed by the electric motor is carried
through the model. With this information the specific nature of
equations 2.2.2(a), (b) and (c) is determined; that is

11 - A-(Pa-PZ) 2.2.4(a)
Qz‘ifi LLMM
Q3s%% Laud

When formulating a general macro replacement for FLDLIN we need to

consider the internal resistance to flow (l-port R) and the flexibility

of the line walls as well as possible compressibility of the fluid
itself (modeled as a l-port C). If the pressure varies rapidly or if
great accuracy in prediction of dynamics is required it is necessary
to include fluid inertia in the line (1-port I). The resulting bond
graph replacement model is shown in Figure 9.

Concluding remarks concerning the assemblage of the entire system

of macro elements is offered in Section 2.4.

2.3 Auto Drive Train Example

A second example well suited to illustrate the modeling and simula-
tion technique is an automobile drive train [12]. A macro bond graph of a
drive train system is given in Figure 10.

Before proceeding to a more detailed description of the example it
is important to emphasize here that we are considering the drive line as
an example of usage of the REPLACE function. In this paper we will
therefore be interested in rather simple models of the macro elements.
Yet when they are assembled into a system model, they are sufficiently
accurate representations of the macro element to allow prediction of
the effects of changes in the component parameters on the overall drive
line dynamics. Thus the macro models used herein will not be as detailed

as the engineering state of the art will allow.

The input and output from GRAPH is illustrated in Figure 11 and
confirms our intentions regarding the power assignments in Figure 10.
It also determines our macro numbering scheme (i.e., ENGINE is macro l,
LWHEL is macro 6; see Appendix A). 1

Detailed output equations for the macro elements are not obtainable

until each has been defined in terms of the standard set of bond graph

10

elements. However, the following is one possible set of general relations

for each macro in the drive train.

ENGINE m1 = @11(11) 2.3.1
CLUTCH T1 = ¢21(w19w2) 2.3.2(a)
12 = O22(m],m2) 2.3.2(b)
TRANS ”2 3 431(rz,t3) 2.3.3(a)'
m3 = @32(12,T3) 2.3-3(b)
SHAFT T3 3 O41(w3,m4) 2.3.4(a)
T4 8 042(w3gw4) 2.304(b)
DIFF Q4 8 051(T4gm59w6) 2.3-5(a)
T5 ' Q52(T4,m5.w6) 2.3-5(b)
16 8 053(14,w5,w6) 2.3.5(c)
RWHEL m5 8 ¢61(T59U7) 2.306(a)
T7 8 ¢62(TSQM7) 2.306(b)
VEHCLE N7 3 °71(T7’T8) 2.3.7(&)

”8 . 072(17918) 2.307(b)

11

The next step is to develop models for macro replacement. A
minimum dynamic model for the engine results by coupling the l-port I
element which represents the equivalent moment of inertia for the fly-
wheel and other reciprocating parts with a source of torque (l-port Se)
representing the driving effort of the engine. A 3-port l junction
represents simultaneously the information that a comnon speed of rotation
exists for the three bonds and that the sum of the three torques is
zero (i.e., that the net of the engines torque less that which is
applied to the rotary inertia is applied down stream to the clutch).

The bond graph replacement for macro 1 is given in Figure 12.

The next macro element is the drive line in the clutch (macro 2,
CLUTCH). The three port 0 junction in Figure 13 indicates that a single
torque is present on all three bonds and that the proper sum of m1, m2,
and m23 is zero. The l-port resistance is a nonlinear element with a
relationship between the common transmitted torque r and the clutch
slip speed “23’ with a modulating variable which may be taken to
represent the Position of the clutch linkage. For illustrative simpli-
city the resistance will be modeled as non-modulated. The clutch plate
has mass; however, one of the plates is coupled to the engine flywheel
and therefore may be taken to be included in the engine equivalent mass.
The other half of the clutch plate is stiffly coupled to the transmission
and therefore may be lumped with the mass of the gears. Now that the
macro CLUTCH has been defined in terms of the standard bond graph elements,

Equations 2.3.2(a) and 2.3.2(b) can be rewritten as:

T1 ’ T2 ‘ ”“23

where b is a constant for a linear resistance.

12

Next we consider the transmission (macro 3, TRANS). Typically, the
transmission is thought of as a torque/angular velocity manipulator,
with small power losses. The macro replacement bond graph is shown in
Figure 14. Notice that the transformer, which is the heart of the trans-
mission effect, has a finite number of gear ratios which may be selected.
In some situations geat tooth compliance, backlash, and power losses
must be included in order to make precise predictions of the dynamics of
the transmission. However, in this case only the relatively simple
model shown in Figure 14 will be used. Note that the rotary inertia
has been lumped in a l-port I element.

We are now faced with formulating the replacement macro definition
for SHAFT. Because we already have the replacement models for ENGINE,
CLUTCH, and TRANS, we have in effect determined the input causality
to SHAFT. Observe in Figure 15 the causal input to SHAFT is angular
velocity. To insure integral causality (See [1]), the group of possible
causal models for SHAFT replacement has been reduced. TWo possible
replacement models are shown in Figure 16. Where the I element repre-
sents the rotational inertia (J) and the C element represents the
equivalent stiffness effect, observe in Figure 16(a) the shaft is modeled
as a spring transmitting power to a lumped mass, yielding the replacement
model in Figure 16(b). The output causality in this model is a flow
(i.e., a angular velocity). Alternatively (See Figure 16(c)) the shaft
may be modeled as having two springs, each on either side of a lumped
mass. Each spring represents half of the shaft‘s stiffness effect. The
so-called pi network [1, p. 87] is a parallel-series-parallel circuit
which will impose an effort causality on the differential. Our choice
between these two models will depend on the preferred input causality to

the differential. We therefore need to model those macros downstream of SHAFT.

13

The last macro in the drive train bond graph is VEHCLE. This
component will include the mass of the vehicle, the resistance to motion
which acts on the vehicle and load disturbances. Since the dynamics
of a vehicle can be complicated when three dimensional motions are
considered, we will use the minimum dynamic model illustrated in Figure 17,
which is one dimensional. A 5-port l-junction, indicating that a
common speed exists for all 5 bonds, is used to sum the forces involved
in the air and rolling resistance, the mass of the vehicle and the
forces due to the road gradients (a net force dependent of the displacement,
x, and thus representable as a nonlinear spring). The preferred causality
is also indicated in Figure 17.

The next macro elements to consider are the wheels, represented
in Figure 10 as RWHEL and LWHEL. If all the deformations a pneumatic
tire and wheel experiences could be considered, the complexity of the
model would cloud the purpose of this example. The transformation from
rotary mechanical motion to translational velocity is simply modeled
as a transformer whose constant modulus is determined by the dimension
of the wheel and tire. The force-slip characteristic is contained in a
non-linear resistance element (R). The rotational inertia is modeled as
a I element. Notice in Figure 18 the causality imposed by the VEHCLE
model is carried through the wheel models.

Macro DIFF is used to model the differential of the drive train.

Its function is to transmit the torque from the drive shaft to the wheels.
The macro DIFF replacement model is shown in Figure 19. With this model

at hand Equations 2.3.5(a), (b) and (c) can be rewritten as follows:

14

This completes the macro definitions downstream of macro SHAFT.
Notice in Figure 20 that when the rules of causality are applied to those
models, the resulting preferred causal input to the differential is a
torque, thereby requiring the replacement model for SHAFT illustrated
in Figure 16(d), to insure integral causality.

2.4 Simulation using ENPORT-S

The actual simulation of bond graph models is carried out by using the
ENPORT-S computer program. This is a successor to ENPORT-4 [3], which
simulated linear multiport systems specified by standard bond graph elements.

The input format for the GRAPH function is identical to that described
in "A User's Guide to ENPORT-4“ with the major extension that non-standard
elements may now be used.

The general bond graph describing the motor-pump system that is
illustrated in Figure 5 is input into the GRAPH function (see Figure 21).
The output of GRAPH is shown in Figure 22 and is an echo of Figure 5.
The macro elements are defined using the REPLACE function, as outlined
in terms of standard line code Appendix A, the input to REPLACE is
shown in Figure 23. The output of the REPLACE function is the complete
system in terms of standard bond graph elements, shown in Figure 24.
'This output is verified by the complete system bond graph shown in Figure
25, that was assembled from the original modeling effort described in
section 2.2.

The general bond graph describing the auto drive line example is

Shcnnlin Figure 10. and output of the GRAPH function as illustrated in

15

Figure 11. Notice the equality between the output of the GRAPH and

the general system bond graph (Figure 10). The REPLACE function input

is shown in Figure 26. The entire system with all macro elements defined
is illustrated in Figure 27 and is an echo of the output of the REPLACE

function shown in Figure 28.

16

Electric Pump

Motor Long Line

 

 

    
 

Controler Reservoir

Filter

Figure 1. Electric motor and pump system

 

vgrif

V

36> r f, MOTOR +7
“ a

(b)

 

 

 

 

 

 

 

 

Figure 3. (a) Hydraulic pump (b) Macro bond graph

17

P2 P3
P P
02 a. ‘63 -—Q-::7' FLDLIN—‘63“?
3
(a) (b)
Figure 4. (a) fluid line (b) macro bond graph
P2
FLDLIN ——zl——78£
/ O2 L
t Rf
MOTOR —-w-v-PUMP
P
\—l—l‘——SE
(1l 1
Rr
Figure 5. motor pump system

Figure 6.

——71 /If

i

,1 ———7- MGY ——-71——-7

 

:2\ 12:”

m Rm

model for electric motor

Figure 7. Replacement model for macro MOTOR

P2

f--§—121FF-—-7-l

(T) T
P1

Figure 8. Replacement model for macro PUMP
P P
2 1 5 3 2
-3 I: 6
I R C

Figure 9. Replacement model for macro FLDLIN

19

mguzm>

x
/

Aux:

4/
x

mzzm

:_ugu o>psu m.u.em> sow cameo econ we. wanna;

“Earn: Ea Isl. mzaTlal as: J1 use.“

20

07/31/78 "’ M S U E N P B R T V E R 500 "'0100510 8.
*GRAPH
*ENGINE I : CLUTCH I 2 3 TRANS 2 3 a SHAFT 3 4 o

*DIFF 4 5 6 , LNHEL 6 8 D RWHEL S 7 1 VEHCLE 7 8 o
*GREND

NUMBER OF ELEMENTS IS 8
NUMBER OF BONDS IS 8
NUMBER OF MACRG ELEMENTS IS 8

THE BOND GRAPH STRUCTURE IS

ENGINE l
CLUTCH l
TRANS 2
SHAFT 3
DIFF 4
LWHEL 6
RWHEL S
VERCLE 7

m-JOMJI>UID—e
QQQMDUN
0

Figure 11. input/output of the GRAPH function
I

T

s2 ——:111——::—7
Figure 12. replacement model for macro ENGINE

U-€>—-R

“’23
H70 —-a7|

Figure 13. replacement model for macro CLUTCH

21

I
3

1 ’iliT’TFi—W

9:91:92993!94

 

Figure 14. replacement model for macro TRANS

I R 1
T l T
Sefilkfiofiul—wm-psmnwmn

Figure 15. forward causal environment of macro SHAFT

k J ' 1-3—r0—lll—iv
W fr: ‘5 :-

(a) tr)

[(6,213 xzél—ifan—zo —»1

C
(C) (d)

Figure 16. (a) replacement model for macro SHAFT option 1
(b) bond graph for macro SHAFT option 1
(c) replacement model for macro SHAFT option 2

(d) bond graph for macro SHAFT option 2 (Pi network)

22

>1/\711

Figure 17. replacement model for macro VEHCLE

 

C

I R

3 6
fill—I’TFi—EVOT'A

Figure 18. replacement model for macros RWHEL and LWHEL

, ms
-“’3—-»11F ——»10
(T)

m6

Figure 19. replacement model for macro DIFF

23

lF—vlFl—vO/R
_,.._,.1 >2;
12.11... I

Figure 20. aft causal environment of macro SHAFT

24

07/31/78 -" M S U E N P O R T V E R 500 "'oIIoISoI7o
*GRAPH
*MOTOR I O l 3 7 8 O R 8 O SE 7 O PUMP l 2 3 O
mFLDLIN 2 4 O 1 4 S 6 O SE 5 O R 6 O
*GREND

Figure 21. Input to GRAPH function, motor pump example

NUMBER OF ELEMENTS IS 9
NUMBER OF BONDS IS 8
NUMBER OF MACRO ELEMENTS IS 3

THE BOND GRAPH STRUCTURE IS

I I 3 7 8
2 R 8

3 SE 7

4 I 4 S 6
5 SE 5

6 R 6

7 MOTOR l

8 PUMP I 2 3
9 FLDLIN 2 4

Figure 22. Output of GRAPH function, motor pump example

*REPLACE

OMOTOR I /
*MACRQ’I/SE29123450139R4O

* 6Y5691.16780179R8’

*PUMPIZS/

*MACRO I 2 I I 2 3 4 O T? I 4 /

*FLDLIN 2 4 I
“ACRO/a/II345OI3OR490256OC6/
*MCEND ,

Figure 23. Input to REPLACE function, motor mpmp example

25

NUMBER OF ELEMENTS IS 21
NUMBER OF BONDS IS 20

THE BOND GRAPH STRUCTURE IS

1 1 3 7 3

2 R a

3 s: 7

4 1 4 s a

5 se 5

s R 6

7 st 9

~a 1 9 1O 11 12
9 1 1o

10 R 11

11 or 12 13

12 1 1 13 14 1s
13 I 14

14 R 15

1s 1 2 3 15

16 TF 1 16

17 1 ‘ 2 17 18 19
13 r 17

19. R 18
20 o 4 19 2o
21 c 20

Figure 24. Output of REPLACE function, motor pump example.

 

Figure 25. Complete motor pump system.

26

REPLACE

*ENGINEI/
#MACRO/l/II23OSE2OI3/
IUICLU‘I‘OI'IIQI

OMACRO / 2 / O I 2 3 O R 3 /
*TRANSZB/
MACRO/3/II34OI3OTF42/
*SHAF'T34/
MACRO/4/0135OCSOI346O
IDIFF456/

“MRO / 5 / TF I 4 O 0 2 3 4 /
*LHHEL 6 8 I

HACRO / 6 / I I 3 5 O I 3 O TF 5 6 O
*RUHEL 5 7 /

*HACRO / 7 / I I 3 5 O I 3 O TF 5 6 O

OVEHCLETBI
”IACRG/S/II2345OR3OI4O
MCEND

I600247

0624OR4/

0624OR4/

CSI

Figure 26. Input to REPLACE function, auto drive train example

I. R I

1 1: 1m in in I

SE-aleT’O-T’ill'fi’TF 1—370 fill—WU ‘71

I . R
’\2u 25

PfeTFF—vo/

.1.” .1315 \Z? c
J: 8 \1

22 23
20 °
R

Figure 27. Complete auto drive train system.

OCT/

27

NUMBER OF ELEMENTS IS 30
NUMBER OF BONDS IS 30

THE BOND GRAPH STRUCTURE IS

I I I 9 IO
2 SE 9
3 I 10
4 O I 2 II
5 R 11
6 I 2 12 I3
7 I 12
8 TE 13 3
9 O 3 I4. 16
IO C 16
II I 14 15 I7-
12 I 17
I3 0 4 IS 18
14 C 18
IS TF 4 19
16 O S 6 19
17 I 6 2O 22
18 I 20
19 TE 22 23
2O 0 23 8 21
21 R 21
22 I 5 24 26
23 I 24
24 TE 26 27
2S 0 27 7 25
26 R ‘ 25
27 I 7 8 28 29 3O
28 R 28 '
29 I 29
30 C 30

Figure 28. Output of REPLACE function, auto drive train example.

Chapter 3

Micro Replacement

3.1 Introduction

A particular problem of interest arises when there are some trans-
mission elements to be considered in a system model. Models of such
components typically have a high degree of repetitiveness involved in
them. For elementary models the MACRO approach would suffice; however,
when there are more than two or three repetitions of the same subsystem
the need for an automated approach is evident.

When using the MICRO option in the REPLACE subroutine the user needs
to specify the unit MICRO (i.e., that portion of the model that is
repeated) model and a number of indicating the number of repetitions of
the micro in cascade. (See Appendix A) The micro model must be a two
port (i.e., it must have exactly two interfaces with the rest of the
system), and the MACRO elements that results from cascading a number of
MICRO elements is also a two port. The number of repetitions needed
(L) is a function of the modeling accuracy required and the computational
resources available. With this option the user has the ability to build
a very large system quite easily; this requires that large system
models be stored. A change in the data storage scheme from that of
ENPORT-4 to a list packed format incorporated in ENPORT-S provides the

necessary support.

3.2 SHAFT Example and Implementation in ENPORT-S
An example to illustrate the MICRO operation is the macro shaft in
the auto-drive line example. The original two-port shaft can be divided

28

29

into as many lumps as seems appropriate. As a unit MICRO model, the
MACRO replacement model shown in Figure 15(d) will be used. The physical
significance of the model has not changed. However, when assigning
parameter values care should be used to assign only that amount re-
presented by each lump (i.e., if the shaft is homogeneous with constant
cross-sectional area, JL = JtotaI/L) by judicious use of parameter
assignments for each lump, such devices as stepped and tapered shafts can
be handled in a highly automated way.

By cascading a set of L lumps, shown in Figure 29 symbolically, the
shaft model can be constructed and is inserted in the system bond graph.
For purposes Of simplification the front end of the drive line will be
modeled as a speed source and the aft end as a resistance as shown in
Figure 30.

The implementation of the MICRO option is discussed thoroughly in

Appendix A. The system for this example is input into the GRAPH
function as shown in Figure 31(a). The GRAPH routine output is shown in
Figure 31(b) and is easily verified to be an exact echo of Figure 30.
'SHAFT 1 2' is defined by the MICRO function, in which the unit element
is given in Figure 29. Four such lumps are called for in the MACRO as
illustrated by the input to the REPLACE function shown in Figure 32.
The entire system is defined in terms of the standard set of bond graph
elements by the output of REPLACE (Figure 33). The reader may wish to
verify that the bond graph shown in Figure 34 is that expected from the
original modeling effort.

L

4

C I C

.1

 

 

 

Figure 29. Micro shaft
s:=l—+smm-—2-;]R

Figure 30. Abridged auto drive train system.

07/31/78 "' H S U E N P O R T V E R 500 ---.10.46.30.
*GRAPH
‘SFIOSHAFTI2OR2O
*GREND '

--

(a)

NUMBER OF ELEMENTS IS 3
NUMBER OF BONDS IS 2
NUMBER OF MACRO ELEMENTS IS I

THE BOND GRAPH STRUCTURE IS

I SF 1
2 R 2
3 SHAFT 1 2

(b)
Figure 31. (a) Input (b) Output of GRAPH function, micro example

.—.. > i

*REPLACE
*SHAFT I 2 I
*HICRO / I / Ls
* I 5 O O 2 6 7
*MCEND

-_ _-_.
- ——.

4 / O
O C 7

Figure 32. Input to the REPLACE function, micro example

J I

NUMBER OF ELEMENTS IS 26
NUMBER OF BONDS IS 25

THE BOND GRAPH STRUCTURE IS

1 SF 1

2 R . 2

3 o 1 3 4
4 c 3

s 1 4 s 6
6 1 5

7 O 3 6 7
3 c 7

9 o 3 9 1o
10 c 9

11 1 1o 11 12
12 I 11

13 o 14 12 13
14 c 13

15 O 14 15 16
16 c 15

17 1 16 17 13
13 1 17

19 o 20 13, 19
20 c 19
21 o 20 21 22
22 c 21
23 1 22 23 24
24 1 23
25 o 2 24 2s
26 c 25

Figure 33. Output of REPLACE function, micro example.

c: L)
Q

1‘
F4 —' ~—
$110
:3 c)

32

Figure 34. Complete SHAFT system

Chapter 4

Conclusions and Recommendations

4.1 Conclusions

The MACRO and MICRO feature described in this work is part of the
ENPORT-S computer program supporting the engineer in the direct simulation
of systems containing both lumped-parameter and power transmission com-
ponents. The designer concentrates on choosing a suitable type of macro
(or micro) element, insight for which choice can be obtained from causal
considerations at the system level, and on selecting an appropriate
assemblage of standard bond graph elements to Obtain satisfactory
accuracy at a reasonable cost. When using the micro option to model
transmission components the user can, by judicious use of parameter

assignments, model such devices as tapered and notched shafts.

4.2 Recommendations
This project is an open ended one, and the possibilities for future

development are extensive. The following is a list of possible directions.

(1) Parameter specification. Consider the usefulness of having the
parameters of a cascaded element assigned automatically by an equation
defined by the user. As an example recall the micro SHAFT. If the
stiffness (k1) associated with each lump were assigned by the relation

k 3 110-101, 1 8 1,10,

1

the result would be characteristic of a tapered shaft. Or

33

34

could be used in modeling a stepped shaft.

(2) Library. A computer library of typical macro-micro models could be
developed for use with the ENPORT-S simulation program. This would
enable the user to call the library for macro-micro replacement. Where

applicable, three models could be catalogued - ideal, static and dynamic.

(§)__§xtensions to the MICRO option. At the present stage of development
the MICRO feature is restricted to cascading two port lumps. The value
of extending this feature to more than two port expansion is Obvious.
Consider a two dimensional plate being stressed as shown in Figure 35(a).
A typical lump, involving internal resistance to deformation and capacitance
is shown in Figure 35(b).

The plate can be represented by an m-by-n array shown symbolically
in Figure 35(c). The plate model can be assembled from a two dimensional
cascading of lumps and the imposition of the appropriate boundary conditions
at the edge ports.

35

 

 

 

Y
«)1/ 1'1/ ./ g/ Olor/ /' 1 I 1’
1 (3 C2 _fig;__ C)
‘3...
F x <—-
go) ' (’9) Pg)
:1, C) C] 4‘1-' X

 

 

 

 

 

 

 

SE "'l”" """“" O'---7- -E317' SE

 

 

4 0:0
SF

Figure 35. Illustration of geometric reticulation for a plate

 

10.

11.

12.

REFERENCES

Karnopp. D.C., and Rosenberg, R.C., System Dynamics, Wiley, New
York, 1975.

Gebben, V.D., "Bond Graph Bibliography for 1961-1976“, Journal of
Dynamic Systems Measurement,_and Control, Trans. ASME, Vol. 99,
No. 2, June 7 . pp. 143-145.

Rosenberg, R.C., A User's Guide to ENPORT-4, Wiley, New York, 1974.

Thoma, J.V., Introduction to Bond Graphs and Their Applications,
Pergamon Press, 1975.

Rosenberg, R.C. and Devlin, J.E., "Simulation of Engineering Systems
Containing Lumped Components and Transmission Elements", Fifth World
Conference on Machines and Mechanisms, Canada, July 1979.

Bowers, J.C. and Sedore, S.R., SCEPTRE: A Computer Program for Circuit
and System Analysis, Prentice-Hall, 1971.

Smith, C.K., "Digital Computer Simulation of Complex Hydraulic Systems
Using Multiport Component Models', Department of Mechanical Engineering,
Oklahoma State University, Ph.D. thesis, 1975.

Sheth, P.N., Vicker, Jr. J.J., "IMP (Integrated Mechanisms Program),
A Computer-Aided Design Analysis System for Mechanisms and Linkage",
Journal of Engineering for Industry, Trans. ASME, June 1971.

Dix, R.C., “MADUSA. Mechanism—Dynamics-Universal System Analyzer".
Van Dixhoorn, J.J., "Simulation of Bond Graphs on Minicomputers",
Journal of Dynamic Systems, Measurement, and Control, Trans. ASME,

rc 9
Rosenberg, R.C., "The Bond Graph as a Unified Data Base for Engineering
System Design“, Journal of Engineering for Industry, Trans. ASME,
Vol. 97, No. 4, 5. DP. 3 3- 3 .

Karnopp. D., Rosenberg, R.C., "Application of Bond Graph Techniques
to the Study of Vehicle Drive Line Dynamics", Journal of Basic En-
gineering, Trans. ASME, June 1970, pp. 355-362.

 

36

For micro replacement the second card (or line) starts with MICRO
followed by the macro/micro index number in the same format as the macro
replacement code. Following the index number and contained within
slashes is that number j which indicates the number of repetitions of
the micro in cascade. This number must be preceded by a space and "L=".
The remainder of this card is standard line code numbered in the same

manner as in the macro replacement, followed by a slash.
Example of Usage -

REPLACE
CLUTCH 11 12 /
MACRO / 1 / 0 1 2 3, R 3
BKBOX 12 4 8 /
MACRO/2/11234,I4/
SHAFT 7 8 /
MICRO / 3 / L = 2 / 0 1 2 3, C 3 /
MCEND

This code will produce the fOllowing replacements:

—-——.—-” CL111c11-——-7‘2 —-7‘ o———=-2 ‘

where bond 1 corresponds to 11, 2 to 12.

—‘i-7 BKBOX ——4—7

\1/2/
x \3

8

where bond 1 corresponds to 12, 2 to 4 and 3 to 8.

7 3 ""l"7"[)"7£‘7"0 "il‘j7"
"""17’ SIUM:T '—--:7' 51’ 5
C C

where bond 1 corresponds to bond 7 and 2 to 8.

We will use a two index reference for macro bonds as follows:
(i,i) refers to macro k, bond i. A three index reference is used for
micro bonds. (k, j, i) refers to micro k, lump j, and bond 1.

In the examples above I(2,4) refers to the I-element in the BKBOX
macro. E(l,3) refers to the effort on the resistance in the CLUTCH.
And C(3,2,3) refers to the C-element on the second lump of SHAFT.

Note: REPLACE must start in column 1.

All other data may start in any column.

I

APPENDIX A
A User's Guide to REPLACE

REPLACE is used to define macro and micro elements in terms of the
standard elements. The order of replacement must be the same as the
macros-micros were input into GRAPH. Macro/micro element replacement
must end with MCEND. Each macro-micro replacement uses at least two cards

(or lines); note that spaces are used as separators.

name b1 b2 ... bp /
MACRO / k / standard line code /
or

MICRO / k / L = j / standard line code/

The first card lists the macro (micro) name, followed by the port
bonds (1 through P in the same order as was input into GRAPH) and ter-
minates with a slash. This card is used regardless of which operation is
being used. At least one space must separate each specific data item.

For macro replacement the second card starts with MACRO followed
by a slash and the macro/micro index number (k). Macro/micro numbering
is sequential starting with one. Following the macro index number, and
contained within slashes, is the replacement standard line code. Bonds
must be numbered consecutively starting with one. Bond 1 in the
replacement code corresponds to macro port b1, bond 2 with b2, and so on
through the pin-port bond. The internal bonds of the macro element are
then numbered (p+1) through n, where n is the total number of bonds in

h

the kt macro element.

APPENDIX B
Glossary of REPLACE

The following is a list of important variables found in subroutine

REPLACE.

ICKLST
IMCNAM

MBIMX

MCBDCT
MCOPTS

MNI
' MPTRA(k)

MPTRB(k)

array containing NPTR information on nonstandard elements
array containing nonstandard elements names

nonstandard elements counter

number of nonstandard element open ports

number of bonds in standard system code

array containing NBIMX bond numbering conversion in-

formation in the’fOrm; MBIMX

 

 

l—I

number of bond ends in present macro element

array containing absolute bond numbers for present
micro element

number of nodes for present macro element

array points to first entry of the kth macro element
in the NBIMX array

h

array points to first entry of the kt macro element in

the MBIMX array

MTYP

NBDLK

NBIMX

NI

NCMCR

equals 1 for MACRO replacement equals 2 for micro

replacement

number of bond ends in total system
Node-bond incidence array

Counter of standard elements as they are
macro elements

Counter of macro elements

used to replace

APPENDIX C

Li stings of Programs

“‘5

33626 czczl _:u:uou I a: poo 11.“ c6
anausz
rpnhxmz
("—2
“nae:
an.m.~.szm~ 6o rm
:u.~.~.x::~
ova—.xouz
.+ono
cmzz.fin_ me on
c“? Q Ca
zOHLqR~3«_»_2_ 111w
\>o:a.u~:~. ~:~.=:H. umza.amzm.a:_. 2:4. o:_\.o .u _.._.i>»z. «has a m
m
.am.>c_: aohmzozuc
.m.op.m2 onmzmzac
.o.a>pz zcfimzm:_o o
.o...zpaz. aczz....co.x:m_+ cm
..c=~.>z_mz..om.z<znna..em .pmnnu_.omnz.aoaz.cmz.noz\mxm\ reasoo
m moon: -1 ucco xo<mo ozcm a<uz w
om_.»m_.bxuz.z~oaaz._n +
.Sooz.>ux.¢:on<u.4<um.pz~..us.nac<n..mscquS o<m¢zxmxc\ ratsou m.
m guano 1. 22oz_ ouzusp<xzca 6
.cmcoauz..gmcpmnza_.u¢¢m_.anzz.czzz.cnz:.4uzz.~:o.z_ \.xaa zozzou
_ econx :1 2ozzao “mooxza 3<omzmu c
c
mmocz 344 do mango asahanua w>xnmmzo 44_: hmam 6 cg
mew—4 supm>m do zo_pom c
op mpzuzunu CH ma>p exam cp m~ arses: exam a: amcoaao ...c
ozoa >3_m<u ma mou~o2<z¢o new; a» ze_pao~m_acz . o
deco nape» 2:» azu ems: azumo . o
220 pm<4 4822 .<zzou < :paa 922 Fan: aaoxc czam upzuzmnu Io<u O. c o
nmxu madam .. o
.xz_m2 .pm44u_ 34—:m oz< mooo :aamo azom aqua a» m_ amaazzo ...w
omega: u2_»=cxa:m n .

.uma<u¢ 66.666236“ to 66.6633 ._ o_nap

:5" c» cc .c.uz..P.hz_.xza_.d_ we

 

uzc zzanou z— anzgpzzouzm hzmzunm pmzad p23 1 xsr~ u~<uzo 111%
. u
aommznmmz
~2—n.mm2.x:~mz an" cm
9
.1 9.3 op cc
mafinummwfilll --1 -.
m: op oc .: .L2.>ux.u— mm“
ace oh cc m2
«Anndazu—
«NH o» co ..cmzz.nn. p2—..:z< c.po.»z~..u~
=c~ c» cc ..zn. u. “:4uzqa.u_
Juan 44<u
uzznpzou mm“ 2 ch
cacao czo: machm :24 hue 111E
u
nuzzn.~z z«zrnn. .
d>pun ._z.pm44u— omau we
M242 az< ua>b pzm:.aan uxcpm 111w
~+muzznmuzz
sana>p~ co
mar—pzcc ad"
an" o» co ..m>p_.a>hz. cu.auzz. an
an a>e~ c- o:
ara4<_n4uzz he“
ace c» cc mu
ofipumxmu~
pea op co .nuzz.u4._z~ UH Goa
. cc: Op cw
«danummuu
mod a» co .o.u4.4cuz. an :3
can 0» ca .::uzm.m.cu.<ra4<~. an
ummu Agau
mmzn.—z.¢_az u
cacao 2— 32¢: Ame—m dc zo~h¢oon mt» mupz~oa z~ weepm 111w a:
~+_zu—z cc"

.A.6.o=oov _ o_nap

.mpwzhczuuz
AH—vzgraum1ap;.u~
A-.hm44um:ah44u—
zomhdzxcuz— zu~m>m c~ ua>h u>mzpux cuhducq uuzo . .

"1 xux
cNm Ch cc and. uZoammvpm 44.u~. mm

whzmzudm 19 mark ;h<uca

~1H+4uzn-
4L2.—1— emu 3c

LUU
If?
(\I
'—

emu

909

9 man
cmw

«mm

CH2

emu

D"
I&# "(Ck—HCFQC

nmm Op om Ana uzoazvp.
.mz.

~+muz21._u

‘Z nzfiGHfiKXF¢HKF
3:: xan-ZXC.Z::U

«on ch ow “anew-muzzv uh can
«U1214u2u0hw2 U

mhmug tu~m>m Lo ZChPCQ ah wpzmzusu cm uu>h hmcw 111%

N
IN

~32~3mc H

XPIXth 22

2

C
LG
:2

LI"

9

CO

H: a
mavmcuc a
~¢LHCM¢

m

cm. a» co .c..z..m o¢.

I—C‘Ji-fl-Nv-H:
Z—vz—H¢ H‘
w x—

...u.u=cu. _ m_auh

Table I (cont'd.).

?25

IRCNFL*1)) GO TO

130

C'. U

A

UP LISTS. SINCE TYPE 10 REHOVED

X'D
(v

Htx

I35:

..Jn-a
ALHZQ‘.
man-‘2
1—122"
wofin
CZZNH
r-v-I'DJv-LLJ
a: ~¢=
Zfioai—Z
H "fit-.11— u;
pazxc-n-In— V2
IIH< 131-2 0
#5220240 ..I
.4355 U U

C
n
WOUL—
II: c
I“. «3'
'1- w

an
o-u—
4‘ #1
rut-1
nil—O
r-tH
V“
F:
(1)4

H-l-J
XLUU
01-11—11
I-nll H
Han
IIHH
HMO-1
Hun-4

#11ka

"1.014?
I~1'.12~
mad.“-
I. 1.1.3“?
nor-mo

XE:

145

24"

150

 

NPIMY!J)ZNPIMY(L)

L")

J41
CONTINUE

J:

945

160

TR(L+1)-NHEL
HPTR-NBEL

RCK)

MINQLHLX

' :MPIR
MPTPCNEL+1)=NPTR(NFL+])-NBEL

NPTR
MPT

165

TO BOTTOM OF SYSIFM LISIS

INFORMATION

f
1

RELOCATE TYPE 10 SYSTE‘

LULQ

(D.CL
Ph-
...]?
4..)
wk;
1-11-4
HM
“A
XX’
VV
t—SI
m<z
A?
..l..l

H.—

170

Table I (cont'd.).

'-
0‘4
#0
<
NO.
NZ
02
A x:
1i P-
o \m
L" *0
.13 01“.!
O on:
< 9L.
11.1
a: LJI—
2‘1...
(f; 2’ HO
O N .1
1.1‘. c. 2 (‘1: O
U: \C b O (C 1 11-0-
2 1", IO CD I"? o- 7
H \ZAJZ
U C1 O O C human
2 1- V- 1...] 1- "xx:
LJ Q c 0:: o
: ‘3 C 2 C C HU—J
:- L5 L9 1..) (.2 c. 5!.“ J
U I I.“ {-5.3de
U) A A L... A L'C C}
H O C _l C O 2" ILH
|>.a~ C3 0 O G o I'- 20-1130"
.J<I- Z O '- 2 O .Z'vr- .I
b.5831: 0 saw O 0-! 1.4 3 LL UZWU
{zlv C CS 0 G o 030 0 LI: mazwuz
Z'Q PA GA CA zfiHh:
+21— 0: 2H 1121-! 0:201 4'1 11.11.124.-
AAt-u-n c: o o 2 0 C32 9 C; 2 ~m~¢d©
XXLCJ 1L HH "3 L ’H 0:; C 'LLJ OU> o
w”$2 Hv u-nv Mir 2 1— C 3 C
are!" 1| L.) a: fix LC 11xmmu‘c Xllxm LP 061:: '— 013nc>m
Phtflv-‘D Lu' U Slush fizbh—tb; 00-23 C CHC‘ U caac..ro
cc. 3’+2 2 u Gxam'fiv—l :12! HQ’ hJ at? 9" Luv-c 1.1 €~¢V<J
2.32Lv—u- 2 I d‘r-ZZ lxu—u— H Icahn-«D .11 0‘} I- 11-0..“
I1 Hwa-xt— .— U antOh-u:~!-OLLO Oxvr-CIOHHLLO mquqt—Z
HZXNZHZ '— t-hl-HVO z1—x1— IO Z’Zl—lvmr- a: P.-t-2'~V
111-ch who 2 3 CmZQ C2 LG I: Z! LLC-T. 1-4 or. O Hxi-mi
~£ZCCXU O C OF‘OCAOCDCHUOUC CCHUHC-IILLJC a: moacccu.
xzzcz U 2 UZCL‘ZC 191-11.: 2:: Hwth-c a: BLLdeu-a
L
c. I o C.
c N u-o c: 11‘ cc :2 r. <2 mm I ON M111
\3 OJ C. \D \D \D F- N <1 as: 0 CC C.
(\1 Lat—39"“) IO 70 I" '0 HUI“: 7’) Kh‘) Lat-£33? d'L'
LC :5 If G If? C Ln C
P- d. x O O t L 0- 1-1
0—1 H H 1— 0-6 N N (\. Cu

 

32w
rmzpka
.wm. x .o<.>w.n~. :fi.»<smam omcm. .
.oz.:<24u~ :: :424k_.1.cmcm upnmz cum nmm
.mz.xc~zumz
Anzvxc—zunz
.m.5.xzmuumz
.~.s.xzm_u~z -
omz.~ua cum as com
“\«nzuau «qum 02c: oavhgzmom o¢cm
agam wh_m3 n_m
mam: Acapzcu pmgza muoz: xzc~ —z_ma w
..>o\¢~m~.c.xm.m<.x~.n_ xfi.pazzam mmcm mqm
msznhzou omm
.m_.._u a..a.xz_mz...~.z<24u~. —.mn=m wp~wz new
cc um
n¢m oh om ._~.mc .m_. u_ -
~1 ~+~vmhaznm~ cam
._.x_¢zu_~
Auz.z~z_n~ “mm on
~¢o~mzuzmzm
m m cw so .o.wu.zurz. um mum
..xc\e~n~.e. xm.m<.x~.n~ x~.»<:¢au amen mam
uzznbzcu cum
.m~.-ua..a.x:Hm2. .~.2424u_.~.=rcn upnaz mam
n1nn+auz.mpazum~
can cw cw ..~+4Lz.mpaz.»4.-. my
~1.~+_.mpazn- cam
.—.mpazn-
chmz.flu~ cgm as
"am ch ac .c.3u.opmz. an
.x. mm umzhuzzhw :¢<ma ozam at» cc.h«zmau swam .
anew u-zz mm“
.e~.. mm mpzu2u4u ozu<z no «wars: «. hizmou =¢cm
muzz.aocm up—z:
.c~.. wh mozom mo mumzaz ¢\e—.. mm mpzurugu mo mumzaz c..»«zzou eacm
omz.4wz.o~cm uphaz cam .
u amm
2o-uum zmapgm 4<zmoz 111%

eunomz acocuoomz. um
.A.u.»=cuv._ apaap

~u.~.rm_m:

ha: uraccz

._¢Auz.¢paznpaz
Luz cc

gu—z

zuz214uzuopwz

zo~h<N~J<_p—z~
\>¢:mom»:nontfiocznomm:w.wm:m.m:~.~:~.u1.\amonunaa-a>bzv <p<o

mm

b L—UU

cm

.or.
..ac~.>z_mz..om.:«24u~..cm.pc44u_..m42.cnaz
r xucgm

oacuzo>w2o<zma<~ndqumopzuoAmhvuum<do“Nb.“wwg

A. .

Acmuo<uzpacmvhm4¢mmo uzmumomnzzoczzx carioauzzohz
a zuoam 11 20::

pzcu 11 xzmmz
«mm 11 xqcmz

mm_u 111 ha:

:32 11 huesu:
c muxzaz 11 t
c

h

n

p-g
UH ODCDODO

<
hi
1
L:

CN

(DP-Cdm'j n I-I-u-n-u-u-n

omzu zo—mz m—

mhz<hm uu<

>zou z
Apzu 2_ mom 4_<
aux _

.J)-I.L
43 >4”

c—
hzuzuau ozu<t :hx wzb u; an
b2wzu4u omu<t Ihx qu no u—

LJ Cl-ZI-ILJZLAJ‘V-t)

H uuaazza «ac.

whv—A zuhw>w oz<oz<hm ahzn mum—4 zuhm>m 4 m
Lz—paomczm n

L1.)
L":
S
D
Z
I
I
.J
LUUUL'U UUUULUUUUL‘ U

uu<4¢u¢ m=.u=oga=m kc a=_um.4 .N n.5u»

 

ccr 0p cc
«ennumaum u
gnu c» Cu ..4+~x._w4xu_.xs_m7.cu. ~2_. kw mm
whacm zuao cmu<z xuuzu w
ego ch co .xzq.au..~.4uaq4. m—
uumu 44<u «cm
and cow ca
ocm op cc
;, magnum“;—
u
can oh cc ..x.x<zu:_.au.:<zur. my
uz<2 cmu<r xumzu w mh
onmz u.x.<¢h;:
n+xux
<zma<_u z<zuz _
mm: c» cc .azuuz:w.cu.<:aa<~. um c>
muck Aqqu u
p2uzuag ozuqz pwuz >u~pzuo~ w
uzznpzcu ac“ wc
H+4n4 mo
:.¢pazna4 pmeu—
auzpz~z~un mo co
~+auzz14uzuzmzm cc
and u
xuazu as; cut“ ozom caucz uxcpw . w
"+4"; ow mm
.~.:<zgu~n.4.tazuz~
4m: z—z~n_ cm on
H+ohmzuzwzfl
1 u c:
xuqzu xom wmz<z :zu«: uxcpm %
ou.w._.xzm~ mm
on“..—.xzm~
omz:.~u~ mm on me
:mzuz

.A 6.283 N «Bah

Table 2 (cont'd;);

10

(‘9

90

STD CODE MACRO DFFINITION

2
5-.
D
<14
Lu'uJ
1%
I11.
.—
11...:
“-1
P‘.
(AU
C:
C
UUUF‘IL.‘
If
3‘

0-0.: N
II II (2
mac '1
>->-Lu
l—P- . O
SEQ 1—

>- C.
‘60— L31")
OCS‘ c
mafv an
UL) O \
<v—1: IO
EEO q-fl-
]:3‘: 0 00
UK?!" co
O O'— L‘-
CG 0 on
MUG! 8!
0 0140.1 pt 0 C:
(4 0:. UC’OJC-
:IQHCUJNCLD
QG.>- £3qu OP"

.1..11-1111‘.1zn1—113
<<zu uqzuh
hot—9m 3 ..lv—z
vvv ((1-4 ‘1'sz
L'CJ 1.1.1:;
LLlLLLJ—QL‘ULLLM
1—1—1—1 01—1—1

{‘4
C
'0

100
105

6010 308

l).[0o1Hl)

sane.
1.1412410
AIL-H
01.2. I! if;
L‘LLI-
AVG-C3
..J luL‘.‘

«nu—0
01-1

r-‘)
c:
UFO

119

O
K
U
<1
E
\n
c- if)
#1 <
C 0-
: 0- c
:1 3 1.1.1
'0 C a:
y.-
0 A 1—
1- H I?"
O .J (Av-10
O I (II)-
N .1...»-
A o J) 2
v- C- I
0 Lu 1—r—a
O 0 >Ho-1
1.1.1 < U30
OLJI 2'.’ our:
CLL-JC. 91.11.11
>0:..li-J)a’ can

I—LL'JZUJLJXLI' L

.J H)- .1347-
LL‘LLTCLLLILdUZ'
HUN—1' HFUIX

3N1

115
120

x

2-

I—o

m

E

2

H

(A

P

a:

C,

a.
O.
+ 2'
..J L:
* CL
A O
x
‘I' LI...J
IL OH
I A
’- mas
L1. 1.1::
1' Ev
II 212
A 3%
F ‘n
9 G.
x '11»: (II
'- 1v 9
a: C>‘ --0
a: 1—1‘ 2‘
t- (fiv— II
C. I. '-
2 E 2

1x
(‘

L.) LL; LP‘L.

Lf"

130

Eo21 GO TO 315

A
O
U
2

U

u
H

Table 2 (cont'd.).

; 9
a fiTYP1ITYP11 GO TO 32%

p1.
oqau c
#OI>0 Kc
(NDthJsam
H .JHUBH

Had ZDHO
thh«:22nLh
a "Numm

moqn hm:
mom uzuc

F!:ZO_N:H
2O U
If. C‘-
P! N
n n
m c
r" c
F" F!

STORE NODE TYPE AND NAME

>4
PM
“2

H"
AA
“H
32

+0

HCO
+PF
WW
HZ?
Z'v
SP:
m<
H42
VJJ
ZLU
Sum

m

N
UUUM

145

 

NC
CTN
n:
GO
PF
Q
3 CC
3 Q6
1
O AA
0\
D I
Z dd
C to
C Cc
mm
U 00
x AA
0 HA
P we
W MAJ
LUUM
a 3mm:
2 ZNL<<R
< h-.441
D-wai
P 2
U C<&L
@ LUNA
C
n
Ugh”

155

335

IF (KEYorflol) GO TO

106

GO TO 500
NBIM¥(NBDLK)=INT

IFRKF

m
n
”U

J=1

A
’

160

A
3
1
U
m
c b
F 1
¢H C
A U
Cd‘ 2
P H
D A
cr- 3
w 5
C +
A@ A
3‘ x
fiA v
'4 I
G o 1
Uh Uh
O¢ Cu
POfies
25+ v
nvvacx
~~3hx
H h
muficc
H~5¢Z
0 C
C A
¢
m
w
g-I

END

NBDLK‘I
MCBDCT+1

COUNI BOND
NBDLK:
MCBDCT:

1-1
F

.170

GO TO 330

INDEX

M

0ND NUMBERING

1+1)

B
1

N

{U03 Q UL?

175

Table 2 (cont'd.).

GOTO 100

IF MICRO: COMPLETE IMPLIED MACRO

180

MICRUR SUBROUlINE

DATA Fnk THIS MACRO

185

0A1 SYSTEM
NI +1LM-111MNI
LK= NBDLK+1LM~11tHCflDCT
DCT=LM1MCBUCT
+(MCRDCT-Lll?
To 140
HRAP-UP FOR MCEND

190

195

CONVERT NBIMX TO ABSOLUTE BOND NUMBERS

200

L+1l

A+
AA
HI-O
vv.3
1m”
KKK 0“"
Ol-l-c-lll
HQQNA
HZXHH
y—wva—a
XX "
{3:27.00}
C hat-oil-

if.

p

10

PavA

A P

x~ x 02

<3 < PM
c..a:'~ Hi" v 2:
13>: 1:: CU) 1?
whfii 0’ Ch A
On?" H2 0 I
Anti—om A+AAAC l—
”.fo HHXF-JU P.’
~~7H ~~x¥o£ H
0.311116 «(Hun-II II
man-1'3 mmnch»A
0-1-35 l—t—XZ 01-10111-
0.0- vfilc. 1-1—x‘wx

1'5." (‘0) § Y2“ ET?"
II N val-3 ll HNZHXOX
NQmNQV-UZXFCLUZXN H WED-Z"

-

Oll~< 0111-14 1"- t— '—

O ll 11' 3031£3U322C2LCCW
C-JZ Oifififictfixxcfi-HZQZ

7"5

205

210

71n

[D

(‘4‘

730

226

,;>huuu

Table 2 (cont'd.

MU

22
Fifi-I
FF-
29

U0

ISO
(MC.

CREATE IBHX - PUT FIRST ELEMENT ENCOUNTERED IN COLUMN ONE

\

N

I-H-a A 0A

x
q "(‘1
2 IA

2 0 Fur-#3
+FU~+~~L
CNflHHX
h—wvfiz
”DIEM rm
ZCW—l- cm:
H ¢O.G.v-12'
xxzzcm

<

p

:0 flNOZ'
HCHI-‘Qh

i
!

C L;
'N '0
CC“ 112‘
O O
P’ P
O 3
L9 L9
A A
C; 0
o 0
U LIJ
Z Z
O O
A A
F- (‘11
Oh. ..—
hfll PM
2 A 2 A
HA MN

050
x pnxhuwcor
zzmzznacnm
m1— 1:11—22 ll
AvOHv—HOuO
VXPVXFPPKP
2 222 a
umcmmocouc
m—oHv-IUUCAG

CDC—Q
AC

%¢

2
830

Q

255
240

ERROR RETURN SECTION

UUUU

245

REPLACE.*)
VT LINEOOO*’ICXQ72A1)

6
l
E

mm

C

250

SECTION

NORMAL RETURN

C..--

C

*olll)

m
A
W
O
2
O
Q
k
O
z A
U \
m ‘
z
D m
2 A
F1
m N
O 1: H
\ D ’
c I'- 0-4
H U H
o D H
i z 5
p o
(0 03 AA
i-t 'DA
: v>
m Q x:
P d {A
Z x ~\
M O m?
2 4H
m C “m
J 2 0A
“A O A-
C N‘
Ll. U 0
C U Z@
O 2 <<
mm P 2'
NZm I Ax
\ «:1 0 L140]
“J? X4 flu¢
nu: Hm 19m
lZZ OZ AHA
mg. ‘0 A00

ZJOGOIHA+OX

+QQ¢CCIIHHQK
uoazvmw—vvcv
DFZW Q xxw
2m» b hchp P
h? uau<¢azu<
PHHFZPEQZZPE
ZJOHmHX “MHZ
cumaomconmao
0223L3LQMFBL

6"00
LOCO

O
u
m
€

GOO
F6“

?65
260

Table 2 (cont'd.).

ELNAM(N21

I
6

0‘!

0ND*93X9*FIRSTig2X9*SLC0ND*/1XgtNUMBERi92X¢*N00F*

Q I— O
a, 910
AZAAHH
\ 0—1910 o
C CH O 00x
1D¢LJHHHQN

U*91XQ*B

unmx IIHHQW%:

COCOv-(‘JOC'O 11.12

Juoozzaumm
+

c a
1D to
«0 NP-
“; 1.1.43

11‘. c
~13 I~
N N

e:z_»2cu an"
mar—hzou :5 rs
.H+mpa_.z<zaum u._+m~.:.24u_
.—+xp¢avhm44ufi n.~+r~.hm44u_
m4+ .~+xpa~.x—az n.~+:~.m~;2
HZXO HUN (0 3C
.H1a.1aag um; on
~22..~1s.+m_a_.umH
:4omu1 o:_ a:
buocuzuacd
hzz1~z+opmz napg~ .\
702214uz "chm: u mm
guzuzcum 1:24 2— mpm—A use: mrp :2<mxm w
. - . .cm.mpm2n muzz..~.om.xzm~ +
..cca.»z~;z..cm.z<zgp~..cm._m44mm.cm42.wamz cmz 4m: \nxm\ 7ozzou cm
x zueem 11 acou :aazc azom a<um u
an ~.»m..»xm:..‘~mzez._a 1
.quz. >Lx. <r¢q<~.4<mm. pzh..-.4um<4 .w~.uz_4.:¢u a: \mxa\ zozzcu
w gucac 11 t :12. mu¢e1~<szaa e
.cm.c<ur..om.pmaz&~.m¢xu~.maz:.czzz.cnzz.4u22.h:oozm \dxmx zoxzau ma
~ xuca: 11 zetzcu uncamnm Jamwzuc w
sag~z z- ._1mc2cm murzzz. 111 a: u
emu”: so mpzca «mean: 1111 a u 7
min; omu~z quzn zmpm>m z~ m.coz ohm zuctaz Japop 111 H2 9 cu
.41szam. scum: 2~ mozu 22c: mumzaz 1 79:20: 9
cmu_z z~ wgooz muzzaz 11 ~27 u
omu<z 2— meta; zuzszz 111 :4 w
Juan 744¢u u m
uu<4auz >c12u44<u u
~<zzom omu<z ep2~ its; axon: czqaxm CF v~ uwommaa .aaaw
.4._z.puomuz.~22.:4.7o¢u_z uzppacxmzm a

mozu_z a:.»=cgn=m Lo m=_um.d .m a_aap

Table 3 (cont'd.).

EXPAND THE BOND LIST IN LUMP SEQUENCE

N
O
m 2
”4 4
...
0-0
on A
I h m
V '25
A x :3
fl i O
+ 0-0 CD
H m
9'4 A?! '2." I—
I I a
N ¢+gn O
\ A 21H“ ;
Aid—APP- 9C
J-JIHQQVQ U
+03|HMH+ U
PN~1~VHHU d
Uflibzmhv: J
afi4ah~ X? Q
C!) IIQLQEP u.)
UCJfiZZCHP a
2L HmZ
UNHHHH 26 3
H mmmuc U C
COJHHHC 2
70
CD
TC
PNQQU
C- .u" C.
U a m

nu
mm
”H —H
v-Cu‘ Cu
my Huh
AAA
AA AAA
Hm dmd
.- III
CC N572
mm *VVJ
no. £¥v
Han indJfi
OMH Jammq
mvv 'IAJI
HXX m7++4

NZZLH~HN+
HHHDfi«—~m
6&2 C~V~
O7ZHC1xxs
h~vPH :2
fl znnmnz
mic amm—
CHHUCHZ?m
C C 2

n
31"

55
60

fl+LM*LPL

3