Power Directions

[Image: bond_power.png]

The half arrow head indicates the direction of power.

When both effort and flow acquire positive values, then power goes from the tail

to the arrow head. Whereas for mixed signs of the variables, the power direction

is reversed.

Note: The interpretation of the relative orientation of positive effort

and flow may be subjective depending on whether the analysis is carried out from

the stand point of the junction or element.

Causality

[Image: bond_causal.png]

Causality establishes the cause and effect relationships between the factors of

power.

In the bond graph images above, the vertical stroke at one end of the power bond

is called causal stroke. This causal stroke is used to indicate the

direction in which the effort signal is directed. Causality is a symmetric

relationship. When one side "causes" effect, the other side "causes" flow.

Junctions

In a 0-junction, only one bond can cause the effort (ie. causal stroke is at the

junction side, away from the element); whereas in a 1-junction, only one bond can

cause the flow (ie. causal stroke is away from junction, at the element side).

This one bond is called the strong bond. If the causality of this strong

bond of a junction is known, the causality of the others bond is also known.

[Image: 1-strongBond.png]

[Image: 0-strongBond.png]

Elements

For inductance I type storage element, the flow is proportional to the time

integral of the effort [f = (1/I) p]. Therefore, an I element receives

effort (cause) and generate flow (effect).

For Capacitive C type storage element, the effort is proportional to the time

integral of the flow [e = (1/C) q]. Therefore, a C element receives flow

(cause) and generates effort (effect).

For Resistive R type element, there is no time integral form of constitutive

law. The flow and effort are algebraically related and can thus have any type of

causal structure. Causal stroke at the junction end indicates a resistive causality

[e = R * f]; whereas stroke at the resistive element end indicates a

conductive causality [f = (1 / R) * e].

As discussed above, the causal strokes for I, C and R elements are as shown

below:

[Image: J-I.png]

[Image: J-C.png]

[Image: J-R1.png]

[Image: J-R2.png]

See also Bond Types.

Guideline to Building a Bond Model

As described before, bond graph modelling must first be understood to build a

Bond model. In order for causality to be established correctly, bond elements must

be connected in specific ways to ensure the correctness of a bond model.

To prevent users from causing causality to fail when building a bond model, MADE

has rules in place to guide users to build a Bond model by indicating to the user

which two components, hence two Bond types, are not to connect to each other. When

these rules are violated, error markers in the "problem" view are created to warn

user of possible problems.

Bond Connection Rules

On a system diagram, Bond connections are created between two components, where

each component has a Bond type assigned to

it. The rules for connecting between two Bond types are listed in the table below.

Bond Types	Allowable connecting TO/FROM
0-J	0-J, 0-R, 1-* (e.g. 1-J, 1-R, 1-IR, 1-IRC), SF, SFSINK, TF, GY
0-C	0-R, 1-* (e.g. 1-J, 1-R, 1-IR, 1-IRC), SF, SFSINK, TF, GY
0-R	All Bond Types
0-CR	0-R, 1-* (e.g. 1-J, 1-R, 1-IR, 1-IRC), SF, SFSINK, TF, GY
1-J	1-J, 1-R, 0-* (e.g. 0-J, 0-R, 0-CR), SE, SESINK, TF, GY
1-R	All Bond Types
1-IR	1-R, 0-* (e.g. 0-J, 0-R, 0-CR), SE, SESINK, TF, GY
1-IRC	1-R, 0-* (e.g. 0-J, 0-R, 0-CR), SE, SESINK, TF, GY
TF / NLTF	0-* - TF - 1-, 1- - TF - 0-, SE - TF - 1-, SF - TF - 0-, 1- - TF - SESINK, 0-* - TF - SFSINK
GY	0-* - GY - 0-, 1- - GY - 1-, SF - GY - 1-, SE - GY - 0-, 1- - GY - SFSINK, 0-* - GY - SESINK
SE	1-*, TF, GY
SF	0-*, TF, GY
SESINK (Same as SE)	1-*, TF, GY
SFSINK (Same as SF)	0-*, TF, GY

Control Connection Rules

Control connection can be established between any Bond type except for sources

and sinks, and another Bond Type or Passive Element consisting of at least one of

Resistor, Capacitor or Inductor in it.

Source	1-, 0-, TF, GY
Target	0-C, 0-R, 0-CR, 1-R, 1-IR, 1-IRC

When a control connection is created, the equivalent connection in its bond

graph model will be connection from the main junction of the source component to

the selected control element of the target component.

The target element is controlled by the source junction. As a result, the

constant value of the target element of a control connection will no longer be a

single constant value but becomes a variable in which its response is viewable via

[View Simulation

Response](03-03-08-DynamicActions.html#viewSimulationResponse).

See also: [Settings

for Control Connection](03-03-07-DynamicSettings.html#dynamicControlSetting)

Steps to Bond Modelling

Before entering the world of bond modelling and bond analysis, the following set

up is required:

1. To build a system structure. To learn how to build a system structure, refer to System Structure Diagram.
2. Define function definition for each component. Refer to Functional Modelling.
3. Define Bond types for each component and connection. Refer to Dynamic Setting.
4. The different actions that can be performed on this bond model is listed in this page.

An example system structure is shown below:

[Image: samplesystemdiagram.png]

The equivalent bond model of the above system structure is shown below:

[Image: samplebond.png]