Bond Graph - Junctions

Junctions

Power bonds may join at one of two kinds of junctions: a 0 junction and a 1 junction.

In a 0 junction, the flow sums to zero and the efforts are equal. This corresponds to a node in an electrical circuit (where Kirchhoff's current law applies), or to a mechanical "stack" in which all the forces are equal.
In a 1 junction, the efforts sum to zero and the flows are equal. This corresponds to an electrical loop, or to a force balance at a mass in a mechanical system.

For an example of a 1 junction, consider a resistor in series:

In this case, the flow (current) is constrained to be the same at all points, and when the implied current return path is included the efforts sum to zero. Power can be computed at points 1 and 2, and in general some power will be dissipated in the resistor. As a bond graph, this becomes

$\overset{\textstyle v_1}{\underset{\textstyle i_1}{-\!\!\!-\!\!\!-\!\!\!\rightharpoondown}} \stackrel{\textstyle\stackrel{\textstyle R}{\upharpoonright}}{1} \overset{\textstyle v_2}{\underset{\textstyle i_2}{-\!\!\!-\!\!\!-\!\!\!\rightharpoondown}}$

From an electrical point of view, this diagram may seem counterintuitive in that flow is not preserved in the same way across the diagram. It may be helpful to consider the 1 junction as daisy chaining the bonds it connects to and power bond up to the R as a resistor with a lead returning back down.

Regardless of the problem domain, bond graph modeling typically proceeds from the identification of key 1 and 0 junctions associated with identifiable efforts and flows in the system, then identifying the dissipative (R) and storage elements (I and C), power sources, and drawing bonds wherever power or information flow between the sources, junctions, and storage/dissipative components. Then sign conventions (arrow heads), and causality are assigned, and finally equations describing the behavior of the system can be derived using the graph as a kind of guide or map.