BGMod handbook

Reading a bond graph

A bond graph describes energy exchange. Each bond carries a pair of variables: effort e and flow f. Their product is power. A block expresses a physical law; a junction connects those laws through conservation equations. A bond is an energy connection, so a one-port resistance can represent a device with two pipe fittings.

Power variables by domain
Domain	Effort e	Flow f	Power e · f
Hydraulic	Gauge pressure p [Pa]	Volume flow Q [m³/s]	pQ [W]
Mechanical, translational	Force F [N]	Velocity v [m/s]	Fv [W]
Electrical	Voltage v [V]	Current i [A]	vi [W]

One bond carries two conjugate variables. The half-arrow and the perpendicular causal stroke have different meanings. Labels e and f above/below the line are explanatory annotations; BGMod’s canvas labels bonds by ID.

Shapes and labels

Circles 0 and 1 are junctions. R, C, I, Se, Sf are one-port primitives. Larger rounded blocks such as 7A, ACC and CYL are compound components with named ports. A caption identifies the block; primitive values and units appear beneath it.

Ports and line styles

Small circles are energy ports. Solid blue connections are hydraulic; dashed amber connections are mechanical. M always marks a mechanical port in the current library. Red highlights identify invalid objects or ports; green indicates selection.

Named ports keep connections unambiguous. The shown half-arrows choose positive power into A and out of B/M during extension; local QA = AAv, QB = −ABv and fM = −v. Actual power also depends on effort. Causal strokes are omitted here.

Pressure reference. Every hydraulic port uses gauge pressure relative to one document-wide reference: p_abs = p + reference_pressure_abs. The default reference is 101325 Pa. Accumulator precharge and initial pressure are entered as absolute values. A tank modeled by Se = 0 Pa is at the reference pressure.

Violet bonds and E ports are electrical. Mechanical primitives describe translation; rotational mechanics is not a separate domain in this library.

Arrows and signs are reference choices

The half-arrow defines positive bond power, not a one-way valve or a guarantee of positive flow. Negative e·f means power travels against the half-arrow. Each bond keeps two ordered endpoints, a and b, and a separate direction value.

direction = +1: a → b · direction = −1: b → a
s_a = −1 · s_b = +1
f_local = s · direction · f · e_local = e
P_absorbed = e · f_local

Component equations use flow into the component, f_local. For example, a bond from a source (a) to a resistance (b), with direction = +1 and positive f, removes power from the source and delivers it to the resistance.

Editor action	What changes	What stays fixed
Reverse reference	Half-arrow; the signs of bond f and e·f.	Endpoints a/b, local physical flows, states and 1-junction port signs.
Delete and recreate in reverse endpoint order	Which end is a or b; the fixed port signs. This can change a 1-junction’s physical connection.	Block parameters, unless edited separately.

All arrows here have direction = +1. At a 1-junction, + means the junction is endpoint b; − means endpoint a. Equality at a junction is spatial, at each instant: pressure or flow may still vary with time. Causal strokes are omitted in this topology illustration.

A 0-junction imposes equal efforts and zero sum of local flows. A 1-junction imposes equal reference flows direction·f and zero signed effort sum Σ(s·e). The visible +/− labels on a 1-junction record endpoint order; they do not flip when you reverse the half-arrow.