# Bond Graph

A bond graph is a graphical representation of a physical dynamic system. It is similar to the better known block diagram and signal-flow graph, with the major difference that the arcs in bond graphs represent bi-directional exchange of physical energy, while those in block diagrams and signal-flow graphs represent uni-directional flow of information. Also, bond graphs are multi domain and domain neutral. This means a bond graph can incorporate multiple domains seamlessly.

The Bond Graph is composed of the "bonds" which link together "single port", "double port" and "multi port" elements (see below for details). Each bond represents the instantaneous flow of energy (dE/dt) or power. The flow in each bond is denoted a pair of variables called 'power variables' whose product is the instantaneous power of the bond. For example, the bond of an electrical system would represent the flow of electrical energy and the power variables would be voltage and current, whose product is power. Each domain's power variables are broken into two types: "effort" and "flow". Effort multiplied by flow produces power, thus the term power variables. Every domain has a pair of power variables with a corresponding effort and flow variable. Examples of effort include force, torque, voltage, or pressure; while flow examples include velocity, current, and volumetric flow. The table below contains the most common energy domains and the corresponding "effort" and "flow".

A bond has two other features described briefly here, and discussed in more detail below. One is the "half-arrow" sign convention. This defines the assumed direction of positive energy flow. As with electrical circuit diagrams and free-body diagrams, the choice of positive direction is arbitrary, with the caveat that the analyst must be consistent throughout with the chosen definition. The other feature is the "causal stroke". This is a vertical bar placed on only one end of the bond. It is not arbitrary. As described below, there are rules for assigning the proper causality to a given port, and rules for the precedence among ports. Any port (single, double or multi) attached to the bond shall specify either "effort" or "flow" by its causal stroke, but not both. The port attached to the end of the bond with the "causal stroke" specifies the "flow" of the bond. And the bond imposes "effort" upon that port. Equivalently, the port on the end without the "causal stroke" imposes "effort" to the bond, while the bond imposes "flow" to that port. This is made more clear with the illustrative examples below.

Energy Domain effort e symbol e unit (metric) e unit (imperial) flow f symbol f unit (metric) f unit (imperial)
Mechanical, translation Force F N lb Linear velocity v m/s ft/s, mph
Mechanical, rotation Torque τ N·m ft·lb Angular velocity ω rad/s rad/s
Electrical Electromotive force V or u V V Current I or i A A
Magnetic Magnetomotive force Flux rate
Hydraulic Pressure P Pa psi Volumetric flow rate Q m³/s ft³/s
Thermal temperature T °C or K °F entropy flow rate S W/°C ft·lb/s·°F

If the dynamics of the physical system to be modeled operate on widely varying time scales, fast continuous-time behaviors can be modeled as instantaneous phenomena by using a hybrid bond graph.

Read more about Bond Graph:  History, Basics, Junctions, Example

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