Nomenclature and Introduction (Modeling for Bond Graph Simulation User Guide)

Version: 3.9.1 (MADE — Maintenance Aware Design Ecosystem)

1 Nomenclature

Term	Definition
FCM	Fuzzy Cognitive Maps
GY	Gyrator
LOI	Level of Indenture
MADE	Maintenance Aware Design Ecosystem
SE	Source Effort
SF	Source Flow
TF	Transformer

2 Introduction

This guide is aimed at presenting the modeling approach for Bond Graph Simulations in MADE to create and analyze the functional model of a complex system. Bond Graph modeling is an energy-based technique used to represent power transmission across a system. This guide aims to answer the following question:

"What is Bond Graph modeling and how should the user create a Bond model?"

Modeling for Bond Graph Simulation in MADE serves as the basis for:

• Developing a functional model of a system
• Manipulating the system functional model (simplification & integration)
• Defining parametric simulation data/inputs
• Analyzing or troubleshooting system behavior response of each flow property for each injected functional failure mode, including:
  • Initial (transient) responses
  • Final (steady-state) responses
• Verification of the results by comparison with test results

Bond Graph is a domain-independent graphical representation of the dynamic behavior of physical systems. It is a powerful tool for modeling power transmission systems, especially when different physical domains are involved. Bond models use uniform notations for all types of physical systems based on energy flows.

Bond Graph is a graphical approach to represent the actions and interactions, static and dynamic, taking place within a powered system. The Bond Graph approach is based on the concept that the dynamic behavior of a system which comprises of interconnected items is dictated by the power being interchanged between items or items and the environment.

The power flow between items is the product of two variables: a potential – effort – and a flow variable. This implies a dual-variable approach to modeling, unlike FCM modeling and other techniques such as transfer functions, block diagrams or signal flow diagrams.

To create a Bond Graph that utilizes a functional model, the user must first understand basic Bond Graph principles and how to build a system model.

(Figure 1 "Bond Graph Modeling Summary" is a diagram showing three inputs — Bi-directional Exchange of Power, Power Transmission Systems, Multidisciplinary Engineering Domains — converging into "Bond Graph"; no additional extractable text.)

2.1 Power & Power Flow

Bond Graph modeling is used to map the flow of power through a system.

"What exactly is flow of power?"

In engineering, the flow rate of energy is called power. One widely accepted and descriptive concept is that power flows. An electric motor draws energy at a required rate from the electric power supply mains i.e. power flows from the mains to the motor and subsequently to the load being driven by the motor.

"Why use power?"

Power is a convenient entity for modeling since it is the multiplication of two conjugate variables — namely, effort and flow — regardless of the engineering domain. When a Bond Graph maps the power flow through a system, it also describes the relationships between conjugate variables in each Bond Graph branch in the system. The consideration of power flow in a system as well as the conjugate variable relationships enables the development of dynamic equations for a system.

Power flow magnitude is described by the product of the two simultaneous variables:

Power = Effort × Flow

2.2 Power Bonds

Bond Graphs represent the power flow through a system by using a series of connections called power Bonds. Power flowing from an element A to an element B is represented using a Bond that carries the two conjugate variables associated with the power: effort and flow.

Figure 2: Power Bond with the flow of power from A to B — depicted as A --effort/flow--> B (a half-arrow with "effort" over "flow" labeling the Bond).

The direction of the arrow indicates the direction of power flow. The Bond (arrow) links two elements — one item sets the effort and the other sets the flow. The vertical bar at the end of an arrow is called a "causal stroke" and is used to indicate which element sets the effort/flow for each Bond.

Figure 3: Power Bond with flow of power from A to B including causality (causal stroke) — shown as A |--effort/flow--> B with the causal stroke placed at the A end.

In figure 3, element B sets the effort and element A sets the flow. Effort is the cause, and flow is the resulting effect for the A element. In this configuration, a Bond arrow can only contain one causal stroke.

2.3 Effort & Flow Definitions for Multiple Domains

The benefits of modeling for Bond Graph Simulation are the ability to model systems that cross engineering domains by keeping track of the conjugate efforts & flows in multi-disciplinary systems.

Energy Domain	Effort	Flow
Hydraulic	Pressure	Flow Rate
Pneumatic	Pressure	Mass Flow Rate
Mechanical – Linear	Force	Velocity
Mechanical – Rotational	Torque	Angular Velocity
Electrical	Voltage	Current
Thermal	Temperature	Heat Flow Rate
Generic	Effort	Flow