DM312: Week 3 Bond Graphs

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What is the purpose of the bond graph theory?

To model energy conservation, transformation, and interaction among components in different energy domains.

What are the fundamental concepts in bond graph theory?

Effort and flow

What does the short straight line at only one end of a bond in a bond graph indicate?

It indicates a causal relationship for that bond.

What does the term 'causality' define in the context of bond graph elements?

Causality defines a relationship of interaction between two bond graph elements, indicating which energy co-variable causes change in the system.

What are the one-port standard elements in a bond graph and what do they represent?

The one-port standard elements are Resistors (R-elements), Inductors (I-elements), and Capacitors (C-elements). They represent the dissipation of energy in the system.

How are the ports classified in bond graph standard elements, and what do they represent?

The ports in bond graph standard elements are classified as one-port, two-ports, and multi-ports. Ports represent the junction between the bond and the element, facilitating the flow of energy within the system.

Explain the difference between an Effort source and a Flow source, and provide examples of each.

Effort source (SE) supplies effort independent of flow and provides power to the system, while Flow source (SF) supplies flow independent of effort. An example of an Effort source is a constant speed driven pump, and an example of a Flow source is a dc motor.

What is the purpose of using Bond graphs in mechatronic design?

To represent physical and engineering components, and their interconnections, emphasizing on energy and power.

How are components represented in Bond graphs?

Components are represented by nodes that store, transmit, or dissipate energy.

Give an example of how Bond graphs are used in a practical application.

A table saw is used to convert electrical power into the rotation of a saw blade to cut through wood.

What are the two types of Bond graphs and how do they differ?

Bond graphs can be either general and descriptive, or specific and quantitative.

What is the SE and SF for Mechanical Translations

Effort: Force Flow: Velocity

What is the SE and SF for Mechanical Rotational

Effort: Torque Flow: Angular Velocity

What is the SE and SF for Electrical

Effort: Voltage Flow: Current

What is the SE and SF for Hydraulic

Effort: Pressure Flow: Volumetric Flow Rate

What is the SE and SF for Thermal

Effort: Temperature/ Pressure Flow: Entropy change rate/Volume change rate

What is the SE and SF for Chemical

Effort: Chemical potential/ Enthalpy Flow: Mole flow rate/ mass flow rate

What is the SE and SF for Magnetic

Effort: Magneto motive force (MMF) Flow: Magnetic flux

How are the arrows annotated in Bond graphs

Half arrow indicates the direction the power flows when the product of e and f is positive. Half arrows are written on same side as effort variables.

What are the table headings for a Bond graph in order

Component, Explain function, Energy Domain, Energy variable, Effort Energy variable Flow

What does "R" stand for in Bond Graphs in relation to One port elements and give examples

Resistors dissipate energy. (causes energy to be lost through its conversion to heat).

Examples of this are: • Electrical resistor • Friction force, Dashpot (mechanical damping); Mechanical translation • Brakes (disc brakes): Mechanical rotation

What does "C" stand for in Bond Graphs in relation to One port elements and give examples for their equations

C-elements store and give up energy without loss.

Electrical=C Mechanical= 1/k Hydraulic= A/pg

What does "I" stand for in Bond Graphs in relation to One port elements and give examples for their equations

• I-elements store and give up energy without loss.

• Electric inductor • Fluid inertia • Mechanical inertia • rectilinear (sliding block – mass action) • Rotary

Explain One port effort sources

Sources of energy are capable of introducing energy to the system: • Effort source – SE • Supply effort independent of flow • Supply power to the system • Represented by dotted line

Explain one port flow sources

Flow source – SF • Supply flow independent of effort Represented by straight bold line

Study Notes

  • Bond Graphs is a unified approach to modeling energy conservation, transformation, and interaction among components in different energy domains.
  • Traditional engineering disciplines have common generalized energy variables in different domains.
    • Mechanical: Effort (Force), Flow (Velocity), Momentum (Momentum), Displacement (Position)
    • Hydraulic: Pressure, Volume flow rate, Pressure momentum, Volume
    • Electrical: Voltage, Current, Flux linkage variable, Charge
  • Bond Graphs provide a graphical and topological description of energy interaction, storage, and dissipation within a dynamic system.
  • Effort and flow are two fundamental concepts.
  • One-port elements:
    • Source Effort (Se): Provides constant voltage or force input.
    • Source Flow (Sf): Provides constant current or volume flow rate input.
  • Two-ports elements:
    • Transformer (TF): Transfers rotational or hydraulic energy between two domains.
    • Gyrator (GY): Transforms electrical energy to rotational energy and vice versa.
  • Common Effort Junctions (0 junctions): Used to represent a sum of zero effort or torque inputs.
  • Common Flow Junctions (1 junctions): Used to represent a sum of zero flow or current inputs.
  • Bond Graph elements and their meaning in different energy domains.
  • Mechanical Translation: Represents translational motion and force in mechanical systems.
  • Mechanical Rotation: Represents rotational motion and torque in mechanical systems.
  • Hydraulic: Represents hydraulic pressure, volume flow rate, and energy transfer in hydraulic systems.
  • Electrical: Represents electrical voltage, current, resistance, and energy transfer in electrical systems.
  • Pneumatic: Represents pneumatic pressure and volume flow rate in pneumatic systems.
  • Causality: Defines the relationship of interaction between two bond graph elements.
  • Interaction between two bond graph elements can be represented by straight lines at only one end to indicate causal relationships.
  • The following diagram shows a representation of a DC motor, where GY indicates the crossover relationship between the electrical input energy co-variables (v and i) and output energy co-variables (torque and rotational speed).
  • The bond to the right of GY has a short vertical stroke, indicating that the load (torque) determines the energy flows through the energy pipe – bond.
  • Functional Synthesis with Bond Graph concepts.
  • Bond Graphs are used for representing physical and engineering components, interconnections between components, and managing different types of energy and power in a compatible fashion.
  • The bonds represent power interactions between components, and the components are represented by nodes that store, transmit, or dissipate energy.
  • Bond graphs are used to design complex systems like a self-regulated drug infuser.
  • Bond Graphs are used to convert electrical power into rotational motion, like a table saw, where mechanical rotation provides rotational motion and adjusts speed and torque.

Test your knowledge on traditional engineering disciplines and their commonalities, as well as the generalised energy variables in different energy domains. Explore concepts related to energy variables, power, mechanical translation, and mechanical rotation.

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