Week 3 DM312 Mechatronic Design and Applications Lecture Notes PDF

DM312 Mechatronic Design and Applications Lecture 3: Introduction to Bond Graphs Dr Aleksandar Josifovic Week 3 - DM312 In this lesson: Part 1 Bond graphs Sources of energy Bond graphs examples Practical exercise Part 2 Defining standard elements Sf, Se, I, R, C Bond graph tutorial Part 1: Bond Grap...

DM312 Mechatronic Design and Applications Lecture 3: Introduction to Bond Graphs Dr Aleksandar Josifovic Week 3 - DM312 In this lesson: Part 1 Bond graphs Sources of energy Bond graphs examples Practical exercise Part 2 Defining standard elements Sf, Se, I, R, C Bond graph tutorial Part 1: Bond Graphs Introducing Bond graphs Mechatronic products integrate aspects from several distinct domains – mechanical, electrical, hydraulic etc. Power is transferred across these domains and is used to define a common representation. Introducing Bond graphs Used for representing: physical and engineering components Interconnections between components Can be either: General and descriptive Specific and quantitative Emphasis is on energy and power Bond graphs – basic concepts The bonds represent power interactions between components. The components are represented by nodes that store, transmit or dissipate energy. Generally start as being purely descriptive. Develop to represent the flow of power through the components. Can manage different types of energy and power in a compatible fashion. Simple example – table saw Used to convert electrical power into the rotation of a saw blade to cut through wood. Nodes Wall socket Electrical Power Bonds Motor Belt Rotational Power Load Sources of energy Sources of energy introduce energy into the system For example the wall socket in the table saw Energy is provided theoretically without limit Two different kinds of energy sources: Sources of effort (e) (Se) Sources of flow (f) (Sf) Sources differ for energy domain (mechanical/electrical/hydraulic etc…) Sources of energy (Se and Sf) Energy Domain Effort (e)(Se) Flow (f)(Sf) Mechanical Translational Force (F) Velocity (v) Mechanical Rotational Torque () Angular velocity () Electrical Voltage (V) Current (i) Hydraulic Pressure (P) Volumetric flow rate (Q) Sources of energy (Se and Sf) Energy Domain Effort (e)(Se) Temperature (T) Thermal Pressure (P) Chemical Chemical potential (μ) Enthalpy (h) Magnetic Magneto-motive force (em) Flow (f)(Sf) Entropy change rate (ds/dt) Volume change rate (dV/dt) Mole flow rate (dN/dt) Mass flow rate (dm/dt) Magnetic flux (φ) Bond representation Half arrow indicates the direction the power flows when the product of e and f is positive. e f F v V i P Q General Energy Mechanical Energy Electrical Energy Hydraulic Energy Half arrow written on same side as effort variables. Descriptive Bond Graphs First step is to construct a bond graph whose nodes describe the components. Example motor car: Engine Gear box Shaft Wheels Road Engine   Gear box   Shaft   Wheels F v Road Descriptive Bond Graphs First step is to construct a bond graph whose nodes describe the components. Example – Internal combustion Engine Fuel μ dN/dt Cylinder F v Crankshaft   Driveshaft Descriptive Bond Graphs First step is to construct a bond graph whose nodes describe the components. Example – Pressure washer Power source V i Electric motor   Hydraulic pump P Q Storage tank P Q Valve P Q User Descriptive Bond Graphs – Energy co-variables Example – Pressure washer Power source V i Component Electric motor   Hydraulic pump Explain function P Q Energy Domain Storage tank P Q Energy variable Effort Valve P Q Energy variable Flow Electric socket Power source Electric V (voltage) i (current) Electric motor Drive the pressurizing system. Provide rotational motion Pressurize water Mechanical rotation τ (torque) ω (rotational speed) Hydraulic P (pressure) Q (volumetric flow) Contain pressurized water Control water flow Hydraulic P (pressure) Q (volumetric flow) Hydraulic P (pressure) Q (volumetric flow) Hydraulic pump Storage tank Valve User Descriptive Bond Graph example – table saw Wall socket V i Motor 𝜏 𝜔 Belt Electrical Power Component Explain function Load Rotational Power Energy Domain Electric socket Power source Electric motor Drive the pressurizing system. Mechanical rotation Provide rotational motion Adjust speed and torque Mechanical rotation Belt 𝜏 𝜔 Electric Energy variable Effort Energy variable Flow V (voltage) i (current) τ (torque) ω (rotational speed) τ (torque) ω (rotational speed) Part 1: Practical exercise Exercise on system energies Design Bond Graph diagram for Car Battery Charging system using stationary exercise bike. Energy co-variables 1. 2. 3. Identify what form of energy exist in the system Define how you can work out the power of the system and translation of energy; Identify key energy related variables in the system (Se and Sf); Example 1 Example 2 Component Centrifugal Pump Explain function Energy Domain Provide pressure, Hydraulic transfer fluid Energy variable Effort P (pressure) Energy variable Flow Q (volumetric flow) Part 2: Defining standard elements Bond Graph Standard Elements Next step is to replace words with standard elements Classified by the number of bonds as: one-port, two-ports, multi-ports. Ports represent the junction between the bond and the element. One-port elements Elements with only one bond/port are: Resistors e R- elements Inductors I-elements Capacitors C-elements f e f e f Effort and Flow sources R I C SE SF One port R-elements Resistors dissipate energy. Examples from different domains Electrical resistor, Friction force, Dashpot (mechanical damping) and, Brakes (disc brakes) V i R F v R   R The arrow indicates that the power is positive and flowing into the resistor. Hence: e=R×f & Power = e×f = R×f2 One port R-elements Resistors dissipate energy. Electrical Mechanical Hydraulic v V Q V – voltage i – current R - Resistor Q – Flow rate P – Pressure R - Resistor F – Force v – velocity R - Resistor V i R Q F v R P Q R One port C-elements C-elements store and give up energy without loss. Examples from different domains are: Capacitor, Hydraulic accumulator Linear or Rotary Springs. Torsional compliance of a shaft V i P Q   C C C One port C-elements C-elements store and give up energy without loss. Electrical Mechanical V Hydraulic v Q V i C F v C:1/k P Q C: A/ρ g One port I-elements I-elements also store and give up energy without loss Examples from different domains are: Electric inductor Fluid inertia Mechanical inertia rectilinear (sliding block – mass action) Rotary (fly wheel used to smooth rotation V i P Q F v I I I One port I-elements I-elements also store and give up energy without loss Electrical Mechanical , V i I   I Hydraulic x F m F v I P Q I One port Effort and Flow 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 SE Gravity Pressure regulator Flow source – SF Supply flow independent of effort… dc motor Constant speed driven pump SF Mechanical system – Bond graph example Part 2: Tutorial - individual Tutorial - hydro‐electric power station Produce a descriptive word bond‐graph showing the different elements and relationships between them within a hydro‐electric power station. Once this has been completed replace the words with bond‐graph and include the relevant energy co‐variables. Component Centrifugal Pump Explain function Provide pressure, transfer fluid Energy Domain Hydraulic Energy variable Effort Q (volumetric flow) Energy variable Flow P (pressure) Lecture material on Myplace