EEE343: Electro-Mechanical Devices and Machines I Practice Flashcards

Principle of Electro-Mechanical Energy Conversion

• Fundamental Law of Conservation of Energy: Within engineer and science environments, it is an accepted fact that energy can neither be created nor destroyed. It can only change from one form to another, a process known as energy conversion.
• Conversion Parameters: The energy conversion process depends on specific parameters, with the conversion device playing the major role.
• Energy Losses: During the conversion process, energy losses are recorded based on physical and non-physical parameters produced during the process.
• Device Structure: While various conversion devices operate on similar principles, their configuration or structure depends on their specific function.
• The Role of Electrical Energy: Electrical energy is a primary concern in the field due to the flexibility it offers in transportation, manipulation, and the conversion process. It serves as a major interface between types of energy.
• Common Energy Conversion Relationships:
  • Chemical to Electrical: Battery.
  • Sound to Electrical: Speaker and Microphone.
  • Electrical to Heat: Electric iron, Water heater.
  • Mechanical to Electrical: Generator.
  • Electrical to Mechanical: Motor (the focus of this material).

Electromechanical Energy Conversion Systems

• Definition: The conversion of electrical energy into mechanical energy or vice versa.
• Motoring Operation: Conversion of electrical energy (Input) to mechanical energy (Output).
• Generating Operation: Conversion of mechanical energy (Input) to electrical energy (Output).
• Classification Criteria: Systems can be classified based on:
  1. Device type.
  2. Motion type.
  3. Excitation type.

Device Type Classification

• Transducers: Used solely for energy conversion in measurement and control environments. Energy signals are converted into another form solely for measurement or process control. This group is sometimes referred to as MEMS (Micro Electro-Mechanical System).
• Force Generating/Producing Devices: Includes solenoid actuators and relays. These devices convert electrical energy into linear or angular displacement.
• Continuous Energy-Conversion Devices: These are electrical motors and generators capable of continuous operation.

Motion Type Classification

• Linear Motion System: Converts electrical energy into mechanical displacement in a straight line.
• Rotating Motion System: Converts electrical energy into rotating or circular motion.

Excitation Type Classification

• Single Excited System:
  • Possesses only one source of excitation (one coil for excitation).
  • These are not continuous energy devices; they perform the conversion or movement only once (single action).
  • Movement can be linear or angular.
  • Commonly referred to as actuators.
  • Reset Mechanism: When the excitation is de-excited, the actuator's moving part resets to its initial position via a mechanically loaded spring.
• Multiple Excited System:
  • Systems with more than one source of excitation (two or more coils).
  • Double Excited System: A two-source type which is a simplified example of continuous rotating machines.
  • Represents the fundamental concept of all rotating electrical machines.
  • Rotation is continuous for the duration of the excitation.

The Medium of Conversion and Energy Balance

• Conversion Interface: The electromechanical energy conversion process occurs through a medium of magnetic or coupling field. Stored energy in the magnetic field serves as the medium.
• Energy Balance Principle: In physics, energy describes the amount of work done by a force in a system. The energy balance is a systematic presentation of energy flow and transformations.
• Engineering Application: Energy balance is a tool used to quantify energy used or produced, aimed at optimizing conversion and increasing system efficiency ("economy of energy conversion").
• General Energy Balance Equation:
  • $E_{input} = E_{output} + E_{stored} + E_{loss}$

Induced Voltage and Electrical Energy Input in Singly Excited Systems

• Theoretical Representation: Electromagnetic force or torque is represented in terms of variables like currents and mechanical displacement ($x$).
• System Components (Singly Excited):
  1. Electric Terminal: Characterized by voltage ($e_i$) and current ($i$).
  2. Mechanical Terminal: Characterized by a force field ($F$) and a position ($x$).
• Loss Modeling: Real systems include electrical losses (ohmic losses in windings represented by resistors) and mechanical losses (friction and windage).
• Electrical Equations:
  • Input Voltage: $V = Ri + L\frac{di}{dt} + e_i$
  • Where $Ri$ is the winding voltage drop, $L\frac{di}{dt}$ is the stored field voltage, and $e_i$ is the induced e.m.f.
  • Induced e.m.f.: e_i = \frac{d\text{\lambda}}{dt} = N\frac{d\text{\phi}}{dt}
  • Input Electrical Energy ($E_E$): $E_E = E_{loss} + E_{stored} + E_{w1}$
  • Where $E_{loss} = i^2 R$, $E_{stored}$ is magnetic field energy, and $E_{w1}$ is energy transferred to the coupling field.
• Formulae for Energy Components:
  • Total Energy supplied: E_E = \text{\int} V i dt
  • Winding Loss ($E_{loss}$): \text{\int} R i^2 dt
  • Stored Energy ($E_{stored}$): \text{\int} i d\text{\lambda} = \frac{1}{2} L i^2
  • Transferred Energy ($E_{w1}$): \text{\int} e_i i dt = \text{\int} i d\text{\lambda} = \text{\int} i N d\text{\phi}

Magnetic Field Energy in Electro-Mechanical Systems

• Interface Role: Magnetic energy is the agent of conversion. According to Michael Faraday, relative motion (mechanical) between a magnetic field (magnetic) and a conductor produces an e.m.f. (electrical) via induction.
• Economic Basis: Although both electric and magnetic fields can carry out conversion, the magnetic field is chosen because it is more economical.
• Balance Components:
  • Electrical Port: Receiving energy (motoring) or delivering energy (generating).
  • Mechanical Port (Shaft): Delivering energy (motoring) or receiving energy (generating).
  • Coupling Field: The electromagnetic field interface.
• Specific Heat Losses:
  • Electrical Port: $I^2R$ losses.
  • Mechanical Port: Friction and windage losses.
  • Coupling Field: Core-losses.

Mathematical Relationships in Magnetic Circuits

• Magnetomotive Force (M.M.F): $F = Ni$
• Permeance (\text{\rho}): \text{\rho} = \frac{\mu \mu_o A}{l_g}
• Inductance ($L$): L = N^2 \text{\rho} = \frac{\text{\lambda}}{i}
• Magnetic Field Energy ($E_m$):
  • E_m = \frac{1}{2} L i^2 = \frac{1}{2} F \text{\phi} = \frac{1}{2} \text{\lambda} i = \frac{1}{2} \frac{\text{\phi}^2}{\text{\rho}}
• Mechanical Force ($F_s$): The force offered against a stretched spring is related to the change in field energy relative to displacement:
  • $F_s = \frac{dE_m}{dx} = \frac{1}{2} i^2 \frac{dL}{dx}$
  • A mechanical force exists only if the coil inductance depends on the extension ($x$).

Multi-Coil Systems (Linear)

• Total Field Energy: $E_m = \frac{1}{2} L_{11} i_1^2 + \frac{1}{2} L_{22} i_2^2 + L_{12} i_1 i_2$
• Mechanical Force: $F_s = \frac{1}{2} i_1^2 \frac{dL_{11}}{dx} + \frac{1}{2} i_2^2 \frac{dL_{22}}{dx} + i_1 i_2 \frac{dL_{12}}{dx}$

Worked Examples: Case Studies

• Example 1: Electromagnetic Relay
  • Parameters: $N = 800$, $Area = 5\,cm \times 5\,cm$, \mu = 4\text{\pi} \times 10^{-7}.
  • Condition: Air gap $l_g = 0.5\,cm$. Current $i = 1.25\,A$.
  • Calculated Permeance: $6.284 \times 10^{-7}$.
  • Coil Inductance: $0.402\,H$.
  • Field Energy: $0.314\,Joules$.
  • Field Force: Calculation result $62.84\,N$.
  • Slow Movement Scenario ($x$ changes to $0.25\,cm$): Mechanical energy output based on field energy changes equals $0.314\,Joules$.
• Example 2: Varying Inductor
  • Variable Inductance Formula: $L = \frac{2L_o}{1 + x/x_o}$, where $L_o = 50\,mH$ and $x_o = 0.05\,cm$.
  • Resultant Energy at $x=0.075\,cm$ and $i=3\,A$: $0.18\,Joules$.
  • Energy Change when $x$ increases to $0.15\,cm$ at constant current: $\Delta E_m = 0.0675\,Joules$.
• Example 3: Coupled Coils
  • Given: $L_{11} = \frac{1}{x} + 1$, $L_{22} = \frac{0.5}{x} + 1$, $L_{12} = L_{21} = \frac{1}{x}$.
  • Excitation: $i_1 = 20\,A$, $i_2 = -10\,A$.
  • Mechanical work done from $x=0.5\,cm$ to $x=1.0\,cm$: $-50\,Joules$ (energy dissipated).

DC Machine Construction

• Yoke (Frame): Offers mechanical support for poles and protects the machine from moisture and dust. Materials: Cast iron, cast steel, or rolled steel.
• Poles and Pole Core: Electromagnets energized by field windings to produce magnetic flux. Built with annealed steel laminations to reduce eddy current losses.
• Pole Shoe: Enlarges the pole region to spread flux across the air-gap towards the armature.
• Field Windings: Copper coils wound around the pole core. When energized, they generate the required magnetic flux.
• Armature Core: Contains slots for armature conductors and provides a low-reluctance path for flux. Laminated to decrease eddy current losses.
• Armature Winding: Conductors (copper) interconnected. Voltage is induced here when turned by a prime mover.
• Commutator: Collects current from armature conductors and supplies it to the load via brushes. It ensures uni-directional torque in motors. Made of hard-drawn copper segments insulated with thin mica layers.
• Brushes: Graphite or carbon blocks that collect current from the commutator. They wear over time and require frequent inspection.

Types of DC Machines and EMF Equation

• Separately Excited: Field coils activated by a separate DC source.
• Self-Excited: Current for field winding is supplied by the machine itself. Includes Shunt, Series, and Compound wound types.
• Shunt Wound: Field coils parallel to the armature; made of many turns of fine wire.
• Series Wound: Field coils in series with the armature; made of few turns of thick wire.
• Compound Wound: Includes both series and shunt fields within every pole.
  • Short Shunt: Shunt field parallel only to the armature.
  • Long Shunt: Shunt field parallel to both the armature and series field.
• EMF Equation:
  • Let \text{\Phi} = flux per pole, $P$ = number of poles, $Z$ = total armature conductors, $n$ = speed (rev/sec), $A$ = number of parallel paths.
  • Generated Voltage: E = n \times P \times \text{\Phi} \times \frac{Z}{A}

Losses in DC Machines

• Electrical/Copper Losses: Losses in windings due to resistance.
• Core/Iron Losses: Losses within the magnetic core material.
• Mechanical Losses: Friction and windage associated with moving parts.
• Brush Losses: Power loss across the brush contacts.
• Stray Load Losses: Miscellaneous losses from flux distortion and eddy currents.