EE361-Electromechanical Energy Conversion

class: center, middle

# EE-361 ELECTROMECHANICAL ENERGY CONVERSION

## Ozan Keysan

[keysan.me](http://keysan.me)

Office: C-113 <span class="meta">•</span> Tel: 210 7586
---
# Review

## Magnetic circuits are analogous to electric circuits:

<img src="magnetic_electric_circuit.png" alt="Drawing" style="width: 800px;"/>
---
# Ampere's Law

### \$\oint_C {\vec{H}.d\vec{\ell}} = \sum I_n = NI \$

### Integral of H around a closed contour C is equal to the net current passing through the path.

### Remember the right hand rule!
---
# Ampere's Law

## Magneto-Motive Force (\$\mathcal{F}\$)

## \$ \mathcal{F} = NI \$
--

## Electric Circuits: \$\quad \quad V=IR\$

## Magnetic Circuits: \$ \quad \quad \mathcal{F} = \Phi \mathcal{R} \$
---
# Assumptions we make in this courses

--
### - All flux contained in magnetic circuit (no leakage)
--

### - Uniform flux distribution in the core
--

### - Flux travels straight in airgaps (no fringing)
--

### - In some cases infinite permeability is assumed

---
# Exercise

## With the same dimensions of the previous example:
--

## Assume Nt=5, I=10 A

## Find B and H in the core.

---
## What happens if you double the current?
--

## \$ \mathcal{F} = NI \$
--

## Current is doubled --> MMF is doubled
--

## \$ \mathcal{F} = \Phi \mathcal{R} \$
--

### [Breaking Bad - Magnets](https://youtu.be/J0IqVC8mTwk?t=47s)

---

# Linearity vs. Non-linearity
--

## $$\vec{B} = \mu \vec{H} $$
--

# Linear B-H Characteristics

- ## Air

---
# B-H Curve of Air/Vacuum (Linear)
--

<img src="http://www.coolmagnetman.com/images/magfund071.gif" alt="Drawing" style="width: 400px;"/>
--

- ## Slope gives permeability (\$\mu = \frac{B}{H}\$)
--

- ## Constant Slope = Linear Material

---
## Non-Linear B-H Characteristics

- ### Iron, Cast-Steel ...
- ### B limit => Saturation
--

---

# Faraday's Law of Induction
--

### \$\nabla \times \vec{E}  = - \dfrac{\partial \vec{B}}{\partial t}\$

### which equals to:

--
### $$\oint_C \vec{E} dl  = - \dfrac{d\Phi}{dt} = -\dfrac{d}{dt}\iint \vec{B} dA$$

### !! The most important equation for EE362

---
# Faraday's Law of Induction

### Induced Voltage in a Coil

## $$ e= \oint \vec{E} dl = -\dfrac{d \Phi}{dt}$$

## $$ e = -\dfrac{d \Phi}{dt} = -\dfrac{d}{dt}\int \vec{B} dA$$
---
# Ways to generate voltage in a coil
--

- ## Time variation of flux (e.g. AC excitation)
--

- ## Due to conductor movement in a stationary field
--

- ## Rotation (e.g. motors)
--

- ## Deformation of coil (Area changes)

---
# Faraday's Law of Induction

## Total voltage in a coil with N turns
## \$V_{coil} = N\dfrac{d \Phi}{dt} = \dfrac{d \lambda}{dt}\$
---

# Flux Linkage
--

### \$\lambda\$ : Flux Linkage
### \$\Phi\$ : Flux (per turn)

### \$\lambda = N_{turns} \Phi \$ (turn. Weber)

<img src="http://img.tfd.com/mgh/cep/thumb/B-magnetic-flux-field-of-a-short-coil.jpg" alt="Drawing" style="width: 300px;"/>
---
# Kircchoff's Voltage Law

---
# Kircchoff's Voltage Law Out!
# Faraday's Law In!

#### For more, watch: [Walter Lewin-part1](https://www.youtube.com/watch?v=eqjl-qRy71w), [part2](https://www.youtube.com/watch?v=1bUWcy8HwpM)

---
<!--
## Relation between Magnetic and Electric Circuits

# \$ L = \dfrac{d \lambda}{d I}\$

## Relation between Magnetic and Electric Circuits

## What happens if you double the number of turns?

## Inductance increases with \$N^2\$

# Inductance

## Inductance is the flux linkage created per ampere

## \$ L =  N \dfrac{d \Phi}{dI}= \dfrac{d \lambda}{d I}\$

## \$ L =  \dfrac{N^2}{R}\$
-->

## You can download this presentation from: [keysan.me/ee361](http://keysan.me/ee361)