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

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# Lorenz Force

## \\(\vec{F} = q (\vec{E} + \vec{v} \times \vec{B})\\)
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### In a purely magnetic system (no electric field) :
## \\(\vec{F} = q \vec{v} \times \vec{B}\\)
--

### or alternatively force density (\\(N/m^3\\))):
## \\(\vec{f} = \rho \vec{v} \times \vec{B} = \vec{J} \times \vec{B}\\)

#### \\( \rho \\): Charge density (C/m3) , \\( \vec{v} \\): velocity

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#Lorenz Force

## \\(\vec{F} = \vec{J} \times \vec{B}\\)

![](http://sharkphysics.weebly.com/uploads/8/5/9/5/8595301/265734720.png?452)
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# Lorenz Force Applications

- ### [Force Demo](http://www.youtube.com/watch?v=K9ks_DNPAFQ)
- ### [Homopolar Motor](http://www.youtube.com/watch?v=kJKuNcgbW-o)
- ### [Wolrd's Simplest Electric Train](https://www.youtube.com/watch?v=J9b0J29OzAU)

- ### [Electromagnetic Aircraft Launcher](https://www.youtube.com/watch?v=T1Icd3MFmWc)
- ### [Navy Railgun](https://www.youtube.com/watch?v=NmFeRYPNP88), [Railgun-2](https://www.youtube.com/watch?v=_VvXXtT3HoU)
- ### [Aselsan Tufan](https://www.youtube.com/watch?v=O5GtuQk3t44)
- ### [Aselsan Tufan-2](https://www.youtube.com/watch?v=MxloiA5mSSk)

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# Determine the direction of rotation

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#What would happen in the device below?

<img src="./images/emec_double_relay.png" alt="Drawing" style="width: 800px;"/>
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#What would happen in the device below?

<img src="https://m.media-amazon.com/images/I/61F-Pso5wvL._AC_SL1001_.jpg" alt="Drawing" style="width: 550px;"/>
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# Basics

- ## Forces and Torque
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- ## Energy Balance
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- ## Stored Energy (Magnetic and Mechanical)
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- ## Losses
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# Losses

- ## Electric Losses (Ohmic Losses)
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- ## Magnetic Losses (Hysteresis Loss)
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- ## Mechanical Losses (Friction etc)

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# Lossless System

### Electric Energy Input = Stored Magnetic Energy + Mechanical Work

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# Energy Balance

![](./images/emec_horizontal.png)
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# Energy Balance

### Ignore resistive and friction losses
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### \\(\Delta W\_{electrical} = \Delta W\_{magnetic} + \Delta W\_{mechanical}\\)
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### \\( Vi\, \mathrm{d}t = i \, \mathrm{d}\lambda = \Delta W\_{magnetic} +  f_{mech} \, \mathrm{d}x\\)

### or
--

## \\( \Delta W\_{magnetic} =  i \, \mathrm{d}\lambda -  f_{mech} \, \mathrm{d}x\\)

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# Energy Balance
## Same can be obtained from the power relations

## \\( \dfrac{\partial W\_{magnetic}}{\partial t}  =  V.i - f_{mech} \dfrac{\partial x}{\partial t} \\)
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## \\( \dfrac{\partial W\_{magnetic}}{\partial t}  =  i \dfrac{\partial \lambda}{\partial t} - f_{mech} \dfrac{\partial x}{\partial t} \\)

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# Review: Magnetic Energy
![](http://upload.wikimedia.org/wikipedia/commons/thumb/1/12/Coenergy.svg/640px-Coenergy.svg.png)
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# Review: Magnetic Energy

## \\(W\_{stored} = \int_0^\lambda i(\lambda) d\lambda \\)
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## or from B-H curve

## \\(W\_{stored} = \int \_{volume } (\int_0^B H dB) \\)
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# Magnetic Energy

### In Linear Systems:
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## Magnetic Energy = Magnetic Co-Energy
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## Magnetic Energy + Magnetic Co-Energy = \\(\lambda i\\)
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### Thus (only in linear systems)
## W(magnetic) = \\(\dfrac{1}{2} \lambda i = \dfrac{1}{2} L i^2 =\dfrac{1}{2L} \lambda^2 \\)

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# Singly-Excited Electromechanical System

<img src="./images/emec_relay.png" alt="Drawing" style="width: 800px;"/>
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# Example:

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# Example:

### Find magnetic stored energy as a function of x. (I=10 A)

<img src="./images/emec_ex2.png" alt="Drawing" style="width: 800px;"/>
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# Example Cont:

### Find magnetic stored energy if N=1000, g=2mm, d=15cm, l=10cm

<img src="./images/emec_ex2.png" alt="Drawing" style="width: 800px;"/>
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# Force from the Stored Energy

## Derivative of Energy w.r.t. position gives the force!
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# Force from Stored Energy
## \\(W\_{magnetic} = i d\lambda - f dx\\)
### Take derivative
--

### Some useful reading:

- #### [MIT From Lasers to Motors](http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-007-electromagnetic-energy-from-motors-to-lasers-spring-2011/readings/MIT6_007S11_forces.pdf)

- #### [Fitzgerald-Electromechanical Energy Conversion](https://feevuted.edu.vn/wp-content/uploads/2018/02/Fitzgerald-2002-Electric-Machinery_Cambrige.pdf)

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# Force from Stored Energy
### \\(Force = - \dfrac{\partial W\_{mag}(\lambda, x)}{\partial x} |\_{\lambda = constant}\\)

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## For Linear Systems
### \\(Force = - \dfrac{\partial}{\partial x} (\dfrac{\lambda^2}{2 L(x)}) =\dfrac{ \lambda^2}{2 L(x)^2} (\dfrac{d L(x)}{dx}) \\)
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### \\(Force = \dfrac{i^2}{2} \dfrac{d L(x)}{dx} \\)
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# Example: Previous Example

### Derive the force as a function of position

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# Example: [Junkyard Magnet](https://www.youtube.com/watch?v=XBWy9gzGGd4)
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### Derive the force:

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# Virtual Work Method

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## When \\(\Phi\\) is constant:

### \\(Force = - \dfrac{\partial W\_{mag}(\Phi, x)}{\partial x} |\_{\Phi = constant}\\)

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# Virtual Work Method
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## Use Co-energy (\\(W\_{mag}'\\)) instead of Magnetic Energy

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## When MMF (\\(NI\\)) is constant:

### \\(Force = \dfrac{\partial W'\_{mag}(\mathrm{F}, x)}{\partial x} |\_{\mathrm{F} = constant}\\)
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# Some Applications
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## How a speaker works?

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## Speaker is just a solenoid

<img src="https://animagraffs.com/wp-content/uploads/loudspeaker/magnet.gif" alt="Drawing" style="width: 500px;"/>
## [How Speakers Work](http://animagraffs.com/loudspeaker/)

#### ([Reading assignment](http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-007-electromagnetic-energy-from-motors-to-lasers-spring-2011/lecture-notes/MIT6_007S11_lec13.pdf))
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# Who is this guy?

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# [Amar Bose](http://www.rle.mit.edu/bose/)

### Founder of Bose Corp, MIT Professor, Electrical Engineering

### [How Amar Bose used research to build better speakers](https://www.cnbc.com/2016/03/24/how-amar-bose-used-research-to-build-better-speakers.html)

### Now MIT owns the [majority shares](http://archive.boston.com/business/technology/articles/2011/04/30/mit_is_new_majority_owner_of_bose/) in Bose Corp. 
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# Magnetism in Medicine:
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# [Malaria](https://www.youtube.com/watch?v=A2-XTlHBf_4)

<img src="http://3.bp.blogspot.com/-gUOAxhCXjP0/UAfo1I4Y1uI/AAAAAAAAHGo/tO885WRQXrc/s1600/Malaria+Disease2.jpg" alt="Drawing" style="width: 300px;"/>
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# Malaria vs Permeability
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## Diagnosis using Magnetic Alignment

### [Magnets diagnose malaria in minutes](http://news.mit.edu/2014/new-method-diagnose-malaria-0831)
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# Malaria vs Permeability

## Diagnosis using Magnetic Alignment

### [Physicists detect malaria using light and magnets](http://physicsworld.com/cws/article/news/2012/oct/30/physicists-detect-malaria-using-light-and-magnets)
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# Malaria Treatment

### [Malaria's Magnetic Properties May Pull Treatments Forward](http://www.cmu.edu/news/stories/archives/2016/june/malaria-magnetic-treatment.html)

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# Rail Gun Example:

###[Mini Coil Gun](http://www.youtube.com/watch?v=lIEgg7d8ZsU), [Large Rail Gun](http://www.youtube.com/watch?v=wa_vuX5_oAk), [Part-2](http://www.youtube.com/watch?v=rAwvnXYH488), [How it works](http://www.youtube.com/watch?v=PQNHsS-BNs4)

### [Reading assignment](http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-007-electromagnetic-energy-from-motors-to-lasers-spring-2011/lecture-notes/MIT6_007S11_lec14.pdf)

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# Summary

## Magnetic Circuit Tries
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- ## To reduce \\(W\_{magnetic}\\) if \\(\Phi\\) is constant
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- ## To maximize the inductance
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- ## To minimize the reluctance (\\(L=N^2/R\\))

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