EE362-Electromechanical Energy Conversion-II

class: center, middle

# EE-362

# Review of Electromechanical Energy Conversion

## Ozan Keysan

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

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

---
#Lorenz Force

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

![](http://sharkphysics.weebly.com/uploads/8/5/9/5/8595301/265734720.png?452)
---
# 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=8UKk84wjBw0)
- ### [Aselsan Tufan](https://www.youtube.com/watch?v=O5GtuQk3t44)
- ### [Aselsan Tufan-2](https://www.youtube.com/watch?v=m4jd8K6M92k)

---
# Determine the direction of rotation

---
#What would happen in the device below?

---
# Link Between Electrical and Mechanical Systems

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

---

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

## \\(W\_{stored} = \int_0^\lambda i(\lambda) d\lambda \\)
--

## or from B-H curve

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

### In Linear Systems:
--

## Magnetic Energy = Magnetic Co-Energy
--

## Magnetic Energy + Magnetic Co-Energy = \\(\lambda i\\)
--

### Thus (only in linear systems)
## W(magnetic) = \\(\dfrac{1}{2} \lambda i = \dfrac{1}{2} L i^2 =\dfrac{1}{2L} \lambda^2 \\)

---
# Force from the Stored Energy

## Derivative of Energy w.r.t. position gives the force!
---
# Force from Stored Energy
### Take derivative of magnetic energy
--

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

### 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)

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

--
## 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}) \\)
--

### \\(Force = \dfrac{1}{2} i^2 \dfrac{d L(x)}{dx} \\)

---
# Summary

## Magnetic Circuit Tries
--

- ## To reduce \\(W\_{magnetic}\\) if \\(\Phi\\) is constant
--

- ## To maximize the inductance
--

- ## To minimize the reluctance (\\(L=N^2/R\\))
---
# Some Applications
--

## How a speaker works?

---

## You can think it is just a basic solenoid, but it's more complex than that.

## [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))

---
# Who is this guy?

---
# [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. 
---
# Magnetism in Medicine:
--

# [Malaria](https://www.youtube.com/watch?v=A2-XTlHBf_4)

---
# 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)

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

---
# Malaria Treatment

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

---

# Summary

## Magnetic Circuit Tries

- ## To reduce \\(W\_{magnetic}\\) if \\(\Phi\\) is constant

- ## To maximize the inductance

- ## To minimize the reluctance (\\(L=N^2/R\\))

---

## Mechanical Power & Energy:
--

## Linear Motion: 
--
\\(P = F v = F \dfrac{dx}{dt}\\) Watt
--

## Rotational:
--
\\(P=T \omega = T \dfrac{d\theta}{dt} \\) Watt
--

## Linear Motion: \\(W = \int P dt = F x \\) Joule
--

## Rotational: \\(W=  \int P dt = T \theta \\) Joule
---

## Linear Acceleration: 
--

## \\(F = m a = m \dfrac{dv}{dt}\\)
--

## Rotational Acceleration:
--

## \\(T=J \dfrac{d\omega}{dt} \\) Watt

## J: Rotational Inertia (\\(kgm^2\\))
---

##  Can you guess the torque expression in this circuit?

---
# Rotational Sytems:
--

## Remember in linear systems:

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

### In rotational systems, just take the derivative wrt \\( \theta \\) not \\( x \\):
--

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

#### [More information](http://engineering.nyu.edu/mechatronics/Control_Lab/Criag/Craig_RPI/SenActinMecha/EM_Motion_Fundamentals_2.pdf)

---
# Rotational Sytems:

## Take the derivative wrt \\( \theta \\) not \\( x \\):
--

## \\(T = - \dfrac{1}{2}\Phi^2\dfrac{d R(\theta)}{d \theta} |\_{\Phi = constant}\\)

### or  alternatively

## \\(T = \dfrac{1}{2}I^2\dfrac{d L(\theta)}{d \theta} |\_{i = constant}\\)

---
# How can we achieve a constant rotation?
--

## Reluctance Motors
--

---
# Single Phase Reluctance Motor
--

### [Magnetic Flux](https://www.youtube.com/watch?v=hDJnLt7cBTY),  [Micro-stepping for higher accuracy](https://www.youtube.com/watch?v=eyqwLiowZiU)

---
# Reluctance Motors

### [More info](http://electrical-engineering-portal.com/characteristics-and-work-principles-of-switched-reluctance-sr-motor)
---
## Magnetorquer: How small satellites align themselves?

[Magnetorquer](https://blog.satsearch.co/2019-08-21-magnetorquers-an-overview-of-magnetic-torquer-products-available-on-the-global-marketplace-for-space.html)

[CubeSat Magnetorquer](https://nanoavionics.com/cubesat-components/cubesat-magnetorquer-satbus-mtq/)

---
# Who is this guy?

---
# James Dyson

### [Digital Motor](https://www.youtube.com/watch?v=-zg593Zw6PQ), [Operating Principle](https://www.youtube.com/watch?v=xMtXrIqlGO0), [Manufacturing](https://www.youtube.com/watch?v=bSdbsnEt70c)
---
# Dyson uses Reluctance Motors

### [Digital Motor](https://www.youtube.com/watch?v=-zg593Zw6PQ), [Operating Principle](https://www.youtube.com/watch?v=xMtXrIqlGO0), [Manufacturing](https://www.youtube.com/watch?v=bSdbsnEt70c)

---
# Summary

## Magnetic Circuit Tries
--

- ### To maximize the inductance, to minimize the reluctance (\\(L=N^2/R\\))

- ### To decrease the magnetic energy (increase co-energy)

## Rotational systems are similar to linear systems, but take the derivative of magnetic energy in terms of \\(\theta\\) instead of \\(x\\).

---
## You can download this presentation from: [keysan.me/ee362](http://keysan.me/ee362)