EE361-Electromechanical Energy Conversion

class: center, middle

# EE-361
# Magnetic Stress
# Rotational Motion

## Ozan Keysan

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

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

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# Example:
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# Magnetic Stress (or Pressure)
## Independent of Area

##\\(P=\dfrac{\mu_0 H^2}{2} = \dfrac{B^2}{2\mu_0}\\)
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## Stress x Area = Force
##\\(F=\dfrac{1}{2}A\mu_0 H^2 = \dfrac{B^2}{2\mu_0} A \\)
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#Magnets
### Why some magnets have backplates?
<img src="http://upload.wikimedia.org/wikipedia/commons/4/4d/Neodymag.jpg" alt="Drawing" style="width: 400px;"/>

- [Why magnets attract?](http://www.youtube.com/watch?v=uTcuDprmues)

- Why magnets repel?
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## Mechanical Power & Energy:
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## Linear Motion: 
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\\(P = F v = F \dfrac{dx}{dt}\\) Watt
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## Rotational:
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\\(P=T \omega = T \dfrac{d\theta}{dt} \\) Watt
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## Linear Motion: \\(W = \int P dt = F x \\) Joule
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## Rotational: \\(W=  \int P dt = T \theta \\) Joule
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## Linear Acceleration: 
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## \\(F = m a = m \dfrac{dv}{dt}\\)
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## Rotational Acceleration:
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## \\(T=J \dfrac{d\omega}{dt} \\) Watt

## J: Rotational Inertia (\\(kgm^2\\))
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# What would happen in this circuit?

<img src="https://raw.githubusercontent.com/ozank/ozank.github.io/master/presentations/images/single_phase_reluctance_motor.png" alt="Drawing" style="width: 700px;"/>
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# Can you guess the torque expression?

<img src="https://raw.githubusercontent.com/ozank/ozank.github.io/master/presentations/images/single_phase_reluctance_motor.png" alt="Drawing" style="width: 700px;"/>
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# Rotational Sytems:
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## Remember in linear systems:

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

### or  alternatively use Co-energy:

### \\(f = \dfrac{\partial W'\_{mag}(\mathcal{F}, x)}{\partial x} |\_{\mathcal{F} = constant}\\)

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# Rotational Sytems:

## Take the derivative wrt \\( \theta \\) not \\( x \\):
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### \\(T = - \dfrac{\partial W\_{mag}(\Phi, \theta)}{\partial \theta} |\_{\Phi = constant}\\)

### or  alternatively

### \\(f = \dfrac{\partial W'\_{mag}(\mathcal{F}, \theta)}{\partial \theta} |\_{\mathcal{F} = constant}\\)

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

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

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# How can we achieve a constant rotation?
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## Single Phase Reluctance Motor
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[Magnetorquer](https://blog.satsearch.co/2019-08-21-magnetorquers-an-overview-of-magnetic-torquer-products-available-on-the-global-marketplace-for-space.html)
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# Single Phase Reluctance Motor
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### [Magnetic Flux](https://www.youtube.com/watch?v=hDJnLt7cBTY),  [Micro-stepping for higher accuracy](https://www.youtube.com/watch?v=eyqwLiowZiU)

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# Reluctance Motors

### [More info](http://electrical-engineering-portal.com/characteristics-and-work-principles-of-switched-reluctance-sr-motor)
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# Reluctance Motors

### [ABB High efficiency reluctance motors](https://new.abb.com/news/detail/71053/abb-ie5-synrm-motors-are-awarded-efficient-solution-label)

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# Who is this guy?

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# James Dyson

### [Digital Motor](https://www.youtube.com/watch?v=_YDArV2M5EU), [Digital Motor 2](https://www.youtube.com/watch?v=-zg593Zw6PQ), [Manufacturing](https://www.youtube.com/watch?v=ttjKjnthDuY)

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# Dyson uses Reluctance Motors

### [Digital Motor](https://www.youtube.com/watch?v=_YDArV2M5EU), [Digital Motor 2](https://www.youtube.com/watch?v=-zg593Zw6PQ), [Manufacturing](https://www.youtube.com/watch?v=ttjKjnthDuY)

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# Reluctance Motor Example:

## Calculate the torque expression
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###  with constant current.
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### with sinusoidal current
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### [Torque Graphs](https://docs.google.com/spreadsheets/d/1MDdJiaDq6uIzYzGMhTugNqbFBcJJClO-m_LqdGe1ZQ4/edit?usp=sharing)

### [Solutions](https://github.com/ozank/ozank.github.io/raw/master/files/ee361_emec_reluctance_motor_example.pdf)

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# Summary

## Magnetic Circuit Tries
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- ### 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\\).

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