EE361-Electromechanical Energy Conversion

class: center, middle

# EE-361
# DC Machines

## Ozan Keysan

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

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

---
## Review

## Electromagnetic systems try to increase inductance (and reduce reluctance)

## \\(T \propto \dfrac{d \mathrm{L}}{d \theta} \\)

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## Review

## For multiply excited systems consider the total inductance : (Self + Mutual)

## \\(T \propto \dfrac{d \mathrm{L}}{d \theta} + \dfrac{d \mathrm{M}}{d \theta} \\)
--

### \\(T\_{mech}= \dfrac{1}{2} \dfrac{dL\_{11}}{d\theta}i\_1^2 + \dfrac{1}{2} \dfrac{dL\_{22}}{d\theta}i\_2^2\\)
### \\(\quad\quad\quad + \dfrac{dM}{d\theta} i\_1 i\_2\\)

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## Coupled mechanical and electrical systems

### \\(V_o = Ri + L \dfrac{di}{dt}\\)

### \\(T\_{elec} =  \dfrac{\partial W'\_{mag}}{\partial \theta} \\)

### \\(f\_{mech} = K (x-x_0) + B \dfrac{dx}{dt} + M \dfrac{d^2x}{d^2t}  \\)

#### [Flywheels for satellite orientation](http://www.youtube.com/watch?v=n_6p-1J551Y)
---

#Introduction to Electric Machines
--

## Generators = Motors

## No difference between a [DC motor and generator](http://www.youtube.com/watch?v=6kgzrXFSDwA)

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#Introduction to Electric Machines
<img src="./images/ee361/enercon.jpeg" alt="Drawing" style="width: 400px;"/>
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# Types of Electric Motors
![](http://www.electrical4u.com/electrical-motor/images/electrical-motor.gif)
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# DC Machines

## Design a DC motor

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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)

#### [Relation between Magnetic Force and Relativity](http://www.youtube.com/watch?v=1TKSfAkWWN0)
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# Lorenz Force in Macroscopic Scale

## Force in a conductor 
## \\(F\_{total} = \int\_{vol} \vec{J} \times \vec{B}\\)
--

### If J and B are orthogonal and homogeneous:
## \\(F\_{total} = (J.Area)\;B.\;length \\)
## \\(F\_{total} = I\;B\;l \\)

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# DC Motor Animation
<img src="./images/ee361/dc_motor.gif" alt="Drawing" style="width: 800px;"/>

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# DC Motor Parts

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#DC Machine Parts
- ## Armature
- ## Field
- ## Commutator (Brushes)
- ## Rotor
- ## Stator
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# DC Machine Parts

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# Electric Commutator
![](http://1.bp.blogspot.com/-13XK9MkbZHA/T6_omiWJm7I/AAAAAAAAB_c/A6GBqsp2700/s640/COMMUTATOR+EXAMPLE.JPG)

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# DC Machine Working Principle
<img src="http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/imgmag/dcmop.gif" alt="Drawing" style="width: 550px;"/>

### [How DC motors work?](http://www.youtube.com/watch?v=LAtPHANEfQo)
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# Induced Voltage in a Rotating Coil 
## (i.e. Generator Mode)

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# How can you calculate maximum flux \\(\Phi_{max} \\)?

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# Induced Voltage in a Rotating Coil

# \\(\Phi_{max} = 2 \hat{B} r L\\)
--

### When the coil is rotating with \\(\omega_r\\)
 
# \\(\Phi(t) = \Phi_{max} cos(\omega t)\\)

### \\(V\_{coil}= -N \dfrac{d\Phi}{dt}=N \omega \Phi_{max} sin(\omega t)\\)

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<!--
## You can have more than 2 poles in a machine

## A) 2-pole (or 1-pole-pair), B) 4-pole (or 2-pole-pairs)

# Flux per-pole & Induced Voltage

## \\(B\_{av} =  \dfrac{2}{\pi} \hat{B}\\)

## \\(A\_{pole} =  \dfrac{2 \pi r L }{p}\\)  (p: pole number)

## \\(\Phi\_{pole} = B\_{av}A\_{pole}= \dfrac{4 \hat{B} r L }{p}\\)

-->

# Induced Voltage Waveform
--

## For single coil with commutator (brushes)

## Mechanical brushes works as a diode rectifier

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# Induced Voltage Waveform
--

## In a two pole machine:
--

## \\(E\_{av} =  \dfrac{2}{\pi} E\_{max}\\)

## \\(E\_{av} =  \dfrac{2}{\pi} N \omega \Phi\_{max}\\)

---

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# How can you increase the torque of a DC Machine?

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# Ways to increase torque in a DC Motor?
--

- ## Increase Field Density (More Magnet, or less reluctance)
--

- ## More Current (Limited by cooling)
--

- ## Increase the length (force increases)
--

- ## Increase the radius (torque increases)
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# Torque in a DC Motor

## Q: Can you plot the torque waveform?

## Q: How can you smooth the torque output?

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# Torque in a DC Motor

## Q: How can you smooth the torque output?
--

### [How DC motors work?](https://youtu.be/LAtPHANEfQo?t=1m20s)

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# Model of DC Motors

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#Simplest Equivalent Circuit of a DC Machine

## A voltage source (proportional to speed) connected in series with a resistance (Armature resistance)
--

### Under constant flux (as in permanent magnet DC machine)
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# Induced Voltage in Armature

--
# \\(E\_a = K\_a \omega\_m \Phi\_{pp}\\)
--

- ### \\(E\_a\\): Induced armature voltage
- ### \\(K\_a\\): Armature Constant
- ### \\(\omega\_m\\): Mechanical Speed (rad/s)
- ### \\(\Phi\_{pp}\\): Flux per-pole

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# DC Machines
--

## Motor Action: Electrical Energy is converted to Mechanical Energy

--
## Generator Action: Mechancial Energy is converted to Electrical Energy

--
## No difference between a [DC motor and generator](http://www.youtube.com/watch?v=6kgzrXFSDwA)
## Just a mode of operating point

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# Induced Voltage in Armature

--
# \\(E\_a = K\_a \omega\_m \Phi\_{pp}\\)
--

- ### \\(E\_a\\): Induced armature voltage
- ### \\(K\_a\\): Armature Constant
- ### \\(\omega\_m\\): Mechanical Speed (rad/s)
- ### \\(\Phi\_{pp}\\): Flux per-pole

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# Equivalent Circuit of a DC Motor

## When the flux is generated by another coil (Field Winding)
--

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# Equivalent Circuit of a DC Motor

## If \\(V\_a > E\_a\\) motoring action
--

## If \\(E\_a > V\_a\\) generating action
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# Losses in the Machine
<img src="./images/ee361/dc_motor1.png" alt="Drawing" style="width: 600px;"/>

## Copper Loss = Armature Loss + Field Loss
--

## \\(P\_{copper} = I\_a^2 R\_a + I\_f^2 R\_f \\)
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# Electromechanical Power
<img src="./images/ee361/dc_motor1.png" alt="Drawing" style="width: 600px;"/>

### Electromechanical Power = Armature Power - Armature Losses
--

## \\(P\_{e} = V\_a I\_a - I\_a R\_a = E\_a I\_a  \\)

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# Electromechanical Power
<img src="./images/ee361/dc_motor1.png" alt="Drawing" style="width: 400px;"/>

## Electromechanical Power = \\(E\_a I\_a  \\)
### Either converted from electrical energy to mechanical energy (motoring mode)

### or converted from mechanical energy to electrical energy (generating mode)

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# Torque Relations

## \\(P\_{mech} = \\)
--
\\( T \omega = E\_a I\_a   \\)
--

## \\( T \omega = K\_a \omega \Phi\_{pp} I\_a \\)
--

## \\(T =K\_a  \Phi\_{pp} I\_a \\)
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# Torque Proportional to Current

# \\(T =K\_a  \Phi\_{pp} I\_a \\)
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# What happens to DC motor at start-up?
--

## Rotor speed is zero: \\(\omega =0 \\)

### Induced armature voltage:
--
\\(E\_a = K\_a \omega\_m \Phi\_{pp}=0\\)

--
## Armature Current: \\(I\_a = (V\_t -E\_a)/R\_a\\)
--

## Maximum Current and Torque at Startup

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# Maximum Torque at Startup
--

## Result: Never attempt a drag race with an electric car.

- [White zombie drag race](https://youtu.be/FtrpBJbLT9M?t=120)
- [White zombie](https://youtu.be/crfEecV1YFA?t=46)
- [White zombie inside](https://youtu.be/OfbPf3WExwU?t=1m25s)
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# You need to wait until EE362, but

## Electric Cars: [Tesla Model S Induction Motor](https://youtu.be/NaV7V07tEMQ?t=18s)

![](http://www.plugincars.com/sites/default/files/model-s-review-620a.jpg)

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## [Tesla vs Lamborghini LP570-4 Super Trofeo](https://youtu.be/r4CnSS4OG4A?t=34s)
<img src="http://www.dsf.my/wp-content/uploads/2014/03/Lamborghini-BlancpainSuper-Trofeo-Race-Series8.jpg" alt="Drawing" style="width: 360px;"/><img src="http://images.thecarconnection.com/med/2014-tesla-model-s_100436548_m.jpg" alt="Drawing" style="width: 350px;"/>

#### [Tesla Insane Mode](https://youtu.be/LpaLgF1uLB8?t=38s), [Tesla Insane Mode- Slow Motion](https://youtu.be/Y8-S7FghyEA?t=27s)

#### More info: [Tesla Model S 0-100 km in 3.4 seconds](http://www.gizmag.com/tesla-model-p85d-driver-assist/34123/), [Tesla Induction Motor Info](http://my.teslamotors.com/roadster/technology/motor)

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# Summary

- ## Induced Voltage Proportional to Speed
## \\(E\_a = K\_a \omega\_m \Phi\_{pp}\\)
--

- ## Torque Proportional to Armature Current
## \\(T =K\_a  \Phi\_{pp} I\_a \\)

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MT2 questions on transformers
#Exercises

## [EX1](https://raw.githubusercontent.com/ozank/ee361/master/images/mt2_ex1.jpg)
## [EX2](https://raw.githubusercontent.com/ozank/ee361/master/images/mt2_ex2.jpg)
## [EX3](https://raw.githubusercontent.com/ozank/ee361/master/images/mt2_ex3.jpg)
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## You can download this presentation from: [keysan.me/ee361](http://keysan.me/ee361)