EE462-Utilization of Electtrical Energy

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# EE-462 UTILIZATION OF ELECTRICAL ENERGY

# DC Motors

## Ozan Keysan

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

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

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# Operation Principle of DC Motors
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#Lorenz Force

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

![](http://upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Regla_mano_derecha_Laplace.svg/400px-Regla_mano_derecha_Laplace.svg.png)

#### [Magnetic Force and Relativity](http://www.youtube.com/watch?v=1TKSfAkWWN0)
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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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# How can you increase the torque of a DC Machine?

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# Ways to increase torque in a DC Motor?
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- ## Increase Field Density (More Magnet, or less reluctance)
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- ## More Current (Limited by cooling)
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- ## Increase the length (force increases)
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- ## Increase the radius (torque increases)
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# DC Machine Parts

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

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# \\(E\_a = K\_a \omega\_m \Phi\_{pp}\\)
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- ### \\(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
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## Motor Action: Electrical Energy is converted to Mechanical Energy

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

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## 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

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# \\(E\_a = K\_a \omega\_m \Phi\_{pp}\\)
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- ### \\(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
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## If \\(E\_a > V\_a\\) generating action
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# Losses in the Machine
<img src="http://cnx.org/resources/1a0fc7a424e633c62ac4fb3e20d75ceb/graphics1.png" alt="Drawing" style="width: 600px;"/>

## Copper Loss = Armature Loss + Field Loss
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## \\(P\_{copper} = I\_a^2 R\_a + I\_f^2 R\_f \\)
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# Electromechanical Power
<img src="http://cnx.org/resources/1a0fc7a424e633c62ac4fb3e20d75ceb/graphics1.png" alt="Drawing" style="width: 600px;"/>

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

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# Electromechanical Power
<img src="http://cnx.org/resources/1a0fc7a424e633c62ac4fb3e20d75ceb/graphics1.png" alt="Drawing" style="width: 300px;"/>

## 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} = \\)
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\\( T \omega = E\_a I\_a   \\)
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## \\( T \omega = K\_a \omega \Phi\_{pp} I\_a \\)
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## \\(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?
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## Rotor speed is zero: \\(\omega =0 \\)

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

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## Armature Current: \\(I\_a = (V\_t -E\_a)/R\_a\\)
## Maximum Torque at Startup
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# Maximum Torque at Startup
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## Result: Never attempt a drag race with an electric car.

- [White zombie drag race](https://youtu.be/vGQSQAz9v6c?t=5s)
- [White zombie](https://www.youtube.com/watch?v=zLjnRj2Dhwk)
- [White zombie inside](https://youtu.be/OfbPf3WExwU?t=1m25s)

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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 \\)

### [How to read a datasheet](http://www.maxonmotor.com/maxon/view/category/motor?target=filter&filterCategory=DC-max)

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# DC Machine Types
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## Everthing is same just different ways of connecting the field winding!
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<img src="images/dc_machine_types.jpg" alt="Drawing" style="width: 800px;"/>

### As a result \\(\Phi\_{pole} \\) is not constant but a function of field current.

### For more information [EE361 Notes](http://keysan.me/ee361)
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# Separately Excited DC Machines

### Field is excited with a separate source
### Flexible Control (Field Current controls \\(\phi\_{pp}\\))

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# Magnetization Characteristics
## What is the relation between \\(I_f\\) and \\(E_a\\)?
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![](http://www.electrical4u.com/wp-content/uploads/2013/10/magnetic-curve-of-dc-generator-25.10.13.png)

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#Magnetization Characteristics
### In the Linear Region

## \\(\phi = K_f I_f\\)
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### Induced Voltage
## \\(E_a = K_a \omega_m \phi = K_a \omega_m K_f  I_f\\)
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### Torque
## \\(T = K_a K_f I_a I_f\\)
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# Separately Excited DC Machines

## \\(\omega_m  = \dfrac{V_t}{K_a \Phi} - \dfrac{R_a}{(K_a \Phi)^2}T \\)

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# Series Wound DC Machine

## Field winding in series with armature

## Field current = Armature Current  ==> \\(I_f = I_a\\)
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# Series Wound DC Machine

## What happens if AC is applied to series DC motor?
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# Universal Motor

## Series DC motors work both with DC and AC

## [Universal Motor](https://www.youtube.com/watch?v=0PDRJKz-mqE)

[More Information](https://en.wikipedia.org/wiki/Universal_motor)
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# Series Wound DC Motor

### \\(V\_t = E_a + (R\_a + R\_f) I_a\\)
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### \\(E_a = K_a \omega_m \phi \\) ==> \\(\phi = K_s I_a\\)
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### \\(T_e = K_a \phi I_a = K_a K_s I_a^2\\)

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# Series DC Motor

## Never run a series DC motor at no load!

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# Series DC Motor

## Torque increases with the square of the armature current
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# Series DC Motor

### High starting torque
### Applications: Traction motors,cranes, [example1](http://www.cgglobal.com/frontend/ProductDetail.aspx?id=j7Cu6ITnQ60=),[example2](http://www.kirloskar-electric.com/products/traction/dc-traction-motor-ktm-15250.html#),[example3](http://www.tulomsas.com.tr/en/main.php?kid=198&rid=103)
### At no load speed increases dangerously

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## Speed Control of DC Motors
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- ## Armature Voltage Control (\\(V_t\\))
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- ## Field Current Control (\\(I_f\\)) (and hence flux)
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- ## Vary Both

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# Armature Voltage Control

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- ## Speed Control over a wide range
- ## Commonly used

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# Armature Voltage Control

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# Field Current Control

- ## An external resistor or variable voltage supply
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- ## Usually used to achieve higher speeds -->
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Decrease \\(I_f\\) (Flux weakening)
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- ## Speed control over a narrow range
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# Field Current Control

<img src="http://www.electrical4u.com/electrical/wp-content/uploads/2013/04/Field-Flux-Control-of-DC-Motor-9-3-15.gif" alt="Drawing" style="width: 800px;"/>
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# Field Current Control
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### Which one is larger \\(L_a\\) or \\(L_f\\)?
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### Field current is easier to control due to low current values, but has a much higher electrical time constant -> sluggish response

### \\(\tau_a = 50ms \quad\quad \tau_f = 1s\\)
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## Armature-Field Current Control

### Armature Voltage Control region is also known as Constant Torque region
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### Field Current Control region is also known as Field Weakening or Constant Power region.
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## Armature-Field Current Control

<img src="http://www.electrical4u.com/electrical/wp-content/uploads/2013/04/torque-power-characteristic-9-3-15.gif" alt="Drawing" style="width: 500px;"/>
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## Armature-Field Current Control

### For standard motors: \\(\omega\_{max} \approx 1.15 \omega\_{base}\\)
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### For special motors: \\(\omega\_{max} \approx 1.7 \omega\_{base}\\)

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## Overloading Capability

### It is possible to achieve higher drive performance by exploiting overloading capacity

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## Permanent Magnet DC Motors

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## You can download this presentation from: [keysan.me/ee462](http://keysan.me/ee462)