EE564-Design of Electrical Machines

class: center, middle

# EE-564 Design of Electrical Machines

## Ozan Keysan

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

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

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# Suitable Airgap
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### There is not a definite answer
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### \\(\delta = 0.2 + 0.01 P^{0.4} \\)mm when p=1
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###  \\(\delta = 0.18 + 0.006 P^{0.4} \\)mm  when p > 1
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### Smallest airgap is 0.2 mm

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# Suitable Airgap

### For heavy duty motors increase the gap by 60 %.
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### For converter driven motors airgap can be increased by 60 % to reduce rotor surface losses.
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### For high speed machines increase airgap (eqn. 6.25 of the textbook)
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### For very large diameter machines airgap is equal to D/1000.

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# Mechanical Constraints

## Tip Speed

### What is the rotational speed of a machine with 0.5m diameter rotor, to reach the tip speed reach to the speed of sound (1 Mach)?
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### Max allowable tip speed: 75m/s for high-strength non-magnetic alloy sleeves, and 100 m/s for carbon-fiber sleeves

Reading: Section 6.1 of textbook
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# Mechanical Loadability
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### Rotor material should withstand centrifugal forces (especially at high speeds).
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## Centrifugal Stress:

## \\(\sigma\_{mech} = C' \rho  r\_r^2 \Omega^2 \\)

### \\(\Omega\\): Mechanical speed in rad/s
### \\(\rho\\): Density of the material
 
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## Centrifugal Stress:

## \\(\sigma\_{mech} = C' \rho  r\_r^2 \Omega^2 \\)
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#### \\(C'= 1\\) for a thin cylinder
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#### \\(C'= (3+v)/8\\) for a smooth homogenous cylinder
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#### \\(C'= (3+v)/4\\) for a cylinder with a small bore
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### \\( v \\): Poisson's ratio
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### [Poisson's ratio](https://www.youtube.com/watch?v=hBnzrBhnzVo), [deflection of a golf ball](https://www.youtube.com/watch?v=aMqM13EUSKw), [deflection of a face, 2:15](https://www.youtube.com/watch?v=On1CsbTwlDs)
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### Poisson Ratios of metals: Aluminium=0.34, Steel=0.29, Copper=0.34

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# Ex. 6.3:

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# Other Mechanical Constraints

### Bending Modes

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# Dynamics of Mechanical Systems: Resonance

### [Transfer function and mathematical modelling](https://www.slideshare.net/vishalgohel12195/transfer-function-and-mathematical-modeling)
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### [Tacoma Bridge](https://www.youtube.com/watch?v=lXyG68_caV4)

### [Forced vibration-1](https://www.youtube.com/watch?v=OaXSmPgl1os), [Resonant Freq.](https://www.youtube.com/watch?v=LV_UuzEznHs)

### [Torsional Resonance](https://www.youtube.com/watch?v=JLY-yQOpL20)
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# Resonant Modes

### [Cantilever Vibration](https://www.youtube.com/watch?v=lKT3wBIUFhA)

### [Resonant Modes](https://www.youtube.com/watch?v=uWoiMMLIvco)

### [Modal Shapes](https://www.youtube.com/watch?v=kvG7OrjBirI)
### [Modal Shapes](https://www.youtube.com/watch?v=d3U_m-4XOtg)

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# Critical Speeds

### The rotational speed should be below the critical speed (preferably with a safety factor)
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### Usually the limiting factor for very high-speed machines:
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# Ex 6.5

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# Aspect Ratio
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## \\(\chi = \dfrac{L'}{D}\\)
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# Typical Aspect Ratios
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## Asynchronous Machines:

## \\(\chi \approx \dfrac{\pi}{2p} \sqrt[3]{p}\\\)
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## Synchronous Machines:

## \\(\chi \approx \dfrac{\pi}{4p} \sqrt{p}\\\)
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# Define \\(D_i\\) and \\(L\\)
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## Usually \\(0.5 < D_i/L < 2.5\\)
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## Small diameter for high-speed or servo-type motors, why?
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### Small inertia,
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### Low tip speed!
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### Bending Modes

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# How to define Outer Diameter \\(D_o\\)?
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# How to define \\(D_o\\)?
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Source: T.Miller - Electric Machine Design Course, Lecture-5, Slide4

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# Typical Flux Density Values

Source: Traditional Design of Electrical Machines, Slide-12
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# Stator Slot Pitch:
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- ## Induction Machines and small PMSMs:  7-45 mm
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- ## Synchronous Machines and large PMSMs:  14-75 mm
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- ## DC Machines:  10-30 mm
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### Tooth thickness can be initially assumed as the half of the slot pitch
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### Slot pitch gets bigger as the power rating of the machine increases

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# Example:

## Define the rough dimensions, and a select suitable stator windings for the 30 kW, 4-pole induction machine.

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# Reading Assignment
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## Ch-7 Introduction summarizes the first steps in machine design

## Ch-7-1 For rotor current calculations

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# Where are we? Rough Design Steps
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# Stator Slot Types:
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<img src="./images/ee564/slot_types.png" alt="Drawing" style="width: 800px;"/>
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- ### Open Slots: Constant width, easy repair and assembly
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- ### Semiclosed Slots: Difficult to assembly but better magnetic characteristics
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- ### Tapered Slots: Varying width (constant tooth width)
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# Production of Electric Machines

### [TES Generators and Motors](https://www.youtube.com/watch?v=5Mu42TzHy8M)

### [Induction Motors: Overhauling a Motor](https://www.youtube.com/watch?v=yPvYd03cKJU)

### [Rewinding a Large Motor](https://www.youtube.com/watch?v=_65mXQ-GNVM)

### [Automatic Coil Insertion](https://www.youtube.com/watch?v=Kih3hyl8CUg)

### [E-propulsion System](https://www.youtube.com/watch?v=d5cEIGDg2Co)

### [BMW i-8](https://youtu.be/w_p8Y1YrrfI?t=1m14s)

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# Selection of number of stator slots
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## Advantages of Low number of slots:

- ### Reduced manufacturing cost
- ### Less space lost due to insulation and slot opening

## Disadvantages of low number of slots

- ### Increased leakage inductance
- ### Reduced breakdown torque
- ### Larger MMF harmonics

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# Selection of number of stator slots

## Advantages of High number of slots:

- ### Reduced tooth pulsation
- ### Higher overload capacity 
- ### Better Cooling
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## Disadvantages of high number of slots

- ### Increased magnetizing current
- ### Poor Cooling
- ### Difficult manufacturing

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## Motor Harmonics

<img src="./images/ee462/torque_pulsations.png" alt="Drawing" style="width:750px;"/>
### Torque Pulsations
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## Crawling Speed

<img src="http://www.eeeguide.com/wp-content/uploads/2016/10/Cogging-and-Crawling-1.jpg" alt="Drawing" style="width:650px;"/>
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### Cogging Torque
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### Why does the rotor is skewed?

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# Acoustic Noise
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: Fan Blades

## Can you guess the frequency of the noise?
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## \\(f= N\_{blades}*f\_{rotor}\\)

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# Number of Slots vs Winding Factor
<img src="./images/fundamental_winding_factors_for_different_slot_numbers.png" alt="Drawing" style="width: 850px;"/>

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# Selection of Number of Slots

## for induction machines
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## \\(Q_s \\) : Stator Slot Number

## \\(Q_r \\) : Rotor Slot Number

## \\(p \\) : Number of pole pairs

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# Selection of Number of Slots
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## It is preferred to have 
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## \\(Q_r \approx 0.8 Q_s \\) for 2,4 poles
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## \\(Q_r \approx 1.2 Q_s \\) for higher poles
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## A minimum of 5-7 rotor bars per pole is preferred.

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# Selection of Number of Slots

## Combinations to avoid
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## Cogging Problem created by slot harmonics
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## \\(Q_s = Q_r \\)
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## \\(Q_s = 2 Q_r \\)
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## \\(Q_s = 0.5 Q_r \\)

### [Ref](https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=5253054)
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## Combinations to avoid
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## Causes slot harmonics 
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## \\(Q_r = Q_s \pm 2 p\\)
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## \\(Q_r = 2 Q_s \pm 2 p\\)
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## \\(Q_r = Q_s \pm p\\)
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## \\(Q_r = 0.5 Q_s \pm p\\)

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## Combinations to avoid
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## Causes mechanical noise and vibrations
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## \\(Q_r =   6 p g  \pm 1\\)

## \\(Q_r =   6 p g  \pm 2p \pm 1\\)

## g: Integer
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# Selection of Number of Slots

## Combinations to avoid

## Cusps in torque speed curve
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## \\(Q_r =  Q_s  \pm p\\)
## \\(Q_r =  Q_s + 5 p\\)

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## Preferred Combinations 
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## In smaller sizes:

## \\(Q_r = Q_s + 4 p \\) with 1 rotor slot skew to reduce cusps and cogging.

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## Common Combinations: \\(Q_s / Q_r\\)

## 2 Pole: 36/28, 48/38, 54/46, 60/52
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## 4 Pole: 48/40, 48/56, 60/44, 60/76, 72/58
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## 6 Pole: 54/42, 54/66, 72/88, 72/54, 72/84
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## 8 Pole: 54/70, 72/58, 72/88
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## 10 Pole: 72/88, 72/92
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## 12 Pole: 72/92

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# Selection of Number of Slots

<img src="./images/slot_combinations.png" alt="Drawing" style="width: 700px;"/>
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# Selection of Number of Slots

<img src="./images/slot_combinations2.png" alt="Drawing" style="width: 600px;"/>
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# Selection of Number of Slots

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# Further Reading

# Selection of Phases - Poles

## T.Miller Electric Machine Design Cource, Lecture 10-12

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## You can download this presentation from: [keysan.me/ee564](http://keysan.me/ee564)