Rotor induction machine for high speed drive applications

ISTANBUL TECHNICAL UNIVERSITY_{F GRADUATE SCHOOL OF SCIENCE} ENGINEERING AND TECHNOLOGY

CONTRIBUTIONS TO REDUCE ROTOR HARMONIC LOSSES IN SOLID ROTOR INDUCTION MACHINE

FOR HIGH SPEED DRIVE APPLICATIONS

Ph.D. THESIS

Mehmet Onur GÜLBAHÇE

Department of Electrical Engineering Electrical Engineering Programme

ISTANBUL TECHNICAL UNIVERSITY_{F GRADUATE SCHOOL OF SCIENCE} ENGINEERING AND TECHNOLOGY

CONTRIBUTIONS TO REDUCE ROTOR HARMONIC LOSSES IN SOLID ROTOR INDUCTION MACHINE

FOR HIGH SPEED DRIVE APPLICATIONS

Ph.D. THESIS

Mehmet Onur GÜLBAHÇE (504122011)

Department of Electrical Engineering Electrical Engineering Programme

Thesis Advisor: Dr. Ö˘gr .Üy. Derya Ahmet KOCABA ¸S

˙ISTANBUL TEKN˙IK ÜN˙IVERS˙ITES˙I F FEN B˙IL˙IMLER˙I ENST˙ITÜSÜ

YÜKSEK HIZLI TAHR˙IK S˙ISTEMLER˙I ˙IÇ˙IN KÜTLESEL ROTORLU ASENKRON MOTORUN ROTOR HARMON˙IK KAYIPLARINI AZALTMAYA YÖNEL˙IK KATKILAR

DOKTORA TEZ˙I Mehmet Onur GÜLBAHÇE

(504122011)

Elektrik Mühendisli˘gi Anabilim Dalı Elektrik Mühendisli˘gi Programı

Tez Danı¸smanı: Dr. Ö˘gr .Üy. Derya Ahmet KOCABA ¸S

Mehmet Onur GÜLBAHÇE, a Ph.D. student of ITU Graduate School of Science En-gineering and Technology 504122011 successfully defended the thesis entitled “CON-TRIBUTIONS TO REDUCE ROTOR HARMONIC LOSSES IN SOLID ROTOR INDUCTION MACHINE FOR HIGH SPEED DRIVE APPLICATIONS”, which he prepared after fulfilling the requirements specified in the associated legislations, before the jury whose signatures are below.

Thesis Advisor : Dr. Ö˘gr .Üy. Derya Ahmet KOCABA ¸S ... Istanbul Technical University

Jury Members : Prof. Dr. Ahmet Faik MERGEN ... Istanbul Technical University

Prof. Dr. Güven KÖMÜRGÖZ KIRI ¸S ... Istanbul Technical University

Prof. Dr. ˙Ibrahim ¸SENOL ... Yıldız Technical University

Prof. Dr. Feriha ERFAN KUYUMCU ... Gedik University

Date of Submission : 8 May 2019 Date of Defense : 18 June 2019

To my spouse Hatice Merve for her boundless love, endless support and encouragement...

FOREWORD

In the name of Allah, Most Gracious, Most Merciful.

First and foremost, I would like to thank God Almighty my creator, my strong pillar, my source of inspiration, wisdom, knowledge and understanding. If he didn’t, I would never wish. Without his blessings, this research study would not have been completed satisfactorily.

This is the study revealed by a human. Everything was revealed by human contains a slight error. Although this thesis has been reviewed repeatedly, there may still be some form and content errors in the thesis. Therefore, I ask forgiveness from God and I apologize to all readers for any possible errors.

I am indepted to many people who helped me for completion of this thesis. In the following, some of them are greatfully acknowledged. I wish to state my gratitude to my advisor Dr. Derya Ahmet Kocaba¸s for his enormous guidance throught the work. He has been there providing his heartfelt support and guidance at all times and has given me invaluable guidance, inspiration and suggestions in my quest for knowledge. Without his able guidance, this thesis would not have been possible and I shall eternally be grateful to him for his assistance.

I also thank the pre-examiners Prof. Dr. Ahmet Faik Mergen from Istanbul Technical University and Prof. Dr. ˙Ibrahim ¸Senol from Yildiz Technical University.

I would like to thanks all jury members separetly. But special thanks to Prof. Dr. Feriha Erfan Kuyumcu from Gedik University and Prof. Dr. Güven Kömürgöz Kırı¸s from Istanbul Technical University for valuable corrections and contributions.

I wish to express my gratitude to Yahya Hamurcu for his valuable strategy. Not only for this research but also for my whole life, he illuminated my way with "Experiential Design Teaching".

I would like to express my gratitude to Prof. Dr. ˙Ibrahim Eksin from Istanbul Technical University for his valuable support, encouragement, life vision and "Big Bang-Big Crunch Algorithm".

Special thanks to R.A. Daniel Tunç Mcguiness, Elec. Eng. Ahmet Hakan O˘guz (M.Sc.) , Elec. Eng. Barı¸s Yıldız, Elec. Eng. Cem Demiro˘glu and Elec. Eng. O˘guz Ka˘gan Kele¸s for their valuable contribution in the thesis.

For the realization of project I also thank to Mech. Eng. Metin Usan from Altınay Robot Teknolojileri A. ¸S., R.A. ˙Ismethan Hanedar and Elec. Eng. Evren Soydan (M.Sc.) from Wat Motor A. ¸S.

This research is supported by Scientific Research Projects Unit of Istanbul Technical University in the framework of "Contributions to Increase in Efficiency in Solid Rotor Induction Motor" with project number 39800. I would like to thank for their support. This research has been carried out at the Department of Electrical Engineering of Istanbul Technical University during the years 2014-2019. During this period, the

help and invaluable guidance of all current and former colleagues of department was gigantic. But I have to mention some personalities, I am deeply greatful to them: R.A. Kubilay Atalay, R.A. Abdullah Polat, R.A. Gökhan Altınta¸s, R.A Handan Nak. Most of all, I am deeply greatful to my wife Hatice Merve and my mothers Necla and Meral and sister Melike for their endless support and encouragement, boundless patience.

June 2019 Mehmet Onur GÜLBAHÇE

TABLE OF CONTENTS Page FOREWORD... x TABLE OF CONTENTS... xi ABBREVIATIONS ... xiii SYMBOLS ... xv

LIST OF TABLES ... xix

LIST OF FIGURES ... xxi

SUMMARY ... xxv ÖZET ...xxvii 1. INTRODUCTION ... 1 1.1 Purpose of Thesis ... 3 1.2 Literature Review ... 5 1.3 Hypothesis ... 8

2. DESIGN AND PERFORMANCE CALCULATION OF CONVEN-TIONAL HIGH SPEED SOLID ROTOR INDUCTION MOTOR... 9

2.1 Determination of Main Dimensions of Rotor... 10

2.2 Losses of SRIM and Cooling Performance ... 14

2.3 Space Harmonics in Solid Rotor Induction Motor ... 18

2.4 Finite Element Modelling of a SRIM ... 26

2.4.1 Rotor end impedances in finite element modelling of a SRIM ... 31

3. DESIGN OF CONVENTIONAL HIGH SPEED SOLID ROTOR INDUCTION MOTOR HAVING DIFFERENT ROTOR TYPES... 33

3.1 Design of Smooth-SRIM ... 33

3.2 Design and Optimisation of High Speed Axially Slitted SRIM (AS-SRIM) . 34 3.2.1 Slit geometry optimisation ... 37

3.2.2 Number of slits optimization ... 45

3.3 Design and Optimisation of High Speed Copper Coated SRIM (CC-SRIM) 49 3.4 Design and Optimisation of High Speed Shielded Axially Slitted Coated SRIM (SAS-SRIM) ... 54

3.4.1 Slit geometry optimisation ... 56

3.4.2 Number of slits optimization ... 59

3.4.3 Coating thickness optimization ... 62

3.5 Performance Comparison of High Speed SRIM Designs ... 63

4. OPTIMISATION IN AIR-GAP HARMONIC FIELD ... 71

4.1 Conventional Winding Analysis ... 71

4.2 Complex Winding Factor of Asymmetrical Stator Windings... 75

4.3 Optimisation Principles ... 78

4.5 Optimisation Results ... 81

5. DESIGN OF THE NOVEL HIGH SPEED SLITTED ROTOR SRIM WITH DECREASED HARMONIC EFFECT... 87

5.1 Basic Design Concepts ... 87

5.2 Principles of Novel Design... 87

5.3 Principles of Slot and Tooth Design ... 88

5.4 Initial Slot and Tooth Design... 90

5.5 Slot and Tooth Optimization... 92

5.6 Winding Design Concepts ... 94

5.7 Yoke Design and Optimization... 94

6. ANAYSIS AND RESULTS OF NOVEL HIGH SPEED SOLID ROTOR INDUCTION MOTOR... 97

7. CONCLUSIONS ... 105

REFERENCES... 109

ABBREVIATIONS

SR : Solid Rotor

SRIM : Solid Rotor Induction Motor CRIM : Caged Rotor Induction Motor

AS-SRIM : Axially Slitted Solid Rotor Induction Motor CC-SRIM : Copper Coated Solid Rotor Induction Motor

SAS-SRIM : Shielded Axially Slitted Solid Rotor Induction Motor FEM : Finite Element Method

SYMBOLS

T : Torque

σts : Tangential stress of electromagnetic rotor surface

L : Length D : Diameter ρ : Mass density ω : Angular speed p_c : Poisson coefficient nc : Critical speed J_in : Modulus of inertia S_A : Cross section k_{sa f e} : Safety factor

D_s : Stator bore diameter

C_mech : Mechanical utilication factor

S : Complex power

J : Current density

k_{ω 1} : Fundamental winding factor Bair−gap : Peak value of air-gap flux density

I : Current

m : Number of phases

N_s : Number of turns per stator phase

τp : Pole pitch

P : Power

η : Efficiency

cosφ : Power factor P_{sha f t} : Shaft power P_out : Output power Pin : Input power

P_Loss : Total loss Ps,Loss : Stator loss

PCu,s : Stator copper loss

P_Fe,s : Stator iron loss P_exc : Excess loss P_δ : Air-gap power

T_em : Electromagnetic torque induced in air-gap Pr,Loss : Total rotor loss

Pf und,r : Fundamental resistive losses of rotor

P_{sur f,r} : Surface losses of rotor P_hyst,r : Hysteresis losses of rotor Pf r,r : Friction loss of rotor

P_J,r : Total joule loss of rotor

V : Volume

s : Slip

n_r : Rotor speed

f_slip : Rotor slip frequency f_s : Stator supply frequency ηf und,r : Rotor fundamental efficiency

P_mech : Mechanical output power

w_r : Mechanical angular speed of the rotor

r : Radius of rotor

kf : Surface roughness coefficient

C_T : Torque coefficient P_f,a : Additional power loss

k2 : Velocity factor

q_m : Mass flow rate of the cooling gas u : Peripheral speed of the rotor P_f,end : Rotor-ends loss

Q_s : Total number of stator slots F_R, FS, FT : MMF of each phases

θ : Winding position

q : Slots per pole per phase

I_R, IS, IT : Effective value of current to the one phase

e : Order of space harmonic n_se : Speed for harmonic order e s_e : Slip of the harmonic

f2e : Frequency of the induced rotor voltage

E : Induced voltage

E₁ : Induced voltage for fundamental component F1 : MMF for fundamental component

φ1 : Magnetic flux for fundamental component

B₁ : Magnetic flux density for fundamental component kw1 : Winding factor for fundamental component

X_m1 : Magnetizing reactance for fundamental component X_r1 : Rotor reactance for fundamental component Ee : Induced voltage for eth harmonic

F_e : MMF for eth harmonic

φe : Magnetic flux for eth harmonic

Be : Magnetic flux density for ethharmonic

k_we : Winding factor for eth harmonic

X_me : Magnetizing reactance for eth harmonic

Xre : Rotor reactance for eth harmonic

H : Magnetic field strength µ : Magnetic permeability σ : Electrical conductivity

¯

H_xe : Tangential magnetic field strength ¯

E_ze : Axial electric field strength ¯

Fe : Harmonic MMF

¯

I_Re0 : Harmonic rotor current ¯

U_Re0 : Harmonic order induced voltage ¯

BRye : Normal magnetic flux density

¯

Z_Re0 : Rotor harmonic impedance ¯

¯

U_2e0 : Induced air-gap voltage of ethharmonic order

¯

Is0 : Stator phase current

¯

P_ind,e0 : Air-gap power of eth harmonic order

T_e : eth harmonic torque component

A : Magnetic vector potential

B : Magnetic field

ν : Magnetic reluctivity ex, ey, ez : Unit vector with direction

R : Resistance of the winding

ψ : Flux linkage

u : Aplied voltage to the stator winding i : Stator phase current

L_end : End-winding inductance

F : Force

W_co : Virtual displacement in the virtual work l_end : Average coil length of the winding ρR : Resistivity of the rotor material

ρR0 : Equivalent resistivity including the end-effect

k_Russell : Russell factor k_{f e} : Stacking factor

R₁, R2, R3 : Resistance of stator winding per phase

L₁, L2, L3 : Inductance of stator winding per phase

τtooth : Tooth pitch

δtooth : Tooth width

δslit : Slit width

δcoat : Coating thickness

d_slit : Slit depth

D_r : Diameter of rotor Ds : Diameter of stator

Q_r : Rotor slit number Q_s : Stator slit number

p : Pole pairs

λ : Slot position

Θ : MMF step value

[z] : Conductor matrix [r] : Slot position matrix

[S] : Complex effective conductor matrix Xc : Centre of mass

N : Number of candidates l : Upper boundry of parameter

r : Normal random number

k : Step of iteration

T HD : Total harmonic distorsion r_slot : Slot end radius

h_slot : Slot depth

LIST OF TABLES

Page Table 2.1 : Obtaining of variable rotor frequency due to space harmonic. ... 21 Table 3.1 : Parameters of CRIM... 34 Table 4.1 : Harmonic winding factors (kwe) and THDs for the best three

solution sets (except triplen harmonics). ... 82 Table 4.2 : Difference between winding factors of conventional and Solution

Set 2. ... 84 Table 4.3 : Information about one phase MMF distribution. ... 84 Table 5.1 : Information about one phase MMF distribution. ... 88 Table 5.2 : Information about one phase MMF distribution. ... 90 Table 5.3 : Initial slot dimensions. ... 92 Table 5.4 : Optimized Slot Dimensions. ... 93 Table 5.5 : Optimized Tooth Dimensions at Tooth Beginning. ... 93 Table 6.1 : Comparison of Losses for novel and conventional motors. ... 101 Table 6.2 : Comparison of material weights for novel and conventional motors.. 101 Table 6.3 : Comparison of operational parameters for novel and conventional

LIST OF FIGURES

Page Figure 1.1 : Most common rotor types for SRIM: a)Smooth SR, b)Smooth SR

with end rings, c) Slitted SR and d) Coated SR... 2 Figure 2.1 : Power- rotational speed boundry both solid and laminated rotors. ... 10 Figure 2.2 : Mechanical stress versus surface velocity. ... 11 Figure 2.3 : Change of utilization factor for 2-poles high speed SRIM: A)

Solid rotor with copper cage, B) Slitted solid rotor with copper end rings, C) slitted solid rotor, D) Smooth solid rotor and dashed line shows that the utilization factor for conventional 50 Hz 2-poles induction motor. ... 13 Figure 2.4 : Reduced power consumption diagram... 15 Figure 2.5 : Equivalent circuit of SRIM for space harmonics. ... 23 Figure 3.1 : 2D Transient magnetic model of Smooth-SRIM... 35 Figure 3.2 : Skin-depth based mesh structure of Smooth-SRIM. ... 35 Figure 3.3 : Geometric optimisation parameters of AS-SRIM. ... 36 Figure 3.4 : Magnetic flux lines and densities for different slit depths a)0mm,

b)5mm, c)10mm, d)15mm, e)20mm... 38 Figure 3.5 : Electromagnetic torque for different slit widths and depths for

AS-SRIM. ... 39 Figure 3.6 : Input current per unit torque for different slit widths and depths

for AS-SRIM... 39 Figure 3.7 : Rotor loss for different slit widths and depths for AS-SRIM... 40 Figure 3.8 : Power factor for different slit widths and depths for AS-SRIM... 40 Figure 3.9 : Efficiency for different slit widths and depths for AS-SRIM. ... 41 Figure 3.10 : Radial component of air-gap flux density for different slit depth

values under constant slit width (δslit= 1.2 mm) for AS-SRIM. ... 42

Figure 3.11 : Radial component of air-gap flux density for different slit width values under constant slit depth (d_slit= 15 mm) for AS-SRIM. ... 42 Figure 3.12 : Harmonic spectrums for different slit depth values under constant

slit width (δ_slit = 1.2 mm) for AS-SRIM... 43 Figure 3.13 : Harmonic spectrums for different slit depth values under constant

slit width (δslit = 1.2 mm) except fundamental component for

AS-SRIM. ... 43 Figure 3.14 : Harmonic spectrums for different slit width values under constant

slit depth (dslit = 15 mm) for AS-SRIM. ... 44

Figure 3.15 : Harmonic spectrums for different slit width values under constant slit depth (d_slit = 15 mm) except fundamental component for AS-SRIM. ... 44

Figure 3.16 : Torque as a function of rotation angle for different number of odd slits for AS-SRIM. ... 47 Figure 3.17 : Torque as a function of rotation angle for different number of even

slits for AS-SRIM. ... 47 Figure 3.18 : Torque and current/torque (torque efficiency) for different

number of slits for AS-SRIM... 48 Figure 3.19 : Rotor loss for different number of slits for AS-SRIM... 48 Figure 3.20 : Efficiency for different number of slits for AS-SRIM... 49 Figure 3.21 : Electromagnetic torque and "input current per unit torque" for

different coating thickness for CC-SRIM. ... 50 Figure 3.22 : Rotor loss for different coating thickness for CC-SRIM... 51 Figure 3.23 : Power factor for different coating thickness for CC-SRIM... 51 Figure 3.24 : Efficiency for different coating thickness for CC-SRIM... 51 Figure 3.25 : Radial component of air-gap flux density for different coating

thickness for CC-SRIM... 52 Figure 3.26 : Harmonic spectrums for different coating thickness (including

fundamental) for CC-SRIM. ... 53 Figure 3.27 : Harmonic spectrums for different coating thickness (excluding

fundamental) for CC-SRIM. ... 53 Figure 3.28 : The geometric optimisation parameter of SAS-SRIM and

differ-ent rotor types of SRIM; b)SAS-SRIM, c)AS-SRIM, d)CC-SRIM. .. 55 Figure 3.29 : Electromagnetic torque for different slit widths and depths for

SAS-SRIM. ... 57 Figure 3.30 : Current/Torque (torque efficiency) for different slit widths and

depths for SAS-SRIM. ... 57 Figure 3.31 : Rotor loss for different slit widths and depths for SAS-SRIM... 58 Figure 3.32 : Power factor for different slit widths and depths for SAS-SRIM... 58 Figure 3.33 : Efficiency for different slit widths and depths for SAS-SRIM... 59 Figure 3.34 : Torque as a function of rotation angle for different number of slits

for SAS-SRIM. ... 60 Figure 3.35 : Torque and current/torque (torque efficiency) for different

number of slits for SAS-SRIM. ... 61 Figure 3.36 : Rotor loss for different number of slits for SAS-SRIM. ... 61 Figure 3.37 : Efficiency for different number of slits for SAS-SRIM. ... 62 Figure 3.38 : Torque and current/torque (torque efficiency) for different coating

thickness for SAS-SRIM... 63 Figure 3.39 : Rotor loss for different coating thickness for SAS-SRIM... 63 Figure 3.40 : Power factor for different coating thickness for SAS-SRIM... 64 Figure 3.41 : Efficiency for different coating thickness for SAS-SRIM... 64 Figure 3.42 : Change of radial component of air-gap flux density versus

mechanical angle... 65 Figure 3.43 : Harmonic spectrums for three types of rotor (including

funda-mental). ... 66 Figure 3.44 : Harmonic spectrums for three types of rotor (excluding

funda-mental). ... 66 Figure 3.45 : Torque-power-speed curve for different types of motors. ... 67 Figure 3.46 : Rotor loss for different types of motors... 67

Figure 3.47 : Efficiency for different types of motors... 68 Figure 3.48 : Power factor for different types of motors... 68 Figure 4.1 : MMF distribution of conventional winding for one phase. ... 72 Figure 4.2 : The winding scheme for reference motor for one pole pairs... 72 Figure 4.3 : MMF distribution of reference conventional high-speed SRIM. ... 73 Figure 4.4 : The spectrum of the calculated harmonics for a conventional

high-speed SRIM. ... 74 Figure 4.5 : Angular position of slots... 76 Figure 4.6 : Targeted MMF wave after optimization. ... 79 Figure 4.7 : The first 35 harmonics of the 3 best solutions. ... 83 Figure 4.8 : The first 35 harmonics of the 3 best solutions except fundamental... 83 Figure 4.9 : MMF distributions of conventional and optimised high speed SRIM. 84 Figure 5.1 : Winding scheme of designed novel motor... 89 Figure 5.2 : Sections and dimensions of novel slot... 91 Figure 5.3 : Initial slot and tooth design (no attention is paid for constant tooth

with). ... 92 Figure 5.4 : Optimised slot and tooth design. ... 93 Figure 6.1 : Conventional (left hand side) and optimized (right hand side) high

speed SRIM... 97 Figure 6.2 : Magnetic flux densty distributions of conventional (left hand side)

and optimized (right hand side) high speed SRIM. ... 98 Figure 6.3 : Magnetic flux lines of conventional (left hand side) and optimized

(right hand side) high speed SRIM. ... 98 Figure 6.4 : Rotor Eddy current density distributions of conventional (left

hand side) and optimized (right hand side) high speed SRIM... 98 Figure 6.5 : Air-gap flux density solution of conventional motor. ... 99 Figure 6.6 : Air-gap flux density solution of optimised motor... 99 Figure 6.7 : Harmonic spectrum of non-3rd order radial air-gap flux density

(T HDconv= 31.8%, T HDopt= 30%)... 100

Figure 6.8 : Harmonic spectrum of non-3rd order radial air-gap flux density components except fundamental (T HDconv = 31.8%, T HDopt =

CONTRIBUTIONS TO REDUCE ROTOR HARMONIC LOSSES IN SOLID ROTOR INDUCTION MACHINE

FOR HIGH SPEED DRIVE APPLICATIONS SUMMARY

In recent years, improvements in industries have brought about an increase in the optimum operating speed for drive systems. In this respect, the recently developed, high-speed, gearless or direct electrical drives are currently very popular, because of the reduction in the total structural volume of the drive system.

Depending on its excellent mechanical and thermal capabilities to withstand stress, solid rotor induction motors (SRIM) are widely used in demanding high-speed and high-pressure applications. Solid rotor is mainly made of one type ferromagnetic material as single-piece. Due to their single material rotor structure, solid rotor induction motor are easy to manufacture, cost-effective and reliable alternatively to other types of high-speed machines. In addition, even if they operate in high speed, they have low level of noise and vibrations. Another main advantage of this motor type is the ability to operate without a speed sensor unlike most of permanent magnet machines.

Since eddy currents are set free in SRIMs, great part of rotor losses is caused by space harmonics created in the air-gap. Rotor losses are increased tremendously in high speed applications with the remarkable increase in driving frequency. It is obvious that elimination of prominent air-gap MMF harmonics can improve the total efficiency of SRIM in high speed applications.

In this thesis, fistly high speed solid rotor induction motor with different convenient types of rotor, i.e., smooth solid, slitted solid and coated solid rotor were designed and analysed in cases where the geometrical size was kept constant. After that, a novel solid rotor structure with slits in axial directions, of which the top of rotor iron teeth is coated with copper named as Shielded Axially Slitted SRIM (SAS-SRIM) was designed and optimised in details. Performance of the motor with the novel rotor design is compared with those of the equivalent motors having axial-slits and copper coated solid rotors. In order to calculate and compare the performances of all motors, the systems were simulated by 2D time stepping finite element analysis (FEA). In the novel structure, the fundamental flux can penetrate much deeper than that of a smooth-type IM because of the presence of slits. In addition, because of the existence of coating on the top of the teeth, the rotor creates decreased torque ripple resulting in less vibration. Novel rotor design serves a better efficiency with less rotor loss together with a disadvantage of decreased power factor.

The second part of thesis contains an innovative design representing a novel stator and rotor combination that is not achieved in previous studies and it is proposed by structural changes to stator to eliminate major effective space harmonics. An unconventional stator slotting pattern and winding distribution was calculated by nature inspired numerical optimization techniques while keeping the fundamental

winding factor relatively high. Unlike previus studies, highest fundamental winding factor was investigated while eliminating space harmonics in the air-gap mmf. A sample design where novel concepts were implemented is presented and a comparison is given in terms of important operational quantities with those of a standard SRIM. Proposed innovative design contributes to reducing rotor losses and increasing the efficiency of high-speed solid rotor induction motors. In addition to that, proposed innovative design increases the electrical performance of high-speed solid rotor induction motor. Use of high-performance and high-efficiency solid rotor induction motors provides contribution to national economy and power quality. Besides these national contributions, this thesis also has scientific contributions to analysis of harmonic power loss calculation in solid rotor induction motor and methods of eliminating harmonic power loss in rotor surface.

YÜKSEK HIZLI TAHR˙IK S˙ISTEMLER˙I ˙IÇ˙IN KÜTLESEL ROTORLU ASENKRON MOTORUN ROTOR HARMON˙IK KAYIPLARINI AZALTMAYA YÖNEL˙IK KATKILAR

ÖZET

Son yıllarda, imalat ula¸sım ve süreç endüstrisindeki geli¸smeler tahrik sistemleri için en uygun çalı¸sma hızında artı¸sı beraberinde getirmi¸stir. Bu ba˘glamda, yeni geli¸stirilen yüksek hızlı, di¸slisiz, kayı¸s-kasnak düzene˘ginin bulunmadı˘gı veya do˘grudan tahrikli elektriksel sürü¸s sistemlerinin yapısal hacimlerindeki azalma nedeniyle ¸su sıralar oldukça bilinirli˘gi artmı¸stır.

Kütlesel Rotorlu Asenkron Motorlar mekanik ve ısıl baskılara kar¸sı oldukça dayanıklı olması nedeniyle yüksek hız ve yüksek basınç talep eden uygulamalarda yaygın olarak kullanılmaktadır. Kütlesel rotor genellikle tek tip ferromanyetik bir malzemeden tek parça olarak imal edilir. Sahip oldu˘gu rotor yapısından dolayı kütlesel rotorlu asenkron motorlar, di˘ger yüksek hızlı makinelere göre üretimi kolay, dü¸sük maliyetli ve güvenilirdir. Ayrıca, yüksek hızda çalı¸smalarına ra˘gmen dü¸sük seviyede gürültü ve titre¸sime sahiptirler. Bu motor tipinin bir ba¸ska üstünlü˘gü ise sürekli mıknatıslı makinelerin ço˘gundan farklı olarak rotor hız-konum algılayıcısı olmadan sürülebilmesidir.

Girdap akımları kütlesel rotor üzerinde serbestçe akabildi˘gi için, rotor kayıplarının büyük kısmı hava aralı˘gında olu¸san uzay harmoniklerinden kaynaklanmaktadır. Yüksek hız uygulamalarına gelince, sürü¸s frekansındaki artı¸stan dolayı rotor kayıplarında da ciddi bir artı¸s vardır. Hava aralı˘gı akı yo˘gunlu˘gundaki harmoniklerinin azaltılması, yüksek hızlı uygulamalarda Kütlesel Rotorlu Asenkron Motor’un toplam verimini arttıraca˘gı a¸sikardır.

Bu tezde, öncelikle Yüksek Hızlı Kütlesel Rotorlu Asenkron Motor’un tasarım ve ba¸sarım hesapları ile ilgili kısa bir bilgi verilmi¸stir. Bu ba˘glamda; Kütlesel Rotorlu Asenkron Motor’un temel boyutlarının belirlenmesi, kayıpları, so˘guma kabiliyeti, uzay harmoniklerinin analizi, harmonik moment ifadesinin elde edilmesi ve sonlu elemanlar yöntemi ile modellenmesi gibi konular kısaca açıklanmı¸stır. Literatürde var olan geleneksel rotor yapılarından olan düz, eksenel yarıklı ve bakır giydirilmi¸s rotor tiplerine sahip Kütlesel Rotorlu Asenkron Motorlar geometrik boyutları sabit kalmak ko¸sulu ile tasarlanıp analiz edilmi¸stir. Daha sonra, eksenel yarıklı yapıdaki rotor di¸s yüzeylerinin bakır ile kaplandı˘gı Siperli-Eksenel Yarıklı Kütlesel Rotorlu Asenkron Motor olarak adlandırılan yeni bir kütlesel rotor yapısı önerilmi¸s, önerilen bu yapı detaylıca tasarlanıp en uygunla¸stırılmı¸stır. Tüm rotor tasarım parametreleri incelenmi¸s, yarık derinli˘gi-geni¸sli˘gi, sayısı ve kaplama kalınlı˘gı gibi rotor ba¸sarımına etki eden tüm geometrik parametreleri için en uygun parametreler belirlenmi¸stir. Yeni rotor tasarımının manyetik ve i¸sletme ba¸sarımı, ona muadil olabilecek eksenel-yarıklı ve bakır giydirilmi¸s Kütlesel Rotorlu Asenkron Motorlar ile kar¸sıla¸stırılmı¸stır. Dahası tüm rotor tiplerinin manyetik akı yo˘gunlu˘gu ve hava aralı˘gındaki akı yo˘gunlu˘gu harmonik spektrumu da verilmi¸stir. Ba¸sarım kar¸sıla¸stırmaları için iki boyutta geçici hal sonlu elemanlar analizi (SEA) kullanılmı¸stır.

Eksenel Yarıklı Kütlesel Rotorlu Asenkron Motor için yapılan analizler yarık derinli˘ginin arttırılıp geni¸sli˘ginin dar tutulmasının moment üretimini %250-300 arttırabildi˘gini göstermektedir. Bununla birlikte, moment üretimi ve mil gücündeki artı¸s ile beraber rotor kaybında artı¸s ya¸sanmaktadır. Ayrıca, yarık geni¸sli˘ginin de˘gi¸stirilmesi güç faktörü ve verim üzerinde büyük bir etkiye sahiptir. Dar ve daha derin yarıklar, güç faktöründe ve verimde artı¸sa neden olur. Yapılan rotor en uygunla¸stırması sonucunda, yarık geni¸sli˘ginin yarık adımının %15’i ve yarık derinli˘ginin rotor yarıçapının %40’ı olarak seçilmesi gerekti˘gi görülmü¸stür.

Bakır Giydirilmi¸s Kütlesel Rotorlu Asenkron Motor için yapılan analizlerde giydirme kalınlı˘gındaki artı¸sın moment üretiminde artı¸s sa˘gladı˘gını görülmü¸stür. Rotor kaybı, 0-1 mm giydirme kalınlı˘gı aralı˘gında artmı¸s, 1-2.5 mm arasında dü¸smü¸s ve 2.5 mm’den sonra tekrar artmı¸stır. Hesaplanan sonuçlar di˘ger tüm performans parametreleri için tutarlı olmasına ra˘gmen rotor kaybı ve kaplama kalınlı˘gı arasında önemli bir ili¸ski kurulamamı¸stır. Bu rotor tipinin güç faktörü ve verimi, kaplama kalınlı˘gının belirli bir seviyeye kadar artmasıyla artarken daha sonra dü¸smeye ba¸slamı¸stır. Motor ba¸sarımını en üst seviyeye çıkarmak için tüm ölçütlere ait en uygun giydirme kalınlı˘gının 1,5 ile 2,5 mm arasında seçilmesi gerekti˘gi görülmü¸stür.

Önerilen yeni rotor yapısında akı, yarıkların varlı˘gı nedeniyle düz kütlesel rotorlu asenkron motora nazaran çok daha derine nüfuz etmektedir. Ayrıca, di¸slerin yüzeyindeki bakır siperin varlı˘gı nedeniyle azaltılmı¸s moment dalgalılı˘gı rotorun daha az titre¸simli bir ¸sekilde çalı¸smasını sa˘glar. Rotor di¸slerindeki yapılan bu de˘gi¸siklik rotor kayıplarını hatırı sayılır derecede azaltmı¸stır. Yapılan rotor en uygunla¸stırması sonucunda, yarık geni¸sli˘ginin yarık adımının %40’ı ve yarık derinli˘ginin rotor yarıçapının %45’i olarak seçilmesi gerekti˘gi görülmü¸stür. Önerilen yeni rotor tasarımı, dü¸sük güç faktörüne sahip olmasına ra˘gmen di˘ger rotor yapılarına kar¸sı daha iyi verim ve daha az rotor kaybına sahiptir.

˙Imalat sorunları açısından bu üç rotor tipi kar¸sıla¸stırıldı˘gında en kolay imal edilen yapının giydirilmi¸s rotor yapısı oldu˘gu görülür. Fakat bu yapı beraberinde getirdi˘gi yüksek rotor kayıplarından dolayı ısıl zorlanma ve so˘guma ba¸sarımı olarak di˘gerlerine göre daha kötü durumdadır. Eksenel Yarıklı Rotor yapısı ise içerdi˘gi hava aralı˘gı akı yo˘gunlu˘gu harmonikleri açısından di˘gerlerine göre oldukça ba¸sarımı dü¸süktür. Bu harmonikler motorda titre¸simli çalı¸smaya ve gürültüye neden olabilece˘gi gibi kalkı¸s anında da motor ba¸sarımını kötüle¸stirmektedir. Tüm bu sonuçlar göz önüne alındı˘gında Siperli-Eksenel Yarıklı Rotor yapısının yüksek hızlı uygulamalar için iyi bir seçim olabilece˘gini göstermektedir.

Tezin ikinci kısmı literatürde daha önce üzerinde çalı¸sılmamı¸s yeni bir stator-rotor kombinasyonunu içeren yenilikçi bir tasarım içermektedir. Ayrıca ba¸slıca uzay harmoniklerini ortadan kaldırmak için rotor yapısındaki de˘gi¸sikliklerden ziyade stator üzerinde bir yapısal de˘gi¸siklik önerilmi¸stir. Alı¸sılmadık stator oluk dizili¸si ve sargı da˘gılımı do˘gadan esinlenen sayısal optimizasyon tekniklerinden olan Big Bang- Big Crunch algoritması yardımıyla hesaplanmı¸stır. Bu hesap yapılırken sargı faktörünün temel bile¸seninin olabildi˘gince yüksek tutulması hedeflenmi¸stir. Literatürkeki var olan çalı¸smaların aksine, bu çalı¸smada hava aralı˘gındaki akı yo˘gunlu˘gu harmonikleri yok edilirken, sargı faktörünün temel bile¸seninin en yüksek de˘geri ara¸stırılmı¸stır. Daha az harmonik bozunum ve yüksek sargı faktörü sa˘glayan en iyi 3 çözüm 10000 sonuç arasından seçilmi¸stir. Stator tarafından hava aralı˘gında olu¸sturulan en belirgin uzay harmonikleri daha yüksek derecelere kaydırılarak etkileri ortadan kaldırılmı¸stır veya

azaltılmı¸stır. Hala hava aralı˘gı akı yo˘gunlu˘gunda bulunan harmonikler ise daha dü¸sük senkron hız de˘gerlerine dü¸sürülmü¸stür. Faz sargılarının birbirinin içine geçti˘gi sıradı¸sı bir oluk da˘gılımı ortaya çıkmı¸stır.

Önerilen yeni stator-rotor kombinasyonunun yer aldı˘gı örnek bir Kütlesel Rotorlu Asenkron Motor tasarımı detaylıca verilmi¸s ve geleneksel oluk ve sargı yapısına sahip Kütlesel Rotorlu Asenkron Motor ile elektriksel, manyetik ve i¸sletme ba¸sarımı açısından kar¸sıla¸stırma yapılmı¸stır. Önerilen yenilikçi tasarım, Yüksek Hızlı Kütlesel Rotorlu Asenkron Motorlar’da hava aralı˘gı harmoniklerinin bozucu etkisini azaltarak rotor kayıplarını azalmasına ve verim artı¸sına katkıda bulunmaktadır. Dahası, mildeki moment dalgalılı˘gının da azalması yeni tasarımın ba¸sarımındandır. ˙I¸sletme ba¸sarımı arttırılmı¸s ve yüksek verimli kütlesel rotorlu asenkron motorların kullanılması ulusal ekonomiye ve güç kalitesine katkı sa˘glayacaktır. Tezin Ulusal ekonomiye katkılarının yanı sıra, Kütlesel Rotorlu Asenkron Motorlar’da rotor yüzeyindeki harmonik güç kaybı hesabında ve rotor yüzeyindeki harmonik güç kayıplarının azaltılması yöntemlerine bilimsel katkısı mevcuttur.

1. INTRODUCTION

In recent years, improvements in manufacturing, transportation and process industry technologies bring about an increase in optimal operation speed in drive systems. In this respect, recently developed high speed gearless or direct drive electrical drives are currently very trendy based on the reduction in the total structural volume of the drive system. Because of the significant development of cost-effective, fast switching and compact variable frequency drives technology, wide speed range operations of different type AC motors has become feasible.

In literature, there are several descriptions for the term “high-speed”. As a mechanical engineer, peripheral speed over 150 m/s is considered to be high speed [1]. From the motor manufacturer’s point of view, a two-pole machine which is supplied higher than 50-60 Hz, can be considered as a high-speed machine. However, the most important point of view for the high-speed term is explained by development at power electronics. Nowadays, up to few hundereds hertz frequencies can be produced by variable frequency drives. However, voltage qualities of these are not satisfactory due to limited switching frequency of high-power IGBT technology. Thus, high-speed levels might be calculated for frequencies in the range of 100-400 Hz which are considered to be high-frequencies [2].

Owing to brush and commutator structure causing mechanical and electrical problems, dc drives are not allowed to be used for high-speed applications. In addition to that, the structure is not appropriate for large centrifugal forces. Neverthless, as high-speed drive applications there are different type of ac motor consepts [1–4]:Laminated/solid induction, permanent magnet synchronous and switched reluctance synchronous motors.

As it can easily be understood from the name, solid rotor induction motors (SRIM) have unconventional cylindirical mass of iron rotor construction and are mechanically very robust depending on its nature. On the contrary, electromagnetic properties of this type of rotors are impoverished, rated slip of the rotor intends to be large causing an

Figure 1.1 : Most common rotor types for SRIM: a)Smooth SR, b)Smooth SR with end rings, c) Slitted SR and d) Coated SR.

increase in rotor losses and bring about a poor power factor. Neverthless, permanent magnet synchronous motors (PMSM) attempt to better efficiency and torque density [4]. Besides, solid rotor motor is very robust than PMSM and it can be operated without speed sensor or rotor position estimation algorithm.

The most uncomplicated solid rotor type is smooth-steel cylinder (Fig. 1.1a) which is easy to manufacture and has the best mechanical and fluid-dynamical properties due to low air friction [1–6]. Besides, it also has a superior heat resistance. However, its electro-magnetic properties are not as good as the other types, thus its slip value is much higher. As a result of the skin effect and travelling eddy currents at the surface of the ferromagnetic material, induced magnetic field is pushed through the outer layers of the rotor. Therefore, the depth of magnetic flux penetration into the rotor surface is very low. The magnetic flux and the torque producing eddy-currents are concentrated on the surface layer and the inner layers of the rotor become an electrically inert. Developed electromagnetic torque of solid rotor induction motor can be increased by means of copper end-rings which can be seen in Fig. 1.1b. Copper end-rings align the rotor current flowth into the axis-parallel direction and it increases the Lorentz force induced on rotor. Placing copper end-ring on rotor doubles electromagnetic torque at a certain slip when compared with that of the same rotor without end-ring [7–9]. Additional performance improvement can be menaged by

axially-slitting the rotor which can be seen in Fig. 1.1c. This brings about a better magnetic flux penetration into the rotor [10–13] and low frequency impedance of rotor decreases, hence this results in developing more electromagnetic torque at very low slip values, but less torque at higher slip values [8]. High frequency surface impedance of rotor is increased, thus the rotor eddy current losses which are caused by time and space harmonics are relatively reduced. However, the robustness of solid rotor is partially lost and air friction between rotating rotor and air increases notably. Besides, slitting the rotor increases the cooling surface and cooling capability [14]. Another method of reducing rotor losses is chamfering radial grooves on rotor surface and the path of high frequency rotor harmonic currents is cut. Further method of reduction of rotor losses is coated rotor (Fig. 1.1d) which is an option for high-speed drive applications. The coating of rotor with ferromagnetic material decreases the impact caused by air-gap harmonics while increasing electro-magnetic performance of the motor [15–17].

1.1 Purpose of Thesis

SRIM has a very low power factor and high order time and spatial harmonic losses. The rotor structure cannot supress any of the time-space harmonics of magneto-motive force in the main air gap. The harmonics in a SRIM generates remarkable losses in solid-rotor. Even if the supply voltage is pure sinusoidal, the air-gap flux density can be distorted by spatial harmonics s [1,2,7,8]. Therefore it leads to high rotor losses and low efficiency. The major causes of rotor losses can be categorized into the following three groups [9].

•Winding harmonics caused by the discrete coil distribution in the periphery of the stator yoke.

•Permeance harmonics caused by the slot openings.

•Slot harmonics, (if the winding harmonics are of the same order with that of the permeance harmonics then the slot harmonics must be taken into consideration) These harmonics are the function of time and position in the air gap and they all have adverse effects on the performance of an induction machine. These effects appear in the form of current, torque and rotor loss [17].

In this thesis, low-order air-gap harmonics caused by winding, permeance and slot openings were eliminated and their total effect was reduced while first seen harmonics was shifted to higher orders and their reduced total effect was compressed to lower speeds. This reduction is performed mainly by optimisation in stator structure while the effect of rotor structure on air-gap harmonics was also investigated . Firstly, conventional rotor types for SRIMs were analysed in detail and main rotor structural effects on motor performance were studied. Main rotor design criterions were optimised parametrically and optimum motor performance limits were obtained for all types of rotors used in SRIMs. Afterwards, a novel rotor structure which is one of the main contributions of this thesis was proposed to improve motor performance and its structure was also optimised according to its design criterions.

In the second part of thesis, a novel stator and rotor combination for SRIM was obtained while using conventional solid rotor structure together with a novel stator core. New unconventional slot positions and numbers of turns per slots were calculated by using a numerical optimisation method while targeted air-gap harmonics created by stator winding were all eliminated. The calculated results for the chosen number of slots per pole were re-analysed in order to obtain the maximum fundamental winding factor while eliminating the targeted harmonics. The new calculated and designed geometry serves a novel stator structure and a novel stator-rotor combination serving innovation to the literature. In addition to that, metaheuristic solution algorithm inspired by nature was used for analysis in order to achieve a reliable solution. Optimum solution was chosen to implement to numerical simulation model and the novel design was analysed numerically to understand the pros and cons of the purposed method. The proposed method will also contribute to optimisation of all conventional SRIM performance.

With the completion of the study, a novel unconventional high speed solid rotor induction motor design was achieved and it was proven that the novel design provides an improved operational performance. Proposed new model contribute to reducing rotor losses, increasing the total efficiency and improving general performance of high-speed solid rotor induction motors. Use of this high-performance and high-efficiency solid rotor induction motors will provide contribution to national economy, power quality and energy efficiency. Besides these national contributions,

this thesis also has scientific contributions to analysis and optimisation of harmonic power loss calculation in solid rotor induction motor and methods of eliminating and/or reducing harmonic power loss in rotor. Consequently, an optimised novel solid rotor induction motor design having an unconventional stator core and winding structure and providing reduced space harmonic effect was obtained.

1.2 Literature Review

Scientific reasearches related to SRIM have increased around the 1960s due to the rising towards SR technology. Most of fist studies on SRs were suppose rotor unsaturated having a constant permeability. Because of fact that the eddy currents and magnetic flux density distributions in rotor body have non-linear distributions, the assumptions about rotor concluded in weak validty. In order to consider characteristics of rotor materials accurately, non-linearities of magnetic material and end-effects of rotor must be taken into account. First studies including the effect of magnetic non-linearities were proposed by Nechleba [18], McConnell and Svedrup [19], Wood and Concordia [20, 21] and Heller [22]. First two and three dimensional magnetic field distribution anaylsis was introduced by Wilson [6]. Non-linear rotor permeability was taken into account for magnetic field anaysis by a computer-aided program. The study was shown that the developed torque rises when the material of rotor has high conductivity and low permeability. However, the impact of saturation of rotor material on performance of motor was not investigated.

In 2D FEA calculations, rotor is assumed as infinitely long solid piece of material and rotor end impedances and 3D nature of SR are not taken into account in coupled electric and magnetic circuit. In order to consider the effect of finite length, dimensionless rotor conductivity correction factors were proposed by Trickey [23], Yee [24], O’Kelly [25], Woolley [26] and Russell [27] that are mostly related to geometrical parameters of SR. Besides, Wood [28] applied a specific approximation but it is questionable. Later, Ducreux [29] used boundry integral method to obtain 3D magnetic field distributions of rotor end regions. Obtained results were compared with 2D FEM calculations using different rotor conductivity correction factors and it is revealed that rotor conductivity correction factor is frequency depend. Suggested rotor conductivity correction factor menage to estimate developed electromagnetic

torque approximately. However, calculating the motor power factor does not estimate correctly.

The most prominent problems of SRIM are concerned about low electrical and magnetic performance of rotor. Due to either need for improved performance or limits of cage rotor induction machine theory for solid rotor performance calculation, further research has been continuing. First studies for obtaining solid rotor performance contained analytical methods which were achieved by Agarwal [30], Wood [31], Angst [32], Heller [22], Jamieson [33, 34], Rajagopalan [35], Chalmers [36], Yee and Wilson [37], Sarma [38]. Despite of fact that these studies were based on limiting non-linear theory, many remarkable observations were achieved. Expecially, Agarwal’s theory of determination of equivalent circuit parameters is still accepted for many people. Apart from these studies, different method which considers the non-linear behaviour of rotor material was proposed by Pipes [39]. In multi-layer transfer-matrix method (MLTM) rotor was devided into layers in radial directions. Electromagnetic equations are calculated for each layer and calculated initial values is used for following calculation of upper layer. Pyrhönen [3] applied MLTM in a smooth solid rotor and it was reported that high saturation flux density and high conductivity of material could be increased the electromagnetic performance or SRIM. After that, Huppunen [40] improved the MLTM and facilitated it for SRIM. Also he showed that the calculation method could be applied for slitted-SRIM and motor electromagnetic performance can be increased by adding copper end-rings on the end of SR body.

In order to increase the motor performance, change in rotor geometry was investigated. Slitting rotor body was proposed to decrease to rotor eddy current losses. First study about slitted rotor belongs to Peesel [41]. Later the impact of axial slitted solid rotor was investigated by Dorairaj and Krihnamurty [10–12] by considering the geometrical parameters of rotor such as slit width, depth and slit number without end-rings. Besides, Rajagopalan and Murty [35] were performed a study about calculations and tests. The real shape of BH curve was used in calculations by [42] and Laporte [43] and they were investigated a slitted SRIM by a software using FEM.

Lähteenmäki [2] and Huppunen [40] did comprehensive studies on SRIM designs. All these studies were established by test and FEM results. In 2006, Bumby introduced an anaylsis based on equivalent circuit approach. All stator parameters were obtained

by classical approach, rotor parameters were calculated by field equaitons. Similar traditional approach for determining rotor parameters were proposed by Russell [27], Agarwal [30], Chalmers and Woolley [26, 36] and O’Kelly [25]. Nevertheless, due to rotor structure, calculation of equivalent circuit parameter is not easy.

In high speed drive applications, motors were supplied by a frequency converter. This stuation causes an increasing excessive eddy current loss on solid rotor surface. In order to decrease this losses layered rotor structure was proposed by Wilson [6], Sarma [38] and Sharma [44]. All these studies consist of several solid layer of different material. Proposed layered rotor would have better operation characteristics than a smooth solid rotor. Moreover, McConnell [19] and Heller [22] developed the equivalent circuit for layered rotor accurately.

Additional performance boost was obtained by coating rotor body with low permeability and resistivity material. Copper coated SRIM were investigated comprehensively by Lähteenmäki [2]. An analytical model for selection of coating thickness was improved by Shah [45]. In addition that rotor could be coat with high resistive ferromagnetic material. High resistive coating layer increases rotor surface impedance and weakens the air-gap harmonic fields before penetration of magnetic flux into well-conducting material. Pyrhönen and Kurronen [46] used a high resistance aluminium-iron alloy as a coating material on SR body. Due to high resistivity of the material, rotor surface impedance increased and eddy current losses were decreased. Jokinen and Arkkio [47] were also concluded that it would be possible to menage additional performance improvements, if rotor surface is coated material having high resistivity and high permeability.

Stator windings of SRIM are common with that of a conventional cage rotor induction motor which cannot prevent the existence of space harmonics. Effect of space harmonics are well studied in literature. Most-known method is chording the coil by shortening the coil pitch than pole pitch [48]. Shildneck [49] analysed several winding arrangements with their benefits and his results were confirmed theoretically. Krebs [50] proposed a non-uniformly distributed winding while changing the number of conductors per slot and keeping the stator core and slot distribution same. Smith and Layton [51] refined Krebs’ method by allowing the distribution of number conductors per slot to vary sinusoidal. Chalmers [52] presented interspersed windings

for odd numbers of slots per pole per phase. His arrangement had a conspicuous reduction in harmonic winding factors whilst keeping the fundamental slightly reduced. Hughes [53] placed two star and delta connected windings in the same stator by dividing the phase spread into two. He connected the phase windings parallel and obtained a 6-phase distribution providing a relatively high fundamental winding factor. Kocabas [17] altered both the winding distribution and slot arrangement providing an unconventional winding arrangement. Air-gap magnetomotive force (MMF) distribution is optimised to eliminate a number of space harmonics. Eliminated number of harmonics is related to the number of slots per pole per phase. The method is applicable to the motors having the slot numbers of orders of 12. However, investigation about fundamental winding factor for being maximum and singular is not provided.

1.3 Hypothesis

The efficiency of SRIM is directly related to magnetic flux and eddy current distribution and naturally to space harmonics. A reduction or elimination in air-gap harmonics can assist the electrical, electromagnetic and mechnical performance of SRIM. The hypothesis of this thesis is to eliminate the winding, permeance and slot harmonics, which exist in the airgap mmf wave while searching for a maximum winding factor by innovative constructional changes and unused methods used for optimisation of an electrical machine. Proposed new model will contribute to reducing rotor losses and increasing the efficiency of high-speed solid rotor induction motors. In addition to that, proposed new model will increase the electrical performance of high-speed solid rotor induction motor.

2. DESIGN AND PERFORMANCE CALCULATION OF CONVENTIONAL HIGH SPEED SOLID ROTOR INDUCTION MOTOR

Since, the high speed solid rotor induction motors are produced from a massive piece of steel, the impact of centrifugal force may not be disregarded. The mechanical tangential streses on rotor body must be reduced in allowed level. Therefore, mechanical limitations bring to restrictions dimensions of rotor geometrical properties, selection of rotor material, increasing precision for quality of manufacturing processes. The application area of high speed SRIM rests in the speed range in which laminated structures can not withstand centrifugal forces. The mechanical abilities of slicon steel bound the surface velocity about 150 m/s. Therefore, laminated rotors are operated from 10 000 min−1to 50 000 min−1 while output power varies from several kilowatts to magawatts range. But FeCo (Iron-Cobalt) laminations with CuCrZr (Copper Chromium Zirconium) alloy bars can be used at high speeds, but it is not economic. On the contrary of laminated rotor, upper speed limit for SRIM is defined by mechanical constraint and is 20 000 min−1 to 100 000 min−1. This mechanical constraint can be determined by maximal speed for a certain rotor volume. Moreover, this mechanical restirictions and power limits may lead to themal design of SRIM. Jokinen [1] calculated the speed boundry both solid and laminated rotors and related curves are given in Figure 2.1. All calculations are done for steel having 700 MPa yield stress and operation speed is selected 20% lower than the first critical speed. The SRIM ensures a robust solution for challenging environments in which other rotor types are obstructed or suspicious. However, most prominent problem on SRIM is low electrical performance of the rotor. As mentioned in introduction, there are methods to improve the performance of a SRIM. One of them is placing end rings on rotor ends. Rotor resistance can be reduced by welding or soldering high conductive end ring such as copper or aluminium. However, additional end rings can not witstand under high mechanical tangential forces, thermal stresses and corrosive environment. Therefore, rotor should be manufactured with single piece massive ferromagnetic material without and additional end rings. In addition, slitting the rotor axially or coating the rotor with

Figure 2.1 : Power- rotational speed boundry both solid and laminated rotors. a conductive material are the other performance improving methods. For high-speed applications, the choice between axial slits and coating rotor is made depending on the type and demands of the application.

2.1 Determination of Main Dimensions of Rotor

As it can be mentioned before, the shaft torque is determined by mechanical tangential stress on rotor body. The torque on rotor body can be expressed as in (2.1) where σtsis

tangential stress of electromagnetic rotor surface, L is length of rotor and R is diameter of rotor [54].

T =1

2· σts· L · D

2

(2.1) As can be seen in (2.1), an inceasing in rotor diameter or length cause the rise in shaft torque. However, mechanical strength and elasticity of rotor material, and tangential forces are limited the rotor diameter and length. Solid rotor structure can withstand higher mechanical stress. Ylinen (1970) estimates mechanical stress of a solid rotor as in (2.2) where ρ is mass density of solid rotor material and ω is angular speed of rotor [54].

σts=

1

4·Cts· ρ · D

2_{· ω}2 _(2.2)

In smooth homogenous cylinder, maximum stress is obtained at the centre of cylinder. But, if the cylinder is hollow, maximum stress is obtained at the inner radius of

Figure 2.2 : Mechanical stress versus surface velocity.

cylinder. Cts coefficient can be calculated as in (2.3)-(2.5) where pc is poisson

coefficient for rotor material [54]. C_ts=3 + pc

8 (smooth homogenous cylinder) (2.3) C_ts= 3 + pc

4 (cylinder with a small bore) (2.4)

C_ts= 1 (thin cylinder) (2.5)

Poisson coefficient of steel is 0.29 and for copper end rings, it is 0.34. Figure 2.2 illustrates the surface velocity versus mechanical stress of rotor [54]. Steel Fe52 (ρ = 7870 kg/m3) and copper (ρ = 8960 kg/m3) are used in calculations. Tensile strength of Fe52 is 520 MPa and copper used as end ring is 220 MPa. It can be inferred from figure, the impact of mechanical tangential stress on copper end ring is very high and solid rotor must be manufactured single piece of massive material. Elasticity and densty of material are impact on rotor rigidity. Young’s modules E defines the elesticty of rotor material. Estimation of the maximum length of rotor as given in (2.6) where S_Ais cross section of rotor and ncis critical speed, Jinis modulus of inertia, k is defined

as ratio between the nth_c critical frequency and the rated angular velocity [54].

L2= n2_c π 2 k· ω s E· Jin ρ · SA (2.6) k= ωc ωn (2.7)

The ratio between rotor length and rotor diameter can be written as in (2.8) considering the safety factor ksa f e[54].

L D = 2 · π · nc· r ksa f e k · 4 r C_ts· E 4 · σ (2.8)

Taking into account the critical speed, thick and short rotor structure will be better choice in order to obtain high speeds without any mechanical problem. First critical speed must be overhead the operation range of the rotor. On the other hand, high speed motors are generally operated above its lowest critical speed between the first and second specific frequencies. Whereas, the rotor should pass through one, two or more lateral critical speeds while motor is start-up.

Selection of stator core length (actuallay same as rotor length) L and stator bore diameter (Ds) is very important design parameter which is directly related torque

capability of SRIM. In order to determine these parameters efficiently, the mechanical utilication factor C, which describes power (S) versus motor size, is defined. According to Vogt (1996) the mechanical utilization factor is expressed in (2.9) where Js stator

linear current density, kw1is fundamental winding factor, Bair−gapis the peak value of

air-gap flux density [40].

S= Cmech· D2s· L · n = π2 √ 2· kw1· J · Bair−gap· D 2 s· L · ns(kVA) (2.9)

By (2.9), the mechanical utilization factor can be written as in (2.10) [40]. C_mech= π

2

√

2· kw1· J · Bair−gap(kVA) (2.10) The current density J is a fictional current layer which rests on the stator surface. This current layer conducts a definite amount of current per inner stator surface length unit. The current density J also is described with stator current Is, number of phases m,

number of turns per stator phase Nsand pole pitch τp[40, 54].

J= m· Ns· Is p· τp

(2.11)

The shaft power of SRIM is calculated from the air-gap power considering fundamental power factor cosϕ1and efficiency η in (2.12) and (2.13) [40, 54].

P_{sha f t}= η · cosϕ1· U EPim= π2 √ 2· kw1· J · Bair−gap· D 2 s· L · ns· η · cosϕ1· U E (2.12)

Figure 2.3 : Change of utilization factor for 2-poles high speed SRIM: A) Solid rotor with copper cage, B) Slitted solid rotor with copper end rings, C) slitted

solid rotor, D) Smooth solid rotor and dashed line shows that the utilization factor for conventional 50 Hz 2-poles induction motor.

P_{sha f t}= C_mech· D2_s· L · n_s (2.13) So, the mechanical utilization factor of SRIM is expressed as in (2.14) [54].

C_mech= Psha f t D2

s· L · ns

(2.14) Selection of stator current density strongly related to the cooling. A good cooling systems can rise the allowed stress values on SRIM. When the SRIM geometrical size increases, cooling surface also increases and loadability of motor is increased. Therefore, the utilization factor is function of geometrical size. Since different kind of rotor structure give very wide range of motor operational quantities, the utilization factor also depends on solid rotor construction. In Figure 2.3 the utilization factor for two-pole different high-speed SRIMs tested at Lappeenranta University of Technology (LUT) [40]. All tested high speed motors have open air-cooling system and all calculated values valid between 50-400 Hz supply frequencies. Cooling system can increase the utilization factor. Similar curves can be found in [55].

When the size of rotor reduces, loss density of motor rises, that brings to cooling problem. Therefore, the termal capabilities must be taken into account, since friction

losses becomes dominant in high and medium speed SRIM. Unlike conventional caged rotor induction motor, SRIM can tolerate high thermal stresses. Since solid rotor has good thermal conductivity, it is better for heat transfer. But, rotor resistance highly depends on rotor tempereture. In order to obtain over heating of stator and rotor, cooling channels and cooling systems are selected carefully.

2.2 Losses of SRIM and Cooling Performance

Electric motor efficiency (η) is a ratio of how much the motor converts electrical energy into mechanical energy and is calculated by dividing the power into the motor (Pin) by the power out of the motor (Pout) [54].

η = Pout Pin

.100% (2.15)

Electromechanical energy conversion theory is the keystone for the analysis of electromechanical motion devices so it is convenient to evaluate the power absorbed in the electric motor on account of the basic principles of electromechanical energy conversion. During the process of energy conversion, some of the energy is converted into heat and it lost from the system. The total loss in an electric motor is explained as absorbed power in an electric motor throughout the process of energy conversion and it can be given as a difference between supplied power and mechanical output power [54].

PLoss= Pin− Pout (2.16)

It is inevitable fact that both stator and the rotor affect the performance characteristics of an electric motor. Figure 2.4 shows that a reduced power consumption diagram of an induction motor. To begin with, supplied electrical input power is consumed by the stator copper losses PCu,s and the iron losses PFe,s. Pexcsembolize the excess losses in

the stator. In the power loss diagram of an induction motor, supplied input power Pin

is divided into two part as stator losses and air-gap power P_δ.On the rotor side, part of the air-gap power is lost in the resistive losses PCu,r and in the iron losses PFe,r. Also,

the mechanical losses expressed as Pf r,rresult from bearing, windage and gas friction.

Finally, after the total loss power of the motor are deducted from the supplied electrical input power Pin, the mechanical output power of the motor Pout is remaining [54]. An

Figure 2.4 : Reduced power consumption diagram.

electrical power needed. At first, part of the supplied electrical power is consumed in the stator windings. Copper loss PCu,s the iron loss PFe,sand the excess losses Pexc

existing on the stator side create the stator loss [54].

Ps,Loss= PCu,s+ PFe,s+ Pexc (2.17)

The air-gap power P_δ transfers the power from the stator to the rotor via the air-gap. The air-gap power can now be written as in (2.18) [54].

P_δ = P_in− Ps,Loss = Temwr (2.18)

The electromagnetic torque Tem comprises the axial output torque and the loading

torque which result from the friction of the bearings and the windage of the rotating rotor.

As for the rotor, part of the air-gap power is consumed in resistance of the rotor, rotor iron losses, and in the rotor friction losses. After that, the remainder of the air-gap power transfer into mechanical output power Pout. The rotor total electrical losses Pr,loss, seperate fundamental resistive losses Pf und,r, which are related with the

electromagnetic torque production. Core losses include hysteresis losses Physt,r, which

result from reorientation of the magnetic field within the motor’s lamination steel and surface losses Psur f,r resulting from eddy-currents produced between laminations due

to the presence of a changing magnetic field by the air-gap harmonics. Besides the electrical rotor losses, mechanical losses caused by the bearing and windage result in

extra power losses [54].

P_r,Loss= Pf und,r+ Psur f,r+ Physt,r+ Pf r,r (2.19)

The ferromagnetic solid rotor materials do not have a laminated structure to restrict the induced eddy-currents by contrast with the laminated rotor bodies. Due the eddy-current losses are related with the square of the frequency, are significantly high. Because the friction losses are proportional to the cube of the speed, can be a main part of high-speed motor losses.

The electrical resistivity of the applied material affects the resistive losses on the rotor. The rotor resistive losses which are the major losses are also known as rotor Joule losses. They include rotor fundamental losses and rotor surface losses. In the total rotor volume V , the total Joule loss PJ,rcan be expressed by the volume integral of the

current densities squared where ρ is the resistivity of the material [54].

P_J,r= Z Z Z

ρ J 2

dV (2.20)

The electrical losses of the solid steel rotor are strictly connected to the slip of the rotor. The ratio of the rotor slip frequency to the stator supply frequency fsgives the per unit

slip s [54]. s= ns− nr ns = fslip fs (2.21) In (2.21) explains ns terms which are the synchronous speed of the machine corresponding to the supply frequency fs and nr the mechanical speed of the loaded

rotor, respectively.

Rotor basic losses Pf und,rin conjunction with the surface loss Psur f,rrepresent the main

part of the total solid rotor losses Pr,loss. The fundamental rotor losses are proportional

to the per-unit slip value. Due to the weak electromagnetic properties of the solid rotor, the per-unit slip tends to be large in comparison with the slip of a squirrel-cage rotor. Hence, in order to reduce the rotor losses and to acquire a high electrical efficiency, the nominal operation point of the motor should occur at a low value of per-unit slip. Considering the air-gap power and the per-unit slip, the rotor fundamental losses can

be calculated by using the well-known relationship between them [54].

Pf und,r= Pδ.s (2.22)

As a consequence, the rotor fundamental efficiency is obtained as in (2.23) [54].

ηf und,r=

P_δ− P_{f und,r}

P_δ = 1 − s (2.23)

On the other hand, in the machines with a solid rotor, eddy-currents that have a low penetration depth is generated by the air-gap harmonics. Because the rotor hysteresis loss is small, the effects may be ignored without making a big mistake. The surface losses Psur f,r can now be written by (2.23) [54].

Psur f,r= Pr,loss− Pf und,r (2.24)

The mechanical output power Pout of the rotor can be expressed by the input power and

the losses generated [54].

P_out= Pdelta− Pr,Loss− Pf und,r+ Pf r,r (2.25)

The electromechanical output power Pmech at the rated speed of the motor can be

expressed as a product of the electromagnetic torque Tem and the wr mechanical

angular speed of the rotor [54].

P_mech= Temwr (2.26)

The friction between a rotating rotor and a cooling gas raises significantly at very high speeds. Saari [14] and Kuosa [56] performed the analyses of friction losses in the air-gap of high-speed solid motors. Rotor dimensions affect the the friction loss caused by the rotating surface of the rotor extremely, so the angular rate of the rotor. As a result of the high angular velocity of the rotor, estimating of the friction losses is crucial. The calculation of friction and cooling loss is completed by means of analytical formulas based on experimental research. As stated by Saari [14] and Aglen [57], the friction power Pf r,rheld by the resisting drag torque of a rotation cylinder with the radius r can

be expressed in a basic case according to (2.27) where wr is the angular velocity of the

rotor, r is the rotor radius and Lr is the axial length of the slitted rotor part [54].

The torque coefficient CT depends on the tip Reynolds number and the coefficient

should be chosen separately for different flow regimes. Bilgen [58] suggested instance the torque coefficients for the active rotor core part. The surface roughness coefficient k_f is 1.0 for a smooth rotor and approximately 2.5 with an axially slitted rotor surface, according to [3]. The friction losses are proportional to the cube of the speed and the rotor forces the axial cooling gas flow into a tangential movement, as well. This causes an additional power loss Pf,a which reliably be calculated with equation (2.28)

where k2is the velocity factor, qmis the mass flow rate of the cooling gas and u is the

peripheral speed of the rotor [54].

P_f,a = k2qmu2 (2.28)

Additionally, the ends of the rotor have friction losses. The power needed to rotate the rotor end is expressed as in (2.28) where r2and r1are the outer and inner radius of the

end, respectively. CT is the corresponding torque coefficient which is referred to the

rotor end can be formed for instance from Kreith [59]. Not only the free space for the rotor ends in the end-winding area is generally large but also the rotor end acts like a centrifugal pump in electrical machines [54].

P_f,end = 1 2CTρ w

3_(r5

2− r15) (2.29)

The total loss in view of gas friction is a sum of the below loss components [54]. P_{f r},total= Pf r,r+ Pf,a+ 2Pf,end (2.30)

The power loss, caused by the gas friction losses, is taken from the axle power of the motor. Hence, smooth rotor surfaces are preferred over slitted ones at high speeds [54].

2.3 Space Harmonics in Solid Rotor Induction Motor

Harmonic analysis of air-gap MMF of SRIM is one of the principle topics in generalized electrical machine theory. MMF function can be considered to increase as a step function at the central axis of a slot. This increase is equal to the multiplication of number of turns per slot and the current passing through one turn. This approximation puts the MMF waveform into a step function [17]. Fourier series expansion is quite sufficient for the integral-slot winding predominantly used for induction machines. In