Induction Motor Analysis

Master Thesis

Time-stepping FE-analysis of a 22kW Variable

Impedance Induction Motor (VZIM) and thermal

analysis

Mehdi Hajinoroozi

Advisors:

Prof. Dr.-Ing. habil. h.c. Andreas Binder

Dipl.-Ing. Hooshang Gholizad

Novemebr 2011

ii

Summary

Variable Impedance Induction Motor consists of a sectionalized rotor, with 3 different

sections and each section has its own bars and end-rings which have different geometry and

materials, in order to achieve high starting torque and high efficiency at the rated operating

point together with high breakdown torque. In order to investigate the electromagnetic and

thermal characteristics of this motor (22 kW VZIM), three different motors VZIM1, VZIM2

and VZIM3 with the same stator but different rotors have been considered and analyzed.

Electromagnetic and thermal analyses of a 22kW Variable Impedance (Z) Induction Motor

(VZIM) are the aim of this master thesis. Finite element method is a precise and useful

approach to analyze electrical machines, therefore the electromagnetic analysis of the VZIM

motor is done using Flux2D software and the thermal analysis is done by ANSYS software.

Furthermore all the calculation results obtained by finite element method and relevant tools

are compared with analytical calculations, carried out by KLASYS program. In order to do

steady state AC and time stepping electromagnetic analysis of the 22kW VZIM motor, first

the geometries of three assumed independent motors VZIM1, VZIM2 and VZIM3 are

generated in Flux2D and with assigning the materials and meshing the geometries, the models

are solved and relevant torque-slip, fundamental stator phase current-slip, input power-slip,

efficiency-slip and power factor-slip characteristics are calculated by Flux2D and compared

with the results of the KLASYS software.

In addition, for thermal calculations due to the existence of the measured values of the 5.5kW

VZIM motor, first the 5.5kW motor is analyzed with the ANSYS tool and the results are

compared with measured values, afterwards the 22kW VZIM motor is analyzed with ANSYS

tool and the results are compared with a simplified thermal equivalent circuit model results.

To carry out the simulation with ANSYS, first the geometries of three assumed independent

motors VZIM1, VZIM2 and VZIM3 are generated and after assigning the materials and

meshing the geometries, the models are solved with assigning the loss densities of different

parts of the motors as heat sources. At the end the values of analytical calculations and finite

element method are compared to make sure that the temperature rise in the stator winding

does not exceed the thermal limit of the insulations.

iii

Contents

Table of Contents

List of Symbols

List of Figures

List of Tables

1 Introduction

1.1 Preface 1

1.2 Electromagnetic and thermal analysis of the 22kW VZIM 3

1.3 Introduction to finite element method 3

1.4 Electrical and mechanical parameters and dimensions of the 22kW VZIM 6

1.5 Procedure of the project 10

2 Geometry and mesh generation with Flux2D

2.1 Introduction 11

2.2 Geometry creation 11

2.3 Meshing the geometry 12

2.4 Material assignment 14

2.5 Electrical circuit for the motor 15

2.6 Calculation of values of circuit’s elements 16

2.6.1 Stator resistance 16

2.6.2 Inductance of stator winding overhang 16

2.6.3 Rotor end-ring leakage inductance 17

2.6.4 Resistance of the end-Ring Segment VZIM1 17



3 Steady state electromagnetic analysis

3.1 Introduction 20

3.2 Steady state AC analysis of the 22kW VZIM 21

3.2.1 Steady state AC analysis of the VZIM1 21



4 Time stepping analysis of VZIM

4.1 Introduction 32

4.2 Stator and rotor field spatial harmonics 32

4.3 Asynchronous harmonic torques 32

4.4 Synchronous harmonic torques 33

4.5 Derived slips used for time stepping analysis 34

4.6 Time-stepping analysis of induction motors 35

4.6.1 Time-stepping analysis of VZIM1 35



iv

4.7 Instantaneous Torque wave forms at different rotor speeds 50

4.8 Synchronous harmonic torque assessment in VZIM 54

4.9 Power losses in different parts of the motor 61

4.9.1 Losses of VZIM at different speeds 63

5 Thermal analysis

5.1 Preface 65

5.2 Temperature rise calculation by thermal equivalent circuits 65

5.2-1 Calculation of and for VZIM2 (22kW) 69

5.2-2 Calculation of and for VZIM3 (22kW) 70

5.3 Numerical calculation of temperature rise 71

5.3.1 Thermal analysis of 5.5kW VZIM2 72

5.3.2 Thermal analysis of 5.5kW VZIM3 75

5.3.3 Thermal analysis of 22kW VZIM2 79

5.3.4 Thermal analysis of 22kW VZIM3 82

6 Conclusion 87

7 Bibliography 88

8 Appendix

8.1 Appendix I 89

8.2 Appendix II 91

8.3 Appendix III 109

8.4 Appendix IV 111

v

List of Symbols

- number of parallel baranches of winding

- parallel wires per turn B T magnetic flux density

H A/m magnetic field strength

A Vs/m Magnetic vector potential

m inner stator diameter f Hz electric frequency

h m height of stator slot opening

- distribution factor

- slot fill factor, frequency coefficient

- pitching factor

- winding factor

m Pole pitch

l m axial length

L m self-inductance

L m overall length

- permeance /unit length

m length of the winding overhang

m - number of phases

m mean diameter of the end-ring

m length of the end-ring segment

m cross section area of end-ring

m end-ring thickness

m end-ring height

M N.m. torque

n 1/s rotational speed

- number of turns per phase

- number of turns per coil

p - number of pole pairs

P W power

q - number of slots per pole and phase

Q - number of slots

R Ohm electric resistance and thermal resistance

s - slip

m slot opening

t s time

u,U V electric voltage

, - current/voltage transformation ratio

V A magnetic voltage (m.m.f.)

m circumference co-ordinate

m air gap width

S/m electric conductivity

density

Ohm.m electric resistivity

- ordinal number of rotor space harmonics

Vs/(Am ) magnetic permeability

- ordinal number of stator space harmonics

vi

1/s electric angular frequency

K/W Heat resistance

temperature

K temperature rise

W Copper losses

W iron losses

W/( ) heat transfer coefficient

j A/ current density

i A current

W volume density of instantaneous power loss

Ws/( ) hysteresis coefficient

1/(Ohm.m)) coefficient of losses in excess

T peak value of the magnetic flux density

m/s wind speed over stator outer surface and winding overhang

d m thickness of slot insulation and stator and rotor lamination W/(m. ) Thermal conductivity

vii

List of Figures

1.1-1 Cross-section of variable impedance induction motor, rotor position at stand still

[6] 2

1.1-2 Cross-section of variable impedance induction motor rotor position at nominal

speed [6] 2

1.4-1 Cross-section of Variable Impedance Induction motor (VZIM1), Prepared by

ANSYS 8


ANSYS 9


ANSYS 9

2.2-1 Created geometry of VZIM1, by Flux2D 11 2.2-2 Created geometry of VZIM2, by Flux2D 11 2.2-3 Created geometry of VZIM3, by Flux2D 12 2.3-1 Generated mesh of VZIM1 in the air-gap using Flux2D 12 2.3-2 Generated mesh of VZIM1 using Flux2D 13 2.4-1 B-H characteristic of M270-50A iron sheets, which are used in stator and rotor

lamination [7] 14

2.5-1 Star connected stator electrical circuit of the motor, by Flux2D 15 3.1-1 Nonlinearity relation of B and H [5] 20 3.1-2 Static and equivalent B-H curves for different cases [5] 21 3.2.1-1 Torque-slip characteristics of VZIM1, comparison of the steady state calculation

results of Flux2D and the analytical calculations by KLASYS 22

3.2.1-2 Torque-slip characteristics of VZIM1, comparison of skewed and unskewed rotor,

obtained by KLASYS 23

3.2.1-3 Phase current-slip characteristic of VZIM1, comparison of the steady state

calculation results of Flux2D and the analytical results of KLASYS

23

3.2.1-4 Normal component of air-gap flux density for one pole pair of VZIM1 at a

slip of 0.0253, calculated by Flux2D

24

3.2.1-5 Numerically calculated flux lines in VZIM1 at a slip of 0.0253, obtained

by Flux2D 25

3.2.2-1 Torque-slip characteristics of VZIM2, comparison of the steady state calculation




27



27

3.2.2-4 Numerically calculated flux lines in VZIM2 at a slip of 0.0253, obtained by

Flux2D 28

3.2.3-1 Torque-slip characteristics of VZIM3, comparison of the steady state calculation




30



30

3.2.3-4 Numerically calculated flux lines in VZIM3 at a slip of 0.0253, obtained by

Flux2D 31

4.3-1 Asynchronous harmonic torques of the 5th and 7th stator field harmonics,

which are superimposed on fundamental asynchronous torque [2] 33

4.4-1 Typical effects of synchronous and asynchronous harmonic torques in induction

machines [2]

34

viii

4.6.1-1 Torque-slip characteristic of unskewed VZIM1, calculated with Flux2D time-

stepping, the effects of the synchronous harmonic torques at slips

, and of the the motor are observable

36

4.6.1-2 Torque-slip characteristic of unskewed VZIM1, calculated with KLASYS, the

effects of the synchronous harmonic torques at slips , and

of the the motor are observable

36

4.6.1-3 Torque-slip characteristic of unskewed VZIM1, time-stepping and AC analysis

results obtained by Flux2D, the harmonic torque effects at lower speeds of the

motor are obvious

38

4.6.1-4 Stator phase current of unskewed VZIM1, time stepping analysis results

calculated by Flux2D and KLASYS 38

4.6.1-5 Input power-slip of VZIM1, comparison of the analysis results calculated by

Flux2D and KLASYS 38

4.6.1-6 Output power-slip of VZIM1, comparison of the analysis results calculated by


4.6.1-7 Efficiency-slip of VZIM1, comparison of the analysis results calculated by


4.6.1-8 Power factor-slip of VZIM1, comparison of the analysis results calculated by


4.6.2-1 Torque-slip characteristic of unskewed VZIM2, obtained by KLASYS and Flux2D

time-stepping calculations, the harmonic torque effects at lower speeds of the

motor are observable

41




41



motor are obvious

42

4.6.2-4 Stator phase current of unskewed VZIM2, comparison of the time stepping

analysis results calculated by Flux2D and KLASYS 43







4.6.2-8 Power factor-slip of VZIM2, comparison of the analysis results calculated by


4.6.3-1 Torque-slip characteristic of unskewed VZIM3, calculated with Flux2D time-

stepping, the effects of the synchronous harmonic torques at slips

, and of the the motor are observable

46




46



motor are obvious

47

4.6.3-4 Stator phase current of unskewed VZIM2, comparison of the analysis results

calculated by Flux2D and KLASYS 47





ix



4.6.3-8 Power factor of VZIM3, comparison of the analysis results calculated by Flux2D

and KLASYS 49

4.7-1 Torque-time characteristic of VZIM2 at 1462rpm, calculated by Flux2D, torque

oscillates around a constant mean value after reaching the steady state 50

4.7-2 Torque-time characteristic of VZIM2 at 1462rpm, calculated by Flux2D, zoomed

view after steady state is reached 51


oscillates around a constant mean value after reaching the steady state 51


view after a steady state is reached 52


oscillates around a constant mean value 52


view after a steady state is reached 53

4.7-7 Torque-time of VZIM2 at 205.5rpm, calculated by Flux2D, where break down slip

of the 7th asynchronous torque harmonic happens at slip 0.863 or 205.5rpm

53

4.8-1 First and second positions of the rotor bars with fixed stator position to

calculate the synchronous harmonic torques, prepared by Flux2D

54

4.8-2 Torque-time of unskewed VZIM2 at , calculated by Flux2D, rotor

position step 1

54


position step 5

55


position step 7

55

4.8-5 Variation of synchronous torque at as a function of rotor position 56 4.8-6 Variation of synchronous torque at a function of rotor position 56 4.8-7 Variation of synchronous torque at as a function of rotor position 56

4.8-8 Torque-time of unskewed VZIM2 at speed 224.28 rpm, calculated by Flux2D 58

4.8-9 Torque-time of unskewed VZIM2 at speed 10 rpm, calculated by Flux2D 59

4.8-10 Torque-time of unskewed VZIM2 at speed -97.14 rpm, calculated by Flux2D 59

4.9.1-1 Comparison between losses of VZIM1 at speed equal to 1390.9 calculated

with Flux2D and KLASYS

63



64



64

5.2-1 The simplified thermal equivalent network for an induction motor 66 5.2-2 Output power-slip characteristics of 22kW VZIM2 and VZIM3 and the average of

the powers 67

5.2-3 Calculated output power of the VZIM motor with the supper-position and

equivalent circuit methods 68

5.3.1-1 2D model of the 5.5kW VZIM2 and meshing, by ANSYS 72 5.3.1-2 3D model of the 5.5kW VZIM2, by ANSYS 72 5.3.1-3 3D model meshing of the 5.5kW VZIM2, by ANSYS 73 5.3.1-4 The thermal solution of the 5.5kW VZIM2 under nominal operation, by ANSYS 74 5.3.1-5 The calculated temperature in the winding overhang of VZIM2, by ANSYS 75 5.3.2-1 2D model of the 5.5kW VZIM3 and meshing, by ANSYS 75 5.3.2-2 3D model of the 5.5kW VZIM3, by ANSYS 76 5.3.2-3 3D model meshing of the 5.5kW VZIM3, by ANSYS 76 5.3.2-4 The thermal solution of the 5.5kW VZIM3 under nominal operation, by ANSYS 78 5.3.2-5 The calculated temperature in winding overhang of 5.5kW VZIM3, by ANSYS 78

x

5.3.3-1 2D model of the 22kW VZIM2 and meshing, by ANSYS 79 5.3.3-2 3D model of the 22kW VZIM2, by ANSYS 79 5.3.3-3 3D model meshing of the 22kW VZIM2, by ANSYS 80 5.3.3-4 The thermal solution of the 22kW VZIM2 under nominal operation, by ANSYS 81 5.3.3-5 The calculated temperature in the winding overhang of 22kW VZIM2, by ANSYS 82

5.3.4-1 2D model of the 22kW VZIM3 and meshing, by ANSYS 82 5.3.4-2 3D model of the 22kW VZIM3, by ANSYS 83 5.3.4-3 3D model meshing of the 22kW VZIM3, by ANSYS 83 5.3.4-4 The thermal solution of the 22kW VZIM3 under nominal operation, by ANSYS 85 5.3.4-5 The calculated temperature in the winding overhang of 22kW VZIM3, by ANSYS 85

xi

List of Tables

1.4-1 Stator dimensions 6 1.4-2 Stator winding details 6 1.4-3 The rotor dimensions and parameters of VZIM1 7 1.4-4 The rotor dimensions and parameters of VZIM2 7 1.4-5 The rotor dimensions and parameters of VZIM3 7 1.4-6 VZIM material details 8 2.4-1 B-H characteristic data of the iron sheet type M270-50A [7] 14 2.6-1 Electrical values of VZIM stator circuit 19 4.8-1 Maximum, minimum and peak to peak values of synchronous torque for

VZIM2 in two different methods of calculation (rotation and oscillation

methods) for the slip

57

4.8-2 Maximum, minimum and peak to peak values of synchronous torque for



57




58


VZIM1 (oscillation method) 58


VZIM3 (oscillation method) 58


VZIM1, at the slip , the comparison of the calculated values by

KLASYS and Flux2D

60


VZIM1, at the slip , the comparison of the calculated values by KLASYS

and Flux2D

60



KLASYS and Flux2D

60



KLASYS and Flux2D

60



and Flux2D

60



KLASYS and Flux2D

60



KLASYS and Flux2D

61



and Flux2D

61



KLASYS and Flux2D

61

4.9-1 Values of specific total losses according to the data sheet of the M270-

50A [7], and calculated power losses, in frequencies 50Hz, 100Hz and

200Hz

62

xii

5.2-1 Heat transfer coefficient for one side of the winding overhang close to the

centrifugal mechanism 67

5.2-2 Losses in different parts of the VZIM2 and VZIM3 in the speed equal to

1467.36 rpm 68

5.2.1-1 Thermal conductivities of the materials used in VZIM2 thermal model 69

5.2.2-1 Thermal conductivities of the materials used in VZIM3 thermal model 70 5.2.2-2 Temperature rise in the stator winding of VZIM2 and VZIM3 calculated based

on simplified thermal equivalent circuit in the nominal operating speed equal to

1467.36 rpm

71

5.3.1-1 Loss densities in different parts of the 5.5kW VZIM2 73 5.3.1-2 Heat transfer coefficient at different boundary conditions of the 5.5kW VZIM2 74

5.3.2-1 Loss densities in different parts of the 5.5kW VZIM3 76 5.3.2-2 Heat transfer coefficient at different boundary conditions of the 5.5kW VZIM3 77

5.3.2-3 Temperature rise in stator slot of 5.5kW VZIM2 and VZIM3 calculated by

ANSYS 78

5.3.3-1 Loss densities in different parts of the 22kW VZIM2 80

5.3.3-2 Heat transfer coefficient at different boundary conditions of the 22kW VZIM2 81

5.3.4-1 Loss densities in different parts of the 22kW VZIM3 83

5.3.4-2 Heat transfer coefficient at different boundary conditions of the 22kW VZIM3 84 5.3.4-3 Temperature rise in stator slot of 22kW VZIM2 and VZIM3 calculated by

ANSYS 85

5.3.4-4 Temperature rise in stator slot of 22kW VZIM2 and VZIM3 calculated by

ANSYS 86

Appendix II Synchronous harmonic torque slip 91 Appendix II Stator ordinal numbers and related asynchronous harmonic torque slips 92 Appendix II Stator ordinal numbers and related asynchronous harmonic torque slips 96 Appendix II Stator ordinal numbers and related asynchronous harmonic torque slips 101 Appendix II Slips which are used to perform time-stepping analysis of VZIM1 106 Appendix II Slips which are used to perform time-stepping analysis of VZIM2 107 Appendix II Slips which are used to perform time-stepping analysis of VZIM3 108 Appendix III Losses in VZIM1 calculated by Flux2D and KLASYS 109 Appendix III Losses in VZIM2 calculated by Flux2D and KLASYS 109 Appendix III Losses in VZIM3 calculated by Flux2D and KLASYS 110

- 1 -

Chapter 1: Introduction

1.1 Preface

Due to the robustness and reliability with low production and maintenance costs of the line

operated induction motors, this type of machines are used in more than 80% of motor

applications worldwide.

Making use of current displacement effect by designing induction motors with deep bar or

double cage rotors results in desirable starting torque and efficiency at nominal speed

operation, but reduction of breakdown torque is not favorable which happens in this case

because of increased rotor leakage reactance. One possible solution is Variable Impedance

Induction Motor (VZIM).

The Variable Impedance Induction Motor has high starting torque, in addition to high

efficiency at the nominal operating point. This type of induction motor includes a

sectionalized cage rotor with different bar shapes for each sub-cage section is used. At

standstill, sub-cages with high resistances are placed inside the stator bore to increase the

starting torque and reduce the starting current. By increasing the rotational speed, a

centrifugal mechanism moves the rotor in the axial direction and brings the other sections of

the rotor cage with low resistances inside the stator bore to reduce the rotor losses at rated

speed. This leads to increased efficiency at nominal operation [6]. Figures 1.1-1 and 1.1-2

show the cross section view of a 3-section VZIM motor at standstill and nominal speed.

The rotor length is 1.5 times the stator length, and it is composed of three different sub-cages

(“A”: starting sub-cage, “B”: middle sub-cage and “C”: final sub-cage). At standstill, the sub-

cages “A” and “B” are inside the rotor bore; means they are active at start-up of the motor).

By increasing the speed, a centrifugal axial rotor shifter mechanism pulls the rotor in the axial

direction and brings the third section of the rotor cage inside the stator bore. At the nominal

speed the sub-cage “A” is put completely out of the stator bore and only the sub-cages “B”

and “C” are active.

- 2 -

Fig 1.1-1: Cross-section of variable impedance induction motor, rotor position at stand still [6]

Fig 1.1-2: Cross-section of variable impedance induction motor rotor position at nominal speed [6]

- 3 -

1.2 Electromagnetic and thermal analysis of the 22kW VZIM

A 4 pole, 22kW VZIM operating with a nominal voltage of 400V and a nominal frequency of

50Hz has been designed. The rotor has 3 sections with different rotor bar shapes. The first

rotor section has round bars, the middle cage has deep bars and the final cage has wedge bars.

The electromagnetic characteristics and thermal effects of the electrical losses in this motor

has been analyzed and investigated.

With the help of Flux2D and ANSYS which are suitable tools for electromagnetic and thermal

analysis and are based on finite element method, the motor’s characteristics and features are

calculated and the results of the electromagnetic analysis prepared by Flux2D are compared

with analytical calculations which mostly are obtained by KLASYS tool.

In this analysis it has been assumed that there are three motors with the same stator but

different rotor bars, therefore three motors VZIM1, VZIM2 and VZIM3 are analyzed.

1.3 Introduction to finite element method [4]

In engineering and science there are many physical phenomena which can be described with

Partial Differential Equations (PDE), solving these equations with analytical methods for

arbitrary shapes is almost impossible. The Finite Element Method (FEM) is a numerical

approach by which these PDE can be approximately solved.

Solving a PDE by FEM method is done by dividing the calculation domain in finite elements

in which a known variation of the physical values is assumed. This variation is usually a

polynomial variation with an arbitrary power but in practical applications the maximal degree

Three is used. In conclusion the field distribution is assumed to be a polynomial variation of

first order in most of the cases, of second order in more rare situation and extremely rare of

the third order.

To have a good FEM calculation some general rules must be followed. After dividing the

calculation domain in finite elements with meshing the area of calculation, first of all the

finite elements have to cover the entire calculation domain, the elements must not overlap and

the nodes of one element cannot be found on the lines of the adjacent elements but must have

the same position with the adjacent elements nodes.

In case of magneto static problems, the field is described by the following Maxwell equations,

and the constitutive law for material,

From we can write B as,

because it is always true , where is called the magnetic vector potential.

From , and the differential equation that describes a magneto

static problem can be obtained,

- 4 -

Each field is defined by its sources , and by related eddies , so

may be chosen free. The coulomb gauge is often used as

Further, if a constant vector is added to , still and are valid,

so the magnetic vector potential is defined by choosing the value for one node from

domain. This is necessary in order to obtain a correct solution. The unknown of the problem is

the value of in the grid nodes and the field source is given by the current density in the

elements volumes (areas for 2D).

After solving the linear system of equations the values of the flux density B are obtained.

Afterwards the field strength H due to is calculated and by integration over the

domain the energy and generated force can also be calculated.

In FEM the stored magnetic energy is calculated by integrating the energy density as a

volume integral for 3D-FEM or as an area integral for 2D-FEM. The volume energy density is

defined as: .

The energy density can be integrated on the calculation domain for the 3D-FEM as it follows

As is calculated as derivative of , is constant within each element. Via

also H is constant within each element. So considering that inside one element the

values for B and H are constant, can be transformed into:

For 2D-FEM the equation is valid, if we consider that we have a length of the

model in the z direction equal with :

The energy in is measured in , whereas the energy in is measured in

. In order to get the value of the stored magnetic energy in a volume from a 2D-FEM

calculation, one has to multiply the calculated value with the length of the model in the z-

direction.

For the magneto static calculation the magnetic field is considered to be constant and no eddy

currents are induced in the conductive materials. This stationary situation is sufficient to

describe only the problems with slow varying fields and problems where the effects of the

variation of the fields are considered negligible. For the rest of the problems consideration of

- 5 -

the variation of the fields is necessary and calculation in time domain or in frequency domain

is applied. The time domain calculation is actually a succession of static calculations for

different time moments. The time variable cannot be considered continuously and has to be

considered using a certain time step. Each static calculation that is performed during a

transient calculation is called a non-linear iteration and for each iteration the results from the

previous iteration are considered as starting point. The variation of magnetic field between

two iteration steps determines the variation speed of the magnetic field. In order to calculate

this influence the Maxwell equations must be written in a form that considers the magnetic

field variation in time

and the constitutive law for material

Like for magneto static problems we can write the flux density as a curl of vector potential

Using in we obtain

which is the electric field strength determined by the time-varying field. It represents the

electromotive force induced in the conductor due to the magnetic field variation. From

we can calculate the current density induced by the magnetic field variation

using

The current density has 2 components:

-The source component that is given as entry data for the problem at the beginning of the

calculation. It is represented by the current density in the conductors that are exciting the

primary magnetic field model.

-The component that is induced due to the magnetic field variation .

Considering these two components results in

This is the differential equation to be solved by the FE program, in a time-step solution. In

practice with usage of a finite element tool there are some steps to solve the problem. The

geometry is prepared, then geometry must be meshed and afterwards material are assigned to

the regions, finally by linking an external electrical circuit the model is ready to be solved. To

create the geometry, symmetry and periodicity must be taken into account. If the geometry

- 6 -

has periodicity, type of the periodicity (symmetric or anti-symmetric conditions) must be

defined.

1.4 Electrical and mechanical parameters and dimensions of the 22kW VZIM

Due to three rotor sections the names VZIM1 for the first cage, VZIM2 for the middle cage

and VZIM3 for the last cage, are assigned to each part of the rotor.

Stator dimensions are given in Table 1.4-1. The stator winding details, which has a star

connection are listed in Table 1.4-2. Tables 1.4-3, 1.4-4 and 1.4-5 list the rotor dimensions

and parameters of the VZIM1, VZIM2 and VZIM3. The rotor sub-cages are not skewed. Table

1.4-6 consists of the material details used in VZIM.

Table 1.4-1: Stator dimensions

Description parameter Dimension Value

Stack length mm 240

Inner stator diameter mm 170

Outer stator diameter mm 270

Air gap width mm 0.45

Number of stator slots - 36

Width of stator slot opening mm 3.1

Height of stator slot opening mm 0.737

Stator slot heit mm 22.6

Stator slot width mm 10.277

Radius of stator slot opening mm 3.606

Table 1.4-2: Stator winding details


Number of phases m - 3

Number of pole pairs p - 2

Number of slots per pole and phase q - 3

Number of turns per coil - 12

Number of parallel branches a - 1

Type of winding - - Single layer

Winding pitch - - Full pitch

Number of turns per phase - 72

Length of overhang mm 226.6

Number of parallel wires per turn - 9

Diameter of conductor mm 1

Winding connection - - Star

- 7 -

Table 1.4-3: The rotor dimensions and parameters of VZIM1


Outer rotor diameter mm 169.1

Inner rotor diameter mm 80

Number of rotor bars - 28

Bar shape - - Round

Bar material - - Bronze

Width of rotor slot opening mm 4.5

Height of rotor slot opening mm 1

Rotor bar diameter mm 10.2

End-ring thickness mm 4.3

End-ring height mm 44






Bar shape - - Deep

Bar material - - Copper

Width of rotor slot opening mm 4


Height of rotor bar mm 8.2

Width of rotor bar mm 9.2

End-ring thickness mm 4.6







Bar shape - - Inverse wedge

Bar material - - Copper

Width of rotor slot opening mm 2


Height of rotor bar mm 17.7

Width of rotor bar mm 10.2

End-ring thickness mm 6


- 8 -

Table 1.4-6: VZIM material details


Conductivity of bronze at 110 S 1.69E+7

Conductivity of copper at 110 S 4.22E+7

Lamination type - - M270-50A

Conductivity of lamination S 1.818E+6

Loss at 50Hz, 1T W/kg 1.07

Loss at 50Hz, 1.5T W/kg 2.52

Cross-sections of the motors have been depicted in figures 1.4-1, 1.4-2 and 1.4-3. The first

motor VZIM1 has round rotor bars made of bronze and second and third motor VZIM2 and

VZIM3 have rotor bars made of copper.

Fig 1.4-1: Cross-section of Variable Impedance Induction motor (VZIM1), prepared by ANSYS

- 9 -



- 10 -

1.5 Procedure of the project

In order to simplify the simulation, three separate induction motors have been considered, in

this simulation VZIM1, VZIM2 and VZIM3 each one has a full length rotor and stator.

With the help of Flux2D, electromagnetic analysis and with ANSYS, thermal analysis has been

done.

Two types of electromagnetic analysis have been carried out:

-Steady state magnetic AC analysis

-Time stepping analysis.

All results from Flux2D have been compared with the analytical results of KLASYS tool.

- 11 -

Chapter 2: Geometry and mesh generation with Flux2D

2.1 Introduction

Electromagnetic analysis based on finite element method is done with Flux2D. In this chapter

the creation of geometry, mesh generation, electrical circuit determination and material

assignment is explained.

2.2 Geometry creation

The variable impedance induction motor which is analyzed has 4-poles, 36-stator slots and 28

rotor bars, three different motors with the same stator but different rotors are being

considered. Based on this consideration 3 models has been created.

Because of simplicity and according to Anti-cyclic boundary condition, ¼ of the motor is

modeled. Three models which have been prepared as VZIM1, VZIM2, and VZIM3 are

depicted in Fig 2.2-1, Fig 2.2-2 and Fig 2.2-3.

Fig 2.2-1: Created geometry of VZIM1, by Flux2D Fig 2.2-2: Created geometry of VZIM2, by

Flux2D

- 12 -

Fig 2.2-3: Created geometry of VZIM3, by Flux2D

2.3 Meshing the geometry

An automatic mesh generator is in charge of meshing the faces. With the help of the mesh

points, it is possible to have fine and dense meshing in the areas which the higher accuracy is

needed. Fine mesh in the air-gap, at the top of the rotor bars, and the stator teeth, is necessary

because of accuracy of the results, air-gap must be fine meshed, to have accurate torque

calculation. The top of the rotor bars near the air gap are densely meshed, to taking into the

account the current displacement effect. In addition the stator teeth must be meshed fine

enough to consider the saturation effect because of high flux density in this area. In Fig.2.3-1

and Fig.2.3-2 generated mesh for VZIM1 is shown. The fine mesh in the air-gap is observable

in Fig.2.3-1.

Fig 2.3-1: Generated mesh of VZIM1 in the air-gap using Flux2D

- 13 -

Fig 2.3-2: Generated mesh of VZIM1 using Flux2D

- 14 -

2.4 Material assignment

Stator and rotor lamination in 22kW VZIM are made of M270-50A [7]. B (H) curve and

values are shown in Fig.2.4-1 and table 2.4-1.

Table 2.4-1: B-H characteristic data of the iron sheet type M270-50A [7]

H/(A/ ) B/Tesla H/(A/ ) B/Tesla

0 0 2119.027 1.516379

21.73374 0.454861 2668.102 1.534915

43.46748 0.7016061 3354.447 1.556988

73.65323 0.902243 4212.377 1.582977

111.3854 1.048599 5284.791 1.613156

158.5506 1.157766 6625.307 1.647613

217.5072 1.240593 8300.953 1.686154

291.2029 1.304297 10395.51 1.728191

383.3224 1.353865 13013.71 1.772635

498.472 1.392849 16286.45 1.817807

642.4088 1.42385 20377.38 1.861388

822.3299 1.448816 25491.05 1.900418

1047.231 1.469241 31883.13 1.931347

1328.358 1.486302 43860.55 1.955117

Fig.2.4-1: B-H characteristic of M270-50A iron sheets, which are used in stator and rotor lamination

[7]

0

0.5

1

1.5

2

2.5

0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000

B/T

esla

H/A ^(− )

B-H Characteristic of M270-50A iron sheets

- 15 -

VZIM1 has rotor bars which are made of bronze, VZIM2 and VZIM3 have rotor bars made of

copper. This special alloy of bronze has the electrical resistivity equal to 0.588E-07 Ohm.m.

Copper has the electrical resistivity equal to 0.237E-07 Ohm.m.

2.5 Electrical circuit of the motor

Three phase winding in 22kW VZIM is star connected. The electrical circuit which is created

in Flux2D, is depicted in Fig.2.5-1.

Fig.2.5-1: Star connected stator electrical circuit of the motor, by Flux2D

The resistances R1, R2 and R3 represent the winding overhang resistances; also the

inductances L1, L2 and L3 represent the overhang inductances. In addition stator phase

windings under stator slots are shown as BPA, BPB and BMC.

VA, VB and VC are three phase voltage sources with 230 V and 120 degree phase shift with

each other; moreover Q1 represents the squirrel cage rotor which is connected to common

point of voltage sources.

- 16 -

2.6 Calculation of values of circuit’s elements

The values of the circuit components are calculated and assigned to the circuit. In this section

the values of the stator resistance, inductance of stator winding overhang, rotor end-ring

leakage inductance and resistance of the end-ring segments are calculated.

2.6.1 Stator resistance

Stator winding resistance per phase is sum of resistance of the coil under stator slots

(also ) and winding overhang (also and ). Resistance per phase

is calculated according to [1]:

Resistance of one phase under stator slot at 20 equals to:

and the resistance of one phase under slot of stator in 110 is given by:

Resistance of the winding overhang at 20 is calculated as below:

and the resistance of winding overhang at 110 is equal to:

2.6.2 Inductance of stator winding overhang

Inductance of the winding overhang is calculated according to [1], using following equation:

where is the length of the winding overhang and is the permeance /unit length which is

calculated as below:

where is the diagonal of the cross-section of the coils in the winding overhang and is

calculated as following:

- 17 -

According to [1] for a single phase winding with q=3, c is equal to 0.67 and is calculated

as below:

Therefore the inductance of the winding overhang equals to:

2.6.3 Rotor end-ring leakage inductance

Rotor end-ring leakage inductance is calculated according to [1] as following:

where and , hence:

2.6.4 Resistance of the end-ring segment of VZIM1

First of all the mean diameter of the end-ring is calculated which is the mean value of

the inner diameter and the outer diameter of the end-ring:

With the number of the rotor bars and the mean diameter of end-ring, the length of

the end-ring segment is calculated as below:

the end-ring thickens is and the end-ring height is using end-

ring thickness and height, the cross section area of end-ring is calculated as:

.

Then resistance of the end-ring is calculated as:

2.6.5 Resistance of the end-Ring Segment VZIM2

The mean diameter of the end-ring is calculated using the mean value of the inner

diameter and the outer diameter of the end-ring:

- 18 -

With the number of the rotor slots and the mean diameter of end-ring, the length of

the end-ring segment is calculated as:

end-ring thickens is, and the end-ring height is .using end-

ring thickness and height, the cross section area of end-ring is calculated as:

conductivity of copper in 110 is calculated as:

Then resistance of the end-ring is calculated as:

2.6.6 Resistance of the end-ring segment VZIM3

The mean diameter of the end-ring is calculated using the mean value of the inner

diameter and the outer diameter of the end-ring,

with the number of the rotor slots and the mean diameter of end-ring, the length of

the end-ring segment is calculated as:

end-ring thickens is and the end-ring height is .using end-ring

thickness and height, the cross section area of end-ring is calculated as:

conductivity of copper in 110 is calculated as:

Then resistance of the End-Ring is calculated as:

All the values derived from formulas in sections 2.6.4 to 2.6.6 are shown in Table 2.6-1.

- 19 -

Table 2.6-1: Electrical values of VZIM stator circuit

Parameter value description

, 0.116 Ω Resistance per phase of the coil under stator slot

, , 0.1095 Ω Resistance per phase of winding overhang

, , 0.424 mH Inductance pre phase of winding overhang

End-ring leakage inductance

Resistance of the end-ring segment, VZIM1



- 20 -

Chapter 3: Steady state electromagnetic analysis

3.1 Introduction

In steady state electromagnetic analysis, it is assumed that variables are changing purely

sinusoidal with time and there are no harmonics. Due to the saturation effect of magnetic

material, electromagnetic flux density B and electromagnetic field strength H, could not be

sinusoidal at the same time. If the electric circuit had voltage source the B would be

considered as sinusoidal variable and therefore because of B (H) curve, H would not be a

sinusoidal variable with time. Fig.3.1-1 shows that how B and H curves change if one of them

is sinusoidal.

Fig. 3.1-1: Nonlinearity relation of B and H [5]

The above contradictions are dealt by using an equivalent B(H) characteristic, which is

different for the original B(H) characteristic and based on the energy equivalence method, as

shown in Fig.3.1-2. For the two extreme cases of B sinusoidal and H sinusoidal the B(H)

curve is modified and shown in Fig.3.1-2 based on the above method. The results obtained

with the equivalent curves calculated in the two extreme cases most often include the exact

result. The equivalent curve can equally be calculated by means of a linear combination

between these two extreme cases as shown in Fig.3.1-2. Only the numerical values of the

post-processed quantities, that depend on energy, are correct. The instantaneous values

computed by this analysis are approximations as they are sinusoidal.

- 21 -

Fig. 3.1-2: Static and equivalent B-H curves for different cases [5]

3.2 Steady state AC analysis of the 22kW VZIM

As previously was mentioned the VZIM motor is considered as three different motors with

the same stator and different rotor bars. Therefore three different motors VZIM1, VZIM2 and

VZIM3 are analyzed and the results are compared with analytical calculations obtained from

KLASYS tool.

3.2.1 Steady state AC analysis of the VZIM1

Fig.3.2.1-1 shows the torque-slip characteristic of VZIM1, which compares the steady state

AC analysis results calculated by Flux2D and KLASYS. It is apparent that the values

calculated by KLASYS are higher than values obtained using Flux2D. In lower slips the

difference between the values of KLASYS and Flux2D are less than 10% and in slips higher

than 0.3 the difference reaches to around 12%. In addition the breakdown torque in both

calculation methods happens around slip equal to 0.65, for the unskewed rotor cage. The

calculation results for the skewed rotor with one stator slot pitch obtained by KLASYS shows

that the breakdown slip is close to one as depicted in Fig.3.2.1.2. As the rotor is equivalently

skewed by shifting the sub-cages in the circumferential direction with respect to each other

by half a stator slot pitch, , which is equivalent to one sator slot

pitch skewing, therefore in the design phase, the optimization has been done for the skewed

rotor case to achieve the maximum starting torque at stand still.

- 22 -

The stator phase current-slip characteristics of VZIM1 which are prepared by Flux2D and

KLASYS are depicted in Fig.3.2.1-3. Maximum deviation between results of the KLASYS and

Flux2D is less than 4%, which shows a good precision.

In Fig.3.2.1-4 the normal component of the air-gap flux density of VZIM1 at a slip of 0.0253

for one pole pair or 180 mechanical degrees has been depicted.

Fig.3.2.1-5 shows the numerically calculated flux lines in VZIM1 by 2 pole pairs at a slip of

0.0253 or 1462.05 , obtained by Flux2D.

Fig.3.2.1-1: Torque-slip characteristics of unskewed VZIM1, comparison of the steady state

calculation results of Flux2D and the analytical calculations by KLASYS

- 23 -

Fig.3.2.1-2: Torque-slip characteristics of VZIM1, comparison of skewed and unskewed rotor,

obtained by KLASYS

Fig.3.2.1-3: Phase current-slip characteristic of unskewed VZIM1, comparison of the steady

state calculation results of Flux2D and the analytical results of KLASYS

- 24 -

Fig.3.2.1-4: Normal component of air gap flux density in the center of the air gap, for one

pole pair of VZIM1 at a slip of 0.0253, calculated by Flux2D

- 25 -

Fig.3.2.1-5: Numerically calculated flux lines in VZIM1 at a slip of 0.0253, obtained by

Flux2D

- 26 -




calculated by KLASYS are higher than values obtained using Flux2D. The difference between

values of KLASYS and Flux2D are around 15%. In addition the breakdown torque in both

calculation methods happens at around a slip of 0.3.

In Fig.3.2.2-2 stator phase current-slip characteristics of VZIM2 which are calculated by

Flux2D and KLASYS are shown. In lower slips the difference of the values in KLASYS and

Flux2D is around 12%, but in higher values of slips the difference is lower than 4%.

In Fig.3.2.2-3 the normal component of air-gap flux density of VZIM2 at a slip of 0.0294 for

one pole pair or 180 mechanical degrees has been depicted.

Fig.3.2.2-4 shows the numerically calculated flux lines in VZIM2 at a slip of 0.0294 or

1455.8 , obtained by Flux2D.



- 27 -

Fig.3.2.2-2: Phase current-slip characteristic of unskewed VZIM2, comparison of the steady state


Fig.3.2.2-3: Normal component of air gap flux density in the center of the air gap, for one pole

pair of VZIM2 at a slip of 0.0253, calculated by Flux2D

- 28 -


Flux2D

- 29 -




calculated by KLASYS are higher than values obtained using Flux2D. The difference between

values of KLASYS and Flux2D are around 12%. In addition the breakdown torque in both

calculation methods happens at around a slip of 0.2.

In Fig.3.2.3-2 stator phase current-slip characteristics of VZIM3 which are prepared by

Flux2D and KLASYS are shown. In lower slips the difference of the values in KLASYS and

Flux2D is around 11%, but in higher values of slips the difference is lower than 3%.

In Fig.3.2.3-3 the normal component of the air gap flux density of VZIM3 at a slip of 0.0169

for one pole pair or 180 mechanical degrees has been depicted.

Fig.3.2.3-4 shows the numerically calculated flux lines in VZIM3 at a slip of 0.0169 or

1474.65 , obtained by Flux2D.



- 30 -

Fig.3.2.3-2: Phase current-slip characteristic of unskewed VZIM3, comparison of the steady state


Fig.3.2.3-3: Normal component of air gap flux density in the center of the air gap, for one pole

pair of VZIM3 at a slip of 0.0253, calculated by Flux2D

- 31 -


Flux2D

- 32 -

Chapter 4: Time stepping analysis

4.1 Introduction

Despite the fact that stator voltage and current are sinusoidal, spatial distribution of flux

density in the air gap is not sinusoidal but step-like, as winding is located in slots.

In steady state analysis only the fundamental sine wave of air gap flux density distribution

was considered which gives a rough estimation of motor characteristics, but more precise and

accurate results are obtained by consideration of higher space harmonics of the stator and

rotor field distribution.

4.2 Stator and rotor field spatial harmonics

The step-like air gap flux density distribution generated by stator, along stator

circumference co-ordinate is represented by Fourier series [2]

Furthermore the step-like air gap flux density distribution generated by rotor along

rotor circumference co-ordinate is represented by Fourier series [2]

.

4.3 Asynchronous harmonic torques

Rotor harmonic currents produce not only additional cage losses, but also due to Lorentz

forces with stator field harmonic additional torque, which is called asynchronous

harmonic torque. For the special case this is the asynchronous torque of KLOSS

- 33 -

function. The stator harmonic field induces the rotor harmonic current and the rotor harmonic

current produces torque with the stator harmonic field.

Asynchronous harmonic torque follows a KLOSS function, depending on harmonic slip , at

this torque is zero. At torque is positive and adds to fundamental torque. At

the torque is negative and is breaking the machine. At harmonic break down slip:

torque reaches positive and negative maximum values. As harmonic break

down slip is small.

Fig.4.3-1: Asynchronous harmonic torques of the 5th and 7th stator field harmonics, which are

superimposed on fundamental asynchronous torque [2]

4.4 Synchronous harmonic torques

Rotor field harmonic of step like air gap flux density distribution, excited by rotor

fundamental current , Will also produce parasitic torque with the stator field harmonics.

Like asynchronous harmonic torque, the condition for constant torque generation is:

-the same wave length

-the same velocity (means also same direction of movement) of the stator and rotor field

wave.

Therefore conditions for slip where synchronous harmonic torque occurs are as following:

- 34 -

Fig.4.4-1: Typical effects of synchronous and asynchronous harmonic torques in induction machines

[2]

Time stepping simulation of the motors is done in the slip range from 0 to 2. In between of

these 2 operating points some important slips corresponding to synchronous and

asynchronous torques are taken into account.

Asynchronous and synchronous harmonic torques happen in slips that have been calculated in

Appendix II and they are considered in the simulation of the motors (VZIM1, VZIM2, and

VZIM3). Fig.4.4-1 shows typical effects of synchronous and asynchronous harmonic torques

in induction machines.

4.5 Derived slips used for time stepping analysis

The sets of slips to perform the time stepping analysis of VZIM1, VZIM2 and VZIM3 motors

have been derived and are given in Table V, Table VI and Table VII in Appendix II. In these

sets of slips the asynchronous and synchronous harmonic torque slips and breakdown slips of

asynchronous harmonic torques are included.

- 35 -

4.6 Time-stepping analysis of induction motors

Time-stepping analysis of the VZIM motor has been done to observe the transients and

harmonic effects on the characteristics of the motor. When the time step is in the order of

1/32th of the electrical cycle, fairly accurate and good results are provided. In our analysis the

motor is line fed and the frequency is 50Hz, and the corresponding electrical cycle is

1/50=0.02s; therefore with consideration of 40 time steps per one cycle,

would be an acceptable time step. Time stepping analysis has been done for some

speeds of the motor, in the range of -1500rpm to 1500rpm corresponding to the slips given in

Table II, Table III and Table IV in Appendix II. In this analysis the friction and windage

losses and load inertia are neglected.

4.6.1 Time-stepping analysis of VZIM1

Time stepping analysis of the VZIM1 motor has been done in different speeds which are

given in Table V in Appendix II. The results consist of the output torque, input phase current,

input power, efficiency, and power factor which have been compared with the results of the

KLASYS tool. The synchronous harmonic torques which happen at slips, ,

and are calculated with Flux2D as explained in the section 4.8 of this chapter.

In Fig.4.6.1-1 the torque slip characteristic of VZIM1, derived from time stepping analysis

with Flux2D, is shown. The effects of the synchronous harmonic torques at slips ,

and are clearly observed. In Fig.4.6.1-2 the torque slip characteristic of

VZIM1, derived from KLASYS, is shown. The effects of the synchronous harmonic torques at

slips , and are clearly observed.

The values of synchronous torque calculated by Flux2D and KLASYS at slips ,

and , are compared in Table 4.8-6, Table 4.8-7 and Table 4.8-8. It is

noticeable that the synchronous torque values calculated by KLASYS are in most of the cases

much higher than the values calculated by Flux2D. The values of Flux2D are more reasonable

and acceptable.

- 36 -

Fig.4.6.1-1: Torque-slip characteristic of unskewed VZIM1, calculated with Flux2D time-stepping, the

effects of the synchronous harmonic torques at slips , and of the

the motor are observable

Fig.4.6.1-2: Torque-slip characteristic of unskewed VZIM1, calculated with KLASYS, the effects of

the synchronous harmonic torques at slips , and of the the motor

are observable

In Fig.4.6.1-3 the torque slip characteristics calculated by time stepping and steady state AC

analysis are compared. The effects of the field harmonics lead to considerable deviations in

the calculated values.

In Fig.4.6.1-4 the fundamental phase current prepared by Flux2D and KLASYS are compared.

The results match very well and maximum difference is less than 5.5%.

- 37 -

Fig.4.6.1-5 shows the input power-slip characteristic of VZIM1 obtained from Flux2D and

KLASYS. At lower slips the calculated results of KLASYS are lower than Flux2D and at higher

slips results of KLASYS are higher. The values match well and the maximum difference is less

than 5%. In addition Fig.4.6.1-6 shows the output power-slip characteristic of VZIM1

obtained from Flux2D and KLASYS.

Fig.4.6.1-7 shows the efficiency calculated by Flux2D and KLASYS. Maximum efficiency

achieved from Flux2D results is 91.41% at a slip of 0.3 and maximum efficiency calculated

by KLASYS is 90.5% at the slip equal to 0.3. The results match very well.

Fig.4.6.1-8 compares the power factor values obtained from Flux2D and KLASYS. The

maximum power factor calculated by KLASYS equals 0.924 which at slip equal to 0.12

happens, and in Flux2D maximum power factor is equal to 0.962 which at slip equal to 0.1

happens, which is higher than KLASYS maximum power factor.

Fig.4.6.1-3: Torque-slip characteristic of unskewed VZIM1, time-stepping and AC analysis results

obtained by Flux2D, the harmonic torque effects at lower speeds of the motor are obvious

- 38 -

Fig.4.6.1-4: Stator phase current of unskewed VZIM1, time stepping analysis results calculated by

Flux2D and KLASYS

Fig.4.6.1-5: Input power-slip of unskewed VZIM1, comparison of the analysis results calculated by

Flux2D and KLASYS

- 39 -

Fig.4.6.1-6: Output power-slip of unskewed VZIM1, comparison of the analysis results calculated by

Flux2D and KLASYS

Fig.4.6.1-7: Efficiency-slip of unskewed VZIM1, comparison of the analysis results calculated by

Flux2D and KLASYS

- 40 -

Fig.4.6.1-8: Power factor-slip of unskewed VZIM1, comparison of the analysis results calculated by

Flux2D and KLASYS


Similar to VZIM1, time-stepping analysis of VZIM2 has been done with Flux2D and results

have been compared with results of the KLASYS tool. In this analysis the considered slips

similarly vary from 0 to 2 and in between additional 50 slips have been considered for

calculations, which have been given in table VI in Appendix II. The synchronous harmonic

torques which happen at slips, , and are calculated with Flux2D as

explained in the section 4.8 of this chapter.




VZIM2, derived from KLASYS, has been shown. The effects of the synchronous harmonic

torques at slips , and are clearly observed.





and acceptable.

- 41 -

Fig.4.6.2-1: Torque-slip characteristic of unskewed VZIM2, obtained by KLASYS and Flux2D time-

stepping calculations, the harmonic torque effects at lower speeds of the motor are observable



are observable

To observe the effect of the harmonics, the torque-slip characteristic of VZIM2 prepared from

time-stepping and steady state AC analysis have been depicted in Fig.4.6.2-3. A considerable

- 42 -

difference happens at the slip 0.857 and 1.071 due to the synchronous harmonics at these

points.

Fig.4.6.2-4 depicts the comparison between fundamental stator phase current calculated by

KLASY and Flux2D. The difference between results is below 10% which mostly happens at

high values of slip ( ).

Fig.4.6.2-5 shows the input power-slip characteristic of VZIM2, calculated by KLASYS and

Flux2D. At higher slips the values of Flux2D are around 11% lower than values of KLASYS.

In addition Fig.4.6.2-6 shows the output power-slip characteristic of VZIM2 obtained from

Flux2D and KLASYS

Fig.4.6.2-7 depicts the efficiency-slip characteristic of VZIM2, prepared by KLASYS and

Flux2D. The efficiency calculated by Flux2D at rated speed of VZIM2 (1455.8 rpm) is equal

to 0.9104 is higher than that of KLASYS which is equal to 0.905.

Fig.4.6.2-8 depicts the power factor-slip characteristic of VZIM2, prepared by KLASYS and

Flux2D.



- 43 -

Fig.4.6.2-4: Stator phase current of unskewed VZIM2, comparison of the time stepping analysis

results calculated by Flux2D and KLASYS


Flux2D and KLASYS

- 44 -


Flux2D and KLASYS


Flux2D and KLASYS

- 45 -

Fig.4.6.2-8: Power factor-slip of unskewed VZIM2, comparison of the analysis results calculated by

Flux2D and KLASYS


Similar to VZIM1 and VZIM2, time-stepping analysis of VZIM3 has been done with Flux2D

and results have been compared with the results of the KLASYS tool. In this analysis the

considered slips similarly vary from 0 to 2 and in between additional 50 slips have been

considered for calculations, which are given in table VII in Appendix II. The synchronous

harmonic torques which happen at slips, , and are calculated with

Flux2D as explained in the section 4.8 of this chapter.




VZIM3, derived from KLASYS, is shown. The effects of the synchronous harmonic torques at

slips , and are clearly observed.





and acceptable.

To observe the effect of the harmonics, the torque-slip characteristic of VZIM3 prepared from

time-stepping and steady state AC analysis have been depicted in Fig.4.6.2-2. A considerable

difference happens at the slip equal to 0.857 and 1.071 due to the synchronous harmonics at

these points.

Fig.4.6.3.3 shows the comparison between fundamental phase current prepared by KLASYS

and Flux2D. The difference between the results is below 5% which mostly happens at high

slip values ( ).

- 46 -

Fig.4.6.3-1: Torque-slip characteristic of unskewed VZIM3, calculated with Flux2D time-stepping, the

effects of the synchronous harmonic torques at slips , and of the

the motor are observable



are observable

- 47 -



Fig.4.6.3-4: Stator phase current of unskewed VZIM2, comparison of the analysis results calculated by

Flux2D and KLASYS

Fig.4.6.3-4 depicts the input power-slip characteristic of VZIM3, prepared by KLASYS and

Flux2D. At higher slips the values of Flux2D are around 4% lower than values of KLASYS. In

addition Fig.4.6.3-5 shows the output power-slip characteristic of VZIM3 obtained from

Flux2D and KLASYS.

- 48 -


Flux2D and KLASYS


Flux2D and KLASYS

Fig.4.10.3-6 depicts the efficiency-slip characteristic of VZIM3, prepared by KLASYS and

Flux2D. The efficiency calculated by Flux2D at rated speed of VZIM3 (1474.65 rpm) is equal

to 0.912 is lower than that of KLASYS which is equal to 0.925.

- 49 -


Flux2D and KLASYS

Fig.4.6.3-7 depicts the input power factor-slip characteristic of VZIM3, prepared by KLASYS

and Flux2D.The maximum power factor is equal to 0.956 which happens at a slip equal to

0.025 in Flux2D calculated results and in case of KLASYS the maximum power factor is equal

to 0.937 which happens at a slip equal to 0.03.

Fig.4.6.3-8: Power factor of unskewed VZIM3, comparison of the analysis results calculated by

Flux2D and KLASYS

- 50 -

4.7 Instantaneous torque wave forms at different rotor speeds

In order to draw the torque-slip characteristic, the average value of the torque over one period

of the stator electrical cycle has been considered. In order to observe the oscillations and

ripple of the torque over time in some sample operating speeds of the motors, the torque-time

characteristics are shown in Fig.4.7-1 to Fig.4.7-7.

From these figures the influence of the harmonics on the torque characteristics is clearly

observable, the lower the speed, the higher the influence of the harmonics and therefore the

ripple on the torque-time characteristics increases. At the speed equal to 1462 in Fig.4.7-1 the

average torque is lower than the average torque at the speed equal to 1200 in Fig.4.7-4 and the

ripple has also lower amplitude. At the speed equal to 205.5 rpm in Fig.4.7-7 the influence of

the synchronous harmonic torques is quite clear. This operating point where the peak of the

7th

asynchronous harmonic torque occurs, is quite near the slip where the

synchronous harmonic torque happens. Therefore the result is a quite oscillating torque-time

characteristic.

Fig.4.7-1: Torque-time characteristic of unskewed VZIM2 at 1462rpm, calculated by Flux2D, torque

oscillates around a constant mean value after reaching the steady state

- 51 -

Fig.4.7-2: Torque-time characteristic of unskewed VZIM2 at 1462rpm, calculated by Flux2D, zoomed

view after steady state is reached


oscillates around a constant mean value after reaching the steady state

- 52 -


view after a steady state is reached


oscillates around a constant mean value

- 53 -


view after a steady state is reached

Fig.4.7-7: Torque-time of unskewed VZIM2 at 205.5rpm, calculated by Flux2D, where break down

slip of the 7th asynchronous torque harmonic happens at slip 0.863 or 205.5rpm

- 54 -

4.8 Synchronous harmonic torque assessment in VZIM

Synchronous harmonic torques of VZIM, happen at the slips, , and

. In this section the torque time characteristics of VZIM1, VZIM2 and VZIM3 at these

slips are studied. For VZIM2 the synchronous harmonic torques are studied and derived by

varying the rotor position with respect to a fixed stator position, for a rotor slot pitch (we call

this method the rotation method). The step for each position is taken as one tenth of a rotor

slot pitch i.e. = 360/28/10 = 1.2857 mechanical degrees. The average torque for a stator

period is calculated for each of the eleven steps. Fig.4.8.1 shows first and second positions of

the rotor bars with fixed stator position.

Fig.4.8-1: First and second positions of the rotor bars with fixed stator position to calculate the

synchronous harmonic torques, prepared by Flux2D

Fig.4.8.2 to Fig.4.8.4 show the variation of the torque for the rotor position steps 1, 5 and 7 of

VZIM2 at the slip respectively. It is clear that the average value of the

synchronous torque at each step is a constant value. Similar procedure has been done for

VZIM2 at slips and , and the torque time values have been calculated for

eleven positions. The calculated synchronous torques, for three different slips of VIM2 are

shown in Fig.4.8-5 to Fig.4.8-7.

Fig.4.8-2: Torque-time of unskewed VZIM2 at , calculated by Flux2D, rotor position step

1

- 55 -


5


7

- 56 -

Fig.4.8-5: Variation of synchronous torque at as a function of rotor position

Fig.4.8-6: Variation of synchronous torque at a function of rotor position

Fig.4.8-7: Variation of synchronous torque at as a function of rotor position

-100

0

100

200

300

400

500

0 20 40 60 80 100

Torq

ue/

N.m

Rotor position at percentage of rotor slot pitch

440

460

480

500

520

540

560

580

0 20 40 60 80 100

Torq

ue/

N.m


250

270

290

310

330

350

0 20 40 60 80 100

To

rqu

e/N

.m


- 57 -

Furthermore the synchronous torque of the VZIM2 has been calculated with another method

(we call this method the oscillation method). The torque time characteristics of VZIM2 have

been calculated in three different speeds and each speed is 10 rpm higher than the speed

where synchronous harmonic torque happens. For VZIM2 the synchronous harmonic torques

happen at 214.28 rpm ( ), 0 rpm ( ) and -107.1428 ( ). Therefore the

torque time characteristic of the VZIM2 at speeds 224.28 rpm, 10 rpm and -97.1428 are

calculated. As the oscillation of the torque time characteristic occurs because of the

synchronous harmonic torque; therefore the maximum and minimum of the variation of the

average torque in the torque time characteristic, equals to the maximum and minimum values

of the synchronous harmonic torques.

Fig.4.8.8 to Fig.4.8.10 show the torque time characteristic of VZIM2 at three different speeds

224.28 rpm, 10 rpm and -97.1428. At speed 224.28 rpm the maximum value of the average

torque is 438.4 Nm and the minimum value is -20.88 Nm and the peak to peak value is

459.28Nm. On the other hand the maximum value of synchronous harmonic torque calculated

by changing the position of the rotor related to fixed stator method is 448.24 Nm and the

minimum value is -20.8 Nm with the peak to peak value equal to 469.04 Nm. The difference

between two methods of synchronous torque calculation of peak to peak value is around 2.1%

at speed 224.28 rpm. The values are summarized in Table 4.8-1.

The torque values for speeds 10 rpm and -97.1428 rpm are calculated in similar way and are

shown in Table 4.8-2 and Table 4.8-3. Clearly the calculated values with two different

methods (rotation and oscillation methods) have a maximum difference of 7.66%.

Due to the reasonable differences of the results of two calculation methods for VZIM2, the

calculation of the maximum and minimum and peak to peak values of synchronous torques at

the slips where synchronous torques of VZIM1 and VZIM2 happen are done by the

oscillation method due to the low calculation time of this method. Table 4.8-4 and Table 4.8-5

show the values of synchronous torques for VZIM1 and VZIM3, calculated by oscillation

method in three different slips, where synchronous harmonic torques happen ( ,

and ).

Table 4.8-1: Maximum, minimum and peak to peak values of synchronous torque for VZIM2 in two

different methods of calculation (rotation and oscillation methods) for the slip

Oscillation method Rotation method Difference %

Maximum torque (N.m) 438.4 448.24 2.19%

Minimum torque(N.m) -20.88 -20.8 0.3%

Peak to peak value (N.m) 459.28 469.04 2.08%





Minimum torque(N.m) 244.56 262.16 6.7%


- 58 -





Minimum torque(N.m) 470.88 461.4 2.01%


Table 4.8-4: Maximum, minimum and peak to peak values of synchronous torque for VZIM1

(oscillation method)

Maximum torque (N.m) 605.56 456.24 629.72

Minimum torque(N.m) 130.8 406.28 499.8

Peak to peak value (N.m) 474.76 49.96 129.92

Table 4.8-5: Maximum, minimum and peak to peak values of synchronous torque for VZIM3

(oscillation method)

Maximum torque (N.m) 370 300.88 458.32

Minimum torque(N.m) -42.44 185.68 351.72

Peak to peak value (N.m) 412.44 114.32 107.6

Fig.4.8-8: Torque-time of unskewed VZIM2 at speed 224.28 rpm, calculated by Flux2D

- 59 -

Fig.4.8-9: Torque-time of unskewed VZIM2 at speed 10 rpm, calculated by Flux2D

Fig.4.8-10: Torque-time of unskewed VZIM2 at speed -97.14 rpm, calculated by Flux2D

In addition, the values of synchronous harmonic torques for VZIM1, VZIM2 and VZIM3 in

three different slips, where synchronous harmonic torques happen are calculated by KLASYS.

In Table 4.8-6 to Table 4.8-14 the calculated values with KLASYS and Flux2D are compared.

It is noticeable that the synchronous torque values calculated by KLASYS are in the most of

the cases much higher than the values calculated by Flux2D.The values of Flux2D are more

reasonable and acceptable.

- 60 -

Table 4.8-6: Maximum, minimum and peak to peak values of synchronous torque for VZIM1, at the

slip , the comparison of the calculated values by KLASYS and Flux2D

Maximum torque

(N.m)

Minimum torque

(N.m)

Peak to peak value

(N.m)

Flux2D 606.56 130.8 474.76

KLASYS 1165.215 -208.695 1373.91

Difference 558.655 338.659 899.15



Maximum torque

(N.m)

Minimum torque

(N.m)

Peak to peak value

(N.m)

Flux2D 456.24 406.28 49.96

KLASYS 526.085 473.915 52.17

Difference 69.845 67.635 2.21



Maximum torque

(N.m)

Minimum torque

(N.m)

Peak to peak value

(N.m)

Flux2D 629.72 499.8 129.92

KLASYS 899.99 230.427 669.564

Difference 270.27 269.373 539.644



Maximum torque

(N.m)

Minimum torque

(N.m)

Peak to peak value

(N.m)

Flux2D 438.4 -20.88 459.28

KLASYS 1083.33 -316.67 1400

Difference 644.93 296.67 940.72



Maximum torque

(N.m)

Minimum torque

(N.m)

Peak to peak value

(N.m)

Flux2D 313.32 244.56 68.76

KLASYS 474.995 341.665 133.33

Difference 161.675 70.105 64.57



Maximum torque

(N.m)

Minimum torque

(N.m)

Peak to peak value

(N.m)

Flux2D 574.2 470.88 103.32

KLASYS 624.995 291.665 333.33

Difference 50.795 179.215 230.01

- 61 -



Maximum torque

(N.m)

Minimum torque

(N.m)

Peak to peak value

(N.m)

Flux2D 370 -42.44 412.44

KLASYS 907.13 -464.29 1371.42

Difference 537.13 421.85 958.98



Maximum torque

(N.m)

Minimum torque

(N.m)

Peak to peak value

(N.m)

Flux2D 300.88 185.68 114.32

KLASYS 358.925 198.215 160.71

Difference 58.045 12.535 46.39



Maximum torque

(N.m)

Minimum torque

(N.m)

Peak to peak value

(N.m)

Flux2D 458.32 351.72 106.6

KLASYS 353.57 246.43 107.14

Difference 104.75 105.29 0.54

4.9 Power losses in different parts of the motor

In order to determine the efficiency of the motor, it is necessary to calculate the losses in

different parts of the motor, these loss components are:

-stator and rotor ohmic losses

-friction and windage losses

-iron losses (mainly in stator iron)

-additional no-load losses such as tooth pulsation and surface losses

-additional load losses such as stator and rotor eddy current losses in conductors.

In simulation by Flux2D the mechanical losses are neglected.

Tables I, II and III in Appendix III show the iron losses which include eddy-current losses and

hysteresis losses in addition to the stator and rotor ohmic losses, which have been calculated

by Flux2D and compared with the results of KLASYS tool.

In Flux2D regarding the iron losses, the volume density of the instantaneous power loss

, is written as [5]:

which is composed of losses by hysteresis, classical losses and losses in excess, where

- 62 -

- is the coefficient by hysteresis

- is the coefficient of losses in excess

- is the conductivity of the material

-d is the thickness of the lamination

- is the peak value of the magnetic flux density

Within the frame of the flux computation,

- is the stack fill factor (close to 1), this coefficient considers the electrical insulation of the

lamination of the magnetic core.

In addition, in steady state AC magnetic application the volume density of the average power

is:

where:

- is the coefficient by hysteresis

- is the coefficient of losses in excess

- is the conductivity of the material

-d is the thickness of the lamination

-f is frequency

- is the peak value of the magnetic flux density

Coefficients , and are necessary to calculate the iron losses with Flux2D, according to

the data sheet of the M270-50A [7] which is the material of the stator and rotor lamination

and with consideration of the equal to 1.5T and with solving , in three different

frequencies 50Hz, 100Hz and 200Hz the values of , and are calculated.

The values of the specific total losses in frequencies 50Hz, 100Hz and 200Hz, according

to the data sheet of the M270-50A [7] are given in Table 4.9-1. In addition the density of the

iron sheet M270-50A is and the power loss is , the calculated

values of the power losses for the frequencies 50Hz, 100Hz and 200Hz and are shown in

Table 4.9-1.

Table 4.9-1: Values of specific total losses according to the data sheet of the M270-50A [7],

and calculated power losses, in frequencies 50Hz, 100Hz and 200Hz

50Hz 100Hz 200Hz

19.45

- 63 -

after the calculations the following results are obtained:

(Ws/( ))

(1/(Ohm.m)), (W/( ))

When these values are available with the help of the Flux2D iron losses are calculated.

4.9.1 Losses of VZIM at different speeds

In this section the losses of VZIM1, VZIM2 and VZIM3 in three different speeds which have

been calculated by Flux2D and KLASYS are compared. Here the components of stator and

rotor iron and copper losses have been considered.

Tables I, II and III in Appendix III show the losses of VZIM1, VZIM2 and VZIM3.

Apparently there are differences between losses calculated by KLASYS and Flux2D, at 22kW

nominal output power operation. In VZIM2 the stator copper losses are around 14%, the rotor

copper losses about 30% and stator iron losses about 11%, calculated by Flux2D are higher

than values calculated by KLASYS. In VZIM3 the stator copper losses are around 18%, the

rotor copper losses about 30% and stator iron losses about 21%, calculated by Flux2D are

higher than values calculated by KLASYS.

Fig.4.9.1-1 shows the comparison between losses of VZIM1 at rated speed equal to 1390.9

rpm calculated with Flux2D and KLASYS, Fig.4.9.1-2 shows the comparison between losses

of VZIM2 at the rated speed equal to 1455.8 rpm calculated with Flux2D and KLASYS and

Fig.4.9.1-3 shows the comparison between losses of VZIM3 at the rated speed equal to

1474.65 rpm calculated with Flux2D and KLASYS.

Fig.4.9.1-1: Comparison between losses of VZIM1 at speed equal to 1390.9 rpm calculated


- 64 -





- 65 -

Chapter 5: Thermal analysis

5.1 Preface

Calculating the temperature rise in electrical machines which occurs due to electrical and

mechanical losses, is one of the important steps in design of electrical machines. According to

Arrhenius’ law, velocity of chemical decomposition of materials increases exponentially with

temperature and for solid insulation materials Montsinger’s rule is valid, that the insulation

life span L decreases by 50% with increase of temperature by . Due to the high

sensitivity of insulation materials to over-temperature, thermal classes for different types of

insulation materials are defined, which gives the maximum permissible temperature limit in

hot spot of insulation. For example in class F maximum temperature rise is 105 for

the machines in the power range of [1].

Cooling system of electrical machines influences their thermal utilization and with a high

efficient cooling system, power per mass of electrical machines can be raised. There are

different possibilities to propel the coolant flow in electrical machines. In case of motors

without fan, cooling is done due to the natural convection and heat radiation. With shaft

mounted fan motors the speed of air flow depends on the velocity of motor. The external fan

is another way for cooling the electrical machine.

According to the second fundamental law of thermodynamics, the natural heat flow is only

possible from a hot to a cold region. Basic principles for heat transfer are

-Conduction, by heat conducting materials

-Convection, by moving coolants like air or water

-Radiation, which does not need any medium for heat transfer.

Calculating the temperature in electrical machines may be done either by numerical methods

or equivalent circuits. Calculation by numerical method in this project has been done by

ANSYS tool.

5.2 Temperature rise calculation by thermal equivalent circuits

To have an estimation of temperature rise in the stator winding simplified thermal networks

are used.

- 66 -

In a simplified thermal network only copper and iron losses in the stator and thermal

resistances between copper and iron due to the slot insulation, heat convection from winding

overhang to air and heat convection from the stator iron to air are considered. Stator copper

losses in the winding ( ) and stator iron losses in the stator iron stack ( ) are loss sources.

Fig.5.2-1 shows the simplified thermal equivalent network for an induction motor.

Fig.5.2-1: The simplified thermal equivalent network for an induction motor

Heat resistances are, between stator iron and ambient cooling air, given by convection,

according to [1] where is the surface of the stator iron housing and is

the heat transfer coefficient which describes the cooling effect of flowing coolant.

between slot conductor copper and iron stack, mainly determined by heat resistance of the slot

insulation, according to [1] , where is the slot surface, is the

thermal conductivity of the slot insulation and is the thickness of the slot insulation.

and are thermal resistances between winding overhang and surrounding air given by

convection. Due to special structure of the VZIM, as this motor is totally enclosed, at one side

of the winding overhang, the heat transfer coefficient is considered as for natural

convection and heat radiation and at the other side, the rotating centrifugal mechanism leads

to a better cooling due to the convection. Therefore in order to calculate the heat transfer

coefficient, with try and error and comparison with measured values, is estimated for the

5.5kW VZIM ( ). For the 22kW VZIM due to similar structure with the

5.5kW VZIM, a proportional ratio of was considered, the calculations are presented in

Appendix IV and the values are shown in Table 5.2-1.

- 67 -

Table 5.2-1: Heat transfer coefficient for one side of the winding overhang close to the centrifugal

mechanism

Winding overhang VZIM2 22kW VZIM3 22kW

Heat transfer

coefficient

63.32 62.86

and are unknown temperature rises, which is the temperature

difference between motor local temperature and ambient temperature of surrounding air. In

this calculation ambient temperature is considered to be 20 .

With consideration of the steady state temperature rise only two algebraic linear equations

have to be solved,

As VZIM2 and VZIM3 are active in rated operating speed of the motor, thermal calculations

of VZIM2 and VZIM3 are done in an operating speed which the average of the output power

produced by VZIM2 and VZIM3 in this speed is equal to 22kW.Therefore as it is depicted in

Fig.5.2-2, the average of output power of VZIM2 and VZIM3 versus slip is calculated and at

a speed of 1467.36 rpm the average power is equal to 22kW. The losses of VZIM2 and

VZIM3 in this speed (1467.36 rpm) have been calculated and are shown in Table 5.2-2. Based

on those losses the temperature rise and for VZIM2 and VZIM3 are calculated in

the following sections.

Fig.5.2-2: Calculated output power-slip characteristics of 22kW VZIM2 and VZIM3 and the average

of the powers

-60000

-40000

-20000

0

20000

40000

60000

80000

0 0.5 1 1.5 2 2.5

Ou

tpu

t p

ow

er/

W

Slip

Power-Slip characteristic

VZIM2 power

VZIM3 power

Average power

- 68 -

Table 5.2-2: Losses in different parts of the VZIM2 and VZIM3 in the speed equal to 1467.36 rpm

/W //W /W /W /W

VZIM2 492.073 466.2 192.6 31.36 16894.2

VZIM3 1395.6 760.52 159.64 33.8 27374.75

Average 943.83 613.36 162.62 32.58 22134.47

In calculation of the average output power in Fig.5.2-2, it is assumed that the equivalent

output power of the VZIM motor can be estimated using super-position method. More

accurate calculations based on an equivalent circuit model [6] show that the super-position

method overestimates the equivalent torque and output power of the VZIM motor, especially

at lower speeds. But it is quite accurate at the rated operating region of the motor, as shown in

Fig.5.2-3. As here, only the calculation of the output power in the operating region of the

VZIM motor is required, hence more simple method of super-positioning is used.

Fig.5.2-3: Calculated output power of the VZIM motor with the supper-position and equivalent circuit

methods

- 69 -

5.2-1 Calculation of and for VZIM2 (22kW)

The materials used in construction of VZIM2 and the related thermal conductivities are shown

in Table 5.2.1-1.

Table 5.2.1-1: Thermal conductivities of the materials used in VZIM2 thermal model

Material Air Iron stack Insulation Copper

Thermal

conductivity,

W/(m.K)

0.031 40 0.2 380

After determination of materials, calculation of thermal resistances is done as following.

is the heat resistance between the stator iron stack and the ambient cooling

air, is the surface of the stator iron housing and is the heat transfer coefficient, is

equal to 203472 , and according to [1] is calculated by ( in

, in ) for moving air over bare metallic hot surface. The speed of wind flow

over the stator body, based on an empirical rule [9], is equal to 70 percent of the linear speed

of the top point of the fan blade, therefore

R is the radius of the fan blade and n is the rotational speed of the VZIM2 with 22kW output

power. Consequently heat transfer coefficient can be calculated as:

,

where is slot surface, is thermal conductivity of slot insulation and

is the thickness of the slot insulation.

According to equations (5.2-1) and (5.2-2) we get:

The maximum temperature rise for class F of insulations is 105 . Here the value is much

lower than the maximum allowable temperature rise; therefore insulation is in the safe side.

The reason for this low temperature rise is the fact that the middle cage (VZIM2) is working

under rated load (16.89kW instead of 22kW) at the rated speed of 1467.36 rpm. The final

temperature rise will be the average value of both VZIM2 and VZIM3.

- 70 -

5.2-2 Calculation of and for VZIM3 (22kW)

The materials used in construction of VZIM3 and the related thermal conductivities are shown

in Table 5.2.2-1.

Table 5.2.2-1: Thermal conductivities of the materials used in VZIM3 thermal model

Material Air Iron stack Insulation Copper

Thermal

conductivity,

W/(m.K)

0.031 40 0.2 380

Calculations are similar to calculations for VZIM2 in the previous section.

is the heat resistances between the stator iron stack and the ambient cooling air, is the

surface of the stator iron housing and is the heat transfer coefficient, is equal to 203472

, and according to [1] can be calculated by ( in , in )

for moving air over bare metallic hot surface. The speed of wind flow over the stator body,

based on an empirical rule [9], is equal to 70 percent of the linear speed of the top point of the

fan blade, therefore

R is the radius of the fan blade and n is the rotational speed of the VZIM2 with 22kW output

power. Consequently heat transfer coefficient can be calculated:

,

where is slot surface, is thermal conductivity of slot insulation and

is the thickness of slot insulation.

According to equations (5.2-1) and (5.2-2) we get:

The calculated temperature rise in the winding is lower than the temperature rise limit

105 for class F insulations used in this motor. Therefore the insulation operates in the safe

side, although the motor operates at overload condition (27.37kW instead of 22kW).

Table 5.2.2-2 shows the temperature rise in the stator winding and iron of VZIM2 and VZIM3

calculated based on simplified thermal equivalent circuit and the average values.

- 71 -

Table 5.2.2-2: Temperature rise in the stator winding of VZIM2 and VZIM3 calculated based on

simplified thermal equivalent circuit in the nominal operating speed equal to 1467.36 rpm

VZIM2 VZIM3 Average value

The average value of the temperature rise of VZIM2 and VZIM3, which is equal to ,

is considered as the temperature rise of the 22kW VZIM motor, which is well below the

temperature rise limit of the used insulation materials (Thermal class F).

5.3 Numerical calculation of temperature rise

In ANSYS as a finite element tool, first of all the geometry of the model has to be prepared,

assigning the materials and meshing the areas are next steps. The loss density is used as heat

source, therefore based on the different losses of the motor, the loss densities for different

parts of the motor are calculated using the formula , where P is the calculated losses

in each part, and V is the volume in which the losses occur.

Electromagnetic analysis of 22kW VZIM is done with Flux2D in previous chapters and just

2D model of the VZIM motors was prepared but in this section for thermal analysis 3D

models of VZIM2 and VZIM3 are built to consider the thermal effect of the winding-

overhangs and end-rings. As usual, the number of the stator teeth and rotor teeth are not equal,

hence a symmetry can be considered if for the simplification, the number of rotor teeth is

assumed to be 36 instead of the 28 which is the real number of rotor teeth. With this

simplification simulation of a half of the stator and rotor slots is enough to do the thermal

analysis of the VZIM motor. In order to take into account the extra losses which appear due to

the simplification in this new model, the rotor copper losses are multiplied by the factor to

compensate the extra losses added to the simulating model.

In this section, first of all the numerical calculation of the temperature rise based on the finite

element method with ANSYS tool for the 5.5kW VZIM is done and compared with measured

values, because the 5.5kW VZIM was already manufactured and tested. Afterwards the

numerical calculation of temperature rise in 22kW VZIM has been carried out using ANAYS

tool.

In three dimensional models considered for thermal analysis of 5.5kW and 22kW VZIM, the

convection heat transfer at the stator outer surface, the outer surface of the winding overhang

and the end rings are considered as the boundary conditions of the thermal model. For

simplification the heat transfer due to heat conduction, through the motor shaft is neglected.

Clearly due to the thermal conduction between the motor shaft and rotor, in case of modeling

the motor shaft, the calculated rotor temperature would be lower than values are presented

with the simplified model in following sections.

- 72 -

5.3.1 Thermal analysis of 5.5 kW VZIM2

First a 2D geometry of 5.5kW VZIM2 is prepared and after assigning the material and

meshing the geometry, by extruding the 2D model, the 3D model is constructed.

In Fig.5.3.1-1 the 2D model and meshing of VZIM2 are depicted, the 3D model and meshing

are depicted in Fig.5.3.1-2 and Fig.5.3.1-3.

Fig.5.3.1-1: 2D model of the 5.5kW VZIM2 and meshing, by ANSYS

Fig.5.3.1-2: 3D model of the 5.5kW VZIM2, by ANSYS

- 73 -

Fig.5.3.1-3: 3D model meshing of the 5.5kW VZIM2, by ANSYS

Loss densities in all volumes of VZIM2 have been calculated and assigned to the simulation

model before solving the thermal model. Table 5.3.1-1 shows the thermal loss densities in

VZIM2 5.5kW.

Table 5.3.1-1: Loss densities in different parts of the 5.5kW VZIM2

Stator

winding

Winding

overhang

Rotor bars Stator iron Rotor iron

Loss density

W/

0.000453318 0.00023955 0.00082892 0.000045299 0.000000566

The air flow in three areas including, the stator outer surface, winding overhang and end-rings

surfaces are considered and the heat transfer coefficients due to the convection are calculated

for those areas.

- The heat transfer coefficient for the stator outer surface is calculated as below:

-The heat transfer coefficients for winding overhangs are considered as below:

For one side of the motor the heat transfer coefficient over winding overhang is

for natural convection and heat radiation, but for the other side of the motor,

because of the rotating centrifugal mechanism, the heat transfer coefficient for winding

overhang was drawn with try and error, considering the value of the maximum temperature

rise of the winding overhang, already measured. By choosing the heat transfer coefficient

, the calculated and measured values match well together, hence

consideration of is acceptable.

- 74 -

-The heat transfer coefficient for the end-ring surface is considered as below:

As in area near the end ring air is nearly not moving, therefore is

considered.

Table 5.3.1-2 shows the heat transfer coefficient at different boundary conditions of the 5.5kW

VZIM2.

Table 5.3.1-2: Heat transfer coefficient at different boundary conditions of the 5.5kW VZIM2

Stator outer

surface End ring

Winding

overhang far

from

centrifugal

mechanism

Winding

overhang close

to centrifugal

mechanism

83.11 15 15 50

Fig.5.3.1-4 shows the thermal solution of the 5.5kW VZIM2, temperature changes from

84.5 on the stator body to 147.89 inside the rotor. For thermal class F of insulations the

maximum allowable temperature rise is 105 . For VZIM2 the maximum temperature rise in

the stator winding is 72.28 as it has been shown in Fig.5.3.1-5, and assures that insulation

lies in a safe side. The measured value of the maximum overhang temperature rise is 67.7 ,

which is 6.3% lower than the finite element calculated value. The ambient temperature is

considered to be 20 .

Fig.5.3.1-4: The thermal solution of the 5.5kW VZIM2 under nominal operation, by ANSYS

- 75 -

Fig.5.3.1-5: The calculated temperature in the winding overhang of VZIM2, by ANSYS

5.3.2 Thermal analysis of 5.5kW VZIM3

Similar to 5.5kW VZIM2, first a 2D geometry of 5.5kW VZIM3 is prepared and after

assigning the material and meshing the geometry, by extruding the 2D model, the 3D model is

constructed.

In Fig.5.3.2-1 2D model and meshing of 5.55kW VZIM3 are depicted, also in Fig.5.3.2-2 and

Fig.5.3.2-3 the 3D model and meshing are depicted.

Fig.5.3.2-1: 2D model of the 5.5kW VZIM3 and meshing, by ANSYS

- 76 -

Fig.5.3.2-2: 3D model of the 5.5kW VZIM3, by ANSYS

Fig.5.3.2-3: 3D model meshing of the 5.5kW VZIM3, by ANSYS



5.5kW VZIM3.

Table 5.3.2-1: Loss densities in different parts of the 5.5kW VZIM3

Stator

winding

Winding

overhang


Loss density

W/

0.00047015 0.00024844 0.0003707 0.00004544 0.000000461

The air flow in three areas including the stator outer surface, winding overhang and end-rings

surfaces are considered and the heat transfer coefficient due to the convection are calculated

for those areas.

- 77 -

- The heat transfer coefficient for the stator outer surface is calculated as below:

- The heat transfer coefficients for winding overhangs are considered as below:

For one side of the motor the heat transfer coefficient over winding overhang is

, for the other side of the motor, because of the rotating centrifugal mechanism,

the heat transfer coefficient for winding overhang was drawn with try and error, considering

the value of the maximum temperature rise of the winding overhang was already measured,

by consideration of heat transfer coefficient the calculated values and

measured values match well together, hence consideration of is acceptable.


As in this area air is nearly not moving, therefore is considered.

Table 5.3.2-2 shows the heat transfer coefficient at different boundary conditions of the 5.5kW

VZIM3.

Table 5.3.2-2: Heat transfer coefficient at different boundary conditions of the 5.5kW VZIM3

Stator outer

surface End ring

Winding

overhang far

from

centrifugal

mechanism

Winding

overhang close

to centrifugal

mechanism

83.65 15 15 50

Fig.5.3.2-4 shows the thermal solution of the VZIM3, temperature changes from 80.17 on

the stator body to 121.969 inside the rotor. For thermal class F of insulations the maximum

allowable temperature is 105 . For VZIM3 the maximum temperature rise in stator winding

overhang is 63.35 as it has been shown in Fig.5.3.2-5, and assures that insulation lies in a

safe side. The measured value of the maximum overhang temperature rise is 67.7 , which is

6.42% higher than the calculated value by finite element method. The ambient temperature is

considered to be 20 .

- 78 -

Fig.5.3.2-4: The thermal solution of the 5.5kW VZIM3 under nominal operation, by ANSYS

Fig.5.3.2-5: The calculated temperature in winding overhang of 5.5kW VZIM3, by ANSYS

Table 5.3.2-3 shows the temperature rise in stator slot of 5.5kW VZIM2 and VZIM3 stator

slot calculated by ANSYS.

Table 5.3.2-3: Temperature rise in stator slot of 5.5kW VZIM2 and VZIM3 calculated by ANSYS


The average value of the temperature rise of VZIM2 and VZIM3 which is equal to , is

considered as the temperature rise of the 5.5kW VZIM motor. The measured value of the

maximum overhang temperature is which obviously shows a very good fitting

between the measured value and calculated values of temperature rise by ANSYS tool.

- 79 -

5.3.3 Thermal analysis of 22kW VZIM2

First a 2D geometry of 22kW VZIM2 is prepared and after assigning the material and

meshing the geometry, by extruding the 2D model, the 3D model is constructed. In Fig.5.3.3-

1 2D model and meshing of it are depicted, also in Fig.5.3.3-2 and Fig.5.3.3-3 the 3D model

and its meshing are depicted.

Fig.5.3.3-1: 2D model of the 22kW VZIM2 and meshing, by ANSYS

Fig.5.3.3-2: 3D model of the 22kW VZIM2, by ANSYS

- 80 -

Fig.5.3.3-3: 3D model meshing of the 22kW VZIM2, by ANSYS



22kW VZIM2.

Table 5.3.3-1: Loss densities in different parts of the 22kW VZIM2

Stator

winding

Winding

overhang


Loss density

W/ 0.000169 0.0001074 0.0007152 0.00002834 0.000007678

The air flow in three areas including the stator outer surface, winding over hang and end-rings


for those areas.

-The heat transfer coefficient for the stator outer surface is calculated as below:


At one side, the heat transfer coefficient for winding overhang is , for the

other side of the motor due to the rotating centrifugal mechanism, as already was

discussed .



Table 5.3.3-2 shows the heat transfer coefficient at different boundary conditions of the 22kW

VZIM2.

- 81 -

Table 5.3.3-2: Heat transfer coefficient at different boundary conditions of the 22kW VZIM2

Stator outer

surface End ring

Winding

overhang far

from

centrifugal

mechanism

Winding

overhang close

to centrifugal

mechanism

102.52 15 15 63.32

Fig.5.3.3-4 shows the thermal solution of the 22kW VZIM2, temperature changes from

59.7929 on the stator body to 150.95 inside the rotor. For thermal class F of insulations

the maximum allowable temperature rise is 105 . For VZIM2 the maximum temperature rise

in the stator winding overhang is 42.73 as it has been shown in Fig.5.3.3-5, and assures that

insulation lies in a safe side. The calculated value of the stator winding temperature rise is

35.31 which is 17.3% lower than finite element calculated value.

Fig.5.3.3-4: The thermal solution of the 22kW VZIM2 under nominal operation, by ANSYS

- 82 -

Fig.5.3.3-5: The calculated temperature in the winding overhang of 22kW VZIM2, by ANSYS

5.3.4 Thermal analysis of 22kW VZIM3

Similar to 22kW VZIM2, first a 2D geometry of 22kW VZIM3 is prepared and after

assigning the material and meshing the geometry, by extruding the 2D model, the 3D model is

constructed. In Fig.5.3.4-1 2D model and meshing of 22kW VZIM3 are depicted, also in

Fig.5.3.4-2 and Fig.5.3.4-3 the 3D model and meshing are depicted.

Fig.5.3.4-1: 2D model of the 22kW VZIM3 and meshing, by ANSYS

- 83 -

Fig.5.3.4-2: 3D model of the 22kW VZIM3, by ANSYS

Fig.5.3.4-3: 3D model meshing of the 22kW VZIM3, by ANSYS



22kW VZIM3.

Table 5.3.4-1: Loss densities in different parts of the 22kW VZIM3

Stator

winding

Winding

overhang


Loss density

W/ 0.00048 0.000304 0.000606 0.00002349 0.00000934

- 84 -

The air flow in three areas including the stator outer surface, winding over hang and end-rings


for those areas.

-The heat transfer coefficient for the stator outer surface is calculated as below:


At one side, the heat transfer coefficient for winding overhang is , for the

other side of the motor due to the rotating centrifugal mechanism, as already was

discussed .

- The heat transfer coefficient for the end-ring surface is considered as below:


Table 5.3.4-2 shows the heat transfer coefficient at different boundary conditions of the 22kW

VZIM3.

Table 5.3.4-2: Heat transfer coefficient at different boundary conditions of the 22kW VZIM3

Stator outer

surface End ring

Winding

overhang far

from

centrifugal

mechanism

Winding

overhang close

to centrifugal

mechanism

102.52 15 15 62.86

Fig.5.3.4-4 shows the thermal solution of the 22kW VZIM3, temperature changes from

98.7877 on the stator body to 224.19 inside the rotor. For thermal class F of insulations

the maximum allowable temperature rise is 105 . For VZIM3 the temperature in stator

winding overhang is 85.72 as it has been shown in Fig.5.3.4-5, and assures that insulation

lies in a safe side. The calculated value of the stator winding temperature rise is 90.57

which is 5.5% higher than calculated value by finite element method.

- 85 -

Fig.5.3.4-4: The thermal solution of the 22kW VZIM3 under nominal operation, by ANSYS

Fig.5.3.4-5: The calculated temperature in the winding overhang of 22kW VZIM3, by ANSYS

Table 5.3.4-3 shows the temperature rise in stator slot of 22kW VZIM2 and VZIM3 stator slot

calculated by ANSYS.

Table 5.3.4-3: Temperature rise in stator slot of 22kW VZIM2 and VZIM3 calculated by ANSYS


- 86 -

The average value of the temperature rise of VZIM2 and VZIM3 ( ) is considered as

the temperature rise of the 22kW VZIM motor which is well below the maximum temperature

rise for the insulation class F ( ). The mean value of the calculated values of the

maximum overhang temperature with simplified equivalent thermal circuit is , which

shows a 1.99% difference between finite element method calculations and the calculations

based on the simplified thermal circuits.

In order to summarize the thermal calculations of 5.5kW and 22kW VZIM, the values of the

stator maximum winding temperature rise and the rotor maximum temperature rise are shown

in Table 5.3.4-4. The thermal analyses of 5.5kW VZIM2 and VZIM3 motors are done in the

operation point of the motor where the output power of each motor is 5.5kW. But the thermal

analyses of 22kW VZIM2 and VZIM3 motors are done in an operation point of the motor,

where the average output power of 22kW motors (VZIM2 and VZIM3) is 22kW. Therefore

according to the previous description and calculation in section 5.2, as it is shown in Table

5.2-2, the 22kW VZIM2 is analyzed in an operation point, that its output power is 16.89kW

and the 22kW VZIM3 is analyzed in an operation point, where its output power is 27.37kW.

Therefore the 22kW VZIM3 motor with the output power 27.37kW is clearly overloaded,

therefore the temperature rise of the rotor and stator of 22kW VZIM3 is relatively high. As

previously mentioned, the average temperature rise of VZIM2 and VZIM3 in the rated

operating point of the VZIM is important and shows the temperature rise of the real motor.

Table 5.3.4-4: Temperature rise in stator slot of 22kW VZIM2 and VZIM3 calculated by ANSYS

5.5kW

VZIM2

5.5kW

VZIM3

Average

value of

5.5kW

VZIM

22kW

VZIM2

22kW

VZIM3

Average

value of

22kW

VZIM

Stator max.

winding

temperature

rise

Rotor max.

temperature

rise

- 87 -

Chapter 6: Conclusion

Electromagnetic and thermal analyses of Variable Impedance Induction Motor (VZIM) have

been done for a 4 pole 22kW motor. The electromagnetic analyses show that the expected

goals of the high starting torque and high efficiency at the rated operating point of the VZIM

motor are fulfilled.

Electromagnetic analysis of the 22kW VZIM motor is carried out with consideration of three

independent motors VZIM1, VZIM2 and VZIM3, using the finite element software Flux2D

and the results are compared with the analytical calculations performed by KLASYS tool. In

the steady state AC analysis the torque-slip, stator phase current-slip, normal air-gap flux

density and flux lines in the electromagnetically active parts of the motors are drawn. The

results of the analytical and finite element method, are compared which shows a good match

between them. Moreover in time stepping analysis torque-slip, fundamental stator phase

current-slip, input power-slip, efficiency-slip and power factor-slip characteristics are drawn

and compared.

Comparison of torque-slip characteristics in steady state AC and time stepping analysis show

that the KLASYS tool always predicts higher values than Flux2D. The efficiency-slip, phase

current-slip, input power-slip and power factor-slip characteristics of the VZIM motor in time

stepping and steady state AC analysis, calculated by Flux2D and KLASYS match very well in

all slips.

Thermal calculations have been done for VZIM with the help of the ANSYS tool which is a

finite element method tool. Comparing the results obtained by ANSYS and simplified thermal

circuits of the 22kW VZIM motor shows a low difference about 1.99%, and the results assure

that the insulation of the stator winding always stays in a safe side, and the temperature never

exceeds the critical values. In addition, the average value of the temperature rise of VZIM2

and VZIM3 ( calculated by ANSYS, is considered as the temperature rise of the

22kW VZIM motor which is well below the maximum temperature rise for the Thermal Class

F ( ).

- 88 -

Bibliography

[1] Binder, A. ,‘‘CAD and system dynamics of electrical machines,’’ Lecture script, TU

Darmstadt, 2010.

[2] Binder, A. ,‘‘Motor development for electrical drive systems, ’’ Lecture script, TU

Darmstadt, 2010.

[3] Binder, A. ,‘‘Electrical Machines and Drives, ’’ Lecture script, TU Darmstadt, 2009.

[4] Binder, A. ; Funieru, B. ‚‘‘Design of Electrical Machines and Actuators with Numerical

Field Calculations, ’’ Seminary notes, TU Darmstadt, 2010.

[5] Flux2D Application‚‘‘Induction machine tutorial calculations in Flux2D,’’ Cedrat

corporation, 2011.

[6] Gholizad, H. ; Binder, A. ,“Analytical Modeling of Variable Impedance Induction

Motors’’, in proc. IEEE IEMDC, 15-18 May 2011, Niagara Falls, Canada, pp. 1504-1509.

[7] Data sheet, Power Core M270-50A, Elektroband NO / NGO electrical steel.

[8] Xyptras, J. ; Hatziathanassiou, V. ,“Thermal analysis of an electrical machine taking into

the account the iron losses and the deep bar effect,’’ IEEE Transactions on Energy

Conversion vol. 14, no. 4, December 1999, pp. 996-1003.

[9] Huai, Y. ; Melnik, R. ; Thogersen, P. ,“Computational analysis of temperature rise

phenomena in induction motors’’, Applied Thermal engineering vol. 23, no. 7, May 2003, pp.

779-795.

- 89 -

8. Appendix

8.1 Appendix I: Calculation of magnetizing main and stray inductances

Magnetizing main inductance for infinite iron permeability is only determined by air

gap. According to [1] the magnetizing main inductance is calculated as:

Stator harmonic stray inductance is calculated as:

where stator harmonic stray coefficient is calculated:

where rotor stray harmonic inductance is calculated as:

Rotor harmonic stray coefficient is calculated:

Inductance of stator winding overhang is calculated as below:

End-ring stray inductance of the rotor cage is calculated:

,

Slot stray inductance of stator winding is calculated:

- 90 -

Rotor slot stray inductance of VZIM1 (Round bar) calculation:

Rotor slot stray inductance of VZIM1 (round bar) is calculated according to [1]

Rotor slot stray inductance of VZIM2 (Deep bar) calculation:

Rotor slot stray inductance of VZIM2 (Deep bar) is calculated according to [1]

where:

(At standstill)

Rotor slot stray inductance of VZIM3 (Wedge bar) calculation:

Rotor slot stray inductance of VZIM2 (Wedge bar) is calculated according to [1]

where:

(At standstill)

- 91 -

8.2 Appendix II: a) Calculation of slips, where a synchronous harmonic torque of

VZIM1, VZIM2, VZIM3 happens

In order to derive the slips that synchronous harmonics of the VZIM occur, according to [2],

Stator ordinal numbers are derived as,

Rotor ordinal numbers are derived as,

Condition for slip where synchronous harmonic occurs is derived as,

After deriving the slips, the related speeds of synchronous harmonic torque is calculated as

In Table I synchronous harmonic torque slips which are the same for VZIM1, VZIM2, and

VZIM3 are shown.

Table I: Synchronous harmonic torque slip

Harmonic slip Rotor speed(rpm)

13 0.857 214.5

-29 1.071 -106.5

b) Calculation of the slips which asynchronous harmonic torque happens in VZIM1

Slips that asynchronous harmonic torques of the VZIM1 occur are calculated according to [2].

Stator ordinal numbers are derived as

The asynchronous harmonic slips are derived as

- 92 -

Table II: Stator ordinal numbers and related asynchronous harmonic torque slips

1 -5 7 -11 13 -17 19 -23 25 -29 31 -35 37

0 1.2 0.857 1.09 0.92 1.0588 0.947 1.043 0.96 1.034 0.96 1.028 0.072

Harmonic break down slips, are calculated for each asynchronous harmonic torque, according

to [2] as

where is calculated as

.

For all ordinal numbers the breakdown slips are calculated as following:

For :

For :

- 93 -

For :

For :

- 94 -

For :

For :

- 95 -

For :

For :

For :

- 96 -

All slips, in which asynchronous harmonic torques happen, and the related slips of the

breakdown harmonic torques, in addition to selected slips for time stepping calculation of the

VZIM1, are shown in Table V.

c) Calculation of the slips, where an Asynchronous harmonic torque happens in VZIM2

Similar to VZIM1 all the calculations have been done for VZIM2.


The asynchronous harmonic slips are derived as

Table III: Stator ordinal numbers and related asynchronous harmonic torque slips

1 -5 7 -11 13 -17 19 -23 25 -29 31 -35 37

0 1.2 0.857 1.09 0.92 1.0588 0.947 1.043 0.96 1.034 0.96 1.028 0.972

Harmonic break down slips are calculated for each asynchronous harmonic torque, according

to [2] as


,


:

- 97 -

:

:

- 98 -

:

:

- 99 -

:

:

- 100 -

:

:

- 101 -



VZIM2 are shown in Table VI.

d) Calculation of the slips where an Asynchronous harmonic torque happens in VZIM3

Similar to VZIM1and VZIM2 all the calculations have been done for VZIM3.


The asynchronous harmonic slips are derived as,

Table IV: Stator ordinal numbers and related asynchronous harmonic torque slips

1 -5 7 -11 13 -17 19 -23 25 -29 31 -35 37

0 1.2 0.857 1.09 0.92 1.0588 0.947 1.043 0.96 1.034 0.96 1.028 0.972

Harmonic break down slips are calculated for each asynchronous harmonic torque, according

to [2] as


.


:

- 102 -

:

:

:

- 103 -

:

:

- 104 -

:

:

- 105 -

:



VZIM2, are shown in Table VII.

- 106 -

Table V: Slips, which are used to perform time-stepping analysis of VZIM1

Slip Speed(rpm)

0.00001 1500

0.01 1485

0.02 1470

0.0253 1462

0.03 1455

0.04 1440

0.05 1425

0.06 1410

0.08 1380

0.1 1350

0.12 1320

0.15 1275

0.2 1200

0.3 1050

0.45 825

0.65 525

0.843 235.5

0.857 214.5

0.871 193.5

0.917 124.5

0.92 120

0.923 115.5

0.94 90

0.947 79.5

0.954 69

0.958 63

0.96 60

0.962 57

0.987 19.5

1 0

1.013 -19.5

1.034 -51

1.0344 -51.6

1.0348 -52.2

1.037 -55.5

1.043 -64.5

1.054 -81

1.0588 -88.2

1.063 -94.5

1.071 -106.5

1.077 -115.5

1.084 -126

1.09 -135

1.096 -144

1.174 -261

1.2 -300

1.226 -339

1.33 -495

1.66 -990

2 -1500

- 107 -

Table VI: Slips, which are used to perform time-stepping analysis of VZIM2

Slip Speed(rpm)

0.00001 1500

0.01 1485

0.02 1470

0.0253 1462

0.03 1455

0.04 1440

0.05 1425

0.06 1410

0.08 1380

0.1 1350

0.12 1320

0.15 1275

0.2 1200

0.3 1050

0.45 825

0.65 525

0.85 225

0.857 214.5

0.8633 205.05

0.9166 125.1

0.92 120

0.9234 114.9

0.944 84

0.947 79.5

0.95 75

0.9587 61.95

0.96 60

0.961 58.5

0.995 7.5

1.0044 -6.6

1.013 -19.5

1.0344 -51

1.03432 -51.48

1.03463 -51.94

1.041 -61.5

1.043 -64.5

1.045 -73.5

1.057 -85.5

1.0588 -88.2

1.0606 -90.9

1.0643 -96.45

1.071 -106.5

1.077 -115.5

1.088 -132

1.09 -135

1.093 -139.5

1.1887 -283.05

1.211 -316.5

1.33 -495

1.66 -990

2 -1500

- 108 -

Table VII: Slips, which are used to perform time-stepping analysis of VZIM3

Slip Speed(rpm)

0.00001 1500

0.01 1485

0.02 1470

0.0253 1462

0.03 1455

0.04 1440

0.05 1425

0.06 1410

0.08 1380

0.1 1350

0.12 1320

0.15 1275

0.2 1200

0.3 1050

0.45 825

0.65 525

0.855 217.5

0.859 211.5

0.8633 205.05

0.9168 124.5

0.92 120

0.9232 115.2

0.9466 80.1

0.947 79.5

0.9474 78.9

0.9595 60.75

0.96 60

1.34 -51

1.03438 -51.57

1.0344 -51.6

1.034418 -51.62

1.042 -63

1.043 -64.5

1.044 -66

1.058 -87

1.0588 -88.2

1.0596 -89.4

1.071 -106.5

1.089 -133.5

1.09 -135

1.091 -136.5

1.191 -286.5

1.2 -300

1.209 -313.5

1.33 -495

1.66 -990

2 -1500

- 1

09

-

8.3

Ap

pen

dix

III

: C

alc

ula

ted

lo

sses

of

VZ

IM1

, V

ZIM

2 a

nd

VZ

IM3

Tab

le I

: L

oss

es i

n V

ZIM

1 c

alcu

late

d b

y Flux2D

and KLASYS

Me

tho

d

Sp

ee

d/r

pm

I1

/A

Co

s(F

i)

Pin

/W

I2'/

A

Po

ut/

W

To

rqu

e/N

m

Eff

icie

ncy

LO

SS

cu1

/W

LOS

Scu

2/W

LO

SS

fes/

W

LOS

Sfe

r/W

Flu

x2

D

13

90

,9

37

,39

0

,96

7

25

05

3,7

3

7,1

34

3

21

60

5,2

3

14

8,4

68

0

,86

9

46

,17

1

49

7,4

4

16

1,1

2

25

,32

Kla

sys

37

,4

0,9

15

2

36

95

,5

35

,66

2

04

92

,4

14

0,7

0

,86

5

94

7

16

45

,6

11

6

2,0

34

Flu

x2

D

14

62

15

,49

0

,87

2

93

68

,97

1

2,8

2

91

75

,23

9

55

,64

0

,97

93

1

62

,39

1

97

,76

1

26

,52

1

2,5

2

Kla

sys

16,3

6

0,7

69

8

72

2,3

1

2,8

4

7892

5

1,5

5

0,9

05

1

81

,2

213

,3

119

,7

0,6

69

Flu

x2

D

52

5

20

0,9

9

0,8

07

1

11

24

00

2

03

,17

2

42

19

,76

2

44

3,7

2

0,2

15

4

27

34

0,6

7

43

03

1,4

8

13

6,2

88

3

8,4

4

Kla

sys

208

,6

0,8

05

1

15

43

9,3

2

07

,2

298

73

,1

543,4

0

,20

8

294

40

,1

558

36

,4

78,0

2

15,7

2

Flu

x2

D

-15

00

29

0,9

7

0,6

1

12

31

00

2

88

,06

-5

81

27

,68

3

55

,52

-0

,47

2

57

30

0,2

8

95

58

0

31

9,1

1

24

,92

Kla

sys

306

,6

0,5

95

1

26

10

4,2

305

-6

33

92

,4

403

,6

-0,5

03

6

36

44

,6

124

69

3,8

58,8

2

6,5

1

Tab

le I

I: L

oss

es i

n V

ZIM

2 c

alcu

late

d b

y Flux2D

and KLASYS

Me

tho

d

Sp

ee

d/r

pm

I1

/A

C

os(

Fi)

P

in/W

I2

'/A

P

ou

t/W

T

orq

ue

/Nm

E

ffic

ien

cy

LOS

Scu

1/W

LO

SS

cu2

/W

LOS

Sfe

s/W

LO

SS

fer/

W

Flu

x2

D

14

55

,8

35

,91

0

,97

2

41

88

3

4,3

1

22

02

1,0

51

1

44

,52

0

,91

04

8

72

,75

8

33

,24

2

00

,08

3

7,3

2

Kla

sys

32

,38

0

,91

6

20

42

5,1

3

0,4

4

18

48

6,2

1

21

,3

0,9

05

7

09

,8

57

5,7

1

77

,9

0,7

24

Flu

x2

D

14

62

31

,20

2

0,9

7

21

10

0

30

,61

2

01

01

,05

7

12

6,0

4

0,9

5

65

8,9

08

6

25

,17

2

20

1,8

52

3

3,5

6

Kla

sys

28,4

3

0,9

04

1

77

04

,8

26,3

2

160

98

,2

105

,1

0,9

09

5

46

,9

430

,1

179

,2

0,6

15

Flu

x2

D

52

5

28

4,0

4

0,6

7

13

30

00

2

87

,5

17

19

0,5

58

3

18

,76

0

,12

92

5

46

03

,35

4

09

38

,52

1

27

,01

6

38

,72

Kla

sys

300

,6

0,7

14

1

47

78

9,1

2

98

,8

301

33

,2

548

,1

0,2

04

6

11

50

,9

562

22

,1

88,0

1

7,9

76

Flu

x2

D

-15

00

33

6,3

6

0,5

3

12

40

00

3

33

,57

7

-39

41

3,2

8

23

6,3

6

-0,3

17

7

65

71

,83

6

83

82

,89

2

29

1,7

76

1

31

,08

Kla

sys

369

,2

0,5

46

1

39

37

8,3

3

67

,1

-471

68

,6

300

,3

-0,3

38

9

22

48

,7

933

73

7

3,8

9

13,0

5

- 1

10

-

Tab

le I

II:

Loss

es i

n V

ZIM

3 c

alcu

late

d b

y Flux2D

and KLASYS

Me

tho

d

Sp

ee

d/r

pm

I1

/A

co

s(Fi

) P

in/W

I2

'/A

P

ou

t/W

T

orq

ue

/Nm

E

ffic

ien

cy

LOS

Scu

1/W

LO

SS

cu2

/W

LOS

Sfe

s/W

LO

SS

fer/

W

Flu

x2

D

14

74

,65

36

,62

0

,95

25

2

41

66

,01

3

0,3

4

22

04

0,7

1

43

,13

2

0,9

12

9

07

,60

5

48

7,8

16

1

40

,12

4

23

,75

6

Kla

sys

33

,02

0

,91

8

20

93

1,6

3

1,3

3

19

36

7,3

1

25

,4

0,9

25

7

38

,1

33

8,2

1

78

,2

0,6

07

Flu

x2

D

14

62

52

,63

0

,95

7

34

90

0

53

,08

3

17

49

,14

2

02

,44

0

,90

9

18

74

,67

9

98

,45

1

67

,16

3

6,9

2

Kla

sys

47,4

0

,93

2

303

81

,1

45,9

1

276

12

1

80

,4

0,9

09

1

52

0,9

7

26

,7

173

,2

0,9

44

Flu

x2

D

52

5

30

3,9

29

0

,59

3

12

50

00

3

02

,9

11

27

7,9

38

2

08

,88

0

,09

2

62

51

7,9

3

30

44

5,9

28

1

10

,28

3

3,9

6

Kla

sys

318

,6

0,5

84

1

28

48

6,7

3

16

,5

207

74

,3

377

,9

0,1

62

6

87

13

,5

387

76

,4

82,2

9

7,7

99

Flu

x2

D

-15

00

34

2,6

1

0,5

22

1

24

00

0

33

7,7

5

-36

27

3,2

8

23

1,0

4

-0,2

92

7

94

43

,87

5

63

65

7,0

52

2

22

,44

1

12

,88

Kla

sys

360

0

,50

7

126

30

7,7

3

58

,1

-388

38

,9

247

,3

-0,3

07

8

77

37

,7

767

32

,1

76,2

2

18,5

2

- 111 -

8.4 APPENDIX IV: Estimation of the heat transfer coefficient at the winding-overhang

close to the centrifugal mechanism

Although VZIM motor is totally enclosed, at one side of the winding overhang, heat transfer

coefficient is considered as for the natural convection and heat radiation, but

at the other side of the motor, the rotating centrifugal mechanism leads to a better cooling due

to the forced convection. Therefore in order to calculate the heat transfer coefficient for this

winding overhang close to the centrifugal mechanism, with try and error and comparison with

measured values, is calculated for 5.5kW VZIM ( ) and for 22kW VZIM

due to the similar structure with 5.5kW VZIM, a proportional value of is considered. In the

following, it is described how the value of heat transfer coefficient is derived.

Measured values at the rated load thermal test for 5.5kW VZIM shows that the maximum

temperature rise for the winding overhang is 67.7 . According to this value a finite element

model of 5.5kW VZIM is prepared using ANSYS, and the value of is adjusted, and finally

with a heat transfer coefficient about the calculated values, based on the

finite element method with ANSYS and measured values are matched together. For 5.5kW

VZIM2 (nominal speed for 5.5kW VZIM2 is equal to 1455.2rpm) with consideration of the

centrifugal mechanism as a standard fan, the heat transfer coefficient is equal to

, besides for 22kW VZIM2 motor (nominal speed

for 22kW VZIM2 is equal to 1467.36 rpm) the heat transfer coefficient for winding overhang

with considering the mechanical part of the motor, as a standard fan, is equal to

. Therefore due to the similarity of the 2 types of the motor

(5.5kW and 22kW) the applied value of for VZIM2 22kW is

.

For 5.5kW VZIM3 (nominal speed for 5.5kW VZIM3 is equal to 1470rpm) with

consideration of the centrifugal mechanism as a standard fan, the heat transfer coefficient is

equal to . Besides for 22kW VZIM3 motor

(nominal speed for 22kW VZIM3 is equal to 1467.36rpm) the heat transfer coefficient for the

winding overhang, with considering the mechanical part of the motor as a standard fan, is

equal to . Therefore due to the similarity of

the 2 types of the motor (5.5kW and 22kW) the applied value of for VZIM2 22kW is

.

Documents

Induction Motor Analysis