Torque Ripple Reduction in Reluctance Synchronous Machines using Magnetic Wedges

Torque Ripple Reduction in Reluctance

Synchronous Machines using Magnetic

Submitted to the Department of Electrical Engineering in partial fulfilment of the

requirements for the Baccalaureus Technologiae in Electrical

SUPERVISOR: E. VOSS



Wedges

By

Robert Albert Smith


requirements for the Baccalaureus Technologiae in Electrical Engineering at the

SUPERVISOR: E. VOSS

NOVEMBER 2010




Engineering at the

ii

DECLARATION

I declare that Torque ripple reduction in reluctance synchronous machines using magnetic

wedges is my own, unaided work and that all the sources I have used or quoted have been

indicated and acknowledged as complete references. This thesis has not been submitted before

for any degree or examination at any other University.

Robert Albert Smith

_______________________________________________

(Signature of candidate)

Signed in Cape Town the _________ day of ________________ 2010

iii

ACKNOWLEDGEMENTS

I would like to thank those who I believe have assisted me getting to this point in my academic

career and therefore with my thesis.

My Heavenly Father

Jesus Christ, without You none of this would have been possible and I thank You for Your

guidance, support and endless love You have given me throughout these years.

Mr. Egon Voss

Thank you for your help and supervision throughout the whole research process. I appreciate all

the time and effort you put aside for me and all the assistance you have given me. You are an

inspiration to many at this institution.

My university friends

Thank you, Deon Heyns, Albertu Prins and all of my fellow BTech engineering students for your

assistance, guidance and support throughout this year.

My family

Thank you for giving me the opportunity to be educated in a tertiary institution doing what I love

most. Your support, love and belief in me made all of this possible.

iv

ABSTRACT

This paper compares different types of magnetic wedges within a reluctance synchronous

machine’s (RSM) stator to determine the effect they have on the torque ripple, as well as the

average torque produced. The torque ripple in any motor is a major disadvantage and it is,

therefore, an important task to find methods of reducing this ripple without considerably

affecting the average torque. The role of magnetic wedges in the stator slots are discussed in

detail. Various case studies were performed and their torques compared. This was completed in

linear and non-linear materials of different permeabilities. The different magnetic materials were

also combined, without changing the wedge geometry, to form double wedges in the stator. This

determined the effect that linear- and non-linear materials have on the torque ripple. From these

case studies, an optimum linear permeability was found, while from the range of non-linear

permeabilities, the lowest torque ripple was produced for a mild steel wedge. After determining

the optimum wedge materials for the specified application, the effect which these different

magnetic materials have on the motor’s torque was also determined.

Index Terms—magnetic wedges, permeability, reluctance synchronous machine, torque ripple.

v

TABLE OF CONTENTS

Declaration.................................................................................................................. ii

Acknowledgements..................................................................................................... iii

Abstract....................................................................................................................... iv

List of figures.............................................................................................................. vii

List of tables................................................................................................................ viii

List of symbols............................................................................................................ ix

List of abbreviations.................................................................................................... x

1. Introduction...................................................................................................... 1

1.1 The history of the RSM....................................................................... 1

1.2 General RSM operation....................................................................... 1

1.3 The effect of magnetic wedges............................................................ 3

2. Research statement.......................................................................................... 4

3. Methodology.................................................................................................... 5

3.1 Simulation specifications..................................................................... 5

3.2 Description of case studies................................................................... 7

3.3 Linear wedge material.......................................................................... 8

3.4 Non-linear wedge material................................................................... 9

3.5 Flux barrier materials............. ............................................................. 10

4. Results............................................................................................................. 10

4.1 Linear materials for single wedge…………….……………………… 10

4.2 Non-linear materials for single wedge……………………………….. 11

vi

4.3 Combined linear- and non-linear materials for double wedge………. 13

4.4 Flux barrier permeabilities.................................................................. 14

5. Analysis of results…………………………………………………………… 15

5.1 Linear materials for single wedge…………….……………………….… 15

5.2 Non-linear materials for single wedge………………….…………..…… 16

5.3 Combined linear- and non-linear materials for double wedge………….. 16

5.4 Flux barrier permeabilities........................................................................ 16

6 Conclusion…………………………………………………………..……… 17

7 References……………………………………………………………..…….. 18

Appendix A: Geometry of RSM…………………………………………….….. 20

Appendix B: Torque results for linear materials……………………………….. 21

Appendix C: Torque results for non-linear materials………………………...… 22

vii

LIST OF FIGURES

Figure 1.2-1 A quarter of the RSM representing its d- and q-axes……………..... 2

Figure 1.2-2 Example of torque ripple without wedges………………………….. 3

Figure 1.3-1 The effect on the flux density of a stator with (a) and without (b)

magnetic wedges………………………………………….………… 4

Figure 3.1-1 Calculation path inside the air-gap along contour Γ……….……….. 6

Figure 3.1-2 Procedure for acquiring RSM torque values………………………… 6

Figure 3.2-1 RSM with a single wedge…………………………………………… 7

Figure 3.2-2 RSM with a double wedge…………………..………………………. 8

Figure 3.4-1 Maximum relative permeability……………………………..……… 9

Figure 4.1-1 The torque comparison for a range of linear magnetic wedges…….. 10

Figure 4.1-2 The torque graph for a linear magnetic wedge compared to the

absence of a magnetic wedge……………………………………….. 11

Figure 4.2-1 The torque comparison for a range of non-linear magnetic

wedges……………………………………………………………..... 12

Figure 4.2-2 The torque graph for a non-linear magnetic wedge compared

to the absence of a magnetic wedge………………………………… 12

Figure 4.4-1 Average torque as a function of the relative permeability of the

flux barriers.………………………………………………………… 14

viii

LIST OF TABLES

Table 4.2-1 List of non-linear materials to be simulated…………………….…… 11

Table 4.3-1 Combined wedge torque values……………………………………… 13

Table 5-1 Summary of findings for lowest torque ripple………………………. 14

ix

LIST OF SYMBOLS

Γ – Gamma (contour) [m]

�max – Maximum relative permeability

�0 – Permeability of vacuum [Vs/Am]

�r – Relative permeability

π – Pi

Bt – Magnetic flux density (tangential component) [Vs/m2]

Br – Magnetic flux density (radial component) [Vs/m2]

B – Magnetic flux density [Vs/m2]

F – Force [N]

H – Magnetic field strength [A/m]

I – Current [A]

ℓs – Stack length [m]

S – Surface contour [m2]

TAVG – Average torque [Nm]

TMAX – Maximum torque [Nm]

TMIN – Minimum torque [Nm]

Tm – Torque (Maxwell stress tensor) [Nm]

%TRIPPLE – Percentage torque ripple [%]

V – Voltage [V]

x

LIST OF ABBREVIATIONS

d – Direct

FEA – Finite element analysis

RSM – Reluctance synchronous machine

Rms – Root mean square

q – Quadrature

1

1 INTRODUCTION

1.1 The history of the RSM

Although the theory of magnetic reluctance has been known for more than 150 years, research on

the RSM has been conducted only since the early days of the 20th

century, with the researchers’

attention mainly focused on the geometry and structure of the rotor. At first, these findings were

only theoretical, but as technology advanced, more computer-based analysis methods were made

possible, giving the engineer fewer restrictions to experiment with the RSM’s parameters. A

large percentage of the research performed on the RSM covered the effect of changes in the rotor

geometry which included the analysis of inductances, magnetic fields, high anisotropy, high

torque-per-volume values, and permeance harmonics. Research on torque harmonics, however,

has not yet received adequate attention and this is the reason for this paper. [1, 2]

1.2 General RSM operation

As the name implies, the RSM operates on the principle of magnetic reluctance. This reluctance,

which is the reciprocal of permeability, is similar to electric resistance in the sense the magnetic

flux always tends to flow through the path of least reluctance [3]. The RSM rotor consists of

magnetic steel laminations, with no conducting windings, and is designed in such a manner that

the inductance varies as it rotates [4]. This is caused by its internal flux barriers and external cut-

outs and is what defines the rotor’s d- and q-axes. These axes (Figure 1.2-1) guide the magnetic

flux, produced by the current in the stator windings, and cause the rotor to move in the direction

of the stator phase sequence which finally reaches the speed synchronous to that of the stator

frequency. Consequently, this magnetic flux, that in effect “pulls” the rotor along the stator,

produces the RSM’s torque. Figure 1.2-1 also illustrates how the flux lines tend to follow the

path of least reluctance which is in effect through the d-axis. The key below the RSM shows the

range of the flux density throughout the stator and rotor. From this it can be seen that the flux

density is the largest around phase B’s winding slots and is distributed along the RSM, around

the flux barriers, and through the stators d-axis.

2

Figure 1.2-1: A quarter of the RSM representing its d- and q-axes

Although the RSM has the advantage not to produce any copper loss in the rotor, it also has the

disadvantage of producing an inherently high torque ripple [4]. This torque ripple (Figure 1.2-2)

is defined as the “deviation of the maximum and minimum torque from the average value” [5]

and is given by the equation [2]:

%��

� � 100% (1)

For equation (1) TMAX, TMIN, and TAVG is the maximum-, minimum-, and average torque

respectively. This torque ripple is caused by the combination of the rotor flux barriers and slots

in the stator which produce a “non-sinusoidal air-gap permeance variation”. Because this ripple

in the torque means an uneven pull, vibrations, and acoustic noise it is desirable to reduce it to a

minimum without reducing the average torque considerably [2], [4], [5].

Phase B

3

Figure 1.2-2: Example of torque ripple without wedges

There have been numerous contributions towards the reduction of the torque ripple, for instance

skewing of the rotor, or changing the flux barrier geometry within the rotor [1], [2], [4-8].

Although electronic drives have been developed, which are of tremendous help, the electrical

engineer still tries to do research on the roots of the problem.

1.3 The effect of magnetic wedges

Similar to the stator rotor, the wedges are made of a magnetic material which makes the air-gap

magnetically smooth. The absence of these magnetic wedges causes the radial force between the

rotor and stator to constantly change as the rotor turns, which in effect produces a ripple in the

torque [1]. A wedge, however, would reduce the average torque, but also produces a smoother

output torque. The mutual flux through the air-gap is now evenly distributed and hence reduces

the torque ripple. The challenge here is to find the optimum material which would distribute

enough magnetic flux to the rotor to maintain the average torque, whilst reducing the variation in

the d- and q-axes inductances. Figure 1.3-1 (a) and (b) illustrate the difference a magnetic wedge

makes to the flux distribution in the slotted region. It can also be seen that the flux density

between the tooth region and the rotor becomes less for the magnetic wedge’s presence. The low

average torque that these wedges create is a result of this reduced flux density.

40

42

44

46

48

50

52

54

56

58

0 30 60 90 120 150 180

Torq

ue (N

m)

Angle (elec°)

Ripple Torque

Avg Torque

Figure 1.3-1: The flux density

For Figure 1.3-1 (a) it can be seen that a certain region in the air

highlighted region covers five flux lines which are transferred from the stator teeth to

The same size region is highlighted in Figure 1.3

eight flux lines is found. This example clearly indicates how the magnetic wedges reduce the

RSM’s average torque.

2 RESEARCH STATEMENT

There have been numerous papers [1

within the stator slots have on the torque ripple. In

method for the reduction of the torque ripple by inserting magnetic wedges within the stator slots

whilst keeping the stator and rotor geometr

“magnetically smooth” which should theoretically produce sinusoidal flux linkages between the

stator and the rotor [5].

Experiments with several different types of linear and non

simulated to cover a variety of permeabilities. These materials will be simulated for single

wedges as well as combined double wedges with different permeabilities.

a

Wedge

4

The flux density in the air-gap with (a) and without (b) magnetic wedges

1 (a) it can be seen that a certain region in the air-gap is highlighted. This

highlighted region covers five flux lines which are transferred from the stator teeth to

The same size region is highlighted in Figure 1.3-1 (b), but in this case, an increased value of

found. This example clearly indicates how the magnetic wedges reduce the

TATEMENT

There have been numerous papers [1], [4], [5] dealing with the effect which magnetic wedges

within the stator slots have on the torque ripple. In this paper, however, the author


whilst keeping the stator and rotor geometries in its initial form. These wedges make the air


xperiments with several different types of linear and non-linear magnetic materi

of permeabilities. These materials will be simulated for single

wedges as well as combined double wedges with different permeabilities. The effect of a change

b

Air-gap with more flux lines

Wedge

Air-gap with

less flux lines

No wedge

with (a) and without (b) magnetic wedges

gap is highlighted. This

highlighted region covers five flux lines which are transferred from the stator teeth to the rotor.

n this case, an increased value of

found. This example clearly indicates how the magnetic wedges reduce the

magnetic wedges

this paper, however, the author proposes a


ies in its initial form. These wedges make the air-gap


linear magnetic materials will be

of permeabilities. These materials will be simulated for single

The effect of a change

gap with ore flux lines

5

in the flux barrier permeability will also be researched to determine the effect it has on the

average torque.

3 METHODOLOGY

3.1. Simulation specifications

A 3-phase, 4-pole, 380V RSM with single layer windings will be simulated at a rms current of

16A and modelled using a Finite Element Analysis (FEA) software. The RSM is also simulated

as a two-dimensional model with the assumption that any fringing effects as well as end leakages

are neglected.

For optimum torque ripple results it was proposed [1] that the RSM rotor has an angle of 26°

between adjacent flux barriers and that the current angle be simulated at 50°. Appendix A gives a

description of the RSM’s specifications and geometries.

FEA produces 180 instantaneous torque values over a range of 180°el, which is equivalent to

90°mech (Figure 1.2-1). FEA calculates these individual torques using Maxwell’s stress tensor

which is derived from the resultant stress tensor σs, for a closed surface, S [1].

� !" ·" $% (3)

This equation is then simplified to a line integral along the closed contour Γ in the centre of the

air-gap (4), because only a two-dimensional slice of the RSM is simulated and then multiplied

with the effective stack length of the rotor [1].

�& '()

*+ ,-,.$Γ / ℓ" (4)

Where μ0 is the permeability of vacuum, Γ is the contour length of the defined path at which each

individual torque is calculated, r is the radius from the centre of the shaft to the contour Γ, Br and

Bt are the radial and tangential components respectively and ℓs the effective stack length of the

rotor [1]. Figure 3.1-1 illustrates the refined mesh description along the air-gap along with the

defined path. This path runs through the centre of the air-gap.

Figure 3.1-1: Calculation path inside the air

These instantaneous torque values are used to calculate the average torque and also to find the

maximum and minimum torque values.

procedure illustrated in Figure 3.1

Figure 3.1-2:

6

: Calculation path inside the air-gap along contour Γ


maximum and minimum torque values. The torque ripple values are acquired using the

3.1-2.

: Procedure for acquiring RSM torque values

Refined air-gap mesh

Contour (Γ)

Γ


acquired using the

7

The average torque, TAVG, can be calculated from the equation:

�123 ∑ �567)°58)°

9 (2)

Where Tn is the value (Nm) for each individual torque and n is the number of torque values

acquired ranging from 0°el to 180°el.

3.2. Description of case studies

The magnetic wedges are simulated with both linear- and non-linear permeabilities. Both of

these wedge materials will be simulated with single- as well as double wedges in the slots. The

double wedges will consist of a combination of both wedge materials. These combinations will

be determined by the best performing wedge, with low torque ripple as the main performance

parameter. It is important to note that the wedge height remains at 1.22 mm throughout the

various case studies. For the final case study, however, a RSM without any magnetic wedges will

be simulated with various flux barrier materials. Practically, this method can be considered as the

insertion of magnetic materials inside the flux barrier region. Figure 3.2-1 and Figure 3.2-2,

single- and double wedge respectively, show how the wedges fit into the stator slots.

8

Figure 3.2-1: RSM with a single wedge

Figure 3.2-2: RSM with a double wedge

3.3. Linear wedge material

The different linear magnetic wedges will be simulated for relative permeabilities ranging from

0.1 to 1 in steps of 0.2, followed by a range of 2 to 10 in steps of 2, after which the steps increase

from 10 to 100 in steps of 10, and finally increasing from 100 to 1000 000 by multiplication

factors of 10. This is to get an approximation of how the torque reacts to such a wide range of

linear permeabilities. The aim of this range is to find an optimum value for the linear wedges

used. The relative permeability for the wedges used in the stator can be calculated using equation

[9]

�. :(); (3)

Where B is the magnetic flux density, μ0 is the permeability of air, and H is the magnetic field

strength. The relative permeability is defined as “the ratio of the permeability of a specific

medium to the permeability of free space given by the magnetic constant μ0 = 4π*10-7

” Vs/Am

[10].

1

2

9

3.4. Non-linear wedge material

Equation (3) causes a non-linear material to have a vast range of relative permeabilities as the

values of B or H change along the B-H curve. According to McLyman [11], theses various

relative permeabilities can be categorized in more than one way. One of these methods

determines the B-H curve’s maximum relative permeability (µmax) which is defined as “the slope

of a straight line drawn from the origin tangent to the curve at its knee.” This means that the

values of both B and H are obtained at the point where the straight line is equal to the curve at

the knee-point. These values are then used to calculate the maximum relative permeability using

equation (3). Figure 3.4-1 is an example of a B-H curve and illustrates how the maximum

relative permeability of a non-linear material is obtained.

Figure 3.4-1: Maximum relative permeability [11]

The various non-linear materials were limited to the list of B-H curves supplied by FEA. From

these materials, a careful selection was used that ranged from a maximum relative permeability

of 100 to 260000.

10

3.5. Flux barrier materials

For this case study it is not necessary to find the material that produces the lowest torque ripple.

This case study is to purely determine how the average torque is affected. The insertion of the

magnetic materials inside the flux barriers will therefore only consist of linear magnetic

materials to provide a wide range of materials.

The linear materials are initially increased by relative permeable steps of 10 up to a value of 50

to illustrate the graph’s initial gradient. From 50 it is increased in larger steps to fit the average

torque values over a larger range of permeabilities.

4 RESULTS

4.1 Linear materials for single wedge

This specific range of linear materials is selected to provide a wide scope of permeabilities. The

graph below (Figure 4.1-1) shows the results for the whole range of linear materials that were

simulated. It is interesting to note how the percentage torque ripple decreases to a specific value

and then rises to a value where it saturates at a constant torque ripple.

Figure 4.1-1: The torque comparison for a range of linear magnetic wedges

4041424344454647484950

0%5%

10%15%20%25%30%35%40%45%50%

0.2

0.4

0.6

0.8 1 2 4 6 8

10

20

25

30

40

50

60

70

80

90

10

010

00

100

00

1000

00

10

00…

Aver

age Torq

ue (N

m)

Torq

ue Rip

ple (%

)

Relative Permeabilty

Linear Material Results

Average Torque

%Torque Ripple

11

Throughout the vast range of linear relative permeabilities it was found that the lowest torque

ripple occurred at a relative permeability of μr = 25. Using equation (2) it can be calculated that

this material produces a torque ripple percentage of 10.67% with an average torque of 44.38 Nm.

This is a remarkable result, as a RSM typically operates between relative permeabilities of 3 500

and 5 000. It is therefore interesting to note that the lowest torque ripple is produced for a

magnetic wedge with such a low relative permeability. For comparative reasons Figure 4.1-2

illustrates the torque ripple and average torque that this material produces as well as the torque

produced with no magnetic wedges. The average torque and torque ripple for the linear wedge is

denoted as “Avg torque 25” and “torque ripple 25” respectively. The same notation applies for

air.

Figure 4.1-2: The torque graph for a linear magnetic wedge compared to the absence of a

magnetic wedge

4.2. Non-linear materials for single wedge

Table 4.2-1 shows the different non-linear materials used as wedges for the RSM. These

materials are acquired from FEA software’s database. The method of obtaining the materials’

maximum relative permeabilities previously described is used. These values obtained are

rounded off to give an estimation of the material’s B-H curve and saturation region.

Table 4.2-1: List of non-linear materials to be simulated

40424446485052545658

0 30 60 90 120 150 180

Torq

ue (N

m)

Angle (elec°)

Torque comparison graph - Linear

Torque Ripple Air

Avg Torque Air

Torque Ripple 25

Avg Torque 25

12

Wedge Material

Maximum Relative

Permeabilty µmax

Wedge Material

Maximum

Relative

Permeabilty µmax

Unisil 27M4 100 A36 Steel 4000

Unisil 30M2H 400 M19FP 26GA 4500

Unisil Grain Orient 800 Newcor 32 4600

Unisil 23M3 1500 Losil 1000 5500

HCR Alloy 2000 EN9 Steel 6000

Cast Iron 2200 Grade 450 Steel 6200

Mild steel 2800 Alnico YCM-9B 34000

Unisil 27MOH 3500 Ferixite 260000

Rolled Steel 3800

Figure 4.2-1 shows the lowest percentage torque ripple of 10.20% was acquired for mild steel

which effectively produced an average torque of 43.41 Nm.

Figure 4.2-1: The torque comparison for a range of non-linear magnetic wedges

This low torque ripple mild steel produces is shown in figure 4.2-2. Again, the blue waveform is

the torque produced with no magnetic wedge inserted. This gives an idea of the effect the

magnetic wedges have.

40

41

42

43

44

45

46

47

48

49

50

0%

5%

10%

15%

20%

25%

10

0

40

0

80

0

15

00

20

00

22

00

28

00

35

00

38

00

40

00

45

00

46

00

55

00

60

00

62

00

34

00

0

26

00

00

Aver

age Torq

ue (N

m)

Torq

ue Rip

ple (%

)

Maximum Relative Permeabilty

Non-linear Material Results

Average Torque

%Torque Ripple

13

Figure 4.2-2: The torque graph for a non-linear magnetic wedge compared to the absence of a

magnetic wedge

4.3. Combined linear- and non-linear materials for double wedge

For the final two case studies the optimum wedges for the two previous case studies, with the

torque ripple as the main performance parameter, will be combined. It should be noted that the

total physical wedge geometry will remain constant and that each wedge material will only be

divided along the breadth of the wedge as illustrated in Figure 3.2-2. The order in which this set

of wedges is placed is also taken into account.

Table 4.3-1 shows the results for the two separate wedge combinations with wedge 1 being the

wedge furthest from the air-gap and wedge 2 closest to the air-gap as displayed in Figure 3.2-2.

Table 4.3-1: Combined wedge torque values

Wedge 1 Non-linear Linear

Wedge 2 Linear Non-linear

%TRIPPLE 10.92% 10.64%

TAVG (Nm) 43.92 43.95

40424446485052545658

0 30 60 90 120 150 180

Torq

ue (N

m)

Angle (elec°)

Torque comparison graph - Non-linear

Torque Ripple Air

Avg Torque Air

Torque Ripple Mild Steel

Avg Torque Mild Steel

14

4.4. Flux barrier permeabilities

According to the theory of magnetism, a force is created when a magnetic flux runs through two

materials having different permeabilities. In the case of the RSM, the rotor, having a relative

permeability of 4500, produces a force onto the flux barrier region, having a relative

permeability of 1. The force created in this specific case contributes to the torque produced by

the RSM.

By increasing the permeability of the flux barrier (which, in this case, would be inserting

different linear magnetic materials) the force produced between the rotor and flux barrier

decrease, which consequently decreases the overall torque. At the point where the flux barrier’s

permeability is equal to that of the rotor, the average torque would be expected to drop to 0 Nm.

As this permeability is increased even further, a force is created in the opposite direction. The

question in this case would be how this increased force between these two materials affects the

average torque produced. Figure 4.4-1 illustrates the decreasing average torque for an increase in

the flux barrier’s permeability.

Figure 4.4-1: Average torque as a function of the relative permeability of the flux barriers

-2

0

2

4

6

8

10

12

10

20

30

40

50

1 0

00

2 0

00

3 0

00

4 0

00

5 0

00

10

00

0

15

00

0

20

00

0

25

00

0

30

00

0

35

00

0

40

00

0

45

00

0

50

00

0

10

0 0

00

20

0 0

00

30

0 0

00

40

0 0

00

50

0 0

00

Avg T

orq

ue (N

m)

Relative Permeability

15

5 ANALYSIS OF RESULTS

Table 5-1 summarises the findings for the paper’s first four case studies. The materials that

produced the lowest torque ripples are documented with their respective average torque values.

For the bottom two rows, the combined wedges are categorised in the order in which each wedge

is inserted i.e. the linear & non-linear row represent the findings for the linear wedge closest to

the air-gap, while the non-linear & linear row represents the non-linear wedge closest to the air-

gap.

Table 5-1: Summary of findings for lowest torque ripple

Material type µr/µmax %TRIPPLE TAVG (Nm)

Linear 25 10.67% 44.38

Non-linear 2800 10.20% 43.41

Linear & non-linear 2800/25 10.92% 43.92

Non-linear & linear 25/2800 10.64% 43.95

5.1 Linear materials for single wedge

With the lowest torque ripple at a value of 10.67%, it was also noted that the average torque

reduced to 44.38 Nm when compared to a RSM with no magnetic wedges. This implies that

while the torque ripple was reduced by 67.1%, the average torque also reduced by 6.2%. It is

interesting to note how the torque ripple decreases up to a certain permeability (μr = 25) and then

rises to a point where the percentage ripple remains constant. It can also be seen that the average

torque is at its maximum where the relative permeability is equal to one, which is equivalent to

the absence of a magnetic wedge. As discussed in section 1.3, the reason for this is the increased

distribution of flux lines within the stator teeth.

16

5.2. Non-linear materials for single wedge

From all of the performed case studies, the non-linear wedge, Mild steel, produced the lowest

torque ripple (10.20%) and, unfortunately, the lowest average torque (43.41 Nm) as well. When

comparing these values to a RSM without any magnetic wedges, a reduction of 68.6% and 8.3%

was calculated for the torque ripple and average torque respectively.

Ferixite, the material with the highest maximum relative permeability, produced the highest

average torque of all the other materials. The interesting fact about this discovery is the

material’s ability to produce almost the exact same average torque as a RSM without any

wedges. The average torque only decreased by 0.4% while the torque ripple reduced by 29.2%.

Depending on the application, this material still produces a high percentage torque ripple

(22.97%), but is a considerable decrease for applications where high average torque is an

important design factor. These findings agreed with that of Voss’ [5] in saying that the non-linear

materials hardly affect the average torque but produces significant reductions in the torque

ripple.

It is interesting to note that these materials do not follow a specified pattern as their respective

permeabilities increase. This is because the shape of their B-H curves has different

characteristics regarding its saturation region and knee-point.

5.3. Combined linear- and non-linear materials for double wedge

The results for the combined wedges show the torque ripple to be higher and lower when

compared to a single material wedge. It is also noted that a slight difference occurs for the order

in which the wedges are placed. A linear wedge close to the air-gap produces a larger percentage

torque ripple as well as a smaller average torque than with the case of a non-linear wedge closest

to the air-gap. This implies that a non-linear wedge being placed closest to the air-gap produces

better results in terms of its torque ripple and average torque.

5.4. Flux barrier permeabilities

As expected, the average torque is almost completely reduced where the flux barrier and rotor

have equal permeabilities. However, when the flux barrier’s permeability is increased even

further it can be seen that the average torque remains at a low value of around 0 Nm. From these

17

results it is clear that, for the permeabilities higher than that of the rotor’s permeability, the force

produced between the two materials do not contribute to the torque. When a further analysis is

conducted, it can be seen that the higher permeable values in the flux barrier create a magnetic

short circuit which, in effect, draw more magnetic flux. The magnetic flux between the rotor and

stator consequently reduces which reduces the torque.

6 CONCLUSIONS

The objective of this paper was to determine the effects magnetic wedges have on the torque

ripple. Along with previous papers, these results confirmed a definite reduction in the torque

ripple. It was also clear that the non-linear magnetic material provided to be more effective in

terms of reducing the torque ripple. From these results different conclusions can be drawn

depending on the RSM designer’s application. A RSM which is dependent on its torque but

needs to reduce the ripple torque would ideally need to employ Fexirite wedges which proved to

keep the average torque constant. A RSM which needs to operate on a more constant torque for

applications that require precision would possibly be employed with a Mild steel wedge. Finally

it can be concluded that the insertion of magnetic wedges seems essential and should be

considered in most RSM designs.

Although certain alterations were made on the materials of the flux barriers, the main objective

of this paper was to determine the effects magnetic wedges have on the torque ripple. Finally, it

can be concluded that a torque is only produced when the permeability of the flux barrier is less

than the rotor’s permeability.

18

7 REFERENCES

[1] A.N. Hanekom, “A torque ripple analysis on reluctance synchronous machines” master’s

thesis, Dept. of Electrical Engineering, Cape Peninsula University of Technology, Cape Town,

South Africa, September 2006

[2] A. Vagati, M. Pastorelli, G. Franceschini, and S. C. Petrache, “Design of Low-Torque-

Ripple Synchronous Reluctance Motors,” in IEEE Transactions on Inustry Applications, 1998,

pp. 758-764.

[3] T.R. Kuphaldt, “Reluctance motor,” 2003,

http://www.allaboutcircuits.com/vol_2/chpt_13/4.html

[4] E. Chiricozzi, G. Conti, F. Parasiliti, M. Villani, “Design solutions to optimize torque

ripple in synchronous reluctance motors” in Proceedings in International Conference on

Electrical Machines, Vigo, Spain, 1996, pp 148-153.

[5] E. Voss and M. Kamper, “On the use of magnetic wedges in synchronous reluctance

machines” in Southern African Universities Power Engineering Conference, University of

Stellenbosch, January 2004

[6] T. Ishikawa and G. R. Slemon, “A Method of Reducing Ripple Torque in Permanent

Magnet Motors without Skewing,” in IEEE Transactions on Magnetics, 1993, pp. 2028-2031.

[7] N. Bianchi, S. Bolognani, D. Bon and M. Dai Pré, "Rotor Flux-Barrier Desing for Torque

Ripple Reduction in Synchronous Reluctance and PM-Assisted Synhronous Motors," in IEEE

Transactions on Inustry Applications, 2009, pp. 921-928.

[8] J. W. Lee, H. S. Kim, B. I. Kwon and T. Kim, “New Rotor Shape Design for Minimum

Torque Ripple of SRM using FEM,” in IEEE Transactions on Magnetics, 2004, pp. 754-757.

[9] E. Voss, The Voss lectures on electrical machine design, 2nd

ed., Cape Peninsula

University of Technology, 2010

19

[10] Anon, “Relative Permeability,” July 2010;

http://en.wikipedia.org/wiki/Relative_permeability

[11] T. McLyman, Transformer and inductor design handbook, 2nd

ed., California Institute of

Technology, New York: Marcel Dekker, Inc., 1988

20

Appendix A: Geometry of RSM

aw = air-gap width (0.34mm)

ba = barrier angle (54.34°)

bh = barrier height (38.65mm)

bp = barrier pitch (11.9°)

ca = cut-out angle (51.26°)

ch = cut-out height (49.15mm)

cp = cut-out pitch (23.5°)

db = diagonal barrier length

(21.0mm)

dw = diagonal barrier width

(5.76mm)

hb = horizontal barrier lenght

(25.38mm)

hw = horizontal barrier width

(7.49mm)

rr = radius of rotor (63.15mm)

rs = radius of stator (101.6mm)

sh = slot height (19.913mm)

sp = slot pitch (10°)

sw = slot width (5.46°)

tw = tooth widht (4.54°)

wh = wedge height (1.22mm)

yh = yoke height (18.197mm)

21

Appendix B: Torque results for linear materials

Relative Permeability Tmax (Nm) Tmin (Nm) Tripple (%) Tavg (Nm)

0.1 57.21 35.83 46.04% 46.44

0.2 57.22 36.65 44.01% 46.75

0.3 57.07 37.82 41.01% 46.93

0.4 57.06 38.61 39.21% 47.04

0.5 56.84 39.35 37.11% 47.14

0.6 56.75 39.69 36.13% 47.21

0.7 56.61 40.07 35.00% 47.26

0.8 56.49 40.35 34.12% 47.28

0.9 56.33 40.60 33.24% 47.31

1 56.17 40.81 32.45% 47.33

2 54.91 42.03 27.25% 47.28

3 53.99 42.49 24.46% 47.02

4 53.08 42.84 21.88% 46.84

5 52.28 43.02 19.84% 46.65

6 51.58 43.13 18.17% 46.48

7 50.98 43.19 16.81% 46.31

8 50.45 43.17 15.78% 46.15

9 49.99 43.12 14.93% 46.00

10 49.58 43.07 14.19% 45.86

20 47.08 42.10 11.13% 44.76

30 46.34 41.37 11.29% 44.06

40 46.17 40.57 12.86% 43.55

50 46.09 39.97 14.19% 43.17

60 46.05 39.34 15.66% 42.88

70 46.05 38.72 17.18% 42.64

80 46.05 38.26 18.35% 42.45

90 46.07 37.93 19.24% 42.30

100 46.09 37.65 20.01% 42.17

1000 46.74 34.24 30.43% 41.07

10000 46.86 33.77 31.96% 40.95

100000 46.88 33.73 32.13% 40.93

1000000 46.88 33.72 32.14% 40.93

22

Appendix C: Torque results for non-linear materials

Wedge Material Tmax (Nm) Tmin (Nm) Tripple (%) Tavg (Nm)

Maximum Relative

Permeabilty

Unisil 27M4 48.84 41.49 16.69% 44.05 100

Unisil 30M2H 48.9 41.94 15.68% 44.37 400

Unisil Grain Orient 48.31 41.73 14.97% 43.95 800

Unisil 23M3 48.56 41.46 16.15% 43.96 1500

HCR Alloy 48.77 41.73 15.94% 44.14 2000

Cast Iron 52.25 43.49 18.97% 46.21 2200

Mildsteel 46.44 42.01 10.20% 43.41 2800

Unisil 27MOH 46.28 41.58 10.89% 43.16 3500

Rolled Steel 48.39 41.82 14.91% 44.08 3800

A36 Steel 48.35 41.86 14.71% 44.09 4000

M19FP 26GA 48.79 41.94 15.47% 44.30 4500

Newcor 32 48.76 41.54 16.37% 44.13 4600

Losil 1000 48.3 41.72 14.95% 44.02 5500

EN9 Steel 49.24 41.98 16.31% 44.47 6000

Grade 450 Steel 48.96 41.88 15.95% 44.34 6200

Alnico YCM-9B 52.63 43.36 19.92% 46.58 34000

Ferixite 53.77 42.94 22.97% 47.15 260000

Documents

Torque Ripple Reduction in Reluctance Synchronous Machines using Magnetic Wedges