Acoustic Noise and Vibration Reduction on Switched Reluctance Machines Through Hole Placement in Stator

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ACOUSTIC NOISE AND VIBRATION REDUCTION ON SWITCHED

RELUCTANCE MACHINES THROUGH HOLE PLACEMENT IN STATOR/

ROTOR LAMINATIONS

A Thesis

Presented to

The Graduate Faculty of The University of Akron

In Partial Fulfillment

of the Requirements for the Degree

Master of Science

Didem Tekgun

May, 2017 ACOUSTIC NOISE AND VIBRATION REDUCTION ON SWITCHED

RELUCTANCE MACHINES THROUGH HOLE PLACEMENT IN STATOR/

ROTOR LAMINATIONS

Didem Tekgun

Thesis

Approved: Accepted:

Adviser Interim Department Chair Dr. Yilmaz Sozer Dr. Joan Carletta

Committee Member Interim Dean of the College Dr. Malik Elbuluk Dr. Donald P. Visco Jr.

Committee Member Dean of the Graduate School Dr. Alexis De Abreu-Garcia Dr. Chand Midha

Date

ii ABSTRACT

Switched reluctance motors (SRMs) are used in numerous applications due to their simple and robust structure. In addition to being mechanically and thermally robust, features such as high torque density, efficiency, and reliability, coupled with their fault tolerant structure and low manufacturing cost make SRMs quite attractive. SRMs are double salient pole motors. The stator has simple concentrated excitation windings, and there is no winding or magnet on the rotor.

Although SRMs have many features and advantages, large torque ripple, vibration, and acoustic noise are the major disadvantages of these machines. The vibration and acoustic noise of SRMs are mainly generated by the radial forces. The radial forces cause deformation on the stator yoke, which results in vibrations and consequently, frame deformation. When these vibrations resonate with the motor body’s natural frequencies, the amplitude of the oscillations and the deformations are intensified. Hence, the acoustic noise increases significantly. The vibration and acoustic noise of

SRMs have been deeply investigated throughout the years, and various methods are reported based on modifications on the motor structure and motor control for reducing them. Since this thesis is focused on the acoustic noise reduction techniques from the design perspective, the acoustic noise and vibration mitigation techniques based on the motor structure modifications are investigated.

Existing methods are focused on the radial force reduction, motor natural frequency manipulation, and stator damping effect improvement. Although, improving one of these factors also improves the others, most previous studies focus on a single factor.

In this thesis, a new vibration and acoustic noise mitigation method is proposed. This method combines the radial force reduction and damping improvement on the stator. The radial force

iii is reduced by introducing rectangular windows on the rotor and the stator poles, which result in a reduction on the stator deformation. In addition, damping elements that are diamond shaped air gaps are inserted into the stator back iron. The number, size, the distance between the elements, and the distance from the stator outer surface to the first air gap are adjusted to achieve the minimum stator deformation and consequently, the minimum acoustic noise. Analyses are performed with 2D/3D electromagnetic and mechanical finite element (FEAs) and vibration analyses tools, and the acoustic noise is reduced successfully.

iv DEDICATED

To the greatest blessings of my life: my husband, Burak, for his endless love, unconditional support, and encouragement, and

my son, Selim Mete, who is the ultimate joy in our lives.

v ACKNOWLEDGEMENTS

I would like to express special thanks to my advisor, Dr. Yilmaz Sozer, for his support, help, and continuous encouragement throughout my studies.

I also would like to thank my thesis committee members, Drs. Malik Elbuluk and Alexis De

Abreu-Garcia for their valuable comments and suggestions to improve the quality of the thesis.

I must also thank my colleagues Yusuf Yasa and Mohamed Ali Al-Amin for their valuable technical support.

Finally and most importantly, I want to thank my dear husband Burak Tekgun, my parents, and all my colleagues for their support and encouragement that have tremendously helped my studies.

vi TABLE OF CONTENTS

Page

LIST OF TABLES ...... x

LIST OF FIGURES ...... xi

CHAPTER

I. INTRODUCTION ...... 1

II. LITERATURE REVIEW ...... 3

2.1. Basic Principles and Classification of SRMs ...... 5

2.2. Operation of SRM...... 7

2.3. Design Considerations to Reduce Acoustic Noise and Vibration in SRM ...... 13

2.3.1. Structural Stator Spacer ...... 13

2.3.2. Stator Yoke Design...... 14

2.3.3. Radial Force Damping ...... 15

2.3.4. Frame Design ...... 18

2.3.5. Pancake Shaped SRM...... 19

2.3.6. Parallel Path Windings ...... 19

2.3.7. Stator Pole Sealing ...... 20

2.3.8. Number of Stator and Rotor Pole Optimization ...... 21

2.3.9. Segmented Rotor SRM ...... 22

vii 2.3.10. Double Stator ...... 24

2.3.11. Skewing ...... 25

2.3.12. Cylindrical Rotor Design of SRM ...... 28

2.3.13. Stator and Rotor (Pole) Geometry ...... 29

2.3.13.1. Windowing ...... 29

2.3.13.2. Pole Shoe ...... 32

2.3.13.3. Pole Arc Optimization ...... 33

2.3.13.4. Pole Tip Optimization ...... 34

2.3.13.5. Tapering the Stator Poles ...... 35

2.3.13.6. Shifted Lamination Layer Method ...... 36

2.3.13.7. SR-Shark Machine...... 37

2.4. Summary ...... 38

III. PROPOSED WORK ...... 39

3.1. Electromagnetic Force Generation Mechanism ...... 39

3.2. Windows on the Stator and Rotor Poles ...... 45

3.3. Distributed Air Gaps on the Stator ...... 49

3.4. Summary ...... 52

IV. ANALYSIS AND RESULTS ...... 53

4.1. Analysis Procedure ...... 53

4.2. Modal Frequency Analysis ...... 54

4.3. Window on the Rotor Pole ...... 55

viii 4.4. Window on the Stator Pole ...... 57

4.5. Analysis of the Distributed Air Gaps ...... 60

4.6. Analysis of the Distributed Air Gaps with Stator and Rotor Windows ...... 63

4.7. Summary ...... 65

V. CONCLUSION AND FUTURE WORK ...... 66

5.1. Conclusion ...... 66

5.2. Future Work ...... 68

REFERENCES ...... 69

ix LIST OF TABLES

Table Page

4.1. Comparison of the distributed air gap locations...... 61

4.2. Comparison of the conventional SRM, windowed SRM, and SRMs that have various types of distributed air gap placed on the stator back iron...... 62

4.3. Comparison of conventional, windowed, and distributed air gap SRMs...... 65

x LIST OF FIGURES

Figure Page

2.1. Diagram of 6/4 and 8/6 pole of SRM [23]...... 5

2.2. The classification of the SRM...... 6

2.3. Short flux path SRM [23]...... 7

2.4. The operation of SRM when (a) phase c and (b) phase a aligned with the rotor pole...... 8

2.5. Single-phase equivalent circuit of SRM...... 9

2.6. Inductance vs. rotor position [37]...... 11

2.7. Existing design of SRM to reduce the vibration the and acoustic noise...... 13

2.8. Principal idea with curved structural stator spacer [31]...... 14

2.9. Seven different stator yoke structures [34]...... 15

2.10. Simple E-core mechanism [35]...... 16

2.11. Three different laminated test models [34]...... 16

2.12. Current and vibration for model A (conventional), model B (two sets of laminations), model C (two sets of laminations and damping material) [35]...... 17

2.13. Illustration of an SRM stator with interlaminated damping material and ...... 17

2.14. Active vibration damping system [35]...... 18

2.15. Four different frame shapes for vibration analysis [38]...... 18

2.16. The proposed switched reluctance motor, whole motor and rotor [39]...... 19

2.17. Cross-section of the analyzed motor and distribution of coil groups (left), ...... 20

2.18. Coil connections of different winding methods [40]...... 20

2.19. The sealing structure used in the stator: 1-stator poles; 2-stator core; 3-the gap; 4- insulation board for sealing winding; 5-evaporative cooling medium [41]...... 21

xi 2.20. Construction of segment type SRM (left), flux distributions (8◦) (right) [45]...... 22

2.21. Construction of dual rotor SRM (left), magnetic flux lines (right) [47]...... 23

2.22. Geometry of CSSSRM (left), aligned flux plot of CSSSRM (right) [49]...... 23

2.23. Geometry of 12/8 pole axial flux segmented rotor SRM (left), ...... 24

2.24. Cross section of a four-phase DSSRM [50]...... 24

2.25. Cross section of (left) conventional SRM and (right) DSSRM [52]...... 25

2.26. Skewed slot structure of rotor with 3-D (left) and 2-D (right) [53]...... 26

2.27. Four SRM structures. (a) Conventional SRM. (b) SR-SRM...... 27

2.28. Prototypes of the stators and rotors. (a) Normal stator. (b) Skewed stator (22.5°). (c) Normal rotor. (d) Skewed rotor (22.5°) [55]...... 28

2.29. Conventional rotor (left) and the proposed cylindrical rotor (right) [56]...... 29

2.30. Classification of stator and rotor pole shaping methods...... 29

2.31. (a) Type-A, (b) Type-B, and (c) Type-C windows placed in a rotor pole of 6/4 SRM [57]. 30

2.32. (a) Radial force, (b) torque profile and (c) performance index NF comparison of ...... 30

2.33. (a) Type-D, (b) E, and (c) F windows placed in the rotor pole [57]...... 31

2.34. (a) Radial force, (b) torque profile and (c) performance index NF comparison of Types D E, and F windows [57]...... 31

2.35. Rectangular windows placed in the rotor poles and flux paths [60]...... 31

2.36. V-shaped window in rotor pole [61]...... 32

2.37. (a) Simple stator pole, (b) modified stator pole [65]...... 32

2.38. Nonuniform air gap profile (left), Pole shoe attached to the lateral face of the rotor pole (right) [66]...... 33

2.39. (a) Section of the motor without pole shoe and notch, (b) Section of the motor with pole shoe, (c) Section of the motor with pole shoe and notch [68]...... 33

2.40. Geometry parameters of SRM [69]...... 34

2.41. The convex sine stator pole design [70]...... 34

2.42. (a) Polygon shape on the stator yoke, (b) trapezoidal shape on the stator pole, ...... 35

xii 2.43. Tapering parameters effecting the natural frequencies [72]...... 36

2.44. Tapered stator poles (a) with modified stator yoke and (b) with rounding and adding rotor pole shoes [74]...... 36

2.45. Shifted rotor laminations [75]...... 37

2.46. (a) SR-Shark machine pole and (b) regular SRM pole [76]...... 37

3.1. (a) Typical switched reluctance machine and (b) its integration surface...... 42

3.2. (a) Idealized phase current, (b) radial force, and (c) the deformation of SRM...... 43

3.3. Air pressure variation around the motor body...... 44

3.4. Amplitude and phase plots of the acoustic sound pressure levels...... 45

3.5. Windows on both stator and rotor poles...... 46

3.6. Radial force profiles for three different window designs [57]...... 46

3.7. Torque profiles for three different window designs [57]...... 47

3.8. Performance index for three different window designs [57]...... 47

3.9. (a) Radial torque, (b) torque profiles, and (c) the performance index of the SRM versus the window position [57]...... 48

3.10. Windows on both stator and rotor poles...... 49

3.11. The illustration of the effect of the distributed air gaps placed on the stator pole...... 50

3.12. Stretched rigid body...... 50

3.13. The effect of the distributed air gaps on the stator back iron...... 51

4.1. A general schematic of the acoustic noise and vibration analysis...... 54

4.2. Modal analysis of an SRM...... 55

4.3. Natural frequencies of the 24/16 SRM...... 55

4.4. Windows on the rotor poles...... 56

4.5. Window size and position on the rotor poles...... 56

4.6. Radial force variation with the rotor window size and position variation...... 57

4.7. Torque variation with the rotor window size and position variation...... 57

4.8. Windows on the stator poles...... 58

xiii 4.9. Windows size and position on the stator poles...... 58

4.10. Windows on both the stator and rotor poles...... 58

4.11. Percent peak to peak radial force reduction versus percent torque reduction...... 59

4.12. Total deformation of the conventional and windowed motors...... 60

4.13. Total acceleration of the conventional and windowed motors...... 60

4.14. Windows on both the stator and rotor poles and the distributed air gaps on the stator back iron...... 63

4.15. Distributed air gaps on the stator back iron...... 64

4.16. Total deformation and acceleration of the optimized SRM...... 65

xiv CHAPTER I

INTRODUCTION

Due to SRM’s robust construction, high operation reliability, high efficiency, high torque to inertia ratio, and low manufacturing costs, they have been attracting substantial attention over the last two decades [1]. Their simple brushless structure and the absence of commutators can be considered as the principal advantage that leads to their stable operation. Since SRMs have no winding or permanent magnet on the rotor, the rotor losses are low, and as such they require no rotor cooling[2]. The SRM simple rotor structure also maximizes the torque to inertia ratio. Another important feature of the SRM is that its stator phases are electrically independent, thereby making

SRMs more tolerant to faults than any other drive system. The stator phases are also magnetically independent from each other, which provides an advantage of controller flexibility to the drive system [3], [4]. Moreover, the absence of rotor windings or magnets makes it possible to achieve very high speeds. The torque-speed characteristics of the motor can be customized based on the application requirements more easily during the design stage due to their inherent flux weakening capabilities [5]. These attractive features make SRMs potential candidates for applications in industrial and commercial markets. However, dealing with the large torque ripple, high vibration, and acoustic noise are the biggest problematic issues of SRMs. The main causes of vibration and acoustic noise are the radial force and the torque pulsation due to flux switching between the phases.

Abrupt variations in the radial forces deflect the stator back iron, which cause a pressure change in the surrounding air giving rise to acoustic noise.

1 Numerous methods for the reduction of vibration and acoustic noise are proposed in the literature. These methods can be grouped as design and control methods. This thesis mainly focuses on the vibration and acoustic noise reduction of SRMs from the machine design perspective.

The radial force is reduced by introducing rectangular shaped windows on the stator and rotor.

This reduces the total deformation on the stator back iron and the motor frame. The total deformation is further reduced by introducing diamond shaped holes on the stator. These distributed air gaps act like little springs on the stator, whose spring coefficients change with the location and size of the holes. Consequently, the natural frequencies of the motor body change, allowing the acoustic noise to be reduced by pushing the vibrations out from the audible spectrum. The sizes and the positions of the distributed air gaps are adjusted such that the motor average torque is not affected while the stator deformation is minimized. The electromagnetic, structural, and harmonic analyses are performed on ANSYS Maxwell and ANSYS Mechanical FEA software packages.

A comprehensive review of the SRM noise reduction methods from the design consideration point of view is provided in Chapter II. Additionally, some comparison studies are investigated to be able to choose the proper design to achieve the minimum vibration and acoustic noise. In Chapter

III, the proposed method for reduction of the vibration and acoustic noise of SRMs is explained in detail. Chapter IV provides the FEA results obtained from 2D/3D electromagnetic and mechanical analyses. Conclusion and future work are presented in Chapter V.

CHAPTER II

LITERATURE REVIEW

Over the past two decades, SRMs have been intensely developed. The origin of SRMs can be tracked back to 1838, but the SRM concept was not fully implemented due to the lack of the necessary power electronic devices and high power switching techniques [1]–[4], [6], [7]. Over the past decades, the progress made in motor design and high power switching devices made SRMs more attractive to researchers; therefore, SRMs became popular in both academia and industry.

Robust and straightforward construction is the most attractive feature of SRMs, which contain no rotor windings, permanent magnets, brushes, or commutators. The rotor is basically made of a piece of steel with laminations which are shaped to form salient poles without any windings.

Because of the absence of brushes, SRMs provide a long life. Due to the lack of a permanent magnet and windings, SRMs have a low manufacturing cost, high power to weight ratio, high efficiency over a wide speed range, high speed and acceleration capabilities, and high fault tolerance [8]. The advantages that are mentioned above make SRMs attractive and favorable for researchers and various industrial applications.

SRMs can address unique and varied requirements such as speed-torque relationship and high fault tolerance, which make them an ideal candidate for utility vehicles, golf carts, electric cars, buses, and trains [5], [9], [10]–[13], [14]. Furthermore, SRMs are well suited to the aerospace field due to their high-speed capability and robustness [15].

For a smooth movement, the SRM`s phases need to be excited at certain rotor angles.

Conventionally, the position of the rotor is measured using mechanical sensors mounted on the rotor shaft. Aside from increasing the cost and making the drive system more complex, most of the

3 times the mechanical position sensors cause reliability issues. Although sensorless position estimation methods exist in the literature [16], these methods make the control even more complex as they require excessive calculations.

Another disadvantage of an SRM is the high level of torque ripple at low speeds, especially when it is operated in single-pulse voltage control mode that contributes to speed ripple and vibration in the stator. Compared with the sinusoidal AC machines, the torque ripple is higher in

SRMs [17]. The torque ripple is mainly due to the nonlinear behavior of the inductance based on the position of the rotor and the excitation current. The existence of the torque ripple causes accuracy problems, especially on the servo systems [18]. There are various known torque ripple reduction methods in the literature. Torque ripple reduction is achieved with different approaches such as improving the motor design, improving the control [19]–[21] strategy, and selecting a higher number of commutation phases [17]. A better design may include optimizing the rotor and stator pole arcs, inserting pole shoes into the rotor poles, etc. Minimizing the torque ripple through the control may cause average torque reduction [18]. Selecting a higher number of phases increases the number of required power electronic components, which raises the cost of the drive system

[22].

The main reason for vibration and acoustic noise is the radial force due to the switching excitations [23]. During the commutation, the active phase current goes to zero, and the following phase current goes to its maximum value, which leads to one of the stator poles to be pulled and the other to be released right after the maximum radial force is applied. This sudden release of the stator pole causes oscillating deformations on the stator back iron and the motor frame, which generate vibration and acoustic noise [24].

In [25]–[27], researchers addressed the point that the acoustic noise of electrical machines could be electrical-magnetic, mechanic, or aerodynamic. The gearbox, bearing, and mechanical misalignment-eccentricity are the main reasons for the mechanical noise. Aerodynamic noise is

4 usually observed at high speeds. Electrical-magnetic noise results from the vibrations caused by the radial magnetic forces. Here, the SRM noise mainly results from magnetic sources [28]–[30].

Due to the limitations of the SRM listed above, different techniques are applied to mitigate these effects so as to increase the competition of SRMs in the variable speed drives market.

Considerable improvements can be achieved with better motor and controller design, but the best results can be obtained by considering them as a whole system.

The rest of this chapter is organized as follows: Section 2.1 introduces the basics of SRMs.

Section 2.2 discusses the operation of SRMs. Section 2.3 covers the design considerations to minimize the acoustic noise and the vibration in SRMs.

2.1. Basic Principles and Classification of SRMs

An SRM is a doubly-salient singly excited reluctance motor that has salient poles on both the rotor and stator sides. The rotor part of the SRM does not include any windings, magnet, or cage.

However, it is implemented with a stack of salient pole laminations. The rotating motion is generated due to the difference of the variable reluctance in the air gap between the rotor and the stator [23]. A typical SRM structure is presented in Figure 2.1. As seen from the figure, both the stator and rotor have salient poles, which makes it a doubly salient machine.

6/4 Pole 8/6 Pole

Figure 2.1. Diagram of 6/4 and 8/6 pole SRM [23].

Switched Reluctance Motors (SRMs)

Rotary SRMs Linear SRMs

Radial Field Axial Field

Short flux path Single-stack Multi-stack machine: Adjacent pole Basic structure: Doubly windings are in series salient with concentric to form a phase windings winding.

Figure 2.2. SRM classification.

SRMs can be categorized as rotary and linear as shown in Figure 2.2. Rotary type SRMs are also classified by the nature of the magnetic field path. If the magnetic field path is perpendicular to the shaft, it is classified as a radial field; if the flux path is in the axial direction, the machine is clasified as an axial field rotary-based SRM.

Radial field SRMs, which are most widely used, can be classified into shorter and longer flux paths based on the placement of the phase coil. In long flux path SRMs, the phase coil is placed at diametrically opposite slots, as shown in Figure 2.1. In short flux path SRMs, as illustrated in Figure

2.3, the phase coil is placed in slots adjacent to each other. Short flux path SRMs introduce lower core losses because the flux reversals do not exist in the stator back iron in addition to short flux paths. However, they have slightly higher mutual inductance and possible higher unbalanced magnetic pull on the rotor.

Figure 2.3. Short flux path SRM [23].

The axial configuration of an SRM is suitable for a ceiling fan or propulsion applications where the total length may be constrained. The weakness of this configuration is the stator laminations that are required to be folded one on top of the other, unlike the radial field configuration where the laminations are simply stacked on each other.

Single-phase SRMs are also used in many applications due to their low-cost manufacture and resemblance to single-phase induction and universal machines. Single-phase SRMs are particularly utilized in high-speed applications. In single-phase SRMs, in case the stator and rotor poles are aligned, the current is turned off, and the rotor continues to rotate due to the stored kinetic energy.

The stator winding again is reenergized if the poles become unaligned and produce an electromagnetic torque. An issue arises in single-phase SRMs, an operation when the stator and rotor poles are aligned at stand still, or the rotor is positioned at starting when the produced torque is lower than the load torque. This issue can be overcome by integrating a permanent magnet into the stator to avoid rotor alignment and, thus, achieve maximum electromagnetic torque.

Single-phase SRMs run with a maximum duty cycle of 0.5, and thus, they introduce torque discontinuity, which leads to high torque ripple and noise. Applications insensitive to this shortcoming, such as hand tools and home appliances, are ideal for this machine.

2.2. Operation of SRMs

Exciting the phases in the diametrically opposite stator poles causes the rotor poles to align as the rotating part prefers to come to the minimum reluctance position at the instance of excitation.

However, in a 6-4 structure, if two rotor poles are aligned with two stator poles, the other two rotor poles are out of alignment with respect to a different set of stator poles. Then, this set of stator poles needs to be excited to align the consequent rotor poles. Figure 2.4.a considers that the rotor poles r1 and r1′ and stator poles c and c′ are aligned. When a current is applied to phase a, with the current direction shown in Figure 2.4.a, a flux is established through stator poles a and a′ and rotor poles r2 and r2′, which tends to pull the rotor poles r2 and r2′ toward the stator poles a and a′, respectively.

When they are aligned, the stator current of phase a is turned off, and the corresponding situation is shown in Figure 2.4.b. Now the stator winding b is excited, pulling r1 and r1 ′ toward b and b′, respectively, in a clockwise direction. Likewise, energizing phase c winding results in the alignment of r2 and r2′ with c and c′, respectively. Accordingly, by switching the stator currents in such a sequence, the rotor is rotated. Similarly, the switching of current in the sequence acb will result in the reversal of the rotor rotation. Torque is generated by switching currents in the stator winding depending on the reluctance variation profile of the rotor, thus resulting in a variable speed motor referred to as a switched reluctance motor (SRM).

(a) (b)

Figure 2.4. The operation of SRM when (a) phase c and (b) phase a aligned with the rotor pole.

Figure 2.5 shows the one phase equivalent circuit of an SRM. A simple version of the equivalent circuit can be derived by neglecting the mutual inductances between the phases. The

8 phase voltage is expressed as the addition of the resistive voltage drop and the rate of change of flux linkage as follows:

di(,) VRi (1) s dt where Rs is the phase resistance and λ is the flux linkage of one phase, expressed as:

 L( i i, ) (2) where L is the phase inductance, which depends on the position of the rotor and phase current.

Hence, the phase voltage can be re-written as:

d{}LididdLi(, )i(, )  VR iR i Lii(, )  ssdt dtdtd   did L(, )i  Ri Lii(,) s dtd  m

In this equation, the resistive voltage drop, inductive voltage drop, and induced emf are represented as three different terms. The last term, induced emf (e), is expressed as:

dL(,) i (4) eKii d mbm

L Rs

+ V e -

Figure 2.5. Single-phase equivalent circuit of an SRM.

The essential electromechanical energy conversion principle can be used for explaining the torque production of an SRM. The mechanical energy in rotating electric machines can be expressed in terms of the electromagnetic torque and the rotor position variation as follows:

WTme   (5)

9 where Te is the electromagnetic torque and Δθ is the incremental rotor angle. Therefore, the electromagnetic torque can be calculated as:

W (6) T  m e 

The change of the mechanical energy is equal to the change in the coenergy when the magneto motive force is constant, and represented as:

` WW  mf (7)

For the linear operating region, the coenergy can be expressed as:

1 (8) W L`2 i i ( , ) f 2 where Li( , ) is the stator inductance at a certain position, and i is the stator phase current. Hence, the electromagnetic torque is as follows:

W WW``Lii(,) 2 (9) T m ff . e  2

Equation (9) has the following implications:

1. The torque is proportional to the square of the phase current and hence, a unipolar current

can be used to produce unidirectional torque.

2. The torque is generated during the rising region of the inductance profile.

3. The stator inductance of a stator winding is a function of both the rotor position and stator

current, thus making it quite nonlinear.

4. A generation action is possible by exciting the stator phase with a unipolar current during

the negative slope of the inductance profile. As a result, this machine is suitable for four-

quadrant operation with a converter.

5. Because of its dependence on a power converter for its operation, this motor is an inherently

variable-speed motor drive system.

The torque characteristics of SRMs are dependent on the relationship between the stator flux linkages and the rotor position as a function of the stator current. A typical phase inductance vs. rotor position is shown in Figure 2.6 for a fixed phase current. The inductance corresponds to that of a stator phase coil of the motor neglecting the fringing effect and saturation. The stator and rotor arcs and the number of rotor poles significantly affect the inductance profile.

(a) (b)

Figure 2.6. Inductance vs. rotor position [37].

From Figure 2.6.a and b, the various angles are derived as:

12 (10) 1 [()] sr 2 Pr

21s (11)

32 ()rs (12)

43  s (13)

2 (14) 541 Pr where βs and βr are the pole arcs of the stator and rotor, respectively, usually βr > βs, and Pr is the number of rotor poles.

There are four distinct inductance regions:

1. 0 ~ θ1 and θ4 ~ θ5: The stator and rotor poles are not overlapping, and the inductance is minimum and almost a constant. Therefore, these regions do not contribute to the torque production.

2. θ1~ θ2: The stator and rotor poles are overlapping; hence, the flux passes through the stator and rotor laminations, which leads the inductance to increase and gives it a positive slope. A current pushed into the winding produces a positive torque during this period. The end of this region comes when the overlapping is complete.

3. θ2~ θ3: In this region, the movement of the rotor pole is not different than it was when a complete overlap occured on the stator pole. This provides the advantage of keeping the inductance maximum and constant, and torque generation is zero, which in turn provides enough time for the stator current to reach zero value when it is commutated. Thus, negative torque generation is avoided in the negative slope region of the inductance.

4. θ3~ θ4: In this region, the rotor pole is moving away from the overlapping the stator pole.

The inductance decreases, which makes a negative slope on the inductance that results in negative torque.

The inductance profile given in Figure 2.6 is an ideal inductance profile. It is not possible to achieve such an inductance profile in an actual motor due to saturation. The saturation affects the linear inductance increase at the saturation point; hence, it reduces the torque constant.

The motoring torque is produced in pulsed form when the rectangular currents are applied to the phases. These pulsating torques combined with the commutation leads to large torque ripples that can cause other problems such as vibration, metal fatigue on the shaft and the stator body, speed oscillations, acoustic noise, etc. Torque ripple reduction can be done by designing the machine such that the inductance profiles of two consequent phases overlap, where the ending of one coincides with the beginning of the other. This can be achieved through the correct choice of the number of stator and rotor poles and their pole arcs. Current profiling could also be used as an alternate technique to reduce the torque ripple.

2.3. Design Considerations to Reduce Acoustic Noise and Vibration in SRMs

Over the last two decades, many studies have reported evaluating the causes of acoustic noise, vibration, and the high torque ripple of SRMs. Researchers have spent much effort to find solutions to these problems by developing the various SRM design and control methods. Several papers address the concept of these designs and control aspects.

Noise and vibration reduction studies from the design perspective are classified in Figure 2.7.

Design Aspects of SRM to Reduce the Acoustic Noise and Vibration

Structural Stator Yoke Pancake Parallel Path Damping Frame Design Stator Spacer Design Shape Design Windings

Number of Segmented Stator and Sealing Stator and Double Stator Skewing Cylindrical SRM Rotor (Pole) Rotor Pole Design of Optimization Rotor Optimization

Figure 2.7. Existing design of SRM to reduce vibration and acoustic noise.

2.3.1. Structural Stator Spacer

In 2001, an idea to reduce the acoustic noise and vibration of electrical machines by introducing improved slot wedges referred to as structural stator spacers, was presented in [31], [32]. The structural stator spacer idea focuses on the classic slot wedges, which are used to fix the stator windings in the motor and reduce windage losses. These wedges are typically made of plastic or wood. The authors aimed to fix the windings problems and increase the stiffness of the stator structure using a solid dielectric and nonmagnetic material. The modified wedges are referred to as structural stator spacers. In Figure 2.8 an example of curved arc stator spacers is shown for a 6/4

SRM.

Figure 2.8. Principal idea with curved structural stator spacer [31].

Improved slot wedges or structural stator spacers can be used to keep the windings in place and reduce windage losses. Also, they can also stiffen the stator to lessen the amount of noise produced by the machine. These structural stator spacers are constructed from a ceramic or laminated nonmagnetic metal, are positioned and installed between the teeth of the electric machine stator in a manner which creates a compressive force in a ring comprised of the spacers and the inner ends of the stator teeth. Such spacers can be considered as a part of the total stator structure.

To verify the effectiveness of the spacers, the authors built two SR motors with and without spacers. Both motors are tested statically and dynamically under no load condition and acoustic noise reductions by the spacers are measured to be 14.1 and 9.2 dBA, respectively. Analysis showed that the structural spacers would work on classic machines like the 6/4, 8/6, and 12/8 but not so effectively for two-phase motors. Finally, this study needs more practical experience to explore the idea and verify the noise/vibrational model on machines with a higher number of poles.

2.3.2. Stator Yoke Design

Vibrations and acoustic noise in SRMs result from deformations on the stator caused by the radial forces. Therefore, designing a proper stator shape that minimizes deformations and radial force would decrease the produced vibrations and acoustic noise. Hence, the stator yoke shape plays a key role in its stiffness [33], [34].

In [34], seven different stator designs with their inner and outer shapes have been studied

(Figure 2.9). Using transient and structural FEAs, the ‘c’ type stator shape is found to be the best shape as it has the least radial force and vibration.

Figure 2.9. Seven different stator yoke structures [34].

2.3.3. Radial Force Damping

The sudden release of the SRM poles after attracting them creates an oscillation called ringing.

These oscillations cause the motor to vibrate and cause the acoustic noise to increase. The oscillation frequencies that are in the audible frequency range contribute the most to the acoustic noise. The duration of these oscillations is dependent on the damping of the motor body. Usually, the sinusoidal fed AC and DC electric machines have rich harmonic content that is spread through a broad frequency range, which improves the damping. However, SRMs have non-sinusoidal excitations that make the harmonic content of the forces fortify at certain frequencies. Studies can be found in the literature to spread the SRM’s natural frequencies through a wider spectrum and increase the damping. Inserting damping materials between the stator laminations is one of the ideas that improves the damping reported in [35]. The authors built simple magnetic structures that have a similar noise production mechanism as that of an SRM (Figure 2.10).

Figure 2.10. Simple E-core mechanism [35].

This way, the system is mathematically modeled, and the natural frequencies (modes) of the structures are determined with the help of FEA. Three different samples are built; the first one is the conventional magnetic structure without damping material, the second one has different size beams stacked together, and the third one has again different size beams stacked with damping materials between them as shown in Figure 2.11. The applied current and the vibration of the structures are given inFigure 2.11 Figure 2.12. It can be clearly seen from the figures that the damping of the structure is improved significantly with the help of the damping material. One disadvantage of this method is that the stack length is almost doubled with the damping material inserted between the laminations as shown in Figure 2.13.

Figure 2.11. Three different laminated test models [34].

Figure 2.12. Current and vibration for Model A (conventional), Model B (two sets of

laminations), Model C (two sets of laminations and damping material) [35].

Figure 2.13. Illustration of an SRM stator with interlaminated damping material and

different stiffness in the laminations [35].

Active damping is also considered for better damping performance [36], [37]. Piezoelectric actuators are assigned to generate the vibration in the opposite direction of the stator back iron based on the feedback information taken from an accelerometer as presented in Figure 2.14. The idea is first put forward in [36], and a coupling model is introduced which is the combination of the magneto-elastic model that includes magneto-striction strains, the piezoelectric model, the

FEM, and the control of the piezoelectric actuator. Later an optimization for the placement of the piezoelectric actuator is carried out to achieve better damping in [37].

Figure 2.14. Active vibration damping system [35].

2.3.4. Frame Design

The radial force is directly related to the stator and frame shape of the motor. Similar with the stator shape of SRMs, the frame structure has also an effect on radial force and deformation.

Therefore, design of the motor frame can also be considered to suppress the vibration and acoustic noise of SRMs. In [38], vibration and acoustic noise have been investigated by changing frame shapes with different structures and materials. In this study, the vibrations of electric motors are mainly based on two factors, radial force excitation and structure borne transfer function. From the four frame shapes, given in Figure 2.15, that were investigated it was concluded that frame thickness, using radial ribbed frame and smooth steel frame could increase stiffness of the frame.

Among these shapes the most effective frame shape for reducing the vibrations is selected as smooth steel.

Figure 2.15. Four different frame shapes for vibration analysis [38].

2.3.5. Pancake Shaped SRM

Axial flux SRMs are considered for reducing the radial force and therefore the acoustic noise.

A particular type of axial flux SRM, called pancake shape SRM, is reported in [39]. In this work, a 5 phase 15/12 axial flux SRM is proposed. This machine, as shown in Figure 2.16, has 15 c-cores on the stator that have individually wound coils. The rotor is made out of a material that has low relative permeability, and there are 12 pieces placed on the rotor as rotor poles which have high permeability. The torque is produced by exciting two coils when the rotor poles are aligned with the c-cores as is the case in regular SRMs.

Figure 2.16. The proposed switched reluctance motor, whole motor and rotor [39].

The reluctance force developed at the rotor pole has only the tangential component. Hence, the vibration and the acoustic noise is minimized.

2.3.6. Parallel Path Windings

The air gap of the SR machines is relatively smaller than the air gaps of the permanent magnet

(PM) machines and induction machines, which makes SRMs more sensitive to the eccentricity. A method for reducing the acoustic noise caused from the eccentricity is reported in [40]. In this work, unbalanced magnetic forces in the rotor are compensated by introducing parallel paths in the windings. A 12/8 SRM with some eccentricity is analyzed through the finite element analysis

(FEA). The winding arrangement and the effect of the eccentricity on the flux are observed and presented in Figure 2.17.

Figure 2.17. Cross-section of the analyzed motor and distribution of coil groups (left),

unbalanced flux density and flux contours (right) [40].

Typically, the coils that belong to a certain phase are connected in series. In this work, they are connected in various series/parallel configurations to balance the currents, and consequently, balance the forces. The winding configurations given in Figure 2.18 are simulated separately to find the optimal configuration. The authors verified that the method effectively reduces the vibration caused by the unbalanced magnetic forces.

Figure 2.18. Coil connections of different winding methods [40].

2.3.7. Stator Pole Sealing

The damping feature of liquids is also used for reducing the stator vibrations. In [41], stator slots are filled with an evaporative cooling medium and sealed without disturbing the air gap of the

SRM, as presented in Figure 2.19. The evaporative medium helps both cooling the motor and

20 reducing the vibrations. The given motor`s vibration and radial force are analyzed through FEA, and it is proved that the acoustic noise is reduced significantly.

Figure 2.19. The sealing structure used in the stator: 1-stator poles; 2-stator core; 3-the gap;

4-insulation board for sealing winding; 5-evaporative cooling medium [41].

2.3.8. Number of Stator and Rotor Pole Optimization

In the literature, some researchers focused on the selection of the proper stator and rotor pole number to achieve the minimum vibration. The researchers pushed forward the idea that selecting a high number of stator and rotor poles results in lower vibration. In [42], the authors investigated the proper number of stator and rotor poles, and they compared the 12/8 and 6/4 SRMs. Two- dimensional (2D) transient magnetic FEA was performed in both the time and frequency domains to compute the radial force, which is the main source of vibration. Comparing the radial force of the 6/4 SRM and the 12/8 SRM it is found that the radial force of the 6/4 SRM is more than two times the 12/8 SRM’s radial force for the same output power. Therefore, it can be concluded from the analysis that the maximum total deformation could be reduced to 1/26 if the motor is designed with a 12/8 structure instead of a 6/4 as the vibration and noise are dramatically reduced for a 12/8

SRM.

Another study in [43] recommends designing the SRM with a higher rotor pole number than the stator pole number. Several combinations of the stator and rotor poles have been proposed. The

21 simulation and experimental results for the prototype 6/10 configuration have been presented and compared to a conventional 6/4 design for verification. It has been observed that a 6/10 machine produces higher torque per unit volume and lower torque ripple compared to a conventional 6/4

SRM with a similar number of phases and volume constraints. Results have shown a significant improvement in increased performance and decreased acoustic noise.

Similar to [41] and [42], estimation and reduction of the stator displacement caused by the radial force is investigated in [44]. In the latter, the authors compared 18/12 poles and 24/16 poles

SRMs. They found that by increasing the number of stator and rotor poles from 18/12 to 24/16, the displacement decreased 21% at the tip of the stator tooth and yoke.

2.3.9. Segmented Rotor SRM

Rotor segmentation is another method of vibration and acoustic noise reduction in SRMs. The effect of a segmented rotor is investigated in various studies [45], [46]. In [45], the segmented rotor is embedded into the aluminum rotor block to increase the structural strength and simplify the manufacturing process. The proposed motor shown in Figure 2.20 is compared with a conventional variable reluctance SRM (VRSRM) based on the torque density, vibration, and the acoustic noise, and proved that the proposed motor is superior to the conventional one in all the mentioned aspects.

Figure 2.20. Construction of segment type SRM (left), flux distributions (8◦) (right) [45].

One disadvantage of this motor is the high copper loss due to the full pitch windings. To decrease the copper loss, the toroidal coil windings in the stator and dual rotor structure given in

Figure 2.21 are proposed in [47].

Figure 2.21. Construction of dual rotor SRM (left), magnetic flux lines (right) [47].

Similar approximations for higher torque density electric vehicle applications can be found in the literature [48], [49]. In [48], the average torque has been improved almost 100% of that for the same frame size conventional SRM by using a full pitched winding structure on with specially designed circular slots segmented rotor SRM(CSSSRM) (Figure 2.212). Circular slots confine the flux to circular paths, resulting in a reduction of actual iron weight. Segmented rotor structure is also adopted to an axial flux SRM (Figure 2.23) [49]. The vibration is reduced while improving the torque density.

Figure 2.22. Geometry of CSSSRM (left), aligned flux plot of CSSSRM (right) [49].

Figure 2.23. Geometry of 12/8 pole axial flux segmented rotor SRM (left),

Flux pattern (a) unaligned position (b) aligned position [49].

2.3.10. Double Stator

Double-stator SRMs (DSSRMs) can be considered as another solution to vibration and acoustic noise problems by incorporating an improved magnetic configuration [50]–[52]. The idea is based on the optimization of the motional forces that requires sophisticated electromechanical energy conversion process. A close examination of force densities of the SRMs shows that most of the radial component of the produced force does not contribute to the rotation. A larger rotational force can be generated by directing some of the normal forces in the direction of rotation. In [50], the double stator design is investigated regarding fundamentals and magnetic force analysis as shown in Figure 2.24.

Figure 2.24. Cross section of a four-phase DSSRM [50].

Multi-Physics analysis of DSSRMs has been introduced in [51], which includes the electromagnetic analysis, structural analysis, and acoustic analysis. In [52], a comparative mechanical vibration study between a DSSRM and a conventional SRM has been proposed (Figure

2.25)

Based on the analysis results given in [50]–[52], it has been proved that the DSSRM is superior to the conventional SRM regarding high power density and low vibration due to decreased radial forces.

Figure 2.25. Cross section of (left) conventional SRM and (right) DSSRM [52].

2.3.11. Skewing

The majority of the research in the literature shows that the main source of acoustic noise and vibration is the rapid change of radial magnetic force along the air gap between the stator and rotor poles. The radial force is aggravated around the salient poles on the stator. Therefore, a skewing stator or rotor can lessen the rapidly changing radial force by distributing the radial force around the skewed surface; hence, the peak value of the radial force can be decreased [53]–[55].

In [53] the authors present a new rotor design with a skewed slot structure (Figure 2.26). In this work, electromechanical and structural FEAs and Matlab are used to optimize the rotor skew angle.

It is found that exceeding a certain level of skewing angle intensifies the torque ripple, which results in a higher vibration.

Figure 2.26. Skewed slot structure of rotor with 3-D (left) and 2-D (right) [53].

The skewing idea is applied to both stator and rotor for acoustic noise and vibration reduction of SRM in [54]. The motor has the same skew angle for both the stator and rotor laminations. In this work, three different skew angles (0◦, 30◦, 64◦) have been analyzed on the prototype motors, and it is validated that the proposed designs are effective in mitigating acoustic noise and vibration.

Another study that investigates skewing the stator and/or rotor on the vibration reduction of three-phase SR motor has been reported in [55]. In this work, including a conventional SRM, four different three-phase 12/8-pole SRMs as skewed rotor-SRM (SR-SRM), skewed stator-SRM (SS-

SRM), and skewed stator and rotor-SRM (SSR-SRM) are introduced and designed, to investigate the effect of skewing on the radial vibration force (Figure 2.27). The radial forces distributed on the stator yoke under different skewing angles for the skewed motors are compared using 3-D FEM models. The radial force in the conventional SRM, SR-SRM, SS-SRM, and SSR-SRM with different skewing angles are compared. The motor`s skewing angles are selected as 7.5°, 11.25°,

15°, and 22.5°, respectively. It has been observed that the force is reduced gradually when the skewed angle increases from 0° to 22.5°. Experimental results also showed that the radial force distributed on the stator yoke is smaller at the 22.5° skew angle than at other angles, which can reduce the stator vibration and therefore the deformation.

Figure 2.27. Four SRM structures. (a) Conventional SRM. (b) SR-SRM.

The conventional SRM and the skewed SRM, which have the best angle (22.5°) based on the simulation results, are shown in Figure 2.28.

According to the simulations and the experimental results, skewing can reduce the vibration of the SRMs, and the radial forces of the all skewed SRMs are reduced with the skewing angle. It is observed that to reduce the vibration skewing the SRM stator is more efficient than skewing the

SRM rotor.

Figure 2.28. Prototypes of the stators and rotors. (a) Normal stator. (b) Skewed stator (22.5°).

2.3.12. Cylindrical Rotor Design of SRM

A switched reluctance motor is one of the major candidates of rare-earth-free motors for high- speed applications in electric machines. An SRM has salient poles in the rotor which results in high windage loss and acoustic noise caused by salient poles at high-speeds.

A cylindrical shape rotor is designed to reduce the windage loss and acoustic noise in [56]. The windage loss and the acoustic noise of the salient pole SRM are measured, and it is found that salient pole SRMs have higher loss at maximum rotational speed. The windage loss resulted in the decrease of efficiency at high speeds and for the low power region. In the literature, some studies, which evaluate the total losses, are reported to reduce the windage loss by inserting ribs between the rotor poles [17]. Thin ribs are placed between the salient poles in the rotor to reduce the windage loss and the acoustic noise level (Figure 2.29). The thickness of the ribs is one of the most significant design parameters and needs to be selected carefully. The mechanical strength at the maximum rotational speed needs to be analyzed to maintain the structural integrity while reducing

28 the windage loss and radial force. According to analysis results, the efficiency is improved by 3.9% and the acoustic noise is reduced by 14.2 dB.

Figure 2.29. Conventional rotor (left) and the proposed cylindrical rotor (right) [56].

2.3.13. Stator and Rotor (Pole) Geometry

Since the conventional SRM`s geometry tends to generate abruptly changing radial forces, the stator and rotor pole geometry modifications are proposed to smooth out this radial force variation.

Methods based on pole shaping on the stator and rotor are presented in Figure 2.30 and explained in detail under seven sub-topics.

Stator and Rotor (Pole) Optimization

Pole Arc Windowing Pole Shoe Pole Tip Tapering the Optimization Optimization Stator Poles

Shifted Lamination SR-Shark Layer Method Machine

Figure 2.30. Classification of stator and rotor pole shaping methods.

2.3.13.1. Windowing

Since the pole shaping approaches are based on smoothing out the radial force and suppressing the peak radial force, one of the most efficient methods is placing holes into the stator and/or rotor poles. The peak radial force occurs when the stator and rotor poles are aligned. The window

29 constraints the maximum flux passing through the poles and reduces the peak radial force amplitude. However, the window also affects the average value of the produced torque. The first study on optimization of the window size and position on the rotor pole for the performance index of average torque / peak radial force (NF) is reported in [57], [58]. In [57], three different window shapes are placed on the rotor pole of a 6/4 SRM (Figure 2.31) and the results are compared as shown in the Figure 2.32.

(a) (b) (c)

Figure 2.31. (a) Type-A, (b) Type-B, and (c) Type-C windows placed in a rotor pole of 6/4 SRM [57].

(a) (b) (c)

Figure 2.32. (a) Radial force, (b) torque profile and (c) performance index NF comparison of

Types A, B, and C windows [57].

Additionally, the distance of the window from the air gap is also analyzed, and another three types of windows are compared as shown in Figure 2.33 and Figure 2.34, and concluded that the best performance could be achieved with the Type-E window that is placed in the rotor pole. In

[58], the acoustic noise is analyzed in detail for the same window types and the improvement is verified.

(a) (b) (c)

Figure 2.33. (a) Type-D, (b) E, and (c) F windows placed in the rotor pole [57].

(a) (b) (c)

Figure 2.34. (a) Radial force, (b) torque profile and (c) performance index NF comparison of

Types D E, and F windows [57].

A similar approach is reported in [59] with circular windows on the rotor (Figure 2.35). The window position and the diameter are optimized for the lower radial force. In another study, with circular windows in the rotor poles [60], the diameter of these windows and pole arcs are optimized to reduce the torque ripple.

Figure 2.35. Rectangular windows placed in the rotor poles and flux paths [60].

The shape of the window is further improved by introducing “V” shaped windows into the rotor poles (Figure 2.36) [61]. The effect of this shape is compared with the rectangular window

31 shape, and it is concluded that the V-shaped window avoids the excessive saturation on the rotor poles while reducing the radial force.

Figure 2.36. V-shaped window in rotor pole [61].

2.3.13.2. Pole Shoe

Stator and rotor pole tooth tip shaping is considered and investigated deeply to mitigate the acoustic noise in [62]–[64]. Adding tooth tips on the stator and rotor poles further improved the torque profile, consequently reduced the vibration. In [65], a tooth tip (also called pole shoe) is placed on the stator pole as shown in Figure 2.37. The authors have analyzed the flux linkages and torque profile of the motor using various pole tip geometries and proposed a design method.

Following an optimization process, they were able to enhance the torque ripple and obtained lower acoustic noise.

Figure 2.37. (a) Simple stator pole, (b) modified stator pole [65].

A similar approach is made for the rotor poles in [66]. In this work, rotor pole shoes are attached to the lateral face of the rotor, in addition to a non-uniform air gap stator structure, as shown in

Figure 2.38. The geometry is optimized using a response surface optimization method [67]. Hence, the average torque and torque ripple improved significantly.

Figure 2.38. Nonuniform air gap profile (left), Pole shoe attached to the lateral face of the

rotor pole (right) [66].

A stator structure having a notch in addition to the stator pole shoe is reported in [68]. Inspired from the shaded pole single phase induction motors, a notch is included into the stator pole as given in Figure 2.39. As a result, the radial force amplitude and torque ripple have been reduced without affecting the average torque.

(a) (b) (c)

Figure 2.39. (a) Section of the motor without pole shoe and notch, (b) Section of the motor with

pole shoe, (c) Section of the motor with pole shoe and notch [68].

2.3.13.3. Pole Arc Optimization

A method which mainly aims to find the optimum pole arc to estimate the vibration in SRMs is proposed in [69]. In this method, the area of flux path varies. This way the inductance changes with the geometrical parameters of the machine such as the thickness of the stator, the pole arc of stator and rotor. Additionally, these geometrical parameters would also affect the mechanical characteristics, which in turn, change the mechanical response of the machine with respect to the electromagnetic force. An 8/6 SRM has been demonstrated with different pole arcs to prove the accuracy and the efficiency of the proposed method in FEA. In order to study the effects of the

33 geometrical parameters on the mechanical response, the thickness of the stator yoke, the pole arc/pole pitch ratio of the stator (SR) and pole arc/pole pitch ratio of the rotor (RR) are defined as design variables (Figure 2.40). From this analysis, it has been observed that the vibration is very sensitive to the pole arc/pole pitch ratio of the stator. Furthermore, acoustic noise with different pole arcs is computed and the results showed that higher pole arc/pole pitch ratio of the stator would reduce acoustic noise in this SRM.

Figure 2.40. Geometry parameters of SRM [69].

2.3.13.4. Pole Tip Optimization

The geometry of the SRMs has a significant effect on reducing the vibration and the acoustic noise; hence, the design of the stator and/or rotor shape can be considered as a noise reduction method. Therefore, an SRM with a new stator pole shape is introduced in [70]. When the convex sine stator pole shape as shown in Figure 2.41 is used, the magnetic field is changed, which leads to a change of the radial force. The analysis revealed that the radial force is decreased dramatically without any significant reduction in average torque. Therefore, the torque ripple is decreased and the vibration is reduced.

Figure 2.41. The convex sine stator pole design [70].

A modified shape of the stator pole and an improved stator yoke structure are proposed in [71].

In this study, the analysis is based on the relationship between the sound pressure level and the maximum displacement of the stator. According to analysis results, the trapezoidal shape of the stator pole, that can reduce the bias of the stress, and a polygon shape of the stator yoke, that can increase the mechanical strength of the stator, are introduced as an appropriate model to reduce the acoustic noise (Figure 2.42).

(a) (b) (c)

Figure 2.42. (a) Polygon shape on the stator yoke, (b) trapezoidal shape on the stator pole,

2.3.13.5. Tapering the Stator Poles

Mitigating the acoustic noise by improving the structural strength of the SRMs is another method in the literature. Based on the structural modal analysis, the natural frequency components of the machine can be obtained through the FEAs. The acoustic noise is elevated when the natural frequency components resonate with the radial force components in the audible spectrum.

Therefore, the stator pole shapes can be optimized to eliminate the dominant frequency components in the audible spectrum. In [72], tapering the stator pole from top to bottom and rounding the bottom edge of the pole is proposed. Further, the effects of the parameters ec, α, β, Rj (Figure 2.43) on the natural frequencies is analyzed, then the parameters are optimized to reduce the acoustic noise.

Figure 2.43. Tapering parameters effecting the natural frequencies [72].

In [73], a design methodology, similar to that of [72], is proposed. The dominant modal frequencies are pushed beyond the audible frequency range. This method uses four design ratios that are defined in terms of the dimensions of the machine geometry to optimize the given objectives. The tapering approach is combined with the stator yoke shaping and adding pole shoes to the rotor [74], [75]. Since the radial force is concentrated behind the stator teeth, the stator yoke is widened in this region; therefore, the structural strength is improved, which leads to a reduction in the acoustic noise (Figure 2.44).

(a) (b)

Figure 2.44. Tapered stator poles (a) with modified stator yoke and (b) with rounding and adding

rotor pole shoes [75].

2.3.13.6. Shifted Lamination Layer Method

A similar approach to the pole shaping approaches is reported in [76], where the rotor laminations are stacked with a zigzag shift as shown in Figure 2.45. The shifted rotor laminations distribute the radial force through the structure thereby reducing the vibrations. The shifting angle is optimized using 3D FEA to achieve the minimum radial force. Hence, the acoustic noise and the torque ripple are reduced without reducing the average torque.

Figure 2.45. Shifted rotor laminations [76].

2.3.13.7. SR-Shark Machine

The pole shape modifications for stator and rotor in the X-Y plane are mentioned above.

Another stator and rotor pole modification are proposed in the Z (axial) direction [77]. This type of

SRM is called an SR-Shark machine, where the stator and rotor poles look like shark`s teeth, as shown in Figure 2.46.

Figure 2.46. (a) SR-Shark machine pole and (b) regular SRM pole [77].

The magnetic analysis and FEA reveal that the motor can increase the average torque, reduce the torque ripple, and the vibration at non-saturated operating conditions. The major disadvantage of the machine is that manufacturing the machine is challenging, as the stator needs to be at least two pieces and aligned with the rotor very carefully.

2.4. Summary

In this chapter, the basic principles, classification, and the operation of SRMs are explained.

Then SRM acoustic noise and vibration reduction techniques are investigated in detail from the machine design perspective. The acoustic noise reduction techniques are classified under thirteen main topics. Stator and rotor pole geometry considerations are deeply investigated under seven subtopics. The effects of these techniques are explained, including their advantages, disadvantages, and the manufacturing challenges of the proposed models.

CHAPTER III

PROPOSED WORK

In this chapter, holes in the stator and rotor laminations are introduced to reduce the radial force and mechanical vibration in SRMs. The placement of the holes can be optimized to maximize the benefits. Reducing the radial force is one way to reduce the vibration. However, there is a tradeoff between the radial force reduction and the torque production. A decrease in the radial force leads the tangential force and torque to decrease. Therefore, while reducing the radial force, the reduction in the average torque should be observed, and thus an optimization process needs to be introduced.

Other than the radial force reduction, the damping effect of the motor body can be improved to reduce the vibration. In this way, the natural frequencies of the motor can be pushed out of the audible spectrum, or at best the amplitudes of these frequency components can be reduced by adding damping elements to the motor body.

The force and acoustic noise generation mechanism of SRMs are explained in Section 3.1.

Section 3.2 gives details of the position and size adjustments of the windows on the stator and rotor poles. The selection of the number of air gaps, air gap sizes, and their positions to achieve the best damping are explained in Section 3.3.

3.1. Electromagnetic Force Generation Mechanism

According to previous studies, the source of the acoustic noise in electrical machines can either be electrical-magnetic, mechanical, or aerodynamic (ventilation). The mechanical noise comes from the gearbox, bearing, or mechanical misalignment (i.e. eccentricity). Aerodynamic noise arises from the air movement in the motor frame, and it usually becomes noticeable at high speeds.

Electrical-magnetic noise is generated from the vibrations due to the radial magnetic forces. Among others, the magnetically stimulated noise constitutes the majority of the SRM noise [28]-[30].

As reviewed in Chapter II, the large torque ripple, high vibration, and the acoustic noise are the main problematic issues of the SRM. The reasons for the vibration and the acoustic noise are the radial force and the torque pulsation due to flux switching between the phases. These are abruptly changing forces on the radial direction which defect the stator back iron, thereby causing a vibration on the motor body. The frequency components of these vibrations resonate with the motor`s natural frequencies and thus their amplitudes intensify. This leads the surrounding air pressure to change, and as a result, acoustic noise is generated.

The traditional methods of electromagnetic force calculation given in the literature focus on the force calculation, but force distribution and the vector analysis are not provided. Using force distribution, force components, the profile of the local forces, and their contribution to the noise, vibration, and deformation of the SRM can be calculated. So far, there are two types of well-known force calculation approaches in electromechanical systems. One is the energy approach, and the other is the field-based approach, which leads to the Lorentz Force Method and Maxwell Stress

Tensor method. In this section, the electromagnetic force mechanism will be investigated based on the Lorentz Force method and Maxwell Stress Tensor method due to its simple calculation procedure and various ways of implementation [78].

The Lorentz Force equation is usually the starting point for the description of the electromagnetic force characteristics. The magnetic force density, as a free current into the magnetic field, is given by Lorentz Force Law, as follows:

FJB (15) where F is the volume force density on the current-carrying conductor in a magnetic field, J is the current density, and B is the flux density. The vector presentation of this force, called

"magnetization force", can be expressed as:

f Jmag B  (16)

According to Ampere`s Law;

  BJ0 (17)

  HJ (18) where μ0 is the permeability of the air and H is the magnetic field intensity.

From Equation (17) and (18);

1 JBH   (19) 0

After substituting (19) in (16), fm a g can be expressed as:

1 fJBBB (20) mag    0

 BB can be expanded as:

11 BBBBBBBBB       2 (21)     22   

The electromagnetic force can be rewritten in the following form by substituting (21) into (20):

11 2 fJBBBBmag    (22) 0 2

To determine the total force acting on the object, we must integrate the force density, F over magV an appropriate volume as follows.

11 F f dV    B  B   B2 dV (23) magV  mag    V 0 2

If the surface S encloses the volume V, the total force can be rewritten in the following form.

11 FF ndSB  n BB n dSTdS 2 (24) magmagSV   SS0 2 where n is the outward-directed unit vector to surface S. It should be noted that, by knowing the forces on the surface of a volume, the total force in volume V can be calculated. This enables one

41 to find the forces affecting the rotor by knowing only the fields on the air gap. The Maxwell Stress

Tensor, T can be represented as:

11 (25) TBnBBn 2    2 0 

Finally, the magnetic force Fm a g can be divided into two components as,

11 (26) FBndSBBdS 222 rrt    2200

11 (27) FBnBdSBB dS t    rt 00

The diagonal element Fr is often called the traction stress, normal stress, or radial force, which

causes radial deflection in the electric machine. The off-diagonal element Ft is shear stress or tangential stress, or tangential force, which is responsible for the torque production.

∬ 푑푆

(a) (b) Figure 3. 1. (a) Typical switched reluctance machine and (b) its integration surface.

Here, Br and Bt represent the radial and tangential components of the flux density in the air gap.

The force components are calculated on each tooth tip of the stator poles as shown in Figure 3. 1.

So the integration can be applied for each surface of the stator pole.

I phase

F rad Time

Time

X(t) X(t)

Time

Figure 3.2. (a) Idealized phase current, (b) radial force, and (c) the deformation of SRM.

Figure 3.2 presents the radial force generation based on the phase current and the alignment of the stator and rotor poles. To generate a torque to pull the rotor pole at the beginning of the overlapping region, the phase current is built in the phase. The radial force increases slowly until the poles start to overlap. When that happens, the phase current is kept constant for generating a constant torque. At the same time, the radial force increases proportional to the overlapping area and reaches its maximum value when the stator and rotor are fully overlapped. Then, the phase current is reduced to zero after, and thus the radial force goes down to zero. The radial force pulls the stator back iron through the motor`s center; this pulling effect leads to deformation on the back iron as shown in Figure 3.2.c. By the time the radial force reaches the zero value, the back iron tries to go back to its original position. However, under the influence of the negative acceleration, the

43 material starts to oscillate, and this oscillation dies down in a short time. The stator acts like an elastic rubber band; the stored energy is released after the pulling force (radial force) becomes zero.

The combination of these oscillations from all the phases resonates with the motor`s natural frequencies and generates powerful vibrations on the motor body. These vibrations lead to the air pressure change in the surrounding air, as shown in Figure 3.3. The air pressure has various frequency components that have different amplitudes.

Surrounding air

Motor Frame

Figure 3.3. Air pressure variation around the motor body.

Figure 3.4 shows an example that consists of the amplitude and phase plot of the acoustic sound pressure levels. Audible noise has harmonics between 4 kHz – 20 kHz frequency spectrum.

Figure 3.4. Amplitude and phase plots of the acoustic sound pressure levels.

3.2. Windows on the Stator and Rotor Poles

The insertion of the windows into the rotor poles is a known method for reducting the radial force that is analyzed in various designs, as explained in Section 2.3.13.1. The research group at

UA introduced windows on both the stator and rotor poles to provide an additional degree of freedom for the radial force reduction. The windows on the stator and rotor poles obviously reduce the radial force; however, radial force reduction leads to a significant decrease of the produced torque. A higher torque average and a lower peak-to-peak radial force variation are desirable. The position and the size of the windows can be adjusted in such a way as to maximize the following design ratio, N:

Tavg N  (28) Frad, pp where Tavg is the average torque and Frad, pp is the peak-to-peak radial force variation of the SRM.

An optimization process that maximizes the design ratio N is necessary to achieve the best performance while reducing the vibration.

In [57], the window on the rotor pole is introduced, and the effect of the size and the position of the rectangular window is analyzed in detail. Figure 3.5 shows a window placed on the rotor pole. Here, xr and yr are the width and height of the window, respectively, and hr is the distance from the air gap.

yr,3

hr yr,2

yr,1

Figure 3.5. Windows on both stator and rotor poles.

First, the hr is kept constant, and the bottom of the window is aligned with the lower part of the rotor pole. Also, the yr is fixed to one-third of the rotor pole width. The radial force and torque are analyzed for three different window height sizes, which are one-third, two-thirds, and full rotor pole heights (types A, B, and C). The radial force and torque profiles of these three types of windows inserted in a 6-4 SRM are given in Figure 3.6 and Figure 3.7 respectively. The performance index is provided in Figure 3.8.

Figure 3.6. Radial force profiles for three different window designs [57].

Figure 3.7. Torque profiles for three different window designs [57].

Figure 3.8. Performance index for three different window designs [57].

As it can be concluded from Figures 3.6-3.8, the window may cause a good radial force reduction and a very high torque fluctuation as in type-C, or low radial force reduction and a good torque generation as in type-A. The window size in type-B gives the best performance among others, which means that the window size should not be too large to allow a sufficient flux to pass through the pole and should not be too small to provide enough radial force reduction.

The position of the window; that is, the distance from the air gap, hr, is varied and its effect is analyzed. According to the results presented in Figure 3.9 for various window positions, bringing the window closer to the air gap provides better radial force reduction; however, the torque fluctuation increases rapidly. It should be noted that the window should never touch or get very

47 close to the air gap surface because it either saturates the material around the pole tips or decreases the overlapping area, which results in a high torque reduction

(a) (b)

(c)

Figure 3.9. (a) Radial torque, (b) torque profiles and (c) the performance index of the SRM versus the window position [57].

The effects of the window size and the position are the same for the stator. The reason an additional window is considered on the stator is to have an additional degree of freedom for the optimization of the average torque per peak-to-peak radial force ratio. Figure 3.10 shows the windows on the stator and rotor poles and their dimensions with positions.

Stator

hs xs

xr hr

Rotor

Figure 3.10. Windows on both stator and rotor poles.

3.3. Distributed Air Gaps on the Stator

Alleviating the radial force helps to reduce the amplitudes of the oscillations on the motor body up to some level. Although the radial force can be minimized, the oscillations on the stator still exist. There are methods in the literature for improving the damping on the stator such as sealing the stator slots and filling them with a liquid that acts as both a cooler and a damping element, tapering the stator poles to have thicker regions on the stator pole ends, or thicker stator back iron regions behind the stator pole. As a new damping method, distributed air gaps are introduced in this thesis, which are small diamond shaped windows distributed through the stator. Similar to other windowing methods, distributed air gaps increase the reluctance and consequently, decreases the radial force. Distributed air gaps generate a spring effect that helps to damp the oscillations.

The reason for selecting the diamond shape for these additional holes is to keep the bridge thicknesses constant. The bridge is the part that is between the two consecutive holes. Therefore, the structure formed by these bridges is similar to a spring in terms of its effect and the physical structure as illustrated in Figure 3.11.

bridge x x

Frad Frad

Figure 3.11. The illustration of the effect of the distributed air gaps placed on the stator pole.

In one direction (radial direction), it is straightforward to calculate the spring constant of a linear object given in Figure 3.12 using Hooke’s Law and Young’s Modulus.

l0 Δl

Figure 3.12. Stretched rigid body.

Hooke’s Law defines the spring constant as:

Fkl (29) where F is the applied force, k is the spring constant or stiffness, l0 is the original length and Δl is the deflection of the rigid body. The stress for the axial load can be expressed as:

 E (30) where E is an elasticity constant of a given material also called Young’s Modulus, ε is the tensile strain that is a fractional increase in the length of the rod.

l (31)   l0

The tensile stress is the outward normal force per area (A) and can be expressed as:

F (32)   A

From (30), (31), and (32) the following equality can be written:

Fl (33)  E Al0

Hence, force can be described as:

l (34) F A E l0

Therefore, the spring constant can be expressed in the following form:

FA (35) kE ll0

In [14], [79] the motor body is assumed to be a plain ring-shaped object and the spring constant per unit length is calculated using a similar approach given above. Then, the natural frequency of this plain ring object is calculated based on the spring constant per unit value, which proves that the spring constants of the stator affects the natural frequencies of the motor.

The distributed air gaps create springs on both the radial and tangential directions as presented in Figure 3.13. Pulling occurs in different directions under the influence of the forces on the different directions.

k5 k8 k2

F y k k9 6 k3

k7 k4 k10

Figure 3.13. The effect of the distributed air gaps on the stator back iron.

Here, the calculation of the spring constants (k1, k2,…) is not as simple as it is in the stator teeth where the spring effect is in one direction or as in the plain ring-shaped object. Therefore, a simpler method can be used to find the optimal numbers, sizes, and positions of the distributed air gaps;

51 that is, the FEA method. It is a fact that these quantities affect the spring constants on both directions. Electromagnetic and structural FEA simulations provide a convenient way to find the optimal values of these parameters for the minimum deflection on the stator outer surface.

3.4. Summary

In this chapter, the proposed acoustic noise mitigation method is presented and explained.

Placing distributed air gaps enhances the damping of the oscillations by changing the natural frequencies of the motor body. In Chapter IV, the analysis is performed and explained in detail.

CHAPTER IV

ANALYSIS AND RESULTS

In this chapter, the analysis and optimization procedure are given for determining the size and position of the distributed air gaps on the stator and rotor. A 24/16, 100 kW, 4250 rpm SRM is selected for the analysis. The following section gives the details of the analysis procedure. The natural frequencies are determined through modal analysis of the SRM. The vibration and acoustic noise analysis of hole placements in the rotor and the stator is provided. Placements of the distributed holes are optimized to get the maximum benefit. Results are presented to get a set of guidelines for the design.

4.1. Analysis Procedure

The analysis starts with a modal analysis, which is used for determining the natural frequencies of the motor. These are the frequencies with which the vibrations coming from the radial forces resonate, hence, generating higher vibrations and acoustic noise.

The rest of the analysis is the combination of electromagnetic, structural, harmonic, and acoustic analyses that are performed using ANSYS Electromagnetics Suite, and ANSYS

Mechanical coupled through ANSYS Workbench shown in Figure 4.1. The electromagnetic analysis is performed with Maxwell. The outputs of this analysis are the radial and tangential forces on the stator pole tooth tips. The harmonic response analysis takes the results from the electromagnetic analysis and determines the surface deformation, acceleration, and velocity of the stator in the frequency domain to feed this information to the acoustic analysis. The results from the harmonic response are loaded to the acoustic analysis toolbox to determine the sound (acoustic) pressure level. The transient structural analysis is also used to analyze the surface deformation,

53 acceleration, and velocity in time domain. It is also possible to determine the acoustic pressure levels using a one-meter microphone test in the transient structural analysis.

Figure 4.1. A general schematic of the acoustic noise and vibration analysis.

4.2. Modal Frequency Analysis

The modal frequency analysis is required for determining the natural frequencies (modes) of the motor. Generated vibrations on the stator poles that are originated from the radial forces become more dominant when they resonate with the natural frequencies of the stator. Therefore, the total deformation on the stator surface increases, which amplifies the acoustic sound pressure. The modal analysis tool is shown in Figure 4.2.

Figure 4.2. Modal analysis of an SRM.

The modal analysis results of the mentioned 24/16 SRM is performed using the ANSYS tool, and the results are presented in Figure 4.3.

Mode 1 Mode 2 Mode 3 Mode 4

198 Hz 544 Hz 1009 Hz 1568 Hz

Figure 4.3. Natural frequencies of the 24/16 SRM.

4.3. Window on the Rotor Pole

The insertion of the windows into the rotor poles is a known method for radial force reduction that is analyzed in various designs, as mentioned in Chapter II. In this section, placing a rectangular window on the rotor poles as shown in Figure 4.4Figure 4.5 is illustrated.

Figure 4.4. Windows on the rotor poles.

The position and the size of the windows are adjusted so as to maximize the following design ratio, N:

Tavg N  (28) Fradpp,

To be able to find the optimum position and size of the window, the optimum performance index, N, should be determined through an optimization method. The electromagnetic FEA,

ANSYS Electromagnetics Suite, repeats the analysis for the parameters that are varying with constant steps within a known range. Figure 4.5 presents the width, xr, the height, yr, and the distance from the air gap, hr, of the windows.

Rotor Pole

hr xr

Figure 4.5. Window size and position on the rotor poles.

The parametric sweep results show that the position and size of the window on the rotor poles have a significant effect on the radial force and the torque production. Figure 4.6 and Figure 4.7 show the results of the radial forces and the average torque based on the parametric sweep.

Figure 4.6. Radial force variation with the rotor window size and position variation.

Figure 4.7. Torque variation with the rotor window size and position variation.

4.4. Window on the Stator Pole

Figure 4.8Figure 4.5 presents the hole placement on the stator poles. The dimensions of the windows in the stator are parametrized as shown in Figure 4.9. The width, xs, the height, ys, and the distance from the air gap, hs are optimized to improve the performance criteria N.

Figure 4.8. Windows on the stator poles.

Stator Pole

hs xs

Figure 4.9. Windows size and position on the stator poles.

The combination of the hole in the rotor and hole in the stator is provided in Figure 4.10. Figure

4.11 presents the parametric sweep of different designs in improving the performance index N. The optimum design provides the maximum reduction in peak-to-peak radial force while achieving minimum reduction in the average torque.

Figure 4.10. Windows on both the stator and rotor poles.

T% vs p2pF% Reduction 80 Windowed Stator and Rotor OPTIMUM VALUE Torque at 300 A: 878.7 Nm (22 % Reduction) 70 Peak to Peak Radial Force: 613.77 N (68 % Reduction) 60 Windowless Stator and Rotor Torque at 300 A: 1136 Nm 50 Peak to Peak Radial Force: 1927.33 N

30 P2PF% REDUCTION P2PF% 20

0 0 5 10 15 20 25 30 35 T% REDUCTION

Figure 4.11. Percent peak to peak radial force reduction versus percent torque reduction.

The tangential and the normal force information are provided from the electromagnetic analysis. While the tangential force is responsible for the torque production, the normal force generates the radial force. Therefore, the outputs of this analysis are the radial and tangential forces on the stator pole tooth tips. These, in turn, are the inputs of the harmonic response analysis, which calculates the surface deformation and acceleration of the stator in the frequency domain.

The second step of the analysis is the harmonic response analysis, which has been performed using ANSYS Mechanical coupled through ANSYS Workbench. The total deformation and the acceleration results have been obtained as an outcome of the mechanical analysis. The total deformation on the stator surface of the conventional machine is found to be 0.27854 μm, while the optimized machine provides 0.17811 μm, as shown in Figure 4.12. These results show that total deformation is reduced by 36 %.

Figure 4.12. Total deformation of the conventional and windowed motors.

The total acceleration on the stator surface is 30880 mm/s2 for the conventional machine, and

18385 mm/s2 for the optimized design. Thus, the total acceleration is improved by 40.46 %.

Figure 4.13. Total acceleration of the conventional and windowed motors.

4.5. Analysis of the Distributed Air Gaps

The effect of the distributed air gaps on the stator for various configurations of the air gap patterns and locations are investigated in this section. First, the distributed air gaps that have the same total area, number, and the size are placed on the stator teeth and back iron separately. For a fair comparison, simulations are performed by adjusting the peak current for a similar average

60 torque production. Table 4.1 compares the FEA results of the motors that have distributed air gaps on the stator teeth and back iron with the conventional SRM.

Table 4.1. Comparison of the distributed air gap locations.

Tavg [Nm] 1136 1142 1132

Peak Current [A] 300 500 300

Frad,p-p [N] 1927 994 1678

Total Deformation [µm] 0.27854 0.25672 0.23867

Total Acceleration [mm/s2] 30880 28653 25581

The peak current is increased to 500 A to match the required torque level. When the distributed air gaps are placed on the stator teeth, the peak-to-peak radial force variation reduces significantly; however, the average torque drops down drastically because the machine goes into saturation. On the other side, when the distributed air gaps are inserted into the back iron, the Frad,p-p is effected slightly but the improvement on the total deformation is significant. It can be concluded that the distributed air gaps reduces the stator surface deformation rather than the radial force.

The effect of various patterns and number of air gaps and sizes are analyzed to minimize the total deformation and acceleration on the stator back iron surface. Simulations are performed using a 300 A phase current for each model as the holes in the back iron would not affect the torque production. Table 4.2 compares four different shaped distributed air gaps placed on the stator back iron with the conventional and windowed SRMs.

Table 4.2. Comparison of the conventional SRM, windowed SRM, and SRMs that have various types of distributed air gap placed on the stator back iron.

Tavg [Nm] 1136 878.70 994 1014 940.8 1061

Peak Current [A] 300 300 300 300 300 300

Frad,p-p [N] 1927 613.77 1485.8 1617 1739.6 1679

Total Deformation [µm] 0.27854 0.17811 0.25692 0.23957 0.26593 0.21965

Total Acceleration [mm/s2] 30880 18385 27989 26122 28354 23778

FEA results show that the distributed air gaps placed on the stator back iron have a significant effect on the reduction of the total deformation and acceleration; however, the radial force cannot be reduced as much as in the windowed SRM. Among others, patterns that have holes clustered in a rectangular outer boundary are superior to the others. The effect of the air gap size, and the distance between the air gaps compared to when the air gaps are clustered in a rectangular outer boundary can also be made from Table 4.2. The best result is achieved with the design that has 14 air gaps. Each air gap has 4 mm2 area, the distance from the first air gap to the stator outer surface is 8 mm, and the distance between the air gaps on the x and y directions are 2 mm and 1.5 mm, respectively. Even a satisfactory reduction on the deformation is achieved with the distributed air gap approach, the radial force / peak-to-peak radial force ratio is not improved much though. Better vibration and acoustic noise mitigation can be realized by combining the windows on the stator and rotor poles with the distributed air gaps. This approach is analyzed and the results are presented in

Section 4.7.

4.6. Analysis of the Distributed Air Gaps with Stator and Rotor Windows

A vibration and acoustic noise analysis is performed with the windows placed on the stator and rotor poles, and distributed air gaps placed on the stator back iron. Combining these vibration reduction techniques provides both improvement on the average torque / peak-to-peak radial force ratio and reduced deformation on the stator outer surface.

Since the window sizes and positions are already optimized in Section 4.5, distributed air gap parameters are optimized in this section. The distributed air gaps are placed to the stator back iron as presented in Figure 4.14.

Figure 4.14. Windows on both the stator and rotor poles and the distributed air gaps on the stator back iron.

The optimal number, the size of the air gaps, the optimal distance between the air gaps on the x and y directions, and the optimal distance from the stator outer surface to the first air gap are not determined through the parameter sweep. The number of simulations that need to be done to cover all the possibilities exceeds several thousand; hence, it is not practical to run a parameter sweep to find the optimal values. Instead, the optimal parameters are determined manually by adjusting their values one at a time.

Figure 4.15 shows the parameters that need to be optimized.

dx hd . . . dy

t y . . .

. . .

......

Figure 4.15. Distributed air gaps on the stator back iron.

In Figure 4.15, Nd is the number of air gaps, dx and dy are the diagonal lengths of the air gaps, tx and ty are the distance between the two consecutive air gaps, and hd is the distance from the outer surface of the stator and the first air gap. These parameters are determined for the minimum deformation and acceleration using the electromagnetic FEA coupled with the transient structural FEA while keeping the optimum window on the rotor and the stator poles. During this optimization process, the average torque is observed, and the percent torque reduction is kept under 20%.

The Mechanical Structural FEA is performed at every iteration, and the minimum deformation and acceleration are achieved. The optimum number and the area of the diamond shaped air gaps

2 have been found as 14 and 4 mm (dx = 4 mm, dy = 2mm), respectively. The optimum distance between the outer diameter of the stator surface and the first diamond shaped air gap hd is found as

8.5 mm. The distance between the end of one diamond shaped air gap and the starting point of the next one in the x and y-axes (tx and ty) are determined as 2 mm and 1.5 mm respectively. The total deformation and total acceleration of the optimized SRM are presented in Figure 4.16.

Figure 4.16. Total deformation and acceleration of the optimized SRM.

4.7. Summary

In this chapter, placement of the distributed air gaps on the stator back iron in combination with the single holes in the stator and rotor poles is proposed and analyzed. Distributed air gaps have diamond shapes. These diamond shaped air gaps act like series-parallel connected springs and damp the oscillations. Therefore, the total deformation and acceleration of the stator outer surface are reduced. The conventional and proposed SRMs are tabulated for comparison purposes in Table

4.3. The total deformation is reduced 36% with the optimized windowed machine and 41.4% with the optimized windowed and distributed air gap machine. The total acceleration is reduced 40% with the optimized windowed machine and 47% with the optimized windowed and distributed air gap machine.

Table 4.3. Comparison of conventional, windowed, and distributed air gap SRMs.

Tavg Peak to Peak Total Deformation Total Acceleration Tavg  F 2 (Nm) Frad (N) rad, pp (μm) (mm/s )

Conventional SRM 1136 1927.33 0.5890 0.27854 30880

Windowed SRM 878.7 613.77 1.4316 0.17811 18385

Windowed SRM with 872.6 692.12 1.2607 0.16317 16338 Distributed Air Gaps

CHAPTER V

CONCLUSION AND FUTURE WORK

5.1. Conclusion

This thesis proposes an acoustic noise and vibration mitigation technique for switched reluctance machines (SRM). SRMs are favored in many applications due to their simple, reliable, and robust structures. However, these machines generate high torque ripples, vibrations, and consequently, high acoustic noise. SRMs have a doubly salient pole structure where the operation relies on exciting stator phases in a switching pattern. Every excitation attracts the appropriate rotor pole, and the rotor rotates through the attraction direction. The force pulling the rotor through the excited pole has two components called tangential and radial forces. The tangential force produces torque while the radial force pulls the stator pole through the center of the motor. During the commutation between the phases, the current that excites the phase suddenly goes to zero, which causes the radial force to decrease abruptly. The potential energy stored on the stator pole when it is pulled is suddenly released, and the stator pole and the stator back iron start to move in the opposite direction and oscillate just like releasing an elastic tape after it is stretched. These oscillations have frequency components that resonate with the motor’s natural frequencies and thus amplify the oscillations at certain frequencies. As a result, acoustic noise is generated. Therefore, the source of the acoustic noise can be considered as the radial force and the motor’s natural frequencies that are on the audible spectrum.

Many researchers investigated the mitigation of the acoustic noise and vibration, and numerous methods are reported based on modifications on the motor structure and motor control. This thesis is focused on acoustic noise reduction techniques from the design perspective. Therefore, a detailed

66 literature survey on design considerations to reduce the acoustic noise and vibration is provided in

Chapter II. In this chapter, the basic principles, classification, and the operation of SRMs are explained. Then, existing methods, which include modifications on stator and rotor poles, modifications on the stator back iron, optimal pole arc design, stator/rotor pole number optimization, skewing, etc. are investigated. The advantages, disadvantages, manufacturing, and structural issues of these methods are discussed. In general, existing methods focus on one aspect, which can be the radial force reduction, or motor natural frequency adjustment, or introduce damping elements on the stator.

In Chapter III, the proposed acoustic noise and vibration reduction method is introduced. The proposed method combines the radial force reduction and the introducing damping elements on the stator. A damping element is a group of diamond shaped holes distributed on the stator back iron.

The reason for diamond shape selection is that it generates zigzag shaped bridges along the stator back iron and these zigzag shaped bridges can be considered as a spring network. The variation in the diamond shape sizes, positions, and the distance between the elements affect the spring constants. Consequently, the damping and the motor’s natural frequencies are affected. Thereby, diamond shape sizes, positions, and the distance between the elements are optimized for minimum total deformation and total acceleration on the stator outer surface while having less than 20% average torque reduction.

The proposed method is applied to a 100 kW, 24/16 SRM using coupled electromagnetic and structural finite element analysis (FEA) software packages from ANSYS.

The combination of distributed air gap with the hole placement in the stator and rotor is proposed and analyzed. The dimensions and the placement of the holes are optimized to reduce the vibration and deformation without significantly impacting the torque production. The performance

index developed as average torque over peak-to-peak radial force variation ( NTF avgrad/ pp , ) is

67 improved from 0.589 to 1.26.7 with the optimized design, and consequently, the total deformation on the stator surface is reduced by 47 %.

In conclusion, the proposed method provides satisfactory acoustic noise and vibration reduction without having an intolerable effect on the torque production. Moreover, the method does not require a complicated manufacturing process, as it only requires the insertion of rectangular and diamond-shaped holes into the stator and rotor laminations.

5.2. Future Work

The possible extensions of this study can be listed as follows:

 An advanced optimization method can be used to improve the optimization process. A

multivariable optimization can be performed for adjusting the window parameters and

distributed air gap parameters altogether.

 The spring constants of the zigzag shaped bridges between the distributed air gaps can

be computed analytically, and the motor’s natural frequencies can be manipulated

using the analytical model.

 The effects of the window and distributed air gap shapes can be analyzed.

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