72 oluklu, 2 kutuplu asenkron motorlarda farklı sayıda rotor oluklarının uzay harmonikleri üzerine olan etkilerinin tespti
Investigation of the space harmonic effects of different numbers of rotor slots for a 2-pole induction motor having 72 stator slots
Yazar: GÜVEN ONUR
Danışman: DOÇ. DR. DERYA AHMET KOCABAŞ
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Elektrik Mühendisliği Ana Bilim Dalı / Elektrik Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2023
Konu: Elektrik ve Elektronik Mühendisliği = Electrical and Electronics Engineering

Özet:
Günümüz dünyasında artan nüfusun en önemli getirisi enerjiye olan ihtiyacın giderek artmasıdır. Fosil yakıtların gerek doğaya zararlı etkileri gerekse dünya üzerinde sınırlı miktarda bulunması, yenilenebilir enerji sistemlerinin giderek daha popüler olmasına sebep olurken, enerji dönüşümü yapılmasını sağlayan araçların da verim ve performans artışını zorunlu hale getirmiştir. Elektrik enerjisi ve mekanik enerji arasındaki dönüşümde şüphesiz en önemli rolü üstlenen elektrik makineleri arasında; üretim kolaylığı, bakım gerektirmemesi, düşük maliyeti sebebiyle asenkron makineleri yaygın olarak kullanılan bir elektrik makinesi haline getirmiştir. Asenkron makineler durağan kısmı stator ve hareketli kısmı rotor olmak üzere iki temel bileşenden oluşur. Statorda oluşturulan manyetik alan, stator ve rotor arasındaki hava aralığından rotora geçerek, rotor manyetik devresi üzerinden tekrar statora geri dönerek devreyi tamamlar. İdealde, hava aralığında bulunan manyetik akı yoğunluğunun saf sinüs biçimli olması istenir ancak motor sargıları saf sinüs biçimli bir kaynak ile beslense dahi oluşan manyetik alan saf sinüs biçimli olamaz. Bunun sebebi makine içerisindeki oluk yapısı ve yerleştirilen sargıların sinüs biçimli olmamasıdır. Hava aralığında oluşan manyeto motor kuvvet sinüs biçimini andıran basamaklı periyodik bir dalga olarak şekillenir. Oluşan bu basamaklı dalga şekli Fourier Dönüşümü ile açıldığında harmonik bileşenleri elde edilecektir. Elde edilen bu harmonik bileşenler kaynak geriliminden bağımsız olarak motor geometrisi sebebiyle 
ortaya çıktığından uzay harmonikleri olarak isimlendirilirler. Uzay harmoniklerinin varlığı makinede birçok istenmeyen etkilere sahiptir. Bu etkiler istenmeyen titreşim ve akustik gürültüler olarak özetlenebilir. Titreşim ve akustik gürültülerin varlığı ile hem makinenin çıkış performansını hem de verimini azaltacaktır. Sadece kararlı çalışma durumunda değil aynı zamanda kalkış ve frenleme 
durumlarında da meydana gelebilecek bu zararlı etkileri azaltmak adına birçok yöntem mevcuttur. Bu yöntemlerden en yaygın olarak kullanılanlar, sadece çift tabakalı sargılara uygulanabilecek olan kirişleme yöntemi, rotor iletkenlerine uygulanan kaykı örnek verilebilir. Bu yöntemlerden bir tanesi de motorun tasarım başlangıcında belirlenen uygun stator/rotor oluk kombinasyonu seçimidir. Bu çalışmada 72 stator oluklu, 2 kutuplu, 3 fazlı asenkron motor farklı oluk sayılarına sahip rotorlar ile analitik ve sonlu elemanlar yöntemi ile analiz edilmiştir. Sonlu elemanlar yöntemi kullanılarak elde edilen hava aralığı manyetik akı yoğunluğu dalga şekilleri Fourier Dönüşümü ile harmoniklerine açılmış rotor oluk sayılarının harmonik bileşenlere olan etkileri karşılaştırma yapılarak tespit edilmiştir. Buna ek olarak, tasarlanan her motorun verimi, moment dalgalılığı gibi performans kriterleri karşılaştırılarak bahsedilen stator yapısına ve seçilen motor kriterlerine göre en uygun rotor oluk sayıları tespit edilerek, literatürde stator/rotor oluk sayısı kombinasyonu seçiminde belirlenen kurallar ile ne kadar uygun olduğu karşılaştırılmıştır. Yapılan karşılaştırma sonucunda 3 fazlı, 2 kutuplu ve 72 stator oluğuna sahip bir asenkron motor için 58, 60, 78, 86, 94, 96, 98 rotor oluklu tasarımların diğer tasarımlara göre moment dalgalılıkları ve geçici hal çalışma durumlarında üretilen elektromanyetik momentin tepe değerleri daha düşüktür. Seçilen bu 5 farklı rotor oluk tasarımları arasında 94 rotor oluğu en düşük moment dalgılılığına sahiptir ve en uygun rotor oluk 
sayısı olarak belirlenmiştir.

Abstract:
In today's world, the most significant consequence of the increasing population is the growing demand for energy. The detrimental effects of fossil fuels on the environment and their limited availability on Earth have led to the increasing popularity of renewable energy systems. This, in turn, has made it necessary for the tools enabling energy conversion to have improved efficiency and performance. Among the electric machines that play an undoubtedly crucial role in the conversion between electrical energy and mechanical energy, asynchronous machines have become widely used due to their ease of production, low maintenance requirements, and low cost. Asynchronous machines consist of two fundamental components: the stationary part called the stator and the moving part called the rotor. The magnetic field created in the stator passes through the air gap between the stator and the rotor, completes the circuit by passing through the rotor's magnetic circuit, and returns to the stator. Ideally, it is desired for the magnetic flux density in the air gap to have a pure sinusoidal waveform. However, even if the motor windings are fed with a pure sinusoidal source, the resulting magnetic field cannot be pure sinusoidal. This is due to the slot structure inside the machine and the fact that the windings placed in them are not sinusoidal. The resulting magneto motive force in the air gap takes the form of a periodic step function resembling a sinusoidal shape. When this stepped waveform is analyzed using by Fourier Transform, the harmonic components can be obtained. These obtained harmonic components, which are independent from the source voltage and arise due to the motor's geometry, are called space harmonics. The presence of space harmonics in the machine leads to various undesirable effects. These effects can be summarized as undesired vibrations and acoustic noise. The existence of vibrations and acoustic noise will reduce both the machine's output performance and efficiency. To mitigate these harmful effects that can occur not only during steady-state operating conditions but also during starting and braking, several methods are available. One of these methods is the selection of an appropriate stator/rotor slot combination determined at the beginning of the motor's design. In a three-phase motor, each phase winding in the stator creates an ampere-turn force that does not change with time but varies in magnitude due to being supplied with AC voltage. When each phase winding is placed in slots with a phase difference of 120 degrees and fed with voltage having a phase difference of 120 degrees, the resulting composite ampere-turn function will become a function that does not change with time but changes in position. This composite magneto-motive force is solely generated by the stator. However, currents flowing through the conductors placed in the rotor slots also create a magnetic field, so the resulting ampere-turn force in the air gap occurs through the combination of the stator and rotor. In this study, designs were created using rotors with different numbers of slots but with the same stator structure and winding shape, and these designs were analyzed using the finite element method. The radial components of the magnetic flux density in the air gap were decomposed into harmonic components using Fourier transform, and the effects of different rotor slot 
numbers on the harmonics and the impact on motor output performance were examined and compared.
In the first stage of the study, the plate values of a 150 kW 3-phase 2-pole asynchronous motor used in the industry and produced in mass production were determined as design criteria. Then, an asynchronous motor design that meets the specified criteria was performed analytically. Different prototype motors were designed by only changing the number of rotor slots while keeping the stator geometry and basic dimensions such as the inner and outer diameters of the motor, air gap, and axial length constant. The reason for keeping the parameters other than the number of rotor slots constant is to accurately compare the effects of rotor and stator slot combinations on space harmonics. After obtaining the magnetic flux density in the air gap through finite element analysis, a code was prepared in MATLAB licensed software to perform Fourier Transform. All data obtained from finite elements were transferred to MATLAB, and the harmonic components of the relevant waveforms were obtained and compared. As a result of the comparison, it was observed that the 71st and 73rd harmonic components were dominant in all analyzed magnetic flux density waveforms. This is because the designed motors have 72 stator slots. Furthermore, it was determined that even though to a small extent, even harmonics exist based on the Fourier Transform analysis. The reason for this is that the waveform of the magnetic flux density in the air gap obtained from the analysis does not have quarter-wave symmetry. Ideally, when the waveform of the magnetic flux density created by the stator is analytically obtained and Fourier transformed to its harmonics, it is observed that the waveform has quarter-wave symmetry, resulting in the even harmonic components being zero. Additionally, in each design, the harmonic degrees corresponding to one less and one more rotor slot were found to be dominant. Furthermore, the electromagnetic moment, induced voltage, and currents flowing through the rotor bars were compared for all analyzed designs. Based on the comparisons, it was observed that in designs where the number of rotor slots is very close to the number of stator slots, the torque ripples reached very high levels between 30% and 40% during stable operating conditions. Additionally, it was observed that as the number of rotor slots increases, the torque ripple decreases. However, it should be noted that a very large number of rotor slots would make 
production more challenging. In addition, during transient states such as starting, the motor produced large moments that could damage the mechanical system and drew high currents. The rotor slot numbers of 58, 60, 78, 86, and 94, which can be designed according to the 72 stator slots, were found to be suitable. Among these 5 different rotor slot numbers, the design model with 94 rotor slots has the lowest torque ripple among other designs. Based on a literature review, it was determined that these slot numbers comply with the equations given in the rules to determine the appropriate stator/rotor slot combination. In addition, the increasing number of rotor slots shows improvement in terms of torque ripple and air gap magnetic flux density harmonic components. 
However, the determination of high number of slots according to the determined magnetic rotor core diameter may cause difficulties in terms of production and may cause the rotor bars to break during operation.