Üniversal motorun sonlu elemanlar yöntemi ile magnetik alan incelemesi
Magnetic field analysis of an universal motor buy finite elements method
- Tez No: 75394
- Danışmanlar: PROF. DR. R. NEJAT TUNÇAY
- Tez Türü: Yüksek Lisans
- Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1998
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Elektrik Mühendisliği Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 117
Özet
ÖZET Bu tez çalışmasında 1000 W, 220 V, 18.000 d/d nominal değerlere sahip kuru ıslak bir elektrik süpürgesine ait üniversal motorun, iki boyutlu kartezyen koordinatlarda magnetik alan incelemesi sonlu elemanlar yöntemi ile yapılmıştır. Tezde ilk olarak üniversal motorun çalışma prensibi ve üniversal motora ait karakteristikler anlatılmıştır. Üniversal motorlar doğru akımda doğru akım motoru, alternatif akımda tek fazlı kollektörlü alternatif motor karakteristiklerini gösteren elektrik motorlarıdır. Her iki işletmede de seri karakteristik gösterirler başka bir deyişle ürettikleri moment her hızda değişik ve hızla ters orantılıdır. Çok yüksek hızlara çıkabildiklerinden düşük güçlerde imal edilirler. Bu durum elektrik süpürgesi, mutfak robotları gibi ev uygulamalarında ideal bir durum oluşturur. Bu yüzden tek başlarına ticari olarak satılmayıp daha çok elektrikli ev aletlerinin bir parçası olarak piyasada yer alırlar. Magnetik alan teorisi, elektrik makinalarının çalışma prensibinin dayandığı temeldir. Bu nedenle elektrik makinasına ait magnetik alan incelemesi makinanın davranışını anlamada ve performansını geliştirmede büyük rol oynar, tasarımın temelini oluşturur. Magnetik alan incelemelerinde karşılaşılan Laplace ve Poisson gibi ikinci dereceden diferansiyel denklemlerin çözümü analitik olarak çok zor, bazende imkansızdır. Bunun üstesinden gelmek için birçok sayısal yöntem geliştirilmiştir. Bunların arasında hem kolaylığı hem de doğruluğu bakımından sonlu elemanlar yöntemi günümüzde üzerinde en çok uğraşılan sayısal yöntemdir. Sonlu elemanlar yönteminin temeli, magnetik enerjiyi minimum yapan magnetik vektör potansiyeli A'nın aynı zamanda Laplace ve Poisson denklemini sağlayan değer olduğudur. Sonlu elemanlar yöntemi, incelenecek bölgenin sonlu küçük geometrik şekillere (üçgen, dörtgen, çokgen) bölünerek, her şekilde (eleman) alanın sürekli olduğu göz önüne alınarak tüm bölge için bir alan ifadesi bulmaktır. Bunu gerçekleştirmek için vektör potansiyele her eleman için bir yaklaşım polinomu belirlenir. Bu polinoma ait katsayıların bulunması ile elemanlar birleştirilir ve tüm bölge için çözüm bulunur. Polinom derecesini artırmak ile çözüm gerçek değere yaklaşır fakat çözüm süresi çok uzar. Çözümün vektör potansiyelini bulmaya yönelik oluşunun en büyük nedeni potansiyelin iki boyutlu x ve y koordinatlarında sadece z yönünde bileşeni oluşu ve böylece bilinmeyen sayısının en az yapılmasıdır. Tez çalışmasında son olarak sonlu elemanlar paket programı ile magnetik incelemesi yapılmış üniversal motora ait sonuçlar gözlenmiş ve yorumlanmıştır. Motor tasarımında önemli rol oynayan endüktans, magnetik akı, magnetik akı yoğunluğu, moment değerleri hesaplanmıştır. Bu değerler daha sonra kontrol için deney sonuçlan ile karşılaştırılmıştır. Ayrıca bu sonuçlara bakılarak tasarımcı optimum ampersarıma, sac kullanımına yöneltililebilir. Bu değerler tasarımda tasarımıncının başvuracağı en önemli değerler olacağından sonlu elemanlar yöntemi artık tasarımın parçası olmuştur. xu
Özet (Çeviri)
SUMMARY MAGNETIC FIELD ANALYSIS OF AN UNIVERSAL MOTOR BY FINITE ELEMENTS METHOD The aim in this master thesis is, to examine the magnetic field of an universal motor by finite elements method (FEM) in two dimensional cartesian coordinates and to evaluate the results. The analized motor in the thesis is produced by Senur A.Ş. as the motor of wet-dry type vacuum cleaner and its two dimensional geometry is shown in figure 1. In order to reach the aim, the subjects have been mentioned in the following sequence; 1. Universal motors have been introduced and the description of their characteristics have been given. 2. General concepts of magnetic field theory have been discussed. 3. Static and dynamic magnetic field analysis with finite element method in two dimensional cartesian coordinates have been explained. 4. General structure of Computer Aided Design (CAD) packet programs for finite elements method has been described. 5. Magnet 5.2 finite elements packet program has been introduced. 6. The examination of magnetic field analysis has been achieved by Magnet 5.2 packet program and the results have been evaluated. / ( ) ( ; O / /'( \ V rJ I C^-,\>\ W tip' Ao :B ) '--XiT; A< V Kİ M fco- ^o ( ) ( ) ry Figure 1 The cross section of the analized motor. XHlThe name universal for the motor comes from the ability to operate on both direct and alternating current. They are characterized by their ability to operate, with substantially the same performance, on direct as well as alternating current of frequencies up to 60 Hz. These motors are series wound and have series characteristics on both direct and alternating current. No load speeds are high, sometimes well over 20.000 rpm, but the armatures are designed so that they will not be damaged at these speeds. They are usually designed for full load operating speeds of 4.000 to 16.000 in larger power ratings, and up to 20.000 or more in smaller power ratings. At the higher speeds better universal characteristics, that is nearly the same performance characteristics on both direct and alternating current, can be obtained. Universal motors are generally custom-built for a specific application and are very often sold as parts rather than as complete motors. Very popular applications for universal motors include portable drills, saws, vacuum cleaners, sewing machines, food mixers, blenders, and many other household appliances. There used to be two major types of universal motors, noncompansated and compansated, but the latter has now all but disappeared. The noncompansated motor usually is built with concentrated or salient poles. The speed-torque characteristic of a noncompansaetd motor is given in figure 2. Similar speed-torque curves for a compansated motor are given in figure 3. It is to be noted that the compansated universal motor has better universal characteristics than the noncompansated universal motor. The noncompansated motor is less expensive and simpler in costruction so it is more generally used for these reasons. Figure 2 Speed-torque characteristic of a noncompansated motor It is to be noted that with either type, the speed drops o IT rapidly with an increase in load and increases with a decrease in load. Phis characteristic is most desirable in vacuum cleaner, for if the cleaner is used under conditions which decrease the volume of air handled, the load on the motor decreases. This decrease in motor load is accompanied by increased motor speed and increased vacuum, so that the xivcleaner will actually handle more air than it would if a constant motor were used. Likewise, this characteristic of speeding up on light loads is very desirable in the case of portable drills, for the motor will drive small drills at high speed and larger drills at a lower speed. b B O 12 14 16 18 Torque, oı-f t Figure 3 Speed-torque characteristics of a compansated motor Magnetic field theory forms the basic principle of the operation of electrical machines. For this reason, the examination of magnetic field of an electrical machine helps to understand the behaviour and the performance characteristics of the machine. Maxwell equations, which are introduced in chapter 3 in the thesis, are the basic equations in magnetic field theory. Laplace and Poisson type partial differential equations are derived from Maxwell equations and they describe the behaviour of static fields. d2A d2A - r + - r = 0 dx~ dy~ Laplace equation (D d2A 32A + -^-r = uJ Poisson equation ox2 dy2 (2) These types of differential equations are named Boundary Value Problems and are solved according to the boundary conditions of the field. Mostly the analytic solution approach is impossible to solve these equations whereas the numerical analysis can easily handle the problem. For this reason there are many numerical methods improved to overcome the solution difficulties. Todays most advanced and easiest method is the Finite Elements Method on which many studies were made. The basic idea of finite elements method is, to find the values of potentials that are the solutions of Laplace and Poisson equations, by minimizing the energy in the magnetic circuit. So the solution is, to find electrical scalar potential V in electrostatic problems and magnetic vectoral potential A in magnetic field problems. Magnetic vectoral potential A has only z component in two dimensional x and y coordinates like the current density and it is defined as the curl of magnetic flux density B. For these reasons, the number of unknowns in the problem can be reduced if the solutions are directed toward to find A values in the magnetic field problems.Finite elements method can be summarized in the following steps; 1. The discretization of the region by finite elements, generation of mesh. 2. To obtain matrix values of each element. 3. The combination of all elements and the solution of the equations. The first thing to do is, to choose the shape of the finite element. In one dimensional problems a line, in two dimensional problems triangle, rectangle, in three dimensional problems cube, prism, rectangular prism, tetrahedrals can be chosen. The corners of the element are named as 'node' and each node and element are given a number for identification. The mesh generation is achieved by the discretization of the region by finite elements. There exists many improved techniques in packet programs to form fine meshes, the tecnique used in Magnet 5.2 is the Delaunay tecnique which has been explained in chapter 6 in thesis. Figure 4. Mesh generation by Delaunay technique To obtain the values of vectoral potential A on the nodes, an approximation function is assigned to vectoral potential. So A, is assumed to change in the element as a function of coordinates. This function can be first order or higher order polynominal function. The first order approximation functions of A in cartesian coordinates; In one dimensional problem : A=a+bx In two dimensional problem : A=a+bx+cy In three dimensional problem : A=a+bx+cy+dz (Second order polynominal in two dimensional problem : A=a+bx+cy+dx2+cy2+fxy) The higher order polynominal functions can be obtained by increasing Ihc node number of an element. The accuracy of solution becomes better as the order of polynominal increases. To assign a first order polynominal means the potential changes in the element linearly, thus the magnetic flux density is constant everywhere in the element. From these coefficients of x and y in polynominal equations in the element, an cofficient matrix is found for each element. The next step is the combination of elements and formation of global nodes of mesh. The coefficient matrix of each element is combined to form global coefficient matrix (Stiffness matrix). Derivating the magnetic energy and equating to zero cause an equation group to appear. These equations, which are linear or nonlinear related to the problem type, can be solved by many mathematical methods. The next step in the thesis is, the introduction of finite elements program used in the analysis of the universal motor. The program named Magnet 5.2 can solve electrostatic, magnetostatic and time harmonic, axisymmetric problems in two xvidimensional cartesian or cylinderical coordinates. It has two main parts; FastTrack and Toolbox. FastTrack is for the novice user who has a little knowledge about CAD programs and finite elements. It has three modules which are activited in sequence: The Describe module, The Solve module and The Post module. Describe module allows the user to draw the device, assign materials to regions and specify coils which form part of a circuit containing current or voltage sources. The result is a complete description of the problem ready for the Solve module, which generates the finite element mesh automatically and then solves the field equations for the required potential function. In Magnet 5.2 an adaptive solution is made where the solver automatically refines the mesh until a specified error criterion is satisfied. This is explained in chapter 6 in the thesis. The solution generated by Solve is passed to the post processor module Post which allows the user to inspect and display field quantities such as flux density and permeability, and to calculate global quantities such as energy, force and inductance. Toolbox is for the advanced user who has experience in Magnetics and CAD programs. Toolbox gives the user total control over all phases of the analysis: Geometric description, finite element mesh generation, problem description ( material properties and excitations), solution and post processing. The user can create macros, known as User Defined Verbs to control the operation of the modules. The final part of thesis consists of the anaysis results of the universal motor. First only the stator windings have been excited with 5A full load current in the simulation to find the magnetic flux values per pole and the stator self inductance and these results have been compared to the experimental results. Then both rotor and stator windings have been excited without brush shift to see the armature reaction. Next, for the full load condition in 5A, the brushes have been shifted to magnetic neutral axis and the torque of the motor has been calculated, also the flux lines, magnetic flux density distribution, permeability distribution outputs have been obtained. The same simulations have been achieved for alternating current. 3A no load condition results both for DC and AC have been shown in Appendix A. Also graphical outputs of absolute value of magnetic flux density B in the air gap can be examined in Appendix B. xvn
Benzer Tezler
- Çamaşır makinesi uygulaması için konsantre sargılı mıknatıs destekli senkron relüktans motor tasarımı, üretimi ve doğrulaması
Design, manufacturing and verification of a concentrated winding magnet assisted synchronous reluctance motor for washing machine application
ÖMER FARUK PAYZA
Yüksek Lisans
Türkçe
2018
Mekatronik MühendisliğiKocaeli ÜniversitesiMekatronik Mühendisliği Ana Bilim Dalı
DOÇ. DR. METİN AYDIN
- Cogging torque and performance optimization of an interior permanent magnet synchronous motor used in commercial washing machines
Ticari çamaşır makinelerinde kullanılan gömülü daimi mıknatıslı senkron motorların tutunma momenti ve performans en uygunlaştırması
EGE ÜNLÜTEPE KESKİN
Yüksek Lisans
İngilizce
2021
Elektrik ve Elektronik Mühendisliğiİstanbul Teknik ÜniversitesiElektrik Mühendisliği Ana Bilim Dalı
DOÇ. DR. DERYA AHMET KOCABAŞ
- Çok disiplinli yaklaşımla katı yakıtlı roket motoru yapısal dayanım ve iç balistik performans optimizasyonu
A multidisciplinary approach in optimization of a solid rocket motor for structural strength and internal ballistic performance
CEYHUN TOLA
Doktora
Türkçe
2017
Uçak Mühendisliğiİstanbul Teknik ÜniversitesiUçak ve Uzay Mühendisliği Ana Bilim Dalı
PROF. DR. MELİKE NİKBAY
- Üniversal motorun benzetişim ve tasarımı
The Simulation and design methods of universal motor
MURAT YILMAZ
Yüksek Lisans
Türkçe
1999
Elektrik ve Elektronik Mühendisliğiİstanbul Teknik ÜniversitesiElektrik Mühendisliği Ana Bilim Dalı
PROF. DR. R. NEJAT TUNCAY
- Modeling and forced vibrations for a universal electric motor
Üniversal elektrik motorunun zorlanmış titreşimlerinin sayısal modelinin kurulması
CİHAN ORHAN
Yüksek Lisans
İngilizce
2011
Makine Mühendisliğiİstanbul Teknik ÜniversitesiMakine Mühendisliği Bölümü
PROF. DR. KENAN YÜCE ŞANLITÜRK