Değmesiz ulaşım sistemlerinde elektromagnetler ile magnetik asılım

Abstract

Bu çalışmada Degmesiz Ulaşım sistemlerinde aracın magnetik asılı mı nda kullanılan elektromagnetler incelen miştir, önce basitleştirilmiş bir magnet incelemesi yapıldıktan sonra kenar etki-leri incelenmiş ve örnek olarak bir elektromagnetin akı dağılımı sonlu elemanlar yöntemi ile bulunmuştur. Aracın hareketi durumunda rayda endüklenen girdap akımlarının etkilerinin incelenmesi yapılmıştır. Daha sonra dinamik magnet modeli ve asılımı kararlı yapan basit bir denetim kuralı verilmiştir.

The concept and basic technology for magnetic levitation and propulsion has existed for many decades. The practical application of this technology for trans portation system has been pursued on a significant scale since the beginning of seventies. There are several possibilities for magnetic levitation. One of them is electromagnetic levitation. Electromagnetic levetation uses the attractive force between a dc magnet and an armature rail. The electromagnets for noncontact suspension and guidance are mounted in the vehicle, the armature rails are implanted in the guideway. Electromagnetic levitation systems are unstable without control. An electromagnet energized with a constant current will either clamp to the rail or fall because the attractive force decreas with increasing air gap. Hence a control system is required to control the current to the magnet as a function of the air gap. In Chapter £ simple best -case calculations for an electromagnet are given. A typical U core electromagnet is considered. It is assumed that there is neglible iron reluctance and no fringing effete. Ideal attraction force is B2 CNID2 F=- P1= »0 £ P1 'o -v- The power dissipation in the winding and the magnet weight are calculated. In order to predict power/force and force/weight ratios,it is made some assumptions about the mode of operation of the magnets. The flux density in the iron is taken to be IT. This makes efficient use of the iron and places the operating point on a steep portion of the core magnetisation curve. Thus it is allowed stabilization of attactive magnetic suspensions with small control current. Considerations of the economy of guideway materials necessitate long narrow magnets. A major practical limitation in magnet operation is the current density in the windings. For copper windings J =10 A/m has been used as the maximum current density achievable without a forced cooling system. For aluminum windings, a current density of 5 2 J=8-10 A/m has been used in order to maintain the same power density. In general, the power /force ratio is low and does not limit the operation of the controlled electromagnet i cally suspended vehicles. Electromagnetic suspensions are limited primarily by their force/weight ratio. Clearly this must be greater than unity, and a value of at least 5 is desirable for an appreciable payload. There is an advantage in using aluminum windings rather than copper windigs to reduce magnet weight. By increasing current density in the magnet windings may be essential to produce acceptable force/weight ratios at moderate air gaps. However, a current density above 10 A/m would necessitate forced cooling of the magnets. Due to these restrictions suspention systems with vehicle-borne iron- cored electromagnets appear to be limited to maximum clearance of 10-20 mm and must be opareted close to minimum clearance dictated by guideway roughness and passanger comfort specif i cat i ons. As a concl us i on -vi- power /force ratios are low, however the practical engineering restrictions of conductor current denstity, magnetic flux density in iron and magnet size result in poor force/weight ratios and limit operation to low suspension clearance. Corner effects are analysed using conform transformation in Chapter 3. The problem is reduced one- or two-corner problem under the assumption the pole surface are so close to rail that the field in -the air gap is uniform in some interval between corners. Lift and side forces are also calculated. In Chapter 4 flux distribution of an electromagnet are given. It assumed that magnet is so long that the entry end exit end corner effects is negligible. Thus the field can be considered in two dimension The differential equation describing magnetic field is -V- VA = tu J Ur J ° Here A is. vector potential, J is current density." To solve this equation f i nete element method is employed. An analysis of eddy current induced by the magnetic fields of the - electromagnets in the rail is.made in Chapter S. Eddy current weakens the field, particularly near the leading end of the magnet, and decreas the attracting force as the magnet speed becomes higher. Eddy current also generates drag. Ahalitical solutions of the field equations are derived.The equation given below can -vi i - be written for the magnetic field within air gap of an electromagnet moving x-di recti on. d2B d2B SB !d2B d2B dB L + 1 _ k -± = * + î - K -. ax2 dz2 dx 9x2 âz2 ax Here B, B is induced and excited compenent of the flux r © density. It is assumed that the excited compenent B is constant in the air gap and has no fringing. Then B is expressed by step functions and extented to Fouier series for z-di recti on. The equation is solved by separating variables. The calculated field distribution shows that eddy current in the rail weakens the excited field near entry end and in the middle of the witdh of the air gap. The formulas for caltulating attracting and drag forces are also obtained. Speed characteristics of the magnet, such as attracting force versus speed curves, drag versus speed curves, are calculated. It is shown how parameters, such as magnet lenght, rail thickness, etc., affect the speed characteristics of the magnet. When the length of the magnet is short, the attracting force decreases considerably at higher speed. Longer length reduces the drag. Larger rail thickness decreases attracting force more at higher speed. Dynamic magnet models and a simple control scheme are given in Chapter 6. An analysis of the dynamic behavior of the magnet is particularly important since it is "a part of the controlled system. The voltage and force equation ~ ~- -vi 1 1 - dyj u = R-iC*,<5D + - dt f l= fCi,<5D are taken as the basis for the model. The input quan tities are voltage and air gap, the output quantities are force and current. The relations between current i, flux linkage y, and air gap & and force f, current and air gap, which are contained in the voltage and force equation, can be determined with numerical field calcula tion and can be expressed approximated anal i tic functions For the investigation of processes in the vicinities of the working point, a linear approximation is sufficient. The equation describing the vertical motion of a singel suspended magnet m z = f, - f 1 m 6 = z - z r m where z, z : vertical distance from a" absolute m r referance to magnet and rail m : mass of singel magnet plus load f. : vertical disturbance force f : vertical force produced by magnet Linearizing these equation in the vicinity of working point and solving for the air gap yields Cs+k.İ>s2 Az Cs3 - Cs+kö/m f/CsD -k. AuCsZ) AÖCsD = 1 L : -1 1 ±__ s3 + klS2 - k2s - k3 -IX- This system is unstable as indicated by the change in sign of the coefficient of the characteristic equation Various method for stabilizing this system are possible. Letting the magnet voltage be a linear combination C possibly frequency dependent? of several variables,, e.g., air gap, magnet current, acceleration, or velocity, allows one to completely specify the closed loop characteristic equation. A contol law requiring the derivative of a variable should be avoided since excessive noise will be introduced. Using feedback only from the air gap and the magnet acceleration a control law can be derived as follow K s K T Au = K AS + - - A6 - - - Az - K A z ^ Ts+1 Ts+1 -x- BöLUM 1 GÎRIS Yol ile araç arasındaki tahrik, taşıma ve yöneltme kuvveti aktarımının değme olmaksızın yapıldığı yol yöneltimli ulaşım sistemleri Değmesi z Ulaşım olarak adlandırılır. Değmesi z ulaşım sistemleri 70*1 i yılların başlangıcından beri geliştirilmektedir. Hem 500 km/h* ye kadar yüksek hız ulaşımı hem de düşük hız kenti çi ve yakın ulaşımda uygulama alanı bulunan değmesi z ulaşım sistemlerinin yol yöneltimli ulaşımda bir çok kazanç sağlayacağını yapılan araştırmalar göstermektedir [13-C43. Tahrik kuvveti lineer maki nal ar ile üretilen değme- siz ulaşım sistemlerinde aracın yola değmeden hareketini sağlamak için yoldan yükseltilip belirli bir yükseklikte taşınması ve yol yörüngesini izlemesi için yönlendi r- dirilrnesi gerekmektedir. Taşıma ve yönlendirmede de magnetik düzenlerden yararlanır. Magnetik taşıma ve yönlendirme yerine bundan sonra Magnetik Asılım terimi k ul 1 anı 1 acak 1 1 r. Bu tez çalışmasında magnetik asılımda kullanılan çekme ilkesine dayalı elektromagnetler incelenmiştir. Araç üzerinde bulunan magnet ile yola saptanmış ferromagnetik ray arasındaki çekme kuvveti asılımı gerçekleştirir.