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Hibrid adım motorunun modellenmesi ve simülasyonu

Modelling and simulation of hybrid stepping motors

  1. Tez No: 14351
  2. Yazar: AYLİN TÜLAY USTA
  3. Danışmanlar: PROF.DR. TAMER KUTMAN
  4. Tez Türü: Yüksek Lisans
  5. Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1991
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 112

Özet

ÖZET Günümüzde dijital elektronikteki gelişmeler sayesinde, elektrik motorlarının kontrol sistemlerinde tahrik elemanı olarak kolaylıkla ve hassasiyetle kul lanılmalarına olanak sağlanmıştır. Klasik AC ve DC motorlar, büyük miktarda hareket gerektiren sistemlerde çok iyi sonuç alınmasını sağlarken, duyarlık gerektiren küçük hareketler için yeterince kullanışlı değildirler. Bunun nedenleri arasında tüm çalışma koşullarında bu motorların konumlarından geri besleme alınmasının gerekli olması ye sürülmelerinin ancak analog olması sayılabilir. Adım motorları ise, girişlerine uygulanan her hareket darbesi için sadece bir adım atmaları nedeniyle duyarlık konusunda büyük bir avantaja sahiptirler ve özellikle küçük miktarda hareket gerektiren hassas kont rol sistemlerinde güvenilirlikle kullanılırlar. Adım büyüklükleri sabit olduğundan ve uygun kontrol edildik lerinde attıkları adım sayısı, girişlerine uygulanan 'darbe sayısına eşit olduğundan, hareket miktarları kolay lıkla belirlenebilir, açık çevrim çalıştırılabilirler. Adım motorlarının performansı, kendi karakteris tik değerlerinden sonra tamamen s-ürücü devrelerine ve kontrol yöntemlerine bağlıdır. Bu yüzden adım motor1arı- nın uygun işaretler ve yöntemlerle sürülmeleri ve kontrol edilmeleri, motorlardan maksimum verim alınmasını sağlar. Bir adım motoruna uygulanacak optimal kontrol yönteminin belirlenebilmesi için ise, motorun matematiksel modelinin elde edilmesi gereklidir. Bu ayrıca, motorun bir kontrol sisteminde kullanılırken nasıl bir davranış göstereceği nin bilinmesi için de yararlıdır. Bu nedenle, bu tez çalışmasında en yaygın kul lanılan iki -fazlı bi-filar sargılı, 1.8° adım açılı hibrid adım motorunun dinamik davranışını en doğru şe kilde yansıtan bir matematiksel modelinin oluşturulmasına ve bu model yardımıyla adım motorunun bilgisayarda simü- lasyonuna çalışılmıştır. Bu si mül asyonun motorun gerçek davranışını ne derece yansıtığını belirleyebilmek için ise, motorun miline bağlanan bir encoder yardımıyla motorun tek adım cevabı incelenmiş, bu cevap, simülasyon sonuçlarıyla karşı laştırılmıştır.

Özet (Çeviri)

SUMMARY Modelling and Simulation o-f Hybrid Stepping Motors Accurate positioning is one o-f the most important problems in position control systems. As an actuator, DC or AC motor is widely used when the settling points are ?far -from the starting points, but if the positioning requires very small movements, conventional motors capabilities.fail. Accurate positioning with very small movements have been achieved a-fter the development o-f the stepping motors. Stepping motors are electromagnetic incremental motion actuators which convert digital pulse inputs to analog output motion. Stepping motors are devices which, when energized by a voltage and current input, move in given angular or linear increments. When properly controlled, the output steps o-f a step motor are always equal in number to the number o-f inputs pulses. Each pulse advances the rotor sha-ft one step increment and latches it magnetically at the precise point to which it is stepped. The devices have been in ex i stance at least 50 years. Step motors are inherently low-e-f -f iciency electromagnetic energy converti on devices when compared wiht conventional AC and DC motors. But, since they can use digital input pulses, they are widely used in numerical control systems, computer peripheral equipments; such as printers, plotters, disk drivers, etc., process control systems, CMC machine tools and robots. Types o-f stepping motors 8 Al thought there is a wide range o-f stepping motor designs, most motors can be identified as variation on the two basic types; variable reluctance (VR) or hybrid. VR step motors also have two typess the multi- stack VR and the single-stack VR motors. These motors VIhave magnetic -field which is produced solely by the winding currents. For the hybrid motor the main source of magnetic -flux is a permanent magnet and DC currents.flowing in one or more windings direct the -flux along alternative paths. In both types of step motors accurate positioning o-f the rotor is generally achieved by magnetic allignment o-f the iron teeth on the stationary and rotating parts o-f the motor. Hybrid motors have a small step length (typically 1. S° ), which can be great advantage when high resolution angular positioning is required. The torque producing capability o-f the hybrid motors arm generally greater than the VR motors, so the hybrid motor is a natural choice -for applications requiring a small step length and high torque in a restricted working space. When the windings o-f the hybrid motor are unex cited the magnetic ?flux produces a small“detent torque”which retains the rotor at the step position. This can be a use-ful -feature in applications where the rotor position must be preserved during a power -failure. In VR step motors, step lengths (typically 15°) are longer than in the hybrid type so less steps are required to move a given distance. A reduction in the number of steps implies less excitation changes, and the speed o-f motor improves. The VR step motor has a lower rotor mechanical inertia than the hybrid type, because there is no permanent-magnet on its rotor. The need o-f mathematical model -for the hybrid motors s In recent years, hybrid stepping motors have become predominant in many applications that require incremental motion control. The increased applications o-f hybrid stepping motors, as integral components o-f high performance incremental motion control systems, has prompted e-f -forts to produce a mathematical model capable o-f predicting reliably the dynamic performance of such machines. While approximate analysis can be useful for indicating the general trends in dynamic behaviour, there is a need for a model of the hybrid motor capable of representing accurately the electromagnetic conditions existing with in the machine at all practical levels of excitation. The reliable prediction of the important dynamic characteristics of the motor necessitates a precise representation of the flux- linkage data. A good example is single step damping, which can be predicted satisfactorily only if the current disturbance and associated power loss in each stator circuit are calculated correctly. This requires that the rate of change of flux linkage be defined accural ety for any combination of system variables. VI ıI. E. D. PICKUP and A.P.RUSSEL have proposed a mathematical model -for the hybrid stepping motor in İ9S0 on this thesis has been based.“' The measurement of the motor parameters, which are used in this model, has been the first step in this work. The simulation results o-f the transient state -for a single step response have been achieved using these parameters. The experimental results have been obtained by using a driver circuitry which has been designed according to the inputs in the model. Description o-f the hybrid stepping motor s Figure 1 illustrates the construction o-f the hybrid motor. The stator has eight salient poles which are wound with a 2 phase, 4 pole winding. The rotor is constructed o-f two stacks, each having 50 equally spaced teeth, separated by an axially magnetised permanent magnet. The path o-f the homopol ar permanent magnet -flux is indicated in -figure l.a. Permanent Permanent rooQnet ^- Stotor Stotor (a) (d) Figure 1. Cross section o-f hybrid stepping motor (a) Paralel to the rotor sha-ft dt where iAo is the current di-fference iA _ tC. Now, the.four first order di-f -fer ant i al equations describing the system dynamics asş, du;/dt = 1/3 j”< T + T(iBO,85 - Kv-u; - Tl - x> vB Vd ı bd' r u>- (6) J s moment of inertia, Ks, s coefficient o-f viscous -friction, Tı_ s load torque 5 instantaneous angular velocity o-f rotor, ii =Xt-cos(p-9) + ^2cos2-(p-e) (10) where; Ai = 100.06*10-“* Weber >^ = -1.08*10-* Weber By this -function, average discepancy per experimental point o-f 0.44*10-* Weber which is comparable with with the eKperimental accuracy o-f measurement. Current dependent linkage o-f phase A was measured by using the bi -filar wound coils o-f phase C as a closely coupled search coil connected to a -flux meter. Because o-f the equal numbers of turns on phases A and C this arrangment gives a direct reading of the flux linkage changes which occur in phase A. Initially the rotor and stator were set up in the reference position, (p 0=0°) A positive current of 0.15 A was switched on in phase A and the associated change in.flux linkage was recorded on the -flux meter connected to the bi -filar winding. The current dependent flux linkage at other positions of rotor relative to stator was obtained in a similar manner» The complete test was then repeated for several different values of phase current. A general expression -for the flux linkage -for Aa(İaciÖ) must be an odd function of iAc and be symmetrical in p 6-=0° and p 0=100° as; k r =0 L r= cosr.(p-©)| (11) The optimum values of the j and k can be determined using an adapted version of the least square error method, as j=7 and k=2. The flux linkages for negatif values of i«c in phase A (which is equivalent to positive current in phase C) are obtained by substituting the appropriate iAC into equation (11) and replacing p Ö by p 0-tt. Simulation t By using the mathematical representation of the.flux linkage which are determined from experiments, with the mathematical model and solving this di -f f eranti al XIequation system by Kutta-Simpson -formulas, the single step response of stepping motor can be find. On -figure 2 a single step response o-f the hybrid motor which is obtain with simulation of one phase excited may be seen. tet (ongie) 3.6”İ.8 JL r\ i \ i \ A A A A /. '?-..-..?.-. V V V v v ^ 1Ü 30 40 50 70 m ioo t glt) W i \ *n İ.8 10 20 30 40 m 70 90 103 t (as) Figure 4. Single step response o-f the step motor 5-il 1 1

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