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An Improved Performance Analysis of a Shaded Pole Motor

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An Improved Performance Analysis of a Shaded Pole Motor View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by UGD Academic Repository AN IMPROVED PERFORMANCE ANALYSIS OF A SHADED POLE MOTOR Vasilija Sarac, Lidija Petkovska, Milan Cundev "Sts. Cyril & Methodius" University Faculty of Electrical Engineering, P.O.Box 574, 1000 Skopje, Macedonia e-mail: [email protected] Abstract: In this paper a methodology for an im- 2. Physical Model of the Shaded-pole Motor proved performance analysis of the shaded pole mo- tor is presented. They are used different approaches The rated data of the shaded pole motor which is to the computation of the motor characteristics. By going to be analyzed are: 220 [V] voltage supply, using them, a complex analysis of the single phase 24 [W] input power, 2200 rpm speed and 2p=2 shaded-pole motor is presented. On the basis of the number of poles. The authors suggest a method- resolving field theory, a circuit model of the motor is derived. The FEM model of the motor is also devel- ology for an improved and deepened perform- oped. By using the Finite Element Method, a set of ance analysis of the shaded pole motor. The calculations is carried out and the distribution of the cross section of the motor is presented in Fig. 1. magnetic flux density in the air gap is obtained. The shaded-pole motor under consideration is studied 1 3 experimentally, too. The obtained results, are mutually compared. A special emphasis is given to the investi- gation of the shading portion of the pole and on its effect on the motor performance characteristics. 2 1. Introduction The development of automatic control devices, robotics and computer techniques recently, as well as different appliances, has caused an ap- Fig. 1. Cross-section of the shaded pole motor pearance and an expansion of special different types of fractional horsepower motors (micro- The first winding is the main stator winding (1) motors) with enormous possibilities for their ap- and the second one is the bar squirrel cage rotor plications, hence, interesting for research. A de- winding (2); the third winding is the auxiliary sta- sign and a performance analysis of these motors tor winding with one shading coil per pole (3). are considerably different from the design and the performance of the classic ones, although One pole pitch of the shaded pole motor, in the their operation bases on the same principles of developed view, is presented in Fig. 2. the electromechanical energy conversion. One of π these particular motors is the shaded-pole motor which appertains to the class of the asymmetrical single-phase induction motors. θ θ m s • × I1 The shaded pole motor is well recognized as simple in construction but complicated for an • analysis. Compared to other types of induction • × I3 motors, the shaded-pole motor is more compli- cated by the fact that there exist three mutually Fig. 2. Developed view of motor pole pitch coupled windings and an asymmetrical elliptic rotating magnetic field. The application of exact The pole of the motor is spanned to an angle of π analytical methods is almost improper. Many au- radians. The angle θs is the angle of shaded pole thors over the past made a lot of research efforts arc in the electrical radians, meaning the shading [1] for an analysis and the design of this motor. pole portion. The angle θm is the angle of the rest But, so far, it has not been established an univer- of the pole pitch, considering the unshaded part sal method of analysis [2]-[5]. of the pole arc in electrical radians, too. The common effect of the main stator winding The current in the main stator winding is: and the shading coil to the rotor circuit is equiva- = U lent to that when the first (main) winding only is I1 (3) ZZRjXX+++( '' +2 ) carrying the current Is = I1 - I3, where, I1 and I3 are mt 1 4 the main stator winding current and the shading coil current in primary terms, respectively. where: U = 220 [V] is the voltage supply; R is the main stator winding resistance. 3. Circuit Model of the Shaded-pole Motor According to the circuit model of the motor, the following impedances are introduced: Starting from the elliptic character of the rotating 1 Z = ()Z + + Z − (4) field, the modeling of shaded pole motor is car- m 2 1 1 ried out according to the revolving field theory. By ' coupling the phenomena caused by the forward = − j C1 ()− Zt Z1+ Z1− (5) and backward components of the magnetic field 2 C1 in the air-gap [1], the common equivalent circuit is derived in the form presented in Fig. 3. R jX 1 + jX' m1 1− S 1 Z = (6) 1+ R 1 ++jX( ' X ) 1− S 11m R jX 1 + jX" m1 1+ S 1 Z = (7) 1− R 1 + j()X" + X 1+ S 1 m1 Where the variable S is the ratio of actual rotor speed n to synchronous speed of the rotating fundamental flux wave ns . Considering that the rotor slip s is expressed by these quantities, as: Fig. 3. Equivalent circuit of the shaded pole motor − based on the revolving field theory ns n s = ns Note that the signs "+" and "-" are used for the the following equations are obvious: forward and backward sequence components, respectively; although both currents and imped- s+ = s = 1− S ances are not specially marked, they are com- prehended as complex quantities. s− = 2 − s = 1+ S According to the revolving field theory the forward In equations (6) and (7) R1 is the rotor resistance and the backward components of the auxiliary and Xm1 is the mutual reactance between the circuit currents are calculated as follows: main stator winding and the short circuit coil. There are four types of stator leakage reac- ' 1 C tances. The first one is the leakage reactance I = ()I − I 1 − jI (1) 1+ 1 3 1 X ' , due to the leakage flux linked with the stator 2 C1 1 coil only, which is going to be calculated as: ' 1 C = ()− 1 + 3,19W + span1 + I1− I1 I3 jI1 (2) Ks1 2 C1 − 2p 2p X' = 2πfC210 8 ⋅ − X (8) 1 3,19Wλ θ m1 + p ⋅ m = ()θ π where: C1 C sin m 2 is the effective number 4lg p of conductors of the main stator winding; Where: W is a length of the core stack; ' = ()θ C1 C sin s 2 is the effective number K s1 is a primary winding slot constant; of conductors of shading coil, i.e. the λ is the pole pitch; auxiliary stator winding; p while, C is the actual number of the main l g is an effective length of the air gap; stator winding conductors. p is the number of poles. ' Where: S is the number of rotor conductors; The second one is leakage reactance X2 , due to s the leakage flux linked with the shading coil only, K s is a rotor slot constant; θ calculated as: sk is an angle of the rotor slots skew; '' ' 2 −8 3,19W span Tf is a width of the rotor tooth face. X = 2πfC 10 ⋅K + 2 (9) 2 4p s2 2p The shading coil current is calculated from: In this case: K is a shading coil slot constant; s2 − = Za Zt span2 is a coil span of shading coil. I3 I1 (17) Z + Z + j()X ' + 2X ' s a 3 4 The third component links the leakage fluxes be- In the above equation, Ra is the shading ring tween the main winding coil and shading ring resistance, and the following impedances are placed on the same pole. introduced: 2 ' = + ( ' − ' ) − 3,19Wλ θ C Za Ra j X 2 X 4 (18) X' = 2πfC210 8 p ⋅ s − X ⋅ 1 (10) 3 π m1 4plg C1 2 ' C1 Z = ()Z + + Z − (19) ' s 1 1 The stator leakage reactance X 4 , linking one C1 shading coil with two stator coils (placed on a pair The static electromagnetic torque is calculated of poles), is calculated as: from the circuit parameters, as follows: ' 2 −8 3,19W d1 X = 2πfC 10 ⋅ (11) 9,55 2 2 4 M = I R − I R 4p e1 em 1+ 1+ 1− 1− (20) n1 where, e1 is the slot opening between adjacent In the equation (20), the currents I1+ and I1− are poles and d1 is the depth of the slot opening. calculated from the equations (1) and (2); R1+ and R are the resistive components of Z and The circuit model of shaded-pole motor is de- 1− 1+ scribed by the rotor parameters included in the Z1− previously given by the equations (6) and (7), equivalent circuit, too. The rotor leakage reac- respectively. '' tance X1 is calculated as a sum: Power factor is calculated as: '' = '' + '' + '' + '' X1 X1slot X1end X1skew X1zigzag (12) I cos ϕ = 1 (21) The particular components are: the slot reac- I1 " " tance X1slot , the end regions reactance X1end , Input power is determined from, " = ϕ the reactance due to the slot skewing X1skew and P1 UI1 cos (22) the "zigzag" reactance X"1zigzag , known as teeth while output power on the motor shaft is given by leakage reactance. The corresponding equations ()1− s n M for their calculation are given below: P = s em (23) 2 p% 9,55 ⋅1+ '' = π 2 −8 6,38W ⋅ 100 X1slot 2 fC1 10 Ks (13) S s considering that mechanical losses of the motor usually are p%=15-25% of the output power. λ '' = π 2 −8 ⋅ p X1end 2 fC1 10 (14) 2p Output torque on the motor shaft is calculated θ from the expression: λ sin sk '' 2 −8 0,647W p 9,55P X = 2πfC 10 ⋅1− 2 (15) M = 2 (24) 1skew 1 θ 2 ()− lg p sk ns 1 s 2 and the efficiency factor is calculated as: '' − 6,38W T '' = π 2 8 ⋅ f P2 X1zigzag 2 fC1 10 (16) η = (25) S 4l s g P1 4.
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