details about rotating magnetic field related with electrical machine

1. Rotating Magnetic Field
EI-DEPT, SRMCEM, LUCKNOW 1
2) INTRODUCTION
Rotating magnetic field can be defined as field or flux having constant amplitude but whose axis
rotates in a plane at a certain speed .e.g. Permanent magnet rotating in a space produces a rotating
magnetic field .similarly if an arrangement made to rotate the poles, with constant excitation
supplied, the resulting magnetic field is rotating magnetic field .so a field produces in a air gap of a
rotating field type alternator is of rotating type. But this is all about production of r.m.f.by
physically rotating poles or magnet .in practice such a rotating magnetic field can be produced by
exciting a set of stationary coils or windings with the help of polyphase A.C. supply .this resultant
flux produces in such a case has constant magnitude and its axis rotates in a space without
physically rotating the windings. [1]
A rotating magnetic field is a magnetic field that has a moving polarities in which its opposite poles
rotate about a central point or axis. Ideally the rotation changes direction at a constant angular rate.
This is a key principle in the operation of the alternating-current motor. [2]
Rotating magnetic fields are often utilized for electromechanical applications such as induction
motors and electric generators; however they are also used in purely electrical applications such as
induction regulators. [1]
3) FIGURE DESCRIPTION
FIGURE: 1. MODEL OF 3 PHASE SYNCHRONOUS ELECTRIC MOTOR [1]
4) WORKING
3 phase synchronous electric motor with animated vector adding of stator coil magnetic fields.
Stator phases R, S and T have sine current shifted by 120° degrees between each. Magnetic field is
Sine wave current in each of the coils produces sine
varying magnetic field on the rotation axis. Magnetic
fields add as vectors.
Vector sum of the magnetic field vectors of the stator
coils produces a single rotating vector of resulting
rotating magnetic field.

2. Rotating Magnetic Field
EI-DEPT, SRMCEM, LUCKNOW 2
proportional to current in linear approximation. Magnetic field vectors of the phases add up on the
axis of the motor as vectors, combining into single rotating vector according to parallelogram law,
which is clearly visible. Rotor has a constant current and hence constant magnetic field, which
shows the inclination to follow rotating magnetic field of the stator coils, causing rotor to rotate.
This particular image shows phase vectors change in time, the other one sums them using
parallelogram theorem.
The result of adding three 120-degrees phased sine waves on the axis of the motor is a single
rotating vector. The rotor has a constant magnetic field. The N pole of the rotor will move toward
the S pole of the magnetic field of the stator, and vice versa. This magneto-mechanical attraction
creates a force which will drive the rotor to follow the rotating magnetic field in a synchronous
manner.
A permanent magnet in such a field will rotate so as to maintain its alignment with the external
field. This effect was utilized in early alternating current electric motors. A rotating magnetic field
can be constructed using two orthogonal coils with a 90 degree phase difference in their AC
currents. However, in practice such a system would be supplied through a three-wire arrangement
with unequal currents. This inequality would cause serious problems in the standardization of the
conductor size. [4]
5) THREE-PHASE ROTATING FIELDS
FIGURE: 2. THREE-PHASE, Y-CONNECTED STATOR. [4]
The three-phase induction motor also operates on the principle of a rotating magnetic field.
The following discussion shows how the stator windings can be connected to a three-phase ac input

3. Rotating Magnetic Field
EI-DEPT, SRMCEM, LUCKNOW 3
And has a resultant magnetic field that rotates.
Figure 2, views A-C show the individual windings for each phase. Figure 2, view D, shows how
the three phases are tied together in a Y-connected stator. The dot in each diagram indicates the
common point of the Y-connection. You can see that the individual phase windings are equally
spaced around the stator. This places the windings 120° apart.
The three-phase input voltage to the stator of figure 4-4 is shown in the graph of figure 3.
Use the left-hand rule for determining the electromagnetic polarity of the poles at any given instant.
In applying the rule to the coils in figure 4-4, consider that current flows toward the terminal
numbers for positive voltages, and away from the terminal numbers for negative voltages.
FIGURE: 3. - THREE-PHASE ROTATING-FIELD POLARITIES AND INPUT VOLTAGES. [4]
The results of this analysis are shown for voltage points 1 through 7 in figure 3. At point 1, the
magnetic field in coils 1-1A is maximum with polarities as shown. At the same time, negative
voltages are being felt in the 2-2A and 3-3A windings. These create weaker magnetic fields, which
tend to aid the 1-1A field. At point 2, maximum negative voltage is being felt in the 3-3A windings.
This creates a strong magnetic field which, in turn, is aided by the weaker fields in 1-1A and 2-2A.
As each point on the voltage graph is analyzed, it can be seen that the resultant magnetic field is
rotating in a clockwise direction. When the three-phase voltage completes one full cycle (point 7),
the magnetic field has rotated through 360°. [4]

4. Rotating Magnetic Field
EI-DEPT, SRMCEM, LUCKNOW 4
6) PRODUCTION OF ROTATING MAGNETIC FIELD
Consider a three phase winding displaced in a space by 120°, supplied by a three phase A.C.
supply. The three phases currents are also displaced from each other by 120°.the flux produced by
each phase currents is also sinusoidal in nature and all three flux are separated from each other by
120°if the phase sequence of the windings is1-2-3, then the mathematical equation for the
instantaneous values of the fluxes ∅1, ∅2, ∅3 can be given as,
…………………………………………………………………. (1)
………………………………………… (2)
………………………………………… (3)
As windings are identical and supply is balanced the amplitude of each flux is same i.e. ∅m. the
wave form of three fluxes are shown in the figure.(4) while the assumed positive direction of these
fluxes in space are shown in the figure .(5) assumed positive direction means whenever the
instantaneous value of the flux is positive,in vector diagram it must be represented along its
assumed positive direction.aand if flux has negative instantaneous value then must be represented
in opposite direction to the assumed positive direction,in the vector diagram. [1]
FIGURE: 4. ASSUMED POSITIVE DIRECTION [1]
FIGURE: 5. WAVE FORM OF THREE FLUXES [1]

5. Rotating Magnetic Field
EI-DEPT, SRMCEM, LUCKNOW 5
Let ∅1, ∅2, and ∅3 be the instantaneous values of the fluxes. The resultant flux ∅T, at any instant is
given by phasor combination of ∅1, ∅2, and ∅3 at that instant .let us find out ∅T at four different
instant 1, 2, 3, and 4 as shown in the fig.5 i.e. respectively at
θ= 0°, 60°, 120°, and 180°.
CASE 1: θ=0°
Substituting in equation (1), (2), (3) we get,
=0
And ……………………………..vector sum
Show positive values in assumed positive directions and negative in opposite directions to assumed
positive directions.
Hence vector diagram looks like as shown in fig. 6.
BD is perpendicular drawn from B on „∅T’
FIGURE: 6. VECTOR DIAGRAM FOR =0° [1]
Since OD=DA=∅T/2
Since in OBD, BOD=30°
So =OD/OB = (∅T/2)
0.866∅m
∅T = 2*0.866∅m *
∅T = 1.5∅m
So magnitude of resultant flux is 1.5 times the maximum value of an individual flux.

6. Rotating Magnetic Field
EI-DEPT, SRMCEM, LUCKNOW 6
CASE 2: θ=60°
Substituting in equations 1), (2), (3) we get,
=
So is positive and is negative so vector diagram looks like as shown in the fig.7.
FIGURE: 7. VECTOR DIAGRAM FOR =60° [1]
It can be seen from the fig.7, that,
∅T = 1.5∅m
So magnitude of the resultant is same as before but it is rotated in space by 60° in space in
clockwise direction, from its previous position.
CASE 3: θ=120°
Substituting in equations 1), (2), (3) we get,
=
0
So is positive and is zero and is negative. so vector diagram looks like as shown in the
fig.8.from fig 8 it can be prove easily that,

7. Rotating Magnetic Field
EI-DEPT, SRMCEM, LUCKNOW 7
FIGURE: 8. VECTOR DIAGRAM FOR =120° [1]
∅T = 1.5∅m
So magnitude of the resultant is 1.5∅m, same as before but it is rotated in space by 60° in space in
clockwise direction, from its previous position.
CASE 4: θ=180°
Substituting in equations 1), (2), (3) we get,
= 0
So is zero and is positive and is negative. So vector diagram looks like as shown in the
fig.9.
From fig 9 it can be prove easily that,
∅T = 1.5∅m
So magnitude of the resultant flux is once again 1.5∅m but it is further rotated by 60° in clockwise
direction from its position for θ=120°.
7) CONCLUSION
So for a half cycle of the fluxes, the resultant has rotated through 180°.This is applicable for 2 pole
winding. From this discussion we can have following conclusion:
a) The resultant of the three alternating fluxes, separated from each other by 120°, has constant
amplitude of 1.5∅m where ∅m is maximum amplitude of an individual flux due to any phase.
b) The resultant always keeps on rotating with a certain speed in space.

8. Rotating Magnetic Field
EI-DEPT, SRMCEM, LUCKNOW 8
This is nothing but satisfying the definition of a rotating magnetic field. Hence we can conclude
that the three phases stationary winding when connected to a three phase A.C. supply produces a
rotating magnetic field.
The speed of the resultant is 180° in space, for 180° electrical of the fluxes for a 2 pole winding as
discussed above. [1]
8) KEY POINT: this is nothing but,
 °MECHANICAL=°ELECTRICAL FOR 2 POLE CASE.
If winding is wound for p poles, then resultant will complete
2/p revolutions for 360°electrical of the fluxes. So resultant flux bears a fixed relation between
speed of rotation, supply frequency and number of poles for which winding is wound. So for a
standard supply frequency of f Hz of a three phase A.C. supply and „P‟ poles of the three phase
windings, the speed of the rotating magnetic field is Ns R.P.M.
FIGURE: 9. VECTOR DIAGRAM FOR =180° [1]
9) DIRECTION OF ROTATING MAGNETIC FIELD
The direction of the rotating magnetic field is always from is always from the axis of the leading
phase of the three phases winding towards the lagging phase of the winding. In the example above
the phase sequence is 1-2-3 i.e. phase 1 leads 2 by 120° and phase 2 leads 3 by 120°.so rotating
Ns= r.p.m.

9. Rotating Magnetic Field
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magnetic field rotates from axis of 1 to axis of 2 and then to axis of 3 i.e. in the clock wise
direction as seen above. This direction can be reversed by changing any two terminals of
three phases winding while connecting them to three phase supply. So in practice for a phase
sequence of R.Y.B, the rotating magnetic field is rotating in clockwise direction, then by
changing any two terminals of the winding it can be changed to anticlockwise, as shown in the
fig.10 and 11. [1]
FIGURE: 10. REVERSAL OF DIRECTION R.M.F. (CLOCKWISE) [1]
FIGURE: 11. REVERSAL OF DIRECTION R.M.F. (ANTICLOCKWISE) [1]

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10) REFERENCES
o Off line books resources
[1] Electromechanical Energy Conversion-2nd
,Technical Publications, second edition –august
2011
[2] D. P. Kothari & I.J. Nagrath, Tata McGraw- Hill & 1995,” Electrical Machines”.
[3] Dr.P.S. Bimbara, Khanna Publication, “Electrical Machinery”.
o On line books resources
[4] Thomas Parke Hughes, Networks of power: electrification in Western society, 1880-1930, page
117
[5] Encyclopedia Americana: Meyer to Nauvoo, Scholastic Library Pub., 2006, page 558
o On line sites resources
[6] http:// www.scribd.com 8.3 Rotating Magnetic Field Due to 3-Phase Currents for Principles of
Electrical Machines (V.K MEHTA)
[7] http:// www.en.wikipedia.org/wiki/Rotating_magnetic_field Rotating magnetic field - Wikipedia, the
free encyclopedia