In the case of a hetero-polar generator the induced emf in a conductor goes through a cyclic change in voltage as it passes under north and south pole polarity alternately. The induced emf in the conductor therefore is not a constant but alternates in magnitude. For a constant velocity of sweep the induced emf is directly proportional to the flux density under which it is moving. If the flux density variation is sinusoidal in space, then a sine wave voltage is generated. This principle is used in the a.c generators. In the case of dc generators our aim is to get a steady d.c. voltage at the terminals of the winding and not the shape of the emf in the conductors. This is achieved by employing an external element, which is called a commutator, with the winding.
Fig. 5 shows an elementary hetero-polar, 2-pole machine and one-coil arma- ture. The ends of the coil are connected to a split ring which acts like a commutator. As the polarity of the induced voltages changes the connection to the brush also gets switched so that the voltage seen at the brushes has a unidirectional polarity. This idea is further developed in the modern day machines with the use of commutators. The brushes are placed on the commutator. Connection to the winding is made through the commutator only. The idea of a commutator is an ingenious one. Even though the instantaneous value of the induced emf in each conductor varies as a function of the flux density under which it is moving, the value of this emf is a constant at any given position of the conductor as the field is stationary. Similarly the sum of a set of coils also remains a constant. This thought is the one which gave birth to the commutator. The coils connected between the two brushes must be ”similarly located” with respect to the poles irrespective of the actual position of the rotor.
This can be termed as the condition of symmetry. If a winding satisfies this condition then it is suitable for use as an armature winding of a d.c. machine. The ring winding due to Gramme is one such. It is easy to follow the action of the d.c. machine using a ring winding, hence it is taken up here for explanation.
Fig. 6 shows a 2-pole, 12 coil, and ring wound armature of a machine. The 12 coils are placed at uniform spacing around the rotor. The junction of each coil with its neighbor is connected to a commutator segment. Each commutator segment is insulated from its neighbor by a mica separator. Two brushes A and B are placed on the commutator which looks like a cylinder. If one traces the connection from brush A to brush B one finds that there are two paths. In each path a set of voltages get added up. The sum of the emfs is constant (nearly). The constancy of this magnitude is altered by a small value corresponding to the coil short circuited by the brush. As we wish to have a maximum value for the output voltage, the choice of position for the brushes would be at the neutral axis of the field. If the armature is turned by a distance of one slot pitch the sum of emfs is seen to be constant even though a different set of coils participate in the addition. The coil which gets short circuited has nearly zero voltage induced in the same and hence the sum does not change substantially. This variation in the output voltage is called the ’ripple’. More the number of coils participating in the sum lesser would be the ’percentage’ ripple.
Another important observation from the working principle of a heterogeneous generator is that the actual shape of the flux density curve does not matter as long as the integral of the flux entering the rotor is held constant; which means that for a given flux per pole the voltage will be constant even if the shape of this flux density curve changes (speed and other conditions remaining unaltered). This is one reason why an average flux density over the entire pole pitch is taken and flux density curve is assumed to be rectangular.
A rectangular flux density wave form has some advantages in the derivation of the voltage between the brushes. Due to this form of the flux density curve, the induced emf in each turn of the armature becomes constant and equal to each other. With this back ground the emf induced between the brushes can be derived. The value of the induced in one conductor is given by
where
Bav = Average flux density over a pole pitch, Tesla.
L = Length of the active conductor, m.
v = Velocity of sweep of conductor, m/sec.
If there are Z conductors on the armature and they form b pairs of parallel circuits between the brushes by virtue of their connections, then number of conductors in a series path is Z/2b. The induced emf between the brushes is
But v = (2p).Y.n where p is the pairs of poles Y is the pole pitch, in meters, and n is the number of revolutions made by the armature per second.
This can be termed as the condition of symmetry. If a winding satisfies this condition then it is suitable for use as an armature winding of a d.c. machine. The ring winding due to Gramme is one such. It is easy to follow the action of the d.c. machine using a ring winding, hence it is taken up here for explanation.
Fig. 6 shows a 2-pole, 12 coil, and ring wound armature of a machine. The 12 coils are placed at uniform spacing around the rotor. The junction of each coil with its neighbor is connected to a commutator segment. Each commutator segment is insulated from its neighbor by a mica separator. Two brushes A and B are placed on the commutator which looks like a cylinder. If one traces the connection from brush A to brush B one finds that there are two paths. In each path a set of voltages get added up. The sum of the emfs is constant (nearly). The constancy of this magnitude is altered by a small value corresponding to the coil short circuited by the brush. As we wish to have a maximum value for the output voltage, the choice of position for the brushes would be at the neutral axis of the field. If the armature is turned by a distance of one slot pitch the sum of emfs is seen to be constant even though a different set of coils participate in the addition. The coil which gets short circuited has nearly zero voltage induced in the same and hence the sum does not change substantially. This variation in the output voltage is called the ’ripple’. More the number of coils participating in the sum lesser would be the ’percentage’ ripple.
Another important observation from the working principle of a heterogeneous generator is that the actual shape of the flux density curve does not matter as long as the integral of the flux entering the rotor is held constant; which means that for a given flux per pole the voltage will be constant even if the shape of this flux density curve changes (speed and other conditions remaining unaltered). This is one reason why an average flux density over the entire pole pitch is taken and flux density curve is assumed to be rectangular.
A rectangular flux density wave form has some advantages in the derivation of the voltage between the brushes. Due to this form of the flux density curve, the induced emf in each turn of the armature becomes constant and equal to each other. With this back ground the emf induced between the brushes can be derived. The value of the induced in one conductor is given by
Ec = Bav.L.v Volts ---------------- 7
where
Bav = Average flux density over a pole pitch, Tesla.
L = Length of the active conductor, m.
v = Velocity of sweep of conductor, m/sec.
If there are Z conductors on the armature and they form b pairs of parallel circuits between the brushes by virtue of their connections, then number of conductors in a series path is Z/2b. The induced emf between the brushes is
E = Ec ( Z/2B ) -------------------- 8
E = Bav . L . v ( Z/2B ) Volts ----- 9
But v = (2p).Y.n where p is the pairs of poles Y is the pole pitch, in meters, and n is the number of revolutions made by the armature per second.
Also Bav can be written in terms of pole pitch Y , core length L, and flux per pole as
Bav = phi / (L.Y) Tesla -------- 10
Substituting in equation Eqn. 9,
E = [phi / (L.Y)] . L . ( 2p . Y .n ) . ( Z/2b )
E= phi . p . Zn / b Volts ---------------- 11
The number of pairs of parallel paths is a function of the type of the winding chosen.
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