A Simple Rotating Loop Between Curved Pole Faces

A Simple Rotating Loop between Curved Pole Faces•It consists of a singleloop of wire rotatingabout a fixed axis.

•The rotating part iscalled rotor, and thestationary part is thestator.

•The magnetic fieldfor the machine issupplied by themagnetic north andsouth poles.

•Since the air gap isof uniform width, thereluctance is thesame everywhereunder the pole faces.

The simplest rotating dc machine is shown below:

EE41 – ELECTROMECHANICAL ENERGY CONVERSION Engr. Elvin D. Dulce Department of Electrical Engineering, CEAT, UPLB

The Voltage Induced in a Rotating Loop

•If the rotor is rotated, a voltage will be induced in the wire loop.•To determine the total voltage etot on the loop, examine each segment ofthe loop separately and sum all the resulting voltages.•The voltage on each segment is given by

eind = (v x B) lEE41 – ELECTROMECHANICAL ENERGY CONVERSION Engr. Elvin D. Dulce Department of Electrical Engineering, CEAT, UPLB


•SEGMENT ab: eba = (v x B) l = vBl (+ into the page)•SEGMENT bc: ebc = 0•SEGMENT cd: edc = (v x B) l = vBl (+ out of the page)•SEGMENT da: eda = 0

etotal = 2vBlEE41 – ELECTROMECHANICAL ENERGY CONVERSION Engr. Elvin D. Dulce Department of Electrical Engineering, CEAT, UPLB


•SEGMENT ab: eab = (v x B) l = vBl (+ out of the page)•SEGMENT bc: ebc = 0•SEGMENT cd: ecd = (v x B) l = vBl (+ into the page)•SEGMENT da: eda = 0

etotal = -2vBl

When the loop rotates by 180:


The Voltage Induced in a Rotating Loop•The graph of the resulting voltage is shown below:

•Alternative way of to express the equation for eind which relates the behaviorof larger, real DC machines:

•Thus, the voltage generated in the machine is equal to the product of the fluxinside the machine and the speed of rotation of the machine, multiplied by aconstant representing the mechanical construction of the machine.

2

0inde

Under the pole faces

beyond the pole edges


Getting DC voltage out of the Rotating LoopCOMMUTATION is the process of converting the ac voltages and currents in the rotor of a dc machine to dc voltages and currents at its terminals.


The Induced Torque in the Rotating LoopSuppose a battery is now connected to the machine:


The Induced Torque in the Rotating Loop•Force will be induced in each segment of the loop at the instant the switch isclosed:

•SEGMENT ab: Fab = i(l x B) = ilB = rF sinθ = rilB•SEGMENT bc: Fbc = 0 = 0•SEGMENT cd: Fcd = i(l x B) = ilB = rF sinθ = rilB

•SEGMENT da: Fda = 0 = 0

ind = 2rilB = under the pole faces

ind = 2rilB beyond the pole edges

2i


The Induced Torque in the Rotating Loop•In general, the torque in any real machine will depend on the same 3factors:

1. The flux in the machine2. The current in the machine3. A constant representing the construction of the machine.


Commutation in a Simple Four-Loop DC Machine•A simple 4 loop, 2 pole dc machine is shown below:

•This machine has 4 complete loops buried in slots carved in the laminatedsteel of its rotor.•The pole faces of the machine are curved to provide a uniform air-gap widthand to give a uniform flux density everywhere under the faces.

•The 4 loops of this machineare laid into the slots in aspecial manner.•The “unprimed” end of eachloop is the outermost wire ineach slot, while the “primed”end of each loop is theinnermost wire in the slotdirectly opposite.


Commutation in a Simple Four-Loop DC Machine•At t = 0, the 1, 2, 3’ and 4’ ends of the loops are under the north pole face,while the 1’, 2’, 3 and 4 ends are under the south pole face.

•The voltage in each of the 1, 2, 3’ and 4’ ends of the loops is given by:eind = vBl (positive out of page)

•The voltage in each of the 1’, 2’, 3 and 4 ends of the loops is given by:eind = vBl (positive into the page)

E = 4e t = 0

Commutation in a Simple Four-Loop DC Machine•At t = 45, the 2 and 4’ ends of the loops are under the north pole face, the2’ and 4 ends are under the south pole face, while the 3, 3’, 1, 1’ ends arebeyond the pole edges.

•The voltage in each of the 2 and 4’ ends of the loops is given by:eind = vBl (positive out of page)

•The voltage in each of the 2’ and 4 ends of the loops is given by:eind = vBl (positive into the page)



•The loops 1 and 3 have rotated into the gap between the poles, so thevoltage across each of them is zero.•The brushes of the machine are shorting out commutator segments ab andcd. This happens just at the time when the loops between these segmentshave 0V across them, so shorting out the segments creates no problem.


The total voltage across the brushes is:

E = 2e t = 45


Commutation in a Simple Four-Loop DC Machine•Now, let the rotor continue to turn another 45°. The resulting situation isshown below:

•Here, the 1’, 2, 3, and 4’ ends of the loops are under the north pole face, andthe 1, 2’, 3’ and 4 ends of the loops are under the south pole face.•The voltages are still built up out of the page for the ends under the northpole face and into the page for the ends under the south pole face.

E = 4e t = 90EE41 – ELECTROMECHANICAL ENERGY CONVERSION Engr. Elvin D. Dulce Department of Electrical Engineering, CEAT, UPLB

Commutation in a Simple Four-Loop DC Machine•The voltages on loops 1 and 3 have reversed between the 2 pictures (fromωt=0° to ωt=90°), but since their connections have also reversed, the totalvoltage is still being built up in the same direction as before.•This is the heart of every commutation scheme.

ωt=0° ωt=90°


Commutation in a Simple Four-Loop DC Machine•The terminal voltage of this 4-loop DC machine is shown below:

•As the number of loops on the rotor increases, the approximation to aperfect DC voltage continues to get better and better.

•COMMUTATION is the process of switching the loop connections on the rotorof a DC machine just as the voltage in the loop switches polarity in order tomaintain an essentially constant DC output voltage.


“Commutation and armature construction in real dc machines”

a. The number of parallel current paths within the rotorb. The output voltage of the rotorc. The number and position of the brushes riding on the

commutator segments

•There are severalways in which theloops on the rotor(armature) can beconnected to itscommutatorsegments.

•These different connections affect:


THE ROTOR COILS•Consist of diamond-shaped coils which are inserted into the armature slots.•The number of conductor on a machine’s armature is given by:

Z = 2CNCZ=# of cond. on rotorC=# of coils on rotorNc=# of turns per coil



THE ROTOR COILS



•Commutator Pitch (YC) – the distance (in number of segments) between thecommutator segments to which the two ends of acoil are connected.

•Progressive vs. Retrogressive Winding•Progressive – the end of the coil is connected to a commutator segment

ahead of the one its beginning is connected to.

•Retrogressive - the end of the coil is connected to a commutator segmentbehind the one its beginning is connected to.

If everything else is identical, the direction of rotation of aprogressive wound rotor will be opposite to the direction of rotationof a retrogressive wound rotor.

•Plex of Windings – the number of complete and independent set of rotorwindings (i.e; simplex, duplex, triplex; multiplex)




# of Poles: 2

# of Slots: 8

# of Commutators: 8

Winding Type: lap

Multiplicity: simplex

Rotation: progressive

DC GENERATORS

Main fields in DC generators are supplied by:1. Electromagnets2. Permanent magnetsEE41 – ELECTROMECHANICAL ENERGY CONVERSION Engr. Elvin D. Dulce Department of Electrical Engineering, CEAT, UPLB

DC GENERATORSElectromagnets or Field Poles:•Built up of stack of steel laminations having good magnetic qualities fastened together.

Field Coils:•Excited with direct current to provide main flux to the armature.


A Simple Rotating Loop Between Curved Pole Faces

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