1. DC Machines Fundamentals
ELECTRICAL MACHINES
DET 204/3
JIMIRAFIZI BIN JAMIL
CHAPTER 2
DC Machines Fundamentals

2. A DC Machines can be used as either a DC generator or a DC motor.
Electrical Machines
Introduction
A DC Machines can be used as either a DC generator or a DC motor.
DC generators
- To convert mechanical energy to electrical energy.
- Limited use due to solid state rectifier.
DC motors
- To convert electrical energy to mechanical energy
- Widely used
- Main feature: speed control is simple and cheap

3. Electrical Machines
Construction

4. Electrical Machines
Construction

5. DC Machine = Stator + Rotor (armature)
Electrical Machines
Construction
DC Machine = Stator + Rotor (armature)
- Stator: stationary part ~ does not move, the outer frame of the machines is made of ferromagnetic materials.
Rotor (Armature): rotating part ~ free to move, the inner part of the machine is made of ferromagnetic materials.
Field winding: is wound on the stator poles to produce magnetic field (flux) in the air gap.
Armature winding: is composed of coils placed in the armature slots.

6. Electrical Machines
Construction
Commutator: is composed of copper bars, insulated from each other. The armature winding is connected to the commutator.
- Brush: placed against the commutator surface. Brush is used to connect the armature winding to external circuit through commutator.

7. Electrical Machines
Construction
The conductor placed in the slots of the stator or rotor are interconnected to form windings.
The winding in which voltage is induced is called the armature winding.
The winding through which a current is passed to produce the primary source of flux in the machine is called the field winding.

8. Electrical Machines
Construction
In the DC machine, the field winding is placed on the stator and the armature winding on the rotor.
DC motor stator

9. Electrical Machines
DC motor rotor

10. Cutaway view of a dc motor
Electrical Machines
Cutaway view of a dc motor

11. Details of the commutator of a dc motor
Electrical Machines
Details of the commutator of a dc motor

12. A coil is formed by connecting several turns in series.
Electrical Machines
Armature Windings
A turn consists of two conductors connected to one end by an end connector.
A coil is formed by connecting several turns in series.
A winding is formed by connecting several coils in series.

13. Cut and unroll of DC machine
Electrical Machines
Armature Windings
Cut and unroll of DC machine

14. Electrical degree and mechanical degree
Electrical Machines
Armature Windings
Electrical degree and mechanical degree
Pole pitch is the distance between the centers of two adjacent poles

15. Two basic sequences of armature winding connections: Lap windings
Electrical Machines
Armature Windings
Two basic sequences of armature winding connections:
Lap windings
Wave windings

16. Electrical Machines
Lap Winding

17. Electrical Machines
Lap Winding
Consider coil shown by the dark lines with one end connected to the commutator bar no 2. The coil is placed in slots 2 and 7 such that the coils sides are placed in similar positions under adjacent poles. This is called lap winding because as the winding progresses the coils laps back on itself.

18. Electrical Machines
Lap Winding
We can conclude, in a lap winding, the number of parallel paths, “a” is always equal to the number of poles, “P” and also to the number of brushes.

19. Electrical Machines
Wave Winding
The coil arrangement and the end connections are illustrated by the dark lines shown in figure above for two coils. One end of the coil starts at commutator bar 2 and the coil sides are placed in slots 7 and 12. The other end of coil is connected to commutator bar 13. The second coil starts at this commutator bar and is placed in slots 18 and 2 and ends on commutator bar 3. This winding is called a wave winding because the coils are laid down a wave pattern.

20. Electrical Machines
Wave Winding
In wave windings, the number of parallel paths, ”a” is always two and there may be two or more brush positions.

21. DC machines operates as a generator
Electrical Machines
DC machines operates as a generator
A simple rotating loop between curved poles faces
Perspective view
Magnetic for DC machine is supplied by the magnetic north and south poles shown on the stator (field winding)

22. A simple rotating loop between curved poles faces
Electrical Machines
A simple rotating loop between curved poles faces
View of field lines
Top view

23. A simple rotating loop between curved poles faces
Electrical Machines
A simple rotating loop between curved poles faces
Front view

24. The Voltage Induced in a Rotating Loop
Electrical Machines
The Voltage Induced in a Rotating Loop
If the rotor of this machine is rotated, a voltage will induced in the wire loop.
Concepts: A moving wire in the presence of a magnetic field has a voltage induced in it.
The loop of wire shown in rectangular, with sides ab and cd perpendicular to the plane of the page and with sides bc and da parallel to the plane of the page

25. The Voltage Induced in a Rotating Loop
Electrical Machines
The Voltage Induced in a Rotating Loop
The induced voltage for one conductor is
where
B = magnetic flux density (T)
v = velocity of the conductor (ms-1)
l = length of conductor (m)
The induced voltage depends on three factor:
1. The flux, Ф in the machine
2. The speed ω of the rotor
3. A constant depending on the construction of the machine

26. The internal generated voltage
Electrical Machines
The internal generated voltage
The voltage out of the armature is
where
Z = the total number of conductors
a = the number of current paths
We know , v =rω, r = radius of the rotor

27. The internal generated voltage
Electrical Machines
The internal generated voltage
The flux of the pole is equal to the flux density under the pole times the pole’s area:
The rotor of the DC machine is shaped like a cylinder, so its area is
If there are P poles on the machine, then the portion of the area associated with each pole is

28. The internal generated voltage
Electrical Machines
The internal generated voltage
The total flux per pole in the machine is
The internal generated voltage is

29. The internal generated voltage
Electrical Machines
The internal generated voltage
where or

30. DC machines operates as a motor
Electrical Machines
DC machines operates as a motor
The induced torque in the rotating loop
A battery is now connected to the machine. When the switch is closed and a current is allowed into conductor loop. The torque will be induced on the conductor loop.
Concepts: a current carrying wire in the presence of a magnetic field has a force induced on it
Lorentz Law : use right hand rule.
Index finger – vector l
Middle finger – Magnetic flux density
Thumb - Force

31. The induced torque in the rotating loop
Electrical Machines
The induced torque in the rotating loop
The force for one conductor is
where
i = magnitude of current in the segment
l = length of the segment, with direction of I defined to be in the direction of current
B = magnetic flux density vector

32. The induced torque in the rotating loop
Electrical Machines
The induced torque in the rotating loop
The torque on that segment is
The induced torque depends on three factors:
1. The flux Ф in the machine
2. The armature (or rotor) current IA in the machine
3. A constant depending on the construction of the machine

33. The torque in any single conductor under the pole faces is
Electrical Machines
The induced torque
The torque in any single conductor under the pole faces is
If there are “a” current paths in the machine, then the total armature current Ia is split among the “a” current paths, so the current in a single conductor is
The torque in a single conductor on the motor is

34. Since there are Z conductors, the total induced torque in rotor is
Electrical Machines
The induced torque
Since there are Z conductors, the total induced torque in rotor is
The total flux per pole in the machine is
The total induced torque is

35. The total induced torque is
Electrical Machines
The induced torque
The total induced torque is
where

36. Power flow and losses in DC machines
Electrical Machines
Power flow and losses in DC machines
DC generators take in mechanical power and produce electric power while DC motors take in electric power and produce mechanical power
Efficiency

37. Power flow and losses in DC machines
Electrical Machines
Power flow and losses in DC machines
The losses that occur in DC machine can be divided into 5
categories:
Copper losses (I2R)
Brush losses
Core losses
Mechanical losses
Stray load losses
Ia = armature current
If = field current
Ra = armature resistance
Rf = field resistance
VBD = brush voltage drop
- Usually assumed to be 2V

38. Core losses – hysteresis losses and eddy current losses
Electrical Machines
Power Losses
Core losses – hysteresis losses and eddy current losses
Mechanical losses – the losses that associated with mechanical effects. Two basic types of mechanical losses: friction & windage. Friction losses caused by the friction of the bearings in the machine. Windage are caused by the friction between the moving parts of the machine and the air inside the motor casing’s
Stray losses (Miscellaneous losses) – cannot placed in one of the previous categories.

39. Electrical Machines
The Power Flow Diagram
Pout = VTIL
For generator

40. Electrical Machines
The Power Flow Diagram
For motor

41. Equivalent circuit of DC generator
Electrical Machines
Equivalent circuit of DC generator
Vf = field voltage
If = field current
Rfw = rheostat resistance
Rf = Rfc + Rfw = field circuit resistance
Ra = armature resistance
Ea = KФω
where Ф = flux generated by field current, If
VT = terminal voltage
Ia = armature current

42. Equivalent circuit of DC motor
Electrical Machines
Equivalent circuit of DC motor
Vf = field voltage
If = field current
Rfw = rheostat resistance
Rf = Rfc + Rfw = field circuit resistance
Ra = armature resistance
Back EMF, Eb = KФω
where Ф = flux generated by field current, If
VT = terminal voltage
Ia = armature current

43. If the armature is lap wound, determine: a. the armature constant K
Electrical Machines
Example
A 4 pole DC machine has an armature of radius 12.5cm and effective length of 25cm. The poles cover 75% of the armature periphery. The armature winding consists of 33 coils, each coil having seven turns. The coils are accommodated in 33 slots. The average flux density under each pole is 0.75T.
If the armature is lap wound, determine:
a. the armature constant K
b. the induced armature voltage when the armature rotates at 1000 rpm.
c. the current in the coil and the electromagnetic torque developed when the armature current is 400A.

44. d. The power developed by the armature.
Electrical Machines
Example
d. The power developed by the armature.
2) If the armature is wave wound, repeat parts a. to d. above. The current rating of the coils remains the same as in the lap wound armature.
Solution
1. Lap wound DC machine a.
Always equal number of poles
( 2 x 33 coils x 7 turns)

45. Electrical Machines
Example b. c.

46. Electrical Machines d. or
2. Wave wound DC machine a. b. c.

47. Electrical Machines d.

48. Magnetizing curve of a DC machine
Electrical Machines
Magnetizing curve of a DC machine
The internal generated voltage, Ea of a DC motor or generator is
The internal generated voltage, Ea is proportional to the flux in the machine and the speed of rotation of the machine.
Magnetization curve of a ferromagnetic material (Ф vs F)
Magnetomotive Force, F = NfIf

49. Electrical Machines
Most motors and generator are designed to operate near the saturation point on the magnetization curve. This implies that a fairly large increase in field current is often necessary to get a small increase in Ea when operation is near full load.

50. Classification of a DC machine
Electrical Machines
Classification of a DC machine
Separately Excited DC Machine
Shunt DC Machine
Series DC Machine
Compounded DC Machine