Dr. Adel Gastli
Electromechanical Systems & Actuators
DC MACHINES These slides are the contributions of: Dr. A. Gastli, Dr. A. Al-Badi, and Dr. Amer Al-Hinai
DC Machines LEARNING GOALS
Introduction Application of DC Machine Advantages & Disadvantages of DC Machine
Construction of DC Machine Field System Armature Commentator Brush
Principle of Operation Faraday’s Law Armature Voltage & Developed Torque
Classification of DC Machine Permanent Magnet Self-Excited Separately-Excited
DC Machine Representation Magnetization Curve (Saturation) DC Motor & Generator Equations Power Flow & Efficiency Torque-Speed Characteristics Dr. Adel Gastli
MCTE3210: Electromechanical Systems & Actuators Starting of DC Machine
2
Introduction Most of the electrical machine in service are AC type. DC machine are of considerable industrial importance. DC machine mainly used as DC motors and the DC generators are rarely used. DC motors provides a fine control of the speed which can not be attained by AC motors. DC motors can developed rated torque at all speeds from standstill to rated speed. Developed torque at standstill is many times greater than the torque developed by an AC motor of equal power and speed rating. MCTE3210: Electromechanical Systems & Actuators
Dr. Adel Gastli
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Application of DC Machines
The d.c. machine can operate as either a motor or a generator, at present its use as a generator is limited because of the widespread use of ac power. Large d.c. motors are used in machine tools, printing presses, fans, pumps, cranes, paper mill, traction, textile mills and so forth. Small d.c. machines (fractional horsepower rating) are used primarily as control device-such as tachogenerators for speed sensing and servomotors for position and tracking. Dr. Adel Gastli
MCTE3210: Electromechanical Systems & Actuators
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Application of DC Machines DC Motor Paper Mills Oil Rigs
Steel Mills
Dr. Adel GastliMining
Robots
MCTE3210: Machine Electromechanical ToolsSystems & Actuators
Petrochemical
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Advantages & Disadvantages Of D.C. Motors Advantages • High starting torque • Rapid acceleration and deceleration. • Speed can be easily controlled over wide speed range. • Used in tough gobs (traction motors, electric trains, electric cars,….) • Built in wide range of sizes. Disadvantages • Needs regular maintenance • Cannot be used in explosive area • High cost Dr. Adel Gastli
MCTE3210: Electromechanical Systems & Actuators
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Introduction Electric Machine
Mechanical Input
Electrical Output
Generator
Electrical Input
Motor
Mechanical Output
Electromechanical Energy Conversion + Electrical system v _
i Ideal Electric Machine
ω
T Mechanical system
Motor Energy Flow
v i=T ω
Generator
MCTE3210: Electromechanical Systems & Actuators
Dr. Adel Gastli
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Construction of DC Machine
Parts of a DC Machine Armature core Leading pole tip
Armature winding
Field coil Rotation Pole axis Shaft
Pole core Trailing pole tip
Pole face
Dr. Adel Gastli
Field yoke
MCTE3210: Electromechanical Systems & Actuators
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Construction of DC Machine Shaft
Armature
Commutator
Stator
Field coil
Dr. Adel Gastli
MCTE3210: Electromechanical Systems & Actuators 2 Pole DC Machine
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Construction of DC Machine: Field System The field system is to produce uniform magnetic field within which the armature rotates. This consists of Yoke or frame: Acts as a mechanical support of the machine
2000HP DC Motor field System Dr. Adel Gastli
MCTE3210: Electromechanical Systems & Actuators
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Construction of DC Machine: Armature The rotor or the armature core, which carries the rotor or armature winding, is made of sheet-steel laminations. The laminations are stacked together to form a cylindrical structure Teeth
Slots
The armature coils that make the armature winding are located in the slots
Slots for wedges
Non-conducting slot liners are wedged in between the coil and the slot walls for protection from abrasion, electrical insulation and mechanical support Cooling ducts for air circulation
Portion of an armature lamination of a dc machine showing slots and teeth Dr. Adel Gastli
MCTE3210: Electromechanical Systems & Actuators
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Construction of DC Machine: Armature
Armature of a DC Machine Dr. Adel Gastli
MCTE3210: Electromechanical Systems & Actuators
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Construction of DC Machine: Commutator Commutator: is a mechanical rectifier, which converts the alternating voltage generated in the armature winding into direct voltage across the brush. It is made of copper segments insulated from each other by mica and mounted on the shaft of the machine. The armature windings are connected to the commutator segments.
Commutator Dr. Adel Gastli
MCTE3210: Electromechanical Systems & Actuators
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Construction of DC Machine: Brush
The purpose of the brush is to ensure electrical connections between the rotating commutator and stationary external load circuit. It is made of carbon and rest on the commutator.
Commutator and Brushes Dr. Adel Gastli
MCTE3210: Electromechanical Systems & Actuators
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Construction of DC Machine: Armature Winding
Top coil sides
Top coil sides
Bottom coil sides
Commutator
1
2
3 Brush
Elements of Lap Winding
1
2 Brush
Elements of Wave Winding
MCTE3210: Electromechanical Systems & Actuators
Dr. Adel Gastli
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Construction of DC Machine: Armature Winding
End connection
Conductors
Turn
Dr. Adel Gastli
Coil
Winding
MCTE3210: Electromechanical Systems & Actuators
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Construction of DC Machine: Armature Winding Lap Winding a b c d e a b c d 1
2 3
4
5
6
7
g
9 10
11 12 13 14 15 16 17 18 19 20
S
N
S
N f
8
e
h
g
f
19 20 21 1
2
3
4
5
6
+
8
9 10 11 12 13 14 15 16 17 18 19
-
+
+
-
-
7
-
+
+
h
+
+
-
Ia +
-
a=b= p
Icoil // paths
brushes
poles
-
+
- Systems - & Actuators MCTE3210: Electromechanical
Dr. Adel Gastli
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Construction of DC Machine: Armature Winding a
d
c
b
1
Wave Winding
e
2 3
4
5
6
7
8
j
b
c
S
N
k
g
f
h g f
17 18 19 20 21 1
2
3
4
-
+
+
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19
+
+
-
-
-
j k
+
Ia
+
i
h
+
-
+ Icoil
Dr. Adel Gastli
e
d
11 12 13 14 15 16 17 18 19 20 21
S
N i
9 10
a
MCTE3210: Electromechanical Systems & Actuators -
a=2 Nb. of // paths 18
Principle of Operation The Faraday Disk and Faraday’s Law An emf is induced in a circuit placed in a magnetic field if either: • the magnetic flux linking the circuit is time varying • or there is a relative motion between the circuit and the magnetic field such that the conductors comprising the circuit cut a cross the magnetic flux lines.
φ
Magnet
+ N ω
S
V Brush
• 1st form of the law is the basis of transformers. • 2nd form is the basic principle of operation of electric generators.
Copper disk Conducting shaft
_
MCTE3210: Electromechanical Systems & Actuators
Dr. Adel Gastli
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Principle of Operation The right-hand rule and generator action V
Velocity, u
Voltmeter Flux density, B
Conductor rails
Φ = B.A Φ = B.l.s
d Φ dB .l.s = dt dt ds ds e = B.l. ,u = dt dt e=
Faraday’s law or flux cutting rule Dr. Adel Gastli
u emf, e
Moving conductor
B
e
l
e=Blu MCTE3210: Electromechanical Systems & Actuators
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Principle of Operation
ω
Without Commutator
φ
N
S
l1
Field pole
N-turn coil
Slip rings
v
brushes
v
External circuit
t
MCTE3210: Electromechanical Systems & Actuators
Dr. Adel Gastli
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Principle of Operation
With Commutator
ω S
N
v
coil Commutatorb segments
a brushes
t v
Dr. Adel Gastli
MCTE3210: Electromechanical Systems & Actuators
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Single-Phase Full wave Rectifier
MCTE3210: Electromechanical Systems & Actuators
Dr. Adel Gastli
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Multi-Pole Machines
If p is the number of poles, then p/2 cycles of variation of the flux are encountered every complete mechanical rotation.
360 o md One pole pitch = 180 ed = p o
θ
B(θ)
N Pole pitch
θ ed
p = θ md 2
N
π
N S
2π
3π
θ S
4π
θed θmd
π
S
S
N
2π
θed : electrical degrees or angular measure in cycles θmd : mechanical degrees or angular measure in space
Dr. Adel Gastli
MCTE3210: Electromechanical Systems & Actuators
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Principle of Operation: Armature Voltage Emf conductor =
Emf Total =
p.Φ . N m Flux / Re v. p.Φ = = 60 time / Re v. (60 / N m )
Emf conductor Number of conductor / path ⎛ p.Φ . N m ⎞ ⎛ Z ⎞ p.Φ .Z . N m Emf Total = ⎜ ⎟ /⎜ ⎟ = 60 60 a ⎝ ⎠ ⎝a⎠
where p = number of poles Z = total number of armature conductors a = number of parallel paths, 2 for wave and p for lab. Φ = flux per pole (Weber) Nm = speed of the motor in the revolutions per minute (rpm) time of 1 revolution = 60/Nm (sec)
MCTE3210: Electromechanical Systems & Actuators
Dr. Adel Gastli
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Principle of Operation: Armature Voltage Let
ωm =
2 .π . N m ω .60 ⇒ Nm = m 60 2 .π
ωm= speed of the motor in radians per second
Emf Total =
p.Φ .Z .ω m p.Φ .Z ω m .60 = . 60 a 2 .π 2 .π .a
Emf Total = K a .Φ .ω m
Ka: armature constant
Ka =
p .Z 2 .π .a
Generated voltage : generator operation Back emf : motor operation
Dr. Adel Gastli
MCTE3210: Electromechanical Systems & Actuators
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Developed (or Electromagnetic) Torque Consider the turn shown in the following Figure.
2πrl p
Area per pole A =
pΦ Φ = A 2π r l
B=
Flux density
Ic =
Current / conductor is
Ia a
fc = B l
The force on a conductor is
Ia a
Tc = f c r = B l
The torque developed by a conductor is
Te =
The total torque developed is
Φ p Ia Ia r = a 2π a
Zp Φ I a E I = K aΦ I a = a a ωm 2π a
MCTE3210: Electromechanical Systems & Actuators
Dr. Adel Gastli
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Production of Unidirectional Torque and Operation of an Elementary ω
ω
N
+
F
a b b
a
F
S
I 1
2
Position of conductor a under N-pole
N
F
+b F
a I 1
S
b a
2
Position of conductor a under S-pole
B I
F
With this configuration the torque is unidirectional and independent of conductor position
Left-hand rule Dr. Adel Gastli
MCTE3210: Electromechanical Systems & Actuators
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Classification of DC Machine
Separately excited
DC Machine
Self-excited
Short Shunt
Long Shunt
Shunt
Series Cumulative
Permanent magnet
Differential
Compound
MCTE3210: Electromechanical Systems & Actuators
Dr. Adel Gastli
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Classification of DC Machine
Field
Field
Armature
Field Armature
Shunt
Separately excited
A1
φf F1
Series
A1
φf
φs S1
F2
Armature
S2
F1
S1
F2
S2
A2
A2
Short-shunt
Dr. Adel Gastli
φs
Motor operation Generator operation
Long-shunt
MCTE3210: Electromechanical Systems & Actuators
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Classification of DC Machine
A1
φf F1
φs S1
F2
A1
φf S2
S1
F2
F1
φs S2
A2
A2
Cumulative compound
Differential compound
Motor operation Generator operation
MCTE3210: Electromechanical Systems & Actuators
Dr. Adel Gastli
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DC Machine Representation The mmf’s produced by the field circuit and the armature circuit are in quadrature.
q-axis d-axis
q-axis
Field Armature d-axis
Armature mmf
Field mmf
φa
Armature mmf
Φ
Field mmf
φf
Dr. Adel Gastli
Saturation Linear
Flux-mmf relation in a dc machine
Fp
MCTE3210: Electromechanical Systems & Actuators
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Magnetization (or Saturation) Curve of a DC Machine Ea
Φ
Speed ωm
Saturation Linear
0.5 ωm
If Nf
Flux-mmf relation in a dc machine
If Magnetization curve
The magnetizing curve is obtained experimentally by rotating the the dc machine at a given speed and measuring the open-circuit armature terminal voltage as the current in the field winding is changed. Magnetization Curve
Represents the saturation level in the magnetic system of the dc machine for various values of excitation mmf . MCTE3210: Electromechanical Systems & Actuators
Dr. Adel Gastli
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Dc Motors Equations Separately Excited DC Motor It +
Ia Ra Rfw ωm
E a = Vt − I a R a Vt
Rfc If
+ Vf −
Vf = Rf I f
−
E a= K aΦωm Te = K a Φ I a
¾ Rfw: resistance of field winding. ¾ Rfc: resistance of control rheostat used in field circuit. ¾ Rf=Rfw+Rfc: total field resistance ¾ Ra: resistance of armature circuit, including the effect of brushes. Sometimes
Ra is shown as the resistance of armature winding alone; the brush-contact voltage drop is considered separately and is usually assumed to be about 2V. Dr. Adel Gastli
MCTE3210: Electromechanical Systems & Actuators
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Dc Motors Equations Shunt or Self-Excited DC Motor
If
It Ia Ra
Rfc
Vt ωm
E a = Vt − I a R a
−
E a= K aΦω m , Vt = I t R L ,
+
Rfw
V f = R f I f = Vt
+
Te = K a Φ I a
−
Ia = It − I f
MCTE3210: Electromechanical Systems & Actuators
Dr. Adel Gastli
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Dc Generator Equations Separately Excited DC Generator
Ia
Vf =(Rfw + Rfc)I f = Rf I f
IL +
Ea =Vt + Iara
ra + ωm Rfw Rfc If
Dr. Adel Gastli
Vt Ea
− −
RL
Ea= KaΦ ωm Vt = ILRL Ia = IL
+ Vf −
MCTE3210: Electromechanical Systems & Actuators
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Dc Generator Equations Self-Excited DC Generators
1. Shunt generator If
Vf = RfI
IL
Rfc
ra Rfw
+ ωm
RL
Vt
E a= K aΦ ω m Vt = I L RL
Ea
−
− −
Ia = IL + I
MCTE3210: Electromechanical Systems & Actuators
Dr. Adel Gastli
= Vt
E a = V t + I a ra
+
Ia
f
f
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Dc Generator Equations 2. Series Generator
Ia
IL
Vt = Ea − Ia (ra + Rs )
+ ra + Ea
Rs Vt
−
RL
I L = Ia = I f Ea = KaΦsωm
−
Dr. Adel Gastli
MCTE3210: Electromechanical Systems & Actuators
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Dc Generator Equations 3. Compound DC Generator If
If
IL
Rfc Rs
+
Vt
−
Rfw
−
Short Shunt
Vt
Ea
−
E a = K a (Φ
Vt = Ea − I a Ra − I L Rs
Rs
+
Ea Rfw
+
Ia Ra
+
Ia Ra
Rfc
IL
sh
± Φ
s
)ω
−
Vt = Ea − I a (Ra + Rs )
m
IL = Ia − I f
IL = Ia − I f If =
Long Shunt
Ea − I a Ra R fw + R fc
−
+
If =
Differential
Cumulative
Vt R fw + R fc
Ea = K a (Φ sh ± Φ s )ωm
E = K (Φ sh ± Φ s )ωm
a a Dr. Adel Gastli
MCTE3210: Electromechanical Systems & Actuators
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Power Flow and Efficiency IL
If
DC Generators
+
Ia
Rfc
Ra +
Rs Vt
Ea −
Rfw
Ea I a
Pinput= Pmech = Pshaft Rotational losses
η= η=
Dr. Adel Gastli
η=
Va I a
Pinput
=
Vt I L +
Vt I L
Poutput= Pelectrical
I 2f R f I L2 Rs
I a2 Ra
Poutput
Va I L
−
Poutput Poutput + Losses
∑
Vt I L I 2 R + Rotational Losses
Vt I L Electromechanical Systems & Actuators EMCTE3210: I + Rotational Losses a a
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Power Flow and Efficiency IL
If
DC Motors
+
Ia
Rfc
Ra Rs
+
Vt
Ea −
Rfw
Pinput = Pelectrical
Vt IL
Va IL
I 2f Rf
IL2 Rs
η = η = η =
Dr. Adel Gastli
Poutput Pinput
=
Vt I L −
Va Ia
−
Ea Ia
Poutput= Pmech= Pshaft
Ia2 Ra Rotational losses
Pinput − Losses
∑
Pinput I 2 R − Rotational Vt I L
Losses
E a I a − Rotational Losses MCTE3210: Electromechanical Systems & Actuators Vt I L
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Torque-Speed Characteristics
Separately excited & Shunt motors (φ is independent of the load torque )
V t = E a + I a ra E a = K aΦ ω m
ωm =
Ia
Vt − I a ra K aΦ
T = K aΦ I a
ωm
Vt K aΦ Therefore ,
V ra ωm = t − T K aΦ (K aΦ)2
ra
Slope ( K Φ ) 2 a T
Dr. Adel Gastli
MCTE3210: Electromechanical Systems & Actuators
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Torque-Speed Characteristics
Series motors E a = Vt − I a ( R a + R s ) E a = K aφ ω m
φ = K1I f = K1I a
Neglecting saturation
E a = K a K 1 I aω m = K s I aω m Vt R + Rs − a KsIa Ks
ωm =
But T = K aφ I a = K a K 1 I a2 = K s I a2 ∴ωm =
Vt Ks T
Dr. Adel Gastli
−
Ra + Rs Ks
MCTE3210: Electromechanical Systems & Actuators
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Torque-Speed Characteristics
Compound motors Cumulative Compound
AT t = AT shunt ± AT series Differential Compound
φ t = φ shunt ± φ series ωm =
Dr. Adel Gastli
Shunt motor
Vt ra − T K aφ t ( K aφ t ) 2
MCTE3210: Electromechanical Systems & Actuators
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Starting of DC Machine If a d.c. motor is directly connected to a d.c. power supply, the starting current will be dangerously high.
Ia =
Vt − E a ra
∴ Ia
ω = 0 → Ea = 0
at starting
Starting
=
Vt ra
Since ra is small, the starting current is very large. The starting current can be limited by the following methods: 1- Use a variable-voltage supply. 2- Insert an external resistance at start, as MCTE3210: Electromechanical Systems & Actuators Dr. Adel Gastli shown in the Figure.
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