感应电机induction+motors

n = 0,
s =1
T
2 1
R2U Tst = K 2 2 R2 + X 2 （Nm）
Start ability
Example An induction machine p=3，the frequency of the source f1=50Hz，the rated speed of the motor n=960r/min. Find: fractional speed s, the frequency of rotor current f2 Solution
Current in rotor conductors
T = K T Φ m I 2 cos φ 2
2 R 2 + ( sX 20 ) 2 R2 cos φ 2 = 2 2 R 2 + ( sX 20 )
I2 =
sE 20
E20 = 4.44f1N2Φm
U1 Φm = 4 .44 f 1 N 1
sR2 2 T=K 2 × U1 2 R2 + ( sX 20 )
iA
A Z X Y
iA
iB
iC
t
Im
B
iC
iB
C
A Y
N
Z
ωt = 0
合成磁场方向：
B
C
S
X
向下
iA
iB
iC
t
Im
n1
A Y
60°
Z Y
n1
A Z
n1
Y C
A
S
N
X
Z B
N
C
S
B C
S
X
N
X
B
ω t = 60 °
ω t = 120 °
ω t = 180 °
iA
A
iA
Z X Y
iB
iC
t
Im
B
iC
Z'
N
• •
B
iC
iB
X'
S
• •
S
N
A' Y
X
B'
C
Im
iA i B iC
t
Z
ωt = 0
p =2
4. Rotation Speed of Magnetic Field
A
30°
A
Y' C'
X'
•
Z
•
•
N
B
C' S
n0
Z N
• •
S
•
S
N
A' Y
X'
X
•
X
B' Z'
•
C S Z' N
C
ωt = 0
5. Fractional Slip
⎛ n1 − n ⎞ ⎟ × 100 % s=⎜ ⎟ ⎜ n 1 ⎠ ⎝
At the beginning of start:
n = 0,
The range of slip:
s =1
0 ≤ s <1
(maximum slip)
Usually
s = 1 ~ 9%
关于相对转速
iA
A
Y
A
N
Z
iC
iB
Z X Y C B
C
B
S
X
p =1
n1 = 60 f ( 转 / 分）
p changes
iA
C'
A X A' Z' Y' Z X' B' Y B
iC
iB
Y' C' X' B'
Z
A
Z'
B X C
C
A' Y
iA
A X A' Z' X' C' Y Y' Z B' B C
A Y'
C'
转子相对磁场的转速 转子电流频率 转子电流产生的旋转磁场相 对于转子的转速
n1 − n = n1 s
f 2 = sf1
60 f 2 60sf1 n2′ = = = sn1 p p
转子电流产生的旋转磁场相 对于空间、定子的转速
n2 = n2′ + n = sn1 + (1 − s)n1 = n1
实际上电机的磁场是由定子电流和转子电流共同产生的
导体在磁场中运动，会产生感应电势和感应电流 （右手定则 n
1
f
n
f
e, i e, i
带电导体在磁场中会受到磁场力的作用 （左手定则）
1. 结论： 转子跟着磁场转→两者转动方向一致 2. 转子比磁场转得慢
n < n1
Asynchronous
n1
f
n
f
e, i e, i
(•)电流出
A Y
1. Rotating Magnetic Field
a Motor
Stator windings in the slots
Stator
A three-phase induction motor with a wound rotor
A three-phase induction motor with a squirrel-cage rotor
Three-phase stator windings: 给空间对称的定子绕组通三相交流电，使之产 生旋转磁场
磁场转速(相对空间、定子) 定子导体电流频率
60 f ( 转/分） n1 = p
转子转速(相对空间、定子)
n1 f1 = p 60
转子电流频率
n = n1 (1 − s )
转子相对磁场的转速
n1 − n n1 × p = sf1 f2 = n1 60
n1 − n = n1 s
n1 − n f2 = p 60
n1
改变电机的旋转方向：换接其中两相。
电源 A B C
电源 A B C
M 3~
n1
M 3~
n1
一个电流周期，旋转磁场在空间转过360°
n1 = 60 f ( 转 / 分）
n1----synchronous speed
f = 50 Hz , n1 = 3000转 / 分
3. Pairs of poles of rotating magnetic field
TN
PN PN ( 千瓦 ) TN = = 9550 2π n N nN (转 / 分 ) 60
（Nm）
Max. torque Tmax
n1
n
Tmax
U =K⋅ 2X2
2 1
T
（Nm）
Tmax
Overload coefficient
Tmax λ= TN
Starting torqueTst
n1 n
A→C→B phase sequence
A→B→C phase sequence
The rotation direction of magnetic field produced by the three-phase currents is coincided with the phase sequence.
n1
Z B
(×)电流入
A Z X Y C B
C
X
A
X
B
Y
C
Z
i B = I m sin (ω t − 120 ° )
i A = I m sin ω t
iA
A Z X Y
iC = I m sin (ω t − 240 ° )
iA
iB
iC
t
iC
iB
C
Im
B
Three-phase balanced current
iB
C
Balanced three-phase current flowing in the three-phase symmetric winding will produce a rotating magnetic field
2. The rotation direction of magnetic field
60 f1 60 × 50 n1 = = = 1000r / min p 3
n1 − n 1000− 960 = = 0.04 s= n1 1000
f 2 = sf1 = 0.04 × 50 = 2 Hz
8.1 The Structure of Three-phase Induction Motor 8.2 The Operational Principle of Induction Motor 8.3 Induction-motor Equivalent Circuit (*) 8.4 Torque and Torque-speed Characteristic 8.5 The Starting of Three-phase Induction Motor 8.6 Speed Control of Induction Motor 8.7 Braking of Three-phase Induction Motor 8.8 The Data of Induction Motor 8.11 Single-phase Induction Motor
2. Torque-speed Characteristic
n1 − n s = n1
sR2 2 T=K 2 × U1 2 R2 + ( sX 20 )
n
n1
T
T = f (S )
n = f (T )
s
0 1
T
3. Important Torques Rated torque TN
nN
n1
n
T
额定功率
iA
iB
iC
Imห้องสมุดไป่ตู้
t
iA
iC
iB
t
Im
n1
n1
Changing the phase sequence of three-phase currents can change the rotation direction of magnetic field
iA
iB
iC
Im
t
iA
iC
iB
t
Im
n1
改变电机的旋转方向：换接其中两相。
8.4 Torque and Torque-speed Characteristic 1. Magnetic torque T pf of rotor circuit （Nm）
T = K TΦ I 2 cos φ 2 m
constant Max. value of magnetic flux under each pole
Rotor 在旋转磁场作用下，转子导体产生感应电动势 并有感应电流；该带电导体在磁场中受到磁场 力的作用，产生转矩而旋转
A
Stator windings
C
Y
Z
rotor
B
stator
X
A
X
B
Y
C
Z
8.1 The Structure of Three-phase Induction Motor 8.2 The Operational Principle of Induction Motor 8.3 Induction-motor Equivalent Circuit (*) 8.4 Torque and Torque-speed Characteristic 8.5 The Starting of Three-phase Induction Motor 8.6 Speed Control of Induction Motor 8.7 Braking of Three-phase Induction Motor 8.8 The Data of Induction Motor 8.11 Single-phase Induction Motor
Chapter 8
Induction Motors
8.1 The Structure of Three-phase Induction Motor 8.2 The Operational Principle of Induction Motor 8.3 Induction-motor Equivalent Circuit (*) 8.4 Torque and Torque-speed Characteristic 8.5 The Starting of Three-phase Induction Motor 8.6 Speed Control of Induction Motor 8.7 Braking of Three-phase Induction Motor 8.8 The Data of Induction Motor 8.10 Single-phase Induction Motor
A'
ω t = 60 °
Im
iA i B
iC
60 f n1 = (转/分） p
t
Synchronous (同步转速)
60 f n1 = ( 转/分） p
极对数 每个电流周期 磁场转过的空间角度 同步转速
( f = 50 Hz )
n1
p =1
p =2 p =3
360 °
3000 (转/分）
180 °
iA
iB
iC
t
iA
iC
iB
t
Im
Im
i A = I m sin ωt
iB = I m sin (ωt − 120 ° )
iA = I m sin ω t
iC = I m sin (ωt − 240 ° )
iC = I m sin ( ω t − 120° ) iB = I m sin ( ω t − 240° )
120 °
1500 (转/分）
1000 (转/分）
Rotor speed and magnetic field speed
电动机转速（额定转速）:
n
电机转子转动方向与磁场旋转的方向一致， 但
n < n1
异步电动机
提示：如果
n = n1
转子与旋转磁场间没有相对运动 无转子电动势（转子导体不切割磁力线） 无转子电流 无转矩
8.1 The Structure of Three-phase Induction Motor Types of motors AC motors Induction motor Motor with wound rotor Synchronous motor DC motors Motor with a squirrel-cage rotor