This video describes the Torque - Slip / Torque- Speed Characteristics of three phase squirrel cage induction motor and slip ring induction motor- also describes the Condition for the maximum torque - Pullout torque and Pullout torque equation

1. TORQUE- SPEED CHARACTERISTICS OF SQUIRREL CAGE & SLIP RING IM
(OR)
TORQUE- SLIP CHARACTERISTICS OF SQUIRREL CAGE & SLIP RING IM
Basic Torque Equation of DC motor
𝐓 = 𝐤 ∗ ∅ ∗ 𝐈
Basic Torque Equation of AC motor
𝐓 = 𝐤 ∗ ∅ ∗ 𝐈 * cos
Power in DC Circuit
V* I
Power in AC Circuit
V* I * cos
Torque - Multiplication of
2 magnetic fluxes
Power – Multiplication of
Voltage and Current

2. Torque Equation of AC Induction Motor
𝐓 = 𝐊 ∗ ∅ ∗
𝐄 𝟐
𝐙 𝟐
∗
𝐑 𝟐
𝐙 𝟐
𝐓 = 𝐤 ∗ ∅ ∗ 𝐈 𝟐* cos
𝐓 =
𝐊 ∗ ∅ ∗ 𝐄 𝟐 ∗ 𝐑 𝟐
𝐙 𝟐
𝟐
𝐓 =
𝐊 ∗ ∅ ∗ 𝐄 𝟐 ∗ 𝐑 𝟐
𝐑 𝟐
𝟐
+ 𝐗 𝟐
𝟐
𝐓 =
𝐊 ∗ ∅ ∗ 𝐒 𝐄 𝟐 ∗ 𝐑 𝟐
𝐑 𝟐
𝟐
+ ( ሻ𝐒 𝐗 𝟐
𝟐
Slip speed (SNs) = Ns- N
𝐈 𝟐 =
𝐄 𝟐
𝐙 𝟐
; 𝐂𝐨𝐬𝛗 =
𝐑 𝟐
𝐙 𝟐
𝒁 𝟐 = 𝑹 𝟐
𝟐
+ 𝑿 𝟐
𝟐

3. 𝐓 ∝
𝐊 ∗ ∅ ∗ 𝐒 𝐄 𝟐 ∗ 𝐑 𝟐
𝐑 𝟐
𝟐
𝐓 =
𝐊 ∗ ∅ ∗ 𝐒𝐄 𝟐 ∗ 𝐑 𝟐
𝐑 𝟐
𝟐
+ ( ሻ𝐒𝐗 𝟐
𝟐
𝐓 ∝
𝐊 ∗ ∅ ∗ 𝐒𝐄 𝟐 ∗ 𝐑 𝟐
൫ ሻ𝐒𝐗 𝟐
𝟐
𝐓 ∝
𝐊 ∗ ∅ ∗ 𝐄 𝟐 ∗ 𝐑 𝟐
𝐒 ∗ 𝐗 𝟐
𝟐
SLIP
TORQUE
01
0
Ns
SPEED
Low SlipHigh Slip
LOW SLIP REGION
HIGH SLIP REGION
Min speed N= 0
@ which slip S = 1
Max speed N= Ns
@ which slip S = 0
Starting
Torque
Critical Slip
Pull out
Torque
(𝐒𝐗 𝟐ሻ 𝟐
≪ 𝐑 𝟐
𝟐
(𝐒𝐗 𝟐ሻ 𝟐
≫ 𝐑 𝟐
𝟐
General Torque Equation

4. Slip ring Induction Motor
(or)
Torque –Speed characteristics of Slip ring Induction motor
Decreasing
Increasing
𝐓 ∝
𝟏
𝑹
𝐓 ∝ 𝐑

5. What is the Condition
for Maximum Torque?
𝐝𝐓
𝐝𝐒
= 𝟎
𝐝
𝐝𝐬
𝐊 ∗ ∅ ∗ 𝐒𝐄 𝟐 ∗ 𝐑 𝟐
𝐑 𝟐
𝟐
+ ( ሻ𝐒𝐗 𝟐
𝟐
= 𝟎
൯( 𝐑 𝟐
𝟐
+ ሻ𝐒𝐗 𝟐
𝟐 ∗ (𝐊 ∗ ∅ ∗ 𝐄 𝟐 ∗ 𝐑 𝟐ሻ − 𝐊 ∗ ∅ ∗ 𝐒𝐄 𝟐 ∗ 𝐑 𝟐 ∗ (𝟐𝐒𝐗 𝟐
𝟐
𝑹 𝟐
𝟐
+ 𝑺 𝟐 𝑿 𝟐
𝟐 𝟐
= 𝟎
V U’ U V’
𝐕 𝟐
_

6. 𝐊 ∗ ∅ ∗ 𝐄 𝟐 ∗ 𝐑 𝟐
𝟑
+ 𝐊 ∗ ∅ ∗ 𝐄 𝟐 ∗ 𝐑 𝟐 ∗ 𝐒 𝟐 𝐗 𝟐
𝟐
− 𝐊 ∗ ∅ ∗ 𝐒𝐄 𝟐 ∗ 𝐑 𝟐 ∗ 𝟐𝐒𝐗 𝟐
𝟐
= 𝟎
𝐊 ∗ ∅ ∗ 𝐄 𝟐 ∗ 𝐑 𝟐 (𝐑 𝟐
𝟐
+ 𝐒 𝟐
𝐗 𝟐
𝟐
− 𝟐𝐒 𝟐
𝐗 𝟐
𝟐
ሻ = 𝟎
𝐑 𝟐
𝟐
− 𝐒 𝟐
𝐗 𝟐
𝟐
= 𝟎
𝐒 𝟐
=
𝐑 𝟐
𝟐
𝐗 𝟐
𝟐
𝐒 =
𝐑 𝟐
𝐗 𝟐
CRITICAL SLIP =
𝐑 𝟐
𝐗 𝟐
൯( 𝐑 𝟐
𝟐
+ ሻ𝐒𝐗 𝟐
𝟐 ∗ (𝐊 ∗ ∅ ∗ 𝐄 𝟐 ∗ 𝐑 𝟐ሻ − 𝐊 ∗ ∅ ∗ 𝐒𝐄 𝟐 ∗ 𝐑 𝟐 ∗ (𝟐𝐒𝐗 𝟐
𝟐
𝑹 𝟐
𝟐
+ 𝑺 𝟐 𝑿 𝟐
𝟐 𝟐
= 𝟎

7. 𝐓 =
𝐊 ∗ ∅ ∗ 𝐒𝐄 𝟐 ∗ 𝐑 𝟐
𝐑 𝟐
𝟐
+ ( ሻ𝐒𝐗 𝟐
𝟐
𝐓(𝐦𝐚𝐱ሻ =
𝐊 ∗ ∅ ∗
𝐑2
𝐗2
𝐄2 ∗ 𝐑2
𝐑2
2
+
𝐑2
2
𝐗2
2 ∗ 𝐗2
2
𝐓(𝐦𝐚𝐱ሻ =
𝐊 ∗ ∅ ∗ 𝐄2 ∗ 𝐑2
2
2𝐑2
2
∗ 𝑿2
𝐓 𝐦𝐚𝐱 𝐨𝐫 𝐩𝐮𝐥𝐥𝐨𝐮𝐭 𝐭𝐨𝐫𝐪𝐮𝐞 =
𝐊 ∗ ∅ ∗ 𝐄 𝟐
𝟐 𝑿 𝟐
PULL OUT TORQUE EQUATION
(Irrespective of rotor resistance 𝐑 𝟐)