Torque-Speed Characteristics - GATE EE Electrical Machines Free MCQ Test

Concept:

The ratio of maximum torque to full load torque is

Where sm is the slip at maximum torque.

sfl is the slip at full load torque.

Slip at maximum torque, 

R2 is the rotor resistance

X2 is the rotor reactance

Calculation:

Given that, Tm = 2.5 Tfl

Tst = 1.5 Tfl

When full load slip is 0.03

Concept:

The ratio of maximum torque to full load torque is

Where s_m is the slip at maximum torque.

s_fl is the slip at full load torque.

Slip at maximum torque, 

R₂ is the rotor resistance

X₂ is the rotor reactance

Calculation:

Given that, Number of poles (P) = 24

Frequency (f) = 50 Hz

Rotor resistance (R₂) = 0.016 Ω

Rotor reactance (X₂) = 0.265 Ω

Slip at maximum torque, 

Speed corresponding to full load torque (N_r) = 247 rpm

X₂ = 2πfL

X₂ = 2π × 50 × 3.61 × 10^-3 = 1.13 Ω

The synchronous speed, 

When the rotor speed is 1140 rpm, slip 

When the rotor speed is 1000 rpm, slip 

From the equivalent circuit of induction motor, if the value of  remains the same, the rotor current I­₂ and the stator current I₁ will remains the same and the machine develops the same torque.

If the rotational losses are neglected, the developed torque is the same as the load torque.

Therefore, for unity turns ratio,

Concept:

• Protective maintenance will generally involve lubricating, cleaning and checking for sparking brushes, vibration, loose belts, high temperature and unusual noises.
• So a planned inspection and maintenance are needed for a vast of electrical equipment to keep in proper working condition.

The maintenance program for every week  of induction motor follows:

• Examine the commutator and brushes.
• Examine the starter switch, fuses, and other controls; tighten loose connections.
• See if the machine is brought up to rated speed in normal time or not. Examine the commutator and brushes.
• Check the level of oil in the bearings

The Torque vs Speed characteristics of the V/f controlled Induction motor:

• Whenever frequency is varied in order to control speed, the terminal voltage is also varied so as to maintain the V/f ratio constant.
• Thus by maintaining a constant V/f ratio, the maximum torque of the motor becomes constant for changing speed.

​Formula:

The induced emf is

Ф = air-gap flux

B_max = Maximum flux density

f = Supply frequency

n= No.of turns

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The Torque vs Speed characteristics of the V/f controlled Induction motor is shown below.

Fig: BratedBrated size 12{B rSub { size 8{ ital "rated"} } } {}" id="MathJax-Element-49-Frame" role="presentation" style="display: inline; font-size: 14px; position: relative;" tabindex="0">The Torque vs Speed characteristics of the V/f controlled Induction motor

Thus maintaining the V/f ratio constant helps us to maintain a constant maximum torque while controlling the speed.

Concept:

• When T_m = T_L then motor runs at constant speed.
• When Tm > T_L then motor will accelerate & speed will increase.
• When Tm < T_L then motor will retard & speed will decrease.

where, T_m = motor torque & T_L = Load Torque

Explanation:

At point 'P'-

If speed slightly increased, then T_L > T_m As a result there will be retardation & it will come back to point P

If speed slightly decreased, then T_L < T_m As a result, there will be acceleration & it will come back to point P

Therefore operation is STABLE at operating point 'P'.

At point Q - 

If speed is slightly increased, then TL < T_m so, there will be acceleration & the speed will further increase.

If speed is slightly decreased, then T_L > T_m then there will be retardation & the speed will decrease further.

Therefore, operation is UNSTABLE at operating point 'Q'.

At point 'R'

If speed slightly increased, then T_L > T_m. there will be Acceleration & motor's speed will increase

Therefore, operation is UNSTABLE at point 'R'.

At point 'S'

If speed slightly increased, then T_L > T_m, then there will be retardation & motor's speed will decrease. As a result motion will back to original speed. therefore, operation is STABLE at point 'S'.

• Induction motor is a type of electric motor in which alternating current from a power source is fed through a primary winding and induces a current in a secondary winding, with the parts arranged so that the resulting magnetic field causes a movable rotor to rotate with respect to a fixed stator.
• The torque-slip characteristics is represented by a rectangular hyperbola.
• For the immediate value of slip, the graph changes from one form to another.
• The torque equation of the induction motor is:

The torque slip characteristic curve is divided into three regions:

• Low slip region
• Medium slip region
• High slip region

Low slip region:

At synchronous speed, slip = 0, therefore the torque is zero.

When there is a light load, the speed is very near to synchronous speed.

The slip is very low and (sX₂₀)² is negligible in comparison with R2. Therefore

i.e. T ∝ S

Medium slip region:

As the slip increases, the speed of the motor decreases with the increase in load.

The term (sX₂₀)² becomes large.

The term R²₂ may be neglected in comparison with the term (sX₂₀)² and the torque equation becomes

Hence for heavy loads, torque is inversely proportional to slip.

High slip region:

Beyond the maximum torque point, the value of torque starts decreasing. As a result, the motor slows down and stops.

At this stage, the overload protection must immediately disconnect the motor from the supply to prevent damage due to the overheating of the motor.

Note:

The motor operates for the values of the slip between s = 0 and s = sm, where sm in the value of slip corresponding to maximum torque.

Torque-Speed Characteristics:

At the low slip region, the torque is proportional to slip. Hence, in the normal working region of the motor, the value of the slip is small. The torque slip curve is a straight line.

Torque ∝ slip

The speed control of three-phase induction motor from the stator side are classified as:

• V/f control or frequency control
• Changing the number of stator poles
• Controlling supply voltage
• Adding rheostat in the stator circuit

The speed controls of three-phase induction motor from rotor side are classified as:

• Adding external resistance on the rotor side
• Cascade control method
• Injecting slip frequency emf into rotor side