Three phase Induction Motor torque/slip HELP NEEDED

[callum76wood]

Hi, I'm really stuck on this assignment question and could do with a hand on the step by step process of how to get the answers.

A three phase induction motor as 2 poles, a standstill voltage of 121 v/phase (Er), rotor resistance of 0.15Ω/phase (Rr) and a standstill rotor reactance of 1.2Ω/phase (Xr)

1. Plot the torque against slip characteristic when the supply frequency is 50Hz for slip values of 1.0, 0.75, 0.5, 0.25, & 0.05

2. Determine the current in each phase of the rotor
A) At start
B) At maximum torque
C) At full load torque if this occurs at a slip of 4%

 

[Babadag]

Neglecting skin and proximity effect in rotor winding-or squirrel cage-
Irot=s*Er/sqrt(Rr^2+s^2*Xr^2) [A] Er[V] ,Rr,Xr [ohm]
Tqmot=3*Irot^2*Rr/s/(2*pi()*f/p) [Nm] p=no.of pole pairs=1
For s=1 [at start] Ir=100 A Tq= 14.33 Nm
For s=0.04 [rated] Ir=30.73 A Tq= 1691 Nm

 

[Babadag]

Sorry, I forgot the maximum torque slip calculation.
The maximum torque slip it is the slip calculated from dTq/ds=0.
If Tq=3*I^2*R/s/(2*PI()*f/p) and I=s*Er/sqrt(R^2+s^2*X^2) then
Tq =3*s^2*Er^2/(R^2+s^2*X^2)/s*R/(2*pi()*f/p)
dTq/ds=3*Er^2/(2*pi()*f/p)*[(R^2+s^2*X^2)-2*s^2*X^2]=0
X^2*s^2=R^2
s=R/X
sm=0.15/1.2=0.125

 

[Babadag]

correction:
s=0.04 Tq= 33.81 !
s=0.125 Tq= 58.25
Sorry!

 

[alphy]

Hi there,

To start, it would be helpful to have a basic understanding of how a three phase induction motor works. This type of motor works by inducing a magnetic field in the rotor through the use of a rotating magnetic field in the stator. As the rotor turns, it tries to "catch up" to the rotating magnetic field, creating a torque that drives the motor.

To plot the torque against slip characteristic, you will need to use the following formula: T = (3V^2)/(2πfRr) * (s/(s^2 + (Xr + Rr)^2)), where T is torque, V is voltage, f is frequency, Rr is rotor resistance, Xr is rotor reactance, and s is slip.

1. To plot the characteristic, you will need to plug in the given values for V, f, Rr, and Xr into the formula and then solve for T for each given slip value. This will give you a set of points that you can plot on a graph, with slip on the x-axis and torque on the y-axis. Once you have all the points plotted, you can connect them to create a curve, which will be the torque against slip characteristic.

2. To determine the current in each phase of the rotor, you can use the following formula: I = (V - Er)/(Zr + Zs), where I is the current, V is the supply voltage, Er is the rotor voltage, Zr is the rotor impedance (Rr + jXr), and Zs is the stator impedance.

A) At start, the rotor voltage will be equal to the supply voltage, so you can plug in the given values for V and Er, and then solve for I. This will give you the current in each phase of the rotor at start.

B) At maximum torque, the slip will be at its minimum value, which is 1-slip. So, you can plug in the given values for V, f, Rr, and Xr, and then solve for T at a slip value of 1-slip. Once you have the torque value, you can use it to solve for the current in each phase of the rotor using the formula above.

C) At full load torque, you can use the given slip value of 4% and plug it into the formula for T. Once you have the torque value, you can use it