Pull Up Torque - Induction Motor

I want to know why you did not look elsewhere for the answer, first?

May be some good explanations here, from credible sources, not strangers.

Torque Speed Curve - Apogee Interactive

Pull-up torque - Encyclopedia Magnetica

Torque Characteristics of NEMA A,B,C,D & E Motors

Good hunting.

Dear Lyn, first I want to ask you to read question first. And FYI I had read all of these link before posting. (Googling is easy compared to posting).

Now just go to the link

http://electrical4u.com/torque-equation-of-three-phase-induction-motor/

as per this site and all good books, torque equation is

Now you can plot curve of T vs slip by any program like excel or matlab.

Why I am not able to see any drop in torque after staring torque ? drop is only after maximum torque.

I don't have a clue.

You might be reading the graph differently than I would. You x axis shows "slip" and thus is relative to the source frequency.

From your graph, once slip is higher than 0.16 (that is to the left of that point on the x axis)the available torque is constantly decreasing.

Thus, once the load causes more slip than 0.16, then the motor would stall since the applied load will then continue to exceed the available torque.

From memory (and it's really a long time ago) once a motor is slipping like that, there is a progressively greater period of time in each second where the rotor is moving through a reduced magnetic field and thus provides less torque.

From your graph, the motor must work between 0.16 slip and 0.00. More slip, it stalls, less slit means that it's performing in a braking mode.

stator and rotor slot combination can lead to this distorsion of T_S Curve.There are designs where you will find absolutely no pull up but a staright continuous increase of T with speed.

The stator produces a rotating magnetic field and the rotor "chases after it". So the rotor sees a variable frequency that decreases to zero as it approaches the synchronous speed. The torque is proportional to the stator field strength and the rotor field strength (which depends on the rotor current).

The induction motor therefore acts like a transformer with a variable frequency that depends on the motor speed, and the torque is proportional to the current in the rotor. Rotor resistance is one factor that can control the torque-speed curve. The desired torque-speed curve can be controlled by different rotor construction.

http://www.purduecal.edu/cpmi/NSF%20Courses/ECET-212/CLASSPRESENTATION/InductionMotors.pdf

In my opinion since R2=a+b*s^2 due to skin effect then for s=1 R2start=a+b and for s~0[for rated s] R2rated=a [then b=R2start-R2rated].

T=K*(a+b*s^2)/((a+b*s^2)^2+s^2*X2^2)

In order to find minimum and maximum T we'll put dT/ds=0 and finally we will get:

b^2*s^4-2*a*b*s-(a^2*b+a*x)=0

Four results: maximum as motor[s>0], maximum as generator[s<0], minimum as motor [pull up slip>0], minimum as generator [pull up slip<0]

Correction:

In my above post I omitted the slip[s] factor from the original formula of torque.

So T=K*s*(a+b*s^2)/((a+b*s^2)^2+s^2*X2^2) instead of T=K*(a+b*s^2)/((a+b*s^2)^2+s^2*X2^2)

And the final equation will be:

a^3+(a^2*b-a*X2^2)*s^2+(b*X2^2-a*b^2)*s^4-b^3*s^6=0

If we shall substitute y=s^2 we shall get three results of y and s=+/-sqrt(y1,y2,y3).

I suggest you may refer to Electrical Machines by Fitzerald and Kingsley, a text book used in colleges which deals with the subject very well bot the theoretical and actual aspects

Maximum motor torque is developed during "locked-rotor" condition because the angle between the rotor field and stator field (slip) is at maximum value.

When the motor reaches design speed the magnetic flux has decreased, the stator and rotor fields are synchronized, and the motor slip factor is at minimum value thereby the torque required to keep the rotor rotating is at whatever the minimum value required to drive the load.

Of course this is only true if the motor load is maintained within design HP rating.

The motor design class A, B, C, D determines where the motor develops it's peak torque value and the magnitude of torque available during starting and/or running.