Speed-Torque Curve

[DFordPE]

Can anyone tell me where to get a simple description of what is happening during the various parts of the induction motor speed-torque curve? I have found some info using equivalent circuits, but:
a. I don't need anything that precise
b. It's been forty years since I graduated and longer than that since I had to use Thevenin.

Case in point, I believe that when the motor starts to rotate and the torque drops to "pull-up," that's where the torque stays until full speed is reached. Others tell me that the torque increases again to "breakdown" and then falls to running torque. I can't see why that would happen. What could possibly cause such a torque increase without a load increase.

 

[electricpete]

What could possibly cause such a torque increase without a load increase.

It is only during steady state where we must assume motor torque = load torque. In contrast, during transient conditions, the motor torque can be different than load torque and the difference represents the accelerating torque.

Ironically, the motor “torque speed curve” is derived from a steady state circuit model but often used for transient analysis. True transient analysis would require a different model, but for many purposes it is sufficient to use quasi-steady state analylsis where we assume motor torque and load torque at a given time are each purely a function of speed at that exact time (and not of history and rates of change).

Can anyone tell me where to get a simple description of what is happening during the various parts of the induction motor speed-torque curve?

Consider the equivalent circuit. Neglect magnetizing imedance for simplicity. All that is left is the resistive impedance R2/s (responsible for torque production and rotor I^2*R losses) and the series inductive reactance Xseries = X1+X2.

At relatively low slip, then R2/s >> Xseries.
As s increases, current increases roughly linearly with slip. I~V/(R2/s) ~ s.
Power factor is roughly constant (predominantly resistive).
So power input is roughly constant
Neglect losses, so power output is roughly constant
Since speed is varying only over a narrow range (under small slip assumption), we can say speed is roughly constant and therefore
Torque = Power / Speed is roughly proportional to slip.

At relatively high speed (s close to 1)
Xseries >>R2/s
As s changes there is very little change in total impedance, but there is an increase in power factor.
This increase in power factor means increase in torque with slip.

In between the very high slip and very low slip extremes, neither effect dominantes and there is gradual transition from one to the other. As a result we see torque increasing with respect to slip on one side of breakdown torque and torque decreasing with slip on the other side of breakdown torque. Monotonic change on each side.

You’ll notice above description didn’t say anything about pullup torque (which is a relative minimum of torque between locked rotor and breakdown torque). It is not predicted by the equivalent circuit with constant parameters. It occurs only if the parameters R2 and L2 themselves vary with frequency due to skin effect. Roughly speaking we can say the skin effect increases power factor at start and gives locked rotor torque a boost. Then as skin effect decreases during start the torque drops initially.


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(2B)+(2B)' ?

 

[bimr]

https://www.youtube.com/watch?v=LzqUJgvqPKw