DC and AC Motors, Back emf

Hi,

I am trying to understand what effect the induced EMF in a DC and AC motor has on rotation.

As an example, here is what I've understood about DC motor operation: If I assume a single loop of wire (equipped with commutator, etc.) and it is in between the N and S pole of two permanent magnets, and the ends of the wire are hooked up to a DC battery, I understand that the current through the wire and the magnetic field due to the magnets will result in a force on the wire and the loop will spin.

Once the loop is spinning though is where I get confused. So now, the flux through the loop is changing, and there is an induced emf in the loop. Based on Faraday's law:

∫E*dl = -V + IR = -Nd(phi)/dt

So the back-emf is equal to the battery voltage less the voltage drop due to the resistance fo the wire. If the resistance is very small, then the back-emf nearly equals the battery voltage, and the result would be very little current flowing in the cirucit, and thus very little torque. How does the motor get away with this?

Also, how can the rotor turn smoothly if it is constantly challenged by the back-emf?

Finally, in an AC motor, where the current is varying sinusoidally, how is the force on the rotor constant?

Thanks in advance for your help!

The back EMF is only (nearly) equal to the supply when the motor is running at it's speed (for that given voltage).

It's the back EMF that sets the speed for a particular voltage, which is why DC motors can easily be speed controlled by varying the supply voltage.

When free running, as you say there is very little torque. When a load is applied to the motor, the speed drops - so the back EMF reduces and the current rises.

That will keep happening (more torque loading = less speed & more current) all the way down until the motor stalls and it is taking the full current allowed by the resistance of the circuit with zero back EMF.

Where the motor speed is critical, some motors have built-in speed control, either simple centrifugal switches or electronics. Others may have tachometers or encoders to allow the speed to be accurately regulated by external electronics.

For AC motors, with a single phase motor the torque is not constant, it relies on the inertia of the motor and mechanical load to maintain a steady speed.

With three phase motors, there is always torque as there is always power in some combination between phases.

Thanks for the response! Let me see if I'm understanding...

So, at no load, the back emf is 0 when the rotor is at rest, but goes up when current begins to flow in the rotor and there is thus torque. But then, almost as fast, the back-emf lowers the current from the battery and reduces the torque. But then, wouldn't you just get the same situation repeating itself over and over, because with the torque reduced, the back-emf reduces, and the current raises, and then the torque raises and so does the back-emf, so the current reduces again. I don't see why there is an equilibrium in this situation. But I'm guessing there is...is that what you meant by this statement?

"The back EMF is only (nearly) equal to the supply when the motor is running at it's speed (for that given voltage)."

So, at the point when the back-emf equals the battery emf, is there no current? Wouldn't that imply no toruqe and bring the rotor to a halt?

Also for this statement: "When free running, as you say there is very little torque. When a load is applied to the motor, the speed drops - so the back EMF reduces and the current rises."
So, if the motor at no load is hardly spinning at all because there is not much current, and then it spins even less when there is a load connected and the back-emf reduces even more, so now more current can flow and the motor picks up again and starts spinning? But then, more back-emf, less current! I keep digging myself deeper when I start thinking like that because the cycle seems to be never ending: more current, more torque, more back-emf, less current, less torque, less back-emf, and so on and so on!

Maybe it would help to think what happens if you spin the motor with no electrical input. Or maybe not, but it is a different perspective.
The motor would act as a dynamo. With the connections open the motor would spin easily. If they were shorted it would be harder to turn.

The back emf is directly proportional to speed, not torque.

I guess I'm confused because for a motor, the speed of the rotor depends on the amount of current flowing through the rotor and the strength of the magnetic field it is imersed in. I am assuming the magnetic field strength is constant because it is being supplied by 2 permanent magnets. The current through the rotor, as I see it, is not constant.

So the battery is supplying the current to the rotor...what is the maximum value that this current can have? Can the back-emf ever be equal to the supply current (but opposite in magnitude of course)? Why won't the speed of the rotor (in revolutions per unit time) be constantly alternating because you have battery current flowing one way, followed by a back-emf and its resulting current which opposes the battery current, followed by more battery current. Is that not an accurate representation of what is happening inside the motor?

Brief definition: EMF = electromotive force, a term used to describe the origin of voltage in electrical devices

As the Back EMF is *voltage*, the motor draws full current when starting from standstill and the current gradually reduces as the speed increases.

It reaches a balance point where the back EMF is just under the supply and the current (resulting from the difference between supply & back EMF, and the circuit resistance) is sufficient to maintain that speed.

The speed is self regulating to some extent, as an increase in load causes a reduction in EMF and a proportional increase in current.

Remember that the motor current controls torque not speed.

The maximum current is when the motor is stalled, it's then simply the supply voltage divided by total circuit resistance.

If the motor speed exceeds its speed due to the supply voltage, it starts to act as a generator. The back EMF is higher than the battery voltage so the current reverses and the battery is charged instead of discharging.

This is used for braking the motor in speed control system - the supply to the motor is reduced and the motor is actively slowed down as current is drawn from it.

because for a motor, the speed of the rotor depends on the amount of current flowing through the rotor and the strength of the magnetic field it is imersed in.

Click to expand...

replace speed with torque in the above.

Speed is a function of the motor's ability to generate the counter EMF.

It's been described in several ways already;

At stall, when current is the highest, you will have the highest torque, because, as you say, the strength of the proportional field.

As the motor winds up, it's generated voltage offsets the applied voltage and current drops, until it reaches a speed where the current flow from the resultant voltage, imparts enough torque to overcome losses and applied load.

The motor typically will not see saw back and forth because it never peaks over the supply, being held back by at least it's internal losses.

It could be pushed over supply if overdriven by the load, as mentioned in the last post, but then those same losses work equally in the opposite direction. If your load became a supply that matched the electrical supply, you may have some hunting going on.

Sorry i'm so late on replying, it took some time to sink in but i think i'm understanding it now. thanks for your help.

still having great difficulty with torque/speed characteristics of an induction motor, but that's for another post.