Why is maximum output power constant in field resistance control method?

[nazia_f]

There are three speed control methods in a shunt DC motor -
Field resistance control
Terminal voltage control
Armature resistance control

In the field/flux control method induced torque decreases and speed increases due to decrease in flux, that is why power remains constant. This is what I got from the book.

I want to know if there is any other explanation about why the output power remains constant or is there any mathematical proof?

 

[NascentOxygen]

In the field/flux control method induced torque decreases and speed increases due to decrease in flux, that is why power remains constant. This is what I got from the book.

I want to know if there is any other explanation about why the output power remains constant or is there any mathematical proof?

It's easy to imagine that starting torque would be reduced when field current is less, there now being reduced repulsion between the armature and weaker field flux.

If we overlook losses, then the rotor of a DC motor will speed up until the rotational speed generates an emf that exactly opposes that of the power supply. If the field's magnetic strength is reduced by reducing the field current, then the rotor must spin faster in that weaker field to generate the same back emf. So it's rotating faster, but the force that is causing this rotation (repulsion between armature and field) is less because you have reduced the field's strength.

I think that is the qualitative question you are asking. The answer suddenly came to me as I was walking to the beach yesterday. It must have been playing on my subconscious mind.

 

[nazia_f]

Maximum torque is proportional to maximum armature current but armature current in inversely proportional to rotational speed. So we can write
T = k/ω
Again P = Tω = (k/ω)*ω = k
So the power remains constant. This answer is what our teacher was expecting from us.
Thanks a lot for your answer but there's something that I didn't clearly get. Could you please explain "less repulsion between armature and field due to reduced field strength" in details to me? How are armature and field repulsing each other?
And I'm really sorry for replying this late.

 

[NascentOxygen]

Could you please explain "less repulsion between armature and field due to reduced field strength" in details to me? How are armature and field repulsing each other?

I used that phrase instead of saying "motor action".

After all, isn't that what causes the rotor to spin--repulsion between the rotor (i.e., armature) and field? The strength of this repulsive force being proportional to the current in each.

 

[nazia_f]

Ah I get it now. :)
Thank you for trying to help me out. ^_^