More on fans and voltages.

For a regular DC brushed motor this is fundamental, albeit a reduction to absurdity. If the applied voltage equals the back EMF the motor is stationary and both speed and voltage are zero. In operation there is _always_ a net applied voltage, it is that voltage which powers the motor. The only theoretical time the two could be equal in motion if if the motor is itself 100% efficient

- no resistive or frictional losses - and has no load, in which case it is also doing no work.

This is basic high school level stuff - if the two voltages are equal no current flows. Therefore no power is consumed and in turn that means no work is done.

For a BLDC - basically the only game in town for computer fans - the two are unconnected. BLDCs are synchronous motors and as such the speed is directly controlled by the pulse train from the (on-fan) controller. The fans can't exceed that speed (unless externally driven) as there is nothng to accelerate it above that speed. If the applied torque is such the fan cannot maintain that programmed speed, it does not slow down but stall, as the phase relationship between the rotor and stator is lost.

This is utterly meaningless. If you drop the voltage to 60% original and current remains constant then power is also 60% of the original. If the current did drop by the same proportion then at that point you end up at 36% power. The high school level error is in the assumption that a motor remotely obeys Ohm's law - it's not true even to a first approximation.

To cut a long story short a computer fan is a BLDC motor and its operation is governed in its entirety by the behaviour of the controller, and that is resistant to naive analysis. As I said I haven't actually measured this on more than a few samples over the years - perhaps half a dozen - but assuming a constant current draw has generally proven a good starting point.

Incorrect

You havent understood anything have you?

No work is done if a perfect motor is spinning at a constant speed.

You really dont understand it at all do you?

The fans can't exceed that speed (unless externally

No, it doesn't. Once again you have no idea how the controller works.

It is hopeless to try and educate someone who has absorbed so little knowledge that he thinks he understands everything.

It certainly is in your case.

As I said I

I have measured it on dozens of samples over the years. As I said I used to design model aircraft with BLDC motors and occasionally still do. I have an MA in electrical engineering.

Grandmothers, eggs, suck.

I'm not going to waste too much time with this, I gave some concrete arguments. Lack counter evidence you respond with insults.

Instead let me be the first to congratulate you in advance on your Nobel prize. You've just broken the conservation of energy. I have a motor connected to a pully lifting a weight. I begin by lifting a moderate amount - a metre say, enough to get it to constant speed. I now need apply no more energy to continue to lift that weight to an infinite height.

True but not very interesting since there is no such thing.

Sigh - he hadn't until you added that weight before then it was just conservation of energy and momentum in a friction free environment.

Why don't you two stop trying to one-down each other ? Nobody is right all the time, and very few people are wrong all the time so working together tends to be more productive than antagonism and point scoring.

Exactly! With the air moved by the fan we were originally talking about being the load equivalent to the weight in your example. Continuous moving air for no expenditure of energy. Oddly enough, if the power source (that isn't delivering any power) is turned off, the fan stops. Hmmm... ;-)

And even if no external work were being done, just an unloaded motor spinning at constant speed, frictionless for the sake of argument, flux in the ferromagnetics (or whatever if the materials are exotic) armature and field cores are still changing and that requires power.

All in all I'd say there is no "perfect" motor possible even in theory

- perfect meaning drawing no power when operating - because even absent friction there are going to be core losses from the changing magnetic field.

To be way overly generous here, I'm guessing some sort of ChatGPT output was requested and misinterpreted and no explanation will suffice for NP since the knowledge required to understand it seems to be lacking.

Actually he had... tho he didn't realize it, and neither do you... since core losses occur when flux is changed, a requirement for a motor (or transformer), work is done to change the flux and heat the core as a result, even if there is no friction or no load.

Sometimes nonsense is too much to keep quiet about.

He specified "perfect" so no core losses.

I'm not going to waste too much time with this, I gave some concrete >arguments. Lack counter evidence you respond with insults.

Oh dear. Really scraping the barrel aren't we? Where in my post hqd I a pulley connected to a weight?

The issue is that under no load a motor is best analysed as 'perfect' with a few quantifiable 'imperfections'.

That is how it is done.. for very good reason. We add in 'idle current' which represents fixed losses due to magnetic hysteresis and friction, and we add in resistive loses due the the resistance of the windings. That gives a very accurate pitcure of moror behavior, and along with the Kv - the back EMF constant, defines the motor behaviour theoretically and experimentally. Kv, Io and Ro - those are the motors characteristic. Nowhere is it speed defined by frequency, for the simple reason that the frequency is controlled by the motors rotational speed. A brushless DC motor is simple DC motor whose commutator has been replaced by an H bridge of power FETs, and a sensor circuit that senses the position of the rotor either by sensors or by monitoring the unenergised pole(s) of the motor. To confuse it with a synchronous motor is akin to saying that you control a cars speed by varying the ignition timing.

People want to know if their fans will run safely on 3V. I have tried to explain why this is (probably) true. RPM and current draw is deeply sensitive to applied voltage.

I had assumed since the OP claimed at least high school physics that he understood the term.

The ideal motor has frictionless bearings, runs in a vacuum and has superconducting windings and no hysteresis losses in its core - in fact many motors do not use iron at all for that reasons.

It only draws current when it has to drive a load. Its speed will never vary under load. It runs at the speed where the back emf equals the applied voltage. Adding more load simply increases the current it draws.

Same as a 'perfect' transformer. The output voltage doesn't vary under load, only the input current does.

I have no idea where the OP got his so called 'knowledge' from. Mine comes from absolutely standard high school electrical motor theory. At least, in my day, it was high school. These days its probably PhD standard material that the student 'rediscovers' after reading 20th century text books.