Hi TerryW,
I won't be mean for the sake of insult or otherwise, but I do have some contributions, contradictions, and general rip-shred response to your post. Sorry, I must have too much time on my hands.
I seem have ended up writing a small introductory thesis on fans and motors below
But my intent is really just to pony-up what strange tidbits I have collected over the years, to the public good and for general interest and curio sake. This is a fan forum after all.
(fan of technology, pun intended 
) I am also not trying to talk down to anyone with this post, I just want to be clear enough for any readers who might not have all the background.
I will use
rotor to indicate the spinning part of a motor/fan, and
stator to indicate the stationary part. On most motors the outer shell part stays still (stator is the magnets or coils), and the part in the center spins (rotor, is coils or magnets). Most computer cooling fans are sort of the other way, where the hub of the fan spins (rotor is magnets), and it is outside of the stationary parts up the middle which include the stator (coils in this case), and the shaft and bearings (at the very very center).
A
commutator is a ring of metal pads around the shaft of a motor. The brushes ride on this same ring, and the pads are connected to coils on the rotor, forming a circuit from brush to pad to coil to oppsite pad to opposite brush. The brushes are aligned to the stator coils/poles such that as the commutator pads turn under the brushes, a rotor coil/pole is energised to attract or repel a nearby stator coil/pole. From the point of view of any one
rotor coil, it is getting energised one way then the other, back and forth, as it spins under opposite brushes. This is called commutating, and that ring of metal pads picks up the namesake.
In a modern DC cooling fan there is no commutator, and the rotor has permanent magnets, so the stator coils/poles have to be commutated (alternated) by an electronic circuit. An oscillator in the circuit will determine how fast to commutate the poles, and that sets the RPM. AC fans use the Alternations of the supply Current to commutate the stator coils/poles; they likewise spin (RPM) at some multiple of 60Hz, somewhat regardless of voltage changes (a dimmer switch might not work right).
Slip rings are seperate continuous metal rings mounted on the rotor, one per brush. They pass electricity from brush to ring, allowing an uncommutated connection to the rotor. Outside of motors the same principal is used in any swivelling wire connector, like ones for phone cords.
Brushless is the most common, meaning no brushes and uses a slip commutator to make electrical connections to the armature. Similar concept as the starter motor in your car. These types of fans generally are inexpensive and usually do not have RPM monitoring (2-wires).
I have
never seen a slip ring DC fan. Also, it would still have brushes for the slip rings, and hence not be brushless. Furthermore, slip rings
are not commutators. As far as I know, slip rings are used to power the rotor in automotive alternators; and in very huge AC motors that need active (not feild excited) rotors but do not need commutation. Car starters are
always commutated, they have to be, there is no cheap/sane/practical way to make a very high current DC series motor (= very high torque) other than brushes+commutator.
In short, electrical contact of moving parts (slip ring
or commutator) =
has brushes.
Brushless = permanent magnet rotor (DC), feild excited rotor (AC), or seperate field coils replacing slip rings (AC generators).
The only
not-brushless DC fans I have ever seen in anything except car radiator fans had small seperate DC motors, with plastic fan blades stuck on the small shafts, very easy to spot. As far as I can tell these are now 100% obsoleted by standard compact brushless hub-rotor fans, like what we are used to in all modern PC equipment. No cooling fans we discuss here
ever use the small seperate DC motors which almost always use brushes. They are
always hub-rotors, lined with cheap ceramic permanent magnets. Ok, except for the YS-Tech tip drives. A permanent magnet rotor means you have to commutate (alternate N-S-N-S...) the stator fields. The stator sits still, so you don't need the brushes+commutator to get electricity to it, but it still needs to be commutated. As far as I know, an IC based circuit is always used (Wow,
solid state man), and it was their ever decreasing cost combined with the trend to surface mount (=small) than enabled the near complete takeover of these fans from the old seperate motor (has brushes) type fans. If the IC used is a recent enough design, then it will probably support recent enhancements like RPM monitoring or stall detection, and/or external speed control. This will likewise require more connections than the basic 2 wire + & - arrangement.
So, all modern DC cooling fans are brushless. All AC fans are brushless. And that sets the stage for noise and motor effects at low voltages...
As most computer fans are marked @ 12VDC working, they could operate reliably at a lower voltage. However, the fans could start making noises at the lower voltages. I.E. The whining or clicking sounds could be caused by the low DC voltage generating oscillations in the inductors in the direct drive / servo motors, etc.
As far as I can tell, the majority of noise in DC cooling fans is from bearings or blades (ie. mechanical sources), although some is definitely from motor effects (electronic origins).
Ball bearing type fans have one or two ball bearing sets, similar to any other normal self contained ball bearing set, but always quite small. With low cost items such as fans, read "cheap bearings" too, not like VCR head bearings (amazing). These bearings are known to be very prone to mechanical shock damage, and the usual symptom is noise, although the manufacturers say that the service life is realatively un-affected. I would guess that the lower the RPM's, the lower the bearing velocity, the more distinct and audible will be the clicking and chattering of these bearings. I once re-oiled a small CPU cooler fan several times, each time it got noisy, until at last it died of bearing failure such that the balls were jammed and the fan was seized solid. The behaviour was that of cheap bearings, and most of the fan noise came from them. I bet that some companies use larger and better grade bearings (Papst?) but that will be the wild exception, not the rule.
Sleave bearing fans are another and different matter, especially considering modern hydrodynamic wave designs. Sleaves tend to be quieter, but they might dry up and/or wear out in less time than ball bearings. With hydrodynamic wave designs, I will wildly speculate that these may have a functional RPM below which the linear velocity of the bearing surfaces is less than the propagation rate of the fluid waves. In this event the collapse of fluid/wave support could lead to cyclycal/resonant effects that might allow bearing contact and/or reach audability. Who knows.
In both ball and sleave fans, blade count, blade spacing, spider design, and many other factors lead to many and varied resonant effects at different fan speeds. These resonant (likely accoustic) effects can certainly be badly exascerbated at lower RPM's where often more of the sounds slide down into the higher sensitivity (lower frequency) ranges of human hearing.
With the electronic drive systems, I will speculate on probable design principals and practicalities, leading up to motor noise effects vs. voltage. The IC's are likely analog, and would function well across a wide range of voltages, just like transistors, diodes, linear regulators, op-amps, and 555'ish timers. They have no need for fixed 1 vs. 0 logic thresholds which bind digital IC's. It would also be unwise to get too picky about 12v (or 24 or 48 for that matter) since these are often unregulated battery power system voltages where 12v can be anything from 10v to 16v or worse, and you want the fans to run if there is even a hint of juice sniffing around. Still, they might have funny behavior at low voltages where some parts of the IC might work properly, but others might crap out in strange and undesigned ways. This could explain wierd pulsing, chattering and vibrating drive effects.
With respect to the waveform supplied to the coils, it's very unlikely that anything more than timed on/off modulation is supplied, plus maybe polarity reversal. The coils would be wound to supply enough feild strength (set by coil resistance) to move the designed amount of air (work load), at the designed supply voltage, and at a fairly high duty cycle (coils on most of the time). Now, since a fan's work load is probably directly proportional to RPM, and the available stator feild strength will decrease with decreasing supply voltage (fixed coil resistance), you would expect that less voltage => weaker stator magnets => less available power => less RPM. The control circuit needs to adjust itself somehow to cope with changing voltages, keeping synchronized (or nearly so) with the rotor. I can think of three methods for this to work.
The oscillator could be adjustable, from some very low minimum (startup from still), and programmed to always try to ramp up in speed. Holding it back would be a magnetic sensor, which would not allow it to slip ahead of the rotor's actual movement. This system alone would stabilize at whatever RPM the supply voltage could support, as determined by the stator coil resistance and air resistance. Alone however, it would be completely dependant on supply voltage for it's speed regulation. I suspect that this mechanism would be the basis for spinning a brushless motor, and that the following two stategies would simply bias the above process in order to regulate it more sensibly.
The oscillator could be deliberately slowed down as the voltage drops, in order to avoid slippage and maintain sync between the commutations of the stator, and the poles of the rotor. There could be a minimum frequency/attempted RPM that the IC will slow to. If the voltage is too low to dive the fan at that speed, the rotor will slip cycles, spinning slower than the stator asks it to. This condition would surely lead to cyclycal/resonant weirdness and noise, and would well explain low voltage growlies on some fans. A fan that slows its oscillator as the voltage drops would have wide voltage tolerance, but variable airflow.
Another low voltage compensation scheme would be to have the stator coils over powered, but normally under driven by modulation (lower % duty cycle), so that as input voltage drops, the duty cycle can be increased to maintain constant effective power/RPM/airflow. This would still lead to slippage when 100% duty cycle is reached, but the voltage falls too low to drive the rotor at the stator's frequency. Fans using only duty cycle compensation for lowered supply voltage would keep constant airflow, probably over a narrow voltage range, but then might falter/slip badly as voltage becomes too low to maintain that set power output, even at 100% duty cycle.
I suspect that various combinations and/or blends of the above voltage compensation methods would be used by different manufacturers and for different target applications. You could even have a fan that tries to keep up speed within a nominal voltage range (12v-10v = increase duty cycle), but then gracefully ramps down when more seriously undervolted (<10v = slow down oscillator to suite).
RPM slippage is likely a factor in generating motor noise. Slippage is when the cyclycal rotor-stator alignments 'slip' a notch. This is impossible in mechanical brush+commutator motors. Most electrically commutated motors have many poles around the outside and are designed to spin at a multiple of the input frequency x number of poles etc.,
minus a few percent of slippage. Slippage is standard fare in AC motors, where it varies with the load on the motor, increasing the feilds generated in the rotor as the motor slips more under load, thus helping to regulate RPM. In electronic controlled DC motors I doubt that slippage is designed or expected, but it wouldn't hurt anything much, save for generating some beat frequencies between the stator's attempted drive RPM and the rotor's actual lagging RPM. These could easily turn into noise in the audio spectrum. Slippage would also seem more likely at marginal/out of tolerance drive voltages.
Finally, I suspect that there may be an interplay between low RPM's or voltages and the IC's startup functions. Maybe on some fans, at either extreme low RPM's or very low voltages, the startup frequency-ramping function gets erroneously engaged even though the fan is spinning. If this were the case, the fan would get repeated pulses of mis-phased stator input, which would normally only be applied to bring the rotor from stand still to RPM. An already spinning blade would absorb the energy and keep spinning, but might make some funny sounds doing it. Here I draw attention to fans that get strange on 5v but run well on 7v. To see the startup pulses yourself, hold a fan rotor still (gently) with your finger for a few seconds with the power on, and see the blade make little kicks, pausing breifly after each kick until the IC does its startup sequence again. Works with some fans, but maybe not all?
All in all, there are tons of ways for all the above factors to interplay harmonically within range of our hearing: singing, or whining, or organ grinding, as the case may be. Annoying noises aside, I don't think you can hurt these fans by undervolting, and they obviously don't burn up even if their bearings seize, so they can handle indefinite locked rotor. If however you find some really noisy sour spot where bearings sing bad songs at you, you might be slowly trashing the fan, and heck, who needs to do that? The rest is only permanent total hearing loss, and who around here give's a damn about that? We know that some fans work well and fairly quiet, some stutter, some suck when they out blow (not literally:) ).
In the end methinks that empirical testing is the only way to really find out what works well, in the morass of products in this crazy and diverse world. And to that effort, I thank Mike Chin profusely for his excellent and generous work on this site.
I am a very long time tech nerd, and have been since about age 4. How machines, any machines, work. I had really great older friends/tech tutors growing up. Physics, chem, math, I read thermodynamics books on the toilet for fun... you get the picture. I think of it as a useful (?) personality defect, bordering on obsessive compulsive behaviour. So please forgive me for spewing the fruits of my 'disfunction' here, but it's a nice place to share/vent with a really nice regular crew of smart people.
, with those keyboards and cameras, multimeters and notes from comparative listening. Let's see those article submissions!