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The brushless electric motor is a simple beast. At its simplest, it's just a simple bar magnet attached to a bearing mounted shaft. Around the outside is a series of electromagnets that are switched with all those fancy power electronics that exist nowadays. Anyhow, they're nearly always designed with
precise balance so that they can spin at huge speeds. However, with a balanced motor, you require a balanced load. Should the load not be balanced, you need a suitable counterweight (mass). However, in some applications an unbalanced load is advantageous. For example, should you wish to carefully match a single cylinder internal combustion engine with a hybrid electric motor, or to power a single bladed propeller.
So, the simple bar magnet can be bent, as horseshoe magnets are, but not as much, this is more of a V magnet, or a much wider angle, whatever is appropriate for the load balancing. Now you have an intrinsically unbalanced motor, useful for smoothly powering your single bladed propeller, or for creating deliberate vibrations in your personal devices without the added complexity of the deliberate addition of a weight.
||The balancing is still going to be a problem, but this time
along the axial direction of the output shaft, unless you can
locate your propeller blade at the axial center of inertia of
your unbalanced rotor.
||I actually have a purposely unbalanced motor at home in
my scavenged electronics box. It's a pager vibrator
motor. Most of those now days are a balanced motors
with an unbalanced weights on the end, but the one I
have is a pancake style motor. It has a stationary
magnet (unlike your suggestion) and is laid out to have 4
flat coils in a spinning disk. However one of these coils is
intentionally missing to unbalance it. I think the one I
have has brushes. The chip to make it brushless might be
pretty small, but it you strapped a circuit board on this,
it could increase the size by 20% easily.
||It seems to me that your idea is an improvement on this
for a vibrating motor since the magnet is probably
heavier than the coils, and if not, the magnet can be
made heavier by using a cheaper heavier (not rare earth)
magnet. It makes a lot of sense to use part of the motor
as the counterweight rather than including a separate
counterweight in addition to the motor.
||The biggest downside is that if phones and pagers
adopted unbalanced motors, that might eliminate the
cheap source of small powerful motors that is currently
available by removing the counterweight from mass
produced phone vibrator motors.
||// unless you can locate your propeller blade at the axial
center of inertia of your unbalanced rotor //
||That's not too hard. Lay it out like a typical computer fan.
Remove all but one fan blade and remove part of the
magnetic ring to keep it balanced. Obviously the
proportions will need to be quite different in the drone
propeller application suggested.
||//(I did a bit of flux modelling in my youth)//
||We've all been there. Short of cash, along comes a smooth-
talking electronics supplier and before you know it you're
posing suggestively with a pot of heavy duty super-activated
||I knew a fellow who built a piece of process equipment for produce handling that required an unbalanced motor to provide the vibration necessary to move the product a little so it would settle properly.