Brushed motors can be powered by DC voltage because the commutation is done by static mechanic-contacts. However the graphite brush wears out over time (and causes ugly EMC noise). And it drags, what results in a bad efficiency (P_electric = P_mechanic + P_losses). Brushless DC motors are therefore more reliable and have a better over all performance. But, the commutation-timing is a challange.
Brushless motors use a rotating outer-rotator (out-runners) with embedded permanent magnets and a stator holding the coils. Three coils build up a rotating electrical field that drags the permanent magnets with it.
Ideally this rotating field gets generated by three sinusoidal 120º shifted currents. The here used method is a so called trapezoidal approximation which is close enough to the ideal sinusoidal coil current (with a bit more power losses).
The motor shown above has 14 permanent magnets (nuts N) and 12 poles (P). One Periode of the coil current does not result in a 360º rotation of the motor. There is a fix relationship between f_electrial to f_mechanical wich is number_of_nuts / 2 (in our case 14/2 = 7).
The above motor is a 14N12P BLDC out-runner Type 2216 with 800kV. kV is a characteristic quantity that tells us how big the number of revolutions is per volt power. So I use a LiPo 4S battery with about 15V. So with no load (!) I could (ideally) get a max 12’000 turns/min. kV in fact talks about the self induced voltage on the coils when you turn the stator mechanically; use the motor as a generator. The induced voltage (moving conductor in a static field – d_phi/d_t) is called back electromagnetic force (BEMF). V_BEMF = B * N * v * l (V_BEMF = induction * number of coil windings * velocity * length).
And then we should know, that the higher the torque of the motor the coil-current increases. The max turns/min also drop with the torque. And the coil current drops with the discharging of the battery. A few things to consider designing a perfect system.