Measuring the frequency of motor vibration
Eugene Sh. is correct (see comments), measuring motor vibration using an accelerometer on the motor body is the only real way to measure vibration directly.

I disagree that the method of measurement is inaccurate.  The peaks that you are seeing are the individual commutations.  If you know the motor pole/slots configuration, you can easily use this to determine the actual shaft speed.  I have been doing this for years and can attest to the accuracy if you know your motor.  Your article is correct.

Your resistance of 1.5 ohms is very high for a motor.  This should probably be on the order of 0.1ohms or less.  You are restricting the motor speed/torque by placing this resistor in series with your motor.

There are various sources of motor vibration which are always present, but you can only guess as to the relative amplitude if you don't measure them.


The first is the vibration at fundamental frequency, which is the frequency that you were trying to calculate.  This is usually the result of mechanical imbalance in the rotor, just like a wheel imbalanced on your car.
Another source of imbalance is 'cogging'.  This is caused when the rotor magnets line up with the stator and then continue and is a harmonic of the fundamental rotational frequency.  You can feel cogging when you turn the shaft by hand and feel the slight differences in torque applied to your hand.
Commutation method also causes a vibration.  Those peaks on your current waveform are actually changing currents, which causes changing torque on your motor at those frequencies.  Torque is directly proportional to current, so a current applied at frequency causes a torque ripple, causing vibration.
The bearings are a small contributor to motor vibration and are usually only observed once the other three have been minimized.  Ball bearings can sometimes be identified on a Bode plot of the motor vibration by looking at the number of balls in the bearing and multiplying that by the fundamental frequency.  Funny things happen with bearings at high speeds, though, so this one is difficult.  Probably no need to even look here.


There are a couple of other potential sources, but these are dominant.  Without actually placing a three-axis accelerometer on the motor case and measuring, you can't be sure.  Once you get the vibration data, you can usually determine the source of the frequency just by looking at its relationship to the fundamental.


If highest vibration is at fundamental, rotor imbalance
If the highest vibration is at cogging, you should be able to count the cogs as you rotate by hand, multiply that by the fundamental, and get the frequency of vibe.
If the vibration is at the same frequency as the current peaks, then you are seeing a result of a differential torque applied via the commutation method.