Efficiency of Keppe motor: simple and easy estimate

Hi,

After some thinking, I would like to present a very easy formula to estimate the Keppe motors’ mechanical efficiency. The formula does not predict efficiency but provides a fair guess based upon the measurement of 2 parameters only.

Theory tells us the following about the force and induced voltage on an electrical conductor that is moving in an EM field:

Force F = B*l*i (induction x length x current)
Voltage E = B*l*v (induction x length x velocity)

With a given motor layout, the coil length and induction (by the magnet) can be assumed to be constant so we can write that:

B*l = E/v so F = (E/v) * i

In these equations i and E are the instantaneous values of current and induced voltage. To estimate efficiency, we have to work with average values. With :
I = average value of i
Uac = rms value of induced voltage = ê * 2/PI (ê = amplitude, assume a sine pattern)
U = battery voltage
R = radius (distance from shaft to coil in radial direction)
w = angular velocity (rad/sec)
v = w * R
Pe = U*I (electrical power consumed, approximation)
Pm = w * T (mechanical power = torque * angular velocity)

This way with E/v = Uac / (w * R ) the average force and torque on the rotor become:
F = Uac * I / (w * R )
T = F * R

The overall efficiency (in %) = 100 * Pm / Pe
= w * F * R *100 / (U * I)
= w * Uac * I * R *100 / ((w * R ) * (U * I) )
= Uac * 100 / U
= ê * 200 / (PI * U)

The values of ê and U can easily be read for an oscilloscope screen. According to this formula, if motor efficiency = 100%, on the oscilloscope the amplitude of the induced voltage and the battery voltage would be equal.

Example calculation: see gmeast post of April 18 for data:
ê = 8 volts
U = 16 V
Result:
* estimated efficiency = 8 * 200 / (3.14 * 16) = 31.8 %
* measured efficiency was about 40%

Please inform me of any errors in the above.

Hi jgreef,

The analysis looks intriguing. I only followed it in part but will continue to work through it. The relationship between battery voltage and induced voltage is an eye opener though. I'll hook my motor back up and peek at this.

Great post,

Greg

Hi,

I am sorry to announce I already found 2 errors in my post. However, they basically won't change the outcome of it.

Error 1:
I stated that the rms value of a sine signal = peak value * 2/Pi. That is incorrect, it was the formula for the average value of the signal. The rms value = peak value * (square root of 2). What value (average or rms) is to be used in my efficiency formula is open for discussion. Since the idea is to calculate the average value of the induced voltage, I would be tempted to use the average value so not the rms value.

Error 2:
I stated : "According to this formula, if motor efficiency = 100%, on the oscilloscope the amplitude of the induced voltage and the battery voltage would be equal." That is incorrect too; if you look at the formula you'll note that to make efficiency = 100%, the amplitude of the induced voltage should be Pi/2 times the battery voltage.

In the meantime, I did some extra testing and it seems that the value "B * l" is indeed more or less a constant (for my motor at least. The parameters I changed to check that were battery voltage, switch closing moment and minor rotor adjustments.

RMS = .707 X Vpeak or Vpeak/1.414, assuming a near perfect sine wave.

JA