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.

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.