Goodness factor

Goodness factor is a metric developed by Eric Laithwaite to determine the 'goodness' of an electric motor.^[1][2] Using it he was able to develop efficient magnetic levitation induction motors.^[3]

$G={\frac {\omega }{{\mathrm {resistance}}\times {\mathrm {reluctance}}}}={\frac {\omega \mu \sigma A_{{\mathrm {m}}}A_{{\mathrm {e}}}}{l_{{\mathrm {m}}}l_{{\mathrm {e}}}}}$

where

G is the goodness factor (factors above 1 are likely to be efficient)

A_m, A_e are the cross sections of the magnetic and electric circuit

l_m, l_e are the lengths of the magnetic and electric circuits

μ is the permeability of the core

ω is the angular frequency the motor is driven at

σ is the conductivity of the conductor

From this he showed that the most efficient motors are likely to be relatively large. However, the equation only directly relates to non-permanent magnet motors.

Laithwaite showed that for a simple induction motor this gave:

$G\propto {\frac {\omega \mu _{0}p^{2}}{\rho _{{\mathrm {r}}}g}}$

where p is the pole pitch arc length, ρ_r is the surface resistivity of the rotor and g is the air gap.

References

1. ER Laithwaite (1965). "The Goodness of a Machine". Electronics and Power. 11 (3): 101–103. doi:10.1049/ep.1965.0071.
2. DJ Patterson; CW Brice; RA Dougal; D Kovuri (2003). "The "Goodness" of Small Contemporary Permanent Magnet Electric Machines" (PDF). Proceedings of the International Electric Machines and Drives Conference. 2: 1195–1200. doi:10.1109/IEMDC.2003.1210392.
3. ER Laithwaite (1965). "Electromagnetic levitation". Electronics and Power. 11 (12): 408–410. doi:10.1049/ep.1965.0312.