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)
Am, Ae are the cross sections of the magnetic and electric circuit
lm, le 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

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, ρr 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". Proceedings of the International Electric Machines and Drives Conference 2: 1195–1200. doi:10.1109/IEMDC.2003.1210392. http://vtb.engr.sc.edu/vtbwebsite/downloads/publications/IEMDCpaper.pdf. 
  3. ^ ER Laithwaite (1965). "Electromagnetic levitation". Electronics and Power 11 (12): 408–410. doi:10.1049/ep.1965.0312. http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5176480.