Post by: klugesmith on December 08, 2019, 11:41:00 AM
Based on Wheeler's formula, basic electrical conductance, and simple finite-element analysis using the FEMM program.
A similar investigation for crushable beverage cans, done more then 10 years ago, never got reported.
The test disk diameters are the same as in a recent post under Sense Coil Fabrication.
To play nicely with Wheeler's formula, inside and outside diameters are 1 and 3 inches, so the mean radius and "winding width" are both 1 inch.
As a 1-turn coil (N=1), the inductance by Wheeler's formula is 1/19 uH, or 52.6 nH.
The shorted-turn resistance is 201 micro-ohms, if 0.05 inches thick and made of 6061-T6 alloy at 20 degrees C.
(conductor length = 2 pi inches, area 0.05 in^2, conductivity 24.59 MS/m.)
The L/R time constant is 262 us; that's how fast a circulating current would decay if there were nothing to keep it going.
Corresponding corner frequency is 608 Hz, so at frequencies far above that the disk behaves like an inductor.
Doubling the metal thickness, to 0.10 inches, would halve the resistance and not (per Wheeler) change the inductance.
So R = 101 u-ohm, L/R = 523 us, corner frequency 304 Hz.
The effective R values could be slightly larger because of skin effect in the aluminum alloy.
For 100, 1000, and 10000 Hz, I figure skin depth of 0.4", 0.13", 0.04" ( 10, 3.2, 1.0 mm).
Just starting to be significant for single HDD platters.
Here's a representative picture from a FEMM run with 0.04" thick disk, declared as 50 turns:
For other values of N, other than 1 which seems to be a problem case, the indicated L and R values are proportional to N^2.
In this case L = 126 uH (50.4 nH for single turn), which is 96% of that according to Wheeler.
R is 0.629 ohms (251 u-ohm for single turn), exactly matching the simple resistance computation above.
For what it's worth, the inductance (flux linkage per ampere) in FEMM simulation was closer to the Wheeler formula for thinner disks.