Hi,
Yes nice link there. They state outright that it is and i quote, "a shading or short circuit ring", that is used to delay the fall of the flux when used with AC.
The basic theory for this would come from the simple inductor:
V=L*di/dt
and solving for the time delay dt:
dt=L*di/V
With a normalized L*di we have:
dt=1/V
so with the voltage V equal to 10 volts it takes time:
dt=1/10
or 0.1 second to decrease the current i (and thus the flux) by some amount di. But if the voltage is lower, like 1v, we get:
dt=1/1=1 second
which is a full second now. Decreasing the voltage to 0.1 volts we get:
dt=1/0.1=10 seconds
which is much longer now. So as the voltage is decreased the time delay gets longer and longer until we reach zero volts:
dt=1/0 => +infinity
and then the relay would never open. But of course in a real relay the coupling of the field to the ring is going to be minimal (no where near a perfect 1) so the time delay will be much less.
It's also of side interest that it should cause more current to flow in the relay wires when it is energized. How much more would depend on the degree of coupling and the resistance of the winding vs the resistance of the ring.
However, it would still be interesting to see this run with and without the ring to see just how much better this particular relay works with the ring. A video with and without the ring would be nice