I don't understand how shading coils work

[fubar.gr]

https://en.wikipedia.org/wiki/Shading_coil

If I understand correctly, the sum of the two magnetic fluxes (main and 90deg shifted) is still a sinewave that passes through zero. So the chattering problem in contactors should persist.

[Berni]

If you take a closer look at the photo in the Wikipedia article you will notice that the shading coil only goes around half of the exposed magnetic core.

So when the unshaded half is crossing 0 and providing 0 attraction force, the shaded part is 90 deg out and providing some attraction. Then when the shaded part is crossing zero, the unshaded part is again out of phase and so it providing some amount of attraction. Once you sum together both of the forces never goes truly to 0.

Or a more mathematical way of explaining it. Yes you always get a normal zero crossing sine wave if you sum two sine waves. But you don't always get a zero crossing is you do "abs(sine1) + abs(sine2)"