Hi Boncuk,
Really? Since when is the force curve for the armature a linear function of the applied voltage?
In most relays (maybe all) as the armature pulls in the force increases until it pulls in all the way,
and there it forms a complete magnetic circuit with low reluctance which keeps it all the way pulled
in with lower current than before when the armature was not that close to the core.
That's the way most relays work, and that means a lower voltage will keep it pulled in, with just
the same force on the contacts themselves.
Sure, it may require more than 6v to keep pulled in, but if it does than it will open completely.
It will open completely because if it opens just a little then the current requirement to hold it there
goes up again, which means it opens even more, and that causes another increase in the
current requirement, and it opens more, until fully open or near so.
I guess there is always the possibility though that the cap is not given enough time to charge up
and so the relay wont operate that one time, when it would be assumed that it would.
I think it at least deserves some testing.
If there is a 12v rail somewhere of course a transistor could be used to turn on the new relay.
Alternately perhaps the relay can be replaced with a lower voltage coil type.