The roller nut was tested, and results are not as good as I expected. Strings get still out of tune after bendings. Reason for that may well be the type of strings that I use: coated ones.
The specific breed, that I use, is Elixir Polyweb, as they seem to have most durable coating.
As the sweat from my fingers is like battery acid, uncoated strings are ruined in just few days.
This type of roller nut, with bearing balls, might work a lot better with metal-to-metal contact, as with uncoated strings.
But enough of that. I think that using real rollers instead of static bearing balls could be a better bet in this case, and therefore forthcoming subject for testing.
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Ongoing, 'tongue in cheek' -test subject is this:
So, it's basically a part of a tremolo, thrown together from the parts, that were at hand. Exception is the spring, that had to be made.
At first, I tried the Strat-style tremolo springs, but even six of them together hadn't enough tension, to get the strings tuned for a standard tuning.
Next I looked for online spring tension calculator, only to find out, that it produces plenty of values of different variables, that I have no idea about
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Numbers aside, it was again time for parking the ball in the dark.
Strat-style springs, that I have, are made of 1.4mm spring wire. To have a single spring to take care of the combined strings tension, it needed to be stout, so 3mm wire/round bar was used.
Surprisingly, with the spring on above pic, the 'sweet spot' is a lot closer. In practice, when tuning the strings, they don't go higher than G(when using 'A' tuning fork).
As it's intentionally a 'floating' system, perhaps adding an adjustment screw to pull the springs' opposite end away from the bridge to 'compensate'.
In the end, if nothing else, this is an attempt to find the pitfalls, that many of the tremolo designers must have stumbled upon.