no fiber washers... curved base of tuner, that fits into curved recess of headstock....
i hope i explained that right.
Sometimes the fiber washers are the culprit on that type of tuner. There should be 2 to each tuner, and they tighten against the wood of the pegbox to hold the string in tune. Try Ken's idea first -- it's easy and might do the trick.
No need to remove/clean/oil those tuners; just tighten them up say a quarter or half turn to start. Then try things to see if they hold the tuning better. If you crank down on them too hard you may break the "plastic" knobs (but replacements are cheap and easy to find).
jp, if you are able to post photos, it may help folks offer the most helpful advice.
i have an old ... old... MD. i am restoring it only really needs a new bridge which i have from Folkcraft... will have to do some sanding to get it to fit.... it has what i believe are banjo friction mechanical tuning mechanisms they seem to semi hold the tone... i believe the screw holding the tuner head on is how to tighten the tuner.... should i remove them clean and oil them... any other suggestions? thanks kindly.