Effects of a worm chain on sprockets comes up often and I think
looking at mechanics of it might resolve some some of the problems.
Sprockets have a pitch diameter that exactly meshes with a half inch
pitch chain in which the gaps between teeth are larger than the chain
rollers to make noise free running when used with a worn (elongated
chain) and to allow the chain to exit at an angle, as with crossing
from a right sprocket to the left chainwheel. Cross-over from one
extreme to the other accelerates chain and sprocket wear. The chain
to enter rear sprockets at an angle is taken care of by the derailleur
which accepts incoming chain at angles on its plastic idlers. Large
chain angles cause more rapid wear here.
As a chain wears, its pitch elongates, the length increase occurring
between inner links, the ones that carry two rollers between side
plates and remain at a half inch regardless of wear. It is the pins
and sleeves that wear and cause pitch elongation between inner links.
The chain DOES NOT STRETCH from tension, but rather gets longer as its
pivots wear.
With increasing pitch (spacing between roller centers) the chain
describes a larger pitch diameter as it rides higher on sprocket teeth
than when new. Besides riding higher, so that you can see light under
the chain when it is pulling, it is loading every second tooth because
only every second roller pair is out of pitch.
Pockets are worn in the sprocket from chain contact, not at the root
diameter for half inch pitch chain, but at a higher pitch diameter.
This does not come to bear immediately because the case hardening of
the sprocket wears slowly, but once that is gone, these pockets that
match the worn chain and lie on a larger pitch diameter develop
rapidly.
When a new chain with correct pitch is used, it idles nicely until it
transmits force against the worn teeth. At that time it rolls up the
last tooth of engagement, there where the chain departs and travels
straight to the chainwheel, and seats in the worn pocket that is at a
larger pitch diameter. Tooth pockets are often not readily
discernible because the sprocket form is circular and deviation from
that circle is hard to detect.
A new, in-pitch chain, rides high on the exit cog of the sprocket so
that the incoming roller of the chain cannot enter because it is ahead
of the cog that it should engage. It remains not engaged, riding on
top of that tooth, which makes certain that subsequent teeth cannot
begin to enter from the exaggerated pitch diameter of riding over the
tops of teeth.
Under high chain load, even small wear pockets made by an out-of-pitch
chain will prevent engagement. Regularly replacing the chain can
prevent this because the wear pockets will be at the correct pitch
diameter, but this can become expensive. The alternative is to
replace the chain at 1/16" per foot (which is in effect 1/8" since
only every second link wears) and replace only those sprockets that
won't mesh.
In earlier times, when sprockets were separate and symmetrical, one
could turn a worn sprocket around and use its unworn flank and get
twice the mileage. With teeth shaved and ramped to make shifting
under load possible, most sprockets don't work well when reversed.
Also multi sprocket units cannot be reversed.
Worn chains do not significantly affect shifting or engagement with
chainwheels, chainwheels having forced engagement and don't care
whether the chain rides high or out of engagement on exit. One thing
that occurs with worn chainwheels is that a new chain can cause "chain
suck" because the chain rides in hooked chainwheel teeth that do not
want to release. This is especially so with small chainwheels.
Loss of exact and quick shifting can occur because a strongly worn
chain can bend sideways and defy being pushed to an adjacent sprocket
by the derailleur, but this requires substantial wear and too long a
path between derailleur and sprocket cluster.
Jobst Brandt