why teeth break...
Here's some info from Jobst Brandt about chain and cog wear. I've also posted quite a bit on chain wear, including my scheme to alternate the use of three chains to avoid mating a new chain with worn cogs. I hope to get 10-15,000 miles from a cassette, but I may encounter excessively hooked teeth before I get to 15,000. What's not covered in Brandt's writing is the fact that some chains (current Campy models) have such hard pins that they may show little elongation, even after 6,000 miles. That doesn't mean the chain isn't worn out. A check of the distance between rollers and side clearance will show an extremely worn chain that still has a pitch that's well within tolerance. One of my chains in this condition wore out one steel cog in 6000 miles. Another wore out two Ti cogs in only 4000 miles. This proves that monitoring chain pitch won't guarantee that the cogs are still useable with a new chain. Thes cogs will still work fine with a chain that has even a few hundred miles of use, but not a new one.
The small chainrings on an MTB increase chain tension and the chances of breaking teeth.
From Jobst Brandt:
Chain life is almost entirely cleanliness and lubrication related
rather than load related. For most bicycles the effect of load
variations is insignificant compared to the lubricant and grit
effects. For example, motorcycle primary and timing chains, operated
under oil in clean conditions, last years while the exposed rear
chains must be replaced often.
The accurate way to test whether a chain is worn is by measurement. A
new chain has a half inch pitch so that it has a pin at exactly every
half inch. As the pins and sleeves wear, this spacing increases and
becomes damaging to sprockets. When the chain pitch grows over one
half percent, it is time for a new chain. At one percent, sprocket
wear progresses rapidly because this length change occurs only between
pin and sleeve so that it is concentrated on every second pitch. The
pitch of the link containing the rollers remaining constant. By
holding a ruler along the chain on the bicycle, align an inch mark
with a pin and see how far off the mark the pin is at twelve inches.
An eighth of an inch (0.125) is a little over the one percent limit
while more than a sixteenth is a prudent time to get a new chain.
Skipping Chain
That a new chain does not want to engage used sprockets may be
obvious, but in theory a new chain cannot freely engage a new rear
sprocket under load even though it has the same pitch as the chain.
That is because the tooth being engaged would be under load and this
is a contradiction in itself. Therefore, a slightly worn sprocket,
that has pockets in its load bearing face is even more reticent to
engage a new chain with perfect 1/2 " pitch.
Sprockets, by the way, do not change pitch when they wear, only the
tooth form changes because the number of teeth remains the same and
the base circle remains essentially unchanged for normal sprocket
wear. On fixed gear bicycles that are ridden until the chain is 5%
out of pitch, the base circle may be slightly reduced but this only
makes the fit of a new chain worse.
Without a strong chain tensioner or a non derailleur gear, the chain
has insufficient tension on its slack run to engage the sprocket when
under tension. In contrast, engagement on the tension side, as on the
crank sprocket, generally succeeds even with substantial tooth wear
because the tension encourages engagement. This condition, however,
enhances "chainsuck", the failure of the chain to disengage the
chainwheel. This can generally not occur without a long arm
derailleur, common to most MTB's and therefore, road bicycles normally
experience a grunchy disengagement instead of a chain jam.
A new chain has a pitch of exactly one half inch. A sprocket, worn by
a longer pitch (worn) chain, has hooked teeth but with the correct
pitch. The hooked profile is formed by the rollers of a worn chain as
they exit the sprocket under load, whereas rollers of a new chain with
correct pitch exit under no load because the load is transferred to
the next roller before disengagement. However, with hooked sprockets
the new chain cannot engage under load because its pitch doesn't allow
it to get over the hook and into the next pocket. These differences
are only a few thousandths of an inch but enough to prevent engagement
when the previous roller is fully engaged.
As a chain wears it concentrates more of its load on the last tooth of
a sprocket before disengagement because the chain pitch no longer
matches the pitch of the sprocket. This effect sometimes breaks off
sprocket teeth. The load concentration on the sprocket also
accelerates wear and is another reason to replace a chain at 1/16th
inch wear.
Jobst Brandt