Elevation of Roller Contact, and Effective Tooth Pitch

Copyright Jonathan Levy, 2000. All rights reserved.

Roller elevation causes increased tooth pitch

This diagram is schematic to illustrate effective tooth-pitch, so tooth pressure-faces are shown straight, even though they are curved.

The pressure-faces are also shown sloping, ie not at right-angles to the alignment of the chain-wrap because most modern teeth, even though they have a "steep" angle at their roots, still contact the rollers at an angle there ; this contact angle changes along their curved shape (when unworn) becoming "flatter" as the roller moves up towards the tooth tip. With tension placed on the chain, the tendency is to eject chain-rollers (ie they ride up the pressure-faces). This effect is not unduly strong with unworn teeth (because of the "steep" angle at the roots) - it is restrained by the overall geometry of the chain wrap - such behaviour being inherent to the overall design.

However, the changed shape of worn and/or failed tooth pressure-faces usually forms ramps from the tooth-roots at a much "flatter" angle which, in turn, drive the chain-rollers up the tooth faces more strongly ("flat"-ramped section from root of tooth is not illustrated on the schematic). This results in an equilibrium contact point for the roller at an increased elevation on the tooth face. The elevation of the equilibrium point depends on a number of factors including how much tension is being placed on the chain, and the increase in elevation can be substantial.

The worn ramps often terminate in indentations worn or failed into the teeth at a higher elevation. Under high chain tension, the rollers usually move up to the indentations, being thereby prevented from rising further; and also prevented from disengaging easily.

Because the effective pitch circle diameter at this contact point is larger than the normal pitch circle diameter when the roller is near the root of the tooth, its effective tooth-pitch is also increased. This, in turn, causes the rollers (which are now in tight contact the bottom teeth) to pull the links/rollers slightly away from the upper teeth, as a result of which load on the upper and middle teeth is reduced to a degree and transferred to the bottom teeth. A new chain or one with little stretch will increase this effect even more, because it further increases the mismatch in tooth-vs-chain pitch.

As little as a 1mm (0.04") increase in the roller's position up the tooth face of a small granny-ring results in the effective tooth pitch increasing by more than 2%. By comparison, a chain is considered to be very badly worn when it has only 1% stretch (and it has usually trashed the teeth of all sprockets and chain-rings by this stage of wear) ; thus it is clear that very small changes in roller elevation can have a profound effect on where it contacts the teeth and how it loads them.

Also in practice, some teeth are loaded more highly than others by the varying force applied during the crank cycle, and thus wear/fail somewhat more than others. As a result, the situation varies as the crank cycles around. And in practice, the chain locates "higher" on the teeth at one or other end of its loop around the chain-ring, depending on whether its pitch is shorter or longer than the effective tooth pitch. Nonetheless, the overall consequences of the behaviour described here, remain valid. The face-to-face pitch of the effective tooth contact point increases if the rollers move "up" the teeth.

Technical discussions often state that as the chain and teeth wear together, the chain finds its own position on the teeth ; this is true. However, implicit in such statements, it often seems taken for granted that the chain load somehow remains quite favourably distributed over the teeth ; this only holds sometimes, and very often is far from the case. There is no fundamental reason why the wear of these two very different components should be so closely synchronised as to result in a favourable load distribution ; materials, stresses, failure-points, and abrasion characteristics can differ greatly for the two components. Usually one or other component wears faster, leading to a mismatch in pitch and transfer of more load to the top or bottom teeth depending respectively on whether the chain or the teeth has the greater effective pitch. An extreme (but fairly common) illustration of this, is metal failure of the pressure faces of aluminium (or normal steel) granny ring teeth on a totally new drive-train after only a very few rides ; the chain remains essentially unworn, while the effective tooth-pitch increases considerably (together with an increase in mechanical resistance to disengagement, due to indentations in the pressure-faces and friction) ; and hence chain-suck.

In a workshop test, increasing loads were applied to small chain-rings (both worn & unworn) using chains with varying degrees of stretch to see how they interacted.

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