Simple guide to worn rear cassette

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Brucey
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Re: Simple guide to worn rear cassette

Post by Brucey »

its what was suggested upthread, isn't it? The question is really when to try this. Ideally you want the chain to be worn near to but not past the point of no return, as it were.

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CJ
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Re: Simple guide to worn rear cassette

Post by CJ »

Brucey wrote:IIRC the rollers on any one inner half-link (IHL) don't quite stay the same distance apart when pushed in the same direction; the reason for this is that the half bushings which support the rollers also wear unevenly. The extent to which this occurs seems to vary with the chain and the usage conditions. I think it is most likely that IHL rollers stay about the same distance apart if the chainring and (single) sprocket both have even tooth counts, because this will allow every other tooth to wear as the pin joints wear. However in a derailleur system or with odd tooth counts, the chain can sit any way it feels like on the sprocket/chainring teeth and there is no way for the teeth to wear that makes it favourable for IHL rollers to remain the same distance apart; should this happen the rollers are immediately unevenly loaded so as to promote wear in the half-bushings.

I like your theory that the one side of each roller/bush bearing (the inward facing sides relative to the inner link plates these half-bushes are formed in) will wear more (than the outer link facing sides) so as to keep the effective length of the inner links in step with the outer links, as the latter elongate due to pin wear. I guess that will be happening, to some extent, on even toothed derailer cogs and chainrings as well as odd-toothed ones in constant mesh. But given the much smaller surface area of pin/bush bearing, I would expect these to wear faster than inner link elongation can keep up with.

P.S. Please don't call a link a half-link, it confuses me.

Brucey wrote:Another factor that is seldom discussed is that once the chain rollers are worn (and to some extent on new chains with sloppy rollers) it is clear that the chain links articulate around the pin centres, but the pin centres are no longer coincident with the roller centres. This is (to my mind) guaranteed to make a mess of the relationship between the actual tooth geometry and the involute curve described by the pin centre of each half link as it engages and disengages with the sprocket. That this is associated with bad (hooking/ramping) wear of the sprocket teeth is clear enough, but for the above reason are sloppy rollers (even in chains of the correct pitch) also associated with faster tooth wear too?

My measurements reveal that rollers have so much slop already in a new chain (almost ten times the clearance outside of the bushes compared to pins internally), that rollers never were concentric with pins to start with! If that mattered, I think they'd have made them a closer fit in the first place. And when I look at how a chain actually meshes with a sprocket (I have also measured an 18T cassette sprocket very carefully and used a basic CAD program to analyse how a chain transmits force to it) I do not see any mis-match or tendency to load the tips of the teeth, arising from roller eccentricity, because the centres simply line up in the direction of tooth contact.

Involute is such a lovely word, I don't blame you for wanting to use it! Chain rollers however, unwrap from sprockets in a connected series of arcs, gaining half an inch in radius as each succeding roller lifts off its tooth. And although that approximates to an involute curve over the large scale, a roller clears its own tooth in the first simple half-inch radius arc, and the direction of its motion after that is immaterial. Okay, the origin of this arc does shift a bit as the next roller in line also rolls up its tooth, so not quite so simple. And this is what causes sprocket teeth to deform as chains elongate. With a longer link, the departing roller remains in contact with the tooth beyond the section that is curved to fit it, and as the next roller shifts likewise the departing roller still carries a lot of chain tension. So you have a high contact stress on that bit of tooth, which deforms to fit the roller.

Thus the curved section migrates towards the tooth tip - on every tooth - such that the driving rollers now sit at a slightly greater radius from the centre of the sprocket. Note however, that the chain, from new to wearing out, never rides on its true pitch circle radius, but always at a slightly smaller radius. A new derailer sprocket (with T teeth and rollers of diameter D) is a fraction of a mm smaller at the roots of its teeth, than 12.7/SIN(180/T)-D. And the roots are wider than the rollers, being curved to fit them closely only on the driving side (also on the other side but only to make space for a slack chain). The centre of the driving curve is nearer to the theoretical pitch circle, but still slightly lower. This is necessary on a derailleur sprocket in order that a slack chain can feed smoothly onto the sprocket. Because the chain is sitting below its pitch circle, slack builds up so that only the two or three rollers before the departing roller carry significant amounts of chain tension. Further back from there, the chain falls slack into the roots of the teeth and this loose condition in the area where the chain feeds onto the sprocket ensures that a slack chain can feed on without conflicting with a tooth tip.

Remember how the roller-fitting curve migrates up the teeth under the pressure of a worn chain? The curved section is, in effect, chasing the growth in chain pitch circle diameter. It never can get there, but if the chain is allowed to wear beyond a certain amount, those curves, by which I mean the centres of rollers sitting snugly on those curves, (or the centres of pins sitting snugly in the bushes in the rollers...) may migrate beyond the pitch circle of a new unworn chain. So when a new chain is fitted, and tension applied to it, it takes up it's maximum theoretical pitch circle. There is thus no slack at the point where slack chain must feed on, so as an empty tooth rotates up toward the next roller in line, the roller contacts the flank of the tooth and is gently nudged outwards. The next roller in line lands on a tooth tip, the next also, and then one drops in and slack chain can now feed on okay... Until the last engaged roller, before the hump of unmeshed chain riding on the tooth tips, gets to the top and is snatched from its tooth, pulling taut the hump. And repeat! It feels like the chain is repeatedly slipping. It isn't actually, its humps of slack unmeshed chain releasing with a jerk, but it might as well be slipping for all the differnce it makes! At least now you have the grim satisfaction of knowing exactly how it got that way.

Needless to say, its very hard to tell, from looking at the teeth, whether the sweet spot on the roller-fitting curve is where the manufacturer wanted it to be, or half a mm higher than there. Because that's all it takes for new chain to jump on a worn sprocket. Sometimes though, you can see a little ridge of metal pushed out to the side of the pressure face of a tooth, or projecting slightly from its tip, and that's a pretty good indication that this sprocket is too far gone.
Chris Juden
One lady owner, never raced or jumped.
Brucey
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Joined: 4 Jan 2012, 6:25pm

Re: Simple guide to worn rear cassette

Post by Brucey »

Image

links, half-links... bound to be confusion... :wink:

It seems to me that the derailleur spring tension pulls unloaded rollers into the tooth valleys and this allows (slightly less worn) chains to mesh with slightly hooked sprockets. If the sprocket/chain wrap is small, there isn't much slack generated this way so skipping is more likely. Because as you say the chain and sprocket are rarely equally worn, the rollers tend to sit on slight 'ramps' in the tooth profile except when they see high loads. Under high loads the loaded roller is pulled up the ramp and drags the other rollers up the ramps too. This is resisted by derailleur spring tension and friction in the roller bushings. Overcoming this presumably makes the chain drive less efficient, as well as causing skipping.

I've mentioned this before but I fairly recently fitted a very accurately made chain (exactly 5.000" for ten er, links) to a very lightly used IGH sprocket. Not only did this grumble under load, it actually caused burrs to be cast inwards on each tooth, such were the loads seen as the chain engaged. I'm sure the chain would have run without fuss had it been less accurately made.

BTW because the pin bushing is free to move slightly within a slack-fitting roller (as the loading direction changes) and the roller can likewise move on an imperfect tooth flank, it could be argued that the curves that the pins describe as the chain engages/disengages aren't quite simple arcs and are a kind of involute.

cheers
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CJ
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Re: Simple guide to worn rear cassette

Post by CJ »

Brucey wrote:Image

links, half-links... bound to be confusion... :wink:

Thanks for the understanding wink - and for providing a nice illustration of why to minimise confusion, we must stick to calling the element of chain connecting two pivots one whole LINK, never mind if its an inner link, an outer link, or a jogged link as shown.
Chris Juden
One lady owner, never raced or jumped.
Brucey
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Joined: 4 Jan 2012, 6:25pm

Re: Simple guide to worn rear cassette

Post by Brucey »

I shall still not be sure what folk mean when they say 'just take a link out of the chain' until I see them doing it; my suspicion is that they don't often mean removing two links and then adding a joggled link. I've no special axe to grind regarding this, except to note that whichever convention you use, it is normally necessary to make it clear by some other means what you really mean. Otherwise it seems to me that a lot of people tend to use 'link' one way when discussing chain length for derailleur gearing, and quite another way when it comes to shortening chains for singlespeed/fixed/IGH use.

Language is defined by usage; in this case 'badly', I'd say. Just for fun I stuck 'joggled link' and 'half-link' into a search engine. The former generated a little over 1/3 the hits and most of them appear to have been for the wrong thing. The same with an image search. The only relevant 'joggled link' images were of things that looked like this;

Image

which is of a thing that is twice as long as your 'joggled link'. It is also twice as long as most of the things that come up when you search for 'half link' although to be fair there are some hits for 'half link' that are the same as the above.

Overall it is a bit of a mess, semantically speaking.

cheers
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CJ
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Re: Simple guide to worn rear cassette

Post by CJ »

Brucey wrote:I shall still not be sure what folk mean when they say 'just take a link out of the chain'...

Oh come off it, they obviously don't mean anything more precise than when they say "I'll just take a bite out of this pie". If they thought about it they'd say two links, and if challenged with: "Do you really mean two links?" they'll respond with a slightly annoyed "Oh yes of course and don't be such a pedant!" For goodness sake, I expect that I've often said "take a link out" myself, when of course I meant two.

It seems to me that a lot of people tend to use 'link' one way when discussing chain length for derailleur gearing, and quite another way when it comes to shortening chains for singlespeed/fixed/IGH use.

It doesn't seem that way to me at all. A 116 link chain is always what it says on the box and does not become a 58 link chain when you take it out of the box and offer it up to a derailleur geared bike. At which point I have never heard anyone say "I think we need to take three links out of this chain".

Language is defined by usage; in this case 'badly', I'd say.

All the more reason to say it better oneself!

Just for fun I stuck 'joggled link' and 'half-link' into a search engine.

Actually I called it a 'jogged link', and although that describes the thing just as well it seems that 'offset' or 'cranked' link are more customary terms.

See page seven of this Renold catalogue for a clear naming of parts and types of roller chain. And although item 30 is (like the item you illustrated) called some kind of 'link', the qualification of 'double' or 'two pitch' makes it clear that we're really talking about two links here.

The Wikipedia page is also very clear about what a link is. So sloppy usage by a few cyclists has not yet blunted the terminology of chains to the point where we cannot be sure how much chain we're talking about!
Chris Juden
One lady owner, never raced or jumped.
Brucey
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Joined: 4 Jan 2012, 6:25pm

Re: Simple guide to worn rear cassette

Post by Brucey »

jogged link, offset link, cranked link: all these terms are used but when it is explained what it means in a bicycle context the usual explanation is 'often known as a half-link'. Asking for anything else in a bike shop is likely to result in a puzzled expression, and indeed if you want to find such link for a bicycle chain, 'half link' is the term that is likely to be most productive when searching the interweb. So be it strictly right or wrong, that is the term in common use.

Put it this way, I have never known anyone be confused by the term 'half link' but I have known pretty much any other term used to refer to chain links be misunderstood at times.

FWIW the roller chain as we know it was a relative late-comer to the chain game; bicycles used all kinds of different chains to start with and with many of these it is impossible to have a half-link, thus an assembly comprising the smallest repeating unit in the chain is 'a link', i.e. comprising an inner and outer set of side plates. Inch-pitch track chain is a case in point. That this smallest repeating unit (usually, but not always because there are such things as skip-tooth designs) occupies two teeth on the chainrings/sprockets is arguably neither here nor there.

cheers
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CJ
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Re: Simple guide to worn rear cassette

Post by CJ »

Brucey wrote:...if you want to find such link for a bicycle chain, 'half link' is the term that is likely to be most productive when searching the interweb.

Thank you for inviting me to the Humpty Dumpty world ("when I use a word, it means just what I choose it to mean") of BMX! Common use of the term 'half-link' appears mostly confined to BMXers, some of whom, so I have recently learned, will pay three times as much for a chain entirely composed of offset links (that they call a 'half-link chain' or an 'interlock chain') that doesn't work any better than a normal chain - but might look cool. :roll:

These are also a very few normal cyclists who need to shorten or lengthen a normal chain by just one link. And the one time I needed to do that (thank you Haden Bros for making your tandem eccentrics not quite eccentric enough :x ), I did force the word 'half-link' past my lips. Not that it did me any good though, because such links, so I was told, have never been made for 3/32 derailleur chain, were available only for 1/8, and not readily available even for that in the 1970s! (So I simply let the chain run slacker until it was worn enough to take out two links - while I designed and had made a sufficiently eccentric eccentric to fit the same shell :D .)

So as far as most of us are concerned, the existence of these funny links is academic, so the wrong-headed cycling term for them does not need to be promulgated beyond the small number of cyclists who actually need them. And in the unlikely event of any BMXer finding this forum, please use 'interlock' instead - it's kinda closer to the correct terms for this kinda chain.

Finally: there is absolutely no need, it would be REALLY confusing, since it would rob the term of what little utility it has, to start calling the normal links of normal chains, 'half-links' too!

I rest my case. :wink:
Chris Juden
One lady owner, never raced or jumped.
Brucey
Posts: 44521
Joined: 4 Jan 2012, 6:25pm

Re: Simple guide to worn rear cassette

Post by Brucey »

some 3/32" half-links

https://www.sjscycles.co.uk/chains/jtek-chain-half-link-332-inch-each/

https://www.tandems.co.uk/m8b0s16p24/KMC-CHAINS-Half-Link-for-3-32%5C-inch-chain-1-2-link

1/8"

https://www.sjscycles.co.uk/chains/chain-half-link-18-inch-each/

Half-links are commonly used in tandem timing chains, IGH, singlespeed, fixed road and fixed track applications. Folk running 'magic gears' on road frames with vertical dropouts use them as well.

If running an old style 1x 5/6 speed derailleur system there is something to be said for using a fully bushed 3/32" chain (KMC and wippermann make them) and also using a half link in the chain if the chainring has an even number of teeth.

I think they were called half-links before BMX existed; maybe old catalogues will tell us when this term came into usage?

They are indeed a problem semantically speaking, but they are quite handy little blighters too.

cheers
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