Chain harmonics - what does this mean?

[rmurphy195]

Can anyone help me understand Tinnishills comment "13t is a prime number, and so extends chain life by eliminating chain harmonics. " What does a prime number have to do with anything, and what are chain harmonics in the context of bicycles?

[Tompsk]

I saw that too and was wondering what is meant by that. My only (big) guess is that having a prime number in the mix would mean that the chain would not keep lining up with the same links on the same teeth. However I think this is only true if the number of links in the chain is a prime number as then, whatever the number of teeth on the sprocket, it will reduce the times the same tooth goes into the same link. However I may have got completely the wrong end of the stick!

PS The number of links will be an even number, which is not prime. But it may be that the number of links is better if it is not a exact multiple of the sprocket or chain ring as this will lead to the same link being on the same tooth every time the chain goes round. E.g. 13t x 39 with a 104 link chain. More important on single spocket systems like hub geared or fixies where the chain could stay permanently in sync.

[Brucey]

I think that is along the right tracks. Motorcyclists have long been almost obsessed with this kind of talk, but amongst cyclists it should be of most interest only to users of IGHs and singlespeeds; with derailleurs (that have more than one chainring), the chain doesn't see the same chain links on the same sprocket for long provided you change gear often enough.

I think that ideally the chainring and sprocket are both prime numbers to allow the chain to have the fewest harmonics. However this view isn't shared by everyone; Sheldon Brown reckoned that it might be best to have an even sprocket tooth count and an even chainring tooth count, and that it was positively beneficial to have the same chain links on the same teeth, because every other half-link in the chain stretches differently, because of the way the links are constructed. He reckoned that a singlespeed drive ran smoother for longer (when it was basically knackered, admittedly) with this setup, which is arguably the exact converse of the 'avoiding chain harmonics' idea.

cheers

[Vorpal]

When something operates on a fundamental/natural frequency and its multiples (harmonics), it can set up a vibration pattern that is especially noisy, and may lead to early failure. It can and does happen in all kinds of systems. It's entirely possible to avoid it through analysis and testing.

If you think of something like a piano, that is meant to make noise... The strings for the A keys vibrate at 55 hertz, 110 hertz, 220, hz, 440 hz, etc.

If you have one part in a drivetrain that has a natural frequency of 440 and another that has a natural frequency of 220, and the chain also runs on a divisor (mode) of the same 'note', then, you might get a very noisy drivetrain. Under the right circumstances, it could likely cause the chain to jump.

Having 13 teeth can't eliminate chain harmonics; it just changes the natural frequency of a single component. That may make it easier to avoid harmonics, but it's not something I am especially familiar with in bicycle design.

Modern technology means we can use computer tools like modal analysis to avoid harmonics during design, whether a sprocket has 11, 12, 13 or 50 teeth.

[Tinnishill]

Yeah, sorry. That was off topic. What I was rambling about is gear mesh frequency harmonics. I should say that I am not a qualified engineer; I suffer from having attended a course of lectures back in the late 70's.

This is my understanding of what is happening. Please feel free to disagree.

Chain wears at a varying rate according to levels of lubrication, dirt contamination and the amount of power being applied. Getting lubrication and cleaning right will extend the chain life. In normal use we assume that lubrication and dirt remain equal round the length of the chain, so I will pretend to ignore that for a bit.

The difference between a bicycle power train and the gear train in something with a steady power supply like a watermill or electric winch is that in a bicycle the applied power level changes as the pedals revolve; there are two pulses of power for each revolution of the cranks. If you search Google Images for the phrase "bicycle pedal power stroke" you will see several illustrations of this power pulse. Maximum wear takes place where the various components mesh together as the power is being applied.

Gear harmonics occur when the number of teeth on one component in the train is a multiple of the number of teeth on another component. For instance if you look at tooth 1 of a 20t cog it will harmonise with tooth 1 of a 40t cog at every second revolution of the 20t cog. Constantly applying the increase of power at the same spot increases wear at that spot compared to other spots which have received less power. Using gear numbers which can divide or multiply into each other will (I was told) result in uneven wear. Prime numbers are indivisible. Inserting a cog with a prime number of teeth into the gear train prevents a harmonic from occurring.

Useful prime numbers for cyclist gear sprockets are:- 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59. Possible chain length prime numbers are 97, 101, 103, 107, 109, 113.

Chain length is usually dictated by the size of the bike frame and it is hard to find chain rings in prime number size, so that leaves us usually with the option to use primes for rear drive sprockets.

That's a fine theory. My real life experience (ie, I don't keep proper records and rely on my fallible memory) is that the difference in wear to the chain is negligible compared to a good cleanliness and lube regime, but the difference in wear to the smaller rear sprockets is noticeable.

Regardless of where the prime number is in the rest of the gear train, the chainring will wear unevenly because it has a fixed angle to the power stroke being delivered through the cranks. This wear can be spread and the chainring life extended by occasionally shifting the ring around the spider.

Where I reckon that some benefit can be obtained is on simple drive trains; single chain ring and epicyclic gear, for instance.

Apologies again for mentioning this, as it can only really be proved in a proper lab.

[Trebor]

I think that is along the right tracks. Motorcyclists have long been almost obsessed with this kind of talk, but amongst cyclists it should be of most interest only to users of IGHs and singlespeeds; with derailleurs (that have more than one chainring), the chain doesn't see the same chain links on the same sprocket for long provided you change gear often enough.

I think that ideally the chainring and sprocket are both prime numbers to allow the chain to have the fewest harmonics. However this view isn't shared by everyone; Sheldon Brown reckoned that it might be best to have an even sprocket tooth count and an even chainring tooth count, and that it was positively beneficial to have the same chain links on the same teeth, because every other half-link in the chain stretches differently, because of the way the links are constructed. He reckoned that a singlespeed drive ran smoother for longer (when it was basically knackered, admittedly) with this setup, which is arguably the exact converse of the 'avoiding chain harmonics' idea.

cheers

The linked article deals with higher powers than any cyclist could produce but illustrates the concept. Basically, if the chainwheel has an even number of teeth then the sprocket should have an odd number in order to minimise harmonics - except in the special case of 1:1 gearing. As a counterfactual you also have to consider chain wrap ie. number of teeth engaged which determines chain tension. The first graph in the article uses a semi-logarithmic scale for the Y axis but illustrates the fact that 10-12 tooth sprockets may be a stupid idea, unless the manufacturer wishes to reduce durability - lower durability = increased sales, what could be the possible attraction of such a business model?

http://www.cross-morse.co.uk/pdf/DriveD ... -Morse.pdf

[NATURAL ANKLING]

Hi,
On motorcycles and single speed chain drive with even sprocket numbers, adjacent teeth will always see adjacent chainlinks in that pattern, thus one tooth on a sprocket will only see half of the chain links at best.
I inserted a half link in my motorcycles if both sprockets were even, but even with an odd sprocket number it might well be that the sprocket will go into the chain length exactly after a few turns.
Odd chain links is a best of all bet as its possible that a driver sprocket teeth could see all links.

The effect of a worn chain on most motorcycles was dramatic that you set chain tension at tight spot but loose spot meant that chain would flap around and you could certainly hear that when driving, whirring sounds one of the characteristics.
Even new set ups showed visible rise and fall of chain due to the slight eccentricity of sprockets.
You would need to carefully calculate sprocket and chain link numbers to get an ideal situation where a sprocket tooth shift phases to next adjacent link every chain turn.

Theres probably a program out there somewhere that will make it easy.

Derailleur set ups are not a problem as said, the front chainring teeth as said can easily show signs of leg max torque, and which leg is the stronger.

[Brucey]

I think that in theory bicycle chains can wear harmonically, but it has always seemed to me that they are less likely to resonate harmonically, because when pedalling the speed (and load/tension) of the chain is not constant. Perhaps it is one of the things that may occur more often with e-bikes.

cheers

[NATURAL ANKLING]

Hi,
Deraillieur chains are sprung, single speed chain drives with no tensioner are more likely to vibrate.
Add as said contantly varying loads and sychronisity means its not a problem.

Put your bike on a stand, engage top gear pedal with your hand like mad.........let go........thats as good as it gets

[bovlomov]

In the light of this - how long before someone starts offering a bicycle tuning service? For the record, my frame is tuned to A♯, and my wheels are both E natural (I try to avoid flats). The brakes are set to B natural (an octave apart) in their relaxed state, and under tension they rise to F♯. The gear ratios are set to a pentatonic scale.

[Vorpal]

and my wheels are both E natural (I try to avoid flats).

I think that most of us do. Too many sharps can be a problem, too

[rmurphy195]

Thank you for all of your replies - I now know a little more than I knew yesterday

Would this explain, I wonder, the following - I used to have a 7-speed setup with 11-28 on the back, and 24/34/44 on the front ( a Dawes Galaxy).

I used to notice a slight thrumming/humming when using the 44/11 combination when pedalling hard. Is this what down to the chain harmonics, or am I being a bit fanciful? (Don't recollect having it in any other gear combination on that or any other bike)

Cheers - Richard

[Brucey]

probably chordal effects on the 11T sprocket, may have been resonating too (speed variations with each pedal stroke tend to be lower in high gears). They are not every efficient, 11T sprockets.

cheers

[NATURAL ANKLING]

Hi,

probably chordal effects on the 11T sprocket, may have been resonating too (speed variations with each pedal stroke tend to be lower in high gears). They are not every efficient, 11T sprockets.

cheers

Spot on! even on the Old Raliegh

[Brucey]

BTW I can think of several reasons why MTB drivetrains went to 11-up cassettes and similarly smaller chainrings;

1) they are lighter in weight

and

2) there is more ground clearance

and

3) you can get a wider range of gears for any given total derailleur capacity (in teeth)

The above don't really apply to touring bikes in quite the same way. That such drivetrains have been fitted to touring bikes is arguably more an indication that there isn't much else that is available off the shelf at reasonable cost, than anything else. The downsides to those transmissions are that you get faster wear and lower efficiency when you use small sprockets. Again it doesn't apply to MTBs in quite the same way, because they will use lower gears more of the time (i.e. larger sprockets) and wear rates are dominated by muck and rubbish on the MTB parts, not other design details.

Fact is that (provided you can get the gear range you want) larger sprockets and chainrings are more efficient, wear longer, and better overall despite their increased weight. Even if your ride comprises solely of climbing steep hills, you would be better off (in round numbers) with a transmission that has +0.5% better average efficiency even if it weighs 0.5 kg more or so.

Back in the days of screw-on freewheels most folk (apart from a few racers who could probably have fitted bigger chainrings instead) were happy with a 14T smallest sprocket.

Overall, (given a free choice) most folk are probably better off with a 46-50T big ring and a 13 or 14 to something cluster for touring purposes. Not only is it more efficient gear-for-gear (than smaller sprockets and chainrings), but if you are fussy about your gear gaps, 2T intervals in the cassette give you better spaced gears in the cruising range when you are using slightly larger sprockets.

It is a source of some annoyance that it is almost impossible to buy a suitable cassette off the shelf, BTW.

cheers