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I want to use bicycle chain sprockets for a non-bicycle related project and I'm trying to figure out what is the maximum torque I can apply.

I did a quick calculation taking a real life example - I know for a fact an 80kg person can stand with his full weight on a pedal and the chain would not snap, so that amounts to:

T = l_p * F_p
T = 0.17 * 80 * 9.81
T = ~133 Nm

Where $T$ is torque at the axis, $l_p$ is length of the crank and $F_p$ is force due to weight.

A 44 tooth sprocket is 180mm in diameter, so the force on its teeth would be approximately:

F_t = T / l_s
F_t = 133 / 0.09
F_t = ~1477 N

Where $F_t$ is force at the teeth and $l_s$ is radius of the sprocket.

Looking at the packaging of my chain it claims that it can withstand up to 900kgf which is in the realm of 9kN. I have currently determined that the sprocket can hold up to 1.5kN but what is the approximate maximum before teeth start flying off?

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  • This paper reports ~250Nm torque at the crankset for sprinters: sportsmedicine-open.springeropen.com/articles/10.1186/… If the chain and sprocket are new and the chain is properly tensioned and wrapped around the sprocket I’d assume you’d need a huge amount of force to rip the teeth off. I think the chain is probably going to be the weaker link by far. Single speed sprockets and chains should be wider and stronger.
    – Michael
    Mar 14, 2022 at 20:34
  • An 80 kg rider can put down more than 80 kg of pressure to the crank. Some can come from lifting the rear pedal, and some comes from the arms pulling on the bars Empirical testing might be suggested, for rigor.
    – Criggie
    Mar 14, 2022 at 21:40
  • Another requirement - bike chains are under tension from the derailleur. Your application needs either a chain tensioner, or some other way to weight the load-sprocket. WIthout this the chain could ride off the teeth easier, especially if the whole system is free to move and oscillate, or experiences vibrations.
    – Criggie
    Mar 14, 2022 at 21:45
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    @Criggie undoubtedly but it's hard to determine how much more than 80kg the force will be, so I just took the weight for the calculation. Also, yes, I found out, through trial and error, that without tension the chain drive creates all kinds of trouble, so I made tensioners - thankfully they are pretty easy to make and springs are cheap af.
    – php_nub_qq
    Mar 15, 2022 at 11:56

2 Answers 2

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what is the approximate maximum before teeth start flying off?

Bicycle drive train parts - for reference:
enter image description here

By "a 44 tooth sprocket" I'm assuming the chainring is meant.

This question is not answerable as it is written.

  1. Most chainrings are made of either aluminum or steel of different alloys. Some are made of titanium or carbon fiber.
  2. There are several manufacturing techniques for each of the metal types

Given the wide variety of chainring types there is no single approximate maximum.
In order to approximate the maximum force before the chainring teeth start flying off specific chainrings would need to be selected for testing and an apparatus for testing would need to be built.

Bicycle chain breaking load min/max data can be found in several places. Here is one example. enter image description here

It is very difficult to find chainring tooth breaking load min/max data.
The chain is the weak link in this system.

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    The chain isn't always the weakest link. If the chain has "stretched" through wear and its length is allowed to go out of specification due to lack of maintenance, then the force applied by the chain can be more concentrated on one tooth of a chainring or rear cog. I've seen teeth snapped off a rear cog.
    – rclocher3
    Mar 14, 2022 at 21:36
  • I'd assume these chains were brand new. When I've broken a chain it tends to be an old one, perhaps with a couple of pins pushed in/out over time, and a side plate starts slipping off a pin. At that point leg power is enough to tear it apart easily.
    – Criggie
    Mar 14, 2022 at 21:43
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    @rclocher3 is right, a worn out chain can kill a sprocket within a megameter. Even if the sprocket is made out of steel. Or, to put it more concisely: The chain is stronger than a single tooth, but half the teeth of a sprocket are stronger than the chain. Btw, the weakest point of a single speed sprocket is not its outer teeth, but rather its inner teeth which it uses to turn the axle. Which makes sense because the chain tugs on more than half a dozen of teeth, but there are only three small inner teeth that have to withstand the same amount of torque. Mar 14, 2022 at 22:26
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    @rclocher3 You are correct. In the context of this question, building an unknown machine using bicycle parts and speaking from a design perspective I think it's accurate to say the chain is the weakest link in the system.
    – David D
    Mar 15, 2022 at 0:45
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    Fair enough @DavidD, for a simple non-bicycling project it's reasonable to assume, for design purposes, that the parts are new and perform to their specifications. In that case the chain would absolutely be the limiting factor.
    – rclocher3
    Mar 15, 2022 at 1:06
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From reality, I think the chain would skip at the rear cog well before it breaks or "the teeth start flying off". This may be at quite a low force if cogs and and chain are worn, even below the power required to sustain the easy acceleration.

I suspect that also new gear would simply skip, at least for the faster gears. It wraps only a 1/3 turn around a sprocket in some cases, so would be somewhat 3 teeth on a 10 teeth sprocket and there is a spring-driven tension mechanism. Easy to jump over.

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    With sufficient chain tension and wrap-around this should be impossible without something breaking.
    – Michael
    Mar 17, 2022 at 13:54
  • There is actually not much wrap around the smaller cogs at the rear. For the big climbing cogs, yes.
    – nightrider
    Mar 17, 2022 at 14:19
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    The logic certainly applies for OP's "non-bicycle related project"
    – ojs
    Mar 17, 2022 at 14:31
  • If both axes are fixed and wrap around is big, it may not be possible to jump over the tooth without breaking something. But the chain gets longer as it wears, so such a device is unlikely. If there is a tension regulator, the question is which one.
    – nightrider
    Mar 17, 2022 at 14:44
  • Sprinters can achieve >2kW power and >200Nm torque at the crankset. A quick napkin calculation tells me that this means something between 1–4kN of chain force at the rear sprocket, depending on sprocket size and gear ratios. With a properly designed tooth shape the chain shouldn’t tend to “climb” the teeth, even under heavy load (it should also be load independent). I guess at high speeds you could run into problems with spring loaded chain tensioners having insufficient force to counteract the centrifugal force on the chain.
    – Michael
    Mar 17, 2022 at 15:21

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