Sunday, January 27, 2013

Can I instrument a Carbon Crank?

I noticed a lot of traffic from which I found out is a huge forum on cycling. One of the largest I’ve ever seen. Someone mentioned my summary post here. I figured I’d sign up and thank them for all the traffic. A question emerged and I’ve been working on it in the back of my mind. Can I instrument a carbon crank? I’ve learned that Stages have mentioned hysterisis which is that the deformation while loading is different than the deformation while unloading. I’ve done some searching and found out that part of the answer (well one here) to this question depends on essentially the loading cycles.

Lets assume a constant sinusoidal loading. Assuming that this is constant eventually the crank will fail at some point. This is referred to as fatigue life. Below is a curve for the fatigue life of aluminium. At a given stress (Left hand scale) it’ll only survive so many repeated loadings. E.G: 200Mpa Stress = 1000 cycles, or 150MPA = 10000 cycles. You’ll notice how a small loading change can make a significant impact in the life before fatigue.

More after the break.

Carbon fiber is a bit more complicated if you look at figure 7 from the mentioned paper.


If N is the number of used cycles and N_f is the number of cycles to failure, at very low usage, approximately 0.1 = N/N_f (10% of it’s designed life) the crank is essentially elastic. This means that if the crank is brand new and hasn’t experienced much fatigue then you could use it as a power meter. If you look at the paper at 0.5 = N/N_f the loading is no longer elastic. At 0.99 shown above the deformation is quite large and follows two different curves. The question is what is the design life of a carbon crank. Is it at 0.1N/N_f after 1 year, 2 years, 5 years, etc?

Lets guess!

SRAM Warranty is 2 years. They would assume heavy usage, and lets assume a consumer safety factor of approximately 3, (99% alpha for failure for normal failure distribution), that brings down the two year maximum usage to a N/N_f of 0.33. However, they would have to assume very heavy usage, so lets say TdF levels of 200km a day for 7 days a week. Lets assume an average rider of 300km a week then we can estimate it’s down to (1400/300)*0.33 = 0.07 for N/N_f at the assumed end of life of 2 years. So could a pro have a carbon arm instrumented… maybe, could a more casual cyclist, most likely – if those assumptions were valid, which they are NOT. It’s just an example

That was just a guess. Realistically you only get a full loading – unloading cycle when you apply force then stop applying force. So lets say you ride with perfect efficiency and constant rotational velocity and never stop applying force. Essentially I’ve said you’ve loaded your crank with force and never unload it until you are done riding. Quite hypothetical, that would only count as N = 1. Say N_F = 1E6 for that loading (A guess with NO BASIS), that means that you used up 0.000001 of it’s design life of 1.0, or 0.0001%. Without integral knowledge of the design life of carbon you can’t make a call. You need to know a lot.

When you ride a carbon frame over rough road that act is using up the life of the frame for fatigue. If you are a Clydesdale type (heavier) on a super light frame riding the cobbles you’ll be quickly using up a fatigue life of the frame. How much? I’d love to know! Over the years it will “sag” and start feeling inconsistent near the end of it’s usable life. It will deflect more and have non-linear spring like qualities to it. Will it be noticeable by a person? I honestly don’t know.

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