The user estimated that he would have put a little more than 100 hours of time on these pedals, all during home use at fairly low pedaling intensities. He is a fairly big person, at 6'2" and weighing 217 pounds.
When it broke, he had been standing on the pedals for want of some variation and was putting forth moderate effort. But he remarked that despite cycling since the 1980's, this is the first pedal he has ever broken. He has other Crank Brothers pedals in stock for outdoor riding but this event has diminished his confidence in those as well. Natural.
The pedal features a chromoly spindle. I do not know its geometrical specifications. Curious enough, I visited the Crank Brothers website (its very well developed actually, so Kudos to them!) and obtained a screen-shot of the spindle from one of their servicing videos. The failure, as I see it, happened just where the cross section started to step down :
Loads & Stresses : The spindle acts like a simplistic cantilever beam with the concentrated reaction force R and pedal force F as I show below.
Then, for a solid spindle acting like a beam, maximum shear stress at the neutral axis would be about :
where V is shear force and A is the cross sectional area of the round section.
By looking at the length of the spindle above compared to its depth (L>>d), one might be able to say that what would be more concerning than the shear stress itself is the spindle's bending stress at one or two critical locations (sites where part sees high stress risers). The designer would then multiply the concentration factors necessary for these stress risers to the equation for maximum bending stress at the spindle's outer fiber given by :
where c = outer radius of section, M = bending moment & I = moment of inertia
High Cycle Fatigue (HCF) : Since the user told me that he uses this moderately at home, the correct technique to analyze the spindle would be in HCF, in a mode of fluctuating loads. Here, the stresses seen would be much below the yield of the spindle material but the loading would gradually accumulate until failure. This happens because of local yielding at critically stressed locations.
To generate a rough idea of fluctuating load on the spindle, I made some assumptions. Research has shown that a good figure for average pedal force for long periods is about 1/5th of body weight. If this is the average, then an approx. max force could perhaps be 75% of body weight. So for a 217 lb person riding moderately like the individual here, a possible range of forces could be as follows :
Fig.1 : Peak forces are seen roughly when the crank is forward, 90-100 degrees past top dead center. These peak forces are a resultant of effective force (radial) and ineffective forces (tangential). For specific illustration, mean component of foot load, Fm, is 43.4 lb and in tension. The alternating component is given by Fa = (Fmax - Fmin) /2 = 119.4 lb. Mean and alternating components of the reaction force Rm and Ra is same as for the foot loading forces. Time period is given by t = 1/frequency. Note : Blue region for upstroke has been exaggerated whereas in reality, peak magnitude might not be so high.
The shear and bending stresses can then be derived from these alternating and mean loads. A Von Mises stress calculation can be done for both alternating and mean stresses. These V M stresses can then be plotted on a modified Goodman diagram along with the corrected endurance limit and yield strength to check visually where in relation to failure boundaries this pair of stresses lie. The safety factor of the part in service comes specifically due to how this pair of stresses vary with each other.
Since the material is steel with a knee in the S-N diagram, a good estimate for design pedal life for infinite life in steel would be a capability to withstand the maximum stresses shown in the figure above for 2 million cycles and over. A normal 90 RPM cadence equates to 1.5 Hz frequency or 1.5 cycles/second. So a designer can make a pedal spindle with chromoly to sustain itself for the range of life shown below.
2 million cycles / (1.5 cycles/sec) = 1.3 million seconds = 370.37 hrs.
200 million cycles / (1.5 cycles/sec) = 133.3 million seconds = 37037.03 hrs.
If a company has the time and money, they'll design for higher life than 200 million cycles.
The point I'm trying to make here is that given the rough loading curve for one rider above you, the actual pedal spindle would have had to be designed to withstand much higher amplitudes of stress cycles for many different riders across a broad spectrum. This should also arrive after providing for fudge factors to account for geometrical & environmental influences!
However in this case, the spindle locally yielded at lower stresses in a matter of 100 hours of life to failure. This was in a controlled environment. This does not correspond suitably with the range for HCF life calculated. On the surface, it appears the spindle might not have been designed/manufactured properly which brought down the strength of the spindle considerably from its predicted life.
What do you think? Should the pedal spindle be beefed up in size to accommodate heavier people, designed with milder cross-sectional variations or heat treated appropriately to overcome this dangerous scenario? And what are your experiences with this particular pedal?
RELATED RESOURCES :
4130 Normalized Steel Alloy Material Properties
Spindle Shear & A Related Injury
Falling Out of Love With Crank Brother's Pedals
Integrated Sensors In Intelligent Bike Parts
How A Clipless Pedal Works
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