Fatigue failure of a star–ratchet gear

• We model the fatigue failure of a star–ratchet gear from a mountain bike.
• Pedaling loads are converted to tooth stresses using a relationship derived using finite element analysis.
• Fractography was used to location failure initiation on the gear teeth, indicating fatigue crack propagation.
• X-ray analysis and hardness testing, as well as metallography, were used to determine the alloy composition of the gear.
• Pedaling loads for the trail rides were derived using a publicly available data base, and translated into loading segments for a block-load fatigue failure analysis.

We present an analysis of the fatigue failure of an 18 tooth star–ratchet gear (SRG). The subject gear was implemented in the freewheel assembly of a mountain bicycle. After 6 years of service, the gear failed unexpectedly during a typical off-road ride. The unique geometry of SRGs precluded a simple comparison to existing gear lifetimes. Scanning Electron Microscopy (SEM) analysis of the failed gears showed crack initiation at the root of the gear teeth, followed by fatigue crack propagation and eventual chip-out. A biomechanical analysis of pedaling forces, coupled with explicit power data obtained from instrumented rides over the same trails, in conjunction with a Finite Element Analysis (FEA) of the gear, were used to determine stress amplitudes for fatigue calculations. Energy dispersive spectroscopy (EDS) determined the alloy composition of the gear and thus set the strength and fatigue properties of the gear. Basquin’s law, Goodman’s mean stress correction, and Miner’s rule were used to estimate the lifetime, in bike rides, of the gear. Our analysis led to an estimate of 2288 rides, while failure was reported after roughly 312 rides. Given the uncertainties in fatigue life estimation and service use, we find this estimate acceptable.