Topology-Optimized Differential Sprocket

The fatigue cycle driving the optimization is a superposition of two things: the chain-engagement cycle (which varies with wheel rotation frequency, and where tooth-to-tooth load increases exponentially from first to last engaged tooth due to hysteresis and chain wear) and the car’s acceleration/deceleration cycle over a lap. Engine braking — which can reach 50% of engine power once pumping, thermal, viscous, and valvetrain losses are accounted for — had to be modeled too, since it’s weaker than drive torque and is exactly why the optimized geometry ends up asymmetric.

Topology optimization on a thin structure like this pays off doubly: the resulting geometry is both lighter and simple to manufacture. The final part, cut from AISI 7075-T6 aerospace aluminum via waterjet (chosen for precision without disturbing the material’s thermal treatment), got a 60µm hard-anodized layer for a 560HV surface microhardness — enough to resist crack growth from chain engagement while cutting friction and wear at the contact surface.

Topology optimization earns its keep fastest on thin, highly-loaded structural parts like this one — where the “obvious” shape almost never survives contact with a real fatigue-cycle model, and where the optimized result is often cheaper to manufacture, not more expensive.