loadbending: cracks start at the rootpitting
Lewis parabolaBending hot spotsContact zoneUnder load a tooth is a short cantilever, fixed at the root and pushed near the tip. The tangential part of the load bends it, so the bending stress peaks at the root fillet, and that is where fatigue cracks start. Lewis's trick: a parabola drawn from the load point is a beam of constant strength, and where it touches the tooth outline is the weakest section. Separately, the flanks press together under very high contact (Hertzian) pressure, and near the pitch line that eventually pits the surface. A gear has to pass both checks.