Why the conveyor gearbox keeps pitting: a gear stress check

Orbis fits a two-stage helical reducer to its standard 30 kW belt conveyor. The motor runs at 1,470 rpm and the gearbox reduces speed about 25:1 to drive the head pulley. Over the past year, seven gearboxes at three quarry sites came back with pitted teeth on one pinion after about 6,500 running hours. The design life is 30,000 hours.

Stage 1 has a 3 mm normal module, 19 and 96 teeth, a 15° helix angle and a 45 mm face width. Stage 2 has a 5 mm module, 18 and 89 teeth, a 12° helix and a 70 mm face width. All gears are case-carburised alloy steel. The datasheet allows 1,350 MPa contact stress and 430 MPa bending stress for 10⁷ cycles. Conveyors start under full load several times a shift, so the design rules call for an application factor of 1.5.

Orbis's chief engineer wants to know: - which stage is undersized, and whether it is bending or contact that governs; - whether the problem is the design or the duty, because one quarry may be overloading its belts; - the cheapest fix that gives 30,000 hours, such as a wider face, a different ratio split or a better material.

You will do this with hand methods based on the Lewis bending equation and Hertz contact stress, written as a Python script so it can be re-run for other gearboxes. The approach follows the logic of ISO 6336 and AGMA rating, simplified. You do not need the gearbox. All data is in this brief.

Done looks like a script that rates both stages, a clear statement of which stage fails and why, a shaft and bearing sanity check, and a one-page recommendation with the fix and its effect on life.