Sizes a symmetrical conveyor pulley shaft from belt forces T₁ and T₂ using a CEMA 7th-edition stress reference (Eq. 8.33) and a user-selected bearing-slope limit. The larger calculated diameter governs and is rounded up to the next listed shaft size.
The design load is the resultant of the two belt-strand forces — T₁ (tight) and T₂ (slack) — pulling on the drum, combined over the wrap angle θ by the CEMA trigonometric method: R = √(T₁²+T₂²−2T₁T₂·cos θ). Drive torque = (T₁−T₂)·D/2.
Bearings support the shaft; the two end-disc hubs share the belt resultant equally. This reference model assumes symmetric hub and bearing positions and no overhung load.
Common shafting steels. CEMA's deflection limit depends only on geometry and E — not strength — so a stronger steel will not fix a slope failure.
Corrected fatigue limit Sf = ka·kb·kc·kd·ke·kf·kg·Sf*. The reference defaults use ka = 0.8 for a machined shaft, automatic kb, kc = 0.897 and Sf* = 0.5Sut. Verify the keyway factor kf for the actual keyway and heat treatment.
Set the allowable shaft slope from the selected bearing and supplier documentation. The 0.0015 rad option is a preliminary reference value, not a universal bearing limit.