Power-transmission shaft sizing engine for mechanical designers: torque from power and speed, midspan bending from radial load, required diameter by the ASME allowable-stress equation and the distortion-energy Goodman fatigue criterion with full Marin modification factors (surface, size, reliability), standard-size selection, static yield and deflection checks — every input with selectable universal units and reference-standard values, every report with the full audit trail.
SectorCalc SC-026 sizes a rotating power-transmission shaft under combined torsion and bending. The engine resolves torque from power and speed, bending moment from a midspan radial load on a simply supported span, then returns the governing diameter from two independent criteria: the ASME allowable-stress shaft equation and the distortion-energy Goodman (DE-Goodman) fatigue criterion with Marin surface, size and reliability factors. It rounds to the next preferred standard diameter and verifies static yield and midspan deflection at that size. Results are reference-grade design estimates — final dimensions, keyways, shoulders and fillet radii must be verified with full stress-concentration analysis before drawing release.
Torque — not power — stresses the shaft. Halving the speed at constant power doubles the torque and roughly doubles the required diameter's cube, so gearbox output shafts are always the critical members. Use the shaft speed after any transmission ratio, and multiply motor nameplate power by the driven machine's service factor when duty is severe.
SC-026 models the shaft as simply supported at the bearing centres with the radial load (gear mesh force, belt tension, rotor weight, or their vector sum) acting at midspan — the worst-case position:
Real shafts carry the load off-centre; M = F·a·b/L reaches its maximum F·L/4 exactly at midspan, so the midspan model is conservative for any single load position. Multiple loads (two gears plus a coupling) require superposition or a shear-moment diagram — this engine covers the dominant single-load case and flags long spans where deflection, not stress, governs.
The ASME transmission-shaft code approach limits shear stress to the lower of 0.30·Sy or 0.18·Sut, with combined shock and fatigue factors Kb and Kt:
This is the quick, inherently conservative screening diameter. It embeds fatigue allowance inside the reduced allowable stress and the K factors rather than an explicit endurance-limit calculation.
Fatigue sizing starts from the rotating-beam endurance limit and corrects it to the real part:
Because kb depends on the unknown diameter, SC-026 iterates: it starts with kb = 1, solves for d, recomputes kb at that diameter, and repeats until the value stabilizes — typically three iterations to better than 0.1% convergence.
For a rotating shaft, bending is fully reversed (alternating) while steady torque is mean torsion. The distortion-energy Goodman criterion gives the required diameter directly:
SC-026 reports both the DE-Goodman and ASME diameters and takes the larger as the required minimum. DE-Goodman usually governs on long spans with high bending; ASME can govern on short, high-torque shafts with ductile materials.
The required diameter is rounded UP to the next preferred size (…45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 110, 120 mm…). At that selected size the engine re-verifies:
The static check uses the factored loads (Kb, Kt) so a single shock event cannot yield the shaft. Both safety factors are reported in the results table and the audit trail.
General machinery shafts target δ ≤ 0.001·L; machine-tool spindles and gear shafts demand far less (gear mesh misalignment limits are typically 0.0001–0.0003·L). SC-026 computes midspan deflection at the selected diameter and warns beyond the general guideline. Critical (whirling) speed is not evaluated — for shafts above ~3600 rpm or with L/d > 15, run a dedicated critical-speed analysis before release.
Either can govern. DE-Goodman with Marin factors typically governs long spans where reversed bending dominates, especially with rough surfaces (hot-rolled, as-forged). The ASME equation can govern short, torque-dominated shafts because its 0.18·Sut shear cap is severe for high-strength steels. SC-026 always reports both and selects the larger diameter.
No — directly at the keyway the stress concentration (Kf ≈ 2–2.5 for a sled-runner keyseat in bending) and the removed section must be checked separately. Shop practice is to size the shaft body with this engine, then add one standard size step or verify the keyed section explicitly. The audit report lists the un-notched body diameter; treat it as the minimum between stress raisers.
The engine sizes solid circular sections. For a hollow shaft with bore ratio k = di/do, section modulus scales by (1 − k⁴): multiply the required solid d³ by 1/(1 − k⁴) and solve for the outer diameter. Weight saving is substantial (up to 40% at k = 0.8) but buckling of thin walls and bore concentricity must then be checked.
Because fatigue cracks start at the surface. An as-forged surface on 625 MPa steel retains only about 35% of the rotating-beam endurance limit (ka ≈ 0.35), versus about 77% for a machined finish — more than a factor of two in allowable alternating stress, and roughly 25% in required diameter since stress scales with 1/d³. Surface finish is the cheapest fatigue upgrade available: grinding a hot-rolled shaft can recover most of the difference.
From the driven machine, not the motor. Fans, centrifugal pumps and generators are steady (Kb 1.5, Kt 1.0). Conveyors, mixers and reciprocating machinery with even loading are minor shock (2.0/1.5). Crushers, presses and machinery with sudden load reversals are heavy shock (3.0/2.0). When in doubt, select the more severe class — the diameter penalty is under 15% while an undersized shaft costs the whole machine.
