Repeated conveyor drive shaft failures after a motor uprate
A 37 kW belt conveyor drives its head pulley through a helical gearbox. The gearbox-side shaft has failed twice in 14 months. The shaft is 1045 cold-drawn (Sut ≈ 630 MPa), 90 mm at the bearings and 80 mm through the keyway; the keyway is end-milled with a 1.0 mm corner radius and a standard parallel key. The fracture started at the keyway corner, shows ratchet marks and beach marks over roughly 60 % of the section, and ends in a small ductile shear zone on the opposite side. At that section the steady torque is 3.2 kN·m and the rotating shaft carries a constant 6.0 kN·m bending moment at 75 rpm. Two years ago the conveyor was uprated from 30 kW to 37 kW by changing only the motor and the motor sheave. Maintenance proposes remaking the shaft in 4140, through-hardened to 40 HRC, at identical dimensions and running it. Production wants the conveyor back within 48 hours.
1. Estimate the nominal bending and torsion stresses, the corrected endurance limit, and the fatigue safety factor at the keyway. What does the result predict?
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Nominal stresses at d = 80 mm. πd³ = π × 0.080³ = 1.609 × 10⁻³ m³.
- Bending, fully reversed (rotating shaft): σ = 32M/(πd³) = 32 × 6000 / 1.609 × 10⁻³ = 119 MPa.
- Torsion, steady: τ = 16T/(πd³) = 16 × 3200 / 1.609 × 10⁻³ = 31.8 MPa, giving a von Mises mean of √3 × 31.8 ≈ 55 MPa.
Corrected endurance limit. Se' = 0.5 × 630 = 315 MPa; surface factor ka = 4.51 × 630⁻⁰·²⁶⁵ ≈ 0.82 (machined); size factor kb = 1.24 × 80⁻⁰·¹⁰⁷ ≈ 0.78; load and temperature factors 1. Se ≈ 315 × 0.82 × 0.78 ≈ 200 MPa.
Notch. An end-milled keyway with r = 1 mm at 80 mm diameter has Kt ≈ 2.0–2.2 in bending; with q ≈ 0.85, Kf ≈ 1.9–2.0.
Modified Goodman with Kf applied to the alternating term only: 1/n = (1.95 × 119)/200 + 55/630 = 1.16 + 0.09 = 1.25, so n ≈ 0.80.
The section cannot achieve infinite life; finite life in the 10⁵–10⁷ cycle range is expected, which matches two failures in 14 months at 75 rpm. The calculation and the beach marks agree, so this is a stress-concentration problem, not a metallurgical mystery.
2. Diagnose the root cause. Is the proposed 4140 / 40 HRC change an adequate fix? Justify with numbers.
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Root cause. The detail was never designed for the uprated duty. Going from 30 kW to 37 kW raised torque about 23 %, and belt tension and therefore bending moment rose with it, while only the motor and sheave changed - the shaft, keyway and bearings were not re-verified. The 1 mm keyway corner with Kf ≈ 2 turns a 119 MPa nominal stress into an effective 230 MPa against a 200 MPa endurance limit. The fractography supports this: initiation at the keyway corner with ratchet marks (multiple crack origins at the notch), beach marks over 60 % of the section (stable fatigue growth), and a small final shear zone (short overload phase). Nothing in that appearance indicts the material.
Would 4140 at 40 HRC fix it? For Sut ≈ 1,050 MPa: Se' = 525 MPa, but ka falls with hardness (4.51 × 1050⁻⁰·²⁶⁵ ≈ 0.71) and kb stays ≈ 0.78, giving Se ≈ 290 MPa. A harder, stronger steel is also more notch-sensitive, q ≈ 0.95, so Kf ≈ 2.1. Then 1/n = (2.1 × 119)/290 + 55/1050 = 0.86 + 0.05 = 0.91, n ≈ 1.1.
That is a marginal gain against a target of n ≥ 2 for a shock-loaded conveyor, and it leaves no allowance for misalignment, belt tension variation or start-up torque. Also, an 80 mm 4140 section through-hardened to 40 HRC will have a softer core, and the keyway is still a sharp notch. Verdict: not adequate as a stand-alone fix. Change the geometry first; material selection is secondary.
3. Give the redesign and the verification steps you would require before the conveyor restarts.
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Geometry (dominant lever). Stress scales as 1/d³: increasing the keyway section from 80 to 95 mm cuts bending stress by (80/95)³ = 0.60, i.e. to about 71 MPa, and Kf drops because the notch is blunter relative to section size. Specify either a sled-runner keyway or an end-milled keyway with corner radius ≥ 3 mm and a relieved key end, and consider replacing the key with a shrink disc or taper-lock hub, which removes the keyway notch entirely. Add generous fillets and undercuts at all diameter transitions.
Material and surface treatment. If 4140 is used, specify induction-hardened fillets to leave residual compressive stress at the notch, and require hardness verification at the surface and core. Do not rely on through-hardening of an 80–95 mm section.
Recalculation and evidence. Re-run the Goodman check with the new dimensions and Kf to demonstrate n ≥ 2 at infinite life, including start-up torque and any plugged-chute shock. Then verify the real loads: laser-align motor and gearbox, measure actual belt tension against the design value, check gearbox output runout and bearing clearance, and confirm that the uprate did not change start/stop frequency.
Before restart. NDT the remaining shaft (magnetic particle at the keyway and fillets), check the spare for the same detail, instrument the drive for torque or motor current during the first loaded runs, set a vibration/oil-debris check at 200 h, and record the measured values against the design assumptions. If geometry cannot change before restart, run at reduced throughput and document the restriction with a dated action plan.