Fatigue Failure at a Shaft Shoulder on a Conveyor Drive

Nominal stresses at the 45 mm section

• Bending moment: M = 6.5 kN × 0.120 m = 0.78 kN·m.
• Section modulus: Z = πd³/32 = π(45)³/32 ≈ 8,946 mm³, so σ = 780,000/8,946 ≈ 87 MPa.
• Polar modulus: Zp = πd³/16 ≈ 17,892 mm³, so τ = 900,000/17,892 ≈ 50 MPa.
• Von Mises nominal stress: sqrt(87² + 3×50²) ≈ 123 MPa, versus Sy = 530 MPa.

Why fatigue still occurs

A rotating shaft reverses the bending stress every revolution, so σa ≈ 87 MPa nominal. The torque is steady, so it contributes mean stress. At the shoulder, D/d = 1.125 and r/d = 0.027, giving a bending Kt of roughly 1.85. With a notch sensitivity q ≈ 0.8, Kf ≈ 1.68, so the local alternating stress is about 146 MPa. A modified endurance limit is approximately Se = 315 × 0.85 × 0.85 × 1.0 × 0.9 ≈ 205 MPa (surface, size, load, and reliability factors). Goodman with mean equivalent stress sqrt(3)×50 ≈ 87 MPa gives 146/205 + 87/630 ≈ 0.85, i.e. n ≈ 1.18. That is a thin margin: a 15–20% belt overload, a jam, or a poor bearing fit during the recent repair pushes n below 1. Beach marks confirm high-cycle fatigue, and the small shear lip shows fast final fracture. Yield strength is not the governing criterion; notch stress, surface condition, and mean stress are.

Ranking

1. Increase the fillet radius and relieve the shoulder. A radius of 3 mm instead of 1.2 mm (r/d ≈ 0.067) reduces bending Kt from about 1.85 to roughly 1.45–1.5. Local alternating stress falls to about 125 MPa, raising the Goodman factor to roughly 1.3–1.4. This is the cheapest change and attacks the failure origin directly. Check that the larger fillet clears the bearing inner ring and seal; a relief groove or undercut shoulder can provide the radius without changing the bearing seat.
2. Increase the shaft diameter at the shoulder, e.g. 45 to 50 mm. Bending and torsional stress scale with 1/d³, so stress drops by about 27%. This also stiffens the shaft and reduces misalignment, but it requires new bearing, seal, and coupling sizes, so it is more expensive and slower.
3. Improve surface and material. Grinding or shot peening the fillet raises the surface factor and can add 15–20% to fatigue strength; switching to 4140 quenched and tempered raises Sut and Se. These are useful but do not remove the stress concentration, so they rank below geometry.

Bearing fit and alignment should be checked as a maintenance action: excessive interference or misalignment adds stress and can explain why failure followed the bearing replacement. Do not simply install the same drawing.

Verification

• Recalculate fatigue life with a documented method, using the actual Kf, mean and alternating stresses, and a Goodman or Gerber criterion. Show the assumed belt tension and starting/jam torque, not only steady operation.
• Confirm the load path: measure belt tension, check pulley alignment, and review the bearing replacement for fit, clearance, and misalignment. A recent repair that changes preload or alignment is a credible contributing cause.
• If the geometry is changed, perform FEA or a strain-gauge check at the fillet, and inspect the first articles with magnetic particle inspection.
• Consider a vibration or torque monitor during the first weeks and a scheduled inspection of the fillet.

Communication

Issue an engineering change notice rather than reinstalling to the old drawing. State the root cause, the interim risk, and the permanent fix. Tell production and maintenance plainly that the identical spare is likely to fail and why, and give a restart date. Record the concession or deviation if a temporary shaft is used, with a defined life limit. The final report should note that nominal stress was only 123 MPa versus 530 MPa yield, so the lesson is about notch fatigue and load assumptions, not about material strength.