Headshaft Hub Fretting on a 75 kW Conveyor Drive
A primary crushed-stone conveyor is driven through a 25:1 helical gearbox by a 75 kW, 1480 r/min motor. Headshaft speed is about 59 r/min, giving roughly 12.1 kN·m at the shaft. The headshaft is 150 mm diameter solid EN8 (Sy ≈ 280 MPa) and carries a 250 mm OD, 140 mm long steel hub located by a 25 × 14 × 140 mm parallel key plus a diametral interference of 0.09 mm measured at 20 °C. After nine months the drive began to slip under starting shock. Strip-down shows the key intact but the keyway widened by about 0.5 mm, heavy fretting scars and reddish oxide debris on the hub bore, and no sign of torque overload. Thermography shows the shaft runs near 75 °C while the hub stays near 40 °C. Take E = 207 GPa, α = 11.5 × 10⁻⁶ /K, and a friction coefficient of 0.12 for the fit.
1. Show whether the interference fit was adequate when cold, and explain why the key did not shear.
Read the worked answer
For a solid shaft in a hub of outer diameter D with diametral interference δ, the contact pressure is:
p = δ·E·(D² − d²) / (2·d·D²)
p = 0.09 × 207 000 × (62 500 − 22 500) / (2 × 150 × 62 500) = 0.09 × 207 000 × 40 000 / 18 750 000 = 39.7 MPa
Friction torque capacity: T = μ·p·(π·d·L)·(d/2)
- Contact area = π × 150 × 140 = 65 973 mm²
- Normal force = 39.7 × 65 973 ≈ 2.62 MN
- T = 0.12 × 2.62 × 10⁶ × 75 = 23.6 × 10⁶ N·mm ≈ 23.6 kN·m
Against 12.1 kN·m running torque that is a factor of 1.95 - adequate at 20 °C. So the fit, not the key, was carrying normal torque. The key has clearance in its keyway, so it only picks up load after relative movement starts (starting shock); at that point it sees impact and bearing load on the keyway wall, not steady shear. That is exactly the evidence found: an intact key, widened keyway, and fretting on the bore - slip and micro-motion first, key damage second.
2. Using the temperature data, reconstruct the failure mechanism and explain the oxide debris.
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The fit loses interference when the shaft runs hotter than the hub. Differential expansion reduces diametral interference by:
Δδ = α·ΔT·d = 11.5 × 10⁻⁶ × 35 × 150 ≈ 0.060 mm
Remaining interference at operating temperature = 0.09 − 0.060 = 0.030 mm.
Pressure scales linearly with interference: p = 39.7 × (0.030/0.09) ≈ 13.2 MPa.
Torque capacity = 23.6 × (13.2/39.7) ≈ 7.9 kN·m, which is well below the 12.1 kN·m running torque. So at steady operating temperature the hub is slipping on every start and probably under load fluctuations.
Mechanism: slip → micro-motion → fretting; the reddish oxide debris is fretting product (fine hematite-rich powder) that is abrasive and cannot escape, so it grinds the bore and keyway, clearance grows, slip amplitude grows, and the damage accelerates. The 0.5 mm keyway widening is the visible end point. The lesson is that a fit checked only at 20 °C on the bench is a fit with an unknown service capacity - thermal derating, not steel quality, caused this failure.
3. Specify the repair you would release, sized to survive the thermal condition, and check the hub stress.
Read the worked answer
Design target: carry 2.0 × 12.1 = 24.2 kN·m by friction alone at the 75 °C operating condition.
Required pressure at operating temperature: p = 2T / (μ·π·d²·L) = 2 × 24.2 × 10⁶ / (0.12 × π × 150² × 140) = 48.4 × 10⁶ / 1.19 × 10⁶ ≈ 40.8 MPa
Required interference at 75 °C: δ = p × 2·d·D² / (E·(D² − d²)) = 40.8 × 18 750 000 / (207 000 × 40 000) ≈ 0.092 mm
Add back the thermal loss of 0.060 mm → required cold interference ≈ 0.152 mm on 150 mm (about 0.001 mm/mm).
Hub stress check at p = 40.8 MPa: σ_hoop = p·(D² + d²)/(D² − d²) = 40.8 × (62 500 + 22 500)/40 000 = 40.8 × 2.125 ≈ 87 MPa, against 280/1.5 ≈ 187 MPa allowable - acceptable, so the hub can take the tighter fit.
Specification I would release: machine and fit to 0.15–0.16 mm interference by thermal shrink or oil injection, verify by measurement on both parts, re-cut the keyway to 28 × 16 with a matched key for back-up only (check bearing stress on the keyway wall against the shock torque), and control heat: cooler oil flow or a heat shield between gearbox and hub to reduce the 35 K differential. Better still, replace the shrink fit with a taper-lock/Ringfeder-type friction element whose capacity is stated at temperature, and add soft-start so the shock that exposed the problem is reduced.