A spur gear slipped on its shaft after four months of service. The gear was 2.5 module, 40 mm bore, 20 mm face, mounted on a ground shaft with an H7/p6 interference fit and a key. The drive transmitted 120 Nm. The gear had turned a few degrees relative to the shaft — visible as a scuffed ring around the hub and a shifted keyway contact mark. The customer’s first call was “the key sheared.” The key hadn’t sheared. The interference fit had let go, and the key, which was only ever a backup, took the load until the bore wore.

The drawing said H7/p6. The machinist had bored the gear to H7 and ground the shaft to p6. On paper that’s 0.026 to 0.051 mm of interference for a 40 mm bore. On the bench, it pressed together fine. Four months later it slipped. The tolerance was right. The contact wasn’t.

What the fit actually needs to do

An interference fit transmits torque through friction at the bore-shaft contact. The torque capacity depends on the contact pressure and the friction coefficient:

T = (π/2) x μ x p x L x d²

where μ is the friction coefficient, p the contact pressure, L the hub length, d the shaft diameter. The contact pressure from the interference, using the thick-cylinder formula, is roughly:

p = E x δ / (d x (1 + Q²))

with δ the diametral interference, E Young’s modulus, Q the ratio of hub outer to bore diameter. For this gear: d = 40 mm, hub outer ≈ 64 mm (Q = 1.6), E = 210 GPa, δ = 0.038 mm average. That gives a contact pressure around 55 MPa. With μ = 0.10 (typical for steel on steel, pressed, lightly oiled), torque capacity is:

T = 1.571 x 0.10 x 55 x 20 x 40² = 2,765,000 Nmm ≈ 2765 Nm

2765 Nm of capacity against a 120 Nm load. A 23x margin. The fit should have been welded on by friction alone. It slipped anyway. The margin calculation was right, and one of the inputs was wrong.

The two inputs that failed

First, the surface finish. The shaft was ground to 0.4 Ra, fine. The gear bore was bored to 1.6 Ra — the drawing didn’t specify a finish on the bore, so the shop left it as-bored. The effective interference of a rough bore is lower than the nominal: the roughness peaks crush and deform during pressing, eating 60-70% of the interference. Instead of 0.038 mm of real interference, the contact had maybe 0.012 mm. That drops the contact pressure to about 18 MPa and the torque capacity to 900 Nm. Still above 120 Nm, but the margin collapsed from 23x to 7x, and friction on a worn, polished bore is lower than the book value.

Second, the direction of the load. The drive reverses. Every reversal, the key takes a momentary blow before friction re-engages. Each reversal micro-shocks the joint. Over four months at 20 reversals a minute, that’s millions of micro-shocks. The bore polished, the effective friction dropped, and the fit let go.

What fixed it

The rework was simple once the diagnosis was clear:

  1. The bore was specified and ground to 0.8 Ra. Real interference went back to the nominal 0.038 mm.
  2. The fit was assembled by heating the gear to 90°C in an oven and dropping it on, instead of pressing at room temperature. Heating expands the bore by about 0.05 mm, so the gear slides on without scoring the surfaces. Pressing a rough, tight fit cold tends to gall and wipe the peaks, destroying the interference you just paid for.
  3. The key was kept — the design needs it for the reversal shocks — but the keyway was broached with a radius at the corners so it doesn’t become a fatigue crack starter, same lesson as every keyed shaft in a reversing drive.

The drive has run two years without slip. The rework cost a re-ground bore and a new key. The original failure cost a day of downtime and a replacement gear.

The general fit rules

For gear-to-shaft fits that carry reversing or shock loads:

  • Specify the bore finish. 0.8 Ra or better. The interference you design is only as real as the surface it lands on.
  • Heat assembly when the fit is above about H7/p6. The temperature change is cheap insurance against galling.
  • Check the hub length. A short hub (this one was 20 mm on a 40 mm bore, L/d = 0.5) concentrates the contact pressure at the hub edges and reduces effective capacity. L/d of 0.8 to 1.0 is better for torque.
  • Treat the key as a backup for shock, not as the primary torque path. If the key is doing the work, the fit has already failed.

The 23x margin on paper collapsed because a rough bore ate 70% of the interference and a reversing load polished the rest. Grind the bore, heat the gear, keep the key for shocks. A fit that slips at 120 Nm isn’t a fit problem. It’s a surface finish problem wearing a tolerance’s clothes.