A keyway on a 40 mm shaft that sheared after three months of operation. The drive was a 5.5 kW motor at 1450 RPM. The customer thought the key was made of soft material. It wasn’t — the keyway was undersized for the torque. The key was 12×8 mm (standard for 40 mm shaft), but the design load included shock from a reciprocating compressor. This is how I size keyways for torque transmission.
The basic torque formula
The shear stress in a rectangular key is:
τ = 2T / (d · b · L)
Where T is the torque (N·mm), d is the shaft diameter (mm), b is the key width (mm), and L is the key length (mm). For a standard square key on a 40 mm shaft: b = 12 mm, L = 36 mm (typical). The torque from 5.5 kW at 1450 RPM: T = 9550 × 5.5 / 1450 = 36.2 N·m = 36,200 N·mm.
Shear stress: τ = 2 × 36,200 / (40 × 12 × 36) = 36,200 / 17,280 = 2.1 MPa. That’s way below the allowable shear stress for steel (about 80 MPa). So why did it fail?
The crushing stress, not shear
The key doesn’t fail in shear — it fails by crushing on the sides. The bearing stress on the key is:
σ_b = 2T / (d · 0.5h · L)
Where h is the key height (8 mm for a 12×8 key). The contact height is h/2 = 4 mm. σ_b = 2 × 36,200 / (40 × 4 × 36) = 72,400 / 5,760 = 12.6 MPa. Still low. But that’s steady-state torque. The compressor has a starting torque of 3x rated (5.5 kW compressor). Shock torque: T = 3 × 36,200 = 108,600 N·mm. Crushing stress: σ_b = 2 × 108,600 / 5,760 = 37.7 MPa. Still below yield for a standard C45 key (355 MPa). But repeated shock cycles work-harden the key surface. After thousands of cycles, the key material flows. The keyway walls wear. The key loosens. Then it impacts each cycle. The key shears.
What I changed
1. Increased key length. I doubled the key length from 36 to 70 mm. The crushing stress dropped by half: σ_b = 18.9 MPa under shock load. The longer key distributes the load over more contact area.
2. Used a Woodruff key or two parallel keys. For high-shock applications, I use two keys spaced 180° apart. The load splits between them. Each key sees half the torque. The crushing stress drops by another factor of two.
3. Specified the key material. I call out C45 (1045) steel, quenched and tempered to HB 220-250. Not mild steel. The yield strength is 355 MPa, and the fatigue limit is about 180 MPa. With the longer key and two-key design, the working stress is well below fatigue limit.
The keyway in the hub
The hub material is often weaker than the key. A cast iron hub has a bearing stress limit of about 80 MPa. If the hub is aluminum, it’s 30 MPa. I check the hub, not just the key. For our 40 mm shaft with a cast iron pulley, the crushing stress under shock (37.7 MPa) is fine for steel but marginal for cast iron. I specified a cast steel pulley instead.
Standard key sizes
| Shaft dia (mm) | Key b×h (mm) | Standard length (mm) | Max torque (N·m) at σ_b=50 MPa |
|---|---|---|---|
| 20 | 6×6 | 20 | 30 |
| 30 | 8×7 | 28 | 85 |
| 40 | 12×8 | 36 | 190 |
| 50 | 14×9 | 44 | 340 |
| 60 | 18×11 | 54 | 620 |
The stress I check: crushing on the keyway side, not shear. And I multiply the rated torque by a shock factor (2-3x for reciprocating loads, 1.5x for centrifugal). The keyway that sheared after 3 months wasn’t undersized for steady-state torque — it was undersized for the shock cycles. A longer key or two keys spaced 180° fixes it.
