The Keyway That Sheared Off Under Torque
We designed a shaft to drive a conveyor pulley. The shaft was Ø25 mm steel. The keyway (for the pulley’s key) was 8 mm wide. We used a standard square key (8×7 mm). On the bench, it held. On the floor, the key sheared off after a week of 24/7 operation. The torque was 30 N·m. We calculated the key shear stress: τ = 2T/(d × b × L) = 2×30,000 / (25 × 8 × 20) = 150 N/mm². The key’s shear strength (mild steel) is about 100 N/mm². We were over the limit. We upsized the key to 10×8 mm and the keyway to match. The shear stress dropped to 80 N/mm². The mistake was picking a standard key size without checking the shear stress.
Shaft and keyway design is a classic machine-design calculation. The key is often the weakest link. This article covers the numbers.
The Keyway Loads
A key (square or rectangular) sits in a keyway on the shaft and a keyseat in the hub. It transmits torque from the shaft to the hub. The key sees two failure modes:
- Shear: The key shears across its width (at the shaft surface).
- Crushing: The key (or the keyway walls) crushes (compression) on its side.
For a standard square key, shear is usually the limiting factor.
Step 1: Shear Stress Calculation
The shear stress on the key is:
τ = 2T / (d × b × L)
Where:
- T = torque (N·mm, so 30 N·m = 30,000 N·mm)
- d = shaft diameter (mm)
- b = key width (mm)
- L = key length (mm, the engaged length, not the total key length)
For T = 30,000 N·mm, d = 25 mm, b = 8 mm, L = 20 mm: τ = 2×30,000 / (25 × 8 × 20) = 60,000 / 4,000 = 150 N/mm².
The allowable shear stress for a steel key (mild steel, 1045) is about 80–100 N/mm² (with safety factor). At 150 N/mm², the key shears.
With a 10×8 mm key (b = 10 mm, L = 25 mm): τ = 60,000 / (25 × 10 × 25) = 60,000 / 6,250 = 96 N/mm². Acceptable.
Step 2: Crushing (Bearing) Stress
The key also crushes against the keyway wall. The bearing (crushing) stress is:
σ = 2T / (d × 0.5h × L)
Where h is the key height (about b for a square key). The 0.5h is because the key contacts the hub on half its height and the shaft on the other half.
For h = 7 mm (8×7 key): σ = 60,000 / (25 × 3.5 × 20) = 60,000 / 1,750 = 34 N/mm². Well within the allowable crushing stress (about 150 N/mm² for steel). So crushing isn’t the issue — shear is.
Step 3: Shaft Diameter and Torsion
The shaft itself must also resist torsion. The shaft’s torsional shear stress:
τ_shaft = 16T / (π × d³)
For T = 30,000 N·mm, d = 25 mm: τ = 16×30,000 / (π × 15,625) = 480,000 / 49,087 = 9.8 N/mm². Very low. The shaft is fine (steel allows 40–50 N/mm² in shear). The key was the weak point, not the shaft.
The keyway rule: The key is the weakest link. Calculate τ = 2T/(d × b × L). Keep it under 100 N/mm² for steel. The key that sheared was at 150 N/mm² — too high. Upsize the key (wider and longer). For high torque, use two keys (180° apart) or a spline.
Step 4: Keyway Types
- Square key (parallel key): Standard. A square bar in a square keyway. Simple, cheap. For most applications.
- Woodruff key: A half-moon key. Self-aligning. For smaller shafts (up to Ø20 mm).
- Spline: Multiple teeth (integral with the shaft). For high torque (the load is shared over many teeth). More expensive.
- Tapered key: A key that wedges (locks axially). For shafts that can’t use a hub screw. Less common now.
| Key Type | Torque Capacity | Best For |
|---|---|---|
| Square parallel key | Standard | Most shafts, general |
| Woodruff key | Low (small shafts) | Ø20 mm and under, self-aligning |
| Spline | High | High torque, frequent shifting |
| Two keys (180°) | ~2× single key | High torque, space-limited |
Step 5: Keyway Stress Concentration
The keyway is a stress riser (the sharp corners concentrate stress). For shafts under fatigue (reversing torque), the keyway corners initiate cracks. Use a radius in the keyway corners (not a sharp corner). For fatigue-critical shafts, specify a ground (not milled) keyway with generous radii.
For a shaft that rotates at constant torque (a conveyor), fatigue isn’t an issue. For a reversing servo axis (article 101), fatigue matters — use a larger radius and a higher safety factor.
A Keyway Design Checklist
- What is the torque? (Continuous and peak.)
- Shaft diameter? (Standard, matches the bearing?)
- Key width b? (From the shaft standard: Ø25 → 8 mm key.)
- Key length L? (Engaged length.)
- Shear stress τ = 2T/(d b L)? (Under 100 N/mm²?)
- Crushing stress? (Under 150 N/mm²?)
- Shaft torsion τ = 16T/(π d³)? (Under allowable?)
- Keyway corners have a radius? (Fatigue?)
- One key or two? (For high torque?)
- Hub length long enough? (Key engagement?)
- Set screw or clamp? (Holds the hub axially?)
- Is the key material specified? (Steel, not cast iron?)
The Bottom Line
Shaft and keyway design makes the key the checked link, not an afterthought. The key that sheared was at 150 N/mm² shear stress — over the limit. Calculate τ = 2T/(d × b × L) and keep it under 100 N/mm². Upsize the key (wider, longer) or use two keys for high torque. Add a radius in the keyway corners for fatigue. The shaft itself is usually fine — the key is the weak point. The shaft that never sheared a key wasn’t the thickest one — it had the right key size.
