Keyway Stress Calculator Formula
Understand the math behind the keyway stress calculator. Each variable explained with a worked example.
Formulas Used
Tangential Force on Key
tangential_force = forceShear Stress on Key
shear_stress = force / (key_width * key_length)Bearing (Compressive) Stress
bearing_stress = force / ((key_height / 2) * key_length)Variables
| Variable | Description | Default |
|---|---|---|
torque | Transmitted Torque (T)(N-m) | 200 |
shaft_dia | Shaft Diameter (d)(mm) | 40 |
key_width | Key Width (w)(mm) | 12 |
key_height | Key Height (h)(mm) | 8 |
key_length | Key Length (L)(mm) | 40 |
force | Derived value= 2 * torque * 1000 / shaft_dia | calculated |
How It Works
Parallel Key Stress Analysis
A key transmits torque between a shaft and a hub (gear, pulley, coupling).
Formulas
The tangential force at the shaft surface: F = 2T / d
Shear stress = F / (w x L) (shear across the key width)
Bearing stress = F / ((h/2) x L) (crushing on half the key height)
where T is torque, d is shaft diameter, w is key width, h is key height, and L is key engagement length. Bearing stress is usually the governing criterion.
Worked Example
A 12x8 mm key, 40 mm long, on a 40 mm shaft transmitting 200 N-m.
torque = 200shaft_dia = 40key_width = 12key_height = 8key_length = 40
- 01F = 2 x 200,000 / 40 = 10,000 N
- 02Shear stress = 10,000 / (12 x 40) = 20.8 MPa
- 03Bearing stress = 10,000 / (4 x 40) = 62.5 MPa
- 04Bearing stress governs. For mild steel key (allowable bearing ~90 MPa), the key is adequate.
Ready to run the numbers?
Open Keyway Stress Calculator