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.
- 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.
Frequently Asked Questions
How do I select the correct key size?
Standard key sizes are based on shaft diameter. For a 40 mm shaft, the standard parallel key is 12 x 8 mm (DIN 6885 / BS 4235). Consult the relevant standard for your shaft diameter.
What is the minimum key length?
Key length should be at least 1 to 1.5 times the shaft diameter. Too-short keys create excessive bearing stress and can fail by crushing. Maximum length is limited by the hub width.
What material should the key be?
Keys are typically made from medium-carbon steel (e.g., AISI 1045). The key should be weaker than the shaft and hub so it acts as a sacrificial element, protecting more expensive components.
Ready to run the numbers?
Open Keyway Stress Calculator