Keys and splines are mechanical features used to lock rotating parts, such as gears, pulleys, and couplings, to a shaft. Their main job is to transmit torque without allowing the hub to slip around the shaft. A key fits into matching slots called keyways in the shaft and hub, while splines use many matching teeth around the shaft.
These parts matter because a small connection detail can control the strength, alignment, and reliability of an entire machine.
A keyed joint transmits torque by pushing on the sides of the key, which creates shear stress in the key and bearing stress between the key, shaft, and hub. If the torque is too high, the key may shear across its length or crush the contact surfaces. Splines spread the load over multiple teeth, so they are often used when higher torque, better centering, or sliding axial motion is needed.
Good design checks both strength and fit, including key size, keyway depth, material, stress concentration, and assembly clearance.
Key Facts
- Torque is related to tangential force by T = F r.
- For a shaft of diameter d, the tangential force at the shaft surface is F = 2T/d.
- Key shear stress can be estimated by tau = F/(w L) = 2T/(d w L).
- Key bearing stress can be estimated by sigma_b = F/((h/2) L) = 4T/(d h L).
- A keyway weakens a shaft because it removes material and creates a stress concentration.
- Splines transmit torque through multiple teeth, which distributes load better than a single key.
Vocabulary
- Key
- A removable machine element placed between a shaft and hub to transmit torque by preventing relative rotation.
- Keyway
- A slot cut into a shaft or hub that holds part of a key.
- Spline
- A series of ridges or teeth on a shaft that mesh with matching grooves in a hub to transmit torque.
- Shear stress
- Stress caused by forces that try to slide one part of a material past another.
- Bearing stress
- Compressive contact stress that occurs where two machine parts press against each other over an area.
Common Mistakes to Avoid
- Using only shear stress to size a key is wrong because bearing stress can be the limiting failure mode.
- Assuming the full key height carries bearing load is wrong because standard approximations usually use about half the key height in contact.
- Ignoring the shaft keyway is wrong because the slot reduces shaft strength and raises local stress.
- Choosing a spline only for higher torque is incomplete because spline selection also depends on alignment, axial sliding, manufacturing cost, and fit accuracy.
Practice Questions
- 1 A shaft has diameter d = 40 mm and transmits torque T = 300 N m. Find the tangential force at the shaft surface using F = 2T/d. Use d in meters.
- 2 A rectangular key has width w = 12 mm, height h = 8 mm, and length L = 50 mm on a shaft of diameter d = 40 mm. If T = 300 N m, estimate the key shear stress and bearing stress using tau = 2T/(d w L) and sigma_b = 4T/(d h L).
- 3 A machine currently uses a single sunk key, but the hub must slide along the shaft while still transmitting torque. Explain why a splined shaft may be a better design choice.