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.
Understanding Engineering: Keys and Splines
Torque becomes a real contact force at the outside of the shaft. A larger shaft radius gives that force more leverage, so the same torque produces less force at its surface. This is one reason shaft diameter matters so much.
In a keyed joint, one side of the key is pressed by the shaft and the opposite side presses on the hub. The key does not transmit useful torque through its top and bottom faces. Its side faces do the important work.
Designers estimate the surface force by saying force equals twice the torque divided by shaft diameter. They then check whether the key can resist being cut across its width and whether its contact faces can resist being crushed.
A key can fail in more than one way. Shear failure occurs when the force slices through the key, much like scissors cutting a strip of material. Bearing failure occurs when the pressure dents or deforms the sides of the keyway.
A short key has less contact area, so it experiences higher stress. A wider or longer key usually carries more load, but there are limits. Making the keyway too deep removes more shaft material.
The corners of a keyway create places where stress gathers during repeated rotation. A shaft may then crack from fatigue even when the key itself remains intact. Rounded keyway ends and suitable heat treatment can reduce this risk.
Splines are useful when a hub must move along the shaft while continuing to rotate with it. A vehicle gearbox provides a familiar example. Some gears slide on splined shafts during gear selection.
Drive shafts, steering columns, aircraft controls, machine tool spindles, and electric motor connections may use splines for the same reason. Straight sided splines are simpler to make. Involute splines use curved tooth shapes similar to gear teeth.
Their shape helps teeth share load more smoothly and makes accurate centering easier. In practice, load is not always shared equally across every spline tooth. Small errors in machining, bending, or alignment can cause a few teeth to carry too much force.
Fit is as important as calculated strength. A joint with too much clearance can move slightly each time the direction of torque changes. This motion is called backlash.
It can create impact loading, noise, and wear. Tiny movements may rub away material through fretting, leaving reddish debris on steel parts. A fit that is too tight can be difficult to assemble and may create unwanted stress before the machine even runs.
Lubrication is often needed for sliding splines, while fixed splines may need corrosion protection. When studying these joints, trace the load path from motor to shaft, from shaft to key or spline, then into the hub. This habit makes it easier to identify the part most likely to limit safe torque.
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.