Stress Concentration at a Keyway
Stress Concentration at a Keyway
A keyway cut into a shaft to seat a key for a pulley, gear, or coupling creates an abrupt local discontinuity in the otherwise smooth shaft geometry, and that discontinuity concentrates stress well above the nominal stress the shaft would see if it were uniform. Stress concentration factors, determined experimentally or from charts for standard geometries, let designers estimate this local peak stress from the simpler nominal stress calculation.Keyways are one of the most common sites for shaft fatigue failure in rotating machinery precisely because they combine a geometric stress riser with a location that already sees the shaft's full torque and bending — overlooking the stress concentration factor and designing to the nominal stress alone routinely leads to fatigue cracks initiating at the keyway corner well before the expected shaft life.
The local peak stress at the keyway is sigma_max = K_t·sigma_nom, the stress concentration factor times the nominal (unconcentrated) stress. where K_t is the stress concentration factor for the keyway geometry, sigma_nom is the nominal stress computed from the shaft's gross section properties, and sigma_max is the resulting local peak stress at the keyway root.
Inputs
K_t := 2.0=2
sigma_nom := 80 MPa=80 MPa
Multiplying the nominal stress by the stress concentration factor gives the actual local peak stress the material experiences right at the sharp corner of the keyway, which is what governs fatigue crack initiation.
sigma_max := K_t·sigma_nom=160 MPa
Results
A peak stress of 160 MPa here — double the nominal value — shows just how significant this local effect is: a shaft that looks adequately sized using nominal stress alone can be dangerously under-designed once the keyway concentration is applied. Because K_t depends strongly on the keyway corner radius, a sharp-cornered keyway concentrates stress far more than one cut with a generous fillet radius, making corner radius one of the most cost-effective design changes available to reduce this peak stress. This static peak-stress check is typically followed by a fatigue analysis using this same concentrated stress, since keyways in rotating shafts almost always see cyclic rather than static loading in service.
Assumptions & limitations
- Stress concentration factor K_t taken from standard charts for the given keyway geometry and shaft diameter ratio.
- Static peak stress check only — fatigue analysis (often using a reduced notch sensitivity factor) is a separate step.
- Nominal stress is assumed already correctly computed from the shaft's gross section properties away from the keyway.
- Keyway assumed to be a standard sled-runner or profiled type matching the K_t chart used.