TAHA Engineering Toolsby TAHA Knowledge Lab

Mechanical Engineering

Parallel Key Length Estimator

Minimum parallel-key length for shear and crushing, or the stresses in a given key.

Inputs

Cross-section of a hub around a shaft with a rectangular key sitting half in the shaft keyway and half in the hub keyway.bhFdshafthub
Section through shaft, key and hub. The torque is carried as a force F = 2T ÷ d at the shaft surface. The key can fail by shear across its width b, or by crushing on its sides (about h ÷ 2 bears on the hub). Diagram not to scale.

From the key standard for your shaft size (for example ISO/R 773 or DIN 6885 in metric, ASME B17.1 in inch). Not built in.

Key material shear strength ÷ your factor of safety, or the value from your design code.

Use the weakest of key, shaft and hub materials.

Result

Minimum key length
31.25
Length needed for shear
17.3611
Length needed for crushing
31.25
Force at the shaft surface
12.5
Governing check
Crushing (bearing) governs
Working
F = 2T ÷ d = 2 × 250 ÷ 40 mm = 12.5 kN L shear = F ÷ (b × τ) = 12,500 ÷ (12 × 60) = 17.361 mm L crushing = F ÷ (h/2 × σ) = 12,500 ÷ (4 × 100) = 31.25 mm

The key must be at least 31.25 mm long (crushing (bearing) governs). Round up to a standard key length that fits within the hub.

Educational estimate — check the assumptions below.

About this calculator

A key locks a gear, pulley or coupling hub onto a shaft and carries the torque between them. It can fail in two ways: by being sheared across its width, or by crushing (bearing) on the side faces in the shaft or hub keyway. This estimator uses the standard textbook method to find the shortest key that keeps both stresses within your allowable values — or checks the stresses in a key of known length.

Choose the key width and height from your key standard for the shaft diameter; they are not built in.

Formula

F = 2T ÷ d    Lshear = F ÷ (b × τallow)    Lcrush = F ÷ ((h/2) × σallow)

T = torque, d = shaft diameter, F = tangential force at the shaft surface, b = key width, h = key height (about half of it bears against the hub), τallow = allowable shear stress, σallow = allowable crushing stress. The required length is the larger of the two.

Worked example

250 N·m on a 40 mm shaft, key 12 × 8 mm, allowable shear 60 MPa, allowable crushing 100 MPa:

  • F = 2 × 250 ÷ 0.040 = 12.5 kN
  • Shear: L = 12 500 ÷ (12 × 60) = 17.4 mm
  • Crushing: L = 12 500 ÷ (4 × 100) = 31.3 mm → crushing governs; choose a standard length of at least 32 mm.

Assumptions and limitations

  • Parallel (feather) key, with the force acting at the shaft surface and stress spread evenly along the key length. In practice the load is uneven, so many designers limit key length to about 1.5 × shaft diameter and use two keys or a spline for higher torque.
  • Allowable stresses are your inputs; they should include a factor of safety and account for shock loads. Fatigue, stress concentration in the shaft keyway and fit of the key are not checked.
  • Taper, gib-head and Woodruff keys have different geometry and are not covered.

References

  • Key shear and crushing analysis (e.g. Shigley’s Mechanical Engineering Design; Bhandari, Design of Machine Elements).
  • Key dimensions: ISO/R 773, DIN 6885-1 (metric), ASME B17.1 (inch).