Design parallel keys and keyways. Calculate required key length, check shear and crushing stresses, and get recommended standard key sizes based on shaft diameter (ISO / DIN 6885).
Parallel rectangular / square key transmitting torque between shaft and hub
SI units: N·mm, MPa, mm
Nominal shaft diameter at the key location.
Torque to be transmitted (1 N·m = 1000 N·mm).
Width of the key (b).
Height of the key.
Active length of the key in contact.
Allowable shear stress of key material.
Allowable compressive stress of key material.
Governing Required Length
Shear Stress
20.41 MPa
Crushing Stress
63.49 MPa
Required length (governing) = 37.04 mm (Shear: 23.81 mm / Crushing: 37.04 mm)
def key_stresses(T, d, w, h, L):
"""
Parallel key shear & crushing stresses
T : N·mm
d, w, h, L : mm
Returns τ and σc in MPa
"""
tau = (2 * T) / (d * w * L)
sigma_c = (4 * T) / (d * h * L)
return tau, sigma_c
# Example
T = 500000
d = 50
w = 14
h = 9
L = 70
tau, sigma = key_stresses(T, d, w, h, L)
print(f"Shear stress: {tau:.2f} MPa")
print(f"Crushing stress: {sigma:.2f} MPa")function [tau, sigma_c] = key_stresses(T, d, w, h, L)
% Parallel key stresses (MPa)
% T in N·mm, dimensions in mm
tau = (2 * T) / (d * w * L);
sigma_c = (4 * T) / (d * h * L);
end
% Example
T = 500000;
d = 50;
[tau, sigma] = key_stresses(T, d, 14, 9, 70);
fprintf('Shear: %.2f MPa, Crushing: %.2f MPa\n', tau, sigma);Shear: =2*T/(d*w*L) | Crushing: =4*T/(d*h*L)Quickly calculate and analyze parameters for your ohms law requirements.
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A rectangular key sheared after only three months of service. Investigation showed the key length had been sized only for crushing; the shear length requirement was significantly longer.
Always calculate both shear and crushing lengths and use the larger value. Never size a key on only one criterion.
A designer used a key sized for a 40 mm shaft on a 55 mm shaft. The resulting high contact stress caused fretting and eventual hub cracking.
Always select the key cross-section from the standard table that corresponds to the actual shaft diameter.
Shear is the tendency of the key to be cut across its width. Crushing is the compressive bearing stress on the contact faces between key, shaft and hub.
Use ISO 773 or DIN 6885 tables. The calculator suggests the appropriate width and height based on shaft diameter.
Typical values for steel keys: shear 40–70 MPa, crushing 80–150 MPa depending on material and load type (steady / shock).