Considering a square key connecting the shaft hub.
Let, T = Torque transmitted by shaft
F = Tangential force acting at the circumference of
d = Diameter of shaft l = Length of key
w = Width of key
t = Thickness of key
for square key, we have,
w = t
Let τ , σc be the permissible shear and crushing stress for key material respectively.
A little consideration will show that due to power transmitted by the shaft the key may fail either due to shearing or crushing.
Considering shearing of key, the tangential shearing force acting on the shaft is
= Area resisting shearing x Shear stress = l x w x r …………(.a)
Also, Torque transmitted =
Considering crushing key, the tangential crushing force acting on the shaft is,
Fix the dimension of key from the standard shaft diameter, and as per the requirement square or rectangular key can be selected,
w= width of key
t = thickness of key
l=length of key =1.5d by proportion……………(1)
1. For Square key , w=t=d/4………………………..(b)
2. For rectangular key, w=d/4 & t=2/3w…………….(c)
3. & length of key can be obtained by shearing and crushing failure of key.
Considering shearing of key,
T=Ï„×w×l×d/2 ………………….. (2)
Considering crushing failure of key,
T=σc×l×d/2×t/2………………….. (3)