It is required to design a square key for fixing a gear on a shaft of 25 mm diameter The shaft is transmitting 15 kW power at 720 rpm to the gear The key is made of st 60 and the factor of safety is 3 For key material, the yield strength in compression can be assumed to be equal to the yield strength in tension Determine the dimensions of the key
Solution
St60 𝜎𝑢=600𝑁⁄𝑚𝑚2
𝜎𝑦=0.7𝜎𝑢=420𝑁/𝑚𝑚2
𝜎𝑚𝑎𝑥=𝜎𝑦𝐹.𝑆=4203=140𝑁/𝑚𝑚2
𝜏𝑚𝑎𝑥=𝜎𝑚𝑎𝑥2=70𝑁/𝑚𝑚2
Transmission Torque M t = Power/2 π n
M t = 15000/2 π *(720/60)= 198 943.68 N.mm
Key dimensions
b=h= d/4 = 25/4=6.25 mm or 6 mm
From Shear stress, then
𝑙=2𝑀𝑡𝜏.𝑏.𝑑=34.6𝑚𝑚
Check by Bearing stress,
𝑙=4𝑀𝑡𝜎𝑏.𝑏.𝑑=34.6𝑚𝑚
Then The key dimensions 6*6*35 mm