A 5hp 1725rpm electric motor has a 0875indiameter shaft exte

A 5-hp, 1725-rpm electric motor has a 0.875-in-diameter shaft extension with a sled runner keyseat for a 0.1875-in-square key. The shaft is made of cold-drawn AISI 1040 steel with S(ut)= 100,000 psi and S(yt)= 88,000 psi. The motor is used to drive a machine that frequently requires a torque that is steady but about 120% of that corresponding to the rated horsepower. Based on average material properties, what is the factor of safety? Why is the factor of safety so high?

Solution

Torque by motor   =   3728.5 / pi * 1725 / 30    = 20.64 Nm

Actual torque = 1.2 * 20.64 = 24.77 Nm   or 18.27 ft lbs

Shear Strength   = Sy / 2   = 44000

Torsional shear stress in shaft   = 16 * T / pi * d^3   =   44000 / FS

                                              =   16 * 18.27 * 12 / pi * 0.875^3    = 44000 / FS

Therefore FS (factor of safety) against torsion = 26.4

Factor of safety is so high because a very high diameter shaft is being used to carry a relatively low amount of torque.