Determine maximum internal diameter of hollow shaft:

A solid shaft of mild steel which is 200 mm in diameter is to be replaced by hollow shaft of alloy steel for which the allowable shear stress is 22 percent greater. If power which is to be transmitted is to be increased by 20 percent and the speed of rotation increased by 6 percent, determine maximum internal diameter of hollow shaft. The external diameter of hollow shaft is to be 200 mm.

Sol.: Solid shaft diameter d = 200mm

Outer diameter of Hollow shaft = d_o  = 200mm

Inner diameter of Hollow shaft = d_i  = ?

Allowable shear stress τ H  = 1.22  S

Power transmitted P_H = 1.20P_S

Shaft speed N_H  = 1.06N_S

Now use P_H = 1.20P_S

i.e.;                         

2  .N_HT_H/60 = 1.2 [2  .N_ST_S/60]

N_HT_H = 1.2 N_ST_S

As N_H  = 1.06NS, putting this values