A machine is driven by a 2kW electric motor running at 1440 r/min through a 2,5:1 helical reduction gearbox. The helical gears are machine cut with a 20 degree normal pressure angle and helix angle of 30 degrees with a normal gear module of 2,5mm. The pinion has 18 teeth of right hand helix and is keyed directly to the electric motor shaft of diameter 19,8mm as shown. If the shaft of the electric motor is machined from EN8 carbon steel and has the dimensions shown determine whether or not there is a reserve factor at the critical section by means of the residual stress method and Goodman relationship. The following fatigue stress concentration factors Kf may be applied 1,7 for bending and 1,9 for axial and 1,4 for torsion. Assume that the endurance limit of the EN8 steel shaft is 180MPa and neglect the effect of the keyway. Provisional calculations estimate that the forces between mating gears are Tangential force Ft=510N Separating force Fr=215N Axial force Fa=295N 02 Electric motor shaft 24 45 teeth 250 18 teeth 20- 55 32 Critical section