A pulley is keyed to a shaft midway between two anti-friction hearings. The bending moment at the pulley vanes from – 170 N-m to 510 N-m and the torsional moment in the shaft varies from 55 N-m to 165 N-m. The frequency of the variation of the loads is the same as the shaft speed. The shaft is made of cold drawn steel having an ultimate strength of 540 MPa and a yield strength of 400 MPa. Determine the required diameter for an indefinite life. The stress concentration factor for the keyway in bending and torsion may be taken as 1.6 and 1.3 respectively. The factor of safety is 1.5. Take size factor = 0.85 and surface finish factor = 0.88.

Given Data

Bending Moment at pulley varies from 170N-m to 510 N-m

Torsional moment in shaft varies from 55N-m to 165N-m

Ultimate Strength = 540 MPa

Yield Strength = 400 MPa

Stress concentration factor in bending = 1.6

Stress concentration factor in torsion = 1.3

Factor of safety = 1.5

Size factor = 0.85

Surface finish factor = 0.88