Shafts & Keys

1. Shafts & Keys • Shafts in general • Fatigue • Deflection • Keys • Critical Frequencies

2. Shafts shoulders, keys, bending, torsion, deflection

3. Shaft Power Power = (Torque)(Angular Velocity) P=T W = (Nm)(radians/s) 1 hp = 745.7 W

4. Stresses in Shafts • normal, bending, alternating,a • normal, bending, mean, m • shear, torque, alternating, a • shear, torque, mean, m

5. Fatigue Data Reversed Torsion Static Torsion

6. Shaft Fatigue Failure

7. Shaft Design Strategy • Find correct equation for dshaft • Identify critical points along shaft • Find Ma, Mm, Ta, Tm • Find Kf, Kfs, Kfm, Kfsm • Find Se (as a function of dshaft) • Solve for dshaft (iterative)

8. Some General Rules of Shaft Design • Length/positioning • keep length as short as possible, avoid overhangs/cantilevered sections • Hollow shafts • greater stiffness/mass and higher natural frequency (but has greater cost and diameter) • Stress concentrations • place where bending moment is low, use generous radii

9. More General Rules • Gears • deflection less than 0.005 in., relative slope differ by less than 0.03 degrees • Bearings • deflection important for sleeve/journal bearings • slope important for roller bearings • Natural Frequency • first natural frequency > 3x(forcing frequency)

10. Key Design Strategy • For Direct Shear Failure • Find Fkey from F=T/rshaft • you now have Fa and Fm • Find a and b (=F/Ashear) • Find ´a and ´m • For Bearing Failure • F=Fm+Fa • Find  (=F/Abearing)

11. Natural Frequencies • Bending • Lateral • Whirl • Torsional

12. Lateral assumes external excitation set potential energy equal to kinetic energy

13. Shaft Whirl

14. Whirl

15. Bending Frequency Strategy • Find maximum static deflection • static, but be realistic • Find n using Lateral Deflection • Find /n

16. Torsional Frequency Strategy • Find Im of mass (ignore shaft) • Find Kt • Find J for each section • Kt,section=GJ/L • Find 1/Kt,total = 1/K1 + 1/K2 + 1/K3 + …