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

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

3. Shaft Power P=T  Power = (Torque)(Angular Velocity) 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 Static Torsion Reversed Torsion

6. Shaft Fatigue Failure

7. Shaft Design Strategy  Find correct equation for d shaft  Identify critical points along shaft  Find M a, M m, T a, T m  Find K f, K fs, K fm, K fsm  Find S e (as a function of d shaft )  Solve for d shaft (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 F key from F=T/r shaft »you now have F a and F m  Find  a and  b (=F/A shear )  Find  ´ a and  ´ m  For Bearing Failure  F=F m +F a  Find  (=F/A bearing)

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 I m of mass (ignore shaft)  Find K t  Find J for each section  K t,section =GJ/L  Find 1/K t,total = 1/K 1 + 1/K 2 + 1/K 3 + … 