1. Vibration Control 1) Control of Excitation Control of Vibration Source. Example: Balancing of Machines 3) Control of System Parameters Change of system parameters such as m, c and k 2) Control of System Configuration Change of system order with vibration absorbers 4) Reduction of Force Transmission to the Machine Vibration Isolation

2. 1) Sources of Vibration Unbalance Misalignment Resonance Bent shaft Bearings Fluid induced instabilities (oil whirl/whip) Gears Looseness Belts & Pulleys Motor vibrations Fans Blade/vane passing Piping Cavitation

3. Causes of Unbalance: Porosity in casting. Nonuniform density of material. Manufacturing tolerances. Gain or loss of material during operation. Maintenance actions (e.g. cleaning, changing bearings). Changing bolts. Machining. Loose material moving around. Keys and couplings.

9. Misalignment: Sources of Vibration (Cont’d)

10. Misalignment Frequency Spectrum:

11. Misalignment Time and Frequency:

12. Misalignment vs. Unbalance

13. 2) Control of System Configuration Vibration Absorbers

14. We add a mass (undamped vibration absorber):

15. Equations: Solution: where

16. To make X 1 to be zero: Or,

18. 4) Reduction of Force Transmission Vibration Isolation Equation of Motion:

19. Force Transmitted to Foundation = Assume that Then And where Transmissibility = = Phase Angle

21. Now Assume that Then transmitted force becomes where