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

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

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.

Misalignment:

Sources of Vibration

(Cont’d)

Misalignment

Frequency Spectrum:

Misalignment

Time and Frequency:

Misalignment vs. Unbalance

2) Control of System Configuration

Vibration Absorbers

We add a mass (undamped vibration absorber):

Equations:

Solution:

where

To make X1 to be zero:

Or,

4) Reduction of Force Transmission

Vibration Isolation

Equation of Motion:

Force Transmitted to Foundation =

Assume that

Then

And

where

Transmissibility =

= Phase Angle

Now Assume that

Then transmitted force becomes

where