1. The design of anti-vibration systems
VIBRATION ISOLATION
The design of anti-vibration systems

2. Introduction
Most mechanical devices such as fans, pumps, etc. produce vibration.
Vibration is easily transmitted through solid materials and may ‘appear’ elsewhere producing troublesome vibration and/or noise.
To prevent this, vibrating machines must be de-coupled from their supports and other connections

3. DEFINITIONS Free Vibration Forced Vibration Resonance Damping
A mass on a spring, a tuning fork or cymbal all vibrate at their natural frequency, f0 when displaced or struck.
Forced Vibration
A system excited by the application of an external periodic force of frequency, f will be forced into vibration.
Resonance
When a system is forced into vibration at its natural frequency, i.e. when f = f0 (The amplitude of vibration increases with each cycle)
Damping
Any influence which extracts energy is known as damping.

4. Damping Ratio
Critical damping is when the mass returns to zero in the shortest time without overshoot.
Damping Ratio = Damping Present
Critical Damping

5. TRANSMISSIBILITY
The performance of a spring isolation system is given by its ability to transmit the forces due to vibration of a machine through the anti-vibration springs.
This is the FORCE TRANSMISSIBILITY, T
T = Force Transmitted
Force Applied
The VIBRATION ISOLATION EFFICIENCY,  is given by:
 = (1-T) x 100 %
Decibel reduction (N dB) by an isolator is given by:-
N (dB) = 20 lg (1/T)
spring
isolator
Force Applied
Force Transmitted

6. Example
Find the transmissibility and the reduction in dB of a spring isolator that gives a vibration isolation efficiency of 99%
 = (1-T) x 100 % so, T = 1 - /100
T = 1 – 99/100
T = 0.01
Reduction in level = 20lg(1/0.01) = 40 dB

7. Static Deflection
The static deflection, s is the deflection causes when a mass is placed upon a spring isolator
Gravity force = m.g
Spring force = k.s
Equating forces we get k.s = m.g or k = m.g/ s
spring
isolator
free height
static deflection (s )

8. Natural Frequency, f0
The natural frequency of a spring mass system (from SHM) is:
Substituting the static deflection for k (k =m.g/s) we get,
Cancelling and combining constants, f0 is found from:

9. Force Transmissibility Graph
Transmissibility, T
Amplification, T 1.0
1.0
Isolation, T  1.0
f/f0
(f = f0)
1.414
Isolation only when f is greater than f02

10. Example
Find the force transmissibility for a machine running at 3000 rpm if it is on a spring isolator with a natural frequency of 10 Hz.
The force transmissibility equation
f = 3000/60 = 50 Hz, f0 = 10 Hz
T = 0.042, Isolation Efficiency,  = (1-T) x 100  96 %

11. PROBLEMS
The amplitude of vibration at resonance can cause mechanical damage
More of a problem with machines which run-up slowly, or that operate at different frequencies which may be close to resonance.
Solution – damping or amplitude limiters
Amplitude limiter with rubber buffers
Friction damping
Visco-elastic damping
(dash-pot)

12. EFFECT OF DAMPING
If damping is increased the resonance amplitudes are reduced, but unfortunately so is the isolation at higher frequencies
f / f0

13. ISOLATOR DESIGN Start with required isolation efficiency, 
Calculate the required transmissibility, T
- From =(1-T)x100 therefore, T = 1- [/100]
Use the transmissibility equation and the forcing frequency, f to find the natural frequency, f0 if the isolator
From T= 1/{(f/f0)2 -1) therefore,
Calculate the static deflection required
From therefore

14. /Continued
A suitable vibration isolation mount can then be selected from a manufacturer’s catalogue which give the static deflections for different machine masses.
Alternatively, the spring stiffness can be found from:
k=m.g/s
Remember, that this will be split between the number of mounts used (usually 4, one at each corner)

15. Example
Find the static deflection of the spring isolators required to give 90% isolation efficiency for a pump with mass of 10kg running at 3000 rpm & give the reduction in dB
Isolation efficiency of 90% means transmission of 10%, so required T = 0.1
Reduction = 20lg(1/0.1) = 20 dB
f = 3000 rpm = 3000/60 = 50 Hz
mass = 10kg (2.5kg per spring)

16. From before natural frequency needed
Substituting for f & T
static deflection required
= m or 1mm

17. The isolator can then be selected from a manufacturers catalogue for the mass of the machine.
Need a spring that will deflect by 1mm under the weight of 2.5kg (assuming 4 springs supporting the pump)
Petrol driven water pump with
rubber isolation mounts

18. INERTIA BASES Machines are often isolated using an inertia base
Spring Isolators
Machines are often isolated
using an inertia base
(concrete)
These add mass which reduces the vibration amplitude
Increased mass allows stiffer springs which will help prevent rocking
The extra mass reduces the centre of gravity also preventing rocking
Flexible coupling

19. CENTRING THE MACHINE MASS OVER THE ISOLATORS
Inertia Base
Centre of
Gravity
Centre of Gravity
INCREASE IN MASS REDUCES THE VIBRATION AMPLITUDES
EXTENDING THE FRAME TO CENTRE THE MASS TO PREVENT ROCKING

20. Dynamic Vibration Damping
Electronically controlled (active) with force applied to oppose that creating the vibration and thus prevent metal fatigue or
Stockbridge dampers – use an additional spring-mass system tuned to the natural frequency of the vibrating system – parasitic spring-mass vibrates instead of actual system.
Masses on springy arms used for power lines and the suspension cables on the old Severn Bridge

21. Wobbly Millennium Bridge

22. THE END