Vibration Isolation Theory
MASS SPRING SYSTEM
A mass spring system may be represented by a mass “M”, excited by a force ”F” and supported on an elastic stiffness
element “K” with a dampening factor “C”. The frequency of the mass spring system is equal to:
The effectiveness of the suspension may be measured by transmissibility, i.e. by the force which is transmitted by the machine to the ground or floor. It is defined as the ratio between the force transmitted to the ground, FOT, and the
original force produced by the vibration FO. Another practical term is often used to describe the efficacy of an anti-vibration mount, namely the degree of insulation, which is:
Transmissibility Equation: E=(1-T)x100%
Examining this curve allows us to reach basic conclusions for an effective isolation.
If the frequency of excitation is times less the natural frequency, transmissibility is greater than one, then the force
transmitted is greater than the excitation force, there is magnification of the vibrations. When we work in this area, the existing damping in the system is important. The greater the latter, the smaller the magnification of the vibrations will be.
If the frequency of excitation is times greater than the natural frequency, transmissibility is less than one, or in other words the force transmitted is less than the force originated in the system, then we are in the damping area. To achieve the greatest isolation, the lowest possible natural frequencies should be sought. There are two ways of doing this:
- By increasing the system mass.
- By reducing the stiffness of the anti-vibration mount.
To increase the efficacy of the isolation in the damping area, it is advisable to have low damping, although weak damping generates greater displacement when passing through the resonance, it is advisable to use a damping coefficient t so that passage through the resonance does not give rise to inadmissible displacement for the machine.
STATIC AND DYNAMIC STIFFNESS: All elastomers suffer dynamic stiffening but metallic springs have a very low dynamic stiffening due to the low internal friction of the metals. Therefore we can consider that the springs have identical static and dynamic stiffness.
DAMPING: The metallic springs have very low damping. As we have mentioned previously, the metal spring coils, do not show any internal friction and therefore there is no energy dissipation through this phenomenon. Dynamic laboratory tests have shown in practice that the damping for this kind of mounts is almost null and this is the reason why these mounts have been combined with viscous dampers for applications where more damping is demanded. For example genset suspensions.
CREEPING AND LONG-TERM BEHAVIOUR: The spring mounts do not have the creeping and continuous increase of deflection all elastomers have, but spring coils have also certain relaxation that depend on the applied load and the temperature. The higher the load and temperature are, the higher is the relaxation. Temperatures above 80ºC and high loads, may cause a small loss of height in the spring. This set is always lower than the usual values of elastomers.
