# Fan response

The fan and its parts may be likened to a spring-mass system.

An understanding of this fact is useful in resolving many vibra­tional problems. It is also of importance in revealing the causes

Of resonance.

Every fan will have three basic properties:

A) Mass “m” measured in kg or lbf. sec2/in. The force due to the mass of the system is an inertia force or a measure of the tendency of the body to remain at rest.

B) Damping “C” is the damping force per unit velocity of a

System. It is a measure of the slowing down of vibrations and is given in N. sec/mm or Ibf. sec/in.

C) Stiffness “k” is a measure of the force required to deflect

Part of the fan through unit distance. Measured in N/mm or Ibf./in.

The combined effects of these restraining forces determine

Howa fan will respond to a given vibratory force e. g. unbalance.

Thus we may state that:

 Cden
 • kep = l41co2r sin (cot — (|>)
 Dt dt
 Md2e„
 Or
 Mepco2 sin cot + Cepcosin ^cot + ~J + kep = IV^o/r sin (cot -<(>)= Mco2e sin (cot — (|>) Property Definition ISO Marine/Defence Acceleration R -|AdB L-20,t4tJ A0 = 10’6 m/s2 > O II © 3 T/T Velocity R v T L*=:20109 y V0= IO 9 m/s Cn E Ц O >

Table 15.3 Vibration definitions for decibel scales

 Equ 15.1

 = Mcd e sin (cot-) Equ 15.2

 Where: E Ep M Mu R -relationship of units

From Section 15.2.1, it can be seen that there is a relationship between any measured quantity such as displacement, velocity or acceleration for a single frequency event.

This can also be extended to the logarithmic scales noting the appropriate reference levels.

Again, it should strictly be for a single frequency simple har­monic motion. However, where one property such as unbal — displacement of centre of gravity from centre of rotation

Displacement of part due to vibratory force

Mass of rotating parts

Mass of residual unbalance

Distance of unbalance from rotating centre

(j) = phase angle between exciting force and actual

Vibration

Or

Inertia force + Damping force + Stiffness force = Vibratory force

It will be seen that the three restraining forces are not working together and that the inertia and stiffness forces are 180° out of phase and tending to cancel each other out. At the frequency where they are equal “resonance” occurs, and there is only the damping (which is 90° out of phase) to keep the system vibra­tions down.

All fans together with their supporting bases consist of a num­ber of different spring-mass systems each having its own natu­ral frequency possible with various degrees of freedom and a different resonant frequency for each. So far we have only con­sidered unbalance as the exciting force, but there will be nu­merous other sources such that resonance can be a common problem.

Posted in Fans Ventilation A Practical Guide