## How to Calculate How Much Vibration is Needed for Your Application

Using the following formulas, you can determine how much vibration will be sufficient. Remember, the goal is to provide just enough vibration to do the job. Excessive vibration can cause excessive wear on surrounding systems.

1. Linear Motion (Contra-Rotating Twin Vibrators)
Vibrators with their axes in the same plane and wired to contra-rotate will produce a linear motion at right angle to the vibrator axes. Amplitudes are given by the formulas below.
2. Circular Motion (Single Vibrators)
True circular motion is only obtained when the center of the vibrator coincides with the center of gravity of the structure. When vibrators are fixed in non-center of gravity positions, the motion will be in the form of an ellipse which varies at different points on the structure. Amplitudes given by the formulas below are an average value suitable as an approximation.

## Diagnostic Instrumentation Technical Data

### Formula – please select a formula from these choices

Amplitude Formula

 For 864 CPM, App. 0.0945 x CF/LOAD For 1152 CPM, App. 0.0530 x CF/LOAD For 1728 CPM, App. 0.0236 x CF/LOAD For 3456 CPM, App. 0.0059 x CF/LOAD cf*/14.2 x (CPM/1000)2 x LOAD Any Frequency, App. Use CF at required frequency i.e. CF = CF at max. freq. x (Required Freq/max. vibrator freq.)2 In no case should amplitudes exceed the following values: Speed App. 864 CPM...1152 CPM...1728 CPM...3456 CPM 1.42"........0.795"..........0.354".........0.088" Any Frequency 1.06(1000/CPM)2

Centrifugal Force Required

If the frequency of vibration, load, and amplitude required are known, the centrifugal force required can be calculated from the following:

 For 864 CPM, CF App. x LOAD/0.0945 For 1152 CPM, CF App. x LOAD/0.0530 For 1728 CPM, CF App. x LOAD/0.0236 For 3456 CPM, CF App. x LOAD/0.0059 Any Frequency, CF App. x 14.2 x (CPM/1000)2LOAD

Power Requirements

The power required from a vibrator depends on the nature of the application and the degree of damping present. It can be shown that for any application there is a peak power requirement when damping is at an optimum level. The power required then is:

 For Linear vibration, Watts max. App. x CF x CPM/676 For Circular vibration, Watts max. App. x CF x CPM/338

In most applications the power required can be taken as one-fifth of the above values since damping rarely reaches an excessive level. If the vibrator current is found to be too high, the out-of-balance weights should be set back until it reaches an acceptable figure.

Vibrator Isolation

When using vibrator(s) on vibratory equipment, it is necessary to allow freedom of movement and also to prevent unwanted damaging vibrations being transmitted to surrounding equipment and steelwork. Generally, 95% isolation is satisfactory and will be obtained using the resilient mountings having the following static deflections under the weight of the structure, load, and vibrator(s):

 For 864 CPM, CF d = 0.990" For 1152 CPM, CF 0.557" For 1728 CPM, CF d = 0.248" For 3456 CPM, CF d = 0.062" For other values of deflection and frequencies isolation % 100 - 100/(d x 25.4)(CPM/950)2 - 1 Total transmitted force is given by P Trans = (100 - isolation %) / 100 x CF

Working Moment

 The working moment values given in the tables are twice the working moment used to calculate the centrifugal force and are used as another method for calculating the amplitude peak to peak from: App. = Working moment/LOAD Also, Working moment required App. x LOAD

Notation

App. = Amplitude peak to peak (inches)
CF = Total Centrifugal Force (pounds)
CPM = Frequency of Vibration (cycles per minute)