The static moment (kg.cm) is determined by the mass of counterweights (kg) multiplied by the radius from the centre of the shaft to the centre of gravity of the counterweights (cm).

The dynamic moment is always always double the static moment. i.e.: it represents the mass of the counterweghts multiplied by the diameter to the centre of gravity of the counterweigthts.

The vibrating stroke of the screen (cm) can be calculated by the total mass of the screen (kg) divided by the dynamic moment (kg.cm).

The centrifugal force of a screen is a function of the dynamic moment and the operating speed (rpm). See my reply to your earlier posted question "centrifugal force and amplitude". ■

John,

Don't you mean that the stroke is the dynamic moment divided by the total mass of the screen? How do you determine the affect of the stiffness of the springs in this calculation. Certainly using stiffer support springs would reduce the overall stroke of the screen (due to the fact that the support structure would increase the effective mass of the system). Also it seems that the rotational speed would have an affect on the amplitude, or is this only true near resonant frequencies? Speaking of which, how are the resonant frequencies of the screen and support structure calculated, or is that too involved of a question for a quick answer? ■

Ooops !!!

You are quite correct in that “stroke is calculated by the dynamic moment divided by vibrating mass” (and not the other way around as I said). Thanks for picking this up ….. I must have had a few drinks that night.

As for determining the stiffness of a steel coil spring?

This is usually expressed as the “spring rate” or the “spring constant” (k), and is the load (kg or Newtons) that is needed to deflect the spring by 1mm.

Things that are going to affect the spring rate are:

·The wire diameter

·The number of active coils (total coils less the closed end coils)

·The mean diameter of the spring (the outside dia less the wire dia)

·The spring material specification

The formula to calculate the spring rate will vary depending on the units that you are using (and spring steel specification), but for a typical spring steel, and where all measurements are in mm, and the result (k) is in kg/mm

k = (8000 x wire dia^4) divided by (8 x number of active coils x mean spring dia^3)

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For all practical purposes the spring stiffness does not affect the stroke. For vibrating equipment soft springs are required to isolate the dynamic loads from the support structure, and if the spring used was stiff enough to effectively alter the stroke, I think the other associated problems would be so great that this would be the least of them!!!

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Likewise rotational speed will have negligible effect on screen throw within the normal screen operating range. It is true that the vibrating characteristics will be effected if the screen is operating at or near the natural frequency of the spring, but soft springs would have a typical natural frequency of say between 100 to 200 rpm, which is well below the normal screen operating range. You can observe the effect of the springs natural frequency coinciding with the screen rpm by the exaggerated “bounce” as the screen starts up and passes through the natural frequency of the spring, and to a greater extent at shutdown as the screen more slowly coasts down through the natural frequency of the springs.

The calculation of the spring natural frequency is not overly complicated, but probably a little too much detail to go into here (unless you are particularly interested).

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As to calculating the natural frequency of the screen and support structure, you are right in that in all but very straightforward beams and simple plate shapes this involves complicated calculations that these days are best done by computer modeling programmes.

In summary - a screen or support structure with members having a natural frequency which is close to the operating frequency of the screen can be a very serious (and expensive) problem, but this is not directly related to the screen throw.

All this is one poor mans opinion – always keen to hear others ■