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Vibrating Screen Bed Depth Calculation STEP by STEP – VSMA Method Guide

Maximize Your Screening Performance – Learn to Calculate Vibrating Screen Efficiency Step by Step.

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Section summary
1. Introduction
2. Vibrating screen theoretical bed depth calculation methodology STEP by STEP
3. Vibrating screen theoretical bed depth Excel calculator

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This page provides a detailed methodology for calculating the discharge end bed depth of vibrating screens, essential for in mining, quarrying, and mineral processing operations.

1. Introduction

The theoretical bed depth, also known as the discharge end bed depth, is a critical parameter in the operation of vibrating screens used in mining applications. It refers to the depth of the material layer on the screen surface at the discharge end, which significantly influences the screening efficiency and capacity.

Calculating the theoretical bed depth is essential for process engineers to optimize screen performance, ensure efficient material separation, and prevent issues such as screen blinding and reduced throughput. The bed depth is determined by several factors, including the screen's inclination, the material's bulk density, the screen aperture size, and the feed rate. A deeper bed depth can hinder the passage of undersized material, while a shallower depth may reduce screening efficiency.

The Vibrating Screen Manufacturers Association (VSMA) provides a standard formula for calculating the discharge end bed depth: DBD=5×T×WO×C​, where DBD is the discharge end bed depth, O is the oversize material in short tons per hour (STPH), C is the cubic feet per ton of material, T is the rate of travel, and W is the width of the screening area in feet. This formula helps engineers determine the optimal bed depth to maintain efficient screening operations.

For materials with a bulk density of 100 lbs. per cubic foot, the bed depth should not exceed four times the size of the screen aperture. For lighter materials, such as those with a bulk density of 50 lbs. per cubic foot, the bed depth should not exceed three times the aperture size. Adhering to these guidelines ensures that the screen operates efficiently, maintaining high throughput and effective material separation.

The theoretical bed depth calculation must be used to control and finalized the vibrating screen sizing calculation, explained on this other page of www.powderprocess.net

2. Vibrating screen theoretical bed depth calculation methodology STEP by STEP

How to calculate the Discharge End Bed Depth (DBD) of a vibrating screen ?

The discharge end bed depth of a vibrating screen can be calculated thanks to the following formula :

DBD = (O.C)/(5.T.W)

Where :

• DBD = Discharge End Bed Depth (inches)
• O = Oversize in STPH
• C = Cubit feet per ton of material
• 5 = Constant
• T = Rate of travel (fpm)
• W = width of the scree area (ft)

Step 1 : Define the characteristics of your feed

It is important to analyse 1st the characteristics of the feed, especially :

- The size distribution and especially the % of the feed that is larger than the aperture you consider which allows to calculate the factory O

- The bulk density ρ of the feed material (lb/ft3) -> it allows to calculate C (ft3/t).

Example : 100 lb/ft3 = 1/100 ft3/lb = (1/100/0.454) ft3/kg = 0.022 ft3/kg = 22 ft3/t

Step 2 : Define the rate of travel T on the vibrating screen

The rate of travel depends on the inclination of the vibrating screen. Consider as typical :

• 75 fpm for inclined screens with slope 18° to 20° with flow rotation.
• 45 fpm for horizontal screens

Step 3 : Determine or assume a screen width

If the calculation is done one an existing screen, W is known and is simply the width of the existing sieve. If the calculation is done during a design, the width must be assumed, for example referring to a manufacturer's catalogue to know in which size are existing their products.

Step 4 : Calculate the Discharge End Bed Depth

DBD = (O.C)/(5.T.W)

Example :

• The aperture of the screen is 1 inch
• The deck is fed with 300 STPH of material with 15% oversize : O = 300*0.15 = 45 STPH
• The bulk density is 100 lb/ft3, which gives C = 22 ft3/t (see above)
• The screen is inclined : T = 75 fpm
• The width is assumed to be 6 ft
• DBD = (45*22)/(5*75*6) = 0.44 inch

Step 5 : check the bed depth is ok

VSMA is giving a rule of thumb :

• For a material with a density of ~100 lb/ft3, the DBD should be < 4*aperture size (in the example above 0.44 inch < 4*1 inch, so ok)
• For a material with a density of ~50 lb/ft3, the DBD should be < 3*aperture size

3. Vibrating screen theoretical bed depth Excel calculator

What are the key process parameters to consider ?

Please access here the vibrating screen theoretical bed depth Free Excel calculation tool : tool access

Warning : this calculator is provided to illustrate the concepts mentioned in this webpage, it is not intended for detail design. It is not a commercial product, no guarantee is given on the results. Please consult a reputable designer for all detail design you may need.

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Sources

VSMA