CHAPTER 3: CALCULATE AND DESIGN SCREENING SYSTEM
3.1 Calculate the working surface of screener
Firstly, sand is a naturally occurring granular material composed of small and fine particles of rock and minerals.
Sand is mainly mined in nature, yet as the status over-exploitation, natural sand resources are becoming gradually scarce and replaced by other materials on the market.
Sand is mined mainly in rivers and seas.
The working surface of the screener is the main part for material sorting. Currently, two are main types of shape: knitted nets, perforated plates.
Knitting mesh: Used for fine sieving and small sieving of loose, dry materials. Knitting mesh has square, rectangular or hexagonal holes. Commonly used knitting fibers are fabric fibers, silk fibers, metal fibers.
Figure 3. 1. Knitting mesh
Perforated plate: Made from steel plate or copper plate. Sieve holes can be round, square, rectangular or oval holes. Perforated sheets are often used for sorting to sizes larger than 5mm. The holes are usually 5-10mm in size and arranged on the plate can be parallel or alternate. Rectangular holes are usually 2.3 times larger in length than in width.
Figure 3. 2. Perforated mesh
24 3.1.1. Parameters for grains of sand
Based on the grain size, the sand is further classified into variety of types.
Below is the standard table about the dimension for grains of sand by two main scales:
Dimension(*) 0,0625–0,0125 0,125–025 0,25–0,5 0,5–1 1–2 Wentworth scale Very fine sand fine sand medium
sand
coarse sand
very coarse sand Kachinskii scale
0,05 ≤ fine sand ≤ 0,25 medium sand
coarse sand 3.1.2. Influential factors in the screening process
3.1.2.1. The effects of shape and size for meshing cell
Depending on the yield and magnitude of the material, we choose the shape and size of the grid appropriately.
Experiments have shown that in order for the material to easily pass through the mesh hole, it is recommended that the mesh hole be slightly larger than the size of the lump of material, which can be from 1 mm to 5 mm depending on the material being sifted.
Here, we determine that the objective is very coarse sand so we choose the dimension for the meshing cell range from 2 mm to 6 mm to get high performance.
In addition, the size of the knitting mesh should be less than the size of the material that passed through the screening hole (except for sand).
Therefore, we choose the diameter for the meshing is: D = 4 mm.
25 3.1.2.2. The effects of incline screener
Figure 3. 3. Illustration of material that can pass through the holes
From the above figures, the minimum diameter of the hole allowing the material to easily pass through is:
d = D ∙ cosα − e ∙ sinα (3.1) By which: d(mm): size of material
D(mm) = 4: size of meshing
e(mm) = 1: thickness of knitting mesh
𝛼 = 200: the standard angle of screener with the ground So, all of materials that have d > 3,4 cannot pass through the hole of screener.
3.1.2.3. The effects of humidity
The moisture content of the material affects directly to the screening process.
In some materials when screener is wet, the ability to pass through the sieve increases because the limiting causes of passing through the hole are improved such as the resistance coefficient of the screener (similar to the coefficient of friction). In addition, moisture on the outside of the sieve wetting material, creating a water film in the meshing cell, this can hinder the passage through the hole of the sieve material.
The amount of physical moisture (i.e. moisture that envelops the outer surface of the material) has an adverse effect on the sieving process. The smaller and finer the sieving material, the more surface moisture affects the sieving process. Surface moisture causes fine material particles to stick together into larger lumps that not only do not get through, but also seal the sieve holes, so the sieving efficiency is reduced.
To minimize the effect of moisture, we increase the revolutions number of the shaft of the screener depending on the moisture content of the material accordingly.
26 3.1.3. The efficiency in the screening process
The efficiency of the sieving process, also known as the screening efficiency, is the ratio of the amount of material that can pass through to the mixture of materials transmitted to the screener, calculated in % and expressed by the symbol η.
The performance of the sieving process depends on many factors such as: the size of the sieve surface, the shape and size of the mesh hole, the velocity of movement of the material on the sieve surface. The thickness of the layer of material on the sieve, the coefficient of friction of the material on the sieve.
From the equilibrium condition, we have:
Q = C + T (3.2)
By which: Q (N): Weight of the starting material mixture C (N): Weight of the mixture below screener
T (N) : Weight of the mixture transmitted on the screener
Let a be the figure for the product after filter in the initial mixture, b is the figure for the rest of product located in the grid of the screener, then the total weight of the original mixed product is Q.a
100, and the weight of the product located in the product layer on the grid is T.b
100
Thus, the screening efficiency will be expressed as follow:
C 𝑄 ∙ 𝑎
100
∙ 100 = 𝐶
𝑄 ∙ 𝑎. 104% (3.3)
Material balance equation calculated by product under screener:
𝑄 ∙ 𝑎
100 = 𝐶 +𝑇 ∙ 𝑏
100 (3.4)
⇔ 𝑄 ∙ 𝑎 = 100 + (𝑄 − 𝐶) ∙ 𝑏
⇔ 𝐶
𝑄 = 𝑎 − 𝑏 100 − 𝑏
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Replacing the above ratio to ( 3.3) we get the screening efficiency:
η = 𝑎 − 𝑏
𝑎 ∙ (100 − 𝑏)∙ 104% (3.5)
Depending on the working area of the machine, the material on the sieve or under the screener is different. From the experiment shows that: a̅ = 70%, b̅ = 30%
⇒ η = a̅ − b̅
𝑎̅ ∙ (100 −b̅)∙ 104 = 70 − 30
70 ∙ (100 − 30)∙ 104 = 81.63 % The screener has an efficiency is: 𝛈 = 80%.
3.1.4. Dimension of mesh and velocity of objects on the screener
The thickness of the material on the screener greatly affects the filtering process. If the layer of mesh is too thick, and the mixture is smaller than the meshing hole located on the surface will not be able to pass through the hole. The thinner the layer of material, the higher the efficiency, resulting in low productivity as not only sand but also others kind trash will be moved out from the holes. Therefore, it is necessary to control the thickness of the material layer on the sieve surface reasonably.
The length of the screening surface also affects the screening process, but here we use knitting mesh, so the working surface of the screener is knitting mesh with square-shaped holes.
Choose the preliminary width is B = 620mm.
Let n is the number of materials transmitted to the screener:
n = B ∙ h
0.785 ∙ d2 (3.6)
⇒ n = 620 ∙ 100
0.785 ∙ 3.42 ≈ 78981(grains) By which: B is the width of screening frame
h = 100mm is the maximum thickness of material
d = 1mm is the dimension for the materials can pass through the hole (very coarse sand)
Then, the number of rows are:
Z = 𝑛
𝑛0 (3.7)
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𝑛0 is the number for grain of sand pass through a hole.
If with D = 4 mm and e = 1 mm due to sand containing garbage, the number of sand through the screener will less than the initial mixture, so according to research, only about 34% of the mixture will go through the sieve then we have:
n0 =D2∙ h
e (3.8)
𝑛0 =42∙ 100
1 ∙ 34% = 544 (𝑔𝑟𝑎𝑖𝑛𝑠) From formula (3.7), we get:
Z =78981
544 = 145(holes) Let t is the step of hole, then the length of screener is:
L = Z ∙ t (3.9)
L = Z ∙ t = 145 ∙ (4 + 1) = 725mm
The fact that lumps of material get through the hole is not entirely easy, but many times get stuck, so it is necessary to include more and the coefficient k. So the actual length of the sieve surface will be:
L = k ∙ Z ∙ t (3.10) L = 1.131 ∙ 725 ≈ 820 mm
With: k = 1.05 – 1.2.
In order to make the working surface has suitable size, a length is chosen to be from 1.2 to 1.5 times larger than the width:
B = L
1.322 ≈ 620 mm Therefore, the dimensions of the mesh are:
Mesh { e = 1mm, D = 4mm L = 820mm, B = 620mm
I use square steel 30 x 30, stainless steel, and thickness 2mm to fixed and support mesh not to slack:
Total dimension of screening frame: {L = 820 + 30 = 850mm B = 620 + 30 = 650mm Estimating the weight of screening frame:
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From the dimension, the total length is 3m for both length and width.
Therefore, weight of screening frame 30x30 (mm), thickness 2mm is: