CHAPTER 3: CALCULATE AND DESIGN SCREENING SYSTEM
3.2 Design the screening system
Vibrating screener: the purpose of using vibrating sieves is to sort and transport materials, consuming little energy but loud noise. Main part of the vibrating screener is springs, which is installed to four corners of screener. This type of screener is popular with construction field.
Rotating screener: The advantages of rotary screener are simple structure, stable movement, no vibration, no noise, low energy costs. The disadvantage is that it is not possible to separate mixtures of nearly equal size, the failure rate is large, the work is difficult to observe, the coefficient of using the sieve surface is small, easy to plug the sieve hole. This type of screener is popular with factories.
Shaking screener: producing the highest efficiency, has the best durability and is capable of sorting many types of items at the same time, but the price is quite high. The screener shakes when the material is put on the screen and then falls throughout the grid, the operating motor pulls the eccentric arm to create a shift, the four shaking bars are responsible for shaking back and forth rhythmically to help the sand get through the holes, and the garbage will go upwards.
We choose the shaking screener because of its high performance and easy for installation.
The structure of system consists of four rotating rods connected at the four corners of the vibrating screening frame, the other four ends attached to the frame chine and driven directly through eccentric shaft.
30 3.2.2. Determine the number of revolution n
Figure 3. 4. Force diagram when the object moves up
Dividing the force P⃗⃗ into two functions via horizontal part and vertical part according to the declination of the screener, when the objects move up, P⃗⃗ is created by inertial a, so we have:
{P⃗⃗ a1 = P⃗⃗ a∙ sinα
⃗⃗ Pa2 = P⃗⃗ a∙ cosα (3.11) When the objects move up , the friction force is created:
F = f(G ∙ cosα − Pa ∙sinα) (3.12) By which: 𝑓 = (0.3 − 0.4) ∙tanφ : coefficient of friction
G is the total weight of mixtures on the screener Pa (N): inertial force of object caused by inertial a
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Types of sand USCS
Friction angle [°]
min max Specific value Sandy gravel with little or no fines GW 33 40
Sandy gravel with little or no fines GP 32 44
Sandy gravels – Loose (GW, GP) 35
Sandy gravels – Dense (GW, GP) 50
Silty sandy gravels GM 30 40
Clayey sandy gravels GC 28 35
Gravelly sand with little or no fines SW 33 43
Loose sand (SW, SP) 29 30
Medium sand (SW, SP) 30 36
Dense sand (SW, SP) 36 41
Silty sands SM 32 35
Table 3. 1. Table of friction angle for sandy soil (according to USCS).
The Unified Soil Classification System (USCS) is a soil classification system used in engineering and geology to describe the texture and grain size of a soil. The classification system can be applied to most unconsolidated materials, and is represented by a two-letter symbol.
Via the target of design, the main objective of the machine is the mixture including waste and sand. With sand, I consider it is sandy gravels which is the combination of coarse sand, gravel, and even rocks in variety of sizes.
From the table 3.1, I choose friction angle = 500 with 𝑓 = (0.3 ÷ 0.4) According to the figure 3.3, the force equation is:
Pa ∙ cosα > f(G ∙ cosα + Pa ∙ sinα) + G ∙ cos ∝ (3.13)
⇒ n > 30 ∙ √tan(φ + α)
r (3.14)
32 By which:
𝛼 = 200, 𝜑 = 500
r = 0,025mm: eccentricity of shaft
⇒ n > 314,49(rev/min)
Let the objects can move up, the minimum number of revolutions of eccentric shaft is:
𝐧 ≥ 𝟑𝟏𝟓(𝐫𝐞𝐯/𝐦𝐢𝐧)
3.2.3. Determine the weight and velocity of mixture moved on the screener 3.2.3.1 The total weight of mixture
Figure 3. 5. Simulation for mixture in the process of moving up screener From the calculated above, I have:
{
B = 850mm = 0.85m L = 650mm = 0.65m
Let h = 100mm: the working depth
Assuming the level of mixture moving up the screener continuously, then I have the volume of mixture on the screener is:
Von screener =h ∙ L
2 ∙ B + 0,3 ∙h ∙ L
2 ∙ B(m3) (3.15) Von screener =0.1 ∙ 0.82
2 ∙ 0.62 + 0,3 ∙0.1 ∙ 0.82
2 ∙ 0.62 Von screener = 0.03 (m3)
Therefore, the total weight of mixture that brought on the screener is:
Gmixture = Von screener ∙ ρ ∙ g (3.16) Gmixture = 453.22 (N)
By which: ρ = 1400 kg/m3: bulk density of sand g = 9.81 (m/s2) : gravitational acceleration 3.2.3.1 The velocity of mixture
v = 2.36√d = 2.36√3,4 ∙ 10−3= 0.14 (m/s)
33 3.2.4. Determine the power of screener
Here, I determine the power expended for the screener is mainly to generate kinetic energy for the vibrating screener.
The power that generates kinetic energy for the screener, also known as the consumable power to shake the whole block, is calculated by the formula:
N = A ∙ n
60 ∙ 75=G ∙ n3∙ r2
4050000(kW) (3.17) By which:
A (Nm): kinetic energy creates the vibration for screener.
n = 500 (rev/min): the number of revolutions r = 0.015 (m): eccentricity of shaft
G = Gmixture+ Gscreening frame + G𝑠𝑎𝑛𝑑 𝑎𝑒𝑟𝑎𝑡𝑜𝑟 𝑠ℎ𝑎𝑓𝑡
G (N): total of weight needs to be shaken Gscreening frame = 150 (N)
Gmixture = 453.22 (N) Gsand aerator shaft = 11 (N) From the equation (3.17), kinetic energy is:
Nkinematic = 7.58 (kW)
The tangential velocity on eccentric shaft is:
v1 = π ∙ r ∙ n
30 = 1.31 (m/s)
The power to overcome friction in the pillow supporting the eccentric shaft is determined by the formula as:
Nfriction =f ∙ Pa∙ v1
103 =0,06 ∙ 2558.33 ∙ 1,31
103 = 0.2 (kW) The efficiency of the screener is: 𝜂𝑠𝑐𝑟𝑒𝑒𝑛𝑒𝑟 = 81.63%
The power of motor is:
Nmotor preliminary =Nkinematic + Nfriction
𝜂𝑠𝑐𝑟𝑒𝑒𝑛𝑒𝑟 = 9.53 (kW) Choose the motor:
From the calculations {N motor preliminary = 9.53 (kW) n = 500 (rpm)
The power of motor must greater than the necessary power Pmotor > Pnecessary
By which: Pnecessary = Nmotor
η
34 Find the efficiency for the system
✓ Drive efficiency:
𝜂 = 𝜂𝑐ℎ𝑎𝑖𝑛 𝑑𝑟𝑖𝑣𝑒 . 𝜂𝑏𝑒𝑎𝑟𝑖𝑛𝑔𝑠 = 0.93 ∙ 0,9952 = 0.92
✓ Following the table 3.3 in page 60 document [1] , we get:
𝜂𝑐ℎ𝑎𝑖𝑛 𝑑𝑟𝑖𝑣𝑒 = 0.93 ∶ the efficiency of the chain drive 𝜂𝑏𝑒𝑎𝑟𝑖𝑛𝑔𝑠 = 0.995 ∶ the efficiency of pairs of bearing Therefore,
Pnecessary =Nmotor
η =9.53
0.92= 10.36 (kW) Distribute the ratios for transmission
Overall transmission ratio for preliminary system: uG = uchain drive = 2
Number of spins of the working shaft: n = npreliminary ∙ uG = 1000 (rev/min) From the motor that have P 𝑛𝑒𝑐𝑒𝑠𝑠𝑎𝑟𝑦= 10.36 (kW), we can determine the number of revolutions and other specification of 4 different motors via the table 3.1 in page 53 document [1] :
ID motor Power 𝐏(𝐊𝐰)
Revolution n(rpm)
𝐓𝐦𝐚𝐱/𝐓𝐝𝐧
160L 11 970 2.5
Table 3. 2. Motor SGA (Company CMG, Australia) 3.2.5. Specifications of screener
Characteristics Parameters
Dimension (mm) 850 × 650 (length × width)
Weight (N) 150
Material of frame Steel square tube 30x30x2 (mm)
Motor 160L (motor SGA)
Transmission Chain drive
Type Shaking screener, steel knitting mesh (holes 4mm) Supporting parts Bearings installed in four corners of sieve
Rod connected with motor shaft to change rotary motion into linear motion
Table 3. 3. Technical table
To facilitate the maintenance, cleaning, replacement of screening mesh, there is a screening frame that contains the meshing screener. Both of parts are connected by two eye bolts. These eye bolts are installed in back corners of the screening frame.
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Figure 3. 6: Screening frame