### Conveying and Sieving

The functionality and choice of the external vibrators at the conveying and sieving is identical and therefore is looked at together also. The external vibrator is only used differently at sieving. At conveying and sieving the working conditions are rough, large material quantities have to be processed and little room is available for the vibration drive.

Whether 1000, 1500 or 3000 vibrations/min is worked with, depends on the bulk material to be processed and the velocity of conveying to be achieved.Here applies the following rule:

High vibration speed at about 3000 vibrations/min is appropriate for fine-grained goods and low vibration frequency at about 1000 vibrations/min for coarse-grained goods.

### Mode of Operation and Choice of External Vibrators

Two counter-rotating external vibrators are attached at a certain attack angle under a conveyor through. The attack angle corresponds to the throwing angle which is important at the analysis of the conveying movement. The two external vibrators must be attached in such a way, that the working direction of the centrifugal forces goes to the centre of gravity of the conveyor through. This one resulting force (linear motion), like fig. 6 points out, moves the vibration equipment (chute or sieve) to and fro. A prerequisite for this linear motion is that both external vibrators run exactly synchronously as figure 41 shows.

Förderrinne Fig. 41: Conveying trough The chute (sieve) must be an all-side free moving system, be hung up vibration isolated, and both external vibrators have to be connected with each other vibration rigidly. The vibration isolated mounting of the chute is achieved with steel springs or rubber swing elements (soft fastening important!). If these conditions are fulfilled, the two external vibrators synchronize themselves at running independently due to laws of mass action.

### Conveying Procedure

Now the bulk material from a sieve, bunker or conveyor belt reaches the conveyor through, which under the influence of the external vibrators creates a linear vibration with a certain frequency and acceleration.

In order to make the conveying process better graspable, only one conveying good particle will be considered here. The motion of the conveying good particle is represented by fig. 42.

A conveying good particle reaching the conveyor through is subject of the acceleration a, which the chute undergoes by the centrifugal forces of the external vibrators. Since the external vibrators are attached at an attack angle of 25° to 30°, the conveying good particle is also accelerated at this angle.At the moment at which the vertical component of this acceleration (vertical acceleration av) exceeds the gravitational acceleration, the conveying good particle lifts off the chute ground (loosening point L). It flies a certain time (tw) at a trajectory of a parabola and covers a throw distance until it hits the chute surface at the next vibration period of the chute again (point A).

The produced throwing range and the size of the acceleration have essential influence on the obtainable conveying good stream. The particle of the material to be conveyed stays as long in connection with the chute till the vertical acceleration component of the chute again gets bigger than the gravitational acceleration.

Then a new throwing phase takes place. These procedures take place till the conveying good particle leaves the gutter. Because of the small throwing ranges and the high frequencies the individual shots are not perceived by the human eye. The material flow therefore appears like a continuously running stream in the conveying through. The conveying characteristics can be influenced by change of the acceleration a and the attack angle α.

To clarify these facts, two edge cases are considered. If the point of impact A of the conveying good particle is very near to the lower stationary point, the conveying speed is low. Little friction emerges between the chute bottom and conveying good particle. Since tR is great, a low velocity of conveying is achieved, instead, however, the chute and conveying goods are conserved.

If the conveying good particle hits the chute near the next Lösepunkt L', the velocity is high. The friction between the chute surface and the conveying good particle is high. Thus a high velocity of conveying is achieved; but the chute and conveying good are, however, stressed much more.

A compromise, as illus. 42 shows, is most favourable.

### Choice of External Vibrators

How to determine the right external vibrators for a chute or a sieve, a calculation example best points out.

The following data must be familiar:

Conveyor capacity L_{F} in t/h or m^{3}/h

Bulk density ρ' in t/m^{3}Chute breadth b in m

Chute length l in m

Chute inclination β in°

Dumping height h in m

For the dumping height h empirical values are used:

h = 0,1 m at a chute breadth up to 0,4 m

h = 0,15 at a chute breadth up to 0,6 m

h = 0,2 at a chute breadth up to 1,0 m

**Now can be calculated:**

Chute height H

H = h ⋅ 1,30 - 1,4 in (m)

Conveying velocity v (in m/min)

Centrifugal force F_{c} (in kN)

v = L_{F} / ( b ⋅ h ⋅ 60 ⋅ F_{w }⋅ F_{ÃŸ} ⋅ F_{h} ⋅ 0,9)

v = conveying velocity in m/min

L_{F} = conveyor capacity in m^{3}/h

b = Chute breadth in m

h = dumping height in m

F_{w} = factor for die conveying willingness of bulk good

1,0 = excellent, e.g. wet sand

0,3 = very poor, e.g. at dust-like, dry materials like cement

F_{ÃŸ} = factor for the angle of inclination

F_{h} = factor for the dumping height

The factors F_{w}, F_{ÃŸ} and F_{h} are empirically determined values. The result for the velocity of conveying has to be compared with table 8. In any case, at the prior determined vibration speed of 3000, 1500, 1000 l/min, v should lie in the green colored area since the acceleration a should not exceed the value of 60 m/s2 (destruction danger of chute or sieve).

If the calculated values are too large for a and v, the angle of inclination and dumping height can be corrected till v and with that a lie in the favourable area.

With a the centrifugal force has F_{c} (in kN) can be calculated now.

Fc = m ⋅ a / 1000

m = weight of chute + weight of vibrator (estimated) + 10-15% of the conveying good (in kg) lying in the chute

a = acceleration in m/s^{2}

Since two external vibrators because of the linear vibrations must be used, the centrifugal force per external vibrator is F_{c} /2.

Since the weight of the external vibrators is known now, too, a correction calculation with the actual m, again can be made.

a |
a |
α° |
v in m/min at |
s in mm at |
remark | ||||

n = 1000 |
n = 1500 |
n = 3000 |
n = 1000 |
n = 1500 |
n = 3000 | ||||

15 20 25 30 35 |
12,6 14,6 16,4 17,7 19 |
57 47 41 36 33 |
4,18 8,42 12,6 16,4 21 |
1,86 3,74 5,6 7,28 9,35 |
0,93 1,87 2,8 3,64 4,68 |
2,7 3,6 4,5 5,4 6,3 |
1,2 1,6 2 2,4 2,8 |
0,3 0,4 0,5 0,6 0,7 |
v small. Application, when a small performance meets the requirement or not sufficient centrifugal force is available.Conveying good is preserved, low chute tear |

40 45 50 |
20,5 21,5 22,7 |
31 28,5 27 |
26,1 29,8 34,2 |
11,6 13,24 15,2 |
5,8 6,62 7,6 |
7,2 8,1 9 |
3,2 3,6 4 |
0,8 0,9 1 |
Favorable application field |

60 80 |
25,4 30 |
24 22 |
42,6 - |
18,96 26,82 |
9,48 13,41 |
10,8 14,4 |
4,8 6,4 |
1,2 1,6 |
v big. Chute loading and a very high, high chute tear |

a = acceleration in m/s a α = attack angle in ° v = conveying velocity in m/min s = vibration breadth |

### Application Conveying

To ensure an efficient function of the chute (or the sieve), in addition, the following points have to be taken into account at the construction of a conveying chute (or a sieve).

- The front and the back hanging should be equally far away from the center of gravity, but as far as possible from each other.
- The relation between length and height of a conveying chute should be 5:1.
- Another condition for the synchronization of the two external vibrators is that they are connected with each other absolutely vibration-rigid. The conveying chute also must be extremely stiff because of the dynamic load. In order to fulfil this requirement at an acceptable weight, free-running conveying chuts are maximal 6 m long.

### Application Sieving

Vibrating screens are used to sieve out bulk materials, in order to e.g. to separate different material sizes or for draining of gravel or sand. The function of vibrating screens is similar to conveying chutes; the bottom, however, is a sieve. The sieve bottom is constructed in many forms and variations (round hole, slot, quadrangle) according to the material to be sieved. There are sieves with several, under each other arranged screen floors, dewatering screens, analysis screen, etc.

The difference to conveying technique is the attack angle of the external vibrators which again are attached in pairs and are counter rotating. The attack angle at sieving is steeper so that the conveying good particle hits the sieve as vertically as possible at the screen bottom; thus the conveying good particle goes better through the screen. Moreover, a better self-cleaning of the screen is given this way since particles being stuck are lifted easier at the next vibration. The attack angle at sieving should be 45°. The throwing range must correspond to the mesh width of the sieve screen.