G. Mitev, Kr. Bratoev, J. Demirev, V. Dobrinov, T. Todorov

MACHINE INJECTION OF WATER HOLDING MATERIALS UNDER THE PLOUGH LAYER – THEORETICAL MOTIVATION OF THE PIPELINE PARAMETERS

G. Mitev, Kr. Bratoev, J. Demirev, V. Dobrinov, T. Todorov

“Angel Kanchev” University of Ruse

1. Abstract :The modern agriculture soil tillage tendency is to combine several operations within one process and reduction the machinery traffic throughout the soil surface to its minimum.

From the other hand there is a trend to minimize the soil tillage operations. The aim of the applied techniques is to reduce the soil compaction, improve soil physical properties, protection from the soil erosion and increasing the yield [4].

An innovation method for minimizing soil tillage is offered. Simultaneously with the deep subsoiling the machine inject natural water holding materials (WHM) at one time in three interconnected layers.

The method application is made by machine which in its construction is combination between subloiler and fertilizer. Similar constructions are known [5], but the material movement from the dose apparatus to the injection tool needs more investigation.

Important feature of the WHM injection is creation of three separated and interconnected layers.

The necessity quantity of the lay substances and their starting state (powder or granular) are asked in the technology aimed to improve the soil properties.

According to their baseline, WHM are attributable to the group of flowing materials with all their physical properties.

The process of laying those materials include filling of the dose device and after that the specified quantity of materials by free fall in line and camera enters the shaped by pruning - laying a paw feed.

Like the seed pipes in the drills and in this machine significant impact on the transportation of specified quantity of material to the channel formations have structural parameters of the pipeline, as well as the interaction of the material with each other and with the walls of the pipeline [2,3].

Using the similarity of pipelines with seed pipes, as the most of his major parameters affecting on the WHM transport through it may be acceped the diameter and shape.

2.  Materials and method

In the theoretical motivation of the diameter and shape of the pipeline's attention is paid to the possibility of optimizing the time to move the WHM through it subject to specified limits, and ​​the following assumptions they have made:

a)  The shape of the particles in BAM is assumed to be spherical with a size equal to their unit (average diameter);

b)  The pipeline has a circular cross-section and the distance between the input and output remains constant.

c)  The metering device made ​​constant and steady stream of WHM in the pipeline at the maximum rate.

d)  The movement of particles in the pipe is frictionless.

The task of determining the shape of the pipe is reduced to mathematical representation of the path of the WHM at which the time they move from the input to the output of the pipeline is the smaller.

Make - up spermatic analogy between the drill pipe and the presented machine allows the use of known mathematical relationships [3].

From these relationships, it is clear that the line of the most rapid descent of the WHM flow from the input to the output of the pipeline is the arc of the cycloid (Figure 1).

Figure 1. Path of the most rapid descent

Therefore, in order to be able particle p. M (Fig. 1) to move without friction from the entrance (p. A) to output (p. B) of the pipeline needs its form (represented by the dotted line) corresponds to the trajectory of the particle. The differential equation of moving under its own weight particle trajectory is presented in the form [3].

, (1)

where is the ordinate of p.;

- the ordinates of any point on the curve (p., Figure 1);

- the first derivative of the ordinate in p. ();

- the gravity.

From equation (1) is displayed expression in which, the time required to move the particle from point to point, ie represented by the integral is determined - the shortest time that the particle will move through the pipeline.

(2)

To find this arc of the cycloid, in which the flow of WAM will be lowered for most - a short time is needed to determine the formation cycloid radius circle.

The beginning and the end of the arc is specified by the coordinates of the points and (Fig. 1), which in the general case of structural considerations (available device dosage and body working against the machine frame) imposed restrictions.

These restrictions may be waived when designing a new machine in that, given a shape and position of the pipe shall be placed on the design elements that are associated with it.

The presence or absence of a restriction indicated that in defining the pipe shape may be solved the pulverized or reverse task. In this case, the justification of the pipeline form is connected with solving the inverse problem, where there are restrictions.

The limits may be represented by the coordinates of the inlet and outlet of the conduit relative to the frame of the machine, which is represented by the coordinate system in Figure 1. The total recording coordinates input will be, and the outcome -. Consequently, the arc of the cycloid for each pipe, should be so located in the space, that the beginning and the end to pass through the coordinates of the input and output of the respective conduit.

This condition is checked by introducing a correlation between the parametric equations of the cycloid separately for early (p.) and the end (p.) of the rainbow:

(3)

where is the radius of the circle forming the cycloid;
and - the angles of rotation of the circle forming the passage of
cycloid in p. A and p. B.

The argument from the trigonometric functions given by the equations (3) is amended in the range -. Therefore, asking different values of ​​need to find this important meaning that satisfies the specific ratio of coordinates. With the established value of the argument and one of the two parametric equations of the cycloid the radius is determined that there should have to be forming a circle:

(4)

Justification by the described above lines form should provide the - fastest, respectively evenly move the WAM before entering the working bodies of the machine.

Another important step in justifying the parameters of lines is the determination of their diameter. The diameter of the pipes must be grounded so that they can be met:

a) maximum amount at the rate of a given species of the WHM could pass in the pipeline the

b) Do not impede the particles movement along their trajectory at - fast descent through the pipeline

Therefore, the diameter of the pipe must be justified separately for each of the conditions. Important is that of them (usually – the large), where conditions remain satisfied. By imposing these conditions are set the boundaries within which the diameter should remain as the first of them to justify the lower limit and the second - the top.

To determine the diameter of the pipeline in accordance of the first condition using the known formula for a mass flow rate

, (5)

where is the maximum quantity of kind of material passing for unit time throughout the pipeline;

- the cross section of the pipeline;

- the velocity of the material movement through the pipeline;

- the bulk density of the material.

The speed of movement of the material with the specified pipeline shape and the manner of movement of the particles therein is determine by using the equation:

, (6)

where the parameters have the same meaning as in the expression (1).

After detailed development of the expression (5) and to carry out certain modifications to give the expression, that is justified minimum value of the diameter.

(7)

It is necessary in justifying of the to paid attention to the following two features: as the value of to bet that most of the material - a great rate, to examine gender ordinate of the starting point and the radius of the circle forming

The first feature allows to unify lines in the machine, ie all be of the same diameter, irrespective of the material being transported.

The second peculiarity rice from the property of the inverted cycloid called tautohronnost, which states that the body placed in various points of the cycloid, reaches the horizon at the same time.

Relative to the operation of the pipeline, this property indicates that the justification of the diameter according to expression (7) must be performed on the output of the pipeline and not to the input. Otherwise, to the input quantity of the material can cause clogging of the pipeline.

In justification of the maximum diameter of the pipeline on the one hand seeks to fulfill the condition for the smooth flow of the particles, and on the other by him can be justified grain size of the material.

Assuming that the flow of WHM in the pipeline has a round cross-section in each of which there are an equal number of particles and in order to avoid contact between the stream and the walls is necessary the radius of the pipeline () be bigger - than the minimum radius () the flow, i.e. . This condition will always be satisfied if the circle radius is presented as recorded, and the circle with radius, as described around right n - gon (, Figure 2) with the side . Output equation from which to derive expression is as follows:

, (8)

where is the area of the central right dodecagon

- the area of the rings ;

- the area of the most outline irregular dodecagon.

The area is divided by a polygon, and, and and from and

The areas of the polygons, and are selected so that they can fit a circle with a diameter equal to the modulus of the particles (- Figure 2).

The shape of such polygons is respectively triangular, square and diamond. In the center of n - gon forming a regular hexagon with sides and area represented by the expression:

(9)

Around the hexagon formed ring (s) of alternating squares and triangles, the area of ​​the implement while n - gon.

Between the number of sides of the hexagon and central dodecagon exist an increasing exponentially geometric progression with the private and the first article that applies only to the first ring, ie the second article in a row ():

(10)

The equation for determining the area of is presented as follows:

, (11)

where is the number of triangles in the central dodecagon

- number of squares in the central dodecagon

The number of squares in the ring is determined by the sum of the first member of the geometric progression [1], from which first member is disconnected:

(12)

When at the expression (12) is added the number of triangles in the central hexagon then the number of equilateral triangles in the correct dodecagon is obtained:

(13)

After the ring the figures, which are formed by the rings being incorrect dodecagon whose circumference increases. Especially in these rings is that the number of squares is the same in all of them, but only changes the number of triangles. The area of the rings can be represented as follows:

, (14)

where is the number of the triangles in the rings ;

- the number of squares into the rings .

The change of the number of triangles in rings is changed in geometric progression [1]. Respectively their number in the rings is determined by the sume of the first n-regression members where the first member is extracted from:

, (15)

Where is the difference in the progression, which in the case of Figure 2 is equal to 12;

- the number of rings..

The number of squares in the rings is determined by the sum of the first n - members of a geometric progression with quotient equal to one:

(16)

Fig. 2. Scheme to justify the incremental pipeline diameter

After substituting expressions (11) and (14) in expression (8) can be written:

(17)

When the interior polygons (,and) have equal sides, then their areas area is valid the true inequality:

(18)

The size of the sides of the inner polygon is derived from the expression for the radius of the inscribed equilateral triangle in a circle, in which case the diameter is:

(19)

Assuming that each of the inner polygon is covered only by a particle having diameter, then from (18) it follows that the particles at the intersection are not contact with each other. Another effect that is derived from this is that the number of inner polygons is to be equal to the number of particles in the cross section of flow, i.e.

(20)

Representing the intersection from expression (5) by MIDOLOVO section () of a particle, then for the particle number can be written equality:

(21)

When is known and after some substitution and transformation of expression (20) appears formula for determining the number of rings: