STUDY OF THE PROCESS OF PREPARING FEEDING MIXTURES USING THE COMPOSITE MIXER

Current constructions of feed mixers for cattle do not meet all the zootechnic requirements to the preparation of multi-component balanced complete feeding mixtures because they are characterized by high energy losses as well as speci c consumption of materials. Therefore, the studies, aimed at elaborating the working bodies for feed mixers which will ensure the creation of highly ef cient feeding foundation with low expenses of energy and materials, are of economic value [4–6]. The aim of the studies is enhancing the quality and improving the technological process of mixing feeds using the new construction of the mixer and substantiating its rational parameters.


INTRODUCTION
Enhancing the ef¿ ciency of animal breeding as an industry depends considerably on the quality of preparing mixtures, as their share takes 30-60 % of expenses in the structure of production costs [1][2][3]. Progressive technologies, providing for complete implementation of genetic potential of animals, have not been widely applied in Ukraine due to the absence of required technical provisions.
Current constructions of feed mixers for cattle do not meet all the zootechnic requirements to the preparation of multi-component balanced complete feeding mixtures because they are characterized by high energy losses as well as speci¿ c consumption of materials. Therefore, the studies, aimed at elaborating the working bodies for feed mixers which will ensure the creation of highly ef¿ cient feeding foundation with low expenses of energy and materials, are of economic value [4][5][6].
The aim of the studies is enhancing the quality and improving the technological process of mixing feeds using the new construction of the mixer and substantiating its rational parameters.

MATERIALS AND METHODS
The methods of mathematical modeling theories and fundamentals of machinery use in feeds mixing were applied in theoretical studies.

RESULTS AND DISCUSSION
The estimated model of the functioning of a constructive-technological scheme of a composite mixer and the mathematical model of the dynamic interaction of mixer paddles and the solid mass of feeds were elaborated. It was established that the technological ef¿ ciency of preparing the homogeneous mixture depends on physical and mechanic properties of its components, the impact and interaction between the form and geometric parameters of the attacking surface of the paddles, the slope angle, the setting increment and working modes of the mixer [7][8][9].
An improved mixer with a combined scheme of the À ow of raw materials using multi-section helical, line and À at paddles is suggested for elimination of current drawbacks of traditional mixers (Fig. 1).
To expand the mass, to intensify the process and to enhance the dynamics of mixing the components in the microvolumes, the helical and À at paddles were additionally equipped with radial paddles.
The process of mixing feeds using the improved mixer is done as follows. The corresponding doses of the components of the feeding mixture are loaded in layers into the tank using the composite transporter with gradual leveling of the raw material using the long line helical paddles with ¿ ngers and then are supplied into the multi-section mixer with À at paddles (Fig. 2). The paddles of the upper range with the right slope angle separate the mixture portion along the width of the paddle and transport it in radial, circular, and axial directions towards the right end of the mixer, and the second range, with the left slope angle -towards the left end of the mixer, creating a large microvolume mass of the mixture with the discrete content of the shares of the mixture components along with the radial ¿ ngers. Here the shares of each mixture component enter the area of interaction of complicated movements, crossings, and collisions, and are periodically transported from one À ow to the other which ensures the intense mass exchange and accelerates the process of feed mixing.
The translocation of a feed mixture along the surface of paddles with different slope angle in the zone  of inertial (free) motion is made in the mode of increased dynamics of the process and the increased number of collisions and crossings in the radial and axial directions which is determined by the form and sizes of the attaching paddle, their setting increment, the slope angle and kinematic modes of the work of paddles (Fig. 3).
The determination of kinematics of the motion of a mixture share was conducted with the consideration of the friction forces and the slope angle for paddles [10][11][12]. In case of friction, depending on the slope angle of the paddle towards the shaft axis a the translocation of the material point of the mixture component in the axial direction will occur while the paddle moves by the value of ( where Į -the slope angle of the paddle; ĳ -the angle of the particle friction along the paddle surface; S -projection of the paddle width.
The axial velocity of the translocation of the mixture share is de¿ ned using the equation: where ȝ -coef¿ cient of the axial lagging behind of the shares depending on the angles Į and ĳ.
The analysis of equations (1), (2) and (4) demonstrates that the translocation of mixture shares in the axial direction and the axial velocity of their translocation depend on the slope angle of the paddles towards the shaft axis of the mixer Į, the friction angle for the mixture along the paddle surface and the coef-¿ cient of axial lagging behind of the material shares of the mixture ȝ (Fig. 5, 6). With the increase in the angle Į on condition of constant coef¿ cient of friction f the axial lagging behind of the translocation of mixture shares decreases, and with the constant slope angle of the paddle Į on condition of increasing the coef¿ cient of friction f, there is also an increase in  For À at paddles with the slope angle Į = 40 ... 50º there occur dead spots at the coef¿ cient of friction f 0.6 ... 0.7, which does not correspond to the technological requirements to mixing the feeds, and discrete particles have only rotational movements.
In the process of the movement of the mixer, when the mixture is separated by paddles, the shares receive the impulse from radial and normal effort P‫މ‬p = P H ÂcosĮ and P‫މ‬p = P H ÂsinĮ (Į -the slope angle for the paddle towards the rotation axis of the shaft).
In addition, the normal component of the force R in the plane of the movement of shares along the paddle leads to the friction force F = f Â P H , which is directed against the relative movement of shares along the paddle. The friction force F is divided into the circular and axial components: Taking the received vectors into consideration by the movement directions, we receive the circular and axial efforts: In case of incomplete ¿ lling of the mixer tank the normal component P H is de¿ ned using the formula: where h aver. -average depth of the largest depression on the paddle, m; F l. -projection of the paddle area on the direction of the rotation of the mixer, m 2 ; ĳ -internal friction angle, degrees; Ȗ -bulk weight of the mixture, kg/cc.
The required power of the drive of the mixer paddles is de¿ ned using the equation, kilowatt: where Z p -the number of paddles, which are simultaneously submerged into the feeding mixture.
Therefore, the total power of the mixer drive is de-¿ ned as follows: N m = N hp + N fp + N hfr + N fst + N f + N hor.p + where N hp , N fp , N hst , N fst , N f , N hor.p , N f , N Ș m -power losses on the drive regarding the helical and À at paddles, frames of helical and À at paddles, radial ¿ ngers, horizontal pipes, friction of the mixer from the body and bearings of the shaft, kilowatt.
The power on the drive of helical and À at paddles: where P p , P o -circular and axial effort, ɇ; ‫ׇ‬ p , ‫ׇ‬ o -circular and axial velocity of the mixture movement, m/s; Z p -number of simultaneously submerged paddles.
The power on the drive of frames of helical and À at paddles  where l -frame length, m; -ratio of the frame length to the resistance force, m; h aver . -average depth of submerging the frame into the feed mass, m; Į -frame width, m; ĳ -angle of feed slope, degrees.
The power on the drive of radial ¿ ngers, kilowatt: where M n -rotational moment from the force of resistance of the ¿ nger, H · m.
where P fthe relative resistance of the mixture, H/m 2 ; R f -average radius of rotation for the ¿ ngers, m.
The power on the drive of horizontal pipes, kilowatt: where M p -rotational moment from the resistance force of the horizontal pipe, H/m.