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size Definition skola a small particles as a result of their skew impact in a working area of counter crossed streams


As it was already marked, in a tangential branch pipe of a centrifugal counterflow mill separate movement of particles is carried out: coaxial movement and front impact of large particles and movement in crossed trajectories of a small particles.

We will consider process of interaction of a material in a working area of movement of a small particles in crossed trajectories.

Change of speed 9частицы a material at skew blow can be described, being based on the second law of dynamics:

Where m - mass of a particle of the material, equal, kg:

zdes_ - Density of a particle of a material, kg/m3;

- The initial size of a particle of a material, m;

F - Force, n, impacts on a particle of a material at the moment of skew impact which we will express through size of arising tangent lines of pressure σ, the Pas: where S0 - a contact area of particles of a material at skew blow, м2.

Taking into account (2.79) and (2.80) formula (2.78) it is possible to give the following sort:

On the basis of the settlement scheme presented in drawing 2. 9, we find, that:

Where β - the running corner of turn, hailstones.


Drawing 2.9. The settlement scheme for the description of process of levigating of a material in a working area of counter crossed streams: Ω — a corner of turn of the rectilinear blade from a point of loading to a point of a descent of a particle, hailstones; β - the running corner of turn, hailstones; - distance from a point of loading to an axis

Rotor rotations, m; R - rotor radius, m

On the basis of (2.82) and the settlement scheme on fig. 2.9 it is possible to receive following parities:

Where hn - co-ordinate of a point of loading of a particle of a material on the rectilinear blade;

- Co-ordinate of a point of a descent of a particle of a material from the rectilinear blade.

The corner of turn of the rectilinear blade Ω from a point of loading by a material to a point of a descent of a particle from the blade is equal:

Here τι - a time interval for which the material particle passes a way r - r from a point of loading to a point of a descent from the rectilinear blade, with.

According to result of work [44]:

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Substitution (2.86) in (2.85) leads to a parity:

According to result of work [51], size of tangent lines of pressure in a working area of skew impacts of particles it is defined as follows:

Where μ - factor of pseudo-viscous levigating; μ =2618 Pases-with [51].

Substitution (2.88) in (2.81) taking into account that:

Leads to a following differential equation:

Let's consider, that as a result of skew impacts speed of a particle of a material will change from value &0 to size Uo, where and - an airspeed equal

Here, according to [69]

Where hp - height of the rectilinear blade, m,

R - Rotor radius, m.

Substitution (2.92) in (2.91) leads to following result:

Integration of the equation (2.90) in certain limits leads to the following:

Calculation of integral (2.94) allows to receive the following result:

On the basis of (2.95) it is possible to find size of a contact area of particles at skew blow S0:

On fig. 2.10 the settlement scheme of interaction of spherical particles is presented at skew blow.

Drawing 2.10. The settlement scheme of interaction of particles at skew blow:

dH - The initial size of a particle of a material, m; So - a particle contact area at skew blow, м2; r - radius of a contact area of particles, m; hmin, Hmax - minimum and a maximum size of a particle after impact, m

As the scheme on fig. 2.10 has a symmetry vertical axis, formation process skola we will consider for one particle of a material. On fig. 2.10
The settlement scheme for interrelation definition between the area and radius skola is presented.

Drawing 2.10. The settlement scheme for interrelation definition between the area

And radius skola particles.

According to the scheme, the contact area, obrazuemogo as a result of skew impact of particles is connected with radius size rсоударений a parity

The minimum size skola particles is defined from following expression:

Considering, that the deformation size hminявляется in small size in comparison smozhno on the basis of (2.98) to within sizes of the first order malosti to receive a following parity:

Where hmin - the minimum value of the size of a particle of the material formed at skew impacts, on the basis of (2.97) and (2.99) will be defined:

n

And size Hmax - a maximum size of a particle of a material as a result of skew impacts will be defined by a following parity:

On fig. 2.11 graphic dependence of size skola particles as a result of skew impact from distance L0между by rotors and their rotating speeds of the item is presented

Drawing 2.11. Dependence of size skola hminот distances Lo

Between rotors and item rotating speeds

From schedules it is visible, that the minimum dimension hmin skola particles increases under the linear law with frequency growth p rotations of rotors and from distance Lo between rotors. For example, at a rotor rotating speed p = 1oo с-1 the size hminскола is equal 0,00017 m, at increase of a rotating speed to 200 с-1 the size hmin skola particles increases to 0,00035 m. At the interaxal distance Lo equal 0,24м the size hmin skola is equal 0,00011 m, at increase in interaxal distance to 0,4м the size hmin skola increases to 0,00036м.

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A source: CHUNGUROVA TATYANA LEONIDOVNA. PERFECTION of the DESIGN And GRINDING PROCESS In the CENTRIFUGAL COUNTERFLOW MILL. The DISSERTATION on competition of a scientific degree of a Cand.Tech.Sci. Belgorod - 2017. 2017

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