阅读说明：本技术 一种在线计算三产品旋流器分配曲线的方法 (Method for calculating distribution curve of three-product cyclone on line ) 是由 杨硕 高俊梅 高鹏 杨树朝 李一鑫 张卫军 郭秀军 吕秀丽 蔡先锋 张海涛 王文 于 2019-09-26 设计创作，主要内容包括：本发明公开了一种在线计算三产品旋流器分配曲线的方法,该方法通过建立相应粒级与密度级的理论模型计算旋流器分配曲线,根据分配曲线得到旋流器一段、二段实际分选密度,以及根据分配曲线计算得到分选效率。与传统的人工采样并进行浮沉实验获得旋流器分配曲线的方法相比,本发明更加准确、快捷、方便,并能够实时监测旋流器分选效果。(The invention discloses a method for calculating a distribution curve of a three-product cyclone on line, which calculates the distribution curve of the cyclone by establishing theoretical models of corresponding size grades and density grades, obtains the actual separation density of a first section and a second section of the cyclone according to the distribution curve, and calculates the separation efficiency according to the distribution curve. Compared with the traditional method for obtaining the distribution curve of the cyclone by manually sampling and carrying out a sink-float experiment, the method is more accurate, quicker and more convenient, and can monitor the sorting effect of the cyclone in real time.)

1. A method of calculating a three product cyclone distribution curve on-line comprising the steps of:

step one, on-lineMeasuring and obtaining the feed density rho of one section of the three-product cyclone _f1Overflow density rho _o1And underflow density ρ _u1And the feeding density rho of the two sections _f2Overflow density rho _o2And underflow density ρ _u2；

Step two, calculating the density rho of the medium in the first section and the second section of the cyclone _mi

H _tiThe radius of the first section and the second section of the cyclone; r is _iThe radial distance of the coal particles from the outer wall of the cyclone;

step three, calculating the effective gravity value G of the coal particles in the heavy medium suspension liquid _dpDielectric resistance R _dpArchimedes number Ar, Reynolds number Rep, drag coefficient C _DAnd the density grade rho of the medium in the first section and the second section of the cyclone _miCalculating the free terminal velocity v of coal particles in the first and second sections of the cyclone _ti

Wherein d is _pIs the volume equivalent diameter, rho, of the coal particles _sIs the coal particle density;

step four, calculating a given size fraction d _pOf the total amount of light (heavy) products entering the coal washing particles

Wherein x and y are radial distances from the coal particles to the outer wall of the cyclone;

step five, calculating RD50 _(1/2)

The probability distribution theory of free settling of coal particles can be used for obtaining, aiming at the coal particles with large particle size, the density of the coal particles is equal to the density of a medium at the point position in an effective separation area in the cyclone, and the following results are obtained:

step six, assuming the introduction coefficient of ξ, calculating the single particle size d _pOf coal particles of

Step seven, calculating the probability (distribution rate) of the sediment falling under the condition of given particle size

Wherein H _siIs given a certain coal particle density ρ _sThe separation boundary of each medium layer in the cyclone is far from the inner wall of the cyclone, the floating or sinking probability of coal particles is 50 percent, delta _csiIs at (0, H) _si) Mass fraction of coal particles separated within the range of δ _cAverage value of (d); h _tiIs the width of the separation region, δ _ctiIs at (0, H) _ti) Mass fraction of coal particles separated within the range of δ _cAverage value of (d); in summary, the following results can be obtained: h _siδ _csiIs the mass fraction of the sediment in the cyclone, H _tiδ _ctiThe total mass fraction of coal particles in the cyclone;

step eight, judging whether PN is equal to 0.5, namely whether the probability of sediment in the total feed amount is 50%, and if not, carrying out iterative hypothesis calculation on ξ, and after ξ is obtained through calculation, calculating a distribution curve of the three-product cyclone under the full density grade of the coal particles with a certain particle size grade;

step nine, calculating the particle size distribution of the coal as the raw material to be washed

By measuring the instantaneous flow Q1 and a certain size fraction d of the raw coal entering the washing _pThe above coal particle flow rate Q2 is calculated as d _pThe above cumulative mass percentage of coal particles

And can be obtained by Gaudin-Schuhmann law, and the full-scale particle size distribution is

Where n is the number of distributions and k is the largest particle of the coal as washed, known as R, d _pAnd k, n can be calculated;

step ten, calculating the distribution coefficient of the three-product cyclone

Wherein, PN _iIs the distribution coefficient of the ith particle size in the total size fraction; m _iThe mass fraction of the ith fraction in the total fraction;

and step eleven, drawing a distribution curve of the tri-product cyclone on line according to the distribution coefficient of the tri-product cyclone.

2. The method for calculating the distribution curve of a three-product cyclone in-line as claimed in claim 1, further comprising the following steps in step three:

s1, calculating the effective gravity value of the coal particles in the heavy medium suspension liquid

Wherein d is _pIs the volume equivalent diameter of the coal particles; rho _sIs the coal particle density; rho _miIs the relative density of the dense medium in the cyclone; g is the acceleration of gravity;

s2, calculating the resistance of the coal particles in the heavy medium

Wherein, C _DIs the drag coefficient; v. of _rThe real speed of the fluid in the medium layer in the cyclone, namely the empty section speed of the fluid; v. of _pIs the velocity of the coal particles; v is the free settling velocity of the coal particles;

s3, calculating the Archimedes number Ar

The archimedes number is only related to the inherent properties of the coal particles and the heavy medium, wherein mu is the viscosity of the heavy medium inside the cyclone, and the calculation process is as follows:

V _e+V _c+V _H＝1

wherein, V _eIs the volume of ferromagnetic substance per unit volume; v _cIs the volume of the coal slurry in unit volume; v _HIs the volume of the coal slurry in unit volume;

V _eρ _e+V _cρ _c+V _Hρ _H＝ρ _f1

where ρ is _eIs the density of the ferromagnetic substance; rho _cThe density of the coal slurry is obtained; rho _HIs the density of water;

wherein G is _e＝V _eρ _eIs the content of ferromagnetic substance in the medium, and is obtained by a magnetic substance detector; g _c＝V _cρ _cIs the coal slime content in the medium, so that

s4, calculating Reynolds number

When the coal particles and the dense medium move relatively, the coal particles are subjected to shear stress resistance and shape resistance at the same time, and the magnitude of the resistance depends on the Reynolds number of the movement between the dense medium and the coal particles and the shape of the coal particles.

When the effective gravity value of the coal particles in the heavy medium is equal to the resistance force, the velocity of the coal particles reaches the terminal velocity of free sedimentation, and the following can be obtained:

from drag coefficient C _DAnd Reynolds number Rep, the obtained Reynolds number is:

(1) when Ar is less than 1.83, Rep is Ar/18, and the solution is obtained: rep is less than 0.1;

(2) when Ar is more than 1.83 and less than 3.5X 10 ⁵，Rep+0.14Rep ^1.7Ar/18, to give: rep of 0.1 < 3X 10 ³；

(3) When 3.5 is multiplied by 10 ⁵＜Ar＜3.25×10 ¹⁰，

(4) When Ar is more than 3.25X 10 ¹⁰，

S5, calculating drag coefficient

The drag coefficient is the drag coefficient of the dense medium fluid and is related to the shape of the coal particles and the Reynolds number, since the cyclone feeds raw coalAre generally treated by a crusher, which is understood here to mean approximately polygonal particles of different size fractions but similar shape, in which case the drag coefficient C _DIs a function of Reynolds number Rep; from C _DRep relation curves, where the coal particles are smooth curves similar to spherical particles, only the difference in coordinate positions of the curves.

The drag coefficient C can be obtained according to different Reynolds numbers _DComprises the following steps:

s6, calculating the free end velocity of the coal particles

Effective gravity value G of coal particles in heavy medium _dpEqual to the resistance R experienced _dpWhen the velocity of the coal particles reaches the free end velocity v _tiBy solving for rho _miAnd C _DIn the case of knowing the particle size and density fractions of the raw coal to be washed, the following are obtained:

wherein the content of the first and second substances,

3. the method for calculating a distribution curve of a three product cyclone in-line according to claim 1, wherein from the distribution curve:

actual separation density of first stage of cyclone

4. The method of claim 1, wherein the separation efficiency is calculated from the distribution curve as:

The technical field is as follows:

the invention belongs to the technical field of gravity coal separation, and particularly relates to a method for calculating a distribution curve of a three-product cyclone on line.

Background art:

the mineral is a mineral particle group composed of different particle diameters and densities, the movement forms of the mineral particles are different due to different gravity, hydrodynamic force and mechanical force applied to the particles in a flowing medium, and the gravity coal separation is a process for realizing the separation of the mineral particle group according to the different movement forms of the particles. The coal dressing with heavy medium cyclone is the most efficient method in gravity coal dressing, and has obvious effect on the dressing and desulfurization of raw coal, fine coal and high-sulfur coal which are difficult to be dressed. The three-product cyclone is formed by assembling two-product cyclones in series, and has no difference in sorting principle. The first section is main washing and sorting with low density suspension, the second section is rewashing, and the result of the concentration of the suspension in the first section is taken as high density suspension in the second section. Under the action of external pressure, the medium in the cyclone generates a centrifugal field and a density field, so that the process for separating clean coal, middlings and gangue is realized.

The distribution curve is an effective method for evaluating the sorting effect of mineral aggregates in the cyclone according to density or particle size, the actual yield, ash content, density and particle composition of the coal product can be calculated through the distribution curve, and the method is the theoretical basis of coal sorting production and design. Density delta at 50% distribution in the distribution curve given clean coal ash ₅₀The method is a theoretical basis for checking the reasonability of the density setting of the suspension in the dense medium coal separation automatic control system for the actual separation density of the washed raw coal, and the clean coal, the middlings and the gangue are accurately separated by controlling the density of the suspension. The calculation method of distribution curve of conventional three-product cyclone includes respectively processing raw coal, clean coal, middlings andand sampling the gangue, performing a floating-sinking experiment to obtain corresponding density composition and yield of each density level occupying the level, and calculating the distribution rate by taking the yield as basic data. Because the raw coal sorting process can take place to dissociate and the argillization phenomenon, and artifical sampling can have error and time lag, and high manual work, time and economic cost can not realize the meaning of real-time supervision swirler sorting effect.

The invention content is as follows:

in order to solve the above disadvantages, the present invention provides a method for calculating a distribution curve of a three-product cyclone on-line by establishing theoretical models of the corresponding size fraction and density fraction.

The invention is realized by the following technical scheme:

a method of calculating a three product cyclone distribution curve on-line comprising the steps of:

step one, obtaining the feeding density rho of one section of a three-product cyclone by online measurement _f1Overflow density rho _o1And underflow density ρ _u1And the feeding density rho of the two sections _f2Overflow density rho _o2And underflow density ρ _u2；

Step two, calculating the density rho of the medium in the first section and the second section of the cyclone _mi

H _tiThe radius of the first section and the second section of the cyclone; r is _iThe radial distance of the coal particles from the outer wall of the cyclone;

step three, calculating the effective gravity value G of the coal particles in the heavy medium suspension liquid _dpDielectric resistance R _dpArchimedes number Ar, Reynolds number Rep, drag coefficient C _DAnd the density grade rho of the medium in the first section and the second section of the cyclone _miCalculating the free terminal velocity v of coal particles in the first and second sections of the cyclone _ti

Wherein d is _pIs the volume equivalent diameter, rho, of the coal particles _sIs the coal particle density;

step four, calculating a given size fraction d _pOf the total amount of light (heavy) products entering the coal washing particles

Wherein x and y are radial distances from the coal particles to the outer wall of the cyclone;

step five, calculating RD50 _(1/2)

The probability distribution theory of free settling of coal particles can be used for obtaining, aiming at the coal particles with large particle size, the density of the coal particles is equal to the density of a medium at the point position in an effective separation area in the cyclone, and the following results are obtained:

step six, assuming the introduction coefficient of ξ, calculating the single particle size d _pOf coal particles of

Step seven, calculating the probability (distribution rate) of the sediment falling under the condition of given particle size

Wherein H _siIs given a certain coal particle density ρ _sThe separation boundary of each medium layer in the cyclone is far from the inner wall of the cyclone, the floating or sinking probability of coal particles is 50 percent, delta _csiIs at (0, H) _si) Mass fraction of coal particles separated within the range of δ _cAverage value of (d); h _tiIs the width of the separation region, δ _ctiIs at (0, H) _ti) Mass of coal particles separated in rangeFraction delta _cAverage value of (d); in summary, the following results can be obtained: h _siδ _csiIs the mass fraction of the sediment in the cyclone, H _tiδ _ctiThe total mass fraction of coal particles in the cyclone;

step eight, judging whether PN is equal to 0.5, namely whether the probability of sediment in the total feed amount is 50%, and if not, carrying out iterative hypothesis calculation on ξ, and after ξ is obtained through calculation, calculating a distribution curve of the three-product cyclone under the full density grade of the coal particles with a certain particle size grade;

step nine, calculating the particle size distribution of the coal as the raw material to be washed

By measuring the instantaneous flow Q1 and a certain size fraction d of the raw coal entering the washing _pThe above coal particle flow rate Q2 is calculated as d _pThe above cumulative mass percentage of coal particles

And can be obtained by Gaudin-Schuhmann law, and the full-scale particle size distribution is

Where n is the number of distributions and k is the largest particle of the coal as washed, known as R, d _pAnd k, n can be calculated;

step ten, calculating the distribution coefficient of the three-product cyclone

Wherein, PN _iIs the distribution coefficient of the ith particle size in the total size fraction; m _iThe mass fraction of the ith fraction in the total fraction;

and step eleven, drawing a distribution curve of the tri-product cyclone on line according to the distribution coefficient of the tri-product cyclone.

Further, the third step includes the following steps:

s1, calculating the effective gravity value of the coal particles in the heavy medium suspension liquid

Wherein d is _pIs the volume equivalent diameter of the coal particles; rho _sIs the coal particle density; rho _miIs the relative density of the dense medium in the cyclone; g is the acceleration of gravity;

s2, calculating the resistance of the coal particles in the heavy medium

Wherein, C _DIs the drag coefficient; v. of _rThe real speed of the fluid in the medium layer in the cyclone, namely the empty section speed of the fluid; v. of _pIs the velocity of the coal particles; v is the free settling velocity of the coal particles;

s3, calculating the Archimedes number Ar

The archimedes number is only related to the inherent properties of the coal particles and the heavy medium, wherein mu is the viscosity of the heavy medium inside the cyclone, and the calculation process is as follows:

V _e+V _c+V _H＝1

wherein, V _eIs the volume of ferromagnetic substance per unit volume; v _cIs the volume of the coal slurry in unit volume; v _HIs the volume of the coal slurry in unit volume;

V _eρ _e+V _cρ _c+V _Hρ _H＝ρ _f1

where ρ is _eIs the density of the ferromagnetic substance; rho _cThe density of the coal slurry is obtained; rho _HIs the density of water;

wherein G is _e＝V _eρ _eIs the content of ferromagnetic substance in the medium, and is obtained by a magnetic substance detector; g _c＝V _cρ _cIs the coal slime content in the medium, so that

Obtaining:

s4, calculating Reynolds number

When the coal particles and the dense medium move relatively, the coal particles are subjected to shear stress resistance and shape resistance at the same time, and the magnitude of the resistance depends on the Reynolds number of the movement between the dense medium and the coal particles and the shape of the coal particles.

When the effective gravity value of the coal particles in the heavy medium is equal to the resistance force, the velocity of the coal particles reaches the terminal velocity of free sedimentation, and the following can be obtained:

from drag coefficient C _DAnd Reynolds number Rep, the obtained Reynolds number is:

(1) when Ar is less than 1.83, Rep is Ar/18, and the solution is obtained: rep is less than 0.1;

(2) when Ar is more than 1.83 and less than 3.5X 10 ⁵，Rep+0.14Rep ^1.7Ar/18, to give: rep of 0.1 < 3X 10 ³；

(3) When 3.5 is multiplied by 10 ⁵＜Ar＜3.25×10 ¹⁰，

Obtaining by solution: 10 ³＜Rep＜3×10 ³；

(4) When Ar is more than 3.25X 10 ¹⁰，

Obtaining by solution: rep > 10 ⁶。

S5, calculating drag coefficient

The drag coefficient is the drag coefficient of the dense medium fluid, and is related to the shape and Reynolds number of the coal particles, since the raw coal fed to the cyclone is generally processed by the crusher, which is approximately understood to mean polygonal particles with different size fractions but similar shapes, and in this case, the drag coefficient C _DIs a function of Reynolds number Rep; from C _DRep relation curves, where the coal particles are smooth curves similar to spherical particles, only the difference in coordinate positions of the curves.

The drag coefficient C can be obtained according to different Reynolds numbers _DComprises the following steps:

s6, calculating the free end velocity of the coal particles

Effective gravity value G of coal particles in heavy medium _dpEqual to the resistance R experienced _dpWhen the velocity of the coal particles reaches the free end velocity v _tBy solving for rho _miAnd C _DIn the case of knowing the particle size and density fractions of the raw coal to be washed, the following are obtained:

wherein the content of the first and second substances,

further, according to the distribution curve, the following results are obtained:

rotational flowActual sorting density of first stage And actual separation density of two stages of the cyclone

The optimal separation of clean coal, middlings and gangue is completed by adjusting the entering density.

Further, the separation efficiency is calculated according to the distribution curve:

the invention has the advantages and beneficial effects that:

the method can calculate the distribution curve of the three-product cyclone on line, avoids the complexity of traditional manual sampling and floating and sinking experiment, is more accurate, quicker and more convenient, and can monitor the sorting effect of the cyclone in real time.

Description of the drawings:

FIG. 1 is a flow chart of the present invention for on-line calculation of a three product cyclone distribution curve.

FIG. 2 is a schematic diagram of the separation boundary of the present invention.

Fig. 3.1 is a graph showing the comparison effect between the distribution curve of a cyclone section calculated on line by using the method of the present invention and the distribution curve obtained by a float-sink experiment.

Fig. 3.2 is a graph showing the comparative effect of the distribution curve of the second cyclone section calculated on line by using the method of the present invention and the distribution curve obtained by a sink-float experiment.

For a person skilled in the art, other relevant figures can be obtained from the above figures without inventive effort.

The specific implementation mode is as follows:

in order to make the technical solution of the present invention better understood, the technical solution of the present invention is further described below with reference to specific examples.

As shown in fig. 1, a method for calculating a distribution curve of a three-product cyclone on-line comprises the following steps:

s1, respectively collecting the material feeding density rho of one section of the three-product cyclone _f1Overflow density rho _o1And underflow density ρ _u1And the feeding density rho of the two sections _f2Overflow density rho _o2And underflow density ρ _u2Wherein the concentration result of the suspension in the first section of the three-product cyclone is used as the high-density suspension in the second section to obtain rho _u1＝ρ _f2The invention realizes rho pair by a drainage method of medium at the middle section of the cyclone _u1The measurement of (2).

S2, calculating the relative density level of the heavy medium in the cyclone

Here, we assume that the structural parameters of the first and second stages of the three-product cyclone are fixed, and under the condition that the process parameters such as the density and pressure of the dense medium suspension feed of the cyclone are stable, a uniform centrifugal force field and a medium turbulent flow field are formed in the cyclone.

Where ρ is _fiThe density of the heavy medium feeding materials of the first section and the second section of the cyclone (i is equal to 1 or 2), kg/m ³；ρ _oiThe overflow density of heavy medium in kg/m in the first and second sections of the cyclone ³；ρ _uiIs the dense medium underflow density of the first section and the second section of the cyclone in kg/m ³；r _iThe radial distance, m, of the coal particles from the outer wall of the cyclone; h _tiIs the radius of the first and second sections of the cyclone, m.

S3, calculating the effective gravity value of the coal particles in the heavy medium suspension liquid

Wherein d is _pIs the volume equivalent diameter, m, of the coal particles; rho _sIs coal particle density, kg/m ³；ρ _miOf heavy medium in cyclonesRelative density, kg/m ³(ii) a g is the acceleration of gravity, m/s ²。

S4, calculating the resistance of the coal particles in the heavy medium

Wherein, C _DIs the drag coefficient; v. of _rThe real speed of the fluid in the medium layer in the cyclone, namely the empty section speed of the fluid, m/s; v. of _pThe velocity of the coal particles, m/s; v is the free settling velocity of the coal particles, m/s.

S5, calculating the Archimedes number Ar

From equation 4, the archimedes number is only related to the intrinsic properties of the coal particles and the dense medium, where μ is the viscosity of the dense medium inside the cyclone, and the calculation process is as follows:

V _e+V _c+V _H＝1 (5)

wherein, V _eIs the volume of ferromagnetic substance per unit volume; v _cIs the volume of the coal slurry in unit volume; v _HIs the volume of the coal slurry in unit volume.

V _eρ _e+V _cρ _c+V _Hρ _H＝ρ _f1(6)

Where ρ is _eIs the density of the ferromagnetic substance; rho _cThe density of the coal slurry is obtained; rho _HIs the density of water. Rho _H＝1kg/m ³According to the sampling assay values at different sites, p _e≈4.5kg/m ³，ρ _c＝1.5kg/m ³。

Wherein G is _e＝V _eρ _eIs the ferromagnetic content of the medium, consisting ofObtaining a magnetic substance detector; g _c＝V _cρ _cIs the coal slime content in the medium, so that

Obtaining:

s6, calculating Reynolds number

When the coal particles and the dense medium move relatively, the coal particles are subjected to shear stress resistance and shape resistance at the same time, and the magnitude of the resistance depends on the Reynolds number of the movement between the dense medium and the coal particles and the shape of the coal particles.

When the effective gravity value of the coal particles in the heavy medium is equal to the resistance force, the velocity of the coal particles reaches the terminal velocity of free sedimentation, and then the velocity is obtained by the following formulas 1, 2, 4 and 10:

from drag coefficient C _DAnd Reynolds number Rep, in combination with equation 12, the Reynolds number can be found as:

(1) when Ar is less than 1.83, Rep is Ar/18, and the solution is obtained: rep is less than 0.1;

(2) when Ar is more than 1.83 and less than 3.5X 10 ⁵，Rep+0.14Rep ^1.7Ar/18, to give: rep of 0.1 < 3X 10 ³；

(3) When 3.5 is multiplied by 10 ⁵＜Ar＜3.25×10 ¹⁰， Obtaining by solution: 10 ³＜Rep＜3×10 ³；

(4) When Ar is more than 3.25X 10 ¹⁰，

Obtaining by solution: rep > 10 ⁶。

S7, calculating drag coefficient

The drag coefficient is the drag coefficient of the dense medium fluid, and is related to the shape and Reynolds number of the coal particles, since the raw coal fed to the cyclone is generally processed by the crusher, which is approximately understood to mean polygonal particles with different size fractions but similar shapes, and in this case, the drag coefficient C _DIs a function of Reynolds number Rep; from C _DRep relation curves, where the coal particles are smooth curves similar to spherical particles, only the difference in coordinate positions of the curves.

The drag coefficient C can be obtained according to different Reynolds numbers _DComprises the following steps:

s8, calculating the free end velocity of the coal particles

Effective gravity value G of coal particles in heavy medium _dpEqual to the resistance R experienced _dpWhen the velocity of the coal particles reaches the free end velocity v _tiBy solving for rho _miAnd C _DIn the case of knowing the particle size and density fractions of the raw coal to be washed, the following are obtained:

wherein the content of the first and second substances,

s9, calculating a given size fraction d _pTotal amount of light (heavy) products in coal washing particles

The geometric meaning of the curved surface integral can be obtained, and a certain rho is obtained in a given cyclone one-section structure and two-section structure _miHeavy product particles in the coal particlesTerminal velocity v of free settling of son _tThe instantaneous flow rate through the curved surface of the outer wall of the cyclone, i.e. the total amount of coal particles per unit time (V) can be calculated _tSt, t 1), yielding:

wherein x and y are the radial distance of coal particles from the outer wall of the cyclone, and x belongs to (0, H) _ti)，y∈(0,H _ti)。

S10, calculating the single particle size d _pThe mass fraction of the coal particles is as follows:

wherein ξ is an introduction coefficient.

S11, calculating the probability (distribution ratio) of the sediment falling under the condition of given particle size

Wherein H _siIs given a certain coal particle density ρ _sThe distance between the separation boundary of each medium layer in the cyclone and the inner wall of the cyclone (the floating or sinking probability of coal particles is 50 percent at the moment), delta _csiIs at (0, H) _si) Mass fraction of coal particles separated within the range of δ _cAverage value of (d); h _tiIs the width of the separation region, δ _ctiIs at (0, H) _ti) Mass fraction of coal particles separated within the range of δ _cAverage value of (a). In summary, the following results can be obtained: h _siδ _csiIs the mass fraction of the sediment in the cyclone, H _tiδ _ctiThe total mass fraction of coal particles in the cyclone.

From experimental data, it can be derived for a given particle size d _pComprises the following steps:

s12, calculating RD50

The probability distribution theory of free settling of coal particles can be used for obtaining, aiming at the coal particles with large particle size, the density of the coal particles is equal to the density of a medium at the point position in an effective separation area in the cyclone, and the following results are obtained:

RD50＝ρ _f+0.26(ρ _u-ρ _o) (18)

s13, calculating an introduction coefficient ξ

1. By measuring rho _f1(cyclone feed), ρ _o1(clean coal port), ρ _u1＝ρ _f2(intermediate cyclone Density), p _o2(middle coal gap), ρ _u2(gangue gap) equal density values, and respectively calculating RD50 ₍₁₎And RD50 ₍₂₎；

2. From equation (15), let us assume that the coefficient ξ is introduced to define ρ _p1＝RD50 ₍₁₎，ρ _p2＝RD50 ₍₂₎Substituting the result into a formula (16), calculating whether PN is equal to 0.5, namely whether the probability of deposition in the total feeding amount is 50%, and if not equal to 0.5, performing iterative hypothesis calculation aiming at ξ;

3. after ξ is calculated, the distribution curve of the 3-product cyclone at full density grade for a certain particle size grade of coal particles is calculated by the formulas (15) to (16).

S14, calculating the particle size distribution of the coal as the raw material to be washed

1. Measuring the instantaneous flow Q1 of the washed raw coal by a washing belt weigher;

2. obtaining a certain size fraction d by means of a classifying screen _pThe above coal particle flow rate Q2;

r is d _pThe above cumulative mass percentage of coal particles.

3. The full scale particle size distribution, as derived from Gaudin-Schuhmann's law, is

Where n is the number of distributions and k is the largest particle of the coal as washed, known as R, d _pAnd k, n can be calculated.

S15, calculating the distribution coefficient of the three-product cyclone

Wherein, PN _iIs the distribution coefficient of the ith particle size in the total size fraction; m _iThe mass fraction of the ith fraction in the total fraction is shown.

And S16, drawing a distribution curve of the three-product cyclone by the formula (21), and obtaining the distribution curve:

1. actual separation density of cyclone 1 and 2 sections

And

the optimal separation of clean coal, middlings and gangue is completed by adjusting the entering density;

2. calculating the sorting efficiency:

FIG. 3.1 is a graph showing the comparative effect of the distribution curve of a cyclone section calculated on line by the method of the present invention and the distribution curve obtained by a sink-float experiment; fig. 3.2 is a graph showing the comparative effect of the distribution curve of the second cyclone section calculated on line by using the method of the present invention and the distribution curve obtained by a sink-float experiment. As can be seen from fig. 3.1 and 3.2, the method of the invention for calculating the distribution curve of a cyclone section on-line is accurate and effective.