Mineral particle size measurement (3)

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Example galena in the lead zinc ore, as measured by using a particle diameter of the cross-sectional diameter d (A) i and (N A) i as shown in Table 2, the test meter -
Calculate the (N V ) j and d (V) of the galena.

- 1
d(V) = —— Σ(NV)j·(dv)j = 204.68mm/2267.21 = 0.0903mm
Nv

Table 2     Galena diameter method measurement results

Serial number

Section perimeter diameter interval d (A)i /mm

Number of sections in 1mm 2

Particle diameter

Number of spherical particles in 1mm 3 N (V)j /mm -3

N (A)i /mm -2

D (V)j /mm

1

0～0.018

0

0.018

0

2

0.018~0.036

18

0.036

198.71

3

0.036～0.054

twenty four

0.054

98.83

4

0.054～0.072

43

0.072

438.98

5

0.072～0.090

50

0.09

601.53

6

0.090～0.108

44

0.108

619.05

7

0.108~0.126

19

0.126

281.42

8

0.126～0.144

2

0.144

28.69

total

　

200

　

2267.21

Here k = 8; △ = 0.018 mm; α ji lookup table (table in mineral particle size measurement (2)) and Nv calculation data are listed in Table 2. An example of the calculation of (Nv)j is as follows:

[next]

In summary, the measurement and calculation steps for solving the particle size of spherical mineral particles by the diameter method can be summarized as follows:
(1) measuring the perimeter of each particle section of the mineral on the A T area of ​​the light (thin) sheet under an image analyzer;
(2) Converting the section length into the section perimeter diameter d(A)i, and finding d(A)max from it;
(3) Grouping the perimeter diameters of the sections, the number of groups k is preferably not more than 10~15, and the group distance â–³ = d(A)max/k

d (A)i = i â–³,i = 1,2,3...,k.

(4) Measure and calculate (NA)i. That is, the number of d(A)i cross sections in the field of view area AT is measured. Ni.(NA)i = ——. Depending on the density of the mineral particles and the uniformity of the distribution, the image analyzer can be either all-optical (thin) or partially mineral particles. The mineral particles in the AT field are usually not less than 200~300.
k
(5) Calculate (Nv)j, Nv = Σ(N v ) j and (d v ) according to the format of Table 1 of equation (10 ).
j=1
2. The area measurement method CACалтъΙκοв improved the above diameter measurement method, and used the area measurement method to derive a simpler measurement and calculation formula. Because it can be proved that the spatial size distribution of the small 闰 does not obey the normal distribution, but obeys the lognormal distribution. Therefore, for the grouping of particle sizes, the number of equal groups is not used, and the method of equal series is used. For example, when CACалтъΙκοв uses a ratio of the cross-sectional diameter d(A)i or the cross-sectional area Ai of 10 -0.1 or (10 -0.1 ), that is:

d (A)i+1
—————— = 10 -0.1 = 0.7943
d (A)i

Ai+1
Or ————— =( 10 -0.1 )2 = 0.6310 (11)
Ai

From this, the coefficients in the equation (10) can be derived. When k = 12, the formula for (N v ) j is 1
(N v ) j = ————[1.6461(N A ) i - 0.4561(N A ) i - 1 - 0.1162(N A ) i - 2
d (v)j

- 0.0415(N A ) i - 3 - 0.0173(N A ) i - 4 - 0.0079(N A ) i - 5

- 0.0038(N A ) i - 6 - 0.0018(N A ) i - 7 - 0.0010(N A ) i - 8

- 0.0003(N A ) i - 9 - 0.0002(N A ) i - 10 - 0.0002(N A ) i - 11 ] [next]

In the formula, j and i are also group ordinal numbers, except that the particle diameter (or cross-sectional area) at which j (or i) = 1 is the largest. (NA)i is the measured value, i = j of the first term. i = 1...j(i ≤ j); j = 1...k.
The lead-zinc ore in the second example is tested by the area method for the lead ore. The test data and calculation results are shown in Table 3.

table 3   Galena area method measurement results

Serial number

Particle cross-sectional area interval Ai(μ 2 )

Number of sections in 1mm 2

Particle diameter

Number of spherical particles in 1mm 3 N (V)j /mm -3

N (A)i /mm -2

D (v)j /mm

1

9500～5994.5

40

0.10998

598.69

2

5994.5～3782.53

57

0.08736

865.2

3

3782.53～2386.78

45

0.0694

625.78

4

2386.78～1506.06

15

0.05513

-74.67

5

1506.06～950.32

19

0.04379

368.76

6

950.32～599.65

12

0.03478

177.54

7

599.65～378.38

10

0.02763

245.27

8

378.38～238.76

2

0.02195

-198.42

total

　

200

　

2608.15

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