g sampling for size analysis (new)

7/27/2019 G Sampling for Size Analysis (New)

1/10

SIZE-01

THE DETERMINATION OF THEPARTICLE SIZE DISTRIBUTION OF A

LOT IS OFTEN ONE OF THE MOST

IMPORTANT CRITERIA

1 Quality of a product,

2 Efficiency of a process,

3 Compliance with the clause of a

commercial contract,

4 Assessment of the accuracy of a

sampling system,

5 Assessment of the representativity of asample,...


2/10

SIZE-02

CANCELLATION AND MINIMIZATION OF

SAMPLING ERRORS

1 IPE: Preventive elimination

2 IDE: Correct delimitation

3 IEE: Correct extraction HFE1

4 GSE: Homogenization

Many increments

5 HFE2: Optimization of the sampling

interval

6 HFE3: Choose the appropriate sampling

selection mode =

Systematic random,

Stratified random,

Simple random.


3/10

SIZE-03

THE FUNDAMENTAL ERROR FE

NEVER CANCELS

m (FSE) 0

Definitions:

Lc: Particle size class of interest

aLc: Proportion of Lc in the lot L

MLc: Weight of the class of interest

NLc: Number of fragments in LcFj: A fragment of Lc

MFj: Weight of the fragment Fj

aFj: For each fragment of Lc aFj = 1

FLc: Average fragment of the class Lc

MFLc: Weight of FLc


4/10

SIZE-04

CALCULATION OF

I HL

ai aL

aLi

Mi

ML

2

2 2

*

I HL

L c ai aF j 1in

out of L c ai 0

I H L

aL c

aL c

j

Mj

ML

Mi

MLi

12

2

2 2

*

I H L

aL c

aL cj

Mj aL c

ML c

Mi

M Li

12

2

2 2

*

XL cXLconstant

I HL

aL c

aL c

XL c XL

1

2


5/10

SIZE-05

a

L c

2: very small

I HL

aL c

aL c

XL c XL

1 2

XL c XL

Mi Mj

and should be expressed in

practical terms because and are

not known.

It is relatively easy when we have a

rough idea of the particle size

distribution.

It is sufficient to substitute or

of a given particle class by the average

fragment of this class.

Fi Fj


6/10

SIZE-06

First lets define:

: number of fragments in the class

: average fragment of the class

: weight of the average fragment

: proportion of in the lot .

By definition: ,then

changing by the average fragments:

NL x L x

L xFL x

FL xMF L x

aL x L xL

M M NF L x L x L x /

Mi

XM

M

N M M

M

M M

ML

i

Li

L x F L x F L x

Lx

F L x L x

Lx

2

M M aL L x L x /

X M aL F L x L x x

But , then


7/10

SIZE-07

In the same way:

XM

M

N M M

M

M M

ML c

j

L cj

L c F L c F L c

L c

L c F L c

L c

2

X ML c F L c

Then we can write:

I H aa

M M aL L c

L cF L c F L x L x

x

1 2

All terms in this formula can either becalculated or estimated when we have, at

our disposal, a rough idea of the particle

size distribution.


8/10

SIZE-08

The average weight of the fragments of a particle size

class can be estimated in two different ways:

1. By direct measurement of the weight of a given

number of fragments selected at random within

the clkass.

2. By calculation using the following two formulas:

3

FLcFLcFLc dfvM

3

FLxFLxFLx dfvM

With:

3

33

2

openingloweropeningupperdFLc

samedFLx

x

LxFLxFLc

Lc

L adda

fIH 3321


9/10

SIZE-09

If is small: , thenaL c aL xx

1

I H fa

d gdLL c

F L c

12

3 3

Now we may calculate the variance of the

Fundamental Sampling Error:

332 2

111gdd

af

MMs FLc

LcLs

FSE

This formula can often be simplified:

If

If is not much different from

If is small, then

M ML s 10

dF L c d

aL c

322

1

FLc

Lcs

FSE daM

fs


10/10

SIZE-10

Important remark: if the coarse fragments

represent a large proportion of the lot, saymore than 20%, the term should be

kept.

gd3

Assessment of the representativity of a

sample

If we want a sample to be representative ofall the fragment size fractions, then it should

be representative of the largest fragments,

which is the most difficult condition to fulfill.

Thus, by definition we may write:

d dF L c

aL c 5% 0 05.and

Then:

s

FSEM

dfs

3

2

18

Of course we assume that the investigated

material is not calibrated: .g 0 25.

g sampling for size analysis (new)

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