rosin rammer regression

7/30/2019 Rosin Rammer Regression

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CALCULATION COVER SHEET Date: ########

Author: Alex Doll

Project: General Engineering Calc No:

Title: Fitting Rosin-Rammler parameters to a sieve analysis

Purpose:

Basis / Assumptions:

Method: Fit the data set entered to the equation:

Y = n * X + n*ln(DN)

where: Y = ln(-ln(R))

X = ln(D)

Refer to Appendix 1 for derivation.

D R X Y

Sieve, m

Cumulative

%Retained Fitted Y

Fitted

%retained

1000 1.0% 0.0%500 37.0% 6.21 -0.01 0.11 32.7%

250 48.4% 5.52 -0.32 -0.44 52.5%

180 61.6% 5.19 -0.72 -0.70 60.8%

150 61.6% 5.01 -0.72 -0.84 65.0%

75 76.0% 4.32 -1.29 -1.39 78.0%

63 82.1% 4.14 -1.62 -1.53 80.5%

53 84.6% 3.97 -1.79 -1.67 82.8%

43 86.0% 3.76 -1.89 -1.83 85.2%

35 87.0% 3.56 -1.97 -1.99 87.3%

30 88.0% 3.40 -2.06 -2.12 88.7%

0 100.0% 100.0%

n= 0.791612

R = 0.9833

(Note: R is relative to the

n * ln(DN) -4.8093 derived X and Y, and not D and R.)

DN = 0.002299

1

Given a data set from a sieve analysis, determine the RosinRammler parameters by regression

Data set is assumed to follow a Rosin-Rammler distribution. Thisdistribution is commonly seen in mineral grinding circuits as cycloneoverflow or SAG mill feed streams. Plotting the data set on a Rosin-Rammler chart (like the one available at http://www.sagmilling.com)should result in a straight line if the data is suitable for fitting by thismethod.


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Result:

References:

The Rosin-Rammler plotting system available at

http://www.sagmilling.com will permit plotting data

on a Rosin-Rammler Y-axis. Refer to Appendix 2 for

instructions on how to paste data from this calc

into the website.

http://www.codecogs.com/d-ox/engineering/materials/rosin_rammler.php

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%80.0%

90.0%

100.0%

1 10 100 1000

Cumulative%retaine

d

Sieve, m

Rosin Rammler Regression Check

The equation was originally published under:Rosin, P. and Rammler, E., The Laws Governing the Fineness of PowderedCoal, J. Inst. Fuel, Vol.7, No. 31, pp.29-36, 1933


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30 12 88

53 15.4 84.6

63 17.9 82.1

75 30.9 69.1

150 38.4 61.6

180 38.4 61.6

250 51.6 48.4

500 63 37

1003 99 1


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CALCULATION APPENDIX 1 Date: ########

Author: Alex Doll



Derivation of the plotting equations:

General form of the Rosin-Rammler equation:

Where: R is the cumulative %retained at a size D

and DN and n are fitting parameters.

In computer programming notation, write as:

R = exp(-(D/DN)^n)

Now, start solving for an equation in the form of

(R) = c1*(D) + c2 where c1 and c2 are constants

step 0 R = exp(-(D/DN)^n)

step 1 ln(R) = -(D/DN)^n

step 2 ln(1/R) = (D/DN)^n

step 3 ln[ln(1/R)] = n*ln(D/DN)

step 4 ln[ln(1/R)] = n*ln(D) - n*ln(DN)

Done. In this expression, (R) = ln[ln(1/R)]

(D) = ln(D)c1 = n

c2 = n*ln(DN)

Note that if R is expressed as a decimal (0.04 instead of 4%),

then the term ln(1/R) will be negative and the second logarithm

will fail. This is fixed by modifying the (R) term:

(R) = ln[ -ln(1/R)]

and the equation becomes:

ln[ -ln(1/R)] = n*ln(D) - n*ln(DN)

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CALCULATION APPENDIX 2 Date: ########

Author: Alex Doll



Using the SAGMILLING.COM Rosin-Rammler plotting system

Requirements:

Web browser and Internet access

Sun Java (just about any version should work)

Method:

Browse http://www.sagmilling.com

Select "Design Tools" from the menu on the left

Select Particle Size Plot from the menu on the left.

Should see the screenshot below:

Select "I have %retained. Don't calculate anything."

Select "Manually enter particle sizes" and press "Next"

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Paste the info on the right 1000

into the entry box on the website: 500

250

180

150

75

6353

43

Press "Next" 35

30

0

0.01

0.37

0.484

0.616

0.616

0.760.821

0.846

0.86

Press "Validate" 0.87

0.88

1

Select "Rosin-Rammler" plot type

Click "Next"

Done. You should see the Java Applet load and display this:

Paste the info on the right into the right-most entry box on the web page (the"Cum. % Retained" column). Don'tworry about the weird spacing or theodd decimal places.

rosin rammer regression

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