ISO 9276-2-2014 pdf free download.Representation of results of particle size analysis — Part 2:Calculation of average particle sizes/ diameters and moments from particle size distributions
Representation de données obtenues par analyse granulometrique — Partie 2: Calcul des tailles/diamètres moyens des particules et des moments a partir de distributions granulométriques.
7 Accuracy of calculated particle size distribution parameters
Any of the below points can cause particle size distributions and their characteristic values to differ significantly if they come from different techniques.
For instance when comparing results from different techniques, it is necessary to convert particle size distribution parameters, such as mean sizes or distribution percentile values, from one type of measured size distribution into another type. e.g. from a volume-based distribution into a number- based distribution. Mathematically, these conversions typically can be done with an accuracy of within 1 %. However, the errors in the parameters are strongly increased by the following:
— if the size distribution is truncated by small cut-offs at either end of the distribution (e.g. 0,05 — 0,3 % r/r), often applied in view of limited measurement precision or deconvolution problems);
— if the measured size distribution contains only few particles at the upper size end, which quantities therefore have a great uncertainty;
— if the size distribution contains phantom peaks due to presence of heterogeneities within the particles sample or to application of inaccurate models for conversion of measured signals into a size distribution;
— if the type of size distribution (dimensionality r) is changed considerably in the conversion of wide size distributions; (volume to surface gives lower errors than volume to number)
— If the size distribution contains only few, wide size classes;
— if significant measurement errors are present.
Further explanations and examples are given in Annex C.
The upper boundary of the distribution is assumed to be 25,0 urn. The truncated volume fraction above this boundary is 0,000 64. The distribution is also truncated at the lower boundary of the seventh class of the R5 series, being 0,995 27 urn. The truncated volume fraction below this boundary is 0,000 62. The total truncated volume fraction is thus 0,001 26.
The numbers in Table A.1 forx,; Qj ax,; :Li. i1Q,, (normalized) and q (R5 series) have been used to calculate the moments represented by Formulae (35) to (38). Note that the Q data are not normalized, due to the truncation of the distribution. The ExceP) function LOGNORMDIST(x,mean,standard_dev) was used to calculate the Qj – values:
Q:ii LOGNORMDIST(x1, ln(xo,3),s) = LOGNORMDIST(x1 1,609 44;0,5)
(A.4)
The analytical values of the moments have been calculated by introducing the lognormal distribution into Formula (1) and integrating between Xmjn = 0 and Xmax = Co. i.e. without truncation. The values obtained are given in TabIA2. Column 2 represents the values of the four moments as calculated from the analytical function. Columns 3 and 5 represent the figures obtained in the numerical calculation
1) Excel Is the trade name of a product supplied by Microsoft. This Information Is given for the convenience of users of this document and does not constitute an endorsement by ISO of the product named. Equivalent products may be used ii they can be shown to lead to the same results.ISO 9276-2-2014 pdf free download.