1、 BRITISH STANDARD BS ISO 9276-1:1998 ISO 9276-1: 1998 Incorporating Corrigendum No. 1 Representation of results of particle size analysis Part 1: Graphical representation ICS 19.120BS ISO 9276-1:1998 This British Standard, having been prepared under the direction of the Sector Board for Materials an
2、d Chemicals, was published under the authority of the Standards Board and comes into effect on 15 October 1998 BSI 2006 ISBN 0 580 30558 9 National foreword This British Standard reproduces verbatim ISO 9276-1:1998, including Corrigendum February 2004, and implements it as the UK national standard.
3、The UK participation in its preparation was entrusted by Technical Committee LBI/37, Sieves, screens and particle sizing, to Subcommittee LBI/37/4, Sizing by methods other than sieving, which has the responsibility to: aid enquirers to understand the text; present to the responsible international/Eu
4、ropean committee any enquiries on the interpretation, or proposals for change, and keep UK interests informed; monitor related international and European developments and promulgate them in the UK. A list of organizations represented on this subcommittee can be obtained on request to its secretary.
5、Cross-references The British Standards which implement international publications referred to in this document may be found in the BSI Catalogue under the section entitled “International Standards Correspondence Index”, or by using the “Search” facility of the BSI Electronic Catalogue or of British
6、Standards Online. The first edition (1990) of ISO 9276-1 was not implemented as a British Standard. Several additional Parts of ISO 9276 were in preparation at the time of publication of the second edition of this Part, no other Parts having been published. This publication does not purport to inclu
7、de all the necessary provisions of a contract. Users are responsible for its correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. Summary of pages This document comprises a front cover, an inside front cover, pages i and ii, the ISO title
8、 page, page ii, pages 1 to 9 and a back cover. This standard has been updated (see copyright date) and may have had amendments incorporated. This will be indicated in the amendment table on the inside front cover. Amendments issued since publication Amd. No. Date Comments 15735 Corrigendum No. 1 28
9、April 2006BS ISO 9276-1:1998 BSI 2006 i Contents Page National foreword Inside front cover Foreword ii 1S c o p e 1 2 Normative reference 1 3S y m b o l s 1 4 Particle size, measures and types 2 5 Graphical representation 3 6 Graphical representation of cumulative and density distributions on a loga
10、rithmic abscissa 6 Annex A (informative) Example of graphical representation of particle size analysis results 8 Figure 1 Coordinates for the representation of particle size analysis data 2 Figure 2 Histogram of a density distribution function 4 Figure 3 Cumulative distribution Q r (x) 5 Figure 4 De
11、nsity distribution q r (x) 6 Figure A.1 Histogram by mass plotted on graph paper with a linear abscissa 9 Figure A.2 Cumulative distribution Q 3 (x) by mass plotted on graph paper with a logarithmic abscissa 9 Figure A.3 Histogram by mass plotted on graphic paper with a logarithmic abscissa 9 Figure
12、 A.4 Cumulative distribution Q 3(In x) by mass plotted on graph paper with a logarithmic abscissa 9 Table 1 Symbols for distributions 3 Table A.1 Calculation of the histogram and the cumulative distribution 8 q r x () q * 3 x () q * 3 In x ()ii blankBS ISO 9276-1:1998 ii BSI 2006 Foreword ISO (the I
13、nternational Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee
14、has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnica
15、l standardization. Draft International Standards adopted by the technical committees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. International Standard ISO 9276-1 was prepared by Tech
16、nical Committee ISO/TC 24, Sieves, sieving and other sizing methods, Subcommittee SC 4, Sizing by methods other than sieving. This second edition cancels and replaces the first edition (ISO 9276-1:1990), of which it constitutes a technical revision. ISO 9276 consists of the following parts, under th
17、e general title Representation of results of particle size analysis: Part 1: Graphical representation; Part 2: Calculation of average particles sizes/diameters and moments from particle size distributions. Annex A of this part of ISO 9276 is for information only. Descriptors: Sieving, sieve analysis
18、, grain size analysis, test results, data representation, graphic methods.BS ISO 9276-1:1998 BSI 2006 1 1 Scope This part of ISO 9276 specifies rules for the graphical representation of particle size analysis data in histograms, density distributions and cumulative distributions. It also establishes
19、 a standard nomenclature to be followed to obtain the distributions mentioned above from the measured data. This part of ISO 9276 applies to the graphical representation of distributions of solid particles, droplets or gas bubbles covering all size ranges. 2 Normative reference The following standar
20、d contains provisions which, through reference in this text, constitute provisions of this part of ISO 9276. At the time of publication, the edition indicated was valid. All standards are subject to revision, and parties to agreements based on this part of ISO 9276 are encouraged to investigate the
21、possibility of applying the most recent edition of the standards indicated below. Members of IEC and ISO maintain registers of currently valid International Standards. ISO 565:1990, Test sieves Metal wire cloth, perforated metal plate and electroformed sheet Nominal sizes of openings. 3 Symbols 3.1
22、General In this part of ISO 9276, the symbol x is used to denote the particle size or the diameter of a sphere. However, it is recognized that the symbol d is also widely used to designate these values. Therefore, in the context of this part of ISO 9276, the symbol x may be replaced by d where it ap
23、pears. Symbols for the particle size other than x or d should not be used. Subscripts with different meanings are divided by the comma sign in this and all other parts of ISO 9276. 3.2 Symbol explanation d particle size, diameter of a sphere (see 3.1) i (subscript) number of the size class with uppe
24、r limit x i : %x i= x i x i1 v (integer, see subscript i) n total number of size classes q 0 (x) density distribution by number q 1 (x) density distribution by length q 2 (x) density distribution by surface or projected area q 3 (x) density distribution by volume or mass q r (x) density distribution
25、 (general) (In x) density distribution in a representation with a logarithmic abscissa average density distribution of the class %x i : histogram (general) Q 0 (x) cumulative distribution by number Q 1 (x) cumulative distribution by length Q 2 (x) cumulative distribution by surface or projected area
26、 Q 3 (x) cumulative distribution by volume or mass Q r (x) cumulative distribution (general) q* r q ri , q r x ()BS ISO 9276-1:1998 2 BSI 2006 4 Particle size, measures and types 4.1 General In a graphical representation of particle size analysis data, the independent variable, i.e. the physical pro
27、perty chosen to characterize the size of the particles, is plotted on the abscissa (see Figure 1). The dependent variable, which characterizes measure and type of quantity, is plotted on the ordinate. 4.2 Particle size x Regarding the denotation of particle size, see 3.1. There is no single definiti
28、on of particle size. Different methods of analysis are based on the measurement of different physical properties. Independently of the particle property actually measured, the particle size is reported as a linear dimension. In this part of ISO 9276, the particle size is defined as the diameter of a
29、 sphere having the same physical properties; this is known as the equivalent spherical diameter. The physical property to which the equivalent diameter refers shall be indicated using a suitable subscript, for example: The different measures are Other definitions are possible, such as those based on
30、 the opening of a sieve or a statistical diameter, e.g. the Feret diameter, measured by image analysis. Q r,i = Q r (x i ) %Q r,i increment of cumulative distribution within the class %x i : %Q r,i= %Q r (x i 1 x i ) = Q r (x i ) Q r (x i 1 ) r type of quantity x particle size, diameter of a sphere
31、(see 3.1) x min size below which there are no particles x max size above which there are no particles x i upper size of a particle size interval x i 1 lower, size of a particle size interval %x i = x i x i1 , width of the particle size interval = K (x) transformed coordinate x s : equivalent surface
32、 area diameter; x v : equivalent volume diameter. Figure 1 Coordinates for the representation of particle size analysis dataBS ISO 9276-1:1998 BSI 2006 3 4.3 Measures and types The measures and types are distinguished with respect to the dependent variables by symbols as shown below. The different m
33、easures are Each measure can be one of several types. The type is indicated by the general subscript, r, or by the appropriate value of r as follows: The summary of the symbols used to designate density and cumulative distributions is shown in Table 1. Table 1 Symbols for distributions 5 Graphical r
34、epresentation Examples of the graphical representation of particle size analysis data are shown in Figure 2 to Figure 4. 5.1 Histogram Figure 2 shows the normalized histogram, , of a density distribution q r (x). It comprises a successive series of rectangular columns, the area of each of which repr
35、esents the relative quantity %Q r,i(x), where or The sum of all the relative quantities, %Q r,i , forms the area beneath the histogram , normalized to 100 % or 1 (condition of normalization). Therefore, the following equation holds: Q: cumulative measures, and q: density measures. number: r = 0 leng
36、th: r = 1 area: r = 2 volume or mass: r = 3 Type Mathematical symbol for density distribution cumulative distribution Distribution by number length area volume or mass General symbol q 0 (x) q 1 (x) q 2 (x) q 3 (x) q r (x) Q 0 (x) Q 1 (x) Q 2 (x) Q 3 (x) Q r (x) (1) (2) (3) q r(x ) q r x () q r x ()
37、BS ISO 9276-1:1998 4 BSI 2006 5.2 Cumulative distribution Q r (x) Figure 3 shows a typical normalized cumulative distributions, Q r (x). If the cumulative distribution is calculated from the histogram data, only individual points Q r,i= Q r (x i ) are obtained, as indicated in Figure 3. Each individ
38、ual point of the distribution, Q r (x i ), defines the relative amount of particles smaller than or equal to x i . The continuous curve is calculated by suitable interpolation algorithms. A first approximation is obtained by connecting successive points by straight lines. The normalized cumulative d
39、istribution extends between 0 and 1, i.e. 0 and 100 %. with 1 k v k i k n. Figure 2 Histogram of a density distribution function (4) q r x ()BS ISO 9276-1:1998 BSI 2006 5 5.3 Density distribution q r (x) Under the presupposition that the cumulative distribution, Q r (x), is differentiable, the conti
40、nuous density distribution, q r (x), is obtained from q r (x) is plotted in Figure 4. Conversely, the cumulative distribution, Q r (x), is obtained from the density distribution, q r (x), by integration: Figure 3 Cumulative distribution Q r (x) (5) (6) q r x () dQ r x () dx - - =BS ISO 9276-1:1998 6
41、 BSI 2006 6 Graphical representation of cumulative and density distributions on a logarithmic abscissa Owing to the fact that a size distribution can cover several decades between its smallest particle size, x min , and its largest particle size, x max , plotting the data on a linear abscissa may no
42、t be suitable. In such a case, therefore, the results shall be plotted on graph paper with a logarithmic abscissa. 6.1 Cumulative distribution on a logarithmic abscissa When plotted on graph paper with a logarithmic abscissa the cumulative values, Q r,i,i.e. the ordinates of a cumulative distributio
43、n, do not change. Meanwhile, the course of the cumulative distribution curve changes but the relative amounts smaller than a certain particle size remain the same. Therefore, the following equation holds: Figure 4 Density distribution q r (x) Q r (x) = Q r (In x) (7)BS ISO 9276-1:1998 BSI 2006 7 6.2
44、 Density distribution on a logarithmic abscissa The density values of a histogram, = (x i 1 , x i ), shall be recalculated using equation (8) which indicates that corresponding areas underneath the density distribution curve remain constant. In particular, the total area is equal to 1 or 100 %, inde
45、pendent of any transformation of the abscissa. where K is any function of x. Thus the following transformation shall be carried out to obtain the density distribution with a logarithmic abscissa: Equation (9) also holds if the natural logarithm is replaced by the logarithm to the base 10. (8) (9) q*
46、 ri , q* rBS ISO 9276-1:1998 8 BSI 2006 Annex A (informative) Example of graphical representation of particle size analysis results The example in Table A.1, based on the data obtained by a sieve analysis, illustrates the application of this part of ISO 9276 Table A.1 Calculation of the histogram an
47、d the cumulative distribution The values for x igiven in column 2 represent the standardized test sieve openings specified in ISO 565. NOTE The notation w used in ISO 565 has been replaced by x i ; in this part of ISO 9276. The different amounts of particles retained between two sieves were obtained
48、 by weighing, and the relative weights, %Q 3,i , are listed in column 3 for each particle size interval %x i . The particle size intervals, %x i , were determined from %x i= x i x i 1and listed in column 4. The histogram ordinates (see column 5) were then calculated using equation (2). and Q 3 (x) a
49、re plotted in Figure A.1 and Figure A.2. The values were calculated from equation (9) (see column 7). (In x)and Q 3 (In x) are plotted in Figure A.3 and Figure A.4. 1 2 3 4 5 6 7 i x i %Q 3,i %x i Q 3,i mm mm %Q 3,i / %x i 1/mm 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0,063 0,09 0,125 0,18 0,25 0,355 0,5 0,71 1 1,4 2 2,8 4 5,6 8s 11,2 16 0,001 0 0,000 9 0,001 6 0,002 5 0,005 0 0,011 0 0,018 0 0,037 0 0,061 0 0,102 0 0,160
