1、BRITISH STANDARD BS ISO 9276-4:2001 Representation of results of particle size analysis Part 4: Characterization of a classification process ICS 19.120 NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBS ISO 9276-4:2001 This British Standard, having been prepared under the direc
2、tion of the Sector Policy and Strategy Committee for Materials and Chemicals, was published under the authority of the Standards Policy and Strategy Committee on 15 January 2002 BSI 15 January 2002 ISBN 0 580 38846 8 National foreword This British Standard reproduces verbatim ISO 9276-4:2001 and imp
3、lements it as the UK national standard. 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: A list of organizations represented on th
4、is committee can be obtained on request to its secretary. Cross-references The British Standards which implement international or European publications referred to in this document may be found in the BSI Standards Catalogue under the section entitled “International Standards Correspondence Index”,
5、or by using the “Find” facility of the BSI Standards Electronic Catalogue. A British Standard does not purport to include all the necessary provisions of a contract. Users of British Standards are responsible for their correct application. Compliance with a British Standard does not of itself confer
6、 immunity from legal obligations. aid enquirers to understand the text; present to the responsible international/European committee any enquiries on the interpretation, or proposals for change, and keep the UK interests informed; monitor related international and European developments and promulgate
7、 them in the UK. Summary of pages This document comprises a front cover, an inside front cover, the ISO title page, pages ii to v, a blank page, pages 1 to 17 and a back cover. The BSI copyright date displayed in this document indicates when the document was last issued. Amendments issued since publ
8、ication Amd. No. Date CommentsReference number ISO 9276-4:2001(E) ISO 2001 INTERNATIONAL STANDARD ISO 9276-4 First edition 2001-07-15 Representation of results of particle size analysis Part 4: Characterization of a classification process Reprsentation de donnes obtenues par analyse granulomtrique P
9、artie 4: Caractrisation dun processus de triageii ISO -67294:(1002)Eiii Contents Page Foreword.iv Introduction.v 1 Scope 1 2 Symbols 2 2.1 Symbols for specific terms.2 2.2 Subscripts 3 3 Characterization of a classification process based on error-free distribution curves and mass balances3 3.1 Densi
10、ty distribution curves representing a classification process3 3.2 Mass and number balances4 3.3 Definitions of cut size, x e 5 3.4 Grade efficiency, T, the grade efficiency curve, T(x), (Tromps curve).6 3.5 Measures of sharpness of cut7 4 The influence of systematic errors on the determination of gr
11、ade efficiency curve9 4.1 General9 4.2 Systematic error due to a splitting process in the classifier 10 4.3 Incomplete dispersion of the feed material 11 4.4 The influence of comminution of the feed in the classifier.11 Annex A (informative) The influence of stochastic errors on the evaluation of gr
12、ade efficiency curves12 Bibliography17 Page3 ISO92764:2001 15January2002ISO -67294:(1002)E iv Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carrie
13、d out through ISO technical committees. Each member body interested in a subject for which a technical committee 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. IS
14、O collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 3. Draft International Standards adopted by the technical committ
15、ees 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. Attention is drawn to the possibility that some of the elements of this part of ISO 9276 may be the subject of patent rights. ISO shall
16、 not be held responsible for identifying any or all such patent rights. International Standard ISO 9276-4 was prepared by Technical Committee ISO/TC 24, Sieves, sieving and other sizing methods, Subcommittee SC 4, Sizing by methods other than sieving. ISO 9276 consists of the following parts, under
17、the general title Representation of results of particle size analysis: Part 1: Graphical representation Part 2: Calculation of average particle sizes/diameters and moments from particle size distributions Part 3: Fitting of an experimental cumulative curve to a reference model Part 4: Characterizati
18、on of a classification process Part 5: Validation of calculations relating to particle size analyses using the logarithmic normal probability distribution Annex A of this part of ISO 9276 is for information only. Page4 ISO92764:2001 15January2002ISO -67294:(1002)Ev Introduction In classification pro
19、cesses used in particle size analysis, such as occurring in impactors, sieves, etc., the mass of the supply or feed material, m s , or its number, n s , of particles, the particle size distribution of which is described by its density distribution, q r,s (x), is separated into at least one fine frac
20、tion of mass, m f , or number, n f , and of density distribution, q r,f (x) and a coarse fraction of mass, m c , or number, n c , and a density distribution, q r,c (x) .T h et y p eo f quantity chosen in the analysis is described by the subscript, r, the supply or feed material and the fine and coar
21、se fractions by the additional subscripts: s; f and c respectively. See Figure 1. Figure 1 Fractions and distributions produced in a one step classification process For the characterization of processes with more than one coarse fraction, e.g. cascade impactors, s, f and c can be replaced by numbers
22、 0, 1 and 2. In this case e.g. number 3 describes a second coarse fraction containing larger particles than fraction 2. It is assumed that the size, x, of a particle is described by the diameter of a sphere. Depending on the problem, the particle size, x, may also represent an equivalent diameter of
23、 a particle of any other shape. Page5 ISO92764:2001 15January2002blank 6egaP ISO92764:2001INTENRATIONAL TSANDADR ISO -67294:(1002)E1 Representation of results of particle size analysis Part 4: Characterization of a classification process 1 Scope The main object of this part of ISO 9276 is to provide
24、 the mathematical background for the characterization of a classification process. This part of ISO 9276 is not limited to an application in particle size analysis, the same procedure may be used for the characterization of a technical classification process (e.g. air classification, centrifugal cla
25、ssification) or a separation process (e.g. gas or hydrocyclones). In clause 3 the characterization of a classification process is described under the presupposition that the density distribution curves describing the feed material and the fractions, as well as the overall mass balance, are free from
26、 errors. In clause 4 the influence of systematic errors on the efficiency of a classification process is described. The effect of stochastic errors in the characterization of a classification process is described in annex A. 7egaP 1002:46729OSI Page3 ISO92764:2001 15January2002ISO -67294:(1002)E 2 2
27、 Symbols 2.1 Symbols for specific terms See Table 1. Table 1 Symbols for specific terms Symbol Term A Parameters derived from cumulative distribution curves E Mass balance error, cumulative distributions I Imperfection K(x) Corrected cumulative distribution m Mass n Total number of size classes, num
28、ber of particles q r (x) Density distribution curve Q r (x) Cumulative distribution curve Q r,i Difference of two cumulative distribution values, relative amount in the ith particle size interval, x i s 2 Variance t Students factor T Grade efficiency T o Overall classification or separation efficien
29、cy T(x) Grade efficiency curve x Particle diameter, diameter of a sphere x a Analytical cut size x e Equiprobable cut size, median particle size of a grade efficiency curve x i Upper particle size of the ith particle size interval x i 1 Lower particle size of the ith particle size interval x i Width
30、 of the ith particle size interval x max Particle size above which there are no particles in a given size distribution x min Particle size below which there are no particles in a given size distribution Angle of slope, weighted sum of variances Mass balance error, density distributions r,i Q r,s,i Q
31、 r,c,i Variable Sharpness of cut parameters formed with characteristic particle sizes v Relative amount r,i Q r,f,i Q r,c,i Variable Amount of particles not participating in a classification process Variable Page8 ISO92764:2001 15January2002ISO -67294:(1002)E3 2.2 Subscripts See Table 2. Table 2 Sub
32、scripts Symbol Significance c Coarse fraction (second subscript after r) f Fine fraction (second subscript after r) i Number of the size class with upper particle size: x i r Type of quantity of a density distribution a (general description) s Supply or feed material (second subscript after r) 0 Rep
33、laces s in case of more than one coarse fraction 1 Replaces f in case of more than one coarse fraction 2 Replaces c in case of more than one coarse fraction a For example, r 3ifty peofq uan t ity volume or mass. 3 Characterization of a classification process based on error-free distribution curves a
34、nd mass balances 3.1 Density distribution curves representing a classification process In a classification process a given supply or feed material (subscript s) is classified into at least two parts, which are called the fine (subscript f) and the coarse (subscript c) fractions. If an ideal classifi
35、cation were possible, the fine fraction would, as shown in Figure 2, contain particles below or equal to a certain size, x e , the so-called cut size, and the coarse fraction would contain all particles above that size. Figure 2 Weighted density distributions of the feed material q r,s (x) and the f
36、ine and coarse fractions of an ideal classification process Page9 ISO92764:2001 15January2002ISO -67294:(1002)E 4 The shaded areas beneath the weighted density distributions of the fine and the coarse product represent the relative mass, v 3,f , or number, v 0,f , of the fine, v r,f , and the coarse
37、 fraction, v r,c , the sum which equals 100 % or unity. In reality, however, in a certain range of sizes x min,c x x max,f particles of the same size, x, are present in both the fine and the coarse fractions. The density distribution curves of the fine and the coarse fractions overlap and intersect
38、each other in this size range, The point of intersection as shown in Figure 3 corresponds to a cut size, which is called the equiprobable cut size, x e (see 3.3.2). The particles below the cut size, x e , in the coarse or above x e in the fine fraction have been incorrectly classified. Figure 3 Weig
39、hted density distributions of feed material, q r,s (x),a ndthefine ,v r,f q r,f (x), and the coarse fraction, v r,c q r,c (x),ofanreal classification process 3.2 Mass and number balances 3.2.1 Mass and number balance in the size range from x min to x max Due to the classification process, the mass,
40、m s , or number, n s , of the feed material, is split into the mass, m f ,o r number, n f , of the fine material and the mass, m c , or number, n c, of the coarse material. One obtains: sfc mmm or sfc nnn (1) and c f ss 1 m m mm or c f ss 1 n n nn (2) 3,f 3,c 1vv or 0,f 0,c 1vv (3) v r,f represents
41、the relative amount of the fine fraction, v r,c the relative amount of the coarse fraction. In Figures 2 and 3, v r,f and v r,c are represented by the areas beneath the weighted density distribution curves of the fine, v r,f q r,f (x), and the coarse, v r,c q r,c (x), fractions. The area beneath the
42、 density distribution curve of the feed material, q r,s (x), equals unity. Page10 ISO92764:2001 15January2002ISO -67294:(1002)E5 3.2.2 Mass and number balance in the size range from x to x dx Particles of a certain size, x, present in the feed material, are either transferred in the classification p
43、rocess to the fine or to the coarse fractions. The amount of these particles in the feed material, dQ r,s (x), is therefore split into two fractions: v r,f dQ r,f (x) and v r,c dQ r,c (x). ,s ,f ,f ,c ,c d( )d( )d( ) rrrrr QxvQxvQx (4) Replacing dQ r (x) by equation 5: d() () d rr Qx qxx (5) one obt
44、ains: ,s ,f ,f ,c ,c () () () rr rr r qxvqxvqx (6) Equation 6 must be used to construct the set of density distribution curves of Figure 3. It should be realized that in plotting Figure 3 only three of the variables of equation 6 can be chosen arbitrarily. If, two density distributions and the relat
45、ive amount of the fine or the coarse material, e.g., q r,s (x), q r,f (x) and v r,f are given, q r,c (x), and v r,c are fixed. 3.2.3 Mass and number balance in the size range from x min to x Integrating equation 6 between x min and x yields: ,s ,f ,f ,c ,c () () + () rr rr r QxvQxvQx (7) 3.2.4 The i
46、ndirect evaluation of v r,f and v r,c In many cases of practical application v r,f and v r,c cannot be calculated from the relevant masses or mass flow rates, due to the fact that these are not available or difficult to measure, etc. If however, representative samples of the feed material and the fi
47、ne and the coarse fraction have been measured equations 3 and 6 or 7 may be used to calculate v r,f or v r,c . Introducing equation 3 into equations 6 and 7 and solving with respect to v r,f yields: ,s ,c ,s ,c ,f ,c ,f ,c ,f ,c () () () () 1 () () () () rrrr rr rrrr QxQxqxqx vv QxQxqxqx (8) If the
48、cumulative distributions Q r,s (x), Q r,f (x) and Q r,c (x) are free from errors, i.e. the mass balance according to equations 6 or 7 leave no remainder, v r,f or v r,c will be constant and independent of size x. 3.3 Definitions of cut size, x e 3.3.1 General In principle, any value of x between x m
49、in c and x max f , i.e. the size range in which the density distributions of the fine and the coarse fractions overlap, can be used as cut size. Two definitions are commonly used as described in 3.3.2 and 3.3.3. 3.3.2 The equiprobable cut size, x e , the median of the grade efficiency curve In Figure 3 the weighted density distribution curves of the fine and the coarse fraction intersect at a certain size x e . This par
