- Email: [email protected]
Characterisation of fragments produced by the comminution of metals especially considering the fragment shape
Powder Technology 122 Ž2002. 177–187 www.elsevier.comrlocaterpowtec
Characterisation of fragments produced by the comminution of metals especially considering the fragment shape St. Sander, G. Schubert ) , G. Timmel Institute of Mechanical Process Engineering and Mineral Processing, Freiberg UniÕersity of Mining and Technology, Agricolastraße 1, D-09599 Freiberg, Germany Received 25 July 2000; received in revised form 6 October 2000; accepted 25 October 2000
Abstract During the comminution of metals, intensive deformation of the material takes place resulting in wide fragment size distributions and a large range of fragment shapes and states of compactness. Thus, the characterisation of the products is a very demanding task. In this paper, the most common methods for the determination of characteristics describing the results of the comminution as well as of the deformation are explained. q 2002 Elsevier Science B.V. All rights reserved. Keywords: Characterisation; Comminution; Shredders; Recycling
1. Introduction The comminution of materials with nonbrittle behaviour, especially of metals, plays an important role in recycling processes. The scientific investigation of these processes is—in comparison to the comminution of brittle materials—still at the beginning. The fact that the characterisation of the fragments produced during comminution is very difficult may be one of the reasons for that. The Chair of Mineral Processing and Recycling ŽATRec. at the Freiberg University of Mining and Technology has attended to the basic research in the field of the comminution of metals and scrap in shredders of the swing hammer mill type for a longer period of time. Platy test bodies of metal sheets are usually utilised as model materials. One essential result of the present research is the finding that very intensive bending and other deformation processes, which cause the formation of initial flaws and crack initiation, take place before a real fragmentation can occur inside this kind of equipment. Only as a second step, the cracks formed propagate until breakage. Due to this kind of stressing, the fragments produced are of very wide fragment size distributions, a large range of fragment shapes and—depending on the material properties and the conditions inside the zone of comminution—of a varying state of compactness. Therefore, the determination of the
properties of these fragments is a very demanding task. Besides the characteristics usually utilized in order to describe the results of the comminution, such as fragment size and fragment mass distributions, fragment shape and crack and fracture surface area, respectively, characteristics describing the compaction have to be determined too. These are the bending radii distribution, the bending length, the degree of bending and the degree of compaction, which is equal to a relative fragment density. The scope of this paper is to introduce the determination methods of the characteristics listed in Table 1 and to judge their applicability.
2. Determination of characteristics describing the results of comminution 2.1. Description of the fragment shape The fragment shape is an important granulometric property which affects most technological processes. Therefore, a great number of investigations have been done in order to describe this characteristic in a suitable manner. Frequently, the determination of shape factors is based on: v
)
Corresponding author. Fax: q49-3731-39-2815. E-mail address: [email protected] ŽG. Schubert..
v
the evaluation of the triaxial dimension relationships, the comparison between the properties Žsuch as area of projection, volume, etc.. of the irregularly shaped
0032-5910r02r$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 Ž 0 1 . 0 0 4 1 4 - 4
St. Sander et al.r Powder Technology 122 (2002) 177–187
178
Table 1 Characteristics describing the results of the comminution and of the compaction of fragments resulting from the stressing of metals Characteristic quantity
Determination method
Characteristics describing the results of the comminution Fragment shape Assignment to a phenomenologically determined classification of fragment shapes v Sieve analysis Fragment sizerfragment size distributions v Image analysis Fragment massrfragment mass distributions Weighing of single fragments Crack lengthrcrack length distribution Measuring after bending open using flexible steel belt rulers Crack and fracture surface area Measuring after bending open using flexible steel belt rulers Characteristics describing the compaction of the fragments Bending radiirbending radii distribution Measuring using gauges Bending length Measuring using flexible steel belt rulers Degree of bending Calculation from area of projection and mass v Calculation from area of projection and mass Degree of compaction v Embedding of fragments into a bulk of monodisperse spheres
v
fragment and those of a geometric body Žsuch as the sphere with equal mass. or the evaluation of the change in behaviour Že.g. settling velocity. as a result of the irregular shape.
Other concepts deliver characteristics describing the so-called roundness by measuring the radius of curvature of the projection of the fragments w1,2x. All the shape factors mentioned above are inadequate if applied to fragments formed by comminution of metals. This is due to the fact that the different fragment shapes are results of the varying states of compaction, too. Schubert w3–8x has been dealing with the comminution of metals and scraps for a considerable period of time. In
order to characterise the products of comminution, he suggested to assign the fragments to the shape classification shown in Fig. 1. For the process-related evaluation, this phenomenologically determined classification is suited better than the utilisation of shape factors, which, moreover, are difficult to determine. Starting from that, for the following investigations, a fragment shape classification was used in order to describe the products of the comminution, which is not only suitable for shape characterisation but also helps to distinguish the state of compaction ŽFig. 2.. Since the portions of the fragment shapes present in a given product allow conclusions concerning the deformation and breakage processes taking place, this concept especially provides advantages
Fig. 1. Shape classification for the characterisation of products of comminution Žaccording to Schubert.: Ža. compact Žcubic.; Žb. compact–strongly compacted; Žc. platy–even; Žd. platy–slightly to strongly deformed; Že. rod-shaped–straight; Žf. rod-shaped–slightly to strongly deformed.
St. Sander et al.r Powder Technology 122 (2002) 177–187
179
Fig. 2. Shape classification of fragments formed by comminution of sheet metals: Ža. platy–even; Žb. platy–slightly deformed; Žc. platy–strongly deformed; Žd. platy–strongly deformed, partially compacted; Že. compacted; Žf. spherical.
for the evaluation of comminution tests with platy test bodies. 2.2. Determination of the fragment size and the fragment size distribution Every fragment can be described by its three dimensions a, b and c, which represent the edge lengths of the enveloping parallelepiped of smallest volume ŽFig. 3.. By definition, a G b G c has to be fulfilled. In order to make the determination of the fragment size practicable, the medium dimension b, which is of significance for the sieve analysis, was assumed to be a close estimate of the fragment size x. The objective of the investigations was to find a method for the determination of dimension b that not only has a high accuracy but is also time-saving. Therefore, as a reference for judging the examined methods, fragment size distributions were used, which had been determined by
sticking the fragments through a geometric series of square perforated plates. Care was taken so that the fragments passed the apertures without abutments according to their dimension b. In this paper, this procedure will be called Adirect measurementB. As test materials, products formed from platy tin sheet test bodies of the initial dimensions Ž a = b = c . s Ž200 = 200 = 1. mm3 , which had been stressed at different periods of time Ž3, 8, 15, 30 and 60 s. in a small-scale horizontal shaft shredder, were utilised. The determination of the fragment size distributions Q 3 Ž b . was conducted by means of two different kinds of test sieving equipment, a suspended sieving machine producing a circular movement in the horizontal plane and a laboratory trommel screen, as well as two devices using image analysis. The suspended sieving machine is equipped with 400-mm-diameter sieves. It is suspended by a rope and the circular movement in the horizontal plane is caused by the action of an unbalance drive. The assumption can be made that in this case, the classification takes place according to dimension a or in between a and b. Due to the height of the sieves, the machine is equipped to handle a maximum of five sieves at a time resulting in six fractions of fragment size. The sieving time was limited to 10 min, because after that, the portion of the finest size fraction would not increase more than 0.2%rmin. The laboratory trommel screen operates discontinuously and is equipped with two octahedral trommels Žwidest diameter D s 570 mm and D s 960 mm.. The aperture size of the bigger trommel is w G 20 mm and of the smaller one is w F 16 mm. Both were operated at a rotational speed of n s 0.8 n crit , in which the critical rotational speed can be derived from n crit s
Fig. 3. Fragment of the fragment shape class Aplaty –strongly deformedB with its three dimensions.
(
g 2p 2 D
.
Ž 1.
Therewith, cataracting and, consequently, the separation according to dimension b should be secured. Since the test
180
St. Sander et al.r Powder Technology 122 (2002) 177–187
Fig. 4. Devices utilised for image analysis: Ža. Haver & Boecker CPA-4 Žaccording to Ref. w9x.; Žb. Proposal of ATRec.
sieving caused the fragments to be deformed or even to be secondarily broken, the sieving time was limited to 5 min per fraction. During the last years, devices using image analysis have become an alternative to be taken into account as compared with sieving. The initial objective was to employ a commercially available image analyser for the characterisation of fragments formed by comminution of sheet metals. Because of its wide measuring range, the CPA-4 ŽFig. 4a. manufactured by Haver & Boecker in Oelde, Germany was examined in detail. In this device, the material is dropped past a linear source of light Ž3. after being transported from the feed bin Ž1. by means of a vibrating conveyor Ž2.. The line camera Ž4. installed opposite to the source of light is connected to the computer Ž5., which is needed for evaluating the data and for controlling purposes w9x. The device was operated in the shape analysis mode without presupposing of the material density. In this mode, the area of projection reconstructed from the line images are used for measurement. For further investigations, the cumulative distributions of the spheres of equal area of projection of the quantity type volume and number of fragment, respectively, were obtained. In addition to the products from the batch tests concerning the comminution kinetics, spheres and cylinders as well as fragments of approximately equal size but varying fragment shapes were analysed. Since problems appeared during determination of the fragment size using the equipment mentioned above, an apparatus using image analysis was assembled in order to meet the specific requirements of the characterisation of the fragments formed by comminution of metals ŽFig. 4b.. It consists of a scales Ž1. utilised for measuring the fragment mass, above which a high-resolution CCD matrix camera Ž2. is installed. The fragments are laid on a flat source of light Ž3. installed at the scales in such a way that dimensions a and b are visible in the projection. The signals of the camera and the scales are processed by means of a PC Ž4.. The software Scion Image of Scion is used for evaluating the images with respect to the fragment
area of projection and dimensions aell and bell of the best fitting ellipse ŽFig. 5.. The latter has an area equal to the area of projection of the fragment and, moreover, maximally overlaps the projection of the fragment. Its dimension bell is assumed to be a good estimation for dimension b of the fragment. Exemplary for the results obtained in the determination of the fragment size distributions using the aforesaid equipment, the mean fragment size b50.3 can be seen in Table 2 as a function of the stressing time. Moreover, the deviations of the values from those obtained by direct measurement DŽ b50.3 . are to be found, which can be calculated by
D Ž b50 .3 . s
Ž b50 .3,direct measurement y b50.3,method . b50 .3,direct measurement
100%.
Ž 2. Due to the low height of the sieves, the suspended sieving machine could not be employed for the comparably coarse fragments obtained after a stressing time of only 3 s. The deviations of the results from those obtained by
Fig. 5. Dimensions aell and bell of the best fitting ellipse.
St. Sander et al.r Powder Technology 122 (2002) 177–187
181
Table 2 Mean fragment size b50.3 as a function of stressing time—comparison of the results obtained using different kinds of equipment and deviation of the results from those obtained by direct measurement DŽ b50.3 . Stressing time Žs.
3 8 15 30 60
Specific energy consumption ŽkJrkg.
Direct measurement
Mean fragment size b50.3 Žmm. Suspended sieving machine
Trommel screen
Haver & Boecker CPA-4
Proposal of ATRec
48.3 112.3 181.6 301.6 484.3
92.8 24 13.2 8.2 6.3
n.d. 20.5 11.6 7.8 6.1
54.2 21.2 13.0 8.4 6.2
52.2 25.5 13.7 8.3 6.2
91.5 22.5 13.4 8.0 6.1
Deviation from the values obtained by direct measurement DŽ b50.3 . Ž%. Suspended sieving machine
Trommel screen
Haver & Boecker CPA-4
Proposal of ATRec
n.d. 14.6 12.1 4.9 3.2
41.6 11.7 1.5 y2.4 1.6
43.8 y6.3 y3.8 y1.2 1.6
1.4 6.5 y1.7 2.7 3.2
Zinc, initial size of test bodies Ž200 = 200 = 1. mm3 ; batch tests with a small-scale horizontal shaft shredder at a circumferential speed of 50 mrs; n.d.s not determinable.
direct measurement are relatively high for longer-stressed products, too. The values of DŽ b50.3 . decrease with increasing stressing time but still are the highest if compared to those obtained using the other equipment. The reproducibility of the results is low even for the product obtained at a stressing time of 15 s, as was found in investigations conducted according to Rasemann w10x. Because of the results shown, it can be stated that test sieving utilising a suspended sieving machine, producing a circular movement in the horizontal plane, does not provide reliable characteristics for fragments formed by comminution of metals. Problems also arose if the trommel screen was employed to products obtained after short stressing times Ž3 and 8 s.. The fragments were subject to deformation and in some cases, breakage occurred. Therefore, the values of DŽ b50.3 . are high for these products. The fragment size of the materials stressed at longer times is smaller and most of the fragments are more compact. Consequently, the
deviations of the results from the values obtained by direct measurement are considerably smaller. Since only one fraction can be obtained at a time, this method is very time consuming. Moreover, its applicability is limited to smaller, more compact fragments. Having this in mind, the utilisation of a trommel screen does not seem to represent a real alternative as compared with the direct measurement. The results of the determination of the fragment size distributions using the Haver & Boecker CPA-4, which is designed for on-line applications, are in good agreement with the values obtained by direct measurement for products obtained at stressing times of t B G 8 s. In contradiction to that, the deviations of DŽ b50.3 . s 43.8% are very high for products stressed at shorter times Ž3 s.. In order to examine this effect, monodisperse bodies of known dimensions were analysed. For steel and glass spheres, the results are in good agreement with the diameters ŽFig. 6a.. The plot of the fragment size distribution Q 0 Ž x A . measured at cylindrical plates Ždiameter D s 2
Fig. 6. Size distributions Q0 Ž xA . measured using the Haver & Boecker CPA-4 Žaccording to Ref. w11x.: Ža. glass Ž D s 8 mm, D s 20 mm. and steel Ž D s 13.5 mm. spheres; Žb. cylindrical plates of plastic Ž D s 20 mm, L s 1.25 mm. Žcomputed distribution: random orientation, according to Vickers w12x..
182
St. Sander et al.r Powder Technology 122 (2002) 177–187
Fig. 7. Size distributions Q0 Ž xA . measured for different feeding orientations using the Haver & Boecker CPA-4 Žaccording to Ref. w11x.: Ža. cylinders of plastic Ž D s 20 mm, L s 40 mm.; Žb. cylinders of plastic Ž D s 20 mm, L s 120 mm. Žcomputed distributions: random orientation, according to Vickers w12x..
mm, height H s 1.25 mm. shows the expected course ŽFig. 6b.. The latter matches well with the one calculated according to Vickers w12x for a random orientation. However, it becomes obvious that it is impossible to derive the real dimensions of the plates from the plot alone. Investigations conducted with cylinders of equal diameter Ž D s 20 mm. but different lengths Ž L s 40 mm and L s 120 mm. showed that an additional influence of the feeding orientation has to be taken into account for this irregularly shaped test bodies ŽFig. 7.. For both kinds of test bodies, the fragment size distributions Q 0 Ž x A . of the cylinders fed lengthwise and transverse significantly vary from each other. Moreover, they do not match to the computed distributions for random orientation as well as the ones of the cylindrical plates. Certainly, there is no clue regarding the real dimensions of the cylinders to be derived from the plots.
For further investigations, fragments which are of approximately equal size but can be assigned to different fragment shape classes were singled out and analysed separately. From the results shown in Fig. 8a, it becomes obvious that the deviations of the determined fragment sizes b50.3 from the values obtained by direct measurement are very high for platy–even and platy–slightly deformed fragments. The sphericities c U,3 determined simultaneously during the size analysis, which is calculated from the area of projection A and the circumference U using
CU ,3 s
4p A U2
.
Ž 3.
can be seen for the examined fragment shape classes in Fig. 8b. It becomes clear that this device is of limited
Fig. 8. Deviations of the fragment size from the values obtained by direct measurement Ža. and mean sphericity Žb. of measurements conducted with the Haver & Boecker CPA-4 analysing fragments of different fragment shape classes Žzinc, wall thickness 1 mm; batch test with a small-scale horizontal shaft shredder at a circumferential speed of 50 mrs..
St. Sander et al.r Powder Technology 122 (2002) 177–187
183
Fig. 9. Fragment size b50 Ža. and fragment mass m 50 Žb. versus specific energy consumption with initial size of the test bodies as a parameter Žzinc, wall thickness 1 mm; batch test with a small-scale horizontal shaft shredder at a circumferential speed of 50 mrs..
value only for the characterisation of the products obtained by comminution of metals. The device utilised for the determination of the fragment size at the Chair of Mineral Processing and Recycling ŽATRec. shows relatively low deviations from the values obtained by direct measurement for all analysed products ŽTable 2.. The assumption that the dimension bell of the best fitting ellipse is a good estimate for the dimension b of the fragments has proven to be applicable for products obtained by comminution of metals. First results for products of wood are similarly promising. In the future, a further automation of the measurement is planned, which will make this method less time-consuming. 2.3. Determination of the fragment mass and fragment mass distributions The change of the medium dimension b is a result of the deformation as well as the breakage processes taking
place inside the zone of comminution. In comparison to that, the fragment mass is altered by breakage alone. Therefore, for the evaluation of the processes taking place during the stressing, the measurement of the fragment mass of every single fragment and the subsequent calculation of the fragment mass distributions Q3 Ž m. is obligatory. Using this method, Kirchner w13x was able to demonstrate that a deformation of the material takes place before breakage occurs. The former causes the medium fragment size to decrease without any loss of fragment mass during the first stage of comminution ŽFig. 9.. The calculation of the fragment mass distributions from the fragment size distributions is impossible since there has to be found a correlation for every single fragment shape class ŽFig. 10a.. However, the portions of the fragment shape classes vary strongly within one product depending on the size fraction under examination ŽFig. 10b.. Moreover, they depend on the material properties and the conditions during comminution.
Fig. 10. Fragment mass versus fragment size with fragment shape as a parameter Ža. and portions of the shape classes within the fragment size fractions Žb. Žzinc, initial size of test bodies Ž200 = 200 = 1. mm3 ; comminution with a small-scale vertical shaft shredder at a circumferential speed of 50 mrs..
184
St. Sander et al.r Powder Technology 122 (2002) 177–187
Fig. 11. Specific energy per unit surface area wA versus the increase in surface area for zinc and steel St14 Ža. and crack length distributions with the specific energy consumption as a parameter Žb. Žinitial size of test bodies Ž200 = 200 = 1. mm3 ; comminution with a small-scale horizontal shaft shredder at a circumferential speed of 50 mrs..
In this context, the device utilised for the determination of the fragment size at ATRec has proven to be well suited, since the mass of every single fragment is measured too. Consequently, the fragment mass distributions and the fragment size distributions are available simultaneously.
the research of the microprocesses and principles of comminution of metals.
3. Determination of characteristics describing the deformation processes
2.4. Determination of the crack and fracture surface area The increase in surface area A Br caused by comminution represents an important characteristic for describing the result of the process. It is essential to emphasise, that in the case of metals, A Br results from the surface area of cracks and fractures. It can only be determined by bending open the fragments and measuring the length of fractures and cracks. By multiplication with the thickness, the surface area can be calculated. Increase in surface area attributable to abrasion cannot be taken into consideration. The characteristic obtained is well suited to measure the progress of comminution. Looking at Fig. 11a, the specific energy per unit surface area wA required for the increase in surface area under equal conditions can be compared for the steel St14 and zinc. The courses of the curves are similar. Therefore, a similar behaviour of both materials during comminution can be assumed. The evaluation of the crack lengths LC plays an important role in the investigation of the microprocesses. After assigning to crack length classes, the crack length distribution of the quantity type crack surface area Q 2 Ž LC . can be determined. As can be derived from Fig. 11b, at the beginning of the stressing Ž wm s 10–20 kJrkg., a predominant portion of the cracks is shorter than 20 mm. With increasing specific energy consumption Ž wm s 30–40 kJrkg., the portion of the longer cracks rises. At a value of wm s 55 kJrkg, no cracks longer than LC s 60 mm are observed. It seems reasonable that these had been extended until breakage. Finally it has to be stressed that the named methods are too time-consuming to be routinely employed; but their purposeful utilisation can provide valuable information for
3.1. Determination of the bending lengths and bending radii distributions The deformation processes mentioned above are mainly caused by bending, buckling and torsion. As a result, linear kinks are formed in the platy material, which also can branch or cross each other. The sum of the lengths of these kinks is called bending length L B . This characteristic can only be determined by measuring using flexible steel belt rulers. In most cases, the fragments have to be bent open at least partially. In order to estimate the intensity of the deformation a kink was subject to, the bending radii
Fig. 12. Bending radii distributions with the specific energy consumption as a parameter Žinitial size of test bodies Ž200=200=1. mm3 ; comminution with a small-scale horizontal shaft shredder at a circumferential speed of 50 mrs..
St. Sander et al.r Powder Technology 122 (2002) 177–187
185
material of these spots is damaged stronger. Again, these investigations are too time-consuming to be applied generally. The results, however, help to gain a better understanding of the processes taking place. 3.2. Determination of the degree of bending For each fragment of the mass m, the equivalent fragment area A eq can be calculated from the wall thickness of the feed c and the material density r M using Eq. Ž4.: m A eq s . Ž 4. rM c
Fig. 13. Degree of bending of single fragment mass fractions as a function of the specific energy consumption Žaccording to Ref. w14x. Žinitial size of test bodies Ž200=200=1. mm3 ; comminution with a small-scale horizontal shaft shredder at a circumferential speed of 50 mrs..
distributions have to be determined. For that, all ranges of the kinks that have a bending angle of more than 908 are examined with radii gauges. The bending radii classes are equivalent to the gradation of these gauges. The lengths of the kinks having the corresponding bending radius can be assigned to the mentioned classes. Eventually, the bending radii distribution of the quantity type length Q1Ž r B . can be presented. When comparing products obtained after subjecting them to a varying amount of specific energy, it becomes obvious that with increasing specific energy, the bending radii become smaller ŽFig. 12.. This implies that the intensified bending results in sharper kinks and, hence, the
With this characteristic and the area of projection of the fragment A Pr as well as the area of projection of the sphere of equal mass A Sph , the degree of bending B can be determined according to w14x: Bs
A eq y A Pr A eq y A Sph
.
Ž 5.
The latter is equal to 0 for an even plate and equal to 1 for a dense sphere. Therefore, B is well suited for describing the deformation. If, for example, the degree of bending of single fragment mass fractions are regarded dependent on the specific energy consumption ŽFig. 13., it becomes obvious that the smallest fragments formed by breakage are hardly deformed. However, a higher supply of specific energy results in an increasing degree of bending in the smaller fragment mass fractions. Because this characteristic does not depend on any variables apart from the fragment mass and the area of projection of the fragments, it can easily be calculated from the results obtained determining the fragment size and mass.
Fig. 14. Height of a bulk of monodisperse spheres before Ža. and after Žb. embedding a set of fragments Žschematically..
St. Sander et al.r Powder Technology 122 (2002) 177–187
186
3.3. Determination of the degree of compaction As mentioned above, the degree of bending is suited to describe the deformation, but it cannot be utilised in order to determine the resulting compaction. For this purpose, the degree of compaction K has been introduced. This characteristic represents a fragment density r Fr related to the material density r M : r Fr K s r Fr ,rel s . Ž 6. rM As the fragment density is the quotient of the fragment mass m and the envelope volume V E , the degree of compaction can be written as m Ks . Ž 7. r M VE It is obvious that the degree of compaction is dependent on the method used for determining the envelope volume. For that, two methods have proven to be practicable: v
v
the embedding of fragments into bulks of monodisperse spheres and the calculation of the ellipsoid of rotation having the dimensions aell and bell w14x.
The former method is based on the fact that the embedding of fragments into a bulk of monodisperse spheres results in a change in its bulk volume. This change in bulk volume can be assumed to be a good estimate of the envelope volume of the fragments embedded. Hence, the degree of compaction K BS can be determined from the difference of the heights Ž H1 y H0 ., the inner diameter of the vessel D i and the mass of fragments embedded ŽFig. 14. using K BS s
4m
r M p D i2 Ž H1 y H0 .
.
Ž 8.
This method is sufficiently accurate only if employed for sets of fragments, which have to be a representative sample of the product under examination. Moreover, the size of the spheres and of the vessel has to be adapted to the fragment size. As a result, an integral value of the envelope volume of the embedded set of fragments is obtained. In comparison to that, the method of calculating the envelope volume is based on the assumption that the volume of the ellipsoid having the dimensions aell and bell provides a good approximation of VE . The degree of compaction K ell then can be calculated using K ell s
6m 2 pr M aell bell
.
Ž 9.
Again, this characteristic can be calculated from the results obtained determining the fragment size and mass. Using
Fig. 15. Distributions of the degree of compaction with the stressing time as a parameter Žinitial size of test bodies Ž200=200=1. mm3 ; batch tests using a small-scale horizontal shaft shredder at a circumferential speed of 50 mrs..
this method, it can be demonstrated that with increasing time of stressing, the fragments are compacted more intensive ŽFig. 15.. It must be stressed that for strongly compacted and very small fragments, values of K ell ) 1 can occur. Using the method of embedding of fragments into bulks of monodisperse spheres, however, high values of K BS are obtained for even plates. Therefore, it has to be decided in every case which of the methods can be utilised. Both degrees of compaction introduced can be calculated from each other within the range of 0.2 F K BS F 0.6 by means of K BS s 0.8818 K ell q 0.1641.
Ž 10 .
4. Summary During the comminution of metals, deformation and breakage occurs simultaneously. Therefore, characteristics both for describing the results of comminution and of the deformation processes makes the characterisation of the products obtained a highly sophisticated task. In correspondence to the characterisation of minerals, the former task is solved by the determination of the fragment size and fragment mass distributions, the fragment shape and as well as the increase in surface area. However, the methods utilised are different. For the determination of the fragment size distributions, sieving has shown to be of limited applicability. In contradiction to that, the utilisation of image analysis has proven to be successful. However, the known commercial devices cannot be used. It rather has to be taken care that the largest and medium dimensions a and b are visible in the projection of the fragments. For many purposes, the determination of the fragment mass distributions is essential in order to distinguish the effects of deformation and break-
St. Sander et al.r Powder Technology 122 (2002) 177–187
age. Having this in mind, a device was assembled and tested successfully, with which every single fragment can be weighed and analysed regarding its fragment size simultaneously. For the evaluation of the fragment shape, it was found to be of advantage to use a phenomenological classification suited to describe the shape as well as the state of compaction. The determination of the increase in surface area is most time-consuming since it only can be measured using flexible steel belt rulers after bending open the fragments. The evaluation of the deformation processes can be conducted by means of the bending radii distribution and the bending length, the degree of bending as well as the degree of compaction. The latter two characteristics can easily be calculated from those obtained in determining the fragment size and mass. References w1x M.H. Pahl, G. Schadel, H. Rumpf, Zusammenstellung von Teil¨ formbeschreibungsmethoden. Aufbereitungstechnik 14 Ž1973. 5, S. 257–264; 10, S. 672–683; 11, S. 759–764. w2x R. Davies, A simple feature–space representation of particle shape. Powder Technology 12 Ž1975. S. 111–124. w3x G. Schubert, Ergebnisse verfahrenstechnischer Untersuchungen an einer Stahlschrott-Shredderanlage. Neue Hutte ¨ 25 Ž1980. 6, S. 201– 206.
187
w4x G. Schubert, Aufbereitung metallischer Sekundarrohstoffe: 1. Au¨ flage. Dt. Verlag fur ¨ Grundstoffindustrie, Leipzig, 1984. w5x G. Schubert, Mechanische Zerkleinerung der GußeisenschrotteGrundlagen. Neue Hutte ¨ 20 Ž1975., S. 235–242. w6x G. Schubert, H. Schubert, Grundlagenuntersuchungen zur Zerkleinerung metallischer Sekundarrohstoffe. Dechema-Mono¨ graphien, Nr. 1549–1575, Bd. 79, S. 167–182. w7x K. Gopel, G. Schubert, Zerkleinerung der Metallspane. ¨ ¨ Neue Hutte ¨ 37 Ž1992. 3, S. 93–97. w8x J. Kirchner, G. Schubert, Comminution of scrap and metals by shredders. Proceedings of the XX. IMPC, 21–26 Sept., 1997, Aachen, Band 2. 1997, S. 37–47. w9x G. Unland, T. Folgner, R. Stenger, Bestimmung der Kornform und Bruchflachigkeit. ZKG International 51 Ž1998. 12. ¨ w10x W. Rasemann, C. Preuße, A. Muller, Zum Einfluß der Teilchenform, ¨ Teilchengroße ¨ und ihrer Mischungsanteile auf die Reproduzierbarkeit der Bewertung von stuckigen und kornigen Mischgutern. ¨ ¨ ¨ Aufbereitungstechnik 38 Ž1997. 3, S. 418–428. ¨ w11x T. Kuntzsch, Ubertragung verschiedener Methoden der Stuckgroßen¨ ¨ analyse auf Zerkleinerungsprodukte von Stoffen mit nicht-sprodem ¨ Verhalten, Thesis, Freiberg University of Mining and Technology, 1999. w12x G.T. Vickers, The projected areas of ellipsoids and cylinders. Powder Technology 86 Ž1997., S. 195–200. w13x J. Kirchner, Mikroprozesse und Einflußgroßen bei der Zerkleinerung ¨ der Schrotte und Metalle in Shreddern mit horizontal angeordnetem Rotor, PhD Thesis, Freiberg University of Mining and Technology, 2000. w14x F. Silbermann, Grundlagenuntersuchungen zu den im Zerkleinerungsraum des Shredders auftretenden Beanspruchungen, Thesis, Freiberg University of Mining and Technology, 1998.
Characterisation of fragments produced by the comminution of metals especially considering the fragment shape St. Sander, G. Schubert ) , G. Timmel Institute of Mechanical Process Engineering and Mineral Processing, Freiberg UniÕersity of Mining and Technology, Agricolastraße 1, D-09599 Freiberg, Germany Received 25 July 2000; received in revised form 6 October 2000; accepted 25 October 2000
Abstract During the comminution of metals, intensive deformation of the material takes place resulting in wide fragment size distributions and a large range of fragment shapes and states of compactness. Thus, the characterisation of the products is a very demanding task. In this paper, the most common methods for the determination of characteristics describing the results of the comminution as well as of the deformation are explained. q 2002 Elsevier Science B.V. All rights reserved. Keywords: Characterisation; Comminution; Shredders; Recycling
1. Introduction The comminution of materials with nonbrittle behaviour, especially of metals, plays an important role in recycling processes. The scientific investigation of these processes is—in comparison to the comminution of brittle materials—still at the beginning. The fact that the characterisation of the fragments produced during comminution is very difficult may be one of the reasons for that. The Chair of Mineral Processing and Recycling ŽATRec. at the Freiberg University of Mining and Technology has attended to the basic research in the field of the comminution of metals and scrap in shredders of the swing hammer mill type for a longer period of time. Platy test bodies of metal sheets are usually utilised as model materials. One essential result of the present research is the finding that very intensive bending and other deformation processes, which cause the formation of initial flaws and crack initiation, take place before a real fragmentation can occur inside this kind of equipment. Only as a second step, the cracks formed propagate until breakage. Due to this kind of stressing, the fragments produced are of very wide fragment size distributions, a large range of fragment shapes and—depending on the material properties and the conditions inside the zone of comminution—of a varying state of compactness. Therefore, the determination of the
properties of these fragments is a very demanding task. Besides the characteristics usually utilized in order to describe the results of the comminution, such as fragment size and fragment mass distributions, fragment shape and crack and fracture surface area, respectively, characteristics describing the compaction have to be determined too. These are the bending radii distribution, the bending length, the degree of bending and the degree of compaction, which is equal to a relative fragment density. The scope of this paper is to introduce the determination methods of the characteristics listed in Table 1 and to judge their applicability.
2. Determination of characteristics describing the results of comminution 2.1. Description of the fragment shape The fragment shape is an important granulometric property which affects most technological processes. Therefore, a great number of investigations have been done in order to describe this characteristic in a suitable manner. Frequently, the determination of shape factors is based on: v
)
Corresponding author. Fax: q49-3731-39-2815. E-mail address: [email protected] ŽG. Schubert..
v
the evaluation of the triaxial dimension relationships, the comparison between the properties Žsuch as area of projection, volume, etc.. of the irregularly shaped
0032-5910r02r$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 Ž 0 1 . 0 0 4 1 4 - 4
St. Sander et al.r Powder Technology 122 (2002) 177–187
178
Table 1 Characteristics describing the results of the comminution and of the compaction of fragments resulting from the stressing of metals Characteristic quantity
Determination method
Characteristics describing the results of the comminution Fragment shape Assignment to a phenomenologically determined classification of fragment shapes v Sieve analysis Fragment sizerfragment size distributions v Image analysis Fragment massrfragment mass distributions Weighing of single fragments Crack lengthrcrack length distribution Measuring after bending open using flexible steel belt rulers Crack and fracture surface area Measuring after bending open using flexible steel belt rulers Characteristics describing the compaction of the fragments Bending radiirbending radii distribution Measuring using gauges Bending length Measuring using flexible steel belt rulers Degree of bending Calculation from area of projection and mass v Calculation from area of projection and mass Degree of compaction v Embedding of fragments into a bulk of monodisperse spheres
v
fragment and those of a geometric body Žsuch as the sphere with equal mass. or the evaluation of the change in behaviour Že.g. settling velocity. as a result of the irregular shape.
Other concepts deliver characteristics describing the so-called roundness by measuring the radius of curvature of the projection of the fragments w1,2x. All the shape factors mentioned above are inadequate if applied to fragments formed by comminution of metals. This is due to the fact that the different fragment shapes are results of the varying states of compaction, too. Schubert w3–8x has been dealing with the comminution of metals and scraps for a considerable period of time. In
order to characterise the products of comminution, he suggested to assign the fragments to the shape classification shown in Fig. 1. For the process-related evaluation, this phenomenologically determined classification is suited better than the utilisation of shape factors, which, moreover, are difficult to determine. Starting from that, for the following investigations, a fragment shape classification was used in order to describe the products of the comminution, which is not only suitable for shape characterisation but also helps to distinguish the state of compaction ŽFig. 2.. Since the portions of the fragment shapes present in a given product allow conclusions concerning the deformation and breakage processes taking place, this concept especially provides advantages
Fig. 1. Shape classification for the characterisation of products of comminution Žaccording to Schubert.: Ža. compact Žcubic.; Žb. compact–strongly compacted; Žc. platy–even; Žd. platy–slightly to strongly deformed; Že. rod-shaped–straight; Žf. rod-shaped–slightly to strongly deformed.
St. Sander et al.r Powder Technology 122 (2002) 177–187
179
Fig. 2. Shape classification of fragments formed by comminution of sheet metals: Ža. platy–even; Žb. platy–slightly deformed; Žc. platy–strongly deformed; Žd. platy–strongly deformed, partially compacted; Že. compacted; Žf. spherical.
for the evaluation of comminution tests with platy test bodies. 2.2. Determination of the fragment size and the fragment size distribution Every fragment can be described by its three dimensions a, b and c, which represent the edge lengths of the enveloping parallelepiped of smallest volume ŽFig. 3.. By definition, a G b G c has to be fulfilled. In order to make the determination of the fragment size practicable, the medium dimension b, which is of significance for the sieve analysis, was assumed to be a close estimate of the fragment size x. The objective of the investigations was to find a method for the determination of dimension b that not only has a high accuracy but is also time-saving. Therefore, as a reference for judging the examined methods, fragment size distributions were used, which had been determined by
sticking the fragments through a geometric series of square perforated plates. Care was taken so that the fragments passed the apertures without abutments according to their dimension b. In this paper, this procedure will be called Adirect measurementB. As test materials, products formed from platy tin sheet test bodies of the initial dimensions Ž a = b = c . s Ž200 = 200 = 1. mm3 , which had been stressed at different periods of time Ž3, 8, 15, 30 and 60 s. in a small-scale horizontal shaft shredder, were utilised. The determination of the fragment size distributions Q 3 Ž b . was conducted by means of two different kinds of test sieving equipment, a suspended sieving machine producing a circular movement in the horizontal plane and a laboratory trommel screen, as well as two devices using image analysis. The suspended sieving machine is equipped with 400-mm-diameter sieves. It is suspended by a rope and the circular movement in the horizontal plane is caused by the action of an unbalance drive. The assumption can be made that in this case, the classification takes place according to dimension a or in between a and b. Due to the height of the sieves, the machine is equipped to handle a maximum of five sieves at a time resulting in six fractions of fragment size. The sieving time was limited to 10 min, because after that, the portion of the finest size fraction would not increase more than 0.2%rmin. The laboratory trommel screen operates discontinuously and is equipped with two octahedral trommels Žwidest diameter D s 570 mm and D s 960 mm.. The aperture size of the bigger trommel is w G 20 mm and of the smaller one is w F 16 mm. Both were operated at a rotational speed of n s 0.8 n crit , in which the critical rotational speed can be derived from n crit s
Fig. 3. Fragment of the fragment shape class Aplaty –strongly deformedB with its three dimensions.
(
g 2p 2 D
.
Ž 1.
Therewith, cataracting and, consequently, the separation according to dimension b should be secured. Since the test
180
St. Sander et al.r Powder Technology 122 (2002) 177–187
Fig. 4. Devices utilised for image analysis: Ža. Haver & Boecker CPA-4 Žaccording to Ref. w9x.; Žb. Proposal of ATRec.
sieving caused the fragments to be deformed or even to be secondarily broken, the sieving time was limited to 5 min per fraction. During the last years, devices using image analysis have become an alternative to be taken into account as compared with sieving. The initial objective was to employ a commercially available image analyser for the characterisation of fragments formed by comminution of sheet metals. Because of its wide measuring range, the CPA-4 ŽFig. 4a. manufactured by Haver & Boecker in Oelde, Germany was examined in detail. In this device, the material is dropped past a linear source of light Ž3. after being transported from the feed bin Ž1. by means of a vibrating conveyor Ž2.. The line camera Ž4. installed opposite to the source of light is connected to the computer Ž5., which is needed for evaluating the data and for controlling purposes w9x. The device was operated in the shape analysis mode without presupposing of the material density. In this mode, the area of projection reconstructed from the line images are used for measurement. For further investigations, the cumulative distributions of the spheres of equal area of projection of the quantity type volume and number of fragment, respectively, were obtained. In addition to the products from the batch tests concerning the comminution kinetics, spheres and cylinders as well as fragments of approximately equal size but varying fragment shapes were analysed. Since problems appeared during determination of the fragment size using the equipment mentioned above, an apparatus using image analysis was assembled in order to meet the specific requirements of the characterisation of the fragments formed by comminution of metals ŽFig. 4b.. It consists of a scales Ž1. utilised for measuring the fragment mass, above which a high-resolution CCD matrix camera Ž2. is installed. The fragments are laid on a flat source of light Ž3. installed at the scales in such a way that dimensions a and b are visible in the projection. The signals of the camera and the scales are processed by means of a PC Ž4.. The software Scion Image of Scion is used for evaluating the images with respect to the fragment
area of projection and dimensions aell and bell of the best fitting ellipse ŽFig. 5.. The latter has an area equal to the area of projection of the fragment and, moreover, maximally overlaps the projection of the fragment. Its dimension bell is assumed to be a good estimation for dimension b of the fragment. Exemplary for the results obtained in the determination of the fragment size distributions using the aforesaid equipment, the mean fragment size b50.3 can be seen in Table 2 as a function of the stressing time. Moreover, the deviations of the values from those obtained by direct measurement DŽ b50.3 . are to be found, which can be calculated by
D Ž b50 .3 . s
Ž b50 .3,direct measurement y b50.3,method . b50 .3,direct measurement
100%.
Ž 2. Due to the low height of the sieves, the suspended sieving machine could not be employed for the comparably coarse fragments obtained after a stressing time of only 3 s. The deviations of the results from those obtained by
Fig. 5. Dimensions aell and bell of the best fitting ellipse.
St. Sander et al.r Powder Technology 122 (2002) 177–187
181
Table 2 Mean fragment size b50.3 as a function of stressing time—comparison of the results obtained using different kinds of equipment and deviation of the results from those obtained by direct measurement DŽ b50.3 . Stressing time Žs.
3 8 15 30 60
Specific energy consumption ŽkJrkg.
Direct measurement
Mean fragment size b50.3 Žmm. Suspended sieving machine
Trommel screen
Haver & Boecker CPA-4
Proposal of ATRec
48.3 112.3 181.6 301.6 484.3
92.8 24 13.2 8.2 6.3
n.d. 20.5 11.6 7.8 6.1
54.2 21.2 13.0 8.4 6.2
52.2 25.5 13.7 8.3 6.2
91.5 22.5 13.4 8.0 6.1
Deviation from the values obtained by direct measurement DŽ b50.3 . Ž%. Suspended sieving machine
Trommel screen
Haver & Boecker CPA-4
Proposal of ATRec
n.d. 14.6 12.1 4.9 3.2
41.6 11.7 1.5 y2.4 1.6
43.8 y6.3 y3.8 y1.2 1.6
1.4 6.5 y1.7 2.7 3.2
Zinc, initial size of test bodies Ž200 = 200 = 1. mm3 ; batch tests with a small-scale horizontal shaft shredder at a circumferential speed of 50 mrs; n.d.s not determinable.
direct measurement are relatively high for longer-stressed products, too. The values of DŽ b50.3 . decrease with increasing stressing time but still are the highest if compared to those obtained using the other equipment. The reproducibility of the results is low even for the product obtained at a stressing time of 15 s, as was found in investigations conducted according to Rasemann w10x. Because of the results shown, it can be stated that test sieving utilising a suspended sieving machine, producing a circular movement in the horizontal plane, does not provide reliable characteristics for fragments formed by comminution of metals. Problems also arose if the trommel screen was employed to products obtained after short stressing times Ž3 and 8 s.. The fragments were subject to deformation and in some cases, breakage occurred. Therefore, the values of DŽ b50.3 . are high for these products. The fragment size of the materials stressed at longer times is smaller and most of the fragments are more compact. Consequently, the
deviations of the results from the values obtained by direct measurement are considerably smaller. Since only one fraction can be obtained at a time, this method is very time consuming. Moreover, its applicability is limited to smaller, more compact fragments. Having this in mind, the utilisation of a trommel screen does not seem to represent a real alternative as compared with the direct measurement. The results of the determination of the fragment size distributions using the Haver & Boecker CPA-4, which is designed for on-line applications, are in good agreement with the values obtained by direct measurement for products obtained at stressing times of t B G 8 s. In contradiction to that, the deviations of DŽ b50.3 . s 43.8% are very high for products stressed at shorter times Ž3 s.. In order to examine this effect, monodisperse bodies of known dimensions were analysed. For steel and glass spheres, the results are in good agreement with the diameters ŽFig. 6a.. The plot of the fragment size distribution Q 0 Ž x A . measured at cylindrical plates Ždiameter D s 2
Fig. 6. Size distributions Q0 Ž xA . measured using the Haver & Boecker CPA-4 Žaccording to Ref. w11x.: Ža. glass Ž D s 8 mm, D s 20 mm. and steel Ž D s 13.5 mm. spheres; Žb. cylindrical plates of plastic Ž D s 20 mm, L s 1.25 mm. Žcomputed distribution: random orientation, according to Vickers w12x..
182
St. Sander et al.r Powder Technology 122 (2002) 177–187
Fig. 7. Size distributions Q0 Ž xA . measured for different feeding orientations using the Haver & Boecker CPA-4 Žaccording to Ref. w11x.: Ža. cylinders of plastic Ž D s 20 mm, L s 40 mm.; Žb. cylinders of plastic Ž D s 20 mm, L s 120 mm. Žcomputed distributions: random orientation, according to Vickers w12x..
mm, height H s 1.25 mm. shows the expected course ŽFig. 6b.. The latter matches well with the one calculated according to Vickers w12x for a random orientation. However, it becomes obvious that it is impossible to derive the real dimensions of the plates from the plot alone. Investigations conducted with cylinders of equal diameter Ž D s 20 mm. but different lengths Ž L s 40 mm and L s 120 mm. showed that an additional influence of the feeding orientation has to be taken into account for this irregularly shaped test bodies ŽFig. 7.. For both kinds of test bodies, the fragment size distributions Q 0 Ž x A . of the cylinders fed lengthwise and transverse significantly vary from each other. Moreover, they do not match to the computed distributions for random orientation as well as the ones of the cylindrical plates. Certainly, there is no clue regarding the real dimensions of the cylinders to be derived from the plots.
For further investigations, fragments which are of approximately equal size but can be assigned to different fragment shape classes were singled out and analysed separately. From the results shown in Fig. 8a, it becomes obvious that the deviations of the determined fragment sizes b50.3 from the values obtained by direct measurement are very high for platy–even and platy–slightly deformed fragments. The sphericities c U,3 determined simultaneously during the size analysis, which is calculated from the area of projection A and the circumference U using
CU ,3 s
4p A U2
.
Ž 3.
can be seen for the examined fragment shape classes in Fig. 8b. It becomes clear that this device is of limited
Fig. 8. Deviations of the fragment size from the values obtained by direct measurement Ža. and mean sphericity Žb. of measurements conducted with the Haver & Boecker CPA-4 analysing fragments of different fragment shape classes Žzinc, wall thickness 1 mm; batch test with a small-scale horizontal shaft shredder at a circumferential speed of 50 mrs..
St. Sander et al.r Powder Technology 122 (2002) 177–187
183
Fig. 9. Fragment size b50 Ža. and fragment mass m 50 Žb. versus specific energy consumption with initial size of the test bodies as a parameter Žzinc, wall thickness 1 mm; batch test with a small-scale horizontal shaft shredder at a circumferential speed of 50 mrs..
value only for the characterisation of the products obtained by comminution of metals. The device utilised for the determination of the fragment size at the Chair of Mineral Processing and Recycling ŽATRec. shows relatively low deviations from the values obtained by direct measurement for all analysed products ŽTable 2.. The assumption that the dimension bell of the best fitting ellipse is a good estimate for the dimension b of the fragments has proven to be applicable for products obtained by comminution of metals. First results for products of wood are similarly promising. In the future, a further automation of the measurement is planned, which will make this method less time-consuming. 2.3. Determination of the fragment mass and fragment mass distributions The change of the medium dimension b is a result of the deformation as well as the breakage processes taking
place inside the zone of comminution. In comparison to that, the fragment mass is altered by breakage alone. Therefore, for the evaluation of the processes taking place during the stressing, the measurement of the fragment mass of every single fragment and the subsequent calculation of the fragment mass distributions Q3 Ž m. is obligatory. Using this method, Kirchner w13x was able to demonstrate that a deformation of the material takes place before breakage occurs. The former causes the medium fragment size to decrease without any loss of fragment mass during the first stage of comminution ŽFig. 9.. The calculation of the fragment mass distributions from the fragment size distributions is impossible since there has to be found a correlation for every single fragment shape class ŽFig. 10a.. However, the portions of the fragment shape classes vary strongly within one product depending on the size fraction under examination ŽFig. 10b.. Moreover, they depend on the material properties and the conditions during comminution.
Fig. 10. Fragment mass versus fragment size with fragment shape as a parameter Ža. and portions of the shape classes within the fragment size fractions Žb. Žzinc, initial size of test bodies Ž200 = 200 = 1. mm3 ; comminution with a small-scale vertical shaft shredder at a circumferential speed of 50 mrs..
184
St. Sander et al.r Powder Technology 122 (2002) 177–187
Fig. 11. Specific energy per unit surface area wA versus the increase in surface area for zinc and steel St14 Ža. and crack length distributions with the specific energy consumption as a parameter Žb. Žinitial size of test bodies Ž200 = 200 = 1. mm3 ; comminution with a small-scale horizontal shaft shredder at a circumferential speed of 50 mrs..
In this context, the device utilised for the determination of the fragment size at ATRec has proven to be well suited, since the mass of every single fragment is measured too. Consequently, the fragment mass distributions and the fragment size distributions are available simultaneously.
the research of the microprocesses and principles of comminution of metals.
3. Determination of characteristics describing the deformation processes
2.4. Determination of the crack and fracture surface area The increase in surface area A Br caused by comminution represents an important characteristic for describing the result of the process. It is essential to emphasise, that in the case of metals, A Br results from the surface area of cracks and fractures. It can only be determined by bending open the fragments and measuring the length of fractures and cracks. By multiplication with the thickness, the surface area can be calculated. Increase in surface area attributable to abrasion cannot be taken into consideration. The characteristic obtained is well suited to measure the progress of comminution. Looking at Fig. 11a, the specific energy per unit surface area wA required for the increase in surface area under equal conditions can be compared for the steel St14 and zinc. The courses of the curves are similar. Therefore, a similar behaviour of both materials during comminution can be assumed. The evaluation of the crack lengths LC plays an important role in the investigation of the microprocesses. After assigning to crack length classes, the crack length distribution of the quantity type crack surface area Q 2 Ž LC . can be determined. As can be derived from Fig. 11b, at the beginning of the stressing Ž wm s 10–20 kJrkg., a predominant portion of the cracks is shorter than 20 mm. With increasing specific energy consumption Ž wm s 30–40 kJrkg., the portion of the longer cracks rises. At a value of wm s 55 kJrkg, no cracks longer than LC s 60 mm are observed. It seems reasonable that these had been extended until breakage. Finally it has to be stressed that the named methods are too time-consuming to be routinely employed; but their purposeful utilisation can provide valuable information for
3.1. Determination of the bending lengths and bending radii distributions The deformation processes mentioned above are mainly caused by bending, buckling and torsion. As a result, linear kinks are formed in the platy material, which also can branch or cross each other. The sum of the lengths of these kinks is called bending length L B . This characteristic can only be determined by measuring using flexible steel belt rulers. In most cases, the fragments have to be bent open at least partially. In order to estimate the intensity of the deformation a kink was subject to, the bending radii
Fig. 12. Bending radii distributions with the specific energy consumption as a parameter Žinitial size of test bodies Ž200=200=1. mm3 ; comminution with a small-scale horizontal shaft shredder at a circumferential speed of 50 mrs..
St. Sander et al.r Powder Technology 122 (2002) 177–187
185
material of these spots is damaged stronger. Again, these investigations are too time-consuming to be applied generally. The results, however, help to gain a better understanding of the processes taking place. 3.2. Determination of the degree of bending For each fragment of the mass m, the equivalent fragment area A eq can be calculated from the wall thickness of the feed c and the material density r M using Eq. Ž4.: m A eq s . Ž 4. rM c
Fig. 13. Degree of bending of single fragment mass fractions as a function of the specific energy consumption Žaccording to Ref. w14x. Žinitial size of test bodies Ž200=200=1. mm3 ; comminution with a small-scale horizontal shaft shredder at a circumferential speed of 50 mrs..
distributions have to be determined. For that, all ranges of the kinks that have a bending angle of more than 908 are examined with radii gauges. The bending radii classes are equivalent to the gradation of these gauges. The lengths of the kinks having the corresponding bending radius can be assigned to the mentioned classes. Eventually, the bending radii distribution of the quantity type length Q1Ž r B . can be presented. When comparing products obtained after subjecting them to a varying amount of specific energy, it becomes obvious that with increasing specific energy, the bending radii become smaller ŽFig. 12.. This implies that the intensified bending results in sharper kinks and, hence, the
With this characteristic and the area of projection of the fragment A Pr as well as the area of projection of the sphere of equal mass A Sph , the degree of bending B can be determined according to w14x: Bs
A eq y A Pr A eq y A Sph
.
Ž 5.
The latter is equal to 0 for an even plate and equal to 1 for a dense sphere. Therefore, B is well suited for describing the deformation. If, for example, the degree of bending of single fragment mass fractions are regarded dependent on the specific energy consumption ŽFig. 13., it becomes obvious that the smallest fragments formed by breakage are hardly deformed. However, a higher supply of specific energy results in an increasing degree of bending in the smaller fragment mass fractions. Because this characteristic does not depend on any variables apart from the fragment mass and the area of projection of the fragments, it can easily be calculated from the results obtained determining the fragment size and mass.
Fig. 14. Height of a bulk of monodisperse spheres before Ža. and after Žb. embedding a set of fragments Žschematically..
St. Sander et al.r Powder Technology 122 (2002) 177–187
186
3.3. Determination of the degree of compaction As mentioned above, the degree of bending is suited to describe the deformation, but it cannot be utilised in order to determine the resulting compaction. For this purpose, the degree of compaction K has been introduced. This characteristic represents a fragment density r Fr related to the material density r M : r Fr K s r Fr ,rel s . Ž 6. rM As the fragment density is the quotient of the fragment mass m and the envelope volume V E , the degree of compaction can be written as m Ks . Ž 7. r M VE It is obvious that the degree of compaction is dependent on the method used for determining the envelope volume. For that, two methods have proven to be practicable: v
v
the embedding of fragments into bulks of monodisperse spheres and the calculation of the ellipsoid of rotation having the dimensions aell and bell w14x.
The former method is based on the fact that the embedding of fragments into a bulk of monodisperse spheres results in a change in its bulk volume. This change in bulk volume can be assumed to be a good estimate of the envelope volume of the fragments embedded. Hence, the degree of compaction K BS can be determined from the difference of the heights Ž H1 y H0 ., the inner diameter of the vessel D i and the mass of fragments embedded ŽFig. 14. using K BS s
4m
r M p D i2 Ž H1 y H0 .
.
Ž 8.
This method is sufficiently accurate only if employed for sets of fragments, which have to be a representative sample of the product under examination. Moreover, the size of the spheres and of the vessel has to be adapted to the fragment size. As a result, an integral value of the envelope volume of the embedded set of fragments is obtained. In comparison to that, the method of calculating the envelope volume is based on the assumption that the volume of the ellipsoid having the dimensions aell and bell provides a good approximation of VE . The degree of compaction K ell then can be calculated using K ell s
6m 2 pr M aell bell
.
Ž 9.
Again, this characteristic can be calculated from the results obtained determining the fragment size and mass. Using
Fig. 15. Distributions of the degree of compaction with the stressing time as a parameter Žinitial size of test bodies Ž200=200=1. mm3 ; batch tests using a small-scale horizontal shaft shredder at a circumferential speed of 50 mrs..
this method, it can be demonstrated that with increasing time of stressing, the fragments are compacted more intensive ŽFig. 15.. It must be stressed that for strongly compacted and very small fragments, values of K ell ) 1 can occur. Using the method of embedding of fragments into bulks of monodisperse spheres, however, high values of K BS are obtained for even plates. Therefore, it has to be decided in every case which of the methods can be utilised. Both degrees of compaction introduced can be calculated from each other within the range of 0.2 F K BS F 0.6 by means of K BS s 0.8818 K ell q 0.1641.
Ž 10 .
4. Summary During the comminution of metals, deformation and breakage occurs simultaneously. Therefore, characteristics both for describing the results of comminution and of the deformation processes makes the characterisation of the products obtained a highly sophisticated task. In correspondence to the characterisation of minerals, the former task is solved by the determination of the fragment size and fragment mass distributions, the fragment shape and as well as the increase in surface area. However, the methods utilised are different. For the determination of the fragment size distributions, sieving has shown to be of limited applicability. In contradiction to that, the utilisation of image analysis has proven to be successful. However, the known commercial devices cannot be used. It rather has to be taken care that the largest and medium dimensions a and b are visible in the projection of the fragments. For many purposes, the determination of the fragment mass distributions is essential in order to distinguish the effects of deformation and break-
St. Sander et al.r Powder Technology 122 (2002) 177–187
age. Having this in mind, a device was assembled and tested successfully, with which every single fragment can be weighed and analysed regarding its fragment size simultaneously. For the evaluation of the fragment shape, it was found to be of advantage to use a phenomenological classification suited to describe the shape as well as the state of compaction. The determination of the increase in surface area is most time-consuming since it only can be measured using flexible steel belt rulers after bending open the fragments. The evaluation of the deformation processes can be conducted by means of the bending radii distribution and the bending length, the degree of bending as well as the degree of compaction. The latter two characteristics can easily be calculated from those obtained in determining the fragment size and mass. References w1x M.H. Pahl, G. Schadel, H. Rumpf, Zusammenstellung von Teil¨ formbeschreibungsmethoden. Aufbereitungstechnik 14 Ž1973. 5, S. 257–264; 10, S. 672–683; 11, S. 759–764. w2x R. Davies, A simple feature–space representation of particle shape. Powder Technology 12 Ž1975. S. 111–124. w3x G. Schubert, Ergebnisse verfahrenstechnischer Untersuchungen an einer Stahlschrott-Shredderanlage. Neue Hutte ¨ 25 Ž1980. 6, S. 201– 206.
187
w4x G. Schubert, Aufbereitung metallischer Sekundarrohstoffe: 1. Au¨ flage. Dt. Verlag fur ¨ Grundstoffindustrie, Leipzig, 1984. w5x G. Schubert, Mechanische Zerkleinerung der GußeisenschrotteGrundlagen. Neue Hutte ¨ 20 Ž1975., S. 235–242. w6x G. Schubert, H. Schubert, Grundlagenuntersuchungen zur Zerkleinerung metallischer Sekundarrohstoffe. Dechema-Mono¨ graphien, Nr. 1549–1575, Bd. 79, S. 167–182. w7x K. Gopel, G. Schubert, Zerkleinerung der Metallspane. ¨ ¨ Neue Hutte ¨ 37 Ž1992. 3, S. 93–97. w8x J. Kirchner, G. Schubert, Comminution of scrap and metals by shredders. Proceedings of the XX. IMPC, 21–26 Sept., 1997, Aachen, Band 2. 1997, S. 37–47. w9x G. Unland, T. Folgner, R. Stenger, Bestimmung der Kornform und Bruchflachigkeit. ZKG International 51 Ž1998. 12. ¨ w10x W. Rasemann, C. Preuße, A. Muller, Zum Einfluß der Teilchenform, ¨ Teilchengroße ¨ und ihrer Mischungsanteile auf die Reproduzierbarkeit der Bewertung von stuckigen und kornigen Mischgutern. ¨ ¨ ¨ Aufbereitungstechnik 38 Ž1997. 3, S. 418–428. ¨ w11x T. Kuntzsch, Ubertragung verschiedener Methoden der Stuckgroßen¨ ¨ analyse auf Zerkleinerungsprodukte von Stoffen mit nicht-sprodem ¨ Verhalten, Thesis, Freiberg University of Mining and Technology, 1999. w12x G.T. Vickers, The projected areas of ellipsoids and cylinders. Powder Technology 86 Ž1997., S. 195–200. w13x J. Kirchner, Mikroprozesse und Einflußgroßen bei der Zerkleinerung ¨ der Schrotte und Metalle in Shreddern mit horizontal angeordnetem Rotor, PhD Thesis, Freiberg University of Mining and Technology, 2000. w14x F. Silbermann, Grundlagenuntersuchungen zu den im Zerkleinerungsraum des Shredders auftretenden Beanspruchungen, Thesis, Freiberg University of Mining and Technology, 1998.