Experimental tudy on the ractal haracteristics of ocks rushing

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1 MATEC Web of Conferences 25, ( 2015) DOI: / matecconf/ C Owned by the authors, publshed by EDP Scences, 2015 Expermental tudy on the ractal haracterstcs of ocks rushng Gapn Ca*, Yang Xong & Longfe Ln School of Mechancal and Electrcal Engneerng, Jangx Unversty of Scence and Technology, Ganzhou, Jangx, Chna ABSTRACT: A fractal model for the sze dstrbuton was proposed based on the fractal character of the crushng granularty of rocks. The crushng tests of three dfferent rocks were conducted. And the test results of rock sze dstrbuton were used to conduct a statstcal analyss. The results ndcate that the fractal characterstcs of rock are unversal. The fractal dmenson s one of perfect ndcators to evaluate crushng, reflectng the whole process of the rock crushng. Subsequently, the relatonshp between fractal dmenson and both of sze of rock and energy consumpton s establshed. It gves a better explanaton from the aspect of mechansm. What s more, the fractal dmenson represents the effect and the rule of the sze dstrbuton of crushng and provdes a theoretcal foundaton for controllng the sze dstrbuton of rock. Keywords: fractal dmenson; sze dstrbuton; crushng test; broken ndcators 1 INTRODUCTION Snce the 1970s, fractal theory as a study of the rregular geometrcal shape was put forward by a French mathematcan Mandelbort. At present, ths theory was wdely used n the physcal, metallurgy, mnng, materals, computer graphcs, and other felds [1]. Because the rock after crushng has good fractal structure, the fractal theory has been wdely used on the rock mechancs. Accordng to the theory, the rock partcle sze, unform degree was respectvely descrbed by the broken fractal dmenson. At present, some basc theores have been establshed n the rock crushng, partcle sze dstrbuton [2], energy consumpton and other respects. Wth the rapd development of modern experment technques and advanced computer technology, the research and analyss of fractal theory n the feld of broken becomes possble. Ths provdes the correspondng theoretcal and practcal sgnfcance for the better research of rock crusher. Ths partcle sze dstrbuton of the crushed rock ore s an mportant ndcator of the crushng effect, whch drectly affects the economc benefts of some enterprses. Accordng to the rock block dstrbuton of fractal characterstcs, Xe H [3], the peak [4] and Wang L [5] proposed a method to predct the partcle sze dstrbuton after the study of crushed ore and rock fragmentaton. Wu Xanzhen et al. [6] explored the crushng process of acoustc emsson by usng fractal characterstc sequence of rock falure process of acoustc emsson. Fractal dmenson D can reflect the statstcal evoluton of rock nternal mcro gap. A.Tasdemr [7] evaluated the fractal characterstcs of partcle sze dstrbuton of Jaw crusher, cone crusher, hammer crusher and the ball mll equpment. The result ndcates that the partcle sze dstrbuton of chromte have fractal rule and the range of fractal dmenson are dfferent. Xu Jnyu et al. [8] analyzed fragmentaton of rock by usng fractal geometry approach after the shock loadng on the marble fractal geometry test. The rock crushng process was conducted a quanttatve descrpton. Wang L et al. [9] proposed the methods to establsh a damage model accordng to the self-smlarty after the fragmentaton of rock. The rock fracture damage parameter was defned accordng to the dstrbuton of rock fragmentaton. Lu Yu [10, 11] establshed an mpact crusher coal partcle sze analyss model accordng to the fractal theory, whch can do a good descrpton of the mpact of coal partcle sze dstrbuton after crushng. The fractal dmenson can do a good evaluaton of the mpact of coal crushng effect. In ths paper, the test study on the mpact ndcators broke (the average partcle sze, the yeld of fne-szed partcles and the crushng rato) relatonshps between the fractal dmenson through the experment of Nobum tantalum ore, grante and cobbles. The analyss about the relatonshp among the fractal dmenson and the both broken rock partcle sze and energy consumpton s obtaned accordng to the partcle sze dstrbuton. 2 BROKEN CALCULUS D DIMENSION Accordng to the basc defnton of fractals by [12] and the materal after crushng ts fractal sze, experts can use dfferent fractal dmensons to represent ts characterstcs. For example, as shown [13] n Katz formula: V ( d ) d A d max 3D (1) *Correspondng author: cgp4821@yahoo.com.cn 4 Artcle avalable at or

2 MATEC Web of Conferences V d Where: ( represents one whch s less than the ) sze of the volume d ; A s the form factor of partcles; D s the partcle fractal dmenson; d represents the average value of gran sze n between; d max represents the maxmum partcle sze after crushng (mm). By Equaton (1), t shows that the mass dstrbuton of the crushed rock can be expressed as: M V d d ( ) d A d max 3D (2) M d Where: ( s the crushed rock mass dstrbuton; s the densty of rock. ) Assumng that the total mass of rock s M T, so: M lm M A (3) T ( d ) Smultaneously, dvde (2) by (3) to obtan the used partcle sze whch s less than d, a mnute qualty dmenson whch represents the cumulatve probablty: M ( d ) d MT dmax 3D (4) By Formula (4), we obtaned the logarthmc transformaton: M ( d ) d ln ln (5) M T dmax M ( d ) Wth d ln and ln M beng ordnate T d max and abscssa respectvely, the expermental data were analyzed accordng to the fttng whose slope s K. Then ts subsze fractal dmenson D s 3-K. 3 ROCK CRUSHING SQUEEZE TEST PROGRAM The rock crushng squeeze test equpment s shown n Fgure 1. Ths equpment s composed of motor, reducer, feed plate and roller. When rollers are smoothly ran n the motor drve, the feed conveyor rollers wll squeeze the rock crushng and collect data by usng wreless torque sensor. The broken evaluaton s estmated to quantfy the broken amount n the actual producton. The stuaton of rock crushng s used to adjust the crushng equpment accordng to the requrement of producton n real tme [14]. Commonly-used ndcators are the broken average partcle sze, the fne-szed partcles yeld and the broken rate. For the same external condtons, the rock crushng process and the fractal characterstcs of crushed rock granularty have a certan relatonshp wth attrbutes themselves. And for dfferent types of rock partcles sze multlevel control experments, t s necessary to let the board crusher be under the same workng condton. In ths paper, we use three dfferent knds of rock to conduct the crushng squeeze tests, and the tantalum-nobum ore wth fve dfferent partcle szes s used to conduct the squeeze crushng experments. Fgure 1. Expermental equpment for crushng 4 ANALYSIS OF TEST RESULTS In order to study the partcle sze dstrbuton characterstcs of crushed rock, we explore whether the fractal dmenson can be used as ndcators to evaluate the crushng rato of rock. In ths paper, we respectvely squeeze and crush three knds of rock such as the tantalum and nobum ore, grante and pebble, and the crushed forms thereof are shown n Fgure 2. Through usng a standard seve, the sze of rock partcles s dvded nto fve grades, ncludng +11mm, the range of 8 11mm, the range of 5 8mm, the range of 2 5mm and 2mm. The amount of qualty product n each class on the screen and the record of expermental data are shown n Table Partcle sze dstrbuton of rock crushng squeeze The sze dstrbuton of three knds of dfferent rocks after beng squeezed and crushed s shown n Fgure 3 and Table 1. Fgure 3 shows the dfferent rocks under the same condton due to dfferent propertes and fragmentaton of dstrbuton. By comparng the expermental data after crushed, the results ndcates that cobblestone have a large percentage of total qualty large partcle mass and uneven partcle sze dstrbuton. However, the Ta-Nb ore partcles after crushed have the largest group of fne partcles and few large partcles. The amount of fne partcles grante s between that of the cobblestone and the Ta-Nb ore. Ths s because the cobblestone wth hghest hardness has the p.2

3 EMME 2015 (a) Cobblestone (b) Grante (c) Ta-Nb ore Fgure 2. Broken forms of dfferent rocks Table 1. Sze dstrbuton of rock Partcle mass dstrbuton/g Experment No. >11mm 11-8mm 8-5mm 5-2mm <2mm Total 1(Cobblestone) 2(Grante) 3(Ta-Nb ore) largest resstance to avod beng crushed. However, the tantalum-nobum ore wth low hardness and beng brttle wll be more easly crushed when broken nto many small partcles. Fgure 4. Mass and sze dstrbuton n logarthmc coordnates Fgure 3. Fragment sze dstrbuton of three dfferent rocks It s descrbed n logarthm wth the data n Table 1 and the mass dstrbuton n Formula (5). Then the data are ftted to obtan the relatonshp between the qualty and the partcle sze dstrbuton after rock beng crushed, as shown n Fgure 4: Fgure 4 shows the double logarthmc curves whch are calculated based on the fractal dmenson of three knds of dfferent rock sze. It can be seen from the fgure that a sgnfcant lnear relatonshp between ponts ndcates the crushed rock n the partcle sze dstrbuton wth good characterstcs of fractal dstrbuton. Ths feature wll not change the type of rock. Accordng to the relatonshp between the fractal dmenson D and the slope of the ftted lne K, the fractal dmenson s calculated wth three rocks, as shown n Table p.3

4 From Table 2, dfferent fractal dmenson D s correspondng to dfferent rocks because of the rock nature tself. In a sense, t characterzes the dfference between rock propertes wthn the materal. Table 2. Fractal dmenson of the experment Ore Cobblestone Grante Ta-Nb ore Lnear ft K Fractal dmenson D MATEC Web of Conferences 4.2 Broken fractal dmenson and broken ndex correlaton analyss (c) In order to evaluate the crushng effect of pebbles, grante and the tantalum-nobum ore, the evaluaton ndex of an average partcle sze, the yeld below 8mm and the broken rate are respectvely calculated accordng to the data of Table 1. The results are shown n Table 3: Table 3. Dfferent ndexes for crushng Experment NO. The average partcle sze/ mm The yeld below 8mm Broken rate (d) Fgure 5. Relatonshp between the fractal dmenson and the crushng ndex (a) The evaluaton ndexes of an average partcle sze, the yeld below 8mm and the broken rate are contrasted accordng to the dfferent rock fractal dmenson n Table 2. Four broken evaluaton ndexes of the sze and trends are observed, as shown n Fgure 5. Accordng to Fgure 5, the crushed fractal dmenson of three dfferent types of rock s almost dentcal wth the crushng rate of followng 8 yeld trends. The average partcle sze s just the opposte trend due to the descrpton of the trend of the object n dfferent drectons. The result llustrates that the better the rock crusher s, the smaller the average partcle sze s; the greater the fragmentaton rate s and the more yeld below 8mm s. The fractal dmenson of crushng s also greater. The fractal dmenson better llustrates that the evaluaton of the fragmentaton degree s consstent wth several other tradtonal evaluaton methods when after crushng. 4.3 Fractal dmenson relatonshp between the rock and the partcle sze (b) In order to explore the fractal dmenson of dfferent prmary partcle szes of the same knd of rock after beng crushed, the tantalum and nobum ore rock experments were conducted wth partcles whose p.4

5 dameters are respectvely 18mm, 21mm, 24mm, 27mm and 30mm. The partcles carry out an extruson crushng test on plate roller vbro-crosher, and the correspondng expermental groups were numbered as 1, 2, 3, 4 and 5. The partcle sze of Ta-Nb ore s respectvely counted n the range of <2mm, 2 5mm, 5 8mm, 8 11mm and >11mm. The mass fracton of Ta-Nb ore s calculated after seved usng a standard seve. The partcle sze dstrbuton s shown n Fgure 6: EMME 2015 Fgure 8. Relatonshp between the broken energy and the sze Fgure 6. Fragment sze dstrbuton of tantalum nobum ore Based on Fgure 6, there are some changes about dfferent partcle szes of tantalum and nobum ore rock after crushng. The larger the prmary partcles are, the fewer a large proporton of partcle mass s and the more the yeld of fne partcle s. The partcle sze dstrbuton of the crushed mass s calculated accordng to the method of fractal dmenson. The fractal dmenson s calculated for each group experment. The data of each test are processed through energy detecton devce. Accordng to the experment data, the broken power s counted. Accordng to the results of each broken experment, we can respectvely draw fractal dmenson of dfferent rock partcles sze of the tantalum and nobum ore. The fractal dmenson of dfferent tantalum and nobum ore and crushng energy s also drawn. The partcle sze curve s shown n Fgures 7 8: As can be seen from the chart, the fractal dmenson represents an upward trend wth the ncrease of the partcle s dameter, and ths s roughly a lnear relatonshp. And we compare the broken partcle sze dstrbuton chart, t shows that the greater the degree of partcle breakage s, the greater the fractal dmenson s. But the crushed fractal dmenson ncreases, and the crushng effect s enhanced. As the energy of broken rock consumpton s decreased, the approxmate lnear decrease gradually appears. Ths s because the rock partcles are smaller, the partcle agglomeraton s closer, and then the rock defects of nternal cracks are fewer. The more dffcult t s to be broken, the more energy t s requred when broken. 5 CONCLUSION (1) Through analyzng three dfferent partcle szes after pressng and crushng, ths paper shows that the partcle sze dstrbuton after crushng rock extruson has fractal characterstcs. Fractal characterstcs are unversal. What s more, fractal dmenson can reflect the squeezng and broken effect well, whch can be used as an ndcator of broken evaluaton. (2) The extruson crushng tests showed that due to the nherent propertes, the broken fractal dmenson of dfferent rocks wll be dfferent after crushed. Wth the ncrease of partcle sze, the broken fractal dmenson of the tantalum and nobum ore crushng rocks tends to ncrease, whch s n the range of 1.5 to 2.0. (3) Wth the reducton of rock partcle dameter, ts nternal crack defects are less. And t s necessary to absorb more energy to make the rock cracks and expanson and eventually cause the fragmentaton effect. Under the condton of absorbng energy, the fractal dmenson of small partcles whch are produced after the rock beng crushed s relatvely small, and the degree of fragmentaton s relatvely low. Fgure 7. Relatonshp between the fractal dmenson and the sze ACKNOWLEDGEMENTS Ths work was supported by the Natonal Scence p.5

6 MATEC Web of Conferences Foundaton of Chna (No ) and the Unversty Technology Buldng Plan Projects of Jangx Provnce, Chna (No. KJLD13045). REFERENCES [1] Zhu Hua Fractal theory and ts applcaton. Bejng: Scence Press, [2] ZHENG Ke-hong, DU Chang-long, & QIU Bng-jng Expermental study on the fractal characterstcs of crushng coal and gangue. Journal of coal, 38(6): [3] Xe H, & Parseau W G Fractal character and mechansm of rock bursts. Internatonal of Rock Mechansm and Mnng Scence & Geomechancs Abstracts, 30(4): [4] WANG We, SU Jng-yu, & MA Dong-hu, et al Evaluaton of rock mass qualty based on fractal nterpolaton model. Journal of Central South Unversty (Scence and Technology), 43(12): [5] WANG L, & GAO Qan Fragmentaton Predcton of rock based on damage energy Dsspaton. Journal of coal, 32(11): [6] WU Xan-zhen, LIU Xang-xn, & LIANG Zheng-zhao, et al Expermental study of fractal dmenson of AE serals of dfferent rocks under unaxal compresson. Rock and Sol Mechancs, 33(12): [7] A. Tasdemr Fractal evaluaton of partcle sze dstrbuton of chromtes n dfferent commnuton envronments. Mnerals Engneerng, 22(9): [8] XU Jn-yu, & LIU Sh Research on fractal characterstcs of marble fragments Subjected to mpact loadng. Rock and Sol Mechancs, 33(11): [9] WANG L, & GAO Qan Fragmentaton Dstrbuton predcton of rock based on damage energy Dsspaton. Journal of rock mechancs and engneerng, 26(6): [10]LIU Yu, ZHOU Ja-we, & DU Chang-long Impact crushng probablty dfference between coal and gangue partcles based on fractal theory. Vbraton and shock, 45(9): [11]LIU Yu, ZHOU Ja-we, & DU Chang-long Fractal character of mpact crushng granularty of coal lumps. Vbraton and shock, 32 (3): [12]Xe Peace Fractal-Introducton to rock mechancs.bejng: Scence Press. [13]ZHANG J-ru, ZHU Je, & HUANG Wen-jng Crushng and fractal behavors of quartz sand-gravel partcles under Confned Compresson. Journal of geotechncal Engneerng, 30(6): [14]M. Rsnen, & M Metamora An evaluaton of the procedure and results of laboratory crushng n qualty assessment of rock aggregate raw materals. Bulletn of Engneerng Geology and the Envronment. 22(1): p.6