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1、煤的冲击式破碎机的分形特征机械与电气工程学院中国矿业大学，中国矿业大学徐州，中国摘要：煤的冲击式破碎机的粒度分布的分形表达是根据分形理论构建。正交试验是通过煤的破碎机冲击粉碎设备的大小和分布进行线性拟合，在双对数坐标分析。结果表明，回归曲线在双对数坐标中是直的并且线性回归是有利的。分形理论对煤的冲击式破碎机的分布规律是合适的。其中影响煤炭的分形维数的因素，冲击的速度是显着的，材料的硬度是第二，冲击频率是非常小的;分形维数随着煤硬度和冲击速度的增加而减小。关键词：冲击式破碎机，分形特性;正交实验;粒度分布介绍随着采矿和煤层夹矸开采的日益机械化，原料煤的质量随大矸石混入煤中含量的增加而下降。煤矸石

2、大量进入选煤影响选煤效率，提高制备成本。同时，煤矸石在制备后被堆放在地面，成为环境污染的危险源。从地下煤矸石中分离不仅可以提高原煤质量，降低制备成本，而且还可以提供材料，并且煤矸石可以充填地下1-2。煤矸石的冲击碰撞是有效的分离的煤矸石和地下岩石的破碎的统计特性，它可以用分形维数的方式来描述3-4。因此，煤和煤矸石的破碎分形分布的研究可以给矸石分离提供理论支持。一些学者在国内外主要探讨了岩石材料在冲击载荷受损的情况下粒度分布的研究的部分分形特征，岩石材料在一般机械破碎损坏的分形特征还没有得到充分的讨论。对岩石碎片装上uiaxial压缩试验的分形特征进行了研究参考文献5，6，对岩石破碎耗能的分形

3、模型中提供了旋转钻井在参考文献7，分形的割煤的分布规律字符大。芯苛瞬慰8。对煤矸石的冲击式破碎机的分形特征的对比研究，是罕见的。因此，煤的冲击式破碎机的分形特征是本文根据冲击试验研究的。粒度分布分形模型有许多模型是对对粒径分布规律的研究，松香Rammler（RR）和盖茨戈丹 - 舒曼模型和Weibull分布的分布规律的研究是常用的9-10。用分形维数描述看似随意的粒度分布是在过去的几十年中岩石粒度分布研究领域的一个重大进展11,12。分形维数的定义如下13： (1)式中：x：松散煤体特征尺度；F: 煤炭坠毁的特征尺度大于或等于x的量;c:比例常数;D:为分形维数。煤颗粒的密度分布函数可以通

4、过分形维数的推导可以得到 (2)从公式2得到的颗粒的质量，其尺寸大于X的质量 (3)XMAX是粒度最大的粒子，长度单位是毫米，密度单位是，g/mm3分别是粒子的形状因子。质量累积速率，其尺寸大于X从公式3得到。 (4)质量累积速率，其尺寸小于x可以从公式4可以得到 (5)粒度大小分布分形维数（D）可以通过线性回归在双对数坐标系中计算。 分形维数的物理意义（D）表示如下：大量的分形维数的表示有许多和小碎片，少量的分形维数表明有越来越大的碎片，因此，分形维数（D）能够在特定的加载模式作为破碎特性指标14。 实验实验设备该装置由输送带，溜槽，高速带加速器，加压装置和粉碎板，它是如图1所示的。煤是通过

5、将沿滑槽皮带高速带加速器进行的，而煤是固定的加压装置。在高速下破碎板的冲击会影响煤的。高速带加速器的速度是通过变频器调整以获得不同的冲击速度。图1 实验装置布装图1破碎板；2压装置；3高速带加速器；4槽；5输送带实验方法煤样来自山东靓装煤炭进出口公司，山东大柳煤矿总公司，徐州夹河煤矿公司和他们的普氏硬度分别为0.84，1.54,2.42。将煤筛选出从50毫米150毫米筛分成9个样品并且获得的平均值。每个样品有200公斤的重量。用正交试验法是直接用冲击式破碎机进行的。煤的硬度，冲击速度，冲击频率设置为因素，每个因素有三个水平。它的因素和水平如表1所示。表1因素水平测试序号.硬度(A)(f)冲击速

6、度(B)(m/s)冲击频率(c)水平10.846121.548232.42103实验是根据所定义的因子水平下的正交表L9（34）进行的。实验结果及分析正交试验的结果示如表2所示。表2 实验结果NO.ABC累积百分比(%)50mm70mm90mm110mm130mm150mm10.846143.659.572.387.293.110020.848264.979.693.710010010030.8410373.487.197.510010010041.546223.637.952.177.491.210051.548354.271.383.191.695.810061.5410151.260.7

7、72.583.796.110072.426316.230.848.770.386.310082.428130.543.965.176.193.710092.4210253.364.879.787.3100100斜率（b）和相关系数（R2）可根据线性拟合曲线和分形维数（D）可以用b相应地计算得到。分形维数（D）的视觉正交实验分析，以找出影响分形维数的主次因素分析。分析的结果示于表3中。表3 实验结果分析序号ABCDR210.84612.230.98220.84822.440.98330.841032.590.94541.54621.530.98751.54832.450.95261.541012

8、.360.99072.42631.310.98982.42811.880.98592.421022.340.993K17.265.076.47K26.346.776.31K35.537.296.35R1.732.220.16在表3中，每个因子（KI）的效果值是各因素的分形维数在i层的总和;范围（R）是各因素的效应值的最大值和最小值的相减得到的，R是测量分形维数的波动的关键指标。其范围是较大的因素的多元化对分形维数更大的影响力。可以从结果中可以看出，其中影响煤的分形维数的因素，冲击的速度是显着的，材料的硬度是第二和冲击频率非常。孀琶旱挠捕鹊脑黾拥姆中挝墙档偷亩寤魉俣鹊脑黾臃中挝窃黾

9、的。结论分形理论是适用于煤的冲击式破碎机的分布规律。其中影响煤炭的分形维数的因素，冲击的速度是显着的，材料的硬度是第二和冲击频率是非常小的。煤的硬度增加分形维数减少，而冲击速度的增加而增加。致谢作者非常感谢国家自然科学基金重点项目（项目编号：50834004）。参考文献1 QIAN Ming-gao, XU Jia-lin, MIAO Xie-xing. Technique of cleaning mining in coal mineJ. Journal of China University of Mining & Technology, 2003, 32(4): 343-348. (in

10、 Chinese) 2 ZHANG Ji-xiong, MIAO Xie-xing, Underground Disposal of Waste in Coal MineJ. Journal of China University of Mining & Technolog, 2006, 35(2): 197-200. (in Chinese) 3 SUN Xi-kui, LI Xue-hua. The New Technology of Waste-filling Replacement Mining on Strip Coal PillarJ. Journal of China Coal

11、Society, 2008, 33(3): 259-263. (in Chinese) 4 PAN Zhao-ke, LIU Zhi-he. Fractal Properties of Size Distribution of Gangue Agmentation and Routine CalculationJ. Journal of Taiyuan University of Technology , 2004, 35(2): 115-117. (in Chinese) 5 DENG Tao, YANG Lin-de, HAN Wen-feng. Influence of Loading

12、Form on Distribution of Marble FragmentsJ. Journal of Tongji University(Natural Science), 2007, 35(1): 10-14. (in Chinese) 6 PAN Zhao-ke, LIU Zhi-he. Fractal Properties of Size Distribution of Gangue Agmentation and Routine CalculationJ. Journal of Taiyuan University of Technology. 2004, 35(2): 115-

13、117. (in Chinese) 7 YAN Tie; LI Wei; BI Xue-liang; LI Shi-bin. Fractal Analysis of Energy Consumption of Rock Fragmentation in Rotary DrillingJ. Chinese Journal of Rock Mechanics and Engineering, 2008, 27(s2): 3649-3654. (in Chinese) 8 LIU Song-yong, DU Chang-long, LI Jian-ping. Fractal Character of

14、 the Distribution Law of the Cutting Coal SizeJ. Journal of China Coal Society, 2009, 34(7): 978-982. (in Chinese) 9 Maciac A, Cuerda E M, Diaz M A. Application of the Rosin-rammler and Gates-gaudin-schuhmann Models to the Particle Size distribution Analysis of Agglomerated CorkJ. Materials Characte

15、rization, 2004, 52: 1592164 10 TAO Chi-dong. Mining Machinery M. Bei Jing: Coal Industry Press, 1993: 35-37. 11 Turcotte D L. Fractals and FragmentationJ. J Geophys Res, 1986, 91 (132): 1 921 1 926. 12 GAO Feng, XIE He-ping, ZHAO Peng. Fractal Properties of Size-frequency Distribution of Rock Fragme

16、nts and the Influence of Meso-structure J . Chinese Journal of Rock and Engineering, 1994, 13 (3) : 240246. (in Chinese) 13 XIE He-ping. Introduction of the Fractals-Rock Mechanics M. Bei Jing: Science Press, 1996: 112-116. (in Chinese) 14 WANG Li, GAO Qian. Fragmentation Predicition of Rock Based o

17、n Damage Energy DissipationJ. Journal of China Coal Society, 2007, 32(11) :1170-1174. (in Chinese)From: Li Jian ping;Zhang Jia-jia;Du Chang-long/Consumer Electronics, Communications and Networks (CECNet), 2011 International Conference onFractal Character of the Impact Crusher of CoalLI Jian-ping, ZH

18、ANG Jia-jia, DU Chang-longCollege of Mechanical and Electrical EngineeringChina University of Mining and Technology,CUMTXuzhou,ChinaAbstract:Fractal expression of the size distribution of impact crusher of coal is built according to fractal theory. Orthogonal experiment is carried out by impactive c

19、rush equipment and size distribution of the crusher of coal is linear fitted and analyzed in double logarithmic coordinates. The results indicate that regression curve in double logarithmic coordinates is straight and linear regression is favorable. The fractal theory is suitable for the distributio

20、n discipline of the impact crusher of coal. Among the factors which affect the fractal dimension of coal, the speed of impact is notable, hardness of materiel is secondly and impact frequency is very little; fractal dimension decreases with the increases of hardness of coal and increases with the in

21、creases of impact speed. Key words:impact crusher; fractal properties; orthogonal experiment; size distribution I NTRODUCTION With the increasing mechanization of mining and the exploitation of coal seam with dirt band, the quality of raw coal decreases as the increases of the content of large gangu

22、e mixed in the coal. The large number of gangue goes into the coal preparation that affects the efficiency of coal preparation and increase the cost of preparation. Meanwhile the gangue is stacked on the ground after preparation, which becomes the hazard sources of environmental Pollution. The separ

23、ation of gangue from coal underground can not only improve the quality of raw coal, decrease the cost of preparation, but also provide materials to the gangue filling underground1 2. The impactive crash of coal and gangue is a effective way to separate gangue from coal underground and the statistica

24、l characteristics of rock crash can described by fractal dimension3 4. Therefore the research of fractal fragmentation distribution of coal and gangue can provide the gangue separation with theoretical support. Scholars at home and abroad mainly probe into the fragments fractal character of rock mat

25、erial damaged under Blast loading for the research of size distribution of particle, fractal character of rock material damaged under general mechanical disruption has not be discussed adequately. The fractal character of rock fragment loading on uiaxial compressive test was studied in reference 5,

26、6, fractal model for consuming energy on rock fragmentation is provided in rotary drilling in reference 7, fractal character of the distribution law of the cutting coal size was studied in reference 8. Research of the fractal character of the impact crusher of coal and gangue is rare in contrast. Th

27、erefore, fractal character of the impact crusher of coal is researched according to impactive experimentation in this paper. FRACTAL MODEL OF SIZE DISTRIBUTION There are many models which study on the distribution law of particle size, Rosin-Rammler (R-R) and Gates-Gaudin-Schuhmann model and Weibull

28、 distribution are in common use9-10. Using fractal dimension to describe the seemingly haphazard size distribution is a significant progress in the field of research on size distribution of rock in the last decades11,12. Fractal dimension was defined the as follows13 (1) Were x is characteristic sca

29、le of crashed coal; F is amount of crashed coal that characteristic scale is greater than or equal to x; c is constant of proportionality; D is fractal dimension. Density distribution function of coal particles can be got by the derivation of fractal dimension (2) Mass of particle whose size is grea

30、ter than x was obtained from Eq.2 (3) Were xmax is the size of the biggest particle, mm; is density, g/mm3; is the shape factor of particle. Mass accumulation rate whose size is greater than x was obtained from Eq.3 (4) Mass accumulation rate whose size is less than x can be got from Eq.4 (5)Fractal

31、 dimension of size distribution (D) can be calculated by linear regression in double logarithmic coordinate system. Physical meaning of fractal dimension (D) is expressed as follows: The large amount of fractal dimension indicates there are many and small fragments, the small amount of fractal dimen

32、sion indicates there are less and big fragments, Therefore, fractal dimension (D) can be used as fragmentation characteristic index under specific loading mode 14.E XPERIMENTATION A. Device of experimentation The device consists of feeding belt, chute, high-speed belt accelerator, pressing device an

33、d crush plate, which is shown in Fig.1. Coal is carried by feeding belt along the chute to the high-speed belt accelerator, while the coal is fixed by pressing device. Coal impacts the crush plates at high speed. The speed of high-speed belt accelerator is adjusted by inverter in order to get differ

34、ent impact speed. Fig.1 Layout of experimental device1 crush plate; 2 pressing device; 3 high-speed belt accelerator; 4 chute; 5 feeding beltB. Experimental methodsThe coal samples came from Shandong Liangzhuang Coal Corporation, Shandong Daliu Coal Corporation, Xuzhou Jiahe Coal Corporation and the

35、ir Protodikonovs hardness are 0.84, 1.54,2.42 respectively. The coal is screened out from 50 mm to 150 mm by sieve and nine samples are obtained on average. Each of the samples is 200Kg weight. Orthogonal test is carried out using directly impact crusher machine. Hardness of coal, impact speed, impa

36、ct frequency are set as the factor and each factor has three level. The factors and levels are shown in Table 1. T ABLE 1 LEVELS OF FACTORSTest No.Hardness(A) (f)Factor impact speed(B)(m/s)Impace frequency(c)level10.846121.548232.42103Experiment was conducted under orthogonal table L9 (34) according

37、 to the levels of factors defined. C. Experimental results and analysis Results of orthogonal experiment are shown in Table 2.T ABLE 2 E XPERIMENTAL FINDINGSNO.ABCCumulative percentage(%)50mm70mm90mm110mm130mm150mm10.846143.659.572.387.293.110020.848264.979.693.710010010030.8410373.487.197.510010010

38、041.546223.637.952.177.491.210051.548354.271.383.191.695.810061.5410151.260.772.583.796.110072.426316.230.848.770.386.310082.428130.543.965.176.193.710092.4210253.364.879.787.3100100Slope (b) and correlation coefficient (R2) can be got according to linear fitting curve and fractal dimension (D) can

39、be calculated by b correspondingly. Fractal dimension (D) is analyzed by visual analysis of orthogonal experiment in order to find out the Primary and secondary factors that affect the fractal dimension. Result of analysis is shown in Table 3.T ABLE 3 ANALYSIS OF EXPERIMENTAL FINDINGSNO.ABCDR210.846

40、12.230.98220.84822.440.98330.841032.590.94541.54621.530.98751.54832.450.95261.541012.360.99072.42631.310.98982.42811.880.98592.421022.340.993K17.265.076.47K26.346.776.31K35.537.296.35R1.732.220.16 In Table 3, effect value of each factor ( ki) is the sum of fractal dimension of each factor under leve

41、l i ; range ( R ) is the subtraction of the max and minimum of the effect value of each factor, R is the key index to measure the fluctuation of fractal dimension. The diversification of the factor whose range is bigger has a bigger influence on fractal dimension. It can be seen from the results tha

42、t among the factors which affect the fractal dimension of coal, the speed of impact is notable, hardness of materiel is secondly and impact frequency is very little; Fractal dimension decreases with the increases of hardness of coal and increases with the increases of impact speed. CONCLUSION 1) The

43、 fractal theory is suitable for the distribution discipline of the impact crusher of coal. 2) Among the factors which affect the fractal dimension of coal, the speed of impact is notable, hardness of materiel is secondly and impact frequency is very little. 3) Fractal dimension decreases with the in

44、creases of hardness of coal and increases with the increases of impact speed. ACKNOWLEDGEMENTSThe authors gratefully acknowledge the Major Project of National Natural Science Foundation (Project No. 50834004).REFERENCES1 QIAN Ming-gao, XU Jia-lin, MIAO Xie-xing. Technique of cleaning mining in coal

45、mineJ. Journal of China University of Mining & Technology, 2003, 32(4): 343-348. (in Chinese) 2 ZHANG Ji-xiong, MIAO Xie-xing, Underground Disposal of Waste in Coal MineJ. Journal of China University of Mining & Technolog, 2006, 35(2): 197-200. (in Chinese) 3 SUN Xi-kui, LI Xue-hua. The New Technolo

46、gy of Waste-filling Replacement Mining on Strip Coal PillarJ. Journal of China Coal Society, 2008, 33(3): 259-263. (in Chinese) 4 PAN Zhao-ke, LIU Zhi-he. Fractal Properties of Size Distribution of Gangue Agmentation and Routine CalculationJ. Journal of Taiyuan University of Technology , 2004, 35(2)

47、: 115-117. (in Chinese) 5 DENG Tao, YANG Lin-de, HAN Wen-feng. Influence of Loading Form on Distribution of Marble FragmentsJ. Journal of Tongji University(Natural Science), 2007, 35(1): 10-14. (in Chinese) 6 PAN Zhao-ke, LIU Zhi-he. Fractal Properties of Size Distribution of Gangue Agmentation and

48、Routine CalculationJ. Journal of Taiyuan University of Technology. 2004, 35(2): 115-117. (in Chinese) 7 YAN Tie; LI Wei; BI Xue-liang; LI Shi-bin. Fractal Analysis of Energy Consumption of Rock Fragmentation in Rotary DrillingJ. Chinese Journal of Rock Mechanics and Engineering, 2008, 27(s2): 3649-3

49、654. (in Chinese) 8 LIU Song-yong, DU Chang-long, LI Jian-ping. Fractal Character of the Distribution Law of the Cutting Coal SizeJ. Journal of China Coal Society, 2009, 34(7): 978-982. (in Chinese) 9 Maciac A, Cuerda E M, Diaz M A. Application of the Rosin-rammler and Gates-gaudin-schuhmann Models

50、to the Particle Size distribution Analysis of Agglomerated CorkJ. Materials Characterization, 2004, 52: 1592164 10 TAO Chi-dong. Mining Machinery M. Bei Jing: Coal Industry Press, 1993: 35-37. 11 Turcotte D L. Fractals and FragmentationJ. J Geophys Res, 1986, 91 (132): 1 921 1 926. 12 GAO Feng, XIE

51、He-ping, ZHAO Peng. Fractal Properties of Size-frequency Distribution of Rock Fragments and the Influence of Meso-structure J . Chinese Journal of Rock and Engineering, 1994, 13 (3) : 240246. (in Chinese) 13 XIE He-ping. Introduction of the Fractals-Rock Mechanics M. Bei Jing: Science Press, 1996: 1

52、12-116. (in Chinese) 14 WANG Li, GAO Qian. Fragmentation Predicition of Rock Based on Damage Energy DissipationJ. Journal of China Coal Society, 2007, 32(11) :1170-1174. (in Chinese)From: Li Jian ping;Zhang Jia-jia;Du Chang-long/Consumer Electronics, Communications and Networks (CECNet), 2011 International Conference on