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(3) Were xmax is the size of the biggest particle, mm; ȡ is density, g/mm3; kv is the shape factor of particle. Mass accumulation rate whose size is greater than x was obtained from Eq.3 3max1( )D xM xMx− >=−
(4) Mass accumulation rate whose size is less than x can be got from Eq.4 3max()D xM xMx− <=
(5) Fractal dimension of size distribution (D) can be calculated by linear regression in max // xMMxx < − 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 dimension indicates there are less and big fragments, Therefore, fractal dimension (D) can be used as fragmentation characteristic index under specific loading mode [14]. III. EXPERIMENTATION A. Device of experimentation The device consists of feeding belt, chute, high-speed belt accelerator, pressing device and 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 different impact speed. Fig.1 Layout of experimental device 1 crush plate; 2 pressing device; 3 high-speed belt accelerator; 4 chute; 5 feeding belt B. Experimental methods The coal samples came from Shandong Liangzhuang Coal Corporation, Shandong Daliu Coal Corporation, Xuzhou Jiahe Coal Corporation and their Protodikonov's 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, impact frequency are set as the factor and each factor has three level. The factors and levels are shown in Table 1. TABLE 1 LEVELS OF FACTORS Test No. Factor Hardness(A) ˄f˅ Impact speed˄B˅ ˄m/s˅ Impact frequency˄C˅ Level 1 0.84 6 1 2 1.54 8 2 3 2.42 10 3 Experiment was conducted under orthogonal table L9 (34) according to the levels of factors defined. C. Experimental results and analysis Results of orthogonal experiment are shown in Table 2. It can be seen from Fig.2 that regression curves of 9 experimental results in double logarithmic coordinate system are all straight line and Linear regression are favorable, which means that fractal distribution is suitable for the distribution discipline of crushed coal fragmentation. Slope (b) and correlation coefficient (R2) can be got according to linear fitting curve and fractal dimension (D) can 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. TABLE 3 ANALYSIS OF EXPERIMENTAL FINDINGS NO. A B C D R2 1 0.84 6 1 2.23 0.982 2 0.84 8 2 2.44 0.983 3 0.84 10 3 2.59 0.945 4 1.54 6 2 1.53 0.987 5 1.54 8 3 2.45 0.952 6 1.54 10 1 2.36 0.990 7 2.42 6 3 1.31 0.989 8 2.42 8 1 1.88 0.985 9 2.42 10 2 2.34 0.993 K1 7.26 5.07 6.47 K2 6.34 6.77 6.31 K3 5.53 7.29 6.35 R 1.73 2.22 0.16 In Table 3, effect value of each factor (ki) is the sum of fractal dimension of each factor under level 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 persification of the factor whose range is bigger has a bigger influence on fractal dimension. It can be seen from the results that 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. IV. CONCLUSION 1) The 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 increases of hardness of coal and increases with the increases of impact speed.