A fractal model method for studying the impact energy and particle size distribution characteristics of minerals

Abstract

A fractal model method for studying the impact energy of minerals and the particle size distribution characteristics, first, according to the mathematical theory of fractal, the fractal model of the particle size distribution of magnetite crushing is established, the fractal dimension D is used to represent the particle size after crushing, then the crushing experiment under different impact crushing energy is repeatedly carried out through the falling weight impact testing machine, and the crushed ore particles are collected, the particle size grading is realized through screening, then the weight of each particle size level is weighed and recorded, then according to the established fractal model, the function equation of ln(M(x) / M) and ln(x / xmax) under different impact energy is established; Further, the function equation of fractal dimension D and different impact crushing energy is established; Through this method, the function relationship between the particle size of magnetite crushing and the impact crushing energy can be constructed, and the function relationship obtained by this method can guide the adjustment of the crushing energy of the crushing equipment, so as to control the particle size of the crushed magnetite.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of analysis of particle size distribution of crushed ore, and particularly relates to a fractal model method for studying impact energy of mineral and particle size distribution characteristics. BACKGROUND

[0002] Ore crushing is the premise of subsequent separation and smelting, and the overall particle size of the post-milling particles formed after the crushing equipment crushes the particles of the ore into the mill covers a certain particle size range, and each particle size level has its own proportion. The crushing process is a process of applying energy to the ore particles by the crushing equipment or the crushing and milling equipment to change the large particles into small particles. If the energy applied by the equipment is too large, the proportion of small particles after crushing is large, and if the energy applied by the equipment is too low, the proportion of small particles after crushing is small. For the crushing and milling of magnetite, the same principle applies. The prior art only has a qualitative understanding of this, and does not provide a quantifiable relationship. How to determine the specific corresponding relationship between the crushing energy and the particle size of the crushed magnetite, and what method to use to analyze and determine this corresponding relationship, has important guiding significance for adjusting the crushing energy of the crushing equipment. SUMMARY

[0003] The purpose of the present application is to solve the above problems and provide a fractal model method for studying impact energy of mineral and particle size distribution characteristics.

[0004] The technical scheme of the present application is a fractal model method for studying impact energy of mineral and particle size distribution characteristics, comprising the following steps:

[0005] a. Establish a fractal model of the particle size distribution of magnetite crushing, and the specific process is as follows:

[0006] From the basic definition of fractal, we can get:

[0007] N=cx -D (1)

[0008] In the formula: x is the characteristic scale of the particle fragment, N is the number of broken particles with characteristic scale x, c is the proportionality constant, and D is the fractal dimension of the broken particle distribution.

[0009] Then the fractal definition is extended to the continuous case:

[0010] N0=cx max -D (2)

[0011] We can get:

[0012] (3)

[0013] Because the number of broken particles is difficult to count, the size-frequency relationship of broken particles is converted into the mass-frequency relationship;

[0014] Because the correlation between the particle mass and the particle size is , the mass-frequency relationship of the particles is:

[0015] (4)

[0016] Thus, D=3b, the fractal dimension of the ore particle size distribution is determined by the mass-frequency relationship; the broken particles are sieved, the total number of the particles is N(x), M(x) is the estimated mass of the broken particles with a diameter less than x, and M is the total mass of the broken particles, then the size-frequency distribution of the broken particles is:

[0017] (5)

[0018] x o is the average size, when x / x0 1, (5) can be transformed into:

[0019] (6)

[0020] The derivative of (6) is:

[0021] (7)

[0022] From the concept of fractal, it is known that:

[0023] (8)

[0024] The relationship between the number of broken particles and the mass is: , then:

[0025] (9)

[0026] Therefore, it is known that:

[0027] D=3-b (10)

[0028] In the formula, b is the slope value in the double logarithmic coordinates, the cumulative mass percentage of the broken particles with a diameter less than x; the establishment of the theoretical model provides a basic operation basis for the operation after obtaining the experimental data.

[0029] b. Use the falling weight impact tester to crush the magnetite sample, classify the crushed ore particles by size, and weigh and record the data for each size classification; detailed experimental data is prepared for subsequent coordinate system point drawing and curve fitting.

[0030] c. Adjust the impact energy of the falling weight impact tester multiple times, repeat step b multiple times; different energy sizes need to be tested to prepare for subsequent analysis of different particle size distributions corresponding to different energies.

[0031] d. According to the data obtained in step c, draw the particle size distribution curve of the crushed magnetite after crushing under different impact energies; this curve provides a visual basis for analyzing and judging the overall trend of particle size under different energies.

[0032] e. According to the fractal model in step a, use the particle formula (6) to draw the ln(M(x) / M)-ln(x / x max ) curve of the particle size distribution characteristics of the crushed magnetite under different impact crushing energies according to the mass distribution of different particle sizes after crushing; according to the curve, establish the function equation of ln(M(x) / M) and ln(x / x max ) under different impact energies;

[0033] f. According to the fractal model in step a, calculate the fractal dimension D under different impact crushing energies, and draw the corresponding relationship diagram of fractal dimension D and different impact crushing energies, fit the curve, and establish the function equation of fractal dimension D and impact crushing energy. This function can intuitively quantify the relationship between the particle size of the crushed magnetite and the crushing energy, and is a linear function, which is easy to operate and can be used to guide the control of the particle size distribution after crushing by controlling the crushing energy, thereby controlling the dissociation degree of the crushed ore.

[0034] Preferably, the method is performed on single-particle magnetite, and the sample in step b is Φ50x25mm, and step b is repeated 5 times under the same impact crushing energy.

[0035] The multiple impact energies in step c are 226.01J, 376.69J, 527.36J, 640.37J, 753.38J, and 866.38J.

[0036] The function equation established in step e under different impact energies is:

[0037] 226.01J y=0.600x+4.393 R 2 =0.95

[0038] 376.69J y=0.531x+4.435 R2 =0.95

[0039] 527.36J y=0.522x+4.609 R 2 =0.98

[0040] 640.37J y=0.472x+4.568 R 2 =0.97

[0041] 753.38J y=0.450x+4,639 R 2 =0.99

[0042] 866.38J y=0.414x+4.568 R 2 =0.98

[0043] where y is ln(M(x) / M), x is ln(x / x max ), R 2 is the fitting coefficient of the equation;

[0044] Step f establishes the function equation of fractal dimension D and impact crushing energy;

[0045] y=0.0003x+ 2.3464 R 2 =0.97

[0046] where y is fractal dimension, x is impact crushing energy, R 2 is the fitting coefficient of the equation.

[0047] According to the data obtained in step d, the particle size distribution curve of single particle magnetite crushed under different impact energy is drawn. As shown in Figure 1 , it is illustrated that with the increase of applied energy, the particle size distribution curve of magnetite crushed gradually shifts to the left, the particle crushing quality gradually increases, the proportion of fine particles gradually increases, and the number of coarse particles decreases.

[0048] Preferably, the method is carried out for a particle group of magnetite, and the magnetite of-2.000+1.180mm particle size is selected in step b, the mass is 150g, and the crushing test under different impact crushing energy is carried out,

[0049] The multiple impact energies in step c are 332.59J, 432.36J, 532.14J, 631.25J,

[0050] 731.69J;

[0051] The function equation established in step e under different impact energy is:

[0052] 332.59J y=0.631x+3.813 R 2 =0.90

[0053] 432.361 y=0.611x+3.918 R 2 =0.92

[0054] 532.14J y -0.576x+3.946 R 2 =0.92

[0055] 631.25J y=0.509x+4.003 R 2 =0.91

[0056] 731.69J y=0.436x+4.042 R 2 =0.90

[0057] where y is ln(M (x) / M), x is ln(x / x max ), R 2 is the fitting coefficient of the equation;

[0058] Step f establishes the function equation of fractal dimension D and impact crushing energy;

[0059] y=4.945E-4x+2.185 R 2 =0.95

[0060] where y is the fractal dimension, x is the impact crushing energy, R 2 is the fitting coefficient of the equation.

[0061] According to the data obtained in step d, the particle size distribution curve of the magnetite ore crushed by the particle group after being crushed under different impact energies is drawn. The particle size distribution of the particle group of magnetite ore crushed under different crushing energies is as shown in Figure 5 , the mass percentage of the intermediate particle size (≤0.90mm) gradually increases in the process of increasing the energy from 332.59J to 731.69J, and the crushing energy gradually increases from 20.65% to 29.98%, with an increase of 45.18%; the mass percentage of the fine particle size (≤0.74mm) also shows a gradually increasing change from 3.24% to 5.52%, compared with the single particle magnetite sample, the damage degree of the particle group sample increases at a smaller amplitude with the increase of energy, and the surface particle crushing exists size effect. According to the particle crushing theory, the particle size decreases, the original crack content is relatively small, the crushing strength is large, and the volume crushing and crack crushing are mainly. The research shows that when the crushing energy reaches a certain value, the increase of energy has little effect on the degree of particle crushing, so the particle size distribution of the crushing products of the particle group of magnetite ore under different crushing energies is not much different.

[0062] The beneficial effects of the present application are:

[0063] The fractal model method for studying the impact energy of minerals and the particle size distribution characteristics, first, according to the mathematical theory of fractal, the fractal model of the particle size distribution of magnetite crushing is established, and the fractal dimension D is used to represent the particle size after crushing, then the crushing experiment under different impact crushing energy is repeatedly carried out through the falling weight impact testing machine, and the crushed ore particles are collected, and the particle size grading is realized through screening, then the weight of each particle size level is weighed and recorded, then according to the established fractal model, the function equation of ln(M (x) / M) and ln(x / xmax) under different impact energy is established; further, the function equation of fractal dimension D and different impact crushing energy is established; through this method, the function relationship between the particle size of magnetite crushing and the impact crushing energy can be constructed, and the function relationship obtained by this method can guide the adjustment of the crushing energy of the crushing equipment, so as to control the particle size of the crushed magnetite. BRIEF DESCRIPTION OF DRAWINGS

[0064] Figure 1 is the particle size distribution curve of the crushed magnetite after different impact energy crushing analyzed by embodiment one of the present application;

[0065] Figure 2 is the ln(M (x) / M)-ln(x / xmax) curve of the particle size distribution characteristics of the crushed magnetite after different impact crushing energy analyzed by embodiment one of the present application;

[0066] Figure 3 is the corresponding relationship diagram of fractal dimension D and different impact crushing energy analyzed by embodiment one of the present application;

[0067] Figure 4 is the particle size distribution curve of the crushed magnetite after different impact energy crushing analyzed by embodiment two of the present application;

[0068] Figure 5 is the ln(M (x) / M)-ln(x / xmax) curve of the particle size distribution characteristics of the crushed magnetite after different impact crushing energy analyzed by embodiment two of the present application;

[0069] Figure 6 is the corresponding relationship diagram of fractal dimension D and different impact crushing energy analyzed by embodiment two of the present application. DETAILED DESCRIPTION

[0070] Embodiment one: refer to Figures 1-3 A fractal model method for studying the impact energy of minerals and the particle size distribution characteristics, comprising the following steps:

[0071] a. The fractal model of the particle size distribution of magnetite ore crushing is established, and the specific process is as follows:

[0072] From the basic definition of fractal:

[0073] N=cx -D (1)

[0074] In the formula: x is the characteristic scale of the particle block, N is the number of broken particles with characteristic scale x, c is the proportionality constant, and D is the fractal dimension of the broken particle distribution;

[0075] Then the fractal definition is extended to the continuous case:

[0076] N0=cx max -D (2)

[0077] We can get:

[0078] (3)

[0079] Because the number of broken particles is difficult to count, the size-frequency relationship of broken particles is converted into the mass-frequency distribution relationship;

[0080] Because the correlation between particle mass and particle size is , the mass-frequency relationship of particles is:

[0081] (4)

[0082] Therefore, D=3b, the fractal dimension of the ore particle size distribution is determined by the mass-frequency relationship; the total number of particles after crushing is N(x), M(x) is the estimated mass of the debris particles with a diameter less than x, and M is the total mass of the broken particles. Therefore, the size-frequency distribution of the broken particles is:

[0083] (5)

[0084] x o is the average size, when x / x0 1, (5) can be transformed into:

[0085] (6)

[0086] Taking the derivative of (6) gives:

[0087] (7)

[0088] From the concept of fractal:

[0089] (8)

[0090] The relationship between the number of broken particles and the mass is: Thus, we have:

[0091] (9)

[0092] Therefore, we know that:

[0093] D = 3 - b (10)

[0094] where b is the slope value in the double logarithmic coordinates, the cumulative percentage mass of broken particles with a diameter less than x; this theoretical model provides the basic operating basis for subsequent data processing.

[0095] b. Use the drop weight impact machine to crush the magnetite sample, and then classify the crushed particles by size. Weigh and record the data for each size classification. Detailed experimental data are prepared for subsequent coordinate system point drawing and curve fitting.

[0096] c. Adjust the impact energy of the drop weight impact machine multiple times and repeat step b multiple times. Different energy levels require experiments to prepare for subsequent analysis of different particle size distributions corresponding to different energies.

[0097] d. According to the data obtained in step c, draw the particle size distribution curve of the crushed magnetite under different impact energies. This curve provides a visual basis for analyzing and judging the overall trend of particle size under different energies. As shown in Figure 1 , it shows that with the increase of applied energy, the particle size distribution curve of the magnetite gradually shifts to the left, the broken particle mass gradually increases, the proportion of fine particles gradually increases, and the number of coarse particles decreases.

[0098] e. According to the fractal model in step a, use the particle formula (6) to draw the ln(M(x) / M)-ln(x / xmax) curve of the particle size distribution characteristics of the crushed magnetite under different impact crushing energies according to the mass distribution of different particle sizes after crushing, as shown in Figure 2 ; According to the curve, establish the function equation of ln(M(x) / M) and ln(x / xmax) under different impact energies.

[0099] f. According to the fractal model of step a, the fractal dimension D under different impact crushing energies is calculated, and the corresponding relationship diagram of the fractal dimension D and the different impact crushing energies is drawn, the curve is fitted, and the function equation of the fractal dimension D and the impact crushing energy is established. The function can intuitively reflect the relationship between the particle size after the magnetite ore crushing and the crushing energy, and is a linear function, which is beneficial to operation, and can be used to guide the control of the particle size distribution after crushing by controlling the crushing energy, so as to control the dissociation degree of the crushed ore.

[0100] The method is performed on single particle magnetite ore, the sample in step b is Φ50*25mm, and step b is repeated 5 times under the same impact crushing energy;

[0101] The multiple impact energies of step c are 226.01J, 376.69J, 527.36J, 640.37J, 753.38J and 866.38J respectively;

[0102] The function equation established in step e under different impact energies is:

[0103] 226.01J y=0.600x+4.393 R 2 =0.95

[0104] 376.69J y=0.531x+4.435 R 2 =0.95

[0105] 527.36J y=0.522x+4.609 R 2 =0.98

[0106] 640.37J y=0.472x+4.568 R 2 =0.97

[0107] 753.38J y=0.450x+4,639 R 2 =0.99

[0108] 866.38J y=0.414x+4.568 R 2 =0.98

[0109] Wherein y is ln(M (x) / M), x is ln(x / x max ), R 2 is the fitting coefficient of the equation;

[0110] Step f establishes the function equation of the fractal dimension D and the impact crushing energy;

[0111] y=0.0003x+ 2.3464 R 2 =0.97

[0112] where y is the fractal dimension, x is the impact breakage energy, R 2 is the fitting coefficient of the equation.

[0113] Example 2:

[0114] Referring to Figures 1-3 , 5, a fractal model method for studying the impact energy of minerals and the particle size distribution characteristics, comprising the following steps:

[0115] a. Establish a fractal model of the particle size distribution of magnetite ore crushing, the specific process is as follows;

[0116] From the basic definition of fractal:

[0117] N = cx -D (1)

[0118] In the formula: x is the characteristic scale of the particle block, N is the number of broken particles with characteristic scale x, c is the proportionality constant, and D is the fractal dimension of the broken particle distribution;

[0119] Then the fractal definition is extended to the continuous case:

[0120] N0 = cx max -D (2)

[0121] We can get:

[0122] (3)

[0123] Because it is difficult to count the number of broken particles, the size-frequency relationship of broken particles is converted into the mass-frequency distribution relationship;

[0124] Because the correlation between particle mass and particle size is , the mass-frequency relationship of the particles is:

[0125] (4)

[0126] Therefore, D = 3b, the fractal dimension of the ore particle size distribution is determined by the mass-frequency relationship; the broken particles are sieved, the total number of particles is N(x), M(x) is the estimated mass of the debris particles with a diameter less than x, and M is the total mass of the broken particles. Therefore, the size-frequency distribution of the broken particles is:

[0127] (5)

[0128] x o is the average size, and when x / x0 1, the (5) formula can be converted to:

[0129] (6)

[0130] The derivative of the (6) formula is:

[0131] (7)

[0132] From the concept of fractal:

[0133] (8)

[0134] The relationship between the number of broken particles and the mass is: Therefore:

[0135] (9)

[0136] Therefore:

[0137] D = 3-b (10)

[0138] In the formula, b is The slope value in the double logarithmic coordinate system, The cumulative percentage of the mass of broken particles with a diameter less than x; the establishment of this theoretical model provides a basic operation basis for subsequent operation after obtaining experimental data.

[0139] b. Use the falling weight impact tester to crush the magnetite sample, and classify the crushed ore particles by size, and weigh and record the data of each size classification. Detailed experimental data is prepared for subsequent coordinate system point drawing and curve fitting.

[0140] c. Adjust the impact energy of the falling weight impact tester several times, repeat step b several times; different energy sizes need to be tested, which prepares for the analysis of different particle size distribution corresponding to different energies.

[0141] d. According to the data obtained in step c, draw the particle size distribution curve of the crushed magnetite after being crushed under different impact energies; this curve provides a visual basis for analyzing and judging the overall trend of particle size under different energies. For example Figure 4As shown, during the increase of crushing energy from 332.59 J to 731.69 J, the mass percentage of intermediate-sized particles (≤0.90 mm) gradually increased, and the crushing energy gradually increased from 20.65% to 29.98%, an increase of 45.18%. The mass of fine-sized particles (≤0.74 mm) also showed a gradual increase, from 3.24% to 5.52%. Compared with single-particle magnetite samples, the degree of damage to particle cluster samples increased less with increasing energy, indicating a size effect in surface particle crushing. According to particle crushing theory, smaller particle size results in less primary fracture content and higher crushing strength, mainly characterized by volumetric crushing and crack crushing. The study shows that when the crushing energy reaches a certain value, further increasing the energy has little effect on the degree of particle crushing. Therefore, the particle size distribution of crushed products from particle cluster magnetite ore does not differ significantly under different crushing energies.

[0142] e. Based on the fractal model in step a, using the particle formula (6), and according to the mass distribution of different particle sizes after crushing, plot the ln(M(x) / M)-ln(x / xmax) curves of the particle size distribution characteristics of magnetite ore after crushing under different impact crushing energies, as shown below. Figure 5 As shown; based on this curve, establish the functional equations of ln(M(x) / M) and ln(x / xmax) under different impact energies;

[0143] f. Based on the fractal model in step a, calculate the fractal dimension D under different impact fracture energies, and plot the correspondence between the fractal dimension D and different impact fracture energies, as shown in the figure. Figure 6 As shown, a fitted curve is obtained, and a functional equation is established between the fractal dimension D and the crushing energy. This function can intuitively and quantitatively reflect the relationship between the particle size distribution of crushed magnetite ore and the crushing energy. Furthermore, it is a linear function, which is easy to calculate. This can be used to guide the control of particle size distribution after crushing by controlling the crushing energy, thereby controlling the degree of liberation of the crushed ore.

[0144] This method is applied to magnetite ore with a particle size distribution. In step b, magnetite ore with a particle size of -2.000 to +1.180 mm and a mass of 150 g is selected, and crushing tests are conducted with different impact crushing energies.

[0145] The impact energies of the multiple impacts in step c are 332.59 J, 432.36 J, 532.14 J, and 631.25 J, respectively.

[0146] 731.69J;

[0147] The functional equations established in step e for different impact energies are as follows:

[0148] 332.59J y=0.631x+3.813 R 2=0.90

[0149] 432.361 y=0.611x+3.918 R 2 =0.92

[0150] 532.14J y -0.576x+3.946 R 2 =0.92

[0151] 631.25J y=0.509x+4.003 R 2 =0.91

[0152] 731.69J y=0.436x+4.042 R 2 =0.90

[0153] Wherein y is ln(M (x) / M), x is ln(x / xmax), R 2 is the fitting coefficient of the equation;

[0154] Step f establishes the function equation of fractal dimension D and the same impact crushing energy;

[0155] y=4.945E-4x+2.185 R 2 =0.95

[0156] Wherein y is fractal dimension, x is impact crushing energy, R 2 is the fitting coefficient of the equation.

[0157] The method of the application, analysis obtains the function relationship between the fractal dimension D representing the surface morphology of the magnetite ore after crushing and the crushing energy, the function relationship can guide to adjust the crushing energy of the crushing equipment, thereby controlling the particle size distribution of the magnetite ore after crushing.

Claims

1. A fractal model method for studying the impact energy of minerals and the particle size distribution characteristics, comprising the following steps: a. establishing a fractal model of the particle size distribution of magnetite crushing, the specific process being as follows; From the basic definition of fractal, we have: N=cx -D (1) In the formula: x is the characteristic scale of the particle fragments, N is the number of broken particles with characteristic scale x, c is the proportionality constant, and D is the fractal dimension of the broken particle distribution; Then the fractal definition is extended to the continuous case: N0 = cx max -D (2) Thus we have: （3） Since the number of broken particles is difficult to count, the scale-frequency relationship of broken particles is converted into the mass-frequency distribution relationship; Since the correlation of the particle mass and the particle size is the mass-frequency relationship of the particles is: （4） Thus we have: D=3b, the fractal dimension of the ore particle size distribution is determined by the mass-frequency relationship; the broken particles are sieved, the total number of particles is N(x), M(x) is the estimated mass of the debris particles with a diameter less than x, and M is the total mass of the broken particles, then the broken particle size-frequency distribution is: （5） x o For average size, when x / x0 1, the equation (5) can be transformed as: （6） Taking the derivative of formula (6) gives: （7） From the concept of fractal, we have: （8） The number and mass relationship of the broken particles is: Thus, there is: （9） Therefore, we have: D=3-b (10) wherein b is the slope value in a double logarithmic coordinate, is the cumulative percentage by mass of broken particles having a diameter less than x; b. Using a drop weight impact testing machine to crush the magnetite sample, sieving the crushed ore particles, and weighing and recording the data of each particle size classification; c. Adjusting the impact energy of the drop weight impact testing machine multiple times, and repeating step b multiple times; d. Drawing the particle size distribution curve of the crushed magnetite under different impact crushing energies according to the data obtained in step c; e. According to the fractal model in step a, the particle formula (6) is used to draw the ln(M (x) / M)-ln(x / x max ) curve of the particle size distribution characteristics of the magnetite after crushing under different impact crushing energies according to the mass distribution of different particle sizes after crushing; and according to the curve, the function equation of ln(M (x) / M) and ln(x / x max ) under different impact energies is established; f. According to the fractal model of step a, calculating the fractal dimension D under different impact crushing energies, and drawing the corresponding relationship diagram of fractal dimension D and impact crushing energy, fitting the curve, and establishing the functional equation of fractal dimension D and impact crushing energy.

2. The method of claim 1, wherein the method is characterized by: This method is for single particle magnetite, the sample in step b is Φ50x25mm, and step b is repeated 5 times under the same impact crushing energy; The multiple impact energies in step c are 226.01J, 376.69J, 527.36J, 640.37J, 753.38J, and 866.38J; The functional equation under different impact energies established in step e is: 226.01 J y = 0.600x + 4.393 R 2 = 0.95 376.69J y = 0.531x + 4.435 R 2 = 0.95 527.36J y = 0.522x + 4.609 R 2 = 0.98 640.37J y = 0.472x + 4.568 R 2 = 0.97 753.38J y = 0.450x + 4,639 R 2 = 0.99 866.38J y = 0.414x + 4.568 R 2 = 0.98 where y is ln(M(x) / M), x is ln(x / x max ), R 2 is the fitting coefficient of the equation; Step f establishes the functional equation of fractal dimension D and impact crushing energy; y = 0.0003x + 2.3464 R 2 = 0.97 where y is the fractal dimension, x is the impact breakage energy, R 2 is the fitting coefficient of the equation.

3. The method of claim 1, wherein: This method is for particle group magnetite, step b selects-2.000+1.180mm particle size of magnetite, the mass is 150g, and the crushing test under different impact crushing energies is carried out, The multiple impact energies in step c are 332.59J, 432.36J, 532.14J, 631.25J, 731.69J； The functional equation under different impact energies established in step e is: 332.59J y = 0.631x + 3.813 R 2 = 0.90 432.361 y = 0.611 x + 3.918 R 2 = 0.92 532.14J y - 0.576x + 3.946 R 2 = 0.92 631.25J y = 0.509x + 4.003 R 2 = 0.91 731.69 J y = 0.436x + 4.042 R 2 = 0.90 where y is ln(M(x) / M), x is ln(x / x max ), R 2 is the fitting coefficient of the equation; Step f establishes the functional equation of fractal dimension D and impact crushing energy; y = 4.945E-4x + 2.185 R 2 = 0.95 where y is the fractal dimension, x is the impact breakage energy, R 2 is the fitting coefficient of the equation.

4. The method of claim 2, wherein the method is characterized by: According to the data obtained in step d, the particle size distribution curve of the crushed single particle magnetite under different impact energies is drawn.

5. The method of claim 3, wherein: According to the data obtained in step d, the particle size distribution curve of the crushed particle group magnetite under different impact energies is drawn.

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