Fractal model method for researching mineral impact energy and particle size distribution characteristics

Abstract

A fractal model method for researching mineral impact energy and particle size distribution characteristics comprises the following steps: firstly, establishing a fractal model of particle size distribution of crushed magnetite according to a fractal mathematical theory, representing the particle size condition after crushing by using a fractal dimension D, and then repeatedly performing crushing experiments under different impact crushing energies through a falling weight impact testing machine to obtain the fractal model of the particle size distribution of the crushed magnetite. The method comprises the following steps of: crushing ore, collecting crushed ore particles, realizing size grading through screening, weighing and recording the weight of the particles of each size grade, and establishing an ln (M (x) / M) and ln (x / xmax) functional equation under different impact energies according to an established fractal model; further establishing a functional equation of the fractal dimension D and different impact crushing energies; by means of the method, the function relation between the magnetic iron ore crushing particle size condition and the impact crushing energy can be constructed, the function relation obtained through the method can further guide and adjust the crushing energy of crushing equipment, and therefore the particle size condition of the crushed magnetic iron ore is controlled.

Description

Technical Field

[0001] The present invention relates to the technical field of analyzing the particle size of ore particles after crushing, and particularly to a fractal model method for studying the impact energy and particle size distribution characteristics of minerals. Background Art

[0002] The crushing and processing of ore is a prerequisite for subsequent separation and smelting. The ground particles formed after the crushing equipment crushes the ore particles to be ground cover a certain particle size range as a whole, and each has its own proportion at different particle size levels. The crushing process is a process in which the crushing equipment or the grinding equipment applies energy to the ore particles to change them from large particles to small particles. If the energy applied by the equipment is too large, the proportion of fine particles after crushing is relatively large; if the energy applied by the equipment is too low, the proportion of fine particles after crushing is relatively small. The same is true for the grinding and processing of magnetite ore. In the prior art, only a qualitative understanding is available, and no quantifiable relationship is given. How to determine the specific corresponding relationship between the crushing energy and the situation of magnetite ore particles after crushing, and what method to use to analyze and determine this corresponding relationship have important guiding significance for adjusting the crushing energy of the crushing equipment. Summary of the Invention

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

[0004] The technical solution of the present invention is: a fractal model method for studying the impact energy and particle size distribution characteristics of minerals, including the following steps:

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

[0006] From the basic definition of fractal, it can be obtained:

[0007] N = cx -D (1)

[0008] In the formula: x is the characteristic scale of the particle fragments, N is the number of crushings with the characteristic scale of x, c is a proportionality constant, and D is the fractal dimension of the crushed particle distribution;

[0009] Let x be the characteristic scale of the particle fragments, and N be the number of fragments with the characteristic scale greater than or equal to x. Then the fractal definition is extended to the continuous case:

[0010] N = cx -D (2)

[0011] Therefore, it can be obtained:

[0012]

[0013] Since the number of broken particles is difficult to count, the scale-frequency relationship of broken particles is transformed into a mass-frequency distribution relationship;

[0014] Since the correlation between particle mass and particle size is M ∝ x 3 , the mass-frequency relationship of particles is:

[0015]

[0016] It can be obtained therefrom that: D = 3b, and the fractal dimension of the ore particle size distribution is determined by the mass-frequency relationship; the broken particles are screened, 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 particle size-frequency distribution of the broken particles:

[0017]

[0018] x o is the average size. When x / x 0 << 1, equation (5) can be transformed into:

[0019]

[0020] Taking the derivative of equation (6) gives:

[0021] dM ∝ x b-1 dr (7)

[0022] From the concept of fractal:

[0023]

[0024] The relationship between the number and mass of broken particles is: dN ∝ x -3 dM, then there is:

[0025] x b-1 dx ∝ x 3 ·x -D-1 dx (9)

[0026] Thus, it can be known that:

[0027] D = 3 - b (10)

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

[0029] b. Use a drop-weight impact testing machine to crush magnetite ore samples. After crushing, the ore particles are classified by particle size, and the particles after each particle size classification are weighed separately and the data is recorded. The detailed experimental data prepares for subsequent coordinate system plotting and curve fitting.

[0030] c. Adjust the impact energy of the drop-weight impact testing machine multiple times, and repeat step b multiple times; for different energy levels, experiments need to be carried out to prepare for the analysis of different particle size distribution situations corresponding to different energies.

[0031] d. According to the data obtained in step c, plot the particle size distribution curve of magnetite ore crushed at different impact energies; this curve provides a visual basis for the analysis and judgment of the overall change trend of particle size under different energies.

[0032] e. According to the fractal model in step a, using particle formula (5.6), based on the mass distribution of different particle size grades after crushing, plot the ln(M(x) / M)-ln(x / x max ) curve of the particle size distribution characteristics of magnetite ore after crushing at different impact crushing energies; according to this 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 plot the corresponding relationship diagram between the fractal dimension D and different impact crushing energies, fit the curve, and establish the function equation of the fractal dimension D and the same impact crushing energy. This function can intuitively and quantitatively reflect the relationship between the particle size situation of crushed magnetite ore and the crushing energy, and is a linear function, which is conducive to calculation. It can be used to guide the control of the particle size distribution by controlling the crushing energy, so as to control the dissociation degree of the ore after crushing.

[0034] Preferably, this method is carried out for single-particle magnetite ore. The sample in step b is Φ50×25mm, and step b is repeated 5 times with 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 respectively;

[0036] The function equations established in step e under different impact energies are:

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

[0038] 376.69J y = 0.531x + 4.435R 2= 0.95

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

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

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

[0042] 866.38J y = 0.414x + 4.568R 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 functional equation of the fractal dimension D and the same impact crushing energy;

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

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

[0047] According to the data obtained in step d, plot the particle size distribution curve of single-particle magnetite ore crushed at different impact energies. As Figure 1 shown, it shows that as the applied energy increases, the particle size distribution curve of magnetite ore crushing 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, this method is carried out for particulate magnetite ore. In step b, magnetite ore with a particle size range of -2.000 + 1.180 mm is selected, and the mass is taken as 150 g for crushing tests with different impact crushing energies,

[0049] The multiple impact energies in step c are 332.59J, 432.36J, 532.14J, 631.25J, and 731.69J respectively;

[0050] The functional equations established in step e under different impact energies are:

[0051]

[0052] where y is ln(M(x) / M), x is ln(x / xmax ),R 2 is the fitting coefficient of the equation;

[0053] Step f: Establish a functional equation for the fractal dimension D and the same impact crushing energy;

[0054] y = 4.945E-4x + 2.185 R 2 = 0.95

[0055] where y is the fractal dimension, x is the impact crushing energy, and R 2 is the fitting coefficient of the equation.

[0056] Based on the data obtained in step d, plot the particle size distribution curve of granular magnetite ore after crushing at different impact energies. The particle size distribution of granular magnetite ore after crushing at different crushing energies is as follows Figure 5 . When the energy increases from 332.59j to 731.69j, the mass percentage of particles with intermediate particle size (≤0.90mm) gradually increases, and the crushing energy gradually increases, rising from 20.65% to 29.98%, with an increase rate of 45.18%; the mass of particles with fine particle size (≤0.74mm) also shows a gradually increasing change characteristic, rising from 3.24% to 5.52%. Compared with the single-particle magnetite sample, the degree of damage of the granular sample increases less with the increase of energy, and there is a size effect in the crushing of surface particles. According to the particle crushing theory, as the particle size decreases, the content of primary cracks is relatively small, the crushing strength is large, and it is mainly volume crushing and crack crushing. Research shows that when the crushing energy reaches a certain value, further increasing the energy has little effect on the crushing degree of particles. Therefore, the particle size distribution of the products of granular magnetite ore under the action of different crushing energies has little difference.

[0057] The beneficial effects of the present invention are:

[0058] The present invention studies the fractal model method for the impact energy and particle size distribution characteristics of minerals. First, according to the mathematical theory of fractals, establish a fractal model for the particle size distribution of magnetite ore crushing, and use the fractal dimension D to represent the particle size situation after crushing. Then, through a drop-weight impact testing machine, conduct crushing experiments under different impact crushing energies repeatedly, collect the crushed ore particles, realize particle size classification through screening, then weigh and record the weights of particles in each particle size level, and then according to the established fractal model, establish a functional equation for ln(M(x) / M) and ln(x / xmax) under different impact energies; further establish a functional equation for the fractal dimension D and different impact crushing energies; through this method, a functional relationship between the particle size situation of magnetite ore crushing and the impact crushing energy can be constructed, and further, the functional relationship obtained through this method can be used to guide the adjustment of the crushing energy of the crushing equipment, so as to control the particle size situation of the crushed magnetite ore. Description of the Drawings

[0059] Figure 1 is the particle size distribution curve of magnetite ore broken at different impact energies obtained from the analysis of Embodiment 1 of the present invention;

[0060] Figure 2 is the ln(M(x) / M)-ln(x / xmax) curve of the particle size distribution characteristics of magnetite ore broken at different impact crushing energies obtained from the analysis of Embodiment 1 of the present invention;

[0061] Figure 3 is the corresponding relationship diagram between the fractal dimension D and different impact crushing energies obtained from the analysis of Embodiment 1 of the present invention;

[0062] Figure 4 is the particle size distribution curve of magnetite ore broken at different impact energies obtained from the analysis of Embodiment 2 of the present invention;

[0063] Figure 5 is the ln(M(x) / M)-ln(x / xmax) curve of the particle size distribution characteristics of magnetite ore broken at different impact crushing energies obtained from the analysis of Embodiment 2 of the present invention;

[0064] Figure 6 is the corresponding relationship diagram between the fractal dimension D and different impact crushing energies obtained from the analysis of Embodiment 2 of the present invention. Detailed implementation manners

[0065] Embodiment 1: Refer to Figures 1-3 , a fractal model method for studying the impact energy and particle size distribution characteristics of minerals, comprising the following steps:

[0066] a. Establish a fractal model of the particle size distribution of magnetite ore broken, and the specific process is as follows;

[0067] According to the basic definition of fractal, it can be obtained that:

[0068] N = cx -D (1)

[0069] In the formula: x is the characteristic scale of the particle fragments, N is the number of fragments with the characteristic scale of x, is the proportionality constant, and D is the fractal dimension of the broken particle distribution;

[0070] Let be the characteristic scale of the particle fragments, and N be the number of fragments with the characteristic scale greater than or equal to x, then the fractal definition is extended to the continuous case:

[0071] N = cx -D (2)

[0072] Therefore, it can be obtained that:

[0073]

[0074] Since the number of broken particles is difficult to count, the scale-frequency relationship of broken particles is transformed into a mass-frequency distribution relationship;

[0075] Since the correlation between particle mass and particle size is M ∝ x 3 , the mass-frequency relationship of particles is:

[0076]

[0077] Thus, it can be obtained that: D = 3b, and the fractal dimension of the ore particle size distribution is determined by the mass-frequency relationship; the broken particles are screened, 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 particle size-frequency distribution of the broken particles is:

[0078]

[0079] x o is the average size. When x / x 0 << 1, equation (5) can be transformed into:

[0080]

[0081] Taking the derivative of equation (6) gives:

[0082] dM ∝ x b-1 dr (7)

[0083] From the concept of fractal:

[0084]

[0085] The relationship between the number and mass of broken particles is: dN ∝ x -3 dM, then:

[0086] x b-1 dx ∝ x 3 ·x -D-1 dx (9)

[0087] Thus, it can be known that:

[0088] D = 3 - b (10)

[0089] In the formula, b is the slope value in the double logarithmic coordinate, is the cumulative mass percentage of broken particles with a diameter less than x; the establishment of this theoretical model provides a basic operation basis for the operation after obtaining experimental data later.

[0090] b. Use a drop-weight impact testing machine to crush magnetite ore samples. After crushing, the ore particles are classified by particle size, and the particles after each particle size classification are weighed separately and the data is recorded; the detailed experimental data is prepared for subsequent coordinate system plotting and curve fitting.

[0091] c. Adjust the impact energy of the drop-weight impact testing machine multiple times, and repeat step b multiple times; for different energy levels, experiments need to be carried out to prepare for the analysis of different particle size distributions corresponding to different energies later.

[0092] d. According to the data obtained in step c, plot the particle size distribution curve of magnetite ore crushed at different impact energies; this curve provides a visual basis for analyzing and judging the overall change trend of particle size under different energies. As Figure 1 shown, it shows that as the applied energy increases, the particle size distribution curve of magnetite ore crushing 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.

[0093] e. According to the fractal model in step a, use the particle formula (5.6), and based on the mass distribution of different particle sizes after crushing, plot the ln(M(x) / M)-ln(x / xmax) curve of the particle size distribution characteristics of magnetite ore after crushing at different impact crushing energies, as Figure 2 shown; according to this curve, establish the function equation of ln(M(x) / M) and ln(x / xmax) under different impact energies;

[0094] f. According to the fractal model in step a, calculate the fractal dimension D under different impact crushing energies, and plot the corresponding relationship diagram between the fractal dimension D and different impact crushing energies, fit the curve, and establish the function equation of the fractal dimension D and the same impact crushing energy. This function can intuitively and quantitatively reflect the relationship between the particle size situation of crushed magnetite ore and the crushing energy, and it is a linear function, which is conducive to calculation, and can be used to guide the control of the particle size distribution by controlling the crushing energy, so as to control the dissociation degree of the ore after crushing.

[0095] This method is carried out for single-particle magnetite ore. The sample in step b is Φ50×25mm, and step b is repeated 5 times with the same impact crushing energy;

[0096] The multiple impact energies in step c are 226.01J, 376.69J, 527.36J, 640.37J, 753.38J, 866.38J respectively;

[0097] The function equation established in step e under different impact energies is:

[0098] 226.01J y=0.600x+4.393R2 = 0.95

[0099] 376.69J y = 0.531x + 4.435R 2 = 0.95

[0100] 527.36J y = 0.522x + 4.609R 2 = 0.98

[0101] 640.37J y = 0.472x + 4.568R 2 = 0.97

[0102] 753.38J y = 0.450x + 4,639R 2 = 0.99

[0103] 866.38J y = 0.414x + 4.568R 2 = 0.98

[0104] where y is ln(M(x) / M), x is ln(x / x max ), R 2 is the fitting coefficient of the equation;

[0105] Step f establishes the functional equation of the fractal dimension D and the same impact crushing energy;

[0106] y = 0.0003x + 2.3464R 2 = 0.97

[0107] where y is the fractal dimension, x is the impact crushing energy, R 2 is the fitting coefficient of the equation.

[0108] Example 2:

[0109] See Figures 1-3 , 5, a fractal model method for studying the impact energy and particle size distribution characteristics of minerals, including the following steps:

[0110] a. Establish a fractal model of the particle size distribution of magnetite ore crushing, and the specific process is as follows;

[0111] From the basic definition of fractal, we can get:

[0112] N = cx -D (1)

[0113] In the formula: x is the characteristic scale of the particle fragments, N is the number of fragments with the characteristic scale of x, is the proportionality constant, and D is the fractal dimension of the broken particle distribution;

[0114] Let \(x\) be the characteristic scale of the particle fragments, and \(N\) be the number of fragments with a characteristic scale greater than or equal to \(x\). Then the fractal definition is extended to the continuous case:

[0115] N = cx -D (2)

[0116] Therefore, it can be obtained that:

[0117]

[0118] Since it is difficult to count the number of broken particles, the scale-frequency relationship of broken particles is transformed into a mass-frequency distribution relationship;

[0119] Since the correlation between particle mass and particle size is \(M\propto x\) 3 , the mass-frequency relationship of the particles is:

[0120]

[0121] From this, it can be obtained that \(D = 3 - b\). The fractal dimension of the ore particle size distribution is determined by the mass-frequency relationship; the broken particles are screened. 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 size-frequency distribution of the broken particles:

[0122]

[0123] x o is the average size. When \(x / x\) 0 << 1, equation (5) can be transformed into:

[0124]

[0125] Taking the derivative of equation (6) gives:

[0126] dM∝x b-1 dr (7)

[0127] From the concept of fractal, it is known that:

[0128]

[0129] The relationship between the number and mass of broken particles is: dN∝x -3 dM, then there is:

[0130] x b-1 dx∝x 3 ·x -D-1 dx (9)

[0131] Thus, it can be known that:

[0132] D = 3 - b (10)

[0133] In the formula, b is the slope value in the double logarithmic coordinate system, and is the cumulative mass percentage of broken particles with a diameter less than x; the establishment of this theoretical model provides a basic operation basis for the subsequent operations after obtaining experimental data.

[0134] b. Use a drop-weight impact testing machine to crush the magnetite ore sample. After crushing, the ore particles are sized, and the particles after each size classification are weighed and the data is recorded; the detailed experimental data prepares for the subsequent plotting of points in the coordinate system and curve fitting.

[0135] c. Adjust the impact energy of the drop-weight impact testing machine multiple times, and repeat step b multiple times; for different energy levels, experiments need to be carried out to prepare for the subsequent analysis of the different particle size distribution conditions corresponding to different energies.

[0136] d. According to the data obtained in step c, plot the particle size distribution curve of the magnetite ore crushed at different impact energies; this curve provides a visual basis for the analysis and judgment of the overall change trend of the particle size under different energies. As Figure 4 shown, during the process of increasing the crushing energy from 332.59 J to 731.69 J, the mass percentage of particles with an intermediate particle size (≤0.90 mm) gradually increases, and the crushing energy gradually increases, rising from 20.65% to 29.98%, with an increase rate of 45.18%; the mass of particles with a fine particle size (≤0.74 mm) also shows a gradually increasing change characteristic, rising from 3.24% to 5.52%. Compared with the single-particle magnetite ore sample, the degree of damage of the particle group sample increases less with the increase of energy, indicating that there is a size effect in the surface particle crushing. According to the particle crushing theory, as the particle size decreases, the relative content of primary cracks is less, the crushing strength is high, and it is mainly volume crushing and crack crushing. Research 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 the crushed products of the particle group magnetite ore under different crushing energies has little difference.

[0137] e. According to the fractal model in step a, use the particle formula (5.6), and based on the mass distribution of different particle sizes after crushing, plot the ln(M(x) / M)-ln(x / xmax) curve of the particle size distribution characteristics of the magnetite ore after crushing at different impact crushing energies, as Figure 5 shown; according to this curve, establish the function equation of ln(M(x) / M) and ln(x / xmax) under different impact energies;

[0138] f. According to the fractal model in step a, calculate the fractal dimension D under different impact crushing energies, and plot the corresponding relationship diagram between the fractal dimension D and different impact crushing energies, as Figure 6As shown, the fitting curve is used to establish the functional equation of the fractal dimension D and the same impact crushing energy. This function can visually and quantitatively reflect the relationship between the particle size of the crushed magnetite ore and the crushing energy, and it is a linear function, which is conducive to calculation. Based on this, it can be used to guide the control of the particle size distribution by controlling the crushing energy, thereby controlling the dissociation degree of the ore after crushing.

[0139] This method is carried out for the particle group magnetite ore. In step b, magnetite ore with a particle size of -2.000 + 1.180 mm is selected, and the mass is 150 g. Crushing tests with different impact crushing energies are carried out.

[0140] The multiple impact energies in step c are 332.59 J, 432.36 J, 532.14 J, 631.25 J,

[0141] 731.69 J;

[0142] The functional equations established in step e under different impact energies are as follows:

[0143] 332.59 J y = 0.631x + 3.813R 2 = 0.90

[0144] 432.361 y = 0.611x + 3.918R 2 = 0.92

[0145] 532.14 J y - 0.576x + 3.946R 2 = 0.92

[0146] 631.25 J y = 0.509x + 4.003R 2 = 0.91

[0147] 731.69 J y = 0.436x + 4.042R 2 = 0.90

[0148] Where y is ln(M(x) / M), x is ln(x / xmax), and R 2 is the fitting coefficient of the equation;

[0149] In step f, the functional equation of the fractal dimension D and the same impact crushing energy is established;

[0150] y = 4.945E - 4x + 2.185R 2 = 0.95

[0151] Where y is the fractal dimension, x is the impact crushing energy, and R 2 is the fitting coefficient of the equation.

[0152] For the method of the invention, the functional relationship between the fractal dimension D representing the surface morphology of the particles after the magnetite ore is broken and the crushing energy is analyzed. This functional relationship can guide the adjustment of 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 and particle size distribution characteristics of minerals, comprising the following steps: a. Establish a fractal model of particle size distribution of magnetite ore crushing. The specific process is as follows; From the basic definition of fractals we can get: N=cx -D (1) Where: x is the characteristic scale of the particle fragments, N is the number of fragments with characteristic scale x, is the proportional constant, and D is the fractal dimension of the distribution of the broken particles; Let x be the characteristic scale of the particle fragments, and N be the number of fragments with characteristic scale greater than or equal to x, then the fractal definition is extended to the continuous case: N=cx -D (2) Therefore, we can get: Since the number of broken particles is difficult to count, the scale-frequency relationship of the broken particles is transformed into a mass-frequency distribution relationship; Since the correlation between particle mass and particle size is M∝x 3 , the mass-frequency relationship of the particle is: From this, we can get: D = 3b, and the fractal dimension of the ore particle size distribution is determined by the mass-frequency relationship; the crushed particles are screened, and 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 crushed particles, then the crushed particle size-frequency distribution is: x o is the average size of one inch. When x / x0<<1, equation (5) can be transformed into: By taking the derivative of (6), we can get: dM∝x b-1 dr (7) From the concept of fractals: N(x)∝x -D , then dN∝x -D-1 dx (8) The relationship between the number and mass of broken particles is: dN∝x -3 dM, then: x b-1 dx∝x 3 ·x -D-1 dx (9) It can be seen that: D=3-b (10) In the formula, b is The slope value in double logarithmic coordinates, is the cumulative percentage of the mass of the broken particles with a diameter less than x; b. Use a falling weight impact tester to crush the magnetite ore sample, classify the crushed ore particles, and weigh the particles after each particle size classification and record the data; c. Adjust the impact energy of the drop weight impact tester several times and repeat step b several times; d. According to the data obtained in step c, a particle size distribution curve of the magnetite ore after crushing at different impact energies is plotted; e. According to the fractal model in step a, using the particle formula (5.6), according to the mass distribution of different particle sizes after crushing, plot the particle size distribution characteristics of magnetite after crushing under different impact crushing energies: ln(M(x) / M)-ln(x / x max ) curve; Based on this curve, the relationship between ln(M(x) / M) and ln(x / x) under different impact energies is established. max ) Functional equation; f. According to the fractal model of step a, calculate the fractal dimension D under different impact crushing energies, draw a corresponding relationship diagram between the fractal dimension D and different impact crushing energies, fit the curve, and establish a function equation between the fractal dimension D and the same impact crushing energy.

2. The fractal model method for studying the impact energy and particle size distribution characteristics of minerals according to claim 1, characterized in that: The method is carried out for single-grain magnetite ore, the sample in step b is Φ50×25 mm, and step b is repeated 5 times with the same impact crushing energy; The multiple impact energies in step c are 226.01 J, 376.69 J, 527.36 J, 640.37 J, 753.38 J, and 866.38 J, respectively; The functional equations under different impact energies established in step e are: 226.01J y=0.600x+4.393R 2 =0.95 376.69J y=0.531x+4.435R 2 =0.95 <h2 style=";text-align:left;direction:ltr">527.36J y = 0.522x + 4.609R<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> <0.98 640.37J and =0.472x+4.568R 2 =0.97 <h2 style=";text-align:left;direction:ltr">753.38J y = 0.450x + 4.639R<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> <0.99 866.38J y=0.414x+4.568R 2 =0.98 where y is ln(M(x) / M) and x is ln(x / x max ), R 2 is the fitting coefficient of the equation; Step f: establishing a function equation between the fractal dimension D and the same impact crushing energy; y=0.0003x+2.3464R 2 =0.97 Where y is the fractal dimension, x is the impact crushing energy, R 2 is the fitting coefficient of the equation.

3. The fractal model method for studying the impact energy and particle size distribution characteristics of minerals according to claim 1, characterized in that: The method is carried out for the particle group magnetite ore. In step b, the magnetite ore of -2.000+1.180mm particle size is selected, the mass is 150g, and the crushing test with different impact crushing energies is carried out. The multiple impact energies in step c are 332.59 J, 432.36 J, 532.14 J, 631.25 J, and 731.69 J, respectively; The functional equations under different impact energies established in step e are: <h2 style=";text-align:left;direction:ltr">332.59J y = 0.631x + 3.813R<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> <0.90 432.361y=0.611x+3.918R 2 =0.92 532.14J y-0.576x+3.946R 2 =0.92 <h2 style=";text-align:left;direction:ltr">631.25J y = 0.509x + 4.003R<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> <0.91 731.69J y=0.436x+4.042R 2 =0.90 where y is ln(M(x) / M) and x is ln(x / x max ), R 2 is the fitting coefficient of the equation; Step f: establishing a function equation between the fractal dimension D and the same impact crushing energy; y=4.945E-4x+2.185R 2 =0.95 Where y is the fractal dimension, x is the impact crushing energy, R 2 is the fitting coefficient of the equation.

4. The fractal model method for studying the impact energy and particle size distribution characteristics of minerals according to claim 2, characterized in that: According to the data obtained in step d, the particle size distribution curve of the single-particle magnetite ore after being crushed at different impact energies is plotted.

5. The fractal model method for studying the impact energy and particle size distribution characteristics of minerals according to claim 3, characterized in that: 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 at different impact energies is drawn.

Images