A method for determining the diameter of steel balls based on the fracture energy of ore

Abstract

The present invention relates to a method for determining the diameter of steel balls based on the fracture energy of ore, belonging to the field of grinding in ore dressing. According to the maximum particle size of the ore fed into the mill, m tons of representative ore samples are taken, and the particle size composition d of the ore fed into the mill is measured. i , the shape factor β of the ore, the density ρ of the ore, and the fracture specific energy E of the ore mi ; various process parameters in the mill and the measured d i , β, ρ, E mi values are substituted into the steel ball diameter calculation formula to accurately calculate the steel ball diameter. The present invention overcomes the defects of calculating the steel ball diameter by traditional empirical formulas, the Allis Chalmers formula, the Knudsen Nord formula, and the Duan's semi-theoretical formula for ball diameter; the grinding process is more targeted and selective, the particle size of the grinding product is more uniform during application, the content of coarser and finer particle sizes is reduced, the content of intermediate easily separable particle sizes is increased, and the metal recovery rate and grade are greatly improved.

Description

Technical Field

[0001] The present invention relates to a method for determining the diameter of steel balls based on the fracture energy of ore, belonging to the field of grinding in ore dressing. Background Technique

[0002] The grinding operation is the core unit for realizing the efficient selective separation of minerals. To achieve the full dissociation of valuable minerals and gangue minerals, efficient grinding treatment must be carried out on them. On the one hand, the energy consumption and steel consumption in the process of grinding minerals are huge. According to statistics, the grinding energy consumption in China accounts for about 1.15% of the total national energy consumption, and the steel consumption accounts for more than 50% of the steel consumption in the concentrator. On the other hand, the particle size characteristics of the grinding products largely determine the subsequent separation indexes. Therefore, how to reduce the energy consumption and steel consumption during the operation of the mill and optimize the particle size characteristics of the grinding products has become a research hotspot in the field of grinding.

[0003] The grinding medium is the most important factor affecting the energy consumption, steel consumption and particle size characteristics of the grinding products in the mill. The grinding medium is the energy transfer body in the grinding process and also the acting body for ore crushing. The grinding efficiency of the mill is affected by the shape, size, ratio, movement form of the medium in the mill and the spatial arrangement between the media. If the energy carried by the medium is not enough to produce a crushing effect, the input energy can only cause elastic deformation of the mineral, and the mineral returns to its original shape after the crushing force is withdrawn. In this process, the energy is dissipated in the pulp in the form of heat; on the contrary, if the energy transferred by the medium is too large, the mineral is prone to through-crushing and over-crushing, resulting in the loss of selectivity in the dissociation of the mineral, and at the same time increasing the energy consumption. Therefore, studying the influence of the size of the medium on grinding and accurately selecting the size of the medium are important issues in the grinding process.

[0004] At present, there are many formulas for calculating the diameter of steel balls in the grinding process. Among them, there are the Rasumov formula (D b =id n ), the Olevsky formula the Davis formula the Bond simple empirical formula and the Dao formula Therefore, there are large errors between the above empirical formulas and actual production. In order to improve the calculation accuracy of the steel ball size, the Aris Chalmers formula widely used in European and American countries is: the Knox Nord formula: The main reasons why these two formulas are difficult to be popularized and applied in the concentrators in China are as follows: (1) Both formulas contain the work index W i, while the beneficiation plants in our country only have the Proctor hardness coefficient f; (2) The feed particle size F in the two formulas uses the 80% sieve - passing size, with the unit of μm, while our country has long used the 95% sieve - passing size, with the unit of cm; (3) Its empirical coefficient was summarized under the condition of foreign large - scale mills. Since the diameter of the mill is large, the potential energy of the steel balls is also greater, so it can make up for the shortage of small balls. However, the diameters of the mills in our country are generally on the small side, and the required diameters are on the large side. Therefore, the empirical coefficient summarized abroad may not be suitable for the beneficiation plants in our country.

[0005] In order to adapt to the actual situation of beneficiation plants in China, Professor Duan Xixiang, in the "Theoretical Calculation Research on the Size of Steel Balls in Ball Mills", derived the semi - theoretical formula for ball diameter based on the classical Davis steel ball theory and the principle of crushing statistical mechanics: This formula uses the compressive strength σ 压 and the 95% sieve - passing size to replace the Bond work index W i and the 80% sieve - passing size commonly used in European and American countries. And the formula takes into account more than a dozen factors. Therefore, the calculation result is in good agreement with the practical result, and it is the most accurate formula for calculating the size of steel balls at present. However, this formula has three problems: ① For the convenience of calculation, the ore is assumed to be spherical particles, ignoring the influence of the ore shape on the fracture energy of the ore; ② It is considered that the mechanical properties of the ore are uniform, and the energy required for ore fracture can be calculated according to the compressive strength and the stress area of the ore. Since there are cracks, defects and holes in the actual ore, there is a large difference between the calculation result and the actual situation; ③ When the ore and rock are stressed, they are in a uniaxial stress state, that is, the formed fracture surface is parallel to the pressure direction and passes through the center of the circle. The actual ore fracture is complex and diverse, and the fracture surface rarely passes through the center of the circle. The above - mentioned problems lead to inaccurate calculation of the energy required for ore fracture, resulting in a difference between the steel ball diameter and the optimal steel ball size. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for determining the steel ball diameter based on the fracture energy of ore. By experimentally detecting the density, shape factor, particle size and fracture energy of the ore, a feasible method for determining the steel ball diameter is provided.

[0007] The technical solution of the present invention is: A method for determining the steel ball diameter based on the fracture energy of ore, and the specific steps of the method are as follows:

[0008] Step1 Determination of the particle size composition of the feed into the mill

[0009] Take m tons of representative ore samples cross - flow from the feed belt into the mill, and use a set of sieves for reduction sieving analysis to obtain the information on the particle size distribution in the ore samples, and measure the geometric mean diameter d of the ore under each particle size grade i ;

[0010] Step2 Determination of the density and shape factor of the ore

[0011] Measure the density ρ of the ore using a helium porosimeter and measure the mass m of the ore under each particle size on an electronic balance. i , according to m i = βρd i 3 , determine the shape factor β of the ore;

[0012] Step3 Determination of the fracture energy of the ore

[0013] Measure the fracture specific energy E of the irregular ore under each particle size on a materials testing machine mi , according to the fracture energy E i = m i E mi Determine the energy required for the ore to fracture;

[0014] Step4 Determination of the steel ball diameter

[0015] The steel ball diameter D required for the feed particle size under specific grinding conditions b Calculation formula:

[0016]

[0017] where ψ is the rotational speed, D0 is the diameter of the intermediate condensation layer, and ρ e is the effective density of the steel ball in the pulp.

[0018] Furthermore, the representative ore sample of m tons is determined according to the maximum particle size fed into the mill, m = Kd 2 , K is a coefficient related to the ore properties, and its value ranges from 0.02 to 0.8.

[0019] Furthermore, the grinding mill is a semi-autogenous mill or a ball mill.

[0020] Furthermore, when measuring the density ρ of the ore, the experiment needs to be repeated no less than 30 times and the average value is taken.

[0021] Furthermore, when measuring the shape factor β of the ore, the experiment needs to be repeated no less than 50 times and the average value is taken.

[0022] Furthermore, when measuring the fracture specific energy of the ore, each particle size needs to be repeated no less than 50 times. Arrange the fracture specific energy E mi from small to large, fit it with the Logistic model, and determine the fracture specific energy corresponding to a fracture probability of 95% by interpolation.

[0023] The working principle of the present invention is:

[0024] The grinding process is a process with intricate influencing factors. There are many aspects that affect the size of grinding steel balls: the fracture energy, particle size, density, shape factor of the ore and rock, the diameter and rotation speed of the mill, the material, density and processing technology of the steel balls, the concentration and viscosity of the pulp, and so on. Only by comprehensively considering the above factors can the size of the steel balls be accurately determined.

[0025] Analyzing from the crushing principle of the ore and rock, the mechanical essence of the crushing process is that the energy applied to the ore and rock is greater than the energy required for its own fracture, and the ore and rock will break. Therefore, the factors affecting the crushing process include: the factors of the crushing object and the crushing power factors.

[0026] The factors of the crushing object include the mechanical strength and geometric size of the ore and rock. The mechanical strength of the ore and rock is generally expressed by the compressive strength and Bond work index, but its measurement procedure is complex and there are large errors in calculating the energy required for the fracture of the ore and rock through them. Therefore, in this invention, the mechanical strength of the ore and rock is directly characterized by measuring the fracture energy of irregular ore.

[0027] The crushing power is mainly implemented by the steel balls, and the magnitude of the crushing force is determined by the normal kinetic energy that the steel ball D b has before crushing, and this normal kinetic energy is related to the mass and speed of the steel ball, and the normal speed is jointly determined by the diameter D0 of the mill and the rotation rate ψ. When the material of the steel ball is determined, the density of the steel ball is constant, but due to the changing pulp concentration inside the mill, the effective density ρ e of the steel ball in the pulp is changing. Therefore, the kinetic energy E carried by the steel ball in the mill = f(D b , D0, ψ, ρ e ). When the energy E of the steel ball is greater than the energy required for the fracture of the ore and rock, the ore and rock will be broken. Therefore, it is reasonable and scientific to determine the size of the steel ball from the energy required for the fracture of the ore and rock.

[0028] The steel ball diameter for crushing ore with a specific particle size d i can be determined by the following formula:

[0029]

[0030] In the formula: D b - The precise ball diameter (m) required for the feed particle size d i under specific grinding conditions; E mi - The specific fracture energy (J / kg) required for the fracture of the ore with particle size d i ; ψ - The rotation rate of the mill (%); ρ - The density of the ore (kg / m 3 ); ρ e - The effective density of the steel ball in the pulp (kg / m 3 ); D0 - The diameter (m) of the "intermediate condensation layer" of the steel balls inside the mill; d i- Feed particle size (m); β- Shape factor of irregular particles.

[0031] The specific derivation process of this formula is as follows:

[0032] (a) Energy E required for ore fracture 断

[0033] Let β be the shape factor of irregular particles, and d i be the diameter of the particle (m), then the volume of irregular ore is:

[0034] V = βd i 3 (1)

[0035] Let ρ be the density of the ore (kg / m 3 ), then the mass of the ore is: M = ρV = ρυd i 3 (2)

[0036] Let E mi be the specific fracture energy of the ore (J / kg), then the energy required for ore fracture is:

[0037] E 断 = βd 3 ρE mi (3).

[0038] (b) Normal impact kinetic energy E of the steel ball falling onto the liner n

[0039] Select a steel ball with a diameter of D b to study. The effective density of the steel ball is ρ e , then the effective mass of the steel ball is:

[0040]

[0041] When the steel ball makes a throwing and falling motion, the normal impact kinetic energy of the steel ball can be solved by using the classical Davis steel ball motion formula. The specific solution process can refer to page 171 of "Ore Crushing and Grinding" compiled by Professor Duan Xixiang. The normal impact kinetic energy E of the steel ball falling onto the liner n is:

[0042]

[0043] Since the breakaway angle α is related to the rotational speed ψ, that is, cosα = ψ 2 ;

[0044] Then formula (5) can be transformed into:

[0045] Where: D0 is the diameter of the intermediate polycondensation layer (m); α is the separation angle of the steel balls (°).

[0046] (c) Calculating the steel ball size from the energy required for ore fracture

[0047] Equation (3) is the energy required for the fracture of ore with a particle size of d i and Equation (6) is the normal energy of a steel ball with a diameter of D b when hitting the ore. When the impact energy carried by the steel ball is greater than the energy required for ore fracture, i.e., E n ≥ E 断 fragmentation occurs, that is

[0048]

[0049] After arrangement, we get

[0050] The beneficial effects of the present invention are as follows:

[0051] It overcomes the defects of calculating the steel ball diameter by traditional empirical formulas, the Allis Chalmers formula, the Knelson Nord formula and the Duan's ball diameter semi-theory formula. Since the fracture energy of irregular ore is directly measured through experiments, no additional error will be introduced, making the energy required for ore fracture more accurate. The steel ball diameter calculated by this method is more targeted and selective in the grinding process. During the application process, the particle size of the grinding product is more uniform, the content of coarser and finer particle sizes is reduced, and the content of intermediate easily selectable particle sizes is increased, greatly improving the metal recovery rate and grade. Description of the Drawings

[0052] Figure 1 is the flowchart of the method for determining the steel ball diameter based on the ore fracture energy of the present invention. Detailed Embodiments

[0053] Example 1: As Figure 1 shown, a method for determining the steel ball diameter based on the ore fracture energy, characterized in that the specific steps of the method are as follows:

[0054] Step1 Determination of the particle size composition of the feed

[0055] Intercept m tons of representative ore samples cross-flow from the feed belt, and use a set of sieves for reduction sieving analysis to obtain information on the particle size distribution of the ore samples, and measure the geometric average diameter d i of the ore for each particle size range;

[0056] Step2 Determination of the ore density and shape factor

[0057] Measure the density ρ of the ore using a helium porosimeter and measure the mass m of the ore for each particle size range on an electronic balancei , according to m i = βρd i 3 , determine the shape factor β of the ore;

[0058] Step3 Determination of the fracture energy of the ore

[0059] Measure the fracture specific energy E of the irregular ore at each particle size on a materials testing machine mi , according to the fracture energy E i = m i E mi Determine the energy required for ore fracture;

[0060] Step4 Determination of the steel ball diameter

[0061] The steel ball diameter D required for the feed particle size under specific grinding conditions b Calculation formula:

[0062]

[0063] Among them, ψ is the rotation rate, D0 is the diameter of the intermediate condensation layer, and ρ e is the effective density of the steel ball in the pulp.

[0064] Specifically, the m tons of the representative ore sample are determined according to the maximum particle size fed into the mill. Generally, to ensure the representativeness of the sample, the minimum mass m = Kd 2 , K is a coefficient related to the ore properties, and its value ranges from 0.02 to 0.8.

[0065] Specifically, the grinding mill is a semi-autogenous mill or a ball mill.

[0066] Specifically, to measure the density ρ of the ore, the test needs to be repeated no less than 30 times and the average value is taken.

[0067] Specifically, to measure the shape factor β of the ore, the test needs to be repeated no less than 50 times and the average value is taken.

[0068] Specifically, to measure the ore fracture specific energy, the test needs to be repeated no less than 50 times for each particle size. Arrange the fracture specific energy E mi from small to large, fit it with the Logistic model, and determine the fracture specific energy corresponding to a fracture probability of 95% by interpolation.

[0069] Example 2: In this example, the raw material is Taihe Iron Ore of Chongqing Iron & Steel Xichang Mining. The method shown in Example 1 is used to determine the steel ball diameter. The specific steps are as follows:

[0070] (1) Determination of the particle size composition of the feed into the mill

[0071] Take 2 tons of representative ore samples by cross-flow cutting on the feed belt into the mill. Use a set of sieves for reduction sieving analysis in the laboratory to obtain information on the particle size distribution in the ore samples, and measure the geometric mean diameter of the ore at the maximum particle size level (generally referring to the particle size corresponding to 95% negative cumulative particle size distribution) as 0.012 m;

[0072] (2) Determination of ore density and shape factor

[0073] Measure 30 groups of ore samples using a helium porosimeter. The average density of the ore is 3800 kg / m 3 , and accurately measure the mass m of 50 ore samples on an electronic balance i . According to m i = βρd i 3 , determine the average shape factor of the ore as 0.395;

[0074] (3) Determination of ore fracture energy

[0075] Determine the fracture specific energy E of 50 groups of irregular ore samples on a materials testing machine mi . According to the fracture energy E i = m i E mi Determine the energy required for ore fracture. The measured fracture specific energy corresponding to a fracture probability of 95% is 2108.02 J / kg;

[0076] (4) Determination of steel ball diameter

[0077] Substitute various process parameters of the ball mill and the measured values of d i , β, ρ, E mi , ψ(75%), D0(3.81 m), ρ e (5610 kg / m 3 ) into the steel ball diameter calculation formula: Calculate the steel ball diameter. The calculated steel ball diameter for a Φ5.03×6.4 m overflow ball mill with a feed of 12 mm is 81.28 mm, and round it up to 80 mm.

[0078] Previously, Chongqing Iron & Steel Xichang Mining Taihe Iron Mine used 100 mm steel balls. The comparison results before and after the test with 80 mm steel balls are shown in Table 1 below:

[0079] Table 1 Comparison table of production rates of Taihe Iron Mine of Chongqing Iron & Steel Xichang Mining using steel balls of different diameters

[0080] Steel ball (mm) Yield of +0.45mm (%) Yield of -0.15 + 0.038mm (%) Yield of -0.038mm (%) Yield of -0.074mm (%) 100 6.59 26.22 25.59 37.48 80 3.29 29.36 21.61 41.97

[0081] It can be seen from the data in the table that after using the more precise 80mm steel balls, the oversize fraction of +0.45mm decreased by 3.3 percentage points, the over-crushed fraction of -0.038mm decreased by 3.98 percentage points, the content of the easily separable fraction of -0.15+0.038mm in the middle increased by 3.14 percentage points, and the qualified fraction of -0.074mm increased by 4.49 percentage points.

[0082] Example 3: In this example, the raw material is the Qibaoshan lead-zinc ore of Jiangxi Copper. The method shown in Example 1 is used to determine the diameter of the steel balls. The specific steps are as follows:

[0083] (1) Determination of the particle size composition of the material fed into the mill

[0084] 1.5 tons of representative ore samples are intercepted crosswise from the incoming grinding belt. In the laboratory, the samples are reduced and sieved using a set of sieves to obtain information on the particle size distribution of the ore samples, and the geometric mean diameter of the ore at the maximum particle size is measured as 0.014m;

[0085] (2) Determination of the ore density and shape factor

[0086] The helium porosimeter is used to measure 30 groups of ore samples. The average density of the ore is 3350 kg / m 3 , and the mass m of 50 ore samples is accurately measured on an electronic balance i . According to m i = βρd i 3 , the average shape factor of the ore is determined to be 0.375;

[0087] (3) Determination of the ore fracture energy

[0088] The fracture specific energy E of 50 groups of irregular ore samples is measured on a materials testing machine mi . According to the fracture energy E i = m i E mi , the energy required for ore fracture is determined. The measured fracture specific energy corresponding to a fracture probability of 95% is 769.01 J / kg;

[0089] (4) Determination of the steel ball diameter

[0090] All kinds of process parameters of the ball mill and the measured d i , β, ρ, E mi , ψ(75%), D0(1.91m), ρ e

[0091]

[0092] To calculate the diameter of steel balls, the diameter of the steel balls obtained when the feed of the Φ2.4×3.6m overflow ball mill is less than 14mm is 81.39mm, and after rounding, it is 80mm.

[0093] Previously, Jiangxi Copper Qibaoshan Lead-Zinc Mine used 100mm steel balls. The comparison results before and after the test with 80mm steel balls are shown in Table 2 below:

[0094] Table 2 Comparison table of the yield of Jiangxi Copper Qibaoshan Lead-Zinc Mine using steel balls of different diameters

[0095]

[0096]

[0097] It can be seen from the data in the table that after using the more accurate 80mm steel balls, the over-coarse particle size of +0.30mm decreased by 10.26 percentage points, the over-crushed particle size of -0.010mm decreased by 2.06 percentage points, the content of the easy-to-select particle size in the middle of -0.074+0.028mm increased by 2.94 percentage points, and the qualified particle size of -0.074mm increased by 8.30 percentage points.

[0098] Example 4: In this example, the raw material is the Heqing Beiya alkaline porphyry-type gold mine in Yunnan. The method shown in Example 1 is used to determine the diameter of the steel balls. The specific steps are as follows:

[0099] (1) Determination of the particle size composition of the feed into the mill

[0100] Take 6 tons of representative ore samples cross-flow from the feed belt into the mill, and use a set of sieves for reduction sieving analysis in the laboratory to obtain the particle size distribution information of the ore samples, and measure the geometric average diameter of the ore under the maximum particle size of 0.188m;

[0101] (2) Determination of the ore density and shape factor

[0102] Measure 30 groups of ore samples using a helium porosimeter. The average density of the ore is 3860 kg / m 3 , and accurately measure the mass m of 50 ore samples on an electronic balance i , according to m i = βρd i 3 , determine the average shape factor of the ore to be 0.352;

[0103] (3) Determination of the ore fracture energy

[0104] Measure the fracture specific energy E of 50 groups of irregular ore samples on a material testing machine mi , according to the fracture energy E i = m i E miDetermine the energy required for ore fracture. The fracture specific energy corresponding to a fracture probability of 95% measured in the test is 3.167 J / kg;

[0105] (4) Determination of the steel ball diameter

[0106] Substitute various process parameters of the ball mill and the measured d i , β, ρ, E mi , ψ(75%), D0(3.97 m), ρ e (5510 kg / m 3 ) values into the steel ball diameter calculation formula: to calculate the steel ball diameter. The calculated steel ball diameter for the Φ5.5×6.6 m semi-autogenous mill with a feed of 188 mm is 141.21 mm, and after rounding, it is 140 mm.

[0107] The comparison results before and after the test of using 120 mm steel balls and 140 mm steel balls in Beiya Gold Mine, Heqing, Yunnan are shown in Table 3 below:

[0108] Table 3 Comparison table of the yields of Beiya Gold Mine, Heqing, Yunnan using steel balls of different diameters

[0109] Steel ball (mm) Yield of +100mm (%) Yield of -80 + 25mm (%) Yield of -0.010mm (%) Yield of -0.074mm (%) 120 44.27 7.39 12.24 25.57 140 36.95 3.89 10.07 28.72

[0110] It can be seen from the data in the table that after using the more accurate 140 mm steel balls, the oversize fraction of +100 mm decreased by 7.32 percentage points, the over-crushed fraction of -0.010 mm decreased by 1.17 percentage points, the content of hard rock in the fraction of -80 + 25 mm increased by 3.50 percentage points, and the qualified fraction of -0.074 mm increased by 3.15 percentage points.

[0111] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge scope of those of ordinary skill in the art.

Claims

1. A method for determining the diameter of steel balls based on the fracture energy of ore, characterized in that: The specific steps of the method are as follows: Step1 Determination of the particle size composition of the material fed into the mill Take m tons of representative ore samples by cross-flow intercepting on the belt feeding into the mill, and use a set of sieves for reduction sieving analysis to obtain the information on the particle size distribution in the ore samples, and measure the geometric mean diameter d of the ore at each particle size fraction i ; Step2 Determination of the ore density and shape factor The density ρ of the ore is measured using a helium porosimeter, and the mass m of the ore under each particle size is measured on an electronic balance. i , according to m i = βρd i 3 , the shape factor β of the ore is determined. Step3 Determination of the ore fracture energy Measure the fracture specific energy E of irregular ore at each particle size on a materials testing machine mi , according to the fracture energy E i = m i E mi Determine the energy required for ore fracture; Step4 Determination of the steel ball diameter Various technological parameters ψ, D0, ρ of the grinding mill e and the measured d i , β, ρ, E mi values are substituted into the steel ball diameter calculation formula: to calculate the steel ball diameter; where ψ is the rotation rate, D0 is the diameter of the intermediate polycondensation layer, and ρ e is the effective density of the steel balls in the pulp.

2. The method for determining the diameter of steel balls based on the fracture energy of ore according to claim 1, wherein: The weight m of the representative ore sample intercepted cross-flow on the belt of the mill is determined by the maximum particle size d of the ore sample fed into the mill, and m = Kd 2 , where K is a coefficient related to the properties of the ore, and its value ranges from 0.02 to 0.

8.

3. The method for determining the diameter of steel balls based on the fracture energy of ore according to claim 1, wherein: The grinding mill is a semi-autogenous mill or a ball mill.

4. The method for determining the diameter of steel balls based on the fracture energy of ore according to claim 1, wherein: To measure the density ρ of the ore, the test needs to be repeated no less than 30 times and the average value is taken.

5. The method for determining the diameter of steel balls based on the fracture energy of ore according to claim 1, characterized in that: To measure the shape factor β of the ore, the test needs to be repeated no less than 50 times and the average value is taken.

6. The method for determining the diameter of steel balls based on the fracture energy of ore according to claim 1, wherein: Measure the fracture specific energy of the ore. For each particle size fraction, the test needs to be repeated no less than 50 times. Denote the fracture specific energy as E mi Arrange them in ascending order, fit them with the Logistic model, and determine the fracture specific energy corresponding to a fracture probability of 95% by interpolation method.

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