JPH11253828A - Working power estimating method of inner and outer cylinder interrotating type ball mill - Google Patents

Abstract

PROBLEM TO BE SOLVED: To inexpensively and efficiently amporphize an inorganic powder with an inner and outer cylinder inter-rotating type ball mill. SOLUTION: At the time of finely pulverizing the powder with the inner and outer cylinder inter rotating type ball mill, the movement of balls 23 in the inner and outer cylinder inter rotating type ball mill 20 is simulated by a discrete element method using a viscoelastic dynamic model to calculate the collision energy E of total balls 23 at the starting of the collision. The working power Y of the inner and outer cylinder inter rotating type ball mill 20 is calculated based on the collision energy E.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION The present invention relates to a method for producing an amorphous powder, which is, for example, an inorganic powder having a crystalline property called a mechanochemical, which is highly pulverized by an inter-rotating ball mill to form an amorphous powder. The present invention relates to a method for predicting the operating power of a rotary ball mill.

[0002]

2. Description of the Related Art In the case of pulverizing powder such as fine pulverization for imparting a chemical reaction activity to inorganic powder, coarse pulverization in the process of refining mineral resources, and coarse pulverization of coal used as a raw material for thermal power generation. For the purpose of improving work efficiency, modifying the properties of powder, and the like, simulation of powder movement during pulverization has been performed. However, since the powder, which is an aggregate of solid particles, repeats discrete and aggregate, it is not easy to derive the relationship between individual powders that repeat discrete and aggregate. However, there is a problem that it is not easy to handle as a continuum.

[0003] For this purpose, the discrete behavior of solid particles is determined by setting a dynamic model for each particle and performing a numerical analysis based on the dynamic model. Based on the discrete element method (individual element method) that calculates the force acting on each particle in a minute time, calculates the equation of motion differentially based on it, and sequentially analyzes the displacement of the particle It has been proposed to simulate the movement of powder. (PACundall and ODL
Strack; Geotechnique, 29, p. 47-65 (1979)).

[0004] Recently, the motion of balls and powder in a ball media type pulverizer has been analyzed by the discrete element method to clarify the pulverization phenomenon theoretically (Junya Kano, Fumiyoshi Saito). Others, Tohoku University Institute of Materials Engineering, Vol. 52, No. 1, No. 2, pp. 112-125.
o, Naoki Chuji and Fumio Saito; Advanced Power Techno
l.Vol.8, No.1, p.39-51 (1997)).

In the discrete element method, the mechanical model acting on particles (balls and powders) is of the utmost importance, and usually
As a viscoelastic mechanical model, a Voigt model is used. In the Voigt model, the force acting on particles is expressed by a spring representing elastic properties and a dashpot representing inelastic properties, and it is necessary to sequentially analyze the particle center coordinates and the displacement of the particle center coordinates in a minute time. Thereby, an acting force on the particles is obtained.

[0006] The behavior of balls and powder in a ball medium type pulverizer by the discrete element method is usually analyzed by a computer in the following procedure. First, the initial parameters indicating the characteristics of the particles (ball and powder) are input to the computer, and the contact between the particles and the wall surface of the cylindrical container is determined to set the initial position of the ball. Next, the contact between the wall surface of the container and the particle is determined, and the contact force (action force) between the target particle and the nearby particle when the particle of interest not in contact with the wall surface of the container comes into contact with the nearby particle is calculated. Then, the average value of the acceleration, velocity, and displacement of the particle is calculated based on the contact force. Thereby, the motion characteristics of the particles are simulated. Also,
If the particles are in contact with the wall of the container when the contact between the particles and the wall of the container is determined, the contact force is calculated and the average value of the acceleration, velocity, and displacement of the particles is calculated based on the contact force. Is calculated, the motion characteristics of the particles are simulated.

[0007] By such a motion simulation of the particles in the ball medium type pulverizer, the contact force of the ball with the powder is analyzed, and the pulverization efficiency and the like of the powder can be improved.

[0008]

Crystalline inorganic powders such as clay minerals and aluminum-containing powders, which are suitably used for civil engineering materials, building materials, etc., are finely pulverized to be amorphous. It is known that high chemical reactivity can be obtained. As a ball medium type pulverizer used for pulverizing such an inorganic powder, an inner / outer cylinder mutual rotation type ball mill is known. The inner / outer cylinder mutual rotating ball mill has an outer cylinder and an inner cylinder arranged concentrically, and a ball is housed between the outer cylinder and the inner cylinder. , The outer cylinder and the inner cylinder are rotated in mutually opposite directions. The ball between the outer cylinder and the inner cylinder is agitated by the outer cylinder stirring blade provided on the inner peripheral surface of the outer cylinder and the inner cylinder stirring blade provided on the outer peripheral surface of the inner cylinder. The powder charged between the and the inner cylinder is finely pulverized.

In such an inner and outer cylinder reciprocating rotary ball mill, the outer cylinder stirring blade provided on the outer cylinder and the inner cylinder stirring blade provided on the inner cylinder give high shear energy to the ball and the powder, and Can be efficiently made amorphous.
However, the shear energy given to the ball and the powder by the outer cylinder stirring blade and the inner cylinder stirring blade depends on the operating conditions of the inner and outer mutual rotating ball mill, for example, the rotation speed of the outer cylinder and the inner cylinder, the filling amount of the ball, and the amount of the ball. It is greatly affected by the material and the like, and if the operating conditions of the inner and outer cylinder reciprocating rotary ball mill are different, the degree of amorphousness of the powder is also greatly changed. Therefore, when the inorganic powder is finely pulverized into an amorphous state, the movement of the ball and the powder in the inner and outer cylinder reciprocating rotary ball mill is simulated and analyzed to improve the pulverization efficiency and the like. Become.

When the inorganic powder is made amorphous by the inner and outer cylinder reciprocating rotary ball mill, the outer cylinder and the inner cylinder need to be rotated in opposite directions to each other, so that the power consumption increases. Amorphous inorganic powder may increase the cost. In order to reduce the cost of amorphizing the inorganic powder, it is important to reduce the power consumption (operating power) of the inner and outer cylinder mutual rotating ball mill. For this purpose, trial and error has been used to reduce the operating power when finely pulverizing the inorganic powder, but in practice, with the operating power of the inner and outer cylinder mutual rotating ball mill reduced, There is a problem that it is not easy to pulverize the inorganic powder efficiently.

The present invention is intended to solve such a problem. It is an object of the present invention to finely pulverize inorganic powders and the like efficiently at low cost by an inner and outer cylinder reciprocating rotary ball mill. It is an object of the present invention to provide a method for estimating the operating power of the inner and outer cylinder mutual rotating ball mill required for the above.

[0012]

SUMMARY OF THE INVENTION The method of predicting the operating power of an inner and outer cylinder reciprocating rotary ball mill according to the present invention is directed to a ball motion in an inner and outer cylinder reciprocating rotary ball mill when finely pulverizing powder by the inner and outer cylinder reciprocating ball mill. Is simulated by a discrete element method using a viscoelastic dynamic model to calculate a collision energy E at the start of collision of all balls. Based on the collision energy E of the balls, the operating power of the inner and outer cylinder mutual rotating ball mill is calculated. It is characterized in that Y is calculated.

The value of the collision energy E is 300 to 800 J /
In the case of the range of s, the operation formula of the operating power Y of the inner and outer cylinder reciprocal rotary ball mill is represented by Y = A · EB (where A is 4.5
B is a constant in the range of 950 to 1050).

[0014]

Embodiments of the present invention will be described below in detail.

According to the present invention, an inorganic powder such as a viscous mineral, an aluminum-containing powder, and a silicon oxide-containing powder is finely pulverized with an inner and outer cylinder reciprocating ball mill, which is a ball medium type pulverizer. This is to predict the operating power of the inner and outer cylinder reciprocating ball mill required to amorphize the ball. The prediction of the operating power is based on the collision energy obtained by the simulation of the ball motion in the inner and outer cylinder reciprocating ball mill. It is calculated based on E.

FIG. 1 shows an example of an inner and outer cylinder mutual rotating ball mill.
Shown in The inner and outer cylinder reciprocating rotary ball mill 20 includes a cylindrical outer cylinder 21 and a cylindrical inner cylinder 22 provided concentrically. The outer cylinder 21 and the inner cylinder 22 rotate in opposite directions to each other. It is supposed to. A plurality of outer cylinder stirring blades 21a are provided on the inner peripheral surface of the outer cylinder 21 at appropriate intervals in the circumferential direction and the axial direction so as to protrude inward. A plurality of inner cylinder stirring blades 22a are also provided on the surface at appropriate intervals in the circumferential and axial directions so as to protrude outward. Each outer cylinder stirring blade 2
1a and each inner cylinder stirring blade 22a are each formed by a flat plate material along the circumferential direction. Many balls 23 are housed between the outer cylinder 21 and the inner cylinder 22.
The inorganic powder is charged between the outer cylinder 21 and the inner cylinder 22 and is finely pulverized by the balls 23 that are rolled by the outer cylinder 21 and the inner cylinder 22 that rotate in opposite directions.

Such an inner / outer cylinder mutual rotating ball mill 2
The motion simulation of the ball 23 accommodated in the outer cylinder 21 at 0 is specifically performed by a discrete element method (individual element method) using a Voigt model as a viscoelastic mechanical model.

FIGS. 2A and 2B are conceptual diagrams of the Voigt model, respectively. FIG. 2A shows a compressive force, and FIG. 2B shows a shear force. In the Voigt model, an elastic spring 14 representing the elastic property of the ball 23 and a viscous dashpot 15 representing the inelastic property are connected in parallel as shown in FIG.
The force acting on the ball 23 is shown. In the shearing force, a friction slider 16 is inserted as a tangential component of the interaction force to represent the frictional interaction associated with the contact of the balls.

In such a Voigt model, when one of the balls 23 is a target ball and the other ball 23 is a target ball at the time of collision of a pair of balls 23, the radius of the target ball 23 is r _i , and the radius of the target ball 23 is
Assuming that r _j and the distance between the centers of the two balls 23 are r _ij , the following equation (1) is satisfied at the start of the collision of the two balls 23.

R _i + r _j = r _ij (1) The acting force at the contact point of the pair of balls 23 is _expressed as a compressive force f _n (
Subscript n indicates the compression direction) and a pair of shear forces f _s1 and f _s2 (the subscripts s1 and s2 indicate the shear direction, respectively). Is represented by the sum of the elastic force e based on the spring 14 and the viscous force d from the Voigt model.

[0021] _{[f n] t = [e} n] t + [d n] t [f s1] t = [e s1] t + [d s1] t [f s2] t = [e s2] t + [ d _s2 ] _t (2) Here, the elastic force [e] and the viscous force [d] based on the spring are expressed as a function of the overlap distance r _d between the balls 23 and the minute time relative displacement speed (Δu / Δt). Become. Therefore, the spring-based elastic force [e] _{t at time t} is the compression elastic constant K _n and the shear elastic constant K
Based on _s , each direction is represented by the following equation (3).

[0022] _{[e n] t = K n} · r d [e s1] t = [e s1] t- Δ t + K s · Δ u s1 [e s2] t = [e s2] t- Δ t + K _s · Δu _s2 (3) Further, the viscous force [d] _t is calculated for each direction based on the compression viscosity coefficient η _n and the shear viscosity coefficient η _s of the dashpot 15 by the following (4) It is represented by an equation.

[0023] _{[d n] t = η n} · (Δu n / Δt) [d s1] t = η s · (Δu s1 / Δt) [d s2] t = η s · (Δu s2 / Δt) ... ( 4) The overlap distance r _d between the pair of colliding balls 23 is (1)
Based on the center-to-center distance r _ij between the radius r _i of the target ball 23 and the radius r _{j of the} target ball shown in the equation, it is expressed by the following equation (5). The distance between the target ball 23 and the target ball 23 is calculated based on the ball center coordinates.

R _d = r _ij − (distance between balls) (5) Further, Δu is obtained from the following formula (6) by the minute time relative displacement of the center coordinates of the pair of colliding balls 23. Here, (u _n ) _i and (u _n ) _j indicate the center coordinates of the pair of colliding balls 23, respectively.

Δu = (u _n ) _i − (u _n ) _j (6) Therefore, in the motion simulation of the ball 23 in the inner and outer cylinder reciprocating ball mill 20 by the Voigt model, the center coordinate of the ball and the minute time By sequentially analyzing the ball center coordinate displacement, it is possible to obtain the acting force on the powder by the balls 23 in the inner and outer cylinder mutual rotating ball mill 20.

In such a Voigt model, a compression elastic constant is
K _n (N / m), shear elastic constant K _s (N / m), compression viscous drag coefficient η _n (N · S / m), shear viscous drag coefficient η _s (N ·
S / m) and the coefficient of friction μ. The compression viscous drag coefficient η _n (N · S / m) and the shear viscous drag coefficient η _s (N · S / m) are expressed by the following equations (7) and (8), respectively. Here, α _n and α _s are constants, respectively.

Η _n = α _n · (m × K _n ) ^1/2 (7) η _s = α _s · (m × K _s ) ^1/2 (8) Inside the inner and outer cylinder mutual rotating ball mill 20 In the motion simulation of the ball 23, the value of each parameter is used in the following range.

That is, the compression elastic constant K _n of the ball 23
The (N / m) and shear elastic constant _{K s (N / m),} 1.0 × 10 7 ~1.0 × 10 range of ¹² (N / m), ^{preferably, 0.5 × 10 8 ~1.5 × 10} 8 (N / M). Compression elastic constant K _n (N / m) and shear elastic constant K
_{If s} is smaller than 1.0 × 10 ⁷ (N / m 2), the rigidity becomes significantly smaller than that of the actually used ball 23, and the movement of the ball 23 in the actually used inner and outer cylinder mutual rotating ball mill 20. Error increases. Conversely, the compression elastic constant K _n (N / m) and the shear elastic constant K _s are 1.0
If it is larger than × 10 ¹² (N / m), the unit time Δt must be reduced when obtaining the acting force per unit time Δt, and as a result, it takes a long time for the calculation, which is not practical. .

The compression viscous drag coefficient η _n of the ball 23 has a constant α _{n in} the range of 1.0 to 10, and the shear viscous drag coefficient η _s
The constant α _s is set in the range of 0.1 to 10, respectively. Constant α _n in compression viscous drag coefficient η _n (N · S / m)
If the value is less than 1.0, and the viscosity of the value of the constant alpha _s at a shear viscosity resistance coefficient eta _s is smaller than 1.0, the powder is mixed into the internal and external cylinders mutual rotation ball mill 20 The target property is not accurately represented, and an error from the actual movement of the ball 23 increases. Conversely, when the value of the constant α _n in the compression viscous drag coefficient η _n (N · S / m) is larger than 10, and when the value of the constant α _s in the shear viscous drag coefficient η _s is larger than 10, Similarly, an error from the actual movement of the ball 23 when the powder is mixed increases.

The friction coefficient μ is in the range of 0.5 to 1.0,
Preferably, it is in the range of 0.7 to 0.9. Friction coefficient μ
If it is not in the range of 0.5 to 1.0, the friction characteristics when powder is mixed into the inner and outer cylinder reciprocal rotation type ball mill 20 will not be accurately represented, and an error from the actual movement of the ball 23 will increase.

Thus, by the Voigt model,
In order to simulate the movement of the balls 23 in the inner and outer cylinder inter-rotating ball mill 20, and to estimate the operating power of the inner and outer cylinder inter-rotating ball mill 20, first, all the balls in the inner and outer cylinder inter-rotating ball mill 20 must be The collision energy E per unit time Δt at the start of the collision is determined. In this case, in the Voigt model, the movement speed of the target ball is u _i , and the movement speed of the target ball is u _i
Assuming that _j is the relative velocity between the two balls, u _ij is represented by the following equation (9).

U _ij = u _i −u _j (9) Let the mass of the target ball 23 be m _i and the mass of the target ball 23 be
Assuming m _j , the collision energy ε at the start of the collision between the two balls 23 is expressed by the following equation (10).

Ε = (1/2) ｛(m _i + m _j ) / 2｝ · u _ij ² (10) All N balls 23 in the inner / outer cylinder mutual rotating ball mill 20 are paired with each other. The total E of the collision energies per unit time Δt at the time of the collision is expressed by the following equation (11).

[0034]

(Equation 1)

In this case, only the collision energy when the target ball collides with the target ball is considered, and the collision energy when the target ball collides with the target ball at that time is ignored.

Based on the thus obtained collision energy E per unit time Δt at the start of collision of all the balls in the inner and outer cylinder reciprocating rotary ball mill 20, the inner and outer cylinder reciprocating ball mill 20 removes the inorganic powder. The predicted value of the working power Y (W) required for amorphization is as follows (1)
It is calculated by equation (2).

Y = A · EB (12) where A and B are constants in the equation (12). For example, the inner and outer cylinder reciprocating rotary ball mill 20 of a specific size is operated under various conditions. It is obtained by a correlation between the operating power measured and the collision energy E obtained by a simulation equivalent to the condition, for example,
All the balls 23 in the inner / outer cylinder mutual rotating ball mill 20
Collision energy E at the start of collision is 300 to 800 (J
/ S), the constant A is 4.5 to 5.5, and B is 950.
~ 1050 range. Therefore, when the inner and outer cylinder mutual rotation type ball mills 20 having different sizes are used, the range of the collision energy E at the start of the collision is different, and the constants A and B also change.

The operating power of the inner / outer cylinder reciprocal rotary ball mill 20 is determined based on the operating power when the ball 23 and the powder are sealed in the outer cylinder 21 and the ball 23 and the powder are sealed in the outer cylinder 21. This is the value obtained by subtracting the idling power when the motor is not running.

By predicting the operating power Y of the inner and outer cylinder reciprocating rotary ball mill 20 in this manner, the civil engineering,
A crystalline inorganic material suitably used as a building material,
The inner and outer cylinder reciprocal rotation type ball mill 20 can significantly reduce the cost of amorphization so as to obtain activation of chemical reactivity.

Examples of the inorganic powder to be amorphized by the inner and outer cylinder reciprocating rotary ball mill 20 include a viscous mineral, an aluminum-containing powder, and an SiO ₂ -containing amorphous phase which is observed by a powder X-ray diffraction method. A single powder or a mixed powder having at least one kind of powder and having an Al / Si molar ratio of 0.4 or more and 4.0 or less is mixed with a powder weight (g) and an inner and outer cylinder reciprocating rotary ball mill 20. Total surface area of the ball filled in (cm
² ) is particularly effective when the ratio is in the range of 0.02 to 0.04.

Examples of the viscous mineral to be amorphized include hydrous silicates containing aluminum, specifically, kaolin mineral, halloysite, pyrophyllite, mica, chlorite, vermiculite, allophane, imogolite and the like. . In particular, the kaolin mineral has a high aluminum content, and thus becomes an activated powder having high reactivity by being amorphous. The average particle size of the viscous mineral is not particularly limited, but is preferably 0.1 to 500 μm, more preferably 0.5 to 1000 μm so that the supplied energy can be effectively used for amorphization.
Should be fine.

The aluminum-containing powder to be amorphized is preferably provided with a mechanical energy of 0.5 to 30 kwh / kg. In this case, an activated powder having high reactivity at room temperature is obtained by the amorphization treatment.

SiO ₂ , in which an amorphous phase is observed in the powder X-ray diffraction method, means that when the powder is subjected to X-ray diffraction by the powder X-ray diffraction method generally used for identifying the crystal structure of the powder. , A broad halo is observed in the pattern S
The powder to be amorphized is iO ₂ , and the content of SiO ₂ is 20% or more as a chemical composition from the viewpoint of reactivity.
It is at most 100%, more preferably at least 40 and at most 100%. The SiO ₂ content powder, ultrafine silica such as aerosil, silica fume, diatomaceous earth, volcanic ash soil such as shirasu or clay, glass, slag, fly ash, metakaolin, various glass ground product, produced by high heat quenching thermal spraying Inorganic powder, abrasive powder and the like. As the average particle diameter of SiO ₂ containing powder is not particularly limited, it can be effectively utilized supplying energy to the amorphous, 0.1 to 500 [mu] m
More preferably, it should be 0.5 to 1000 μm.

The single or mixed inorganic powder to be subjected to the amorphization treatment preferably has a AL / Si molar ratio of 0.4 to 4.0, more preferably 1.0 to 3.5, still more preferably 1.5 to 3.5. ~ 3.0. AL / Si molar ratio is 0.
If it is less than 4, the specific crystallized powder will have reactivity,
In particular, the curability at room temperature is poor. On the other hand, when the molar ratio of AL / Si exceeds 4.0, physical properties such as strength and durability are inferior.

<Experimental Example 1> Kaolin (Georgia, USA, USA) was used as the inner / outer cylinder inter-rotating ball mill 20 shown in FIG. 1 using a trade name "Ultra Fine Mill" (AT-25-WDB manufactured by Mitsubishi Heavy Industries, Ltd.). Produce, average particle size
The operating power of the inner / outer cylinder reciprocating ball mill 20 at the time of pulverizing 2.4 μm, Al / Si molar ratio of 1.0) and performing amorphization treatment was predicted. The inner / outer cylinder mutual rotating ball mill 20 includes the outer cylinder 2
The diameter of 1 is 26cm, the diameter of the inner cylinder 22 is 8cm,
A chromium (Cr) steel ball with a diameter of 10 mm (density 7.8 g / cm ³ )
It is accommodated in the outer cylinder 21 in a sealed amount of kg. The number of balls is 14013. Then, the outer cylinder 21 and the inner cylinder 22
Based on the collision energy E of the ball when the rotation speed of the
The operating power was calculated. Table 1 shows the operating conditions of the inner / outer cylinder mutual rotating ball mill 20 in this case.

[0046]

[Table 1]

Such an inner and outer cylinder mutual rotating ball mill 2
0, in order to reduce the operation time when calculating the operation power, as shown in FIGS. 3A and 3B, four outer cylinder stirring blades 21a provided at equal intervals in the circumferential direction are provided. In the segment 20a having a length of 10 cm including the four inner cylinder stirring blades 22a provided at equal intervals in the circumferential direction, the collision energy E ′ for the fine pulverization of the powder by 2531 balls 23 is determined. The calculated collision energy E ′ was corrected so as to correspond to the actual collision energy E of 14013 balls 23 in the inner and outer cylinder reciprocating ball mill 20.

The collision energy E 'at the segment 20a in the inner and outer cylinder rotating rotary ball mill 20 has a compression elastic constant K _n and a shear elastic constant K _s of 1.
0 × 10 ⁸ (N / m 2), constant α _n and constant α _s of the compression viscous drag coefficient η _n and the shear viscous drag coefficient η _s are 2.0, the friction coefficient μ is 0.76, and the calculation time at the start of collision of the ball 12. (The unit time Δt is 1.0 × 10 ^-5 seconds)
Is calculated based on the equation (11), and based on the collision energy E ′, the actual inner and outer cylinder mutual rotation type ball mill 2 is calculated.
The correction was made so as to correspond to the collision energy E at 0. Then, the operating power Y of the inner and outer cylinder reciprocal rotation type ball mill 20 required for amorphizing carion was calculated based on the equation (12). In this case, the constant A in equation (12) is set to 5.0,
Assuming that the constant B is 1000, the following equation (12 ′) was used.

Y = 5.0 × E−1000 (12 ′) where E is the corrected collision energy.

The collision energy E 'of the ball at the segment 20a in the inner and outer cylinder mutual rotating ball mill 20 based on the equation (11) is 133 (J / S), and the corrected collision energy E is 736 (J / S). S). The operating power Y calculated based on the equation (12 ′) was 2.68 (kW). On the other hand, the measured operating power of the actual inner / outer cylinder mutual rotating ball mill 20 was 2.65 (kW). The results are shown in Table 2 together with the conditions for simulating the movement of the ball 23 in the inner and outer cylinder mutual rotating ball mill 20.

[0051]

[Table 2]

<Experimental Example 2> The rotation speed of the outer cylinder 21 and the inner cylinder 22 in the inner and outer cylinder mutual rotating ball mill 20 was set to 59 r.
Under the same conditions as in Example 1 except that pm was set, the collision energy E ′ of the ball at the segment 20a in the inner and outer cylinder reciprocating rotary ball mill 20 was calculated. The collision energy E ′ was 94 (J / S). The corrected collision energy E was 520 (J / S). Using the corrected collision energy E, the operating power Y calculated based on the equation (12 ′) was 1.60 (kW). On the other hand, the actual measured operation power of the inner and outer cylinder mutual rotating ball mill 20 is 1.36 (k
W). The results are also shown in Table 2.

<Experimental Example 3> 45 kg (14013 pieces) of zirconia spheres (density 6.0 g / cm ³ ) were used as the balls 23 accommodated in the outer cylinder 21 of the inner and outer cylinder mutual rotating ball mill 20. Under the same conditions as in Example 1 except that the rotation speed of the inner cylinder 22 was set to 105 rpm, the collision energy E ′ of the ball in the segment 20a in the inner and outer cylinder mutual rotation type ball mill 20 was calculated. E ′ was 103 (J / S), and the corrected collision energy E was 570 (J / S). The operating power Y calculated based on the equation (12 ′) was 1.85 (kW). On the other hand, the measured operation power of the actual inner / outer cylinder mutual rotation type ball mill 20 was 2.03 (kW). The results are also shown in Table 2.

<Experimental Example 4> 26 kg (14013 pieces) of alumina spheres (density: 3.6 g / cm ³ ) were used as the balls 23 accommodated in the outer cylinder 21 of the inner and outer cylinder mutual rotating ball mill 20. Under the same conditions as in Example 1 except that the rotation speed of the inner cylinder 22 was set to 118 rpm, the collision energy E ′ of the ball at the segment 20 a in the inner and outer cylinder mutual rotation type ball mill 20 was calculated. Is 74 (J / S), and the corrected collision energy E is
410 (J / S). The operating power Y calculated based on the equation (12 ′) was 1.05 (kW). On the other hand, the measured operating power of the actual inner / outer cylinder reciprocating rotary ball mill 20 was 1.10 (kW). The results are also shown in Table 2.

[0055]

As described above, the method for predicting the operating power of the inner and outer cylinder reciprocating rotary ball mill according to the present invention accurately predicts the operating power required when finely pulverizing the powder by the inner and outer cylinder reciprocating rotary ball mill. Therefore, it is possible to greatly contribute to the reduction of power consumption by the inner and outer cylinder mutual rotating ball mill. As a result, inorganic powders such as clay minerals and aluminum-containing powders can be efficiently amorphized at a low cost and efficiently by an inner and outer cylinder reciprocating rotary ball mill. , And can be easily mass-produced industrially.

[Brief description of the drawings]

FIG. 1A is a perspective view showing a schematic configuration of an inner / outer cylinder reciprocating ball mill which is a ball medium type pulverizer, and FIG.
Is a cross-sectional view thereof.

FIG. 2 (a) is a model of a compressive force in a Voigt model as a viscoelastic dynamic model of a discrete element method employed in a method for predicting the operating power of an inner and outer cylinder mutual rotating ball mill of the present invention, and FIG. It is a model of the shear force in the Voigt model.

FIGS. 3 (a) and (b) are explanatory views showing the relationship between an outer cylinder and an inner cylinder in an inner / outer cylinder mutual rotating ball mill, respectively.

[Explanation of symbols]

 REFERENCE SIGNS LIST 20 inner and outer cylinder mutual rotating ball mill 21 outer cylinder 21 a outer cylinder stirring blade 22 inner cylinder 22 a inner cylinder stirring blade 23 ball

Claims (2)

[Claims] A ball motion in an inner / outer cylinder inter-rotation type ball mill when finely pulverizing a powder by an inner / outer cylinder inter-rotation type ball mill is simulated by a discrete element method using a viscoelastic dynamic model, and all balls are simulated. A method for estimating the operating power of an inner and outer cylinder reciprocating rotary ball mill, comprising: calculating a collision energy E at the start of a collision; and calculating an operating power Y of the inner and outer cylinder reciprocating rotary ball mill based on the collision energy E of the ball. . 2. The value of the collision energy E is 300 to 800 J.
/ S range, the operation formula of the operating power Y of the inner and outer cylinder reciprocal rotary ball mill is Y = A · EB (where A is 4.
(A constant in the range of 5 to 5.5, B is a constant in the range of 950 to 1050)
The method for predicting operating power of an inner / outer cylinder mutual rotating ball mill according to claim 1, wherein: