JP2023183816A - Method of estimating appropriate clearance for powder kneading machine and powder kneading machine with appropriate clearance - Google Patents

Abstract

To provide a method of estimating an appropriate clearance for a powder kneading machine using a model; and to provide the powder kneading machine with the appropriate clearance.SOLUTION: A method of estimating an appropriate clearance for a powder kneading machine, in a model for the powder kneading machine composed of rotation blades 1 and a casing 2, comprises: a cell division step to divide a toric area between a rotation locus of the rotation blades 1 and the casing 2 into toric cells Ai (i=1, 2, 3 ... n) of n (n≥3) of a width Δr and define a toric cell of the width Δr on the inside of the cell A1 as a cell A0; a flow rate assumption step; a shear rate calculation step; a shearing stress calculation step; and a flow rate calculation step.SELECTED DRAWING: Figure 1

Description

The present invention relates to a kneader, a mixer, an agitator, and other drive machines (hereinafter referred to as The present invention relates to a method for estimating the appropriate clearance of a powder kneader (simply referred to as a "powder kneader") and a powder kneader equipped with the appropriate clearance.

In recent years, a molded coal blending technology has been put into practical use in which a part of coking coal for blast furnace coke production is mixed with a petroleum-based or coal-based caking filler using a powder mixer, and then pressure-molded and blended.

However, in powder kneaders used in briquette blending technology, wear of the casing due to coal powder has become a problem. As the casing becomes worn, it becomes more susceptible to destruction.

In view of the above-mentioned problems, there is a known method of forming a self-lining layer of powder by providing a clearance between the rotation locus drawn by the tip of the rotary blade and the casing to prevent wear of the casing.

For example, in Patent Document 1, two kneading shafts that are driven to rotate in opposite directions are installed in a parallel arrangement inside a casing, and each of the two kneading shafts has a plurality of stirring shafts each having a blade at the tip. A two-shaft mixer with protruding blades, which has a self-lining layer formed by adhering the kneaded material to the inner surface of the casing between the inner surface of the outer plate of the casing and the rotation locus drawn by the tip of the stirring blade. We provide a twin-shaft mixer that can prevent wear of the casing and significantly improve durability by providing a gap for forming the casing.

Japanese Patent Application Publication No. 2011-25112

However, there is no known method for estimating the clearance value. In order to estimate the clearance at which self-lining can occur in an actual machine, it is first necessary to estimate the theoretical clearance (appropriate clearance) obtained by calculation.

The present invention was made in view of the above-mentioned situation, and an object of the present invention is to provide a method for estimating the appropriate clearance of a powder kneading machine and a powder kneading machine having the appropriate clearance.

The gist of the invention is as follows.

ただし、
γ₀:任意のせん断速度
μ´:せん断速度γ₀における摩擦係数
ｎ:無次元パラメータ
である。
（４）前記せん断速度計算工程では以下の式（３）によって前記セルＡ_ｉ-1と前記セルＡ_ｉとの境界面におけるせん断速度γ_Ai-1⇔Aiを計算し、前記流動速度計算工程では以下の式（４）が全てのi（ｉ＝１、２、３...ｎ）で成立するように収束計算を実施し、前記流動速度を計算する（１）又は（２）に記載の粉体混練機の適正クリアランスの推定方法。

ただし、
△r:セルの幅
V_Ａｉ:セルＡｉの円周に沿った方向の流動速度
V_Ａｉ-1:セルＡｉ－１の円周に沿った方向の流動速度

ただし、
r:回転羽根の半径
（５）回転羽根の回転中心軸を略水平となるように回転羽根を１本以上設けた粉体混練機であって、前記粉体混練機のケーシング内面の点と、前記回転羽根のうち前記ケーシング内面の点に最も先端が近接する回転羽根との間のクリアランスｄが、前記近接する回転羽根の半径ｒに対して式（５）の範囲にあるようなクリアランス適正点が存在し、前記クリアランス適正点からなる面積が、前記回転羽根の回転中心軸を通る水平面より下方の前記ケーシング内面の面積の５０％以上を占めることを特徴とする適正クリアランスを備えた粉体混練機。

ただし、Ｄは適正クリアランスであり、Ｄ=０.１１５×ｒで求める。
（６）回転羽根の回転中心軸と水平面のなす角θが０°＜θ≦９０°となるように回転羽根を1本以上設けた粉体混練機であって、前記粉体混練機のケーシング内面の点と、前記回転羽根のうち前記ケーシング内面の点に最も先端が近接する回転羽根との間のクリアランスｄが、前記近接する回転羽根の半径ｒに対して式（５）の範囲にあるようなクリアランス適正点が存在し、前記クリアランス適正点からなる面積が、前記回転羽根の羽根最上端の回転軸中心部を通る水平面より下方の前記ケーシング内面の面積の５０％以上を占めることを特徴とする適正クリアランスを備えた粉体混練機。ただし、Ｄは適正クリアランスであり、Ｄ=０.１１５×ｒで求める。 (1) A method for estimating the appropriate clearance of a powder kneading machine, in which, in a model of the powder kneading machine consisting of a rotary vane and a casing, an annular region between the rotation locus of the rotary vane and the casing is , divided into n (n≧3) annular cells A _i (i=1, 2, 3...n) with a width Δr, and the annular cells with a width Δr further inside cell A ₁ . Flow in the direction along the circumferential direction for each of the cell division process in which cell A is set to ₀ and the cells A _i (i=0, 1, 2, 3...n) divided in the cell division process S1. A flow velocity assumption step in which the velocity V _i (i=0, 1, 2, 3...n) is assumed, and the i-th cell A _i (i=1, 2, 3... n) from the inner peripheral side A shear rate calculation step of calculating the shear rate γ _{Ai-1 ⇔ Ai} at the interface between and cell A _i-1 , and the shear stress τ(γ) of the powder at the shear rate γ calculated in the shear rate calculation step. a shear stress calculation step to calculate, a shear stress τ (γ _Ai-1⇔Ai ) at the interface between the cell A _i and the cell A _i-1 calculated in the shear stress calculation step, and the cell A _i a flow velocity calculation step of calculating the flow velocity of the cell by convergence calculation such that the product with the inner circumference length is equal for all i (i = 1, 2, 3...n); A method for estimating the appropriate clearance of a powder kneading machine.
(2) The method for estimating the appropriate clearance of a powder kneading machine according to (1), in which self-lining occurs from the cell such that the flow velocity V _i calculated in the flow velocity calculation step is 0.01 V ₀ or less. .
(3) In the shear stress calculation step, the friction coefficient μ(γ) at the shear rate γ is calculated using the following equation (1), and the friction coefficient is multiplied by the powder pressure P using the following equation (2). , the method for estimating the appropriate clearance of a powder kneading machine according to (1) or (2), wherein the shear stress at the shear rate γ is obtained.

however,
γ ₀ : Any shear rate μ′ : Friction coefficient at shear rate γ ₀ n : Dimensionless parameter.
(4) In the shear rate calculation step, the shear rate γ _Ai-1⇔Ai at the interface between the cell A _i-1 and the cell A _i is calculated using the following equation (3), and in the flow rate calculation step, Perform convergence calculation so that the following equation (4) holds true for all i (i=1, 2, 3...n), and calculate the flow velocity described in (1) or (2). Method for estimating appropriate clearance for powder kneading machines.

however,
△r: Cell width
V _Ai : Flow velocity in the direction along the circumference of cell Ai
V _Ai-1 : Flow velocity in the direction along the circumference of cell Ai-1

however,
r: radius of the rotating blade (5) A powder kneading machine having one or more rotating blades so that the center axis of rotation of the rotating blade is substantially horizontal, and a point on the inner surface of the casing of the powder kneading machine, An appropriate clearance point at which a clearance d between the rotary vanes whose tips are closest to a point on the inner surface of the casing is within the range of formula (5) with respect to the radius r of the adjacent rotary vanes. Powder kneading with an appropriate clearance, wherein the area consisting of the appropriate clearance point occupies 50% or more of the area of the inner surface of the casing below a horizontal plane passing through the central axis of rotation of the rotating blade. Machine.

However, D is the appropriate clearance and is determined by D=0.115×r.
(6) A powder kneading machine provided with one or more rotary blades such that the angle θ between the central axis of rotation of the rotary blade and the horizontal plane satisfies 0°<θ≦90°, and the casing of the powder kneading machine A clearance d between a point on the inner surface and a rotary vane whose tip is closest to the point on the inner surface of the casing among the rotary vanes is within the range of formula (5) with respect to the radius r of the adjacent rotary vane. A suitable clearance point exists, and the area formed by the suitable clearance point occupies 50% or more of the area of the inner surface of the casing below a horizontal plane passing through the center of the rotation shaft at the uppermost end of the rotary blade. Powder kneading machine with appropriate clearance. However, D is the appropriate clearance and is determined by D=0.115×r.

According to the present invention, it is possible to provide a method for estimating the appropriate clearance of a powder kneader and a powder kneader having the appropriate clearance.

FIG. 2 is a schematic diagram showing a model for predicting flow velocity distribution from shear force balance. FIG. 2 is an enlarged cell view of the model of FIG. 1 illustrating a cell division process. FIG. 2 is an enlarged cell view of the model of FIG. 1 explained in the flow velocity assumption step; It is a graph showing shear rate dependence of friction coefficient. FIG. 2 is an enlarged cell view of the model of FIG. 1 explained in the appropriate clearance calculation process. It is a graph showing the relationship between the flow rate of the kneaded material and the distance from the tip of the rotating blade in the direction of the inner surface of the casing. FIG. 2 is a schematic diagram showing a self-lining verification test. It is a graph showing the relationship between the appropriate clearance and the diameter of the rotating blade. 1 is a schematic diagram of an actual powder kneading machine to which clearance is applied.

The present inventors have discovered a method for estimating the appropriate clearance of a powder kneader.

Hereinafter, an embodiment of a method for estimating the appropriate clearance between the rotation locus of a rotary blade and a casing in a powder kneading machine according to the present invention will be described in detail. The clearance estimation method of this embodiment includes a cell division step S1, a flow rate assumption step S2, a shear rate calculation step S3, a shear stress calculation step S4, and a flow rate calculation step S5.

(Cell division step S1)
The present inventors have devised the model shown in FIG. 1 as a result of intensive study on a method for estimating the appropriate clearance. The model shown in FIG. 1 is composed of a rotating blade 1, a casing 2 that accommodates the rotating blade 1, and an annular region between the rotating blade 1 and the casing 2. The rotary blade 1 rotates clockwise about the C axis, which is the central axis. FIG. 1 shows a model that predicts the flow velocity distribution in the model diameter direction of the powder being stirred within the casing 2 from the balance of shear forces. In the cell division step S1, in the model of FIG. 1, an annular region B between the rotation locus of the rotary blade 1 and the casing 2 is divided into n annular cells with a width Δr (n≧3). . FIG. 2 is an enlarged view of the cell of the model in FIG. As shown in FIG. 2, the i-th cell from the inner circumferential side is defined as cell A _i (i=1, 2, 3...n). Further, for convenience, a ring-shaped cell with a width Δr located further inside the cell A ₁ is referred to as a cell A ₀ .

(Flow velocity assumption step S2)
A flow velocity in a direction along the circumferential direction is assumed for each of the cells divided in the cell division step S1. Specifically, as shown in FIG. 3, V Ai is the flow velocity of the i-th cell A _i from the inner circumference side, and V _Ai is the flow velocity of the i-th cell A _i from the inner circumference side, and V Ai is the flow velocity of the _{i-th cell A i} from the inner circumference side, and The flow velocity is set as V _Ai-1 , and the flow velocity in the direction along the circumference of cell A _i+1 one outside of cell Ai is set as V _Ai+1 . Each cell is an annular rigid body when viewed from the C-axis direction, and the moving speed of each cell in the center line in the width direction is defined as the flow speed of each cell. There is no speed difference inside the cell. Since each cell has a different flow rate, shear stress is generated between the cells.

式（１）において、△rをセルの幅、Ｖ_ＡｉをセルＡ_ｉの円周に沿った方向の流動速度、Ｖ_Ａｉ-1をセルＡ_ｉ-1の円周に沿った方向の流動速度とする。 (Shear rate calculation step S3)
The shear rate γ _Ai-1⇔Ai between cell A _i and cell A _i-1 can be determined by the following equation (1). Further, as shown in FIG. 3, a boundary passing through the midpoint of Δr is defined as a cell boundary.

In equation (1), △r is the width of the cell, V _Ai is the flow velocity in the direction along the circumference of cell A _i , and V _Ai-1 is the flow velocity in the direction along the circumference of cell A _i-1. shall be.

(Shear stress calculation step S4)
In order to put the model in Figure 1 into practical use, it is necessary to clarify the relationship between shear rate and shear stress. Therefore, the present inventors conducted a shear test to investigate the coefficient of friction of powder at different shear rates. The shear test was conducted under the following conditions.
Sample: Coal/road tar mixture Test method: Constant volume shear test Shear band thickness: 1mm
Temperature: 65℃
The shear rate [1/s] was changed to 0.8, 0.3, and 1.

式（２）において、μ(γ)をせん断速度γにおける摩擦係数、γ₀を任意のせん断速度、μ´をせん断速度γ₀における摩擦係数、αを無次元パラメータとする。
石炭/ロードタール混練物と異なる粉体を処理対象とする場合についても、前記せん断試験と同様の試験を実施することによって、式（２）のようなせん断速度と摩擦係数の関係を得ることができる。 FIG. 4 is a diagram showing the shear rate dependence of the friction coefficient obtained in the shear test. The horizontal axis is the shear rate, and the vertical axis is the friction coefficient, and the friction coefficient increased as the shear rate increased. The graph in FIG. 4 is approximated by the following equation (2).

In equation (2), μ(γ) is a friction coefficient at shear rate γ, γ ₀ is an arbitrary shear rate, μ' is a friction coefficient at shear rate γ ₀ , and α is a dimensionless parameter.
Even when a powder different from the coal/road tar mixture is to be treated, the relationship between shear rate and friction coefficient as shown in equation (2) can be obtained by conducting a test similar to the shear test described above. can.

Next, by multiplying the friction coefficient obtained in (2) by the powder pressure P, the shear stress τ(γ) can be obtained. This is expressed by the following equation (3).

(Flow velocity calculation step S5)
The shear force is calculated by multiplying the area of the shear plane (the contact surface that acts on the shear stress) by the shear stress. In the models shown in FIGS. 1 and 2, the shear force (left side of equation (4)) caused by the shear rate γ _Ai⇔Ai+ 1 between cell A _i and cell A _i+ 1, and _the The shear force (right side of equation (4)) generated by the shear rate γ _Ai-1⇔Ai between cell A _i-1 is balanced in a steady state where A _i neither accelerates nor decelerates. The reason for this will be explained in detail. The cells A _i rotate in the circumferential direction while transmitting the rotational force of the rotating blade 1 to the outer cells by the frictional force between the cells. When sufficient time has elapsed since the rotating blade 1 started rotating and the rotational force of the rotating blade 1 has been sufficiently transmitted to each cell in the casing 2, each cell moves at a constant speed without acceleration or deceleration. Because of the rotational movement in each cell, the shearing force acting from one cell inside is balanced with the shearing force acting one cell outside. This is expressed by the following equation (4). The area of the shear plane is the product of the circumference of the cell and the depth of the cell, but since the depths of each cell are all equal, it is erased from both sides. Here, τ(γ _Ai⇔Ai+1 ) represents the shear stress at the shear rate γ _Ai⇔Ai+1 , and r represents the radius of the rotation locus drawn by the rotating blade 1.

The shearing force is balanced at the interface between all adjacent cells, so if V _Ai (1≦i≦n) that satisfies the following equation (5) is found, the rotational force of the rotating blade 1 is The cell flow velocity at the time when sufficient transmission has been made to each cell in 2 can be determined. The cell flow rate will be explained in detail below.

式（７）の値が収束したと考えられる条件は以下の式（８）が成り立つときである。

図６は、上述したモデル（図１）を用いて計算した、回転羽根の直径を１５０ｍｍ、回転羽根の回転速度を３２ｒｐｍとした場合の各セルの流動速度である。縦軸は混練物流動速度（Ｖ_ｉ／Ｖ_０）、横軸は回転羽根先端からのケーシング内面方向の距離（Ｒ_i－ｒ）を示している。図６から読み取れるように、Ｖ_i＝０．０１Ｖ_０程度のセルを境界として、その外側から急激に流動速度が減少している。実用上は、Ｖ_i≦０．０１Ｖ_０となるセルからセルフライニングが発現するということができる。 Finally, a convergence calculation is performed so that the flow velocity of the cell A _n at the outermost periphery of the casing 2 becomes 0. The appropriate clearance calculation step S6 is calculated as shown in FIG. At this time, r represents the coordinate in the diametrical direction with the center of the rotating blade and the casing as 0, A _i represents the i-th cell, and R _i (=r+i△r) represents the inner coordinate of A _i .
Further, let V _i be the rotational speed of A _i , and let F _i be the product F of the shear stress that A _i receives from A _i-1 and the inner circumference length of A _i is the average of F1 to Fn (n=80). . F _i is expressed by the following equation (6). At this time, V _i is changed so that 1≦i≦79, so that the value of equation (7) becomes the minimum and holds true for all i (i = 1, 2, 3...n). Calculate convergence. At this time, the constraint conditions are V ₀ =rotational speed of the blade tip, 1≦i≦79, V _i+1 ≦V _i , and V ₈₀ =0. Further, V _i is determined by equation (1).

The condition under which the value of Equation (7) is considered to have converged is when Equation (8) below holds true.

FIG. 6 shows the flow velocity of each cell calculated using the above-mentioned model (FIG. 1) when the diameter of the rotary blade is 150 mm and the rotation speed of the rotary blade is 32 rpm. The vertical axis represents the flow rate of the kneaded material (V _i /V ₀ ), and the horizontal axis represents the distance from the tip of the rotating blade toward the inner surface of the casing (R _i -r). As can be seen from FIG. 6, the flow velocity rapidly decreases from the outside of the cell where V _i =0.01V ₀ is the boundary. In practical terms, it can be said that self-lining occurs in cells where V _i ≦0.01V ₀ .

(Self-lining verification test)
In order to confirm the consistency between the above-mentioned model and the actual phenomenon, a self-lining verification test was conducted as shown in FIG. 7. At this time, the size of the container was changed and the flow of the powder was evaluated at each clearance (5, 15, and 25 mm).

Similar to the calculation conditions in FIG. 6, the diameter of the rotary blade was 150 mm, and the rotation speed of the rotary blade was 32 rpm. The motor performance was a rated output of 120 W and a rated torque of 2.2 Nm. The inner side of the boundary surface where the powder flow stagnates was defined as a fluidized bed, and the outer side was defined as a stagnation layer, and the thicknesses of the fluidized bed and stagnation layer were determined. The results are shown in Table 1 below, and the experimental value of the appropriate clearance in the kneading system was about 9 mm. This result matched with good accuracy the estimated value of the appropriate clearance by the model shown in FIG.

In addition, assuming that powder kneading machines of various sizes are used in industrial applications, the model predicted the relationship between the diameter of the rotary blade and the appropriate clearance. The results are shown in Figure 8 below, and it was estimated that a width of 0.115 times the radius of the rotary blade is the appropriate clearance for any size of powder kneader. In addition, in this model, the appropriate clearance did not change depending on the rotation speed.
If the clearance of the powder kneader is smaller than the appropriate clearance, sliding will occur between the inner surface of the casing and the powder, causing wear on the casing. On the other hand, if the clearance of the powder kneading machine is larger than the appropriate clearance, problems such as the kneading performance of the powder will deteriorate or the device will become unnecessarily large will occur.
The horizontal axis of 0.009 in FIG. 6 is the appropriate clearance (powder speed = impeller tip speed x 0.01 times), and at the same time is the boundary between the flowing part and the stagnation part, which was confirmed in experiments. Based on the appropriate clearance (horizontal axis 0.009), if the horizontal axis is decreased to 0.008, 0.007, 0.006, the powder velocity near the casing surface shown on the vertical axis increases, and the casing wear rate increases. increase. On the other hand, as the horizontal axis approaches 0.010, the calculated powder velocity is expected to fall below 1/1000 of the blade tip velocity and become almost 0.
If the clearance is designed and manufactured with a clearance of 0.006, which is smaller than 0.009 on the horizontal axis in Figure 6, the powder velocity will be approximately 10 times the proper clearance (0.009), so the casing will wear out and the clearance will become 0. It is expected that wear will stop when the value approaches .009.
Therefore, the clearance of a powder kneader for industrial use is preferably 90% or more and 115% or less of the appropriate clearance, more preferably 95% or more and 110% or less. If the clearance of the powder kneader is designed to be slightly smaller than the appropriate clearance, the point extending radially outward from the outer circumferential end of the rotary blade should be within the range from the inner surface of the casing to the center of the thickness of the casing. This corresponds to a value of 90% or more of the appropriate clearance. When designing the clearance to be slightly smaller, the clearance may be more preferably 95% or more of the appropriate clearance. In addition, when designing the clearance of a powder kneader to be slightly larger than the appropriate clearance, the point where the outer peripheral end of the rotary blade is extended 110% radially outward from there than the appropriate clearance is from the inner surface of the casing to the center of the casing plate thickness. range. This corresponds to a value of 110% or less of the appropriate clearance. If it is designed to be slightly larger, it is more desirable to extend the length by 105% or 100%.

(Powder kneading machine with appropriate clearance)
Next, an example in which the calculated appropriate clearance is provided in an actual machine will be described.

<Example applied to horizontal powder kneading machine>
The powder kneading machine with appropriate clearance according to the present embodiment is a powder kneading machine in which one or more rotary blades are provided so that the central axis of rotation of the rotary blades is substantially horizontal, and the powder kneading machine is The clearance d between the point on the inner surface of the casing and the rotating blade whose tip is closest to the point on the inner surface of the casing is within the range of formula (9) with respect to the radius r of the adjacent rotating blade. A suitable clearance point exists, and the area formed by the suitable clearance point occupies 80% or more of the area of the inner surface of the casing below a plane passing through the central axis of rotation of the rotating blade. Further, the area formed by the appropriate clearance point may be 50% or more of the area of the inner surface of the casing below the horizontal plane passing through the uppermost end of the rotary blade. However, D is the appropriate clearance and is determined by D=0.115×r.

When the powder kneading machine is provided with two or more rotary blades, the rotary blade with the longest central axis of rotation is set to the radius r of the adjacent rotary blades. Equation (9) indicates that the clearance d of the actual machine is 90% or more and 115% or less of the appropriate clearance.

<Example applied to a vertical powder kneader>
The powder kneading machine with the appropriate clearance according to the present embodiment is a powder kneader in which one or more rotary blades are provided so that the angle θ between the rotation center axis of the rotary blade and the horizontal plane satisfies 0°<θ≦90°. In a kneading machine, the clearance d between a point on the inner surface of the casing of the powder kneading machine and the rotating blade whose tip is closest to the point on the inner surface of the casing among the rotating blades is relative to the radius r of the adjacent rotating blade. It is assumed that there is a suitable clearance point within the range of formula (9), and that the area consisting of the suitable clearance point occupies 80% or more of the area of the inner surface of the casing below the horizontal plane passing through the top end of the rotary blade. Features. Further, the area consisting of the appropriate clearance point may be 50% or more of the area of the inner surface of the casing below the horizontal plane passing through the center of the rotation shaft at the uppermost end of the rotary blade. However, D is the appropriate clearance and is determined by D=0.115×r.

The expression that the central axis of rotation of the rotating blade is substantially perpendicular includes an angular range of 0° or more and 10° or less with respect to the vertical direction. More preferably, the angle range is 0° or more and 10° or less. When the powder kneading machine is provided with two or more rotary blades, the rotary blade with the longest central axis of rotation is set to the radius r of the adjacent rotary blades. Equation (9) indicates that the clearance d of the actual machine is 90% or more and 115% or less of the appropriate clearance.

(Example)
The present invention will be explained in more detail with reference to Examples. The present invention is not limited to these examples in any way. FIG. 9 is a schematic diagram of an actual powder kneading machine 4 to which clearance is applied.
There are two rotating blades 1 at the bottom of the casing 2. The bottom surface of the casing 2 is a cylindrical surface coaxial with the rotating blade 1. In a portion of the casing 2 above the axis of the rotating blade 1, a side wall extends in the vertical direction. A plurality of nozzles 3 are installed on the ceiling wall of the casing 2. In the illustration, a feeder (not shown) is installed on the back side of the rotary blade 1. In the illustration, a discharge port (not shown) is arranged on the near side of the rotating blade 1. The objects to be kneaded by these powder kneaders 4 are both coal and oil. Coal to be kneaded is supplied from a feeder. Further, oil is supplied from the nozzle, and the treated kneaded material is discharged from the opening. In the example, a clearance within a range calculated from the appropriate clearance D using equation (9) was applied. In the comparative example, a clearance outside the range calculated from the appropriate clearance D using equation (9) was applied. In the Examples and Comparative Examples, the wear amount of the casing was evaluated after a certain period of test operation. Table 2 shows the design values (radius r of the rotary blade, clearance d), appropriate clearance D, throughput of the material to be kneaded, and amount of wear in the examples and comparative examples.

As shown in Table 2, in the examples, no amount of wear was detected even though the amount of kneaded materials per day was large. On the other hand, in the comparative example, the amount of abrasion was detected even if the daily processing amount of the kneaded material was small.

According to the present invention, by using the model, it is possible to provide an appropriate clearance for the powder kneading machine. In addition, sliding between the coal powder and the casing wall is suppressed, which is expected to significantly extend the life of the coal powder. Therefore, the present invention has high industrial applicability.

1 Rotating vane 2 Casing 3 Nozzle 4 Powder kneading machine

Claims (6)

A method for estimating the appropriate clearance of a powder kneader, the method comprising:
In the model of the powder kneading machine consisting of a rotary vane and a casing, the annular region between the rotation locus of the rotary vane and the casing is defined by n (n≧3) annular cells A with a width Δr. _i (i = 1, 2, 3...n), and a cell division step in which a ring-shaped cell with a width Δr further inside cell A ₁ is defined as cell A ₀ ;
The flow velocity V _i ( _i =0, 1, 2, 3...n);
a shear rate calculation step of calculating the shear rate γ _Ai-1⇔Ai at the interface between the i-th cell A _i (i=1, 2, 3...n) from the inner circumferential side and the cell A _i-1 ; ,
a shear stress calculation step of calculating the shear stress τ(γ) of the powder at the shear rate γ calculated in the shear rate calculation step;
The product of the shear stress τ (γ _Ai-1⇔Ai ) at the interface between the cell A _i and the cell A _i-1 calculated in the shear stress calculation step and the length of the inner circumference of the cell A _i is equal for all i (i=1, 2, 3...n), a flow velocity calculation step of calculating the flow velocity of the cell by convergence calculation;
A method for estimating the appropriate clearance of a powder kneading machine. The method for estimating appropriate clearance for a powder kneading machine according to claim 1, wherein self-lining occurs from the cells such that the flow velocity V _i calculated in the flow velocity calculation step is 0.01 V ₀ or less. In the shear stress calculation step, the friction coefficient μ(γ) at the shear rate γ is calculated using the following equation (1), and the friction coefficient is multiplied by the powder pressure P using the following equation (2) to calculate the shear stress. The method for estimating an appropriate clearance for a powder kneading machine according to claim 1 or 2, wherein the shear stress at a speed γ is obtained.

however,
γ ₀ : Any shear rate μ' : Friction coefficient at shear rate γ ₀ n : Dimensionless parameter. In the shear rate calculation step, the shear rate γ _Ai-1⇔Ai at the interface between the cell A _i-1 and the cell A _i is calculated using the following equation (3), and in the flow rate calculation step, the following equation is used. The powder kneading machine according to claim 1 or 2, wherein the flow velocity is calculated by performing a convergence calculation so that (4) holds true for all i (i=1, 2, 3...n). How to estimate proper clearance.

however,
△r: Cell width
V _Ai : Flow velocity in the direction along the circumference of cell Ai
V _Ai-1 : Flow velocity in the direction along the circumference of cell Ai-1

however,
r: Radius of rotating blade A powder kneading machine is provided with one or more rotary blades so that the central axis of rotation of the rotary blades is substantially horizontal, and a point on the inner surface of the casing of the powder kneader and a point on the inner surface of the casing among the rotary blades are provided. There exists an appropriate clearance point such that the clearance d between the point and the rotating blade whose tip is closest is within the range of formula (5) with respect to the radius r of the adjacent rotating blade, and from the appropriate clearance point A powder kneading machine with appropriate clearance, characterized in that the area occupies 50% or more of the area of the inner surface of the casing below a horizontal plane passing through the central axis of rotation of the rotating blade.

However, D is the appropriate clearance and is determined by D=0.115×r. A powder kneading machine equipped with one or more rotary blades such that the angle θ between the central axis of rotation of the rotary blade and a horizontal plane satisfies 0°<θ≦90°, wherein a point on the inner surface of the casing of the powder kneading machine and the rotary vane whose tip is closest to the point on the inner surface of the casing among the rotary vanes, such that the clearance d is within the range of formula (5) with respect to the radius r of the adjacent rotary vane. An appropriate clearance point is present, and the area consisting of the appropriate clearance point occupies 50% or more of the area of the inner surface of the casing below a horizontal plane passing through the center of the rotating shaft at the uppermost end of the rotary blade. Powder kneading machine with clearance. However, D is the appropriate clearance and is determined by D=0.115×r.

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