Classifying apparatus

Abstract

An apparatus for classifying fine particles in slurry provides a sharp particle size distribution with few mixed coarse particles and high classification accuracy. The apparatus includes a rotor (15) including classification chambers (17) between blades (16) radially arranged at circumferentially regular intervals, and classifies particles so that a classified particle size is constant in an entire radial region from an outer periphery to an inner periphery of the classification chamber. The blade (16) of the rotor has a circumferential thickness t(d) increasing toward the outer periphery, and the classification chamber (17) has a width increasing toward the inner periphery.

Claims

1. A classifying apparatus comprising a rotor that includes multiple blades radially or eccentrically arranged at circumferential intervals and classification chambers between the blades, the classifying apparatus being configured to move particles having a size larger than a classified particle size toward an outer peripheral side and move particles having a size smaller than the classified particle size toward an inner peripheral side while a fluid flowing into the classification chambers flows from the outer peripheral side to the inner peripheral side, and to classify fine particles in the fluid so that the classified particle size is constant in an entire radial region from an outer periphery to an inner periphery of the classification chamber, characterized in that the blade has a constant height along a rotation axis of the rotor and a circumferential thickness increasing toward the outer periphery, and a blade thickness t(d) in a diameter d position of the classification chamber is obtained by Expression 15 below: $\begin{array}{cc}t\left(d\right)=\frac{1}{N}\left[d-\frac{Q}{T}\frac{1}{D_1^2}\frac{2894}{d.Math.n^2}\frac{18}{9.8\left({}_2-{}_1\right)}\right]& \mathrm{Expression}15\end{array}$ where Q is a flow rate, N is a number of classification chambers in a circumferential direction, D.sub.1 is a classified particle size, n is a rotation speed of the rotor, is viscosity of the fluid, .sub.1 is specific gravity of the fluid, .sub.2 is specific gravity of a particle, and T is a blade height (constant).

2. The classifying apparatus according to claim 1, characterized in that a blade thickness t(d) at the inner periphery of the blade is zero.

3. A classifying apparatus comprising a rotor that includes multiple blades radially or eccentrically arranged at circumferential intervals and classification chambers between the blades, the classifying apparatus being configured to move particles having a size larger than a classified particle size toward an outer peripheral side and move particles having a size smaller than the classified particle size toward an inner peripheral side while a fluid flowing into the classification chambers flows from the outer peripheral side to the inner peripheral side, and to classify fine particles in the fluid so that the classified particle size is constant in an entire radial region from an outer periphery to an inner periphery of the classification chamber, characterized in that the blade has a constant circumferential thickness and a height along a rotation axis of the rotor increasing toward the inner periphery, and a blade height T(d) in a diameter d position of the classification chamber satisfies Expression 11 below: $\begin{array}{cc}T\left(d\right)=\frac{Q}{d-\mathrm{tN}}.Math.\frac{1}{D_1^2}.Math.\frac{2894}{d.Math.n^2}.Math.\frac{18}{9.8\left({}_2-{}_1\right)}& \mathrm{Expression}11\end{array}$ where Q is a flow rate, N is the number of classification chambers in a circumferential direction, D.sub.1 is a classified particle size, n is a rotation speed of the rotor, is viscosity of the fluid, .sub.1 is specific gravity of the fluid, .sub.2 is specific gravity of a particle, and t is a blade thickness.

4. A classifying apparatus comprising a rotor that includes multiple blades radially or eccentrically arranged at circumferential intervals and classification chambers between the blades, the classifying apparatus being configured to move particles having a size larger than a classified particle size toward an outer peripheral side and move particles having a size smaller than the classified particle size toward an inner peripheral side while a fluid flowing into the classification chambers flows from the outer peripheral side to the inner peripheral side, and to classify fine particles in the fluid so that the classified particle size is constant in an entire radial region from an outer periphery to an inner periphery of the classification chamber, characterized in that the blade has a height along a rotation axis of the rotor increasing toward the inner periphery and a circumferential thickness increasing toward the outer periphery, and a blade height T(d) and a blade thickness t(d) in a diameter d position of the classification chamber are obtained by Expressions 18, 19, and 21 below: $\begin{array}{cc}T\left(d\right)=\frac{Q}{E\left(d\right).Math.N}.Math.\frac{1}{D_1^2}.Math.\frac{2894}{d.Math.n^2}.Math.\frac{18}{9.8\left({}_2-{}_1\right)}& \mathrm{Expression}18\\ E\left(d\right)=\frac{}{N}.Math.\left\{b.Math.d_2-\frac{b.Math.d_2-a.Math.d_1}{d_2-d_1}\left(d_2-d\right)\right\}& \mathrm{Expression}19\\ t\left(d\right)=\frac{d}{N}-\frac{}{N}.Math.\left\{b.Math.d_2-\frac{b.Math.d_2-a.Math.d_1}{d_2-d_1}\left(d_2-d\right)\right\}& \mathrm{Expression}21\end{array}$ where a is a coefficient of (d.sub.1Nt.sub.1)/d.sub.1 of a gap between the blades at the inner periphery, b is a coefficient of (d.sub.2Nt.sub.2)/d.sub.2 of a gap between the blades at the outer periphery, d.sub.1 is an inner peripheral diameter of the rotor, d.sub.2 is an outer peripheral diameter of the rotor, t.sub.1 is a blade thickness at the inner periphery, t.sub.2 is a blade thickness at the outer periphery, Q is a flow rate, N is the number of classification chambers in a circumferential direction, D.sub.1 is a classified particle size, n is a rotation speed of the rotor, is viscosity of the fluid, .sub.1 is specific gravity of the fluid, and .sub.2 is specific gravity of a particle.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) FIG. 1 is a cross sectional view of a rotor that constitutes a classifying apparatus.

(2) FIG. 2 is a schematic view of a configuration of a general system including a dry type classifying apparatus.

(3) FIG. 3 is a schematic view of a configuration of a general system including a wet type classifying apparatus.

(4) FIG. 4 is a vertical sectional view of a rotor according to an embodiment of the present invention.

(5) FIG. 5 is a sectional view taken along the line A-A in the rotor in FIG. 4.

(6) FIG. 6 is a vertical sectional view of a rotor according to another embodiment.

(7) FIG. 7 is a sectional view taken along the line B-B in the rotor in FIG. 6.

(8) FIG. 8 is a cross sectional view of a variant of the rotor in FIG. 7.

(9) FIG. 9 shows a rotor used in a classifying apparatus in Example 1 and a size thereof.

(10) FIG. 10 shows a rotor used in a classifying apparatus in Comparative example 1 and a size thereof.

(11) FIG. 11 shows a particle size distribution of a raw material and particle size distributions of particles classified using the classifying apparatuses in FIGS. 9 and 10.

(12) FIG. 12 shows a rotor used in a classifying apparatus in Example 2 and a size thereof.

(13) FIG. 13 shows a rotor used in a classifying apparatus in Comparative example 2 and a size thereof.

(14) FIG. 14 shows a particle size distribution of a raw material and particle size distributions of particles classified using the classifying apparatuses in FIGS. 12 and 13.

(15) FIG. 15 is a vertical section view of a rotor according to another embodiment.

(16) FIG. 16 is a sectional view taken along the line C-C in the rotor in FIG. 15.

DESCRIPTION OF EMBODIMENT

(17) A classifying apparatus of this embodiment is an apparatus using a rotor that includes blades radially or eccentrically provided from a rotation center at circumferentially regular intervals and classification chambers between the blades to rotate the rotor at high speed and to classify fine particles in a fluid flowing into the rotor, in which any of the first to third modes described above is used to classify the particles so that a classified particle size is constant in an entire radial region from an outer periphery to an inner periphery of the classification chamber. Structures of classifying apparatuses used in the modes will be described below.

(18) FIGS. 4 and 5 show a rotor of a classifying apparatus used in the first mode. FIG. 4 is a vertical sectional view of a rotor 23, and FIG. 5 is a sectional view taken along the line A-A in FIG. 4. The rotor 23 in FIG. 5 has the same cross section as the rotor 2 in FIG. 1 but a different vertical section.

(19) A classified particle size D.sub.1 in the rotor 23 is obtained in the same manner as described above. Specifically, in a diameter d position of the rotor 23 in FIG. 5, the classified particle size D.sub.1 at which a centrifugal force F and a drag R are balanced is expressed from Expression 6 above by:

(20) $\begin{array}{cc}{D}_1=\sqrt{\frac{Q}{\left(d-\mathrm{tN}\right)T\left(d\right)}.Math.\frac{2894}{d.Math.n^2}.Math.\frac{18}{9.8\left({}_2-{}_1\right)}}& \mathrm{Expression}7\end{array}$
where T(d) is a height of a blade 21 in a direction perpendicular to the plane of FIG. 5 as a function of a diameter d. As described above, in the diameter d position, particles having a size larger than the classified particle size D.sub.1 are expelled radially outward, while particles having a size smaller than the classified particle size D.sub.1 move radially inward. In Expression 7, Q, N, t, A, n, , .sub.1, .sub.2 are as described in Expression 6, Q is a flow rate of a fluid, N is the number N of classification chambers, n is a rotation speed of the rotor 23, is viscosity of the fluid, .sub.1 is specific gravity of the fluid, t is a thickness of the blade 21, .sub.2 is specific gravity of a particle contained in the fluid.

(21) An arc area A(d) of the classification chamber 22 expressed as a function of the diameter d is expressed by:

(22) $\begin{array}{cc}A\left(d\right)=E\left(d\right).Math.T\left(d\right)=\frac{\left(d-\mathrm{tN}\right)T\left(d\right)}{N}& \mathrm{Expression}8\end{array}$
where E(d) is a gap between the blades and T(d) is the height of the blade 21 in the diameter d position, and thus obtained from Expressions 7 and 8 above by Expression 9 below:

(23) $\begin{array}{cc}A\left(d\right)=\frac{Q}{N}.Math.\frac{1}{D_1^2}.Math.\frac{2894}{d.Math.n^2}.Math.\frac{18}{9.8\left({}_2-{}_1\right)}& \mathrm{Expression}9\end{array}$

(24) For the arc area A(d) in the diameter d position to provide the constant classified particle size D.sub.1, with the flow rate Q, the number N of the classification chambers 22, the rotation speed n of the rotor, the viscosity of the fluid, the specific gravity .sub.1 of the fluid, and the specific gravity .sub.2 of the particle being set values and constant, the arc area A(d) in Expression 9 above is expressed by A(d)=C/d, and is a function of the diameter d and inversely proportional to the diameter d.

(25) The character C refers to a constant expressed by Expression 10 below.

(26) $\begin{array}{cc}C=\frac{Q}{N}.Math.\frac{1}{D_1^2}.Math.\frac{2894}{n^2}.Math.\frac{18}{9.8\left({}_2-{}_1\right)}& \mathrm{Expression}10\end{array}$

(27) From Expressions 8 and 9, the height T(d) of the classification blade 21 as a function of the diameter d is obtained by Expression 11 below:

(28) 0$\begin{array}{cc}T\left(d\right)=\frac{Q}{d-\mathrm{tN}}.Math.\frac{1}{D_1^2}.Math.\frac{2894}{d.Math.n^2}.Math.\frac{18}{9.8\left({}_2-{}_1\right)}& \mathrm{Expression}11\end{array}$

(29) The blade height T(d) to provide the constant classified particle size D.sub.1 in the entire region from the outer periphery to the inner periphery of the classification chamber 22 is obtained by Expression 11. The height T(d) of the blade 21 is a function of the diameter d from Expression 11, and decreases with increasing diameter d toward the outer periphery while increases with decreasing diameter d. Thus, as shown in FIG. 4, the rotor 23 has a sectional shape with an expanded inner peripheral side. A gap E(d) between the blades is expressed by E(d)=(dtN)/N from Expression 8, and increases toward the outer periphery in proportion to the diameter d (FIG. 5).

(30) The rotor 23 of this embodiment with the blade height T increasing toward the inner peripheral side as described above was used, and with a flow rate Q, a blade thickness t, the number N of classification chambers, a rotation speed n of the rotor, viscosity , specific gravity .sub.1 of the fluid, and specific gravity .sub.2 of the particle in Table 4 below being set as in Table 1 and the classified particle size D.sub.1 being a set value in Table 4 below, a simulation calculation was performed using Expressions 3, 8, 9, and 11 above to obtain a linear speed s, an arc area A(d), a gap E(d) between the blades, and a blade height T(d) in the diameter d position. Calculation results are shown in Table 5 below. In Table 4, the classified particle size D.sub.1 is set to 0.92 m to match a classified particle size D.sub.1 on an outer periphery of the rotor in a diameter position of 0.40 m as a minimum value, among classified particle sizes D.sub.1 in Table 2 obtained by a simulation calculation by substituting appropriate items in Table 1 into Expression 6.

(31) TABLE-US-00004 TABLE 4 SET VALUE SPECIFIC NUMBER OF ROTATION GRAVITY SPECIFIC CLASSIFIED DIAMETER FLOW BLADE CLASSIFICATION SPEED OF OF GRAVITY PARTICLE POSITION RATE THICKNESS CHAMBERS ROTOR VISCOSITY PARTICLE OF FLUID SIZE d Q t N n .sub.2 .sub.1 D.sub.1 m Nm.sup.3/s m rpm kg/m .Math. s kg/m.sup.3 kg/m.sup.3 m 0.40 0.00001 0.005 12 2500 0.001 2300 1000 0.92 0.35 0.00001 0.005 12 2500 0.001 2300 1000 0.92 0.30 0.00001 0.005 12 2500 0.001 2300 1000 0.92 0.25 0.00001 0.005 12 2500 0.001 2300 1000 0.92 0.20 0.00001 0.005 12 2500 0.001 2300 1000 0.92

(32) TABLE-US-00005 TABLE 5 CALCULATED VALUE DIAMETER GAP BETWEEN BLADE LINEAR POSITION CENTRIFUGAL ARC AREA BLADES HEIGHT SPEED d EFFECT A(d) E(d) T(d) s m G m.sup.2 m m m/s 0.40 1398 0.00100 0.100 0.0100 0.00084 0.35 1223 0.00114 0.096 0.0118 0.00073 0.30 1049 0.00133 0.073 0.0182 0.00063 0.25 874 0.00159 0.061 0.0261 0.00052 0.20 699 0.00199 0.047 0.0424 0.00042

(33) By Expression 11 of the embodiment, the height T(d) of the blade 21 is obtained to provide a constant classified particle size D.sub.1 in a radial direction in the classification chamber.

(34) FIGS. 6 and 7 show a rotor of a classifying apparatus used in the second mode. FIG. 6 is a vertical sectional view of a rotor 25 and FIG. 7 is a sectional view taken along the line B-B in FIG. 6. As shown in FIG. 6, the rotor 25 is configured so that a blade 26 has a constant height T in a radial direction and a circumferential thickness t(d) of the blade increasing from an inner periphery toward an outer periphery as shown in FIG. 7, and a classification chamber 27 has a width increasing toward an inner periphery and changing in the radial direction. The thickness t(d) of the blade 26 at the inner periphery may not be zero but is preferably zero. This is because the zero thickness of the blade 26 at the inner periphery can reduce a diameter of the inner periphery of the blade 26 and an increased diametrical length of the blade allows sufficient classification in the classification chamber.

(35) In the embodiment for implementing the second mode, an arc area A(d) in a diameter d position is expressed by: Expression 12
A(d)=E(d).Math.T
where E(d) is a circumferential gap between the blades. From Expressions 9 and 12 above as relational expressions of the diameter d and the arc area A(d) to provide a constant classified particle size D.sub.1, the gap E(d) between the blades in the diameter d position is expressed by Expression 13 below:

(36) $\begin{array}{cc}E\left(d\right)=\frac{Q}{T.Math.N}.Math.\frac{1}{D_1^2}.Math.\frac{2894}{d.Math.n^2}.Math.\frac{18}{9.8\left({}_2-{}_1\right)}& \mathrm{Expression}13\end{array}$

(37) The arc area A(d) and the gap E(d) between the blades in the diameter d position obtained by a simulation calculation from Expressions 12 and 13 above, with the same set values as in Table 4 other than the blade height T being constant at 0.0381 m as shown in Table 6 below and a circumferential thickness t(d) of the blade 26 obtained by Expression 15 below, are shown in Table 6 below together with the circumferential thickness t(d) of the blade, a centrifugal effect G, and a linear speed s.

(38) The blade height T is set to 0.0381 m to satisfy a classified particle size D.sub.1=0.92 m like the flow rate Q in Table 4. With a blade thickness t(d)=0 at a diameter d=0.20 m and the number N of classification chambers=12, E(d)=0.052 m from E(d)=d/N. The value of E(d) and appropriate items in Table 4 are substituted into Expression 13 to obtain the blade height T of 0.0381 m at the diameter d=0.20 m. The blade thickness t(d) in the diameter d position is obtained by Expression 14 below:

(39) $\begin{array}{cc}t\left(d\right)=\frac{d}{N}-E\left(d\right)& \mathrm{Expression}14\end{array}$

(40) Expression 13 is substituted into E(d) in Expression 14, and then the thickness t(d) of the blade 26 is expressed by Expression 15 below. A simulation calculation is performed by substituting appropriate items in Table 4 into Expression 15 to obtain a blade thickness t(d) with a constant classified particle size D.sub.1 of 0.92 m from an outer periphery to an inner periphery of the classification chamber.

(41) $\begin{array}{cc}t\left(d\right)=\frac{1}{N}\left[d-\frac{Q}{T}\frac{1}{D_1^2}\frac{2894}{d.Math.n^2}\frac{18}{9.8\left({}_2-{}_1\right)}\right]& \mathrm{Expression}15\end{array}$

(42) TABLE-US-00006 TABLE 6 SET VALUE CALCULATED VALUE DIAMETER CENTRIFUGAL GAP BETWEEN BLADE LINEAR BLADE POSITION EFFECT ARC AREA BLADES HEIGHT SPEED THICKNESS d G A(d) E(d) T s t(d) m m.sup.2 m m m/s m 0.40 1398 0.00100 0.026 0.0381 0.00084 0.0785 0.35 1223 0.00114 0.030 0.0381 0.00073 0.0617 0.30 1049 0.00133 0.035 0.0381 0.00063 0.0436 0.25 874 0.00160 0.042 0.0381 0.00052 0.0236 0.20 699 0.00199 0.052 0.0381 0.00042 0.0000

(43) In the rotor 25 in FIG. 7, the classification chambers 27 are tapered toward the outer peripheral side and radially formed. However, as a rotor 31 in FIG. 8, blades 33 having a sectional area increasing toward an outer peripheral side and tapered classification chambers 32 may be eccentrically formed.

(44) In a further embodiment of a rotor for implementing the third mode described above, the rotor 23 in FIG. 4 and the rotors 25, 31 in FIG. 7 or 8 are combined.

(45) FIGS. 15 and 16 are a rotor for implementing the third mode described above. More specifically, FIG. 15 is the same as FIG. 4 except that line B-B is changed to line C-C, and FIG. 16 is the same as FIG. 7 except that reference numeral 25 and 26 are changed to 23 and 21 respectively. Also, as shown in FIG. 16, the blade 21 has a height T increasing toward an inner peripheral side, and a classification chamber 26 has a width increasing toward the inner peripheral side.

(46) Specifically, a blade has a height gradually increasing toward an inner periphery as shown in FIG. 4 to expand an inner peripheral side of the rotor. Also, as shown in FIG. 7 or 8, the blade has a thickness increasing toward an outer peripheral side, and a classification chamber has a width increasing toward the inner peripheral side.

(47) In this embodiment, an arc area A(d) in a diameter d position is expressed by:

(48) $\begin{array}{cc}A\left(d\right)=E\left(d\right).Math.T\left(d\right)=\frac{\left(d-t\left(d\right)N\right)T\left(d\right)}{N}& \mathrm{Expression}16\end{array}$
where E(d) is a circumferential gap between the blades, and T(d) is a height of the blade. A thickness t(d) of the blade 26 expressed as a function of a diameter d is obtained by Expression 17 below:

(49) $\begin{array}{cc}t\left(d\right)=\frac{1}{N}\left[d-\frac{Q}{T\left(d\right)}\frac{1}{D_1^2}\frac{2894}{d.Math.n^2}\frac{18}{9.8\left({}_2-{}_1\right)}\right]& \mathrm{Expression}17\end{array}$
where T in Expression 15 is replaced by T(d). By substituting Expression 17 into Expression 16, the height T(d) is expressed by:

(50) $\begin{array}{cc}T\left(d\right)=\frac{Q}{E\left(d\right).Math.N}.Math.\frac{1}{D_1^2}.Math.\frac{2894}{d.Math.n^2}.Math.\frac{18}{9.8\left({}_2-{}_1\right)}& \mathrm{Expression}18\end{array}$

(51) The gap E(d) in Expression 18 is obtained by Expression 19 below:

(52) $\begin{array}{cc}E\left(d\right)=\frac{}{N}.Math.\left\{b.Math.d_2-\frac{b.Math.d_2-a.Math.d_1}{d_2-d_1}\left(d_2-d\right)\right\}& \mathrm{Expression}19\end{array}$

(53) In Expression 19, d.sub.1 is an inner peripheral diameter of the classification chamber, d.sub.2 is an outer peripheral diameter, a is a coefficient for gap between the blades at the inner periphery, defined by (d.sub.1Nt.sub.1)/d.sub.1, b is a coefficient for gap between the blades at the outer periphery, defined by (d.sub.2Nt.sub.2)/d.sub.2, t.sub.1 is a thickness of the blade 26 at an inner peripheral end, t.sub.2 is a thickness thereof at an outer peripheral end. Thus, a difference between a circumferential gap on the inner peripheral diameter d.sub.1 and a circumferential gap on the outer peripheral diameter d.sub.2 is expressed by (bd.sub.2ad.sub.1)/N. Any diameter d between the diameter d.sub.2 and the diameter d.sub.1 is obtained by Expression 20 below by proportionally dividing the difference by (d.sub.2d)/(d.sub.2d.sub.1), and Expression 19 above is obtained by Expression 20.

(54) $\begin{array}{cc}\frac{\left({\mathrm{bd}}_2-{\mathrm{ad}}_1\right)}{N}.Math.\frac{d_2-d}{d_2-d_1}& \mathrm{Expression}20\end{array}$

(55) The thickness t(d) of the blade 26 is t(d)={dN.Math.E(d)}/N, and thus obtained by Expression 21 below by substituting the gap E(d) obtained by Expression 19 into Expression 18.

(56) $\begin{array}{cc}t\left(d\right)=\frac{d}{N}-\frac{}{N}.Math.\left\{b.Math.d_2-\frac{b.Math.d_2-a.Math.d_1}{d_2-d_1}\left(d_2-d\right)\right\}& \mathrm{Expression}21\end{array}$

(57) With the same set values as in Table 4 above except the blade thickness and a being set to 1 and b being set to 0.8, a simulation calculation was performed for the blade height T(d) by Expression 18 and the blade thickness t(d) by Expression 21 using the gap E(d) between the blades in the diameter d position obtained by Expression 19, and calculated values are shown together with an arc area A(d) and a centrifugal effect G in Table 7 below.

(58) TABLE-US-00007 TABLE 7 CALCULATED VALUE DIAMETER CENTRIFUGAL GAP BETWEEN BLADE LINEAR BLADE POSITION EFFECT ARC AREA BLADES HEIGHT SPEED THICKNESS d G A(d) E(d) T(d) s t(d) m m.sup.2 m m m/s m 0.40 1398 0.00100 0.084 0.0119 0.00084 0.0209 0.35 1223 0.00114 0.076 0.0150 0.00073 0.0157 0.30 1049 0.00133 0.068 0.0195 0.00063 0.0105 0.25 874 0.00159 0.060 0.0265 0.00052 0.0052 0.20 699 0.00199 0.052 0.0381 0.00042 0.0000

(59) As described in the embodiments for implementing the first to third modes, the rotor is required including a blade of such a shape as to provide a constant classified particle size in the radial direction of the classification chamber.

(60) The shown rotors 23, 25, 31 in the embodiments are used in a vertically oriented classifying apparatus, but may be similarly used in a laterally oriented classifying apparatus.

Example 1

(61) As a rotor in a dry type classifying apparatus 3 in FIG. 2, a rotor 42 of a size in FIG. 9 was produced in which forty blades 41 were radially arranged from a center of the rotor at circumferentially regular intervals. Each blade 41 had a thickness of 5 mm at an outer peripheral diameter of 200 mm and a zero thickness at an inner peripheral diameter of 165 mm, and the thicknesses satisfy Expression 15. A raw material of 73.5 kg/h, which had a mean particle size D50 of 2.50 m and a maximum particle size D100 of 13.20 m, had a particle size distribution in Table 8 and FIG. 11, and were composed of heavy calcium carbonate with physical properties shown in Table 9 below, was supplied together with air of 550 Nm.sup.3/h(0.153 Nm.sup.3/s) to the classifying apparatus 3, and were classified under a set condition based on set values in Table 10 and calculated values in Table 11. Then, fine particles collected in a container 12 were sampled to measure a particle size and a rate of the fine particles. Results are shown in Table 8 below and FIG. 11. The fine particles measured had a mean particle size D50 of 1.24 m and a maximum particle size D100 of 5.86 m. The measurement was performed using a laser diffraction/scattering type particle size distribution measuring apparatus (trade name: LA-700) manufactured by HORIBA, Ltd.

(62) TABLE-US-00008 TABLE 8 COMPARATIVE PERCENTAGE OF EXAMPLE 1 EXAMPLE 1 PARTICLES PERCENTAGE PERCENTAGE PARTICLE IN RAW OF FINE OF FINE SIZE (m) MATERIAL % PARTICLES % PARTICLES % 0.296 0.339 0.00 0.389 0.00 0.11 0.445 0.00 0.17 0.57 0.51 0.11 0.27 1.15 0.584 0.21 0.48 1.95 0.669 0.40 0.87 3.21 0.766 0.79 1.60 5.06 0.877 1.49 2.86 8.41 1.005 2.62 4.75 10.73 1.151 4.14 7.05 12.28 1.318 5.77 9.15 12.46 1.51 7.06 10.34 11.25 1.729 7.69 10.35 9.22 1.981 7.69 9.48 7.06 2.269 7.32 8.27 5.25 2.599 6.90 7.13 3.92 2.976 6.59 6.10 2.76 3.409 6.45 5.29 1.95 3.905 6.42 4.48 1.30 4.472 6.36 3.76 0.80 5.122 6.07 2.95 0.40 5.867 5.39 2.14 0.11 6.72 4.30 1.42 0.00 7.697 2.98 0.81 8.816 1.77 0.29 10.097 0.90 0.00 11.565 0.43 13.246 0.17 15.172 0 17.377

(63) TABLE-US-00009 TABLE 9 SPECIFIC RESIDUE SURFACE FROM 45 m APPARENT DOP AREA MEAN PARTICLE SIZE SCREEN DENSITY ABSORPTION WHITENESS MOISTURE cm.sup.2/g Am Bm % g/ml ml/100 g % % AIR AIR DIAMETER AT 50% JIS JIS K5101 BASED ON JIS SPECTROSCOPIC JIS K0068 PERMEATION PERMEATION IN WEIGHT STANDARD STATIC K5101 (USE COLORIMETER/ METHOD METHOD CUMULATIVE SCREEN METHOD DOP) WHITENESS METER PARTICLE SIZE DISTRIBUTION 21,000 1.1 2.5 0 0.3 33 43 94

(64) TABLE-US-00010 TABLE 10 SET VALUE SPECIFIC NUMBER OF ROTATION GRAVITY SPECIFIC DIAMETER FLOW RATE CLASSIFICATION SPEED OF OF GRAVITY BLADE POSITION OF FLUID CHAMBERS ROTOR VISCOSITY PARTICLE OF LIQUID HEIGHT d Q N n .sub.2 .sub.1 T m m.sup.3/s rpm kg/m .Math. s kg/m.sup.3 kg/m.sup.3 m 0.2000 0.153 40 7000 0.000018 2700 1.2 0.15 0.1942 0.153 40 7000 0.000018 2700 1.2 0.15 0.1883 0.153 40 7000 0.000018 2700 1.2 0.15 0.1825 0.153 40 7000 0.000018 2700 1.2 0.15 0.1767 0.153 40 7000 0.000018 2700 1.2 0.15 0.1708 0.153 40 7000 0.000018 2700 1.2 0.15 0.1650 0.153 40 7000 0.000018 2700 1.2 0.15

(65) TABLE-US-00011 TABLE 11 CALCULATED VALUE CLASSIFIED DIAMETER CENTRIFUGAL BLADE GAP BETWEEN LINEAR PARTICLE POSITION EFFECT THICKNESS ARC AREA BLADES SPEED SIZE d G t(d) A(d) E(d) s D.sub.1 m M m.sup.2 m m/sec m 0.2000 5481 0.0050 0.00161 0.0107 2.38 2.31 0.1942 5321 0.0042 0.00166 0.0111 2.30 2.31 0.1883 5161 0.0033 0.00172 0.0115 2.23 2.31 0.1825 5001 0.0025 0.00177 0.0118 2.16 2.31 0.1767 4842 0.0017 0.00183 0.0122 2.09 2.31 0.1708 4682 0.0008 0.00189 0.0126 2.03 2.31 0.1650 4522 0 0.00194 0.0130 1.97 2.31

(66) The classified particle size D.sub.1 of 2.31 m in Table 11 was a classified particle size on an outer periphery of the classification chamber obtained with a thickness t(d) of the blade 41 at the outer periphery of the classification chamber being set to 5 mm, and obtained by a simulation calculation by substituting appropriate items in Table 10 into Expression 6. The blade thickness t(d) in each diameter position in Table 11 was obtained by substituting the classified particle size D.sub.1 set to be constant in a radial direction of the classification chamber and appropriate items in Table 10 into Expression 15, and an inner peripheral diameter d at t=0 was obtained by Expression 15. A centrifugal effect G was obtained by substituting the rotation speed n of the rotor in Table 10 into G=(d.Math.n.sup.2)/(2894), an arc area A was obtained by substituting the blade thickness t(d) obtained by the above and the appropriate items in Table 10 into Expression 5 with t being replaced by t(d), a linear speed s was obtained by substituting the arc area A obtained by the above and the appropriate items in Table 10 into Expression 3, and a gap E(d) between the blades was obtained from the thickness t(d) and by Expression 14. As shown in Table 8, a maximum particle size 100 in Example 1 at this time was 5.867 m.

Comparative Example 1

(67) A classifying apparatus was used including a rotor 44 that has the same structure and size as the rotor 42 in FIG. 9 except a constant thickness of 5 mm of a blade 43 as shown in FIG. 10 and the same structure as the classifying apparatus in Example 1 other than the rotor, and the same raw material as in Example 1 was used to perform classification under the same condition. Tables 12 and 13 below show items used for a simulation calculation and calculation results. A classified particle size D.sub.1 in Table 13 was obtained by substituting appropriate items in Table 12 into Expression 6, an arc area A(d) was obtained by substituting the appropriate items in Table 12 into Expression 5, a centrifugal effect G was obtained by substituting a rotation speed n of the rotor in Table 12 into G=(d.Math.n.sup.2)/(2894), a linear speed s was obtained by substituting the arc area A(d) obtained and the appropriate items in Table 12 into Expression 3, and a gap E(d) between the blades was obtained by substituting the arc area A(d) and a blade height T in Table 12 into E(d)=A(d)/T.

(68) Results are shown in Table 8 and FIG. 11 together with Example 1. In Comparative example 1, the same measuring apparatus as in Example 1 was used to measure a particle size by the same method as in Example 1. Then, the fine particles collected in the container 12 in FIG. 2 had a mean particle size D50 of 1.79 m and a maximum particle size D100 of 8.81 m.

(69) TABLE-US-00012 TABLE 12 SET VALUE FLOW NUMBER OF ROTATION SPECIFIC SPECIFIC DIAMETER RATE BLADE CLASSIFICATION SPEED OF GRAVITY OF GRAVITY BLADE POSITION OF FLUID HEIGHT CHAMBERS ROTOR VISCOSITY PARTICLE OF LIQUID THICKNESS d Q T N n .sub.2 .sub.1 t m m.sup.3/s m rpm kg/m .Math. s kg/m.sup.3 kg/m.sup.3 m 0.2000 0.153 0.15 40 7000 1.8E05 2700 1.2 0.005 0.1942 0.153 0.15 40 7000 1.8E05 2700 1.2 0.005 0.1883 0.153 0.15 40 7000 1.8E05 2700 1.2 0.005 0.1825 0.153 0.15 40 7000 1.8E05 2700 1.2 0.005 0.1767 0.153 0.15 40 7000 1.8E05 2700 1.2 0.005 0.1708 0.153 0.15 40 7000 1.8E05 2700 1.2 0.005 0.1650 0.153 0.15 40 7000 1.8E05 2700 1.2 0.005

(70) TABLE-US-00013 TABLE 13 CALCULATED VALUE CLASSIFIED DIAMETER CENTRIFUGAL GAP BETWEEN LINEAR PARTICLE POSITION EFFECT ARC AREA BLADES SPEED SIZE d G A(d) E(d) s D.sub.1 m m.sup.2 m m/sec m 0.2000 5481 0.00161 0.0107 2.38 2.31 0.1942 5321 0.00154 0.0102 2.49 2.39 0.1883 5161 0.00147 0.0098 2.61 2.49 0.1825 5001 0.00140 0.0093 2.73 2.59 0.1767 4842 0.00133 0.0089 2.88 2.70 0.1708 4682 0.00126 0.0084 3.03 2.82 0.1650 4522 0.00119 0.0080 3.21 2.95

(71) A dry type classifying apparatus including the rotor in FIG. 9 produced with the constant classified particle size in the classification chamber and the blade thickness satisfying Expression 15, and a classifying apparatus including the rotor with the constant blade thickness were used and compared as described above. Then, as shown in FIG. 11, a particle size distribution in Example 1 was shifted to the left as compared to a particle size distribution in comparative example 1, and finer particles and a sharper distribution were obtained, reducing entering of coarse particles.

Example 2

(72) As a rotor 17 of a wet type classifying apparatus 14 in FIG. 3, a rotor 47 of a size in FIG. 12 was produced in which thirty blades 46 were radially arranged from a center of the rotor at circumferentially regular intervals. Each blade 46 had a thickness of 3 mm at an outer peripheral diameter of 86 mm and a zero thickness at an inner peripheral diameter of 70.2 mm, and the thicknesses satisfy Expression 15. A raw material, which had a mean particle size D50 of 5 m and a particle size D98 of 14 m, had a particle size distribution in Table 14 below and FIG. 14, and were composed of spherical molten silica (trade name: FB-5SDC) manufactured by Denka Company Limited, was mixed into a 0.2 wt % hexametaphosphoric acid aqueous solution, and such a raw material slurry was used to perform an experiment three times under a set condition with set values in Table 15 and calculated values in Table 16 obtained by a simulation calculation from the set values. Results are shown in Table 14 below and FIG. 14. A fine particle slurry collected in a tank 19 was sampled to measure a particle size for each experiment. The mean particle sizes D50 were 2.7, 2.9, and 2.9 m, and the particle sizes D98 were 5.7, 6.6, and 6.8 m. The measurement was performed using a laser diffraction type particle size distribution measuring apparatus (trade name: SALD-3100) manufactured by Shimadzu Corporation.

(73) TABLE-US-00014 TABLE 14 COMPARATIVE PERCENTAGE EXAMPLE 2 OF PERCENTAGE EXAMPLE 2 PARTICLES IN OF FINE PERCENTAGE OF PARTICLE RAW PARTICLES % FINE PARTICLES % SIZE (m) MATERIAL % -est1 -est2 -est1 -est2 -est3 0.233 0 0 0 0 0 0 0.291 0 0 0 0 0 0 0.362 0 0 0.363 0.002 0.003 0 0.451 0.018 0.004 0.059 0.017 0.029 0.002 0.563 0.134 0.074 0.121 0.067 0.134 0.048 0.701 0.524 0.397 0.456 0.21 0.411 0.267 0.874 1.349 1.257 1.21 0.616 0.976 0.912 1.089 2.51 2.705 2.456 1.619 2.01 22 1.356 3.668 4.397 4.086 3.275 3.555 3.976 1.690 4.622 5.993 5.836 4.682 5.025 5.531 2.106 5.504 7.345 7.227 10.357 7.45 7.142 2.625 6.538 8.513 10.039 24.636 20.768 19.047 3.271 7.693 14.273 16.675 27.179 25.734 26.218 4.076 8.605 17.045 18.543 21.959 22.639 24.201 5.079 9.182 13.076 12.547 2.448 5.498 4.425 6.329 13.959 13.503 11.328 1.892 3.412 3.461 7.887 16.615 6.109 5.307 0.824 1.746 1.841 9.828 10.515 3.567 2.723 0.205 0.535 0.614 12.247 5.058 1.382 0.872 0.012 0.075 0.107 15.262 2.555 0.33 0.152 0 0 0.008 19.018 0.814 0.031 0 0 0 0 23.699 0.137 0 0 0 0 0

(74) TABLE-US-00015 TABLE 15 SET VALUE FLOW NUMBER OF ROTATION SPECIFIC SPECIFIC DIAMETER RATE OF CLASSIFICATION SPEED OF GRAVITY OF GRAVITY OF BLADE POSITION FLUID CHAMBERS ROTOR VISCOSITY PARTICLE LIQUID HEIGHT d Q N n .sub.2 .sub.1 T m N m.sup.3/s rpm kg/m .Math. s kg/m.sup.3 kg/m.sup.3 m 0.0860 2.78E06 30 4442 0.001 2300 1000 0.01 0.0834 2.78E06 30 4442 0.001 2300 1000 0.01 0.0807 2.78E06 30 4442 0.001 2300 1000 0.01 0.0781 2.78E06 30 4442 0.001 2300 1000 0.01 0.0755 2.78E06 30 4442 0.001 2300 1000 0.01 0.0728 2.78E06 30 4442 0.001 2300 1000 0.01 0.0702 2.78E06 30 4442 0.001 2300 1000 0.01

(75) TABLE-US-00016 TABLE 16 CALCULATED VALUE GAP CLASSIFIED DIAMETER CENTRIFUGAL BLADE BETWEEN LINEAR PARTICLE POSITION EFFECT THICKNESS ARC AREA BLADES SPEED SIZE d G t(d) A(d) E(d) s D.sub.1 m M m.sup.2 m m/sec m 0.0860 949 0.00300 0.000060 0.0060 0.00154 1.52 0.0834 920 0.00250 0.000062 0.0062 0.00149 1.52 0.0807 891 0.00200 0.000065 0.0065 0.00144 1.52 0.0781 862 0.00150 0.000067 0.0067 0.00139 1.52 0.0755 833 0.00100 0.000069 0.0069 0.00134 1.52 0.0728 804 0.00050 0.000071 0.0071 0.00130 1.52 0.0702 775 0.00000 0.000073 0.0073 0.00126 1.52

(76) The classified particle size D.sub.1 in Table 16 was a classified particle size on an outer periphery of the classification chamber obtained with a thickness t(d) of the blade 46 at the outer periphery of the classification chamber being set to 3 mm, and obtained by a simulation calculation by substituting appropriate items in Table 15 into Expression 6. The blade thickness t(d) in each diameter position was obtained by substituting the classified particle size set to be constant at 1.52 m in a radial direction and appropriate items in Table 15 into Expression 15, and an inner peripheral diameter d at t=0 was obtained by Expression 15. A centrifugal effect G was obtained by substituting the rotation speed n of the rotor in Table 15 into G=(d.Math.n.sup.2)/(2894), an arc area A was obtained by substituting the blade thickness t(d) obtained by the above and the appropriate items in Table 15 into Expression 5, a linear speed s was obtained by substituting the arc area A obtained by the above and the appropriate items in Table 15 into Expression 3, and a gap E(d) between the blades was obtained from the thickness t(d) and by Expression 14. As shown in Table 14, the particle sizes D98 in Example 2 at this time were 5.7, 6.6, and 6.8 m.

(77) TABLE-US-00017 TABLE 17 SET VALUE SPECIFIC NUMBER OF ROTATION GRAVITY SPECIFIC DIAMETER FLOW RATE BLADE CLASSIFICATION SPEED OF OF GRAVITY BLADE POSITION OF FLUID HEIGHT CHAMBERS ROTOR VISCOSITY PARTICLE OF FLUID THICKNESS d Q T N n .sub.2 P.sub.1 t m Xm.sup.3/s m rpm kg/m .Math. s kg/m.sup.3 kg/m.sup.3 m 0.0860 2.78E06 0.01 30 4442 0.001 2300 1000 0.003 0.0834 2.78E06 0.01 30 4442 0.001 2300 1000 0.003 0.0807 2.78E06 0.01 30 4442 0.001 2300 1000 0.003 0.0781 2.78E06 0.01 30 4442 0.001 2300 1000 0.003 0.0755 2.78E06 0.01 30 4442 0.001 2300 1000 0.003 0.0728 2.78E06 0.01 30 4442 0.001 2300 1000 0.003 0.0702 2.78E06 0.01 30 4442 0.001 2300 1000 0.003

(78) TABLE-US-00018 TABLE 18 CALCULATED VALUE GAP CLASSIFIED DIAMETER CENTRIFUGAL BETWEEN LINEAR PARTICLE POSITION EFFECT ARC AREA BLADES SPEED SIZE d G A(d) E(d) s D.sub.1 m m.sup.2 m m/sec m 0.0860 949 0.000060 0.0060 0.00154 1.52 0.0834 920 0.000057 0.0057 0.00162 1.58 0.0807 891 0.000055 0.0055 0.00170 1.64 0.0781 862 0.000052 0.0052 0.00179 1.71 0.0755 833 0.000049 0.0049 0.00189 1.79 0.0728 804 0.000046 0.0046 0.00200 1.88 0.0702 775 0.000043 0.0043 0.00213 1.97

Comparative Example 2

(79) A classifying apparatus was used including a rotor 45 that has the same structure and size as the rotor 47 in FIG. 12 except a constant thickness of 3 mm of a blade 48 as shown in FIG. 13 and the same structure as the classifying apparatus in Example 2 other than the rotor, and the same raw material as in Example 2 was used to perform classification under the same condition.

(80) Tables 17 and 18 show items used for a simulation calculation and calculation results. A classified particle size D.sub.1 in Table 18 was obtained by substituting appropriate items in Table 17 into Expression 6, an arc area A(d) was obtained by substituting the appropriate items in Table 17 into Expression 5, a centrifugal effect G was obtained by substituting a rotation speed n of the rotor in Table 17 into G=(d.Math.n.sup.2)/(2894), a linear speed s was obtained by substituting the arc area A(d) obtained and the appropriate items in Table 17 into Expression 3, and a gap E(d) between the blades was obtained by substituting the arc area A(d) and a blade height T in Table 17 into E(d)=A(d)/T.

(81) Results are shown in Table 14 and FIG. 14 together with Example 2. In Comparative example 2, the same measuring apparatus as in Example 2 was used to measure a particle size twice by the same method as in Example 2. Then, the fine particles collected in the container 19 in FIG. 3 had mean particle sizes D50 of 3.3 and 3.5 m, and particle sizes D98 of 9.1 and 9.7 m

(82) Also in the wet type classifying apparatus, as seen in FIG. 14, a particle size distribution in Example 2 is shifted to the left in FIG. 14 as compared to a particle size distribution in comparative example 2, and much finer particles and a much sharper distribution were obtained, reducing entering of coarse particles.

INDUSTRIAL APPLICABILITY

(83) The classifying apparatus of the present invention can be used in general industry treating wet and dry type classification of any powder of micron to submicron size, for example, metal industry, chemical industry, pharmaceutical industry, cosmetic industry, pigment, food industry, ceramic industry, etc.

REFERENCE SIGNS LIST

(84) 1, 21, 26, 33, 41, 43, 46, 48 blade 2, 17, 23, 25, 31, 42, 44, 47 rotor 9, 22, 27, 32 classification chamber