JP2583780B2 - How to mix powders - Google Patents
How to mix powdersInfo
- Publication number
- JP2583780B2 JP2583780B2 JP63013314A JP1331488A JP2583780B2 JP 2583780 B2 JP2583780 B2 JP 2583780B2 JP 63013314 A JP63013314 A JP 63013314A JP 1331488 A JP1331488 A JP 1331488A JP 2583780 B2 JP2583780 B2 JP 2583780B2
- Authority
- JP
- Japan
- Prior art keywords
- mixing
- calculated
- rotation speed
- powders
- mixer
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Classifications
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
- B01F—MIXING, e.g. DISSOLVING, EMULSIFYING OR DISPERSING
- B01F23/00—Mixing according to the phases to be mixed, e.g. dispersing or emulsifying
- B01F23/60—Mixing solids with solids
Landscapes
- Chemical & Material Sciences (AREA)
- Chemical Kinetics & Catalysis (AREA)
- Mixers With Rotating Receptacles And Mixers With Vibration Mechanisms (AREA)
Description
【発明の詳細な説明】 ＜産業上の利用分野＞ 本発明は回転混合機を用いて粉粒体を均一に混合する
方法に関し、詳しくは回転混合機内に充填される粉粒体
の充填率を変更しても、その充填率に応じて均一に混合
させることができる粉粒体の混合方法に関する。DETAILED DESCRIPTION OF THE INVENTION <Industrial application> The present invention relates to a method for uniformly mixing powders and granules using a rotary mixer. The present invention relates to a method for mixing powders and granules that can be uniformly mixed according to the filling rate even if changed.
＜従来技術とその課題＞ 回転混合機で粉粒体を混合する場合、最適な混合状態
を得る混合機の回転速度は、その混合機に仕込まれる粉
粒体の仕込み重量や見掛け密度によって変化する。従来
はこの最適混合回転速度を得るのに、前記仕込み重量や
見掛け密度が変更される都度、実際に回転させたデータ
から最適混合速度を選んでいた。したがって、非常に煩
わしく、また混合機の大きさや形を変更する都度、各個
々の条件における最適混合回転速度を全て再測定して選
出しなければならないという不都合があった。<Prior art and its problems> When mixing powders and granules with a rotary mixer, the rotation speed of the mixer to obtain an optimum mixing state varies depending on the weight and apparent density of the powders charged in the mixer. . Conventionally, in order to obtain the optimum mixing rotation speed, the optimum mixing speed was selected from the actually rotated data every time the charged weight or the apparent density was changed. Therefore, it is very troublesome, and every time the size or shape of the mixer is changed, the optimum mixing rotation speed under each individual condition must be remeasured and selected.
＜目的＞ そこで本発明は上記従来技術における欠点を解消し、
ある１つの条件における混合機の最適混合回転速度がわ
かれば、他の条件における最適混合回転速度を予測して
粉粒体を混合させることができる方法の提供を目的とす
る。<Objective> Accordingly, the present invention has solved the above-mentioned disadvantages of the prior art,
It is an object of the present invention to provide a method capable of predicting the optimum mixing rotation speed under another condition and mixing the granules if the optimum mixing rotation speed of the mixer under one certain condition is known.
＜課題を解決するための手段＞ 本発明の粉粒体の混合方法は、ある１つの充填率で回
転混合機内に粉粒体を入れて実際に混合した場合に得ら
れた最適混合回転速度と、前記充填率から計算できる粉
粒体の重心回転半径とから、フルード数Frを予め算出し
ておくことにより、他の異なる充填率で粉粒体を入れた
場合の最適混合回転速度を、前記予め算出しておいたフ
ルード数Frと、当該充填率から計算できる粉粒体の重心
回転半径とから、計算のみで求めることを特徴としてい
る。<Means for Solving the Problems> The method for mixing powder and granules according to the present invention is based on the optimum mixing rotational speed obtained when powder and granules are put into a rotary mixer at a certain filling rate and actually mixed. By calculating the Froude number Fr in advance from the rotation radius of the center of gravity of the granular material that can be calculated from the filling ratio, the optimal mixing rotation speed when the granular material is added at another different filling ratio is calculated as described above. It is characterized in that the fluid number Fr is obtained only by calculation from the previously calculated Froude number Fr and the rotation radius of the center of gravity of the granular material that can be calculated from the filling rate.
さらに前記構成においてフルード数Frを下記の式で算
出することを特徴としている。Further, the configuration is characterized in that the Froude number Fr is calculated by the following equation.
ここで下記の式とは、次の式をいう。 Here, the following equation refers to the following equation.
Fr＝ω2Rg/G Fr:フルード数 ω：回転速度（1/sec） Rg:重心回転半径（cm） G:重力加速度（cm/sec2） 本発明の構成をもう少し具体的に説明する。今、第１
図に示すような半径1m、長さ2mの水平回転円筒混合機を
用いた場合において、見掛け密度1.0の粉粒体を1.885ト
ン仕込んで、実際に回転混合させた場合の最適混合に対
応する回転速度、すなわち実績値としての回転速度Ｎが
27rpmであった場合について考える。Fr = ω 2 Rg / G Fr: Froude number ω: Rotation speed (1 / sec) Rg: Rotation radius of the center of gravity (cm) G: Gravitational acceleration (cm / sec 2 ) The configuration of the present invention will be described more specifically. Now the first
In the case of using a horizontal rotating cylindrical mixer with a radius of 1 m and a length of 2 m as shown in the figure, 1.885 tons of powder and granular material with an apparent density of 1.0 were charged, and the rotation corresponding to the optimal mixing when actually rotating and mixing Speed, that is, rotation speed N as an actual value
Consider the case of 27 rpm.
この場合、粉粒体の仕込容積は、 仕込容積＝仕込み重量／見掛け密度 ＝1.885/1 ＝1.885（m3） 一方、回転混合機の内容積は 内容積＝πR2・Ｌ R:半径 L:長さ ＝２π ＝6.284（m3） よって粉粒体の充填率は、 充填率＝30（％） である。そして充填率が30％であると、前記第１図の水
平回転円筒混合機の場合、重心回転半径Rgは、 Rg＝60.2（cm） と計算できる。In this case, the charged volume of the granular material is: charged volume = weight charged / apparent density = 1.885 / 1 = 1.885 (m 3 ) On the other hand, the internal volume of the rotary mixer is the internal volume = πR 2 · LR R: radius L: Length = 2π = 6.284 (m 3 ) Therefore, the filling rate of the powder is 30%. When the filling rate is 30%, in the case of the horizontal rotary cylinder mixer shown in FIG. 1, the rotation radius Rg of the center of gravity can be calculated as follows: Rg = 60.2 (cm).
フルード数Frは Fr＝ω2Rg/G ……（１） で表され、又 ω＝２πN/60 ……（２） であるので、 Fr＝４π2N2Rg/602G ……（３） N:回転速度（rpm） となる。よって前記回転速度Ｎ＝27rpmと、重心回転半
径Rg＝60.2cmを（３）式に代入すると、フルード数Frは Fr＝0.49 となる。この得られたフルード数Fr＝0.49を用いて、別
の条件で粉粒体を第１図の水平回転円筒混合機に入れた
場合の最適混合回転速度Ｎを求めることができる。すな
わち上記式（３）から回転速度Ｎは、 N2＝602FrG/4π2Rg ……（４） であるので、式（４）にFr＝0.49と、各条件における重
心回転半径Rgを代入すればよい。Froude number Fr is expressed by Fr = ω 2 Rg / G ...... (1), also ω = 2πN / 60 ...... are the (2), Fr = 4π 2 N 2 Rg / 60 2 G ...... (3 N: The rotation speed (rpm). Therefore, when the rotational speed N = 27 rpm and the center-of-gravity rotational radius Rg = 60.2 cm are substituted into the equation (3), the Froude number Fr becomes 0.49. Using the obtained Froude number Fr = 0.49, the optimum mixing rotation speed N when the granular material is put in the horizontal rotary cylindrical mixer shown in FIG. 1 under another condition can be obtained. That is, since the rotation speed N is N 2 = 60 2 FrG / 4π 2 Rg from the above equation (3), (4) do it.
今、見掛け密度が１、仕込量が0.628トンの場合
（ａ）、見掛け密度１、仕込量が3.142トンの場合
（ｂ）、見掛け密度1.5、仕込量1.885トンの場合
（ｃ）、見掛け密度0.5、仕込量0.943トンの場合
（ｄ）、見掛け密度２、仕込量5.027トンの場合（ｅ）
についての最適混合回転速度の計算値を表１に示す。Now, when the apparent density is 1, the charged amount is 0.628 tons (a), the apparent density is 1, the charged amount is 3.142 tons (b), the apparent density is 1.5, the charged amount is 1.885 tons (c), and the apparent density is 0.5. , When the charged amount is 0.943 ton (d), when the apparent density is 2, and when the charged amount is 5.027 ton (e)
Table 1 shows the calculated values of the optimum mixing rotation speeds for.
上記の具体的説明においては、第１図に示すような半
径1m、長さ2mの水平回転円筒混合機を用いた場合を示し
たが、他の形状の場合でも、同様にある１つの充填率で
の実績値としての最適混合回転速度が得られれば、他の
充填率での最適混合回転速度が計算で容易に得られる。 In the above specific description, a case where a horizontal rotating cylindrical mixer having a radius of 1 m and a length of 2 m as shown in FIG. 1 is used, but a similar filling rate is also applicable to other shapes. If the optimum mixing rotation speed is obtained as the actual value in the above, the optimum mixing rotation speed at another filling rate can be easily obtained by calculation.
また回転混合機の形状が同じで、スケールアップした
ような場合においても、改めて実績値を得る必要はな
い。すなわち相似形の場合には、それらのスケールの異
なるものにつき、何れかのスケールのものについての最
適混合回転速度の実績値が１つあれば十分である。Further, even when the rotary mixer has the same shape and is scaled up, it is not necessary to newly obtain the actual value. That is, in the case of similar shapes, it is sufficient that there is one actual value of the optimum mixing rotation speed for any of the scales having different scales.
＜作用効果＞ 本発明は以上の構成よりなり、ある１つの充填率にお
ける実績値としての最適混合回転速度を得ることによ
り、他の充填率における最適混合回転速度を、計算によ
って算出することができる。したがって、種々の充填率
に対してその都度予めの実績値を得るといった労力や試
し混合などを必要とすることなく、最初から最適の混合
を行うことができる。<Effects> The present invention is configured as described above, and by obtaining the optimum mixing rotation speed as the actual value at a certain filling ratio, the optimum mixing rotation speed at another filling ratio can be calculated. . Therefore, the optimum mixing can be performed from the beginning without the need for labor or trial mixing to obtain a result value in advance for each of various filling rates.
＜実施例＞ 第２図に示すような二重円錐型混合機で、内容積の異
なる３つの互いに相似形の混合機Ａ、Ｂ、Ｃを用いて、
見掛け密度1.3のスポンジチタンを種々の充填率で混合
した。そして最適の混合度となる実際の回転速度を得
た。またこの最適混合回転速度からフルード数Frを算出
した。一方、混合機Ａにおけるフルード数Frの値（0.2
1）をもって、混合機Ｂ、Ｃにおける最適混合回転速度
を計算した。計算による最適混合回転速度をカッコ内に
示す。なお混合機Ａは内容積が8m3、混合機Ｂは内容積
が4m3、混合機Ｃは内容積が0.05m3である。また混合度
は次に示すレーン（Lacey）の式を使って得た。<Example> In a double cone type mixer as shown in FIG. 2, three similar mixers A, B and C having different internal volumes were used.
Titanium sponge with an apparent density of 1.3 was mixed at various filling rates. Then, the actual rotation speed at which the degree of mixing was optimal was obtained. The Froude number Fr was calculated from the optimum mixing rotation speed. On the other hand, the value of the Froude number Fr in the mixer A (0.2
According to 1), the optimum mixing rotation speed in the mixers B and C was calculated. The calculated optimal mixing rotation speed is shown in parentheses. Incidentally mixer A has internal volume of 8m 3, mixer B is internal volume of 4m 3, mixer C is the internal volume is 0.05 m 3. The degree of mixing was obtained using the following equation of lane (Lacey).
混合度＝（σe 2−σ２）／（σo 2−σ２） σo:混合前の標準偏差 σe:混合後の標準偏差 σ：完全混合状態の標準偏差 結果を表２に示す。Degree of mixing = (σ e 2 −σ 2 ) / (σ o 2 −σ 2 ) σ o : Standard deviation before mixing σ e : Standard deviation after mixing σ: Standard deviation of perfect mixing state The results are shown in Table 2. .
表２から明らかなように、混合機Ａにおける最適混合
回転速度の実績値19rpmから得られたフルード数Fr、0.2
10を用いて計算した他の混合機Ｂ、Ｃにおける各条件で
の最適混合回転速度値カッコ内は、それらの条件におけ
る実際の最適混合回転速度上段と非常によく一致してい
る。 As is clear from Table 2, the Froude number Fr obtained from the actual value of 19 rpm of the optimum mixing rotational speed in the mixer A, 0.2
The values of the optimum mixing rotation speeds in the parentheses of the other mixers B and C calculated using FIG. 10 are in good agreement with the uppermost values of the actual mixing rotation speeds in those conditions.
第１図は本発明の具体的説明に用いた水平回転円筒混合
機の斜視図、第２図は実施例に用いた二重円錐型混合機
の斜視図である。FIG. 1 is a perspective view of a horizontal rotary cylindrical mixer used in the specific description of the present invention, and FIG. 2 is a perspective view of a double cone type mixer used in the embodiment.
Claims (2)
を入れて実際に混合した場合に得られた最適混合回転速
度と、前記充填率から計算できる粉粒体の重心回転半径
とから、フルード数Frを予め算出しておくことにより、
他の異なる充填率で粉粒体を入れた場合の最適混合回転
速度を、前記予め算出しておいたフルード数Frと、当該
充填率から計算できる粉粒体の重心回転半径とから、計
算のみで求めることを特徴とする粉粒体の混合方法。1. An optimum mixing rotation speed obtained when powders and granules are put into a rotary mixer at a certain filling rate and actually mixed, and a center-of-gravity rotation radius of the powders and granules which can be calculated from the filling rate. By calculating the Froude number Fr in advance,
Optimum mixing rotation speed when powders are added at other different filling rates, the Froude number Fr calculated in advance, and the center of gravity rotation radius of the powders that can be calculated from the filling rate, only calculation. A method for mixing powders and granules, wherein the method is obtained by:
を特徴とする請求項１記載の粉粒体の混合方法。 記 Fr＝ω2Rg/G ω：回転速度（1/sec） Rg:重心回転半径（cm） G:重力加速度（cm/sec2）2. The method according to claim 1, wherein the Froude number is calculated by the following equation. Note Fr = ω 2 Rg / G ω: Rotational speed (1 / sec) Rg: Rotation radius of center of gravity (cm) G: Gravitational acceleration (cm / sec 2 )
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP63013314A JP2583780B2 (en) | 1988-01-22 | 1988-01-22 | How to mix powders |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP63013314A JP2583780B2 (en) | 1988-01-22 | 1988-01-22 | How to mix powders |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPH01189341A JPH01189341A (en) | 1989-07-28 |
| JP2583780B2 true JP2583780B2 (en) | 1997-02-19 |
Family
ID=11829710
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP63013314A Expired - Fee Related JP2583780B2 (en) | 1988-01-22 | 1988-01-22 | How to mix powders |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JP2583780B2 (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE4437072C2 (en) * | 1994-10-17 | 1996-11-21 | Loedige Maschbau Gmbh Geb | Process for the treatment of bulk goods that tend to generate dust |
| JP2015003318A (en) * | 2013-04-26 | 2015-01-08 | 第一三共株式会社 | Method for calculating powder mixing condition |
-
1988
- 1988-01-22 JP JP63013314A patent/JP2583780B2/en not_active Expired - Fee Related
Also Published As
| Publication number | Publication date |
|---|---|
| JPH01189341A (en) | 1989-07-28 |
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Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| LAPS | Cancellation because of no payment of annual fees |