JP2009119433A - Medium behavior simulation apparatus of rotary oscillation mill machine - Google Patents

Medium behavior simulation apparatus of rotary oscillation mill machine Download PDF

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JP2009119433A
JP2009119433A JP2007299315A JP2007299315A JP2009119433A JP 2009119433 A JP2009119433 A JP 2009119433A JP 2007299315 A JP2007299315 A JP 2007299315A JP 2007299315 A JP2007299315 A JP 2007299315A JP 2009119433 A JP2009119433 A JP 2009119433A
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spherical
wall surface
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mill
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JP5190251B2 (en
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Fumiyoshi Saito
文良 齋藤
Junya Kano
純也 加納
Tomonari Kobayashi
智成 児林
Masayuki Narumi
雅之 鳴海
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Sumitomo Chemical Co Ltd
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Abstract

<P>PROBLEM TO BE SOLVED: To easily, accurately and sequentially simulate the behavior of each spherical medium in a mill vessel which carries out complex movement of rotation and oscillation, by using a relative coordinate system that is a coordinate system having a symmetric axis of the axisymmetric shaped mill vessel as one of coordinate axes. <P>SOLUTION: The behavior of the spherical medium packed in the axisymmetric shaped mill and carrying out rotation movement and oscillation movement is simulated by defining an absolute coordinate system K1 with the coordinate center fixed and a relative coordinate system K2 using one of axes as a symmetry axis, carrying out judgement of contact between the spherical medium and the mill-vessel wall surface in a coordinate system obtained by converting the coordinates from the absolute coordinate system K1 to the relative coordinate system K2 to obtain the contact angle of the spherical medium and the mill-vessel wall surface in the relative coordinate system K2, and then obtain the coordinates in the absolute coordinate system K1 by coordinate conversion. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

本発明は、軸対称形状のミル容器内に被加工物を多数の鋼球ボール等の球形粉砕媒体（以下、球形媒体という。）とともに装填し、ミル容器を回転させつつ揺動させることにより被加工物を粉砕或いは混合する回転揺動ミル装置におけるミル容器内の球形媒体の挙動をシミュレーションする回転揺動ミル装置の媒体挙動シミュレーション装置に関する。   In the present invention, a work piece is loaded together with a large number of spherical grinding media such as steel ball balls (hereinafter referred to as spherical media) in an axisymmetric mill container, and the mill container is swung while being rotated. The present invention relates to a medium behavior simulation apparatus of a rotary rocking mill apparatus that simulates the behavior of a spherical medium in a mill container in a rotary rocking mill apparatus that pulverizes or mixes a workpiece.

回転ミル装置は、多数個の球形媒体を収納した密閉ミル容器内に被加工物を装填してミル容器を固定された回転軸を中心として回転駆動することにより、被加工物を所定の粒径に粉砕又は混合する。回転ミル装置におけるミル容器内の球形媒体の挙動をシミュレーションする媒体挙動シミュレーション装置としては、例えば発明者等による特許文献１に開示されている。   The rotary mill device loads a workpiece into a sealed mill container containing a large number of spherical media, and rotates the mill container around a fixed rotation axis, thereby causing the workpiece to have a predetermined particle size. Crush or mix. An example of a medium behavior simulation apparatus that simulates the behavior of a spherical medium in a mill container in a rotary mill apparatus is disclosed in Patent Document 1 by the inventors.

この媒体挙動シミュレーション装置は、シミュレーション技術として、微小時間毎に個々の粒子に作用する力を算出し、この算出結果に基づいて運動方程式を差分的に計算し、粒子の変位を逐次数値解析する離散要素法（DEM:Discrete Element Method）が用いられる。なお、離散要素法については、例えば非特許文献１に具体的な計算方法が開示されている。   As a simulation technique, this medium behavior simulation apparatus calculates a force acting on individual particles every minute time, calculates a motion equation differentially based on the calculation result, and performs discrete numerical analysis of particle displacement sequentially. The element method (DEM: Discrete Element Method) is used. As for the discrete element method, a specific calculation method is disclosed in Non-Patent Document 1, for example.

発明者等により提供された特許文献１に開示した媒体挙動シミュレーション装置は、座標系として回転軸を１つの軸とする絶対座標軸系だけを使いミル容器内の球形媒体の挙動をシミュレーションする。   The medium behavior simulation apparatus disclosed in Patent Document 1 provided by the inventors simulates the behavior of a spherical medium in a mill container using only an absolute coordinate axis system having a rotation axis as one axis as a coordinate system.

特開平１１−１４７０４８号公報Japanese Patent Laid-Open No. 11-147048 日本機械学会論文集（Ｂ編）、５７、５３４、６０（１９９１）Transactions of the Japan Society of Mechanical Engineers (B), 57, 534, 60 (1991)

ところで、回転ミル装置については、ミル容器を回転させるとともに揺動させる回転揺動ミルも知られている。この回転ミル装置は、回転軸が揺動するため、ミル容器の挙動が複雑になり、特許文献１のシミュレーションの適用が困難である。   Incidentally, as a rotary mill device, a rotary rocking mill that rotates and rocks a mill container is also known. In this rotary mill apparatus, since the rotation shaft swings, the behavior of the mill container becomes complicated, and it is difficult to apply the simulation of Patent Document 1.

本発明は、軸対称形状のミル容器の対称軸を座標軸の１つとした座標系である相対座標系を利用することにより、ミル容器内の球形媒体の挙動を容易かつ正確に逐次シミュレーションすることを可能とする回転揺動ミル装置の媒体挙動シミュレーション装置を提供することを目的とする。   The present invention makes it possible to sequentially and easily simulate the behavior of a spherical medium in a mill vessel by using a relative coordinate system, which is a coordinate system in which the axis of symmetry of an axially symmetric mill vessel is one of the coordinate axes. It is an object of the present invention to provide a medium behavior simulation apparatus for a rotary rocking mill apparatus that can be used.

上述した目的を達成する本発明にかかる回転揺動ミル装置の媒体挙動シミュレーション装置は、内部に多数の球形媒体を装填した軸対称形状のミル容器と、該ミル容器内を通る回転軸を中心として該ミル容器を回転させる容器回転駆動手段と、ミル容器を回転軸と直交する揺動軸を中心として揺動させる容器揺動駆動手段とを備えた回転揺動ミル装置におけるミル容器内における球形媒体の挙動をシミュレーションする。回転揺動ミル装置の媒体挙動シミュレーション装置は、回転揺動ミル装置に対して、座標中心を固定した座標系である絶対座標系（Ｋ１：ＫＸ１、ＫＹ１、ＫＺ１）を規定するとともにミル容器の対称軸を座標軸の１つとした座標系である相対座標系（Ｋ２：ＫＸ２、ＫＹ２、ＫＺ２）を規定する。   A medium behavior simulation apparatus for a rotary oscillating mill apparatus according to the present invention that achieves the above-described object is an axially symmetric mill container in which a large number of spherical media are loaded, and a rotational axis passing through the mill container. A spherical medium in a mill container in a rotary rocking mill device comprising container rotation driving means for rotating the mill container and container rocking drive means for rocking the mill container around a rocking axis orthogonal to the rotation axis. Simulate the behavior of The medium behavior simulation device of the rotary rocking mill device defines an absolute coordinate system (K1: KX1, KY1, KZ1) that is a coordinate system with a fixed coordinate center with respect to the rotary rocking mill device and is symmetrical with the mill vessel. A relative coordinate system (K2: KX2, KY2, KZ2), which is a coordinate system in which an axis is one of coordinate axes, is defined.

回転揺動ミル装置の媒体挙動シミュレーション装置は、数値解析を行う微小単位時間（Δｔ）、絶対座標系（Ｋ１）における球形媒体の中心位置の座標情報である媒体中心絶対座標情報（Ａ：ＡＸ１、ＡＹ１、ＡＺ１）、絶対座標系（Ｋ１）における球形媒体の運動ベクトル情報（Ｖ）、球形媒体の半径（Ｒ）及び球形媒体をそれぞれ識別する媒体識別指標（Ｆ）を初期情報として入力する入力手段を備える。回転揺動ミル装置の媒体挙動シミュレーション装置は、入力手段により入力された初期情報を記憶する記憶手段を備える。回転揺動ミル装置の媒体挙動シミュレーション装置は、相対座標系（Ｋ２）における、ミル容器の壁面の座標情報である壁面相対座標情報（Ｂ：ＢＸ１、ＢＹ１、ＢＺ１）を求めるとともに、記憶手段に記憶された媒体中心絶対座標情報（Ａ）に基づいて多数の球形媒体のそれぞれについて相対座標系（Ｋ２）における中心位置の座標情報である媒体中心相対座標情報（Ｃ：ＣＸ１、ＣＹ１、ＣＺ１）を求め、該媒体中心相対座標情報（Ｃ）、球形媒体の半径（Ｒ）及び壁面相対座標位置（Ｂ）に基づいて球形媒体のミル容器の壁面への接触を判別する演算・判別手段を備える。   The medium behavior simulation apparatus of the rotary oscillating mill apparatus is a medium unit absolute coordinate information (A: AX1, which is coordinate information of a center position of a spherical medium in a minute unit time (Δt) and an absolute coordinate system (K1) for performing numerical analysis. AY1, AZ1), the motion vector information (V) of the spherical medium in the absolute coordinate system (K1), the radius (R) of the spherical medium, and a medium identification index (F) for identifying the spherical medium as initial information. Is provided. The medium behavior simulation apparatus of the rotary rocking mill apparatus includes a storage unit that stores initial information input by the input unit. The medium behavior simulation device of the rotary rocking mill device obtains wall surface relative coordinate information (B: BX1, BY1, BZ1) which is coordinate information of the wall surface of the mill container in the relative coordinate system (K2) and stores it in the storage means. Based on the obtained medium center absolute coordinate information (A), medium center relative coordinate information (C: CX1, CY1, CZ1) which is coordinate information of the center position in the relative coordinate system (K2) is obtained for each of a large number of spherical media. And a calculation / discrimination means for discriminating contact of the spherical medium with the wall surface of the mill container based on the medium center relative coordinate information (C), the radius (R) of the spherical medium and the wall surface relative coordinate position (B).

回転揺動ミル装置の球形媒体挙動シミュレーション装置は、演算・判別手段による球形媒体のミル容器の壁面への接触判定に基づき、相対座標系（Ｋ２）における球形媒体とミル容器壁面との接触点位置の座標情報である接触点相対座標情報（Ｄ：ＤＸ１、ＤＹ１、ＤＺ１）から絶対座標系（Ｋ１）における球形媒体とミル容器壁面との接触点位置の座標情報である接触点絶対座標情報（Ｅ：ＥＸ１、ＥＹ１、ＥＺ１）を求め、該接触点絶対座標情報（Ｅ）と球形媒体の媒体中心絶対座標情報（Ａ）と媒体識別指標（Ｆ）とに基づいて絶対座標系（Ｋ１）における接触点位置での球形媒体の接触方向（Ｈ）を算出する。回転揺動ミル装置の球形媒体挙動シミュレーション装置は、球形媒体の接触点におけるミル容器の壁面の揺動動作による絶対座標系（Ｋ１）における壁面揺動速度ベクトル（Ｖ１）と回転動作による絶対座標系（Ｋ１）における壁面回転速度ベクトル（Ｖ２）を算出するとともに、これら壁面揺動速度ベクトル（Ｖ１）と壁面回転速度ベクトル（Ｖ２）のベクトル和として絶対座標系（Ｋ１）における接触点位置でのミル容器の壁面の運動速度ベクトル（ＶＴ）を算出する。回転揺動ミル装置の球形媒体挙動シミュレーション装置は、球形媒体の運動速度ベクトル（Ｖ）とミル容器の壁面との接触方向（Ｈ）とミル容器の壁面の運動速度ベクトル（ＶＴ）に基づいて球形媒体が壁面から受ける力（ＪＯ）を算出し、該壁面から受ける力（ＪＯ）と重力（Ｇ）と微小単位時間（Δｔ）とに基づいて運動方程式を数値解析することにより球形媒体の運動速度ベクトル（Ｖ）及び微小時間変位（Ｕ）を求めるとともに、該微小時間変位（Ｕ）から微小単位時間（Δｔ）後の球形媒体の媒体中心絶対座標情報（Ａ）を求め、該媒体中心絶対座標情報（Ａ）及び運動速度ベクトル（Ｖ）を記憶手段に格納し、適宜の出力手段により出力する。   The spherical medium behavior simulation apparatus of the rotary rocking mill apparatus is based on the determination of the contact of the spherical medium with the wall surface of the mill container by the calculation / discrimination means, and the contact point position between the spherical medium and the mill container wall surface in the relative coordinate system (K2). Contact point relative coordinate information (D: DX1, DY1, DZ1) that is the coordinate information of the contact point absolute coordinate information (E) that is the coordinate information of the contact point position between the spherical medium and the mill vessel wall surface in the absolute coordinate system (K1). : EX1, EY1, EZ1) and contact in the absolute coordinate system (K1) based on the contact point absolute coordinate information (E), the medium center absolute coordinate information (A) of the spherical medium, and the medium identification index (F). The contact direction (H) of the spherical medium at the point position is calculated. The spherical medium behavior simulation device of the rotary rocking mill device is a wall rocking velocity vector (V1) in the absolute coordinate system (K1) based on the rocking motion of the wall surface of the mill container at the contact point of the spherical medium and the absolute coordinate system based on the rotational motion. The wall surface rotational speed vector (V2) in (K1) is calculated, and the mill at the contact point position in the absolute coordinate system (K1) is calculated as the vector sum of the wall surface rotational speed vector (V1) and the wall surface rotational speed vector (V2). A velocity vector (VT) of the wall surface of the container is calculated. The spherical medium behavior simulation apparatus of the rotary oscillating mill apparatus has a spherical shape based on the motion speed vector (V) of the spherical medium and the contact direction (H) between the wall surface of the mill container and the motion speed vector (VT) of the wall surface of the mill container. The velocity of the spherical medium is calculated by calculating the force (JO) that the medium receives from the wall surface and numerically analyzing the equation of motion based on the force (JO), gravity (G), and minute unit time (Δt) received from the wall surface. The vector (V) and the minute time displacement (U) are obtained, and the medium center absolute coordinate information (A) of the spherical medium after the minute unit time (Δt) is obtained from the minute time displacement (U). The information (A) and the motion velocity vector (V) are stored in the storage means and output by an appropriate output means.

本発明にかかる回転揺動ミル装置の球形媒体挙動シミュレーション装置によれば、多数の球形媒体を装填した軸対称形状のミル容器が回転動作と揺動動作を行うことによりミル容器内において３次元運動を行う球形媒体の挙動を逐次シミュレーションする。回転揺動ミル装置の球形媒体挙動シミュレーション装置によれば、座標中心を固定した座標系の絶対座標系とミル容器の対称軸を座標軸の１つとした座標系の相対座標系とを規定し、球形媒体とミル容器の壁面との接触判別結果に基づいて当該ミル容器の壁面における球形媒体の運動速度ベクトルを絶対座標系から相対座標系に座標変換した座標系において求めることにより、離散要素法を適用して３次元運動を行う球形媒体の運動解析を容易かつ正確に逐次シミュレーションを行うことが可能となる。   According to the spherical medium behavior simulation apparatus of the rotary rocking mill apparatus according to the present invention, the axially symmetric mill container loaded with a large number of spherical media performs three-dimensional motion in the mill container by rotating and swinging. The behavior of a spherical medium performing the simulation is sequentially simulated. According to the spherical medium behavior simulation device of the rotary rocking mill device, the absolute coordinate system of the coordinate system with the fixed coordinate center and the relative coordinate system of the coordinate system with the symmetry axis of the mill container as one of the coordinate axes are defined. The discrete element method is applied by determining the motion velocity vector of the spherical medium on the wall surface of the mill container based on the result of contact discrimination between the medium and the wall surface of the mill container in a coordinate system obtained by converting the coordinate system from the absolute coordinate system to the relative coordinate system. As a result, it is possible to easily and accurately perform sequential simulation of the motion analysis of a spherical medium that performs three-dimensional motion.

以下、本発明の実施の形態について図面を参照して詳細に説明する。実施の形態として示す球形媒体挙動シミュレーション装置（以下、シミュレーション装置と略称する）１は、図１に示すように入力手段２と、記憶手段３と、演算・判別手段４と、出力手段５を備え、図２に示す回転揺動ミル装置６の軸対称形状のミル容器７内に装填した鋼球ボール等の多数個の球形媒体８の挙動解析を計算処理してその挙動を逐次シミュレーションする。シミュレーション装置１は、実際にはコンピュータとその周辺機器とにより構成され、例えば入力手段２がキーボードであり、記憶手段３が内蔵メモリ或いは外部記憶装置であり、出力手段５がモニタ或いはプリンタである。シミュレーション装置１は、コンピュータにロードされた所定のプログラムソフトウェアにより動作する。   Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. A spherical medium behavior simulation apparatus (hereinafter abbreviated as a simulation apparatus) 1 shown as an embodiment includes an input means 2, a storage means 3, a calculation / discrimination means 4, and an output means 5 as shown in FIG. 2, the behavior analysis of a large number of spherical media 8 such as steel ball balls loaded in the axially symmetric mill container 7 of the rotary rocking mill device 6 shown in FIG. 2 is calculated and the behavior is sequentially simulated. The simulation apparatus 1 is actually composed of a computer and its peripheral devices. For example, the input means 2 is a keyboard, the storage means 3 is a built-in memory or an external storage device, and the output means 5 is a monitor or a printer. The simulation apparatus 1 operates with predetermined program software loaded on a computer.

シミュレーション装置１は、上述した従来のシミュレーション装置と同様に、離散要素法を用いて各球形媒体８のミル容器７内における挙動を逐次シミュレーションする。離散要素法は、各先行文献に詳細に説明されているように、運動方程式を差分的に計算して粒子の微小時間変位を逐次数値解析する方法である。   Similar to the above-described conventional simulation apparatus, the simulation apparatus 1 sequentially simulates the behavior of each spherical medium 8 in the mill container 7 using the discrete element method. The discrete element method is a method in which a numerical equation of motion is differentially calculated and a minute time displacement of particles is sequentially numerically analyzed, as described in detail in each of the prior documents.

回転揺動ミル装置６は、例えば鉱物資源の精製過程において原料鉱石等の被加工物１４を所定の粒径に粉砕する等の各種用途に用いられ、図２に示すように、ミル容器７の対称軸９をこのミル容器７を回転させる回転支軸として、この対称軸９を駆動する容器回転駆動手段１０と、対称軸９を支持する支持機構１１と、この支持機構１１の揺動支軸１２を駆動してミル容器７を対称軸９と直交するの軸方向と直交する揺動支軸１２を中心として揺動させる容器揺動駆動手段１３とを備える。   The rotary rocking mill device 6 is used for various purposes such as pulverizing a workpiece 14 such as raw ore into a predetermined particle diameter in the process of refining mineral resources, for example, as shown in FIG. Using the symmetry axis 9 as a rotation support shaft for rotating the mill container 7, the container rotation drive means 10 for driving the symmetry axis 9, the support mechanism 11 for supporting the symmetry axis 9, and the swing support shaft of the support mechanism 11 And a container swinging drive means 13 for driving the mill container 7 about a swinging support shaft 12 orthogonal to the axial direction orthogonal to the symmetry axis 9.

回転揺動ミル装置６は、ミル容器７を回転動作させながら揺動動作を行うことにより、このミル容器７内において被加工物１４を効率よく粉砕することが可能である。回転揺動ミル装置６においては、このようにミル容器７が回転動作と揺動動作を行うことから、その内部に充填された多数個の球形媒体８もミル容器７内において回転動作に伴うＸ軸方向とＹ軸方向の挙動とともに揺動動作に伴うＺ軸方向の挙動が生じる。   The rotary rocking mill device 6 can efficiently grind the workpiece 14 in the mill container 7 by performing the rocking motion while rotating the mill container 7. In the rotary rocking mill device 6, the mill container 7 performs the rotating operation and the rocking operation in this way, so that a large number of spherical media 8 filled in the mill container 7 can also be rotated in the mill container 7 with the rotational operation. Along with the behavior in the axial direction and the Y-axis direction, the behavior in the Z-axis direction accompanying the swinging motion occurs.

シミュレーション装置１は、ミル容器７内において３次元運動を行う球形媒体８の挙動を、座標中心を固定した座標系である絶対座標系Ｋ１（Ｘ１、Ｙ１、Ｚ１）を規定するとともに、ミル容器７の対称軸９を座標軸の１つとした座標系である相対座標系Ｋ２（Ｘ２、Ｙ２、Ｚ２））を規定する。   The simulation apparatus 1 defines an absolute coordinate system K1 (X1, Y1, Z1), which is a coordinate system with a fixed coordinate center, for the behavior of the spherical medium 8 that performs three-dimensional motion in the mill container 7, and the mill container 7 A relative coordinate system K2 (X2, Y2, Z2)) is defined which is a coordinate system in which the symmetry axis 9 is one of the coordinate axes.

シミュレーション装置１は、球形媒体８とミル容器７の壁面（ミル容器壁面）７Ａとの接触判定を相対座標系Ｋ２において行う。シミュレーション装置１は、ミル容器７の壁面７Ａにおける球形媒体８との接触点相対座標情報Ｄ（ＤＸ１、ＤＹ１、ＤＺ１）を相対座標系Ｋ２において求め、相対座標系Ｋ２から絶対座標系Ｋ１に座標変換して接触点絶対座標情報Ｅ（ＥＸ１、ＥＹ１、ＥＺ１）を求める。シミュレーション装置１は、接触点絶対座標Ｅと媒体中心絶対座標情報Ａ（ＡＸ１、ＡＹ１、ＡＺ１）とから、球形媒体８とミル容器７の壁面７Ａの接触方向Ｈを算出する。シミュレーション装置１は、ミル容器７の回転方向と運動速度ベクトルＶＴを絶対座標系Ｋ１において求める。シミュレーション装置１は、基準となる絶対座標系Ｋ１の座標中心を例えばミル容器７の揺動中心となる揺動支軸１２として規定するが、任意の位置に設定することも可能である。   The simulation apparatus 1 performs contact determination between the spherical medium 8 and the wall surface (mill container wall surface) 7A of the mill container 7 in the relative coordinate system K2. The simulation apparatus 1 obtains contact point relative coordinate information D (DX1, DY1, DZ1) with the spherical medium 8 on the wall surface 7A of the mill container 7 in the relative coordinate system K2, and performs coordinate conversion from the relative coordinate system K2 to the absolute coordinate system K1. Then, the contact point absolute coordinate information E (EX1, EY1, EZ1) is obtained. The simulation apparatus 1 calculates the contact direction H between the spherical medium 8 and the wall surface 7A of the mill container 7 from the contact point absolute coordinate E and the medium center absolute coordinate information A (AX1, AY1, AZ1). The simulation apparatus 1 obtains the rotation direction of the mill container 7 and the motion speed vector VT in the absolute coordinate system K1. The simulation apparatus 1 defines the coordinate center of the reference absolute coordinate system K1 as, for example, the swing support shaft 12 serving as the swing center of the mill container 7, but can be set at an arbitrary position.

シミュレーション装置１においては、周知の離散要素法を用いて微小時間Δｔごとに数値計算を繰り返すことによりミル容器７内における球形媒体８の挙動をシミュレーションする。シミュレーション装置１においては、図３乃至図８に示す手順により、球形媒体８の座標情報について絶対座標系Ｋ１から相対座標系Ｋ２への座標変換の処理を行う。回転揺動ミル装置６は、上述したようにミル容器７が対称軸９を中心として回転動作を行いながら揺動支軸１２を中心として揺動動作を行うことにより、ミル容器７の中心位置が図３に示すように時間経過に伴ってＰｔ０を中心としてＰｔ１〜Ｐｔ２の範囲で変化する。   In the simulation apparatus 1, the behavior of the spherical medium 8 in the mill container 7 is simulated by repeating numerical calculation every minute time Δt using a known discrete element method. In the simulation apparatus 1, coordinate conversion processing from the absolute coordinate system K 1 to the relative coordinate system K 2 is performed on the coordinate information of the spherical medium 8 by the procedure shown in FIGS. 3 to 8. As described above, the rotary rocking mill device 6 swings around the rocking support shaft 12 while the mill container 7 rotates around the symmetry axis 9, so that the center position of the mill container 7 can be adjusted. As shown in FIG. 3, it changes in the range of Pt1 to Pt2 with Pt0 as the center as time elapses.

シミュレーション手順は、図４に示すようにミル容器７の揺動支軸１２を座標中心として固定した絶対座標系Ｋ１（Ｘ１、Ｙ１、Ｚ１）を規定する。ミル容器７に装填されたある球形媒体８は、同図に示すようにこの絶対座標系Ｋ１において、中心位置の座標情報として媒体中心絶対座標情報Ａ（ＡＸ１、ＡＹ１、ＡＺ１）を有する。   The simulation procedure defines an absolute coordinate system K1 (X1, Y1, Z1) in which the swing support shaft 12 of the mill container 7 is fixed as a coordinate center as shown in FIG. A certain spherical medium 8 loaded in the mill container 7 has medium center absolute coordinate information A (AX1, AY1, AZ1) as coordinate information of the center position in the absolute coordinate system K1, as shown in FIG.

シミュレーション手順は、図５に示すように時間経過とともに揺動した位置にあるミル容器７を揺動開始前の初期位置に位置させる回転座標変換の処理を行う。球形媒体８は、この回転座標変換処理により媒体中心絶対座標情報Ａが、同図に示すように媒体中心絶対座標情報Ａ０（ＡＸ１０、ＡＹ１０、ＡＺ１０）として定義される。球形媒体８は、時間経過とともにミル容器７内を移動し、図６に示すように中心位置が移動することにより媒体中心絶対情報Ａ０が媒体中心絶対座標情報Ａ１（（ＡＸ１１、ＡＹ１１、ＡＺ１１）へと変化する。   In the simulation procedure, as shown in FIG. 5, a rotation coordinate conversion process is performed in which the mill container 7 located at a position that has been swung with time has been positioned at an initial position before the start of rocking. In the spherical medium 8, medium center absolute coordinate information A is defined as medium center absolute coordinate information A0 (AX10, AY10, AZ10) as shown in FIG. The spherical medium 8 moves in the mill container 7 as time passes, and the center position moves as shown in FIG. 6 so that the medium center absolute information A0 becomes the medium center absolute coordinate information A1 ((AX11, AY11, AZ11). And change.

シミュレーション手順は、図７に示すように上述した絶対座標系Ｋ１から座標中心を平行移動してミル容器７の中心Ｐ０を原点として対称軸９を座標軸の１つとした座標系である相対座標系Ｋ２（Ｘ２、Ｙ２、Ｚ２）を規定する。球形媒体８は、絶対座標系Ｋ１における媒体中心絶対座標情報Ａに対応して、同図に示すように相対座標系Ｋ２において中心位置の座標情報として媒体中心相対座標情報Ｃ（ＣＸ２、ＣＹ２、ＣＺ２）を有する。   As shown in FIG. 7, the simulation procedure is a relative coordinate system K2 which is a coordinate system in which the coordinate center is translated from the absolute coordinate system K1 described above and the center P0 of the mill container 7 is the origin and the symmetry axis 9 is one of the coordinate axes. (X2, Y2, Z2) is defined. The spherical medium 8 corresponds to the medium center absolute coordinate information A in the absolute coordinate system K1, and the medium center relative coordinate information C (CX2, CY2, CZ2) as the coordinate information of the center position in the relative coordinate system K2 as shown in FIG. ).

シミュレーション手順は、ミル容器７の所定壁面の位置情報である壁面相対座標位置Ｂ（ＢＸ２、ＢＹ２、ＢＺ２）を求める。シミュレーション手順は、図８に示すように壁面相対座標位置Ｂと媒体中心相対座標情報Ｃと球形媒体８の半径Ｒに基づいて、相対座標系Ｋ２において球形媒体８とミル容器７の壁面７Ａとの接触判定を行う。   In the simulation procedure, a wall surface relative coordinate position B (BX2, BY2, BZ2) which is position information of a predetermined wall surface of the mill container 7 is obtained. As shown in FIG. 8, the simulation procedure is based on the relative coordinate position B of the wall surface, the relative center coordinate information C of the medium and the radius R of the spherical medium 8, and the relationship between the spherical medium 8 and the wall surface 7A of the mill container 7 in the relative coordinate system K2. Perform contact determination.

シミュレーション手順は、相対座標系Ｋ２において球形媒体８とミル容器７の壁面７Ａとの接触点位置の座標情報である接触点相対座標情報Ｄ（ＤＸ１、ＤＹ１、ＤＺ１）に基づいて、上述した座標変換処理と逆の座標変換処理を行って絶対座標系Ｋ１における球形媒体８とミル７の容器壁面７Ａとの接触点位置の座標情報である接触点絶対座標情報Ｅ（ＥＸ１、ＥＹ１、ＥＺ１）を求める。シミュレーション手順は、これにより絶対座標系Ｋ１における球形媒体８のミル容器７の壁面７Ａに対する接触角度θを求める。   The simulation procedure is based on the coordinate conversion described above based on the contact point relative coordinate information D (DX1, DY1, DZ1) which is the coordinate information of the contact point position between the spherical medium 8 and the wall surface 7A of the mill container 7 in the relative coordinate system K2. The coordinate conversion process opposite to the process is performed to obtain the contact point absolute coordinate information E (EX1, EY1, EZ1) which is the coordinate information of the contact point position between the spherical medium 8 and the container wall surface 7A of the mill 7 in the absolute coordinate system K1. . The simulation procedure thereby obtains the contact angle θ of the spherical medium 8 with respect to the wall surface 7A of the mill container 7 in the absolute coordinate system K1.

シミュレーション手順は、容器揺動駆動手段１３により揺動支軸１２を中心として揺動動作するミル容器７の壁面７Ａの壁面速度（壁面揺動速度ベクトル）Ｖ１を、絶対座標系Ｋ１において求める。シミュレーション手順は、容器回転駆動手段１０により対称軸９を中心として回転動作するミル容器７の壁面７Ａの壁面速度（壁面回転速度ベクトル）Ｖ２を、絶対座標系Ｋ１において求める。シミュレーション手順は、壁面揺動速度ベクトルＶ１と壁面回転速度ベクトルＶ２のベクトル和として、ミル容器７の壁面７Ａの速度ベクトルＶＴを求める。   In the simulation procedure, a wall surface speed (wall surface swing speed vector) V1 of the wall surface 7A of the mill container 7 that swings around the swing support shaft 12 by the container swing drive means 13 is obtained in the absolute coordinate system K1. In the simulation procedure, a wall surface speed (wall surface rotational speed vector) V2 of the wall surface 7A of the mill container 7 that rotates around the axis of symmetry 9 by the container rotation driving means 10 is obtained in the absolute coordinate system K1. In the simulation procedure, the velocity vector VT of the wall surface 7A of the mill container 7 is obtained as the vector sum of the wall surface swing velocity vector V1 and the wall surface rotation velocity vector V2.

シミュレーション装置１においては、上述した球形媒体８の座標情報について絶対座標系Ｋ１から相対座標系Ｋ２への座標変換の処理を前提条件として、演算・判別手段４において図９に示した手順にしたがって離散要素法を用いて微小時間Δｔごとに数値計算を繰り返してミル容器７内における球形媒体８の挙動をシミュレーションし、その結果を出力手段５により出力する。シミュレーション手順においては、揺動支軸１２を座標中心として固定した座標系である絶対座標系Ｋ１（Ｘ１、Ｙ１、Ｚ１）を規定する（Ｓ−１）とともに、ミル容器７の対称軸９を座標軸の１つとした座標系である相対座標系Ｋ２（Ｘ２、Ｙ２、Ｚ２）を規定する（Ｓ−２）。   In the simulation apparatus 1, the coordinate information of the spherical medium 8 described above is premised on the coordinate conversion process from the absolute coordinate system K 1 to the relative coordinate system K 2, and the calculation / discrimination unit 4 performs discrete processing according to the procedure shown in FIG. Numerical calculation is repeated every minute time Δt using the element method to simulate the behavior of the spherical medium 8 in the mill container 7, and the result is output by the output means 5. In the simulation procedure, an absolute coordinate system K1 (X1, Y1, Z1), which is a coordinate system with the swing support shaft 12 fixed as the coordinate center, is defined (S-1), and the symmetry axis 9 of the mill vessel 7 is the coordinate axis. A relative coordinate system K2 (X2, Y2, Z2), which is one of the coordinate systems, is defined (S-2).

シミュレーション手順においては、入力手段２により、数値解析を行う微小単位時間Δｔと、絶対座標系Ｋ１における球形媒体８の中心位置の座標情報である媒体中心絶対座標情報Ａと、球形媒体８の半径Ｒと、球形媒体８をそれぞれ識別する媒体識別指標Ｆと、球形媒体８の運動速度ベクトルＶを入力する（Ｓ−３）。これらの入力情報は、入力手段２から記憶手段３へと送られて初期情報として記憶される。なお、初期情報として入力される球形媒体８の運動速度ベクトルＶは、通常「０」若しくは極く小さな値である。   In the simulation procedure, the input unit 2 performs minute unit time Δt for numerical analysis, medium center absolute coordinate information A that is coordinate information of the center position of the spherical medium 8 in the absolute coordinate system K1, and the radius R of the spherical medium 8. Then, the medium identification index F for identifying the spherical medium 8 and the motion velocity vector V of the spherical medium 8 are input (S-3). These pieces of input information are sent from the input means 2 to the storage means 3 and stored as initial information. The motion velocity vector V of the spherical medium 8 input as initial information is usually “0” or a very small value.

シミュレーション手順においては、相対座標系Ｋ２における壁面相対座標位置Ｂを求める（Ｓ−４）。シミュレーション手順においては、各球形媒体８について、記憶手段３に記憶した媒体中心絶対座標情報Ａに基づいて、相対座標系Ｋ２における中心位置の座標情報である媒体中心相対座標情報Ｃを算出する（Ｓ−５）。   In the simulation procedure, the wall surface relative coordinate position B in the relative coordinate system K2 is obtained (S-4). In the simulation procedure, medium center relative coordinate information C, which is coordinate information of the center position in the relative coordinate system K2, is calculated for each spherical medium 8 based on the medium center absolute coordinate information A stored in the storage means 3 (S). -5).

シミュレーション手順においては、媒体中心相対座標情報Ｃの算出結果に基づき、上述した壁面相対座標位置Ｂと記憶手段３に記憶した球形媒体８の半径Ｒとを用いて球形媒体８のミル容器７の壁面７Ａの接触を判別する（Ｓ−６）。接触判別は、媒体中心相対座標情報Ｃと壁面相対座標位置Ｂとの距離が球形媒体８の半径Ｒ以下となる場合において、球形媒体８がミル容器７の壁面７Ａの所定位置に接触したと判定する。   In the simulation procedure, based on the calculation result of the medium center relative coordinate information C, the wall surface of the mill container 7 of the spherical medium 8 using the wall surface relative coordinate position B and the radius R of the spherical medium 8 stored in the storage unit 3. 7A contact is discriminated (S-6). In the contact determination, when the distance between the medium center relative coordinate information C and the wall surface relative coordinate position B is equal to or less than the radius R of the spherical medium 8, it is determined that the spherical medium 8 has contacted a predetermined position on the wall surface 7A of the mill container 7. To do.

シミュレーション手順においては、上述した球形媒体８のミル容器７の壁面７Ａへの接触判定に基づいて、相対座標系Ｋ２における球形媒体８とミル容器７の壁面７Ａとの接触点位置の座標情報である接触点相対座標情報Ｄが求められる（Ｓ−７）。シミュレーション手順においては、相対座標系Ｋ２から絶対座標系Ｋ１への座標変換処理を行い、接触点相対座標情報Ｄに基づいて絶対座標系Ｋ１におけるミル容器７の壁面７Ａと球形媒体８との接触点位置の座標情報である接触点絶対座標情報Ｅを求める（Ｓ−８）。   In the simulation procedure, the coordinate information of the contact point position between the spherical medium 8 and the wall surface 7A of the mill container 7 in the relative coordinate system K2 is based on the determination of the contact of the spherical medium 8 to the wall surface 7A of the mill container 7 described above. Contact point relative coordinate information D is obtained (S-7). In the simulation procedure, a coordinate conversion process from the relative coordinate system K2 to the absolute coordinate system K1 is performed, and the contact point between the wall surface 7A of the mill container 7 and the spherical medium 8 in the absolute coordinate system K1 based on the contact point relative coordinate information D. Contact point absolute coordinate information E, which is coordinate information of the position, is obtained (S-8).

シミュレーション手順においては、接触点絶対座標情報Ｅの算出結果に基づき、媒体中心絶対座標情報Ａと媒体識別指標Ｆとを用いて接触点位置における球形媒体８の接触方向Ｈを算出する（Ｓ−９）。また、シミュレーション手順においては、接触点絶対座標情報Ｅの算出結果に基づき、ミル容器７の壁面７Ａと球形媒体８との接触点位置におけるミル容器７の揺動動作によるミル容器７の壁面７Ａの壁面揺動速度ベクトルＶ１を算出（Ｓ−１０）するとともに回転動作によるミル容器７の壁面７Ａの壁面回転速度ベクトルＶ２を算出する（Ｓ−１１）。シミュレーション手順においては、これら壁面揺動速度ベクトルＶ１と壁面回転速度ベクトルＶ２との和として、絶対座標系Ｋ１における球形媒体８の接触点位置におけるミル容器７の壁面７Ａの運動速度ベクトルＶＴを算出する（Ｓ−１２）。   In the simulation procedure, based on the calculation result of the contact point absolute coordinate information E, the contact direction H of the spherical medium 8 at the contact point position is calculated using the medium center absolute coordinate information A and the medium identification index F (S-9). ). Further, in the simulation procedure, based on the calculation result of the contact point absolute coordinate information E, the wall surface 7A of the mill container 7 by the swinging motion of the mill container 7 at the contact point position between the wall surface 7A of the mill container 7 and the spherical medium 8 is obtained. A wall surface swing speed vector V1 is calculated (S-10), and a wall surface rotational speed vector V2 of the wall surface 7A of the mill container 7 is calculated (S-11). In the simulation procedure, a motion speed vector VT of the wall surface 7A of the mill container 7 at the contact point position of the spherical medium 8 in the absolute coordinate system K1 is calculated as the sum of the wall surface swing speed vector V1 and the wall surface rotation speed vector V2. (S-12).

シミュレーション手順においては、球形媒体８の数が多く、相互の衝突を無視することができない場合に、媒体中心絶対座標情報Ａと媒体識別指標Ｆとから球形媒体８間の中心間距離Ｌを求め、この中心間距離Ｌと記憶手段３に記憶した球形媒体８の半径Ｒとを用いて球形媒体８間の接触を判別する（Ｓ−１３）。シミュレーション手順においては、この球形媒体８間の接触判定に基づいて、媒体中心絶対座標情報Ａと媒体識別指標Ｆとから球形媒体８間の接触方向Ｍを算出する（Ｓ−１４）。シミュレーション手順においては、ミル容器７の壁面７Ａの運動速度ベクトルＶＴ、ミル容器７の壁面７Ａにおける球形媒体８の接触方向Ｈ、球形媒体８の運動速度ベクトルＶ及び球形媒体８間の接触方向Ｍとに基づいて、球形媒体８がミル容器７の壁面７Ａから受ける力ＪＯと他の球形媒体８から受ける力ＪＡを算出する（Ｓ−１５）。   In the simulation procedure, when the number of spherical media 8 is large and mutual collision cannot be ignored, the center-to-center distance L between the spherical media 8 is obtained from the media center absolute coordinate information A and the medium identification index F. Contact between the spherical media 8 is determined using the center distance L and the radius R of the spherical media 8 stored in the storage means 3 (S-13). In the simulation procedure, based on the contact determination between the spherical media 8, the contact direction M between the spherical media 8 is calculated from the medium center absolute coordinate information A and the medium identification index F (S-14). In the simulation procedure, the motion speed vector VT of the wall surface 7A of the mill container 7, the contact direction H of the spherical medium 8 on the wall surface 7A of the mill container 7, the motion speed vector V of the spherical medium 8 and the contact direction M between the spherical media 8 Based on the above, the force JO received by the spherical medium 8 from the wall surface 7A of the mill container 7 and the force JA received from the other spherical medium 8 are calculated (S-15).

シミュレーション手順においては、各球形媒体８についてそれぞれ算出したミル容器７の壁面７Ａから受ける力ＪＯと他の球形媒体８から受ける力ＪＡ及び重力Ｇと微小単位時間Δｔとに基づいて運動方程式を数値解析することにより各球形媒体８の運動速度ベクトルＶ及び微小時間変位Ｕを求める（Ｓ−１６）。シミュレーション手順においては、各球形媒体８の運動速度ベクトルＶ及び微小時間変位Ｕを入力手段２を介して順次記憶手段３に格納する（Ｓ−１７）。シミュレーション手順においては、全球形媒体８に関する微小時間変位Ｕに基づいて、ミル容器７内における球形媒体８の挙動のシミュレーション結果を出力手段５により出力する（Ｓ−１８）。   In the simulation procedure, the equation of motion is numerically analyzed based on the force JO received from the wall surface 7A of the mill container 7 calculated for each spherical medium 8, the force JA received from the other spherical medium 8, the gravity G, and the minute unit time Δt. Thus, the motion velocity vector V and the minute time displacement U of each spherical medium 8 are obtained (S-16). In the simulation procedure, the motion velocity vector V and minute time displacement U of each spherical medium 8 are sequentially stored in the storage means 3 via the input means 2 (S-17). In the simulation procedure, a simulation result of the behavior of the spherical medium 8 in the mill container 7 is output by the output means 5 based on the minute time displacement U with respect to the entire spherical medium 8 (S-18).

上述したシミュレーション装置１によるミル容器７内における球形媒体８の挙動シミュレーションは、図１０乃至図１３に示すミル容器７の内部を可視可能とした回転揺動ミル装置６による実験結果との比較により極めて精度が高いことが確認される。この比較は、内部容量が６０リットルのミル容器７内に、半径１５ｍｍ、摩擦係数０．８のポリアミド系合成高分子化合物（ナイロン：商標）からなる球形媒体８を充填率５０％で充填し、それぞれミル容器７を所定の駆動条件で駆動した場合の同一時間における球形媒体８の挙動の経時変化を比較したものである。なお、同比較実験においては、球形媒体８の挙動をより明確に得るために、ミル容器７内に被加工物を充填せずに行った。   The behavioral simulation of the spherical medium 8 in the mill container 7 by the simulation apparatus 1 described above is extremely compared with the experimental result by the rotary rocking mill apparatus 6 that makes the inside of the mill container 7 visible as shown in FIGS. It is confirmed that the accuracy is high. In this comparison, a spherical medium 8 made of a polyamide synthetic polymer compound (nylon: trademark) having a radius of 15 mm and a friction coefficient of 0.8 is filled in a mill container 7 having an internal capacity of 60 liters at a filling rate of 50%. Each of them compares the time-dependent change in the behavior of the spherical medium 8 when the mill container 7 is driven under a predetermined driving condition. In the comparative experiment, in order to obtain the behavior of the spherical medium 8 more clearly, the mill container 7 was not filled with a workpiece.

図１０乃至図１３は、ミル容器７の駆動開始から１．２５sec、２．５０sec、３．７５sec、５．００sec、６．２５sec後のミル容器７内における球形媒体８の挙動をそれぞれ示したものである。図１０は、ミル容器７を、回転数０．４Ｎｃ、１分間に１２回の揺動回数で駆動した場合の球形媒体８の挙動である。図１１は、ミル容器７を、回転数０．６Ｎｃ、１分間に１２回の揺動回数で駆動した場合の挙動を示したものである。図１２は、ミル容器７を、回転数０．８Ｎｃ、１分間に１２回の揺動回数で駆動した場合の球形媒体８の挙動を示したものである。である。図１３は、ミル容器７を、回転数１．０Ｎｃ、１分間に１２回の揺動回数で駆動した場合の挙動を示したものである。   10 to 13 show the behavior of the spherical medium 8 in the mill container 7 after 1.25 sec, 2.50 sec, 3.75 sec, 5.00 sec, and 6.25 sec from the start of driving of the mill container 7, respectively. It is. FIG. 10 shows the behavior of the spherical medium 8 when the mill container 7 is driven at a rotational speed of 0.4 Nc and a swing frequency of 12 times per minute. FIG. 11 shows the behavior when the mill container 7 is driven at a rotation speed of 0.6 Nc and 12 swings per minute. FIG. 12 shows the behavior of the spherical medium 8 when the mill container 7 is driven at a rotational speed of 0.8 Nc and a swing frequency of 12 times per minute. It is. FIG. 13 shows the behavior when the mill container 7 is driven at a rotation speed of 1.0 Nc and 12 swings per minute.

シミュレーション装置１においては、これらの図から明らかなように、ミル容器７をいずれの条件で揺動動作と回転動作を行った場合でも、球形媒体８の挙動を回転揺動ミル装置６における実際の状態と極めて近似した正確なシミュレーションを行う。   In the simulation apparatus 1, as is clear from these drawings, the behavior of the spherical medium 8 is actually measured in the rotary rocking mill apparatus 6 when the mill container 7 is swung and rotated under any conditions. Perform an accurate simulation that closely approximates the condition.

回転揺動ミル装置の軸対称形状のミル容器内における球形媒体の挙動をシミュレーションする媒体挙動シミュレーション装置の構成図である。It is a block diagram of the medium behavior simulation apparatus which simulates the behavior of the spherical medium in the axially symmetric mill container of the rotary rocking mill apparatus. 回転揺動ミル装置の構成図である。It is a block diagram of a rotation rocking mill device. シミュレーション手順の説明図であり、ミル容器の動作図である。It is explanatory drawing of a simulation procedure, and is an operation | movement figure of a mill container. 同絶対座標系Ｋ１の説明図である。It is explanatory drawing of the absolute coordinate system K1. 同時間経過とともに揺動した位置にあるミル容器を揺動開始前の初期位置に位置させる回転座標変換の説明図である。It is explanatory drawing of the rotation coordinate transformation which positions the mill container in the position rocked with progress of the same time in the initial position before rocking | fluctuation start. 同時間経過とともにミル容器内を移動する球形媒体の媒体中心絶対座標情報の変化を説明する説明図である。It is explanatory drawing explaining the change of medium center absolute coordinate information of the spherical medium which moves the inside of a mill container with progress of the same time. 同絶対座標系Ｋ１から座標中心を平行移動してミル容器の回転中心Ｐ０を原点とし、ミル容器の回転支軸である対称軸を座標軸の１つとした座標系である相対座標系Ｋ２を規定する説明図である。A relative coordinate system K2 is defined which is a coordinate system in which the coordinate center is translated from the absolute coordinate system K1 and the rotation center P0 of the mill container is the origin, and the symmetry axis which is the rotation support axis of the mill container is one of the coordinate axes. It is explanatory drawing. 相対座標系Ｋ２においてミル容器の壁面と球形媒体の接触判定結果に基づいて、ミル容器の所定壁面における球形媒体の接触角度を求める説明図である。It is explanatory drawing which calculates | requires the contact angle of the spherical medium in the predetermined wall surface of a mill container based on the contact determination result of the wall surface of a mill container and a spherical medium in the relative coordinate system K2. シミュレーション手順の工程図である。It is process drawing of a simulation procedure. ミル容器の駆動条件（回転数０．４Ｎｃ、揺動回数１２回／ｍｉｎ）での実験装置によるミル容器内における球形媒体の状態とシミュレーション装置により求めた球形媒体の挙動のシミュレーション図である。It is a simulation diagram of the state of the spherical medium in the mill container and the behavior of the spherical medium determined by the simulation apparatus by the experimental device under the driving conditions of the mill container (rotation speed 0.4 Nc, number of swings 12 times / min). ミル容器の駆動条件（回転数０．６Ｎｃ、揺動回数１２回／ｍｉｎ）での実験装置によるミル容器内における球形媒体の状態とシミュレーション装置により求めた球形媒体の挙動のシミュレーション図である。FIG. 6 is a simulation diagram of the state of the spherical medium in the mill container and the behavior of the spherical medium obtained by the simulation apparatus by the experimental device under the driving conditions of the mill container (rotation speed 0.6 Nc, number of swings 12 times / min). ミル容器の駆動条件（回転数０．８Ｎｃ、揺動回数１２回／ｍｉｎ）での実験装置によるミル容器内における球形媒体の状態とシミュレーション装置により求めた球形媒体の挙動のシミュレーション図である。It is a simulation diagram of the state of the spherical medium in the mill container by the experimental device and the behavior of the spherical medium obtained by the simulation device under the driving conditions of the mill container (rotation number 0.8 Nc, number of swings 12 times / min). ミル容器の駆動条件（回転数１．０Ｎｃ、揺動回数１２回／ｍｉｎ）での実験装置によるミル容器内における球形媒体の状態とシミュレーション装置により求めた球形媒体の挙動のシミュレーション図である。FIG. 6 is a simulation diagram of the state of the spherical medium in the mill container and the behavior of the spherical medium obtained by the simulation apparatus by the experimental apparatus under the driving conditions of the mill container (rotation speed: 1.0 Nc, number of swings: 12 times / min).

符号の説明Explanation of symbols

１ シミュレーション装置、２ 入力手段、３ 記憶手段、４ 演算・判別手段、５ 出力手段、６ 回転揺動ミル装置、７ ミル容器、８ 球形媒体、９ 対称軸、１０ 容器回転駆動手段、１１ 支持機構、１２ 揺動支軸、１３ 容器揺動駆動機構、１４ 被加工物   DESCRIPTION OF SYMBOLS 1 Simulation apparatus, 2 input means, 3 memory | storage means, 4 calculation and discrimination means, 5 output means, 6 rotation rocking mill apparatus, 7 mil container, 8 spherical medium, 9 symmetry axis, 10 container rotation drive means, 11 support mechanism , 12 oscillating spindle, 13 container oscillating drive mechanism, 14 work piece

Claims (3)

内部に多数の球形媒体を装填した軸対称形状のミル容器と、該ミル容器内を通る回転軸を中心として該ミル容器を回転させる容器回転駆動手段と、上記ミル容器を上記回転軸と直交する揺動軸を中心として揺動させる容器揺動駆動手段とを備えた回転揺動ミル装置における上記ミル容器内における上記球形媒体の挙動をシミュレーションする球形媒体挙動シミュレーション装置であり、
上記回転揺動ミル装置に対して、座標中心を固定した座標系である絶対座標系（Ｋ１：ＫＸ１、ＫＹ１、ＫＺ１）を規定するとともに上記ミル容器の対称軸を座標軸の１つとした座標系である相対座標系（Ｋ２：ＫＸ２、ＫＹ２、ＫＺ２）を規定し、
数値解析を行う微小単位時間（Δｔ）、上記絶対座標系（Ｋ１）における上記球形媒体の中心位置の座標情報である媒体中心絶対座標情報（Ａ：ＡＸ１、ＡＹ１、ＡＺ１）、上記絶対座標系（Ｋ１）における上記球形媒体の運動ベクトル情報（Ｖ）、上記球形媒体の半径（Ｒ）及び上記球形媒体をそれぞれ識別する媒体識別指標（Ｆ）を初期情報として入力する入力手段と、
上記入力手段により入力された上記初期情報を記憶する記憶手段と、
上記相対座標系（Ｋ２）における、上記ミル容器の壁面の座標情報である壁面相対座標情報（Ｂ：ＢＸ１、ＢＹ１、ＢＺ１）を求めるとともに、上記記憶手段に記憶された上記媒体中心絶対座標情報（Ａ）に基づいて多数の上記球形媒体のそれぞれについて上記相対座標系（Ｋ２）における中心位置の座標情報である媒体中心相対座標情報（Ｃ：ＣＸ１、ＣＹ１、ＣＺ１）を求め、該媒体中心相対座標情報（Ｃ）、上記球形媒体の半径（Ｒ）及び上記壁面相対座標位置（Ｂ）に基づいて上記球形媒体の上記ミル容器の壁面への接触を判別する演算・判別手段とを備え、
上記演算・判別手段による上記球形媒体の上記ミル容器の壁面への接触判定に基づき、上記相対座標系（Ｋ２）における上記球形媒体と上記ミル容器壁面との接触点位置の座標情報である接触点相対座標情報（Ｄ：ＤＸ１、ＤＹ１、ＤＺ１）から上記絶対座標系（Ｋ１）における上記球形媒体と上記ミル容器壁面との接触点位置の座標情報である接触点絶対座標情報（Ｅ：ＥＸ１、ＥＹ１、ＥＺ１）を求め、該接触点絶対座標情報（Ｅ）と上記球形媒体の媒体中心絶対座標情報（Ａ）と上記媒体識別指標（Ｆ）とに基づいて上記絶対座標系（Ｋ１）における上記接触点位置での上記球形媒体の接触方向（Ｈ）を算出し、
上記球形媒体の上記接触点における上記ミル容器の壁面の揺動動作による上記絶対座標系（Ｋ１）における壁面揺動速度ベクトル（Ｖ１）と回転動作による上記絶対座標系（Ｋ１）における壁面回転速度ベクトル（Ｖ２）を算出するとともに、これら壁面揺動速度ベクトル（Ｖ１）と壁面回転速度ベクトル（Ｖ２）のベクトル和として上記絶対座標系（Ｋ１）における上記接触点位置での上記ミル容器の壁面の運動速度ベクトル（ＶＴ）を算出し、
上記球形媒体の上記運動速度ベクトル（Ｖ）と上記ミル容器の壁面との接触方向（Ｈ）と上記ミル容器の壁面の運動速度ベクトル（ＶＴ）に基づいて上記球形媒体が壁面から受ける力（ＪＯ）を算出し、該壁面から受ける力（ＪＯ）と重力（Ｇ）と上記微小単位時間（Δｔ）とに基づいて運動方程式を数値解析することにより上記球形媒体の運動速度ベクトル（Ｖ）及び微小時間変位（Ｕ）を求め、該微小時間変位（Ｕ）から上記微小単位時間（Δｔ）後の上記球形媒体の媒体中心絶対座標情報（Ａ）を求めるとともに、該媒体中心絶対座標情報（Ａ）及び上記運動速度ベクトル（Ｖ）を上記記憶手段に格納し、適宜の出力手段により出力することを特徴とする回転揺動ミル装置の媒体挙動シミュレーション装置。 An axially symmetric mill container in which a large number of spherical media are loaded, container rotation driving means for rotating the mill container around a rotation axis passing through the mill container, and the mill container orthogonal to the rotation axis A spherical medium behavior simulation apparatus for simulating the behavior of the spherical medium in the mill container in a rotary rocking mill apparatus having a container rocking drive device that rocks around a rocking shaft;
An absolute coordinate system (K1: KX1, KY1, KZ1), which is a coordinate system with a fixed coordinate center, is defined with respect to the rotary oscillating mill device, and a coordinate system in which the axis of symmetry of the mill vessel is one of coordinate axes. A certain relative coordinate system (K2: KX2, KY2, KZ2) is defined,
Minute unit time (Δt) for numerical analysis, medium center absolute coordinate information (A: AX1, AY1, AZ1) which is coordinate information of the center position of the spherical medium in the absolute coordinate system (K1), the absolute coordinate system ( Input means for inputting, as initial information, motion vector information (V) of the spherical medium in K1), a radius (R) of the spherical medium, and a medium identification index (F) for identifying the spherical medium;
Storage means for storing the initial information input by the input means;
In the relative coordinate system (K2), wall surface relative coordinate information (B: BX1, BY1, BZ1) which is coordinate information of the wall surface of the mill container is obtained, and the medium center absolute coordinate information ( Based on A), medium center relative coordinate information (C: CX1, CY1, CZ1), which is coordinate information of the center position in the relative coordinate system (K2), is obtained for each of a large number of spherical media, and the medium center relative coordinates are obtained. Computation / discrimination means for discriminating contact of the spherical medium to the wall surface of the mill container based on the information (C), the radius (R) of the spherical medium and the relative wall surface coordinate position (B),
Based on the contact determination of the spherical medium to the wall surface of the mill container by the calculation / discrimination means, the contact point is coordinate information of the contact point position between the spherical medium and the mill container wall surface in the relative coordinate system (K2). Contact point absolute coordinate information (E: EX1, EY1) which is coordinate information of the contact point position between the spherical medium and the mill vessel wall surface in the absolute coordinate system (K1) from the relative coordinate information (D: DX1, DY1, DZ1). , EZ1), and the contact in the absolute coordinate system (K1) based on the contact point absolute coordinate information (E), the medium center absolute coordinate information (A) of the spherical medium, and the medium identification index (F). Calculate the contact direction (H) of the spherical medium at the point position,
The wall surface swing speed vector (V1) in the absolute coordinate system (K1) by the swinging motion of the wall surface of the mill container at the contact point of the spherical medium and the wall surface rotational speed vector in the absolute coordinate system (K1) by the rotating motion. (V2) is calculated, and the motion of the wall surface of the mill container at the position of the contact point in the absolute coordinate system (K1) is calculated as the vector sum of the wall surface swing speed vector (V1) and the wall surface rotational speed vector (V2). Calculate the velocity vector (VT)
Based on the contact velocity (H) between the motion velocity vector (V) of the spherical medium and the wall surface of the mill container and the motion velocity vector (VT) of the wall surface of the mill container (JO) ) And numerically analyzing the equation of motion based on the force (JO), gravity (G), and the minute unit time (Δt) received from the wall surface, the velocity vector (V) of the spherical medium and the minute The time displacement (U) is obtained, the medium center absolute coordinate information (A) of the spherical medium after the minute unit time (Δt) is obtained from the minute time displacement (U), and the medium center absolute coordinate information (A). And the motion speed vector (V) is stored in the storage means and output by an appropriate output means. 上記媒体中心絶対座標情報（Ａ）と上記媒体識別指標（Ｆ）とから各球形媒体間の中心間距離（Ｌ）を求めるとともに、該中心間距離（Ｌ）と上記球形媒体の半径（Ｒ）とから上記各球形媒体間の接触を判定する媒体接触判定手段を備え、
上記媒体接触判定手段による上記各球形媒体間の接触判定に基づいて、上記媒体中心絶対座標情報（Ａ）から上記各球形媒体間の接触方向（Ｍ）を算出し、
上記各球形媒体間の接触方向（Ｍ）と上記球形媒体の上記ミル容器の壁面との接触方向（Ｈ）及び上記球形媒体の上記壁面揺動速度ベクトル（Ｖ１）と上記運動速度ベクトル（Ｖ）とに基づいて上記球形媒体が上記壁面から受ける力（ＪＯ）及び他の上記球形媒体から受ける力（ＪＡ）を算出し、
上記球形媒体が上記壁面から受ける力（ＪＯ）と上記他の上記球形媒体から受ける力（ＪＡ）と上記球形媒体に作用する重力（Ｇ）及び上記微小単位時間（Δｔ）とに基づいて運動方程式を数値解析することを特徴とする請求項１に記載の回転揺動ミル装置の媒体挙動シミュレーション装置。 The center-to-center distance (L) between the spherical media is obtained from the medium center absolute coordinate information (A) and the medium identification index (F), and the center-to-center distance (L) and the radius (R) of the spherical medium are obtained. Medium contact determining means for determining contact between the spherical media from
Based on the contact determination between the spherical media by the medium contact determination means, the contact direction (M) between the spherical media is calculated from the medium center absolute coordinate information (A),
The contact direction (M) between the spherical media, the contact direction (H) of the spherical media with the wall surface of the mill container, the wall surface swing velocity vector (V1) and the motion velocity vector (V) of the spherical media. Based on the above, the force (JO) received by the spherical medium from the wall surface and the force (JA) received from the other spherical medium are calculated,
Equation of motion based on the force (JO) that the spherical medium receives from the wall surface, the force (JA) that the spherical medium receives from the other spherical medium, the gravity (G) that acts on the spherical medium, and the minute unit time (Δt) The medium behavior simulation apparatus for a rotary rocking mill apparatus according to claim 1, wherein the medium is numerically analyzed. 上記絶対座標系（Ｋ１）が、上記容器揺動駆動手段により揺動動作される上記ミル容器の揺動中心を座標中心として固定した座標系により構成されることを特徴とする請求項１又は請求項２に記載の回転揺動ミル装置の媒体挙動シミュレーション装置。   The absolute coordinate system (K1) is constituted by a coordinate system in which a rocking center of the mill container that is swung by the container rocking drive means is fixed as a coordinate center. Item 3. The medium behavior simulation device of the rotary rocking mill device according to Item 2.
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Publication number Priority date Publication date Assignee Title
KR101064604B1 (en) 2009-10-27 2011-09-15 주식회사 위노바 Two dimensional ball mill apparatus and method of manufacturing nano composite
WO2015033739A1 (en) * 2013-09-04 2015-03-12 国立大学法人東北大学 Evaluation method, evaluation device, and program

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JPH04161239A (en) * 1990-10-26 1992-06-04 Aichi Electric Co Ltd Stirring device
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JPH11147048A (en) * 1997-11-18 1999-06-02 Sekisui Chem Co Ltd Apparatus for simulating motion of motion in crusher and apparatus for simulating quantity of energy for actuating crusher

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JPH0784992A (en) * 1993-09-17 1995-03-31 Taiho Yakuhin Kogyo Kk Simulation for particle behavior in rotary mixing container
JPH11147048A (en) * 1997-11-18 1999-06-02 Sekisui Chem Co Ltd Apparatus for simulating motion of motion in crusher and apparatus for simulating quantity of energy for actuating crusher

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR101064604B1 (en) 2009-10-27 2011-09-15 주식회사 위노바 Two dimensional ball mill apparatus and method of manufacturing nano composite
WO2015033739A1 (en) * 2013-09-04 2015-03-12 国立大学法人東北大学 Evaluation method, evaluation device, and program

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