JP4072329B2

JP4072329B2 - Magnetic particle behavior analysis apparatus and behavior analysis method

Info

Publication number: JP4072329B2
Application number: JP2001331915A
Authority: JP
Inventors: 新吾永井
Original assignee: Canon Inc
Current assignee: Canon Inc
Priority date: 2001-10-30
Filing date: 2001-10-30
Publication date: 2008-04-09
Anticipated expiration: 2021-10-30
Also published as: JP2003139829A

Description

【０００１】
【発明の属する技術分野】
本発明は、磁界が印加された領域内を移動する粒子の挙動解析において、特に解析領城中を磁性部材が移動する場合に対して、磁化された磁性部材が磁界に及ぼす影響を考慮して磁性粒子の挙動を求める装置及び方法に関するものである。
【０００２】
【従来の技術】
近年、磁界を印加した状態における磁性粒子の挙動解析が行われ、磁性粒子の圧粉成形の性能予測や電子写真の現象解明等に活用されている。
【０００３】
磁界中の磁性粒子の挙動計算には解析対象に適した様々な方法が用いられており、磁気力の他に重力など各粒子に働く力を求め、それらをもとに各粒子の挙動を逐次求める方法が一般的に行われている。
【０００４】
また、粒子に働く磁気力を求める方法としては、有限要素法などの数値計算を用いて求めた外部印加磁界分布をもとに、各磁性粒子の磁化や磁気力を求める方法などがある。その際、外部印加磁界は定常場として扱い、粒子挙動解析の実施中は変化しないとする場合が多い。また、解析領域内に磁性部材がある場合については、あらかじめ磁性部材を考慮した外部印加磁界分布を求めておくことにより、磁性部材による磁界の変化を考慮した計算を行うことができる。
【０００５】
各磁性粒子の磁化については、磁化が粒子ごとに固定されている場合や外部印加磁界によって磁化される場合などがある。後者については、“永井他，ＪａｐａｎＨａｒｄｃｏｐｙ’９９論文集，１８５（１９９９）”に説明されているように、外部印加磁界に比例していると仮定して、粒子の中心位置での外部印加磁界の値を求める方法が広く用いられている。
【０００６】
以下、磁性粒子の挙動解析の代表的な処理プログラムの構成について、図８、図９を用いて説明する。
【０００７】
図中、符号８０は制御部であり、プログラムの処理全体を制御する。
【０００８】
符号８１は初期条件の設定部であり、磁性粒子の初期配置や磁気特性などの物性値、解析領域を構成する構造物の形状、大きさ、位置、外部印加磁界分布、時間ステップなどの計算条件について設定を行う。
【０００９】
符号１０は磁性粒子に働く磁気力の計算部であり、各磁性粒子の磁気特性（磁化や磁気モーメントなど）及び外部印加磁界分布をもとに、各磁性粒子に働く磁気力の計算を行う。この処理は、図９で示した符号１２及び符号１４の２つの処理で構成されている。符号１２は磁性粒子の磁化の設定部であり、各磁性粒子の磁化及び磁気モーメントを設定する。符号１４は印加磁界や磁性粒子による磁気力の計算部であり、磁性粒子の磁化の値に応じて、外部印加磁界による磁気力や磁性粒子同士の磁気相互作用力の計算を行う。
【００１０】
符号８２は磁性粒子に働く磁気力以外の力の計算部であり、各磁性粒子に働く重力などの計算を行う。符号８３は粒子の速度と変位の計算部であり、各磁性粒子に働く全ての力をもとに運動方程式を解くことにより、各粒子の速度と変位を更新する。
【００１１】
なお、実際の計算では、符号８１を処理した後に、符号１０、８２〜８３の処理を繰り返すことにより、磁性粒子の挙動を求めることができる。
【００１２】
【発明が解決しようとする課題】
しかしながら、粒子を撹拌する部材が磁性体の場合など、磁性部材が解析領域内を移動している場合には、各時間における磁性部材の位置に基づいた磁界分布を考慮して磁性粒子の挙動を計算する必要があった。特に、磁性粒子の磁化が印加する磁界によって決まる場合においては、磁性粒子の磁化を精度良く求めることが重要であり、そのためには磁性部材による影響を考慮した磁性粒子に印加する磁界分布を正確に扱うことが必要となる。
【００１３】
これを上記従来例で実現するためには、あらかじめ磁性部材の移動位置に応じた複数の磁界分布を用意しておく必要があるが、磁界解析に手間がかかるだけでなく、データが膨大となるといった課題がある。また、磁性部材の挙動が磁性粒子との相互作用に影響を受ける場合には、前もって磁性部材の軌跡を予測できないため、あらかじめ磁界分布を用意することは不可能となる。
【００１４】
また、粒子挙動解析の実行中に磁性部材の位置を考慮した磁界計算を逐次行う方法が考えられるが、計算時間の点から実用的な方法ではない。
【００１５】
本発明はこのような問題を鑑みてなされたものであり、磁性粒子に働く磁界を、外部印加磁界と、外部印加磁界により磁化された磁性部材がつくる磁界の重ね合わせで表されるとし、各時間での磁性部材の位置に基づいて、外部印加磁界により磁化された磁性部材がつくる磁界分布と磁性粒子に働く磁気力を求めることにより、移動を伴う磁性部材による磁界の変化を考慮した磁性体粒子の挙動を、簡単かつ精度良く解析することを目的としている。
【００１６】
【課題を解決するための手段】
かかる課題を解決するため、本発明の磁性粒子の挙動解析装置は、以下の構成を備える。すなわち、外部磁界印加手段と磁性部材が存在する領域内を移動する粒子の挙動解析装置において、磁性部材の中心位置データをもとに外部印加磁界により磁化された磁性部材の磁化状態の計算を行う磁性部材の磁化状態の計算部、各粒子の磁化の設定を行う磁性粒子の磁化の設定部、磁化された磁性部材がつくる磁界による各粒子に働く磁気力の計算を行う磁性部材の磁界による磁性粒子の磁気力の計算部、各粒子に働く印加磁界や他の磁性粒子による磁気力の計算を行う印加磁界や磁性粒子による磁気力の計算部、によって構成された磁性粒子に働く磁気力の計算部を有する磁性粒子の挙動解析装置であって、磁性粒子に働く磁界を、外部印加磁界と、外部印加磁界により磁化された磁性部材がつくる磁界の重ね合わせで表し、さらに磁性粒子に働く磁気力を、外部印加磁界や磁性粒子同士による磁気力と、磁性部材による磁気力の重ね合わせで表し、磁性部材の位置データをもとに外部印加磁界による磁性部材の磁化状態を求め、各粒子の位置における磁化された磁性部材がつくる磁界分布に基づいて、磁性部材による磁気力を求めることを特徴とした磁性粒子の挙動解析装置である。
【００１７】
また、本発明の他の様態は、磁性粒子の磁化の設定部、磁性部材の磁界による磁性粒子の磁気力の計算部、及び印加磁界や磁性粒子による磁気力の計算部において、各磁性粒子の中心位置における外部印加磁界と、磁性部材がつくる磁界の和に基づいて各磁性粒子の磁化状態を求め、該磁化状態をもとに磁性粒子に働く磁気力を計算することを特徴とした磁性粒子の挙動解析装置である。
また、本発明の他の様態は、外部磁界印加と磁性部材が存在する領域内を移動する粒子の挙動解析方法において、磁性部材の中心位置データをもとに外部印加磁界により磁化された磁性部材の磁化状態の計算を行い、各粒子の磁化の設定を行い、磁化された磁性部材がつくる磁界による各粒子に働く磁気力の計算を行い、各粒子に働く印加磁界や他の磁性粒子による磁気力の計算を行うことにより、磁性粒子に働く磁気力の計算を行なう磁性粒子の挙動解析方法であって、磁性粒子に働く磁界を、外部印加磁界と、外部印加磁界により磁化された磁性部材がつくる磁界の重ね合わせで表し、さらに磁性粒子に働く磁気力を、外部印加磁界や磁性粒子同士による磁気力と、磁性部材による磁気力の重ね合わせで表し、磁性部材の位置データをもとに外部印加磁界による磁性部材の磁化状態を求め、各粒子の位置における磁化された磁性部材がつくる磁界分布に基づいて磁性部材による磁気力を求めることを特徴とした磁性粒子の挙動解析方法である。
また、本発明の他の様態は、磁性粒子の挙動解析方法の磁性粒子の磁化の設定、磁性部材の磁界による磁性粒子の磁気力の計算、及び印加磁界や磁性粒子による磁気力の計算において、各磁性粒子の中心位置における外部印加磁界と、磁性部材がつくる磁界の和に基づいて各磁性粒子の磁化状態を求め、該磁化状態をもとに磁性粒子に働く磁気力を計算することを特徴とした磁性粒子の挙動解析方法である。
【００１８】
【発明の実施の形態】
（実施例１）
以下に、第１の実施例について詳しく説明する。なお、説明にあたっては、球状の磁性粒子を２次元断面に分布させ、中心軸が断面に垂直になる向きに配置された円柱状の磁性部材が断面内を移動する場合を想定しており、断面と平行な一様磁界を全体に印加した場合について取り扱うこととする。なお、磁性粒子の磁化は各粒子ごとに固定であるとする。
【００１９】
図１は、磁性粒子の挙動解析装置において、本発明の特徴である磁性粒子に働く磁気力の計算部における処理プログラムの構成である。なお、磁性粒子挙動の全体の処理については図８に示した従来の技術と同じであるため、ここでは説明を省略する。
【００２０】
図中、符号１１は磁性部材の磁化状態の計算部であり、磁性部材の中心位置データをもとに外部印加磁界により磁化された磁性部材の磁化状態の計算を行う。ここで、磁性部材の磁化は、磁性部材の中心位置における外部印加磁界Ｈ₀によって決まるし、円柱磁性体が一様磁界中で磁化しているとみなすことにより、解析解を得ることができる。
【００２１】
具体的な磁性部材の内部磁界Ｈ及び磁性部材の磁化がつくる外部磁界ＨｒとＨθよ以下の式で求める（μは磁性部材の比透磁率、ａは磁性部材の半径、ｒとθ１は図５に示すように磁性部材の中心からの変位と角度を表す。なお、本式の導出は共立出版電磁気学演習Ｐ２１７等を参照）。
【００２２】
【数１】

【００２３】
符号１２は磁性粒子の磁化の設定部であり、各粒子の磁化の設定を行う。なお、ここでは磁性粒子の磁化は各粒子ごとに固定であるとしているので、あらかじめ設定してある各粒子の磁化を用いる。
【００２４】
符号１３は磁性部材の磁界による磁性粒子の磁気力の計算部であり、磁化された磁性部材がつくる磁界による各粒子に働く磁気力の計算を行う。ここでは、磁性部材がつくる磁界（式２）（式３）の空間微分をとることにより、並進力ＦｒとＦθ、回転力Ｍθは以下の式で求めることができる（Ｍｉは磁性粒子ｉの磁気モーメント、θ２は図５に示すように磁性部材の中心からの位置ベクトルに対する磁性粒子ｉの磁気モーメントＭｉの角度を表す）。
【００２５】
【数２】

【００２６】
符号１４は印加磁界や磁性粒子による磁気力の計算部であり、各粒子に働く印加磁界や他の磁性粒子による磁気力の計算を行う。なお、具体的な計算方法については、“永井他，ＪａｐａｎＨａｒｄｃｏｐｙ’９９論文集，１８５（１９９９）”に説明されているので、ここでは説明を省略する。
【００２７】
本発明による装置の構成を図２に示す。
【００２８】
本装置は、図２に示すように、ＣＰＵ２０、ＲＡＭ２１、表示装置２２、入力部２３、外部記憶装置２４及びバス２５とを備える構成となっている。更に、上記ＲＡＭ２１は、プログラム格納部２１ａ、磁性粒子データ格納部２１ｂ、外部印加磁界分布データ格納部２１ｃ、磁性粒子の磁化状態データ格納部２１ｄ、磁性部材データ格納部２１ｅ、磁性部材の磁化状態データ格納部２１ｆ、磁性部材と磁性粒子の相対位置データ格納部２１ｇ、磁性粒子に働く磁気力データ格納部２１ｈとを備えている。
【００２９】
上記各部の構成を詳述すると、ＣＰＵ２０は、中央処理装置であり、バス２５を介して接続された上記各部を制御する。ＲＡＭ２１の各格納部２１ａ〜２１ｇには、上記図１に示したプログラム、磁性粒子データ（位置、粒径、磁気特性）、外部印加磁界分布データ、磁性粒子の磁化状態データ、磁性部材データ（形状・寸法、位置、磁気特性）、磁性部材の磁化状態データ、磁性部材と磁性粒子の相対位置データ、磁性粒子に働く力データがそれぞれ格納される。
【００３０】
表示装置２２は、ディスプレイやプリンタ等から構成され、ＣＰＵ２０の制御により表示すべきデータを表示する。入力部２３は、キーボードやマウス等から構成され、外部からの入力データを装置内に入力する。外部記憶装置２４は、ハードディスク等で構成されており、各種データを記憶する。
【００３１】
ここで、各データの内容を説明する。磁性粒子データ（位置、粒径、磁気特性）とは、２次元断面内に分布している各粒子の位置、粒径、磁気特性である。外部印加磁界分布データとは、あらかじめ有限要素法等により求めておいた外部印加磁界の分布である。磁性粒子の磁化状態データとは、各粒子の中心位置における磁化や磁気モーメントの値である。磁性部材データ（形状・寸法、位置、磁気特性）とは、磁性部材の形状や寸法、２次元断面内の各時間ごとの位置、磁気特性である。
【００３２】
磁性部材の磁化状態データとは、磁性部材の位置と外部印加磁界分布より求めた磁性部材の磁化状態のデータであり、磁化した磁性部材がつくる磁界である。磁性部材と磁性粒子の相対位置データとは、磁性部材に対する磁性粒子ｉの相対位置ｒ、θ１、θ２である。磁性粒子に働く力データとは、磁性部材や外部印加磁界による磁気力、磁性粒子同士の磁気相互作用力など、各磁性粒子に働く力である。
【００３３】
図３は本発明における磁性粒子の磁気力の計算部における処理の流れを表すフローチャートであり、本発明の特徴を最も良く表している。以下に、図３を用いて、上記装置を用いて磁性粒子の磁気力を計算する際の処理の流れを説明する。
【００３４】
（１）まず、磁性部材の磁化状態の計算部１１において、外部印加磁界分布データ２１ｃ、磁性部材データ２１ｅをもとに、磁性部材データの中心位置における外部印加磁界Ｈ₀を求め、磁性部材の磁化状態を計算し、磁性部材の磁化状態データ２１ｆに格納する（ステップＳ３０）。
【００３５】
（２）次に、磁性粒子の磁化の設定部１２において、磁性粒子データ２１ｂをもとに、磁性粒子ｉの磁気モーメントＭｉを磁性粒子の磁化状態データ２１ｄに設定する（ステップＳ３１）。
【００３６】
（３）次に、磁性部材の磁界による磁性粒子の磁気力の計算部１３において、磁性粒子データ２１ｂと磁性粒子の磁化状態データ２１ｄ、及び磁性部材データ２１ｅをもとに、磁性部材に対する磁性粒子ｉの中心位置ｒ、θ１、θ２を求め、磁性部材と磁性粒子の相対位置データ２１ｇに格納する（ステップＳ３２）。
【００３７】
（４）次に、磁性粒子データ２１ｂと磁性粒子の磁化状態データ２１ｄ、磁性部材の磁化状態データ２１ｆ、及び磁性部材と磁性粒子の相対位置データ２１ｇをもとに、（式４）〜（式６）に従い、磁性部材の磁界による磁性粒子に働く磁気力を求め、磁性粒子に働く力データ２１ｈの更新を行う（ステップＳ３３）。
【００３８】
（５）次に、外部印加磁界や他の磁性粒子による磁性粒子に働く磁気力を求め、磁性粒子に働く力データ２１ｈの更新を行う（ステップＳ３４）。この処理は、従来技術と同様であるため、説明は省略する。
【００３９】
（６）（２）〜（５）の処理を２次元断面内にある全粒子に対して行う（ステップＳ３５）。
【００４０】
本発明の特徴は、磁性部材に印加している外部印加磁界の大きさによって磁性部制の磁化が決定するとし、さらに解析領域内の磁界を外部印加磁界と磁性部材がつくる磁界に分けて考えたことである。以下、このことについて、図４、図５を用いて更に詳しく説明する。
【００４１】
図４（ａ）は磁性部材に印加されている外部印加磁界を、（ｂ）は外部印加磁界によって磁化された磁性部材がつくる磁界を表しており、４０は外部印加磁界、４１は磁性部材、４２は磁性粒子、４３は外部印加磁界により磁化された磁性部材の磁化を、４４は磁化された磁性部材がつくる磁界を表している。また、図５は磁性部材による磁性粒子に働く磁気力を説明する図であり、５０は磁性粒子の磁化を表す。
【００４２】
本発明では、図４（ａ）に示したように磁性部材４１に外部印加磁界４０が印加されているとみなし、この印加磁界によって図４（ｂ）に示したような磁化４１が磁性部材内部に発生するとしている。これにより、磁性部材の位置における外部印加磁界の大きさをもとに、磁性部材の磁化状態４１と磁性部材によってつくられる磁界４４を、（式１）〜（式３）を用いて容易に求めることができる。
【００４３】
さらに、解析領域内の磁界を、外部印加磁界と磁性部材がつくる磁界に分けて考えることにより、磁性粒子に印加される磁界による磁気力についても、外部印加磁界による磁気力と磁性部材がつくる磁界による磁気力にわけて考えることが可能となる。そして、磁性部材による磁気力については、（式４）〜（式７）を用いて磁性部材による磁界分布と磁性粒子の位置や磁化によって求めることができる。
【００４４】
これまで説明してきたように、磁性部材の位置が特定されると、磁性部材の磁化状態、磁性部材による磁界分布及び、磁性部材による磁性粒子に働く磁気力を全て求めることができる。このため、本発明を用いることにより、磁性部材の位置が逐次変化している場合においても、磁性部材の位置に応じて、磁性粒子に働く磁気力を精度良く求めることが可能となり、移動を伴う磁性部材による磁界の変化を考慮した磁性体粒子の挙動を、簡単かつ精度良く解析することが可能となる。
【００４５】
なお、上記説明では一様磁界を印加した場合について説明しているが、有限要素法や境界要素法等の解析結果を用いることにより、場所に応じて変化する磁界を印加する場合についても簡単に本発明を適用することができる。例えば、有限要素法の場合、各粒子の中心位置を内包する有限要素を求め、その有限要素に対する内挿補間を行うことにより求める方法が一般に用いられている。各粒子の中心位置を内包する有限要素の特定方法としては、“Ｊ．Ｗ．Ｓｌｏａｎ，ＡｆａｓｔａｌｇｏｒｉｔｈｍｆｏｒｃｏｎｓｔｒｕｃｔｉｎｇＤｅｌａｕｎａｙｔｒｉａｎｇｕｌａｔｉｏｎｓｉｎｔｈｅｐｌａｎｅ，Ａｄｖ．Ｅｎｇ．Ｓｏｆｔｗａｒｅ，Ｖｏ１９，Ｎｏ１（１９８７）”に、内挿補間の方法としては“中田、高橋，電気工学の有限要素法”に説明されている。
【００４６】
また、上記説明では磁性部材を円柱状としているが、一様磁界中の磁性体磁化の解析解を求めることができる楕円柱や球状のように、磁界中の磁性体の磁化を求めることが可能な形状については、本発明を容易に適用可能である。同様に、任意の磁界中の磁性体の磁化を求めることができる場合については、３次元解析にも適用可能である。さらに、複数の磁性部材に対しても適用可能である。
【００４７】
（実施例２）
第２の実施例では、磁性粒子が印加磁界によって磁化される場合について説明する。この系を解析する場合のポイントは、磁性粒子の磁化を精度良く求めることであり、そのためには磁性粒子に印加される磁界を正確に扱うことが重要となる。
【００４８】
本発明における解析領域内の磁界における扱いは第１の実施例と同じとする。すなわち、磁性部材に印加している外部印加磁界の大きさによって磁性部材の磁化が決定するとし、さらに解析領域内の磁界を外部印加磁界と磁性部材がつくる磁界に分けて考える。これにより、磁性粒子に印加される磁界は、外部印加磁界と磁性部材がつくる磁界の重ね合わせとして求めることができる。
【００４９】
以下に、磁性粒子の磁化の求め方について、図７を用いて説明する。
【００５０】
図７は、（ａ）は磁性粒子に印加している外部印加磁界と磁性部材がつくる磁界の重ね合わせの磁界を、（ｂ）は磁性粒子に印加した磁界による磁性粒子の磁化を表しており、７０は図４中の外部印加磁界４０と磁性部材がつくる磁界４４を重ね合わせることにより求められた磁界、７１は磁性粒子に印加した磁界による磁性粒子の磁化を表している。なお、４１〜４４は図４と同じである。
【００５１】
図７（ａ）に示したように、外部印加磁界４０と磁性部材がつくる磁界４４の重ね合わせた磁界７０を求めることにより、磁性部材が存在することによる磁界の変化を考慮した磁界分布を求めることが可能となる。これにより、図７（ｂ）に示したように磁性部材の影響を考慮した磁性粒子の磁化を精度良く求めることができる。
【００５２】
以下に本実施例の具体的内容を説明する。なお、本発明の処理プログラムの構成や装置の構成は図１及び図２と同じであり、説明を省略する。
【００５３】
図６は本発明における磁性粒子の磁気力の計算部における処理の流れを表すフローチャートであり、本発明の特徴を最も良く表している。以下に、図６を用いて磁性粒子の磁気力を計算する際の処理の流れを説明する。
【００５４】
（１）まず、磁性部材の磁化状態の計算部１１において、外部印加磁界分布データ２１ｃ、磁性部材データ２１ｅをもとに、磁性部材データの中心位置における外部印加磁界Ｈ₀を求め、磁性部材の磁化状態を計算し、磁性部材の磁化状態データ２１ｆに格納する（ステップＳ３０）。これは実施例１と同じである。
【００５５】
（２）次に、磁性粒子の磁化の設定部１２において、磁性粒子データ２１ｂ、外部印加磁界分布データ２１ｃをもとに、磁性粒子ｉの中心位置にかかる外部印加磁界を求め、磁性粒子にかかる磁界データに格納する（ステップＳ６０）。
【００５６】
（３）次に、磁性粒子データ２１ｂ、磁性部材の磁化状態データ２１ｔをもとに、（式２），（式３）に基づいて磁性粒子ｉの中心位置にかかる磁性部材がつくる磁界を求め、先に求めた磁性粒子にかかる磁界データに加算する（ステップＳ６１、ステップＳ６２）。
【００５７】
これにより、磁性粒子にかかる外部印加磁界と磁性部材による磁界の和Ｈｉが得られたことになる。
【００５８】
（４）次に、磁性粒子データ２１ｂ、磁性粒子にかかる磁界データ２１ｆをもとに、（式８）、（式９）に基づいて磁性粒子ｉの磁化状態を求め、磁性粒子の磁化状態データ２１ｄに格納する（ステップＳ６３）。なお、（式８）（式９）は球状粒子を仮定して得られる式を用いている（Ｊｍは磁性粒子ｉの磁化、Ｍｉは磁性粒子の磁気モーメント、μｉは磁性粒子ｉの比透磁率、ａｉは磁性粒子ｉの半径）。
【００５９】
【数３】

【００６０】
（５）次に、磁性部材の磁界による磁性粒子の磁気力の計算部１３において、磁性粒子データ２１ｂと磁性粒子の磁化状態データ２１ｄ、及び磁性部材データ２１ｅをもとに、磁性部材に対する磁性粒子ｉの中心位置ｒ、θ１、θ２を求め、磁性部材と磁性粒子の相対位置データ２１ｇに格納する（ステップＳ３２）。
【００６１】
（６）次に、磁性粒子データ２１ｂと磁性粒子の磁化状態データ２１ｄ、磁性部材の磁化状態データ２１ｆ、及び磁性部材と磁性粒子の相対位置データ２１ｇをもとに、（式４）〜（式６）に従い、磁性部材の磁界による磁性粒子に働く磁気力を求め、磁性粒子に働く力データ２１ｈの更新を行う（ステップＳ３３）。
【００６２】
（７）次に、外部印加磁界による磁性粒子に働く磁気力を求め、磁性粒子に働く力データ２１ｈの更新を行う（ステップＳ３４）。この処理は、従来技術と同様であるため、説明は省略する。
【００６３】
（８）（２）〜（７）の処理を２次元断面内にある全粒子に対して行う（ステップＳ３５）。
【００６４】
磁性粒子に働く磁気力は磁性粒子の磁化によって決定するため、磁性粒子の磁化が印加する磁界により決まる場合には、磁性粒子に印加する磁界を精度良く解くことが重要となる。
【００６５】
本発明では、解析領域内の磁界を、外部印加磁界と、外部印加磁界により磁化した磁性部材がつくる磁界の重ね合わせで表すことにより、磁性部材が存在することによる磁界分布の変化を考慮した磁界分布を求めることが可能である。その結果、磁性部材による磁性粒子の磁化の影響を考慮することが可能となり、磁性粒子の磁化を精度良く求めることができる。
【００６６】
これまで説明してきたように、磁性部材の位置が特定されると、磁性部材の磁化の状態、磁性部材による磁界分布、磁性粒子の磁化、及び磁性部材による磁性粒子に働く磁気力を全て求めることができる。このため、本発明を用いることにより、磁性部材の位置が逐次変化している場合においても、磁性部材の位置に応じて、磁性粒子に働く磁気力を精度良く求めることが可能となり、移動を伴う磁性部材による磁界の変化を考慮した磁性体粒子の挙動を、簡単かつ精度良く解析することが可能となる。
【００６７】
上記説明では、球状粒子を用いているが、粒子の形状に応じた磁化や磁気モーメントを求めることにより、様々な形状の粒子に適用することが可能となる。
【００６８】
具体的な方法として、印加磁界と平行な磁化ができると仮定し、粒子の反磁界係数Ｎｄを定義することにより、（式１０）、（式１１）を用いて粒子の磁化や磁気モーメントを求める方法などがある（Ｖｉは粒子の体積）。
【００６９】
【数４】

【００７０】
【発明の効果】
以上説明したように、本発明によれば、磁性粒子に働く磁界を、外部印加磁界と、外部印加磁界により磁化された磁性部材がつくる磁界の重ね合わせで表されるとし、各時間での磁性部材の位置に基づいて、外部印加磁界により磁化された磁性部材がつくる磁界分布と磁性粒子に働く磁気力を求めることにより、移動を伴う磁性部材による磁界の変化を考慮した磁性体粒子の挙動を、簡単かつ精度良く解析することができた。
【００７１】
また、磁性粒子が印加磁界によって磁化される場合についても、磁化の大きさを、外部印加磁界と磁化した磁性部材による磁界の重ね合わせで決定するとすることにより、磁性部材の影響を考慮した粒子の磁化を計算することができ、移動を伴う磁性部材による磁界の変化を考慮した磁性体粒子の挙動を、簡単かつ精度良く解析することができた。
【図面の簡単な説明】
【図１】本発明における磁性粒子の挙動を解析する装置における磁性粒子に働く磁気力の計算部に関する処理プログラムの構成図
【図２】本発明の実施例に係わる磁性粒子の挙動を解析する装置の構成図
【図３】本発明の実施例に係わる磁性粒子の挙動を解析する装置における磁性粒子に働く磁気力の計算部に関する処理の流れ図
【図４】（ａ）本発明の実施例に係わる磁性部材に印加されている外部印加磁界を説明する図、（ｂ）本発明の実施例に係わる外部印加磁界によって磁化された磁性部材がつくる磁界を説明する図
【図５】本発明の実施例に係わる磁性粒子に働く磁性部材による磁気力を説明する図
【図６】本発明の第２の実施例に係わる磁性粒子の挙動を解析する装置における磁性粒子に働く磁気力の計算部に関する処理の流れ図
【図７】（ａ）本発明の実施例に係わる外部印加磁界と磁性部材による磁界の重ね合わせた磁界を説明する図、（ｂ）本発明の実施例に係わる磁性粒子に印加した磁界による磁性粒子の磁化を説明する図
【図８】従来例に係わる磁性粒子の挙動を解析する装置に関する処理プログラムの構成図
【図９】従来例に係わる磁性粒子の挙動を解析する装置における磁性粒子に働く磁気力の計算部に関する処理プログラムの構成図
【符号の説明】
ステップＳ３０〜ステップＳ３５、ステップＳ６０〜ステップＳ６３処理を表すブロック
８０制御部１０〜１４
８１〜８３部を表すブロック
２０ＣＰＵ
２１ＲＡＭ
２２表示装置
２３入力部
２４外部記厖装置
２５バス[0001]
BACKGROUND OF THE INVENTION
In the behavior analysis of particles moving in a region to which a magnetic field is applied, the present invention considers the influence of the magnetized magnetic member on the magnetic field, especially when the magnetic member moves in the analysis castle. Determine particle behaviorEquipment andIt is about the method.
[0002]
[Prior art]
In recent years, behavior analysis of magnetic particles in a state where a magnetic field is applied has been performed, which is utilized for predicting the performance of compacting magnetic particles, elucidating the phenomenon of electrophotography, and the like.
[0003]
Various methods suitable for the analysis target are used to calculate the behavior of magnetic particles in a magnetic field. In addition to magnetic force, the force acting on each particle such as gravity is obtained, and the behavior of each particle is sequentially determined based on these forces. The method of obtaining is generally performed.
[0004]
As a method for obtaining the magnetic force acting on the particles, there is a method for obtaining the magnetization and magnetic force of each magnetic particle based on the externally applied magnetic field distribution obtained by numerical calculation such as the finite element method. In that case, the externally applied magnetic field is treated as a stationary field, and often does not change during the particle behavior analysis. Further, in the case where there is a magnetic member in the analysis region, it is possible to perform calculation in consideration of a change in the magnetic field due to the magnetic member by obtaining an externally applied magnetic field distribution in consideration of the magnetic member in advance.
[0005]
Regarding the magnetization of each magnetic particle, the magnetization may be fixed for each particle or may be magnetized by an externally applied magnetic field. As for the latter, as explained in “Nagai et al., Japan Hardcopy '99 Proceedings, 185 (1999)”, it is assumed that the magnetic field is proportional to the external applied magnetic field, and the external applied magnetic field at the center position of the particle is A method for obtaining a value is widely used.
[0006]
Hereinafter, the configuration of a typical processing program for analyzing the behavior of magnetic particles will be described with reference to FIGS.
[0007]
In the figure, reference numeral 80 denotes a control unit that controls the entire processing of the program.
[0008]
Reference numeral 81 denotes an initial condition setting unit, which is a calculation condition such as physical property values such as initial arrangement and magnetic characteristics of magnetic particles, shape, size, position, externally applied magnetic field distribution, time step, etc. of the structure constituting the analysis region. Set for.
[0009]
Reference numeral 10 denotes a calculation unit for the magnetic force acting on the magnetic particles, and calculates the magnetic force acting on each magnetic particle based on the magnetic characteristics (magnetization, magnetic moment, etc.) of each magnetic particle and the externally applied magnetic field distribution. This process is composed of two processes of

reference numerals

12 and 14 shown in FIG. Reference numeral 12 denotes a magnetic particle magnetization setting unit which sets the magnetization and magnetic moment of each magnetic particle. Reference numeral 14 denotes a calculation unit for the magnetic force generated by the applied magnetic field and the magnetic particles, and calculates the magnetic force generated by the externally applied magnetic field and the magnetic interaction force between the magnetic particles in accordance with the magnetization value of the magnetic particles.
[0010]
Reference numeral 82 denotes a calculation unit for forces other than the magnetic force acting on the magnetic particles, and performs calculations such as gravity acting on each magnetic particle. Reference numeral 83 denotes a particle velocity / displacement calculation unit, which updates the velocity and displacement of each particle by solving the equation of motion based on all the forces acting on each magnetic particle.
[0011]
In the actual calculation, the behavior of the magnetic particles can be obtained by repeating the processes of

reference numerals

10 and 82 to 83 after the reference numeral 81 is processed.
[0012]
[Problems to be solved by the invention]
However, when the magnetic member is moving in the analysis region, such as when the member that agitates the particles is a magnetic material, the magnetic particle behavior is considered in consideration of the magnetic field distribution based on the position of the magnetic member at each time. It was necessary to calculate. In particular, when the magnetization of the magnetic particles is determined by the magnetic field to be applied, it is important to accurately determine the magnetization of the magnetic particles. For this purpose, the magnetic field distribution applied to the magnetic particles in consideration of the influence of the magnetic member is accurately determined. It is necessary to handle.
[0013]
In order to realize this in the above-described conventional example, it is necessary to prepare a plurality of magnetic field distributions corresponding to the moving position of the magnetic member in advance. There is a problem. Further, when the behavior of the magnetic member is affected by the interaction with the magnetic particles, it is impossible to prepare the magnetic field distribution in advance because the trajectory of the magnetic member cannot be predicted in advance.
[0014]
In addition, a method of sequentially performing magnetic field calculation in consideration of the position of the magnetic member during execution of the particle behavior analysis can be considered, but it is not a practical method from the viewpoint of calculation time.
[0015]
The present invention has been made in view of such problems, and it is assumed that the magnetic field acting on the magnetic particles is represented by an externally applied magnetic field and a superposition of magnetic fields created by the magnetic member magnetized by the externally applied magnetic field, A magnetic material that takes into account changes in the magnetic field due to movement by obtaining the magnetic field distribution created by the magnetic member magnetized by the externally applied magnetic field and the magnetic force acting on the magnetic particles based on the position of the magnetic member over time The purpose is to analyze the behavior of particles easily and accurately.
[0016]
[Means for Solving the Problems]
  In order to solve this problem, the magnetic particle behavior analysis apparatus of the present invention has the following configuration. That is, in the behavior analysis apparatus for particles moving within the region where the external magnetic field applying means and the magnetic member exist, the magnetization state of the magnetic member magnetized by the external applied magnetic field is calculated based on the center position data of the magnetic member. Magnetization state calculation unit of magnetic member, magnetization setting unit of magnetic particle for setting magnetization of each particle, magnetism by magnetic field of magnetic member for calculating magnetic force acting on each particle by magnetic field created by magnetized magnetic member Calculation of the magnetic force acting on the magnetic particles composed of the magnetic force calculation part of the particles, the applied magnetic field that calculates the magnetic field applied to each particle and the magnetic force of other magnetic particles, and the magnetic force calculation part of the magnetic particles An apparatus for analyzing the behavior of magnetic particles having a portion, wherein the magnetic field acting on the magnetic particles is formed by superimposing an externally applied magnetic field and a magnetic field produced by a magnetic member magnetized by the externally applied magnetic field.RepresentationFurthermore, the magnetic force acting on the magnetic particles can be obtained by superimposing the magnetic force generated by the externally applied magnetic field or magnetic particles and the magnetic force generated by the magnetic memberRepresentationThe magnetic member is magnetized by an externally applied magnetic field based on the magnetic member position data, and the magnetic force by the magnetic member is obtained based on the magnetic field distribution produced by the magnetized magnetic member at each particle position. This is a magnetic particle behavior analysis apparatus.
[0017]
  In another aspect of the present invention, the magnetic particle magnetization setting unit, the magnetic force calculation unit of the magnetic particle by the magnetic field of the magnetic member, and the magnetic force calculation unit of the applied magnetic field or magnetic particle Magnetic particles characterized in that the magnetization state of each magnetic particle is obtained based on the sum of the externally applied magnetic field at the central position and the magnetic field generated by the magnetic member, and the magnetic force acting on the magnetic particle is calculated based on the magnetization state It is a behavior analysis device.
  According to another aspect of the present invention, there is provided a magnetic member magnetized by an externally applied magnetic field based on data on a central position of the magnetic member in a method for analyzing the behavior of particles moving within an area where the magnetic member is present and applying an external magnetic field. The magnetization state of each particle is calculated, the magnetization of each particle is set, the magnetic force acting on each particle by the magnetic field created by the magnetized magnetic member is calculated, the applied magnetic field acting on each particle, and the magnetism caused by other magnetic particles A magnetic particle behavior analysis method for calculating a magnetic force acting on a magnetic particle by calculating a force, wherein a magnetic member acting on the magnetic particle is divided into an externally applied magnetic field and a magnetic member magnetized by the externally applied magnetic field. The magnetic force acting on the magnetic particles is expressed by the superposition of the magnetic force generated by the external magnetic field and magnetic particles and the magnetic force generated by the magnetic member. The magnetic particle behavior analysis method is characterized in that the magnetization state of the magnetic member by an externally applied magnetic field is obtained and the magnetic force by the magnetic member is obtained based on the magnetic field distribution created by the magnetized magnetic member at each particle position. .
  In another aspect of the present invention, in the setting of the magnetization of the magnetic particle in the magnetic particle behavior analysis method, the calculation of the magnetic force of the magnetic particle by the magnetic field of the magnetic member, and the calculation of the magnetic force by the applied magnetic field or magnetic particle, The magnetization state of each magnetic particle is obtained based on the sum of the externally applied magnetic field at the center position of each magnetic particle and the magnetic field created by the magnetic member, and the magnetic force acting on the magnetic particle is calculated based on the magnetization state. This is a method for analyzing the behavior of magnetic particles.
[0018]
DETAILED DESCRIPTION OF THE INVENTION
Example 1
The first embodiment will be described in detail below. In the description, it is assumed that spherical magnetic particles are distributed in a two-dimensional cross section, and a cylindrical magnetic member arranged in a direction in which the central axis is perpendicular to the cross section moves in the cross section. Will be handled when a uniform magnetic field parallel to is applied to the whole. It is assumed that the magnetization of the magnetic particles is fixed for each particle.
[0019]
FIG. 1 shows a configuration of a processing program in a calculation unit of a magnetic force acting on a magnetic particle, which is a feature of the present invention, in a magnetic particle behavior analysis apparatus. Since the entire processing of the magnetic particle behavior is the same as that of the conventional technique shown in FIG. 8, the description thereof is omitted here.
[0020]
In the figure, reference numeral 11 denotes a calculation unit for the magnetization state of the magnetic member, which calculates the magnetization state of the magnetic member magnetized by the externally applied magnetic field based on the center position data of the magnetic member. Here, the magnetization of the magnetic member is determined by the externally applied magnetic field H at the center position of the magnetic member.₀The analytical solution can be obtained by assuming that the cylindrical magnetic body is magnetized in a uniform magnetic field.
[0021]
Specifically, the internal magnetic field H of the magnetic member and the external magnetic field Hr and Hθ created by the magnetization of the magnetic member are obtained by the following equations (μ is the relative magnetic permeability of the magnetic member, a is the radius of the magnetic member, and r and θ1 are FIG. This represents the displacement and angle from the center of the magnetic member, as shown in (For the derivation of this formula, see Kyoritsu Publishing, Electromagnetics Exercise P217).
[0022]
[Expression 1]

[0023]
Reference numeral 12 denotes a magnetic particle magnetization setting unit for setting the magnetization of each particle. Here, since the magnetization of the magnetic particles is fixed for each particle, the magnetization of each particle set in advance is used.
[0024]
Reference numeral 13 denotes a calculation unit for the magnetic force of the magnetic particles by the magnetic field of the magnetic member, and calculates the magnetic force acting on each particle by the magnetic field generated by the magnetized magnetic member. Here, by taking the spatial differentiation of the magnetic field (Formula 2) (Formula 3) generated by the magnetic member, the translational forces Fr and Fθ and the rotational force Mθ can be obtained by the following formulas (Mi is the magnetic property of the magnetic particle i). The moment θ2 represents the angle of the magnetic moment Mi of the magnetic particle i with respect to the position vector from the center of the magnetic member as shown in FIG. 5).
[0025]
[Expression 2]

[0026]
Reference numeral 14 denotes a calculation unit for an applied magnetic field or magnetic force generated by magnetic particles, and calculates an applied magnetic field acting on each particle or a magnetic force generated by other magnetic particles. Since a specific calculation method is described in “Nagai et al., Japan Hardcopy '99 Proceedings, 185 (1999)”, the description is omitted here.
[0027]
The configuration of the apparatus according to the present invention is shown in FIG.
[0028]
As shown in FIG. 2, the present apparatus includes a CPU 20, a RAM 21, a display device 22, an input unit 23, an external storage device 24, and a bus 25. Further, the RAM 21 includes a program storage unit 21a, a magnetic particle data storage unit 21b, an externally applied magnetic field distribution data storage unit 21c, a magnetic particle magnetization state data storage unit 21d, a magnetic member data storage unit 21e, and a magnetic member magnetization state data. A storage unit 21f, a relative position data storage unit 21g of the magnetic member and the magnetic particles, and a magnetic force data storage unit 21h acting on the magnetic particles are provided.
[0029]
The configuration of each unit will be described in detail. The CPU 20 is a central processing unit and controls each unit connected via the bus 25. In each of the storage units 21a to 21g of the RAM 21, the program shown in FIG. 1, magnetic particle data (position, particle size, magnetic characteristics), externally applied magnetic field distribution data, magnetic particle magnetization state data, magnetic member data (shape) (Dimension, position, magnetic characteristics), magnetization state data of the magnetic member, relative position data of the magnetic member and magnetic particles, and force data acting on the magnetic particles are stored.
[0030]
The display device 22 includes a display, a printer, and the like, and displays data to be displayed under the control of the CPU 20. The input unit 23 includes a keyboard, a mouse, and the like, and inputs input data from the outside into the apparatus. The external storage device 24 is composed of a hard disk or the like and stores various data.
[0031]
Here, the contents of each data will be described. The magnetic particle data (position, particle size, magnetic property) is the position, particle size, and magnetic property of each particle distributed in the two-dimensional cross section. The externally applied magnetic field distribution data is a distribution of the externally applied magnetic field that is obtained in advance by the finite element method or the like. The magnetization state data of magnetic particles is the value of magnetization and magnetic moment at the center position of each particle. The magnetic member data (shape / dimension, position, magnetic property) is the shape and size of the magnetic member, the position of each time in the two-dimensional cross section, and the magnetic property.
[0032]
The magnetization state data of the magnetic member is data on the magnetization state of the magnetic member obtained from the position of the magnetic member and the externally applied magnetic field distribution, and is a magnetic field generated by the magnetized magnetic member. The relative position data of the magnetic member and the magnetic particles are the relative positions r, θ1, and θ2 of the magnetic particle i with respect to the magnetic member. The force data acting on the magnetic particles is a force acting on each magnetic particle, such as a magnetic force generated by a magnetic member or an externally applied magnetic field, or a magnetic interaction force between magnetic particles.
[0033]
FIG. 3 is a flowchart showing the flow of processing in the magnetic force calculation unit of the magnetic particles in the present invention, and best represents the features of the present invention. Below, the flow of processing when calculating the magnetic force of magnetic particles using the above-mentioned apparatus will be described using FIG.
[0034]
(1) First, in the calculation unit 11 of the magnetization state of the magnetic member, based on the externally applied magnetic field distribution data 21c and the magnetic member data 21e, the externally applied magnetic field H at the center position of the magnetic member data.₀Is calculated, and the magnetization state of the magnetic member is calculated and stored in the magnetization state data 21f of the magnetic member (step S30).
[0035]
(2) Next, the magnetic particle magnetization setting unit 12 sets the magnetic moment Mi of the magnetic particle i to the magnetic particle magnetization state data 21d based on the magnetic particle data 21b (step S31).
[0036]
(3) Next, in the magnetic particle magnetic force calculation unit 13 by the magnetic field of the magnetic member, the magnetic particle for the magnetic member is based on the magnetic particle data 21b, the magnetization state data 21d of the magnetic particle, and the magnetic member data 21e. The center positions r, θ1, and θ2 of i are obtained and stored in the relative position data 21g between the magnetic member and the magnetic particles (step S32).
[0037]
(4) Next, based on the magnetic particle data 21b, the magnetization state data 21d of the magnetic particles, the magnetization state data 21f of the magnetic member, and the relative position data 21g of the magnetic member and the magnetic particles, (Expression 4) to (Expression 4) According to 6), the magnetic force acting on the magnetic particles due to the magnetic field of the magnetic member is obtained, and the force data 21h acting on the magnetic particles is updated (step S33).
[0038]
(5) Next, the magnetic force acting on the magnetic particles by the externally applied magnetic field or other magnetic particles is obtained, and the force data 21h acting on the magnetic particles is updated (step S34). Since this process is the same as that of the prior art, description thereof is omitted.
[0039]
(6) The processes (2) to (5) are performed on all particles in the two-dimensional cross section (step S35).
[0040]
The feature of the present invention is that the magnetization of the magnetic system is determined by the magnitude of the externally applied magnetic field applied to the magnetic member, and the magnetic field in the analysis region is further divided into the externally applied magnetic field and the magnetic field generated by the magnetic member. That is. Hereinafter, this will be described in more detail with reference to FIGS.
[0041]
4A shows the externally applied magnetic field applied to the magnetic member, FIG. 4B shows the magnetic field generated by the magnetic member magnetized by the externally applied magnetic field, 40 is the externally applied magnetic field, 41 is the magnetic member, Reference numeral 42 denotes magnetic particles, 43 denotes magnetization of a magnetic member magnetized by an externally applied magnetic field, and 44 denotes a magnetic field generated by the magnetized magnetic member. FIG. 5 is a diagram for explaining the magnetic force acting on the magnetic particles by the magnetic member, and 50 represents the magnetization of the magnetic particles.
[0042]
In the present invention, it is assumed that an externally applied magnetic field 40 is applied to the magnetic member 41 as shown in FIG. 4A, and the magnetization 41 as shown in FIG. It is supposed to occur. Thus, based on the magnitude of the externally applied magnetic field at the position of the magnetic member, the magnetization state 41 of the magnetic member and the magnetic field 44 created by the magnetic member can be easily obtained using (Expression 1) to (Expression 3). be able to.
[0043]
Furthermore, by dividing the magnetic field in the analysis region into an externally applied magnetic field and a magnetic field generated by the magnetic member, the magnetic force generated by the magnetic field applied to the magnetic particles is also determined by the magnetic force generated by the externally applied magnetic field and the magnetic member. It is possible to think about the magnetic force due to And the magnetic force by a magnetic member can be calculated | required by the position and magnetization of a magnetic field distribution and magnetic particle by a magnetic member using (Formula 4)-(Formula 7).
[0044]
As described above, when the position of the magnetic member is specified, all of the magnetization state of the magnetic member, the magnetic field distribution by the magnetic member, and the magnetic force acting on the magnetic particles by the magnetic member can be obtained. For this reason, by using the present invention, even when the position of the magnetic member is sequentially changed, the magnetic force acting on the magnetic particles can be accurately determined according to the position of the magnetic member, which is accompanied by movement. It becomes possible to easily and accurately analyze the behavior of the magnetic particles in consideration of the change of the magnetic field due to the magnetic member.
[0045]
In the above description, a case where a uniform magnetic field is applied is described. However, by using analysis results such as the finite element method and the boundary element method, a case where a magnetic field that changes depending on the location is applied can be easily described. The present invention can be applied. For example, in the case of the finite element method, a method is generally used in which a finite element including the center position of each particle is obtained and obtained by performing interpolation for the finite element. As a method for specifying a finite element including the center position of each particle, “JW Sloan, A fast algorithm for constructing Delaunay triangulations in the plane, Adv. Eng. Software, Vo19, 198”, No. 1 The interpolation method is described in “Nakada, Takahashi, Finite Element Method of Electrical Engineering”.
[0046]
In the above description, the magnetic member has a cylindrical shape. However, it is possible to obtain the magnetization of a magnetic material in a magnetic field, such as an elliptical cylinder or a spherical shape that can obtain an analytical solution for the magnetization of a magnetic material in a uniform magnetic field. For various shapes, the present invention can be easily applied. Similarly, the case where the magnetization of a magnetic substance in an arbitrary magnetic field can be obtained can also be applied to a three-dimensional analysis. Furthermore, it can be applied to a plurality of magnetic members.
[0047]
(Example 2)
In the second embodiment, a case where magnetic particles are magnetized by an applied magnetic field will be described. The point in analyzing this system is to obtain the magnetization of the magnetic particles with high accuracy. For that purpose, it is important to accurately handle the magnetic field applied to the magnetic particles.
[0048]
The handling of the magnetic field in the analysis region in the present invention is the same as in the first embodiment. That is, the magnetization of the magnetic member is determined by the magnitude of the externally applied magnetic field applied to the magnetic member, and the magnetic field in the analysis region is further divided into an externally applied magnetic field and a magnetic field generated by the magnetic member. Thereby, the magnetic field applied to the magnetic particles can be obtained as a superposition of the externally applied magnetic field and the magnetic field generated by the magnetic member.
[0049]
Hereinafter, a method of obtaining the magnetization of the magnetic particles will be described with reference to FIG.
[0050]
FIG. 7A shows the superposition of the externally applied magnetic field applied to the magnetic particles and the magnetic field created by the magnetic member, and FIG. 7B shows the magnetization of the magnetic particles by the magnetic field applied to the magnetic particles. , 70 is a magnetic field obtained by superimposing the externally applied magnetic field 40 in FIG. 4 and the magnetic field 44 produced by the magnetic member, and 71 is the magnetization of the magnetic particles by the magnetic field applied to the magnetic particles. 41 to 44 are the same as those in FIG.
[0051]
As shown in FIG. 7A, a magnetic field distribution in consideration of a change in the magnetic field due to the presence of the magnetic member is obtained by obtaining a magnetic field 70 obtained by superimposing the externally applied magnetic field 40 and the magnetic field 44 generated by the magnetic member. It becomes possible. Thereby, as shown in FIG.7 (b), the magnetization of the magnetic particle which considered the influence of the magnetic member can be calculated | required accurately.
[0052]
The specific contents of the present embodiment will be described below. The configuration of the processing program and the configuration of the apparatus of the present invention are the same as those in FIGS.
[0053]
FIG. 6 is a flowchart showing the flow of processing in the magnetic force calculation unit of the magnetic particles in the present invention, and best represents the features of the present invention. In the following, the flow of processing when calculating the magnetic force of the magnetic particles will be described with reference to FIG.
[0054]
(1) First, in the calculation unit 11 of the magnetization state of the magnetic member, based on the externally applied magnetic field distribution data 21c and the magnetic member data 21e, the externally applied magnetic field H at the center position of the magnetic member data.₀Is calculated, and the magnetization state of the magnetic member is calculated and stored in the magnetization state data 21f of the magnetic member (step S30). This is the same as in the first embodiment.
[0055]
(2) Next, in the magnetization setting unit 12 of the magnetic particle, the externally applied magnetic field applied to the center position of the magnetic particle i is obtained based on the magnetic particle data 21b and the externally applied magnetic field distribution data 21c, and applied to the magnetic particle. Store in the magnetic field data (step S60).
[0056]
(3) Next, based on the magnetic particle data 21b and the magnetization state data 21t of the magnetic member, the magnetic field generated by the magnetic member at the center position of the magnetic particle i is obtained based on (Expression 2) and (Expression 3). Then, it is added to the magnetic field data concerning the magnetic particles obtained previously (step S61, step S62).
[0057]
Thereby, the sum Hi of the externally applied magnetic field applied to the magnetic particles and the magnetic field by the magnetic member is obtained.
[0058]
(4) Next, based on the magnetic particle data 21b and the magnetic field data 21f applied to the magnetic particle, the magnetization state of the magnetic particle i is obtained based on (Equation 8) and (Equation 9). 21d (step S63). Note that (Equation 8) and (Equation 9) use equations obtained assuming spherical particles (Jm is the magnetization of the magnetic particle i, Mi is the magnetic moment of the magnetic particle, and μi is the relative permeability of the magnetic particle i. Ai is the radius of the magnetic particle i).
[0059]
[Equation 3]

[0060]
(5) Next, in the magnetic particle magnetic force calculation unit 13 by the magnetic field of the magnetic member, the magnetic particle for the magnetic member is based on the magnetic particle data 21b, the magnetization state data 21d of the magnetic particle, and the magnetic member data 21e. The center positions r, θ1, and θ2 of i are obtained and stored in the relative position data 21g between the magnetic member and the magnetic particles (step S32).
[0061]
(6) Next, based on the magnetic particle data 21b, the magnetization state data 21d of the magnetic particles, the magnetization state data 21f of the magnetic member, and the relative position data 21g of the magnetic member and the magnetic particles, (Expression 4) to (Expression 4) According to 6), the magnetic force acting on the magnetic particles due to the magnetic field of the magnetic member is obtained, and the force data 21h acting on the magnetic particles is updated (step S33).
[0062]
(7) Next, the magnetic force acting on the magnetic particles by the externally applied magnetic field is obtained, and the force data 21h acting on the magnetic particles is updated (step S34). Since this process is the same as that of the prior art, description thereof is omitted.
[0063]
(8) The processes (2) to (7) are performed on all particles in the two-dimensional cross section (step S35).
[0064]
Since the magnetic force acting on the magnetic particles is determined by the magnetization of the magnetic particles, it is important to accurately solve the magnetic field applied to the magnetic particles when the magnetization of the magnetic particles is determined by the applied magnetic field.
[0065]
In the present invention, the magnetic field in the analysis region is represented by superimposing the externally applied magnetic field and the magnetic field created by the magnetic member magnetized by the externally applied magnetic field, thereby taking into account the change in the magnetic field distribution due to the presence of the magnetic member. Distribution can be obtained. As a result, it becomes possible to consider the influence of the magnetization of the magnetic particles by the magnetic member, and the magnetization of the magnetic particles can be obtained with high accuracy.
[0066]
As explained so far, when the position of the magnetic member is specified, the state of magnetization of the magnetic member, the magnetic field distribution by the magnetic member, the magnetization of the magnetic particle, and the magnetic force acting on the magnetic particle by the magnetic member are all obtained. Can do. For this reason, by using the present invention, even when the position of the magnetic member is sequentially changed, the magnetic force acting on the magnetic particles can be accurately determined according to the position of the magnetic member, which is accompanied by movement. It becomes possible to easily and accurately analyze the behavior of the magnetic particles in consideration of the change of the magnetic field due to the magnetic member.
[0067]
In the above description, spherical particles are used. However, by obtaining the magnetization and magnetic moment according to the shape of the particles, it can be applied to particles of various shapes.
[0068]
As a specific method, assuming that the magnetization parallel to the applied magnetic field can be performed, the particle demagnetization coefficient Nd is defined, and the magnetization and magnetic moment of the particle are obtained using (Equation 10) and (Equation 11). There is a method (Vi is the volume of the particle).
[0069]
[Expression 4]

[0070]
【The invention's effect】
As described above, according to the present invention, the magnetic field acting on the magnetic particles is represented by the superposition of the externally applied magnetic field and the magnetic field produced by the magnetic member magnetized by the externally applied magnetic field. Based on the position of the member, by calculating the magnetic field distribution generated by the magnetic member magnetized by the externally applied magnetic field and the magnetic force acting on the magnetic particle, the behavior of the magnetic particle considering the change of the magnetic field due to the magnetic member accompanying the movement can be obtained. It was possible to analyze easily and accurately.
[0071]
In addition, when the magnetic particles are magnetized by the applied magnetic field, the magnitude of magnetization is determined by superimposing the externally applied magnetic field and the magnetic field of the magnetized magnetic member, so that the effect of the magnetic member is considered. The magnetization could be calculated, and the behavior of the magnetic particles considering the change of the magnetic field due to the magnetic member accompanying the movement could be analyzed easily and accurately.
[Brief description of the drawings]
FIG. 1 is a configuration diagram of a processing program related to a calculation unit for magnetic force acting on magnetic particles in an apparatus for analyzing the behavior of magnetic particles in the present invention.
FIG. 2 is a block diagram of an apparatus for analyzing the behavior of magnetic particles according to an embodiment of the present invention.
FIG. 3 is a flowchart of a process related to a calculation unit for a magnetic force acting on a magnetic particle in an apparatus for analyzing the behavior of the magnetic particle according to an embodiment of the present invention.
4A is a view for explaining an externally applied magnetic field applied to a magnetic member according to an embodiment of the present invention, and FIG. 4B is a magnetic member magnetized by an externally applied magnetic field according to an embodiment of the present invention. Diagram explaining magnetic field
FIG. 5 is a diagram for explaining magnetic force generated by a magnetic member acting on magnetic particles according to an embodiment of the present invention.
FIG. 6 is a flowchart of a process related to a calculation unit for a magnetic force acting on a magnetic particle in an apparatus for analyzing the behavior of the magnetic particle according to the second embodiment of the present invention.
7A is a diagram for explaining a magnetic field obtained by superimposing an externally applied magnetic field according to an embodiment of the present invention and a magnetic field by a magnetic member, and FIG. 7B is a magnetic diagram of a magnetic field applied to a magnetic particle according to an embodiment of the present invention. Diagram explaining magnetization of particles
FIG. 8 is a configuration diagram of a processing program related to an apparatus for analyzing the behavior of magnetic particles according to a conventional example.
FIG. 9 is a configuration diagram of a processing program related to a calculation unit for a magnetic force acting on magnetic particles in an apparatus for analyzing the behavior of magnetic particles according to a conventional example.
[Explanation of symbols]
Step S30 to Step S35, Step S60 to Step S63 Block representing processing
80 controller 10-14
Block representing 81 to 83 parts
20 CPU
21 RAM
22 Display device
23 Input section
24 External storage device
25 bus

Claims

In the behavior analysis device for particles moving in the region where the external magnetic field applying means and the magnetic member exist,
Magnetization state calculation unit for the magnetic member that calculates the magnetization state of the magnetic member magnetized by the externally applied magnetic field based on the center position data of the magnetic member, and magnetization setting unit for the magnetic particle that sets the magnetization of each particle Calculating the magnetic force acting on each particle by the magnetic field generated by the magnetized magnetic member, calculating the magnetic force of the magnetic particle by the magnetic field of the magnetic member, calculating the applied magnetic field acting on each particle and the magnetic force by other magnetic particles A magnetic particle behavior analysis device having a magnetic force calculation unit acting on a magnetic particle constituted by an applied magnetic field and a magnetic force calculation unit by a magnetic particle,
The magnetic field acting on the magnetic particles is represented by the superposition of the externally applied magnetic field and the magnetic field created by the magnetic member magnetized by the externally applied magnetic field, and the magnetic force acting on the magnetic particles is expressed as represents a superposition of the magnetic force by the magnetic member,
Based on the position data of the magnetic member, obtain the magnetization state of the magnetic member by the externally applied magnetic field,
A magnetic particle behavior analysis apparatus characterized in that a magnetic force by a magnetic member is obtained based on a magnetic field distribution created by a magnetized magnetic member at each particle position.

In the magnetic particle magnetization setting unit, the magnetic particle magnetic force calculation unit due to the magnetic field of the magnetic member, and the applied magnetic field or magnetic force calculation unit in the magnetic particle behavior analysis device according to claim 1,
The magnetization state of each magnetic particle is obtained based on the sum of the externally applied magnetic field at the center position of each magnetic particle and the magnetic field created by the magnetic member, and the magnetic force acting on the magnetic particle is calculated based on the magnetization state. Magnetic particle behavior analyzer.

In the method of analyzing the behavior of particles moving within the region where the external magnetic field is applied and the magnetic member exists,
Calculate the magnetization state of a magnetic member magnetized by an externally applied magnetic field based on the data on the center position of the magnetic member, set the magnetization of each particle, and use the magnetic field generated by the magnetized magnetic member to act on each particle. A magnetic particle behavior analysis method that calculates the magnetic force acting on the magnetic particles by calculating the force and calculating the magnetic force applied to each particle and the magnetic force by other magnetic particles,
The magnetic field acting on the magnetic particles is represented by the superposition of the externally applied magnetic field and the magnetic field created by the magnetic member magnetized by the externally applied magnetic field, and the magnetic force acting on the magnetic particles is expressed as , Represented by the superposition of magnetic force by magnetic members,
Based on the position data of the magnetic member, obtain the magnetization state of the magnetic member by the externally applied magnetic field,
A magnetic particle behavior analysis method characterized in that a magnetic force by a magnetic member is obtained based on a magnetic field distribution created by a magnetized magnetic member at each particle position.

In the magnetic particle behavior analysis method according to claim 3, the setting of the magnetization of the magnetic particles, the calculation of the magnetic force of the magnetic particles by the magnetic field of the magnetic member, and the calculation of the magnetic force by the applied magnetic field or magnetic particles,
The magnetization state of each magnetic particle is obtained based on the sum of the externally applied magnetic field at the center position of each magnetic particle and the magnetic field created by the magnetic member, and the magnetic force acting on the magnetic particle is calculated based on the magnetization state. Analysis method for magnetic particles.