JP3760380B2

JP3760380B2 - Viscoelastic material belt characteristic analysis apparatus, method, system, program, and recording medium

Info

Publication number: JP3760380B2
Application number: JP2002073124A
Authority: JP
Inventors: 兪　　波
Original assignee: Ricoh Co Ltd
Current assignee: Ricoh Co Ltd
Priority date: 2002-03-15
Filing date: 2002-03-15
Publication date: 2006-03-29
Anticipated expiration: 2022-03-15
Also published as: JP2003270108A

Description

【０００１】
【発明の属する技術分野】
本発明は、非線型特性を有する粘弾性材料ベルトの荷重（応力）−ひずみ特性を高精度に求めるための粘弾性材料ベルト特性解析方法、装置、システム、プログラム及びび記録媒体に関し、例えば粘弾性材料で構成されたタイミングベルトにより駆動伝達を行う場合、または複写機など駆動系の設計の際に、最適化手法を用いたタイミングベルト荷重（応力）−ひずみ特性解析を行う場合等に応用されるものである。
【０００２】
【従来の技術】
一般的な線形弾性材料において、弾性変形（線形）領域では、応力と歪の比であるヤング率は一定であるため、構造物の形状、寸法、ヤング率などの材料定数や、拘束条件、負荷条件などのパラメータにより線形解析を行い、さまざまな条件下における構造物の荷重（応力）−歪特性を求めることができる。
【０００３】
【発明が解決しようとする課題】
しかしながら、前記粘弾性材料ベルトの荷重（応力）−歪特性を解析する場合には、ベルトの粘性などの影響により時間が進行すると共に材料のヤング率が変化を生じるため、単にヤング率のみ入力する場合には、解析計算上誤差が大きくなり、また粘性の影響によるヤング率の変化を予測することによってベルト荷重（応力）−歪特性を求めるのは難しいという問題があった。
また、駆動機構の急速な立上挙動におけるベルトの荷重（応力）−歪特性または微少ひずみ領域におけるベルトの荷重（応力）−歪特性を、普通の引張り試験機で正確に計測できないという問題もあった。
また、最適化手法により、駆動系の実験データと計算データを合わせ込むことによって、ベルトの荷重（応力）−歪特性を求める方法についても、多峰性解空間に最適解を局部に落ちる可能性があり、荷重（応力）−歪特性の解精度が低いという問題もあった。
【０００４】
そこで、本発明は、粘弾性材料ベルトを含み、駆動軸と従動軸から構成された実験装置から、駆動軸の回転をベルトを介して従動軸に伝達し、各軸について回転量と時間との関係を計測し、これに基づいて機構解析モデルを用いて、最適化手法を用いて、従動軸回転量実験データと解析データを比較しながら、大域最適解の探索と局部最適解の探索に分け、各設計変数を反復して、両者が一致するように、短時間で効率よく前記粘弾性材料ベルトの荷重（応力）−歪特性を算出することができる方法およびシステムを提供することを目的とする。
【０００５】
【課題を解決するための手段】
上記の目的を達成するために、本発明による粘弾性材料ベルト特性解析装置は、粘弾性材料で構成されたベルトに任意の負荷が作用することにより発生する荷重（応力）−ひずみ特性を求める粘弾性材料ベルト特性解析装置であって、駆動軸の回転を前記ベルトを介して従動軸に伝達することにより前記ベルトに任意のテンションを発生させるテンション発生手段と、前記駆動軸の回転量と時間との関係及び前記従動軸の回転量と時間との関係を計測する計測手段と、機構解析モデルを用いることにより、ベルト荷重（応力）−ひずみ特性の初期値から前記計測した駆動軸の回転量と時間との関係を用いて前記従動軸の回転量と時間との関係を算出する第１の演算手段と、前記ベルト荷重（応力）−ひずみ特性の初期値にシフト量係数をかけ、シフト量係数を設計変数として順次変化させ、前記算出された従動軸の回転量と時間との関係と計測された回転量と時間との関係とを比較し、各時間における回転量の差分の合計値を最小にすることによって、前記シフト量係数を決定する第一最適化手段と、前記機構解析モデルを用いて、前記算出されたシフト量係数による決定された荷重（応力）−ひずみ特性における各荷重データを設計変数として反復して変化させ、前記算出された従動軸の回転量と時間との関係と計測された回転量と時間との関係とを比較し、各時間における回転量の差分の合計値を最小にすることによって、前記ベルトの荷重（応力）−ひずみ特性を決定する第二最適化手段とを設けている。
【０００６】
また、本発明による粘弾性材料ベルト特性解析方法は、粘弾性材料で構成されたベルトに任意の負荷が作用することにより発生する荷重（応力）−ひずみ特性を求める粘弾性材料ベルト特性解析方法であって、駆動軸の回転を前記ベルトを介して従動軸に伝達することにより前記ベルトに任意のテンションを発生させるステップと、前記駆動軸の回転量と時間との関係及び前記従動軸の回転量と時間との関係を計測するステップと、機構解析モデルを用いることにより、ベルト荷重（応力）−ひずみ特性の初期値から前記計測した駆動軸の回転量と時間との関係を用いて前記従動軸の回転量と時間との関係を算出するステップと、前記ベルト荷重（応力）−ひずみ特性の初期値にシフト量係数をかけ、シフト量係数を設計変数として順次変化させ、前記算出された従動軸の回転量と時間との関係と計測された回転量と時間との関係とを比較し、各時間における回転量の差分の合計値を最小にすることによって、前記シフト量係数を決定する第一最適化を行うステップと、前記機構解析モデルを用いて、前記算出されたシフト量係数による決定された荷重（応力）−ひずみ特性における各荷重データを設計変数として反復して変化させ、前記算出された従動軸の回転量と時間との関係と計測された回転量と時間との関係とを比較し、各時間における回転量の差分の合計値を最小にすることによって、前記ベルトの荷重（応力）−ひずみ特性を決定する第二最適化を行うステップとを設けている。
【０００７】
また、本発明による粘弾性材料ベルト特性解析システムは、粘弾性材料で構成されたベルトの荷重（応力）−ひずみ特性を求める前記粘弾性材料ベルト特性解析システムであって、前記ベルトを介して、駆動軸の挙動を従動軸に伝達する実験装置を有し、前記実験装置の駆動軸と従動軸の回転量と時間との関係を計測できる計測装置を設け、駆動軸の回転量と時間との関係と従動軸の回転量と時間との関係を計測する計測手段と、前記計測して得られた駆動軸の回転量と時間との関係を用いて、前記実験装置の機構モデルにより、ベルト荷重（応力）−ひずみ特性から、従動軸の回転量と時間との関係を算出する機構解析手段と、前記機構解析モデルを用いて、前記ベルト荷重（応力）−ひずみ特性の初期値にシフト量係数をかけ、シフト量係数を設計変数として順次変化させ、前記算出された従動軸の回転量と時間との関係と計測された回転量と時間との関係とを比較し、各時間における回転量の差分の合計値を最小にすることによって、前記シフト量係数を決定する単因子実験法を用いた第一最適化計算手段と、前記機構解析モデルを用いて、前記第一最適化計算手段で算出されたベルト荷重（応力）−ひずみ特性における各荷重データを設計変数として反復して変化させ、前記算出された従動軸の回転量と時間との関係と計測された回転量と時間との関係とを比較し、各時間における回転量の差分の合計値を最小にすることによって、前記粘弾性材料で構成されたベルトの荷重（応力）−ひずみ特性を決定する第二最適化計算手段とを設けている。
【０００８】
また、本発明によるプログラムは、前記粘弾性材料ベルト荷重（応力）−ひずみ特性解析方法を、コンピュータに実行させるためのプログラムである。
【０００９】
また、本発明による記録媒体は、前記プログラムを記録したコンピュータ読み取り可能な記録媒体である。
【００１０】
【発明の実施の形態】
以下、本発明の実施の形態を請求項毎に図面と共に説明する。
〔請求項１、８、２、９に関する構成・動作〕
請求項１、１５に関する粘弾性材料ベルト特性解析装置、方法にあっては、図１のフローチャートに示すような手順で解析を行う。粘弾性材料ベルトに任意の負荷（テンション）が作用することにより発生する荷重（応力）−ひずみ特性解析方法について説明する。
【００１１】
まず、本方法を実行するための請求項２、９に関する粘弾性材料ベルト特性解析装置としての実験装置について図７を参照して説明する。本装置は、粘弾性材料ベルトを介して駆動軸の挙動を従動軸に伝達する実験装置である。
図７の駆動側において、モータ１で回転駆動される駆動軸２には、駆動軸負荷３とプーリ４と計測装置５が設けられている。計測装置５は駆動軸２の回転量と時間との関係を計測する装置である。従動側において、従動軸６には、従動軸負荷７とプーリ８と計測装置９が設けられている。計測装置９は従動軸６の回転量と時間との関係を計測する装置である。計測装置５、９として、例えば回転量と時間との関係を計測できるエンコーダを用いることができる。
プーリ４とプーリ８間には、解析実験対象である粘弾性材料ベルト１０が掛け渡されている。この外に本装置内には、図示せずも制御プログラムを有する制御装置や機構解析モデルを有する演算装置等が備えられているものとする。
【００１２】
次に、本装置を用いた粘弾性材料ベルトの負荷により発生する荷重（応力）−ひずみ特性解析方法について図１と共に説明する。
まず、モータ１により駆動軸２を駆動し、その回転を粘弾性材料ベルト１０を介して従動軸６に伝達し、計測装置５により駆動軸の回転量と時間との関係を計測すると共に、計測装置９により従動軸の回転量と時間との関係を計測する（ステップＳ１、以下、ステップ略）。次に、計測された駆動軸２の回転量と時間との関係曲線（Ｓ２）を、実験装置内の予め構築された機構解析モデルに入力し、ベルト荷重（応力）−ひずみ特性の初期値（Ｓ３）から、機構解析モデルを用いて所定の微少時間間隔毎に解析を行い、従動軸の回転量と時間との関係を算出する。尚、この算出方法については後述する（Ｓ４、Ｓ５）。
【００１３】
次に、前記ベルト荷重（応力）−ひずみ特性の初期値にシフト量係数をかけ、シフト量係数を設計変数として順次変化させ、前記算出された従動軸の回転量と時間との関係と計測された回転量と時間との関係とを比較し、回転量データ差分の合計値を最小にすることによって、前記シフト量係数を決定する第一最適化ステップを含む処理を実行する（Ｓ６、Ｓ７）。次に、前記シフト量係数をかけた従動軸の回転量と時間との関係と計測された回転量と時間との関係とを比較し、各時間間隔における従動軸回転量データ差分の合計値を最小にするように、前記機構解析モデルを用いて、前記制約条件下に前記ベルト荷重（応力）−ひずみ特性における各荷重データを設計変数として反復して変化させる第二最適化ステップを含む処理を実行することにより（Ｓ８、Ｓ９、Ｓ１０、Ｓ３〜Ｓ９）、前記粘弾性材料で構成されたベルトの荷重（応力）−ひずみ特性を決定する（Ｓ１１）。
【００１４】
次に、本実施の形態によるの粘弾性材料ベルト特性解析方法について、具体的な解析例を用いて説明する。
まず、計測装置５により、駆動軸２の回転量（回転速度）と時間との関係を計測して、図２の曲線Ａを得る。また、計測装置９により、従動軸６の回転量（回転速度）と時間との関係をを計測して、図２の曲線Ｂを得る。次に、機構解析モデルに図３に示すようなベルト荷重（応力）−ひずみ特性曲線の初期値Ｃを入力し、この初期値と前記曲線Ａを用いて従動軸６の回転量と時間との関係を算出値する。算出結果を図４の曲線Ｄに示す。
【００１５】
次に、前記ベルト荷重（応力）−ひずみ特性の初期値Ｃにシフト量係数をかけ、シフト量係数を単因子実験変数として、例えば、１から３０（ベルトの物理特性の可能範囲）まで０．１間隔で順次変化させ、前記算出された従動軸６の回転量と時間との関係（図４のＤ) と計測された従動軸６の回転量と時間との関係（図４の曲線Ｅ）とを比較し、回転量データ差分の合計値を最小になるとき、前記シフト量係数を決定する。次に、前記決定されたシフト量係数をベルト荷重（応力）−ひずみ特性曲線の初期値Ｃにかけ、従動軸６の回転量と時間との関係と計測された回転量と時間との関係とを比較し、各時間間隔における従動軸回転量データの差分の合計値を最小にするように、前記シフト量係数をかけたベルト荷重（応力）−ひずみ特性曲線における各荷重値ポイントを設計変数として、前記制約条件下に反復して変化させ、粘弾性材料ベルトの荷重（応力）−ひずみ特性を決定する。
【００１６】
図５に計算が収束する際の従動軸６の回転量と時間との関係曲線の算出値（曲線Ｆ）と、従動軸６の回転量と時間との関係曲線の計測値（曲線Ｇ）の比較を示す。
図６に最後に決定された粘弾性材料ベルトの荷重（応力）−ひずみ特性（曲線Ｈ）と、ベルトの荷重（応力）−ひずみ特性曲線初期値（曲線Ｉ）の比較を示す。
【００１７】
〔請求項３、１０に関する構成・動作〕
請求項３、１０に関する粘弾性材料ベルト特性解析方法における機構解析モデルにおいて、前記計測された駆動軸２の回転量と時間との関係を用いて、機構解析モデルにより、ベルト荷重（応力）−ひずみ特性の初期値から、従動軸６の回転量と時間との関係を算出する方法について説明する。
まず、前記実験装置と対照付けて、次式（１）の運動方程式に基づいて機構解析モデルを構築する。
［Ｊ］［ｄθ² ／ｄ²ｔ］＋［Ｃ］［ｄθ／ｄｔ］+ ［ｋ］［θ］＝［Ｔ］・・・（１）
ただし、
［Ｊ］：各慣性モーメントを含む慣性モーメントマトリックス
［ｋ］：ベルト剛性係数を含むバネ剛性マトリックス
［Ｃ］：ベルト粘性係数を含むバネ粘性マトリックス
［θ］：駆動軸、従動軸の回転角を含む回転角ベクトル
［Ｔ］：トルクベクトル
【００１８】
前記実験装置機構解析モデルの概略図を図８に示す。前記計測された駆動軸２の回転量と時間との関係を機構解析モデルに入力し、ベルト荷重（応力）−ひずみ特性の初期値から従動軸６の回転量と時間との関係を算出する。
【００１９】
〔請求項４、１１に関する構成・動作〕
請求項４、１１に関する粘弾性材料ベルト特性解析方法における機構解析モデルにあっては、前記任意の引張り試験から得られた粘弾性材料ベルトの荷重（応力）−ひずみ特性を計算の初期値として予め定義するものである。機構解析モデルに、粘弾性材料ベルトの弾性体及び粘性体としての挙動を表現するため、図９に示したバネとダッシュポットによるモデルで表現する。前記式（１）におけるベルトの剛性係数マトリックス［ｋ］の初期値は前記図３に示した任意の引張り試験から得られたベルト荷重−ひずみ特性曲線を用いて定義する。
【００２０】
〔請求項５、１２に関する構成・動作〕
請求項５、１２に関する粘弾性材料ベルト特性解析方法における最適化手法にあっては、図１０の第１最適化ステップに示すような手順で解析を行う。ベルト荷重（応力）−ひずみ特性の初期値にシフト量係数をかけ、シフト量係数を設計変数として順次変化させ、前記算出された従動軸の回転量と時間との関係と計測された回転量と時間との関係とを比較し、各回転量データ差分の合計値を最小にすることによって、前記シフト量係数を決定する第一最適化ステップについて説明する。
【００２１】
まず、ベルト荷重（応力）−ひずみ特性の初期値にシフト量係数をかけ、シフト量係数を単因子実験変数として、例えば、１から３０（ベルトの物理特性の可能範囲）まで０．１間隔で順次変化させ、前記算出された従動軸の回転量と時間との関係（図４のＥ）と計測された回転量と時間との関係（図４のＤ）とを比較し、回転量データ差分の合計値を最小になる際、前記シフト量係数を決定する。この決定されたシフト量係数を第二最適化ステップの計算に持ち込む。
【００２２】
〔請求項６、１３に関する構成・動作〕
請求項６、１３に関する粘弾性材料ベルト特性解析方法における最適化手法にあっては、図１０の第二最適化ステップに示すような手順で解析を行う。機構解析モデルを用いて、前記シフト量係数をかけたベルト荷重（応力）−ひずみ特性における各荷重データを設計変数として反復して変化させ、前記算出された従動軸の回転量と時間との関係と計測された回転量と時間との関係とを比較し、各回転量データ差分の合計値を最小にすることによって、粘弾性材料ベルトの荷重（応力）−ひずみ特性を決定する第二最適化ステップについて説明する。
まず、前記シフト量係数をかけたベルト荷重（応力）−ひずみ特性における荷重値（ｘ）、および機構モデルから算出された従動軸の回転量と時間との関係と計測された回転量と時間との関係における各回転量データ差分の合計値（ｙ）の勾配を式２で計算し、これによって適切な探索方向を決定する。
【００２３】
【数１】

【００２４】
次に、決定された探索方向に沿って、新しい設計変数が設定され、算出された従動軸の回転量と時間との関係と計測された回転量と時間との関係における各回転量データ差分の合計値が最小になるまで上記計算を繰り返す。
【００２５】
〔請求項７、１４に関する構成・動作〕
請求項７、１４に関する粘弾性材料ベルト特性解析方法における荷重（応力）−ひずみ特性を決定する決定方法にあっては、前記シフト量係数をかけたベルト荷重（応力）−ひずみ特性における各荷重データを設計変数として反復して変化させる際、前記荷重（応力）−ひずみ特性において、各荷重がひずみ量の増加に伴い、単調増加の制約条件を設け、粘弾性材料ベルトの荷重（応力）−ひずみ特性を決定する計算を行う途中、制約条件の満足を常にチェックし、制約条件を満足するように粘弾性材料ベルトの荷重（応力）−ひずみ特性を決定する計算を繰り返すものである。
【００２６】
〔請求項１５に関する構成・動作〕
請求項１５に関する粘弾性材料ベルトの荷重（応力）−ひずみ特性を求める粘弾性材料特性解析システムの実施の形態について説明する。
図１１に本実施の形態による粘弾性材料ベルト荷重（応力）−ひずみ特性解析システムを示すブロック図である。
この解析システムは、前記実験装置２０、計測装置３０（計測装置５、９）、入力装置４０、演算装置５０、６０、７０及び表示装置８０で構成されている。実験装置２０は実験装置駆動手段を有し、計測装置３０は駆動軸、従動軸回転量と時間との関係計測手段を有し、演算装置５０は機構解析手段、演算装置６０は第一最適化手段、演算装置７０は第二最適化手段とベルト荷重（応力）−ひずみ特性決定手段をそれぞれ有している。前記各手段は予め各装置に組み込まれている。
【００２７】
実験装置は図７にも示すように、モータ１により回転する駆動軸２と、駆動軸２に取りつけたプーリ４と、従動軸６と、従動軸６に取りつけたプーリ８と、プーリ４、８間に掛け渡された粘弾性材料ベルト１０とで構成されている。計測装置３０は各軸の回転量と時間との関係を計測するもので、例えば、エンコーダで構成されている。演算装置５０〜７０は、例えば普通のＰＣで構成される。
【００２８】
まず、前記実験装置駆動手段により、所定の実験条件で実験装置を駆動し、次に、駆動軸２の回転量と時間との関係と従動軸６の回転量と時間との関係計測手段により、駆動軸２と従動軸６の回転量と時間との関係を計測装置３０で計測し、次に、計測された駆動軸２の回転量と時間との関係を入力装置４０により、演算装置５０〜７０に入力し、機構解析手段によりベルト荷重（応力）−ひずみ特性から、従動軸６の回転量と時間との関係を算出する。
【００２９】
次に、前記ベルト荷重（応力）−ひずみ特性決定手段により、機構解析モデルを用いて、ベルト荷重（応力）−ひずみ特性の初期値にシフト量係数をかけ、シフト量係数を単因子実験変数として順次に変化させ、前記算出された従動軸の回転量と時間との関係と計測された回転量と時間との関係とを比較し、各回転量データ差分の合計値を最小にになる際のシフト量係数を第二最適化手段の計算に持ち込む。そして前記ベルト荷重（応力）−ひずみ特性の初期値にシフト量係数をかけ、この曲線における各荷重データを設計変数として反復して変化させ、前記算出された従動軸の回転量と時間との関係と計測された回転量と時間との関係とを比較し、各データ差分の合計値を最小にする。これによって、粘弾性材料で構成されたベルトの荷重（応力）−ひずみ特性を決定し、最後に表示装置８０により決定されたベルトの荷重（応力）−ひずみ特性を表示する。
【００３０】
〔請求項１６に関する構成・動作〕
請求項１６に関する粘弾性材料特性解析システムにあっては、前記実験装置から、駆動軸の回転量と時間との関係と従動軸の回転量と時間との関係を駆動軸と従動軸の回転量と時間との関係計測手段により計測するものである。
【００３１】
〔請求項１７に関する構成・動作〕
請求項１７に関する粘弾性材料特性解析システムにあっては、前記計測された駆動軸の回転量と時間との関係を用いて、実験装置の機構解析モデルにより、ベルト荷重（応力）−ひずみ特性から、前記機構解析手段により従動軸の回転量と時間との関係を算出するものである。
【００３２】
〔請求項１８に関する構成・動作〕
請求項１８に関する粘弾性材料特性解析システムにあっては、機構解析モデルを用いて、ベルト荷重（応力）−ひずみ特性の初期値にシフト量係数をかけ、シフト量係数を設計変数として順次変化させ、前記算出された従動軸の回転量と時間との関係と計測された回転量と時間との関係とを比較し、各回転量データ差分の合計値を最小にすることによって、前記シフト量係数を決定する第一最適化計算手段と、この第一最適化計算手段で算出されたベルト荷重（応力）−ひずみ特性における各荷重データを設計変数として反復して変化させ、前記算出された従動軸の回転量と時間との関係と計測された回転量と時間との関係とを比較し、各回転量データ差分の合計値を最小にすることによって、粘弾性材料ベルトの荷重（応力）−ひずみ特性を決定する第二最適化計算手段により、粘弾性材料ベルトの荷重（応力）−ひずみ特性を決定するものである。
【００３３】
〔請求項１９、２０に関する構成・動作〕
請求項１９、２０に関するプログラム、記録媒体は、請求項１〜７のいずれかに記載の粘弾性材料ベルト荷重（応力）−ひずみ特性解析方法をコンピュータに実行させるためのプログラム及びこのプログラムを記録したコンピュータ読み取り可能な記録媒体である。この記録媒体としては、半導体記憶装置、磁気記録媒体、光記録媒体、光磁気記録媒体等を用いることができる。
【００３４】
【発明の効果】
請求項１、８の発明による粘弾性材料ベルト荷重（応力）−ひずみ特性解析装置、方法によれば、負荷が作用することにより発生する荷重（応力）−ひずみ特性を高精度に解析することができる。
請求項２、９の発明による粘弾性材料ベルト荷重（応力）−ひずみ特性解析装置、方法によれば、前記本発明の解析対象となる粘弾性材料ベルトを含む前記実験装置を構築し、解析のベースとする駆動軸と従動軸の回転量と時間との関係を計測装置により、計測することができる。
請求項３、１０の発明による粘弾性材料ベルト荷重（応力）−ひずみ特性解析装置、方法によれば、前記計測して得られた駆動軸の回転量と時間との関係を用いて、機構解析モデルにより、従動軸の回転量と時間との関係を計算することができる。
【００３５】
請求項４、１１の発明による粘弾性材料ベルト荷重（応力）−ひずみ特性解析装置、方法によれば、解析の初期状態を備えることができる。
請求項５、１２の発明による粘弾性材料ベルト荷重（応力）−ひずみ特性解析装置、方法によれば、大域最適解を探索することができる。
請求項６、１３の発明による粘弾性材料ベルト荷重（応力）−ひずみ特性解析装置、方法によれば、局部最適解を探索することができる。
請求項７、１４の発明による粘弾性材料ベルト荷重（応力）−ひずみ特性解析装置、方法によれば、粘弾性材料ベルト荷重（応力）−ひずみ特性を解析する際、荷重（応力）−ひずみ曲線の形を維持しながら解析を進めることができる。
【００３６】
請求項１５の発明による粘弾性材料ベルト荷重（応力）−ひずみ特性解析システムによれば、粘弾性材料ベルト荷重（応力）−ひずみ特性解析方法を用いて、解析することにより、負荷に応じた粘弾性材料ベルト荷重（応力）−ひずみ特性を解析することができる。
請求項１６の発明による粘弾性材料ベルト荷重（応力）−ひずみ特性解析システムによれば、実験装置駆動手段により実験装置を駆動し、計測手段により駆動軸と従動軸の回転量と時間との関係を計測することができる。
請求項１７の発明による粘弾性材料ベルト荷重（応力）−ひずみ特性解析システムによれば、機構解析手段により、所定の解析微少時間間隔で従動軸の回転量と時間との関係を計算することができる。
請求項１８の発明による粘弾性材料ベルト荷重（応力）−ひずみ特性解析システムによれば、第一最適化手段と第二最適化手段により、負荷による粘弾性材料ベルト荷重（応力）−ひずみ特性を決定することができる。
【００３７】
請求項１９、２０の発明によるプログラム及び記録媒体によれば、前記粘弾性材料ベルト荷重（応力）−ひずみ特性解析プログラムをコンピュータで実行することができ、また、このプログラムを記録した記録媒体によれば、前記各解析方法、手順を記録し、記録媒体を持ち運ぶことでプログラムの移動や更新を容易に行うことができる。
【図面の簡単な説明】
【図１】請求項１、８の発明に関する実施の形態による前記粘弾性材料ベルト特性の解析手順を示すフローチャートである。
【図２】請求項１、８の発明に関する実施の形態による前記駆動軸と従動軸の回転量と時間との関係曲線の計測結果を示す説明図である。
【図３】請求項１、８の発明に関する実施の形態によるベルト荷重（応力）−ひずみ特性の初期値を示す特性図である。
【図４】請求項１、８の発明に関する実施の形態による従動軸の回転量と時間との関係初期計算結果を示す特性図である。
【図５】請求項１、８の発明に関する実施の形態による従動軸の回転量と時間との関係最終計算結果を示す特性図である。
【図６】請求項１、８の発明に関する実施の形態によるベルト荷重（応力）−ひずみ特性の解析結果を示す特性図である。
【図７】請求項２、９の発明に関する実施の形態による実験装置の基本構成を示す構成図である。
【図８】請求項３、１０の発明に関する実施の形態による請求項３実施例に係る前記実験装置の機構モデルの概略を示す構成図である。
【図９】請求項４、１１の発明に関する実施の形態による粘弾性材料ベルトのモデル表現を示す構成図である。
【図１０】請求項５、１２の発明に関する実施の形態による粘弾性材料ベルト特性解析方法の最適化ステップを示す構成図である。
【図１１】請求項１５の発明に関する実施の形態による粘弾性材料ベルト特性解析システムを示す説明ブロック図である。
【符号の説明】
１モータ
２駆動軸
３駆動側負荷
４、８プーリ
５、９計測装置
６従動軸
７従動側負荷
１０ベルト
２０実験装置
３０計測装置
４０入力装置
５０、６０、７０演算装置
８０表示装置[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a viscoelastic material belt characteristic analysis method, apparatus, system, program, and recording medium for obtaining a load (stress) -strain characteristic of a viscoelastic material belt having nonlinear characteristics with high accuracy. It is applied to the case where drive transmission is performed using a timing belt made of materials, or the timing belt load (stress) -strain characteristic analysis using an optimization method when designing a drive system such as a copying machine. Is.
[0002]
[Prior art]
In general linear elastic materials, the Young's modulus, which is the ratio of stress to strain, is constant in the elastic deformation (linear) region. Therefore, the material constants such as the shape, dimensions, and Young's modulus of the structure, restraint conditions, and load By performing linear analysis using parameters such as conditions, the load (stress) -strain characteristics of the structure under various conditions can be obtained.
[0003]
[Problems to be solved by the invention]
However, when analyzing the load (stress) -strain characteristics of the viscoelastic material belt, the Young's modulus of the material changes as time progresses due to the influence of the belt's viscosity and the like, so only the Young's modulus is input. In some cases, the error in analysis calculation becomes large, and it is difficult to obtain the belt load (stress) -strain characteristics by predicting the change in Young's modulus due to the influence of viscosity.
Another problem is that the load (stress) -strain characteristics of the belt in the rapid start-up behavior of the drive mechanism or the load (stress) -strain characteristics of the belt in the micro-strain region cannot be accurately measured with an ordinary tensile testing machine. It was.
Also, there is a possibility that the optimum solution will fall locally in the multimodal solution space for the method of obtaining the load (stress) -strain characteristics of the belt by combining the experimental data and calculation data of the drive system by the optimization method. There is also a problem that the solution accuracy of the load (stress) -strain characteristic is low.
[0004]
Therefore, the present invention transmits a rotation of the drive shaft to the driven shaft through the belt from an experimental apparatus including a viscoelastic material belt and configured with a drive shaft and a driven shaft. Measure the relationship, and based on this, use the mechanism analysis model and use the optimization method to compare the driven shaft rotation amount experimental data with the analysis data, and then divide the search into a global optimal solution and a local optimal solution search It is an object of the present invention to provide a method and system capable of calculating the load (stress) -strain characteristics of the viscoelastic material belt efficiently in a short time so that the design variables are repeated and the two match. To do.
[0005]
[Means for Solving the Problems]
In order to achieve the above object, a viscoelastic material belt characteristic analyzing apparatus according to the present invention is a viscoelastic material belt characteristic analyzing apparatus that obtains a load (stress) -strain characteristic that is generated when an arbitrary load acts on a belt made of a viscoelastic material. An elastic material belt characteristic analysis device, comprising: tension generating means for generating an arbitrary tension on the belt by transmitting the rotation of the drive shaft to the driven shaft via the belt; and the rotation amount and time of the drive shaft. And the measurement means for measuring the relationship between the rotation amount of the driven shaft and the time, and the mechanism analysis model, so that the measured rotation amount of the drive shaft from the initial value of the belt load (stress) -strain characteristic A first computing means for calculating the relationship between the rotation amount of the driven shaft and time using the relationship with time, and multiplying the initial value of the belt load (stress) -strain characteristic by a shift amount coefficient; Sequentially changing the shift amount coefficient as a design variable, comparing the relationship between the rotation amount and time relationship between the measured rotation amount and time of the calculated driven shaft, At each time The first optimization means for determining the shift amount coefficient by minimizing the total difference of the rotation amounts, and the load (stress determined by the calculated shift amount coefficient using the mechanism analysis model )-Each load data in the strain characteristics is repeatedly changed as a design variable, and the relationship between the calculated rotation amount of the driven shaft and time is compared with the relationship between the measured rotation amount and time, At each time Second optimization means is provided for determining the load (stress) -strain characteristics of the belt by minimizing the total value of the difference in rotation amount.
[0006]
The viscoelastic material belt characteristic analyzing method according to the present invention is a viscoelastic material belt characteristic analyzing method for obtaining a load (stress) -strain characteristic generated by an arbitrary load acting on a belt made of a viscoelastic material. A step of generating an arbitrary tension on the belt by transmitting the rotation of the drive shaft to the driven shaft through the belt, the relationship between the rotation amount of the drive shaft and time, and the rotation amount of the driven shaft. The step of measuring the relationship between time and time, and using the mechanism analysis model, the driven shaft is measured using the relationship between the measured rotation amount of the drive shaft and time from the initial value of the belt load (stress) -strain characteristic. The step of calculating the relationship between the amount of rotation and the time, and multiplying the initial value of the belt load (stress) -strain characteristic by a shift amount coefficient, and sequentially changing the shift amount coefficient as a design variable It was to compare the relationship between the rotation amount and time relationship between the measured rotation amount and time of the calculated driven shaft, At each time Performing a first optimization to determine the shift amount coefficient by minimizing a total difference of rotation amounts, and using the mechanism analysis model, the load determined by the calculated shift amount coefficient Each load data in (stress) -strain characteristics is repeatedly changed as a design variable, and the relationship between the calculated amount of rotation of the driven shaft and time is compared with the relationship between the measured amount of rotation and time, At each time Performing a second optimization for determining the load (stress) -strain characteristics of the belt by minimizing the total value of the difference in rotation amount.
[0007]
Further, a viscoelastic material belt characteristic analysis system according to the present invention is the viscoelastic material belt characteristic analysis system for obtaining a load (stress) -strain characteristic of a belt made of a viscoelastic material, through the belt, An experimental device that transmits the behavior of the drive shaft to the driven shaft is provided, and a measuring device that can measure the relationship between the rotation amount and time of the drive shaft and the driven shaft of the experimental device is provided. The belt load is determined according to the mechanism model of the experimental apparatus using the measurement means for measuring the relationship and the relationship between the rotation amount of the driven shaft and the time, and the relationship between the rotation amount of the drive shaft and the time obtained by the measurement. Using the mechanism analysis means for calculating the relationship between the rotation amount of the driven shaft and time from the (stress) -strain characteristics, and the mechanism analysis model, a shift amount coefficient is added to the initial value of the belt load (stress) -strain characteristics. Multiply the shift amount Sequentially changing numbers as design variables, compares the relationship between the rotation amount and time relationship between the measured rotation amount and time of the calculated driven shaft, At each time Rotation amount of First optimization calculation means using a single factor experimental method for determining the shift amount coefficient by minimizing the total difference value, and calculation by the first optimization calculation means using the mechanism analysis model Each load data in the calculated belt load (stress) -strain characteristic is repeatedly changed as a design variable, and the relationship between the calculated amount of rotation of the driven shaft and time and the relationship between the measured amount of rotation and time Compare At each time Rotation amount of Second optimization calculation means is provided for determining the load (stress) -strain characteristic of the belt made of the viscoelastic material by minimizing the total value of the differences.
[0008]
The program according to the present invention is a program for causing a computer to execute the viscoelastic material belt load (stress) -strain characteristic analysis method.
[0009]
The recording medium according to the present invention is a computer-readable recording medium on which the program is recorded.
[0010]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described with reference to the drawings for each claim.
[Configuration / Operation of Claims 1, 8, 2, 9]
In the viscoelastic material belt characteristic analyzing apparatus and method according to the first and fifteenth aspects, the analysis is performed according to the procedure shown in the flowchart of FIG. A method for analyzing a load (stress) -strain characteristic generated when an arbitrary load (tension) acts on the viscoelastic material belt will be described.
[0011]
First, an experimental apparatus as a viscoelastic material belt characteristic analyzing apparatus according to claims 2 and 9 for executing this method will be described with reference to FIG. This device is an experimental device that transmits the behavior of a drive shaft to a driven shaft via a viscoelastic material belt.
On the drive side in FIG. 7, the drive shaft 2 that is rotationally driven by the motor 1 is provided with a drive shaft load 3, a pulley 4, and a measuring device 5. The measuring device 5 is a device that measures the relationship between the amount of rotation of the drive shaft 2 and time. On the driven side, the driven shaft 6 is provided with a driven shaft load 7, a pulley 8, and a measuring device 9. The measuring device 9 is a device that measures the relationship between the amount of rotation of the driven shaft 6 and time. As the measuring devices 5 and 9, for example, an encoder capable of measuring the relationship between the rotation amount and time can be used.
Between the pulley 4 and the pulley 8, a viscoelastic material belt 10 which is an object of an analysis experiment is stretched. In addition to this, it is assumed that a control device having a control program, an arithmetic device having a mechanism analysis model, and the like are provided in the present device.
[0012]
Next, a load (stress) -strain characteristic analysis method generated by the load of the viscoelastic material belt using this apparatus will be described with reference to FIG.
First, the drive shaft 2 is driven by the motor 1, the rotation is transmitted to the driven shaft 6 via the viscoelastic material belt 10, and the relationship between the rotation amount of the drive shaft and time is measured and measured by the measuring device 5. The relationship between the rotation amount of the driven shaft and time is measured by the device 9 (step S1, hereinafter, step is omitted). Next, a relationship curve (S2) between the measured rotation amount of the drive shaft 2 and time is input to a pre-constructed mechanism analysis model in the experimental apparatus, and an initial value of the belt load (stress) -strain characteristic ( From S3), an analysis is performed at predetermined minute time intervals using the mechanism analysis model, and the relationship between the amount of rotation of the driven shaft and time is calculated. This calculation method will be described later (S4, S5).
[0013]
Next, a shift amount coefficient is applied to the initial value of the belt load (stress) -strain characteristic, the shift amount coefficient is sequentially changed as a design variable, and the relationship between the calculated amount of rotation of the driven shaft and time is measured. The processing including the first optimization step for determining the shift amount coefficient is performed by comparing the relationship between the rotation amount and the time and minimizing the total value of the rotation amount data difference (S6, S7). . Next, the relationship between the rotation amount and time of the driven shaft multiplied by the shift amount coefficient is compared with the relationship between the measured rotation amount and time, and the total value of the driven shaft rotation amount data difference at each time interval is calculated. A process including a second optimization step of repeatedly changing each load data in the belt load (stress) -strain characteristic as a design variable using the mechanism analysis model so as to minimize the design data. By executing (S8, S9, S10, S3 to S9), the load (stress) -strain characteristic of the belt made of the viscoelastic material is determined (S11).
[0014]
Next, the viscoelastic material belt characteristic analysis method according to the present embodiment will be described using a specific analysis example.
First, the relationship between the amount of rotation (rotational speed) of the drive shaft 2 and time is measured by the measuring device 5 to obtain the curve A in FIG. Further, the relationship between the amount of rotation (rotational speed) of the driven shaft 6 and time is measured by the measuring device 9 to obtain a curve B in FIG. Next, an initial value C of a belt load (stress) -strain characteristic curve as shown in FIG. 3 is input to the mechanism analysis model, and using this initial value and the curve A, the rotation amount and time of the driven shaft 6 are determined. Calculate the relationship. The calculation result is shown by a curve D in FIG.
[0015]
Next, the initial value C of the belt load (stress) -strain characteristic is multiplied by a shift amount coefficient, and the shift amount coefficient is set as a single factor experimental variable, for example, from 1 to 30 (possible range of physical characteristics of the belt). The relationship between the calculated amount of rotation of the driven shaft 6 and time (D in FIG. 4) and the relationship between the measured amount of rotation of the driven shaft 6 and time (curve E in FIG. 4) is changed sequentially at intervals. And the shift amount coefficient is determined when the total value of the rotation amount data differences is minimized. Next, the determined shift amount coefficient is applied to the initial value C of the belt load (stress) -strain characteristic curve, and the relationship between the rotation amount of the driven shaft 6 and time and the relationship between the measured rotation amount and time are obtained. In comparison, each load value point in the belt load (stress) -strain characteristic curve multiplied by the shift amount coefficient so as to minimize the total difference of the driven shaft rotation amount data in each time interval as a design variable, The load (stress) -strain characteristic of the viscoelastic material belt is determined by repeatedly changing under the constraint conditions.
[0016]
FIG. 5 shows the calculated value (curve F) of the relationship curve between the rotation amount of the driven shaft 6 and time when the calculation converges (curve F), and the measured value (curve G) of the relationship curve between the rotation amount of the driven shaft 6 and time. A comparison is shown.
FIG. 6 shows a comparison between the load (stress) -strain characteristic (curve H) of the viscoelastic material belt finally determined and the initial value (curve I) of the load (stress) -strain characteristic curve of the belt.
[0017]
[Configuration and operation of claims 3 and 10]
11. A mechanism analysis model in the viscoelastic material belt characteristic analysis method according to claim 3, wherein a belt load (stress) -strain is determined by a mechanism analysis model using a relationship between the measured rotation amount of the drive shaft 2 and time. A method for calculating the relationship between the rotation amount of the driven shaft 6 and time from the initial value of the characteristic will be described.
First, in contrast to the experimental apparatus, a mechanism analysis model is constructed based on the equation of motion of the following equation (1).
[J] [dθ ² / D ² t] + [C] [dθ / dt] + [k] [θ] = [T] (1)
However,
[J]: Inertia moment matrix including each moment of inertia
[K]: Spring stiffness matrix including belt stiffness coefficient
[C]: Spring viscosity matrix including belt viscosity coefficient
[Θ]: Rotation angle vector including rotation angle of drive shaft and driven shaft
[T]: Torque vector
[0018]
A schematic diagram of the experimental device mechanism analysis model is shown in FIG. The relationship between the measured rotation amount of the drive shaft 2 and time is input to the mechanism analysis model, and the relationship between the rotation amount of the driven shaft 6 and time is calculated from the initial value of the belt load (stress) -strain characteristic.
[0019]
[Configuration and operation of claims 4 and 11]
In the mechanism analysis model in the viscoelastic material belt characteristic analysis method according to claims 4 and 11, the load (stress) -strain characteristic of the viscoelastic material belt obtained from the arbitrary tensile test is preliminarily used as an initial value for calculation. To define. In order to express the behavior of the viscoelastic material belt as an elastic body and a viscous body in the mechanism analysis model, the mechanism analysis model is represented by a model using a spring and a dashpot shown in FIG. The initial value of the belt stiffness coefficient matrix [k] in the equation (1) is defined using the belt load-strain characteristic curve obtained from the arbitrary tensile test shown in FIG.
[0020]
[Configuration and operation of claims 5 and 12]
In the optimization method in the viscoelastic material belt characteristic analysis method according to the fifth and twelfth aspects, the analysis is performed according to the procedure shown in the first optimization step of FIG. The initial value of the belt load (stress) -strain characteristic is multiplied by a shift amount coefficient, the shift amount coefficient is sequentially changed as a design variable, and the relationship between the calculated rotation amount of the driven shaft and time and the measured rotation amount A first optimization step for determining the shift amount coefficient by comparing the relationship with time and minimizing the total value of the respective rotation amount data differences will be described.
[0021]
First, the initial value of the belt load (stress) -strain characteristic is multiplied by a shift amount coefficient, and the shift amount coefficient is set as a single factor experimental variable, for example, at intervals of 0.1 from 1 to 30 (the possible range of physical characteristics of the belt). By sequentially changing, the relationship between the calculated rotation amount of the driven shaft and time (E in FIG. 4) and the relationship between the measured rotation amount and time (D in FIG. 4) are compared, and the rotation amount data difference When the total value is minimized, the shift amount coefficient is determined. This determined shift amount coefficient is brought into the calculation of the second optimization step.
[0022]
[Configuration / Operation of Claims 6 and 13]
In the optimization method in the viscoelastic material belt characteristic analysis method according to claims 6 and 13, the analysis is performed according to the procedure shown in the second optimization step of FIG. Using a mechanism analysis model, each load data in the belt load (stress) -strain characteristic multiplied by the shift amount coefficient is repeatedly changed as a design variable, and the relationship between the calculated amount of rotation of the driven shaft and time 2nd optimization to determine the load (stress) -strain characteristics of viscoelastic material belt by comparing the relationship between measured rotation amount and time and minimizing the total value of each rotation amount data difference The steps will be described.
First, the load value (x) in the belt load (stress) -strain characteristic multiplied by the shift amount coefficient, the relationship between the rotation amount of the driven shaft calculated from the mechanism model and time, the measured rotation amount and time, The gradient of the total value (y) of the respective rotation amount data differences in the relationship is calculated by Equation 2, thereby determining an appropriate search direction.
[0023]
[Expression 1]

[0024]
Next, a new design variable is set along the determined search direction, and each rotation amount data difference in the relationship between the calculated rotation amount of the driven shaft and time and the relationship between the measured rotation amount and time is calculated. Repeat the above calculation until the total value is minimized.
[0025]
[Configuration and operation of claims 7 and 14]
In the determination method for determining the load (stress) -strain characteristic in the viscoelastic material belt characteristic analysis method according to claim 7 or 14, each load data in the belt load (stress) -strain characteristic multiplied by the shift amount coefficient. In the load (stress) -strain characteristics, each load has a monotonically increasing constraint condition as the strain amount increases, and the load (stress) -strain of the viscoelastic material belt During the calculation for determining the characteristics, the satisfaction of the constraint condition is always checked, and the calculation for determining the load (stress) -strain characteristic of the viscoelastic material belt so as to satisfy the constraint condition is repeated.
[0026]
[Configuration / Operation of Claim 15]
An embodiment of a viscoelastic material property analysis system for obtaining a load (stress) -strain property of a viscoelastic material belt according to claim 15 will be described.
FIG. 11 is a block diagram showing a viscoelastic material belt load (stress) -strain characteristic analysis system according to the present embodiment.
This analysis system is composed of the experimental device 20, the measurement device 30 (measurement devices 5 and 9), the input device 40, the

arithmetic devices

50, 60 and 70, and the display device 80. The experimental apparatus 20 has experimental apparatus driving means, the measuring apparatus 30 has measuring means for measuring the relationship between the drive shaft and the amount of rotation of the driven shaft and time, the arithmetic apparatus 50 is mechanism analysis means, and the arithmetic apparatus 60 is first optimized. The means 70 includes a second optimization means and a belt load (stress) -strain characteristic determination means. Each means is incorporated in each device in advance.
[0027]
As shown in FIG. 7, the experimental apparatus includes a drive shaft 2 rotated by a motor 1, a pulley 4 attached to the drive shaft 2, a driven shaft 6, a pulley 8 attached to the driven shaft 6, and pulleys 4, 8 It is comprised with the viscoelastic material belt 10 hung between. The measuring device 30 measures the relationship between the amount of rotation of each axis and time, and is composed of, for example, an encoder. The arithmetic devices 50 to 70 are configured by, for example, ordinary PCs.
[0028]
First, the experimental apparatus is driven by the experimental apparatus driving means under predetermined experimental conditions, and then the relationship between the rotation amount of the drive shaft 2 and time and the relationship between the rotation amount of the driven shaft 6 and time is measured by the measurement means. The relationship between the rotation amount and time of the drive shaft 2 and the driven shaft 6 is measured by the measuring device 30, and then the relationship between the measured rotation amount of the drive shaft 2 and time is calculated by the input device 40 using the arithmetic devices 50 to 50. Then, the relationship between the rotation amount of the driven shaft 6 and time is calculated from the belt load (stress) -strain characteristic by the mechanism analysis means.
[0029]
Next, the belt load (stress) -strain characteristic determining means uses a mechanism analysis model to multiply the initial value of the belt load (stress) -strain characteristic by a shift amount coefficient, and the shift amount coefficient is used as a single factor experimental variable. By sequentially changing, the relationship between the calculated rotation amount of the driven shaft and time and the relationship between the measured rotation amount and time are compared, and the total value of each rotation amount data difference is minimized. The shift amount coefficient is brought into the calculation of the second optimization means. Then, the initial value of the belt load (stress) -strain characteristic is multiplied by a shift amount coefficient, each load data in this curve is repeatedly changed as a design variable, and the relationship between the calculated amount of rotation of the driven shaft and time is calculated. And the relationship between the measured rotation amount and time, and the total value of each data difference is minimized. Thus, the load (stress) -strain characteristic of the belt made of the viscoelastic material is determined, and finally, the load (stress) -strain characteristic of the belt determined by the display device 80 is displayed.
[0030]
[Configuration and operation of claim 16]
In the viscoelastic material characteristic analysis system according to claim 16, from the experimental apparatus, the relationship between the rotation amount of the drive shaft and time, the relationship between the rotation amount of the driven shaft and time, and the rotation amount of the drive shaft and the driven shaft. It is measured by means for measuring the relationship between time and time.
[0031]
[Configuration / Operation of Claim 17]
In the viscoelastic material characteristic analysis system according to claim 17, the belt load (stress) -strain characteristic is determined by a mechanism analysis model of an experimental apparatus using the relationship between the measured rotation amount of the drive shaft and time. The mechanism analysis means calculates the relationship between the amount of rotation of the driven shaft and time.
[0032]
[Configuration / Operation of Claim 18]
In the viscoelastic material characteristic analysis system according to claim 18, a shift amount coefficient is applied to the initial value of the belt load (stress) -strain characteristic using a mechanism analysis model, and the shift amount coefficient is sequentially changed as a design variable. The shift amount coefficient is determined by comparing the relationship between the calculated rotation amount of the driven shaft and time and the relationship between the measured rotation amount and time, and minimizing the total value of each rotation amount data difference. A first optimization calculating means for determining the load, and each load data in the belt load (stress) -strain characteristic calculated by the first optimization calculating means is repeatedly changed as a design variable, and the calculated driven shaft By comparing the relationship between the amount of rotation and time and the relationship between the measured amount of rotation and time, and minimizing the total value of each rotation amount data difference, the load (stress) -strain of the viscoelastic material belt Characteristic The second optimization calculation means for determining a load (stress) of the viscoelastic material belt - is what determines the distortion characteristics.
[0033]
[Configuration and operation of claims 19 and 20]
A program and a recording medium according to claims 19 and 20 are recorded with a program for causing a computer to execute the viscoelastic material belt load (stress) -strain characteristic analysis method according to any one of claims 1 to 7 and the program. A computer-readable recording medium. As this recording medium, a semiconductor storage device, a magnetic recording medium, an optical recording medium, a magneto-optical recording medium, or the like can be used.
[0034]
【The invention's effect】
According to the viscoelastic material belt load (stress) -strain characteristic analysis apparatus and method according to the first and eighth aspects of the invention, the load (stress) -strain characteristic generated when the load is applied can be analyzed with high accuracy. it can.
According to the viscoelastic material belt load (stress) -strain characteristic analysis apparatus and method according to the inventions of claims 2 and 9, the experimental apparatus including the viscoelastic material belt to be analyzed according to the present invention is constructed and analyzed. The relationship between the amount of rotation of the drive shaft and the driven shaft as a base and time can be measured by the measuring device.
According to the viscoelastic material belt load (stress) -strain characteristic analysis apparatus and method according to the third and tenth aspects of the invention, the mechanism analysis is performed using the relationship between the rotation amount of the drive shaft and the time obtained by the measurement. With the model, the relationship between the amount of rotation of the driven shaft and time can be calculated.
[0035]
According to the viscoelastic material belt load (stress) -strain characteristic analysis apparatus and method according to the inventions of claims 4 and 11, an initial state of analysis can be provided.
According to the viscoelastic material belt load (stress) -strain characteristic analysis apparatus and method according to the inventions of claims 5 and 12, a global optimum solution can be searched.
According to the viscoelastic material belt load (stress) -strain characteristic analysis device and method according to the inventions of claims 6 and 13, a local optimum solution can be searched.
According to the viscoelastic material belt load (stress) -strain characteristic analyzing apparatus and method according to the inventions of claims 7 and 14, when analyzing the viscoelastic material belt load (stress) -strain characteristic, a load (stress) -strain curve is obtained. The analysis can proceed while maintaining the shape of.
[0036]
According to the viscoelastic material belt load (stress) -strain characteristic analysis system according to the invention of claim 15, the viscoelastic material belt load (stress) -strain characteristic analysis method is used to analyze the viscosity according to the load. Elastic material belt load (stress) -strain characteristics can be analyzed.
According to the viscoelastic material belt load (stress) -strain characteristic analysis system of the sixteenth aspect of the present invention, the experimental device is driven by the experimental device driving means, and the relationship between the rotation amount of the drive shaft and the driven shaft and the time by the measuring device. Can be measured.
According to the viscoelastic material belt load (stress) -strain characteristic analysis system according to the seventeenth aspect of the present invention, the mechanism analysis means can calculate the relationship between the rotation amount of the driven shaft and the time at predetermined analysis minute time intervals. it can.
According to the viscoelastic material belt load (stress) -strain characteristic analysis system according to the invention of claim 18, the viscoelastic material belt load (stress) -strain characteristic due to the load is obtained by the first optimization means and the second optimization means. Can be determined.
[0037]
According to the program and the recording medium of the inventions of claims 19 and 20, the viscoelastic material belt load (stress) -strain characteristic analysis program can be executed by a computer, and the recording medium on which the program is recorded is used. For example, it is possible to easily move and update the program by recording each analysis method and procedure and carrying the recording medium.
[Brief description of the drawings]
FIG. 1 is a flowchart showing an analysis procedure of the viscoelastic material belt characteristics according to an embodiment relating to the first and eighth aspects of the invention;
FIG. 2 is an explanatory diagram showing a measurement result of a relationship curve between rotation amounts of the drive shaft and the driven shaft and time according to an embodiment relating to the first and eighth aspects of the present invention;
FIG. 3 is a characteristic diagram showing initial values of belt load (stress) -strain characteristics according to the embodiments of the first and eighth aspects of the invention.
FIG. 4 is a characteristic diagram showing an initial calculation result of the relationship between the amount of rotation of the driven shaft and time according to the embodiment relating to the first and eighth aspects of the present invention;
FIG. 5 is a characteristic diagram showing a final calculation result of the relationship between the amount of rotation of the driven shaft and time according to the embodiment relating to the first and eighth aspects of the present invention;
FIG. 6 is a characteristic diagram showing an analysis result of a belt load (stress) -strain characteristic according to an embodiment relating to the first and eighth aspects of the invention.
FIG. 7 is a configuration diagram showing a basic configuration of an experimental apparatus according to an embodiment relating to the second and ninth aspects of the invention;
FIG. 8 is a block diagram showing an outline of a mechanism model of the experimental apparatus according to claim 3 according to the embodiments of claims 3 and 10;
FIG. 9 is a structural diagram showing a model representation of a viscoelastic material belt according to an embodiment related to the inventions of claims 4 and 11;
FIG. 10 is a block diagram showing optimization steps of a viscoelastic material belt characteristic analysis method according to an embodiment relating to the inventions of claims 5 and 12;
FIG. 11 is an explanatory block diagram showing a viscoelastic material belt characteristic analysis system according to an embodiment relating to the invention of claim 15;
[Explanation of symbols]
1 Motor
2 Drive shaft
3 Driving load
4, 8 pulley
5, 9 Measuring device
6 Driven shaft
7 Driven load
10 belt
20 Experimental equipment
30 Measuring device
40 input devices
50, 60, 70 arithmetic unit
80 Display device

Claims

A viscoelastic material belt characteristic analyzer for obtaining a load (stress) -strain characteristic generated by an arbitrary load acting on a belt composed of a viscoelastic material,
Tension generating means for generating an arbitrary tension on the belt by transmitting the rotation of the drive shaft to the driven shaft via the belt;
Measuring means for measuring the relationship between the rotation amount of the drive shaft and time and the relationship between the rotation amount of the driven shaft and time;
By using the mechanism analysis model, the relationship between the rotation amount of the driven shaft and time is calculated from the initial value of the belt load (stress) -strain characteristic using the measured relationship between the rotation amount of the drive shaft and time. First computing means;
The initial value of the belt load (stress) -strain characteristic is multiplied by a shift amount coefficient, the shift amount coefficient is sequentially changed as a design variable, and the relationship between the calculated rotation amount of the driven shaft and time and the measured rotation amount First optimization means for determining the shift amount coefficient by comparing the relationship between the time and the time, and minimizing the total value of the difference in rotation amount at each time ;
Using the mechanism analysis model, each load data in the load (stress) -strain characteristic determined by the calculated shift amount coefficient is repeatedly changed as a design variable, and the calculated amount of rotation of the driven shaft and The load (stress) -strain characteristics of the belt are determined by comparing the relationship between time and the relationship between the measured rotation amount and time and minimizing the total difference in rotation amount at each time. A viscoelastic material belt characteristic analysis device comprising a second optimization means.

Pulleys are respectively provided on the drive shaft and the driven shaft in the tension generating means, the belt is stretched over each pulley, the drive shaft is driven to rotate by a motor, and this rotation is driven by the driven shaft via the belt. 2. The viscoelastic material belt characteristic analyzer according to claim 1, wherein the measuring device measures a relationship between a rotation amount and a time for each of the drive shaft and the driven shaft.

Using the measured relationship between the rotation amount of the drive shaft and time, the mechanism analysis model calculates the relationship between the rotation amount of the driven shaft and time from the initial value of the belt load (stress) -strain characteristic. The viscoelastic material belt characteristic analyzer according to claim 1 or 2.

The viscosity according to claim 1, 2, or 3, wherein in the structural analysis model, a load (stress) -strain characteristic of the belt obtained from an arbitrary tensile test is defined in advance as the initial value of the calculation. Elastic material belt characteristic analyzer.

The first optimization unit multiplies the initial value of the belt load (stress) -strain characteristic by a shift amount coefficient, sequentially changes the shift amount coefficient as a design variable, and calculates the calculated rotation amount and time of the driven shaft. The shift amount coefficient is determined by comparing the relationship between the rotation amount and the relationship between the measured rotation amount and time and minimizing the total value of the rotation amount differences at each time. The viscoelastic material belt characteristic analysis device according to any one of -4.

The second optimization means repeatedly calculates the load value in the belt load (stress) -strain characteristic multiplied by the shift amount coefficient as a design variable using the mechanism analysis model, and calculates the calculated value. By comparing the relationship between the amount of rotation of the driven shaft and time and the relationship between the measured amount of rotation and time, and minimizing the total difference in the amount of rotation at each time , the load (stress) of the belt 6. The viscoelastic material belt characteristic analyzer according to claim 5, wherein a strain characteristic is determined.

When each load data in the belt load (stress) -strain characteristic multiplied by the shift amount coefficient is repeatedly changed as a design variable, in the load (stress) -strain characteristic, each load increases with the amount of strain. The viscoelastic material belt characteristic analyzing apparatus according to claim 6, wherein a constraint condition for monotonically increasing is provided.

A viscoelastic material belt characteristic analysis method for obtaining a load (stress) -strain characteristic generated by an arbitrary load acting on a belt made of a viscoelastic material,
Generating an arbitrary tension on the belt by transmitting the rotation of the drive shaft to the driven shaft via the belt;
Measuring the relationship between the rotation amount of the drive shaft and time and the relationship between the rotation amount of the driven shaft and time;
By using the mechanism analysis model, the relationship between the rotation amount of the driven shaft and time is calculated from the initial value of the belt load (stress) -strain characteristic using the measured relationship between the rotation amount of the drive shaft and time. Steps,
The initial value of the belt load (stress) -strain characteristic is multiplied by a shift amount coefficient, the shift amount coefficient is sequentially changed as a design variable, and the relationship between the calculated rotation amount of the driven shaft and time and the measured rotation amount Performing a first optimization to determine the shift amount coefficient by comparing the relationship between the time and the time, and minimizing the total difference of the rotation amount at each time ;
Using the mechanism analysis model, each load data in the load (stress) -strain characteristic determined by the calculated shift amount coefficient is repeatedly changed as a design variable, and the calculated rotation amount of the driven shaft and The load (stress) -strain characteristics of the belt are determined by comparing the relationship between time and the relationship between the measured rotation amount and time and minimizing the total difference in rotation amount at each time. A viscoelastic material belt characteristic analysis method, comprising: a step of performing second optimization.

A pulley is provided on each of the drive shaft and the driven shaft, the belt is stretched over each pulley, the drive shaft is driven to rotate by a motor, and the rotation is transmitted to the driven shaft via the belt. 9. The viscoelastic material belt characteristic analysis method according to claim 8, wherein a relationship between a rotation amount and time is measured for each of the drive shaft and the driven shaft.

Using the measured relationship between the rotation amount of the drive shaft and time, the mechanism analysis model calculates the relationship between the rotation amount of the driven shaft and time from the initial value of the belt load (stress) -strain characteristic. The viscoelastic material belt characteristic analysis method according to claim 8 or 9, wherein

The viscosity according to claim 8, 9 or 10, wherein in the structural analysis model, a load (stress) -strain characteristic of the belt obtained from an arbitrary tensile test is defined in advance as the initial value of the calculation. Elastic material belt characteristics analysis method.

In the first optimization, a shift amount coefficient is applied to the initial value of the belt load (stress) -strain characteristic, the shift amount coefficient is sequentially changed as a design variable, and the calculated rotation amount and time of the driven shaft are calculated. by the relationship is compared with the relationship between that has been rotated amount and time measurement, the total value of the difference between the rotation amount at each time to minimize claim 8, characterized by determining the shift amount coefficient The viscoelastic material belt characteristic analysis method according to any one of ˜11.

In the second optimization, using the mechanism analysis model, each load value in the belt load (stress) -strain characteristic multiplied by the shift amount coefficient is repeatedly changed as a design variable, and the calculation is performed. By comparing the relationship between the amount of rotation of the driven shaft and time and the relationship between the measured amount of rotation and time, and minimizing the total difference in the amount of rotation at each time , the load (stress) of the belt The method for analyzing viscoelastic material belt characteristics according to claim 12, wherein the strain characteristics are determined.

When each load data in the belt load (stress) -strain characteristic multiplied by the shift amount coefficient is repeatedly changed as a design variable, in the load (stress) -strain characteristic, each load increases with the amount of strain. The viscoelastic material belt characteristic analysis method according to claim 13, wherein a constraint condition for monotonically increasing is provided.

The viscoelastic material belt characteristic analysis system for obtaining a load (stress) -strain characteristic of a belt made of a viscoelastic material,
An experimental device that transmits the behavior of the drive shaft to the driven shaft via the belt is provided, and a measurement device that can measure the relationship between the rotation amount and time of the drive shaft and the driven shaft of the experimental device is provided. Measuring means for measuring the relationship between the amount of rotation and time and the relationship between the amount of rotation of the driven shaft and time;
Using the relationship between the amount of rotation of the drive shaft obtained by the measurement and time, the relationship between the amount of rotation of the driven shaft and time is determined from the belt load (stress) -strain characteristics by the mechanism model of the experimental apparatus. A mechanism analysis means for calculating;
Using the mechanism analysis model, a shift amount coefficient is applied to the initial value of the belt load (stress) -strain characteristic, the shift amount coefficient is sequentially changed as a design variable, and the calculated rotation amount and time of the driven shaft are calculated. And the relationship between the measured rotation amount and the time, and by using the single factor experiment method for determining the shift amount coefficient by minimizing the total difference of the rotation amount at each time . An optimization calculation means;
Using the mechanism analysis model, each load data in the belt load (stress) -strain characteristic calculated by the first optimization calculation means is repeatedly changed as a design variable, and the calculated rotation amount of the driven shaft The load of the belt made of the viscoelastic material (by comparing the relationship between the rotation time and the measured rotation amount and the time and minimizing the total difference in the rotation amount at each time ( A second optimization calculation means for determining (stress) -strain characteristics, and a viscoelastic material belt characteristic analysis system.

Rotating the drive shaft by the motor, attaching a pulley to the drive shaft, turning the belt to the pulley, driving the driven shaft pulley by the belt, and rotating the driven shaft, the experimental device drive means in the transmission belt experimental device Provided with a measuring device capable of measuring the relationship between the rotation amount and the time on the drive shaft and the driven shaft from the experimental device, the relationship between the rotation amount and the time of the drive shaft, the rotation amount and the time of the driven shaft, The viscoelastic material belt characteristic analysis system according to claim 15, further comprising a measuring unit that measures the relationship between the viscoelastic material belt and the belt.

Using the relationship between the amount of rotation of the drive shaft obtained by the measurement and the time, the relationship between the amount of rotation of the driven shaft and the time is calculated from the belt load (stress) -strain characteristics by the mechanism analysis model of the experimental apparatus. 17. The viscoelastic material belt characteristic analysis system according to claim 15 or 16, further comprising a mechanism analysis unit for calculating.

Using the mechanism analysis model, a shift amount coefficient is applied to the initial value of the belt load (stress) -strain characteristic, the shift amount coefficient is sequentially changed as a design variable, and the calculated rotation amount and time of the driven shaft are calculated. by the relationship is compared with the relationship between that has been rotated amount and time measurement, the total value of the difference between the rotation amount at each time to minimize the first optimization calculation means for determining the shift amount coefficient, Each load data in the belt load (stress) -strain characteristic calculated by the first optimization calculating means is repeatedly changed as a design variable, and the relationship between the calculated amount of rotation of the driven shaft and time is measured. The relationship between the rotation amount and time is compared, and the total value of the difference in rotation amount at each time is minimized to determine the load (stress) -strain characteristic of the belt made of the viscoelastic material. Second most Viscoelastic material belt characterization system according to claim 15, characterized in that it comprises a reduction calculation section.

The program for making a computer perform the viscoelastic material belt load (stress) -strain characteristic analysis method in any one of Claims 8-14.

A computer-readable recording medium on which the program according to claim 19 is recorded.