JP3788231B2 - Evaluation method for radial vibration of rotating body and evaluation apparatus for radial vibration of rotating body - Google Patents

Description

上記式（２）において、｜Ａ｜は複素数Ａの絶対値であり、Ｘ_h ^*及びＹ_h ^*は複素数Ｘ_h及びＹ_hの共役であり、且つＲｅ（Ｂ）は複素数Ｂの実数部である。
【００２３】
このとき、ｘ（ｔ）,ｙ（ｔ）のＮ点の離散値系列が実数値の系列であれば、方位θの径方向振動ｆ（ｔ,θ）の離散値系列｛ｆ（ｎΔｔ,θ）、ｎ＝０,１,…Ｎ−１｝も実数値の系列となるので、周波数点ｈにおける方位θの径方向振動ｆ（ｔ,θ）の周波数サンプル値のＲＭＳ振幅値（Root Mean Square）は２^1/2｜Ｆ_h（θ）｜であり、上記式（２）に基づいて周波数点ｈにおける方位θの径方向振動ｆ（ｔ,θ）の周波数サンプル値のＲＭＳ振幅値は下記式（３）で表される。
【００２４】

この周波数点ｈにおける方位θの径方向振動ｆ（ｔ,θ）の周波数サンプル値のＲＭＳ振幅値を、回転体の径方向振動の周波数点ｈにおける方位θの振幅として算出した後、本処理を終了する。
【００２５】
このとき、回転体の回転方向の全方位に亘って算出された周波数点ｈにおける径方向振動ｆ（ｔ,θ）の周波数サンプル値のＲＭＳ振幅値の中から選択された最大のＲＭＳ振幅値をＮＲＲＯ振動成分の評価におけるＲＭＳ評価値とし、このＲＭＳ評価値を呈する方位θを最大方位θ_maxとする。
【００２６】
また、好ましくは、前記回転体の回転方向における０〜πの方位を細分化した各方位毎に前記所定の周波数に対応する前記２方向の周波数スペクトルに基づいて前記径方向振動の振幅を算出し、該算出された各方位の振幅から前記最大振幅を選択するのがよい。
【００２７】
例えば、回転体の特定の周波数の径方向振動の方位θにおける振幅として、周波数点ｈにおける回転体の回転方向をＭ個に分割したときの方位２ｊπ／Ｍの径方向振動ｆ（ｔ,２ｊπ／Ｍ）の周波数サンプル値のＲＭＳ振幅値を算出するとき、この周波数点ｈにおける方位２ｊπ／Ｍの径方向振動ｆ（ｔ,２ｊπ／Ｍ）の周波数サンプル値のＲＭＳ振幅値は、下記式（４）で表される。
【００２８】

上記式（４）では、方位２ｊπ／Ｍ＝０〜πと方位２（ｊ＋Ｍ／２）π／Ｍ＝２ｊπ／Ｍ＋π＝π〜２πにおいて周波数サンプル値の絶対値｜Ｆ_h（２ｊπ／Ｍ）｜と｜Ｆ_h（２ｊπ／Ｍ＋π）｜は等しいので、方位２ｊπ／Ｍの径方向振動ｆ（ｔ,２ｊπ／Ｍ）の周波数サンプル値のＲＭＳ振幅値は方位２ｊπ／Ｍ＝０〜πで算出すれば十分である。その結果、方位２ｊπ／Ｍの径方向振動ｆ（ｔ,２ｊπ／Ｍ）の周波数サンプル値のＲＭＳ振幅値を回転体の回転方向の全周に亘って算出する必要を無くすことができるので、計算時間をより短縮することができる。
【００２９】
このとき、回転体の回転方向の方位２ｊπ／Ｍ＝０〜πに亘って算出された周波数点ｈにおける径方向振動ｆ（ｔ,２ｊπ／Ｍ）の周波数サンプル値のＲＭＳ振幅値の中から選択された最大のＲＭＳ振幅値をＲＭＳ評価値とし、このＲＭＳ評価値を呈する方位２ｊπ／Ｍを最大方位θ_maxとする。
【００３０】
さらに好ましくは、前記回転体の回転方向における０〜π／２の方位を細分化した各方位毎に前記所定の周波数に対応する前記２方向の周波数スペクトルに基づいて前記径方向振動の振幅を算出し、該算出された各方位の振幅から前記最大振幅を選択するのがよい。
【００３１】
例えば、方位２ｊπ／Ｍをπ／２進めた方位（２ｊπ／Ｍ＋π／２）におけるＲＭＳ振幅値は、ｃｏｓ（２ｊπ／Ｍ）の代わりに−ｓｉｎ（２ｊπ／Ｍ）を、ｓｉｎ（２ｊπ／Ｍ）の代わりにｃｏｓ（２ｊπ／Ｍ）を上記式（４）に代入すれば、下記式（５）で表される。
【００３２】

従って、上記式（４）及び上記式（５）を用いれば、方位２ｊπ／Ｍ＝０〜π／２におけるｓｉｎ（２ｊπ／Ｍ）及びｃｏｓ（２ｊπ／Ｍ）を算出するだけで、方位２ｊπ／Ｍ＝０〜πにおける周波数点ｈの径方向振動ｆ（ｔ,２ｊπ／Ｍ）の周波数サンプル値のＲＭＳ振幅値を算出することができるので、方位２ｊπ／Ｍの径方向振動ｆ（ｔ,２ｊπ／Ｍ）の周波数サンプル値のＲＭＳ振幅値を回転体の回転方向の半周に亘って算出する必要を無くし、計算時間をさらに短縮することができる。
【００３３】
また、好ましくは、前記径方向振動の最大振幅と、前記最大振幅を呈する方位とを前記２方向の周波数スペクトル及び三角関数の加法定理に基づいて導出するのがよい。
【００３４】
ここで、本発明の径方向振動の最大振幅と、最大振幅を呈する方位とを２方向の周波数スペクトル及び三角関数の加法定理に基づいて導出する最大振幅導出処理について説明する。
【００３５】
本発明の最大振幅導出処理において、上記式（２）は、ａ_h＝（｜Ｘ_h｜²＋｜Ｙ_h｜²）／２、ｂ_h＝（｜Ｘ_h｜²−｜Ｙ_h｜²）／２及びｃ_h＝（Ｘ_hＹ_h ^*＋Ｙ_hＸ_h ^*）／２＝Ｒｅ（Ｘ_hＹ_h ^*）を用いて下記式（６）で表される。
【００３６】

上記式（６）において、φ_h＝ｔａｎ^-1（ｃ_h／ｂ_h）である。従って、上記式（６）より、周波数サンプル値の２乗｜Ｆ_h（θ）｜²が最大値となる最大方位θ_maxは下記式（７）で表される。
【００３７】
θ_max＝φ_h／２
＝［ｔａｎ^-1 [ Ｒｅ（Ｘ_hＹ_h ^*）／（｜Ｘ_h｜²−｜Ｙ_h｜²）]］／２
及び
θ_max＝φ_h／２±π …（７）
また、周波数サンプル値の２乗｜Ｆh（θ）｜²の最大値は下記式（８）で表される。
【００３８】

このとき、２^1/2｜Ｆ_h（θ）｜の最大値がＲＭＳ評価値であり、下記式（９）で表される。
【００３９】

従って、上記式（７）及び上記式（９）を用いれば、ＲＭＳ評価値を算出する際に、Ｘ_h及びＹ_hから｜Ｘ_h｜²,｜Ｙ_h｜²,Ｒｅ（Ｘ_hＹ_h ^*）,｜Ｘ_h ²＋Ｙ_h ²｜を算出するだけで最大方位θ_max，ＲＭＳ評価値を算出することができるので、回転体の回転方向における各方位毎にＲＭＳ振幅値を算出する必要を無くし、計算時間を極めて短縮することができる。
【００４０】
さらに好ましくは、前記最大振幅と所定値との比較に基づいて前記回転体の回転性能の良否を判定する。例えば、前記最大振幅が所定値を越えるときには、回転性能不良と判定するのがよい。
【００４１】
このとき、最大振幅が所定値を越えるときには、回転性能不良と判定するので、簡潔に回転性能の良否を判定することができる。
【００４２】
尚、上述したＸ_h及びＹ_hの複素数値を用いる代わりに、それらの振幅及び位相を用いてもよい。このときの回転体の径方向振動の評価方法において、上述した式（１）〜（９）に等価な式を導くのは容易であるために、説明を省略する。
【００４３】
【発明の実施の形態】
以下、本発明の第１の実施の形態に係る評価方法を図面を参照して詳述する。
【００４４】
本発明の第１の実施の形態に係る評価方法は、回転体の径方向振動を互いに異なる２方向から測定し、該測定した２方向の振動成分の各々に基づいて方位に依存するＮＲＲＯ振動成分の最大振幅と、最大振幅を呈する方位とを評価する際に以下の評価装置によって実行される。
【００４５】
本発明の第１の実施の形態に係る評価方法を実行する評価装置の概略構成を図面を用いて説明する。
【００４６】
図１は、本発明の第１の実施の形態に係る評価方法を実行する評価装置の概略構成を示す図である。
【００４７】
図１において、評価装置１００は、非接触光学型である２つの変位センサ１０１と、２つの変位測定装置１０２と、コンピュータ１０３と、モータ１０４と、カップリング１０５と、回転軸１０６を有するスピンドル１０７とによって構成される。
【００４８】
回転軸１０６は水平に配向しており、２つの変位センサ１０１は夫々スピンドル１０７の前面より突出した回転軸１０６に垂直且つ水平（図中のｘ方向）に、回転軸１０６に垂直且つ鉛直（図中のｙ方向）に配置される。従って、２つの変位センサ１０１は互いに直交している。また、２つの変位センサ１０１は夫々変位測定装置１０２を介してコンピュータ１０３に接続される（図１（ａ））。モータ１０４は、その回転軸がカップリング１０５を介して回転軸１０６と接続される（図１（ｂ））。
【００４９】
変位センサ１０１は回転軸１０６の径方向の振動成分を測定し、且つ測定した振動成分を信号として変位測定装置１０２に送信し、変位測定装置１０２は送信された信号を回転軸１０６のｘ方向、若しくはｙ方向に関する変位量に比例する電圧信号に変換し、且つ変換した電圧信号をコンピュータ１０３が内蔵する不図示のＡ／Ｄ変換器に入力する。コンピュータ１０３はＡ／Ｄ変換器に入力された電圧信号を同期的にディジタル値に変換し、且つ変換されたディジタル値を記憶する。さらに、コンピュータ１０３は記憶されたディジタル値に基づいて回転軸１０６の回転方向の方位に依存するＮＲＲＯ振動成分の最大振幅と、該最大振幅を呈する方位とを導出し、回転軸１０６の回転性能の良否を判定する。また、モータ１０４はカップリング１０５を介して回転軸１０６に駆動トルクを伝達し、回転軸１０６を一定速で回転させる。
【００５０】
以下、図１の評価装置１００によって実行される回転軸１０６のＮＲＲＯ振動成分の最大振幅評価処理について図面を用いて説明する。
【００５１】
図２は、図１の評価装置１００によって実行される回転軸１０６のＮＲＲＯ振動成分の最大振幅評価処理のフローチャートである。
【００５２】
まず、回転軸１０６のｘ方向の振動成分の電圧信号ｘ（ｔ）及びｙ方向の振動成分の電圧信号ｙ（ｔ）の離散値系列｛ｘ_n＝ｘ（ｎΔｔ）,ｙ_n＝ｙ（ｎΔｔ）、ｎ＝０,１,…Ｎ−１｝をＡ／Ｄ変換器に同時に取り込み（ステップＳ２０１）、該取り込んだ離散値系列に対してＦＦＴアルゴリズムを用いて離散的フーリエ変換を行いＸ_k,Ｙ_kで表される周波数サンプル値｛Ｘ_k,Ｙ_k、ｋ＝０,１,…Ｎ−１｝を得る（ステップＳ２０２）。
【００５３】
次いで、ＮＲＲＯ振動成分のＰ個の周波数（特定の周波数）｛ｆ_ｉ、ｉ＝１,…Ｐ｝に対応するＰ個の周波数点｛ｋ_ｉ、ｉ＝１,…Ｐ｝の夫々と対応する周波数軸上の離散点の周波数サンプル値｛Ｘ_ki,Ｙ_ki、ｉ＝１,…Ｐ｝を離散的フーリエ変換によって得られた周波数サンプル値｛Ｘ_k,Ｙ_k、ｋ＝０,１,…Ｎ−１｝から選択し、選択された周波数サンプル値Ｘ_ki,Ｙ_kiを用いて｛｜Ｘ_ki｜²,｜Ｙ_ki｜²,Ｒｅ（Ｘ_kiＹ_ki ^*）、ｉ＝１,…Ｐ｝を算出し、これらを不図示のメモリに記憶する（ステップＳ２０３）。
【００５４】
その後、回転軸１０６の回転方向をＭ個に分割した方位のうち、０〜πに相当する方位｛θ_j＝２ｊπ／Ｍ、ｊ＝０,１,…Ｍ／２−１｝の各方位において周波数点ｋ_i毎に上記式（４）に基づいてＲＭＳ振幅値｛２^1/2｜Ｆ_ki（２ｊπ／Ｍ）｜、ｊ＝０,１,…Ｍ／２−１｝を算出する（ステップＳ２０４）。このとき、上述した通り周波数サンプル値の絶対値｜Ｆ_ki（２ｊπ／Ｍ）｜と｜Ｆ_ki（２ｊπ／Ｍ＋π）｜は等しいので、π〜２πに相当する方位ではＲＭＳ振幅値を算出する必要はない。
【００５５】
さらに、算出されたＭ／２個のＲＭＳ振幅値｛２^1/2｜Ｆ_ki（２ｊπ／Ｍ）｜、ｊ＝０,１,…Ｍ／２−１｝から最大のＲＭＳ振幅値を選択する。該選択したＲＭＳ振幅値を周波数点ｋ_iのＲＭＳ評価値Ａ_kiとし、このＲＭＳ評価値Ａ_kiを呈する方位２ｊπ／Ｍ、２ｊπ／Ｍ＋πを最大方位とする（ステップＳ２０５）。
【００５６】
その後、ＮＲＲＯ振動成分の特定の周波数｛ｆ_i、ｉ＝１,…Ｐ｝と、ＲＭＳ評価値｛Ａ_ki、ｉ＝１,…Ｐ｝と、各ＲＭＳ評価値Ａ_kiに対応する最大方位｛２ｊ_ｉπ／Ｍ、ｉ＝１,…Ｐ｝とによって図３に示す表を作成し（ステップＳ２０６）、表における全てのＲＭＳ評価値Ａ_kiが所定値より小さいか否かを判別する（ステップＳ２０７）。
【００５７】
ステップＳ２０７の判別の結果、全てのＲＭＳ評価値Ａ_kiのうち、１つでも所定値より大きければ、回転軸１０６の回転性能を不良と判定し（ステップＳ２０８）、全てのＲＭＳ評価値Ａ_kiが所定値より小さければ回転軸１０６の回転性能は良好と判定する（ステップＳ２０９）。その後、本処理を終了する。
【００５８】
本発明の第１の実施の形態によれば、ｘ、ｙ方向から測定して得られる回転軸１０６の径方向振動のｘ、ｙ方向の振動成分を離散的フーリエ変換によって周波数サンプル値｛Ｘ_k,Ｙ_k、ｋ＝０,１,…Ｎ−１｝に変換し（ステップＳ２０２）、該変換されたｘ、ｙ方向の周波数サンプル値から選択されたＮＲＲＯ振動成分の特定の周波数｛ｆ_ｉ、ｉ＝１,…Ｐ｝に対応する周波数点｛ｋ_ｉ、ｉ＝１,…Ｐ｝の周波数サンプル値に基づいて、０〜πに相当する方位｛θ_ｊ＝２ｊπ／Ｍ、ｊ＝０,１,…Ｍ／２−１｝の各方位毎にＲＭＳ振幅値｛２^1/2｜Ｆ_ki（２ｊπ／Ｍ）｜、ｊ＝０,１,…Ｍ／２−１｝を算出し（ステップＳ２０４）、これらのＲＭＳ振幅値からＲＭＳ評価値Ａ_kiを選択する（ステップＳ２０５）ので、フーリエ変換を各方位毎に行う必要を無くすことができることに加え、π〜２πに相当する方位でＲＭＳ振幅値を算出する必要を無くし、多大な計算を行うことなく、生産ラインの中で回転体の径方向振動のＮＲＲＯ振動成分をリアルタイムに評価することができる。
【００５９】
次に、本発明の第２の実施の形態に係る評価方法を図面を参照して説明する。
【００６０】
本発明の第２の実施の形態に係る評価方法も同様に、方位に依存するＮＲＲＯ振動成分の最大振幅と、最大振幅を呈する方位とを評価する際に、図１の評価装置１００によって実行される。
【００６１】
以下、図１の評価装置１００によって実行される回転軸１０６のＮＲＲＯ振動成分の最大振幅評価処理について図面を用いて説明する。
【００６２】
本処理は、図２の最大振幅評価処理に対して、ステップＳ２０４において算出されるＲＭＳ振幅値が異なる。
【００６３】
図４は、図１の評価装置１００によって実行される回転軸１０６のＮＲＲＯ振動成分の最大振幅評価処理のフローチャートである。
【００６４】
図４のフローチャートにおいて、ステップＳ２０１〜Ｓ２０３、Ｓ２０７〜Ｓ２０９は図２のフローチャートのそれと同じであるので、説明を省略する。
【００６５】
図４の処理において、ステップＳ２０３の後、回転軸１０６の回転方向をＭ個に分割した方位のうち、０〜π／２に相当する方位｛θ_j＝２ｊπ／Ｍ、ｊ＝０,１,…Ｍ／４−１｝の各方位において周波数点ｋ_i毎に上記式（４）及び上記式（５）に基づいてＲＭＳ振幅値｛２^1/2｜Ｆ_ki（２ｊπ／Ｍ）｜,２^1/2｜Ｆ_ki（２ｊπ／Ｍ＋π／２）｜、ｊ＝０,１,…Ｍ／４−１｝を算出する（ステップＳ４０１）。
【００６６】
さらに、算出されたＭ／２個のＲＭＳ振幅値｛２^1/2｜Ｆ_ki（２ｊπ／Ｍ）｜,２^1/2｜Ｆ_ki（２ｊπ／Ｍ＋π／２）｜、ｊ＝０,１,…Ｍ／４−１｝から最大の振幅値を選択する。該選択したＲＭＳ振幅値を周波数点ｋ_iのＲＭＳ評価値Ａ_kiとし、このＲＭＳ評価値Ａ_kiを呈する方位２ｊπ／Ｍ又は２ｊπ／Ｍ＋π／２を最大方位とする（ステップＳ４０２）。
【００６７】
その後、ＮＲＲＯ振動成分の特定の周波数｛ｆ_i、ｉ＝１,…Ｐ｝と、ＲＭＳ評価値｛Ａ_ki、ｉ＝１,…Ｐ｝と、各ＲＭＳ評価値Ａ_kiに対応する最大方位｛２ｊ_ｉπ／Ｍ又は２ｊ_ｉπ／Ｍ＋π／２、ｉ＝１,…Ｐ｝とによって図５に示す表を作成する（ステップＳ４０３）。以後は、図２の処理におけるステップＳ２０７以降の処理を行う。
【００６８】
本発明の第２の実施の形態によれば、方位２ｊπ／Ｍ＝０〜π／２におけるｓｉｎ（２ｊπ／Ｍ）及びｃｏｓ（２ｊπ／Ｍ）を算出するだけで、方位２ｊπ／Ｍ＝０〜πにおけるＮＲＲＯ振動成分の特定の周波数｛ｆ_i、ｉ＝１,…Ｐ｝におけるＲＭＳ振幅値を算出する（ステップＳ４０１）ので、ＲＭＳ振幅値を回転体の回転方向の半周に亘って算出する必要を無くし、もって計算時間をさらに短縮することができる。
【００６９】
次に、本発明の第３の実施の形態に係る評価方法を図面を参照して説明する。
【００７０】
本発明の第３の実施の形態に係る評価方法も同様に、方位に依存するＮＲＲＯ振動成分の最大振幅と、最大振幅を呈する方位とを評価する際に、図１の評価装置１００によって実行される。
【００７１】
以下、図１の評価装置１００によって実行される回転軸１０６のＮＲＲＯ振動成分の最大振幅評価処理について図面を用いて説明する。
【００７２】
本処理は、図２の最大振幅評価処理に対して、ＲＭＳ評価値及び最大方位を三角関数の加法定理に基づいて導出する点で異なる。
【００７３】
図６は、図１の評価装置１００によって実行される回転軸１０６のＮＲＲＯ振動成分の最大振幅評価処理のフローチャートである。
【００７４】
図６のフローチャートにおいて、ステップＳ２０１〜Ｓ２０３、Ｓ２０７〜Ｓ２０９は図２のフローチャートのそれと同じであるので、説明を省略する。
【００７５】
図６の処理において、ステップＳ２０３の後、ＮＲＲＯ振動成分の特定の周波数｛ｆ_ｉ、ｉ＝１,…Ｐ｝毎に、上記式（９）に基づいてＲＭＳ評価値｛Ａ_ki＝２^1/2｜Ｆ_ki（φ_ki／２）｜、ｉ＝１,…Ｐ｝と、上記式（７）に基づいて各ＲＭＳ評価値Ａ_kiに対応する最大方位｛θ_ki＝φ_ki／２,θ_ki＋π、ｉ＝１,…Ｐ｝とを解析的に導出する（ステップＳ６０１）。
【００７６】
その後、ＮＲＲＯ振動成分の特定の周波数｛ｆ_i、ｉ＝１,…Ｐ｝と、ＲＭＳ評価値｛Ａ_ki、ｉ＝１,…Ｐ｝と、各ＲＭＳ評価値Ａ_kiに対応する最大方位｛θ_ki,θ_ki＋π、ｉ＝１,…Ｐ｝とによって図７に示す表を作成する（ステップＳ６０２）。以後は、図２の処理におけるステップＳ２０７以降の処理を行う。
【００７７】
本発明の第３の実施の形態によれば、ＮＲＲＯ振動成分の特定の周波数｛ｆ_i、ｉ＝１,…Ｐ｝毎に、ＲＭＳ評価値｛Ａ_ki＝２^1/2｜Ｆ_ki（φ_ki／２）｜、ｉ＝１,…Ｐ｝と、各ＲＭＳ評価値Ａ_kiに対応する最大方位｛θ_ki＝φ_ki／２,θ_ki＋π、ｉ＝１,…Ｐ｝とを三角関数の加法定理に基づいて解析的に導出する（ステップＳ６０１）ので、回転体の回転方向における各方位毎にＲＭＳ振幅値を算出する必要を無くし、もって計算時間を極めて短縮することができる。
【００７８】
次に、本発明の第４の実施の形態に係る評価方法を図面を参照して説明する。
【００７９】
本発明の第４の実施の形態に係る評価方法も同様に、方位に依存するＮＲＲＯ振動成分の最大振幅と、最大振幅を呈する方位とを評価する際に、図１の評価装置１００によって実行される。
【００８０】
以下、図１の評価装置１００によって実行される回転軸１０６のＮＲＲＯ振動成分の最大振幅評価処理について図面を用いて説明する。
【００８１】
本処理は、図２の最大振幅評価処理に対して、複数のＮＲＲＯ振動成分の周波数における総合的なＲＭＳ評価値及び最大方位を一度に導出する点で異なる。
【００８２】
総合的なＲＭＳ評価値及び最大方位を一度に導出するための計算式は以下の手順によって導出される。まず、算出されたＮＲＲＯ振動成分の特定の周波数｛ｆ_i、ｉ＝１,…Ｐ｝に対応するＰ個の周波数点｛ｋ_i、ｉ＝１,…Ｐ｝の夫々と対応する周波数軸上の離散点における｜Ｘ_ki｜²,｜Ｙ_ki｜²,Ｒｅ（Ｘ_kiＹ_ki ^*）｛ｉ＝１,…Ｐ｝及び上記式（２）に基づいて、以下のパワースペクトルを表現する下記式（１０）を得る。
【００８３】
【数５】

【００８４】
ここで、上記式（２）から上記式（７）を導出した手順と同様に、三角関数の加法定理に基づいた手順により、上記式（１０）から複数のＮＲＲＯ振動成分の周波数における総合的な最大方位θ_maxを表す下記式（１１）が導出される。
【００８５】
【数６】

【００８６】
さらに、上記式（２）から上記式（９）を導出した手順と同様に、三角関数の加法定理に基づいた手順により、上記式（１０）から複数のＮＲＲＯ振動成分の周波数における総合的なＲＭＳ評価値Ａ_totalを表す下記式（１２）が導出される。
【００８７】
【数７】

【００８８】
図８は、図１の評価装置１００によって実行される回転軸１０６のＮＲＲＯ振動成分の最大振幅評価処理のフローチャートである。
【００８９】
図８のフローチャートにおいて、ステップＳ２０１〜Ｓ２０３は図２のフローチャートのそれと同じであるので、説明を省略する。
【００９０】
図８の処理において、ステップＳ２０３の後、ステップＳ２０３で算出されたＮＲＲＯ振動成分の特定の周波数｛ｆ_ｉ、ｉ＝１,…Ｐ｝に対応するＰ個の周波数点｛ｋ_ｉ、ｉ＝１,…Ｐ｝の夫々と対応する周波数軸上の離散点における｜Ｘ_ki｜²,｜Ｙ_ki｜²,Ｒｅ（Ｘ_kiＹ_ki ^*）｛ｉ＝１,…Ｐ｝、上記式（１１）及び上記式（１２）に基づいて総合的な最大方位θ_max、θ_max＋π及びＲＭＳ評価値Ａ_totalを算出する（ステップＳ８０１）。
【００９１】
次いでステップＳ８０２において、ＲＭＳ評価値Ａ_totalが所定値より小さいか否かを判別する。
【００９２】
ステップＳ８０２の判別の結果、ＲＭＳ評価値Ａ_totalが所定値より大きければ、回転軸１０６の回転性能を不良と判定し（ステップＳ８０３）、ＲＭＳ評価値Ａ_totalが所定値より小さければ回転軸１０６の回転性能は良好と判定する（ステップＳ８０４）。その後、本処理を終了する。
【００９３】
この他、総合的なＲＭＳ評価値及び最大方位を一度に導出するのではなく、回転軸１０６の回転方向をＭ個に分割した方位のうち、０〜πに相当する方位｛θ_j＝２ｊπ／Ｍ、ｊ＝０,１,…Ｍ／２−１｝の各方位毎に上記式（１０）に基づいてパワースペクトルを求め、これらのパワースペクトルの中から最大のものをＲＭＳ評価値Ａ_totalとして選択してもよい。
【００９４】
本第４の実施の形態によれば、ＮＲＲＯ振動成分の特定の周波数｛ｆ_ｉ、ｉ＝１,…Ｐ｝における総合的な最大方位θ_max,θ_max＋π及びＲＭＳ評価値Ａ_totalを一度に導出する（ステップＳ８０１）ので、回転体のＮＲＲＯ振動成分の全体的なＲＭＳ値の評価ができる。
【００９５】
次に、本発明の第５の実施の形態に係る評価方法について説明する。
【００９６】
本発明の第５の実施の形態に係る評価方法も同様に、方位に依存するＮＲＲＯ振動成分の最大振幅と、最大振幅を呈する方位とを評価する際に、図１の評価装置１００によって実行される。
【００９７】
本発明の第５の実施の形態に係る評価方法におけるＮＲＲＯ振動成分の最大振幅評価処理は、図２、４、６及び８の最大振幅評価処理に対して、後述するリーケージと、周波数点の不一致とによって生じるスペクトルの分散を考慮する点で異なる。
【００９８】
リーケージとは、分析の対象となる振動成分をサンプリングする際の時間制限に起因する現象であって、単一の周波数の正弦波の周波数スペクトルが本来単一の線スペクトルでなければならないのに対し、複数の周波数点に分散したスペクトルになる現象であり、周波数点の不一致とは、ＮＲＲＯ振動成分の特定の周波数｛ｆ_i、ｉ＝１,…Ｐ｝と、ＦＦＴアルゴリズムによって得られた周波数サンプル値｛Ｘ_k,Ｙ_k、ｋ＝０,１,…Ｎ−１｝の離散的な周波数点｛ｋ_ｉ、ｉ＝１,…Ｐ｝との不一致のことである。
【００９９】
以下、本処理がリーケージと周波数点の不一致とによって生じるスペクトルの分散に対する従来の対策について説明する。
【０１００】
まず、従来のリーケージと周波数点の不一致とによって生じるスペクトルの分散の問題と対策については、米国特許第５，４２０，５０１号明細書に詳述されている。これによれば、ある周波数成分を許容できる誤差内で評価するためには、周波数軸上において評価する振動成分の周波数に近傍であって、互いに隣接する複数の周波数点の周波数サンプル値の２乗和を算出し、該算出した２乗和の平方根に適当な定数（例えば、上記式（３）、（４）、（５）及び（９）における２^1/2と使用するハニング窓等の窓関数に対する補正値）を掛ければよい。
【０１０１】
一方、定常的な振動現象における同一周波数のｘ方向及びｙ方向の振動は、時間軸上において相互の振幅比と位相差との関係は一定であるため、全ての互いに隣接する複数の周波数点に分散したスペクトルにおいて、ｘ方向とｙ方向の周波数サンプル値の対｛Ｘ_k,Ｙ_k｝の相互の振幅比と位相差との関係は一定となる性質を有する。従って、これら複数の周波数点の各々において、評価する振動成分の周波数の最大方位と同じ方位における周波数サンプル値の振幅値は、他のいかなる方位における周波数サンプル値の振幅値よりも常に大きい。
【０１０２】
本処理は、これら上述した米国特許第５，４２０，５０１号明細書の対策と、定常的な振動現象における同一周波数のｘ方向及びｙ方向の振動の性質とに基づいて、リーケージと周波数点の不一致とによって生じるスペクトルの分散を考慮したＮＲＲＯ振動成分の評価を行う。
【０１０３】
以下、図１の評価装置１００によって実行される回転軸１０６のＮＲＲＯ振動成分の最大振幅評価処理について図面を用いて説明する。
図９は、図１の評価装置１００によって実行される回転軸１０６のＮＲＲＯ振動成分の最大振幅評価処理のフローチャートである。
図９のフローチャートにおいて、ステップＳ２０１〜Ｓ２０２、Ｓ２０５〜Ｓ２０９は図２のフローチャートのそれと同じであるので、説明を省略する。
図９の処理において、ステップＳ２０２の後、評価するＮＲＲＯ振動成分の特定の周波数｛ｆ_i、ｉ＝１,…Ｐ｝の各々に対応する周波数点ｋ_ｉに近傍であって、互いに隣接するｍ個の周波数点｛ｋ_i -m/2,ｋ_i -m/2+1,．．．ｋ_i,．．．ｋ_i +m/2-1｝の各々について｛｜Ｘ_ki+l｜²,｜Ｙ_ki+l｜²,Ｒｅ（Ｘ_ki+lＹ_ki+l ^*）、ｌ＝−ｍ／２,−ｍ／２＋１,．．．０,．．．ｍ／２−１｝を算出し、これらを不図示のメモリに記憶する（ステップＳ９０１）。
その後、回転軸１０６の回転方向をＭ個に分割した方位のうち、０〜πに相当する方位｛θj＝２ｊπ／Ｍ、ｊ＝０,１,…Ｍ／２−１｝の各方位毎に上記ｍ個の周波数点ｋ_iの各々について下記式（１３）で表される振動の周波数サンプル値の２乗｜Ｆ_ki+l（２ｊπ／Ｍ）｜²を算出する（ステップＳ９０２）。
｜Ｆ_ki+l（２ｊπ／Ｍ）｜²＝｜Ｘ_ki+l｜²ｃｏｓ²（２ｊπ／Ｍ）
＋｜Ｙ_ki+l｜²ｓｉｎ²（２ｊπ／Ｍ）
＋２Ｒｅ（Ｘ_ki+lＹ_ki+l ^*）ｓｉｎ（２ｊπ／Ｍ）ｃｏｓ（２ｊπ／Ｍ）
…（１３）
次いで、算出されたｍ個の周波数サンプル値の２乗｛｜Ｆ_ki+l（２ｊπ／Ｍ）｜²、ｌ＝−ｍ／２,−ｍ／２＋１,．．．０,．．．ｍ／２−１｝について総和を算出し、該算出した総和の平方根を算出し、さらに該算出された平方根を２^1/2倍することによって下記式（１４）で表される各方位における周波数点ｋiのＲＭＳ振幅値を算出する（ステップＳ９０３）。
【０１０４】
【数８】

【０１０５】
以後は、図２の処理におけるステップＳ２０５以降の処理を行う。
尚、本第５の実施の形態ではｍを暗黙的に偶数としたが、奇数でも同様に評価できることは明らかである。
また、本第５の実施の形態では、上述した本発明の第３の実施の形態のように、ＲＭＳ評価値及び最大方位を三角関数の加法定理に基づいて解析的に導出してもよい。以下、本第５の実施の形態においてＲＭＳ評価値及び最大方位を三角関数の加法定理に基づいて解析的に導出する方法について説明する。
まず、評価するＮＲＲＯ振動成分の特定の周波数｛ｆ_i、ｉ＝１,…Ｐ｝の各々に対応する周波数点ｋ_iに近傍であって、互いに隣接するｍ個の周波数点｛ｋ_i -m/2,ｋ_i -m/2+1,．．．ｋ_i,．．．ｋ_i +m/2-1｝の各々について｛｜Ｘ_ki+l｜²＋｜Ｙ_ki+l｜²,｜Ｘ_ki+l ²＋Ｙ_ki+l ²｜,Ｒｅ（Ｘ_ki+lＹ_ki+l ^*）、ｌ＝−ｍ／２,−ｍ／２＋１,．．．０,．．．ｍ／２−１｝を算出し、上記ｍ個の周波数点｛ｋ_i -m/2,ｋ_i -m/2+1,．．．ｋ_i,．．．ｋ_i +m/2-1｝の各々について下記式（１５）で表される振動の周波数サンプル値の２乗｛｜Ｆ_ki+l（φ_ki／２）｜²、ｌ＝−ｍ／２,−ｍ／２＋１,．．．０,．．．ｍ／２−１｝を算出する。
｜Ｆ_ki+l（φ_ki／２）｜²＝
（｜Ｘ_ki+l｜²＋｜Ｙ_ki+l｜²＋｜Ｘ_ki+l ²＋Ｙ_ki+l ²｜）／２…（１５）
その後、算出されたｍ個の周波数サンプル値の２乗｛｜Ｆ_ki+l（φ_ki／２）｜²、ｌ＝−ｍ／２,−ｍ／２＋１,．．．０,．．．ｍ／２−１｝について総和を算出し、該算出した総和の平方根を算出し、さらに該算出された平方根を２^1/2倍することによって下記式（１６）で表される周波数点ｋ_iのＲＭＳ評価値を算出する。
【０１０６】
【数９】

【０１０７】
また、上述したように周波数サンプル値の対｛Ｘ_ki+l,Ｙ_ki+l｝の相互の振幅比と位相差との関係は、どの周波数点においても一定である。従って、上記周波数点ｋ_iのＲＭＳ評価値を与える最大方位を下記式（１７）により算出できる。
θ_i＝φ_ki／２
＝［ｔａｎ^-1 [ Ｒｅ（Ｘ_kiＹ_ki ^*）／（｜Ｘ_ki｜²−｜Ｙ_ki｜²）]］／２
及び
θπ_i＝φ_ki／２±π …（１７）
本第５の実施の形態によれば、リーケージと周波数点の不一致とによって生じるスペクトルの分散を考慮するので、ＮＲＲＯ振動成分の特定の周波数｛ｆ_i、ｉ＝１,…Ｐ｝に対応するＲＭＳ評価値｛Ａ_ki、ｉ＝１,…Ｐ｝を許容できる誤差内で評価することができる。
【０１０８】
【発明の効果】
以上詳細に説明したように、請求項１記載の回転体の径方向振動の評価方法によれば、２方向から測定して得られた振動成分の各々をフーリエ変換によって周波数スペクトルに変換し、該変換された２方向の周波数スペクトルに基づいて各方位毎に特定の周波数の径方向振動の振幅を算出するので、フーリエ変換を各方位毎に行う必要を無くし、多大な計算を行うことなく、生産ラインの中で回転体の径方向振動のＮＲＲＯ振動成分をリアルタイムに評価することができる。
【図面の簡単な説明】
【図１】本発明の第１の実施の形態に係る評価方法を実行する評価装置の概略構成を示す図であり、（ａ）は正面図であり、（ｂ）は側面図である。
【図２】図１の評価装置１００によって実行される回転軸１０６のＮＲＲＯ振動成分の最大振幅評価処理のフローチャートである。
【図３】図２の最大振幅評価処理で使用される回転軸１０６の回転性能判定表である。
【図４】図１の評価装置１００によって実行される回転軸１０６のＮＲＲＯ振動成分の最大振幅評価処理のフローチャートである。
【図５】図４の最大振幅評価処理で使用される回転軸１０６の回転性能判定表である。
【図６】図１の評価装置１００によって実行される回転軸１０６のＮＲＲＯ振動成分の最大振幅評価処理のフローチャートである。
【図７】図６の最大振幅評価処理で使用される回転軸１０６の回転性能判定表である。
【図８】図１の評価装置１００によって実行される回転軸１０６のＮＲＲＯ振動成分の最大振幅評価処理のフローチャートである。
【図９】図１の評価装置１００によって実行される回転軸１０６のＮＲＲＯ振動成分の最大振幅評価処理のフローチャートである。
【図１０】従来の回転体の径方向振動を評価する方法を説明する図である。
【符号の説明】
１００ 評価装置
１０１ 変位センサ
１０２ 変位測定装置
１０３ コンピュータ
１０４ モータ
１０５ カップリング
１０６ 回転軸
１０７ スピンドル[0001]
BACKGROUND OF THE INVENTION
  The present invention relates to a method for evaluating radial vibration of a rotating body, and in particular, radial vibration of a rotating body that evaluates radial vibration that is asynchronous with the rotational speed of a rotating body such as a bearing or a spindle incorporating a bearing based on frequency analysis. Evaluation methodAnd evaluation device for radial vibration of rotating bodyAbout.
[0002]
[Prior art]
Conventional rolling bearings and rotating bodies such as spindles incorporating them generate radial vibrations caused by the roundness of the bearings, etc., so that significant vibrations of structures such as machine tools that use these components as components May become a vibration source.
[0003]
Such a rotating body generates radial vibration even when rotating at a constant speed, and this radial vibration includes a radial vibration component (NRRO: Non Repeatable Round Out) vibration component that is asynchronous with the rotational speed of the rotating body. Included). The frequency of this NRRO vibration component is determined from a predetermined calculation formula based on the geometric dimensions of rolling elements such as inner and outer rings of a rotating body, balls, and the like, and the shape accuracy of the rotating body, and the constant speed rotation speed of the rotating body. Since a plurality of predetermined calculation formulas are defined, there are a plurality of frequencies of the NRRO vibration component. Of these NRRO vibration components having a plurality of frequencies, the vibration magnitude (amplitude) of some NRRO vibration components changes depending on the direction of rotation of the rotating body (hereinafter referred to as “direction dependent”). ")" Is known.
[0004]
On the other hand, especially in hard disk devices, the disk bearings caused by the vibration of the ball bearings used for the rotating shafts of the disks are the main cause of positioning errors of the magnetic head. Yes.
[0005]
In order to supply ball bearings that satisfy the rotational accuracy required for hard disk drives, it is necessary to quantitatively evaluate the NRRO vibration component and eliminate ball bearings having an NRRO vibration component that is inconvenient for magnetic head positioning. There is. Furthermore, the NRRO vibration component at a frequency in the vicinity of the resonance frequency of the hard disk device (hereinafter referred to as “specific frequency”) is evaluated with particular emphasis to eliminate ball bearings that may cause the hard disk device to resonate. There is a need.
[0006]
Usually, the NRRO vibration component of a specific frequency is composed of an NRRO vibration component that depends on the orientation and an NRRO vibration component that does not depend on the direction, and each NRRO vibration component is composed of a plurality of frequencies. That is, each specific frequency of the NRRO vibration component that depends on the azimuth and the NRRO vibration component that does not depend on the azimuth is composed of a plurality of frequencies. For example, if the NRRO vibration component of a specific frequency depends on the azimuth, , Knowing the magnitude of the NRRO vibration component consisting of a plurality of frequencies depending on the orientation for each direction over the entire direction of rotation of the rotating body, The NRRO vibration component is evaluated by finding the maximum amplitude value and the azimuth exhibiting this amplitude value.
[0007]
As one of the methods for evaluating the radial vibration of the rotating body in all directions in the rotating direction of the rotating body, a displacement sensor such as a displacement measuring instrument for measuring the radial vibration is provided at two locations near the outer periphery of the rotating body. There is known a method of setting different azimuths and evaluating radial vibrations of different third orientations using measured vibration values of two orientations. In this method of evaluating radial vibration, two displacement sensors are installed so as to be able to measure vibrations in directions (x direction and y direction) perpendicular to the rotation axis of the rotating body and perpendicular to each other (FIG. 10). When the vibration measurement time is t and the measured vibration components in the x and y directions are x (t) and y (t), respectively, one of the displacement sensors is installed on the axis x in FIG. The radial vibration f (t, θ) in the azimuth θ that is rotated by an angle θ in the rotational direction of the rotating body from the shaft is expressed by the following equation.
[0008]
f (t, θ) = x (t) cos θ + y (t) sin θ
In addition, the amplitude of the NRRO vibration component is usually evaluated by the maximum value of the fluctuation range when the NRRO vibration component is cut out for each rotation period of the rotating body and superimposed. At this time, the NRRO evaluation value means the maximum amplitude selected from the amplitudes of the NRRO vibration components in each direction, and the maximum direction θ_maxMeans an orientation exhibiting an NRRO evaluation value.
[0009]
Usually, the radial vibration f (t, θ) includes vibration components other than the NRRO vibration component having a specific frequency depending on the direction. Therefore, in order to evaluate the amplitude of the NRRO vibration component having a specific frequency depending on the direction, the amplitude of the NRRO vibration component having a specific frequency depending on the direction is selected from the radial vibration f (t, θ) by frequency analysis. Must be sought.
[0010]
In general, in order to selectively obtain the amplitude of a specific frequency from vibrations including a plurality of frequencies, frequency analysis using Fourier transform is performed. However, in the above-described method for evaluating radial vibration, the maximum orientation θ_maxAnd radial vibration f (t, θ_max) And f (t, θ_max) Is sampled every Δt, and N-point discrete value series {f_n(Θ_max) = F (nΔt, θ_max), N = 0, 1,... N−1}, the frequency spectrum {F_k(Θ_max), K = 0, 1,... N−1}, the maximum azimuth θ_maxThe frequency spectrum corresponding to a specific frequency in the frequency spectrum distribution obtained by the Fourier transform is not necessarily the maximum value in all directions.
[0011]
Because, as mentioned above, a specific frequency usually consists of a plurality of frequencies, the maximum direction θ_maxIs the azimuth in which the combined amplitude determined by the relative relationship between the frequency, amplitude and phase of a specific frequency NRRO vibration component consisting of a plurality of frequencies depending on the azimuth is maximum, but in general, the NRRO vibration of each frequency This is because the components exhibit maximum amplitude in different directions.
[0012]
Therefore, the true maximum orientation θ of each NRRO vibration component of a specific frequency_maxIs obtained for each direction by obtaining a frequency spectrum distribution by frequency analysis using Fourier transform from the radial vibration f (t, θ) {0 ≦ θ <2π} for each direction, and then for a specific frequency for each direction. The frequency spectrum corresponding to each of the frequencies is obtained, the vibration levels of the frequency spectrum are compared in all directions for each frequency, the frequency spectrum exhibiting the maximum vibration level is selected from these, and each selected frequency spectrum is selected. It is necessary to select a frequency spectrum exhibiting the maximum vibration level from the frequency spectrum of the frequency, and obtain an orientation in which the selected frequency spectrum is exhibited.
[0013]
[Problems to be solved by the invention]
However, in frequency analysis using Fourier transform for each orientation, the true maximum orientation θ_maxIf the azimuth θ is fined to increase the accuracy of calculation, FFT (Fast Fourier Transform) operation must be repeated for each azimuth θ. There is a problem that the NRRO vibration component of radial vibration cannot be evaluated in real time.
[0014]
  SUMMARY OF THE INVENTION An object of the present invention is to provide a method for evaluating the radial vibration of a rotating body capable of evaluating in real time the NRRO vibration component of the radial vibration of the rotating body in a production line without performing a large amount of calculation.And evaluation device for radial vibration of rotating bodyIs to provide.
[0015]
[Means for Solving the Problems]
  In order to achieve the above object, the present invention provides a radial vibration whose amplitude changes depending on the orientation of the rotating body in the rotational direction, and the radial vibration having a predetermined frequency asynchronous with the rotational speed of the rotating body. The maximum amplitude of the radial vibration and the azimuth exhibiting the maximum amplitude are evaluated on the basis of vibration components obtained by measuring two different directions from each other.As much as possibleEach of the vibration components obtained by measurement from the two directions is converted into a frequency spectrum by Fourier transform, and the diameter is determined for each azimuth in the rotational direction of the rotating body based on the converted two-direction frequency spectrum. Calculate the amplitude of directional vibrationRelated to evaluation method of radial vibration of rotating body.
[0016]
According to the radial vibration evaluation method for a rotating body of the present invention, each of vibration components obtained by measuring from two directions is converted into a frequency spectrum by Fourier transform, and based on the converted two-way frequency spectrum. The radial vibration amplitude of a specific frequency is calculated for each direction, eliminating the need to perform Fourier transform for each direction, and performing the radial vibration of the rotating body in the production line without performing a large amount of calculation. The NRRO vibration component of can be evaluated in real time.
[0017]
Here, the amplitude calculation processing for obtaining the amplitude in the direction θ of the radial vibration of the specific frequency of the rotating body of the present invention will be described.
[0018]
First, vibration components x (t) and y (t) in the x and y directions are measured, and each of these x (t) and y (t) is divided for each Δt and sampled at N points. {X_n= X (nΔt), y_n= Y (nΔt), n = 0, 1,... N−1} is Fourier transformed. Since the Fourier transform in this process is a discrete Fourier transform by FFT operation, if the discrete point on the frequency axis is k, X_k, Y_kThe frequency spectrum {X_k, Y_k, K = 0, 1,... N−1} (hereinafter referred to as “frequency sample values”).
[0019]
After that, the frequency spectrum X corresponding to the frequency point h corresponding to the specific frequency_h, Y_hTo the frequency spectrum {X_k, Y_k, K = 0, 1,... N−1}, and the selected frequency spectrum X_h, Y_hBased on the above, the square of the frequency sample value of the radial vibration f (t, θ) in the direction θ at the frequency point h is calculated.
[0020]
First, the radial vibration f (t, θ) in the azimuth θ is expressed by the following formula (1) as described above.
[0021]
f (t, θ) = x (t) cos θ + y (t) sin θ (1)
When both sides of the equation (1) are Fourier transformed, the square of the frequency sample value of the radial vibration f (t, θ) of the azimuth θ at the frequency point h | F_h(Θ) |²Is represented by the following formula (2).
[0022]

In the above formula (2), | A | is the absolute value of the complex number A, and X_h ^*And Y_h ^*Is a complex number X_hAnd Y_hAnd Re (B) is the real part of the complex number B.
[0023]
At this time, if the discrete value series of the N points of x (t) and y (t) is a real value series, the discrete value series {f (nΔt, θ) of the radial vibration f (t, θ) in the azimuth θ. ), N = 0, 1,... N−1} is also a series of real values, so the RMS amplitude value (Root Mean Square) of the frequency sample value of the radial vibration f (t, θ) in the direction θ at the frequency point h. ) Is 2^1/2｜ F_h(Θ) |, and the RMS amplitude value of the frequency sample value of the radial vibration f (t, θ) of the azimuth θ at the frequency point h based on the above equation (2) is expressed by the following equation (3).
[0024]

After calculating the RMS amplitude value of the frequency sample value of the radial vibration f (t, θ) of the azimuth θ at the frequency point h as the amplitude of the azimuth θ at the frequency point h of the radial vibration of the rotating body, this processing is performed. finish.
[0025]
At this time, the maximum RMS amplitude value selected from the RMS amplitude values of the frequency sample values of the radial vibration f (t, θ) at the frequency point h calculated over all directions in the rotation direction of the rotating body is obtained. The RMS evaluation value in the evaluation of the NRRO vibration component is used, and the azimuth θ exhibiting the RMS evaluation value is set as the maximum azimuth θ._maxAnd
[0026]
Preferably, the amplitude of the radial vibration is calculated based on the frequency spectrum in the two directions corresponding to the predetermined frequency for each direction obtained by subdividing the directions of 0 to π in the rotation direction of the rotating body. The maximum amplitude is preferably selected from the calculated amplitudes of the respective directions.
[0027]
For example, as the amplitude in the azimuth θ of the radial vibration of a specific frequency of the rotator, the radial vibration f (t, 2jπ / M in the azimuth 2jπ / M when the rotation direction of the rotator at the frequency point h is divided into M pieces. When calculating the RMS amplitude value of the frequency sample value of M), the RMS amplitude value of the frequency sample value of the radial vibration f (t, 2jπ / M) in the azimuth 2jπ / M at the frequency point h is given by the following equation (4) ).
[0028]

In the above formula (4), the absolute value of the frequency sample value | F in the direction 2jπ / M = 0 to π and the direction 2 (j + M / 2) π / M = 2jπ / M + π = π to 2π_h(2jπ / M) | and | F_hSince (2jπ / M + π) | is equal, it is sufficient to calculate the RMS amplitude value of the frequency sample value of the radial vibration f (t, 2jπ / M) in the azimuth 2jπ / M with the azimuth 2jπ / M = 0 to π. . As a result, it is possible to eliminate the need to calculate the RMS amplitude value of the frequency sample value of the radial vibration f (t, 2jπ / M) in the azimuth 2jπ / M over the entire circumference of the rotating body. Time can be further shortened.
[0029]
At this time, it is selected from the RMS amplitude values of the frequency sample values of the radial vibration f (t, 2jπ / M) at the frequency point h calculated over the direction 2jπ / M = 0 to π in the rotation direction of the rotating body. The obtained maximum RMS amplitude value is set as the RMS evaluation value, and the azimuth 2jπ / M exhibiting the RMS evaluation value is set as the maximum azimuth θ._maxAnd
[0030]
More preferably, the amplitude of the radial vibration is calculated based on the frequency spectrum in the two directions corresponding to the predetermined frequency for each direction obtained by subdividing the direction of 0 to π / 2 in the rotation direction of the rotating body. The maximum amplitude is preferably selected from the calculated amplitudes of the respective directions.
[0031]
For example, the RMS amplitude value in an azimuth (2jπ / M + π / 2) advanced by azimuth 2jπ / M is −sin (2jπ / M) instead of cos (2jπ / M), sin (2jπ / M) If cos (2jπ / M) is substituted into the above equation (4) instead of the above, it is expressed by the following equation (5).
[0032]

Therefore, by using the above formula (4) and the above formula (5), simply calculating sin (2jπ / M) and cos (2jπ / M) in the orientation 2jπ / M = 0 to π / 2, the orientation 2jπ / M Since the RMS amplitude value of the frequency sample value of the radial vibration f (t, 2jπ / M) at the frequency point h at M = 0 to π can be calculated, the radial vibration f (t, 2jπ in the azimuth 2jπ / M) can be calculated. / M), it is not necessary to calculate the RMS amplitude value of the frequency sample value over the half circumference in the rotation direction of the rotating body, and the calculation time can be further shortened.
[0033]
Preferably, the maximum amplitude of the radial vibration and the azimuth exhibiting the maximum amplitude are derived based on the frequency spectrum in the two directions and the addition theorem of trigonometric functions.
[0034]
Here, the maximum amplitude derivation process for deriving the maximum amplitude of the radial vibration and the azimuth exhibiting the maximum amplitude according to the present invention based on the frequency spectrum in two directions and the addition theorem of the trigonometric function will be described.
[0035]
  In the maximum amplitude derivation processing of the present invention, the above equation (2) is expressed as a_h= (| X_h｜²+ | Y_h｜²) / 2, b_h= (| X_h｜²− | Y_h｜²) / 2 and c_h= (X_hY_h ^*+ Y_hX_h ^*) / 2= Re (X_hY_h ^*) And is represented by the following formula (6).
[0036]

In the above equation (6), φ_h= Tan^-1(C_h/ B_h). Therefore, from the above equation (6), the square of the frequency sample value | F_h(Θ) |²Is the maximum orientation θ_maxIs represented by the following formula (7).
[0037]
  θ_max= Φ_h/ 2
        = [Tan^-1 [ Re (X_hY_h ^*) / (| X_h｜²− | Y_h｜²)]] / 2
as well as
  θ_max= Φ_h/ 2 ± π (7)
  Also, the square of the frequency sample value | Fh (θ) |²Is represented by the following formula (8).
[0038]

At this time, 2^1/2｜ F_hThe maximum value of (θ) | is the RMS evaluation value, and is represented by the following formula (9).
[0039]

Therefore, when the above formula (7) and the above formula (9) are used, when calculating the RMS evaluation value, X_hAnd Y_hTo | X_h｜², | Y_h｜², Re (X_hY_h ^*), | X_h ²+ Y_h ²Just calculate |_maxSince the RMS evaluation value can be calculated, it is not necessary to calculate the RMS amplitude value for each direction in the rotation direction of the rotating body, and the calculation time can be greatly shortened.
[0040]
More preferably, the quality of the rotation performance of the rotating body is determined based on a comparison between the maximum amplitude and a predetermined value. For example, when the maximum amplitude exceeds a predetermined value, it may be determined that the rotation performance is poor.
[0041]
At this time, when the maximum amplitude exceeds a predetermined value, it is determined that the rotation performance is poor, so it is possible to simply determine whether the rotation performance is good or bad.
[0042]
In addition, X mentioned above_hAnd Y_hThese amplitudes and phases may be used instead of the complex values. In the evaluation method of the radial vibration of the rotating body at this time, it is easy to derive an expression equivalent to the above-described expressions (1) to (9), and thus description thereof is omitted.
[0043]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, an evaluation method according to the first embodiment of the present invention will be described in detail with reference to the drawings.
[0044]
In the evaluation method according to the first embodiment of the present invention, the radial vibration of the rotating body is measured from two different directions, and the NRRO vibration component that depends on the orientation based on each of the measured vibration components in the two directions. This is executed by the following evaluation device when evaluating the maximum amplitude and the orientation exhibiting the maximum amplitude.
[0045]
A schematic configuration of an evaluation apparatus that executes an evaluation method according to a first embodiment of the present invention will be described with reference to the drawings.
[0046]
FIG. 1 is a diagram showing a schematic configuration of an evaluation apparatus that executes the evaluation method according to the first embodiment of the present invention.
[0047]
In FIG. 1, an evaluation apparatus 100 includes a non-contact optical type two displacement sensor 101, two displacement measurement apparatuses 102, a computer 103, a motor 104, a coupling 105, and a spindle 107 having a rotation shaft 106. It is comprised by.
[0048]
The rotation shaft 106 is horizontally oriented, and the two displacement sensors 101 are perpendicular to the rotation shaft 106 protruding from the front surface of the spindle 107 and are horizontal (in the x direction in the figure), and perpendicular to the rotation shaft 106 and vertical (see FIG. In the middle y direction). Therefore, the two displacement sensors 101 are orthogonal to each other. The two displacement sensors 101 are connected to the computer 103 via the displacement measuring device 102 (FIG. 1 (a)). The rotation shaft of the motor 104 is connected to the rotation shaft 106 through the coupling 105 (FIG. 1B).
[0049]
The displacement sensor 101 measures the vibration component in the radial direction of the rotating shaft 106 and transmits the measured vibration component as a signal to the displacement measuring device 102. The displacement measuring device 102 sends the transmitted signal to the x direction of the rotating shaft 106, Or it converts into the voltage signal proportional to the displacement amount regarding ay direction, and inputs the converted voltage signal into the A / D converter not shown which the computer 103 contains. The computer 103 synchronously converts the voltage signal input to the A / D converter into a digital value, and stores the converted digital value. Further, the computer 103 derives the maximum amplitude of the NRRO vibration component that depends on the direction of the rotation direction of the rotating shaft 106 and the direction that exhibits the maximum amplitude based on the stored digital value, and determines the rotational performance of the rotating shaft 106. Judge the quality. Further, the motor 104 transmits driving torque to the rotating shaft 106 through the coupling 105, and rotates the rotating shaft 106 at a constant speed.
[0050]
Hereinafter, the maximum amplitude evaluation process of the NRRO vibration component of the rotating shaft 106 executed by the evaluation apparatus 100 of FIG. 1 will be described with reference to the drawings.
[0051]
FIG. 2 is a flowchart of the maximum amplitude evaluation process of the NRRO vibration component of the rotating shaft 106 executed by the evaluation apparatus 100 of FIG.
[0052]
First, the discrete value series {x of the voltage signal x (t) of the vibration component in the x direction of the rotating shaft 106 and the voltage signal y (t) of the vibration component in the y direction._n= X (nΔt), y_n= Y (nΔt), n = 0, 1,... N−1} are simultaneously taken into the A / D converter (step S201), and discrete Fourier transform is performed on the taken discrete value series using an FFT algorithm. X_k, Y_kThe frequency sample value {X_k, Y_k, K = 0, 1,... N−1} are obtained (step S202).
[0053]
  Next, P frequencies (specific frequencies) of the NRRO vibration component {f_i, I= 1,... P} P frequency points {k_i, I= 1,... P}, the frequency sample values {X of discrete points on the frequency axis corresponding to each of P,._ki, Y_ki,i = 1,... P} is a frequency sample value {X obtained by discrete Fourier transform_k, Y_k, K = 0, 1,... N−1}, and the selected frequency sample value X_ki, Y_ki{| X_ki｜², | Y_ki｜², Re (X_kiY_ki ^*), I= 1,... P} are calculated and stored in a memory (not shown) (step S203).
[0054]
Thereafter, among the azimuths obtained by dividing the rotation direction of the rotation shaft 106 into M, the azimuths {0 corresponding to 0 to π_j= 2jπ / M, j = 0, 1,... M / 2-1} at each frequency point k_iRMS amplitude value {2 based on the above equation (4) for each^1/2｜ F_ki(2jπ / M) |, j = 0, 1,... M / 2-1} are calculated (step S204). At this time, as described above, the absolute value of the frequency sample value | F_ki(2jπ / M) | and | F_kiSince (2jπ / M + π) | is equal, it is not necessary to calculate the RMS amplitude value in the direction corresponding to π to 2π.
[0055]
Further, the calculated M / 2 RMS amplitude values {2^1/2｜ F_kiThe maximum RMS amplitude value is selected from (2jπ / M) |, j = 0, 1,... M / 2-1}. The selected RMS amplitude value is expressed as frequency point k._iRMS evaluation value A_kiThis RMS evaluation value A_kiThe azimuths 2jπ / M and 2jπ / M + π exhibiting are set as the maximum azimuths (step S205).
[0056]
  Then, the specific frequency {f of the NRRO vibration component_i, I= 1,... P} and RMS evaluation value {A_ki, I= 1,... P} and each RMS evaluation value A_kiThe maximum direction {2j corresponding to_iπ / M, i= 1,... P} to create the table shown in FIG. 3 (step S206), and all RMS evaluation values A in the table_kiIs less than a predetermined value (step S207).
[0057]
As a result of the determination in step S207, all RMS evaluation values A_kiIf any one of them is larger than the predetermined value, it is determined that the rotation performance of the rotating shaft 106 is defective (step S208), and all the RMS evaluation values A_kiIs smaller than the predetermined value, it is determined that the rotation performance of the rotating shaft 106 is good (step S209). Thereafter, this process is terminated.
[0058]
  According to the first embodiment of the present invention, the vibration component in the x and y directions of the radial vibration of the rotating shaft 106 obtained by measurement from the x and y directions is subjected to a frequency sample value {X_k, Y_k, K = 0, 1,... N−1} (step S202), and the specific frequency {f of the NRRO vibration component selected from the converted frequency sample values in the x and y directions._i, I= 1,... P} corresponding to the frequency point {k_i, I= 1,... P} based on the frequency sample value of {}, the orientation {θ corresponding to 0 to π_j= 2jπ / M, j = 0, 1,... M / 2-1} for each azimuth, RMS amplitude value {2^1/2｜ F_ki(2jπ / M) |, j = 0, 1,... M / 2-1} are calculated (step S204), and the RMS evaluation value A is calculated from these RMS amplitude values._ki(Step S205), it is possible to eliminate the need to perform the Fourier transform for each direction, and to eliminate the need to calculate the RMS amplitude value in the direction corresponding to π to 2π, and perform a large amount of calculation. In addition, the NRRO vibration component of the radial vibration of the rotating body can be evaluated in real time in the production line.
[0059]
Next, an evaluation method according to the second embodiment of the present invention will be described with reference to the drawings.
[0060]
Similarly, the evaluation method according to the second embodiment of the present invention is executed by the evaluation apparatus 100 of FIG. 1 when evaluating the maximum amplitude of the NRRO vibration component depending on the direction and the direction exhibiting the maximum amplitude. The
[0061]
Hereinafter, the maximum amplitude evaluation process of the NRRO vibration component of the rotating shaft 106 executed by the evaluation apparatus 100 of FIG. 1 will be described with reference to the drawings.
[0062]
This process differs from the maximum amplitude evaluation process of FIG. 2 in the RMS amplitude value calculated in step S204.
[0063]
FIG. 4 is a flowchart of the maximum amplitude evaluation process of the NRRO vibration component of the rotating shaft 106 executed by the evaluation apparatus 100 of FIG.
[0064]
In the flowchart of FIG. 4, steps S201 to S203 and S207 to S209 are the same as those of the flowchart of FIG.
[0065]
In the process of FIG. 4, after step S203, among the azimuths obtained by dividing the rotation direction of the rotary shaft 106 into M, the azimuth {θ corresponding to 0 to π / 2 is obtained._j= 2jπ / M, j = 0, 1,... M / 4-1}, the frequency point k_iRMS amplitude value {2 based on the above formula (4) and the above formula (5) for each^1/2｜ F_ki(2jπ / M) |, 2^1/2｜ F_ki(2jπ / M + π / 2) |, j = 0, 1,... M / 4-1} are calculated (step S401).
[0066]
Further, the calculated M / 2 RMS amplitude values {2^1/2｜ F_ki(2jπ / M) |, 2^1/2｜ F_kiThe maximum amplitude value is selected from (2jπ / M + π / 2) |, j = 0, 1,... M / 4-1}. The selected RMS amplitude value is expressed as frequency point k._iRMS evaluation value A_kiThis RMS evaluation value A_kiIs set to the maximum azimuth 2jπ / M or 2jπ / M + π / 2 (step S402).
[0067]
  Then, the specific frequency {f of the NRRO vibration component_i, I= 1,... P} and RMS evaluation value {A_ki,i = 1,... P} and each RMS evaluation value A_kiThe maximum direction {2j corresponding to_iπ / M or 2j_iπ / M + π / 2, i= 1,... P}, the table shown in FIG. 5 is created (step S403). Thereafter, the processing after step S207 in the processing of FIG. 2 is performed.
[0068]
  According to the second embodiment of the present invention, it is only necessary to calculate sin (2jπ / M) and cos (2jπ / M) in the azimuth 2jπ / M = 0 to π / 2, and the azimuth 2jπ / M = 0 to 0 Specific frequency of the NRRO vibration component at π {f_i, I= 1,... P} is calculated (step S401), so that it is not necessary to calculate the RMS amplitude value over a half circumference in the rotation direction of the rotating body, thereby further reducing the calculation time.
[0069]
Next, an evaluation method according to the third embodiment of the present invention will be described with reference to the drawings.
[0070]
Similarly, the evaluation method according to the third embodiment of the present invention is executed by the evaluation apparatus 100 of FIG. 1 when evaluating the maximum amplitude of the NRRO vibration component that depends on the direction and the direction that exhibits the maximum amplitude. The
[0071]
Hereinafter, the maximum amplitude evaluation process of the NRRO vibration component of the rotating shaft 106 executed by the evaluation apparatus 100 of FIG. 1 will be described with reference to the drawings.
[0072]
This process differs from the maximum amplitude evaluation process of FIG. 2 in that the RMS evaluation value and the maximum direction are derived based on the addition theorem of trigonometric functions.
[0073]
FIG. 6 is a flowchart of the maximum amplitude evaluation process of the NRRO vibration component of the rotating shaft 106 executed by the evaluation apparatus 100 of FIG.
[0074]
In the flowchart of FIG. 6, steps S201 to S203 and S207 to S209 are the same as those of the flowchart of FIG.
[0075]
  In the process of FIG. 6, after step S203, the specific frequency {f of the NRRO vibration component_i, I= 1,... P}, RMS evaluation value {A_ki= 2^1/2｜ F_ki(Φ_ki/ 2) |, i= 1,... P} and the above formula (7) Based on each RMS evaluation value A_kiMaximum orientation corresponding to {θ_ki= Φ_ki/ 2, θ_ki+ Π, i= 1,... P} are derived analytically (step S601).
[0076]
  Then, the specific frequency {f of the NRRO vibration component_i, I= 1,... P} and RMS evaluation value {A_ki, I= 1,... P} and each RMS evaluation value A_kiMaximum orientation corresponding to {θ_ki, θ_ki+ Π, i= 1,... P}, the table shown in FIG. 7 is created (step S602). Thereafter, the processing after step S207 in the processing of FIG. 2 is performed.
[0077]
  According to the third embodiment of the present invention, the specific frequency {f of the NRRO vibration component_i, I= 1,... P} for each RMS evaluation value {A_ki= 2^1/2｜ F_ki(Φ_ki/ 2) |, i= 1,... P} and each RMS evaluation value A_kiMaximum orientation corresponding to {θ_ki= Φ_ki/ 2, θ_ki+ Π, i= 1,... P} are analytically derived based on the addition theorem of trigonometric functions (step S601), eliminating the need to calculate the RMS amplitude value for each direction in the rotational direction of the rotating body, thereby greatly reducing the calculation time. It can be shortened.
[0078]
Next, an evaluation method according to the fourth embodiment of the present invention will be described with reference to the drawings.
[0079]
Similarly, the evaluation method according to the fourth embodiment of the present invention is executed by the evaluation apparatus 100 in FIG. 1 when evaluating the maximum amplitude of the NRRO vibration component depending on the direction and the direction exhibiting the maximum amplitude. The
[0080]
Hereinafter, the maximum amplitude evaluation process of the NRRO vibration component of the rotating shaft 106 executed by the evaluation apparatus 100 of FIG. 1 will be described with reference to the drawings.
[0081]
This process is different from the maximum amplitude evaluation process of FIG. 2 in that a comprehensive RMS evaluation value and maximum direction at a frequency of a plurality of NRRO vibration components are derived at a time.
[0082]
  A calculation formula for deriving the overall RMS evaluation value and the maximum azimuth at a time is derived by the following procedure. First, the specific frequency {f of the calculated NRRO vibration component_i, I= 1,... P} P frequency points {k_i, I= 1,... P} | X at discrete points on the frequency axis corresponding to each_ki｜², | Y_ki｜², Re (X_kiY_ki ^*) {I= 1,... P} and the following formula (10) representing the following power spectrum is obtained based on the above formula (2).
[0083]
[Equation 5]

[0084]
Here, in the same manner as the procedure for deriving the equation (7) from the equation (2), the procedure based on the addition theorem of the trigonometric function is used to comprehensively calculate the frequencies of the plurality of NRRO vibration components from the equation (10). Maximum orientation θ_maxThe following formula (11) representing is derived.
[0085]
[Formula 6]

[0086]
Further, similar to the procedure for deriving the equation (9) from the equation (2), the overall RMS at the frequencies of the plurality of NRRO vibration components from the equation (10) is obtained by the procedure based on the addition theorem of the trigonometric function. Evaluation value A_totalThe following formula (12) representing is derived.
[0087]
[Expression 7]

[0088]
FIG. 8 is a flowchart of the maximum amplitude evaluation process of the NRRO vibration component of the rotating shaft 106 executed by the evaluation apparatus 100 of FIG.
[0089]
In the flowchart of FIG. 8, steps S201 to S203 are the same as those of the flowchart of FIG.
[0090]
  In the process of FIG. 8, after step S203, the specific frequency {f of the NRRO vibration component calculated in step S203._i, I= 1,... P} P frequency points {k_i, I= 1,... P} | X at discrete points on the frequency axis corresponding to each_ki｜², | Y_ki｜², Re (X_kiY_ki ^*) {I= 1,... P}, the overall maximum orientation θ based on the above formula (11) and the above formula (12)._max, Θ_max+ Π and RMS evaluation value A_totalIs calculated (step S801).
[0091]
Next, in step S802, the RMS evaluation value A_totalWhether or not is smaller than a predetermined value is determined.
[0092]
As a result of the determination in step S802, the RMS evaluation value A_totalIs larger than the predetermined value, it is determined that the rotational performance of the rotating shaft 106 is defective (step S803), and the RMS evaluation value A_totalIs smaller than the predetermined value, it is determined that the rotation performance of the rotating shaft 106 is good (step S804). Thereafter, this process is terminated.
[0093]
In addition, the comprehensive RMS evaluation value and the maximum azimuth are not derived at once, but the azimuth {θ corresponding to 0 to π among the azimuths obtained by dividing the rotation direction of the rotation shaft 106 into M pieces._j= 2jπ / M, j = 0, 1,... M / 2-1} for each orientation, a power spectrum is obtained based on the above formula (10), and the largest one of these power spectra is an RMS evaluation value. A_totalYou may choose as
[0094]
  According to the fourth embodiment, the specific frequency {f of the NRRO vibration component_i, I= 1,... P} overall maximum orientation θ_max, θ_max+ Π and RMS evaluation value A_totalAre derived at a time (step S801), the overall RMS value of the NRRO vibration component of the rotating body can be evaluated.
[0095]
Next, an evaluation method according to the fifth embodiment of the present invention will be described.
[0096]
Similarly, the evaluation method according to the fifth embodiment of the present invention is executed by the evaluation apparatus 100 of FIG. 1 when evaluating the maximum amplitude of the NRRO vibration component depending on the direction and the direction exhibiting the maximum amplitude. The
[0097]
The maximum amplitude evaluation process of the NRRO vibration component in the evaluation method according to the fifth embodiment of the present invention is the same as the maximum amplitude evaluation process of FIGS. In that the spectral dispersion caused by
[0098]
  Leakage is a phenomenon caused by the time limit when sampling the vibration component to be analyzed, whereas the frequency spectrum of a single frequency sine wave must be essentially a single line spectrum. Is a phenomenon in which the spectrum is dispersed at a plurality of frequency points. The frequency point mismatch is a specific frequency of the NRRO vibration component {f_i, I= 1,... P} and the frequency sample value {X obtained by the FFT algorithm_k, Y_k, K = 0, 1,... N−1} discrete frequency points {k_i, I= 1,... P}.
[0099]
Hereinafter, conventional measures against spectral dispersion caused by leakage and frequency point mismatch in this process will be described.
[0100]
First, the problem and countermeasure of spectral dispersion caused by conventional leakage and frequency point mismatch are described in detail in US Pat. No. 5,420,501. According to this, in order to evaluate a certain frequency component within an allowable error, the square of the frequency sample values of a plurality of frequency points adjacent to each other and close to the frequency of the vibration component to be evaluated on the frequency axis. The sum is calculated, and a constant appropriate for the square root of the calculated sum of squares (for example, 2 in the above formulas (3), (4), (5) and (9)).^1/2And a correction value for a window function such as a Hanning window to be used).
[0101]
On the other hand, the vibrations in the x and y directions having the same frequency in a steady vibration phenomenon have a constant relationship between the amplitude ratio and the phase difference on the time axis. A pair of frequency samples in the x and y directions {X_k, Y_k} Has the property that the relationship between the mutual amplitude ratio and the phase difference is constant. Therefore, at each of the plurality of frequency points, the amplitude value of the frequency sample value in the same direction as the maximum direction of the frequency of the vibration component to be evaluated is always larger than the amplitude value of the frequency sample value in any other direction.
[0102]
This processing is based on the countermeasures of the above-mentioned US Pat. No. 5,420,501 and the characteristics of the vibration in the x and y directions of the same frequency in the steady vibration phenomenon. The NRRO vibration component is evaluated in consideration of the spectral dispersion caused by the mismatch.
[0103]
  Hereinafter, the maximum amplitude evaluation process of the NRRO vibration component of the rotating shaft 106 executed by the evaluation apparatus 100 of FIG. 1 will be described with reference to the drawings.
  FIG. 9 is a flowchart of the maximum amplitude evaluation process of the NRRO vibration component of the rotating shaft 106 executed by the evaluation apparatus 100 of FIG.
  In the flowchart of FIG. 9, steps S201 to S202 and S205 to S209 are the same as those of the flowchart of FIG.
  In the process of FIG. 9, after step S202, the specific frequency {f of the NRRO vibration component to be evaluated_i, I= 1,... P} corresponding to each frequency point k_iM frequency points {k_i -m / 2, k_i -m / 2 + 1,. . . k_i,. . . k_i + m / 2-1} For each {| X_{ki + l}｜², | Y_{ki + l}｜², Re (X_{ki + l}Y_{ki + l} ^*), L = −m / 2, −m / 2 + 1,. . . 0,. . . m / 2-1} are calculated and stored in a memory (not shown) (step S901).
  Then, for each of the azimuths {θj = 2jπ / M, j = 0, 1,... M / 2-1} corresponding to 0 to π among the azimuths obtained by dividing the rotation direction of the rotation shaft 106 into M pieces. M frequency points k above_iThe square of the frequency sample value of vibration represented by the following formula (13)_{ki + l}(2jπ / M) |²Is calculated (step S902).
  ｜ F_{ki + l}(2jπ / M) |²= | X_{ki + l}｜²cos²(2jπ / M)
  + | Y_{ki + l}｜²sin²(2jπ / M)
  + 2Re (X_{ki + l}Y_{ki + l} ^*) Sin (2jπ / M) cos (2jπ / M)
                                                          ... (13)
  Next, the square of the calculated m frequency sample values {| F_{ki + l}(2jπ / M) |², L = −m / 2, −m / 2 + 1,. . . 0,. . . m / 2-1} is calculated, the square root of the calculated total is calculated, and the calculated square root is calculated as 2^1/2By multiplying, the RMS amplitude value of the frequency point ki in each direction represented by the following formula (14) is calculated (step S903).
[0104]
[Equation 8]

[0105]
  Thereafter, the processing after step S205 in the processing of FIG. 2 is performed.
  In the fifth embodiment, m is implicitly set to an even number, but it is obvious that the evaluation can be similarly performed with an odd number.
  In the fifth embodiment, as in the third embodiment of the present invention described above, the RMS evaluation value and the maximum azimuth may be analytically derived based on an addition theorem of trigonometric functions. Hereinafter, a method for analytically deriving the RMS evaluation value and the maximum azimuth based on the trigonometric addition theorem in the fifth embodiment will be described.
  First, the specific frequency {f of the NRRO vibration component to be evaluated_i,i = 1,... P} corresponding to each frequency point k_iM frequency points {k_i -m / 2, k_i -m / 2 + 1,. . . k_i,. . . k_i + m / 2-1} For each {| X_{ki + l}｜²+ | Y_{ki + l}｜², | X_{ki + l} ²+ Y_{ki + l} ²｜, Re (X_{ki + l}Y_{ki + l} ^*), L = −m / 2, −m / 2 + 1,. . . 0,. . . m / 2-1}, and the m frequency points {k_i -m / 2, k_i -m / 2 + 1,. . . k_i,. . . k_i + m / 2-1}, The square of the frequency sample value of vibration represented by the following formula (15) {| F_{ki + l}(Φ_ki/ 2) |², L = −m / 2, −m / 2 + 1,. . . 0,. . . m / 2-1} is calculated.
    ｜ F_{ki + l}(Φ_ki/ 2) |²=
    (| X_{ki + l}｜²+ | Y_{ki + l}｜²+ | X_{ki + l} ²+ Y_{ki + l} ²|) / 2 ... (15)
  Then, the square of the calculated m frequency sample values {| F_{ki + l}(Φ_ki/ 2) |², L = −m / 2, −m / 2 + 1,. . . 0,. . . m / 2-1} is calculated, the square root of the calculated total is calculated, and the calculated square root is calculated as 2^1/2Frequency point k represented by the following formula (16) by multiplying_iThe RMS evaluation value is calculated.
[0106]
[Equation 9]

[0107]
  In addition, as described above, the frequency sample value pair {X_{ki + l}, Y_{ki + l}}, The relationship between the mutual amplitude ratio and the phase difference is constant at any frequency point. Therefore, the frequency point k_iThe maximum azimuth that gives the RMS evaluation value can be calculated by the following equation (17).
    θ_i= Φ_ki/ 2
    = [Tan^-1 [ Re (X_kiY_ki ^*) / (| X_ki｜²− | Y_ki｜²)]] / 2
  as well as
    θπ_i= Φ_ki/ 2 ± π (17)
  According to the fifth embodiment, since the spectral dispersion caused by the leakage and the frequency point mismatch is considered, the specific frequency {f of the NRRO vibration component is considered._i, I= 1,... P} RMS evaluation value {A_ki, I= 1,... P} can be evaluated within an acceptable error.
[0108]
【The invention's effect】
As described in detail above, according to the radial vibration evaluation method for a rotating body according to claim 1, each vibration component obtained by measuring from two directions is converted into a frequency spectrum by Fourier transform, Since the amplitude of radial vibration at a specific frequency is calculated for each direction based on the converted frequency spectrum in two directions, it is not necessary to perform Fourier transform for each direction, and production can be performed without performing a large amount of calculation. The NRRO vibration component of the radial vibration of the rotating body can be evaluated in real time in the line.
[Brief description of the drawings]
FIG. 1 is a diagram showing a schematic configuration of an evaluation apparatus that executes an evaluation method according to a first embodiment of the present invention, wherein (a) is a front view and (b) is a side view.
FIG. 2 is a flowchart of a maximum amplitude evaluation process of an NRRO vibration component of a rotating shaft 106 executed by the evaluation apparatus 100 of FIG.
3 is a rotational performance determination table of a rotating shaft 106 used in the maximum amplitude evaluation process of FIG.
4 is a flowchart of a maximum amplitude evaluation process of an NRRO vibration component of a rotating shaft 106 executed by the evaluation apparatus 100 of FIG.
5 is a rotational performance determination table of a rotating shaft 106 used in the maximum amplitude evaluation process of FIG.
6 is a flowchart of a maximum amplitude evaluation process for an NRRO vibration component of a rotating shaft 106 executed by the evaluation apparatus 100 of FIG. 1;
7 is a rotational performance determination table of a rotating shaft 106 used in the maximum amplitude evaluation process of FIG.
FIG. 8 is a flowchart of a maximum amplitude evaluation process for an NRRO vibration component of a rotating shaft 106 executed by the evaluation apparatus 100 of FIG. 1;
9 is a flowchart of processing for evaluating the maximum amplitude of the NRRO vibration component of the rotating shaft 106, which is executed by the evaluation apparatus 100 of FIG. 1;
FIG. 10 is a diagram for explaining a conventional method for evaluating radial vibration of a rotating body.
[Explanation of symbols]
100 Evaluation equipment
101 Displacement sensor
102 Displacement measuring device
103 computer
104 motor
105 coupling
106 Rotating shaft
107 spindle

Claims (10)

A radial vibration whose amplitude changes depending on the direction of the rotation direction of the rotating body, and is obtained by measuring the radial vibration having a predetermined frequency asynchronous with the rotational speed of the rotating body from two different directions. In order to evaluate the maximum amplitude of the radial vibration and the direction exhibiting the maximum amplitude based on each of the vibration components, each of the vibration components measured from the two directions is converted into a frequency spectrum by Fourier transform. In the evaluation method for radial vibration of the rotating body, the amplitude of the radial vibration is calculated for each direction of the rotating direction of the rotating body based on the converted frequency spectrum in the two directions . And
The vibration component x (t) in the radial vibration in the x direction and the vibration component y (t) in the radial vibration in the y direction are measured, and the vibration components x (t) and y (t) are divided every Δt. N point discrete value series {x _n = x (nΔt) , y _n = y (nΔt), n = 0 , 1 , ... N−1}
A frequency sample value {X _k , Y _k , k = 0 , 1 , ... N−1} represented by X _k , Y _k is _obtained by performing a discrete Fourier transform on the discrete value series ,
P number of specific frequency _{{f i, i = 1,} ... P} P number of frequency points corresponding to _{{k i, i = 1,} ... P} and the corresponding frequency sample values {X _ki, Y _ki, i = 1 , ... P} is selected from the frequency sample values {X _k , Y _k , k = 0 , 1 , ... N−1}, and {| X _ki | ² , | Y _ki | ² , Re (X _ki Y _ki ^* ), i = 1 , ... P},
Of the orientations obtained by dividing the rotational direction of the rotating body into M pieces, each of the orientations {θ _j = 2jπ / M, j = 0 , 1 , ... M / 2-1} corresponding to 0 to π. RMS amplitude value {2 ^1/2 | F _ki (2jπ / M) |, j = 0 , 1 , ... M / 2-1} is calculated for each frequency point k _{i in the} azimuth ,
A maximum RMS amplitude value is calculated from the RMS amplitude value {2 ^1/2 | F _ki (2jπ / M) |, j = 0 , 1 , ... M / 2-1} calculated for each frequency point k _i. Select as the RMS evaluation value A _ki of the point k _i ,
A method for evaluating radial vibration of a rotating body, wherein the radial vibration of the rotating body is evaluated based on the RMS evaluation value A _ki . The rotating body according to claim 1 , wherein the specific frequency {f _i , i = 1 ,... P} of the NRRO vibration component and the RMS evaluation value {A _ki , i = 1 _,. Evaluation method of radial vibration of the. A radial vibration whose amplitude changes depending on the direction of the rotation direction of the rotating body, and is obtained by measuring the radial vibration having a predetermined frequency asynchronous with the rotational speed of the rotating body from two different directions. In order to evaluate the maximum amplitude of the radial vibration and the direction exhibiting the maximum amplitude based on each of the vibration components, each of the vibration components measured from the two directions is converted into a frequency spectrum by Fourier transform. In the evaluation method of the radial vibration of the rotating body, the amplitude of the radial vibration is calculated for each azimuth of the rotating direction of the rotating body based on the converted two-direction frequency spectrum.
The vibration component x (t) in the radial vibration in the x direction and the vibration component y (t) in the radial vibration in the y direction are measured, and the vibration components x (t) and y (t) are divided every Δt. N point discrete value series {x _n = x (nΔt), y _n = y (nΔt), n = 0, 1,... N−1}
Frequency sample values {X _k , Y _k , k = 0, 1,... N−1} represented by X _k , Y _k are obtained by performing a discrete Fourier transform on the discrete value series,
Frequency points {X _ki , Y _ki , i corresponding to P frequency points {k _i , i = 1 ,... P} corresponding to P specific frequencies {f _i , i = 1 _,. = 1 ,... P} is selected from the frequency sample values {X _k , Y _k , k = 0, 1,... N−1}, and {| X _ki | ² , | Y _ki | ² , Re (X _ki Y _ki ^* ), i = 1 ,...
Of the orientations obtained by dividing the rotational direction of the rotating body into M, orientations corresponding to 0 to π / 2 {θ _j = 2jπ / M, j = 0, 1,... M / 4-1} RMS amplitude values for each frequency point k _i in each orientation _{^{{2 1/2 | F ki (2jπ}} / M) |, 2 1/2 | F ki (2jπ / M + π / 2) |, j = 0,1, ... M / 4-1} is calculated,
RMS amplitude value {2 ^1/2 | F _ki (2jπ / M) |, 2 ^1/2 | F _ki (2jπ / M + π / 2) |, j = 0,1, calculated for each frequency point k _i ... select the maximum amplitude value from M / 4-1} as the RMS evaluation value A _ki of the frequency point k _i ,
Evaluation method of radial vibration of that rotating member to and evaluating the radial vibration of the rotating body on the basis of the RMS evaluation value A _ki. A radial vibration whose amplitude changes depending on the direction of the rotation direction of the rotating body, and is obtained by measuring the radial vibration having a predetermined frequency asynchronous with the rotational speed of the rotating body from two different directions. In order to evaluate the maximum amplitude of the radial vibration and the direction exhibiting the maximum amplitude based on each of the vibration components, each of the vibration components measured from the two directions is converted into a frequency spectrum by Fourier transform. In the evaluation method of the radial vibration of the rotating body, the amplitude of the radial vibration is calculated for each azimuth of the rotating direction of the rotating body based on the converted two-direction frequency spectrum.
The vibration component x (t) in the radial vibration in the x direction and the vibration component y (t) in the radial vibration in the y direction are measured, and the vibration components x (t) and y (t) are divided every Δt. N point discrete value series {x _n = x (nΔt), y _n = y (nΔt), n = 0, 1,... N−1}
Frequency sample values {X _k , Y _k , k = 0, 1,... N−1} represented by X _k , Y _k are obtained by performing a discrete Fourier transform on the discrete value series,
Frequency points {X _ki , Y _ki , i corresponding to P frequency points {k _i , i = 1 ,... P} corresponding to P specific frequencies {f _i , i = 1 _,. = 1 ,... P} is selected from the frequency sample values {X _k , Y _k , k = 0, 1,... N−1}, and {| X _ki | ² , | Y _ki | ² , Re (X _ki Y _ki ^* ), i = 1 ,...
Based on the following formula, RMS evaluation value {A _ki = 2 ^1/2 | F _ki (φ _ki / 2) |, i = 1 ,... P} is calculated for each frequency point k _i .
2 ^1/2 | F _h (φ _h / 2) | = (| X _h | ² + | Y _h | ² + | X _h ² + Y _h ² |) ^1/2
Evaluation method of radial vibration of that rotating member to and evaluating the radial vibration of the rotating body on the basis of the RMS evaluation value A _ki. A radial vibration whose amplitude changes depending on the direction of the rotation direction of the rotating body, and is obtained by measuring the radial vibration having a predetermined frequency asynchronous with the rotational speed of the rotating body from two different directions. In order to evaluate the maximum amplitude of the radial vibration and the direction exhibiting the maximum amplitude based on each of the vibration components, each of the vibration components measured from the two directions is converted into a frequency spectrum by Fourier transform. In the evaluation method of the radial vibration of the rotating body, the amplitude of the radial vibration is calculated for each azimuth of the rotating direction of the rotating body based on the converted two-direction frequency spectrum.
The vibration component x (t) in the radial vibration in the x direction and the vibration component y (t) in the radial vibration in the y direction are measured, and the vibration components x (t) and y (t) are divided every Δt. N point discrete value series {x _n = x (nΔt), y _n = y (nΔt), n = 0, 1,... N−1}
Frequency sample values {X _k , Y _k , k = 0, 1,... N−1} represented by X _k , Y _k are obtained by performing a discrete Fourier transform on the discrete value series,
Frequency points {X _ki , Y _ki , i corresponding to P frequency points {k _i , i = 1 ,... P} corresponding to P specific frequencies {f _i , i = 1 _,. = 1 ,... P} is selected from the frequency sample values {X _k , Y _k , k = 0, 1,... N−1}, and {| X _ki | ² , | Y _ki | ² , Re (X _ki Y _ki ^* ), i = 1 ,...
Based on the following equation to calculate the frequency points _{{k i, i = 1,} ... P} overall RMS evaluation values A _total for,

The overall RMS evaluation value evaluation method of radial vibration of that rotating member to and evaluating the radial vibration of the rotating body on the basis of the A _total. A radial vibration whose amplitude changes depending on the direction of the rotation direction of the rotating body, and is obtained by measuring the radial vibration having a predetermined frequency asynchronous with the rotational speed of the rotating body from two different directions. In order to evaluate the maximum amplitude of the radial vibration and the direction exhibiting the maximum amplitude based on each of the vibration components, each of the vibration components measured from the two directions is converted into a frequency spectrum by Fourier transform. In the evaluation method of the radial vibration of the rotating body, the amplitude of the radial vibration is calculated for each azimuth of the rotating direction of the rotating body based on the converted two-direction frequency spectrum.
The vibration component x (t) in the radial vibration in the x direction and the vibration component y (t) in the radial vibration in the y direction are measured, and the vibration components x (t) and y (t) are divided every Δt. N point discrete value series {x _n = x (nΔt), y _n = y (nΔt), n = 0, 1,... N−1}
Frequency sample values {X _k , Y _k , k = 0, 1,... N−1} represented by X _k , Y _k are obtained by performing a discrete Fourier transform on the discrete value series,
Frequency points {X _ki , Y _ki , i corresponding to P frequency points {k _i , i = 1 ,... P} corresponding to P specific frequencies {f _i , i = 1 _,. = 1 ,... P} is selected from the frequency sample values {X _k , Y _k , k = 0, 1,... N−1}, and {| X _ki | ² , | Y _ki | ² , Re (X _ki Y _ki ^* ), i = 1 ,...
Of the azimuths obtained by dividing the rotation direction of the rotator into M, each of the azimuths {θ _j = 2jπ / M, j = 0, 1,... M / 2-1} corresponding to 0 to π. Calculate the power spectrum for the frequency points {k _i , i = 1 ,...

The largest one of the power spectra is selected as a comprehensive RMS evaluation value A _total ,
The overall RMS evaluation value evaluation method of radial vibration of that rotating member to and evaluating the radial vibration of the rotating body on the basis of the A _total. A radial vibration whose amplitude changes depending on the direction of the rotation direction of the rotating body, and is obtained by measuring the radial vibration having a predetermined frequency asynchronous with the rotational speed of the rotating body from two different directions. In order to evaluate the maximum amplitude of the radial vibration and the direction exhibiting the maximum amplitude based on each of the vibration components, each of the vibration components measured from the two directions is converted into a frequency spectrum by Fourier transform. In the evaluation method of the radial vibration of the rotating body, the amplitude of the radial vibration is calculated for each azimuth of the rotating direction of the rotating body based on the converted two-direction frequency spectrum.
The vibration component x (t) in the radial vibration in the x direction and the vibration component y (t) in the radial vibration in the y direction are measured, and the vibration components x (t) and y (t) are divided every Δt. N point discrete value series {x _n = x (nΔt), y _n = y (nΔt), n = 0, 1,... N−1}
Frequency sample values {X _k , Y _k , k = 0, 1,... N−1} represented by X _k , Y _k are obtained by performing a discrete Fourier transform on the discrete value series,
P frequency points k _i corresponding to each of P specific frequencies {f _i , i = 1 ,... P} and adjacent to each other m frequency points {k _i -m / 2 , k _i -m / 2 + 1,. . . k _i,. . . For each of k _i + m / 2-1 }, {| X _{ki + l} | ² , | Y _{ki + l} | ² , Re (X _{ki + l} Y _{ki + l} ^* ), l = −m / 2, − m / 2 + 1,. . . 0,. . . m / 2-1},
Of the azimuths obtained by dividing the rotation direction of the rotator into M, each of the azimuths {θ _j = 2jπ / M, j = 0, 1,... M / 2-1} corresponding to 0 to π. It said m frequency points _{{ki -m / 2, k i} -m / 2 + 1, depending on the orientation. . . k _i,. . . k _i + m / 2-1 } square of the frequency sample value of vibration {| F _{ki + l} (2jπ / M) | ² , l = −m / 2, −m / 2 + 1,. . . 0,. . . m / 2-1},
The calculated square values {| F _{ki + l} (2jπ / M) | ² , l = −m / 2, −m / 2 + 1,. . . 0,. . . m / 2-1} and an RMS amplitude value based on the following formula,

The RMS amplitude values for each frequency point ^{_{k i {2 1/2 | F ki}} (2jπ / M) |, j = 0,1, ... M / 2-1} from the frequency point k _i a maximum RMS amplitude Select RMS evaluation value A _ki ,
Evaluation method of radial vibration of that rotating member to and evaluating the radial vibration of the rotating body on the basis of the RMS evaluation value A _ki. A radial vibration whose amplitude changes depending on the direction of the rotation direction of the rotating body, and is obtained by measuring the radial vibration having a predetermined frequency asynchronous with the rotational speed of the rotating body from two different directions. In order to evaluate the maximum amplitude of the radial vibration and the direction exhibiting the maximum amplitude based on each of the vibration components, each of the vibration components measured from the two directions is converted into a frequency spectrum by Fourier transform. In the evaluation method of the radial vibration of the rotating body, the amplitude of the radial vibration is calculated for each azimuth of the rotating direction of the rotating body based on the converted two-direction frequency spectrum.
The vibration component x (t) in the radial vibration in the x direction and the vibration component y (t) in the radial vibration in the y direction are measured, and the vibration components x (t) and y (t) are divided every Δt. N point discrete value series {x _n = x (nΔt), y _n = y (nΔt), n = 0, 1,... N−1}
Frequency sample values {X _k , Y _k , k = 0, 1,... N−1} represented by X _k , Y _k are obtained by performing a discrete Fourier transform on the discrete value series,
P frequency points k _i corresponding to each of P specific frequencies {f _i , i = 1 ,... P} and adjacent to each other m frequency points {k _i -m / 2 , k _i -m / 2 + 1,. . . k _i,. . . For each of k _i + m / 2-1 }, {| X _{ki + l} | ² , | Y _{ki + l} | ² , Re (X _{ki + l} Y _{ki + l} ^* ), l = −m / 2, − m / 2 + 1,. . . 0,. . . m / 2-1},
Square values {| F _{ki + l} (φ _ki / 2) | ² , l = −m / 2, −m / 2 + 1,. . . 0,. . . m / 2-1} is calculated based on the following formula,
| F _{ki + l} (φ _ki / 2) | ² = (| X _{ki + l} | ² + | Y _{ki + l} | ² + | X _{ki + l} ² + Y _{ki + l} ² |) / 2
Based on the following formula, the RMS evaluation value A _ki of the frequency point k _i is calculated,

A method for evaluating radial vibration of a rotating body, wherein the radial vibration of the rotating body is evaluated based on the RMS evaluation value A _ki . The method for evaluating radial vibrations of a rotating body according to any one of claims 1 to 8, wherein an azimuth exhibiting a maximum amplitude of the radial vibration is a maximum azimuth. An apparatus for evaluating radial vibration of a rotating body that measures the radial vibration of the rotating body using the method for evaluating radial vibration of the rotating body according to any one of claims 1 to 9 .

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