JP4219162B2 - Active dynamic damper device - Google Patents

Description

【００１３】

【００１４】
床面振動を角周波数ωの正弦波変位ｘ_０とし、また、前記梃子８自体の質量を省略すると、ラプラス演算子ｓを使った運動方程式は次に示す（３）式のように纏められる。ただし、すべての変数（Ｆ_０、Ｆ_１、Ｆ_２、ｘ_０、ｘ、ｄｘ_１、ｘ_２）は交流分のみを表す。
【００１５】

【００１６】
前記（３）式において、第一式は前記錘９の運動方程式、第二式は前記構造物１１の運動方程式、第三式は前記超磁歪素子４の変位で発生した機械応力と制御応力の和、第四と第五式は前記梃子８に作用する各力の平衡式、第六式は前記超磁歪素子４の変位と前記構造物１１の変位と前記錘９の変位との関係式である。
前記（３）式における第一、第四式により、次に示す（４）式のような関係式を求めることができる。
【００１７】

【００１８】
また、前記（３）式における第六、第三、第五と第一式により、次に示す（５）式のような関係式を求めることができる。
【００１９】

【００２０】
前記（５）式から、前記錘９の上下変位ｘ_２と前記構造物１１の上下変位ｘとの関係式は次に示す（６）式のように求められる。
【００２１】

【００２２】
前記（４）と（６）式を前記（３）式における第二式に代入し、整理すると、前記床面の上下変位ｘ_０から前記構造物１１の上下変位ｘまでの閉ループ系伝達関数は次に示す（７）式のように求められる。
【００２３】

【００２４】
ここで、“電気ばね”Ｋ_ｅ(ｓ)を次に示す（８）式のように設計すると、閉ループ系伝達関数Ｇ(ｓ)は次に示す（９）式のように求められる。
【００２５】

【００２６】

【００２７】
ただし、ｙとｚは前記アンプ１０の各ゲイン（Ｋ_Ｐ、Ｋ_Ｉ、Ｋ_Ｄ、Ｋ_２Ｄ）を設計するための中間パラメータ、ｄ（ｓ）は閉ループ系特性多項式、ａ_ｉ（ｉ＝０〜３）は特性多項式の各係数である。
一例として真鍋係数図法により前記中間パラメータｙとｚを設計することができる。真鍋係数図法は制御系設計手法として公知となり、前願の特開２００２−３２５４７１号公報にも記載があり、ここで、その詳細の説明を省略する。
以下、真鍋係数図法により前記中間パラメータｙとｚを設計する。
【００２８】
前記（９）式の閉ループ系特性多項式に対して真鍋係数図法の安定度指標γ_ｉ（ｉ＝１〜２）は次に示す（１０）式となる。
【００２９】

【００３０】
γ_１、γ_２より、前記中間パラメータｙとｚは、次に示す（１１）式の関係がある。
【００３１】

【００３２】
前記（１１）式の数値解を求めるのが困難であるが、幾何作図の手法を用いて（１１）式で表す２組の曲線を描いてその交点を求めることにより前記中間パラメータｙとｚを求めることができる。その詳細は本発明の具体例を参照下さい。
【００３３】
以下、図３と図４を参照し、前記（８）式で表した“電気ばね”Ｋ_ｅ(ｓ)の各定数（−ｋ_１、ｙ、ｚ）から、前記アンプ１０の各ゲインの決定方法を説明する。
図３は制御回路の構成を示す図である。ここで、Ｒ_１とＬ_１は前記励磁コイル５の抵抗とインダクタンス、Ｒ_２とＬ_２は前記信号コイル６の抵抗とインダクタンスである。Ｋ(ｓ)は前記アンプ１０の入、出力間の伝達関数である。
前記アンプ１０の入力インピーダンスが十分大きいので、前記アンプ１０の出力電圧ｕと前記信号コイル６の誘起電圧ｕ_２は次に示す（１２）式の関係がある。
【００３４】

【００３５】
また、前記アンプ１０の出力インピーダンスが十分小さいので、前記出力電圧ｕを前記励磁コイル５の両端に加えると、励磁コイルの電流は次に示す（１３）式のようになる。
【００３６】

【００３７】
逆磁歪効果によって、前記超磁歪素子４の上下変位ｄｘ_１により前記励磁コイル５と信号コイル６に誘起電圧ｕ_１とｕ_２が発生する。ヒステリシスなど非線形現象が存在するが、動作点の近辺で線形特性としてｄｘ_１とｕ_１、ｕ_２の関係を表現すると、次に示す（１４）式が得られる。
【００３８】

【００３９】
ここで、β_１とβ_２は誘起電圧の発生係数である。ラプラス演算子のｓは前記誘起電圧ｕ_１とｕ_２は前記超磁歪素子４の上下変位ｄｘ_１の微分量、即ちｄｄｘ_１／ｄｔに比例することを表す。また、前記超磁歪素子４の上下変位ｄｘ_１で起きた前記磁束変化ｄΦ_１とｄΦ_２は反対の向きを持つから、（１４）式の第二式に“−”を付けた。
【００４０】
一方、磁歪効果によって前記励磁コイル５に流した電流ｉにより前記超磁歪素子４に働く上下方向の制御応力ｆを生成する。同様に動作点の近辺で線形特性として前記電流ｉと応力ｆの関係を表現すると、次に示す（１５）式が得られる。
【００４１】

【００４２】
ここで、ｋ_ｉは制御応力の発生係数である。
前記（１２）式〜（１５）式から、前記超磁歪素子４の変位ｄｘ_１から超磁歪素子に働く制御応力ｆまでの信号流れは図４に示すブロック線図のようになる。
図４から、前記超磁歪素子４の上下変位ｄｘ_１から前記超磁歪素子４に働く制御応力ｆまでの伝達関数、即ち、前記“電気ばね”Ｋ_ｅ(ｓ)は次に示す（１６）式のように求められる。
【００４３】

【００４４】
前記（８）式を前記（１６）式に代入し整理すると、前記アンプ１０の伝達関数Ｋ(ｓ)は前記中間パラメータｙとｚの関数として、次に示す（１７）式のように表すことができる。
【００４５】

【００４６】
前記（１７）式から、本発明の請求項２において、前記アンプ１０の入力から出力までの伝達関数Ｋ(ｓ)は比例、積分、１次微分、２次微分制御によって構成されることが分かる。
【００４７】
以上のまとめとして、本発明のアクティブダイナミックダンパ装置は図１に示すように、永久磁石１と、励磁コイル５と予圧を与える板ばね７を有する超磁歪素子４とを鉄心２、２１で繋がることによって閉磁路を構成し、かつ、該永久磁石１と、該永久磁石１と超磁歪素子４の間に信号コイル６を有する鉄心２１と空気ギャップ３とを鉄心２、２１で繋がることによって内磁路を構成し、前記信号コイル６と前記励磁コイル５をアンプ１０の入、出力とし、前記超磁歪素子４の出力軸には先端に錘９を固着した梃子８を接し、構造物１１に一体支持された支点１２にて上下可動させる。
前記アンプ１０の入力から出力までの伝達関数Ｋ(ｓ)は、比例、積分、１次微分、２次微分制御で構成され、中間パラメータｙとｚにより前記アンプ１０の伝達関数の各ゲイン（ＫＰ、ＫＩ、ＫＤ、Ｋ２Ｄ）を設計すれば、構造物１１の振動抑制制御ができる。
【００４８】
以下、数値例を挙げて、本発明の実施の具体的形態をさらに説明する。
数値例とした試作機の構造物１１の機械定数、アクティブダイナミックダンパ装置の定数、および真鍋係数図法の安定度指標は、構造物１１の質量Ｍ、構造物１１の支持のばね定数ｋ_０、構造物１１の支持の粘性係数ｃ_０、超磁歪素子４の機械ばね定数ｋ_１、超磁歪素子４の機械粘性係数ｃ_１、梃子比ｒ、錘９の質量ｍ、誘起電圧発生係数β_１とβ_２、制御応力発生係数ｋ_ｉ、励磁コイル５の抵抗Ｒ_１、励磁コイル５のインダクタンスＬ_１、安定度指標γ_１、γ_２を次に示す（１８）式の値としたときの中間パラメータｙ、ｚ、およびアンプ１０の伝達関数の各ゲインＫ_Ｐ、Ｋ_Ｉ、Ｋ_Ｄ、Ｋ_２Ｄの決定例について説明する。
【００４９】

【００５０】
（１８）式の各定数を（１１）式に代入し、（１１）式の幾何解は図６に示すように双曲線と双直線との三つの交点として次に示す（１９）式のように求められる。
【００５１】

【００５２】
制御系を安定にするための必要条件として、前記（９）式の分母に示す閉ループ系特性多項式ｄ(ｓ)の各係数はａ_ｉ＞０（または、ａ_ｉ＜０）（ｉ＝０〜３）を満たさなければならないので、該条件をチェックすることにより前記（１９）式に（ｙ_３、ｚ_３）のみが安定解として得られた。
ｙ＝-174.15とｚ＝-2.658、および前記（１８）式に示す各定数を前記（１７）式に代入し計算すると、前記アンプ１０の伝達関数の各ゲイン（Ｋ_Ｐ、Ｋ_Ｉ、Ｋ_Ｄ、Ｋ_２Ｄ）は次に示す（２０）式のように求められる。
【００５３】

【００５４】
（２０）式に示す伝達関数を有するアンプ１０を図１に示すアクティブダイナミックダンパ装置に適用すると、床面の上下変位ｘ_０から構造物１１の上下変位ｘまでの伝達関数の周波数応答特性シミュレーションは図７に示す実線のように構造物１１の固有共振周波数ｆ_０（＝２０Ｈｚ）の近辺でゲイン特性のピークが低く抑えられたことが分かる。ただし、図７に示す破線はアクティブダイナミックダンパ装置を装着しない場合、床面の上下変位ｘ_０から構造物１１の上下変位ｘまでの周波数応答特性シミュレーションである。図８に床面にステップ状の上下変位ｘ_０（＝10μｍ）が発生する場合の構造物１１の上下変位ｘの時間応答シミュレーションを示す。ただし、破線はアクティブダイナミックダンパ装置を装着しない場合、実線はアクティブダイナミックダンパ装置を装着する場合に対応する。図８に示す時間応答シミュレーションから、本発明のアクティブダイナミックダンパ装置を用いると、構造物１１の上下振動が速やかに抑制できることがわかる。
【００５５】
図９に床面の上下変位ｘ_０から超磁歪素子４の上下変位ｄｘ_１までの伝達関数の周波数応答特性シミュレーションを示す。図１０にｘ_０＝10μｍのステップ状の床面変位が発生する場合の超磁歪素子４の上下変位ｄｘ_１の時間応答シミュレーションを示し、超磁歪素子４に最大ｄｘ_１＝76μｍの上下変位が起きる。しかし、超磁歪素子４に大きな上下変位が取れないため、梃子比ｒをｒ＞１のように大きくし、超磁歪素子４の小さな上下変位だけで錘９の上下方向の大変位を生成することによって、構造物１１の上下振動を減衰することができる。以下、梃子比をｒ＝５としたときの設計結果を述べる。
【００５６】
梃子比ｒ＝５の場合、中間パラメータｘとｙを求めるための前記（１１）式の幾何解は、図１１に示すように双曲線と双直線との三つの交点として次に示す（２１）式のように求められる。
【００５７】

【００５８】
制御系を安定にするための必要条件をチェックすることにより前記（２１）式に（ｙ_３、ｚ_３）のみが安定解として得られた。
ｙ＝445とｚ＝-66.44、および前記（１８）式に示す各定数を前記（１７）式に代入し計算すると、アンプ１０の伝達関数の各ゲイン（Ｋ_Ｐ、Ｋ_Ｉ、Ｋ_Ｄ、Ｋ_２Ｄ）は次に示す（２２）式のように求められる。
【００５９】

【００６０】
（２２）式に示す伝達関数を有するアンプ１０を図１に示すアクティブダイナミックダンパ装置に適用すると、床面の上下変位ｘ_０から構造物１１の上下変位ｘまでの伝達関数の周波数応答特性シミュレーションは図１２に示す実線のように構造物１１の固有共振周波数ｆ_０（＝２０Ｈｚ）の近辺でゲイン特性のピークが低く抑えられたことが分かる。図１３に床面にステップ状の上下変位ｘ_０（＝10μｍ）が発生する場合の構造物１１の上下変位ｘの時間応答シミュレーションを示す。ただし、破線はアクティブダイナミックダンパ装置を装着しない場合、実線はアクティブダイナミックダンパ装置を装着する場合に対応する。図１３を図８と比べると、梃子比ｒ＝５の場合はｒ＝１の場合とほぼ同じ程度の制振効果を達成できる。
【００６１】
一方、図１４に床面の上下変位ｘ_０から超磁歪素子の上下変位ｄｘ_１までの伝達関数の周波数応答特性シミュレーションを示す。ただし、ゲイン特性に破線と実線はそれぞれ梃子比ｒ＝１とｒ＝５に対応する。ｒ＝５の場合のゲイン特性（実線）はｒ＝１の場合のゲイン特性（破線）より低いので、梃子比を大きくすれば、超磁歪素子の上下変位が小さくなることがわかる。図１５に床面にｘ_０＝10μｍのステップ状の上下変位が発生する場合の超磁歪素子の上下変位ｄｘ_１の時間応答シミュレーションを示す。ただし、破線と実線はそれぞれｒ＝１とｒ＝５に対応する。ｒ＝１の最大76μｍの超磁歪素子の上下変位に対し、ｒ＝５の場合、超磁歪素子の上下変位の最大値はおよそ五分の一の16μｍに抑えられた。
【００６２】
【発明の効果】
以上説明したように本願の発明によれば、構造物の制振制御に振動センサを使うことなく、しかも、除振機構部を被除振体の下に取り付ける必要もなく、被除振体としての構造物の上に取り付けるアクティブダイナミックダンパ装置を、永久磁石と超磁歪素子と鉄心とコイルとアンプと梃子と錘などで構成し、床面の上下変位から構造物の上下変位までの閉ループ系伝達関数の周波数応答のゲイン特性のピーク値を低く抑えるようにアンプの伝達関数の各ゲインを設計することによって、構造物の上下振動抑制制御を提供することができ、実用上、有用性の高いものである。
【図面の簡単な説明】
【図１】本発明の請求項１記載のアクティブダイナミックダンパ装置の構成図である。
【図２】本発明の制御系を示すモデル図である。
【図３】本発明の制御回路の構成を示す図である。
【図４】超磁歪素子の変位から制御応力までの信号流れを示すブロック線図である。
【図５】従来のダイナミックダンパを示すモデル図である。
【図６】梃子比ｒ＝１のときの中間パラメータｙとｚの幾何解を示す図である。
【図７】梃子比ｒ＝１の制御を適用したときの床面の上下変位から構造物の上下変位までの周波数応答特性図である。
【図８】梃子比ｒ＝１の制御を適用したときの構造物の上下変位の時間応答特性図である。
【図９】梃子比ｒ＝１の制御を適用したときの床面の上下変位から超磁歪素子の上下変位までの周波数応答特性図である。
【図１０】梃子比ｒ＝１の制御を適用したときの超磁歪素子の上下変位の時間応答特性図である。
【図１１】梃子比ｒ＝５のときの中間パラメータｙとｚの幾何解を示す図である。
【図１２】梃子比ｒ＝５の制御を適用したときの床面の上下変位から構造物の上下変位までの周波数応答特性図である。
【図１３】梃子比ｒ＝５の制御を適用したときの構造物の上下変位の時間応答特性図である。
【図１４】梃子比ｒ＝５の制御を適用したときの床面の上下変位から超磁歪素子の上下変位までの周波数応答特性図である。
【図１５】梃子比ｒ＝５の制御を適用したときの超磁歪素子の上下変位の時間応答特性図である。
【符号の説明】
１ 永久磁石
２ 上側の鉄心
２１ 下側の鉄心
２２ 空気ギャップ側の鉄心
３ 空気ギャップ
４ 超磁歪素子
５ 励磁コイル
６ 信号コイル
７ 板ばね
８ 梃子
９ 錘
１０ アンプ
１１ 構造物
１２ 支点
Ｍ 構造物の質量
ｋ_０ 構造物の支持のばね定数
ｃ_０ 構造物の支持の粘性係数
ｍ 錘の質量
ｋ_１ 超磁歪素子のばね定数
ｃ_１ 超磁歪素子の粘性係数
ｘ_０ 床面の上下変位
ｘ 構造物の上下変位
ｄｘ_１ 超磁歪素子の上下変位
ｘ_２ 錘の上下変位
Φ 永久磁石から発生した磁束
Φ_１ 超磁歪素子を通す磁束
ｄΦ_１ 超磁歪素子を通す磁束Φ_１に起きた磁束変化
Φ_２ 空気ギャップを通す磁束
ｄΦ_２ 空気ギャップを通す磁束Φ_２に起きた磁束変化
ｆ 超磁歪素子に働く制御応力
Ｆ_０ 構造物に固定される支点の梃子に対する引張力
Ｆ_１ 超磁歪素子の梃子に対する支持力
Ｆ_２ 錘の梃子に対する圧力
ｆ_０ 構造物の固有共振周波数
ｕ_１ 励磁コイルの誘起電圧
ｕ_２ 信号コイルの誘起電圧
ｕ アンプの出力電圧
ｉ 励磁コイルに流す制御電流
Ｋ_ｅ(ｓ) 超磁歪素子の上下変位から制御応力ｆまでの伝達関数
ｌ 超磁歪素子の梃子に対する支持点から固定支持までの距離
Ｌ 錘から固定支持までの距離
ｒ 梃子比（Ｌ／ｌ）
β_１ 超磁歪素子の上下変位による励磁コイルの誘起電圧の発生係数
β_２ 超磁歪素子の上下変位による信号コイルの誘起電圧の発生係数
ｋ_ｉ 制御応力の発生係数
Ｋ(ｓ) アンプの入力から出力までの伝達関数
Ｋ_Ｐ アンプの伝達関数の比例ゲイン
Ｋ_Ｉ アンプの伝達関数の積分ゲイン
Ｋ_Ｄ アンプの伝達関数の１次微分ゲイン
Ｋ_２Ｄ アンプの伝達関数の２次微分ゲイン
Ｇ(ｓ) 床面の上下変位から構造物の上下変位までの閉ループ系の伝達関数
ｓ ラプラス演算子
d（ｓ） 閉ループ系特性多項式
ａ_ｉ 閉ループ系特性多項式の各係数
γ_ｉ 真鍋係数図法の安定度指標
Ｒ_１ 励磁コイルの抵抗
Ｌ_１ 励磁コイルのインダクタンス
Ｒ_２ 信号コイルの抵抗
Ｌ_２ 信号コイルのインダクタンス
ｙ 中間パラメータのその１
ｚ 中間パラメータのその２[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an active dynamic damper device.
[0002]
[Prior art]
Various methods have been considered in the past to suppress the vertical vibration of the structure. In this structure, instead of directly dissipating the vertical vibration energy of the structure by damping, an auxiliary vibration system is added as shown in FIG. 5 to thereby absorb the vibration energy of the structure. There is a way.
A conventional dynamic damper is a pendulum composed of a spring and a weight, and has a specific resonance frequency. If this is mounted on the structure, when vertical vibration is applied to the structure from the outside, if the vibration frequency is the same as the resonance of the dynamic damper, the excitation force from the outside and the force that the dynamic damper pushes back Cancel each other, and the vertical vibration of the structure can be suppressed. However, the damping effect cannot be exhibited in a frequency band other than the natural resonance frequency of the dynamic damper.
When an external excitation force acts over a wide frequency band, it is necessary to incorporate a damping element in the dynamic damper. As the design method, there are a design method based on a maximum value minimization criterion called fixed point theory and a design method based on a minimum dispersion criterion (see, for example, Non-Patent Document 1).
As a design procedure based on the fixed point theory, the mass m of the additional system attached as a dynamic damper is first determined, the ratio μ (= m / M) between the mass m of the weight and the mass M of the structure is obtained, and then the optimum The spring constant k ₁ of the additional system is determined by the design method, and finally the viscosity coefficient c ₁ is determined. Therefore, different dynamic dampers are required for different structures. That is, if the mass M of the target structure or the spring constant k _{0 of the} support changes, the constants m, k ₁ and c ₁ of the dynamic damper must be changed. When the dynamic damper designed in this way is attached to the structure, the maximum value of the vibration magnification from the vertical displacement of the floor surface to the vertical displacement of the structure is √ ((μ + 2) / μ). For example, when μ = 0.1, the maximum value is 4.58, that is, if the floor surface amplitude is 1 at the frequency causing the maximum value, the amplitude of the structure is 4.58 times. As the mass ratio μ is increased, the maximum amplitude of the structure can be reduced, but the mass of the weight of the dynamic damper cannot be increased too much due to physical limitations such as space.
As a conventional technique, there is an active vibration isolator using a giant magnetostrictive actuator (see, for example, Patent Document 1).
The active vibration isolator includes a base portion, a mounting plate, a small displacement actuator having a giant magnetostrictive element or a piezo element, a large displacement actuator having an air actuator or a linear motor, a vibration sensor such as an accelerometer, and a vibration removal device including a laminated rubber. A vibration mechanism unit and a control device unit that controls the vibration isolation mechanism unit are provided. The mounting plate is supported by a large displacement actuator and laminated rubber so as to be slidable in the vertical direction. The small displacement actuator and the large displacement actuator are arranged horizontally between the base portion and the mounting plate, and the vibration isolation body is isolated by displacing the position of the mounting plate with respect to the base portion in the vertical direction. That is, a vibration sensor is necessary for the active vibration isolator. Moreover, it is necessary to attach the vibration isolation mechanism of the active vibration isolator under the vibration isolation body. The cost due to the use of the vibration sensor increases. On the other hand, when the vibration isolation mechanism is attached under the vibration isolation body, it may be impossible to attach the vibration isolation mechanism.
[0003]
[Non-Patent Document 1]
The Japan Society of Mechanical Engineers, “Vibration damping technology” published by Yokendo Co., Ltd., September 1, 1998, p. 49-56
[Patent Document 1]
JP 2001-50334 A (page 1-3, FIG. 1)
[0004]
[Problems to be solved by the invention]
As described above, the vertical vibration suppression of the structure by the conventional dynamic damper is not an active method, and there is a problem that each constant of the dynamic damper must be changed when the mass of the structure and the spring constant of the support are changed. Moreover, the conventional active vibration isolator requires a vibration sensor, and the vibration isolation mechanism must be attached under the vibration isolator.
[0005]
The present invention has been made in view of the above-mentioned problems of the prior art, and does not require the use of a vibration sensor, and it is not necessary to attach the vibration isolation mechanism part under the vibration isolation body. For the purpose of providing an active dynamic damper device simply by mounting on a vibrating body,
In claim 1, an active dynamic damper device is constituted by a permanent magnet, a giant magnetostrictive element, an iron core, an air gap, a coil, an amplifier, a leaf spring, a weight, an insulator, and the like.
3. The active dynamic damper device according to claim 1, wherein the transfer function K (s) from the input to the output of the amplifier is proportional, integral, first derivative, and second derivative control. .
[0006]
[Means for Solving the Problems] In other words, the means for achieving the object of the present invention is the dynamic damper device mounted on the structure 11 as the vibration isolator in the first aspect. A closed magnetic circuit is formed by connecting the exciting coil 5 and the giant magnetostrictive element 4 having the leaf spring 7 for applying a preload by the iron cores 2 and 21, and the permanent magnet 1, the permanent magnet 1, and the giant magnetostrictive element 4 An inner magnetic path is formed by connecting the iron core 22 having the signal coil 6 between the air gap 3 and the iron cores 2 and 21, and the signal coil 6 and the exciting coil 5 are used as input and output of the amplifier 10, and the super An active dynamic damper device is characterized in that an output shaft of the magnetostrictive element 4 is in contact with a lever 8 having a weight 9 fixed to the tip thereof and is movable up and down at a fulcrum 12 integrally supported by a structure 11.
[0007]
3. The active dynamic damper device according to claim 2, wherein the transfer function K (s) from the input to the output of the amplifier 10 is K (s) = K _P + K _I / s + K _D s + K _2D s ² .
[0008]
1 is a block diagram of an active dynamic damper device for explaining claim 1 of the present invention. In FIG. 1, a permanent magnet 1 is placed on a structure 11 as a vibration isolator. And a super magnetostrictive element 4 having a leaf spring 7 for applying a preload is connected by iron cores 2 and 21 to form a closed magnetic circuit, and the permanent magnet 1, the permanent magnet 1, and the super magnetostrictive element 4, an iron core 22 having a signal coil 6 and an air gap 3 are connected by iron cores 2 and 21 to form an inner magnetic path, and the signal coil 6 and the excitation coil 5 are input and output of an amplifier 10. An active dynamic damper device characterized in that an insulator 8 having a weight 9 fixed to the tip thereof is in contact with the output shaft of the giant magnetostrictive element 4 and is movable up and down at a fulcrum 12 integrally supported by a structure 11 is constructed. Yes. However, if the amplifier 10 cannot be installed on the structure 11 due to the weight or dimensions of the amplifier 10, the amplifier 11 may be installed at another location.
[0009]
Next, claim 2 will be described with reference to FIGS.
First, the operating principle of the active dynamic damper device shown in FIG. 1 will be described, and with reference to FIG. 2, the closed loop transfer function of the control system and how to obtain intermediate parameters (y, z) for control system design will be described. Finally, a method for determining each gain (K _P , K _I , K _D , K _2D ) of the amplifier 10 will be described with reference to FIGS.
[0010]
As shown in FIG. 1, since the inner magnetic path of the air gap 3 having the same magnetic resistance is formed in parallel with the giant magnetostrictive element 4, the magnetic flux Φ from the permanent magnet 1 is evenly Φ1 in the static state. (= Φ / 2) and Φ2 (= Φ / 2) are divided into the giant magnetostrictive element 4 and the air gap 3. Further, an appropriate magnetic bias is applied to the giant magnetostrictive element 4 by the magnetic flux Φ1. On the other hand, preload is applied by a leaf spring 7 at the upper end of the giant magnetostrictive element 4.
When the structure 11 is vibrated up and down by an external force such as vertical vibration (displacement is x0) of the floor surface (displacement is x), the weight 9 also starts to vibrate (displacement is x2). . A force that varies in the vertical direction is applied to the giant magnetostrictive element 4 through the fulcrum 12 of the insulator 8, and a vertical displacement dx1 occurs in the giant magnetostrictive element 4 due to the varying force, and the permeability of the giant magnetostrictive element 4 due to the inverse magnetostrictive effect. Therefore, a magnetic flux change dΦ1 occurs in the magnetic flux Φ1 passing through the giant magnetostrictive element 4. On the other hand, since the magnetic flux Φ from the permanent magnet 1 is constant in the closed magnetic path, the magnetic flux change dΦ2 also occurs in the inner magnetic path of the air gap 3 due to the magnetic flux change dΦ1 of the giant magnetostrictive element 4. Moreover, dΦ2 = −dΦ1. The induced voltages u1 and u2 are generated in the exciting coil 5 and the signal coil 6 by the magnetic flux changes dΦ1 and dΦ2.
When the vertical vibration of the floor surface is a sinusoidal displacement with a constant frequency, each of the above-described changes (x0, x, x2, dx1, dΦ1, dΦ2, u1, u2) also changes at the same frequency.
The induced voltage u2 of the signal coil 6 is input to the amplifier 10, the output voltage u of the amplifier 10 is applied to both ends of the exciting coil 5, and the sum of the output voltage u and the induced voltage u2 By controlling the current i, the control stress f acting on the giant magnetostrictive element is controlled, and the vertical vibration of the structure 11 is suppressed. Hereinafter, the stress f is referred to as a control stress.
[0011]
FIG. 2 shows a control system model.
Here, k ₀ , c _0, and M are the spring constant, the viscosity coefficient, and the mass of the structure 11 for supporting the structure 11. k ₁ and c ₁ are the spring constant and viscosity coefficient of the giant magnetostrictive element 4. K _e (s) is a transfer function from the vertical displacement dx ₁ of the giant magnetostrictive element 4 to the control stress f. Hereinafter, K _e (s) is referred to as an “electric spring”. l and L are length distributions of the insulator 8, and r = L / l is an insulator ratio. m is the mass of the weight 9. F ₀ , F ₁ and F ₂ are forces acting on the insulator 8, and among them, F ₀ is a tensile force due to the fulcrum 12 fixed to the structure 11, and F ₁ is due to the output shaft of the giant magnetostrictive element 4. The supporting force, F _2, is the pressure by the weight 9.
In the static state, the forces F ₀ , F ₁ and F ₂ have a relationship as shown in the following expressions (1) and (2).
[0012]

[0013]

[0014]
The floor vibration and sinusoidal displacement x ₀ of the angular frequency omega, also, omitting the mass of the lever 8 itself, the equation of motion using the Laplace operator s can be summarized as shown below (3). However, all the variables (F ₀ , F ₁ , F ₂ , x ₀ , x, dx ₁ , x ₂ ) represent only AC components.
[0015]

[0016]
In the equation (3), the first equation is the equation of motion of the weight 9, the second equation is the equation of motion of the structure 11, the third equation is the mechanical stress and control stress generated by the displacement of the giant magnetostrictive element 4. The sum, the fourth and fifth equations are the balance equations of the forces acting on the insulator 8, and the sixth equation is the relational expression of the displacement of the giant magnetostrictive element 4, the displacement of the structure 11 and the displacement of the weight 9. is there.
A relational expression such as the following expression (4) can be obtained from the first and fourth expressions in the expression (3).
[0017]

[0018]
Further, a relational expression such as the following expression (5) can be obtained from the sixth, third, fifth and first expressions in the expression (3).
[0019]

[0020]
From the equation (5), the relational expression between the vertical displacement x of the vertical displacement x ₂ and the structure 11 of the weight 9 is determined as shown below (6).
[0021]

[0022]
Wherein (4) and (6) by substituting the second equation in the formula (3), and rearranging, the closed loop transfer function from the vertical displacement x ₀ of the floor surface to the vertical displacement x of the structure 11 It is obtained as shown in the following equation (7).
[0023]

[0024]
Here, when the “electric spring” K _e (s) is designed as shown in the following equation (8), the closed-loop system transfer function G (s) is obtained as shown in the following equation (9).
[0025]

[0026]

[0027]
However, y and z are intermediate parameters for designing each gain (K _P , K _I , K _D , K _2D ) of the amplifier 10, d (s) is a closed-loop system characteristic polynomial, and a _i (i = 0 to 0). 3) is each coefficient of the characteristic polynomial.
As an example, the intermediate parameters y and z can be designed by the Manabe coefficient projection. The Manabe coefficient projection method is known as a control system design method, and is also described in Japanese Patent Application Laid-Open No. 2002-325471 of the previous application, and a detailed description thereof is omitted here.
Hereinafter, the intermediate parameters y and z are designed by the Manabe coefficient projection.
[0028]
The stability index γ _i (i = 1 to 2) of the Manabe coefficient projection with respect to the closed-loop characteristic polynomial of the equation (9) is expressed by the following equation (10).
[0029]

[0030]
From γ ₁ and γ ₂ , the intermediate parameters y and z have the relationship of the following expression (11).
[0031]

[0032]
Although it is difficult to obtain the numerical solution of the equation (11), the intermediate parameters y and z are obtained by drawing the two sets of curves represented by the equation (11) by using the method of geometric drawing and obtaining the intersections thereof. Can be sought. For details, see the specific example of the present invention.
[0033]
Hereinafter, with reference to FIG. 3 and FIG. 4, each gain of the amplifier 10 is determined from each constant (−k ₁ , y, z) of the “electric spring” K _e (s) expressed by the equation (8). A method will be described.
FIG. 3 is a diagram showing the configuration of the control circuit. Here, R ₁ and L ₁ are the resistance and inductance of the exciting coil 5, and R ₂ and L ₂ are the resistance and inductance of the signal coil 6. K (s) is a transfer function between the input and output of the amplifier 10.
Since the input impedance of the amplifier 10 is sufficiently large, the induced voltage u ₂ of the signal coil 6 and the output voltage u of the amplifier 10 is shown below (12) relationship with.
[0034]

[0035]
Further, since the output impedance of the amplifier 10 is sufficiently small, when the output voltage u is applied to both ends of the excitation coil 5, the current of the excitation coil is expressed by the following equation (13).
[0036]

[0037]
Due to the inverse magnetostrictive effect, induced voltages u ₁ and u ₂ are generated in the exciting coil 5 and the signal coil 6 due to the vertical displacement dx ₁ of the giant magnetostrictive element 4. Although nonlinear phenomena such as hysteresis exist, when the relationship between dx ₁ and u ₁ , u ₂ is expressed as a linear characteristic near the operating point, the following equation (14) is obtained.
[0038]

[0039]
Here, β ₁ and β ₂ are generation coefficients of the induced voltage. The Laplace operator s represents that the induced voltages u ₁ and u ₂ are proportional to the differential amount of the vertical displacement dx ₁ of the giant magnetostrictive element 4, that is, ddx ₁ / dt. Further, since the magnetic flux changes dΦ ₁ and dΦ ₂ caused by the vertical displacement dx ₁ of the giant magnetostrictive element 4 have opposite directions, “−” is added to the second expression of the expression (14).
[0040]
On the other hand, a vertical control stress f acting on the giant magnetostrictive element 4 is generated by the current i flowing through the exciting coil 5 due to the magnetostrictive effect. Similarly, when the relationship between the current i and the stress f is expressed as a linear characteristic in the vicinity of the operating point, the following equation (15) is obtained.
[0041]

[0042]
Here, k _i is a generation coefficient of control stress.
From the (12) to (15), the signal flow from the displacement dx ₁ of the super magnetostrictive element 4 to control stress f acting on the super-magnetostrictive element are as the block diagram shown in FIG.
From FIG. 4, the transfer function from the vertical displacement dx ₁ of the super magnetostrictive element 4 to the control stress f acting on the super magnetostrictive element 4, that is, the “electric spring” K _e (s) is expressed by the following equation (16): It is required as follows.
[0043]

[0044]
When the equation (8) is substituted into the equation (16) and rearranged, the transfer function K (s) of the amplifier 10 is expressed as the following equation (17) as a function of the intermediate parameters y and z. Can do.
[0045]

[0046]
From the equation (17), it can be seen that, in claim 2 of the present invention, the transfer function K (s) from the input to the output of the amplifier 10 is constituted by proportional, integral, first derivative, and second derivative control. .
[0047]
As a summary of the above, the active dynamic damper device of the present invention connects the permanent magnet 1 and the super magnetostrictive element 4 having the leaf spring 7 for applying the preload with the iron cores 2 and 21 , as shown in FIG. constitute a closed magnetic path by, and the inner magnetic and the permanent magnet 1, the core 21 and the air gap 3 having a signal coil 6 between the permanent magnet 1 and the super-magnetostrictive element 4 by lead in core 2 and 21 The signal coil 6 and the excitation coil 5 are input to and output from the amplifier 10, and the output shaft of the giant magnetostrictive element 4 is in contact with an insulator 8 having a weight 9 fixed to the tip, and is integrated with the structure 11. The fulcrum 12 is moved up and down.
The transfer function K (s) from the input to the output of the amplifier 10 is constituted by proportional, integral, first-order differentiation, and second-order differentiation control, and each gain (KP) of the transfer function of the amplifier 10 is determined by intermediate parameters y and z. , KI, KD, K2D), the vibration suppression control of the structure 11 can be performed.
[0048]
Hereinafter, specific embodiments of the present invention will be further described with numerical examples.
As a numerical example, the mechanical constant of the prototype structure 11, the constant of the active dynamic damper device, and the stability index of the Manabe coefficient projection are the mass M of the structure 11, the spring constant k ₀ of the support of the structure 11, the structure The viscosity coefficient c ₀ of the support of the object 11, the mechanical spring constant k _{1 of} the giant magnetostrictive element 4, the mechanical viscosity coefficient c ₁ of the giant magnetostrictive element 4, the insulator ratio r, the mass m of the weight 9, the induced voltage generation coefficients β ₁ and β ₂ , intermediate parameter y when control stress generation coefficient k _i , resistance R ₁ of exciting coil 5, inductance L ₁ of exciting coil 5, and stability indices γ ₁ and γ ₂ are values of the following equation (18) , Z, and gains K _P , K _I , K _D , and K _2D of the transfer function of the amplifier 10 will be described.
[0049]

[0050]
Each constant of the equation (18) is substituted into the equation (11), and the geometric solution of the equation (11) is represented by three intersections of a hyperbola and a hyperbola as shown in FIG. Desired.
[0051]

[0052]
As a necessary condition for stabilizing the control system, each coefficient of the closed loop system characteristic polynomial d (s) shown in the denominator of the equation (9) is a _i > 0 (or a _i <0) (i = 0 to 0). Since 3) must be satisfied, only (y ₃ , z ₃ ) was obtained as a stable solution in the above equation (19) by checking this condition.
When y = −174.15, z = −2.658, and the constants shown in the equation (18) are substituted into the equation (17) and calculated, the gains (K _P , K _I , K _D ) of the transfer function of the amplifier 10 are calculated. , K _2D ) is obtained by the following equation (20).
[0053]

[0054]
When an amplifier 10 having a transfer function shown in equation (20) is applied to an active dynamic damper device shown in FIG. 1, the frequency response characteristic simulation of the transfer function from vertical displacement x ₀ of the floor surface to the vertical displacement x of the structure 11 As shown by the solid line in FIG. 7, it can be seen that the peak of the gain characteristic is suppressed low in the vicinity of the natural resonance frequency f ₀ (= 20 Hz) of the structure 11. However, the broken lines shown in FIG. 7 when not wearing an active dynamic damper device, a frequency response characteristic simulation from vertical displacement x ₀ of the floor surface to the vertical displacement x of the structure 11. FIG. 8 shows a time response simulation of the vertical displacement x of the structure 11 when a step-like vertical displacement x ₀ (= 10 μm) occurs on the floor surface. However, the broken line corresponds to the case where the active dynamic damper device is not mounted, and the solid line corresponds to the case where the active dynamic damper device is mounted. From the time response simulation shown in FIG. 8, it can be seen that the vertical vibration of the structure 11 can be quickly suppressed by using the active dynamic damper device of the present invention.
[0055]
Figure 9 shows the frequency response characteristic simulation of the transfer function from vertical displacement x ₀ of the floor surface to the vertical displacement dx ₁ of the super magnetostrictive element 4. FIG. 10 shows a time response simulation of the vertical displacement dx ₁ of the giant magnetostrictive element 4 when a step-like floor surface displacement of x ₀ = 10 μm occurs, and the maximum vertical displacement of dx ₁ = 76 μm occurs in the giant magnetostrictive element 4. . However, since the giant magnetostrictive element 4 cannot take a large vertical displacement, the insulator ratio r is increased so that r> 1, and a large displacement in the vertical direction of the weight 9 is generated only by a small vertical displacement of the giant magnetostrictive element 4. Thus, the vertical vibration of the structure 11 can be damped. The design results when the insulator ratio is r = 5 will be described below.
[0056]
When the insulator ratio r = 5, the geometrical solution of the equation (11) for obtaining the intermediate parameters x and y is expressed by the following equation (21) as three intersections of a hyperbola and a hyperbola as shown in FIG. It is required as follows.
[0057]

[0058]
By checking the necessary conditions for stabilizing the control system, only (y ₃ , z ₃ ) was obtained as a stable solution in the equation (21).
When y = 445, z = -66.44, and the constants shown in the equation (18) are substituted into the equation (17) and calculated, the gains (K _P , K _I , K _D , K, K) of the transfer function of the amplifier 10 are calculated. _2D ) is obtained by the following equation (22).
[0059]

[0060]
(22) Applying the amplifier 10 having a transfer function shown in the expression active dynamic damper device shown in FIG. 1, the frequency response characteristic simulation of the transfer function from vertical displacement x ₀ of the floor surface to the vertical displacement x of the structure 11 It can be seen that the peak of the gain characteristic is suppressed to be low in the vicinity of the natural resonance frequency f ₀ (= 20 Hz) of the structure 11 as shown by the solid line in FIG. FIG. 13 shows a time response simulation of the vertical displacement x of the structure 11 when a step-like vertical displacement x ₀ (= 10 μm) occurs on the floor surface. However, the broken line corresponds to the case where the active dynamic damper device is not mounted, and the solid line corresponds to the case where the active dynamic damper device is mounted. Comparing FIG. 13 with FIG. 8, when the lever ratio r = 5, it is possible to achieve the vibration damping effect of almost the same degree as when r = 1.
[0061]
On the other hand, it shows the frequency response characteristic simulation of the transfer function from vertical displacement x ₀ of the floor surface 14 to vertical displacement dx ₁ of the super magnetostrictive element. However, the broken line and the solid line in the gain characteristic correspond to the lever ratios r = 1 and r = 5, respectively. Since the gain characteristic (solid line) when r = 5 is lower than the gain characteristic (dashed line) when r = 1, it can be seen that when the insulator ratio is increased, the vertical displacement of the giant magnetostrictive element is reduced. FIG. 15 shows a time response simulation of the vertical displacement dx ₁ of the giant magnetostrictive element when a stepwise vertical displacement of x ₀ = 10 μm occurs on the floor surface. However, the broken line and the solid line correspond to r = 1 and r = 5, respectively. In contrast to r = 1, the maximum vertical displacement of the giant magnetostrictive element of 76 μm, when r = 5, the maximum value of the vertical displacement of the giant magnetostrictive element was suppressed to about 1/5 of 16 μm.
[0062]
【The invention's effect】
As described above, according to the invention of the present application, it is not necessary to use a vibration sensor for vibration control of a structure, and it is not necessary to attach a vibration isolation mechanism part under the vibration isolation body. The active dynamic damper device mounted on the structure of the building is composed of permanent magnets, giant magnetostrictive elements, iron cores, coils, amplifiers, insulators, weights, etc., and closed-loop transmission from the vertical displacement of the floor to the vertical displacement of the structure By designing each gain of the transfer function of the amplifier so as to keep the peak value of the gain characteristic of the frequency response of the function low, it is possible to provide the vertical vibration suppression control of the structure, which is practically highly useful It is.
[Brief description of the drawings]
FIG. 1 is a configuration diagram of an active dynamic damper device according to claim 1 of the present invention;
FIG. 2 is a model diagram showing a control system of the present invention.
FIG. 3 is a diagram showing a configuration of a control circuit of the present invention.
FIG. 4 is a block diagram showing a signal flow from displacement of the giant magnetostrictive element to control stress.
FIG. 5 is a model diagram showing a conventional dynamic damper.
FIG. 6 is a diagram showing a geometric solution of intermediate parameters y and z when the insulator ratio r = 1.
FIG. 7 is a frequency response characteristic diagram from the vertical displacement of the floor surface to the vertical displacement of the structure when the control of the insulator ratio r = 1 is applied.
FIG. 8 is a time response characteristic diagram of vertical displacement of a structure when control of an insulator ratio r = 1 is applied.
FIG. 9 is a frequency response characteristic diagram from the vertical displacement of the floor surface to the vertical displacement of the giant magnetostrictive element when the control of the insulator ratio r = 1 is applied.
FIG. 10 is a time response characteristic diagram of vertical displacement of a giant magnetostrictive element when control of an insulator ratio r = 1 is applied.
FIG. 11 is a diagram showing a geometric solution of intermediate parameters y and z when the insulator ratio r = 5.
FIG. 12 is a frequency response characteristic diagram from the vertical displacement of the floor surface to the vertical displacement of the structure when the control of the insulator ratio r = 5 is applied.
FIG. 13 is a time response characteristic diagram of vertical displacement of a structure when control of an insulator ratio r = 5 is applied.
FIG. 14 is a frequency response characteristic diagram from the vertical displacement of the floor surface to the vertical displacement of the giant magnetostrictive element when the control of the insulator ratio r = 5 is applied.
FIG. 15 is a time response characteristic diagram of vertical displacement of a giant magnetostrictive element when control of an insulator ratio r = 5 is applied.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 Permanent magnet 2 Upper iron core 21 Lower iron core 22 Air gap side iron core 3 Air gap 4 Giant magnetostrictive element 5 Excitation coil 6 Signal coil 7 Leaf spring 8 Insulator 9 Weight 10 Amplifier 11 Structure 12 Support point M Mass of structure k ₀ Spring constant of support of structure c ₀ Viscosity coefficient of support of structure m Mass of mass k ₁ Spring constant of super magnetostrictive element c ₁ Viscosity coefficient of super magnetostrictive element x ₀ Vertical displacement of floor surface x Vertical movement of structure Displacement dx ₁ Vertical displacement of the giant magnetostrictive element x ₂ Vertical displacement of the spindle Φ Magnetic flux generated from the permanent magnet Φ ₁ Magnetic flux passing through the giant magnetostrictive element dΦ ₁ Magnetic flux passing through the giant magnetostrictive element Φ ₁ Magnetic flux change Φ ₂ Air gap Magnetic flux to be passed dΦ ₂ Magnetic flux change caused by magnetic flux Φ ₂ passing through the air gap Control stress F ₀ acting on the giant magnetostrictive element Tensile force F ₁ to the insulator of the fulcrum fixed to the structure F ₁ Supporting force F ₂ to the insulator of the giant magnetostrictive element To the insulator of the weight Pressure f ₀ natural resonance frequency of structure u ₁ induction voltage u of excitation coil ₂ induction voltage of signal coil u output voltage of amplifier i control current K _e (s) control stress caused by vertical displacement of giant magnetostrictive element Transfer function to f l Distance from support point to fixed support for insulator of giant magnetostrictive element L Distance from weight to fixed support r Insulator ratio (L / l)
β ₁ Magnetostrictive element induced voltage generation coefficient of exciting coil β ₂ Giant magnetostrictive element vertical coefficient generated coefficient of signal coil induced coefficient k _i Control stress generation coefficient K (s) Output from amplifier input Transfer function K up to _P amplifier transfer function proportional gain K _I amplifier transfer function integral gain K _D amplifier transfer function first derivative gain K _2D amplifier transfer function second derivative gain G (s) Floor Transfer function s Laplace operator from the vertical displacement of the structure to the vertical displacement of the structure
d (s) Closed loop system characteristic polynomial a _i Each coefficient of closed loop system characteristic polynomial γ _i Manabe coefficient projection stability index R ₁ Excitation coil resistance L ₁ Excitation coil inductance R ₂ Signal coil resistance L ₂ Signal coil inductance y of the intermediate parameter
z Intermediate parameter # 2

Claims (2)

In the dynamic damper device for suppressing the vibration of the structure (11) as the vibration isolator,
A closed magnetic circuit is formed by connecting a permanent magnet (1), an exciting coil (5), and a super magnetostrictive element (4) having a leaf spring (7) for applying a preload by an upper iron core (2) and a lower iron core (21). configure and upper and said permanent magnet (1), the air gap (3) and the iron core (22) having a signal coil (6) between said permanent magnet (1) and the super-magnetostrictive element (4) The inner core (2) and the lower iron core (21) are connected to form an inner magnetic path, and an amplifier (10) is provided that receives the voltage of the signal coil (6) and outputs it to the excitation coil (5). An output shaft of the giant magnetostrictive element (4) is in contact with an insulator (8) having a weight (9) fixed at the tip, and is movable up and down at a fulcrum integrally supported by the structure (11). Active dynamic damper device. The transfer function K (s) from the input to the output of the amplifier (10) is

The active dynamic damper device according to claim 1, wherein:

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