BW Professional Cutter Expert www.tool-tool.com

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弊社の全般供給体制及び技術自慢の総合専門製造メーカーに貴方のご体験を御待ちしております。

Bewise Inc. talaşlı imalat sanayinde en fazla kullanılan ve üç eksende (x,y,z) talaş kaldırabilen freze takımlarından olan Parmak Freze imalatçısıdır. Çok geniş ürün yelpazesine sahip olan firmanın başlıca ürünlerini Karbür Parmak Frezeler, Kalıpçı Frezeleri, Kaba Talaş Frezeleri, Konik Alın Frezeler, Köşe Radyüs Frezeler, İki Ağızlı Kısa ve Uzun Küresel Frezeler, İç Bükey Frezeler vb. şeklinde sıralayabiliriz.

BW специализируется в научных исследованиях и разработках, и снабжаем самым высокотехнологичным карбидовым материалом для поставки режущих / фрезеровочных инструментов для почвы, воздушного пространства и электронной индустрии. В нашу основную продукцию входит твердый карбид / быстрорежущая сталь, а также двигатели, микроэлектрические дрели, IC картонорезальные машины, фрезы для гравирования, режущие пилы, фрезеры-расширители, фрезеры-расширители с резцом, дрели, резаки форм для шлицевого вала / звездочки роликовой цепи, и специальные нано инструменты. Пожалуйста, посетите сайт www.tool-tool.com для получения большей информации.

BW is specialized in R&D and sourcing the most advanced carbide material with high-tech coating to supply cutting / milling tool for mould & die, aero space and electronic industry. Our main products include solid carbide / HSS end mills, micro electronic drill, IC card cutter, engraving cutter, shell end mills, cutting saw, reamer, thread reamer, leading drill, involute gear cutter for spur wheel, rack and worm milling cutter, thread milling cutter, form cutters for spline shaft/roller chain sprocket, and special tool, with nano grade. Please visit our web www.tool-tool.com for more info.

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個人分類：學術研究

Feb 27 Fri 2009 14:05
Galego Indutancia www.tool-tool.com

Bewise Inc. www.tool-tool.com Reference source from the internet.

Nun indutor, denomínase indutancia (L), á relación entre o fluxo magnético ( $\mathbf{\Phi}$ ) e a intensidade de corrente eléctrica(I):

$L = {\Phi \over I}$

歡迎來到Bewise Inc.的世界，首先恭喜您來到這接受新的資訊讓產業更有競爭力，我們是提供專業刀具製造商，應對客戶高品質的刀具需求，我們可以協助客戶滿足您對產業的不同要求，我們有能力達到非常卓越的客戶需求品質，這是現有相關技術無法比擬的，我們成功的滿足了各行各業的要求，包括：精密HSS DIN切削刀具、協助客戶設計刀具流程、DIN or JIS 鎢鋼切削刀具設計、NAS986 NAS965 NAS897 NAS937orNAS907 航太切削刀具,NAS航太刀具設計、超高硬度的切削刀具、醫療配件刀具設計、複合式再研磨機、PCD地板專用企口鑽石組合刀具、粉末造粒成型機、主機版專用頂級電桿、PCD V-Cut刀、捨棄式圓鋸片組、粉末成型機、主機版專用頂級電感、’汽車業刀具設計、電子產業鑽石刀具、木工產業鑽石刀具、銑刀與切斷複合再研磨機、銑刀與鑽頭複合再研磨機、銑刀與螺絲攻複合再研磨機等等。我們的產品涵蓋了從民生刀具到工業級的刀具設計；從微細刀具到大型刀具；從小型生產到大型量產；全自動整合；我們的技術可提供您連續生產的效能，我們整體的服務及卓越的技術，恭迎您親自體驗！！

BW Bewise Inc. Willy Chen willy@tool-tool.com bw@tool-tool.com www.tool-tool.com skype:willy_chen_bw mobile:0937-618-190 Head &Administration Office No.13,Shiang Shang 2nd St., West Chiu Taichung,Taiwan 40356 http://www.tool-tool.com / FAX:+886 4 2471 4839 N.Branch 5F,No.460,Fu Shin North Rd.,Taipei,Taiwan S.Branch No.24,Sec.1,Chia Pu East Rd.,Taipao City,Chiayi Hsien,Taiwan

Welcome to BW tool world! We are an experienced tool maker specialized in cutting tools. We focus on what you need and endeavor to research the best cutter to satisfy users’ demand. Our customers involve wide range of industries, like mold & die, aerospace, electronic, machinery, etc. We are professional expert in cutting field. We would like to solve every problem from you. Please feel free to contact us, its our pleasure to serve for you. BW product including: cutting tool、aerospace tool .HSS DIN Cutting tool、Carbide end mills、Carbide cutting tool、NAS Cutting tool、NAS986 NAS965 NAS897 NAS937orNAS907 Cutting Tools,Carbide end mill、disc milling cutter,Aerospace cutting tool、hss drill’Фрезеры’Carbide drill、High speed steel、Compound Sharpener’Milling cutter、INDUCTORS FOR PCD’CVDD(Chemical Vapor Deposition Diamond )’PCBN (Polycrystalline Cubic Boron Nitride) ’Core drill、Tapered end mills、CVD Diamond Tools Inserts’PCD Edge-Beveling Cutter(Golden Finger’PCD V-Cutter’PCD Wood tools’PCD Cutting tools’PCD Circular Saw Blade’PVDD End Mills’diamond tool. INDUCTORS FOR PCD . POWDER FORMING MACHINE ‘Single Crystal Diamond ‘Metric end mills、Miniature end mills、Специальные режущие инструменты ‘Пустотелое сверло ‘Pilot reamer、Fraises’Fresas con mango’ PCD (Polycrystalline diamond) ‘Frese’POWDER FORMING MACHINE’Electronics cutter、Step drill、Metal cutting saw、Double margin drill、Gun barrel、Angle milling cutter、Carbide burrs、Carbide tipped cutter、Chamfering tool、IC card engraving cutter、Side cutter、Staple Cutter’PCD diamond cutter specialized in grooving floors’V-Cut PCD Circular Diamond Tipped Saw Blade with Indexable Insert’ PCD Diamond Tool’ Saw Blade with Indexable Insert’NAS tool、DIN or JIS tool、Special tool、Metal slitting saws、Shell end mills、Side and face milling cutters、Side chip clearance saws、Long end mills’end mill grinder’drill grinder’sharpener、Stub roughing end mills、Dovetail milling cutters、Carbide slot drills、Carbide torus cutters、Angel carbide end mills、Carbide torus cutters、Carbide ball-nosed slot drills、Mould cutter、Tool manufacturer.

ようこそＢｅｗｉｓｅ　Ｉｎｃ.の世界へお越し下さいませ、先ず御目出度たいのは新たな

情報を受け取って頂き、もっと各産業に競争力プラス展開。

弊社は専門なエンド・ミルの製造メーカーで、客先に色んな分野のニーズ、

豊富なパリエーションを満足させ、特にハイテク品質要求にサポート致します。

弊社は各領域に供給できる内容は：

弊社の製品の供給調達機能は：

弊社の全般供給体制及び技術自慢の総合専門製造メーカーに貴方のご体験を御待ちしております。

Bewise Inc. talaşlı imalat sanayinde en fazla kullanılan ve üç eksende (x,y,z) talaş kaldırabilen freze takımlarından olan Parmak Freze imalatçısıdır. Çok geniş ürün yelpazesine sahip olan firmanın başlıca ürünlerini Karbür Parmak Frezeler, Kalıpçı Frezeleri, Kaba Talaş Frezeleri, Konik Alın Frezeler, Köşe Radyüs Frezeler, İki Ağızlı Kısa ve Uzun Küresel Frezeler, İç Bükey Frezeler vb. şeklinde sıralayabiliriz.

BW специализируется в научных исследованиях и разработках, и снабжаем самым высокотехнологичным карбидовым материалом для поставки режущих / фрезеровочных инструментов для почвы, воздушного пространства и электронной индустрии. В нашу основную продукцию входит твердый карбид / быстрорежущая сталь, а также двигатели, микроэлектрические дрели, IC картонорезальные машины, фрезы для гравирования, режущие пилы, фрезеры-расширители, фрезеры-расширители с резцом, дрели, резаки форм для шлицевого вала / звездочки роликовой цепи, и специальные нано инструменты. Пожалуйста, посетите сайт www.tool-tool.com для получения большей информации.

BW is specialized in R&D and sourcing the most advanced carbide material with high-tech coating to supply cutting / milling tool for mould & die, aero space and electronic industry. Our main products include solid carbide / HSS end mills, micro electronic drill, IC card cutter, engraving cutter, shell end mills, cutting saw, reamer, thread reamer, leading drill, involute gear cutter for spur wheel, rack and worm milling cutter, thread milling cutter, form cutters for spline shaft/roller chain sprocket, and special tool, with nano grade. Please visit our web www.tool-tool.com for more info.

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個人分類：學術研究

Feb 27 Fri 2009 13:58
Français Inductance www.tool-tool.com

Bewise Inc. www.tool-tool.com Reference source from the internet.

L'inductance d’un circuit électrique est un coefficient qui traduit le fait qu’un courant le traversant crée un champ magnétique à travers la section entourée par ce circuit. Il en résulte un flux du champ magnétique à travers la section limitée par ce circuit.

L’inductance est égale au quotient du flux de ce champ magnétique par l’intensité du courant traversant le circuit. L’unité de l’inductance est le Henry (H).

Par extension, on désigne par inductance tout circuit électrique ou dipôle électrique qui par sa construction a une certaine valeur d’inductance (grandeur physique). Ces dipôles sont généralement des bobines, souvent appelées inductances ou self (en anglais self inductance qui a donné le mot « self ») par abus de langage (ou métonymie) comme pour la résistance.

Inductance propre [modifier]

symbole de l'inductance

La définition la plus courante d'inductance propre est la suivante : La surface circonscrite par un circuit électrique parcouru par un courant I est traversée par le flux du champ magnétique (appelé autrefois flux d’induction) $\Phi\,$ . L’inductance L du circuit électrique est alors définie comme le rapport entre le flux embrassé par le circuit et le courant :

$L = \frac{\Phi}{I} \,$

Il est important de préciser que le flux $\Phi\,$ en question est celui produit par le courant I et non celui provenant d'une autre source (courant, aimant, etc.).

Malgré sa popularité, cette définition présente deux inconvénients. Le premier est que la définition de l'inductance est donnée en fonction du flux $\Phi\,$ qui est une grandeur physique inaccessible directement. Il n'existe pas de moyen de mesurer le flux magnétique sans le faire varier en fonction du temps. Le second inconvénient est que la « surface circonscrite par le circuit » n'est pas toujours facile à déterminer et, dans certains cas, elle n'existe même pas (par exemple si le circuit « fait un nœud »).

Une deuxième définition qui ne présente pas ces inconvénients est :

$u=-L{di\over dt}\,$

où :

L est l'inductance propre du circuit ou composant.
u est la tension aux bornes du circuit.
${di\over dt}\,$ est la variation du courant qui traverse le circuit avec le temps (mesurée en ampères/seconde).
u et i sont des valeurs instantanées.

nous remarquons que :

Lorsque le courant est constant, di/dt est nul et par conséquent la tension u auto-induite est nulle aussi.
Le signe (-) indique que la tension auto-induite aux bornes de l'inductance s'oppose aux variations du courant qui la traverse.
Quand on applique une tension constante à une inductance, le courant qui rentre par l'extrémité positive augmente avec le temps.

Ce n'est qu'en utilisant cette définition que l'on pourrait mesurer la valeur de l'inductance d'un circuit et, à partir de là, déterminer le flux magnétique équivalent qui traverse la « surface circonscrite » équivalente mais il faudrait pour cela que la tension aux bornes de cette portion de circuit ne dépende que de phénomènes magnétiques. Malheureusement celle -ci dépend d'un grand nombre d'effets physiques très divers (dont l'effet Joule), ce qui empêche toute mesure éventuelle de l'inductance d'une portion de circuit

De plus, cette définition n'est pas valable pour des portions de circuit présentant des non-linéarités (par exemple : des inductances à noyau ferromagnétique). La valeur de l'inductance dépendra alors de la valeur du courant et de son histoire (hystérésis).

Une partie du flux produit par le courant traverse le câble lui-même. Il convient donc de distinguer l’inductance externe et l’inductance interne d’un circuit. L’inductance interne d’un câble diminue lorsque la fréquence du courant augmente à cause de l’effet pelliculaire ou effet de peau. En pratique, l'effet de peau est presque complet à partir d'une ou deux dizaines de kilohertzs et l'inductance ne varie plus.

Inductance mutuelle [modifier]

Lorsqu’un circuit 1 traversé par un courant noté $i_1 \,$ , produit un champ magnétique à travers un circuit 2, on peut écrire :

$M_{1/2} = \frac{\Phi_2}{i_1} \,$

La valeur de cette inductance mutuelle dépend des deux circuits en présence (caractéristiques géométriques, nombre de spires) mais aussi de leur position relative : éloignement et orientation.

Le dipôle « Inductance », ou bobine [modifier]

Son symbole dans les schémas est L. Une inductance L est un dipôle tel que :

$u = L \frac{di}{dt} \,$

Cette relation vient de l’expression du flux du champ magnétique et de la loi de Faraday qui seront vues en magnétostatique :

$u =\frac{d\Phi}{dt} \,$ et de $\Phi= L \cdot i \,$

Cette équation montre que l’intensité du courant traversant une inductance ne peut pas subir de discontinuité, cela correspondrait en effet à une tension infinie à ses bornes, donc à une puissance infinie.

Puissance instantanée [modifier]

Remarque : on ne peut stocker que de l'énergie. Le terme puissance emmagasinée est donc un abus de langage qui correspond en réalité à la puissance que l'on fournit à l'inductance et qui vient augmenter l'énergie emmagasinée dans cette dernière.

La puissance instantanée fournie à l'inductance est égale à :

$P = u \cdot i = L \frac{di}{dt} \cdot i\,$

En utilisant la transformation mathématique suivante :

$\frac{d(i^2)}{dt} =i \cdot \frac{d(i)}{dt} + \frac{d(i)}{dt}\cdot i = 2 \frac{d(i)}{dt}\cdot i \,$

on obtient la relation :

$P = \frac{1}{2} \cdot L \frac{d(i^2)}{dt} \,$

La puissance instantanée fournie à une inductance est liée à la variation du carré de l’intensité qui la traverse : si celui-ci augmente, l’inductance emmagasine de l'énergie. Elle en restitue dans le cas contraire.

L’énergie échangée entre 2 instants ti et tf vaut :

$W = \frac{1}{2} \cdot L (i^2_{tf}-i^2_{ti}) \,$

Il en résulte qu’il est difficile de faire varier rapidement le courant qui circule dans une bobine et ceci d’autant plus que la valeur de son inductance sera grande. Cette propriété est souvent utilisée pour supprimer de petites variations de courant non désirées.

L’effet de l’inductance face aux variations du courant est analogue en mécanique à l’effet de la masse face aux variations de la vitesse : quand on veut augmenter la vitesse il faut fournir de l’énergie cinétique et ceci d’autant plus que la masse est grande. Quand on veut freiner, il faut récupérer cette énergie. Débrancher une bobine parcourue par un courant, c’est un peu arrêter une voiture en l’envoyant contre un mur.

Puissance en régime sinusoïdal [modifier]

En régime sinusoïdal, une inductance idéale (dont la résistance est nulle) ne consomme pas de puissance active. En revanche, il y a stockage ou restitution d’énergie par la bobine lors des variations de l'intensité du courant.

Impédance [modifier]

A chaque instant [modifier]

$\frac{di}{dt} = \frac{U}{L}$ .

On a $u(t) = U\sqrt{2}\sin(\omega t)$ et $i(t) = I\sqrt{2}\sin(\omega t - \varphi)$ .

$\frac{di}{dt} = \frac{U}{L}\sqrt{2}\sin(\omega t)$

Donc $i(t) = \left(\frac{U}{L}\sqrt{2}\right)\left(-\frac{1}{\omega}\cos(\omega t)\right) = \frac{U}{L\omega}\sqrt{2}(-\cos(\omega t))$

On obtient finalement : $i(t) = \frac{U}{L\omega}\sqrt{2}\sin\left(\omega t -\frac{\pi}{2}\right) = I\sqrt{2}\sin(\omega t - \varphi)$ . Donc : $I = \frac{U}{L\omega}$ .

Loi d'Ohm en valeurs efficaces : $U = L\omega I = ZI \Leftrightarrow Z = L\omega = 2\pi Lf$ avec Z en Ohms, L en Henrys, ω en rad/s et f en Hz.

En continu, f = 0: une bobine parfaite se comporte comme un court-circuit (en effet : $Z = 0 \Rightarrow U = 0\cdot I = 0[V]$ ).

Pente de la droite = 2πL

En complexes [modifier]

$\underline{U}=\underline{Z}\,\underline{I}$ avec

$\underline{U} = [U, 0]$
$\underline{I} = [I = \frac{U}{L\omega}, -\frac{\pi}{2} rad]$

D'où : $|\underline{Z}| = Z = \frac{U}{I} = L\omega$ ; et $Arg(\underline{Z}) = \varphi = \frac{\pi}{2}$

On en déduit que $\underline{Z} = \mathbf{j}L\omega$ avec $\underline{Z}$ imaginaire pur de la forme $\underline{Z} = \mathbf{j}X$ et X = Lω > 0.

Ouverture du circuit [modifier]

Articles détaillés : Ouverture d'un circuit inductif et Tension transitoire de rétablissement.

Les inductances s'opposant à la variation du courant qui les traverse, l'ouverture d'un circuit inductif parcouru par un courant peut amener des surtensions. Ces surtensions oscillent avec une pulsation $\textstyle{\omega = {1\over \sqrt{LC}}}$ . $\scriptstyle{{C}}$ représentant les capacités parasites du circuit. La tension maximale de l'oscillation peut être très élevée. Ceci vient du fait qu'après l'interruption du courant l'énergie de l'inductance $\scriptstyle{{1\over 2}LI^2}$ a été transférée aux capacités parasites sous la forme $\scriptstyle{{1\over 2}CV^2}$ .

Voir aussi [modifier]

Liens internes [modifier]

歡迎來到Bewise Inc.的世界，首先恭喜您來到這接受新的資訊讓產業更有競爭力，我們是提供專業刀具製造商，應對客戶高品質的刀具需求，我們可以協助客戶滿足您對產業的不同要求，我們有能力達到非常卓越的客戶需求品質，這是現有相關技術無法比擬的，我們成功的滿足了各行各業的要求，包括：精密HSS DIN切削刀具、協助客戶設計刀具流程、DIN or JIS 鎢鋼切削刀具設計、NAS986 NAS965 NAS897 NAS937orNAS907 航太切削刀具,NAS航太刀具設計、超高硬度的切削刀具、醫療配件刀具設計、複合式再研磨機、PCD地板專用企口鑽石組合刀具、粉末造粒成型機、主機版專用頂級電桿、PCD V-Cut刀、捨棄式圓鋸片組、粉末成型機、主機版專用頂級電感、’汽車業刀具設計、電子產業鑽石刀具、木工產業鑽石刀具、銑刀與切斷複合再研磨機、銑刀與鑽頭複合再研磨機、銑刀與螺絲攻複合再研磨機等等。我們的產品涵蓋了從民生刀具到工業級的刀具設計；從微細刀具到大型刀具；從小型生產到大型量產；全自動整合；我們的技術可提供您連續生產的效能，我們整體的服務及卓越的技術，恭迎您親自體驗！！

BW Bewise Inc. Willy Chen willy@tool-tool.com bw@tool-tool.com www.tool-tool.com skype:willy_chen_bw mobile:0937-618-190 Head &Administration Office No.13,Shiang Shang 2nd St., West Chiu Taichung,Taiwan 40356 http://www.tool-tool.com / FAX:+886 4 2471 4839 N.Branch 5F,No.460,Fu Shin North Rd.,Taipei,Taiwan S.Branch No.24,Sec.1,Chia Pu East Rd.,Taipao City,Chiayi Hsien,Taiwan

Welcome to BW tool world! We are an experienced tool maker specialized in cutting tools. We focus on what you need and endeavor to research the best cutter to satisfy users’ demand. Our customers involve wide range of industries, like mold & die, aerospace, electronic, machinery, etc. We are professional expert in cutting field. We would like to solve every problem from you. Please feel free to contact us, its our pleasure to serve for you. BW product including: cutting tool、aerospace tool .HSS DIN Cutting tool、Carbide end mills、Carbide cutting tool、NAS Cutting tool、NAS986 NAS965 NAS897 NAS937orNAS907 Cutting Tools,Carbide end mill、disc milling cutter,Aerospace cutting tool、hss drill’Фрезеры’Carbide drill、High speed steel、Compound Sharpener’Milling cutter、INDUCTORS FOR PCD’CVDD(Chemical Vapor Deposition Diamond )’PCBN (Polycrystalline Cubic Boron Nitride) ’Core drill、Tapered end mills、CVD Diamond Tools Inserts’PCD Edge-Beveling Cutter(Golden Finger’PCD V-Cutter’PCD Wood tools’PCD Cutting tools’PCD Circular Saw Blade’PVDD End Mills’diamond tool. INDUCTORS FOR PCD . POWDER FORMING MACHINE ‘Single Crystal Diamond ‘Metric end mills、Miniature end mills、Специальные режущие инструменты ‘Пустотелое сверло ‘Pilot reamer、Fraises’Fresas con mango’ PCD (Polycrystalline diamond) ‘Frese’POWDER FORMING MACHINE’Electronics cutter、Step drill、Metal cutting saw、Double margin drill、Gun barrel、Angle milling cutter、Carbide burrs、Carbide tipped cutter、Chamfering tool、IC card engraving cutter、Side cutter、Staple Cutter’PCD diamond cutter specialized in grooving floors’V-Cut PCD Circular Diamond Tipped Saw Blade with Indexable Insert’ PCD Diamond Tool’ Saw Blade with Indexable Insert’NAS tool、DIN or JIS tool、Special tool、Metal slitting saws、Shell end mills、Side and face milling cutters、Side chip clearance saws、Long end mills’end mill grinder’drill grinder’sharpener、Stub roughing end mills、Dovetail milling cutters、Carbide slot drills、Carbide torus cutters、Angel carbide end mills、Carbide torus cutters、Carbide ball-nosed slot drills、Mould cutter、Tool manufacturer.

ようこそＢｅｗｉｓｅ　Ｉｎｃ.の世界へお越し下さいませ、先ず御目出度たいのは新たな

情報を受け取って頂き、もっと各産業に競争力プラス展開。

弊社は専門なエンド・ミルの製造メーカーで、客先に色んな分野のニーズ、

豊富なパリエーションを満足させ、特にハイテク品質要求にサポート致します。

弊社は各領域に供給できる内容は：

弊社の製品の供給調達機能は：

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Bewise Inc. talaşlı imalat sanayinde en fazla kullanılan ve üç eksende (x,y,z) talaş kaldırabilen freze takımlarından olan Parmak Freze imalatçısıdır. Çok geniş ürün yelpazesine sahip olan firmanın başlıca ürünlerini Karbür Parmak Frezeler, Kalıpçı Frezeleri, Kaba Talaş Frezeleri, Konik Alın Frezeler, Köşe Radyüs Frezeler, İki Ağızlı Kısa ve Uzun Küresel Frezeler, İç Bükey Frezeler vb. şeklinde sıralayabiliriz.

BW специализируется в научных исследованиях и разработках, и снабжаем самым высокотехнологичным карбидовым материалом для поставки режущих / фрезеровочных инструментов для почвы, воздушного пространства и электронной индустрии. В нашу основную продукцию входит твердый карбид / быстрорежущая сталь, а также двигатели, микроэлектрические дрели, IC картонорезальные машины, фрезы для гравирования, режущие пилы, фрезеры-расширители, фрезеры-расширители с резцом, дрели, резаки форм для шлицевого вала / звездочки роликовой цепи, и специальные нано инструменты. Пожалуйста, посетите сайт www.tool-tool.com для получения большей информации.

BW is specialized in R&D and sourcing the most advanced carbide material with high-tech coating to supply cutting / milling tool for mould & die, aero space and electronic industry. Our main products include solid carbide / HSS end mills, micro electronic drill, IC card cutter, engraving cutter, shell end mills, cutting saw, reamer, thread reamer, leading drill, involute gear cutter for spur wheel, rack and worm milling cutter, thread milling cutter, form cutters for spline shaft/roller chain sprocket, and special tool, with nano grade. Please visit our web www.tool-tool.com for more info.

beeway 發表在痞客邦留言(0) 人氣()

個人分類：學術研究

Feb 27 Fri 2009 13:33
Suomi Induktanssi www.tool-tool.com

Bewise Inc. www.tool-tool.com Reference source from the internet.

Induktanssi (itseisinduktanssi, tunnus L) kuvaa kelan (solenoidin) tai muun yleisen johdinsilmukan kykyä vastustaa virran muutosta. Induktanssin SI-järjestelmän mukainen yksikkö on henry (1 H).

Sähkövirran muutos indusoi esimerkiksi kelaan induktiojännitteen, jonka suuruus saadaan Faradayn induktiolaista. Induktanssi lasketaan silmukkaan indusoituneen jännitteen E_ind (vastasähkömotorinen voima) ja sähkövirran muutoksen di/dt suhteena:

$L = \frac{E_{ind}}{di/dt}$ .

Mikäli käämin induktanssi on suuri, aiheuttaa pienikin virranmuutos voimakkaan induktiojännitteen, joka vastustaa virran muutosta. Piirin induktanssia lisäämällä voidaan siis vaimentaa äkillisiä sähkövirran muutoksia. Induktanssi voidaan laskea myös kierrosmäärän N ja magneettivuon Φ tulon suhteesta kelan virtaan. Toisinaan puhutaan myös käämivuosta (tunnus Ψ), joka on kierrosmäärä kertaa kelan magneettivuo. Induktanssi L voidaan tällöin ajatella myös käämivuoksi Ψ virtaa I kohti.

L = N·Φ/I = Ψ/I

Ferriittirenkaalle käämityn kelan induktanssi voidaan laskea seuraavasta kaavasta:

$L = {\mu_0 \mu_e N^2 A_e \over l_e}$

missä

μ₀ on tyhjiön permeabiliteetti

μ_e on sydämen tehollinen permeabiliteetti

N on kierrosmäärä

A_e on tehollinen poikkipinta-ala

l_e on tehollinen magneettisen piirin pituus

Kelasydämelle käämityn kelan induktanssin määrittäminen perustuu usein myös A_L-lukuun. Sydämelle ilmoitettava A_L-luku, jonka yksikkönä käytetään usein nH/n² tarkoittaa, miten paljon nanohenrejä induktanssia saadaan käämin kierrosmäärän (n) neliötä kohti.

Kela (vyyhdellä oleva johdin) ja myös suora johdin muodostavat ympärilleen magneettikentän, kun niissä kulkee sähkövirta. Siten niillä on induktanssia ja vaihtovirtapiirissä vastusta, reaktanssia.

歡迎來到Bewise Inc.的世界，首先恭喜您來到這接受新的資訊讓產業更有競爭力，我們是提供專業刀具製造商，應對客戶高品質的刀具需求，我們可以協助客戶滿足您對產業的不同要求，我們有能力達到非常卓越的客戶需求品質，這是現有相關技術無法比擬的，我們成功的滿足了各行各業的要求，包括：精密HSS DIN切削刀具、協助客戶設計刀具流程、DIN or JIS 鎢鋼切削刀具設計、NAS986 NAS965 NAS897 NAS937orNAS907 航太切削刀具,NAS航太刀具設計、超高硬度的切削刀具、醫療配件刀具設計、複合式再研磨機、PCD地板專用企口鑽石組合刀具、粉末造粒成型機、主機版專用頂級電桿、PCD V-Cut刀、捨棄式圓鋸片組、粉末成型機、主機版專用頂級電感、’汽車業刀具設計、電子產業鑽石刀具、木工產業鑽石刀具、銑刀與切斷複合再研磨機、銑刀與鑽頭複合再研磨機、銑刀與螺絲攻複合再研磨機等等。我們的產品涵蓋了從民生刀具到工業級的刀具設計；從微細刀具到大型刀具；從小型生產到大型量產；全自動整合；我們的技術可提供您連續生產的效能，我們整體的服務及卓越的技術，恭迎您親自體驗！！

BW Bewise Inc. Willy Chen willy@tool-tool.com bw@tool-tool.com www.tool-tool.com skype:willy_chen_bw mobile:0937-618-190 Head &Administration Office No.13,Shiang Shang 2nd St., West Chiu Taichung,Taiwan 40356 http://www.tool-tool.com / FAX:+886 4 2471 4839 N.Branch 5F,No.460,Fu Shin North Rd.,Taipei,Taiwan S.Branch No.24,Sec.1,Chia Pu East Rd.,Taipao City,Chiayi Hsien,Taiwan

Welcome to BW tool world! We are an experienced tool maker specialized in cutting tools. We focus on what you need and endeavor to research the best cutter to satisfy users’ demand. Our customers involve wide range of industries, like mold & die, aerospace, electronic, machinery, etc. We are professional expert in cutting field. We would like to solve every problem from you. Please feel free to contact us, its our pleasure to serve for you. BW product including: cutting tool、aerospace tool .HSS DIN Cutting tool、Carbide end mills、Carbide cutting tool、NAS Cutting tool、NAS986 NAS965 NAS897 NAS937orNAS907 Cutting Tools,Carbide end mill、disc milling cutter,Aerospace cutting tool、hss drill’Фрезеры’Carbide drill、High speed steel、Compound Sharpener’Milling cutter、INDUCTORS FOR PCD’CVDD(Chemical Vapor Deposition Diamond )’PCBN (Polycrystalline Cubic Boron Nitride) ’Core drill、Tapered end mills、CVD Diamond Tools Inserts’PCD Edge-Beveling Cutter(Golden Finger’PCD V-Cutter’PCD Wood tools’PCD Cutting tools’PCD Circular Saw Blade’PVDD End Mills’diamond tool. INDUCTORS FOR PCD . POWDER FORMING MACHINE ‘Single Crystal Diamond ‘Metric end mills、Miniature end mills、Специальные режущие инструменты ‘Пустотелое сверло ‘Pilot reamer、Fraises’Fresas con mango’ PCD (Polycrystalline diamond) ‘Frese’POWDER FORMING MACHINE’Electronics cutter、Step drill、Metal cutting saw、Double margin drill、Gun barrel、Angle milling cutter、Carbide burrs、Carbide tipped cutter、Chamfering tool、IC card engraving cutter、Side cutter、Staple Cutter’PCD diamond cutter specialized in grooving floors’V-Cut PCD Circular Diamond Tipped Saw Blade with Indexable Insert’ PCD Diamond Tool’ Saw Blade with Indexable Insert’NAS tool、DIN or JIS tool、Special tool、Metal slitting saws、Shell end mills、Side and face milling cutters、Side chip clearance saws、Long end mills’end mill grinder’drill grinder’sharpener、Stub roughing end mills、Dovetail milling cutters、Carbide slot drills、Carbide torus cutters、Angel carbide end mills、Carbide torus cutters、Carbide ball-nosed slot drills、Mould cutter、Tool manufacturer.

ようこそＢｅｗｉｓｅ　Ｉｎｃ.の世界へお越し下さいませ、先ず御目出度たいのは新たな

情報を受け取って頂き、もっと各産業に競争力プラス展開。

弊社は専門なエンド・ミルの製造メーカーで、客先に色んな分野のニーズ、

豊富なパリエーションを満足させ、特にハイテク品質要求にサポート致します。

弊社は各領域に供給できる内容は：

弊社の製品の供給調達機能は：

弊社の全般供給体制及び技術自慢の総合専門製造メーカーに貴方のご体験を御待ちしております。

Bewise Inc. talaşlı imalat sanayinde en fazla kullanılan ve üç eksende (x,y,z) talaş kaldırabilen freze takımlarından olan Parmak Freze imalatçısıdır. Çok geniş ürün yelpazesine sahip olan firmanın başlıca ürünlerini Karbür Parmak Frezeler, Kalıpçı Frezeleri, Kaba Talaş Frezeleri, Konik Alın Frezeler, Köşe Radyüs Frezeler, İki Ağızlı Kısa ve Uzun Küresel Frezeler, İç Bükey Frezeler vb. şeklinde sıralayabiliriz.

BW специализируется в научных исследованиях и разработках, и снабжаем самым высокотехнологичным карбидовым материалом для поставки режущих / фрезеровочных инструментов для почвы, воздушного пространства и электронной индустрии. В нашу основную продукцию входит твердый карбид / быстрорежущая сталь, а также двигатели, микроэлектрические дрели, IC картонорезальные машины, фрезы для гравирования, режущие пилы, фрезеры-расширители, фрезеры-расширители с резцом, дрели, резаки форм для шлицевого вала / звездочки роликовой цепи, и специальные нано инструменты. Пожалуйста, посетите сайт www.tool-tool.com для получения большей информации.

BW is specialized in R&D and sourcing the most advanced carbide material with high-tech coating to supply cutting / milling tool for mould & die, aero space and electronic industry. Our main products include solid carbide / HSS end mills, micro electronic drill, IC card cutter, engraving cutter, shell end mills, cutting saw, reamer, thread reamer, leading drill, involute gear cutter for spur wheel, rack and worm milling cutter, thread milling cutter, form cutters for spline shaft/roller chain sprocket, and special tool, with nano grade. Please visit our web www.tool-tool.com for more info.

beeway 發表在痞客邦留言(0) 人氣()

個人分類：學術研究

Feb 27 Fri 2009 13:26
Español Inductancia www.tool-tool.com

Bewise Inc. www.tool-tool.com Reference source from the internet.

En un Inductor o bobina, se denomina inductancia, L, a la relación entre el flujo magnético, $\mathbf{\Phi}$ y la intensidad de corriente eléctrica,I:

$L = {\Phi \over I}$

El flujo que aparece en esta definición es el flujo producido por la corriente I exclusivamente. No deben incluirse flujos producidos por otras corrientes ni por imanes situados cerca ni por ondas electromagnéticas.

Desgraciadamente, esta definición es de poca utilidad porque es difícil medir el flujo abrazado por un conductor. En cambio se pueden medir las variaciones del flujo y eso sólo a través del voltaje V inducido en el conductor por la variación del flujo. Con ello llegamos a una definición de inductancia equivalente pero hecha a base de cantidades que se pueden medir, esto es, la corriente, el tiempo y la tensión:

$V_L = L{\Delta I\over \Delta t}$

El signo de la tensión y de la corriente son los siguientes: si la corriente que entra por la extremidad A del conductor, y que va hacia la otra extremidad, aumenta, la extremidad A es positiva con respecto a la opuesta. Esta frase también puede escribirse al revés: si la extremidad A es positiva, la corriente que entra por A aumenta con el tiempo.

La inductancia siempre es positiva, salvo en ciertos circuitos electrónicos especialmente concebidos para simular inductancias negativas.

De acuerdo con el Sistema Internacional de Medidas, si el flujo se expresa en weber y la intensidad en amperio, el valor de la inductancia vendrá en henrio (H).

Los valores de inductancia prácticos van de unos décimos de nH para un conductor de 1 milímetro de largo hasta varias decenas de miles de Henrios para bobinas hechas de miles de vueltas alrededor de núcleos ferromagnéticos.

El término "inductancia" fue empleado por primera vez por Oliver Heaviside en febrero de 1886, mientras que el símbolo L se utiliza en honor al físico Heinrich Lenz.

Valor de la inductancia [editar]

El valor de la inductancia viene determinado exclusivamente por las características geométricas de la bobina y por la permeabilidad magnética del espacio donde se encuentra. Así, para un solenoide, la inductancia, de acuerdo con las ecuaciones de Maxwell, viene determinada por:

$L = \frac{\mu N^2 A} {l}$

donde μ es la permeabilidad absoluta del núcleo (el producto entre la permeabilidad del aire y la permeabilidad relativa del material) N es el número de espiras, A es el area de la sección transversal del bobinado y l la longitud de las líneas de flujo.

El cálculo de l es bastante complicado a no ser que la bobina sea toroidal y aún así, resulta difícil si el núcleo presenta distintas permeabilidades en función de la intensidad que circule por la misma. En este caso, la determinación de l se realiza a partir de las curvas de imantación.

Acoplamiento magnético [editar]

Cuando el flujo magnético de una bobina alcanza a otra, se dice que ambas bobinas están acopladas magnéticamente. Este acoplamiento a menudo es no deseado, pero en ocasiones es aprovechado, como ocurre por ejemplo en los transformadores. En bobinas acopladas, existen dos tipos de inductancia: la debida al flujo de una bobina sobre otra, denominada inductancia mutua, y la debida al propio flujo, denominada autoinductancia. Así, en el caso de dos bobinas se tendría:

L₁₁ - autoinductancia de la bobina 1

L₂₂ - autoinductancia de la bobina 2

L₁₂ = L₂₁ - inductancias mutuas

Para diferenciar la autoinductancia de la inductancia mutua, se suelen designar con L y M respectivamente.

歡迎來到Bewise Inc.的世界，首先恭喜您來到這接受新的資訊讓產業更有競爭力，我們是提供專業刀具製造商，應對客戶高品質的刀具需求，我們可以協助客戶滿足您對產業的不同要求，我們有能力達到非常卓越的客戶需求品質，這是現有相關技術無法比擬的，我們成功的滿足了各行各業的要求，包括：精密HSS DIN切削刀具、協助客戶設計刀具流程、DIN or JIS 鎢鋼切削刀具設計、NAS986 NAS965 NAS897 NAS937orNAS907 航太切削刀具,NAS航太刀具設計、超高硬度的切削刀具、醫療配件刀具設計、複合式再研磨機、PCD地板專用企口鑽石組合刀具、粉末造粒成型機、主機版專用頂級電桿、PCD V-Cut刀、捨棄式圓鋸片組、粉末成型機、主機版專用頂級電感、’汽車業刀具設計、電子產業鑽石刀具、木工產業鑽石刀具、銑刀與切斷複合再研磨機、銑刀與鑽頭複合再研磨機、銑刀與螺絲攻複合再研磨機等等。我們的產品涵蓋了從民生刀具到工業級的刀具設計；從微細刀具到大型刀具；從小型生產到大型量產；全自動整合；我們的技術可提供您連續生產的效能，我們整體的服務及卓越的技術，恭迎您親自體驗！！

BW Bewise Inc. Willy Chen willy@tool-tool.com bw@tool-tool.com www.tool-tool.com skype:willy_chen_bw mobile:0937-618-190 Head &Administration Office No.13,Shiang Shang 2nd St., West Chiu Taichung,Taiwan 40356 http://www.tool-tool.com / FAX:+886 4 2471 4839 N.Branch 5F,No.460,Fu Shin North Rd.,Taipei,Taiwan S.Branch No.24,Sec.1,Chia Pu East Rd.,Taipao City,Chiayi Hsien,Taiwan

Welcome to BW tool world! We are an experienced tool maker specialized in cutting tools. We focus on what you need and endeavor to research the best cutter to satisfy users’ demand. Our customers involve wide range of industries, like mold & die, aerospace, electronic, machinery, etc. We are professional expert in cutting field. We would like to solve every problem from you. Please feel free to contact us, its our pleasure to serve for you. BW product including: cutting tool、aerospace tool .HSS DIN Cutting tool、Carbide end mills、Carbide cutting tool、NAS Cutting tool、NAS986 NAS965 NAS897 NAS937orNAS907 Cutting Tools,Carbide end mill、disc milling cutter,Aerospace cutting tool、hss drill’Фрезеры’Carbide drill、High speed steel、Compound Sharpener’Milling cutter、INDUCTORS FOR PCD’CVDD(Chemical Vapor Deposition Diamond )’PCBN (Polycrystalline Cubic Boron Nitride) ’Core drill、Tapered end mills、CVD Diamond Tools Inserts’PCD Edge-Beveling Cutter(Golden Finger’PCD V-Cutter’PCD Wood tools’PCD Cutting tools’PCD Circular Saw Blade’PVDD End Mills’diamond tool. INDUCTORS FOR PCD . POWDER FORMING MACHINE ‘Single Crystal Diamond ‘Metric end mills、Miniature end mills、Специальные режущие инструменты ‘Пустотелое сверло ‘Pilot reamer、Fraises’Fresas con mango’ PCD (Polycrystalline diamond) ‘Frese’POWDER FORMING MACHINE’Electronics cutter、Step drill、Metal cutting saw、Double margin drill、Gun barrel、Angle milling cutter、Carbide burrs、Carbide tipped cutter、Chamfering tool、IC card engraving cutter、Side cutter、Staple Cutter’PCD diamond cutter specialized in grooving floors’V-Cut PCD Circular Diamond Tipped Saw Blade with Indexable Insert’ PCD Diamond Tool’ Saw Blade with Indexable Insert’NAS tool、DIN or JIS tool、Special tool、Metal slitting saws、Shell end mills、Side and face milling cutters、Side chip clearance saws、Long end mills’end mill grinder’drill grinder’sharpener、Stub roughing end mills、Dovetail milling cutters、Carbide slot drills、Carbide torus cutters、Angel carbide end mills、Carbide torus cutters、Carbide ball-nosed slot drills、Mould cutter、Tool manufacturer.

ようこそＢｅｗｉｓｅ　Ｉｎｃ.の世界へお越し下さいませ、先ず御目出度たいのは新たな

情報を受け取って頂き、もっと各産業に競争力プラス展開。

弊社は専門なエンド・ミルの製造メーカーで、客先に色んな分野のニーズ、

豊富なパリエーションを満足させ、特にハイテク品質要求にサポート致します。

弊社は各領域に供給できる内容は：

弊社の製品の供給調達機能は：

弊社の全般供給体制及び技術自慢の総合専門製造メーカーに貴方のご体験を御待ちしております。

Bewise Inc. talaşlı imalat sanayinde en fazla kullanılan ve üç eksende (x,y,z) talaş kaldırabilen freze takımlarından olan Parmak Freze imalatçısıdır. Çok geniş ürün yelpazesine sahip olan firmanın başlıca ürünlerini Karbür Parmak Frezeler, Kalıpçı Frezeleri, Kaba Talaş Frezeleri, Konik Alın Frezeler, Köşe Radyüs Frezeler, İki Ağızlı Kısa ve Uzun Küresel Frezeler, İç Bükey Frezeler vb. şeklinde sıralayabiliriz.

BW специализируется в научных исследованиях и разработках, и снабжаем самым высокотехнологичным карбидовым материалом для поставки режущих / фрезеровочных инструментов для почвы, воздушного пространства и электронной индустрии. В нашу основную продукцию входит твердый карбид / быстрорежущая сталь, а также двигатели, микроэлектрические дрели, IC картонорезальные машины, фрезы для гравирования, режущие пилы, фрезеры-расширители, фрезеры-расширители с резцом, дрели, резаки форм для шлицевого вала / звездочки роликовой цепи, и специальные нано инструменты. Пожалуйста, посетите сайт www.tool-tool.com для получения большей информации.

BW is specialized in R&D and sourcing the most advanced carbide material with high-tech coating to supply cutting / milling tool for mould & die, aero space and electronic industry. Our main products include solid carbide / HSS end mills, micro electronic drill, IC card cutter, engraving cutter, shell end mills, cutting saw, reamer, thread reamer, leading drill, involute gear cutter for spur wheel, rack and worm milling cutter, thread milling cutter, form cutters for spline shaft/roller chain sprocket, and special tool, with nano grade. Please visit our web www.tool-tool.com for more info.

beeway 發表在痞客邦留言(0) 人氣()

個人分類：學術研究

Feb 27 Fri 2009 13:17
Esperanto Induktanco www.tool-tool.com

Bewise Inc. www.tool-tool.com Reference source from the internet.

Difino

Induktanco estas mezuro de la kvanto de magneta flukso produktita de donita elektra kurento.

$L= \frac{\Phi}{I}$

kie

L estas la induktanco en henroj,

I estas la kurento en amperoj,

φ estas la magneta flukso en veberoj.

Komparu la supran difinon kun tiuj de impedanco, rezistanco, kapacitanco, kaj konduktanco.

La simbolo L uziĝas por induktanco honore al la fizikisto Heinrich Lenz. La termino induktanco estis fabrikita de Oliver Heaviside en februaro 1886. La [[SI]a unito por induktanco estas la henro (simbolo: H).

Precize parole, la kvanto ĵus difinita nomiĝas mem-induktanco, ĉar la magneta kampo estas kreita sole de la konduktanto kiu portas la kurenton.

Kiam konduktanto volviĝas sur si mem N-foje ĉirkaŭ la la sama akso, la kurento postulata por produkti donitan kvanton de flukso reduktiĝas per faktoro de N kompare kun unuopa turno de drato. Tiel, la induktanco de bobeno de drato de N turnoj doniĝas de

$L= \frac{\lambda}{I} = N\frac{\Phi}{I}$

kie λ estas la tuta 'fluksa kuplado'.

Tia bobena konduktanto estas ekzemplo de induktilo.

[redakti] Ecoj de induktanco

La supra ekvacio povas rearanĝiĝi tiele

$\lambda = LI \,$

Farado de la tempa derivaĵo de ambaŭ flankoj de la ekvacio donas:

$\frac{d\lambda}{dt} = L \frac{dI}{dt} + I \frac{dL}{dt} \,$

En plej multaj kazoj, la induktanco estas konstanta tempe kaj tiel

$\frac{d\lambda}{dt} = L \frac{dI}{dt}$

Laŭ la Leĝo de Farady de Induktanco oni havas

$\frac{d\lambda}{dt} = -\mathcal{E} = V$

kie $\mathcal{E}$ estas la elektromova forto (emf) kaj v estas la induktita tensio. Notu ke la emf estas kontrauen al la induktita tensio. Tiel

$\frac{dI}{dt} = \frac{V} {L}$

aŭ

$I(t) = \frac{1}{L} \int_0^tV(\tau) d\tau + I(0)$

Tiuj ĉi ekvacioj kune diras ke, por konstana aplikita tensio v, la kurento ŝanĝas en lineara maniero, ĉe "pokvanto" proporcia al la aplikita tensio, sed inverse proporcia al la induktanco. Male, se la kurento tra la induktilo estas ŝanĝanta ĉe konstanta pokvanto, la induktita tensio estas konstanta.

La efiko de induktanco povas esti komprenita per unuopa maŝo de drato kiel ekzemplo. Se tensio subite aplikiĝas inter la finoj de la maŝo de drato, la kurento devas ŝanĝi de nula al ne-nula. Tamen, ne-nula kurento indukas magnetan kampon per la leĝo de Ampere. Tiu ĉi ŝanĝo de la magneta kampo induktas emf kiu estas direkte kontraŭa al la ŝanĝo de kurento. La grando de tiu ĉi emf estas proporcia al la ŝanĝo de la kurento kaj la induktanco. Kiam la kontraŭantaj fortoj ekvilibriĝas, la rezulto estas kurento kiu pliiĝas lineare kun tempo kie la pokvanto de tiu ĉi ŝanĝo determiniĝas de la aplikata tensio kaj la induktanco.

[redakti] Permeableco

La kvanto de magneta flukso produktita de kurento dependas de fizika eco de la medio ĉirkaŭanta la kurento kiu nomiĝas kel la permeableco, μ. Ju pli granda la permeableco des pli granda la magneta flukso generita de la donita kurento. Certaj materialoj havas multe pli alatan permeablecon de aero. Se konduktilo (drato) estas volvita ĉirkaŭ tia materialo, la magneta flukso estas ĝenerale multe pli granda,do la induktanco estas multe pli granda ol la induktanco de la drato volvita en la aero. La mem-induktanco L de tia solenoido (idealigado de bobeno) povas esti kalkulita de

$L = {\mu_0 \mu_r N^2 A \over l} = \frac{N \Phi}{I}$

kie

μ₀ estas la permeableco de sena spaco (4π × 10^-7 henroj per metre)

μ_r estas la permeableco de sena spaco) (4π × 10^-7 henroj per metro).

μ_r estas la relativa permeableco de la koro (sendimensia)

N estas la nombro de volvaĵoj

A esta la kversekcia areo de la bobeno en [kvadrataj metroj]].

l estas la longo en metroj.

Φ = BA estas la flukso en veberoj (B estas la fluksa denseco, A estas la areo).

I estas la kurento en amperoj.

Tio ĉi, kaj la induktanco de pli komplikitaj formoj, povas deriviĝi de la ekvacioj de Maksvelo.

[redakti] Kuplitaj induktiloj

Kiam la magneta flukso produktita de induktilo ligas al alia induktilo, oni nomas tiujn ĉi induktilojn kuplitaj. Kuplado estas ofte maldezirita sed ofte tia kuplado estas intenca kaj estas la bazo de transformilo. Kiam induktiloj kupliĝas, ekzistas kunan induktancon kiu rilatas la kurento en unu unu induktilo al la fluksa ligo en la alia induktilo. Tiel estas tri induktancoj difineblaj por kuplitaj induktiloj:

L₁₁ - la mem-induktanco de induktilo 1

L₂₂ - la mem-induktanco de induktilo 2

L₁₂ = L₂₁ - la kun-induktanco asociiĝebla kun ambaŭ induktiloj.

[redakti] Derivaĵoj de vektorkampa teorio

[redakti] Reciproka induktanco

Reciproka induktanco estas la tensio induktita en unu cirkvito (la sekundara cirkvito) kiam la la kurento en alia cirkvito (la primara cirkvito) ŝanĝas da unito dum unita tempo. Ĝi estas grava kiel mekanismo per kiu transformilo funkcias; sed ĝi povas ankaŭ kaŭzi nedeziritan kupladon inter la konduktilo en cirkvito.

La interinduktanco (en SI-unuoj) de cirkvito i sur cirkvito j doniĝas de la duobla-integrala NEUMANN-a formulo

$M_{ij} = \frac{\mu_0}{4\pi} \oint_{C_i}\oint_{C_j} \frac{\mathbf{ds}_i\cdot\mathbf{ds}_j}{|\mathbf{R}_{ij}|}$

[redakti] Derivado

$\Phi_{i} = \int_{S_i} \mathbf{B}\cdot\mathbf{da} = \int_{S_i} (\nabla\times\mathbf{A})\cdot\mathbf{da} = \oint_{C_i} \mathbf{A}\cdot\mathbf{ds} = \oint_{C_i} \left(\sum_{j}\frac{\mu_0 I_j}{4\pi} \oint_{C_j} \frac{\mathbf{ds}_j}{|\mathbf{R}|}\right) \cdot \mathbf{ds}_i$

kie

$\Phi_i\ \,$ estas la magneta flukso tra la i-a surfaco per la [[elektra cirkvito] skemita per C_j

C_i estas la entenanta krubo de S_i.

B estas la magnetkampa vektoro.

A estas la vektora potencialo.

Teoremo de Stokes estis uzita.

$M_{ij} \equiv \frac{\Phi_{ij}}{I_j} = \frac{\mu_0}{4\pi} \oint_{C_i}\oint_{C_j} \frac{\mathbf{ds}_i\cdot\mathbf{ds}_j}{|\mathbf{R}_{ij}|}$

tiel ke la induktanco estas pure geometria kvanto sendependa de la kurento en la cirkvitoj.

[redakti] Mem-induktanco

Meminduktanco, notita L, estas speciala kazo de interinduktanco kie, en al supra ekvacio, i = j. Tiel

$M_{ij} = M_{jj} = L_{jj} = L_j = L = \frac{\mu_0}{4\pi} \oint_{C}\oint_{C'} \frac{\mathbf{ds}\cdot\mathbf{ds}'}{|\mathbf{R}|}$

Fizike, la mem-induktanco de cirkvito reprezentas la kontraŭ-emf priskribita de la lego de induktado de Faraday.

[redakti] Uzado

La flukso $\Phi_i\ \!$ tra la i-a cirkvito en aro evidente estas donita de

$\Phi_i = \sum_{j} M_{ij}I_j = L_i I_i + \sum_{j\ne i} M_{ij}I_j \,$

tiel ke la induktita emf, $\mathcal{E}$ , de specifa cirkvito, i, en iu donita aro povas esti donita rekte de:

$\mathcal{E} = -\frac{d\Phi_i}{dt} = -\frac{d}{dt}(L_i I_i + \sum_{j\ne i} M_{ij}I_j) = -(\frac{dL_i}{dt}I_i +\frac{dI_i}{dt}L_i) -\sum_{j\ne i}(\frac{dM_{ij}}{dt}I_j + \frac{dI_j}{dt}M_{ij})$

[redakti] Vidu ankaŭ jenon:

[redakti] Referencoj

Griffiths, David J. Introduction to Electrodynamics (3rd ed.)(1998). Prentice Hall. ISBN 0-13-805326-X
Wangsness, Roald K. Electromagnetic Fields (2nd Ed.)(1986). Wiley Text Books. ISBN 0-471-81186-6.
Hughes, Edward. Electrical & Electronic Technology (8th ed.)(2002). Prentice Hall. ISBN 0-582-40519-X.

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Inductance is that property in an electrical circuit where a change in the current flowing through that circuit induces an electromotive force (EMF) that opposes the change in current (See Induced EMF).

In electrical circuits, any electric current i produces a magnetic field and hence generates a total magnetic flux Φ acting on the circuit. This magnetic flux, due to Lenz's law tends to act to oppose changes in the flux by generating a voltage (a back EMF) that counters or tends to reduce the rate of change in the current. The ratio of the magnetic flux to the current is called the self-inductance which is usually simply referred to as the inductance of the circuit. The term 'inductance' was coined by Oliver Heaviside in February 1886.^[1] It is customary to use the symbol L for inductance, possibly in honour of the physicist Heinrich Lenz.^[2] ^[3]

In honour of Joseph Henry, the unit of inductance has been given the name henry (H): 1H = 1Wb/A.

[edit] Definitions

The quantitative definition of the (self-) inductance of a wire loop in SI units (webers per ampere) is

$\displaystyle L= \frac{N\Phi}{i}$

where Φ denotes the magnetic flux through the area spanned by the loop, and N is the number of wire turns. The flux linkage λ = NΦ thus is

$\displaystyle N{\Phi} = Li$ .

There may, however, be contributions from other circuits. Consider for example two circuits C₁, C₂, carrying the currents i₁, i₂. The flux linkages of C₁ and C₂ are given by

$\displaystyle N_1\Phi_1 = L_{11}i_1 + L_{12}i_2,$

$\displaystyle N_2\Phi_2 = L_{21}i_1 + L_{22}i_2.$

According to the above definition, L₁₁ and L₂₂ are the self-inductances of C₁ and C₂, respectively. It can be shown (see below) that the other two coefficients are equal: L₁₂ = L₂₁ = M, where M is called the mutual inductance of the pair of circuits.

The number of turns N₁ and N₂ occur somewhat asymmetrically in the definition above. But actually L_mn always is proportional to the product N_mN_n, and thus the total currents N_mi_m contribute to the flux.

Self and mutual inductances also occur in the expression

$\displaystyle W=\frac{1}{2}\sum_{m,n=1}^{K}L_{m,n}i_{m}i_{n}$

for the energy of the magnetic field generated by K electrical circuits where i_n is the current in the nth circuit. This equation is an alternative definition of inductance that also applies when the currents are not confined to thin wires so that it is not immediately clear what area is encompassed by the circuit nor how the magnetic flux through the circuit is to be defined.

The definition L = NΦ / i, in contrast, is more direct and more intuitive. It may be shown that the two definitions are equivalent by equating the time derivative of W and the electric power transferred to the system.

[edit] Properties of inductance

Taking the time derivative of both sides of the equation NΦ = Li yields:

$N\frac{d\Phi}{dt} = L \frac{di}{dt} + \frac{dL}{dt} i \,$

In most physical cases, the inductance is constant with time and so

$N\frac{d\Phi}{dt} = L \frac{di}{dt}$

By Faraday's Law of Induction we have:

$N\frac{d\Phi}{dt} = -\mathcal{E} = v$

where $\mathcal{E}$ is the Electromotive force (emf) and v is the induced voltage. Note that the emf is opposite to the induced voltage. Thus:

$\frac{di}{dt} = \frac{v}{L}$

or

$i(t) = \frac{1}{L} \int_0^tv(\tau) d\tau + i(0)$

These equations together state that, for a steady applied voltage v, the current changes in a linear manner, at a rate proportional to the applied voltage, but inversely proportional to the inductance. Conversely, if the current through the inductor is changing at a constant rate, the induced voltage is constant.

The effect of inductance can be understood using a single loop of wire as an example. If a voltage is suddenly applied between the ends of the loop of wire, the current must change from zero to non-zero. However, a non-zero current induces a magnetic field by Ampère's law. This change in the magnetic field induces an emf that is in the opposite direction of the change in current. The strength of this emf is proportional to the change in current and the inductance. When these opposing forces are in balance, the result is a current that increases linearly with time where the rate of this change is determined by the applied voltage and the inductance.

Multiplying the equation for di / dt above with Li leads to

$Li\frac{di}{dt}=\frac{d}{dt}\frac{L}{2}i^{2}=iv$

Since iv is the energy transferred to the system per time it follows that $\left( L/2 \right)i^2$ is the energy of the magnetic field generated by the current.

[edit] Phasor circuit analysis and impedance

Using phasors, the equivalent impedance of an inductance is given by:

$Z_L = V / I = j L \omega \,$

where

j is the imaginary unit,

L is the inductance,

$\omega = 2 \pi f \,$ is the angular frequency,

f is the frequency and

$L \omega \ = X_L$ is the inductive reactance.

[edit] Induced emf

The flux $\Phi_i\ \!$ through the i-th circuit in a set is given by:

$\Phi_i = \sum_{j} M_{ij}I_j = L_i I_i + \sum_{j\ne i} M_{ij}I_j \,$

so that the induced emf, $\mathcal{E}$ , of a specific circuit, i, in any given set can be given directly by:

$\mathcal{E} = -\frac{d\Phi_i}{dt} = -\frac{d}{dt} \left (L_i I_i + \sum_{j\ne i} M_{ij}I_j \right ) = -\left(\frac{dL_i}{dt}I_i +\frac{dI_i}{dt}L_i \right) -\sum_{j\ne i} \left (\frac{dM_{ij}}{dt}I_j + \frac{dI_j}{dt}M_{ij} \right).$

[edit] Coupled inductors

Further information: Coupling (electronics)

The circuit diagram representation of mutually inducting inductors. The two vertical lines between the inductors indicate a solid core that the wires of the inductor are wrapped around. "n:m" shows the ratio between the number of windings of the left inductor to windings of the right inductor. This picture also shows the dot convention.

Mutual inductance occurs when the change in current in one inductor induces a voltage in another nearby inductor. It is important as the mechanism by which transformers work, but it can also cause unwanted coupling between conductors in a circuit.

The mutual inductance, M, is also a measure of the coupling between two inductors. The mutual inductance by circuit i on circuit j is given by the double integral Neumann formula, see #Calculation techniques

The mutual inductance also has the relationship:

$M_{21} = N_1 N_2 P_{21} \!$

where

M₂₁ is the mutual inductance, and the subscript specifies the relationship of the voltage induced in coil 2 to the current in coil 1.

N₁ is the number of turns in coil 1,

N₂ is the number of turns in coil 2,

P₂₁ is the permeance of the space occupied by the flux.

The mutual inductance also has a relationship with the coupling coefficient. The coupling coefficient is always between 1 and 0, and is a convenient way to specify the relationship between a certain orientation of inductor with arbitrary inductance:

$M = k \sqrt{L_1 L_2} \!$

where

k is the coupling coefficient and 0 ≤ k ≤ 1,

L₁ is the inductance of the first coil, and

L₂ is the inductance of the second coil.

Once this mutual inductance factor M is determined, it can be used to predict the behavior of a circuit:

$V_1 = L_1 \frac{dI_1}{dt} + M \frac{dI_2}{dt}$

where

V is the voltage across the inductor of interest,

L₁ is the inductance of the inductor of interest,

dI₁ / dt is the derivative, with respect to time, of the current through the inductor of interest,

M is the mutual inductance and

dI₂ / dt is the derivative, with respect to time, of the current through the inductor that is coupled to the first inductor.

When one inductor is closely coupled to another inductor through mutual inductance, such as in a transformer, the voltages, currents, and number of turns can be related in the following way:

$V_s = V_p \frac{N_s}{N_p}$

where

V_s is the voltage across the secondary inductor,

V_p is the voltage across the primary inductor (the one connected to a power source),

N_s is the number of turns in the secondary inductor, and

N_p is the number of turns in the primary inductor.

Conversely the current:

$I_s = I_p \frac{N_p}{N_s}$

where

I_s is the current through the secondary inductor,

I_p is the current through the primary inductor (the one connected to a power source),

N_s is the number of turns in the secondary inductor, and

N_p is the number of turns in the primary inductor.

Note that the power through one inductor is the same as the power through the other. Also note that these equations don't work if both transformers are forced (with power sources).

When either side of the transformer is a tuned circuit, the amount of mutual inductance between the two windings determines the shape of the frequency response curve. Although no boundaries are defined, this is often referred to as loose-, critical-, and over-coupling. When two tuned circuits are loosely coupled through mutual inductance, the bandwidth will be narrow. As the amount of mutual inductance increases, the bandwidth continues to grow. When the mutual inductance is increased beyond a critical point, the peak in the response curve begins to drop, and the center frequency will be attenuated more strongly than its direct sidebands. This is known as overcoupling.

[edit] Calculation techniques

[edit] Mutual inductance

The mutual inductance by circuit i on circuit j is given by the double integral Neumann formula

$M_{ij} = \frac{\mu_0}{4\pi} \oint_{C_i}\oint_{C_j} \frac{\mathbf{ds}_i\cdot\mathbf{ds}_j}{|\mathbf{R}_{ij}|}$

The constant μ₀ is the permeability of free space (4π × 10^-7 H/m), C_i and C_j are the curves spanned by the wires, R_ij is the distance between two points. See a derivation of this equation.

[edit] Self-inductance

Formally the self-inductance of a wire loop would be given by the above equation with i =j. However, 1 / R now gets singular and the finite radius a and the distribution of the current in the wire must be taken into account. There remain the contribution from the integral over all points where $|R| \ge a/2$ and a correction term,

$L_{jj} = L = \left (\frac{\mu_0}{4\pi} \oint_{C}\oint_{C'} \frac{\mathbf{ds}\cdot\mathbf{ds}'}{|\mathbf{R}|}\right )_{|\mathbf{R}| \ge a/2} + \frac{\mu_0}{2\pi}lY$

Here a and l denote radius and length of the wire, and Y is a constant that depends on the distribution of the current in the wire: Y = 0 when the current flows in the surface of the wire (skin effect), Y = 1 / 4 when the current is homogenuous across the wire. Here is a derivation of this equation.

[edit] Method of images

In some cases different current distributions generate the same magnetic field in some section of space. This fact may be used to relate self inductances (method of images). As an example consider

A) A wire at distance d / 2 in front of a perfectly conducting wall (which is the return)
B) Two parallel wires at distance d, with opposite current

The magnetic field of the two systems coincides (in a half space). The magnetic field energy and the inductance of system B thus are twice as large as that of system A.

[edit] Self-inductance of simple electrical circuits in air

The self-inductance of many types of electrical circuits can be given in closed form. Examples are listed in the table.

Inductance of simple electrical circuits in air

Type
Inductance / μ₀
Comment

Single layer
solenoid
$\frac{r^{2}N^{2}}{3l}\left\{ -8w + 4\frac{\sqrt{1+m}}{m}\left( K\left( \frac{m}{1+m}\right) -\left( 1-m\right) E\left( \frac{m}{1+m}\right) \right) \right\}$

$=\frac {r^2N^2\pi}{l}\left( 1 - \frac{8w}{3\pi} + \frac{w^2}{2} - \frac{w^4}{4} + \frac{5w^6}{16} - \frac{35w^8}{64} + ... \right)$

N: Number of turns
r: Radius
l: Length
w = r / l
m = 4w²
E,K: Elliptic integrals

Coaxial cable,
high frequency
$\frac {l}{2\pi} \ln{\frac {a_1}{a}}$
a₁: Outer radius
a: Inner radius
l: Length

Circular loop
$r \cdot \left( \ln{ \frac {8 r}{a}} - 2 + Y\right)$
r: Loop radius
a: Wire radius

Rectangle
$\frac {1}{\pi}\left(b\ln{\frac {2 b}{a}} + d\ln{\frac {2d}{a}} - \left(b+d\right)\left(2-Y\right) +2\sqrt{b^2+d^2} -b\cdot\operatorname{arsinh}{\frac {b}{d}}-d\cdot\operatorname{arsinh}{\frac {d}{b}} \right)$
b, d: Border length
d >> a, b >> a
a: Wire radius

Pair of parallel
wires
$\frac {l}{\pi} \left( \ln{\frac {d}{a}} + Y \right)$
a: Wire radius
d: Distance, d ≥ 2a
l: Length of pair

Pair of parallel
wires, high
frequency
$\frac {l}{2\pi}\operatorname{arcosh}\left( \frac {d^{2}}{2a^{2}}-1\right)$
a: Wire radius
d: Distance, d ≥ 2a
l: Length of pair

Wire parallel to
perfectly
conducting wall
$\frac {l}{2\pi} \left( \ln{\frac {2d}{a}} + Y \right)$
a: Wire radius
d: Distance, d ≥ a
l: Length

Wire parallel to
conducting wall,
high frequency
$\frac {l}{4\pi}\operatorname{arcosh}\left( \frac {2d^{2}}{a^{2}}-1\right)$
a: Wire radius
d: Distance, d ≥ a
l: Length

The constant μ₀ is the permeability of free space (4π × 10^-7 H/m). For high frequencies the electrical current flows in the conductor surface (skin effect), and depending on the geometry it sometimes is necessary to distinguish low and high frequency inductances. This is the purpose of the constant Y: Y=0 when the current is uniformly distributed over the surface of the wire (skin effect), Y=1/4 when the current is uniformly distributed over the cross section of the wire. In the high frequency case, if conductors approach each other, an additional screening current flows in their surface, and expressions containing Y become invalid.

[edit] Inductance of a solenoid

A solenoid is a long, thin coil, i.e. a coil whose length is much greater than the diameter. Under these conditions, and without any magnetic material used, the magnetic flux density B within the coil is practically constant and is given by

$\displaystyle B = \mu_0 Ni/l$

where μ₀ is the permeability of free space, N the number of turns, i the current and l the length of the coil. Ignoring end effects the total magnetic flux through the coil is obtained by multiplying the flux density B by the cross-section area A and the number of turns N:

$\displaystyle \Phi = \mu_0N^2iA/l,$

from which it follows that the inductance of a solenoid is given by:

$\displaystyle L = \mu_0N^2A/l.$

This, and the inductance of more complicated shapes, can be derived from Maxwell's equations. For rigid air-core coils, inductance is a function of coil geometry and number of turns, and is independent of current.

Similar analysis applies to a solenoid with a magnetic core, but only if the length of the coil is much greater than the product of the relative permeability of the magnetic core and the diameter. That limits the simple analysis to low-permeability cores, or extremely long thin solenoids. Although rarely useful, the equations are,

$\displaystyle B = \mu_0\mu_r Ni/l$

where μ_r the relative permeability of the material within the solenoid,

$\displaystyle \Phi = \mu_0\mu_rN^2iA/l,$

from which it follows that the inductance of a solenoid is given by:

$\displaystyle L = \mu_0\mu_rN^2A/l.$

Note that since the permeability of ferromagnetic materials changes with applied magnetic flux, the inductance of a coil with a ferromagnetic core will generally vary with current.

[edit] Inductance of a coaxial line

Let the inner conductor have radius r_i and permeability μ_i, let the dielectric between the inner and outer conductor have permeability μ_d, and let the outer conductor have inner radius r_o1, outer radius r_o2, and permeability μ_o. Assume that a DC current I flows in opposite directions in the two conductors, with uniform current density. The magnetic field generated by these currents points in the azimuthal direction and is a function of radius r; it can be computed using Ampère's Law:

$0 \leq r \leq r_i: B(r) = \frac{\mu_i I r}{2 \pi r_i^2}$

$r_i \leq r \leq r_{o1}: B(r) = \frac{\mu_d I}{2 \pi r}$

$r_{o1} \leq r \leq r_{o2}: B(r) = \frac{\mu_o I}{2 \pi r} \left( \frac{r_{o2}^2 - r^2}{r_{o2}^2 - r_{o1}^2} \right)$

The flux per length l in the region between the conductors can be computed by drawing a surface containing the axis:

$\frac{d\phi_d}{dl} = \int_{r_i}^{r_{o1}} B(r) dr = \frac{\mu_d I}{2 \pi} \ln\frac{r_{o1}}{r_i}$

Inside the conductors, L can be computed by equating the energy stored in an inductor, $\frac{1}{2}LI^2$ , with the energy stored in the magnetic field:

$\frac{1}{2}LI^2 = \int_V \frac{B^2}{2\mu} dV$

For a cylindrical geometry with no l dependence, the energy per unit length is

$\frac{1}{2}L'I^2 = \int_{r_1}^{r_2} \frac{B^2}{2\mu} 2 \pi r~dr$

where L' is the inductance per unit length. For the inner conductor, the integral on the right-hand-side is $\frac{\mu_i I^2}{16 \pi}$ ; for the outer conductor it is $\frac{\mu_o I^2}{4 \pi} \left( \frac{r_{o2}^2}{r_{o2}^2 - r_{o1}^2} \right)^2 \ln\frac{r_{o2}}{r_{o1}} - \frac{\mu_o I^2}{8 \pi} \left( \frac{r_{o2}^2}{r_{o2}^2 - r_{o1}^2} \right) - \frac{\mu_o I^2}{16 \pi}$

Solving for L' and summing the terms for each region together gives a total inductance per unit length of:

$L' = \frac{\mu_i}{8 \pi} + \frac{\mu_d}{2 \pi} \ln\frac{r_{o1}}{r_i} + \frac{\mu_o}{2 \pi} \left( \frac{r_{o2}^2}{r_{o2}^2 - r_{o1}^2} \right)^2 \ln\frac{r_{o2}}{r_{o1}} - \frac{\mu_o}{4 \pi} \left( \frac{r_{o2}^2}{r_{o2}^2 - r_{o1}^2} \right) - \frac{\mu_o}{8 \pi}$

However, for a typical coaxial line application we are interested in passing (non-DC) signals at frequencies for which the resistive skin effect cannot be neglected. In most cases, the inner and outer conductor terms are negligible, in which case one may approximate

$\frac{dL}{dl} \approx \frac{\mu_d}{2 \pi} \ln\frac{r_{o1}}{r_i}$

[edit] See also

[edit] References

^ Heavyside, O. Electrician. Feb. 12, 1886, p. 271. See reprint
^ Glenn Elert (1998-2008). "The Physics Hypertextbook: Inductance". http://hypertextbook.com/physics/electricity/inductance/.
^ Michael W. Davidson (1995-2008). "Molecular Expressions: Electricity and Magnetism Introduction: Inductance". http://micro.magnet.fsu.edu/electromag/electricity/inductance.html.

[edit] General References

Frederick W. Grover (1952). Inductance Calculations. Dover Publications, New York.
Griffiths, David J. (1998). Introduction to Electrodynamics (3rd ed.). Prentice Hall. ISBN 0-13-805326-X.
Wangsness, Roald K. (1986). Electromagnetic Fields (2nd ed. ed.). Wiley. ISBN 0-471-81186-6.
Hughes, Edward. (2002). Electrical & Electronic Technology (8th ed.). Prentice Hall. ISBN 0-582-40519-X.
Küpfmüller K., Einführung in die theoretische Elektrotechnik, Springer-Verlag, 1959.
Heaviside O., Electrical Papers. Vol.1. – L.; N.Y.: Macmillan, 1892, p. 429-560.

[edit] Links

Clemson Vehicular Electronics Laboratory: Inductance Calculator

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