ارائ ر ش طراحي شبی ساز هیداى هغ اطیسي زهیي ج ت ا جام تست اي هغ اطیسي ها ار
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1 9;1; := هجو ع هقاالت ;: صفح 908-=90 تا اردیب شت ها ارائ ر ش طراحي شبی ساز هیداى هغ اطیسي زهیي ج ت ا جام تست اي هغ اطیسي ها ار 1 ظيد يح د طادق ي ظ ي 2 ي دي يستض ي 1 دا شج ي کازش اظي ازشد ي دظي افضا دا شکد ي دظي افضا دا شگا ط ؼتي اييسکثيس smsadeghmousavi@gmail.com 2 دا شياز دا شکد ي دظي افضا دا شگا ط ؼتي اييسکثيس mortazavi@aut.ac.ir چكید دز ا ي يقا ن پي چ ه نتص ت ػ ا ػا يم ايجادک د ي يدا يغ اطي عي يک ا خت زا يؼس فی د ت تسز ظی ي ؼادالت زيا ضی حاکى تس پي چ ه نتص دا يس ی يست ؼی يي پسداشيى ي يصا دزطد يک اختی ييدا يغ اطيعي حجى يک اختي يت اظس آ زا ت ط زت د ي ح ی ازائ يی د يى. پط اش آ ت تسزظی ز د يحاظثات ح تؼيي پازايتس ا تسای طساحی يک پيچ ه نتص پسداخت شد فه چازت پيش ادی تسای طساحی ظاخت آ ازائ يی گسدد. شثي ظاش ييدا يغ اطيعی پيچ ه نتص كلیدي: اژ اي تعت ای يالحظات طساحی ظاخت يک اختی ييدا يغ اطيعی يغ اطيعی يا از Design Method Proposition of Earth Magnetic Field Simulator For Magnetic Tests of Satellite Seyyed Mohammad Sadegh Mousavi 1 Mahdi Mortazavi 2 1 MSc Student of Aerospace Engineering, Aerospace Engineering Department, Amirkabir University of Technology 2 Associate Professor of Aerospace Engineering Department, Amirkabir University of Technology Abstract In this paper, we introduce Helmholtz coil as a creator of uniform magnetic field and investigate about mathematic equation of circular and square Helmholtz coil, and indicate the percentage of their uniformity and corresponding uniformity volume with two curves. After that we discuss about calculation process and methods of specifying parameters for designing a Helmholtz coil, and suggest a flowchart for designing and manufacturing process. Key words: Helmholtz Coil, Magnetic Field Simulator, Magnetic Field Uniformity, Designing and Manufacturing Requirements, Magnetic Tests of Satellite 9 هقده تا ا ج گ يسي تس ا ي اي ف ضايي فس ظتاد شد يا از ا فضااپي ا اي يلتهاه تا ياداز شياي يمانؼا دز يا زد ييادا يغ اطيعي شيي تأثيسات آ تس ز ي اجعاو فضايي ا يت تيشتسي پ يدا کسد. تا ت ظؼ تک ن ژي ا ظتفاد اش ان ا اي يغ اطي عي ظ يس يگ ت يتس گ شتا ز د د اي يغ اطي عي ي ازد دي گس دز شيسظي عتى تؼ يي ک تسل ضؼيت يا از ا ت کازگيسي يک شثي ظاش ييدا يغ اطيعي ت ي ظ ز تعت آياد ظاشي اط ي ا ياتي اش ػ ه کسد دز ظت ا ي ا جصا ا يت تي شتسي پ يدا د] 1 [ ت ط زي ک يي ت ا گ فت ا يس ش شثي ظاش ي يدا يغ اطي عي ي کي اش تج ياصات اجاة ضاس زي دز شيي ا تعات ااي انکتس يغ اطيعاي يا از ا چ ي شثي ظاشي يحيط يدازي آ ا يي تاشد. پيچ
2 2 ه نتص ت ػ ا ػايم ايجاد يک ييدا يغ اطيعي يک اخت قش ي ي زا دز ا جاو چ ي ت عت ايي اي فا يي ک د. دز ت عيازی اش پس ژ اي ظاخت يا از ک دز کش ز اي يلتهه ا جاو شد يا دز حال ا جاو ا ظت يي ت ا او پي چ ي ه نتص زا دز ک از آشيايشا ات يلتهفا ي کا دز شيي ا ا اي يستا تا تعا ت ا اي انکتس يغ اطي عي شثي ظاشی ي يدا يغ اطي عی ش يي ا جاو يي ش د يا فت] 2 [. تا ت ج ت ز د ک ش ز ػصيص يا ا يسا ت ج غ ک ش ز ای داز د ط ؼت ف ضايی ظاخت ت ظؼ چ ي ا تصاز ايی ايسی ضس زی ت ظس يی زظد. : تعریف پیچ ي لو لتس يک پيچ ه نتص دايس ي اش د ظيى پيچ دايس اي شکم تا شؼاع تؼداد د ز ظيى پيچي يکعا تشکيم يي ش د. اي د ظيى پيچ ت ط زت ى يح ز قساز گسفت جسيا يکعا I اش س د ظيى پيچ ػث ز داد يي ش د. تسآي د ييدا يغ اطيعي اي د ظيى پيچ دز ح اني قم ييا ي آ ا ت ط زت يک ييدا يغ اطيعي تقسيثا يک اخت ي اشي تا يح ز اي ظيى پيچ ا خ ا د ت د. ظيى پيچ ا ت شکم يستؼي يص يي ت ا د ظاخت ش د. پيچ ه نتص يي ت ا د ت ط زت يک يح ز د يح ز يا ظ يح ز ظاخت ش د دز د يا ظ زاظتاي يتؼايد ييدا يغ اطيعي يک اخت ت نيد ايد. اثثات يي ش د ک دز پيچ ه نتص دايس ی تساي داشت تيشتسي ييصا يک اختي الشو اظت تا فاطه د پيچ تايد تساتس شؼاع پيچ ا تاشد] 2 [. شكل 9. ح تغييسات يؤنف يح زی ييدا يغ اطيعي تس ز ي يح ز پيچ ي ه نتص دايس ي تک يح ز شکل:. پيچ ي ه نتص يستؼي ظ يح ز ; هعادالت ریاضی حاکن بر پیچ ی لو لتس ييدا يغ اطيعي تس ز ي يح ز دز قم ي يسکصي پيچ ي ه نتص دايس ي ت تستية تساتس اظت تا] 2 [: )1( )2( ک z فاطه اش يسکص د پيچ a شؼاع پيچ N تؼداد د ز ظيى پيچی µ 0 ضسية ف ذپريسي يغ اطيعي خالء اظت. تا ت ج ت زاتم )1( يي ت ا ي ح ي تغييسات يؤنف يح زي ييدا يغ اطيعي دز زاظتاي يح ز پيچ زا زظى د )شکم 3(. يي تي يى ک دز ح اني قم يسکصي ييدا يغ اطيعي تقسيثا يک اختي ج د دازد. زاتم يؤنف يح زي ييدا يغ اطيعي تس ز ي يح ز چ ي دز
3 B z (Gauss) 3 يسكص پيچ ي ه نتص يستؼي يص ت تستية تا ز اتط )3( )4( شا داد شد اظت] 2 [. )3( 9 x 10-3 فاطه تي د d ظه ضهغ يستغ يؼسف a )4( دز اي ز اتط پازايتس اثثات يي ش د ک تساي زظيد ت تيشتسي ييصا پيچ اظت تاشد] 3 [. a تساتس 0/5445 يقداز آ يک اختي الشو اظت تا z/a شكل ;. ي ح ي تغييسات يؤنف يح زي ييدا يغ اطيعي دز زاظتاي يح ز پيچ ي ه نتص دايس ي تک يح ز شکل>. پيچ ي ه نتص يستؼي تک يح ز دظتگا يلتظات يست ط < یک اختي هیداى هغ اطیسي تساي تيا ييصا يک اختي ييدا يغ اطيعی اش زاتم شيس تس حعة دزطد اظتفاد يي گسدد] 4 [: )5( ک دزآ B 0 ا داش ييدا يغ اطيعي دز يسکص پيچ ه نتص B i ا داش ييدا يغ اطيعي دز س قم اش حجى ي زد ظس اظت ک يي خ ا يى يک اختي ييدا زا دز آ حجى يحاظث اييى. سچ يقاديس B i ا ت يقداز B 0 صديکتس تاش د )يؼ ي سچ دزطد ف ق ک تس تاشد( يک اختي ييدا تيشتس خ ا د ت د ت ط زيک يي ت ا فسع د دز کم حجى ي زد ظس يک ييدا يک اخت ت ا داش B 0 ج د دازد. تا ت ج ت ز اتط فسي ل اي ييدا يغ اطيعي پيچ ي ه نتص يي ت ا كا ت ز اي يك اختي ييدا يغ اطيعي زا دز طفحات يلتهه زظى د] 5[]2 [. ت ػ ا شكم 5 كا ت ز اي يك اختي ييدا يغ اطيعي زا دز طفح ρz )دظتگا يلتظات اظت ا ای( تساي پيچ ي ه نتص دايس ي شا يي د د. اػداد يشلض شد ز ي خم دزطد يك اختي زا دز آ احي شا يي د د. تساي يثال خم طي ك تا اػداد ±1 يشلض شد ا د يسش احي اش ييدا يغ اطيعي زا شا يي د د ك دز داخم آ احي ييصا يك اختي ييدا دز تاش ±1% اظت.
4 4 کا ت ز اي دزطد يک اختي يست ت شکل=. ρz پيچ ي ييدا يغ اطيعي دز طفح B z يؤنف ه نتص دايس ي شکل<. تصزگتسي حجى کس ي شکم ک يي ت ا دز احي ی يک اختي ±1% دز ظس گسفت ييدا يغ اطيعي پيچ ه نتص دايس ي دازاي تقاز ح ل يح ز پيچ ا يي تاشد ت اتساي تا د زا احي اي اش شکم 5 ك يسش آ تا اػداد ±1 يشلض شد اظت )ح ل يح ز پيچ يح زz ( حج ي اش ييدا ک دازاي يک اختي دز تاش ±1% اظت تدظت يي آيد )شکم 6(. حجى شا داد شد دز اي شکم پيچيد ت ظس يي زظد. دز ػ م تساي ظادگي ت تس اظت تا ت جاي اظتفاد اش حجى ف ق اش يک حجى کس ي شکم تساي تيا يک اختي ييدا يغ اطيعي اظتفاد اييى] 4 [. دز اقغ اي تصزگتسي حجى كس ي اظت ك يك اختي ييدا يغ اطيعي دز داخم آ دز تاش ±1% يي تاشد. ت اي تستية يي ت ا تا تيا شؼاع اي كس حجى يحد د يك اختي ي زد ظس زا تيا د. ت ي تستية تساي پيچ ي ه نتص يستؼي يص يي ت ا كا ت ز اي يك اختي زا دز طفحات يلتهفي زظى د ت تسزظی ييصا يک اختی آ پسداخت] 2 [. = تعییي پاراهتر ای اساسی در طراحی پیچ ی لو لتس تا زظى تحهيم شکم ايی ظيس شکم 5 يی ت ا ي ح ی تغييسات دزطد يک اختی زا تسحعة شؼاع کس يک اختی )R( زظى د] 3[]2 [. شکم 7 اي ي ح ی ا زا تسای د پيچ ی ه نتص دايس ی يستؼی شا يی د د. شکل 0. پيچ ي دايس ي پيچ ي يستؼي تا پازايتس a يکعا شکل 7. ي ح ي دزطد يک اختي ييدا يغ اطيعي تس حعة شؼاع عثي کس يک اختي يکعا ی داز د زا a اگس د پيچ ی يستؼی دايس ی ک پازايتس يشلض يی گسدد ک 7 دز ظس تگيسيى تا ت ج ت ي ح ی ای شکم ت اشاي دزطد يک اختي يکعا حجى کس يک اختي ييدا يغ اطيعي دز پيچ ي ه نتص يستؼي تصزگتس اش پيچ ي ه نتص
5 5 دايس ي يي تاشد. تا ت ج ت اي ي ح ی ا تا تؼيي ييصا دزطد يک اختی شؼاع يک اختی ي زد ياش يی ت ا اتؼاد پيچ ی ه نتصی ک اي شسايط زا ازضاء يی ايد يافت. دزطد يک اختی الشو اظت تا R a تؼد اش يشلض شد يقاديس ي زد ياش زا تؼيي د. تؼداد د ز ظيى پيچی ياکصي ى جسيا تؼيي اي يقاديس تعتگی ت ياکصي ى ييدا يغ اطيعی ي زد ياش ت نيدی ت ظط پيچ ا دازد. تا يشلض شد اتؼاد چ ي ياکصي ى ييدا يغ اطيعی ي زد ياش تا ت ج ت ز اتط )2( يا )4( يی ت ا يى ي ح ی ياکصي ى جسيا ي زد ياش تس حعة تؼداد 9 تا فسع ظيى پيچی زا زظى اييى. اي ي ح ی ا دز شکم د ز 50 تساتس تا a گا ض يقداز 1/1 ت نيد ييدا يغ اطيعی ياکصي ى سچ تؼداد تا ت ج ت اي شکم ظا تی يتس زظى شد اظت] 2 [. د ز ظيى پيچی تيشتس تاشد ت ياکصي ى جسيا ک تسی تسای زظيد ز ی ياش دازيى. سکداو اش قا ت ييدا يغ اطيعی ياکصي ى ي ح ی ف ق يی ت ا د يکی اش ا تلاب ای يا تاشد. افصايش يا کا ش تؼداد د ز ياکصي ى جسيا ا تلاتي يي ت ا د يصايا يؼاية خاص خ د زا داشت تاشد. ت ػ ا يثال افصايش تؼداد د ز يي گسدد تاػث افصايش حعاظيت ييدا يغ اطيعي ت تغييسات جسيا تغييسات ا دکي دز جسيا پيچ ا يي ت ا د ي جة تغييسات اش طسفي افصايش تؼداد د ز تاػث تصزگي دز ييدا يغ اطيعي گسدد. کا ش ييصا جسيا ي زد ياش تساي زظيد ت يک ييدا يغ اطيعي يشلض يي گسدد اي ايس يمه تي اظت چسا ک کاز تا جسيا اي تا تؼيي شد کى آظا تس اي تس يؼق ل تس خ ا د ت د. حداکثس جسيا ي زد ياش يی ت ا ظيى تا ظمح يقمغ ي اظة ک اي يقداز جسيا زا تح م يی ک د ا تلاب د. دز ظاخت پيچ اي ه نتص اش ظيى اي الکي يعي اظتفاد يي ش د. ظيى اي يعي تا اظتا دازد اي يلتهفي ت نيد يي ش د. تا ت ج ت جدا ل ي اظة تا قمس ي ج د تسای اي اظتا دازد ا يی ت ا ظيى الکی زا ا تلاب د. يساحم طساحي ظاخت يک پيچ ي تا ت ج ت يمانة ازائ شد يی گسدد. ازائ 10 ت ط زت شکم ه نتص
6 6 شكل 1. ي ح ي ياکصي ى جسيا ي زد ياش تس حعة تؼداد د ز ظيى پيچ 98. شكل فه چازت طساحي پيچ ي ه نتص > تیج گیري دز ا ي يقا ن ت تسز ظی ي ؼادالت ز ا تط زيا ضی حاکى تس پي چ ی ه ا نتص پسداختا شاد ييادا يغ اطيعای ت نيادی يياصا يک اختی آ ي زد تحه يم تسز ظی قساز گس فت تا ت ج ت ا ي تحهيم ا ز اتط حاکى ز د طساحی يک پيچ ه نتص ت ط زت ػاو ازائ گسديد. تدي تستية يقديات ا ني الشو تسای ظاخت شثي ظاش ييدا يغ اطيعی شيي فسا ى يی آيد. ه ابع 1. Fabrizio Piergentili, Gian Paolo Candini, Marco Zannoni, Design, Manufacturing, and Test of a Real-Time, Three-Axis Magnetic Field Simulator, IEEE Transactions on Aerospace and Electronic Systems Vol. 47, No. 2 April ي ظ ی ظيد يح د طادق تسزظی يالحظات طساحی تد ي يدل زياضی پيچ ی ه نتص ج ت تعت گشتا ز د د يغ اطيعی. پايا - اي کازش اظی دا شگا ط ؼتی اييسکثيس دا شکد ي دظی افضا William M. Frix, George G. Karady, Brian A. Venetz, Comparison of Calibration Systems for Magnetic Field Measurement Equipment, IEEE Transactions on Power Delivery, Vol. 9, No. 1, January Marino, Alberto R. Field Homogeneity in Helmholtz Coils, Application Note NAS02-I, Serviciencia, S.L. 21 October Pastena, M, Grassi, M, Optimum Design of a Three-Axis Magnetic Field Simulator, IEEE Transactions on Aerospace and Electronic Systems Vol. 38, No. 2, April 2002.
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