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實(shí)習(xí)報(bào)告 這次認(rèn)識(shí)實(shí)習(xí)，讓我走進(jìn)了工廠、踏進(jìn)了車間，見(jiàn)到了工人是如何生產(chǎn)產(chǎn)品。我想，實(shí)習(xí)只是一種手段，我們更多需要做的是在實(shí)習(xí)過(guò)程中，通過(guò)對(duì)工廠的了解和與工人、技術(shù)人員的交流，得以對(duì)所學(xué)專業(yè)在國(guó)民經(jīng)濟(jì)中所占地位與作用的認(rèn)識(shí)有所加深，培養(yǎng)事業(yè)心、使命感和務(wù)實(shí)精神，激發(fā)為振興中華而刻苦學(xué)習(xí)奮力工作的熱情，為更好地適應(yīng)從學(xué)生到工作者的過(guò)渡準(zhǔn)備條件。 這次認(rèn)識(shí)實(shí)習(xí)，讓我了解機(jī)械零件的基本生產(chǎn)加工方法、機(jī)械制造工藝流程以及主要生產(chǎn)設(shè)備在生產(chǎn)中的作用等知識(shí)。同時(shí)，也得到一次綜合能力的訓(xùn)練和培養(yǎng)。在整個(gè)實(shí)習(xí)過(guò)程中，充分發(fā)揮學(xué)習(xí)主動(dòng)性、積極性，在生產(chǎn)現(xiàn)場(chǎng)細(xì)心觀察，虛心請(qǐng)教，積極思維，多方了解，大膽提出自己的想法，在有限的實(shí)習(xí)時(shí)間里，使諸方面的能力都得到鍛煉。 實(shí)習(xí)已經(jīng)結(jié)束，但作為一名大學(xué)生對(duì)實(shí)習(xí)中的所見(jiàn)所聞以及自己的一些感想做一次總結(jié)也很有必要。 奇瑞汽車有限公司于1997年由5家安徽地方國(guó)有投資公司投資17.52億元注冊(cè)成立；1997年3月18日動(dòng)工建設(shè)，1999年12月18日，第一輛奇瑞轎車下線。2001年，奇瑞轎車正式上市，當(dāng)年便以單一品牌完成銷售2.8萬(wàn)輛；2002年，奇瑞轎車產(chǎn)銷量突破5萬(wàn)輛，成功躋身國(guó)內(nèi)轎車行業(yè)“八強(qiáng)”之列，成為行業(yè)內(nèi)公認(rèn)的“車壇黑馬”。2005年銷售18.9萬(wàn)輛，比上年增長(zhǎng)118%，全國(guó)轎車市場(chǎng)占有率達(dá)6.7%，在我國(guó)轎車行業(yè)排名第七。 目前，奇瑞公司已具備年產(chǎn)65萬(wàn)輛整車、65萬(wàn)臺(tái)發(fā)動(dòng)機(jī)和40萬(wàn)套變速箱的生產(chǎn)能力。奇瑞公司旗下現(xiàn)有奇瑞、瑞麒、威麟和開(kāi)瑞四個(gè)子品牌，產(chǎn)品覆蓋乘用車、商用車、微型車領(lǐng)域。目前，奇瑞已有16個(gè)系列數(shù)十款車型投放市場(chǎng)，另有數(shù)十款儲(chǔ)備車型將相繼上市。奇瑞以“安全、節(jié)能、環(huán)?！睘楫a(chǎn)品訴求，先后通過(guò)ISO9001、德國(guó)萊茵公司ISO/TS16949等國(guó)際質(zhì)量體系認(rèn)證。 “自主創(chuàng)新”是奇瑞發(fā)展戰(zhàn)略的核心，也是奇瑞實(shí)現(xiàn)超常規(guī)發(fā)展的動(dòng)力之源。 “全球化”是奇瑞的戰(zhàn)略發(fā)展目標(biāo)。在積極打造硬實(shí)力的同時(shí)，奇瑞還高度重視培育軟實(shí)力。秉承“大營(yíng)銷”理念，奇瑞全面升級(jí)“品牌、品質(zhì)、服務(wù)”三大平臺(tái)，不斷提升品牌形象和企業(yè)形象。奇瑞汽車將秉承“自主創(chuàng)新、世界一流、造福人類”的奮斗目標(biāo)，繼續(xù)保持艱苦奮斗的“小草房”精神，為實(shí)現(xiàn)成為“自主國(guó)際名牌”第二階段目標(biāo)而努力！ 奇瑞ACTECO 1.9D TCI柴油發(fā)動(dòng)機(jī) 奇瑞ACTECO 1.9D TCI柴油發(fā)動(dòng)機(jī)，直列4缸，每缸4氣門(mén)，雙頂置凸輪軸，滾子搖臂，液壓挺柱。該款發(fā)動(dòng)機(jī)融TCI技術(shù)、高壓共軌直噴技術(shù)、EGR系統(tǒng)等數(shù)項(xiàng)先進(jìn)技術(shù)于一身，并采用TVD、雙質(zhì)量飛輪等結(jié)構(gòu)，提高了發(fā)動(dòng)機(jī)的功率和扭矩，最大限度地減少?gòu)U氣，減少了發(fā)動(dòng)機(jī)的噪音。燃油較點(diǎn)燃式汽油機(jī)減少40-45%，滿足歐Ⅳ排放標(biāo)準(zhǔn)?？胺Q新一代綠色動(dòng)力。 奇瑞ACTECO 2.0D TCI DGI發(fā)動(dòng)機(jī) 奇瑞ACTECO 2.0D TCI DGI發(fā)動(dòng)機(jī)為直列4缸機(jī)，液4缸機(jī)，渦輪 中冷，缸內(nèi)直噴，雙頂置凸輪軸，可變進(jìn)排氣正時(shí)，滾子搖臂，液壓挺柱，每缸4氣門(mén)。該發(fā)動(dòng)機(jī)能夠滿足歐Ⅳ排放標(biāo)準(zhǔn)。在該款發(fā)動(dòng)機(jī)上裝備了電子節(jié)流閥體，使其控制更靈活更適用于裝備自動(dòng)變速器的整車控制系統(tǒng)。 奇瑞ACTECO 4.0 V8汽油發(fā)動(dòng)機(jī) 奇瑞ACTECO 4.0 V8汽油發(fā)動(dòng)機(jī)為V型8氣缸發(fā)動(dòng)機(jī)，全鋁機(jī)身，每缸4氣門(mén)，雙頂置凸輪軸，滾子搖臂，采用CBR，VVT等尖端發(fā)動(dòng)機(jī)燃油、正時(shí)控制系統(tǒng)。此款發(fā)動(dòng)機(jī)能夠滿足歐Ⅳ排放標(biāo)準(zhǔn)。同時(shí)該款發(fā)動(dòng)機(jī)上裝備DOD技術(shù)，可以在高動(dòng)力性和高經(jīng)濟(jì)性之間任意切換。 發(fā)動(dòng)機(jī)事業(yè)部發(fā)動(dòng)機(jī)二廠有一條試制線，總造價(jià)達(dá)5000多萬(wàn)，可試制各種類型的內(nèi)燃發(fā)動(dòng)機(jī)，經(jīng)過(guò)認(rèn)證可以生產(chǎn)航天零件。投入使用后將試制一臺(tái)發(fā)動(dòng)機(jī)的費(fèi)用減少到以前的十分之一。該廠房采用密封全空調(diào)微正壓設(shè)計(jì)，有助于減少粉塵擴(kuò)散，提高產(chǎn)品質(zhì)量。車間里有500多臺(tái)數(shù)控設(shè)備聯(lián)網(wǎng)生產(chǎn)，確保了產(chǎn)品的品質(zhì)。 奇瑞的確在不斷地進(jìn)步，雖然和合資車還有差距，但是價(jià)格的優(yōu)勢(shì)以及逐漸過(guò)硬的質(zhì)量已經(jīng)讓我們有充足的借口購(gòu)買(mǎi)奇瑞，而越來(lái)越少聽(tīng)到“奇瑞奇瑞，修車排隊(duì)”的聲音了。 不過(guò)奇瑞在各個(gè)車型里面相對(duì)做工存在較大差異，這種差異和價(jià)格基本成正比。下面我就談?wù)勎覍?duì)各個(gè)車型的感覺(jué)。 東方之子外觀油漆做工中上乘，空間已經(jīng)達(dá)到標(biāo)準(zhǔn)B級(jí)車范疇，而且?guī)啄昵霸O(shè)計(jì)的車型，目前如果開(kāi)出去，一點(diǎn)不會(huì)顯得過(guò)時(shí)。內(nèi)飾件用材較為精良，中控臺(tái)軟性材料，各種接縫都是令人較為滿意。奇瑞A1當(dāng)時(shí)是奇瑞號(hào)稱真正質(zhì)量飛躍的車型，但是各個(gè)媒體，專家試駕后，看到有些言過(guò)其實(shí)。用料絕對(duì)能對(duì)得起這個(gè)價(jià)格，接縫也屬細(xì)密之列，只是開(kāi)著不太爽，人機(jī)設(shè)計(jì)也有些問(wèn)題，方向盤(pán)感覺(jué)和放置東西都有一些別扭。外觀可以打比較高的分，但是開(kāi)起來(lái)分值較低。噪聲控制還要加強(qiáng)。而A5是你不會(huì)想到這是一臺(tái)最近基本款只要55000元的車，空間很大。用料也絕對(duì)對(duì)得起這個(gè)價(jià)位，電噴系統(tǒng)采用合資件，傳感器也是。車架開(kāi)起來(lái)有些松，原車隔音做得不好，整車噪聲比較大 把所學(xué)的理論知識(shí)，運(yùn)用到客觀實(shí)際中去，使自己所學(xué)的理論知識(shí)有用武之地。只學(xué)不實(shí)踐，所學(xué)的就等于零,理論應(yīng)該與實(shí)踐相結(jié)合.另一方面，實(shí)踐可為以后找工作打基礎(chǔ).通過(guò)這段時(shí)間的實(shí)習(xí)，學(xué)到一些在學(xué)校里學(xué)不到的東西。因?yàn)榄h(huán)境的不同，接觸的人與事不同，從中所學(xué)的東西自然就不一樣了。經(jīng)過(guò)這次實(shí)習(xí)，雖然時(shí)間很短，可我學(xué)到的卻是我一個(gè)學(xué)期在學(xué)校難以了解的。就比如何與同事們相處，相信人際關(guān)系是現(xiàn)今不少大學(xué)生剛踏出社會(huì)遇到的一大難題，于是在實(shí)習(xí)時(shí)我便有意觀察前輩們是如何和同事以及上級(jí)相處的，而自己也盡量虛心求教。這次實(shí)習(xí)經(jīng)歷使我獲益良多,對(duì)我將來(lái)的發(fā)展具有十分積極的作用。 通過(guò)集成磁軸承輔助有限元分析的一種新型飛輪儲(chǔ)能存儲(chǔ)系統(tǒng)的設(shè)計(jì)與建模 C.張，學(xué)生會(huì)員，IEEE，吳平，學(xué)生會(huì)員，IEEE和K. J. Tseng，高級(jí)會(huì)員，IEEE 新加坡共和國(guó), 新加坡639798，南陽(yáng)大道BLK S2，南洋理工大學(xué)，先進(jìn)電力電子研究中心 摘要——本文提出的是緊湊和高效的飛輪存儲(chǔ)系統(tǒng)。該系統(tǒng)是由綜合力學(xué)性能和磁軸承輔助，飛輪作為轉(zhuǎn)子的驅(qū)動(dòng)系統(tǒng)，并且該系統(tǒng)通過(guò)被夾在兩個(gè)磁盤(pán)式定子之間而節(jié)省空間。通過(guò)主動(dòng)磁軸承，轉(zhuǎn)子飛輪旋轉(zhuǎn)和保持在垂直方向的磁懸浮機(jī)械軸承和軸向磁通永磁同步電動(dòng)機(jī)的助攻結(jié)合使用，而限制在徑向方向的其他四個(gè)自由度的機(jī)械。所提出的系統(tǒng)的數(shù)學(xué)模型被推導(dǎo)出來(lái)。三維有限元方法是應(yīng)用于通過(guò)研究和驗(yàn)證數(shù)學(xué)模型系統(tǒng)分析結(jié)果而支持系統(tǒng)可行性。 一 正文 在現(xiàn)代化電力行業(yè)，具有強(qiáng)度高，重量輕的先進(jìn)復(fù)合材料，控制技術(shù)和電子電力，飛輪能量存儲(chǔ)系統(tǒng)（FESS）正在成為一個(gè)傳統(tǒng)的化學(xué)電池系統(tǒng)的可行性替代。其優(yōu)點(diǎn)為儲(chǔ)能密度高，充電放電風(fēng)險(xiǎn)較低，放電深度容易檢測(cè)，能在較寬溫度范圍內(nèi)操作，壽命更長(zhǎng)，有利于環(huán)境。所以FESS被認(rèn)為是對(duì)于現(xiàn)在許多應(yīng)用的一個(gè)有前景的技術(shù)，包括航空航天，交通運(yùn)輸，電力工業(yè)，軍事，建筑服務(wù)。 一般來(lái)說(shuō)，一個(gè)飛輪儲(chǔ)能系統(tǒng)是由一個(gè)磁性的或機(jī)械的軸承支撐的由電機(jī)帶動(dòng)的飛輪，一個(gè)將機(jī)械能和電能內(nèi)部轉(zhuǎn)化系統(tǒng)的飛輪，控制增強(qiáng)電子的器件和觸地軸承組成的。這個(gè)單獨(dú)的除磁性軸承驅(qū)動(dòng)電機(jī)使轉(zhuǎn)子長(zhǎng)，容易產(chǎn)生彎曲振動(dòng)。且大電機(jī)軸承系統(tǒng)使得小型化【5】困難。為了克服這些問(wèn)題，自軸承永磁電機(jī)被引進(jìn)。電機(jī)結(jié)合磁軸承和汽車功能為單一的磁性制動(dòng)器。這樣的設(shè)計(jì)由于不需要機(jī)械軸承可以降低整體的一種電機(jī)長(zhǎng)。因此能夠提高功率密度，減輕重量，降低轉(zhuǎn)子的動(dòng)態(tài)振動(dòng)【6】的敏感性。 如圖1所示，沿x，y，z在飛輪軸有三個(gè)方向，使每一個(gè)軸的位移和旋轉(zhuǎn)受機(jī)械或磁性的幫助來(lái)控制六個(gè)自由度。機(jī)械軸承具有結(jié)構(gòu)簡(jiǎn)單，操作方便的優(yōu)點(diǎn)，但由于摩擦損耗，應(yīng)考慮潤(rùn)滑油的使用。特別是發(fā)生在軸承，沿重力方向上即圖1沿z軸方向的摩擦要比其他方向上的摩擦大得多。由于這個(gè)原因，軸承使用機(jī)械軸承是不現(xiàn)實(shí)的，而其他的軸是可以承受的。主動(dòng)磁軸承相對(duì)于傳統(tǒng)軸承是可以承受的。主動(dòng)磁軸承相對(duì)于傳統(tǒng)軸承有許多優(yōu)點(diǎn)，這些優(yōu)點(diǎn)包括更高的能量效率，降低磨損，延長(zhǎng)壽命，不需要潤(rùn)滑機(jī)械維修和較寬的操作溫度。關(guān)于磁軸承有許多研究，但大多數(shù)人對(duì)待至少有五個(gè)自由度的對(duì)象是控制。由于控制每個(gè)自由度需要一個(gè)傳感器，執(zhí)行器和控制器，整個(gè)系統(tǒng)在機(jī)械/電氣部分和控制系統(tǒng)設(shè)計(jì)變得復(fù)雜。鑒于此，本文提出了一個(gè)新概念磁性軸承。其中軸只有兩個(gè)自由度受主動(dòng)控制，即分別沿平移和旋轉(zhuǎn)方向。其他方向的運(yùn)動(dòng)方向由機(jī)械軸承完全限制。主動(dòng)磁軸承和機(jī)械軸承的結(jié)合使用可以減少控制的復(fù)雜性，使系統(tǒng)運(yùn)動(dòng)更加穩(wěn)定，可行和具有成本效益。 圖1 飛輪的三個(gè)運(yùn)動(dòng)方向 目前，軸向磁通永磁電機(jī)（AFPM）在許多應(yīng)用中 已成為一個(gè)有吸引力的研究場(chǎng)【8】【9】。它們有幾個(gè)獨(dú)特的功能，如效率高，高能，高扭矩密度，低轉(zhuǎn)子損耗和小磁厚度。然而缺點(diǎn)是該分布式繞組具有與線圈導(dǎo)體的有效部分相比的顯著長(zhǎng)度的端繞組。這顯然會(huì)導(dǎo)致機(jī)器性能差。作為本機(jī)顯著成分（即總在大多數(shù)機(jī)器設(shè)計(jì)的50%以上）被產(chǎn)生熱量，但沒(méi)有轉(zhuǎn)矩。集中繞組可以解決這個(gè)問(wèn)題。此外，他們有簡(jiǎn)單的設(shè)計(jì)，更容易安排及更高效率。 有限元分析法（FEM）已被證明是特別靈活，可靠。有效的分析方法是工頻電磁場(chǎng)和機(jī)電裝置的合成。有限元法可以分析任何形狀和材料的PM電路，有限元分析與其他永磁電機(jī)的分析方法相比的一個(gè)顯著優(yōu)點(diǎn)是其準(zhǔn)確計(jì)算電樞反應(yīng)，電磁力和力矩的固有能力。 本文中，一種集成磁軸承輔助新型飛輪儲(chǔ)能系統(tǒng)被介紹。用電動(dòng)機(jī)和發(fā)電機(jī)相結(jié)合并且使飛輪功能作為機(jī)器，以節(jié)省空間的轉(zhuǎn)子。機(jī)械軸承是用來(lái)限制沿徑向方向得位移和旋轉(zhuǎn)，位移和旋轉(zhuǎn)沿軸向方向由主動(dòng)磁軸承控制。利用數(shù)學(xué)模型所提出的系統(tǒng)的結(jié)構(gòu)和電磁設(shè)計(jì)被呈現(xiàn)。三維有限元分析的實(shí)現(xiàn)，驗(yàn)證了數(shù)學(xué)模型和支持體系的可行性。本文中介紹的分析結(jié)果已經(jīng)獲得。 二 建設(shè)與計(jì)算所提出的系統(tǒng) （1）整個(gè)系統(tǒng)的配置 圖2所提出的系統(tǒng)的橫截面圖 圖2示出了所提出的的飛輪儲(chǔ)能系統(tǒng)的橫截面圖。它的組分列于表I項(xiàng)目1和8是固定在該裝置的殼體，其目的是從任何轉(zhuǎn)子碎片消散徑向動(dòng)能，并確保在發(fā)生機(jī)械故障的情況下安全的上部和下部固定件。軸向磁通永磁同步電動(dòng)機(jī)的實(shí)施來(lái)驅(qū)動(dòng)其也用作轉(zhuǎn)子的飛輪。 機(jī)械旋轉(zhuǎn)球軸承安裝在轉(zhuǎn)子上，以限制其徑向運(yùn)動(dòng)和輔助飛輪/轉(zhuǎn)子的旋轉(zhuǎn)的外緣。這種安排使結(jié)構(gòu)不使用軸非常緊湊。但是機(jī)械軸承的孔的最大直徑限制了最大速度。用油膜軸承DN值（孔直徑mm*轉(zhuǎn)速rpm）可以達(dá)到3，000,000【13】。這意味著最高車速小于2000轉(zhuǎn)時(shí)該孔的直徑為150毫米。在更高的速度飛輪系統(tǒng)上，兩個(gè)機(jī)械軸承可以安裝在被固定在所述轉(zhuǎn)子的中間軸的兩端。用這種結(jié)構(gòu)，速度可以高達(dá)60000轉(zhuǎn)以上。 軸向運(yùn)動(dòng)可實(shí)現(xiàn)對(duì)旋轉(zhuǎn)球軸承的輪輞正交安裝的4個(gè)滑動(dòng)球軸承的援助。當(dāng)轉(zhuǎn)子旋轉(zhuǎn)時(shí)（圖中的項(xiàng)目＃2和＃102），非接觸式渦流位移傳感器和光電傳感器在兩個(gè)定子的中空的中心設(shè)置用以檢測(cè)沿z軸的位移和角位置。起動(dòng)操作時(shí)或在磁懸浮軸承故障的情況下，需要著陸軸承。著陸軸承應(yīng)安裝在對(duì)著轉(zhuǎn)子的外緣。在正常操作期間，存在所有的轉(zhuǎn)子表面和觸下軸承之間的小于0.5mm的空氣間隙，從而實(shí)現(xiàn)了機(jī)械接觸式的環(huán)境。 （2） 建議系統(tǒng)的基本特征 圖3顯示了所提出的系統(tǒng)的基本特征。電動(dòng)機(jī)及發(fā)電機(jī)用盤(pán)式幾何組合成一個(gè)單一的電動(dòng)機(jī)，如圖3所示（a）所示。轉(zhuǎn)子兼作飛輪和被夾持兩個(gè)圓盤(pán)型定子之間。此設(shè)計(jì)使盤(pán)式轉(zhuǎn)子的轉(zhuǎn)矩產(chǎn)生區(qū)。 如圖所示在圖3（b）中，每個(gè)上部和下部定子承載的一組三相繞組的銅與正弦電流供給;集中繞組被實(shí)現(xiàn)，以減少功率損耗。如果分布式繞組，繞組-末端將跨越轉(zhuǎn)子的半個(gè)圓周。線圈導(dǎo)體的有效部分比端部是更長(zhǎng)，從而繞組的銅損會(huì)更大。在這個(gè)特定的設(shè)計(jì)中，有6個(gè)線圈，其中每個(gè)線圈都圍繞定子齒。三相和三相電流的方向在特定的實(shí)例中的分布，如圖4顯示。除了提高效率，結(jié)構(gòu)簡(jiǎn)單，安裝方便定子繞組也可實(shí)現(xiàn)這種設(shè)計(jì)。 永久磁鐵被安裝在轉(zhuǎn)子的兩個(gè)表面上，如圖3（c）所示。這些PM的與磁通流過(guò)電動(dòng)機(jī)的結(jié)構(gòu)被描繪在圖4中。預(yù)防性維護(hù)都定居在相反的方向上和下轉(zhuǎn)子面，所以他們會(huì)相互吸引，增加磁路的總光通量。 圖3所提出的飛輪系統(tǒng)的基本組成部分 （a）定子轉(zhuǎn)子組件 （b）定子的繞組（c）轉(zhuǎn)子（d）非磁性的護(hù)環(huán) 采用高強(qiáng)度非磁性材料制成的護(hù)圈是用來(lái)協(xié)助PM在抵抗離心力的作用，如圖3（d）所示。 圖4電機(jī)發(fā)展結(jié)構(gòu)和二維通量模式 磁懸浮軸承可以用吸引力來(lái)實(shí)現(xiàn)。定子和轉(zhuǎn)子場(chǎng)之間的相互作用產(chǎn)生的軸向力，使得在轉(zhuǎn)子和定子相互吸引。每個(gè)定子的電流可以獨(dú)立調(diào)節(jié)，以控制轉(zhuǎn)子上的凈力，并保持它在兩個(gè)定子的中間。沿著軸向軸的凈力可求得 F = F2 ? F1 (1) 其中，F(xiàn)1是較低的定子和轉(zhuǎn)子之間的力; F2是上定子和轉(zhuǎn)子之間的作用力。 電動(dòng)機(jī) - 發(fā)電機(jī)相當(dāng)于兩個(gè)電動(dòng)機(jī)，總轉(zhuǎn)矩T可以寫(xiě)為 T = T1 +T2 (2) 其中，T1和T2分別由上部和下部分別電機(jī)產(chǎn)生的轉(zhuǎn)矩 （3） 電機(jī)尺寸 軸向磁通電機(jī)的尺寸可通過(guò)下式被轉(zhuǎn)換到一個(gè)等效徑向尺寸的機(jī)器得到 D=Do+ Di/2 (3) L=Do- Di/2 (4) 其中DO和DI是軸向磁通盤(pán)式馬達(dá)，D和L的外徑和內(nèi)徑都內(nèi)徑的徑向當(dāng)量機(jī)和長(zhǎng)度。當(dāng)KR = Do / Di = 3 .最大扭矩產(chǎn)生 從電機(jī)的輸出方程，我們可以得到D2L=QCons （5） 然后，我們就可以得到 其中C0是輸出系數(shù)，Q為機(jī)器的千伏安的評(píng)級(jí)，NS是額定轉(zhuǎn)速在RPS 其中Bgav代表的平均磁通密度超過(guò)氣隙的機(jī)器，也被稱為磁載荷，A為電負(fù)荷;千瓦是繞組系數(shù); PN，ηN和cosφN分別表示額定功率，效率和功率因數(shù); KE是感應(yīng)電動(dòng)勢(shì)和電壓之間的比率。在本設(shè)計(jì)中，KE =0.905。 空氣間隙的最小長(zhǎng)度是由機(jī)械約束集并且不大可能小于0.3毫米。磁鐵'的深度一般應(yīng)減少到最低值，以盡量減少磁體的成本。制造業(yè)的限制，很難有磁鐵大于2.0mm更薄。在此設(shè)計(jì)中，GL被選擇為0.5mm時(shí)，與毫升設(shè)定為2.5毫米。 根據(jù)在表II中示出的設(shè)計(jì)要求的數(shù)據(jù)時(shí)，電機(jī)設(shè)計(jì)的結(jié)果可以得到如在表III中。這只是一個(gè)測(cè)試設(shè)計(jì)驗(yàn)證系統(tǒng)結(jié)構(gòu)的可行性和數(shù)學(xué)模型的正確性。所以在額定轉(zhuǎn)速時(shí)只選擇為1500轉(zhuǎn)每分鐘。 三.數(shù)學(xué)模型 如圖3所示，在定子的三相繞組分別記為a，b和c具有相同的匝數(shù)。永久磁鐵被安裝在所述盤(pán)型轉(zhuǎn)子的表面上，一個(gè)非凸轉(zhuǎn)子最后獲得。只有當(dāng)勵(lì)磁繞組被永久磁鐵所取代時(shí)，電機(jī)可以被視為一個(gè)常規(guī)同步電機(jī)， PM電機(jī)可以通過(guò)假設(shè)這里所述轉(zhuǎn)子的永磁體已被替換成等效的轉(zhuǎn)子電流，如果與卷繞數(shù)N F是容易分析。由定子相繞組與等效轉(zhuǎn)子電流產(chǎn)生，如果可以被認(rèn)為是第φ和rφ，相同的繞組[14] [15]的分布的正弦函數(shù)的粗略近似的磁動(dòng)勢(shì)的波形。其中sφ和rφ是從一個(gè)三相定子繞組軸與旋轉(zhuǎn)直軸，分別測(cè)得的角度。假設(shè)極對(duì)數(shù)為P，其功能如下 其中N s是相當(dāng)于匝正弦分布繞組的定子的各相的數(shù)量。 對(duì)于被描繪為圖3的繞組分布（b）所示，音調(diào)因數(shù)KP= 1，分配系數(shù)KD= COS（π/ 6）= 3/2，所以繞組系數(shù)千瓦= KP×KD= 3/2。然后Ns個(gè)可以計(jì)算為 其中NPH是圈串聯(lián)每相的實(shí)際數(shù)目。 由PMs，MMFM，所產(chǎn)生的等效的MMF的最大值被計(jì)算為 其中，LM和HM表示磁體長(zhǎng)度和當(dāng)磁鐵由導(dǎo)磁的鐵短路的磁場(chǎng)強(qiáng)度。然后N個(gè)f如果該值，可以實(shí)現(xiàn)如 B是用于的PM的殘留磁通密度，R，μ為相對(duì)磁導(dǎo)率，μ0為空氣與4π×10-7的值的磁導(dǎo)率。 定子和轉(zhuǎn)子的表面之間的有效氣隙長(zhǎng)度被定義為g時(shí)，磁通密度B與磁通如下圖所示： 作為一個(gè)例子，讓我們判斷，由于電流只在一個(gè)繞組漏感在這里忽略繞組的總磁鏈。 其中Ro和Ri是，定子的外表面和內(nèi)半徑。同樣地，我們可以得到 在a和f繞組之間的互感是通過(guò)確定 在與上述相同的方式，LAF，LBF，LCF可寫(xiě)為 因此，其他的互感可求得 然后 其中L是電機(jī)的電感矩陣，該電感是由（18）（19）確定，（21） - （24）。 （31）的電感表達(dá)式可以當(dāng)它們被表達(dá)的dq0變量方面被簡(jiǎn)化 存儲(chǔ)的磁能可以被計(jì)算為 因此，可以得到的有吸引力的力Fs 從弗萊明左手法則，旋轉(zhuǎn)扭矩Ts可表示為 這里，定子和的PM在平衡點(diǎn)的表面之間的空氣間隙被定義為L(zhǎng)G，所以在定子和轉(zhuǎn)子在平衡點(diǎn)之間的有效氣隙可求得 Kc為卡特的系數(shù)，它是約等于1。然后F1和T1可以通過(guò)代克= G0+ Z，ID = ID1和IQ = IQ1入（28）（29）進(jìn)行計(jì)算，而F2和T2可以通過(guò)替換來(lái)計(jì)算G = G0 - Z，ID = ID 2和 IQ = IQ2到相同的等式，其中z是在垂直方向上的轉(zhuǎn)子的位移?？偟牧土厥怯桑?）和（2）得到的。 在轉(zhuǎn)子的徑向運(yùn)動(dòng)由機(jī)械球軸承的限制。因此，轉(zhuǎn)子的軸向運(yùn)動(dòng)是獨(dú)立的徑向運(yùn)動(dòng)。轉(zhuǎn)子的軸向運(yùn)動(dòng)的動(dòng)力學(xué)方程為 其中FZ是在z軸方向上的外力，而重力被考慮在內(nèi)。 總轉(zhuǎn)矩的方程可以改寫(xiě)為 和 其中J是轉(zhuǎn)動(dòng)慣量，θ是轉(zhuǎn)子角，π是轉(zhuǎn)速。 電壓方程可寫(xiě)為 四. 有限元分析和模型驗(yàn)證 （1）理論 在永磁電機(jī)的磁場(chǎng)總是與瞬態(tài)激勵(lì)和非線性磁性材料相關(guān)。以下三個(gè)麥克斯韋方程有關(guān)的瞬態(tài)的應(yīng)用程序。 其中，H表示磁場(chǎng)密度，J是電流密度，σ是介質(zhì)的電導(dǎo)率，和E是電場(chǎng)強(qiáng)度 從（36）和（37），可以得到 力和力矩可以計(jì)算為存儲(chǔ)磁共能W'相對(duì)于小排量的導(dǎo)數(shù)。助能量可以寫(xiě)成 然后瞬時(shí)力Fs中的偏移量s的方向上的分量是 以小角度旋轉(zhuǎn)位移θ的瞬時(shí)轉(zhuǎn)矩T由下式表示 （2）有限元分析 使用時(shí)步三維有限元模擬[16]在第二節(jié)中描述的提出的系統(tǒng)進(jìn)行了分析。分析模型的網(wǎng)格形狀被示為圖5。只有一個(gè)定子和轉(zhuǎn)子被實(shí)現(xiàn)在有限元分析中，為了節(jié)省計(jì)算時(shí)間，但它是有效的描述整個(gè)系統(tǒng)的性能。 圖5分析模型的網(wǎng)格形狀 圖6有限元模擬的結(jié)果時(shí)，定子伴隨50Hz正弦電流（a）磁鏈（b）引起的電壓（c）轉(zhuǎn)速 在開(kāi)環(huán)的條件下，50赫茲的正弦波電流，并且給定的1500轉(zhuǎn)每分的初始速度，無(wú)論是交鏈磁通量和感應(yīng)電壓是準(zhǔn)正弦，而且速度穩(wěn)定到同步速度最終。有限元法 析結(jié)果如圖6示。事實(shí)證明，電機(jī)可以作為一個(gè)正弦波電機(jī)進(jìn)行分析，數(shù)學(xué)分析是站得住腳的。 圖7（a）和（b）示出了磁通密度在定子和轉(zhuǎn)子。很明顯，有分別具有定子和轉(zhuǎn)子的表面磁通密度較高的區(qū)域4。它代表4極電機(jī)。永久磁鐵NdFe35 與留磁通密度Br=1.23 T的安裝在轉(zhuǎn)子的表面上，所以在根據(jù)的PM的區(qū)域中，磁通密度是肯定比在其他地方更高。 圖7定子和轉(zhuǎn)子的磁通分布（a）定子的磁通密度(b)轉(zhuǎn)子的磁通密度 （3）. 數(shù)學(xué)模型的驗(yàn)證 三個(gè)相電流可被分解為直軸電流，如下所示 其中，θ是轉(zhuǎn)子的電角度。 使得IQ =0，我們得到平均為零的扭矩如圖8所示，（a）所示。顯而易見(jiàn)的是，該扭矩沒(méi)有關(guān)系的id。 分配ID = 0和Q =1時(shí)，力，轉(zhuǎn)矩和轉(zhuǎn)速也可以如圖8（b）中所示獲得的 。（d）所示上的力和力矩是大致恒定的，并且速度線性增加。事實(shí)證明，扭矩是成正比的iq 通過(guò)分配IQ或id到零，然后改變ID或IQ相應(yīng)的值，我們可以得到的軸向磁力和 矩曲線在起點(diǎn)處，如圖9所示。實(shí)線代表從（28）的計(jì)算結(jié)果和（29），以及星標(biāo)記都是在有限元分析的結(jié)果時(shí)，它被分配了。當(dāng)他們比最大額定電流是1.85×2=2.62 A在這樣的設(shè)計(jì)更高的力和力矩偏離的計(jì)算曲線向下。這是由當(dāng)高電流被輸入的磁飽和引起的。 圖8當(dāng)qi=0，di=0的有限元分析結(jié)果（a）qi=0時(shí)扭矩（b）di=0時(shí)的力（c）di=0時(shí)的（d）di=0時(shí)的速度 在圖9（a），用小于電流有限元模型和數(shù)學(xué)模型之間的誤差仍然存在。這是因?yàn)楫?dāng)ID =0，22N f如果在占主導(dǎo)地位（28）所示的力值， N個(gè)之間f小錯(cuò)誤，如果用（14）和有限元分析軟件計(jì)算出的值會(huì)導(dǎo)致對(duì)力值差異較大。圖9（e）及（f）是扭矩和動(dòng)力的變化時(shí)，不同氣隙長(zhǎng)度分配。結(jié)果通過(guò)這兩種方法獲得的幾乎是相同的。 圖9有限元模擬結(jié)果與解析計(jì)算結(jié)果的比較（a）id=0，iq是變量時(shí)的力（b）id=0，iq是變量時(shí)的力矩（c力（d）），id是變量時(shí)的力矩（e）id=0 ，iq=1，氣隙長(zhǎng)度變化時(shí)的力（f）id=0 ，iq=1，氣隙長(zhǎng)度變化時(shí)的力矩 為了進(jìn)一步驗(yàn)證的數(shù)學(xué)模型，Matl ab / Simulink環(huán)境可以采用來(lái)模擬電動(dòng)機(jī)的性能的準(zhǔn)確性，所導(dǎo)出的模擬結(jié)果隨后可被用于與有限元分析的數(shù)據(jù)進(jìn)行比較。 當(dāng)ID = 0和Q =1的電流被分配到定子繞組，通過(guò)Simulink中的仿真結(jié)果示于圖10。電機(jī)在模擬的參數(shù)在表IV中所示。通過(guò)比較從Simulink仿真和有限元分析，這示于圖8（BC）和圖中得到的力和扭矩曲線。10分別當(dāng)相同的電流分配，可以看出，它們的平均值是非常相似的，盡管有在有限元分析結(jié)果有一定的波動(dòng)。 圖10通過(guò)圖8指定相同的電流的仿真結(jié)果圖(a)軸向磁力MATLAB仿真（b）通過(guò)MATLAB仿真扭矩 同樣，我們也可以輸入相同的電壓，這是電角向電動(dòng)機(jī)模型在上述兩種方法的功能，其結(jié)果，得到與圖1所示。 11。力的相應(yīng)的曲線，扭矩是在形狀和價(jià)值觀相似。其結(jié)果是，支持該數(shù)學(xué)模型的正確性的證明。 從有限元分析結(jié)果和有限元法和模擬結(jié)果之間的比較，很顯然，所提出的系統(tǒng)是可行的，并且衍生數(shù)學(xué)模型是準(zhǔn)確的，并且可以被用來(lái)設(shè)計(jì)的驅(qū)動(dòng)系統(tǒng)。 圖11通過(guò)指定相同的電壓的MATLB仿真和有限元分析結(jié)果的比較（a）軸向磁力的MATLB仿真（b）軸向磁場(chǎng)力的有限元分析（c）通過(guò)MATLB仿真扭矩（d）轉(zhuǎn)矩的有限元分析 五.結(jié)論 一種新穎的飛輪儲(chǔ)能系統(tǒng)與局部自支承飛輪轉(zhuǎn)子已經(jīng)提出了這樣的紙張。系統(tǒng)的結(jié)構(gòu)及設(shè)計(jì)方法的細(xì)節(jié) 進(jìn)行了描述。數(shù)學(xué)模型是來(lái)自和三維有限元分析已經(jīng)進(jìn)行，以驗(yàn)證所提出的設(shè)計(jì)和數(shù)學(xué)模型。支持所有的分析結(jié)果所提出的系統(tǒng)的可行性，并證明了數(shù)學(xué)模型的正確性。該系統(tǒng)的原型目前正在開(kāi)發(fā)中。 參考文獻(xiàn) [1]R.Beach和D.A.Christopher，“航空航天應(yīng)用的“飛輪儲(chǔ)能技術(shù)的開(kāi)發(fā)，IEEE aerosp。電子系統(tǒng)雜志 卷13，頁(yè)9-14， 1998年6月。 [ 2 ] j.g.bitterly，“飛輪技術(shù)：過(guò)去，現(xiàn)在，和第二十一世紀(jì)的預(yù)測(cè)，”IEEE aerosp。電子系統(tǒng)雜志，13卷，第13-16頁(yè)， 1998年8月。 [3]J.Beno, R.Hebner and A.Walls, “飛輪電池再次到來(lái)，”IEEE譜，卷39，頁(yè)46-51。2002年4月。 [4] S.Ginter, G.Gisler, J.Hanks, D.Havenhill, W.Robinson 和L.Spina，“宇宙飛船能量存儲(chǔ)系統(tǒng)，IEEE aerosp”。電子系統(tǒng)雜志，13卷，第27-32， 1998。 [5] H. 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Kingsley Jr., 和 S.D.Uman, 電動(dòng)機(jī)械，第五版。紐約：麥格勞山，1992。 [15] P. C. Krouse, O. Wasynczuk 和S. D. Sudhoff分析電機(jī)械傳動(dòng)系統(tǒng)，第二版。IEEE出版社。 [ 16 ]麥斯威爾三維參數(shù)化參考指南，Ansoft公司，2002。 Abstract—A compact and efficient flywheel energy storage system is proposed in this paper. The system is assisted by integrated mechanical and magnetic bearings, the flywheel acts as the rotor of the drive system and is sandwiched between two disk type stators to save space. The combined use of active magnetic bearings, mechanical bearings and axial flux PM synchronous machine assists the rotor-flywheel to spin and remain in magnetic levitation in the vertical orientation, while constrains the other four degrees of freedom in radial directions mechanically. The mathematical model of the proposed system has been derived. Three-dimensional finite element method is applied for studying the performances and verifying the mathematical model of the system. The analysis results support the feasibility of the system. I. INTRODUCTION N modern power industries, with the advances of high strength and light weight composite material, control technology and power electronics, the Flywheel Energy Storage System (FESS) is becoming a viable alternative to traditional chemical battery systems, with its advantages such as higher energy storage density, lower risk of overcharge and over-discharge, easier detection of the depth of discharge, operation over a wider temperature range, longer lifespan and environmental friendliness [1]-[4]. As a result, FESS is now considered a promising technology for many applications including spaceflight, transportation, power industry, military, and building services. In general, a flywheel energy storage system is composed of a flywheel, magnetic or mechanical bearings that support the flywheel, a motor-generator to drive the flywheel and inter-convert the mechanical energy and electrical energy, control and power electronic devices, and touchdown bearings. This separate driving motor-generator in addition to magnetic bearings makes the rotor long and apt to produce bending vibrations. And the large motor-bearing system makes it difficult for miniaturization [5]. To overcome these problems, a self-bearing permanent magnet motor is introduced. The motor combines magnetic bearing and motoring functionality into a single magnetic actuator. Such designs can reduce the overall length of a motor because less mechanical bearings are required, thus increasing power density, reducing weight, and lowering susceptibility to rotor dynamic vibrations [6]. As shown in Fig. 1, there are three directions along x , y and z axes within the flywheel, such that six degrees-of-freedom (DOF) which are the displacement and rotation of every axis should be controlled with the help of mechanical or magnetic bearings. Mechanical bearings have the advantages of simple structure and easy operation, but the frictional loss and thereby, the use of lubrication should always be taken into consideration. Especially, the friction occurring on the bearing which is along the direction of the gravity, i.e., the direction along z axis in Fig. 1, is much greater than those in the other directions. For this reason, it is not practical to use mechanical bearings along this axis, while for the other axes, they can still be tolerated. Active magnetic bearings have many advantages over the conventional bearings. Such benefits include higher energy efficiency, lower wear, longer lifespan, absence of need of lubrication and mechanical maintenance, and wider range of operating temperatures. There are many studies concerning magnetic bearings, but most of them treat the bearing in which at least five DOF of the object are controlled. Since the control of each DOF requires a sensor, an actuator and a controller, the entire system becomes complex in terms of the design of its mechanical/ electrical part and the control system [7]. Considering this, this paper presents a new concept of magnetic bearing, in which only 2 DOF of an axis, namely, the translation and rotation along and about axial directions respectively, are actively controlled. The motions in other directions are entirely restricted by mechanical bearings. The combined use of active magnetic bearings and mechanical bearings can cut down the complexity of control and make the system more stable, viable and cost-effective. Currently, axial flux permanent magnet motors (AFPM) used in many applications have become an appealing research field [8] [9]. They have several unique features such as high efficiency, high power and torque densities, low rotor losses and small magnetic thickness. However, the disadvantage is that the distributed windings have end-windings of significant length compared to the active part of the coil conductors. This FEM Analyses for the Design and Modeling of a Novel Flywheel Energy Storage System Assisted by Integrated Magnetic Bearing C. Zhang, Student Member, IEEE, P. Wu, Student Member, IEEE and K. J. Tseng, Senior Member, IEEE Centre for Advanced Power Electronics, Nanyang Technological University Blk S2, Nanyang Avenue, Singapore 639798, Republic of Singapore I Fig. 1. Three motion directions of flywheel. 0-7803-8987-5/05/$20.00 ?2005 IEEE. 1157 obviously results in poor machine performance, as a significant part of the machine copper (i.e., more than 50% of the total in most machine designs) is producing heat but no torque [10]. Concentrated windings can solve this problem. Furthermore, they have simpler design, easier arrangement and higher efficiency. The finite element method (FEM) has proved to be particularly flexible, reliable and effective in the analysis and synthesis of power-frequency electromagnetic and electromechanical devices [11] [12]. The FEM can analyze PM circuits of any shape and material. A remarkable advantage of FEM analysis over other approaches to analysis of PM motor is the inherent ability to calculate accurately armature reaction effects, electromagnetic force and torque. In this paper, a novel flywheel energy storage system assisted by integrated magnetic bearing is proposed. The motor and generator are combined to be a single machine and the flywheel functions as the rotor in order to save space. Mechanical bearings are used to restrict the displacement and rotation along radial directions, and the displacement and rotation along axial direction are controlled by active magnetic bearings. The structure and electromagnetic design of the proposed system is presented along with the mathematical model. 3D FEM analyses are implemented to verify the mathematical model and support the feasibility of the system. Analysis results have been obtained and are presented in this paper. II. CONSTRUCTION AND GEOMETRY OF THE PROPOSED SYSTEM A. Configuration of the Entire System Fig.2 shows the cross-sectional diagram of the proposed flywheel energy storage system. Its components are listed in Table I. Items 1 and 8 are the upper and lower stators fixed on the system housing which is designed to dissipate radial kinetic energy from any rotor debris and ensure safety in the event of mechanical failure. Axial flux permanent magnet synchronous motor is implemented to drive the flywheel which is also functioning as a rotor. Mechanical rotational ball bearings are mounted on the outer rim of the rotor to constrain its radial motion and assist the rotation of the flywheel/rotor. This arrangement makes the structure very compact without using the shaft. But the large diameter of the bore of the mechanical bearing limits the maximum speed. By using fluid-film bearings, the DN value (bore diameter mm× speed rpm) can reach 3,000,000 [13]. That means the maximum speed is less than 20,000 rpm when the bore diameter is 150 mm. In higher speed flywheel system, two mechanical bearings can be mounted at the ends of the shaft which is fixed in the middle of the rotor. With this arrangement, the speed may reach up to 60,000 rpm and above. The axial motion can be realized with the aid of 4 sliding ball bearings installed orthogonally on the rim of the rotational ball bearing. Non-contact eddy current displacement sensor and photo electrical sensor are set in the hollow center of the two stators to detect the displacement and angular position along z-axis when the rotor spins, (items #2 and #10 in Fig. 2). Touchdown bearings are necessary during starting operation or in the event of magnetic bearings failure. The touchdown bearings shall be mounted against the outer rim of the rotor. During normal operation, there is a less than 0.5 mm air-gap between all rotor surfaces and the touchdown bearings, thus achieving a mechanically contact-less environment. B. Basic Features of the Proposed System Fig.3 shows the basic features of the proposed system. The motor and generator with disk-type geometry are combined into a single electric machine as shown in Fig.3 (a). The rotor doubles as the flywheel and is sandwiched between two disk-type stators. This design maximizes the torque production area of the disk-type rotor. As shown in Fig.3 (b), each of the upper and lower stators carries a set of three-phase copper windings to be fed with sinusoidal currents; concentrated windings are implemented to reduce the power loss. If distributed windings are used, the winding-ends will span half the circumference of the rotor. The ends are much longer compared to the effective parts of coil conductors, and the copper loss of the windings will thus be larger. In this particular design, there are 6 coils, each of which surrounds a stator tooth. The distribution of three phases and directions of the three-phase currents at a particular instance are TABLE I COMPONENTS OF THE PROPOSED SYSTEM Item Number Item Name 1 Upper stator 2 Position sensor 3 Stator windings 4 Touchdown bearings 5 Rotational ball bearing 6 System housing 7 Rotor permanent magnets 8 Lower stator 9 Non-magnetic material guard ring 10 Rotation sensor 11 Flywheel-rotor 12 Fasteners 13 Sliding ball bearing Fig. 2. Cross-sectional diagram of the proposed system. 1158 shown in Fig. 4. Besides improved efficiency, simple structure and easy installation of the stator winding can also be realized in this design. Permanent magnets are mounted on both surfaces of the rotor, as shown in Fig.3 (c). The arrangement of these PMs and the magnetic flux flowing in the motor are depicted in Fig.4. PMs are settled in opposite directions in upper and lower rotor faces, so that they would attract each other and increase the total flux in the magnetic circuits. A guard ring made of high strength non-magnetic material is used to assist the PMs in resisting the centrifugal force, as shown in Fig.3 (d). Magnetic bearings can be realized by using attractive forces. The interaction between the stator and rotor fields produces an axial force that makes the rotor and stator attract each other. The currents of each stator can be independently adjusted to control the net forces on the rotor and keep it in the middle of the two stators. The net force along the axial axis can be obtained as 21 FF F= ? (1) Where 1 F is the force between the lower stator and rotor; 2 F is the force between the upper stator and rotor. The motor-generator is equivalent to two motors, the total torque T can be written as 12 TTT= + (2) Where 1 T and 2 T are torques generated by the upper and lower motor respectively. C. Dimensions of the Motor The size of axial flux motor can be transformed to that of an equivalent sized radial machine by the following formulas 2 oi DD D + = (3) 2 oi DD L ? = (4) where o D and i D are the outer and inner diameters of the axial flux disk-type motor, D and L are the inner diameter and length of the equivalent radial machine. Maximum torque is produced when /3 Roi KDD==. From output equation of the motor, we can get 2 0 s Q DL Cn = (5) and then, we can obtain 3 3 2 0 8 (1)(1) R o RRs QK D KKCn = +? (6) where 0 C is the output coefficient, Q is the rating of machine in kVA, s n is the rated speed in r.p.s. 3 0 11 10 gav w CBAK ? =×, cos EN N N KP Q η ? = (7) where gav B represents the average flux density over the air-gap of the machine, also known as magnetic loading; A is the electric loading; w K is the winding factor; N P , N η and cos N ? represent rated power, efficiency and power factor respectively; E K is the ratio between induced EMF and the voltage. In this design, 0.905 E K = . Minimum length of air-gap is set by mechanical constraints and is unlikely to be less than 0.3 mm. Magnets’ depth should generally be reduced to a minimal value so as to minimize the cost of the magnets. Manufacturing restrictions make it difficult to have magnets thinner than 2.0mm. In this design, g l is selected as 0.5 mm, and m l is set to be 2.5 mm. According to the design requirement data shown in Table II, the motor design results can be obtained as in Table III. This is just a test design to verify the feasibility of the system structure and the correctness of the mathematical model. So the rated Fig. 4. Motor development structure and 2D flux pattern. (a) (b) (c) (d) Fig. 3. Basic parts of the proposed flywheel system. (a) Stator-rotor Assembly. (b) Stator Windings. (c) Rotor-flywheel. (d) Non-magnetic guard ring. 1159 speed is only selected to be 1500 rpm. III. MATHEMATICAL MODEL As shown in Fig.3, the three-phase windings of the stator are denoted as a, b and c with the same winding number. Permanent magnets are mounted on the surface of the disk type rotor, a non-salient rotor is obtained as a result. The motor can be treated as a conventional synchronous motor, only if the field windings are replaced by permanent magnets. The PM motor can be readily analyzed by assuming that the permanent magnets of the rotor here have been replaced by an equivalent rotor current f i with the winding number f N . The waveform of the MMFs produced by the stator phase windings and the equivalent rotor current f i may be considered as coarse approximation of sinusoidal functions of s φ and r φ , the same as the distribution of the windings [14] [15]. Where s φ and r φ are the angles measured from the a phase stator winding axis and rotational d axis, respectively. Assuming the number of pole pairs is P , their functions are as follows cos 2 sin 2 s as as s s as s MMF N iP P N NP φ φ =? = (8) ( ) () 2 cos 3 2 2 sin 3 2 s bs bs s s bs s MMF N iP P N NP φ π φπ =? ? =? (9) ( ) () 2 cos 3 2 2 sin 3 2 s cs cs s s as s MMF N iP P N NP φ π φπ =? + =+ (10) cos 2 sin 2 f f fr f rf r MMF N iP P N NP φ φ =? = (11) where s N is the number of turns of equivalent sinusoidally distributed winding in each phase of the stator. For the winding distribution depicted as Fig.3 (b), the pitch factor 1 p k = , the distribution factor d k = cos( / 6)π = 3/2, so the winding factor 3/2 wpd kkk=×= . Then s N can be calculated as 4 s wph NkN π = (12) where ph N is the actual number of turns in series per phase. The maximum value of the equivalent MMF produced by PMs , m MMF , is calculated to be 2 ff mmm Ni MMF H l P == (13) where, m l and m H denote the magnet length and the magnetic field intensity when the magnet is shorted by permeable iron. Then the value of f f N i can be achieved as 0 22 rm ff mm r B l Ni PHl P μ μ == (14) r B is the remanent flux density for the PMs, r μ is the relative permeability, and 0 μ is the magnetic permeability of the air with the value 7 410π ? × . The effective air gap length between the surfaces of stator and rotor is defined as g , the magnetic flux density B and magnetic flux are shown as below: 0 s MMF B Bds g μφ== ∫ (15) As an example, let us determine the total flux linkages of the winding due to current flowing only in a winding, leakage inductances are ignored here. / 0 22 / 0 () () sin 2 () .[ ]cos 4 s s P s as as s as s s s P so i as s N NdPP NR R iPdd Pg π φπ φ λ φφ φ φ φ μ ξ ξφ + == ? ? ∫∫ ∫ (16) 222 0 2 () 8 as o i s as s as R RN LL i Pg λμπ? === (17) where o R and i R are the outer and inner radius of the stator. Similarly, we can get as bs cs s L LLL= == (18) TABLE III DESIGN GEOMETRICAL DATA No. of pole pairs 2 No. of slots 6 Outer diameter of stator 130 mm Inner diameter of stator 76 mm Permanent magnets length 2.5 mm Air gap length 0.5 mm Slot width 28 mm Slot depth 22 mm Stator yoke thickness 18 mm Rotor core thickness 60 mm Air gap flux density 0.805 T No. of turns per phase 416 TABLE II DESIGN REQUIREMENT DATA Rated power 1 kVA Phase current, rms 1.85 A Power factor 0.9 Efficiency 0.9 Rated speed 1500 rpm Frequency 50 Hz Slot fill factor 0.4 Remanent flux density 1.23 T Magnet recoil permeability 1.05 Carter’s factor 1.05 1160 222 0 2 () 8 f oif ff f as RRN LL i Pg λμπ? === (19) The mutual inductance between the a and f windings is determined by / 0 22 / 0 ()() sin 2 () .[ ]cos() 4 s s P S asf as s f r s s P fo i f s N NdPP NR R iP dd Pg π φπ φ λφφφ φ μ ξ θξφ + == ? ?? ∫∫ ∫ (20) In the same way as above, af L , bf L , cf L can be written as 22 0 2 () cos cos 8 oisf af m RRNN L PL P Pg μπ θ θ ? == (21) 22 0 2 () cos( 2 / 3 ) 8 oisf bf RRNN LP Pg μπ θ π ? =? (22) 22 0 2 () cos( 2 / 3 ) 8 oisf cf RRNN Pg μπ θ π ? =+ (23) Therefore, the other mutual inductances can be obtained as 1/2 ab ba ac ca bc cb s L LLLLL L======? (24) Then, () = ff af bf cf f T af as ab ac a fabc bf bs ac b ba cb cs ccf ca L L L Li L L L Li L L Li L L LiLL λλλλ ?? ?? ?? ?? ?? == ?? ?? ?? ?? ?? ?? λ Li (25) where L is the inductance matrix of the motor, the inductances are determined by(18)(19) and (21)-(24). The inductance expression of (31) can be simplified when they are expressed in terms of 0dq variables 3/2 0 3/2 0 003/2 f fm f dm s d sqq L Li L L i λ λ λ ?? ???? ???? ?? = ?? ?? ?? ?? ???? ?? (26) The magnetic energy stored may be calculated as ()( ) 1 i 2 T fdq f d q Wii λλλ= (27) The attractive force s F can thus be obtained () 22 0 22 22 2 2 2 () 16 53 . 22 oi s ff sffd s d q RRW F g Pg Ni NNii N i i μπ ?? =? = ? ?? +++ ?? ?? (28) From the Fleming’s left-hand rule, the rotating torque s T can be expressed as 22 0 3( ) 3 () 216 oisf s dq qd f q RRNN TPii i Pg μπ λλ ? =× ? = (29) Here, the air gap between the surfaces of the stator and PMs at the equilibrium point is defined as g l , so the effective air gap between the stator and rotor at the equilibrium point can be obtained as 0 (/) cg m r gKllμ= + (30) where c K is the Carter’s coefficient, which is approximately equal to 1. Then 1 F and 1 T can be calculated by substituting 0 g gz= + , 1dd ii= and 1qq ii= into (28)(29) whereas 2 F and 2 T can be calculated by substituting 0 g gz=?, 2dd ii= and 2qq ii= into the same equations, where z is the displacement of the rotor in the vertical direction. The total force and torque are obtained by (1) and (2). The radial motions of the rotor are restricted by mechanical ball bearings. Therefore, the axial motion of the rotor is independent of radial motion. The dynamic equation of the axial motion of the rotor is '' z mz F f= + (31) where z f is the external force in the direction of z-axis, and the gravity is taken into consideration. The equation of total torque can be rewritten as '' Tq TJ Kiθ== (32) And '' , Tq J Kiθ??== (33) where J is the moment of inertia, θ is the rotor angle and ? is the rotational speed. The voltage equations can be written as 1 () q a ddd rq ddd L Rd ivi pi dt L L L ?=?+ (34) 1 () () ad m qqd rd r qqq q RLd ivi pi p dt L L L L λ ? ?=?? ? (35) IV. FEM ANALYSIS AND MODEL VERIFICATION A. Theory Magnetic fields in PM motors are always associated with transient excitations and nonlinear