諧波齒輪減速器設(shè)計(jì)及性能仿真【說明書+CAD+SOLIDWORKS】

諧波齒輪減速器設(shè)計(jì)及性能仿真【說明書+CAD+SOLIDWORKS】,說明書+CAD+SOLIDWORKS,諧波齒輪減速器設(shè)計(jì)及性能仿真【說明書+CAD+SOLIDWORKS】,諧波,齒輪,減速器,設(shè)計(jì),性能,機(jī)能,仿真,說明書,仿單,cad,solidworks 畢業(yè)設(shè)計(jì)（論文） 開題報(bào)告 畢業(yè)設(shè)計(jì)（論文）題目：諧波齒輪減速器設(shè)計(jì)及性能仿真 專 業(yè)： 指導(dǎo)教師： 學(xué)生姓名： 學(xué) 號(hào)： 畢業(yè)時(shí)間： （一）選題的背景及意義 背景：諧波傳動(dòng)是 20 世紀(jì) 50 年代中期隨著空間科學(xué)技術(shù)的發(fā)展，在薄殼彈性變形的理論基礎(chǔ)上發(fā)展起來的一種新型傳動(dòng)技術(shù)。由于諧波減速器具有回差小、單級(jí)減速比范圍大、運(yùn)動(dòng)平穩(wěn)、低噪聲、傳動(dòng)效率高、承載力大、體積小、質(zhì)量輕等多種其他減速器不具備的優(yōu)點(diǎn),因此一經(jīng)問世就立刻引起了各國的普遍重視。美國、前蘇聯(lián)、日本、德國、英國等國家以及我國都開展了諧波減速器的理論、制造、加工、潤滑等技術(shù)研究，美國等先進(jìn)國家已將該項(xiàng)技術(shù)大量應(yīng)用于空間飛行器的各種實(shí)施展開、驅(qū)動(dòng)、精密指向、掃描、空間機(jī)器人活動(dòng)關(guān)節(jié)等運(yùn)動(dòng)機(jī)構(gòu)上,并已推廣應(yīng)用到地面雷達(dá)天線、通訊、電子、醫(yī)療器械、工業(yè)機(jī)器人、儀器儀表等多種行業(yè)中,獲得了巨大的軍事收益和社會(huì)效益。 意義：雖然國內(nèi)外學(xué)者幾乎對(duì)該領(lǐng)域所有問題都進(jìn)行過不同程度的研究，但仍有大量的基礎(chǔ)性工作有待開展。作為決定傳動(dòng)壽命的柔輪疲勞強(qiáng)度的研究問題一直是研究諧波齒輪傳動(dòng)的重心。針對(duì)柔輪軸向尺寸大的問題，國外諧波齒輪傳動(dòng)多采用短杯柔輪，其體積小，重量輕、承載能力高；而國內(nèi)的短杯諧波齒輪存在著軸向尺寸大，承載能力不高的缺點(diǎn)。國內(nèi)的短杯諧波技術(shù)還處于研發(fā)階段，沒有成熟的產(chǎn)品。國外雖然有短杯柔輪，但是由于各國所采用的標(biāo)準(zhǔn)不一致和技術(shù)上的封鎖，并考慮到進(jìn)口產(chǎn)品價(jià)格昂貴等因素，所以研究開發(fā)出可以滿足我國在緊湊空間環(huán)境中尺寸小，承載能力相對(duì)較大的特殊形狀的諧波減速器對(duì)推動(dòng)我國諧波減速器在宇航空間中的應(yīng)用具有重要的意義。 （二）研究內(nèi)容擬解決的問題 本課題在對(duì)諧波傳動(dòng)及齒輪傳動(dòng)相關(guān)知識(shí)熟練掌握的基礎(chǔ)上，主要完成以下幾個(gè)內(nèi)容：確定杯形柔輪的結(jié)構(gòu)、對(duì)柔輪的結(jié)構(gòu)參數(shù)進(jìn)行影響分析、諧波減速器的結(jié)構(gòu)設(shè)計(jì)、諧波減速器的傳動(dòng)比、承載能力、傳動(dòng)效率的性能分析、對(duì)諧波減速器的傳動(dòng)效率、啟動(dòng)力矩、跑合溫升進(jìn)行研究。其結(jié)構(gòu)形式?jīng)Q定著諧波傳動(dòng)的承載能力、傳動(dòng)性能、結(jié)構(gòu)尺寸、使用壽命和加工工藝性等等。根據(jù)使用實(shí)踐和試驗(yàn)研究，諧波齒輪傳動(dòng)最主要的失效形式是柔輪的疲勞斷裂，因此，對(duì)于諧波齒輪中柔輪的進(jìn)一步研究已經(jīng)非常必要。由于諧波減速器有眾多的優(yōu)越性，因此諧波傳動(dòng)得到了廣泛的應(yīng)用。諧波傳動(dòng)有三個(gè)基本運(yùn)動(dòng)構(gòu)件—?jiǎng)傒?、柔輪和波發(fā)生器，如圖 1-1 所示， 圖1-1 三大件結(jié)構(gòu)示意 例如：諧波傳動(dòng)不適用于小速比的傳動(dòng)，由于速比過小，柔輪的徑向變形量增大，容易疲勞破壞；柔輪和波發(fā)生器的加工困難；對(duì)柔性軸承的材料及制造精度要求較高；杯形柔輪雖然應(yīng)用廣泛但是軸向尺寸大；柔輪在苛刻條件下(如高低溫環(huán)境)容易失效。對(duì)于諧波齒輪傳動(dòng)在空間環(huán)境中的應(yīng)用來說，柔輪的軸向尺寸大和柔輪在高低溫環(huán)境下容易發(fā)生強(qiáng)度破壞是兩個(gè)比較明顯的問題。 針對(duì)所設(shè)計(jì)的諧波減速器的具體結(jié)構(gòu)參數(shù)，對(duì)傳動(dòng)比、承載能力、傳動(dòng)效率等參數(shù)做性能分析。分別分析兩大核心部分各自的性能參數(shù)的影響，并給出諧波減速器的性能分析表。 （三）研究方法技術(shù)路線： 研究內(nèi)容：傳統(tǒng)的杯形結(jié)構(gòu)的柔輪在當(dāng)前的諧波減速器中應(yīng)用極其廣泛，具有結(jié)構(gòu)簡單、聯(lián)接方便、制造容易、剛性較大的特點(diǎn)，具體的結(jié)構(gòu)示意圖如圖 2-1 所示。但是就目前的產(chǎn)品來說，傳統(tǒng)杯形的柔輪結(jié)構(gòu)的軸向尺寸大的問題沒有得到很好的解決，相比于國外相同機(jī)型的產(chǎn)品，還是存在較突出的體積大的缺點(diǎn)。這也大大的限制了諧波減速器在小空間中的應(yīng)用。 圖 2-1 杯形柔輪結(jié)構(gòu)圖 針對(duì)傳統(tǒng)杯形柔輪的軸向尺寸較大的問題，本課題設(shè)計(jì)了三種不同于傳統(tǒng)杯形結(jié)構(gòu)的柔輪：直角圓弧回形結(jié)構(gòu)的柔輪結(jié)構(gòu)示意圖如圖 2-2 a)所示；“之”字結(jié)構(gòu)的柔輪結(jié)構(gòu)示意圖如圖 2-3 a)所示；直角直線回形結(jié)構(gòu)的柔輪結(jié)構(gòu)示意圖如圖 2-4 a)所示。這三種結(jié)構(gòu)的特殊點(diǎn)在于改變了傳統(tǒng)柔輪的杯筒和杯底結(jié)構(gòu)，呈現(xiàn)回折的趨勢(shì)。因此，這種提高了諧波減速器可用于結(jié)構(gòu)緊湊的機(jī)構(gòu)。 圖 2-2 直角圓弧回形柔輪 圖 2-3 “之”字結(jié)構(gòu)柔輪 圖 2-4 直角直線回形柔輪 研究方法: 通過改進(jìn)設(shè)計(jì)，根據(jù)柔輪在不同工作條件下進(jìn)行力學(xué)分析，進(jìn)行三維造型。通過對(duì)不同機(jī)型柔輪的有限元分析比較，可以看出，相同機(jī)型、相同軸向尺寸的四種結(jié)構(gòu)中哪種方式的柔輪結(jié)構(gòu)為最優(yōu)分析模型，分析柔輪各結(jié)構(gòu)參數(shù)對(duì)柔輪應(yīng)力的影響。 （三）研究的總體安排和進(jìn)度計(jì)劃 15年第1、2周 畢業(yè)實(shí)習(xí)，提交實(shí)習(xí)報(bào)告、開題報(bào)告 15年第3、4周 網(wǎng)絡(luò)搜集相關(guān)資料，去圖書館查閱資料，有條件去諧波齒輪減速器工廠參觀，確定最終設(shè)計(jì)方案 15年第5、6周 完成文獻(xiàn)綜述以及外文翻譯 15年第7、8周 根據(jù)工作要求，查閱相關(guān)手冊(cè)，對(duì)各部門機(jī)構(gòu)設(shè) 計(jì)、計(jì)算；從各方面對(duì)產(chǎn)品進(jìn)行綜合評(píng)價(jià)，校核，修正。 15年第9~11周 提交CAD,設(shè)計(jì)計(jì)算說明書和三維模型，畢業(yè)設(shè)計(jì)初稿 15年第12周 提交畢業(yè)設(shè)計(jì)定稿 15年第13周 答辯 （二）參考文獻(xiàn) [1] 機(jī)械設(shè)計(jì)手冊(cè)編委會(huì).機(jī)械設(shè)計(jì)手冊(cè)新版第三卷.北京:機(jī)械工業(yè)出版社,2004.9. 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House,1985. 畢業(yè)設(shè)計(jì)（論文） 題目 諧波齒輪減速器設(shè)計(jì)及性能仿真 學(xué)院 機(jī)械設(shè)計(jì)制造及其自動(dòng)化專業(yè) 學(xué)生姓名 學(xué) 號(hào) 指導(dǎo)教師 系 主 任 二級(jí)學(xué)院院長 27 摘 要 諧波齒輪傳動(dòng)具有體積小、重量輕、結(jié)構(gòu)緊湊、傳動(dòng)比大、效率高等優(yōu)點(diǎn)。廣泛應(yīng)用于礦山、冶金、飛機(jī)、輪船、汽車、起重機(jī)、電工機(jī)械、儀表、化工業(yè)等許多領(lǐng)域諧波齒輪傳動(dòng)有著廣泛的發(fā)展前景。 諧波齒輪減速器與普通減速器相比具有體積小、重量輕、傳動(dòng)平穩(wěn)、效率高、傳動(dòng)比范圍大等優(yōu)點(diǎn)。但其設(shè)計(jì)計(jì)算較過程復(fù)雜，軸承的受力較大、壽命較短。所以對(duì)于我們?cè)谠O(shè)計(jì)這類減速器時(shí)如何進(jìn)行參數(shù)的選擇，避免大量繁雜的計(jì)算，如何選擇好軸承使其使用壽命增加具有一定的設(shè)計(jì)意義。 對(duì)諧波減速器國內(nèi)外的發(fā)展現(xiàn)狀、優(yōu)缺點(diǎn)、結(jié)構(gòu)型式和其傳動(dòng)原理進(jìn)行了一定的闡述。在設(shè)計(jì)過程當(dāng)中，對(duì)內(nèi)嚙合傳動(dòng)產(chǎn)生的各種干涉進(jìn)行了詳細(xì)驗(yàn)算；從如何提高軸承的壽命為出發(fā)點(diǎn)，來計(jì)算選擇減速器齒輪的模數(shù)，最終合理設(shè)計(jì)減速器的整體結(jié)構(gòu)。 關(guān)鍵詞：諧波傳動(dòng)；減速器；內(nèi)齒輪副 Abstract 目 錄 摘 要 II Abstract III 第1章 緒論 5 1.1 概述 5 1.2諧波齒輪減速器研究內(nèi)容擬解決的問題 5 1.3 本文研究主要內(nèi)容 6 第2章 諧波齒輪減速器設(shè)計(jì) 7 3.3.1.傳動(dòng)結(jié)構(gòu)形式的選擇 7 3.3.2.幾何參數(shù)的計(jì)算 7 3.4 凸輪波發(fā)生器及其薄壁軸承的計(jì)算 8 3.4.1柔輪齒面的接觸強(qiáng)度的計(jì)算 9 3.4.2柔輪疲勞強(qiáng)度的計(jì)算 9 3.5 軸結(jié)構(gòu)尺寸設(shè)計(jì) 11 3.6 軸的受力分析及計(jì)算 11 3.7 軸承的壽命校核 12 6.2 銷軸的強(qiáng)度校核計(jì)算 14 6.3 輸入軸的強(qiáng)度校核 15 6.4 鍵的校核計(jì)算 17 6.4.1 聯(lián)軸器處鍵的校核 17 6.4.2 偏心套處鍵的校核 17 6.4.3 支座處鍵的校核 17 6.5 軸承的校核計(jì)算 18 第3章 諧波齒輪減速器三維設(shè)計(jì)圖 24 總結(jié) 26 致 謝 27 參考文獻(xiàn) 28 第1章 緒論 1.1 概述 隨著現(xiàn)代工業(yè)的高速發(fā)展，機(jī)械化和自動(dòng)化水平的不斷提高，各工業(yè)部門需要大量的減速器，并要求減速器體積小，重量輕，傳動(dòng)比范圍大，效率高，承載能力大，運(yùn)轉(zhuǎn)可靠以及壽命長等。減速器的種類雖然很多，但普通的圓柱齒輪減速器的體積大，結(jié)構(gòu)笨重；普通的蝸輪減速器在大的傳動(dòng)比時(shí)，效率較低；擺線針輪行星減速器雖能滿足以上提出的要求，但成本較高，需要專用設(shè)備制造；而諧波減速器不但基本上能滿足以上提出的要求，并可用通用刀具在插齒機(jī)上加工，因而成本較低。能適應(yīng)特種條件下的工作，在國防，冶金，礦山，化工，紡織，食品，輕工，儀表制造，起重運(yùn)輸以及建筑工程等工業(yè)部門中取得廣泛的應(yīng)用。 1.2諧波齒輪減速器研究內(nèi)容擬解決的問題 諧波傳動(dòng)是五十年代中期出現(xiàn)的一種新型傳動(dòng)，它隨著空間技術(shù)的發(fā)展而迅速發(fā)展起來。由于諧波傳動(dòng)具有傳動(dòng)比大、體積小、傳動(dòng)精度高的特點(diǎn)，一開始就被運(yùn)用在火箭、導(dǎo)彈、衛(wèi)星等飛行器中，實(shí)現(xiàn)了他的優(yōu)越性。目前這種傳動(dòng)技術(shù)已由航天飛行器，飛機(jī)中的應(yīng)用迅速推廣到原子能、雷達(dá)、通訊、造船、冶金、汽車、坦克、機(jī)床、儀表、防止、建筑、起重運(yùn)輸、醫(yī)療器械等各個(gè)部門。無論是作為數(shù)據(jù)傳遞的高精度傳動(dòng)，還是作為傳遞大轉(zhuǎn)矩的動(dòng)力傳動(dòng)，都得到了比較滿意的效果。特別是，這種傳動(dòng)通過密封壁來傳遞機(jī)械運(yùn)動(dòng)，因而它用于操縱高溫，高壓的管路以及用來驅(qū)動(dòng)工作在高真空，有原子輻射或其他有害介質(zhì)空間的機(jī)構(gòu)，是現(xiàn)有的其他一切傳動(dòng)所不能比擬的。 諧波齒輪傳動(dòng)是五十年代后期隨著航天技術(shù)發(fā)展而出現(xiàn)的一種新型傳動(dòng)。它與一般齒輪傳動(dòng)相比，具有傳動(dòng)比大、體積小、重量輕、精度高、噪音小等優(yōu)點(diǎn)。此外，它還具有通過密封殼體傳遞運(yùn)動(dòng)和動(dòng)力的功能，這一特點(diǎn)是機(jī)械傳動(dòng)所無法比擬的。諧波齒輪傳動(dòng)一問世，就顯示出了它的顯著優(yōu)越性。因此，諧波齒輪傳動(dòng)是一種生命力強(qiáng)、發(fā)展前途十分寬廣的機(jī)械傳動(dòng)。 1.3 本文研究主要內(nèi)容 通過利用網(wǎng)絡(luò)工具、圖書館的書籍和各類期刊、雜志查閱了解諧波減速器的相關(guān)知識(shí)，確定本設(shè)計(jì)符合要求，滿足需要。具體設(shè)計(jì)方法如下： 1、查閱資料、結(jié)合所學(xué)專業(yè)課程，產(chǎn)生諧波減速器結(jié)構(gòu)設(shè)計(jì)的基本思路； 2、查閱各類機(jī)械機(jī)構(gòu)手冊(cè)，確定合理的諧波減速器結(jié)構(gòu)； 3、根據(jù)給定技術(shù)參數(shù)來選擇合適的零部件部位； 4、重點(diǎn)對(duì)驅(qū)動(dòng)機(jī)構(gòu)進(jìn)行設(shè)計(jì)研究； 5、通過研究國內(nèi)外情況，確定本設(shè)計(jì)課題的重點(diǎn)設(shè)計(jì)； 6、完成2D裝配圖的設(shè)計(jì)和繪制，并由此繪制零件圖； 7、編寫設(shè)計(jì)說明書； 8、檢查并完善本設(shè)計(jì)課題。 本設(shè)計(jì)采用的方法是理論設(shè)計(jì)與經(jīng)驗(yàn)設(shè)計(jì)相結(jié)合的方案，所運(yùn)用的資料來源廣泛，內(nèi)容充足。 第2章 諧波齒輪減速器設(shè)計(jì) 諧波減速器： ⑴型號(hào)：XB3-50-100 額定輸出轉(zhuǎn)矩：20N.m 減速比：i1=100 設(shè)諧波減速器的的傳遞效率為：，步進(jìn)電機(jī)應(yīng)輸出力矩為： (3.6) 選擇BF反應(yīng)式步進(jìn)電機(jī) 型號(hào)：55BF003 靜轉(zhuǎn)矩：0.686N.m 步距角：1.5° 3.3.1.傳動(dòng)結(jié)構(gòu)形式的選擇 該減速器是電傳動(dòng)減速的諧波齒輪裝置。要求其傳動(dòng)比較大﹑結(jié)構(gòu)簡單緊湊﹑效率較高﹑承載力較高﹑通用性良好。因此本設(shè)計(jì)方案所選的結(jié)構(gòu)形式為剛輪固定﹑波發(fā)生器主動(dòng)和柔輪從動(dòng)比較合適。為了便于采用標(biāo)準(zhǔn)刀具來加工柔輪和剛輪，特選取壓力角的漸開線齒廓。 3.3.2.幾何參數(shù)的計(jì)算 齒數(shù)的確定 柔輪齒數(shù)： 剛輪齒數(shù)： 已知模數(shù)：，則 柔輪分度圓直徑： 鋼輪分度圓直徑： 柔輪齒圈處的厚度： 重載時(shí)，為了增大柔輪的剛性， 允許將δ1計(jì)算值增加20%，即 柔輪筒體壁厚： 為了提高柔輪的剛度，取 輪齒寬度： 輪轂凸緣長度：取 柔輪筒體長度： 輪齒過渡圓角半徑： 為了減少應(yīng)力集中，以提高柔輪抗疲勞能力，取 由于采用壓力角的漸開線齒廓，傳動(dòng)的嚙合參數(shù)可按考慮到構(gòu)件柔度的計(jì)算公式，即按如下公式進(jìn)行計(jì)算。 3.4 凸輪波發(fā)生器及其薄壁軸承的計(jì)算 滾珠直徑： 柔輪齒圈處的內(nèi)徑： 則： 軸承外環(huán)厚度：由于工藝上的要求，可將外環(huán)做成無滾道的 軸承內(nèi)環(huán)厚度： 內(nèi)環(huán)滾道深度： 式中的是考慮到外環(huán)無滾道而內(nèi)環(huán)滾道加深量。 軸承內(nèi)外環(huán)寬度：所用為滾珠軸承，近似等于齒寬 軸承外環(huán)外徑： 軸承內(nèi)環(huán)內(nèi)徑： 為了便于制造，采用雙偏心凸輪波發(fā)生器。 則凸輪圓弧半徑： 其中ｅ是偏心距： （—?jiǎng)傒喎侄葓A直徑，—柔輪分度圓直徑） 則凸輪圓弧半徑： 凸輪長半軸： 凸輪短半軸： 3.4.1柔輪齒面的接觸強(qiáng)度的計(jì)算 根據(jù)諧波傳動(dòng)傳動(dòng)比大的特點(diǎn)，其柔輪和剛輪的齒數(shù)較多，齒形很接近于直線。故實(shí)際諧波齒輪傳動(dòng)的載荷能力主要應(yīng)由柔輪齒側(cè)工作表面的最大接觸應(yīng)力所限制。因此，諧波齒輪傳動(dòng)的柔輪齒側(cè)面應(yīng)滿足如下接觸強(qiáng)度條件： 接觸強(qiáng)度計(jì)算公式： —輸出轉(zhuǎn)矩 —柔輪節(jié)圓半徑 —柔輪輪齒寬 —?jiǎng)傒唹毫? —接觸系數(shù)（0.4~0.9） 對(duì)于一般雙波傳動(dòng)，輪齒寬許用接觸應(yīng)力 則： 所以滿足齒面的接觸強(qiáng)度要求。 3.4.2柔輪疲勞強(qiáng)度的計(jì)算 諧波齒輪傳動(dòng)中輪齒的工作特點(diǎn)是：齒面的摩擦滑移接觸和柔輪承受著反復(fù)的交變載荷。為了使柔輪在循環(huán)的彈性變形下能正常工作，除滿足耐磨條件外，還必須進(jìn)行柔輪的疲勞強(qiáng)度計(jì)算。 柔輪材料采用 調(diào)制硬度229~269。 計(jì)算柔輪在反復(fù)彈性變形狀態(tài)下工作時(shí)所產(chǎn)生的交變應(yīng)力幅和平均應(yīng)力為 截面處正應(yīng)力： 切應(yīng)力： 由扭矩產(chǎn)生的剪切應(yīng)力： 其中： 則： 驗(yàn)算安全系數(shù)： 疲勞極限應(yīng)力： 應(yīng)力安全系數(shù)： 其中，抗拉屈服極限： 剪切應(yīng)力集中系數(shù)： 則滿足疲勞強(qiáng)度條件。 3.5 軸結(jié)構(gòu)尺寸設(shè)計(jì) 考慮到軸的載荷較大，材料選用45,熱處理調(diào)質(zhì)處理,取材料系數(shù) 所以,有該軸的最小軸徑為: 考慮到鍵槽的影響，所以dmin取值為17MM,具體結(jié)構(gòu)如下： 3.6 軸的受力分析及計(jì)算 軸的受力模型簡化(見圖7)及受力計(jì)算 圖 軸的受力分析知： 3.7 軸承的壽命校核 鑒于調(diào)整間隙的方便,軸承均采用正裝.預(yù)設(shè)軸承壽命為3年即12480h. 校核步驟及計(jì)算結(jié)果見下表: 表1 軸承壽命校核步驟及計(jì)算結(jié)果 計(jì)算步驟及內(nèi)容 計(jì)算結(jié)果 6014 A端 B端 由手冊(cè)查出Cr、C0r及e、Y值 Cr=98.5kN C0r=86.0kN e=0.68 計(jì)算比值Fa/Fr FaA /FrA e 確定X、Y值 XA=1 YA =0 查載荷系數(shù)fP 1.2 計(jì)算當(dāng)量載荷 P=Fp(XFr+YFa) PA=5796.24 PB=6759.14 計(jì)算軸承壽命 763399h 大于 12480h 由計(jì)算結(jié)果可見軸承6014AC、6007均合格，最終選用軸承6014。 四、軸的強(qiáng)度校核 經(jīng)分析知C、D兩處為可能的危險(xiǎn)截面， 現(xiàn)來校核這兩處的強(qiáng)度： （1）、合成彎矩 （2）、扭矩T圖 （3）、當(dāng)量彎矩 （4）、校核 由手冊(cè)查材料45的強(qiáng)度參數(shù) C截面當(dāng)量彎曲應(yīng)力： 由計(jì)算結(jié)果可見C截面安全。 各軸鍵、鍵槽的選擇及其校核 因減速器中的鍵聯(lián)結(jié)均為靜聯(lián)結(jié), 因此只需進(jìn)行擠壓應(yīng)力的校核. 一、 電機(jī)鍵的選擇及校核: 帶輪處鍵:按照帶輪處的軸徑及軸長選 鍵B8X7,鍵長50,GB/T1096 聯(lián)結(jié)處的材料分別為: 45鋼(鍵) 、40Cr(軸) (1) 剛輪處鍵: 按照輪轂處的軸徑及軸長選 鍵B14X9GB/T1096 聯(lián)結(jié)處的材料分別為: 20Cr (輪轂) 、45鋼(鍵) 、20Cr(軸) 此時(shí), 鍵聯(lián)結(jié)合格. (2)輸出軸處鍵: 按照聯(lián)軸器處的軸徑及軸長選 鍵16X10,鍵長100,GB/T1096 聯(lián)結(jié)處的材料分別為: 45鋼 (聯(lián)軸器) 、45鋼(鍵) 、45(軸) 其中鍵的強(qiáng)度最低,因此按其許用應(yīng)力進(jìn)行校核,查手冊(cè)其 該鍵聯(lián)結(jié)合格. 6.2 銷軸的強(qiáng)度校核計(jì)算 由于行星輪與內(nèi)齒輪齒廓曲率半徑很接近，齒輪接觸面積較大，接觸應(yīng)力小，因此常不計(jì)算齒面接觸應(yīng)力。而且在設(shè)計(jì)齒輪計(jì)算齒輪模數(shù)時(shí)就是應(yīng)用彎曲應(yīng)力計(jì)算的，固齒輪的齒面彎曲應(yīng)力是滿足的，在此不必在對(duì)齒輪進(jìn)行校核?，F(xiàn)對(duì)銷軸進(jìn)行校核。 懸臂式銷軸的彎曲應(yīng)力校核公式： 式中：——制造和安裝誤差對(duì)銷軸載荷影響系數(shù) 。＝1.35～1.5，精度低時(shí)取大值，反之取小值，在次?。?.35 ——行星輪對(duì)銷軸的作用力（上節(jié)算得＝3195.67N） ——銷軸直徑（＝28㎜） ——許用彎曲應(yīng)力（銷軸的材料為20CrMnMo，根據(jù)銷軸材料查?。?50～200） L的值從下圖11中取得，約為50㎜，則： 《 因此銷軸的強(qiáng)度是足夠的，其尺寸符合要求。 6.3 輸入軸的強(qiáng)度校核 軸在載荷作用下，將產(chǎn)生彎曲或扭轉(zhuǎn)變形。在進(jìn)行州的強(qiáng)度校核時(shí)，應(yīng)根據(jù)軸的具體受載及應(yīng)力情況采用相應(yīng)的計(jì)算方法，并恰當(dāng)?shù)倪x取許用應(yīng)力。在此，輸入軸受到彎矩和扭矩，按彎扭合成強(qiáng)度條件進(jìn)行計(jì)算，其核算公式為： 式中： ——軸的計(jì)算應(yīng)力，MPa； ——軸所受的彎矩，N·㎜； ——軸所受的扭矩，N·㎜； ——軸的抗彎截面系數(shù)，； ——對(duì)稱循環(huán)變應(yīng)力時(shí)軸的許用彎曲應(yīng)力。 1)做出軸的計(jì)算簡圖（即力學(xué)模型） 在計(jì)算軸所受載荷時(shí)，常將軸上的分布載荷簡化為集中力，其作用點(diǎn)取為載荷分布段的中點(diǎn)。各支承處所受的反力和應(yīng)力集中點(diǎn)的反力、轉(zhuǎn)矩都已在圖中表示出來了。個(gè)支承處與應(yīng)力集中點(diǎn)之間的距離算得結(jié)果在圖中也已表明。如圖12。 2）做出彎矩圖 軸所受的載荷是從軸上的偏心套傳來的，而偏心套所受的力又是行星輪傳遞的。行星輪所受的力在4.1.1已算出，圓周力為（節(jié)圓上）為=5897.78N，徑向力為=4931.31N，即為軸所受的力。為了求出各支承處的水平反力和垂直反力列出以下四個(gè)個(gè)方程： +=5897.78N ×50＝×100 +=4931.31N ×50＝×100 聯(lián)立以上四個(gè)方程可得出：＝3931.85N，=1965.93N，=3287.54，=1643.77N。 彎矩，。 總彎矩為 3）做出扭矩圖 傳遞扭矩T=。 扭矩圖如圖 4）校核軸的強(qiáng)度 在軸上，偏心套聯(lián)接處為危險(xiǎn)截面（即截面B）如圖所示。對(duì)軸的抗彎截面系數(shù)的計(jì)算公式查課本《機(jī)械設(shè)計(jì)》中表15-4得出＝。由附圖可知d=45㎜，b＝14㎜，t=5.5㎜，代入數(shù)據(jù)得出＝7611.3。 在此處的扭轉(zhuǎn)應(yīng)力為靜應(yīng)力，故取，軸的計(jì)算應(yīng)力： 前已選定軸的材料為45鋼，調(diào)質(zhì)處理，查課本《機(jī)械設(shè)計(jì)》中表15-1得出。因此<，故安全。 圖12 輸入軸受力分析簡圖 6.4 鍵的校核計(jì)算 所用到的三個(gè)鍵都是平鍵。設(shè)計(jì)中所涉及的鍵均為靜聯(lián)結(jié)，但有沖擊，故用以下公式校核： 式中：T為傳遞轉(zhuǎn)矩（N·㎜），k——鍵與輪轂的接觸高度（），h——為鍵高（㎜）；，b——為鍵寬（㎜）；d——為軸徑（㎜）。 查得 ，則校核過程如下： 6.4.1 聯(lián)軸器處鍵的校核 此處鍵（C型）傳遞的轉(zhuǎn)矩為聯(lián)軸器的轉(zhuǎn)矩，即T=，b×h×L=10×8×53，l=L-b=43㎜ ，d=35㎜,故有： 故安全 6.4.2 偏心套處鍵的校核 此處鍵（A型）傳遞的轉(zhuǎn)矩為輸入轉(zhuǎn)矩，即T＝，b×h×L=14×9×70，l=L-b=56㎜ ，d=45㎜,故有： 故安全 6.4.3 支座處鍵的校核 此處鍵（A型）傳遞的轉(zhuǎn)矩為輸出轉(zhuǎn)矩，即T＝F·/2＝1200000N·㎜，b×h×L=16×10×60，l=L-b=44㎜ ，d=53㎜，且采用雙鍵聯(lián)接，故有： 故安全 6.5 軸承的校核計(jì)算 根據(jù)傳動(dòng)的結(jié)構(gòu)要求選用的軸承如下表7所示： 滾動(dòng)軸承的壽命校核計(jì)算公式： 式中n ——軸承轉(zhuǎn)速，r/min； ——軸承壽命指數(shù)，對(duì)球軸承＝3，對(duì)滾子軸承＝10/3； ——壽命因數(shù)，按表7-2-8選??； ——速度因數(shù)，按表7-2-9選?。? ——力矩載荷因數(shù)，力矩載荷較小時(shí)，，較大時(shí)，； ——沖擊載荷因數(shù)，按表7-2-10選取； ——溫度系數(shù)，由于卷揚(yáng)機(jī)長期在室外工作，工作溫度小于120°，故取。（查表7-2-11）（據(jù)《機(jī)械設(shè)計(jì)手冊(cè)》第四版第二卷） 。 表7 軸承代號(hào)及基本參數(shù) 型號(hào) 數(shù)目 基本參數(shù) d D B 基本額定動(dòng)載荷/kN GB/T276-1994 6211 2 55 100 21 43.2 GB/T276-1994 6208 2 40 80 18 29.5 GB/T276-1994 6220 1 100 180 34 122 GB286-81 3516 2 80 140 33 104 1）軸承6211（球軸承），與卷筒轉(zhuǎn)速相同，n＝26.53r/min；查得＝4.58，=1.073，=1.5，=1.2，則： 2）軸承6208（球軸承），與端蓋聯(lián)接的軸承的轉(zhuǎn)速n為輸入軸與卷筒的相對(duì)速度，故；且查得＝4.58，=0.324，=1.5，=1.2，則： 而與銷軸盤聯(lián)接的軸承的轉(zhuǎn)速與輸入軸的轉(zhuǎn)速相同，n＝960，則： 3）軸承6220（球軸承），n＝26.53r/min；查得＝4.58，=1.073，=1.5，=1.2， 4）軸承3516（滾子軸承），轉(zhuǎn)速n為輸入軸與行星輪的相對(duì)速度，故；且查得＝3.93，=0.363，=1.5，=1.2，則： 以上對(duì)軸承的校核說明了所選的所有軸承都滿足要求。 （6）潤滑與密封 ① 齒輪的潤滑 采用浸油潤滑，浸油深度為一個(gè)齒高，但不小于10mm。 ② 滾動(dòng)軸承的潤滑 由于軸承周向速度為1m/s <2m/s，所以選用軸承內(nèi)充填油脂來潤滑。 ③ 潤滑油的選擇 齒輪選用普通工業(yè)齒輪潤滑油，軸承選用鈣基潤滑脂。 ④ 密封方法的選取 箱內(nèi)密封采用擋油盤。箱外密封選用凸緣式軸承蓋，在非軸伸端采用悶蓋，在軸伸端采用透蓋，兩者均采用墊片加以密封；此外，對(duì)于透蓋還需要在軸伸處設(shè)置氈圈加以密封。 十、箱體尺寸及附件的設(shè)計(jì) 采用HT250鑄造而成，其主要結(jié)構(gòu)和尺寸如下： 中心距a=154.5mm，取整160mm 總長度L： 總寬度B： 總高度H： 箱座壁厚：，未滿足要求，直接取8 mm 箱蓋壁厚：，未滿足要求，直接取8mm 箱座凸緣厚度b： =1.5*8=12 mm 箱蓋凸緣厚度b1： =1.5*8=12mm 箱座底凸緣厚度b2：=2.5*8=20 mm 箱座肋厚m：=0.85*8=6.8 mm 箱蓋肋厚m1：=0.85*8=6.8mm 扳手空間： C1＝18mm，C2＝16mm 軸承座端面外徑D2：高速軸上的軸承： 低速軸上的軸承： 軸承旁螺栓間距s：高速軸上的軸承： 低速軸上的軸承： 軸承旁凸臺(tái)半徑R1： 箱體外壁至軸承座端面距離： 地腳螺釘直徑： 地腳螺釘數(shù)量n：因?yàn)閍=160mm<250mm，所以n=4 軸承旁螺栓直徑： 凸緣聯(lián)接螺栓直徑： ,?。?0mm 凸緣聯(lián)接螺栓間距L：， 取L＝100mm 軸承蓋螺釘直徑與數(shù)量n：高速軸上的軸承：d3=6, n＝4 低速軸上的軸承： d3=8，n＝4 檢查孔蓋螺釘直徑：,取d4＝6mm 檢查孔蓋螺釘數(shù)量n：因?yàn)閍=160mm<250mm,所以n=4 啟蓋螺釘直徑d5（數(shù)量）：（2個(gè)） 定位銷直徑d6（數(shù)量）： （2個(gè)） 齒輪圓至箱體內(nèi)壁距離： ，取 ＝10mm 小齒輪端面至箱體內(nèi)壁距離： ，取 ＝10mm 軸承端面至箱體內(nèi)壁距離：當(dāng)軸承脂潤滑時(shí)，＝10～15 ，取 ＝10 大齒輪齒頂圓至箱底內(nèi)壁距離：>30～50 ，取 ＝40mm 箱體內(nèi)壁至箱底距離： ＝20mm 減速器中心高H： ，取H＝185mm。 箱蓋外壁圓弧直徑R： 箱體內(nèi)壁至軸承座孔外端面距離L1： 箱體內(nèi)壁軸向距離L2： 兩側(cè)軸承座孔外端面間距離L3： 2、附件的設(shè)計(jì) （1）檢查孔和蓋板 查《機(jī)械基礎(chǔ)》P440表20－4，取檢查孔及其蓋板的尺寸為： A＝115，160，210，260，360,460，取A＝115mm A1＝95mm，A2＝75mm，B1＝70mm，B＝90mm d4為M6，數(shù)目n＝4 R＝10 h＝3 A B A1 B1 A2 B2 h R n d L 115 90 95 70 75 50 3 10 4 M6 15 （2）通氣器 選用結(jié)構(gòu)簡單的通氣螺塞，由《機(jī)械基礎(chǔ)》P441表20－5，取檢查孔及其蓋板的尺寸為（單位：mm）： d D D1 S L l a D1 M22 1.5 32 25.4 22 29 15 4 7 （3）油面指示器 由《機(jī)械基礎(chǔ)》P482附錄31，取油標(biāo)的尺寸為： 視孔 A形密封圈規(guī)格 （4）放油螺塞 螺塞的材料使用Q235，用帶有細(xì)牙螺紋的螺塞擰緊，并在端面接觸處增設(shè)用耐油橡膠制成的油封圈來保持密封。由《機(jī)械基礎(chǔ)》P442表20－6，取放油螺塞的尺寸如下（單位：mm）： d D0 L l a D S d1 M24 2 34 31 16 4 25.4 22 26 （5）定位銷 定位銷直徑 ，兩個(gè)，分別裝在箱體的長對(duì)角線上。 ＝12+12＝24，取L＝25mm。 （6）起蓋螺釘 起蓋螺釘10mm，兩個(gè)，長度L>箱蓋凸緣厚度b1=12mm，取L＝15mm ，端部制成小圓柱端，不帶螺紋，用35鋼制造，熱處理。 （7）起吊裝置 箱蓋上方安裝兩個(gè)吊環(huán)螺釘，查《機(jī)械基礎(chǔ)》P468附錄13， 取吊環(huán)螺釘尺寸如下（單位：mm）： d（D） d1(max) D1（公稱） d2(max) h1(max) h d4 M8 9.1 20 21.1 7 18 36 r1 r(min) l(公稱) a(max) b（max） D2（公稱min） h2(公稱min) 4 1 16 2.5 10 13 2.5 箱座凸緣的下方鑄出吊鉤，查《機(jī)械基礎(chǔ)》P444表20－7得， B=C1+C2=18+16=34mm H=0.8B=34*0.8=27.2mm h=0.5H=13.6mm r2 =0.25B=6.8mm b=2 =2*8=16mm 第3章 諧波齒輪減速器三維設(shè)計(jì)圖 總結(jié) [1].諧波減速器與普通相比具有結(jié)構(gòu)緊湊、體積小、重量輕、傳動(dòng)比范圍大、效率高、 運(yùn)轉(zhuǎn)平穩(wěn)、噪音小、承載能力大結(jié)構(gòu)簡單、加工方便、成本低、安裝和使用較為方便、運(yùn)轉(zhuǎn)可靠、使用壽命長等優(yōu)點(diǎn)。因此，對(duì)于研究和開發(fā)設(shè)計(jì)此類減速器有一定的價(jià)值。 [2].在設(shè)計(jì)減速器過程當(dāng)中，因內(nèi)齒輪和外齒輪的齒數(shù)差很少，內(nèi)外齒輪應(yīng)制成變位齒輪。在選擇變位系數(shù)時(shí)候要充分考慮嚙合傳動(dòng)當(dāng)中的各種干涉問題。我們可以通過試湊法來選取變位系數(shù)，但此方法比較繁瑣。也可以通過查表法來選擇，這種方法簡單，在具體的計(jì)算驗(yàn)證過程中發(fā)現(xiàn)通過查表所得數(shù)據(jù)，雖滿足各種限制條件，卻并非最優(yōu)。所以如何設(shè)計(jì)出高效的減速器，還有待進(jìn)一步研究。 [3].軸承是諧波減速器中的一個(gè)薄弱環(huán)節(jié)，增大齒輪的模數(shù)，可以使行星輪的直徑增大，可選擇較大尺寸的軸承；另外增加兩軸承之間的安裝距離，使軸承上的載荷減小，因此能使軸承的壽命提高。 致 謝 我要感謝我的指導(dǎo)教師XX老師。老師雖身負(fù)教學(xué)、科研重任，仍抽出時(shí)間，不時(shí)召集我和同門以督責(zé)課業(yè)，從初稿到定稿，不厭其煩，一審再審，大到篇章布局的偏頗，小到語句格式的瑕疵，都一一予以指出。是他傳授給我方方面面的知識(shí)，拓寬了我的知識(shí)面，培養(yǎng)了我的功底，對(duì)論文的完成不無裨益。我還要感謝學(xué)院所有教過我的老師，是你們讓我成熟成長；感謝學(xué)院的各位工作人員，他細(xì)致的工作使我和同學(xué)們的學(xué)習(xí)和生活井然有序。 謹(jǐn)向我的父母和家人表示誠摯的謝意。他們是我生命中永遠(yuǎn)的依靠和支持，他們無微不至的關(guān)懷，是我前進(jìn)的動(dòng)力；他們的殷殷希望，激發(fā)我不斷前行。沒有他們就沒有我，我的點(diǎn)滴成就都來自他們。 讓我依依不舍的還有各位學(xué)友、同門和室友。在我需要幫助的時(shí)候他們伸出溫暖的雙手，鼎立襄助。能和他們相遇、相交、相知是人生的一大幸事。 參考文獻(xiàn) [1] 馮桂安等.機(jī)械制造裝備設(shè)計(jì)[M]. 北京:機(jī)械工業(yè)出版社， [2] 齒輪手冊(cè)編委會(huì).齒輪手冊(cè)(上冊(cè))第2版.北京:機(jī)械工業(yè)出版社,2002.5. [3] 漸開線齒輪行星傳動(dòng)的設(shè)計(jì)與制造編委會(huì). 漸開線齒輪行星傳動(dòng)的設(shè)計(jì)與制造.北京:機(jī)械工業(yè)出版社,2002.5. [4] 陳坐模，葛文杰等. 機(jī)械原理第七版.北京:高等教育出版社,2007.12. [5] 濮良貴，紀(jì)名剛. 機(jī)械設(shè)計(jì)第八版.北京:高等教育出版社,2008.4. [6] 卜炎. 螺紋連接連接設(shè)計(jì)與計(jì)算.北京:高等教育出版社,1993. [7] 張春林，曲繼芳.機(jī)械創(chuàng)新設(shè)計(jì)[M].北京:高等教育出版社,2008.4. [8] 成大先.機(jī)械設(shè)計(jì)手冊(cè),第五卷[M]. 北京:化學(xué)工業(yè)出版社， [9] 王昆等.機(jī)械設(shè)計(jì)課程設(shè)計(jì)[M]. 北京:高等教育出版社, [10] 王杰等.機(jī)械制造工程學(xué)[M].北京:北京郵電大學(xué)出版社， [11] 良貴，紀(jì)名剛.機(jī)械設(shè)計(jì)[M]. 北京:機(jī)械工業(yè)出版社， [12] 阮忠唐主編. 連軸器，離合器的設(shè)計(jì)與選用指南[M]. [13] 《機(jī)械設(shè)計(jì)手冊(cè)》聯(lián)合編寫組.機(jī)械設(shè)計(jì)手冊(cè)（上） [14] 中國農(nóng)業(yè)機(jī)械化科學(xué)研究院.實(shí)用機(jī)械設(shè)計(jì)手冊(cè)[M]. rugged, e generation curr guidelines 2 Power System Network Description bine can enter self-excitation operation. The voltage and fre- quency during off-grid operation are determined by the balance between the systems reactive and real power. Downloaded 28 Mar 2008 to 211.82.100.20. Redistribution subject to ASME license or copyright; see http:/www.asme.org/terms/Terms_Use.cfm We investigate a very simple power system network consisting of one 1.5 MW, fixed-speed wind turbine with an induction gen- erator connected to a line feeder via a transformer H208492 MVA, 3 phase, 60 Hz, 690 V/12 kVH20850. The low-speed shaft operates at 22.5 rpm, and the generator rotor speed is 1200 rpm at its syn- chronous speed. A diagram representing this system is shown in Fig. 1. The power system components analyzed include the following: An infinite bus and a long line connecting the wind turbine to the substation A transformer at the pad mount One potential problem arising from self-excitation is the safety aspect. Because the generator is still generating voltage, it may compromise the safety of the personnel inspecting or repairing the line or generator. Another potential problem is that the generators operating voltage and frequency may vary. Thus, if sensitive equipment is connected to the generator during self-excitation, that equipment may be damaged by over/under voltage and over/ under frequency operation. In spite of the disadvantages of oper- ating the induction generator in self-excitation, some people use this mode for dynamic braking to help control the rotor speed during an emergency such as a grid loss condition. With the proper choice of capacitance and resistor load H20849to dump the energy from the wind turbineH20850, self-excitation can be used to maintain the wind turbine at a safe operating speed during grid loss and me- chanical brake malfunctions. The equations governing the system can be simplified by look- ing at the impedance or admittance of the induction machine. To Contributed by the Solar Energy Division of THE AMERICAN SOCIETY OF MECHANI- CAL ENGINEERS for publication in the ASME JOURNAL OF SOLAR ENERGY ENGINEERING. Manuscript received: February 28, 2005; revised received: July 22, 2005. Associate Editor: Dale Berg. Journal of Solar Energy Engineering NOVEMBER 2005, Vol. 127 / 581Copyright 2005 by ASME E. Muljadi C. P. Butterfield National Renewable Energy Laboratory, Golden, Colorado 80401 H. Romanowitz Oak Creek Energy Systems Inc., Mojave, California 93501 R. Yinger Southern California Edison, Rosemead, California 91770 Self-Excitation Wind Power Traditional wind turbines they are inexpensive, tion generators requir is often used. Because the capacitor compensation among the wind turbine, tant aspects of wind content in the output ena and gives some H20851DOI: 10.1115/1.2047590 1 Introduction Many of todays operating wind turbines have fixed speed in- duction generators that are very reliable, rugged, and low cost. During normal operation, an induction machine requires reactive power from the grid at all times. Thus, the general practice is to compensate reactive power locally at the wind turbine and at the point of common coupling where the wind farm interfaces with the outside world. The most commonly used reactive power com- pensation is capacitor compensation. It is static, low cost, and readily available in different sizes. Different sizes of capacitors are generally needed for different levels of generation. A bank of parallel capacitors is switched in and out to adjust the level of compensation. With proper compensation, the power factor of the wind turbine can be improved significantly, thus improving over- all efficiency and voltage regulation. On the other hand, insuffi- cient reactive power compensation can lead to voltage collapse and instability of the power system, especially in a weak grid environment. Although reactive power compensation can be beneficial to the overall operation of wind turbines, we should be sure the compen- sation is the proper size and provides proper control. Two impor- tant aspects of capacitor compensation, self-excitation H208511,2H20852 and harmonics H208513,4H20852, are the subjects of this paper. In Sec. 2, we describe the power system network; in Sec. 3, we discuss the self-excitation in a fixedspeed wind turbine; and in Sec. 4, we discuss harmonics. Finally, our conclusions are pre- sented in Sec. 5. and Harmonics in Generation are commonly equipped with induction generators because and require very little maintenance. Unfortunately, induc- reactive power from the grid to operate; capacitor compensation the level of required reactive power varies with the output power, must be adjusted as the output power varies. The interactions the power network, and the capacitor compensation are impor- that may result in self-excitation and higher harmonic ent. This paper examines the factors that control these phenom- on how they can be controlled or eliminated. H20852 Capacitors connected in the low voltage side of the trans- former An induction generator For the self-excitation, we focus on the turbine and the capaci- tor compensation only H20849the right half of Fig. 1H20850. For harmonic analysis, we consider the entire network shown in Fig. 1. 3 Self-Excitation 3.1 The Nature of Self-Excitation in an Induction Generator. Self-excitation is a result of the interactions among the induction generator, capacitor compensation, electrical load, and magnetic saturation. This section investigates the self- excitation process in an off-grid induction generator; knowing the limits and the boundaries of self-excitation operation will help us to either utilize or to avoid self-excitation. Fixed capacitors are the most commonly used method of reac- tive power compensation in a fixed-speed wind turbine. An induc- tion generator alone cannot generate its own reactive power; it requires reactive power from the grid to operate normally, and the grid dictates the voltage and frequency of the induction generator. Although self-excitation does not occur during normal grid- connected operation, it can occur during off-grid operation. For example, if a wind turbine operating in normal mode becomes disconnected from the power line due to a sudden fault or distur- bance in the line feeder, the capacitors connected to the induction generator will provide reactive power compensation, and the tur- Downloaded 28 Mar 2008 to 211.82.100.20. Redistribution subject to ASME license or copyright; see http:/www.asme.org/terms/Terms_Use.cfm operate in an isolated fashion, the total admittance of the induc- tion machine and the rest of the connected load must be zero. The voltage of the system is determined by the flux and frequency of the system. Thus, it is easier to start the analysis from a node at one end of the magnetizing branch. Note that the term “imped- ance” in this paper is the conventional impedance divided by the frequency. The term “admittance” in this paper corresponds to the actual admittance multiplied by the frequency. 3.2 Steady-State Representation. The steady-state analysis is important to understand the conditions required to sustain or to diminish self-excitation. As explained above, self-excitation can be a good thing or a bad thing, depending on how we encounter the situation. Figure 2 shows an equivalent circuit of a capacitor- compensated induction generator. As mentioned above, self- excitation operation requires that the balance of both real and reactive power must be maintained. Equation H208491H20850 gives the total admittance of the system shown in Fig. 2: Y S + Y M H11032 + Y R H11032 =0, H208491H20850 where Y S H11005 effective admittance representing the stator winding, the capacitor, and the load seen by node M Y M H11032 H11005 effective admittance representing the magnetizing branch as seen by node M, referred to the stator side Y R H11032 H11005 effective admittance representing the rotor winding as seen by node M, referred to the stator side H20849Note: the superscript “ H11032” indicates that the values are referred to the stator side.H20850 Equation H208491H20850 can be expanded into the equations for imaginary and real parts as shown in Eqs. H208492H20850 and H208493H20850: R 1L /H9275 H20849R 1L /H9275H20850 2 + L 1L 2 + R R H11032/SH9275 H20849R R H11032/SH9275H20850 2 + L LR H11032 2 =0 H208492H20850 where Fig. 1 The physical diagram of the system under investigation Fig. 2 Per phase equivalent circuit of an induction generator under self-excitation mode 582 / Vol. 127, NOVEMBER 2005 1 L M H11032 + L 1L H20849R 1L /H9275H20850 2 + L 1L 2 + L LR H11032 H20849R R H11032/SH9275H20850 2 + L LR H11032 2 =0 H208493H20850 R 1L = R S + R L H20849H9275CR L H20850 2 +1 L 1L = L LS CR L H20849H9275CR L H20850 2 +1 R S H11005 stator winding resistance L LS H11005 stator winding leakage inductance R R H11032 H11005 rotor winding resistance L LR H11032 H11005 rotor winding leakage inductance L M H11032 H11005 stator winding resistance S H11005 operating slip H9275 H11005 operating frequency R L H11005 load resistance connected to the terminals C H11005 capacitor compensation R 1L and L 1L are the effective resistance and inductance, respectively, representing the stator winding and the load as seen by node M. One important aspect of self-excitation is the magnetizing char- acteristic of the induction generator. Figure 3 shows the relation- ship between the flux linkage and the magnetizing inductance for a typical generator; an increase in the flux linkage beyond a cer- tain level reduces the effective magnetizing inductance L M H11032 . This graph can be derived from the experimentally determined no-load characteristic of the induction generator. To solve the above equations, we can fix the capacitor H20849CH20850 and the resistive load H20849R L H20850 values and then find the operating points for different frequencies. From Eq. H208492H20850, we can find the operating slip at a particular frequency. Then, from Eq. H208493H20850, we can find the corresponding magnetizing inductance L M H11032 , and, from Fig. 3, the operating flux linkage at this frequency. The process is repeated for different frequencies. As a base line, we consider a capacitor with a capacitance of 3.8 mF H20849milli-faradH20850 connected to the generator to produce ap- proximately rated VAR H20849volt ampere reactiveH20850 compensation for full load generation H20849high windH20850. A load resistance of R L =1.0 H9024 is used as the base line load. The slip versus rotor speed presented in Fig. 4 shows that the slip is roughly constant throughout the speed range for a constant load resistance. The capacitance does not affect the operating slip for a constant load resistance, but a higher resistance H20849R L high=lower generated powerH20850 corresponds to a lower slip. The voltage at the terminals of the induction generator H20849pre- sented in Fig. 5H20850 shows the impact of changes in the capacitance Fig. 3 A typical magnetization characteristic Transactions of the ASME Downloaded 28 Mar 2008 to 211.82.100.20. Redistribution subject to ASME license or copyright; see http:/www.asme.org/terms/Terms_Use.cfm and load resistance. As shown in Fig. 5, the load resistance does not affect the terminal voltage, especially at the higher rpm H20849higher frequencyH20850, but the capacitance has a significant impact on the voltage profile at the generator terminals. A larger capacitance yields less voltage variation with rotor speed, while a smaller capacitance yields more voltage variation with rotor speed. As shown in Fig. 6, for a given capacitance, changing the effective value of the load resistance can modulate the torque-speed characteristic. These concepts of self-excitation can be exploited to provide dynamic braking for a wind turbine H20849as mentioned aboveH20850 to pre- vent the turbine from running away when it loses its connection to the grid; one simply needs to choose the correct values for capaci- tance H20849a high valueH20850 and load resistance to match the turbine power output. Appropriate operation over a range of wind speeds can be achieved by incorporating a variable resistance and adjust- ing it depending on wind speed. 3.3 Dynamic Behavior. This section examines the transient behavior in self-excitation operation. We choose a value of 3.8 mF capacitance and a load resistance of 1.0 H9024 for this simu- lation. The constant driving torque is set to be 4500 Nm. Note that the wind turbine aerodynamic characteristic and the turbine con- trol system are not included in this simulation because we are more interested in the self-excitation process itself. Thus, we fo- Fig. 4 Variation of slip for a typical self-excited induction generator Fig. 5 Terminal voltage versus rotor speed for different R L and C Journal of Solar Energy Engineering cus on the electrical side of the equations. Figure 7 shows time series of the rotor speed and the electrical output power. In this case, the induction generator starts from rest. The speed increases until it reaches its rated speed. It is initially connected to the grid and at t=3.1 seconds H20849sH20850, the grid is discon- nected and the induction generator enters self-excitation mode. At t=6.375 s, the generator is reconnected to the grid, terminating the self-excitation. The rotor speed increases slightly during self- excitation, but, eventually, the generator torque matches the driv- ing torque H208494500 NmH20850, and the rotor speed is stabilized. When the generator is reconnected to the grid without synchronization, there is a sudden brief transient in the torque as the generator resyn- chronizes with the grid. Once this occurs, the rotor speed settles at the same speed as before the grid disconnection. Figure 8H20849aH20850 plots per phase stator voltage. It shows that the stator voltage is originally the same as the voltage of the grid to which it is connected. During the self-excitation mode H208493.1 sH11021t H110216.375 sH20850, when the rotor speed increases as shown in Fig. 7, the voltage increases and the frequency is a bit higher than 60 Hz. The voltage and the frequency then return to the rated values when the induction generator is reconnected to the grid. Figure 8H20849bH20850 is an expansion of Fig. 8H20849aH20850 between t=3.0 s and t=3.5 s to better illustrate the change in the voltage that occurs during that transient. 4 Harmonic Analysis 4.1 Simplified Per Phase Higher Harmonics Representation. In order to model the harmonic behavior of the network, we replace the power network shown in Fig. 1 with the per phase equivalent circuit shown in Fig. 9H20849aH20850. In this circuit representation, a higher harmonic or multiple of 60 Hz is denoted Fig. 6 The generator torque vs. rotor speed for different R L and C Fig. 7 The generator output power and rotor speed vs. time NOVEMBER 2005, Vol. 127 / 583 4.1.2 Transformer. We consider a three-phase transformer with leakage reactance H20849X xf H20850 of 6 percent. Because the magnetiz- Downloaded 28 Mar 2008 to 211.82.100.20. Redistribution subject to ASME license or copyright; see http:/www.asme.org/terms/Terms_Use.cfm by h, where h is the integer multiple of 60 Hz. Thus h=5 indicates the fifth harmonic H20849300 HzH20850. For wind turbine applications, the induction generator, transformer, and capacitors are three phase and connected in either Wye or Delta configuration, so the even harmonics and the third harmonic do not exist H208515,6H20852. That is, only h=5,7,11,13,17,., etc. exist. 4.1.1 Infinite Bus and Line Feeder. The infinite bus and the line feeder connecting the wind turbine to the substation are rep- resented by a simple Thevenin representation of the larger power system network. Thus, we consider a simple RL line representa- tion. Fig. 8 The terminal voltage versus the time. a Voltage during self-excitation. b Voltage before and during self-excitation, and after reconnection. Fig. 9 The per phase equivalent circuit of the simplified model for harmonic analysis 584 / Vol. 127, NOVEMBER 2005 ing reactance of a large transformer is usually very large com- pared to the leakage reactance H20849X M H11032 H11015H11009 open circuitH20850, only the leakage reactance is considered. Assuming the efficiency of the transformer is about 98 percent at full load, and the copper loss is equal to the core loss H20849a general assumption for an efficient, large transformerH20850, the copper loss and core loss are each approximately 1 percent or 0.01 per unit. With this assumption, we can compute the copper loss in per unit at full load current H20849I 1 FullH6018Load =1.0 per unitH20850, and we can determine the total winding resistance of the primary and secondary winding H20849about one percent in per unitH20850. 4.1.3 Capacitor Compensation. Switched capacitors represent the compensation of the wind turbine. The wind turbine we con- sider is equipped with an additional 1.9 MVAR reactive power compensation H208491.5 MVAR above the 400 kVAR supplied by the manufacturerH20850. The wind turbine is compensated at different levels of compensation depending on the level of generation. The ca- pacitor is represented by the capacitance C in series with the para- sitic resistance H20849R c H20850, representing the losses in the capacitor. This resistance is usually very small for a good quality capacitor. 4.1.4 Induction Generator. The induction generator H208491.5 MW,480 V,60 HzH20850 used for this wind turbine can be repre- sented as the per phase equivalent circuit shown Fig. 9H20849aH20850. The slip of an induction generator at any harmonic frequency h can be modeled as S h = hH9275 s H9275 r hH9275 s H208494H20850 where S h H11005 slip for hth harmonic h H11005 harmonic order H9275 s H11005 synchronous speed of the generator H9275 r H11005 rotor speed of the generator Thus for higher harmonics H20849fifth and higherH20850 the slip is close to 1 H20849S h =1H20850 and for practical purposes is assumed to be 1. 4.2 Steady State Analysis. Figure 9H20849bH20850 shows the simplified equivalent circuit of the interconnected system representing higher harmonics. Note that the magnetizing inductance of the transformers and the induction generator are assumed to be much larger than the leakages and are not included for high harmonic calculations. In this section, we describe the characteristics of the equivalent circuit shown in Fig. 9, examine the impact of varying the capacitor size on the harmonic admittance, and use the result of calculations to explain why harmonic contents of the line cur- rent change as the capacitance is varied. From the superposition theorem, we can analyze a circuit with only one source at a time while the other sources are turned off. For harmonics analysis, the fundamental frequency voltage source can be turned off. In this case, the fundamental frequency voltage source H20849infinite busH20850, V s , is short circuited. Wind farm operator experience shows us that harmonics occur when the transformer operates in the saturation region, that is, at higher flux levels as shown in Fig. 3. During the operation in this saturation region, the resulting current can be distorted into a sharply peaked sinusoidal current due to the larger magnetizing current imbedded in the primary current. This nonsinusoidal cur- rent can excite the network at resonant frequencies of the network. From the circuit diagram we can compute the impedance H20849at any capacitance and harmonic frequencyH20850 seen by the harmonic source, V h , with Eq. H208495H20850, where the sign “ H20648 ” represents the words “in parallel with:” Transactions of the ASME Downloaded 28 Mar 2008 to 211.82.100.20. Redistribution subject to ASME license or copyright; see http:/www.asme.org/terms/Terms_Use.cfm ZH20849C,hH20850 = H20849Z line + 0.5Z xf H20850 H20648 H208490.5Z xf + Z C H20648 Z gen H20850H208495H20850 w