喜歡就充值下載吧。。資源目錄里展示的文件全都有，，請(qǐng)放心下載，，有疑問(wèn)咨詢QQ:414951605或者1304139763 ======================== 喜歡就充值下載吧。。資源目錄里展示的文件全都有，，請(qǐng)放心下載，，有疑問(wèn)咨詢QQ:414951605或者1304139763 ======================== 任務(wù)書 （任務(wù)起止日期 02月 ~ 05月） 題 目 純電動(dòng)汽車動(dòng)力傳動(dòng)系統(tǒng)匹配設(shè)計(jì) 學(xué) 院 專 業(yè) 班 級(jí) 學(xué) 生 指導(dǎo)教師 課題內(nèi)容： 本設(shè)計(jì)題目主要針對(duì)某純電動(dòng)汽車，通過(guò)相關(guān)計(jì)算完成純電動(dòng)汽車電機(jī)性能參數(shù)、傳動(dòng)系參數(shù)及動(dòng)力電池參數(shù)的匹配設(shè)計(jì)，并繪制出純電動(dòng)汽車動(dòng)力傳動(dòng)系統(tǒng)的總布置圖和關(guān)鍵零部件圖。其主要內(nèi)容如下： 1．分析純電動(dòng)汽車動(dòng)力傳動(dòng)系統(tǒng)功能總成，提出動(dòng)力傳動(dòng)系統(tǒng)總布置設(shè)計(jì)方案； 2．確定純電動(dòng)汽車的主要技術(shù)參數(shù)； 3．根據(jù)整車動(dòng)力性要求，對(duì)驅(qū)動(dòng)電機(jī)、電池及傳動(dòng)系主要性能參數(shù)進(jìn)行匹配設(shè)計(jì)； 4．繪制動(dòng)力傳動(dòng)系統(tǒng)布置圖（0號(hào)圖幅）和關(guān)鍵零部件圖； 5．撰寫設(shè)計(jì)說(shuō)明書，總結(jié)設(shè)計(jì)方法和步驟。 本設(shè)計(jì)課題所需的計(jì)算機(jī)和MATLAB、CAD軟件已經(jīng)具備，并具備相關(guān)的參考書籍、參考手冊(cè)，可以滿足設(shè)計(jì)需要。 課題任務(wù)要求： 1、總布置圖、關(guān)鍵零部件圖等繪圖工作量不少于2張，至少一張為0號(hào)圖紙； 2、純電動(dòng)汽車英文資料翻譯，工作量少于三千（3000）字； 3、文獻(xiàn)綜述不少于一千五百（1500）字； 4、設(shè)計(jì)計(jì)算說(shuō)明書不得少于一萬(wàn)五千（15000）字。 主要參考文獻(xiàn)（由指導(dǎo)教師選定）： [1] 熊明潔, 胡國(guó)強(qiáng), 閔建平. 純電動(dòng)汽車動(dòng)力系統(tǒng)參數(shù)選擇與匹配[J]. 汽車工程師, 2010, 5: 38-40. [2] Aden Seaman, John Mcphee. Symbolic Math-based Battery Modeling for Electric Vehicle Simulation [C]. Proceedings of the ASME 2010 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, August 15-18, 2010, Canada, DETC 2010-28814: 1-9. [3] 王峰, 方宗德, 祝小元. 純電動(dòng)汽車新型動(dòng)力傳動(dòng)裝置的匹配仿真與優(yōu)化[J]. 汽車工程, 2011, 33(9): 71-74. [4] 查鴻山, 宗志堅(jiān), 劉忠途. 純電動(dòng)汽車動(dòng)力匹配計(jì)算與仿真[J]. 中山大學(xué)學(xué)報(bào), 2010, 5: 52-56. [5] 姬芬竹, 高峰, 周榮. 純電動(dòng)汽車傳動(dòng)系參數(shù)匹配的研究[J]. 汽車科技, 2005, 6: 26-29. [6] 黃菊花, 徐仕華, 劉淑琴. 電動(dòng)汽車動(dòng)力參數(shù)匹配及性能仿真[J]. 南昌大學(xué)學(xué)報(bào), 2011, 4: 89-92. [7] 杜發(fā)榮, 姬芬竹. 電動(dòng)汽車動(dòng)力傳動(dòng)系統(tǒng)評(píng)價(jià)體系參數(shù)[J]. 遼寧工程技術(shù)大學(xué)學(xué)報(bào), 2008, 2: 116-119. [8] 姜輝. 電動(dòng)汽車傳動(dòng)系統(tǒng)的匹配及優(yōu)化[D]. 重慶: 重慶大學(xué), 2006. [9] 張新磊. 電動(dòng)汽車總體設(shè)計(jì)及性能仿真優(yōu)化[D]. 哈爾濱: 哈爾濱工業(yè)大學(xué), 2010. [10] 周保華. 電動(dòng)汽車傳動(dòng)系統(tǒng)參數(shù)設(shè)計(jì)及換擋控制研究[D]. 重慶: 重慶大學(xué), 2010. [11] 余銀輝. 微型電動(dòng)汽車傳動(dòng)系統(tǒng)匹配及驅(qū)動(dòng)優(yōu)化研究[D]. 重慶: 重慶大學(xué), 2010. [12] 夏青松. 電動(dòng)汽車動(dòng)力系統(tǒng)設(shè)計(jì)及仿真研究[D]. 武漢: 武漢理工大學(xué), 2007. 同組設(shè)計(jì)者 無(wú) 注：1. 此任務(wù)書應(yīng)由指導(dǎo)教師填寫。 2. 此任務(wù)書最遲必須在畢業(yè)設(shè)計(jì)開始前一周下達(dá)給學(xué)生。 學(xué)生完成畢業(yè)設(shè)計(jì)（論文）工作進(jìn)度計(jì)劃表 序號(hào) 畢業(yè)設(shè)計(jì)（論文）工作任務(wù) 工 作 進(jìn) 度 日 程 安 排 周次 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 參考文獻(xiàn)收集與查閱 — 2 學(xué)習(xí)參考文獻(xiàn) — — — 3 開題報(bào)告 — — 4 文獻(xiàn)綜述 — — 5 外文翻譯 — — — — 6 提出動(dòng)力傳動(dòng)系統(tǒng)總布置設(shè)計(jì)方案 — — — 7 確定純電動(dòng)汽車的主要技術(shù)參數(shù)并進(jìn)行動(dòng)力傳動(dòng)系統(tǒng)匹配設(shè)計(jì) — — — 8 繪制總布置圖和關(guān)鍵零部件圖 — — — 9 撰寫畢業(yè)論文 — — — 10 準(zhǔn)備答辯相關(guān)材料 — — 注：1. 此表由指導(dǎo)教師填寫。 2. 此表每個(gè)學(xué)生一份，作為畢業(yè)設(shè)計(jì)（論文）檢查工作進(jìn)度之依據(jù)； 3. 進(jìn)度安排請(qǐng)用“—”在相應(yīng)位置畫出。 畢業(yè)設(shè)計(jì)（論文）階段工作情況檢查表 時(shí)間 第一階段 第二階段 第三階段 內(nèi)容 組織紀(jì)律 完成任務(wù)情況 組織紀(jì)律 完成任務(wù)情況 組織紀(jì)律 完成任務(wù)情況 檢 查 情 況 教師 簽字 簽字 日期 簽字 日期 簽字 日期 注：1. 此表應(yīng)由教師認(rèn)真填寫； 2. “組織紀(jì)律”一欄根據(jù)學(xué)生具體執(zhí)行情況如實(shí)填寫； 3. “完成任務(wù)情況”一欄按學(xué)生是否按進(jìn)度保質(zhì)保量完成任務(wù)的情況填寫； 4. 對(duì)違紀(jì)和不能按時(shí)完成任務(wù)者，指導(dǎo)教師可根據(jù)情節(jié)輕重對(duì)該生提出警告或不能參加答辯的建議。 譯文 外文翻譯 題 目 純電動(dòng)汽車動(dòng)力傳動(dòng) 系統(tǒng)匹配設(shè)計(jì) 專 業(yè) 班 級(jí) 學(xué) 生 指導(dǎo)教師 面向?qū)ο髷?shù)學(xué)建模蓄電池的電動(dòng)汽車仿真 Aden N. Seaman, Jone McPhee 摘要： 我們提出了一種在MapleSim軟件中基于數(shù)學(xué)模型設(shè)計(jì)出來(lái)的蓄電池電動(dòng)汽車。這個(gè)模型有個(gè)優(yōu)點(diǎn)是：模型是在一種物理一致的方式下利用因果系統(tǒng)部件進(jìn)行描述的。我們利用一個(gè)由Chen和Rincon-Mora建立的蓄電池模型來(lái)開發(fā)了一個(gè)基于數(shù)學(xué)模型的完整蓄電池組，并開發(fā)簡(jiǎn)單控制器，電動(dòng)機(jī)/發(fā)電機(jī)，地形模型，和驅(qū)動(dòng)循環(huán)模型，以此在不同工況下測(cè)試電動(dòng)車性能。由此產(chǎn)生的微分方程是被象征性地簡(jiǎn)化的，并進(jìn)行數(shù)值模擬來(lái)給出物理一致的結(jié)果，還有便是清楚地表明了蓄電池和縱向車輛動(dòng)力學(xué)的緊密耦合。 1 簡(jiǎn)介 車輛建模是一個(gè)復(fù)雜而又極具挑戰(zhàn)性的工作。汽車公司每年發(fā)布一些新的車型,所有的這些汽車都需要模擬和測(cè)試,然后才能進(jìn)行車輛試制。 隨著推動(dòng)清潔、高效汽車的發(fā)展，傳動(dòng)系統(tǒng)正逐漸包含電機(jī)、發(fā)動(dòng)機(jī)、無(wú)級(jí)變速器、類似電池的能量?jī)?chǔ)存裝置，以及傳統(tǒng)內(nèi)燃機(jī)等。 在此，有一項(xiàng)技術(shù)能夠降低建立復(fù)雜車輛模型難度的便是非因果數(shù)學(xué)模型，該模型是利用控制方程組內(nèi)組成部分動(dòng)作的物理方程組來(lái)描述的。在最終被求出數(shù)值解以產(chǎn)生輸出數(shù)據(jù)之前，這些方程組特征地運(yùn)行。這種方法使設(shè)計(jì)者們指定各部分動(dòng)作，并約束各部分在一個(gè)更物理一致的語(yǔ)言環(huán)境中去描述各部分變得更容易。這使得交換或是修改各部分，甚至于簡(jiǎn)化系統(tǒng)描述更為容易[1]。 Modelica[2]描述語(yǔ)言已被許多作者運(yùn)用在建立混合動(dòng)力汽車系統(tǒng)上了[3-7]，并且絕大多數(shù)運(yùn)用Dymola[8]仿真環(huán)境。 我們選擇運(yùn)用MapleSoft軟件中的MapleSim[9]仿真模塊作為我們的仿真環(huán)境，因?yàn)樵撃K允許我們利用控制BEV系統(tǒng)仿真的基礎(chǔ)的數(shù)學(xué)方程組。 我們選用的這種方法產(chǎn)生一個(gè)簡(jiǎn)化了的基于方程的可有效仿真的系統(tǒng)描述。方程組也可以運(yùn)用在HIL實(shí)時(shí)仿真中，同時(shí)可以被運(yùn)用于靈敏度分析和系統(tǒng)最優(yōu)化中[10,11]。 在本文中，我們提出一個(gè)蓄電池電動(dòng)汽車 (BEV)，這是在軟件MapleSim中我們基于數(shù)學(xué)建模技術(shù)已經(jīng)建立的模型。如圖1中總體BEV系統(tǒng)框圖所示。這是一個(gè)更復(fù)雜的數(shù)學(xué)化的混合動(dòng)力電動(dòng)汽車整車模型建立的開始，我們旨在建立一個(gè)可運(yùn)用的符號(hào)化數(shù)學(xué)模型。 圖1 總體BEV系統(tǒng)框圖 我們將一個(gè)Chen 和 Rincon-Mora[12]建立的鋰離子電路電池模型應(yīng)用到BEV系統(tǒng)中。我們修改電池方程來(lái)模擬一個(gè)電池組，該電池組是由單個(gè)的電池單元通過(guò)串、并聯(lián)方式組合起來(lái)的。為了將電池組和驅(qū)動(dòng)電機(jī)聯(lián)系起來(lái)，我們必須建立一個(gè)能量控制器模型作為系統(tǒng)集成的一部分。我們進(jìn)一步結(jié)合一個(gè)簡(jiǎn)單的在一個(gè)斜面驅(qū)動(dòng)的一維動(dòng)力學(xué)模型，一個(gè)地形模型控制傾斜度、一個(gè)驅(qū)動(dòng)循環(huán)模型控制車輛所期望的速度。 通過(guò)改變驅(qū)動(dòng)循環(huán)和地形模型，我們?cè)诓煌鸟{駛環(huán)境下檢測(cè)了所設(shè)計(jì)BEV純電動(dòng)汽車的性能。 2 系統(tǒng)建模和仿真 我們決定使用的技術(shù)是利用MapleSim 數(shù)學(xué)化模型作為仿真環(huán)境，它有一個(gè)圖形界面互連系統(tǒng)部件。該系統(tǒng)模型通過(guò)Maple數(shù)學(xué)引擎進(jìn)行運(yùn)行，并且最后描述系統(tǒng)的微分方程(DAEs)被用于數(shù)值模擬以產(chǎn)生輸出數(shù)據(jù)。作為三維多體系統(tǒng)仿真，利用以線性圖論為基礎(chǔ)的DynaFlex-Pro引擎對(duì)系統(tǒng)進(jìn)行仿真[1,11]。 2.1 蓄電池 無(wú)論BEV電動(dòng)車還是HEV混合動(dòng)力汽車，其中一個(gè)最重要組成部分是蓄電池。根據(jù)所需保真度和主要研究的電池參數(shù)，這里有很多種建立不同電池化學(xué)物質(zhì)的方法。參考Rao所著論文[13]中總結(jié)的一些建模方法。一般來(lái)說(shuō),隨著計(jì)算設(shè)備精度的提高，模型的精度也必將隨著提高。 一些我們所回顧的電池建模技術(shù)有：Salameh建立的鉛酸蓄電池模型[14]；Rong 和Pedram建立的鋰離子電池?cái)?shù)學(xué)模型[15]，其考慮了電池的SOH值和溫度效應(yīng);在3.1節(jié)PNGV電池測(cè)試手冊(cè)中的集總參數(shù)模型[16]；Piller發(fā)明的卡爾曼濾波技術(shù)[17]；Chen 和 Rin′con-Mora建立的電氣電路模型[12]；Nelson建立的阻抗模型[18]。這些不同的技術(shù)都有其優(yōu)點(diǎn)和缺點(diǎn)，也有其適用范圍。 在此，我們對(duì)電動(dòng)汽車采用鋰離子電池具有極大的興趣，因?yàn)殇囯x子電池質(zhì)量輕并且具有高于鉛酸蓄電池和鎳基蓄電池的重量質(zhì)量比和能量體積比。當(dāng)司機(jī)加速和再生制動(dòng)時(shí)，電池將受到持續(xù)高電流和反復(fù)充電的作用，因此，電動(dòng)汽車對(duì)電池的性能要求很高。而且，隨著駕駛環(huán)境變化，電池溫度大范圍變化可能會(huì)嚴(yán)重影響電池的性能和壽命。 因此我們需要建立一個(gè)鋰離子電池化學(xué)模型，其具有較寬范圍SOC值，能承受較大范圍電流變化，適應(yīng)較大范圍溫度變化。因此，最后我們更傾向于在HIL系統(tǒng)中建立這個(gè)電動(dòng)汽車模型，并且我們需要的是一個(gè)成本不太昂貴，保真度也不十分高的模型。 這些要求把我們注意引向Chen 和 Rin′con-Mora提出的電氣電路蓄電池模型。我們?cè)谲浖﨧apleSim中執(zhí)行這些不同部分并且在充電狀態(tài)和電器元件之間（在他們論文中方程2至6）運(yùn)用常用功能模塊代替非線性關(guān)系。見圖2 電池的框圖。 圖2 電池結(jié)構(gòu)框圖 因?yàn)樗麄兊哪Ｐ褪且粋€(gè)單一的單元,我們通過(guò)調(diào)整他們的方程用串、并聯(lián)的方式來(lái)模擬由若干單元組成的電池。Chen 和 Rin′con-Mora的電池可分為兩個(gè)線性電路以及兩個(gè)線性電路之間的非線性耦合關(guān)系。見圖2不同電路的標(biāo)簽。一個(gè)電路是一種大型的電容器并聯(lián)電阻，這一電路是模擬電池充電狀態(tài)和電池自放電。這可以稱為“電容電路”。另一個(gè)電路是一個(gè)電壓源串聯(lián)一個(gè)電容電阻網(wǎng)絡(luò)，這一電路是模擬電池時(shí)域響應(yīng)。這可以稱為“時(shí)域響應(yīng)電路”。 調(diào)整單個(gè)單元模型來(lái)模擬整個(gè)電池組，令Nparallel是眾單元中的一個(gè)并聯(lián)單元，令Nseries 是許多并聯(lián)單元中的串聯(lián)單元，由此構(gòu)成整個(gè)電池組。在時(shí)域響應(yīng)電路中，開路電壓乘以Nseries 。當(dāng)電流在電容電路中流動(dòng)時(shí)，流經(jīng)電流在時(shí)域響應(yīng)電路中為除以Nparallel 。在時(shí)域響應(yīng)電路中，電阻為乘以Nseries Nparallel 并且電容為乘以Nparallel Nseries 。 電池模型的單個(gè)單元擁有的開路電壓為3.3 V，并且在從100%荷電狀態(tài)以1A的恒定電流放電情況下，其容量為837.5 mAh 。將每8個(gè)電池單元并聯(lián)起來(lái)組成一個(gè)并聯(lián)單元，再將74個(gè)這樣的并聯(lián)單元串聯(lián)起來(lái)組成一個(gè)最大電壓為244.2V和容量為6.7Ah的電池組。如此得到的電池組是可以和應(yīng)用在2007款豐田凱美瑞混合動(dòng)力汽車上的電池組相媲美的[19]。 Chen和Rin′con-Mora的電池模型在短時(shí)間內(nèi)用于仿真是十分簡(jiǎn)單的，然而，在以下提供的方式中是比較復(fù)雜的，如；開路電壓隨SOC值的變化；充電損耗和恢復(fù)的暫態(tài)效應(yīng)；以及電量損耗和電量恢復(fù)對(duì)SOC值的依賴性；電池容量隨放電電流的變化等。此外，因?yàn)榇四Ｐ褪且粋€(gè)電氣電路模型，所以很容易并入BEV電動(dòng)汽車模型的電氣系統(tǒng)，并且，這易于代替利用數(shù)學(xué)建模技術(shù)的方法。 該模型的一個(gè)負(fù)面因素是在沒(méi)有設(shè)置任何溫度影響的情況下建模，盡管Chen和Rin′con-Mora陳述了要包含一個(gè)溫度影響模塊并不是難事。對(duì)于電動(dòng)汽車，其溫度會(huì)隨外部環(huán)境條件，電池內(nèi)部耗散熱量和熱化學(xué)反應(yīng)等變化。我們唯一遇到的明確包括溫度依賴性模塊的數(shù)學(xué)模型是Rong 和Pedram 所建立的[15]，但是他們的模型假定的是一個(gè)恒定的放電電流，因此，并不適合我們的BEV電動(dòng)汽車系統(tǒng)。 Chen和Rincon-Mora的模型也能承受超過(guò)額定電流的充電電流，同時(shí)不用考慮電池內(nèi)部增加的電阻值，因?yàn)槠溆绊懞苄?，即使有?nèi)阻，充電后的電量也接近完全充滿電的狀態(tài)。此外，電池的SOH值隨時(shí)間和充電循環(huán)次數(shù)的變化情況也未建立模型。這些負(fù)面因素是可接受的，考慮到在以后的模型中車輛控制系統(tǒng)將要限制電池的最大充電量，并且盡管本文沒(méi)有研究模型的溫度或者SOH值，但他們應(yīng)該不至于太難編入。 2.2 能量控制器 接下來(lái)，純電動(dòng)汽車的一個(gè)重要組成部分是能量轉(zhuǎn)化器。能量轉(zhuǎn)換器在蓄電池和傳動(dòng)電機(jī)/發(fā)電機(jī)之間起著紐帶作用。在行駛過(guò)程模式下，能量轉(zhuǎn)換器控制大部分能量輸入電機(jī)；當(dāng)在再生制動(dòng)的模式下，大部分制動(dòng)能量回流到電池。 通常，升壓或升壓去磁轉(zhuǎn)換器的使用取決于輸出電壓是高于還是低于輸入電壓[20]。通過(guò)改變高頻切換電路的工作周期，從而可以控制電機(jī)的輸出電壓、電流和功率。 圖3 能量控制器框圖 為避免在MapleSim中建立高頻電路模型，我們決定選用一個(gè)簡(jiǎn)單的近似值，該值能作為能量從電池流向電機(jī)的升壓或是升壓去磁轉(zhuǎn)換器，反之亦然。如圖3所示是能量控制器框圖。盡管當(dāng)前模型擁有一個(gè)100%效率的轉(zhuǎn)換器，但一種Hellgren[3]在其論文中所采用的效率更為現(xiàn)實(shí)的模型是可以被采用的。 在輸出循環(huán)中運(yùn)用一種由信號(hào)驅(qū)動(dòng)的電流源，據(jù)此可以測(cè)量輸出電壓和計(jì)算輸出功率。輸入電流是受PID控制器調(diào)整的，以致根據(jù)輸入功率匹配輸出功率。無(wú)論是對(duì)于決定功率流方向的正向電流還是反向電流，該電路都能很好地工作。當(dāng)輸出電壓和輸出電流趨近于零時(shí)，這個(gè)模型解決了一個(gè)簡(jiǎn)單代數(shù)功率轉(zhuǎn)換器“除以零”的問(wèn)題，并且能適應(yīng)變化的輸入輸出阻抗。但是其并未考慮該部件的物理限制，例如：電池的最大充放電率，電機(jī)、電線或是功率電子元件的電壓、電流限制等。 2.3 電機(jī) 本汽車模型中電機(jī)是選用的Modelica直流永磁電機(jī)，該電機(jī)包括內(nèi)電阻，電感和轉(zhuǎn)子轉(zhuǎn)動(dòng)慣量[21]。 電機(jī)的機(jī)械和電氣動(dòng)作是通過(guò)方程1和2進(jìn)行建模，在方程中Ja是電樞慣性，是點(diǎn)數(shù)轉(zhuǎn)角，Vnom, Inom和 fnom分別是電機(jī)公稱電壓、電流和旋轉(zhuǎn)頻率。是電機(jī)軸扭矩，La和Ra分別是電樞電感和電阻。最后，和分別是電機(jī)輸出端電壓和電流。 我們選擇由L.M.C公司[22]生產(chǎn)的型號(hào)為L(zhǎng)EM-200的D127直流永磁電機(jī)模型。然而，我們需要修改電機(jī)的額定電壓和電流以適應(yīng)我們所選電池電壓。這要求我們用不同的線束和改變電機(jī)自身磁體來(lái)得到重繞線圈電機(jī)。 電機(jī)所用到的參數(shù)已在表1中給出。我們可以注意到電機(jī)的電壓和功率均是各自額定值的兩倍。 2.4車輛動(dòng)力學(xué) 我們所使用的車輛模型十分簡(jiǎn)單。其物理參數(shù)基于2007款豐田凱美瑞混合動(dòng)力汽車。因?yàn)槲覀冎魂P(guān)心傳動(dòng)部件的性能，我們不關(guān)心車輛自身的懸架系統(tǒng)或是轉(zhuǎn)向系統(tǒng)。我們運(yùn)用了一個(gè)具有規(guī)定重量的位于斜面上的無(wú)阻力運(yùn)輸車一維模型。驅(qū)動(dòng)電機(jī)與運(yùn)輸車變形車輪通過(guò)9:1的固定轉(zhuǎn)速比變速器進(jìn)行彈性連接。車胎和凱美瑞汽車輪徑相同，型號(hào)為P215/60V R16.0。 方程3描述了電機(jī)旋轉(zhuǎn)和電機(jī)軸轉(zhuǎn)矩關(guān)系。是電機(jī)軸上轉(zhuǎn)矩，m是汽車的整車質(zhì)量，R是驅(qū)動(dòng)輪的半徑，是電機(jī)到車胎的傳動(dòng)比，是電機(jī)主軸的轉(zhuǎn)動(dòng)位移，g是重力加速度常數(shù)，且是傾斜角度。 表2列出了所用到的參數(shù)值。 在本模型中唯一的一種制動(dòng)方式是再生制動(dòng)，在再生制動(dòng)的過(guò)程中，電機(jī)電流反向流動(dòng)，利用車輛的動(dòng)能給蓄電池充電。我們沒(méi)有將反復(fù)充電時(shí)電池的電流限制考慮在內(nèi)。 對(duì)于這個(gè)車輛模型我們附加上了一個(gè)簡(jiǎn)單的地形模型。根據(jù)時(shí)間查表控制地形的傾斜度，該地形是車輛的行駛環(huán)境。有了這樣的地形模型，我們可以仿真電動(dòng)汽車在平原和丘陵地帶的性能。 駕駛循環(huán)系統(tǒng)是一個(gè)車輛理想速度隨時(shí)間的對(duì)照表。PID控制器將理想速度與實(shí)際速度進(jìn)行對(duì)比，并驅(qū)動(dòng)能量控制器輸入傳送動(dòng)力到電機(jī)或是從電機(jī)獲得動(dòng)力，直到車輛的實(shí)際速度和理想速度相匹配。 如圖1總體BEV框圖所示。 2.5數(shù)值仿真 在MapleSim軟件將車輛模型轉(zhuǎn)換成微分方程組過(guò)后，象征性地降低和減少了系統(tǒng)的方程組。然后用減少了的方程求出數(shù)值解以得到最終的輸出數(shù)據(jù)。 MapleSim 是利用自身的非剛性求解器來(lái)仿真我們建立的車輛系統(tǒng)，該非剛性求解器使用一個(gè)Fehlberg fourth-fifth命令四階插值Runge-Kutta 法。我們采用一種絕對(duì)誤差和相對(duì)誤差值均為1e-7的自適應(yīng)時(shí)間步長(zhǎng)，并打開MapleSim的使仿真程序運(yùn)行更快的自身代碼生成能力。這個(gè)模型是在運(yùn)用適合于Linux系統(tǒng)的MapleSim版本3的3兆英特爾Core2 Duo環(huán)境中運(yùn)行的。它被設(shè)定在一個(gè)仿真超過(guò)30秒時(shí)間間隔，并且需10秒鐘實(shí)際時(shí)間才能完成。 3 仿真結(jié)果 圖4是單一電池單元脈沖放電在MapleSim仿真模型和實(shí)際電池單元中的對(duì)照。實(shí)際電池單元數(shù)據(jù)可以從Chen和Rin′con-Mora論文中圖5提取。類似在他們的論文中一樣，我們的模型也不考慮自放電電阻。最初98% SOC值和實(shí)驗(yàn)結(jié)果很接近，直到電池容量耗盡之前都很貼近實(shí)際值。我們的模型要求一個(gè)放電循環(huán)而不僅僅是實(shí)際上看到的電池終端電壓快速下降。 運(yùn)用我們的車輛模型進(jìn)行了兩個(gè)簡(jiǎn)單而直觀的測(cè)試。表3中列出了在驅(qū)動(dòng)循環(huán)系統(tǒng)中應(yīng)用到的參數(shù)。 3.1加速度 我們所做的第一個(gè)測(cè)試是在平坦地形上以硬和軟的加速度模擬車輛的駕駛狀況。由于內(nèi)部損失，如果是軟加速而硬加速，那么蓄電池電動(dòng)車和內(nèi)燃機(jī)車的效率將更高。硬加速循環(huán)和軟加速循環(huán)的初始加速度是不同的，但是最大速度和減速度是相同的。見圖5是駕駛循環(huán)速度隨時(shí)間變化的硬和軟加速曲線圖 圖6為電池SOC值隨時(shí)間變化圖。曾描述該模型沒(méi)有滾動(dòng)阻力。你可以看到硬加速驅(qū)動(dòng)周期以一個(gè)低于軟加速循環(huán)的SOC值結(jié)束加速狀態(tài)。不相同的地方是由于電阻損失來(lái)自于電機(jī)繞組和電池內(nèi)部化學(xué)損失 3.2山地 我們所做的第二個(gè)測(cè)試是測(cè)試汽車上坡和下坡的情況。當(dāng)汽車上坡時(shí)，電池消耗能量并部分轉(zhuǎn)化為汽車重力勢(shì)能，然而，在下坡的時(shí)候，汽車減少的部分重力勢(shì)能轉(zhuǎn)化到電池當(dāng)中。見圖5駕駛循環(huán)速度隨時(shí)間變化的山地循環(huán)曲線。地形循環(huán)非常簡(jiǎn)單：在t=9.5s時(shí)，車輛遇到陡坡，并駛上陡坡，或是在t=20.5s之前從坡度為8度的斜坡上駛下，返回平地。 圖7為這個(gè)測(cè)試中電池SOC值隨時(shí)間變化曲線。在兩種情況下，電池消耗能量使車輛加速，將電池的能量部分轉(zhuǎn)化為車輛的動(dòng)能。 在上坡的情況下，SOC值減小。駕駛控制器應(yīng)用更多能量到電機(jī)以使車輛的速度和理想速度相匹配，并且電池能量轉(zhuǎn)化成了車輛的重力勢(shì)能。 在下坡的情況下，SOC值增加。駕駛控制器應(yīng)用蓄熱式“制動(dòng)”以使車輛保持速度恒定，并且車輛的重力勢(shì)能隨著轉(zhuǎn)化成電能回流到電池中。 最后，汽車運(yùn)動(dòng)到平緩的地點(diǎn)并利用再生制動(dòng)實(shí)現(xiàn)剎車，同時(shí)將車輛動(dòng)能轉(zhuǎn)化到電池中儲(chǔ)存起來(lái)。 3.3驗(yàn)證 在基于能量守恒的原則下我們對(duì)在MapleSim中的仿真結(jié)果和近似計(jì)算結(jié)果做了一下對(duì)比。對(duì)硬和軟加速循環(huán)做了以下幾點(diǎn)對(duì)比：在車輛啟動(dòng)之前和啟動(dòng)后達(dá)到最大速度開始直至再生制動(dòng)以前。因?yàn)檐囕v在平直道路上無(wú)滾動(dòng)阻力地運(yùn)動(dòng)，僅僅包含車輛動(dòng)能和電機(jī)、電池上必須考慮的阻力損失。 見表4，基于能量守恒的近似理論計(jì)算和MapleSim 軟件為硬和軟加速度循環(huán)做的仿真結(jié)果在以下參數(shù)上做的對(duì)比結(jié)果。J——轉(zhuǎn)化到車輛的能量；P——加速全程的平均功率；SOC——電機(jī)和電池上納入考慮的損失中電池的SOC值變化。詳見Appendix A在硬加速驅(qū)動(dòng)循環(huán)計(jì)算中的步驟。 MapleSim仿真結(jié)果與近似理論結(jié)果比較吻合?？紤]到近似理論公式的使用，出現(xiàn)較小的誤差并不奇怪。 4 總結(jié) 我們利用了運(yùn)用MapleSim軟件的基于數(shù)學(xué)的方法模擬了一個(gè)簡(jiǎn)單的蓄電池電動(dòng)汽車。這項(xiàng)技術(shù)減少了汽車開發(fā)時(shí)間，并使系統(tǒng)更接近物理系統(tǒng)。 運(yùn)用一個(gè)基于Chen和Rin′con-Mora的電池模型建立的完整電池組數(shù)學(xué)模型，一個(gè)簡(jiǎn)單的功率控制器模型和一個(gè)標(biāo)準(zhǔn)Modelica直流電機(jī)模型，我們能夠組成一個(gè)BEV傳動(dòng)系統(tǒng)并將其與一個(gè)簡(jiǎn)單的車輛動(dòng)力學(xué)模型聯(lián)系起來(lái)。 通過(guò)運(yùn)用不同的地形條件和駕駛循環(huán)，對(duì)兩個(gè)不同的情景進(jìn)行測(cè)試以比較我們汽車模型的性能和人們期望的實(shí)際汽車的性能。在兩種情況下，得到的測(cè)試結(jié)果和直覺(jué)想象以及近似理論計(jì)算都是想符合的。 基本的描述系統(tǒng)的數(shù)學(xué)方程能用到靈敏度分析、優(yōu)化或是實(shí)時(shí)HIL仿真等運(yùn)用中。 后續(xù)工作將包括給系統(tǒng)增加內(nèi)燃機(jī)作為一個(gè)增程器，增加功率控制器、電機(jī)模型的保真度，增加更復(fù)雜車輛模型、地形模型和駕駛循環(huán)模型 致謝 我們特別感謝豐田公司，MapleSoft公司以及加拿大自然科學(xué)與工程研究委員會(huì)的大力支助和支持！ - 11 - Proceedings of the ASME 2010 International Design Engineering Technical Conferences &Computers and Information in Engineering ConferenceIDETC/CIE 2010August 15-18, 2010, Montreal, Quebec, CanadaDETC2010-28814SYMBOLIC MATH-BASED BATTERY MODELINGFOR ELECTRIC VEHICLE SIMULATIONAden N. SeamanDepartment of Systems Design EngineeringUniversity of WaterlooWaterloo, Ontario, Canada. N2L 3G1Email: anseamanreal.uwaterloo.caJohn McPheeDepartment of Systems Design EngineeringUniversity of WaterlooWaterloo, Ontario, Canada. N2L 3G1Email: mcpheereal.uwaterloo.caABSTRACTWe present results of a math-based model of a battery elec-tric vehicle (BEV) designed in MapleSim1. This model has thebenefits of being described in a physically consistent way us-ing acausal system components. We used a battery model byChenandRin con-Moratodevelopamath-basedmodelof acom-plete battery pack, and developed simple power controller, mo-tor/generator, terrain, and drive-cycle models to test the vehicleunder various conditions. The resulting differential equationsare simplified symbolically and then simulated numerically togive results that are physically consistent and clearly show thetight coupling between the battery and longitudinal vehicle dy-namics.1IntroductionVehiclemodelingisacomplicatedandchallengingtask. Au-tomotive companies release several new vehicles each year, andall of these need to be simulated and tested before they are actu-ally manufactured.With the push towards cleaner and more energy-efficientvehicles, powertrains are incorporating motors, generators,continuously-variable transmissions, energy storage devicessuch as batteries and fuel-cells, and traditional internal combus-tion engines (ICEs).One of the techniques that can ease the growing complex-ity of vehiclemodelingis acausal math-basedmodelingin which1Maple and MapleSim are trademarks of MapleSoftthe system is described using the physics-based equations thatgovern the behaviour of its components. These mathematicalequations are processed symbolically before finally being solvednumerically to generate output data. This approach makes it eas-ier for designers to specify component behaviour, and constrainsthemtodescribecomponentsinamorephysically-consistentlan-guage. This makes it easier to swap or modify components andsimplifies the description of the system 1.The Modelica 2 description language has been used bymany authors 37 to model hybrid electric vehicle systemsacausally, mostly using the Dymola 8 simulation environment.We have chosen to use MapleSim 9 from MapleSoft asour simulation environment, as this allows us to access the un-derlying mathematical equations which govern the system beingsimulated.Thisapproachyieldsasimplifiedequation-baseddescriptionof the system which can be simulated efficiently. The equationscan also be used in real-time simulationfor hardware-in-the-loop(HIL) applications, and can be used in sensitivity analysis andsystem optimization 10,11.In this paper we present the results of a battery electric ve-hicle (BEV) we have modeled using math-based modeling tech-niquesinMapleSim. See Fig.1forablockdiagramoftheoverallBEV system. This is the beginning of a more complex math-based hybrid electric vehicle (HEV) model we aim to developusing symbolic mathematics.We have incorporated a lithium-ion electric-circuit batterymodel by Chen and Rin con-Mora 12 into the BEV system. We1Copyright c ? 2010 by ASMEProceedings of the ASME 2010 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2010 August 15-18, 2010, Montreal, Quebec, Canada DETC2010-? Downloaded 25 Jun 2011 to 113.204.33.35. Redistribution subject to ASME license or copyright; see http:/www.asme.org/terms/Terms_Use.cfmmodified the battery equations to simulate a battery pack com-posed ofseries and parallel combinationsof single cells. Inorderto connect the battery pack to a motor we had to develop a powercontroller model as part of the system integration. We furtherincorporateda simple one-dimensionalvehicle model that driveson an inclined plane, a terrain model that controls the incline,and a drive cycle model that controls the vehicles desired speed.By varying the drive cycle and terrain model, we tested theBEV under various driving conditions.FIGURE 1.BLOCK DIAGRAM OF OVERALL BEV MODEL2System Modeling and SimulationThe technique we decided to use was math-based model-ing using MapleSim as the simulation environment, which has agraphical interface for interconnecting system components. Thesystem model is then processed by the Maple mathematics en-gine, and finally the differential-algebraic equations (DAEs) de-scribing the system are simulated numerically to produce out-put data. For 3D multibody simulation it uses the DynaFlex-Pro engine, which uses linear graph-theory for system simula-tion 1,11.2.1BatteryOne of the most importantcomponentsof an electric vehicle either BEV or HEV is the battery. There are many ways ofmodeling different battery chemistries depending on the fidelityneeded and the battery parameters of interest. See the article byRao et al. 13 for an overview of some of the techniques. Gen-erally, with increasing model accuracy comes increased compu-tational requirements.Some modeling techniquesthat we reviewed were: the lead-acid model of Salameh et al. 14; the mathematical lithium-ionmodel of Rong and Pedram 15 that incorporates state-of-healthand temperature effects; the lumped-parameter model in section3.1 of the Partnership for a New Generation of Vehicles (PNGV)Battery Test Manual 16; the Kalman filtering techniques ofPiller et al. 17; the electrical circuit modelofChen and Rin con-Mora12; andthe impedancemodelof Nelson et al. 18. Thesedifferenttechniqueshavetheirstrengthsandweaknessesandlim-ited ranges of application.There is a great interest in using lithium-ion batteries inelectric vehicles, as they are light and have a higher power-to-weight and power-to-size ratio than Lead-Acid or Nickel-basedbatteries. Great demands are placed on vehicle batteries as thedriver accelerates and brakes regeneratively,putting the batteriesthrough periods of high current draw and recharge. Dependingon the driving environment,the batteries can also be subjected tolarge temperature variations, which can have a significant effecton the batterys performance and lifetime.Thus we needed to model a lithium-ion battery chemistryover a wide state-of-charge (SOC) range, under widely-varyingcurrents, for various temperatures. Since we would eventuallylike to model this vehicle in a hardware-in-the-loop (HIL) sys-tem, we neededa model that was not computationallyexpensive,and we did not require a high-fidelity model.These requirements led us to the electrical circuit model ofChen and Rin con-Mora. We implemented their components inMapleSimandusedacustomfunctionblocktorepresentthenon-linear relationship between the state of charge and the electricalcomponents (Equations 2 to 6 in their paper). See Fig. 2 for ablock diagram of the battery.FIGURE 2.BLOCK DIAGRAM OF SINGLE-CELL BATTERYMODELSince their model is of a single cell, we modified their equa-tions to simulate a battery of cells in parallel and series. TheChen and Rin con-Mora battery can be divided into two linearcircuits with a non-linear coupling between them. See Fig. 2 forlabels of these different circuits. One circuit is a large capaci-tor in parallel with a resistor that models the charge state of thebattery and self-discharge. This can be called the “capacity cir-cuit”. Anothercircuit is a voltage source in series with a resistor-2Copyright c ? 2010 by ASMEDownloaded 25 Jun 2011 to 113.204.33.35. Redistribution subject to ASME license or copyright; see http:/www.asme.org/terms/Terms_Use.cfmcapacitor network that models the time response of the battery.This can be called the “time response circuit”.To adapt their single cell model to simulate an entire bat-tery pack, let Nparallelbe the number of cells in a parallel pack,and let Nseriesbe the number of parallel packs placed in seriesto make the whole battery. The open circuit voltage in the timeresponse circuit is multiplied by Nseries. The current flowing inthe time response circuit is divided by Nparallelwhen it flows inthe capacity circuit. The resistors in the time response circuit aremultipliedbyNseries/NparallelandthecapacitorsaremultipliedbyNparallel/Nseries.A singlecell ofthebatterymodelhas anopen-circuitvoltageof 3.3 V and a capacity of 837.5 mAh at a 1 A discharge ratestarting at 100% state of charge. By placing 8 cells in parallel,and 74 of these parallel packs in series, a 244.2 V, 6.7 Ah batterypack was created. This pack is comparable to that in a 2007Toyota Camry hybrid 19.The Chen and Rin con-Mora battery model is simple enoughto simulate in a short amount of time while being complexenough to provide the following: variations in the open circuitvoltage with SOC; transient effects of charge depletion and re-coveryandtheir dependenceonSOC; andthe variationin batterycapacity with discharge current. Furthermore, since it is an elec-tricalcircuitmodelitcaneasilybeincorporatedintotheelectricalsystem of the BEV model and is amenable to being representedusing math-based modeling techniques.Oneofthedownsidesofthis modelis thatnotemperatureef-fects of any kind are modeled, although Chen and Rin con-Morastate it would not be difficult to include them. In an electric ve-hicle the temperature will vary with external environmental con-ditions, with heating of the battery due to internal losses, andwith endo- and exothermic chemical reactions. The only modelwe encountered that explicitly included temperature dependencewas the mathematical model of Rong and Pedram 15, but theirmodel assumes a constant discharge current and thus is not suit-able for our BEV system.The Chen and Rin con-Mora model can also be overchargedand does not consider the increasing resistance of the battery asit nears a full charge. Furthermore the variations of the batterysstate-of-health (SOH) with time and charge cycles is not mod-eled. These downsides are acceptable given that in future mod-eling the vehicles control system will limit maximum batterycharge,andalthoughinthis paperwe are notinterested inmodel-ingtemperatureorstate-of-health,theyshouldnotbetoodifficultto incorporate.2.2Power ControllerThe next important component of an electric vehicle is apower converter that acts as an interface between the battery andthe drive motor/generator. This component controls the amountof power going to the motor during driving, and the amount ofpower going back into the battery during regenerative braking.Generally, boost or buck converters are used depending onwhether the output voltage is higher or lower, respectively, thanthe input voltage 20. By varying the duty cycle of a high-frequency switching circuit, the output voltage and thus currentand power can be controlled.Insteadof modelingthe highfrequencycircuit in MapleSim,we decided to use a simple approximation that can serve as botha boost or buck converter with power flowing from the batteryto the motor, or vice-versa. Figure 3 is a picture of the powercontrollerblock diagram. Althoughthe currentmodelhas a fixedconverter efficiency of 100%, a more realistic efficiency modelsuch as the one used by Hellgren 3 can be incorporated.FIGURE 3.BLOCK DIAGRAM OF POWER CONTROLLERMODELUsing a signal-driven current source in the output loop, theoutput voltage is measured and the output power is calculated.The input currentis adjusted by a PID controller so that the inputpower matches the output power. This circuit works both forpositive or negative current, which determines the direction ofpower flow. This model avoids the divide-by-zero problem of asimple algebraic power converter when the output voltage andcurrent goes to zero, and adapts to changing input and outputimpedance. However it does not take into consideration physicallimitations of componentssuch as the batterys maximumchargeor discharge rates, and voltage and current limits of the motor,wires, or power electronics.2.3Electrical MotorThe electrical motor used in the vehicle model is the Model-ica DC permanent magnet motor, which includes internal resis-tance, inductance, and rotor inertia 21.Its mechanical and electrical behaviour are modelled byEquations 1 and 2 where Jais the armature inertia,(t) is thearmaturerotationangle,Vnom, Inom, and fnomare the nominalmo-tor voltage, current, and rotational frequency, respectively.(t)is theshafttorque,andLaandRaare thearmatureinductanceand3Copyright c ? 2010 by ASMEDownloaded 25 Jun 2011 to 113.204.33.35. Redistribution subject to ASME license or copyright; see http:/www.asme.org/terms/Terms_Use.cfmresistance, respectively. FinallyV(t), andI(t) arethe voltageandcurrent at the motor terminals, respectively.Ja(t)30(VnomRaInom)I(t)fnom(t) = 0(1)LaI(t)+RaI(t)V(t)+30(VnomRaInom)(t)fnom= 0(2)We chose to use the physical parameters of the LEM-200ModelD127DCpermanentmagnetmotorfromL.M.C.Ltd22.However we modified the rated current and voltage of the motorto be more compatible with our battery voltage. This would ef-fectively require re-winding the motor with different wire andchanging its magnets.The parameters used for the motor are presented in Table 1.Note that the peak current and power of the motor are twice therated value.TABLE 1.MOTOR MODEL PARAMETERSNameValueResistance0.0175 Inductance13HInertia0.0236 kgm2RPMrated3600 rpmVrated150 VIrated96 APrated12.56 kW2.4Vehicle DynamicsThe vehicle model we used was very simple.Its physi-cal parameters were based on the 2007 Toyota Camry hybrid.Since we were concerned only with the performance of the pow-ertrain components, we did not concern ourselves with vehiclesuspension or steering. We used a one-dimensional model of africtionless cart on an incline under the force of gravity. Thedrive motor is connected to one of the slipless wheels of the cartthrough a fixed transmission with a ratio of 9 motor revolutionsper wheel revolution. The wheels have the same diameter as theP215/60VR16.0 tires on the Camry.Equation 3 describes the relationship between the rotationand torqueof the motor shaft.(t) is the torqueseen at the motorshaft, m is the vehicles mass, R is the drive tire radius,is thegear ratio from the motor to the tire,(t) is the motor shaftsrotational displacement, g is the gravitational constant, and(t)is the terrain inclination angle.Table 2 lists the values used for these parameters.(t) =mR?Rd2dt2(t)+gsin(t)?(3)TABLE 2.VEHICLE MODEL PARAMETERSNameSymbolValuemassm1613 kgtire radiusR32.25 cmgear ratio9gravityg9.8 m/s2The only type of braking included in this model is regener-ative braking where the current to the motor is reversed and thebattery is charged with the kinetic energy of the vehicle. We didnot take into consideration recharge current limits of the battery.To this vehicle model we attached a simple terrain model.A time-dependent lookup table controlled the inclination of theterrainonwhich thevehicletraveled. This allowed us to simulatethe vehicles performance on flat and hilly terrain.Thedrivecycle is a time-dependentlookuptable of the vehi-cles desired speed. A PID controllercomparesthe desired speedto the actual speed and drives the input of the power controller totransfer power to the motor, or to extract power from the motoruntil the vehicles speed matches the desired speed.See Fig. 1 for the block diagram of the overall BEV model.2.5Numerical SimulationAfter MapleSim converts the vehicle model into differentialequations, it simplifies and reduces the system of equations sym-bolically. Then using this reduced equation set it solves themnumerically to produce the final output data.MapleSim simulated our system with its non-stiff solver,which uses a Fehlberg fourth-fifth order Runge-Kutta method4Copyright c ? 2010 by ASMEDownloaded 25 Jun 2011 to 113.204.33.35. Redistribution subject to ASME license or copyright; see http:/www.asme.org/terms/Terms_Use.cfmwith degree four interpolant.We used an adaptive time-stepwith absolute and relative error tolerances of 1e-7, and turned onMapleSims native code generation ability which runs the sim-ulation faster. The model was simulated on a 3 GHz Intel Core2 Duo using MapleSim version 3 for Linux. It was set to simu-late over a 30 second time interval, and took 10 seconds of actualtime to complete.3Results0500010000150002000025000Time (s)33.23.43.63.844.2Voltage (V)ModeledActualFIGURE 4.MODELED-VS-ACTUAL 12 BATTERY UNDERPULSED CONSTANT-CURRENT DISCHARGEFigure 4 is a comparison between the MapleSim model andan actual cell for a pulsed current discharge of a single batterycell. The actual cell data was extracted from Fig. 5 of Chenand Rin con-Moras paper. Like the model in their paper, ourmodel does not include a self-discharge resistor. An initial SOCof 98% gives a close match to the experimental results, trackingthem very well until the battery capacity is almost exhausted.Our model requires one discharge cycle more than the actual tosee a rapid collapse in the battery terminal voltage.Using our vehicle model we performedtwo simple and intu-itive tests. Table 3 lists the parameters used in the drive cycles.3.1AccelerationsThe first test we did was to simulate the vehicle driving un-der hard and gentle accelerations on flat terrain. Battery and in-ternal combustion engine vehicles are more efficient if gentle ac-celeration is used compared to hard acceleration, due to internallosses. The initial accelerations of the hard and gentle cycles aredifferent,but the maximumspeed and rate of decelerationare thesame. See the hard and gentle curves of Fig. 5 for a plot of thedrive cycle speed with time.TABLE 3.DRIVE CYCLE AND TERRAIN MODEL PARAME-TERSNameValueVmax9 m/sahard1.607 m/s2agentle0.968 m/s2hill height8.67 mhill angle8Figure 6 plots the batterys state of charge versus time. Re-call that this model is without rollingresistance. One can see thatthe hard acceleration drive cycle ends up with a lower final stateof charge than the gentle cycle. This difference is due to ohmiclosses in the motor windings and chemical losses in the battery.3.2HillsThe second test we did was to drive the vehicle up and downa hill. The battery should lose energy going uphill as the vehi-cle gains gravitational potential energy, and gain energy goingdownhill as the vehicle loses potential energy. See the hill cyclecurve of Fig. 5 for a plot of the drive cycle speed with time. Theterrain cycle is very simple: at t=9.5 s the vehicle encounters thehill, then it drives up or down an 8incline before returning toflat terrain at t=20.5 s.Figure 7 plots the batterys state of charge versus time forthis test. In both cases the battery loses energy as it accelerates051015202530Time (s)0123456789Velocity (m/s)Hard & Hill cyclesGentle cycleFIGURE 5.DRIVE CYCLE: SPEED-VS-TIME FOR HARD, GEN-TLE, AND HILL CYCLES5Copyright c ? 2010 by ASMEDownloaded 25 Jun 2011 to 113.204.33.35. Redistribution subject to ASME license or copyright; see http:/www.asme.org/terms/Terms_Use.cfmthe vehicle, transferring energy from the battery to the vehicleskinetic energy.In the uphill case the state of charge decreases. The drivecontrollerappliesmore powerto the motorto match the vehiclesspeed tothe desiredspeed, and thebatterys energyis put intothevehicles gravitational potential energy.In the downhill case the state of charge increases. The drivecontroller applies the regenerative “brakes” to keep the vehiclesspeed constant, and the vehicles gravitational potentialenergyistransferred to the battery.Finally the vehicle encounters a flat spot and uses regenera-tive braking to come to a halt, transferring the vehicles kineticenergy to the battery.051015202530Time (s)78.87979.279.479.679.880State of Charge (%)Gentle startHard startFIGURE 6.STATE OF CHARGE FOR HARD AND GENTLE AC-CELERATIONS ON FLAT TERRAIN051015202530Time (s)76777879808182State Of Charge (%)DownhillUphillFIGURE 7.S