左曙光，李多強(qiáng)，毛 鈺，鄧文哲，吳旭東

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考慮機(jī)電耦合的電動(dòng)輪系統(tǒng)縱向振動(dòng)特性建模及驗(yàn)證

左曙光，李多強(qiáng)，毛 鈺，鄧文哲，吳旭東※

（同濟(jì)大學(xué)新能源汽車工程中心，上海 201804）

為了研究機(jī)電耦合對(duì)電動(dòng)輪系統(tǒng)的縱向振動(dòng)特性的影響，該文首先建立了電動(dòng)輪縱扭耦合動(dòng)力學(xué)模型，基于該模型分析了考慮機(jī)電耦合前后電動(dòng)輪系統(tǒng)模態(tài)特征的變化，并通過輪轂電機(jī)驅(qū)動(dòng)電動(dòng)輪系統(tǒng)的振動(dòng)特性試驗(yàn)，驗(yàn)證了該動(dòng)力學(xué)解析模型的準(zhǔn)確性；其次分析了機(jī)電耦合對(duì)電動(dòng)輪系統(tǒng)縱向振動(dòng)的影響，指出轉(zhuǎn)矩波動(dòng)引起定轉(zhuǎn)子發(fā)生相對(duì)運(yùn)動(dòng)，導(dǎo)致電機(jī)發(fā)生偏心，從而產(chǎn)生不平衡磁拉力。不平衡磁拉力的作用導(dǎo)致非簧載部分縱向振動(dòng)出現(xiàn)不同程度的惡化，當(dāng)軸承剛度為12.5 MN/m時(shí)，在定子縱向平移模態(tài)頻率下電機(jī)的定轉(zhuǎn)子、輪胎縱向振動(dòng)加速度分別惡化113.35%、105.69%、27.15%，影響其使用壽命和結(jié)構(gòu)安全，而對(duì)于簧載部分縱向振動(dòng)的影響較小。

車輛；振動(dòng)；模型；機(jī)電耦合；電動(dòng)輪；轉(zhuǎn)矩波動(dòng)；不平衡磁拉力

0 引 言

近年來，隨著電動(dòng)汽車的興起，其關(guān)鍵部件電動(dòng)輪系統(tǒng)成為開發(fā)研究的核心[1-3]。針對(duì)電動(dòng)輪一懸架系統(tǒng)振動(dòng)特性，目前的研究尚不充分，文獻(xiàn)[4-6]考慮了輪轂電機(jī)與輪胎之間的耦合動(dòng)力學(xué)關(guān)系但是分析對(duì)象是路面激勵(lì)下考慮增加電機(jī)質(zhì)量對(duì)垂向振動(dòng)的影響，分析頻率較低，采用的輪胎模型也較為簡(jiǎn)單，均不能反映輪轂電機(jī)高頻轉(zhuǎn)矩激勵(lì)下的電動(dòng)輪振動(dòng)特性。

電動(dòng)輪系統(tǒng)中的輪轂電機(jī)受到高頻轉(zhuǎn)矩波動(dòng)的作用，導(dǎo)致縱向振動(dòng)上的問題相對(duì)于垂向更顯著[7]。張立軍等[8]基于輪轂電機(jī)-輪胎總成非線性動(dòng)力學(xué)模型分析了輪轂電機(jī)轉(zhuǎn)矩波動(dòng)引起的輪胎縱向接地力的階次振蕩。毛鈺等[7]通過臺(tái)架試驗(yàn)揭示了電動(dòng)輪系統(tǒng)縱向振動(dòng)的階次特征和高頻特性，基于剛性環(huán)理論的建立了電動(dòng)輪系統(tǒng)的動(dòng)力學(xué)模型，并進(jìn)行了模態(tài)分析，通過理論解釋了電動(dòng)輪高頻振動(dòng)現(xiàn)象。上述文獻(xiàn)在分析電動(dòng)輪系統(tǒng)的縱向振動(dòng)時(shí)，將電機(jī)作為一個(gè)整體進(jìn)行建模，然而實(shí)際運(yùn)行過程中電動(dòng)輪系統(tǒng)是一個(gè)復(fù)雜的機(jī)電耦合系統(tǒng)。

電動(dòng)輪系統(tǒng)的縱向振動(dòng)引起輪轂電機(jī)的定轉(zhuǎn)子發(fā)生相對(duì)運(yùn)動(dòng)，導(dǎo)致徑向氣隙不再均勻，進(jìn)而產(chǎn)生不平衡磁拉力（unbalanced magnetic pull，UMP）直接作用于在電動(dòng)輪系統(tǒng)電機(jī)的定轉(zhuǎn)子上，這將導(dǎo)致電動(dòng)輪系統(tǒng)的縱向振動(dòng)特性發(fā)生改變。此外不平衡磁拉力會(huì)進(jìn)一步加劇徑向氣隙不均勻性，因此考慮機(jī)電耦合產(chǎn)生的不平衡磁拉力對(duì)電動(dòng)輪系統(tǒng)的振動(dòng)影響尤為重要。

Tan 等[9-10]分析了由輪轂電機(jī)產(chǎn)生不平衡磁拉力對(duì)電動(dòng)汽車的橫向和垂向耦合動(dòng)力學(xué)的影響，指出不平衡磁拉力不同程度惡化垂向和橫向的振動(dòng)，在設(shè)計(jì)輪轂電機(jī)驅(qū)動(dòng)電動(dòng)汽車時(shí)，不平衡磁拉力必須作為一個(gè)重要的考慮因素；Wang等[11-12]分析了開關(guān)磁阻電機(jī)（switched reluctance motor，SRM）不平衡磁拉力與路面激勵(lì)相耦合下的車輛的垂向振動(dòng)，指出SRM不平衡磁拉力與路面激勵(lì)和開關(guān)磁阻電機(jī)氣隙偏心高度耦合，這種耦合效應(yīng)惡化了車輛垂向振動(dòng)。文獻(xiàn)[9-12]指出不平衡磁拉力對(duì)于電動(dòng)輪系統(tǒng)的振動(dòng)具有重要影響，然而他們都是針對(duì)機(jī)電耦合產(chǎn)生的不平衡磁拉力對(duì)垂向和橫向振動(dòng)特性的研究，鮮有學(xué)者考慮不平衡磁拉力對(duì)系統(tǒng)縱向振動(dòng)特性的影響。因此研究考慮機(jī)電耦合產(chǎn)生的不平衡磁拉力對(duì)于電動(dòng)輪系統(tǒng)的縱向振動(dòng)的影響是十分必要的。

為研究機(jī)電耦合產(chǎn)生不平衡磁拉力對(duì)電動(dòng)輪系統(tǒng)的縱向振動(dòng)特性的影響，本文首先建立了電動(dòng)輪縱扭耦合動(dòng)力學(xué)模型，基于該模型分析了考慮機(jī)電耦合前后電動(dòng)輪系統(tǒng)模態(tài)特征的變化，并通過輪轂電機(jī)驅(qū)動(dòng)電動(dòng)輪系統(tǒng)的振動(dòng)特性試驗(yàn)，驗(yàn)證了該動(dòng)力學(xué)解析模型的準(zhǔn)確性；隨后基于建立的動(dòng)力學(xué)模型分析了機(jī)電耦合產(chǎn)生的不平衡磁拉力對(duì)電動(dòng)輪系統(tǒng)縱向振動(dòng)的影響。

1 考慮機(jī)電耦合的電動(dòng)輪系統(tǒng)縱向動(dòng)力學(xué)建模及模態(tài)分析

1.1 電動(dòng)輪系統(tǒng)縱向動(dòng)力學(xué)建模及模態(tài)分析

由前期研究可知[13]轉(zhuǎn)矩波動(dòng)會(huì)通過輪胎與路面的附著作用引起縱向接地力波動(dòng)進(jìn)而激發(fā)電動(dòng)輪縱向振動(dòng)，即電動(dòng)輪在電機(jī)轉(zhuǎn)矩波動(dòng)激勵(lì)下主要表現(xiàn)為扭轉(zhuǎn)和縱向振動(dòng)，又因?yàn)殡姍C(jī)轉(zhuǎn)矩波動(dòng)具有明顯的階次特性[14-15]。因此為了能夠反映輪轂電機(jī)高頻轉(zhuǎn)矩波動(dòng)激勵(lì)下的電動(dòng)輪振動(dòng)特性，建立電動(dòng)輪系統(tǒng)縱扭耦合動(dòng)力學(xué)模型如圖1所示。輪胎和電機(jī)轉(zhuǎn)子通過胎側(cè)連接，胎側(cè)等效為扭轉(zhuǎn)剛度和縱向平移剛度；電機(jī)定子經(jīng)懸架擺臂及襯套與車身在縱向連接；電機(jī)定子與轉(zhuǎn)子通過軸承連接；輪胎扭轉(zhuǎn)自由度和縱向平移自由度通過考慮輪胎松弛特性的瞬態(tài)刷子模型實(shí)現(xiàn)耦合。

圖1 電動(dòng)輪系統(tǒng)縱扭耦合動(dòng)力學(xué)模型

現(xiàn)有的文獻(xiàn)在分析電動(dòng)輪系統(tǒng)的縱向振動(dòng)時(shí)時(shí)通常將電機(jī)的定轉(zhuǎn)子視為整體[16-18]。而實(shí)際運(yùn)行過程中電動(dòng)輪系統(tǒng)是一個(gè)復(fù)雜的機(jī)電耦合系統(tǒng)。為了考慮電動(dòng)輪系統(tǒng)的機(jī)電耦合特性，首先需要建立考慮定轉(zhuǎn)子分開的電動(dòng)輪縱向動(dòng)力學(xué)方程，如式（1）所示。

式中x、x、x為輪胎、輪輞/電機(jī)轉(zhuǎn)子和電機(jī)定子縱向位移，m；θ、θ為電機(jī)轉(zhuǎn)子和輪胎旋轉(zhuǎn)角，rad；F為輪胎縱向力，N。電動(dòng)輪模型參數(shù)如表1所示。

上述模型忽視了機(jī)電耦合產(chǎn)生的不平衡磁拉力?？紤]機(jī)電耦合后，電動(dòng)輪系統(tǒng)的縱向振動(dòng)引起輪轂電機(jī)的定轉(zhuǎn)子發(fā)生相對(duì)運(yùn)動(dòng)，導(dǎo)致徑向氣隙不再均勻，進(jìn)而產(chǎn)生不平衡磁拉力直接作用于在電動(dòng)輪系統(tǒng)電機(jī)的定轉(zhuǎn)子上，導(dǎo)致電動(dòng)輪系統(tǒng)的縱向動(dòng)力學(xué)模型發(fā)生了變化。圖2為輪轂電機(jī)縱向偏心的示意圖。

因?yàn)殍F芯材料的磁導(dǎo)率遠(yuǎn)遠(yuǎn)大于空氣的磁導(dǎo)率，磁力線進(jìn)出定子、轉(zhuǎn)子鐵芯時(shí)基本垂直于鐵芯表面。因此對(duì)本文研究的徑向電機(jī)，氣隙磁通密度的切向分量遠(yuǎn)遠(yuǎn)小于徑向分量，可以忽略不計(jì)。所以根據(jù)麥克斯韋張量方程，切向的電磁力f為0，徑向電磁力f可近似表示為

式中B(,)為電機(jī)的徑向磁密，T；0為真空磁導(dǎo)率。

注：x、z表示坐標(biāo)軸；e表示電機(jī)的偏心量，mm；α表示徑向電磁力與x軸的夾角，rad。

將徑向電磁力沿圓周積分后并化簡(jiǎn)得到總的不平衡磁拉力UMP為

式中l為電機(jī)軸向長(zhǎng)度，m；為電機(jī)氣隙半徑，m。

該電動(dòng)輪系統(tǒng)采用的輪轂電機(jī)為分?jǐn)?shù)槽集中繞組的外轉(zhuǎn)子永磁同步電機(jī)，其參數(shù)如表2所示。圖3為有限元建立有限元模型仿真得出的不平衡磁拉力與縱向偏心間關(guān)系，可知該不平衡的磁拉力與偏心量的大小成正比，而偏心量等于定轉(zhuǎn)子的相對(duì)位移。則不平衡磁拉力可以表示為

式中k為電磁剛度，其大小等于曲線的斜率3.25 MN/m。

表2 永磁同步電機(jī)參數(shù)

圖3 不平衡磁拉力與縱向偏心的關(guān)系

在實(shí)際中，不平衡磁拉力以一對(duì)相互作用力的形式，作用在電機(jī)的定轉(zhuǎn)子上。此時(shí)考慮機(jī)電耦合產(chǎn)生的不平衡磁拉力后的電動(dòng)輪縱向動(dòng)力學(xué)方程如式（5）所示。

將式（1）和（5）表達(dá)成狀態(tài)空間形式，根據(jù)線性系統(tǒng)理論求解出特征值與特征向量，在Matlab中通過振型歸一化和無量綱化判斷振型特征，分析結(jié)果如表3所示。

表3 電動(dòng)輪模態(tài)參數(shù)

由表3可以看出，考慮機(jī)電耦合產(chǎn)生的不平衡磁拉力后，電動(dòng)輪系統(tǒng)的各階振型特征不變，但表現(xiàn)為定子的縱向平移的第五階模態(tài)頻率下降，由130.08降為112.34 Hz，其余階模態(tài)頻率幾乎保持不變。這是因?yàn)椴黄胶獯爬?duì)于電機(jī)的定轉(zhuǎn)子來說是外力，對(duì)于車身和輪胎是內(nèi)力，所以系統(tǒng)的第五階模態(tài)即振型為定子的縱向平移對(duì)應(yīng)的模態(tài)頻率受影響較大。

1.2 試驗(yàn)驗(yàn)證

為驗(yàn)證輪轂電機(jī)驅(qū)動(dòng)電動(dòng)汽車在驅(qū)動(dòng)電機(jī)轉(zhuǎn)矩波動(dòng)激勵(lì)下振動(dòng)特性研究所建解析模型的準(zhǔn)確性，本文通過某電動(dòng)汽車電動(dòng)輪系統(tǒng)的臺(tái)架試驗(yàn)進(jìn)行了驗(yàn)證。該四分之一電動(dòng)輪系統(tǒng)采用雙橫臂懸架，安裝在課題組開發(fā)的懸架試驗(yàn)臺(tái)架上[19]，輪胎直接與轉(zhuǎn)鼓相接觸，如圖4所示。試驗(yàn)過程中輪胎由輪轂電機(jī)驅(qū)動(dòng)，并通過轉(zhuǎn)鼓施加負(fù)載以模擬車輛行駛過程中的阻力。通過加速度傳感器采集了輪胎的縱向加速度信號(hào)。

圖4 電動(dòng)輪臺(tái)架試驗(yàn)布置

試驗(yàn)工況設(shè)定為電機(jī)驅(qū)動(dòng)轉(zhuǎn)矩60 N·m，轉(zhuǎn)速在30 s內(nèi)由0加速到300 r/min。圖5為試驗(yàn)獲取的輪胎縱向加速度的時(shí)頻圖。

由圖5可知，輪胎振動(dòng)表現(xiàn)出階次特征，主要階次為1、5、5.5、6、6.5等，其中6階振動(dòng)最為明顯，主要是由于電機(jī)的6階轉(zhuǎn)矩波動(dòng)引起的。汽車從0起步加速到30 km/h時(shí)，電機(jī)轉(zhuǎn)速從0加速到300 r/min，轉(zhuǎn)矩波動(dòng)頻率可以達(dá)到360 Hz，因此本文的激勵(lì)頻率超過了100 Hz。這里涉及的階次均相對(duì)于電流基頻（轉(zhuǎn)頻與極對(duì)數(shù)的乘積），6階表示電流基頻的6倍頻。另外從圖5中可以看出在整個(gè)頻段內(nèi)輪胎的縱向振動(dòng)存在著3個(gè)明顯的共振區(qū)。提取輪胎縱向振動(dòng)時(shí)頻圖中6階振動(dòng)切片如圖6所示，3個(gè)共振區(qū)對(duì)應(yīng)的頻率分別位于48、94及141 Hz，這與表3中通過解析模型計(jì)算獲取的模態(tài)頻率相接近，從而驗(yàn)證了電動(dòng)輪系統(tǒng)縱向動(dòng)力學(xué)解析模型的準(zhǔn)確性。同時(shí)可以看出，輪胎振動(dòng)顯著的頻段為0～150 Hz，高于150 Hz的頻段內(nèi)振動(dòng)幅值較小。因此本文分析的主要頻率在150 Hz以內(nèi)，而所建解析模型能夠反映該頻段的振動(dòng)特性，可進(jìn)一步用于電動(dòng)輪系統(tǒng)的縱向動(dòng)力學(xué)分析。

圖6 輪胎6階縱向振動(dòng)加速度

2 考慮機(jī)電耦合的電動(dòng)輪系統(tǒng)縱向振動(dòng)特性分析

2.1 電動(dòng)輪系統(tǒng)機(jī)電耦合下不平衡磁拉力

分析振動(dòng)來源[20]可知，轉(zhuǎn)矩波動(dòng)具有明顯的階次特征。轉(zhuǎn)矩波動(dòng)包括電機(jī)繞組不通電時(shí)永磁體和定子開槽相互作用產(chǎn)生的齒槽轉(zhuǎn)矩和由永磁體和電樞反應(yīng)磁場(chǎng)共同作用產(chǎn)生的電磁轉(zhuǎn)矩脈動(dòng)兩部分。由文獻(xiàn)[21-23]可知齒槽轉(zhuǎn)矩的脈動(dòng)頻率為電機(jī)極槽最小公倍數(shù)的整數(shù)倍轉(zhuǎn)頻，由文獻(xiàn)[24-26]可知電磁轉(zhuǎn)矩脈動(dòng)頻率為6（為極對(duì)數(shù)）的整數(shù)倍轉(zhuǎn)頻。對(duì)于本文研究的24極27槽電機(jī)來說，其齒槽轉(zhuǎn)矩的頻率為216f，電磁轉(zhuǎn)矩波動(dòng)的頻率為72f（f為電機(jī)的轉(zhuǎn)頻、為整數(shù)）。由文獻(xiàn)[14]可知，轉(zhuǎn)矩波動(dòng)的基波對(duì)縱向振動(dòng)特性的影響較大，所以為便于后續(xù)分析考慮機(jī)電耦合產(chǎn)生的不平衡磁拉力對(duì)電動(dòng)輪系統(tǒng)縱向振動(dòng)的影響，電動(dòng)輪系統(tǒng)輸入激勵(lì)為轉(zhuǎn)矩

為反映電動(dòng)輪系統(tǒng)在整個(gè)轉(zhuǎn)速范圍內(nèi)的動(dòng)力學(xué)特性，分析輪轂電機(jī)加速工況下氣隙的變化如圖7a所示，圖7b展示了由氣隙變化產(chǎn)生的不平衡磁拉力。

由圖7可知，轉(zhuǎn)矩波動(dòng)引起定轉(zhuǎn)子發(fā)生相對(duì)運(yùn)動(dòng)，即氣隙發(fā)生變化，導(dǎo)致電機(jī)發(fā)生偏心，產(chǎn)生不平衡磁拉力。當(dāng)軸承的剛度為12.5 MN/m時(shí)，輪轂電機(jī)氣隙最大偏心率達(dá)3.5%，不平衡磁拉力的最大值達(dá)119 N。對(duì)比分析發(fā)現(xiàn)不平衡磁拉力亦會(huì)加劇氣隙的變化，二者存在很強(qiáng)的正相關(guān)性；齒槽轉(zhuǎn)矩與不平衡磁拉力共同作用是氣隙在低頻段變化的主要原因，高頻段則主要受電樞與永磁體磁場(chǎng)相互作用產(chǎn)生的轉(zhuǎn)矩波動(dòng)與不平衡磁拉力的共同影響。

圖7 輪轂驅(qū)動(dòng)電機(jī)的氣隙變化及不平衡磁拉力

2.2 不平衡磁拉力對(duì)電動(dòng)輪系統(tǒng)縱向振動(dòng)特性影響

人體對(duì)低頻的縱向振動(dòng)較為敏感，因此車身在2～3 Hz附近的縱向振動(dòng)將顯著影響輪轂電機(jī)驅(qū)動(dòng)電動(dòng)汽車的乘坐舒適性。對(duì)于電動(dòng)輪系統(tǒng)，由于轉(zhuǎn)矩波動(dòng)的作用，輪胎滑移率會(huì)在中高頻附近出現(xiàn)顯著波動(dòng)，中頻波動(dòng)難以準(zhǔn)確測(cè)量或估計(jì)，進(jìn)而使滑移率的辨識(shí)的存在誤差，對(duì)車輛縱向動(dòng)力學(xué)控制（如ABS，TCS等）有顯著影響[27-29]。在電機(jī)的諸多失效形式中，電機(jī)長(zhǎng)時(shí)間工作在中高頻激勵(lì)下引起的結(jié)構(gòu)件（諸如軸承、定轉(zhuǎn)子等）疲勞破壞是主要貢獻(xiàn)之一[30]。為分析考慮機(jī)電耦合產(chǎn)生不平衡磁拉力對(duì)車輛舒適性、電機(jī)結(jié)構(gòu)穩(wěn)定性、縱向滑移率辨識(shí)等影響，仿真得出加速工況下車身、電機(jī)定轉(zhuǎn)子和輪胎縱向加速度時(shí)域圖，進(jìn)而通過短時(shí)傅里葉變換得到對(duì)應(yīng)的頻域結(jié)果如圖8至圖11所示。

注：圖中兩條曲線近似重合。

圖9 定子縱向振動(dòng)加速度

圖10 轉(zhuǎn)子縱向振動(dòng)加速度

由圖8到圖11可知：考慮機(jī)電耦合產(chǎn)生的不平衡磁拉力對(duì)系統(tǒng)的第五階模態(tài)影響較大，表現(xiàn)為頻率下降，且電機(jī)定轉(zhuǎn)子的振動(dòng)幅值在此階模態(tài)處增大許多，即電機(jī)及定轉(zhuǎn)子的縱向振動(dòng)由第五階貢獻(xiàn)增多，因?yàn)殡妱?dòng)輪系統(tǒng)的第五階模態(tài)表現(xiàn)為定子的縱向平移。而機(jī)電耦合產(chǎn)生的不平衡磁拉力對(duì)于車身及輪胎的縱向振動(dòng)影響相對(duì)較小。為定量分析不平衡磁拉力對(duì)車身及簧下部件縱向振動(dòng)的影響，分別取=108.4、93.62 r/min，此時(shí)轉(zhuǎn)矩波動(dòng)頻率分別與考慮機(jī)電耦合產(chǎn)生不平衡磁拉力前后第五階所對(duì)應(yīng)的模態(tài)一致，仿真獲取各響應(yīng)量縱向振動(dòng)加速度均方根值如表4所示。

注：圖11a中，僅在1.7、2.6、5.1 s時(shí)，考慮不平衡磁拉力略大于不考慮不平衡磁拉力的輪胎縱向振動(dòng)加速度；其余時(shí)間段輪胎縱向振動(dòng)加速度幾乎相等。

表4 縱向振動(dòng)加速度惡化程度

注：a表示車身縱向振動(dòng)加速度，m·s-2；a表示轉(zhuǎn)子縱向振動(dòng)加速度，m·s-2；a表示定子縱向振動(dòng)加速度，m·s-2；a表示輪胎縱向振動(dòng)加速度，m·s-2。

Note:aindicates longitudinal vibration acceleration of vehicle body, m·s-2;aindicates longitudinal vibration acceleration of rotor, m·s-2;aindicates longitudinal vibration acceleration of stator, m·s-2; aindicates longitudinal vibration acceleration of tire, m·s-2.

由表4可知，機(jī)電耦合產(chǎn)生的不平衡磁拉力使電機(jī)的定轉(zhuǎn)子、輪胎在第五階模態(tài)頻率處的縱向振動(dòng)加速度都不同程度的增大，分別增加113.35%、105.69%、27.15%，對(duì)于車身縱向振動(dòng)加速度幾乎無影響。

在電動(dòng)輪系統(tǒng)中，由于輪轂電機(jī)驅(qū)動(dòng)的輪胎/車輪等動(dòng)力學(xué)結(jié)構(gòu)存在柔性，反作用于電機(jī)的負(fù)載轉(zhuǎn)矩在45.41及94.28 Hz處使定轉(zhuǎn)子及輪胎縱向振動(dòng)比較顯著，且電機(jī)長(zhǎng)時(shí)間工作下的中高頻激勵(lì)將引起結(jié)構(gòu)件的疲勞破壞，故分析系統(tǒng)在第三、四階模態(tài)下，即轉(zhuǎn)速=37.85、78.75 r/min時(shí)，機(jī)電耦合產(chǎn)生的不平衡磁拉力對(duì)簧下部件縱向振動(dòng)的影響。機(jī)電耦合產(chǎn)生的不平衡磁拉力使電機(jī)的定子、輪胎縱向振動(dòng)加速度在第三階模態(tài)頻率處分別增加6.14%、2.84%，對(duì)轉(zhuǎn)子縱向振動(dòng)加速度幾乎無影響；在第四階模態(tài)頻率處使電機(jī)的轉(zhuǎn)子、定子、輪胎縱向振動(dòng)加速度分別增加21.94%、64.89%、5.71%。

因?yàn)楸疚闹饕紤]機(jī)電耦合對(duì)電動(dòng)輪系統(tǒng)的縱向振動(dòng)特性影響，由模態(tài)頻率分析發(fā)現(xiàn)只有在定子的縱向平移的振動(dòng)特征的模態(tài)頻率有所下降。這是因?yàn)椴黄胶獯爬?duì)于電機(jī)的定轉(zhuǎn)子來說是外力,直接作用在定轉(zhuǎn)子上，對(duì)于車身和輪胎是內(nèi)力，所以振型為定子的縱向平移對(duì)應(yīng)的模態(tài)頻率變化較大。在電機(jī)結(jié)構(gòu)中，定轉(zhuǎn)子只由軸承這一物理結(jié)構(gòu)直接相連，所以模型參數(shù)中只有軸承剛度的改變對(duì)于考慮機(jī)電耦合產(chǎn)生的不平衡磁拉力影響較大，進(jìn)而影響該電動(dòng)輪系統(tǒng)的縱向振動(dòng)特性。由文獻(xiàn)[31]可知，軸承的安裝剛度一般在12.5～22.5 MN/m，因此在不同軸承剛度下，仿真獲取了激勵(lì)頻率分別為考慮機(jī)電耦合前后定子縱向平移模態(tài)的頻率時(shí)簧下質(zhì)量縱向振動(dòng)加速度的均方根值，分析了不同剛度下簧下質(zhì)量縱向振動(dòng)的惡化程度，結(jié)果如圖12所示。

圖12 不同軸承剛度下簧下質(zhì)量縱向振動(dòng)加速度惡化情況

由圖12可知在實(shí)際軸承的安裝剛度范圍內(nèi)，考慮機(jī)電耦合后，簧下質(zhì)量的縱向振動(dòng)加速度出現(xiàn)不同程度的惡化，影響其使用壽命和結(jié)構(gòu)安全。

3 結(jié) 論

本文建立了考慮機(jī)電耦合產(chǎn)生不平衡磁拉力的電動(dòng)輪縱向動(dòng)力學(xué)模型，并分析了考慮前后模態(tài)特征的變化；研究了在轉(zhuǎn)矩波動(dòng)輸入下，機(jī)電耦合產(chǎn)生不平衡磁拉力對(duì)電動(dòng)輪系統(tǒng)縱向振動(dòng)特性的影響，得出以下結(jié)論：

1）基于電動(dòng)輪縱扭耦合動(dòng)力學(xué)模型，分析考慮機(jī)電耦合后，電動(dòng)輪系統(tǒng)各階模態(tài)的變化規(guī)律：表現(xiàn)為定子的縱向平移的振動(dòng)特征的模態(tài)頻率下降，其余階模態(tài)頻率幾乎保持不變。

2）當(dāng)軸承剛度為12.5 MN/m時(shí)，機(jī)電耦合產(chǎn)生的不平衡磁拉力使定子縱向平移模態(tài)頻率下電機(jī)的定轉(zhuǎn)子、輪胎縱向振動(dòng)加速度分別惡化113.35%、105.69%、27.15%；在其余軸承剛度下，機(jī)電耦合導(dǎo)致簧下質(zhì)量的縱向振動(dòng)亦出現(xiàn)了較大程度的惡化，使其控制難度加大，并嚴(yán)重影響其使用壽命和結(jié)構(gòu)安全。因此在電動(dòng)汽車的開發(fā)中考慮機(jī)電耦合產(chǎn)生的不平衡磁拉力很有必要。

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Modeling and validation on longitudinal vibration characteristics of electric wheel system considering electromechanical coupling

Zuo Shuguang, Li Duoqiang, Mao Yu, Deng Wenzhe, Wu Xudong※

(201804,)

Recently, distributed-drive electric vehicle has become one of the development directions of future vehicle with the advantage of miniaturization and high performance. The electric wheel system is a key component of distributed-drive electric vehicle. The longitudinal dynamics of electric wheel system caused by torque ripple of the in-wheel motor is more significant than vertical. The existing studies on longitudinal vibration analysis of electric wheel system are always taking stator and rotor as a whole. Actually, the electric wheel is a complicated electromechanical coupling system. The longitudinal vibration of electric wheel system causes the relative displacement of rotor and stator, resulting in unbalanced magnetic pull (UMP) that acts on the surface of rotor and stator. The induced UMP by electromechanical coupling changes the characteristics of the longitudinal vibration and deteriorates the performance of the electric wheel system further. Therefore, it is important to consider the effects of UMP caused by electromechanical coupling on the longitudinal vibration of the electric wheel system. Longitudinal vibration characteristics of an electric wheel system considering electromechanical coupling was studied in this paper. Firstly, the electric wheel longitudinal-tensional coupling dynamic model was established, and the variation of the modal characteristics for the electric wheel system with and without electromechanical coupling was analyzed. It needs to indicate that the modal shapes of the electric wheel system are identical considering the UMP, but the fifth order modal frequency is decreased obviously. This mode was characterized as the longitudinal translation of the stator. The accuracy of the analytical dynamic model was verified through vibration test of a one-quarter electric wheel system. The electric wheel system adopted a double-wishbone suspension and was installed on the experiment bench developed by the research group. During the test, the tire was driven by the in-wheel motor and directly contacted with the drum. The load on the tire was exerted by the drum to simulate the resistance in the course of vehicle running. The longitudinal acceleration of tire was measured by an acceleration sensor. Time frequency map of the tire longitudinal vibration was then extracted. Three main resonance regions could be found near 48, 94 and 141 Hz, which were consistent with the modal frequencies obtained by the established analytical model. This verified the accuracy of the analytical model on longitudinal dynamics of electric wheel system. When longitudinal vibration frequency of the vehicle driven by in-wheel motor was near 2-3 Hz, it significantly affected the riding comfort as people are sensitive to low-frequency longitudinal vibration. While the high frequency longitudinal vibration is not favorable to the motor. Finally, the longitudinal vibration characteristic of the electric wheel system considering electromechanical coupling was studied. The time and frequency domain acceleration of vehicle body, stator, rotor and tire were obtained by simulation. It inferred from the quantitative analysis that torque ripple caused the relative displacement of stator and rotor, resulting in eccentric of the motor and UMP. The UMP is regarded as external force for the stator and rotor of the motor, while it is regarded as internal force for the vehicle body and tire. As a result, the unbalanced magnetic pull had little influence on the longitudinal vibration characteristic of sprung mass. However, it deteriorated the longitudinal vibration characteristic of unsprung mass sharply, which was harmful to the service life and structure safety. Therefore, it is necessary to consider the unbalanced magnetic pull caused by electromechanical coupling in the development of electric vehicle. This study provides guidance for the design of electric vehicles driven by in-wheel motor.

vehicles; vibrations; models; electromechanical coupling; electric wheel; torque ripple; unbalanced magnetic pull

10.11975/j.issn.1002-6819.2017.22.008

U461.1

A

1002-6819(2017)-22-0061-08

2017-06-23

2017-09-20

國家自然科學(xué)基金資助項(xiàng)目（51375343）；上海市教委科研創(chuàng)新項(xiàng)目（15ZZ015）

左曙光，教授，博士生導(dǎo)師，研究方向?yàn)槠囅到y(tǒng)動(dòng)力學(xué)與控制。Email：sgzuo@#edu.cn

吳旭東，助理教授，研究方向?yàn)槠囌駝?dòng)、噪聲及系統(tǒng)動(dòng)力學(xué)。Email：wuxudong@#edu.cn