籠型感應(yīng)電機(jī)轉(zhuǎn)子軸向分段錯(cuò)開結(jié)構(gòu)削弱同步附加轉(zhuǎn)矩的研究

徐 威 任曉明 寧銀行 鮑曉華

籠型感應(yīng)電機(jī)轉(zhuǎn)子軸向分段錯(cuò)開結(jié)構(gòu)削弱同步附加轉(zhuǎn)矩的研究

徐 威1任曉明1寧銀行1鮑曉華2

（1. 上海電機(jī)學(xué)院電氣學(xué)院 上海 201306 2. 合肥工業(yè)大學(xué)電氣與自動(dòng)化工程學(xué)院 合肥 230009）

特定槽配合感應(yīng)電機(jī)輸出轉(zhuǎn)矩與電機(jī)起動(dòng)位置有關(guān)。為抑制轉(zhuǎn)矩隨起動(dòng)位置周期變化引起的轉(zhuǎn)矩波動(dòng)，提出一種削弱同步附加轉(zhuǎn)矩的軸向分段錯(cuò)開轉(zhuǎn)子結(jié)構(gòu)。建立電磁轉(zhuǎn)矩計(jì)算模型，推導(dǎo)關(guān)于轉(zhuǎn)子初始位置的轉(zhuǎn)矩幅值表達(dá)式，確定產(chǎn)生恒定轉(zhuǎn)矩的磁場(chǎng)階次和電機(jī)轉(zhuǎn)速條件?；诖艅?dòng)勢(shì)線性分布假設(shè)，探討轉(zhuǎn)子分段錯(cuò)開結(jié)構(gòu)減小諧波電動(dòng)勢(shì)的機(jī)理，量化同步附加轉(zhuǎn)矩削弱程度與轉(zhuǎn)子錯(cuò)開段數(shù)的關(guān)系。以四種特殊槽配合為例，仿真分析單斜槽轉(zhuǎn)子、分段錯(cuò)開轉(zhuǎn)子及兩者組合結(jié)構(gòu)轉(zhuǎn)子，對(duì)電機(jī)基波轉(zhuǎn)矩和同步附加轉(zhuǎn)矩的影響。最后，選擇等槽配合方案試制雙斜槽轉(zhuǎn)子樣機(jī)，開展電機(jī)堵轉(zhuǎn)轉(zhuǎn)矩和空載特性試驗(yàn)。結(jié)果表明，轉(zhuǎn)子分段錯(cuò)開結(jié)構(gòu)有效削弱了同步附加轉(zhuǎn)矩，解決了等槽配合感應(yīng)電機(jī)起動(dòng)困難的問題，為抑制電機(jī)轉(zhuǎn)矩波動(dòng)和槽配合選取方法的研究提供了理論參考。

軸向分段錯(cuò)開轉(zhuǎn)子 同步附加轉(zhuǎn)矩 轉(zhuǎn)矩波動(dòng) 槽配合 感應(yīng)電機(jī)

0 引言

近些年，在電動(dòng)汽車等新興應(yīng)用領(lǐng)域中，電機(jī)輸出轉(zhuǎn)矩的平滑性與穩(wěn)定性要求逐漸提高[1-3]。相較于永磁同步電機(jī)，感應(yīng)電機(jī)（Induction Machine, IM）憑借著價(jià)格低廉、可靠性高和過載能力強(qiáng)等優(yōu)點(diǎn)，仍具有一定的競(jìng)爭(zhēng)優(yōu)勢(shì)和應(yīng)用需求[4]。因此，眾多科技工作者開展了抑制感應(yīng)電機(jī)轉(zhuǎn)矩波動(dòng)的理論研究與實(shí)踐驗(yàn)證。感應(yīng)電機(jī)轉(zhuǎn)矩波動(dòng)主要源于氣隙諧波磁場(chǎng)產(chǎn)生的諧波電磁轉(zhuǎn)矩[5]，而諧波磁場(chǎng)可分為由變頻供電方式導(dǎo)致的時(shí)間諧波分量，以及由分布繞組與鐵心開槽結(jié)構(gòu)引起的空間諧波分量[6-7]。相應(yīng)的轉(zhuǎn)矩脈動(dòng)抑制措施可以從諧波磁場(chǎng)來源展開，一方面可以優(yōu)化電機(jī)控制算法，減小諧波電流分量來降低電機(jī)轉(zhuǎn)矩脈動(dòng)[8-9]；另一方面也可以調(diào)整電機(jī)結(jié)構(gòu)參數(shù)來降低由空間諧波磁場(chǎng)導(dǎo)致的轉(zhuǎn)矩脈動(dòng)[10-12]。基于削弱空間諧波磁場(chǎng)的轉(zhuǎn)矩研究，主要從電機(jī)定子側(cè)與轉(zhuǎn)子側(cè)結(jié)構(gòu)優(yōu)化兩個(gè)方向展開。Li Yanxin等探究定子集中繞組與鐵心結(jié)構(gòu)對(duì)轉(zhuǎn)矩特性的影響，對(duì)比分析不同拓?fù)潆姍C(jī)的轉(zhuǎn)矩分量，研究表明齒間不對(duì)稱飽和是導(dǎo)致轉(zhuǎn)矩脈動(dòng)差異的主要原因[10]。T. Gundogdu等優(yōu)化電機(jī)轉(zhuǎn)子槽形參數(shù)，在轉(zhuǎn)子閉口槽槽口處設(shè)置U型槽橋結(jié)構(gòu)，改善轉(zhuǎn)子側(cè)磁場(chǎng)分布來降低磁飽和程度，從而減小電機(jī)轉(zhuǎn)矩脈動(dòng)[11]。G. Joksimovi?等對(duì)比研究定、轉(zhuǎn)子槽配合參數(shù)對(duì)電機(jī)負(fù)載時(shí)轉(zhuǎn)矩脈動(dòng)的影響，根據(jù)轉(zhuǎn)子直槽或斜槽類型，分別總結(jié)八極電機(jī)槽配合參數(shù)的選取范圍，并按照轉(zhuǎn)矩脈動(dòng)大小依次排序[12]?；\型轉(zhuǎn)子軸向斜槽是一種傳統(tǒng)且有效的抑制轉(zhuǎn)矩波動(dòng)的措施?；趩涡辈坜D(zhuǎn)子結(jié)構(gòu)，一種帶中間環(huán)的斜槽轉(zhuǎn)子逐步發(fā)展并應(yīng)用在雙速電機(jī)中，有助于減小電機(jī)高速運(yùn)行時(shí)的轉(zhuǎn)矩脈動(dòng)，并提高電機(jī)低速運(yùn)行時(shí)的輸出轉(zhuǎn)矩[13]。通過對(duì)中環(huán)斜槽轉(zhuǎn)子結(jié)構(gòu)參數(shù)的組合設(shè)計(jì)，優(yōu)化后的轉(zhuǎn)子相較于單斜槽轉(zhuǎn)子進(jìn)一步削弱了空間諧波磁場(chǎng)，從而降低電機(jī)轉(zhuǎn)矩脈動(dòng)[14]。但是，考慮感應(yīng)電機(jī)附加轉(zhuǎn)矩與雜散損耗的槽配合選取矛盾仍然存在[15-16]，已有的轉(zhuǎn)矩脈動(dòng)抑制研究往往基于電機(jī)常規(guī)的槽配合選取范圍。

感應(yīng)電機(jī)結(jié)構(gòu)優(yōu)化措施可以為其他類型電機(jī)抑制轉(zhuǎn)矩脈動(dòng)研究提供思路。永磁同步電機(jī)采用類似于單斜槽轉(zhuǎn)子的軸向分段傾斜磁極，有助于削弱齒槽轉(zhuǎn)矩、減小轉(zhuǎn)矩脈動(dòng)等[17-18]。為避免單向傾斜磁極引起的不平衡磁拉力問題，永磁電機(jī)采用軸向分段錯(cuò)開的非斜極轉(zhuǎn)子，并結(jié)合其他措施抑制電機(jī)齒槽轉(zhuǎn)矩[19-20]。這種轉(zhuǎn)子分段錯(cuò)開的斜槽代替結(jié)構(gòu)也可以抑制感應(yīng)電機(jī)轉(zhuǎn)矩脈動(dòng)[21]。但是，轉(zhuǎn)子軸向分段錯(cuò)開結(jié)構(gòu)減小諧波轉(zhuǎn)矩的工作原理還未明確。相較于隨轉(zhuǎn)子位置周期變化的齒槽轉(zhuǎn)矩[22]，很少有文獻(xiàn)研究感應(yīng)電機(jī)電磁轉(zhuǎn)矩的空間周期性，尤其是針對(duì)起動(dòng)過程中的附加轉(zhuǎn)矩分量，基于削弱附加轉(zhuǎn)矩以拓寬電機(jī)槽配合選取范圍的研究還不夠充分。

本文針對(duì)感應(yīng)電機(jī)輸出轉(zhuǎn)矩隨起動(dòng)位置周期變化的現(xiàn)象，提出一種轉(zhuǎn)子軸向分段錯(cuò)開結(jié)構(gòu)削弱同步附加轉(zhuǎn)矩，降低電機(jī)轉(zhuǎn)矩波動(dòng)。通過建立電磁轉(zhuǎn)矩計(jì)算模型，推導(dǎo)恒定轉(zhuǎn)矩幅值與轉(zhuǎn)子初始位置的關(guān)系，確定典型槽配合電機(jī)恒定轉(zhuǎn)矩的空間周期性。仿真分析單斜槽轉(zhuǎn)子、分段錯(cuò)開轉(zhuǎn)子及其組合結(jié)構(gòu)轉(zhuǎn)子削弱同步附加轉(zhuǎn)矩的效果，并采用等槽配合樣機(jī)試驗(yàn)來驗(yàn)證理論分析的合理性。為抑制電機(jī)轉(zhuǎn)矩波動(dòng)提供設(shè)計(jì)思路，并為探索感應(yīng)電機(jī)新的槽配合選取規(guī)則提供理論參考。

1 電磁轉(zhuǎn)矩解析計(jì)算

1.1 轉(zhuǎn)矩通用表達(dá)式

感應(yīng)電機(jī)電磁轉(zhuǎn)矩可利用虛位移法求解，根據(jù)轉(zhuǎn)矩表達(dá)式的數(shù)學(xué)意義，確定不隨時(shí)間或空間位置角變化的恒定電磁轉(zhuǎn)矩的產(chǎn)生條件。對(duì)于三相籠型感應(yīng)電機(jī)，分別在定子側(cè)和轉(zhuǎn)子側(cè)建立繞組磁動(dòng)勢(shì)坐標(biāo)系，電機(jī)合成氣隙磁動(dòng)勢(shì)包括定子合成磁動(dòng)勢(shì)和轉(zhuǎn)子合成磁動(dòng)勢(shì)，可表示[14]為

其中，定、轉(zhuǎn)子諧波磁動(dòng)勢(shì)的階次可分別表示為

為便于后續(xù)電磁轉(zhuǎn)矩的計(jì)算，將轉(zhuǎn)子磁動(dòng)勢(shì)表達(dá)式轉(zhuǎn)換至定子靜止坐標(biāo)系中。利用空間機(jī)械位置角的變換關(guān)系，轉(zhuǎn)子合成磁動(dòng)勢(shì)又可表示為

式中，為轉(zhuǎn)差率。

根據(jù)虛位移法的定義，電機(jī)電磁轉(zhuǎn)矩等于氣隙磁場(chǎng)能量對(duì)轉(zhuǎn)角的偏導(dǎo)數(shù)。若該角度表示為轉(zhuǎn)子虛位移，忽略磁能中的恒定部分，電機(jī)電磁轉(zhuǎn)矩通用表達(dá)式可化簡(jiǎn)為

式中，0為真空磁導(dǎo)率；l為電機(jī)軸向長(zhǎng)度；0為氣隙的徑向長(zhǎng)度。在此不考慮電機(jī)定、轉(zhuǎn)子開槽等因素引起的氣隙諧波磁導(dǎo)分量。

電磁轉(zhuǎn)矩表達(dá)式可以化簡(jiǎn)為關(guān)于磁動(dòng)勢(shì)的兩項(xiàng)三角函數(shù)乘積項(xiàng)。對(duì)于第一項(xiàng)由不同階次定、轉(zhuǎn)子磁場(chǎng)產(chǎn)生的轉(zhuǎn)矩分量，以及第二項(xiàng)由轉(zhuǎn)子磁場(chǎng)自身產(chǎn)生的轉(zhuǎn)矩分量，轉(zhuǎn)矩幅值在空間周期內(nèi)的平均值恒為零，表現(xiàn)為空間轉(zhuǎn)矩脈動(dòng)分量。僅當(dāng)產(chǎn)生轉(zhuǎn)矩的定、轉(zhuǎn)子磁場(chǎng)階次絕對(duì)值相同，即||=||時(shí)，電磁轉(zhuǎn)矩幅值與轉(zhuǎn)子空間位置角無關(guān)，可表示為

式中，j為定、轉(zhuǎn)子諧波磁動(dòng)勢(shì)初相位之差。

由式（6）可進(jìn)一步分析轉(zhuǎn)矩幅值與時(shí)間無關(guān)的條件，在此分為兩種情況。第一種情況為次轉(zhuǎn)子諧波磁場(chǎng)與感生它的ν次定子諧波磁場(chǎng)相互作用，即式（3）中2=0，該轉(zhuǎn)矩分量可稱為異步轉(zhuǎn)矩[15]。在第二種情況中，轉(zhuǎn)矩由次轉(zhuǎn)子諧波磁場(chǎng)與非感生它的ν次定子諧波磁場(chǎng)相互作用，該轉(zhuǎn)矩分量可稱為同步轉(zhuǎn)矩[15]。若產(chǎn)生同步轉(zhuǎn)矩的兩種磁動(dòng)勢(shì)的轉(zhuǎn)向相同，恒定轉(zhuǎn)矩還應(yīng)滿足電機(jī)轉(zhuǎn)速r=0的條件；若這兩種磁動(dòng)勢(shì)的轉(zhuǎn)向相反，則轉(zhuǎn)速條件應(yīng)滿足

式中，為電源頻率。對(duì)于式（6）中的其他轉(zhuǎn)矩分量，其幅值在時(shí)間周期內(nèi)的平均值恒為零，表現(xiàn)為時(shí)間轉(zhuǎn)矩脈動(dòng)分量。

1.2 恒定轉(zhuǎn)矩的空間周期性

由此可知，轉(zhuǎn)矩幅值隨起動(dòng)位置角變化的空間周期與轉(zhuǎn)子諧波磁動(dòng)勢(shì)階次2成反比，其最小公倍數(shù)為一個(gè)轉(zhuǎn)子齒距。由于產(chǎn)生異步轉(zhuǎn)矩的磁場(chǎng)階次條件為2=0，故轉(zhuǎn)子初始位置變化不影響異步轉(zhuǎn)矩，僅需考慮同步轉(zhuǎn)矩的空間周期性。在此以四極感應(yīng)電機(jī)為例，同步附加轉(zhuǎn)矩的產(chǎn)生條件見表1，分別列出電機(jī)四種槽配合時(shí)，產(chǎn)生主要同步轉(zhuǎn)矩分量的磁場(chǎng)階次和電機(jī)轉(zhuǎn)速條件。氣隙諧波磁場(chǎng)正向與反向旋轉(zhuǎn)的差異性直接反映在階次正負(fù)號(hào)上。當(dāng)r=24時(shí)，同階定、轉(zhuǎn)子諧波磁場(chǎng)轉(zhuǎn)向相同，同步轉(zhuǎn)矩的轉(zhuǎn)速條件均為零。當(dāng)r=26, 28, 16時(shí)，產(chǎn)生同步轉(zhuǎn)矩的定、轉(zhuǎn)子磁場(chǎng)旋轉(zhuǎn)方向相反，由式（7）可知，相應(yīng)的電機(jī)正向轉(zhuǎn)速條件。根據(jù)產(chǎn)生同步轉(zhuǎn)矩的轉(zhuǎn)子磁場(chǎng)階次，可推斷四種槽配合電機(jī)最大同步附加轉(zhuǎn)矩的空間周期分別為1.0、0.5、1.0和1.0個(gè)轉(zhuǎn)子齒距。

表1 四極感應(yīng)電機(jī)同步附加轉(zhuǎn)矩的產(chǎn)生條件

Tab.1 Generation conditions for synchronous parasitic torque of four-pole induction machine

2 軸向分段錯(cuò)開轉(zhuǎn)子

為抑制恒定轉(zhuǎn)矩分量隨起動(dòng)位置周期變化而引起的轉(zhuǎn)矩波動(dòng)，本節(jié)提出一種軸向分段錯(cuò)開轉(zhuǎn)子結(jié)構(gòu)，如圖1所示，轉(zhuǎn)子沿軸向分為段，每段轉(zhuǎn)子軸向長(zhǎng)度為l/，相鄰轉(zhuǎn)子間的圓周錯(cuò)開距離為2/，其中，2為轉(zhuǎn)子齒距。軸向分段錯(cuò)開轉(zhuǎn)子削弱諧波電動(dòng)勢(shì)的工作原理如圖2所示，以錯(cuò)開段數(shù)=4為例，轉(zhuǎn)子任意一根導(dǎo)條沿軸向分為四段導(dǎo)體并相互錯(cuò)開，依次標(biāo)記為1～4。根據(jù)電磁感應(yīng)原理，定子一階和二階齒諧波磁場(chǎng)在各導(dǎo)條中分別感生諧波電動(dòng)勢(shì)ν1和ν2，同階感生電動(dòng)勢(shì)的幅值相等。由于各段導(dǎo)條沿圓周均勻分布，導(dǎo)條12與導(dǎo)條34感生的一階諧波電動(dòng)勢(shì)的方向相反，四段錯(cuò)開轉(zhuǎn)子合成電動(dòng)勢(shì)中的一階齒諧波分量被抵消，二階齒諧波電動(dòng)勢(shì)同理也被抵消。但是對(duì)于兩段錯(cuò)開轉(zhuǎn)子，即單根轉(zhuǎn)子導(dǎo)條分別錯(cuò)開為導(dǎo)條13或?qū)l24，相鄰導(dǎo)條中二階齒諧波電動(dòng)勢(shì)方向相同，故僅能抵消轉(zhuǎn)子一階齒諧波電動(dòng)勢(shì)。通過各段錯(cuò)開轉(zhuǎn)子電動(dòng)勢(shì)之間的合成作用，可以抵消部分階次的諧波電動(dòng)勢(shì)，進(jìn)而削弱由齒諧波磁動(dòng)勢(shì)產(chǎn)生的同步附加轉(zhuǎn)矩。假設(shè)合成轉(zhuǎn)子磁動(dòng)勢(shì)為各段錯(cuò)開轉(zhuǎn)子磁動(dòng)勢(shì)的矢量和，由式（11）可知，此時(shí)感應(yīng)電機(jī)的諧波電磁轉(zhuǎn)矩可以表示為

式中，為考慮轉(zhuǎn)子分段錯(cuò)開效應(yīng)后的諧波電磁轉(zhuǎn)矩最大值；a2為轉(zhuǎn)子齒距角。

圖2 軸向分段錯(cuò)開轉(zhuǎn)子削弱諧波電動(dòng)勢(shì)原理

為描述分段錯(cuò)開轉(zhuǎn)子對(duì)電機(jī)電磁轉(zhuǎn)矩的削弱程度，引入轉(zhuǎn)子錯(cuò)開系數(shù)st，定義該系數(shù)為分段錯(cuò)開轉(zhuǎn)子與完整轉(zhuǎn)子時(shí)電機(jī)諧波轉(zhuǎn)矩的幅值比?？紤]到當(dāng)前電機(jī)制造工藝水平，以錯(cuò)開段數(shù)≤4為例，由式（12）化簡(jiǎn)可知轉(zhuǎn)子錯(cuò)開系數(shù)為

將式（3）代入式（13）中，可計(jì)算軸向分段錯(cuò)開轉(zhuǎn)子對(duì)兩類恒定轉(zhuǎn)矩的削弱程度。對(duì)于2=0時(shí)的異步轉(zhuǎn)矩，諧波階次越低則錯(cuò)開系數(shù)越接近于1，轉(zhuǎn)矩幅值近似不變。對(duì)于2≠0時(shí)的同步轉(zhuǎn)矩，特定諧波階次時(shí)的錯(cuò)開系數(shù)接近于零，轉(zhuǎn)矩分量近似被抵消。若以為正序數(shù)，軸向分段錯(cuò)開轉(zhuǎn)子抵消同步轉(zhuǎn)矩的轉(zhuǎn)子齒諧波磁場(chǎng)階次為

在氣隙磁動(dòng)勢(shì)線性分布的前提下，軸向分段錯(cuò)開轉(zhuǎn)子可以抵消轉(zhuǎn)子諧波電動(dòng)勢(shì)及其產(chǎn)生的同步附加轉(zhuǎn)矩，作用諧波的類型與錯(cuò)開段數(shù)有關(guān)。若考慮錯(cuò)開轉(zhuǎn)子軸向連接區(qū)域?qū)е碌穆┐?，則諧波的削弱程度存在一定的折扣，并且會(huì)引起電機(jī)主磁通部分降低、附加損耗增加等不利因素。

3 削弱同步附加轉(zhuǎn)矩的仿真對(duì)比

3.1 單斜槽轉(zhuǎn)子的影響

傳統(tǒng)感應(yīng)電機(jī)設(shè)計(jì)理論通常采用轉(zhuǎn)子斜槽措施，并限制槽配合參數(shù)的選取范圍，從而避免電機(jī)在起動(dòng)過程中產(chǎn)生較大的同步附加轉(zhuǎn)矩[15]。為對(duì)比不同轉(zhuǎn)子類型削弱同步附加轉(zhuǎn)矩的效果，本文選取表1中的四種非常規(guī)槽配合，建立相應(yīng)的電機(jī)模型，每種槽配合電機(jī)分別采用轉(zhuǎn)子直槽與單斜槽兩種結(jié)構(gòu)，其他參數(shù)完全相同，三相感應(yīng)電機(jī)的主要參數(shù)見表2。在產(chǎn)生最大同步轉(zhuǎn)矩的轉(zhuǎn)速條件下，分別計(jì)算電機(jī)齒距范圍內(nèi)不同起動(dòng)位置時(shí)的轉(zhuǎn)矩。直槽和單斜槽轉(zhuǎn)子感應(yīng)電機(jī)輸出轉(zhuǎn)矩波形如圖3所示，四種槽配合電機(jī)的輸出轉(zhuǎn)矩波形正弦周期變化，周期分別為1.0、0.5、1.0和1.0個(gè)轉(zhuǎn)子齒距，驗(yàn)證了轉(zhuǎn)矩空間周期性的理論結(jié)果。若忽略異步附加轉(zhuǎn)矩分量，輸出轉(zhuǎn)矩的平均值約等于基波轉(zhuǎn)矩，轉(zhuǎn)矩波形的峰-峰值近似等于兩倍最大同步轉(zhuǎn)矩值。相較于直槽轉(zhuǎn)子，單斜槽轉(zhuǎn)子有效削弱了電機(jī)同步附加轉(zhuǎn)矩，四種槽配合電機(jī)的最大同步轉(zhuǎn)矩幅值分別減小了58.2%、55.0%、42.9%和61.8%。但是，單斜槽轉(zhuǎn)子仍無法改變特殊槽配合電機(jī)輸出轉(zhuǎn)矩的空間周 期性。

表2 三相感應(yīng)電機(jī)的主要參數(shù)

Tab.2 Main parameters of three-phase induction machine

3.2 軸向分段錯(cuò)開轉(zhuǎn)子的影響

以兩段和三段錯(cuò)開轉(zhuǎn)子為例，根據(jù)表2中的電機(jī)參數(shù)，分別建立軸向分段錯(cuò)開轉(zhuǎn)子電機(jī)模型，在此忽略錯(cuò)開轉(zhuǎn)子間的軸向連通區(qū)域。電機(jī)輸出轉(zhuǎn)矩隨起動(dòng)位置角的波形如圖4所示。在兩段錯(cuò)開轉(zhuǎn)子情況下，四種槽配合電機(jī)輸出轉(zhuǎn)矩的波形為正弦波，空間周期均為1/2個(gè)轉(zhuǎn)子齒距。在三段錯(cuò)開轉(zhuǎn)子情況下，r=24, 16時(shí)轉(zhuǎn)矩波形的空間周期為1/3個(gè)轉(zhuǎn)子齒距，r=26, 28時(shí)電機(jī)轉(zhuǎn)矩近似為恒定值，轉(zhuǎn)矩脈動(dòng)分別為0.55%和1.0%。轉(zhuǎn)矩空間周期性的變化反映了最大同步轉(zhuǎn)矩類型的改變，特定轉(zhuǎn)子諧波磁場(chǎng)產(chǎn)生的同步轉(zhuǎn)矩近似被消除，驗(yàn)證了兩段錯(cuò)開轉(zhuǎn)子能抵消轉(zhuǎn)子一階齒諧波磁場(chǎng)產(chǎn)生的同步轉(zhuǎn)矩，三段錯(cuò)開轉(zhuǎn)子能分別抵消轉(zhuǎn)子一階和二階齒諧波磁場(chǎng)各自產(chǎn)生的同步轉(zhuǎn)矩分量的分析結(jié)果。

圖4 軸向分段錯(cuò)開轉(zhuǎn)子感應(yīng)電機(jī)輸出轉(zhuǎn)矩波形

不同轉(zhuǎn)子類型時(shí)感應(yīng)電機(jī)的轉(zhuǎn)矩值對(duì)比見表3，分別列出轉(zhuǎn)子類型為直槽、單斜槽、兩段錯(cuò)開和三段錯(cuò)開時(shí)，四種槽配合電機(jī)的基波轉(zhuǎn)矩和最大同步轉(zhuǎn)矩值。通過對(duì)比可知，相較于直槽轉(zhuǎn)子，單斜槽轉(zhuǎn)子有助于削弱不同槽配合電機(jī)的同步轉(zhuǎn)矩，并且略微降低基波轉(zhuǎn)矩；而分段錯(cuò)開轉(zhuǎn)子僅削弱特定槽配合時(shí)的同步附加轉(zhuǎn)矩，基波轉(zhuǎn)矩的幅值近似不變。分段錯(cuò)開轉(zhuǎn)子適用的槽配合范圍取決于同步附加轉(zhuǎn)矩的諧波磁場(chǎng)來源。

表3 不同轉(zhuǎn)子類型時(shí)感應(yīng)電機(jī)的轉(zhuǎn)矩值對(duì)比

Tab.3 Comparison of torque values of induction machines with different rotor types （單位: N·m）

4 等槽配合感應(yīng)電機(jī)仿真與試驗(yàn)

4.1 三維有限元仿真

通過第3節(jié)對(duì)四種槽配合電機(jī)的仿真計(jì)算，驗(yàn)證了單斜槽轉(zhuǎn)子與分段錯(cuò)開轉(zhuǎn)子對(duì)同步附加轉(zhuǎn)矩的削弱效果。為保證附加轉(zhuǎn)矩的削弱程度，本節(jié)將這兩種轉(zhuǎn)子結(jié)構(gòu)結(jié)合，形成兩段錯(cuò)開斜槽結(jié)構(gòu)的雙斜槽轉(zhuǎn)子，轉(zhuǎn)子模型如圖5所示。考慮到電機(jī)等槽配合時(shí)，最大同步附加轉(zhuǎn)矩的產(chǎn)生條件為電機(jī)轉(zhuǎn)速r=0 r/min，為簡(jiǎn)化后續(xù)樣機(jī)的試驗(yàn)過程，在此以24-24等槽配合為例。建立轉(zhuǎn)子單斜槽、兩段錯(cuò)開和雙斜槽時(shí)的電機(jī)對(duì)比模型，轉(zhuǎn)子斜槽距離均為一個(gè)齒距，電機(jī)除轉(zhuǎn)子類型外其他參數(shù)完全相同（見表2）。三臺(tái)電機(jī)堵轉(zhuǎn)轉(zhuǎn)矩仿真波形對(duì)比如圖6所示，轉(zhuǎn)矩幅值隨起動(dòng)位置角近似正弦變化，其空間周期性與二維有限元仿真中的結(jié)果相同。相較于前兩種轉(zhuǎn)子，電機(jī)采用雙斜槽轉(zhuǎn)子組合結(jié)構(gòu)時(shí)，最大同步附加轉(zhuǎn)矩幅值分別減小80.3%和50.2%，轉(zhuǎn)矩空間周期性為半個(gè)齒距。轉(zhuǎn)矩對(duì)比結(jié)果驗(yàn)證了雙斜槽轉(zhuǎn)子削弱一階齒諧波磁場(chǎng)產(chǎn)生同步轉(zhuǎn)矩的優(yōu)越性，其削弱程度優(yōu)于任意一種單獨(dú)轉(zhuǎn)子結(jié)構(gòu)時(shí)的效果。

圖5 籠型轉(zhuǎn)子的三維有限元模型

圖6 等槽配合電機(jī)堵轉(zhuǎn)轉(zhuǎn)矩的仿真波形

在各導(dǎo)條中設(shè)置隨轉(zhuǎn)子旋轉(zhuǎn)的電流橫截面，計(jì)算導(dǎo)條電流在圓周內(nèi)的空間分布。雙斜槽轉(zhuǎn)子導(dǎo)條電流的諧波分析如圖7所示，相較于單側(cè)轉(zhuǎn)子電流，合成轉(zhuǎn)子電流的基波分量略微減小，11次與13次的一階齒諧波電流幅值大幅降低，分別減小84.2%和87.8%，而23次與25次的二階齒諧波電流的減小程度分別為1.15%和0.43%，可近似忽略不計(jì)。諧波電流的對(duì)比結(jié)果驗(yàn)證了轉(zhuǎn)子分段錯(cuò)開結(jié)構(gòu)的作用效果，雙斜槽轉(zhuǎn)子具有削弱轉(zhuǎn)子一階齒諧波電動(dòng)勢(shì)的優(yōu)越效果，但不影響轉(zhuǎn)子二階齒諧波電動(dòng)勢(shì)。

圖7 雙斜槽轉(zhuǎn)子感應(yīng)電機(jī)導(dǎo)條電流諧波分析

4.2 等槽配合樣機(jī)對(duì)比試驗(yàn)

籠型感應(yīng)電機(jī)斜槽轉(zhuǎn)子的最佳斜槽距離通常為一個(gè)齒距，有助于削弱奇次齒諧波磁場(chǎng)。為探討雙斜槽轉(zhuǎn)子組合結(jié)構(gòu)中，轉(zhuǎn)子斜槽度參數(shù)對(duì)同步附加轉(zhuǎn)矩抑制效果的影響，試制兩臺(tái)不同斜槽度的雙斜槽轉(zhuǎn)子樣機(jī)，斜槽距離分別為0.9以及1個(gè)齒距。樣機(jī)轉(zhuǎn)子實(shí)物如圖8所示。搭建如圖9所示的堵轉(zhuǎn)轉(zhuǎn)矩試驗(yàn)平臺(tái)，以目測(cè)讀取的轉(zhuǎn)矩最大值作為該轉(zhuǎn)子位置時(shí)的電機(jī)堵轉(zhuǎn)轉(zhuǎn)矩值。

圖8 閉口槽形的雙斜槽轉(zhuǎn)子

圖9 電機(jī)堵轉(zhuǎn)轉(zhuǎn)矩試驗(yàn)平臺(tái)

樣機(jī)堵轉(zhuǎn)轉(zhuǎn)矩波形如圖10所示，轉(zhuǎn)矩幅值隨轉(zhuǎn)子機(jī)械位置角近似正弦變化，其空間周期約為半個(gè)轉(zhuǎn)子齒距（2/2）。由此推斷，同步附加轉(zhuǎn)矩以二階齒諧波磁場(chǎng)產(chǎn)生的轉(zhuǎn)矩分量為主。相較于4.1節(jié)的仿真結(jié)果，樣機(jī)基波轉(zhuǎn)矩的試驗(yàn)值較為接近，但是最大同步轉(zhuǎn)矩的估算值偏大，導(dǎo)致堵轉(zhuǎn)轉(zhuǎn)矩的最值存在誤差?？紤]轉(zhuǎn)子斜槽設(shè)計(jì)對(duì)樣機(jī)轉(zhuǎn)矩的影響，相較于斜槽距離sk=0.92時(shí)的情況，樣機(jī)轉(zhuǎn)子sk=1.02時(shí)的堵轉(zhuǎn)轉(zhuǎn)矩最小值增加4.7 N·m，最大值減小8.1 N·m。轉(zhuǎn)矩對(duì)比結(jié)果表明，在組合轉(zhuǎn)子結(jié)構(gòu)中，轉(zhuǎn)子導(dǎo)條斜槽效應(yīng)與錯(cuò)開效應(yīng)對(duì)轉(zhuǎn)子諧波磁動(dòng)勢(shì)存在耦合的削弱作用。錯(cuò)開導(dǎo)條結(jié)構(gòu)對(duì)奇次諧波產(chǎn)生同步轉(zhuǎn)矩的抵消效果存在誤差，仍需補(bǔ)充采取最佳斜槽角的轉(zhuǎn)子斜槽設(shè)計(jì)，從而最大程度削弱同步附加轉(zhuǎn)矩。

圖10 雙斜槽轉(zhuǎn)子樣機(jī)堵轉(zhuǎn)轉(zhuǎn)矩的試驗(yàn)波形

為探究雙斜槽轉(zhuǎn)子組合結(jié)構(gòu)對(duì)定子側(cè)磁場(chǎng)的影響，在此開展樣機(jī)空載特性試驗(yàn)。利用測(cè)定的線電壓、相電流和輸入功率參數(shù)，樣機(jī)空載特性曲線如圖11所示，繪制其中一臺(tái)雙斜槽轉(zhuǎn)子樣機(jī)的空載特性曲線。由鐵耗與機(jī)械損耗組成的恒定損耗con近似與電壓比的二次方線性相關(guān)，其擬合曲線的縱軸截距約等于機(jī)械損耗。圖中，0和N分別為空載電壓和額定電壓。兩臺(tái)樣機(jī)空載試驗(yàn)結(jié)果見表4，相較于斜槽距離sk=0.92時(shí)的情況，樣機(jī)轉(zhuǎn)子sk=1.02時(shí)的空載電流增加約2.8%，由此導(dǎo)致定子空載銅耗增加5.5 W，而恒定損耗值共增加7.26 W。樣機(jī)對(duì)比試驗(yàn)表明，雙斜槽轉(zhuǎn)子有助于削弱同步附加轉(zhuǎn)矩，解決等槽配合電機(jī)起動(dòng)困難的問題。但是，錯(cuò)開轉(zhuǎn)子連接區(qū)域會(huì)引起邊緣漏磁，降低了電機(jī)的有效磁通，進(jìn)而導(dǎo)致功率因數(shù)降低和空載損耗增加等。

圖11 樣機(jī)空載特性曲線

表4 雙斜槽轉(zhuǎn)子樣機(jī)空載試驗(yàn)結(jié)果對(duì)比

Tab.4 Comparison of no-load test results of dual skewed rotor prototype machines

5 結(jié)論

本文提出一種轉(zhuǎn)子軸向分段錯(cuò)開結(jié)構(gòu)削弱電機(jī)同步附加轉(zhuǎn)矩，抑制轉(zhuǎn)矩幅值隨起動(dòng)位置周期變化引起的轉(zhuǎn)矩波動(dòng)。通過仿真分析轉(zhuǎn)子單斜槽、分段錯(cuò)開及其組合結(jié)構(gòu)時(shí)的電機(jī)轉(zhuǎn)矩特性，對(duì)比試驗(yàn)兩臺(tái)等槽配合樣機(jī)，可以得到以下主要結(jié)論：

1）感應(yīng)電機(jī)恒定轉(zhuǎn)矩包括異步轉(zhuǎn)矩與同步轉(zhuǎn)矩兩類，僅同步轉(zhuǎn)矩幅值隨電機(jī)起動(dòng)位置周期性變化，其空間周期大小與產(chǎn)生轉(zhuǎn)矩的轉(zhuǎn)子諧波磁場(chǎng)階次成反比，周期最小公倍數(shù)為一個(gè)轉(zhuǎn)子齒距。

2）轉(zhuǎn)子軸向分段錯(cuò)開結(jié)構(gòu)可以減小轉(zhuǎn)子諧波電動(dòng)勢(shì)，改變特殊槽配合電機(jī)輸出轉(zhuǎn)矩的空間周期性，提高輸出轉(zhuǎn)矩最小值。當(dāng)錯(cuò)開段數(shù)=2時(shí)，可近似抵消轉(zhuǎn)子奇次齒諧波磁場(chǎng)產(chǎn)生的同步轉(zhuǎn)矩分量。

3）相較于軸向斜槽和分段錯(cuò)開轉(zhuǎn)子，兩者組合結(jié)構(gòu)削弱同步附加轉(zhuǎn)矩效果更佳。雙斜槽轉(zhuǎn)子斜槽距離為一個(gè)齒距時(shí)，樣機(jī)起動(dòng)轉(zhuǎn)矩比的最小值約為1.5倍，有助于實(shí)現(xiàn)等槽配合電機(jī)正常起動(dòng)，但轉(zhuǎn)子局部漏磁會(huì)引起空載損耗增加等缺點(diǎn)。

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Research on the Reduction of Synchronous Parasitic Torque by the Rotor Axial Piecewise Staggered Structure of Cage Induction Machine

1112

（1. School of Electrical Engineering Shanghai Dianji University Shanghai 201306 China 2. School of Electrical Engineering and Automation Hefei University of Technology Hefei 230009 China）

The smoothness and stability requirements of motor output torque have gradually increased in recent years, especially in emerging applications such as electric vehicles. The induction machine (IM), due to its low price, high reliability, and strong overload capacity, still has certain competitive advantages and application needs. In classical motor design theory, the range of slot combinations is limited to ignore the large synchronous parasitic torque, such as the equivalent slot combination. However, the stray loss of IM is small when the number of stator slots and rotor slots is similar. For some of these special slot combinations, the output torque of the induction machine is related to the starting position of the motor. In order to suppress the torque ripple caused by the periodic torque variation with the starting position, a rotor axial piecewise staggered structure is proposed to weaken the synchronous parasitic torque. The selection range of slot combinations can be expanded by solving the starting difficulty of the IM with an equivalent slot combination.

The electromagnetic torque calculation model is established, the torque amplitude expression about the initial rotor position is deduced, and the magnetic field order and the motor speed conditions for generating constant torque are determined. Based on the assumption of the linearly distributed magnetic potential, the mechanism of weakening the harmonic electromotive force is discussed using a piecewise staggered rotor structure. The relationship between the weakening degree of synchronous parasitic torque and the number of staggered rotor segments is quantified. Taking four kinds of special slot combinations as examples, the effects of the single skewed rotor, the piecewise staggered rotor, and the rotor with the combined structure on the fundamental torque and synchronous parasitic torque are simulated and analyzed. Finally, the dual skewed rotor prototype machines are trial-produced with the equivalent slot combination scheme, and the motor locked-rotor torque tests are carried out.

Simulation results on the torque components show that the single skewed rotor weakens the synchronous torque of the motor with different slot combinations while slightly reducing the fundamental torque. However, the single skewed rotor still cannot change the spatial periodicity of the output torque. For the piecewise staggered rotor, the synchronous torque is weakened only for certain slot combinations, and the amplitude of the fundamental torque remains approximately unchanged. Regarding the combined rotor structure, taking the two-stage staggered skewed rotor as an example, the attenuation degree of the harmonic magnetic field is greater than that of any single rotor structure. Experimental results on the locked-rotor torque show that the offset effect of the staggered bar structure on the synchronous torque generated by the odd harmonics deviates from the simulation results by a degree. An optimal skewed rotor design is necessary to minimize the synchronous parasitic torque.

The following conclusions can be drawn from the simulation analysis and prototype test. (1) The amplitude of synchronous torque changes periodically with the starting position of the motor, and the spatial period is inversely proportional to the order of the rotor harmonic magnetic field that generates torque. The rotor pitch is the least common multiple of the period. (2) The rotor axial staggered structure can reduce the rotor harmonic electromotive force, change the spatial periodicity of the output torque of the motor with certain slot combinations, and improve the minimum output torque. (3) Compared with the skewed rotor and the piecewise staggered rotor, the combined structure of the two has a better effect of weakening the synchronous parasitic torque. When the skewed distance of the dual skewed rotor is one tooth pitch, the minimum value of the starting torque ratio of the prototype is about 1.5 times, thus helping the normal starting of the motor with equal stator and rotor slot number. However, the partial magnetic flux leakage of the rotor may result in certain disadvantages. For example, it may increase no-load loss.

Axial piecewise staggered rotor, synchronous parasitic torque, torque fluctuation, slot combination, induction machine

10.19595/j.cnki.1000-6753.tces.221534

TM343

國家自然科學(xué)基金（51977055）和安徽省科技重大專項(xiàng)（201903a05020042）資助項(xiàng)目。

2022-08-08

2022-09-01

徐 威 男，1994年生，博士，講師，研究方向?yàn)殡姍C(jī)電磁場(chǎng)分析與計(jì)算、電機(jī)優(yōu)化設(shè)計(jì)、電機(jī)諧波磁場(chǎng)理論等。E-mail: xuwei@sdju.edu.cn（通信作者）

任曉明 男，1977年生，博士，副教授，研究方向?yàn)楦唠妷杭夹g(shù)、儲(chǔ)能技術(shù)、工業(yè)控制及圖像處理等。E-mail: renxm@sdju.edu.cn

（編輯 崔文靜）