陳益廣,史翊辰,沈勇環(huán)
有限轉(zhuǎn)角旋轉(zhuǎn)電樞式永磁同步電動(dòng)機(jī)設(shè)計(jì)
陳益廣,史翊辰,沈勇環(huán)
(天津大學(xué)電氣自動(dòng)化與信息工程學(xué)院,天津 300072)
為降低運(yùn)行噪聲,提升仿生魚腰關(guān)節(jié)驅(qū)動(dòng)用電動(dòng)機(jī)(簡稱腰電機(jī))無故障工作時(shí)間,降低維護(hù)成本,腰電機(jī)采用直驅(qū)方式,且還應(yīng)輕質(zhì)高效.根據(jù)仿生魚魚體尺寸、魚體結(jié)構(gòu)及魚尾的拍動(dòng)模式,結(jié)合流體力學(xué)理論,對仿生魚尾鰭部分進(jìn)行了力學(xué)分析.根據(jù)腰電機(jī)的安裝位置、旋轉(zhuǎn)角速度及尾鰭受力,計(jì)算得腰電機(jī)的輸出轉(zhuǎn)矩和輸出功率要求.由于電機(jī)轉(zhuǎn)矩與氣隙處直徑的平方成正比,故針對腰電機(jī)低速大扭矩設(shè)計(jì)要求,選擇外轉(zhuǎn)子電機(jī)結(jié)構(gòu)形式;但是,考慮到安裝空間的限制,以及腰電機(jī)運(yùn)行角度有限的特點(diǎn),提出了一種有限轉(zhuǎn)角旋轉(zhuǎn)電樞式永磁同步電動(dòng)機(jī)用作腰電機(jī),即通過變換傳統(tǒng)外轉(zhuǎn)子永磁同步電動(dòng)機(jī)拓?fù)浣Y(jié)構(gòu),將傳統(tǒng)的永磁外轉(zhuǎn)子變換為定子,將傳統(tǒng)的定子電樞改為在有限轉(zhuǎn)角內(nèi)旋轉(zhuǎn)的轉(zhuǎn)子電樞,在克服安裝空間受限的同時(shí)增大了電機(jī)單位體積的輸出轉(zhuǎn)矩.運(yùn)用有限元方法對一臺(tái)54槽60極有限轉(zhuǎn)角旋轉(zhuǎn)電樞式永磁同步電動(dòng)機(jī)進(jìn)行了電磁設(shè)計(jì),通過選取合適的齒寬達(dá)到腰電機(jī)輕質(zhì)高效的設(shè)計(jì)目的.根據(jù)實(shí)際運(yùn)行工況,分析了腰電機(jī)在仿生魚尾部拍動(dòng)頻率為0.35Hz時(shí)的運(yùn)行效率為75.5%,滿足不低于75%的設(shè)計(jì)要求.最后,對腰電機(jī)樣機(jī)進(jìn)行了壽命試驗(yàn).結(jié)果表明:該電機(jī)滿足仿生魚腰關(guān)節(jié)驅(qū)動(dòng)設(shè)計(jì)要求,且運(yùn)行效率較高.
永磁同步電動(dòng)機(jī);有限轉(zhuǎn)角;旋轉(zhuǎn)電樞;運(yùn)行效率
仿生魚作為人類探索、開發(fā)海洋的設(shè)備,具有噪聲低、對環(huán)境擾動(dòng)小等特點(diǎn),是近年來水下推進(jìn)器的研究熱點(diǎn)之一[1-2].從仿生學(xué)角度看,魚類推進(jìn)方式大多為身體/尾鰭推進(jìn)模式(body and/or caudal fin,BCF)[3].在此模式下,魚類通過魚體彎曲形成延至尾鰭的推進(jìn)波,使尾鰭產(chǎn)生較大游動(dòng)推力.
對于仿生魚的電驅(qū)動(dòng)研究,國內(nèi)外研究較少.文獻(xiàn)[4]認(rèn)為尾鰭驅(qū)動(dòng)電機(jī)的驅(qū)動(dòng)力矩包含水動(dòng)力矩和慣性力矩兩部分.文獻(xiàn)[5-6]給出了仿生魚直線運(yùn)動(dòng)時(shí)電機(jī)的位置角情況.而對于仿生魚高效驅(qū)動(dòng)電機(jī)設(shè)計(jì),國內(nèi)外鮮有涉及.
提高仿生魚驅(qū)動(dòng)電機(jī)運(yùn)行效率,可以延長仿生魚水下作業(yè)時(shí)間,對水下環(huán)境執(zhí)行任務(wù)等具有重要意義.對于采用BCF模式的由魚體、尾柄和尾鰭構(gòu)成的三節(jié)仿生魚驅(qū)動(dòng)系統(tǒng),尾柄和尾鰭各需要一臺(tái)雙軸伸輸出的有限轉(zhuǎn)角裝置驅(qū)動(dòng),尾柄驅(qū)動(dòng)裝置安裝在魚體軀干后端;尾鰭驅(qū)動(dòng)裝置安裝在尾柄內(nèi),其旋轉(zhuǎn)軸在尾柄后端.
本文圍繞一臺(tái)不經(jīng)任何減速和傳動(dòng)機(jī)構(gòu)直接驅(qū)動(dòng)仿生魚尾柄的腰關(guān)節(jié)永磁同步電動(dòng)機(jī)設(shè)計(jì)展開分析.從電機(jī)設(shè)計(jì)要求[7]、提出電機(jī)拓?fù)浣Y(jié)構(gòu)、電機(jī)電磁設(shè)計(jì)以及電機(jī)運(yùn)行效率等方面對腰電機(jī)的設(shè)計(jì)方法進(jìn)行了詳細(xì)分析.有限轉(zhuǎn)角旋轉(zhuǎn)電樞式永磁同步電動(dòng)機(jī)用作腰電機(jī)驅(qū)動(dòng)尾柄,能夠滿足輕質(zhì)高效和安裝空間限制等設(shè)計(jì)要求.
尾鰭和尾柄以相同頻率拍動(dòng),且
圖1?仿生魚簡化模型
尾鰭和尾柄的拍動(dòng)角速度為
根據(jù)文獻(xiàn)[8],由茹科夫斯基升力定理,尾鰭受力符合平板繞流受力情景,尾鰭受到的升力為
式中:為尾鰭受到的升力,N;為流體密度,kg/m3;為尾鰭面積,m2;為相對于尾鰭無窮遠(yuǎn)處的流體速度,等價(jià)于在靜態(tài)流體中壓力中心點(diǎn)的速度,m/s;為流體對平板的沖角,rad.流體中尾鰭受力分析圖如圖2所示.升力方向與來流方向垂直,且升力作用中心點(diǎn)位于尾鰭前端1/4處.
若認(rèn)為魚體沿水平方向游動(dòng)的動(dòng)力來源于尾鰭上下拍打時(shí)與流體作用產(chǎn)生的升力,從動(dòng)力學(xué)角度來看,該升力與魚體參數(shù)有關(guān).本文仿生魚體設(shè)計(jì)參數(shù)列于表1中.
表1?仿生魚設(shè)計(jì)參數(shù)
Tab.1?Parameters of biomimetic fish
由式(5)可知,尾鰭壓力中心點(diǎn)的速度對于升力求解十分關(guān)鍵.當(dāng)尾鰭或尾柄位于圖1中參考線下方時(shí),位置角為負(fù)值,壓力中心點(diǎn)處的速度沿水平和豎直方向分量[9]分別為
對于本文中的仿生魚,認(rèn)為魚體沿水平方向游速與尾鰭拍動(dòng)頻率的關(guān)系[10]為
由式(6)和式(7)可得到壓力中心點(diǎn)處速度
將式(9)代入式(5),得到尾鰭受到的升力
由式(6)~式(10)可得到尾鰭的受力情況,進(jìn)而由圖3可推導(dǎo)出腰電機(jī)所應(yīng)輸出的力矩
腰電機(jī)上的慣性力矩為
綜上,腰電機(jī)應(yīng)輸出轉(zhuǎn)矩為
腰電機(jī)應(yīng)輸出功率為
由仿真結(jié)果可見,尾部每拍動(dòng)一個(gè)周期,腰電機(jī)的輸出轉(zhuǎn)矩變化一個(gè)周期,輸出功率變化兩個(gè)周期;尾柄轉(zhuǎn)速和轉(zhuǎn)矩雖然周期一致,但是存在相位差,故每個(gè)功率變化周期都存在一段瞬時(shí)功率為負(fù)的較短時(shí)間,在這較短時(shí)間內(nèi)出現(xiàn)腰電機(jī)能量回饋過程.腰電機(jī)在兩種拍動(dòng)頻率下的峰值轉(zhuǎn)矩和峰值功率列于表2中.
表2?兩種拍動(dòng)頻率下腰電機(jī)運(yùn)行數(shù)據(jù)
Tab.2 Operation data of waist motor under two flapping frequencies
受安裝空間約束,腰電機(jī)外徑和軸向長度限制在540mm和200mm內(nèi),整體質(zhì)量低于125kg,且腰電機(jī)運(yùn)行效率要高,使仿生魚具備更長的巡游時(shí)間.控制器由電池供電,電池標(biāo)稱電壓為270V.
腰電機(jī)轉(zhuǎn)速低、鐵耗低,永磁體可以表貼,使得極對數(shù)應(yīng)盡可能取得多;瓦形永磁體薄,極弧寬度窄且與齒寬接近,永磁體利用率高;兼作機(jī)殼的永磁定子軛部薄,使氣隙處直徑較大,機(jī)殼輕;電樞繞組采用槽數(shù)比極數(shù)少的分?jǐn)?shù)槽集中繞組[13],繞組端部短,在軸向空間一定時(shí)電樞鐵心軸向疊長能做到最長,在增大轉(zhuǎn)矩同時(shí)端部銅耗小、效率高.
腰電機(jī)橫截面如圖5所示.其中,兼做腰電機(jī)機(jī)殼的永磁定子軛采用導(dǎo)磁的鋼材,電樞鐵心采用高磁感硅鋼片,端蓋和電樞轉(zhuǎn)子支架都采用鋁合金,釹鐵硼永磁體牌號為N38UH.
圖5?有限轉(zhuǎn)角旋轉(zhuǎn)電樞式電機(jī)橫截面
在腰電機(jī)設(shè)計(jì)時(shí),對峰值轉(zhuǎn)矩和轉(zhuǎn)速留有一定裕度,所設(shè)計(jì)的54槽60極有限轉(zhuǎn)角旋轉(zhuǎn)電樞式永磁同步電動(dòng)機(jī)基本參數(shù)如表3所示.
表3?腰電機(jī)設(shè)計(jì)參數(shù)
Tab.3?Parameters of waist motor
電機(jī)的結(jié)構(gòu)型式、槽極配合和基本尺寸確定后,在輸出轉(zhuǎn)矩一定時(shí),電機(jī)的輕質(zhì)高效設(shè)計(jì)工作轉(zhuǎn)化成電樞鐵心齒寬與槽寬的合理分配問題.
電樞鐵心齒距一定時(shí),齒寬大小關(guān)系到齒部磁密飽和程度、鐵心質(zhì)量和鐵耗;同時(shí)也關(guān)系到槽寬大小,影響著電樞繞組銅線質(zhì)量和銅耗.雖然腰電機(jī)極數(shù)多,但轉(zhuǎn)速低,最高工作頻率僅8Hz,因此電機(jī)鐵耗很低,腰電機(jī)的損耗主要為銅耗.故齒部磁密可以比一般電機(jī)高,使得槽面積大一些,以降低導(dǎo)線電流密度,減少銅耗,提高電機(jī)效率.
圖6?齒部最大磁密、電機(jī)質(zhì)量與齒寬關(guān)系曲線
圖7?電機(jī)效率與齒寬關(guān)系曲線
綜合磁密、質(zhì)量、效率及加工工藝因素,所設(shè)計(jì)的腰電機(jī)空載電動(dòng)勢波形如圖8所示.
設(shè)計(jì)方案的一些關(guān)鍵參數(shù)為:永磁體極弧系數(shù)0.867,齒寬11mm,齒部最大磁密1.72T,軛部最大磁密1.42T,氣隙磁密均值0.84T,峰值負(fù)載時(shí)線圈電流密度3.22A/mm2,總質(zhì)量124.4kg,轉(zhuǎn)子轉(zhuǎn)動(dòng)慣量3kg·m2,效率74.15%,輸出轉(zhuǎn)矩脈動(dòng)2.1%.
圖8?腰電機(jī)空載電動(dòng)勢波形
腰電機(jī)運(yùn)行時(shí)采用直軸電流為零(i=0)控制方式.考慮到腰電機(jī)損耗主要來自于繞組銅耗,其次是鐵耗.其中電樞繞組銅耗計(jì)算式為
鐵耗計(jì)算式[17]為
由于腰電機(jī)轉(zhuǎn)速很低,風(fēng)摩損耗、軸承摩擦損耗可忽略不計(jì),腰電機(jī)效率計(jì)算式為
綜上可得到圖9所示的腰電機(jī)效率云圖.
由圖9可見,轉(zhuǎn)矩較低轉(zhuǎn)速較高時(shí)效率較高,這時(shí),輸出功率相對較高,電流較小,銅耗與鐵耗接近,符合電機(jī)內(nèi)部可變損耗與不變損耗相同時(shí),電機(jī)效率最高的原則.腰電機(jī)最高效率已達(dá)88%.
圖9?腰電機(jī)效率云圖
相比于某一工作點(diǎn)的效率,更具實(shí)際價(jià)值的是仿生魚運(yùn)動(dòng)時(shí)腰電機(jī)的運(yùn)行效率[18].運(yùn)行效率的高低決定仿生魚每次投放后在水中巡游時(shí)間的長短.
在工作時(shí)間內(nèi),腰電機(jī)銅耗能、鐵耗能分別為
式中n為腰電機(jī)的極對數(shù).
在內(nèi),腰電機(jī)損耗能量、輸出能量和運(yùn)行效率分別為
仿真可得,魚尾拍動(dòng)頻率0.35Hz時(shí),在30s內(nèi)腰電機(jī)銅耗和鐵耗能量如圖10所示,損耗能量與輸出能量如圖11所示.
圖10?腰電機(jī)銅耗和鐵耗能量
圖11?腰電機(jī)損耗能量和輸出能量
由圖11可見,能量損耗曲線在任意時(shí)刻的斜率皆為正值,而輸出能量曲線存在斜率為負(fù)的時(shí)段,這與圖4(d)中存在能量回饋過程相一致.經(jīng)計(jì)算,拍動(dòng)頻率為0.35Hz時(shí),腰電機(jī)運(yùn)行效率為75.5%.滿足該拍動(dòng)頻率下不低于75%的設(shè)計(jì)要求.
當(dāng)尾部拍動(dòng)幅值一定時(shí),經(jīng)過不同拍動(dòng)頻率下的運(yùn)行效率計(jì)算得到的腰電機(jī)運(yùn)行效率隨尾部拍動(dòng)頻率變化關(guān)系曲線如圖12所示.由圖12可見,腰電機(jī)在0.1~0.4Hz的運(yùn)行頻率范圍內(nèi),運(yùn)行效率先增加后下降,在0.17Hz時(shí)達(dá)到最大值81.45%.
圖12?腰電機(jī)運(yùn)行效率與尾部拍動(dòng)頻率關(guān)系曲線
圖14為壽命試驗(yàn)平臺(tái)示意,腰關(guān)節(jié)電機(jī)為雙軸伸輸出,軸伸兩側(cè)對稱布置.樣機(jī)固定在支撐盤上,軸伸一側(cè)各設(shè)備的聯(lián)接順序依次為轉(zhuǎn)矩轉(zhuǎn)速傳感器、升速機(jī)、飛輪和磁粉制動(dòng)器.為便于安裝樣機(jī),與轉(zhuǎn)矩轉(zhuǎn)速傳感器間使用了帶有中間軸的膜片彈性聯(lián)軸器.使用傳動(dòng)比為10.83的升速機(jī),大幅降低飛輪體積,降低磁粉制動(dòng)器額定轉(zhuǎn)矩.磁粉制動(dòng)器采用水冷方式.添加飛輪后,使得樣機(jī)整個(gè)軸系的轉(zhuǎn)動(dòng)慣量為68kg·m2,與仿生魚的等效轉(zhuǎn)動(dòng)慣量基本相同.試驗(yàn)時(shí),由控制器控制腰電機(jī)轉(zhuǎn)子角位置正弦規(guī)律變化.兩個(gè)磁粉制動(dòng)器線圈串聯(lián)由直流電源通入電流,調(diào)整電流改變磁粉制動(dòng)器的制動(dòng)轉(zhuǎn)矩,給樣機(jī)軸伸兩側(cè)施加相同恒定阻轉(zhuǎn)矩.樣機(jī)的轉(zhuǎn)矩和轉(zhuǎn)速由轉(zhuǎn)矩轉(zhuǎn)速傳感器測得.
圖13?腰電機(jī)壽命試驗(yàn)平臺(tái)(局部)
圖14?樣機(jī)壽命試驗(yàn)平臺(tái)示意
表4?腰電機(jī)壽命試驗(yàn)時(shí)的運(yùn)行效率
Tab.4?Operation efficiency of waist motor during life test
由表4可見,在恒定阻轉(zhuǎn)矩作用下,樣機(jī)實(shí)測運(yùn)行效率值與采用電機(jī)效率云圖數(shù)據(jù)計(jì)算得到的理論值比較接近.試驗(yàn)結(jié)果說明樣機(jī)設(shè)計(jì)與效率分析方法可行.
(1) 以仿生魚動(dòng)力模型為設(shè)計(jì)依據(jù),對仿生魚腰關(guān)節(jié)用永磁同步電動(dòng)機(jī)采用有限轉(zhuǎn)角旋轉(zhuǎn)電樞式結(jié)構(gòu),能夠克服安裝空間限制,且增大電機(jī)單位體積下輸出轉(zhuǎn)矩,滿足了低速大扭矩工況需要.
(2) 合適選取電機(jī)電樞鐵心齒寬,可在滿足轉(zhuǎn)矩要求下達(dá)到驅(qū)動(dòng)電機(jī)輕質(zhì)高效的設(shè)計(jì)要求.
(3) 樣機(jī)試驗(yàn)結(jié)果表明電機(jī)設(shè)計(jì)和運(yùn)行效率分析方法可行,所設(shè)計(jì)的電機(jī)能夠滿足仿生魚特定運(yùn)行頻率下的運(yùn)行效率要求,且在全運(yùn)行范圍內(nèi)具有較高的運(yùn)行效率.為仿生魚高效驅(qū)動(dòng)電機(jī)設(shè)計(jì)提供了方法參考.
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Design of Limited Angle Rotational Armature Permanent Magnet Synchronous Motor
Chen Yiguang,Shi Yichen,Shen Yonghuan
(School of Electrical and Information Engineering,Tianjin University,Tianjin 300072,China)
To minimize operating noise,increase the mean time between failures of biomimetic fish,and save maintenance costs,the electric motor for driving biomimetic fish waist joint(waist motor)was adopted in a direct-drive mode,which should be light weight and efficient. First,mechanical analysis of biomimetic fish caudal fin was conducted in combination with the hydrodynamics theory based on the fish body size and structure and caudal fin flapping pattern.The waist motor output torque and power were acquired through its installation position,rotational angular velocity,and force on the caudal fin.Because the torque was proportional to the square of the air gap diameter,the external rotor structure was selected to meet the low-speed and high-torque demands.The limited angle rotational armature permanent magnet synchronous motor(PMSM)used as the waist motor was proposed to consider the space constraint of the installation and the restricted operating angle of the waist motor.By changing the external rotor motor topology structure,the traditional permanent magnet external rotor was fixed to use as a stator,and the traditional stator armature was transformed to be rotor armature with a limited rotational angle.Thus,the installation space limitation problem was solved while increasing the output torque per unit volume.Using finite element analysis,a 54-slot 60-pole limited angle rotational armature PMSM was designed.Meanwhile,an appropriate tooth width was selected to achieve the design goal of light weight and high efficiency.Through analysis,motor operation efficiency reached 75.5% when the caudal fin flapping frequency was 0.35Hz,which met the requirement of not less than 75%.Finally,the life test of the prototype was conducted.Results show that the motor with this structure can meet the requirement of waist joint drive and possesses high operation efficiency.
permanent magnet synchronous motor;limited angle;rotational armature;operation efficiency
TM351
A
0493-2137(2020)11-1120-08
10.11784/tdxbz201910021
2019-10-13;
2019-11-19.
陳益廣(1963—??),男,博士,教授.
陳益廣,chenyiguang@tju.edu.cn
(責(zé)任編輯:孫立華)