中英文文獻翻譯-一種永磁雙穩(wěn)態(tài)電磁離合器裝置的分析與設計

中英文文獻翻譯-一種永磁雙穩(wěn)態(tài)電磁離合器裝置的分析與設計,中英文,文獻,翻譯,一種,永磁,雙穩(wěn)態(tài),電磁離合器,裝置,分析,設計 附錄A 文 章 一種永磁雙穩(wěn)態(tài)電磁離合器裝置的分析與設計 蔡萬麗，顧成林，胡曉東 先進電磁工程技術國家重點實驗室 華中科技大學電氣與電子工程學院，武漢430074;電子郵件:clgu@mail.hust.edu.cn(C.G.);xdhu@hust.edu.cn(X.H.) *發(fā)件人應向其發(fā)出信函;電子郵件:wlcai@hust.edu.cn; 電話:+ 1 - 86-134-3718-8225。 學術編輯:保羅·斯圖爾特 電話:+86-134-3718-8225。 學術編輯:保羅·斯圖爾特 收到:2015年3月9日/接受:2015年6月1日/出版:2015年6月11日 摘 要 在內燃機車和集中電動汽車中，離合器已被廣泛應用于汽車、汽車、汽車、汽車等領域。本文提出了一種將永磁雙穩(wěn)態(tài)電磁離合器單元(PMBECU)特別引入輪式電動汽車，使輪轂與輪轂之間的剛性連接更加靈活。首先闡述了PMBECU的工作原理。然后，提出并分析了基本的磁路模型，然后通過研究PM漏磁系數(shù)對主要結構參數(shù)進行優(yōu)化設計。此外，根據(jù)PMBECU的基本電磁特性，提出了當前的脈沖電源，并通過改進的有限元方法，分析了使PMBECU的運行及其動態(tài)特性的最小脈沖寬度。最后，研制并測試了樣機，驗證了所有的分析結果。 關鍵詞:離合器單元；動力學分析；電磁設計；有限元法(FEM)；永磁；雙穩(wěn)態(tài)操作 1.介紹 電動汽車(EV)最近密集調查作為潛在解決方案不斷增長的能源危機和環(huán)境污染的問題[1 - 4],專注于傳動形式,電機、控制器、電池、能源系統(tǒng),駕駛舒適,等等。與集中傳動相比,輪電動汽車驅動電動汽車被認為是更有能力的驅動形式在不遠的將來[5 - 7],由于其直接驅動的優(yōu)點(no-gearbox),更靈活的控制策略(每個輪子的扭矩是獨立控制的)，高的機械完整性(與傳統(tǒng)的汽油車有很大的不同)。然而，由于輪轂與電機之間的剛性連接，在突然啟動和停止過程中不可避免地會引入機械沖擊和電磁脈沖，可能會對電機和控制器造成危害，降低驅動舒適性[8-10]。 在傳統(tǒng)汽油車的基礎上，通過在輪轂與電機之間引入離合器，使剛性連接更加靈活的[11]，可以改善這種電動汽車輪轂的機電沖動。仿真和實驗結果之間的傳統(tǒng)離合器電機和負載在(12、13)表明,起動電流和混蛋在離合器耦合不同空閑下開始速度可以減少小于1/2相比,直接開始,電動勢和沖動回控制器可以通過分離消除制動(電動機停止自然斷開后制動負荷)。此外，在混合動力電動汽車中，傳統(tǒng)離合器在空轉時用于切斷發(fā)動機或電機，以避免自旋損失，延長機器[14]的生命周期。此外，在輪內驅動的電動汽車中，在滑行[15]時，采用離合器將電機從輪轂上分離，以減少損失。 然而，傳統(tǒng)的機械式離合器系統(tǒng)[16,17]不適合在集線器中可用的有限空間，并且需要定期維護，這使得它不適合在車輪內的電動汽車驅動器。此外，電磁離合器[18,19]，容易被電流控制，耗能大，同時也存在在轂內調節(jié)形狀的問題。在[20]的其他離合器中，一個人遇到一個或所有上述的問題，因此也不是合適的選擇。本文提出了一種永磁雙穩(wěn)態(tài)電磁離合器單元(PMBECU)，它是由電流控制，由永磁保持在穩(wěn)定狀態(tài)，因此是一種節(jié)能的裝置，并且具有平直結構，使其在有限的空間內的放置成為可能。離合器系統(tǒng)是通過在電動機周圍裝配幾個PMBECUs，結合摩擦或顎對來實現(xiàn)的。 作為離合器系統(tǒng)的關鍵部件，本文重點研究了PMBECU的電磁設計和分析。電磁閥[21]、電動工具[22]、振子[23、24]、換擋器[25-27]等線性電磁裝置的設計與分析，主要采用有限元法(FEM)進行。同樣，為了滿足在輪轂有限空間內適應離合器的需要，F(xiàn)EM對PMBECU的主要結構參數(shù)進行了優(yōu)化設計，重點研究了PM的漏磁系數(shù)。此外，為了實現(xiàn)對PMBECU操作的簡單可靠控制，通過改進FEM計算了PMBECU的動態(tài)特性，表明低功耗電容脈沖電源是非常合適的。分析了溫度對動態(tài)性能的影響。通過對樣機的測量，驗證了分析方法和結果的正確性。 2.工作原理 PMBECUs的裝配實現(xiàn)了輪轂與電機之間的柔性連接如圖1a所示，PMBECU的結構如圖1b所示，其中兩個具有相反極性的PMs安裝在剛性e型鐵磁基的兩側。鐵磁驅動裝置被放置在兩個非磁性的低摩擦滑道中。兩個線圈連接n系，繞在每個滑道上。 圖1所示(a)輪轂與電機的柔性連接(b) PMBECU的結構 Figure 1 (a) Flexible connection of hub and motor (b) Structure of the PMBECU PMBECU的二維(2D)分析模型，其主要結構參數(shù)標注如圖2所示，其中正確的方向為力和運動變量的正方向。 圖2 PMBECU的二維分析模型 Figure 2 2D analysis model of the PMBECU 沒有注入線圈的PMBECU的通量線分布如圖3a所示。顯然，動力裝置由左PM保持在穩(wěn)定狀態(tài)，不消耗能源。當電流方向合適時(即，如圖2所示的當前方向)和訪問線圈的值，移動器極化，相應的通量線分布如圖3b所示。動車機將很快被由此產生的電磁力從左穩(wěn)態(tài)推進到右。同時，位置傳感器自動切斷電流，電機由正確的PM控制，再次不消耗任何能量，雙穩(wěn)態(tài)運行。 圖3磁通線分布(a)穩(wěn)定狀態(tài)(b)運動 Figure 3 Magnetic flux lines distribution. (a) Steady state; (b) Action. 很明顯,PMBECU具有平面結構因此適合放置在一個有限的空間,和接觸和分離之間的轉換是真正可以方便地操縱,因此只有一個即時切換所需電流,但大多數(shù)時間是在一個穩(wěn)定的狀態(tài)由一個點,因此節(jié)能。 3電磁設計 3.1磁路模型 根據(jù)磁通線分布如圖3所示,假設鐵磁材料有無限的滲透率和忽視接觸的空氣間隙,磁路關系的PMBECU線圈開路的情況下可以通過一個簡化的表示磁網絡如圖4所示。 圖4 簡化磁網絡 Figure 4 Simplified magnetic network 磁網絡包括兩個獨立的分支,是Φδj magneto-motive迫使布置點的氣隙,磁通穿過極面發(fā)的每一邊,方程(1)-(3),分別為: Fmj = H c hm δ j ( kσj hm μr + δ j ) (1) L δj = μ0 Sm δ j (2) Br,Hc,μr剩磁、矯頑力,和相對滲透率的點,hm和Sm的厚度和極面區(qū)域點,δj氣隙長度是標記在圖2中,μ0空氣的磁導率,和kσj是漏磁系數(shù)定義為: kσj = F mj F δj (4) Φmj在哪主磁通通過底部的點。 麥克斯韋應力張量由下式[27]給出 t n = (B n2 - Bs2 ) (2μ0 ) (5) t s = B n Bs μ0 式中Bn、Bs分別為動器上通量密度的外法向分量和切向分量。在無限滲透表面之外，通量密度只有一個法向分量。因此,結合方程(3),夾持力(水平)穩(wěn)態(tài)(δ1 = 0,δ2 = lt,lt是旅行的長度mover)可以近似計算: ? ? f H = B δ21 S m - B δ22 S m = B r2 Sm ? 1 - 1 ÷ ? ÷ (6) 2 μ 0 2 μ 0 2μ0 ( lt hm ) 2 è ? ? kσ2 + μr ÷ ? ÷ 迫使規(guī)范化fb = 0.5 br2sm /μ0(下同),夾持力是: f H = 1- 1 (kσ2 + μr lt hm ) 2 (7) 顯然,PMBECU的夾持力是由kσ2(泄漏系數(shù)δ= lt)、旅行長度厚度的比值lt /嗯,下午和晚上的特點。此外,漏通量kσ2系數(shù)是一個函數(shù)的結構參數(shù),并可以通過方程計算。 (4)有限元分析得到的磁通后 通過將電流從0增加，可以得到移動者所經歷的電磁力，進而得到理想的閾值電流，該閾值電流對移動者的作用至關重要，與水平電磁力fmx = 0相對應。本文將電流歸一化為ib = Hchm/N，其中N為一個線圈的匝數(shù)。 3.2主要結構參數(shù)設計 PMBECU在絕大多數(shù)情況下都是穩(wěn)定狀態(tài)，由保持力可靠地維持，因此保持力是最重要的指標。根據(jù)方程(7),漏磁系數(shù)kσ2在分離方面,這是一個結構參數(shù)的函數(shù),在夾持力有很大的影響。此外，漏磁系數(shù)決定了PM的合理使用。因此，主要的結構參數(shù)(如圖2所示)，即點wm的寬度,高度從下午到基地惠普、和旅游發(fā)lt的長度,通過研究kσ2,優(yōu)化結合保持力和閾值電流，其中其他尺寸比(與hm成比例)保持不變，其中一個參數(shù)變化范圍為hp/hm = 1.2, wm/hm = 2.5, lt/hm = 2。 kσ2對不同結構參數(shù)的變化如圖5所示。從圖5a可以看出，當hp大于hm的1.5倍時，泄漏通量系數(shù)增加的非常緩慢，所以hp最好在hm的1-1.5倍以內， 這也說明PMBECU是可以平坦結構的。同樣，wm最好是hm的2.5倍，如圖5b所 示。圖5 c顯示了漏磁系數(shù)與lt kσ2幾乎線性增加,顯示沒有明顯的拐點。但是從圖5d可以看出，當lt比hm大2倍時，保持力增長非常緩慢，同時閾值電流不斷增大，使得動刀的動作更加困難。因此，在1.5-2倍于PM的厚度范圍內的lt是更合理的。 圖5 pimization(a)從PM到base的高度(b)點的寬度(c)旅行長度(d)旅行的長度 Figure 5 Opimization (a) Height from PM to base (b) Width of PM (c) Travel length(d) Travel length. 4.動力學分析 4.1.電磁特性 基于上述分析，設計了一個PMBECU原型，其主要參數(shù)如表1所示，如圖6所示。假設搬家公司是固定在不同的位置，改變線圈中的電流(恒直流波)，用有限元法計算磁場，用(5)計算動刀所受的力，得到動刀對電流i和位移x的電磁力如圖7所示。 表1主要設計參數(shù) Table 1 Leading design parameters Parameter Value Parameter Value Thickness of PM hm 2.5 mm Width of base wb 80 mm Width of PM wm 6 mm Remanence of PM Br 0.4 T Length of PM lm 20 mm Coercivity of PM Hc 318 kA/m Height of PM to base hp 3 mm Turns of coil N 60 Travel length lt 4.8 mm Mass of mover m 56 g 圖6 原型 Figure 6 Prototype 從圖7a可以看出，對于開路條件，i = 0水平力曲線表明PMBECU有兩個穩(wěn)態(tài)狀態(tài)，一個是來自PM的磁力，另一個是不穩(wěn)定的平衡點(半行程長度位置)。當動車超過這個不穩(wěn)定點時，即使關閉電流也可以自動將動車拉到另一個穩(wěn)態(tài)。由于電流增加到理想閾值電流i = 0.49，動車開始移動。線圈的最大電流受PM的消磁曲線的拐點(不可逆退磁的臨界點)限制，在這個原型中，i = 0.77。 事實上，由于垂直方向上的不對稱結構，mover經歷了一個向下的垂直電磁力(如圖7b所示)，它引入了摩擦阻力。因此，計算摩擦力和其他誤差(材料、模型、測量等)，實際的閾值電流大于計算值，即為原型的0.52。此外，為了保證PM的性能，最大電流應該限制為iM = 0.7。 圖7 電磁力(a)水平(b)垂直 Figure 7 Electromagnetic forces. (a) Horizontal; (b) Vertical. 當電流大于閾值電流時，合力為正的水平力開始驅動動車，力是位移單調遞增的函數(shù)。在經過PMBECU的中點后，mover可以到達另一個穩(wěn)定狀態(tài)，電流關閉(即:，脈沖電流只維持行程長度寬度的一半)。此外，考慮到慣性運動和運動摩擦系數(shù)的變化，電流的脈沖寬度可以更小。因此，需要對PMBECU進行動力學分析。 4.2動力學方程和分析方法 由于PMBECU的運動對稱性，只研究了動刀從左向右的運動。假設靜摩擦系數(shù)等于運動摩擦系數(shù)，則確定動力學特性的磁運動學耦合數(shù)學方程為: f mx - f z = mdv dt (8) v = dx dt (9) f mx = q ( x, i ), f my = p ( x, i) (10) f z = μs ( f my + mg) (11) 那么fmx和fmy水平和垂直電磁力推動者,fz阻力,v是發(fā)的速度,μs靜摩擦系數(shù)是0.065,這個原型(測量)和g重力加速度是恒定的。 PMBECU的動力學分析是為了說明磁場與運動的耦合關系。為適應不同結構尺寸的不同摩擦阻力條件，提出了一種改進的有限元分析方法。如圖8a所示，在靠近PMs點處建立兩個lt長度的矩形區(qū)域(即材料變化區(qū))，并將其均勻嚙合成n步的四邊形，即，步長為x = lt/n。左邊和右邊的初始滲透率是設置為鐵(μFe)和空氣(μ0)分別。如圖8b所示，如果第一個x的滲透率與左邊的材料相嚙合變異區(qū)域變成μ0第x網格在正確的μFe,同樣意識到x位移的推動者。因此，一次網格可以覆蓋移動機[23]的移動長度位移。 (a) n·Dx μFe μ0 μ0 μFe μFe μ0 （b） 圖8網格技術 (a)網 (b)原則 Figure 8 Onetime mesh technique (a) Mesh (b) Principle 此外，通過將位移設為已知質量，而將時間設為未知變量，并在每次材料變化前計算時間、速度和電流，整個PMBECU運動過程(即， PMBECU的動力學特性可通過一次網格求解。這種改進后的FEM分析流程圖如圖9所示，其中既考慮了當前的變化，又考慮了電阻的變化，這很容易通過商業(yè)FEM軟件(如ANSYS可編程設計語言)實現(xiàn)。在本文中，在動車的每一邊，材料變化區(qū)域的前部分都被精細地嚙合，后部分被粗略地嚙合(因為前部分位移需要更多的時間)，從而提高精度，減少計算量。 4.3最小驅動脈沖寬度 脈沖閾值電流訪問(在脈沖寬度的計算,給出了位移的長度),可以解決改進的有限元動力學方程,然后脈沖寬度的時候,最后的力和速度曲線和位移和不同的脈沖寬度,都可以獲得。最小脈沖寬度tw是閾值電流的脈沖寬度，該閾值是關鍵的，它支持在接觸和分離之間切換PMBECU，即。，當脈沖寬度小于tw時，動車速度為負值。原型的合力和速度曲線，隨位移和脈寬而變化，如圖10所示。 圖9 用改進的有限元法求解動力學問題的流程圖 Figure 9 Flowchart for solving the dynamics by improved FEM. 圖10 不同脈沖寬度下的動力學特性(a)合成水平力(b)速度 Figure 10 Dynamics characteristic under different pulse width (a) Resultant horizontal force (b) Velocity 被訪問的脈沖電流的寬度越小，電動機所經歷的切換過程就越均勻。當加速位移比減速位移稍長時，則是實現(xiàn)PMBECU在穩(wěn)態(tài)間切換的最小電流脈沖寬度，在本樣機中為tw = 18ms。 5. 實驗驗證 PMBECU的實驗電路和實驗裝置如圖11所示。首先，測量了不同位置的持力，并與有限元法進行了比較。 計算結果(有一個初始氣隙δ1 = 0.1毫米和接觸氣隙的中期部分δ0 = 0.18毫米已占據(jù)在有限元模型),如圖12所示。實驗結果略小于仿真結果，仿真結果主要歸因于PM的圓角，但仍顯示出可接受的工程精度。 圖11 (a)實驗電路(b)實驗平臺①原型②電容器供應③激光位移傳感器 Figure 11 (a) Experimental circuit;(b) Experimental rig① Prototype② Capacitor supply ③ Laser displacement transducer 圖12不同位置的持力比較 Figure 12 Comparison of the holding force at different positions 應用于線圈的脈沖電流近似是由電容器放電產生的低功率脈沖電源。通過改變電容(即，改變脈沖寬度)，調整充電電壓(保持iM = 0.7)，可以得到可行的最小脈沖寬度，在本樣機中為tw = 5.2 ms，對應的放電電流曲線如圖13所示。由于最大放電電流大于閾值電流，且連續(xù)放電電流曲線優(yōu)于矩形脈沖電流，所以小功率電容器電源的最小脈沖寬度要小得多。 錫的動力學實驗PMBECU(環(huán)境溫度為25°C),主要電氣參數(shù)Cb = 8.6 mF,Rb = 1.15?,推動者的位移記錄由一個激光位移傳感器。實際上，改進的FEM也可以得到低功耗電容器電源的動態(tài)特性和最小脈沖寬度，每一步的電流值由電路方程求解。 圖13低功率電源的放電電流曲線對樣機的切換至關重要 Figure 13 Discharge current curve of the low power supply which critically enables the switchover of the prototype 改進的有限元模擬和實驗的比較動力學特征的結果顯示在圖14中,它顯示了一個令人滿意的協(xié)議,除了輕微的反彈的推動者,實驗速度和動態(tài)力發(fā)源于測量位移的微分和二階微分曲線。因此，改進的有限元方法是對PMBECU進行動力學分析的有效方法。更重要的是,在恒流的動力學特征相比,在發(fā)力比較均勻,發(fā)的速度是穩(wěn)定的,和控制更簡單(當前自動衰減沒有斷開的位置檢測),因此代表了PMBECU最優(yōu)供電方案。 圖14 低功率脈沖電源下的動力學特性比較（a）速度 (b)合成水平力 Figure 14 Comparison of dynamics characteristics under low power pulse supply. (a) Velocity(b) Resultant horizontal force 在輪內驅動應用中，該設備工作條件苛刻——振動、溫度變化、電磁干擾等。振動和電磁干擾分別影響PMBECU的機械可靠性和控制可靠性。然而，從電磁分析的角度來看，溫度的變化主要改變了PMBECU的電磁特性。當溫度升高時，電阻大約每攝氏度增加0.43%，電阻Rb 25°C)。最大放電電流imax的對應變化如圖15a所示。如圖所示,當溫度小于0°C,imax是比我大10%將不可逆轉地消磁的點,從而表明釹鐵硼點比鐵氧體點是更好的選擇。當溫度高于150°C,imax小于閾值電流雖然電容器是無限的,這將禁用PMBECU,因此應該避免。圖15 b顯示了最小電容的變化Cmin(Cb 25°C)相比,極度使PMBECU在不同的工作溫度。實驗的四個測點驗證了仿真的有效性。由圖15b可知，當溫度升高時，由于imax的降低，PMBECU的工作需要更大的電容。因此，電容器的尺寸應由最大工作溫度決定。 圖15 電磁特性隨溫度變化(a)最大放電電流(b)最小電容器使PMBECU的工作成為可能 Figure 15 Electromagnetic characteristics variation with temperature (a) Maximum discharge current;(b) Minimum capacitor enables the work of the PMBECU 6.結論 本文提出了一種永磁雙穩(wěn)態(tài)電磁離合器單元，將其引入到輪式電動汽車驅動器中，使輪轂與車輪之間的剛性連接更加靈活。PMBECU的主要結構參數(shù)進行了優(yōu)化,研究泄漏系數(shù),夾持力,和閾值電流,使點的寬度,高度從下午到基地,和旅行的長度最好在分別在2.5，1.2，2次點的厚度。 基于最優(yōu)結構參數(shù)，制作了一個PMBECU原型。基本的電磁特性表明，脈沖電源較好地控制了PMBECU。為此，提出了一種改進的有限元方法，以獲得閾值電流的動態(tài)特性和最小脈沖寬度。通過對原型的實驗測量，驗證了靜態(tài)力和動力學特性的仿真結果。分析和實驗結果均表明，低功率電容器電源非常適合PMBECU，在最大工作條件溫度下決定電容器的尺寸。分析方法和結果為整個離合器系統(tǒng)的進一步設計奠定了堅實的基礎。 參考文獻 1、Chan、C.C.、Bousayle、A、陳、KY、電動、混合動力和燃料電池汽車：結構和建模。IEEE Trime.VEH。技術專家2010, 59, 589—598。 2、Chau、K.T.、Chan、C.C.、劉、C.H.電動和混合動力電動汽車用永磁無刷傳動概述。IEEE Trime.印度電子2008, 55, 2246—2257。 3、李、C.、劉、C.H.、Chau、K.T.：一種用于范圍擴展電動汽車的無磁軸向磁通電機。能量2014, 7, 1483–1499。 4、李，H.D.；Sul，S.K.；CHO，H.S.；李，J.M.先進的換檔和離合器策略的并聯(lián)混合動力汽車。IEEE標準。2000, 6, 26—32。 5、Rahman，K.M.；帕特爾，N.R.；沃德，T.G.；Nagashima，J.M.；CARICCHI，F(xiàn)；Cracimimbi，F(xiàn).用于燃料電池電動和混合動力汽車推進系統(tǒng)的直接驅動輪式電動機的應用。IEEE Trime.印度藥典2006, 42, 1185—1192。 6、薩凱，S，SADO，H.；HORI，Y.運動控制在電動汽車中，四個獨立驅動的輪式馬達。IEEE Trime.機器。1999, 41, 9—16。 7、Ifedi、C.J.、梅克羅、B.C.、布羅克韋、S.T.M.、自夸、G.S.、阿特金森、G.J.、Perovic、D.K. 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E型芯內永磁直線振蕩執(zhí)行器的分析。IEEE Trime.Magn。2009, 45, 4384—4387。 24、Srairi、K.、Feliachi、M.電磁執(zhí)行器行為分析的有限元和參數(shù)化方法。IEEE Trime.Magn。1995, 31, 3497—3499。 25、Kawase、Y、Tatsuoka、S、山口、T.I.交流電磁接觸器工作特性的三維有限元分析。IEEE Trime.Magn。1994, 30, 3244—3247。 26、方、S.H.、林、H.Y.、霍城、S.L.用永磁操動器對低壓斷路器進行瞬態(tài)聯(lián)合仿真。IEEE Trime.Magn。2009, 45, 1242—1245。 27、WO、K.I.；Kwon，B.I.永磁式磁路斷路器的特性分析和修改。IEEE Trime.Magn。2004, 40, 691—694。作者2015；持牌人MDP，巴塞爾，瑞士。本文是一個開放式訪問的文章，在條款和條件下的創(chuàng)作共享屬性許可證（http://Creative VIEMMON.org /許可證/按/ 4）。 附錄B 附錄B Energies 2015, 8, 5598-5612; doi:10.3390/en8065598 OPEN ACCESS energies ISSN 1996-1073 www.mdpi.com/journal/energies Article Analysis and Design of a Permanent Magnet Bi-Stable Electro-Magnetic Clutch Unit for In-Wheel Electric Vehicle Drives Wanli Cai *, Chenglin Gu and Xiaodong Hu State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical & Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China; E-Mails: clgu@mail.hust.edu.cn (C.G.); xdhu@hust.edu.cn (X.H.) * Author to whom correspondence should be addressed; E-Mail: wlcai@hust.edu.cn; Tel.: +86-134-3718-8225. Academic Editor: Paul Stewart Received: 9 March 2015 / Accepted: 1 June 2015 / Published: 11 June 2015 Abstract: Clutches have been used in internal combustion vehicles and concentrated electric vehicles (EVs) to smoothen impulsion while starting and shifting. This paper proposes a permanent magnet bi-stable electromagnetic clutch unit (PMBECU) which is specially introduced into in-wheel EVs to make the rigid connection between hub and wheel more flexible. Firstly, the operation principle of the PMBECU is illustrated. Then, the basic magnetic circuit model is presented and analyzed, followed by optimal design of the main structural parameters by investigating the PM leakage flux coefficient. Further, according to the basic electromagnetic characteristics of the PMBECU, the current pulse supply is put forward, and the minimum pulse width which enables the operation of the PMBECU and its dynamic characteristics are analyzed by an improved finite element method. Finally, a prototype machine is manufactured and tested to validate all the analysis results. Keywords: clutch unit; dynamics analysis; electromagnetic design; finite element method (FEM); permanent magnet; bi-stable operation Energies 2015, 8 5599 1. Introduction Electric vehicles (EV) have been intensively investigated recently as potential solutions for the growing problems of the energy crisis and environmental pollution [1–4], focusing on the drive form, electric motor, controller, battery, energy system, drive comfort, etc. Compared with centralized drive, the in-wheel EV drive is considered the more competent drive form for EVs in the near future [5–7], because of its merits of direct drive (no-gearbox), more flexible control strategy (torque at each wheel is independently controlled), high mechanical integrity (greatly different from conventional gasoline cars). However, the rigid connection between hub and motor, inevitably introduces mechanical shocks and electromagnetic impulsion during sudden start and stop processes, which can potentially harm the motor and controller and reduce drive comfort [8–10]. Referring to traditional gasoline cars, this electromechanical impulsion in in-wheel EV drives can be ameliorated by introducing a clutch between the hub and motor to make the rigid connection more flexible [11]. The simulation and experimental results of a conventional clutch between motor and load presented in [12,13] show that the starting current and jerk in clutch coupling starts under different idle speeds can be reduced to less than 1/2 compared to direct starting, and the impulsive back electromotive force to the controller can be eliminated by detached braking (the motor stops naturally after being disconnected from the braking load). Besides, in hybrid EVs, the conventional clutch has been used to cut off the engine or electrical machine while idling to avoid spin losses and extend the life cycle of the machine [14]. Moreover, in in-wheel driven EVs, clutches have been used to detach the motor from hub to reduce losses while coasting [15]. However, the conventional mechanical clutch system [16,17] is not suitable for the limited space available in a hub and suffers from a need for regular maintenance which makes it unsuitable for in-wheel EV drives. In addition, electromagnetic clutches [18,19], which can be easily manipulated by current control, are energy-consuming and also suffer from the problem of accommodating their shape in the hub. In other clutches [20] one encounters one or all of the aforementioned problems, thus are also not suitable options. This paper proposes a permanent magnet bi-stable electromagnetic clutch unit (PMBECU), which is controlled by current and held by the PM in a steady state, and thus is energy-saving, and it also has a flat structure that makes its placement in a limited space viable. The clutch system is realized by assembling several PMBECUs around motors, combined with friction or jaw pairs. As key parts of the clutch system, this paper focuses on the electromagnetic design and analysis of the PMBECU. The design and analysis of linear electromagnetic devices, such as electromagnetic valves [21], electric tools [22], oscillators [23,24], and switch gears [25–27], are mainly carried out by the finite element method (FEM). Likewise, aiming to satisfy the need to accommodate the clutch in the limited space available in the hub, the optimal design of the main structure parameters of the PMBECU are carried out by FEM which focuses especially on investigating the leakage flux coefficient of the PM. Moreover, in order to realize simple and reliable control of the operation of the PMBECU, the dynamic characteristics of the PMBECU are calculated by improved FEM, which shows that the low power capacitor pulse supply is very suitable. The influence of the temperature on the dynamic performance is also analyzed. The analysis method and results are finally validated by measurements taken on a prototype machine. Energies 2015, 8 5600 2. Operation Principle The assembly of the PMBECUs to realize the flexible connection between hub and motor is shown in Figure 1a, and the structure of the PMBECU, in which two PMs with opposite polarities are mounted on each side of a rigid E-type ferromagnetic base, is shown in Figure 1b. The ferromagnetic mover is placed in two low-frictional slideways which are non-magnetic. Two coils are connected n series and wound around each slideway. Tyre PMBECU Mover Coil PM Wheel motor PM Slideway Base Slideway (a) (b) Figure 1. (a) Flexible connection of hub and motor; (b) Structure of the PMBECU. The 2-dimensional (2D) analysis model of the PMBECU with its main structure parameters labeled is shown in Figure 2, where the right direction is prescribed as positive for force and movement variables. FEM boundary hm wm fz mg fmx hp fmy x(d1) d2=lt-d1 o Figure 2. 2D analysis model of the PMBECU. The flux line distribution of the PMBECU without current injected into the coils is shown in Figure 3a. Apparently, the mover is held by the left PM in a steady state without energy consumption. When current with a suitable orientation (i.e., the current direction shown in Figure 2) and value accesses the coils, the mover is polarized, and the corresponding flux lines distribution is shown in Figure 3b. The mover will soon be propelled from the left steady state to the right by the resultant electromagnetic force. Meanwhile, the current is switched off automatically by the position sensor, and the mover is held by the right PM, again without any energy consumption, thus it is bi-stable. Energies 2015, 8 5601 (a) (b) Figure 3. Magnetic flux lines distribution. (a) Steady state; (b) Action. It is evident that the PMBECU has a flat structure thus is suitable for placement in a limited space, and the switchover between engagement and disengagement is electrically-controlled thus it can be conveniently manipulated, and only an instant current is required for switchover, but most time it is in a steady state which is held by a PM and thus is energy-saving. 3. Electromagnetic Design 3.1. Magnetic Circuit Model According to the magnetic flux line distribution shown in Figure 3a, assuming the ferromagnetic material has infinite permeability and neglecting the contact air gaps, the magnetic circuit relations of the PMBECU under open circuit of the coils conditions can be expressed by a simplified magnetic network as shown in Figure 4. L d1 L d2 Fm1 F d1 F d2Fm2 Figure 4. Simplified magnetic network. The magnetic network comprises two independent branches, where Φδj are the magneto-motive force furnished to the air gap by the PM, magnetic flux pass through the pole face of the mover at each side, Equations (1)–(3), respectively:  Fmj (j = 1, 2), Λδj, and air gap permeance, and which are calculated by Fmj = H c hm δ j ( kσj hm μr + δ j ) (1) L δj = μ0 Sm δ j (2) Energies 2015, 8 5602 F δj = B r S m ? δ j ? (3) ? kσj + μr ÷ è hm ? where Br, Hc, and μr are remanence, coercivity, and relative permeability of the PM, hm and Sm are the thickness and pole face area of the PM, δj is the air gap length as labeled in Figure 2, μ0 is the permeability of air, and kσj is the leakage flux coefficient which is defined as: kσj = F mj F δj (4) where Φmj is main magnetic flux through bottom face of PM. The Maxwell stress tensors are given by the following equation [27]: t n = (B n2 - Bs2 ) (2μ0 ) (5) t s = B n Bs μ0 where Bn, Bs are the outer normal and tangential components of the flux density on the mover, respectively. Out of an infinite permeable surface, the flux density only has a normal component. Hence, combined with Equation (3), the holding force (horizontal) at steady state (δ1 = 0, δ2 = lt, lt is the travel length of the mover) can be approximately calculated by: ? ? f H = B δ21 S m - B δ22 S m = B r2 Sm ? 1 - 1 ÷ ? ÷ (6) 2 μ 0 2 μ 0 2μ0 ( lt hm ) 2 è ? ? kσ2 + μr ÷ ? ÷ With forces normalized to fb = 0.5Br2Sm/μ0 (the same hereafter), the holding force is: f H = 1- 1 (kσ2 + μr lt hm ) 2 (7) Apparently, the holding force of the PMBECU is determined by kσ2 (leakage coefficient at δ = lt), the ratio of travel length to thickness of the PM lt/hm, and the PM characteristics. Moreover, the leakage flux coefficient kσ2 is a function of the structure parameters, and can be calculated by Equation (4) after the magnetic flux derived from FEM analysis. By increasing the current from 0, the electromagnetic force experienced by the mover can be obtained, and then the ideal threshold current iT which critically enables the action of the mover can be obtained by FEM as well, corresponding to the horizontal electromagnetic force fmx = 0. In this paper, current is all normalized to ib = Hchm/N, where N is the number of turns for one coil. 3.2. Main Structure Parameters Design The PMBECU works at steady state most of the time, which is reliably maintained by the holding force, thus the holding force is the most significant index. According to Equation (7), the leakage flux coefficient kσ2 at the detached side, which is a function of the structure parameters, has a great influence on the holding force. Moreover, the leakage flux coefficient determines the reasonable usage of the PM. Thus, the main structure parameters (as labelled in Figure 2), i.e., the width of the PM wm, the height from the PM to the base hp, and the travel length of mover lt, are optimized by studying kσ2, Energies 2015, 8 5603 combined with accounting for the holding force and threshold current, where, other size ratios (proportioned to hm) remain unchanged while one varies the parameters within the ranges hp/hm = 1.2, wm/hm = 2.5, lt/hm = 2. The variation of kσ2 versus different structure parameters is shown in Figure 5. Figure 5a shows that the leakage flux coefficient increases quite slowly when hp is 1.5 times bigger than hm, hence hp would better be within 1–1.5 times of hm, which also indicates the PMBECU is capable of a flat structure. Likewise, wm would better be around 2.5 times of hm as seen in Figure 5b. Figure 5c shows the leakage flux coefficient kσ2 increases almost linearly with lt, which shows no clear inflection point. But from Figure 5d, the holding force increases very slowly when lt is 2 times larger than hm, meanwhile, the threshold current keeps increasing, which makes the action of the mover harder. Hence, lt within 1.5–2 times the thickness of the PM is more sensible. Leakage flux coefficient kσ2 Leakage flux coefficient kσ2  5 4 3 2 1 0 0 1 2 3 Height of PM to base/thickness of PM hp/hm (a) 7 6 5 4 3 2 1 0 0 1 2 3 4 Travel length/thickness of PM lt/hm (c)  10 σ2 8 k coefficient 6 flux 4 Leakage 2 0 0 1 2 3 4 5 6 7 Width of PM/thickness of PM wm/hm (b) value) 1 1 value) 0.8 0.8 (P.U. (P.U. 0.6 fH T 0.6i H force f 0.4 0.4 iT current Holding 0.2 0.2 0 0 Threshold 1 2 3 0 4 Travel length / thickness of PM lt/hm (d) Figure 5. Opimization. (a) Height from PM to base; (b) Width of PM; (c) Travel length; (d) Travel length. 4. Dynamics Analysis 4.1. Electromagnetic Characteristics Based on the aforementioned analyses, a PMBECU prototype designed with the main parameters listed in Table 1 is shown in Figure 6. Assuming the mover is fixed at different positions, changing the Energies 2015, 8 5604 current (constant DC wave) in the coil, computing the magnetic field by FEM and the forces experienced by mover by (5), then the electromagnetic forces on the mover versus current i and displacement x are obtained as shown in Figure 7. Table 1. Leading design parameters. Parameter Value Parameter Value Thickness of PM hm 2.5 mm Width of base wb 80 mm Width of PM wm 6 mm Remanence of PM Br 0.4 T Length of PM lm 20 mm Coercivity of PM Hc 318 kA/m Height of PM to base hp 3 mm Turns of coil N 60 Travel length lt 4.8 mm Mass of mover m 56 g Figure 6. Prototype. From Figure 7a, for open circuit conditions, the i = 0 horizontal force curve indicates that the PMBECU has two steady states held by the magnetic force from the PM, and an unstable equilibrium point (the half travel length location). When the mover exceeds this unstable point, the mover can be drawn to the other steady state automatically even if the current is switched off. Since the current increases to the ideal threshold current (enabling the action of the mover) i = 0.49, the mover starts moving. The maximum current in the coil is limited by the inflection point of the demagnetizing curve of the PM (critical point of irreversible demagnetization), which is i = 0.77 in this prototype. In fact, because of the asymmetric structure in the vertical direction, the mover experiences a downward vertical electromagnetic force (as shown in Figure 7b) which introduces frictional resistance. Hence, accounting for friction, and other errors (material, model, measuring, etc.), the real threshold current iT is bigger than the calculated value, which is iT = 0.52 for the prototype. Moreover, to guarantee the performance of the PM, the maximum current should be limited to iM = 0.7. Energies 2015, 8 5605 Horizontal force fmx (P.U. value)  3 2 1 0 -1 0  i = 0.7 i = 0.49 i = 0 1.2 2.4 3.6 4.8 Displacement x (mm) (a)  Vertical force fmy (P.U. value)  2 1.5 1 0.5 0 0  i = 0.7 i = 0.49 i = 0 1.2 2.4 3.6 4.8 Displacement x (mm) (b) Figure 7. Electromagnetic forces. (a) Horizontal; (b) Vertical. When the current is larger than the threshold current, the resultant positive horizontal force starts to drive the mover, and the force is a monotonously increasing function of the displacement. After moving through the middle point of the PMBECU, the mover can reach another steady state with the current switched off (i.e., the pulse current sustains only half the travel length width). What’s more, considering the inertial motion and variation of the kinetic friction coefficient, the pulse width of the current can be even smaller. Thus, a dynamics analysis of the PMBECU should be carried out. 4.2. Dynamics Equations and Analysis Method Because of the motion symmetry of the PMBECU, only the movement of the mover from left to right is investigated. Supposing the static friction coefficient is equal to the kinetic friction coefficient, then the magnetic-kinematic coupled mathematic equations which determines the dynamics characteristics are described as: f mx - f z = mdv dt (8) v = dx dt (9) f mx = q ( x, i ), f my = p ( x, i) (10) f z = μs ( f my + mg) (11) where fmx and fmy are the horizontal and vertical electromagnetic forces on the mover, fz is the resisting force, v is the velocity of the mover, μs is the static friction coefficient which is 0.065 in this prototype (measured), and g is the acceleration constant of gravity. The dynamics analysis of the PMBECU is to illustrate the coupling of the magnetic field and the movement. To cope with the varying friction resistance conditions of the PMBECU, and give consideration to the convenience of analysis of varied structure sizes, an improved FEM is proposed. As shown in Figure 8a, two lt length rectangular areas (namely, the material variation area) in proximity to the PMs are established and uniformly meshed into n steps of quadrilateral shape, i.e., the step length is x = lt/n. The initial permeability of the left part and the right are set as iron (μFe) and air Energies 2015, 8 5606 (μ0) respectively. As shown in Figure 8b, if the permeability of the first x meshes in the left material variation area is changed into μ0 and the first x meshes at the right into μFe, a x displacement of the mover is equivalently realized. Thus, a onetime mesh can cover the travel length displacement of the mover [23]. Y Z X (a) n·Dx μFe μ0 μ0 μFe μFe μ0 (b) Figure 8. Onetime mesh technique. (a) Mesh; (b) Principle. Further, by setting displacement as a known quality but time as an unknown variable, and calculating the time, velocity, and current before each time of material variation, the whole PMBECU movement process (i.e., the dynamics characteristics of the PMBECU) can be solved by using only a onetime mesh. This improved FEM analysis flow chart is shown in Figure 9, where both the current change and resistance variation can be taken into account, w