基于ANSYS8.0的永磁直線電機的有限元分析及計算

基于ANSYS8.0的永磁直線電機的有限元分析及計算,基于,ansys8,永磁,直線,電機,機電,有限元分析,計算 基于ANSYS8.0 的永磁直線電機的有限元分析及計算學生姓名：沈沉 指導(dǎo)教師：余佩瓊 浙江工業(yè)大學信息工程學院電氣工程系摘 要永磁直線電機是一種具有很高定位精度的新型電機。不同與其他勵磁的直線電機，它采用永磁體作為勵磁源。研究其磁場分布及力特性具有重要意義。相對于傳統(tǒng)的解析法，有限元數(shù)值分析可以縮短電機的設(shè)計周期及減少設(shè)計成本，可對直線電機的磁場及力得出精確的分析。ANSYS8.0是一種在工程中廣泛使用的有限元分析軟件，采用該軟件中的電磁場分析功能對永磁直線電機的磁場進行有限元的分析和計算，并在此分析的基礎(chǔ)上對永磁直線電機的力場做進一步的計算和分析，對永磁直線電機的設(shè)計具有重要的工程意義。通過電磁場的有限元數(shù)值分析方法，利用通用有限元分析軟件ANSYS8.0建立平板型單邊永磁直線電機的有限元模型，分析其2維靜態(tài)磁場，得到初步的分析結(jié)果，并在這個分析的基礎(chǔ)上對永磁直線電機的力場進行了進一步的分析，計算直線電機的推力和法向力，結(jié)合永磁直線電機的靜態(tài)磁場，研究了永磁直線電機推力及法向力和電流變化的相互關(guān)系，對今后永磁直線電機的設(shè)計和研究具有一定的參考意義。關(guān)鍵詞永磁直線電機、有限元、ANSYS、電磁場、推力、法向力Finite Element Analysis and Calcultation of a Permanent Magnet Linear Motor Based on ANSYS8.0Student: Chen Shen Advisor: Peiqiong YuDepartment of Electric Engineering College of Information Engineering Zhejiang University of TechnologyAbstractThe permanent magnet linear motor is a kind of new electrical engineering that has the very high fixed position accuracy.The differents between the permanent linear motor and the type of non-permanent is that it adopts thepermanent be the source of dlux Opposite in traditional resolution method,Finite element analysis can shorten the design period of the electrical engineering and reduce to the design cost,it also can get the analysis of a precision tu the magnetic field and fotce of the linear motor the ansys8.0 is a finitr element analvtical software.Throught the method of the Finite element for the electromagnetic analysis,we use ANSYS8.0 creat a model for the Permanent magnet lineat motor with finite element method.We analysis its 2-D setaic magnetic and get the first result. Then we analysis the force field by finish the analysis of its magetic field We calaulate the thrust and normal force combining the analysis of the permanent magnet linear motor,study the relationship between thecurrent and thrust,normal force.The work for this paper can give some help and advice to the study and design of the permanent linear motor KeywordsPMLSM, ANSYS, FEM,Electromagnetic field, thrust, normal force浙江工業(yè)大學 2005 屆本科畢業(yè)設(shè)計英文翻譯課 題 ：基于 ANSYS8.0 的永磁直線電機的有限元分析及計算學 院：信息工程學院專 業(yè)：電氣工程及其自動化姓 名：沈 沉指導(dǎo)老師：余佩瓊新型直接驅(qū)動管型直線無刷永磁電動機的發(fā)展Won-jong Kim and Bryan C.Murphy摘要：這篇文章介紹了一種新型管型直線無刷永磁電動機的設(shè)計。在這個設(shè)計中，磁體作為運動部件依照NS-NS—SN-SN的方式導(dǎo)向的，這樣在同名極區(qū)域能夠產(chǎn)生更高的磁力。我們發(fā)展了一種分析的方法用來計算這種電動機推力和設(shè)計傳動器的大小。直線電動機與一個位置檢測器，3個功率放大器和一個控制器協(xié)力運行，這樣形成了一個完整的控制緊密致動的解決方案。實時數(shù)字控制器提高了電動機的動態(tài)性能并且增益調(diào)度的使用減少了非線性死區(qū)的影響。在它的初速電流狀態(tài)，電動機對一個5-mm的階躍命令的響應(yīng)具有30ms的上升時間， 60ms的穩(wěn)定延遲時間和25% 超調(diào)量。電動機有1.5m/s的最大速度和最高10g的加速度。它有一個10－cm的工作行程和最大26n的輸出推力。這種電動機緊湊的尺寸顯示它能夠用在需要中等輸出力和精度的機械應(yīng)用中，比如說機器人gripper定位或者傳動. 值得注目的是電動機的移動部分能夠伸展超過它的固定支撐基座。這個延伸的能力使它在需要一個小的，直接驅(qū)動的致動器應(yīng)用中非常有用，因為這種致動器工作環(huán)境是在一個不舒服，拘束的空間環(huán)境中。關(guān)鍵字: 直接驅(qū)動的直流電動機，直線 致動器，永磁電動機，實時數(shù)字控制，管型電動機1. 引言在本文中所記述的工作的目的是發(fā)展一種新型的具有快速，平滑，帶10-cm工作行程緊密定位的致動器。在圖1中所示的直接驅(qū)動的管型直線無刷永磁電動機（LBPMM）有一個無槽的定子，能夠提供沒有頓振的平滑轉(zhuǎn)換。這個設(shè)計選擇犧牲更高的輸出推力的能力，來實現(xiàn)平滑致動。這種致動器的應(yīng)用包括緊密定位和機器人致動的需要。在靈巧的手[1]和終端復(fù)合連接的機器人手臂中直線致動器用來作為機器人的末端受動器。Budig 論述了不同的直線電動機在許多不同的領(lǐng)域中的應(yīng)用[2]。圖1.裝配好的管裝直線電動機安裝在精密光學桌面上，用銅管和右邊的LVDT連接。永磁體放在銅管里面。在電動機后面可以看到放大器直線致動器被用在水壓的或是氣壓泵中，在需要高輸出力的無精確下滑要求的應(yīng)用中相當有效。其他的致動器使用無靜電回轉(zhuǎn)電機和導(dǎo)螺桿或是其他的旋轉(zhuǎn)到直線轉(zhuǎn)換裝置相連接，這就帶來了根多的復(fù)雜因素包括增長的反沖和移動部分因為聯(lián)接或齒輪增加的質(zhì)量。因此, 由永磁體和載流線圈組成的LBPMM,特別適合用來做精密定位上的應(yīng)用。在LBPMM和其他直接驅(qū)動系統(tǒng)的領(lǐng)域（直接驅(qū)動就是指負載由電動機直接推動），以經(jīng)有了很多的貢獻。LBPMM常被應(yīng)用在單自由度和多自由度的精密定位中。 Lequesne調(diào)查了許多按照轉(zhuǎn)換率在5到20mm內(nèi)而設(shè)計的永磁直線電動機性能指標。 [3]Kim和Trumper et. al論證了一個6自由度的平板LBPMM能夠被用在納米級的精密定位中 [4,5]。這個裝置是由包含一個固定基座的載流線圈組成，固定基座在由永磁體陣列組成的滾筒的下面。當給它一定的電壓，線圈輕輕浮在滾筒中，并允許重要的平移和旋轉(zhuǎn)在底盤平面里。Berhan, 等人討論了Halbach磁體陣列[6]在新型無鐵心管型LBPMM中的使用[7,8] 。Halbach 陣列是由軸對稱的八邊形導(dǎo)向矩形永磁體形成的，它可以近似的等效為一個圓柱型的Halbach陣列。本文所提出設(shè)計的的電動機和以上所提到的電動機的主要區(qū)別它有一個更簡單的由圓柱型永磁體組成的mover，具有更緊湊的尺寸，在建筑里的使用也更加容易。Ishiyama, 等人設(shè)計了一種管型LBPMM能夠用來作為驅(qū)動圖像閱讀裝置里的托架和其他用途的工具[9] 。這個設(shè)計遺留下一批空的成放射狀磁化的永磁體，每個磁極與鄰近的磁極相互吸引。這種結(jié)構(gòu)常常被用來制造相關(guān)的長型管型磁鐵陣列，作為電動機的固定組成部分。本次的設(shè)計與其主要不同在于磁體的磁化方向和電機的構(gòu)造。被提到的設(shè)計也包含一個固定的磁體序列和外部線圈作為運動機件。這和本文所討論的的電動機完全不同，因為in the latter 被永磁體包圍的管子能夠自由的伸出超過支撐的底座。Zhu, 等人建立了一個管型LBPMM并討論了最小限度頓振 [10]。在這個設(shè)計中，討論了多相電動機的拓撲結(jié)構(gòu)。和[9]中相似的放射性磁化磁體和 axially-magnetized磁體在作者的設(shè)計中都是作為具體化的選項。這個設(shè)計采用定子鐵心，由此鼓動頓振推力到系統(tǒng)中。[10]中討論的電動機設(shè)計的主要性能目標是最大化力/電流比和力/體積比。這次設(shè)計的目的主要是期望獲得極佳的精密定位性能，輸出力只是作為可供參考的指標。Liaw, 等人開發(fā)了一種魯棒性位置控制LBPMM[11]。Shieh和Tung一個LBPMM 的控制器用在制造業(yè)的系統(tǒng)中[12]。Brückl討論了直線電機在超高精度機床上的應(yīng)用 [13],這也是我們這次設(shè)計的電動機可能的用途之一。Basak和Shirkoohi使用軟件對NdFeB magnets直流無刷直線電動機的磁場進行了分析計算。[14] Lee論證了使用鋸齒狀部件在圓柱型直線電動機設(shè)計中的可行性，使用這種部件的好處在于能夠使裝配容易并且防止電機運行時熱度過高[15]。Trumper等人論述了電磁序列能夠在2維和3維場方向圖中產(chǎn)生通過線圈中變化的電流密度[16]。Ishiyama介紹了一種用于圓柱形直線電動機定子的設(shè)計方法，就是使用一個固定機械裝置來結(jié)合由相鄰永磁體的相對面形成的環(huán)[17]。Akmese等人記述了電機參數(shù)的計算機分析方法和磁場頓振推力的有限元分析[18]。Eastham, 等人 論述了無刷管型直流電動機的最優(yōu)化設(shè)計[19]。上述所提到的設(shè)計概念，特別是在[7-10]中討論過的，在總體性能上和這次設(shè)計有相似的地方，但是這次的設(shè)計和以往還是有重要的區(qū)別之處。本次設(shè)計考慮到緊湊輕薄形圓柱管型致動器的要求，使它能自由的伸展超過支撐底盤。這次使用無鐵心和無槽設(shè)計，大大消除了頓振的產(chǎn)生，使電動機能夠平滑運動。底部采用無鐵心的設(shè)計，因此沒有鐵軛對磁場的集束效應(yīng)，使得電動機效率受到損失。電動機的緊密設(shè)計使其可適用于狹小空間中的機器人技術(shù)領(lǐng)域。系統(tǒng)具有的良好的電壓穩(wěn)定性有助于自身在精密定位領(lǐng)域中的應(yīng)用。在下面的章節(jié)中，我們將通過對控制穩(wěn)定和電動機規(guī)格兩方面的討論來介紹電動機的設(shè)計。然后介紹滿足特殊運動要求的控制器的設(shè)計，同樣的也介紹了滿足2個特殊的機器人致動要求的最優(yōu)化控制器的設(shè)計步驟。通過對一些實驗的數(shù)據(jù)分析結(jié)果來舉例說明系統(tǒng)對不同輸入的響應(yīng)特性，有些還包括了外加負載的影響。當輸出最大推力的時候，電動機還能夠保持穩(wěn)定，對這個工作的討論在[20]中有詳細論述。2．電動機的設(shè)計2.1.概念設(shè)計圖2顯示了電動機概念結(jié)構(gòu)，沒有磁體和線圈的詳細尺寸。圓柱形永磁體被放置成NS-NS—SN-SN的方式并且在每對之間相互間隔。磁體的剖面必須和線圈的剖面相匹配，并且成對的磁體陣列剖面也要和線圈的剖面一致。磁體被固定在一個可以自由滑動的銅管里組成電動機的mover。三相電磁線圈標注為A ，B，C 。每個線圈最外面的和最里面的繞組都由引出導(dǎo)線，線圈按照一定的順序排列，使得每個線圈有三分之一位于同一相。線圈構(gòu)成定子，mover 被放置在定子里。當線圈裝有動力的時候，就會依照洛倫茲力方程對永磁體施加力，從而促使了mover的平移。圖 2磁體的長度（沿Z軸方向）設(shè)定為和線圈一樣。因此需要設(shè)計的參數(shù)為磁體的長度，磁體的外半徑和線圈的內(nèi)半徑（取決與在兩者之間的氣隙），線圈的外半徑。磁體序列固定在銅管里，之間留出空間給磁體和線圈氣隙。2．2電動機推力計算和sizing為了確定詳細的設(shè)計參量，必須制定出量化的期望的性能標準。在這里，概念上的設(shè)計保證了平滑移動的要求，因為沒有能產(chǎn)生頓振的鐵槽。剩下的感興趣的性能參數(shù)是最大輸出力。洛倫茲力方程f = ∫ ( J × B) dV支配了電流線圈和永磁體的互感。輸出力是線圈電流密度向量和永磁體產(chǎn)生的通過整個線圈的磁通密度向量乘積的體積分。單個磁體和單個線圈的互感是對輸出力的主要影響。根據(jù)對稱性進行進一步的擴展和簡化，洛倫茲力方程變?yōu)椋?）。一些幾何的參數(shù)在圖3中給出。詳細的推導(dǎo)過程在[20]中給出，[21,22] 中的材料對此非常有幫助。每個線圈的自感系數(shù)和阻抗分別為0.500 mH和0.552 ?。通過每個線圈的最大限度為3A。經(jīng)過評估我們選擇圓柱的NdFeB永磁體。它最大的能量積為0.4MJ/m3 (50 MGOe).選擇磁體直徑為10.0-mm (0.395”)，長度為9.53-mm (0.375”)，最小剩磁為1.20 T。留下合適的空間給外直徑為11.1-mm (7/16”) 的銅管來放置磁體，使其并能夠不接觸線圈自由滑動，線圈的內(nèi)直徑12.2 mm，外直徑為33.2 mm.。沿Z軸的長度選擇為9.53相對于磁體的長度。使用AWG #21 線圈，179繞數(shù)在設(shè)計封裝里。 圖 3基于以上的規(guī)格尺寸，單個磁體和單個線圈之間的力/電流和對應(yīng)的位移（Z）的函數(shù)關(guān)系可以用（1）來決定。數(shù)學CAD用來求解不同位移下的力/電流。這些結(jié)果在圖4中給出。這些圖中的點是通過在數(shù)學CAD中反復(fù)求解得出的。把這些點經(jīng)過線性插補連成一條連續(xù)直線的線。圖42．3 機械設(shè)計定子由9個線圈（每相3個）組成，在每對磁鐵之間采用鋁使得能和磁體粘合在一塊。磁體和鋁的粘合是涂環(huán)氧的PC-7在外表面。磁體的由4個磁體和兩個組成，共63.3mm。一個銅管被用來裝磁體和。管子的外直徑為11.1-mm(7/16”)，管壁厚0.356 mm (0.014”) ，長305 mm (12.0”)。磁體和spacer在管子中按照NSNS—SN-SN的方向排列。在銅管里的磁體能夠通過9線圈集來轉(zhuǎn)換，如圖2所示。支撐銅管的尼龍軸承用Delrin固定在定子的兩端來保持住。當把線圈面對面的粘合起來的時候，0.787- mm厚的多層pr用來留下一個間隙在在spacer的內(nèi)直徑到外直徑處開槽留下空間給引出的金屬導(dǎo)線。Spacer是縱傾的因此它的內(nèi)直徑就會比線圈的大，外直徑會比線圈的小。這樣就能使銅管在線圈中自由滑動并留下空間給引出的空間導(dǎo)線使其能在周圍適當?shù)牡胤奖话b。被添加的有效厚度為1.03mm 。因此定子由6個線圈和6個spacer 組成共63.3mm ，和磁體一樣。2.4. 整流為了提供平穩(wěn)的三相電流給電動機，一個整流等式關(guān)于基于位置的力和電流是需要的。為了方便，坐標約定和圖2的一樣，相關(guān)的定義在[8]中，這樣變化方程就能夠使用而無需作重大修改。上文提到的交換等式在（2）中給出。這里用C 替換了部分幾何參量。變量1，2，3相對于線圈的三相電流。4.方程2提供了包含一個未知量C的3個等式，當知道了電流，就可以確定位移和力的值。為了找到一個合適的C的值，要完成分析和實驗手續(xù)。在每種情況里，平衡的三相電流和位移是固定的。在統(tǒng)計調(diào)查了C的數(shù)據(jù)，選擇中間值。當c確定下后，控制器的輸出就能變換出3個期望的跟隨輸出電流?？刂破鞯妮敵隽渴橇?線圈電流的最大擺動幅度是3A，和控制器板的輸出電壓成正比。因此，跨導(dǎo)放大器增益為0.333A/v。為了分析確定電動機的力的性能，必須總計每個磁體-線圈互感的單獨貢獻。線圈的pitch和磁體的相適應(yīng)，因此每相的單個線圈的力的貢獻是一樣的。每相力/電流的值要*3。因為每相有3個線圈。從圖4，可以清楚的看到當磁體超過30mm，力的貢獻可以忽略，因此只有每個線圈中最靠近的6個磁體能夠貢獻。表1列舉了在最靠近的6個磁體間的和在每相單個線圈的力貢獻。磁體的相應(yīng)編號被標注在圖2中。通過增加每相的輸出力建立合力。表1顯示了最大輸出力時的位置和電流條件，緩和了平衡3相條件。輸出力的最大限度確定為29.6N，當考慮到平衡的3相條件，最大的輸出力為19.4N。2.5.實驗步驟和使用儀器實驗步驟顯示在圖5中。線性可變微分變壓器（LVDT）通過導(dǎo)螺桿和電動機的mover相連。LVDT輸出模擬位置信號給實驗電路，經(jīng)過conditioning circuit 的整流濾波，再送到DS1104控制器板的模擬數(shù)字轉(zhuǎn)換信道。控制板處理這個位置信號，然后輸出合適的控制信號給PWM放大器。然后放大器產(chǎn)生正比與電壓的電流給線圈，用來對固定在mover中的永磁體施加力的作用，產(chǎn)生平移。下面詳細介紹了步驟所要用到測量儀器。3.控制器的設(shè)計和執(zhí)行在這一節(jié)中，說明了系統(tǒng)建模和控制器的開發(fā)設(shè)計。人們設(shè)計了各種各樣的控制器來更好的達到期望的性能特征在機器人技術(shù)中的應(yīng)用。在每種方案中，核心都是一個典型的控制器。增益的時序安排被用來實現(xiàn)減少響應(yīng)死區(qū)域的影響。有兩個主要的性能指標要考慮。第一個性能指標是在最小位置噪音下的快速上升時間，這也是許多緊密定位應(yīng)用的要求。第二個性能指標是小的或沒有超調(diào)量，在一些超調(diào)量可能意味著不受歡迎的碰撞的機器人技術(shù)應(yīng)用中會有要求。3．1培養(yǎng)模型LVDT允許自身的鐵心無接觸的滑動，因此使得系統(tǒng)中沒有摩擦力的產(chǎn)生。尼龍軸承定位于直線電動機的兩端使得幾乎沒有摩擦給系統(tǒng)，所有摩擦力在最初的系統(tǒng)建模中可以忽略。因此。系統(tǒng)可以建模作為純質(zhì)量系統(tǒng)。動子的質(zhì)量在精密天平上測量為175g。相應(yīng)的平臺 傳遞函數(shù)為（3）3．2 控制器設(shè)計系統(tǒng)被建模為純質(zhì)量的，所有模型在邊上穩(wěn)定的。為了減少上升時間和增加的衰減，加上了一個引導(dǎo)補償器。為了改善系統(tǒng)的穩(wěn)態(tài)性能，包括了一個lag補償器。在可以接受的衰減條件下，系統(tǒng)應(yīng)該有一個超過60度的相位裕度。為了零穩(wěn)態(tài)誤差，一個極點被放在s-平面的原點。要求的最小上升時間限定在較低的系統(tǒng)增益的限度內(nèi)，然而實際上，實際增益比這個限度要高很多。因此剩下的極點和零點通過許多次反復(fù)的誤差實驗來確定。Matlab函數(shù) ‘rlool’用來最終確定控制器的參數(shù)，以達到合適的動態(tài)性能。方程（4）給出了在5-kHz 取樣頻率下的控制器的離散時間域下的變換。（4）這個控制器在轉(zhuǎn)線路頻率為49hz下產(chǎn)生73。6度的相位差，可適用于在一個要求快速階躍響應(yīng)同時可以接受20－30％的超調(diào)量的應(yīng)用中。許多其他的控制器也被發(fā)展并且它們的性能要檢驗以確定它們適用于具體的機器人技術(shù)應(yīng)用中。比如在無超調(diào)量和高數(shù)點對點定位的應(yīng)用。3．3 增益調(diào)度將在第四節(jié)討論的，在實驗的階躍響應(yīng)中，有兩個最總要的問題，高振幅噪音和重大的dead－band區(qū)域prsent。重新設(shè)計了構(gòu)成后，噪音能夠通過軟件過濾器顯著的減小。系統(tǒng)響應(yīng)中 的t是由在系統(tǒng)中的非線性摩擦引起的。當電動機的移動到期望點的附近時。因為電動機在最終位置的附近，誤差是小的，然而，控制器需要時間積累足夠大的命令電流來讓電動機克服摩擦力。結(jié)果產(chǎn)生了一個重大的時間延遲。為了消除這個死區(qū),要就要執(zhí)行增益的時序安排。一個50um以內(nèi)的死區(qū)要保留來防止干擾的劇增當接近期望的最終評估。圖6給了系統(tǒng)響應(yīng)一個20－mm的輸入命令，帶有或沒有增益時序安排執(zhí)行。這里使用的控制器被明確設(shè)計用來實現(xiàn)到達指定位置而無超調(diào)量的目標。然而這導(dǎo)致了它比較慢，特別是在大的階躍時。通過增益時序安排的方法的影響顯著的減小了。同時上升時間從超過7s降低到少于0.8s。4．實驗結(jié)果為了測定電動機適用的范圍有多廣，我們進行了很多的實驗來測試電動機的性能。同時根據(jù)電動機不同的應(yīng)用修改了一些控制的設(shè)置，以便在每個應(yīng)用中能達到最優(yōu)化控制。這些修改包括濾波，增益調(diào)度以及路徑規(guī)劃。應(yīng)該注意到所有讀取的有關(guān)位置的數(shù)據(jù)都是經(jīng)過LVDT過濾的信號。4.1.電動機傳動力的實驗測定為了測定出電動機的最大拉力輸出，實驗中將保持三相線圈中電流恒定，同時通過滑輪和懸掛在上面的負載給電動機提供一個外力，如圖7所示。圖 7通過給懸掛的負荷加上一些小的砝碼，使負荷重量增加直到達到電動機的輸出拉力，這時電動機開始釋放負載，使其落下。移去剛加上去的質(zhì)量，通過天平測出剩下的質(zhì)量。將這個質(zhì)量乘以引力常數(shù)就可以確定輸出拉力。當通過線圈每相的最大電流是3A時，輸出拉力26.3N。通過式（1）計算出來的相關(guān)力的理論值是29.6N。4.2.階躍響應(yīng)階躍響應(yīng)是測量直線傳動器點對點可操作性的有用工具。許多應(yīng)用要求傳動器能夠盡可能快的從一個點移動到另一個點。其他重要的特性是超調(diào)量百分比，穩(wěn)定延遲時間和穩(wěn)態(tài)誤差。圖8中的第一個繪制的是系統(tǒng)對40-um階躍命令的響應(yīng)。響應(yīng)上升時間少于0.3s，穩(wěn)定延遲時間大約是0.4s。這些瞬態(tài)響應(yīng)相對于40赫茲的系統(tǒng)交叉頻率來說是很慢的。相信是尼龍軸承的摩擦和死區(qū)的降低了這個微小運動。在圖8中的第二條線顯示了5-mm的階躍響應(yīng)。在沒有嚴重的非線性影響的條件下，上升時間和穩(wěn)定延遲時間分別為20ms和60ms。很清楚的表明系統(tǒng)的精密定位要好于20um。而對精密定位的限制因素在于LVDT傳感器電的精度和它的電子噪音干擾。采用一臺更好精密度的傳感器就能提高電動機的定位精度。圖9說明了系統(tǒng)對2cm到5cm相互間隔1cm的階躍信號的響應(yīng)。在這些響應(yīng)中，上升時間少于0.1s，穩(wěn)定延遲時間在0.2到1s的范圍內(nèi)，超調(diào)量為20到25％。上升和還原時間的不同是因為在建模中被忽略的因素（比如死區(qū)，軸承摩擦）存在于系統(tǒng)中的關(guān)系。電動機的一個重要的屬性就是在增加的負荷下它的執(zhí)行性能。為了這個目的，我們在一些階躍響應(yīng)中通過滑輪給系統(tǒng)加上了5N的負荷，如圖7所示。圖10給出了帶負荷的系統(tǒng)階躍響應(yīng)，范圍在5mm到5cm之間，與所加負荷方向相反。系統(tǒng)的上升時間，還原時間和超調(diào)量的范圍分別為30到100ms，這個實驗?zāi)軌蛴行У臏y量出電動機在帶負荷階躍條件下的應(yīng)用性能。5．總結(jié)一個對新型直接驅(qū)動永磁管型電動機的設(shè)計已經(jīng)介紹完了。設(shè)計這個電動機的目的是提供許多機器人技術(shù)所需要的致動解決方案；主要是緊湊的，快速的，平滑的，精密定位的。這個設(shè)計由一個位置傳感器，三個功率放大器和一個控制器與設(shè)計的直線電動機協(xié)力運行組成了一個完整的精密致動和控制的解決辦法。Lead-lag控制器的設(shè)計和實現(xiàn)增加了位移速度并減小了穩(wěn)態(tài)誤差和超調(diào)量。增益調(diào)度的實現(xiàn)減少了死區(qū)的影響。電動機能夠通過10-mm工作行程in 67 ms 相當于約1.5 m/s的速度，并且能夠達到10g的加速度。系統(tǒng)對5-mm 階躍命令的響應(yīng)的上升時間，穩(wěn)定延遲時間和超調(diào)量分別為30ms，20ms 和25% 。電動機緊湊的大小和伸展運動部件超過它支撐基座的能力，使它非常適合在許多空間受制約的運動控制中的應(yīng)用。 Development of a Novel Direct-Drive Tubular Linear Brushless Permanent-Magnet Motor 279 Development of a Novel Direct-Drive Tubular Linear Brushless Permanent-Magnet Motor Won-jong Kim and Bryan C. Murphy Abstract: This paper presents a novel design for a tubular linear brushless permanent-magnet motor. In this design, the magnets in the moving part are oriented in an NS-NS—SN-SN fashion which leads to higher magnetic force near the like-pole region. An analytical methodology to calculate the motor force and to size the actuator was developed. The linear motor is operated in conjunction with a position sensor, three power amplifiers, and a controller to form a complete solution for controlled precision actuation. Real-time digital controllers enhanced the dynamic performance of the motor, and gain scheduling reduced the effects of a nonlinear dead band. In its current state, the motor has a rise time of 30 ms, a settling time of 60 ms, and 25% overshoot to a 5-mm step command. The motor has a maximum speed of 1.5 m/s and acceleration up to 10 g. It has a 10-cm travel range and 26-N maximum pull-out force. The compact size of the motor suggests it could be used in robotic applications requiring moderate force and precision, such as robotic-gripper positioning or actuation. The moving part of the motor can extend significantly beyond its fixed support base. This reaching ability makes it useful in applications requiring a small, direct-drive actuator, which is required to extend into a spatially constrained environment. Keywords: Direct-drive DC motor, linear actuator, permanent-magnet motor, real-time digital control, tubular motor. 1. INTRODUCTON The objective of the work described in this paper is to develop a novel linear actuator capable of fast, smooth, precise positioning with a 10-cm actuation range. The direct-drive tubular linear brushless permanent-magnet motor (LBPMM) shown in Fig. 1 has a slotless stator to provide smooth translation without cogging. This design choice sacrifices the higher force capabilities that would be possible with iron slots in the stator in favor of smooth actuation. Applications for this type of actuator include precision positioning and robotic actuation needs. Linear actuators are used in robot end-effectors such as dexterous hands [1] and as the final link in multi-link robotic arms. Budig discusses many types of applications for which linear motors are appropriate [2]. Some linear actuators are comprised of hydraulic or pneumatic rams, which are good for non-precision applications requiring high force. Others use an electric rotary motor with a lead screw or other linkage to convert rotary motion to linear translation, which has serious complications including backlash and increased mass of the moving part due to connecting linkages or gears. Hence, the LBPMM, which is comprised of permanent magnets and current-carrying coils, is especially suited for precision positioning applications. There have been many contributions in the field of LBPMM’s and other direct-drive systems, in which the load is propelled directly by the motor. LBPMM’s __________ Manuscript received April 1, 2004; accepted June 9, 2004. Recommended by Editor Keum-Shik Hong. Won-jong Kim is with the Department of Mechanical Engineering, Texas A&M University, 3123 TAMU, College Station, Texas 77843-3123 USA (e-mail: wjkim@mengr.tamu. edu). Bryan Murphy is with The Boeing Company, International Space Station, Loads, Dynamics, and Mechanisms division, 13100 Space Center Blvd, Houston, TX 77059 USA (e-mail: Bryan.C.Murphy@boeing.com) Fig. 1. Assembled tubular linear motor mounted on aprecision optical table shown with brass tubeconnected to the LVDT at right. Thepermanent magnets are within the brass tube.The amplifiers can be seen in the back. International Journal of Control, Automation, and Systems, vol. 2, no. 3, pp. 279-288, September 2004 280 Won-jong Kim and Bryan C. Murphy are commonly used in single- and multi-degree-of-freedom precision positioning applications. Lequesne investigated a number of performance criteria for permanent-magnet linear motor designs with translation range from 5 to 20 mm [3]. Kim and Trumper, et. al demonstrated that a six-degree-of-freedom planar LBPMM could be used for precision nanopositioning [4,5]. This setup consists of current-carrying coils contained within a stationary base beneath a platen comprised of matrices of permanent magnets. When energized, the coils levitate the platen and allow significant translation and rotation in the plane of the base plate. Berhan, et al. discussed the use of a Halbach magnet array [6] in a novel ironless tubular LBPMM [7,8]. The Halbach array is implemented in the form of axisymmetric octagonally-oriented rectangular permanent magnets, which approximate a cylindrical Halbach array. The primary differences between the cited motor and the proposed design is that the proposed motor has a simpler mover made up of cylindrical permanent magnets, is more compact in size, and is much easier in construction. Ishiyama, et al. designed a tubular LBPMM that can be used to drive a carriage in an image reading device and other applications [9]. This design entails an array of hollow radially-magnetized permanent magnets, with the poles of each magnet aligned with the attractive poles of the adjacent magnets. This configuration is repeated to produce a relatively long tubular array of magnets, which constitutes the fixed part of the motor. The primary differences between this design and the design proposed herein are the magnetization direction of the magnets and the configuration of the motor. The cited design also embodies a fixed array of magnets, with the outer coils as the moving part. This is substantially different from the motor discussed in this paper, as in the latter the tube, which encompasses the permanent magnets, is free to extend out well beyond the support of the base. Zhu, et al. constructed a tubular LBPMM and discussed cogging minimization [10]. In this design multiple motor topologies are discussed. Radially-magnetized magnets similar to those in [9] and axially-magnetized magnets as in the authors’ design were both proposed as options for the embodiment. This design uses an iron core in the stator, which instigates cogging forces into the system. The primary performance goal discussed in [10] is to maximize the force-per-current and force-per-volume ratios. In the proposed design herein, while output force is of appreciable concern, the primary desire is for precise positioning. Liaw, et al. developed an LBPMM with robust position control [11]. Shieh and Tung designed a controller for an LBPMM used in a manufacturing system [12]. Brückl discussed the use of a linear motor for ultra-precision machine tools [13], which is also a possible application for our design. Basak and Shirkoohi used a software package to compute the magnetic field in DC brushless linear motors with NdFeB magnets [14]. Lee demonstrated a cylindrical linear motor design using toothed sections which makes assembly easier and prevents overheating [15]. Trumper, et al. discussed electromagnetic arrays capable of generating field patterns in two and three dimensions by varying current density in the winding [16]. Ishiyama presented a stator design for a cylindrical linear motor in which opposing faces of ring shaped permanent magnets are adjacent and positioned close to each other using a tightening mechanism [17]. Akmese, et al. described computer-aided analysis of machine parameters and the magnetic cogging force using finite element techniques [18]. Eastham, et al. discussed the optimum design of brushless tubular linear machines [19]. The concepts given in the aforementioned papers, particularly those discussed in [7-10], incorporate qualities similar to the design proposed here, but with significant differences. The proposed design allows for compact actuation of a slender cylindrical tube, which is free to extend beyond the support base. As the design is ironless and slotless, there is no cogging, which allows smooth translation. The downside of this ironless design is that there is no iron yoke to concentrate the magnetic field, so the efficiency suffers. The compact design of the motor makes it applicable to space-constrained robotics applications. The potential resolution of the system lends itself to applications in precision positioning. In the following sections, a presentation of the electromechanical design is given with the governing equations and motor sizing discussed. Next, the design of controllers for particular motion requirements is presented, as well as the steps taken to optimize the controllers for two specific robotic-actuation needs. Several experimental results are given illustrating the system response to various inputs, some including externally applied loads. The maximum force for which the motor is capable is also determined. This work is also discussed in detail in [20]. 2. ELECTRO-MECHANICAL DESIGN 2.1. Design concept Fig. 2 represents the conceptual configuration without particular dimensions assigned to the magnets and coils. Cylindrical permanent magnets are placed in an NS-NS—SN-SN fashion with spacers between pairs. The magnet pitch is required to match the coil pitch, and arranging magnets (which were conveniently available) together in pairs allowed the magnet Development of a Novel Direct-Drive Tubular Linear Brushless Permanent-Magnet Motor 281 zdpwhcZRxyρ BCA' B'C' ABCz, z'θ' coil polycarbonate spacer aluminum spacer magnetMOVER o' r θ o r' STATOR 3 2 5 7 4 6 1 8 Fig. 2. Section view of coils and magnets with brass tube hidden. Coordinates are given for the mover frame (primed frame) as well as the stator frame (unprimed frame) that is stationary in space. Fig. 3. Parameters between permanent magnet (left) and current-carrying coil (upper right). The coil is represented with a rectangular cross-section. pitch to match the coil pitch. The magnets are fixed within a freely sliding brass tube which constitutes the mover. Electromagnetic coils are configured in three phases labeled A, B, and C. Each coil has one lead from the outermost turn and one from the innermost turn. The coils are arranged in sequence such that every third coil is in the same phase. The coils constitute the stator, and the mover is placed within the stator. As the coils are powered, they exert a force upon the permanent magnets according to the Lorentz force equation, which causes translation of the mover. The length (along the z-axis) of the magnets is set to be equal to that of the coils. Therefore the required design parameters are the length of the magnets/coils, the outer radius of the magnet and the inner radius of the coil (this pair determines the air gap between them), and the outer radius of the coil. The magnet array is fixed within a brass tube, space for which must be accommodated in the air gap between the magnet and coil arrays. 2.2. Motor force calculation and sizing To determine the particular values for the design parameters, some quantified desired performance criteria must be established. In this case, the conceptual design guarantees the smooth translation requirement, as there are no iron slots, which would introduce cogging. The remaining performance parameter of interest is the maximum output force. The Lorentz force equation, f = ∫ (J × B) dV governs the interaction of the coil current and permanent magnet. The output force is the volumetric integral of the cross product of the current density in the coil with the magnetic flux density generated by the permanent magnet over the whole coil volume. The force of primary interest is the interaction of a single magnet with a single coil current. Upon further expansion and simplifications due to symmetry, the Lorentz force equation becomes (1). Some geometric parameters are given in Fig. 3. A thorough derivation is given in [20], in which material from [21,22] was quite helpful. The coil inductance and resistance are 0.500 mH and 0.552 ?, respectively, per coil. A maximum current of 3 A flow through each coil. The magnets chosen for evaluation were cylindrical neodymium iron boron (NdFeB) magnets. Their maximum energy product (BHmax) is 0.4 MJ/m3(50 MGOe). The magnets chosen are 10.0-mm (0.395”) in diameter, 2222022 200022222 200()4( / 2) 2 cos( )...(/2) 2cos()hwZcRzwhcZRJM df dddrzd r rd d r d dz drzd r rπππμ ρθ ρπρρθφρθρ φρρθφ++??????=??????++? ??????+++? ??∫∫∫ ∫∫∫∫(1)282 Won-jong Kim and Bryan C. Murphy 9.53-mm (0.375”) long, and have a minimum remanence of 1.20 T. To allow adequate space for the 11.1-mm (7/16”) O.D. (outer diameter) brass tube to house the magnets and slide freely without contact within the coils, the I.D. (inner diameter) of the coils was chosen to be 12.2 mm, with an O.D. of 33.2 mm. The length (in the z-direction) was selected to be 9.53 mm to match that of the magnets. Using AWG #21 wire, 179 turns of wire fit within the design envelope. Based on these dimensions, the force per current between a single magnet and single coil as a function of relative displacement (Z) can be determined using (1). MathCAD was used to solve for this force per current for numerous values of Z. These results are illustrated in Fig. 4. The points given in the figure are from iterations solved in MathCAD. The lines connecting the points into a continuous line are from linear interpolation between these points. 2.3. Mechanical design The stator consists of nine coils (three per each phase), corresponding to 1? pitches. To provide the desired travel range of 10-cm, several pitches of magnets are included, so that there are always magnets within appreciable force range on both sides (axially) of each coil. Aluminum spacers were used between pairs of magnets so that the magnets could be glued together. The magnets and spacers were glued in place by coating PC-7 epoxy on the outer surfaces. The magnet pitch consisting of four magnets with two spacers is 63.3 mm. A brass tube was chosen to house the magnets and spacers. The tube has an 11.1-mm (7/16”) O.D., wall thickness of 0.356 mm (0.014”) and is 305 mm (12.0”) in length. The magnets and spacers are positioned in the brass tube in an NS-NS—SN-SN orientation. The magnets within the brass tube will translate through the nine-coil assembly, as shown in Fig. 2. Nylon bearings which support the brass tube are held in Delrin housings fixed to both ends of the stator. When gluing the coils together face-to-face, 0.787-mm-thick multi-layer polycarbonate spacers were used to leave a gap between coils for the lead wire from the innermost coil winding to run along the face of the coil to the outside of the coils. A notch was cut from the inner diameter to the outer diameter of each of the spacers to leave room for the lead wire. The spacers were trimmed so that the inner diameter of the spacers was larger than that of the coils and so that the outer diameter of the spacers was smaller than that of the coils. This allowed the brass tube to slide freely through the coils, and also left room for the wire leads on the outside of the coils to be wrapped around to the appropriate location. The effective thickness of the added polycarbonate spacer (including the glue line on both faces) was 1.03 mm. Thus, the stator pitch consisting of six coils with six spacers is 63.3 mm, the same as the magnet pitch. 2.4. Commutation In order to provide balanced three-phase current to the motor, a commutation equation relating force and current based on position was required. For convenience, the coordinate convention designated in Fig. 2 was chosen to correlate with that defined in [8] so that the commutation equation would be applicable without significant modification. The commutation equation from said paper is given in (2), where C replaces a quotient of geometric parameters. 101020cos13 .sin13AB zdCiziC fziγγ??????????=???????????????(2) The variables iA, iB, and iCcorrespond to the three-phase currents applied to the coils. The parameter γ1is the magnitude of the spatial wave number of the first harmonic, γ1= |2π/l|, where l is the pitch of the motor (63.3 mm). The relative lateral displacement of the mover with respect to the stator is denoted z0, and fzdis the desired axial thrust. Equation (2) provides three equations for only one unknown, C, as the currents are given, and the displacement and force can be readily determined. To find an appropriate value for C, analytical and experimental procedures were executed. In each instance, balanced three-phase currents and a displacement (z0) were fixed. Upon statistical investigation of the data for C, the median value was selected. Once C is determined, the controller output can be converted to the three desired output currents as follows. The output from the controller is force, which is multiplied by the geometric quotient C and the appropriate sinusoidal displacement dependency as in (2). The maximum swing of the current to the coils is ±3 A, proportional to the output voltage from the controller board. Hence the transconductance Fig. 4. Theoretical force per current as a function ofrelative displacement for one magnet with onecoil. -0.70-0.60-0.50-0.40-0.30-0.20-0.100.000 0.005 0.01 0.015 0.02 0.025 0.03 0.035Relative Displacement (m)Force/Current(N/A)Numerically Determined Data PointsLinearly Interpolated PointsDevelopment of a Novel Direct-Drive Tubular Linear Brushless Permanent-Magnet Motor 283 Table 1. Analytical force output. Coil in Phase A Coil in Phase B Coil in Phase CMagnet Distance Force/ Current Distance Force/ Current DistanceForce/Current(mm) (N/A) (mm) (N/A) (mm) (N/A)1 -36.55 0.00 -26.00 -0.05 -15.45 -0.232 -27.03 -0.05 -16.48 -0.20 -5.93 -0.583 -4.90 -0.53 5.65 -0.57 16.20 -0.204 4.63 -0.52 15.18 -0.24 25.73 -0.065 26.75 -0.05 37.30 0.00 47.85 0.006 48.85 0.00 59.40 0.00 69.95 0.00Force/Current (N/A) -1.16 -1.06 -1.07Multiplied by 3 Coils -3.47 -3.17 -3.21Current to Coils (A) -3.00 -3.00 -3.00Force per Phase (N) 10.40 9.51 9.62Total Force (N) 29.60 amplifier gain is 0.333 A/V. To analytically determine the force capabilities of the motor, the individual contributions for each magnet-coil interaction must be summed. Since the pitch of the coils matches the pitch of the magnets, the force contribution from each coil in a single phase is identical. Thus the force per current for each phase is multiplied by three, as there are three coils in each phase. From Fig. 4, it is clear that for magnets beyond 30 mm, the force contribution is negligible, so only the six closest magnets to each coil are taken into consideration. Table 1 enumerates the force contributions between the six nearest magnets and a single coil in each phase. The magnet number corresponds to the magnets as labeled in Fig. 2. The force per current is summed for each representative coil, then multiplied by three because there are three coils in each phase. This force-per-current value for each phase is multiplied by the current sent through that phase to find the force output. The total force is found by adding the force outputs from each phase. Table 1 represents the position and current condition for maximum force output, which relaxes the balanced three-phase condition. The maximum force is determined to be 29.6 N. With the balanced three-phase condition in place, the maximum force is 19.4 N. 2.5. Experimental setup and instrumentation The experimental setup is depicted in Fig. 5. The linear variable differential transformer (LVDT) is connected to the mover of the motor through a threaded rod. The LVDT outputs the analog position signal to the conditioning circuit, which shifts and filters it, then sends it to an analog-to-digital (A/D) channel of the DS1104 controller board. The controller board processes the position signal, and outputs appropriate control signals to the