氣浮墊的研拋工藝及研拋機結(jié)構(gòu)設(shè)計【研磨機】【研磨拋光】【說明書+CAD+3D】

氣浮墊的研拋工藝及研拋機結(jié)構(gòu)設(shè)計【研磨機】【研磨拋光】【說明書+CAD+3D】,研磨機,研磨拋光,說明書+CAD+3D,氣浮墊的研拋工藝及研拋機結(jié)構(gòu)設(shè)計【研磨機】【研磨拋光】【說明書+CAD+3D】,氣浮墊,工藝,研拋機,結(jié)構(gòu)設(shè)計,研磨,拋光,說明書,仿單,cad 摘要 隨著精密、超精密技術(shù)的發(fā)展日益進步,機器及檢測儀器等的精度要求越來越高,對氣浮墊的制造精度也提出更高的要求。目前,由于氣浮墊精密加工技術(shù)的研究還不夠深入,因此,研究氣浮墊的精密制造技術(shù)是氣浮墊領(lǐng)域函須解決的課題。 針對研磨拋光過程，本文深入研究了磨料種類、粒度、拋光液溶劑、研拋壓力、研拋加工時間等因素對加工表面粗糙度的影響。根據(jù)氣浮墊研磨設(shè)備對研磨工藝的要求，本文設(shè)計了一種專門的研磨機，并對研磨機的各個部分進行分析和說明，并對部分零件進行驗證和校核。 關(guān)鍵詞：氣浮墊；研磨；拋光；機械結(jié)構(gòu) Abstract With the development of Precision and ultra-Precise technology, the accuracy of the machinery and the detecting instrument become higher, the Production accuracy of cushion needed also more higher. At present, the research about the cushion Precision finishing technology is not enough. So how to enhance the accuracy it is one of needing to resolve problem of the research area of the floatation cushion. On the surface roughness effects of abrasive type, grain size, polishing liquid solvents, polishing pressure, polishing machining time and so on, are researched in-depth for the process of mechanical polishing. According to gas floating pad grinding equipment requirement for grinding process, this paper designed a kind of special grinding machine, and analyze the various parts of the grinding machine and instructions, and to verify and check parts. Keywords ：Gas floating cushion; Grinding; Polishing; The mechanical structure 氣浮墊的研拋工藝及研拋機結(jié)構(gòu)設(shè)計 前言 1.1研究背景及意義 近年來，功能陶瓷、石英晶片、平面或多面體晶體和光學器件等硬脆材料的精密加工提出了很高要求，不僅要求這些材料有極小的平面度、極小的表面粗糙度、超平滑的表面[1-3]，還要求材料兩端面嚴格平行、無晶向誤差、表面無變質(zhì)層等，有的甚至要求達到納米級或更高的加工精度和無損傷的表面加工質(zhì)量，由于研磨拋光技術(shù)可以獲得很高的精度和超光滑表面，上述的材料均需采用精密研磨拋光技術(shù)[3-8]。 利用研拋工具的亞口徑機械式研拋是目前加工創(chuàng)成復(fù)雜光學曲面主要方法，但無論是在創(chuàng)成原理還是在加工裝置上，都存在著難以逾越的固有缺陷。目前，許多研究主要是針對回轉(zhuǎn)對稱非球面光學零件的加工技術(shù)及裝備。 對于有復(fù)雜幾何特征的光學曲面，研拋去除量總是非均勻變化的。這使得研拋工具與被加工工件之間的變形不一致。難以獲得均勻一致的面形精度研拋工具去除工件材料所形成的加工表面殘高也總是非均勻變化的[9-11]。因而難以獲得均勻一致的加工表面。質(zhì)量為了使所獲得加工表面質(zhì)量和面形精度滿足加工要求，同時機構(gòu)的設(shè)計簡單實用性能可靠勢，必將增加研拋加工時間降低研拋加工效率。 研磨和拋光硬脆材料去除機理比較復(fù)雜，硬脆材料的表面完整性、亞表面層損傷、零件幾何形狀受很多因素的影響[12-15]。研磨和拋光加工工藝參數(shù)成為歐美各大企業(yè)的機密，而且針對不同材料以及不同設(shè)備，其參數(shù)變化非常大，使其難以復(fù)制和模仿[16-19]。目前，我國高檔次精密研磨設(shè)備設(shè)計制造水平不高，國外對高檔次精密加工工藝嚴格保密，這嚴重制約了我國精密加工技術(shù)的發(fā)展。為了加強我國精密研磨、拋光技術(shù)的發(fā)展，除了開發(fā)擁有自主產(chǎn)權(quán)的精密研磨拋光設(shè)備之外，研磨、拋光加工工藝也成為了研究重點[20-23]。 1.2氣浮墊研磨拋光機理 氣浮墊壓力產(chǎn)生的原理:利用壓縮氣體的粘性,提高工作間隙中氣體的壓力從而將物體懸浮起來。如圖1.1所示,氣浮墊可以分為三種:動壓型,靜壓型和壓膜型。如圖1.1(a)所示,動壓氣浮墊是兩個面相對移動,且間隙呈楔狀,沿移動方向間隙逐漸變小。由于相對移動,氣體因其粘性作用,被拖帶壓入楔形間隙中,從而產(chǎn)生壓力,構(gòu)成動壓懸浮。如圖1.1(b)所示,靜壓型氣浮墊是將外部的壓縮氣體通過節(jié)流器導入間隙中,借助其靜壓使之懸浮起來。節(jié)流器的作用是當間隙變化時,調(diào)整間隙內(nèi)的壓力,從而使氣浮墊具有一定的剛度。如圖1.1(c)所示,壓膜型氣浮墊利用了相互接觸的面沿垂直方向的振動,使間隙內(nèi)的壓力的平均值高于周圍環(huán)境壓力這一原理。由于氣體具有粘性,間隙內(nèi)的氣體不能快速出入,從而壓力增高。例如,讓一塊玻璃板平行地落在一塊平滑的板上時,玻璃板會輕輕地落下,從這一現(xiàn)象,就能夠理解壓膜氣浮墊的原理。 圖1.1.氣浮墊的工作原理 在上述結(jié)構(gòu)的氣浮墊形式中,動壓型和靜壓型得到更加廣泛的應(yīng)用。在氣浮墊實際設(shè)計中,氣浮墊的節(jié)流方式也不同。分別利用噴嘴、毛細管、縫隙的阻抗起到供氣孔節(jié)流的作用,而固有孔節(jié)流器是由供氣孔和氣浮墊間隙所形成的假想圓柱面起到節(jié)流器的作用。表面節(jié)流器是在氣浮墊面上設(shè)置與供氣孔連同的極淺的溝槽,溝槽的阻抗就構(gòu)成了節(jié)流。多孔質(zhì)節(jié)流器是氣浮墊的承載面采用了具有透氣性的多孔質(zhì)材料,多孔質(zhì)材料的阻抗起到了供氣孔節(jié)流器的作用。 傳統(tǒng)的研磨一般利用鑄鐵研磨盤，采用手工實現(xiàn)無規(guī)則的運動或靠機床實現(xiàn)模模擬手工的運動軌跡。傳統(tǒng)的拋光一般利用瀝青、聚氯乙烯和無紡布等拋光盤， 采用擺動、行星運動和環(huán)行運動等運動方式。研磨和拋光都是根據(jù)不同的加工條件涂敷不同的磨料，工件至于研磨盤或拋光墊上，用夾具裝夾工件并對工件施加一定的壓力，通過機床的主軸帶動磨盤轉(zhuǎn)動，利用磨盤和工件間的相對運動和磨料的切削作用從工件表面去除一層很薄的材料，從而達到加工的目的，加工示意圖如圖1．2所示。 圖1.2研磨拋光示意圖 按照磨料的附著方式，研磨拋光方法可以分為兩種：固結(jié)磨料研拋和游離磨料研拋。固結(jié)磨料研磨工件主要以耕犁方式去除材料，具有加工效率高、成本低等優(yōu)點，但研磨工具磨損大，容易在工件上留下劃痕，難以得到無損傷表面；游離磨料研磨拋光工件是利用磨料顆粒在研磨盤和工件之間對工件表面滾壓，使工件表面產(chǎn)生微小破碎這種方式來去除材料，能獲得無損傷平滑表面。 1.3研磨拋光加工工藝 1.3.1磨料的選取 磨料一是研磨加工的“刀具”,在加工中的起著切削作用。因此,首先磨料一要有較高的硬度,這是其磨削作用的關(guān)鍵所在,一般情況下磨料硬度大于被磨削工件硬度,再次要具有良好的韌性,保證和其他刃具一樣變鈍后能夠自銳。同時磨料的形狀和粒度應(yīng)該均勻,這由研磨拋光加工的特殊性所決定的,另外還要有高溫穩(wěn)定性和化學穩(wěn)定性,這樣在加工的過程中保持自身的優(yōu)良機械和化學性能。 磨料的粒度也是一個很關(guān)鍵的因素,一般磨料的粒度指磨料的粗細程度。在相關(guān)的標準中都有規(guī)定,磨料的粗細用粒度表示,粒度號數(shù)越大,顆粒越小。粗顆粒用于粗加工。 1.3.2.研磨液的選取 通常,研磨加工時,不能直接用磨料對工件表面進行加工,必須加配其他的化學溶劑或其他輔助填料調(diào)配成研磨液,研磨液具有調(diào)和磨料及冷卻潤滑加工被加工接觸面的作用,如果沒有選擇好合適的研磨液,對精密研磨拋光加工可能會帶來一系列的影響,如溫度升高以損傷氣浮墊試件的被加工表面,降低表面粗糙度、產(chǎn)生劃痕、損傷磨盤等危害。因此,和磨料一樣對研磨液的組成和配比也有要求,例如參與作用的研磨液要有冷卻和潤滑的物理性質(zhì),還要具有一定的粘度,以致有勃附作用。在實際生產(chǎn)中不容易被研磨盤甩出;其物理作用和化學性質(zhì)也要良好,研磨液一般是由磨料和活性劑組成的。用于研磨磨料的硬度必須高于工件的硬度,現(xiàn)在可以作為磨料的材料有金剛石、碳化硼、氧化鋁等。由于研磨過程活性劑在研磨過程中起到很重要的作用,如果只有磨料,沒有合適的活性劑,可能會產(chǎn)生許多問題,所以研磨劑要求應(yīng)該有懸浮、潤滑、冷卻、去損、清洗和防銹性能。 1.3.3研磨工藝 傳統(tǒng)的研磨和拋光，設(shè)備條件只是實現(xiàn)高質(zhì)量研拋的必要條件。工藝條件和操作者的技藝也起著十分重要的作用。通常學者們從研磨拋光的4個基本組成部分：工件、研磨拋光液、磨粒和拋光盤入手研究研磨和拋光加工工藝與加工質(zhì)量的關(guān)系。Yongwu Zhao等人以硅片為研究對象，采用化學機械拋光方法探討了研磨拋光工藝參數(shù)對材料去除率的影響，他指出磨粒大小是影響材料去除率的主要因素，轉(zhuǎn)速和壓力是次要因素；B．J．Hooper等人研究了拋光墊磨損對硅片表面質(zhì)量與材料去除率的影響㈣；H．Y Tam等人研究了轉(zhuǎn)速、磨粒大小等加工參數(shù)光學器件表面粗糙度的影響，并得到Ra=10．7 nln的光滑表面；Nabil Belkhir等人以玻璃為研究對象，探討了磨粒與材料去除量的關(guān)系，他指出磨粒的形狀直接影響其切削行為，磨損后的磨粒材料切削能力明顯降低；A．Q．Biddut等人研究了磨粒大小與加工壓力對硅片表面損傷的影響，并指出能否得出無損傷表面，磨粒大小與加工壓力是關(guān)鍵；浙江工業(yè)大學周兆忠等采用A1203磨料，約50rim的Si02拋光液，以聚胺酯作為拋光墊，鑄鐵盤研磨盤對氮化鋁基片進行研磨，得到表面粗糙度Ra為8nm的超光滑表面；廣東工業(yè)大學袁慧等人研究了工程陶瓷研磨拋光工藝，并指出磨削質(zhì)量主要受到磨粒粒度的影響。 影響研磨效果的因素除了研磨盤、磨料種類、磨料粒度等一系列因素外，研磨壓力、轉(zhuǎn)速、研磨液濃度、研磨液流量、研磨時間等因素對研磨的效果也有很大的影響。由于時間和精力有限，在本論文中就不一一論述。 第二章 氣浮墊拋研機結(jié)構(gòu)設(shè)計 2.1氣浮墊拋研機的結(jié)構(gòu)總體設(shè)計 平面研磨機為精密研磨拋光設(shè)備，被研磨、拋光材料放在研磨盤上，研磨盤逆時鐘旋轉(zhuǎn)，修正輪帶動工件盤自轉(zhuǎn)，重力加壓的方式對工件施加壓力，工件盤與研磨盤作相對摩擦運動來達到加工的效果。圖2.1為本設(shè)計初步設(shè)計的平面研拋機原有的結(jié)構(gòu)示意圖。其工作原理是研磨盤由電機通過減速機構(gòu)帶動旋轉(zhuǎn)，研磨盤上有三個加工工位，并在工件盤上放置加載砝碼，這樣研磨盤在旋轉(zhuǎn)，由于摩擦力矩的作用帶動工件盤的也在旋轉(zhuǎn)，在砝碼加壓的情況下兩者的相互轉(zhuǎn)動摩擦起到材料去除的作用，達到研磨的效果。 圖2.1拋研機結(jié)構(gòu)總體設(shè)計 2.2氣浮轉(zhuǎn)臺的設(shè)計 在精密研磨拋光加工工藝中,離不開研磨盤的存在,研磨盤是加工的場所,幾乎所有的研磨拋光加工都是在研磨拋光盤上進行的,對于研拋盤的選擇也至關(guān)重要。在加工中,磨料對被加工件進行磨削,同時研磨盤也同樣在受到磨損。研磨拋光盤自身的精度對氣浮墊的表面精度影響很大,甚至會把這種精度關(guān)系“復(fù)印”到氣浮墊表面上,故要求研磨盤的加工面要有較高的幾何精度。 氣浮轉(zhuǎn)臺主要包括直流力矩電機。氣浮軸承以及軸承所需要的供氣系統(tǒng)等組成。氣浮轉(zhuǎn)臺的各部件在設(shè)計時考慮了結(jié)構(gòu)對稱性原則，以提高轉(zhuǎn)臺軸系回轉(zhuǎn)時的平穩(wěn)性。轉(zhuǎn)臺軸系選用氣浮軸承支承軸系上，同軸安裝進口無刷直流力矩電機作為直接驅(qū)動元件，轉(zhuǎn)臺部件在設(shè)計制造時力求在形狀尺寸和質(zhì)量分布上對各自的正交坐標平面對稱。并且要求在滿足結(jié)構(gòu)件強度和剛度的前提下同時力求內(nèi)環(huán)軸系質(zhì)量最小盡量減小軸系轉(zhuǎn)動慣量，氣浮轉(zhuǎn)臺利用多孔噴射氣浮墊產(chǎn)生靜壓 支撐待研拋工件由于采用多孔噴射技術(shù)， 平臺表面壓力分布均勻， 具有承載能力強剛度好抗氣振等優(yōu)點 。主要應(yīng)用于精密測量和超精加工等精密氣浮轉(zhuǎn)臺如圖2.2所示。 圖2.2 精密氣浮墊床 氣浮轉(zhuǎn)臺中的核心部件就是氣浮軸承氣浮軸承，又稱為空氣軸承，指的是用氣體。通常是空氣，但也有可能是其它氣體。作為潤滑劑的滑動軸承空氣軸承消除了由摩擦力引起的阻力。磨損提供了極高的徑向和軸向旋轉(zhuǎn)精度由于旋轉(zhuǎn)的轉(zhuǎn)子和靜態(tài)支撐部分之間沒有機械接觸，磨損程度降到了最低，從而確保精度始終保持穩(wěn)定，空氣軸承內(nèi)部的低剪切力能夠在提供極高轉(zhuǎn)速的同時，將動力損失降到最低，使產(chǎn)生的熱量非常小并能同時保持較低的振動水平。在高精度和高速領(lǐng)域上優(yōu)勢十分明顯. 2.3.氣浮墊研磨機傳動機構(gòu)設(shè)計 本設(shè)計所設(shè)計的電動機到研磨臺的傳動才用鏈傳動。鏈傳動具有帶傳動和嚙合傳動的一些特點，其優(yōu)點是：鏈傳動沒有彈性滑動和打滑，能保持準確的平均傳動比；傳動尺寸比較緊湊；不需要很大的張緊力，作用在軸上的載荷較??；承載能力大；效率高（η=0.95～0.98）。同時；鏈傳動能吸振與緩和沖擊，結(jié)構(gòu)簡單，加工成本低廉，安裝精度要求低，適合較大中心距的傳動，并能在溫度較高、濕度較大、油污較重等惡劣環(huán)境中工作。 鏈傳動的缺點是：高速運轉(zhuǎn)時不夠平穩(wěn)；傳動中有沖擊和噪聲；不宜在載荷變化很大和急促反向的傳動中使用；只能用于平行軸間的傳動；安裝精度和制造費用比帶傳動高。 圖2.3 鏈傳動 Figure 2.3 chain 鏈傳動的適用場合：廣泛應(yīng)用于中心距較大、多軸、平均傳動比要求準確的傳動。環(huán)境惡劣的開式傳動、低速重載傳動及潤滑良好的高速傳動，均可采用鏈傳動。滾子鏈傳遞的功率通常在100kw以下，鏈速在15m/s以下，傳動比I<=7。目前其最大傳遞功率可達500kw，最高中心距可達8m。 綜合分析各種傳動方案，從傳動效率、傳動比、傳動速度、制造成本和安裝精度、傳動裝置外廓尺寸等方面綜合考慮，本設(shè)計課題的傳動方案采用鏈傳動。 2.4 選用電動機 電動機的容量（功率）選得是否合適，對電動機的工作和經(jīng)濟性都有影響。當容量小于工作要求時，電動機不能保證工作裝置的正常工作，或電動機因長期過載而過早損壞；容量過大則電動機的價格高，能量不能充分利用，且因經(jīng)常不在滿載下運動，其效率和功率因數(shù)都較低，造成浪費。 根據(jù)機械設(shè)計[1]取 磨臺質(zhì)量： 工件所受重力： 滿載時每個托輪所受切向力： 磨臺線速度： 磨臺所需功率： 查表得： 電動機至磨臺的總效率 電動機所需功率 所以選用電動機額定功率 綜上所述，電動機可選用YTC系列齒輪減速三相異步電動機，根據(jù)額定功率選用YTC502型。 第三章 機械傳動件的設(shè)計計算 3.1 鏈傳動的設(shè)計與計算 鏈輪傳動的示意圖如下圖。 圖3.1 鏈傳動 3.1.1 鏈條的設(shè)計與計算 1.選擇鏈輪齒數(shù) 取小鏈輪齒數(shù) 則大鏈輪齒數(shù)，取 2.確定計算功率 查表得 為工況系數(shù)， 為齒數(shù)系數(shù)， 3.選擇鏈條型號和節(jié)距 根據(jù)查表[3]可選16A型滾子鏈，鏈條節(jié)距為p 4.計算鏈節(jié)數(shù)和中心距 初選中心距： ，取p 鏈條節(jié)數(shù)： ，其中 取 （取偶） 最大中心距為： ，查表 實際中心距為： ,一般 5.計算鏈條速度 有效圓周力為： 作用在軸上的力F 為壓軸力系數(shù)，對于水平傳動 3.1.2 主要失效形式 a）鏈的疲勞破壞 鏈在運動過程中，其上的各個元件都在變應(yīng)力作用下工作，經(jīng)過一定的循環(huán)次數(shù)后，鏈板將會因疲勞而斷裂；套筒、滾子表面將會因沖擊而出現(xiàn)疲勞點蝕。因此，鏈條的疲勞強度就成為決定鏈傳動承載能力的主要因素。 b）鏈條鉸鏈的磨損 鏈條在工作過程中，鉸鏈中的銷軸與套筒間不僅承受較大的壓力，而且還有相對轉(zhuǎn)動，導致鉸鏈磨損，其結(jié)果使鏈節(jié)距增大，鏈條總長度增加，從而使鏈的松邊垂度發(fā)生變化，同時增大了運動的不均勻性和動載荷，引起跳齒。 c) 鏈條鉸鏈的膠合 當鏈速較高時，鏈節(jié)受到的沖擊增大，鉸鏈中的銷軸和套筒在高壓下直接接觸，同時二者相對轉(zhuǎn)動產(chǎn)生摩擦熱，從而導致膠合。因此，膠合在一定程度上限制了鏈傳動的極限轉(zhuǎn)速。 d）鏈條的靜力破壞 當鏈速較低時，如果鏈條負載不增加而變形持續(xù)增加，即認為鏈條正在被破壞。導致鏈條變形持續(xù)增加的最小負載將限制鏈條能夠承受的最大載荷。 3.1.3 滾子鏈的靜強度計算 在低速（）重載鏈傳動中，鏈條的靜強度占主要地位。如果仍用額定功率曲線選擇計算，結(jié)果常不經(jīng)濟，因為額定功率曲線上各點相應(yīng)的條件性安全系數(shù)S為8~20，遠比靜強度安全系數(shù)大。當進行耐疲勞和耐磨損工作能力計算時，若要求的使命壽命過短，傳動功率過大，也需進行鏈條的靜強度驗算。 鏈條靜強度計算公式為 式中 為靜強度安全系數(shù)； 為排數(shù)系數(shù)； 為工況系數(shù)； 為有效圓周力； ,并查表得，， 所以 為許用安全系數(shù)，一般為4-8；如果按最大尖峰載荷來代替進行計算，則可為3-6； 所以滿足要求 3.2 鏈輪基本參數(shù)和主要尺寸 鏈輪齒數(shù) 配用鏈條的節(jié)距 配用鏈條的滾子外徑 小鏈輪分度圓直徑 小鏈輪齒頂圓直徑 取 小鏈輪齒根圓直徑 大鏈輪分度圓直徑 大鏈輪齒頂圓直徑 取 大鏈輪齒根圓直徑 鏈輪齒寬 查表得 , 為內(nèi)鏈節(jié)內(nèi)寬 所以 圖3.2 齒形 3.3 滾子鏈傳動的故障與維修 表5.1 滾子鏈傳動的故障與維修 故障 原因 維修措施 鏈板或鏈輪齒嚴重側(cè)磨 1.各鏈輪不共面 2.鏈輪端面跳動嚴重 3.鏈輪支承剛度差 4.鏈條扭曲嚴重 1.提高加工與安裝精度 2.提高支承件剛度 3.更換合格鏈條 鏈板早期疲勞開裂 潤滑條件良好的中低速鏈傳動，鏈板的疲勞是主要矛盾，但若過早失效則有問題： 1.鏈條規(guī)格選擇不當 2.鏈條品質(zhì)差 3.動力源或負載動載荷大 1.重新選用合適規(guī)格的鏈條 2.更換質(zhì)量合格的鏈條 3控制或減弱負載和動力源的沖擊振動 滾子提前碎裂 1.鏈輪轉(zhuǎn)速較高而鏈條規(guī)格選擇不當 2.鏈輪齒溝有雜物或鏈條磨損嚴重發(fā)生爬齒和滾子被擠頂現(xiàn)象 3.鏈條質(zhì)量差 銷軸磨損或銷軸與套筒膠合 鏈條鉸鏈元件的磨損是最常見的現(xiàn)象之一。正常磨損是一個緩慢發(fā)展的過程。如果發(fā)展過快則 1.潤滑不良 2.鏈條質(zhì)量差或選用不當 1.清除齒溝雜物或換新鏈條 2.更換質(zhì)量合格的鏈條。 續(xù)表5.1 故障 原因 維修措施 外鏈節(jié)外側(cè)擦傷 1.鏈條未張緊，發(fā)生跳動，從而與鄰近物體碰撞 2.鏈箱變形或內(nèi)有雜物 1.使鏈條適當張緊 2.消除箱體變形、清除雜物 鏈條跳齒或抖動 1.鏈條磨損伸長，使節(jié)距和垂度過大 2.沖擊或脈動載荷較重 3.鏈輪齒磨損嚴重 1.更換鏈條或鏈輪 2.適當張緊 3.采取措施穩(wěn)定載荷 鏈輪齒磨損嚴重 1.潤滑不良 2.鏈輪材質(zhì)較差，齒面硬度不足 1.改善潤滑條件 2.提高鏈輪材質(zhì)和齒面硬度 3.把鏈輪拆下，翻轉(zhuǎn)180°再裝上，則可利用齒廓的另一側(cè)而延長使用壽命 卡簧、開口銷等鏈條鎖止元件松脫 1.鏈條抖動過烈 2.有障礙物磕碰 3.鎖止元件安裝不當 1.適當張緊或考慮增設(shè)導板托板 2.消除障礙物 3.改善鎖止件安裝質(zhì)量 振動劇烈、噪聲過大 1.鏈輪不共面 2.松邊垂度不合適 3.潤滑不良 4.鏈箱或支承松動 5.鏈條或鏈輪磨損嚴重 1.改善鏈輪安裝質(zhì)量 2.適當張緊 3改善潤滑條件 4.消除鏈箱或支承松動 5.更換鏈條或鏈輪 6.加裝張緊裝置或防振導板 根據(jù)以上鏈傳動的滾子鏈傳動的故障與維修，當鏈傳動出現(xiàn)故障時，可以根據(jù)以上的內(nèi)容來對鏈輪傳動進行調(diào)整，從而達到鏈輪傳動的最佳效果。 4軸的設(shè)計及計算 4.1 軸的材料 應(yīng)用于軸的材料種類很多，主要根據(jù)軸的使用條件，對軸的強度、剛度和其他機械性能等的要求，采用的熱處理方式，同時考慮制造加工工藝，并力求經(jīng)濟合理來選擇軸的材料。 軸的常用材料是優(yōu)質(zhì)碳素鋼，如35、45和50，其中以45號鋼最為常用。 根據(jù)本設(shè)計的要求，選45號鋼作材料。 4.2 軸的結(jié)構(gòu)設(shè)計 軸的結(jié)構(gòu)設(shè)計是確定軸的合理外形和全部結(jié)構(gòu)尺寸，為軸設(shè)計的重要步驟。 一般軸的結(jié)構(gòu)設(shè)計原則： a）節(jié)約材料，減輕重量，盡量采用等強度外形尺寸或大的截面系數(shù)的截面形狀； b）易于軸上零件的精確定位、穩(wěn)固、裝配、拆卸、和調(diào)整； c）采用各種減少應(yīng)力集中和提高強度的結(jié)構(gòu)措施； d）便于加工制造和保證精度。 由材料力學可知，軸的扭轉(zhuǎn)強度[4]條件為 式中 為軸的扭轉(zhuǎn)切應(yīng)力，單位為; 為軸所受的扭矩，單位為; 為軸傳遞的功率，單位為； 為軸的轉(zhuǎn)速，單位為; 為軸的抗扭截面系數(shù)，單位為； 為許用扭轉(zhuǎn)切應(yīng)力，單位為。 由此推得實心圓軸的基本直徑為： 式中為計算常數(shù)，取決于軸的材料和受載情況，查表知，45號鋼的C的范圍為，取 所以 當軸段上開有鍵槽時，應(yīng)適當增大軸徑以考慮鍵槽對軸的強度的削弱：單鍵槽增大3%，雙鍵槽增大7%，然后將軸徑圓整。 綜合以上取， 軸的結(jié)構(gòu)設(shè)計如下圖： 圖4.1 主軸 4.3軸上鍵的校核 根據(jù)軸和鏈輪配合的要求，初選平鍵A ，對于采用常見的材料組合和按標準選取尺寸的普通平鍵連接（靜連接），其主要失效形式是工作面被壓潰。除非有嚴重過載，一般不會出現(xiàn)鍵的剪斷。因此，通常按工作面上的壓力進行條件性的強度校核計算。 假定載荷在鍵的工作面上均勻分布，普通平鍵連接的強度條件為 （5-18） 式中： T—傳遞的轉(zhuǎn)矩，，； k—鍵與輪轂鍵槽的接觸高度，，此處h為鍵的高度，mm； l—鍵的工作長度，mm，圓頭平鍵，這里L為鍵的公稱長度，mm，b為鍵的寬度，mm； d—軸的直徑，mm； [σp]—鍵、軸、輪轂三者中最弱材料的許用擠壓應(yīng)力。 在軸上傳遞的轉(zhuǎn)矩為電動機的輸出轉(zhuǎn)矩 （5-19） 鍵與輪轂鍵槽的接觸高度 鍵的工作長度 軸的直徑 由《機械設(shè)計》表6-2，選擇 代入公式（5-18）： 滿足條件。 轉(zhuǎn)向箱輸出端鍵的校核 結(jié)構(gòu)與電動機軸端結(jié)構(gòu)相似，選擇 平鍵A 10*10*28 計算公式與上式相同 傳遞的轉(zhuǎn)矩 鍵與輪轂鍵槽的解除高度 鍵的工作長度 L=24mm。 軸的直徑 代入公式（5-18）： 滿足條件。 5 軸承的選擇和潤滑 5.1 軸承的選擇 選擇滾動軸承的類型與多種因素有關(guān)，通常根據(jù)下列幾個主要因素： A.負荷情況 負荷是選擇軸承最主要的依據(jù)，通常應(yīng)根據(jù)負荷的大小，方向和性質(zhì)來選擇軸承。 a)負荷大小：一般情況下，滾子軸承由于是線接觸，承載能力大，適用于承受較大負荷，球軸承由于是點接觸，承載能力小，適用于輕，中等負荷。 b)負荷方向：純徑向力作用，宜選用深溝球軸承，圓柱滾子軸承或滾針軸承。純軸向負荷作用，選用推力球軸承或推力滾子軸承。徑向負荷和軸向負荷聯(lián)合作用時，一般選用角接觸球軸承或圓錐滾子軸承。若徑向負荷較大而軸向負荷較小時，也可選用深溝球軸承和內(nèi)外圈都有擋邊的圓柱滾子軸承。若軸向負荷較大而徑向負荷小時，可選用推力角接觸軸承，推力圓錐滾子軸承。 c)負荷性質(zhì)：有沖擊負荷時，宜選用滾子軸承。 B.高速性能 球軸承比滾子軸承有較高的極限轉(zhuǎn)速，故高速時應(yīng)優(yōu)先考慮選用球軸承。在相同內(nèi)徑時，外徑越小，滾動體越輕小，運轉(zhuǎn)時滾動體作用在外圈上的離心力也越小，因此更適合于較高轉(zhuǎn)速下工作。在一定條件下，工作轉(zhuǎn)速較高時宜選用超輕，特輕系列的軸承。 C.調(diào)心性能 當軸兩端軸承孔同心性差或軸的剛度小，變形較大，以及多支點軸，均要求軸承調(diào)心性好，這時應(yīng)選用調(diào)心球軸承或調(diào)心滾子軸承。 D.允許的空間 徑向尺寸受限制的機械裝置，可選用滾針軸承或特輕，超輕型軸承；軸向尺寸受限制時，宜選用窄或?qū)捪盗械妮S承。 E.安裝與拆卸方便 整體式軸承座或頻繁裝拆時，應(yīng)優(yōu)先選用內(nèi)外圈可分離的軸承。軸承裝在長軸上時，為裝拆方便可選用帶錐孔和緊定套的軸承。 根據(jù)以上所述及本設(shè)計的具體要求，選用調(diào)心球軸承。 5.2 軸承的潤滑 軸承潤滑主要目的是減少摩擦和磨損，同時起到冷卻，吸振，防銹及降噪的作用。 常用的潤滑劑有潤滑油，潤滑脂及固體潤滑劑(二硫化鉬)。選擇潤滑劑應(yīng)當考慮工作溫度，軸承負荷，轉(zhuǎn)速及其工作環(huán)境影響。一般來說，溫度高，負荷大，轉(zhuǎn)速低時選用粘度高的潤滑劑。 潤滑油選擇：常用的潤滑油有--機械油，高速機械油，汽輪機油，壓縮機油，變壓器油，汽缸油等等。一般而言，軸承轉(zhuǎn)速越高，則選用較低粘度的潤滑油。負荷越重，則選用粘度較高的潤滑油。潤滑方法有：油浴潤滑，循環(huán)油潤滑，噴油潤滑及油霧潤滑。 選擇潤滑油或潤滑脂的一般原則如表9.1： 表9.1 選擇潤滑油或脂潤滑的一般原則 影響選擇的因素 用潤滑脂 用潤滑油 溫度 當溫度超過120時，要用特殊潤滑脂。當溫度升高到200-220時，再潤滑的時間間隔要縮短 油池溫度超過90或軸承溫度超過200時，可采用特殊的潤滑油 溫度系數(shù) <400000 〈400000－500000 載荷 低到中等 各種載荷直到最大 軸承形式 不用于不對稱的球面滾子推力軸承 用于各種軸承 殼體設(shè)計 較簡單 需要較復(fù)雜的密封和供油裝置 長時間不需維護的地方 可用。根據(jù)操作條件，特別要考慮工作溫度 不可以用 集中供油 選用泵送性能好的潤滑脂。不能有效地傳熱，也不能作為液壓介質(zhì) 可用 最低轉(zhuǎn)矩損失 如填裝適當，比采用油的損失還要低 為了獲得最低功率損失，應(yīng)采用有清洗泵或油霧裝置的循環(huán)系統(tǒng) 污染條件 可用。正確的設(shè)計可防止污染物的侵入 可用。但要采用有防護、過濾裝置的循環(huán)系統(tǒng) 結(jié)論 我本次的畢業(yè)設(shè)計選題新穎，涉及知識面廣，包括氣浮墊研磨機的總體結(jié)構(gòu)設(shè)計、軸承的選用、電機的選用、鍵的選用與校核、鏈輪傳動的設(shè)計等各個方面的內(nèi)容，基本上涉及了我大學四年所學的各項內(nèi)容同時也涉及到一些書本上不曾涉及的內(nèi)容，是對我大學四年所學知識的一次全面的總結(jié)，也是對我所學知識的進一步拓展。 在本設(shè)計中，執(zhí)行工作的從動件能滿足生產(chǎn)工藝提出的運動形式、運動規(guī)律、功能范圍和運動性能等諸方面的具體要求。結(jié)構(gòu)簡單，尺寸大小適度，在整體布置上占有空間小，布局緊湊。制造加工容易，維修拆裝方便，工作中穩(wěn)定可靠，使用安全，具有足夠的壽命。滾筒與電動機的運動方式，功率、轉(zhuǎn)矩及其載荷特性能夠相互協(xié)調(diào)，與其他相鄰機構(gòu)的銜接正常，傳動運動和力可靠，不會發(fā)生運動干涉。本機符合生產(chǎn)的需要，具有較高的生產(chǎn)率和經(jīng)濟效益。 致 謝 為期三個多月的畢業(yè)設(shè)計已經(jīng)接近尾聲，回顧整個過程，我深有感受。在設(shè)計過程中，我翻閱了很多與我課題相關(guān)的資料，同時將以前所學的有直接聯(lián)系的相關(guān)專業(yè)科目認真的溫習了一邊，豐富了許多理論方面的知識。這次設(shè)計使我四年中學到的基礎(chǔ)知識得到了一次綜合的應(yīng)用，使學過的知識結(jié)構(gòu)得到了科學的組合，同時也從理論到實踐發(fā)生了一次質(zhì)的飛躍，可以說這次設(shè)計是理論知識與實踐運用之間相互過渡的橋梁，是我們即將踏上工作崗位的臺階。 在畢業(yè)設(shè)計的過程中，我發(fā)現(xiàn)自身的許多不足，理論知識不夠扎實，設(shè)計經(jīng)驗不足，同時又缺乏實踐工作的磨礪，從而導致在設(shè)計時難以做出正確的選擇，對課題的內(nèi)容茫然不知所措。對資料的應(yīng)用也不夠確切，對設(shè)計產(chǎn)品的具體形狀、運作方式、性能指標也不能有一個準確的定位。缺乏對具體產(chǎn)品的想象力，當查閱有關(guān)資料時， 設(shè)計思維又受到書本內(nèi)容的束搏，不能得到擴展，始終局限于個別的、單一的理論或?qū)嶓w。這一切都是可能導致我本次設(shè)計的不足之處，懇請老師和同學指正。 由于自己能力所限，時間倉促,設(shè)計中還存在許多不足之處，懇請各位老師同學給予批評指正。 參考文獻 [1] 王軍．單晶藍寶石基片精密研磨工藝研究[D]．大連：大連理工大學，2008． [2] 徐萬孚，劉雨川，李廣宇，等．螺旋槽干運行非接觸氣體密封的理論分析與試驗[J]．機械工程學報，2003，39(4)：124-27． [3] 周圣人，朱維兵，王和順．節(jié)流孔特性對靜壓干氣密封性能的影響[J]．潤滑與密封，2003，21(2)：69-73． [4] 張君安，方宗德．用可變截面均壓槽實現(xiàn)高剛度空氣靜壓軸承的結(jié)構(gòu)設(shè)計[J]．西安石油大學學報，2006，21(6)：96-98． [5] 王偉,欒道成,陳庚.超細硬質(zhì)合金研究進展綜述[J].西華大學學報(自然科學版),2009,28(4):100～104 [6] 鄶吉才,張飛虎.ELID磨削鈍化膜彈簧剛度計算模型研究[J].工具技術(shù),2008,28:29-32 [7] 榮烈潤.超精密研磨拋光方法[J].航空精密制造技術(shù),2005,41(2):4-7. [8] 簡金輝,焦鋒.超精密加工技術(shù)研究現(xiàn)狀及發(fā)展趨勢.機械研究與應(yīng)用,2008:4-8 [9] 任敬心,黃奇.激光陀螺反射鏡基片精密拋光技術(shù)的研究[J].航空精密制造技術(shù),1992, 47 (1):11-13, [10] 徐鋒,左敦穩(wěn),王珉等.CVD金剛石厚膜的機械拋光及其殘余應(yīng)力的分析.人工晶體學報,33(3):437-440. [11] Wang CY, Kuang TC, Qin Z, Wei X. How abrasive machining affects surface characteristics of vitreous ceramic tile. Am Ceram Soc Bull 2003: 920,1–8. [12]Tucci A, EspósitoL.Polishing of porcelain stoneware tile: surface aspects.QUALICER 2000: World Congress on Ceramic Tile Quality. 2000. [13] Ibá?nez MJ, Sánchez E, García-Ten J, Orts MJ, Cantavella V, Sánchez J, et al. Use of pin-on-disk tribometer for studying porcelain tile polishing.QUALICER 2002: World Congress on Ceramic Tile Quality. 2002. [14]朱炳森，王成勇，袁慧．工程陶瓷薄件固著磨料研磨研究[J]．金剛石與磨料磨具工程，2000．1(115)：23-26 [15]何聰華，袁慧．精密金剛石砂輪的制造、修整及其磨削機理研究進展．超硬材料工程[J]．2008，4(20)：30—36 [16]袁巨龍．功能陶瓷的超精密加工技術(shù)[M]．哈爾濱工業(yè)大學出版社,2000．8：40—51. [17]P．S．Sreejith，B．K．A．Ngoi．Material removal mechanisms in precision machining of new materials[J]．International Journal of Machine Tool&Manufacture，2001，41：1831—1843. [18] H．Y.Tam，H．B．Cheng，Y.W.Wang．Removal rate and surface roughness in the lapping and polishing of RB—SiC optical components[J]．Journal of Materials Processing Technology,2007,192-193:277. [19]周兆忠，袁巨龍，鄭家錦，呂冰海．氮化鋁基片超精密加工的實驗研究[J]．金 剛石與磨料磨具工程，2005．4，2：36-38. [20]袁慧，王成勇，魏昕．工程陶瓷的游離磨料研磨加工工藝[J]．機械工藝師，2003．3：19-20. [21]房建國，劉棉，楊志甫，超精密研磨拋光機床的研究與設(shè)計[J].航空精密制造技術(shù)，2005．12，41(6)：4. [22]趙文宏，黃文君，袁巨龍等．修正環(huán)型納米級超精密拋光機智能[J]．控制系統(tǒng)的實現(xiàn)．機電工程，2003，20(3)：38-41. [23] 胡曉珍，胡曉東，李偉．超精密雙面拋光機控制系統(tǒng)的研究[J]．機電工程，2005，22(1 1)：58-62. Robotics and Computer-Integrated Manufac b , f Science, Science In manufacturing industry of wooden furniture, CAD/ machines cannot be applied to the sanding task of the workpiece with free-formed surface. Accordingly, we must depend on skilled workers who can not only perform workers usually use handy air-driven tools such as a double Industrial robots have been progressed remarkably and applied to several tasks such as painting, welding, handling and so on. In these cases, it is important to precisely ARTICLE IN PRESS control the position of the end-effector attached to the tip of the robot arm. On the contrary, when the robots are applied to polishing, deburring or grinding task, it is 0736-5845/$-see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.rcim.2006.04.004 C3 Corresponding author. Tel.: +81836884547; fax: +81836883400. E-mail address: nagataed.yama.tus.ac.jp (F. Nagata). CAM systems and NC machine tools have been introduced widely and generally, so that the design and machining processes are rationalized drastically. However, the sand- ing process after machining is hardly automated yet, because it requires delicate and dexterous skills so as not to spoil the beauty and quality of the surface. Up to now, several sanding machines have been developed for wooden materials. For example, the wide belt sander as shown in Fig. 1 is used for flat workpieces constructing furniture. The profile sander as shown in Fig. 2 is suitable for the sanding around the edge. However, these conventional action sanding tool and an orbital sanding tool as shown in Fig. 4. In order to produce a better surface quality, the double action sander simultaneously performs rotational and eccentric motions. As can be guessed, such tools spread out unhealthy noise, vibration and dust. The most serious problem in the sanding process is that the sanding task in such a bad working environment is extremely hard for skilled workers. From this reason, an advanced sanding machine which can even partially replace the skilled workers is being required in the furniture manufacturing industry. wooden materials constructing furniture. Handy air-driven tools can be easily attached to the tip of the robot arm via a compact force sensor. The robotic sanding system is called the 3D robot sander. The robot sander has two novel features. One is that the polishing force acting between the tool and wooden workpiece is delicately controlled to track a desired value, e.g., 2kgf. The polishing force is defined as the resultant force of the contact force and kinetic friction force. The other is that no complicated teaching operation is required to obtain a desired trajectory of the tool. Cutter location (CL) data, which are tool paths generated by a CAD/CAM system, are directly used for the basic trajectory of the handy tool attached to the robot arm. The robot sander can be applied to the sanding task of free- formed curved surface with which conventional sanding machines have not been able to cope. The effectiveness and promise are shown and discussed through a few experiments. r 2006 Elsevier Ltd. All rights reserved. Keywords: Robotic sanding; CAD/CAM; Cutter location data; Non-taught operation; Surface following control; Polishing force 1. Introduction appropriate force control of sanding tools but also deal with complex curved surface as shown in Fig. 3. Skilled In this paper, a sanding system based on an industrial robot with a surface following controller is proposed for the sanding process of Robotic sanding system for with free-formed Fusaomi Nagata a,C3 , Yukihiro Kusumoto a Department of Electronics and Computer Science, Tokyo University o b Interior received in revised Abstract turing 23 (2007) 371379 new designed furniture surface Yoshihiro Fujimoto b , Keigo Watanabe c Yamaguchi, Daigaku-Dori 1-1-1, Sanyo-Onoda 756-0884, Japan Center, Agemaki 405-3, Ohkawa, Fukuoka 831-0031, Japan and Engineering, Saga University, Honjomachi 1, Saga 840-8502, Japan form 10 March 2006; accepted 7 April 2006 ARTICLE IN PRESS Fig. 2. Conventional profile sander. Fig. 3. Sanding scene by a skilled worker. Fig. 1. Conventional wide belt sander. F. Nagata et al. / Robotics and Computer-Integrated372 indispensable to use some force control strategy without damaging the object. For example, polishing robots and finishing robots were presented in 15. Automated robotic deburring and grinding were also introduced in 610. Two representative force control methods have been ever proposed. They are impedance control 11 and hybrid position/force control 12. The impedance control is one of the most effective strategies for a manipulator to desirably reduce or absorb the impact force with an object. It is characterized by an ability that controls the mechanical impedance such as inertia, damping and stiffness acting between the end-effector and its environment. The impedance control does not have a force control mode or a position control mode but it is a combination of the force and velocity of the end-effector. On the other hand, the Fig. 4. Handy air-driven sanding tools usually used by skilled workers. Manufacturing 23 (2007) 371379 hybrid position/force control method simultaneously con- trols the position and force of a robot manipulator. However, the six constraints which consist of 3-DOF positions and 3-DOF forces in a constrained frame cannot be simultaneously satisfied. In order to avoid the inter- ference between the force control system and position control system, either force control mode or position control mode is selected in each direction. Surface following control is a basic sanding strategy for industrial robots. It is known that two control schemes are needed to realize the surface following control system. One is the position/orientation control of the sanding tool attached to the tip of the robot arm. The other is the force control to stably keep in contact along the curved surface of the workpiece. It should be noted that if the geometric information on the workpiece is unknown, then it is so difficult to satisfactorily control the contact force moving with a higher speed 13. To suppress overshoots and oscillations, for example, the feed rate must be given a small value. Furthermore, it is also difficult to control the orientation of the sanding tool, keeping in contact with the workpiece from normal direction. The authors have conducted relevant fundamental studies. As for force control, impedance model following force control method was proposed for an industrial robot with open architecture concept 14. The force controller adjusts the contact force acting between a sanding tool and workpiece through a desired impedance model. In 15, fuzzy environment model was presented for environments with unknown physical property. The fuzzy environment model is learned with genetic algorithm and can estimate the stiffness of unknown environment. The effectiveness was evaluated through simulations using a dynamic model of PUMA560 manipulator. In 16, a gravity compensator was considered to remove the influence of tool weight from measured force. In 17, concerning tool position and so that we can try to program new functions such as force control, compliance control and so on. The 6-DOF industrial robot shown in Fig. 5 is a FS20N with a PC- based controller provided by Kawasaki Heavy Industries. The proposed robotic sanding system is developed based on the industrial robot whose tip has a compact force sensor. A handy sanding tool can be easily attached to the tip of the robot arm via the force sensor. A PC is connected to the PC-based controller via an optical fiber cable. The PC-based controller provides several Windows API (ap- plication programming interface) functions, such as servo control with joint angles, forward/inverse kinematics and so on. By using such API functions, for instance, the position and orientation at the tip of the robot arm can be ARTICLE IN PRESS F. Nagata et al. / Robotics and Computer-Integrated Manufacturing 23 (2007) 371379 373 orientation control, it was further considered how to realize non-taught operation for industrial robots. Further- more, hyper CL data were also presented to deal with new statements about the regulation of sanding parameters in 18. In this paper, a robotic sanding system is integrated for new designed furniture with free-formed curved surface. The robotic sanding system provides a practical surface following control that allows industrial robots not only to adjust the polishing force through a desired impedance model in Cartesian space but also to follow a curved surface keeping contact with from normal direction. The polishing force is assumed to be the resultant force of contact force and kinetic friction force. We also describe how to apply the sanding system to a sanding task of wooden workpiece without complicated teaching process. A few sanding experiments are shown to demonstrate the effectiveness and promise of the proposed robotic sanding system using the surface following controller. 2. Robotic sanding system Recently, open architectural industrial robots have been proposed to comply with users various requests with regard to application developments. The industrial robot has an open programming interface for Windows or Linux, Fig. 5. Robotic sanding system developed based on controlled easily and safely. In the following section, the surface following controller is implemented for robotic sanding by using the Windows API functions. 3. Surface following control for robotic sanding system The robotic sanding system has two main features: one is that neither conventional complicated teaching tasks nor post-processor (CL data ! NC data) is required; the other is that the polishing force acting on the sanding tool and tool position/orientation are simultaneously controlled along free-formed curved surface. In this section, a surface following control method indispensable for realizing the features are described in detail. 3.1. Desired trajectory Robotic sanding task needs a desired trajectory so that the sanding tool attached to the tip of the robot arm can follow the objects surface, keeping contact with the surface from the normal direction. In executing a motion using an industrial robot, the trajectory is generally obtained in advance, e.g., through conventional robot teaching pro- cess. When the conventional teaching for an object with complex curved surface is conducted, the operator has to input a large number of teaching points along the surface. an open architectural industrial robot FS20N. The desired tool angles y r1 k, y r2 k of inclination and rotation at the discrete time k can be calculated as y rj ky j ify j i 1C0y j ig kx d kC0pik ktik , (11) where j 1;2. If (11) is substituted into (8), (9), (10), we finally obtain o da ksiny r1 kcosy r2 k, (12) o db ksiny r1 ksiny r2 k, (13) o dg kcosy r1 k. (14) x d k and o d k mentioned above are directly obtained from the CL data without any conventional complicated teaching, and used for the desired position and orientation of a sanding tool attached to a robot arm. 3.2. Polishing force In this section, a sanding strategy dealing with polishing force is described in detail. The polishing force vector FkF x k F y k F z kC138 T is assumed to be the resultant force of contact force vector fkf x k f y k f z kC138 T ARTICLE IN PRESS Y 2 afii9826 (i ) Fig. 7. Normalized tool vector ni represented by y 1 i and y 2 i in robot base coordinate system. tegrated Such a teaching task is complicated and time-consuming. However, if the object is fortunately designed and manufactured by a CAD/CAM system and an NC machine tool, then the CL data can be referred as the desired trajectory. In order to realize non-taught operation, we have already proposed a generalized trajectory generator 19,20 using the CL data, which yields the desired trajectory rk at the discrete time k given by rkx T d k o T d kC138 T , (1) where x d kx dx k x dy k x dz kC138 T and o d k o da k o db k o dg kC138 T are the position and orientation components, respectively. o d k is the normal vector at the position x d k. In the following, we detail how to make rk using the CL data. A target workpiece with curved surface is generally designed by a 3D CAD/CAM, so that the CL data can be calculated by the main-processor of the CAM. The CL data are sequential points along the model surface given by a zigzag path or a whirl path. In this approach, the desired trajectory rk is generated along the CL data. The CL data are usually calculated with a linear approximation along the model surface. The ith step is written by CLip x i p y i p z i n x i n y i n z iC138 T , (2) fn x ig 2 fn y ig 2 fn z ig 2 1, (3) where pip x i p y i p z iC138 T and nin x i n y i n z iC138 T are position and orientation vectors, respectively. rk is obtained by using linear equations and a tangential velocity v t k represented by v t kv tx k v ty k v tz kC138 T . (4) A relation between CLi and rk is shown in Fig. 6. In this case, assuming rk2CLi; CLi 1C138 we obtain rk through the following procedure. First, a direction vector ti is given by tipi 1C0pi (5) so that each component of v t k is obtained by v tj kkv t kk t j i ktik j x;y;z. (6) Using a sampling width Dt, each component of the desired position x d k is given by x dj kx dj k C0 1v tj kDt j x;y;z. (7) Next, the desired orientation o d k is considered. We define two angles y 1 i;y 2 i as shown in Fig. 7. y 1 i and y 2 i are the tool angles of inclination and rotation, respectively. Using y 1 i and y 2 i, each component of ni is represented by aisiny 1 icosy 2 i, (8) bisiny 1 isiny 2 i, (9) F. Nagata et al. / Robotics and Computer-In374 gicosy 1 i. (10) Workpiece CL(i-1) r (k) r (k + 1) r (k + 2) CL(i+1) CL(i) Fig. 6. Relation between CL data CLi and desired trajectory rk. X Z O afii9835 (i) afii9835 1 (i) afii9828 (i) afii9825 (i ) Manufacturing 23 (2007) 371379 and kinetic friction force vector F r kF rx k F ry k F rz kC138 T that are given to the workpiece as shown finishing, it is fundamental and effective to stably control the polishing force. When the robotic sanding system runs, the polishing force is controlled by the impedance model following force control with integral action given by v normal kv normal k C01e C0B d =M d Dt e C0B d =M d Dt C0 1 K f B d E f k K fi X k n1 E f n, 19 ARTICLE IN PRESS tegrated Manufacturing 23 (2007) 371379 375 in Fig 8, where the sanding tool is moving along on the surface from (A) to (B). F r k is written by F r kdiagm x ;m y ;m z kfkk v t k kv t kk diagZ x ;Z y ;Z z v t k, 15 where diagm x ;m y ;m z kfkkv t k=kv t kk is the Coulomb friction, and diagZ x ;Z y ;Z z v t k is the viscous friction. m i and Z i i x;y;z are the i-directional coefficients of Coulomb friction per unit contact force and of viscous friction, respectively. Each friction force is generated by fk and v t k, respectively. Fk is represented by FkfkF r k. (16) The polishing force magnitude can be easily measured by using a 3-DOF force sensor attached between the tip of the arm and the sanding tool, which is given by Tip of robot arm Force sensor Sanding tool Workpiece vt F f F r (A) (B) Fig. 8. Polishing force Fk composed of contact force fk and kinetic friction force F r k. F. Nagata et al. / Robotics and Computer-In kFkk f S F x kg 2 f S F y kg 2 f S F z kg 2 q , (17) where S F x k, S F y k and S F z k are the each directional component of force sensor measurements in sensor coordinate system. In the following section, the error E f k of polishing force magnitude is calculated by E f kF d C0kFkk, (18) where F d is a desired polishing force. 3.3. Feedback control of polishing force In the manufacturing industry of wooden furniture, skilled workers usually use handy air-driven tools to finish the surface after machining or painting. These types of tools cause high frequency and large magnitude vibrations, so that it is so difficult for the skilled workers to sand the workpiece keeping the polishing force a desired value. Consequently, undesirable unevenness tends to appear on the sanded surface. In order to achieve a good surface where v normal k is the velocity scalar; K f is the force feedback gain; K fi is the integral control gain; M d and B d are the desired mass and desired damping coefficients, respectively. Dt is the sampling width. Using v normal k, the normal velocity vector v n kv nx k v ny k v nz kC138 at the center of the contact point is represented by v n kv normal k o d k ko d kk . (20) 3.4. Feedforward and feedback control of position Currently, wooden furniture are designed and machined with 3D CAD/CAM systems and NC machine tools, respectively. Accordingly the CL data generated from the main-processor of the CAM can be used for the desired trajectory of the sanding tool. The tool path (CL data) as shown in Fig. 9, which are calculated in advance based on a zigzag path, is considered to be a desired trajectory of the sanding tool. Fig. 10 shows the block diagram of the surface following controller implemented in the robot sander. The position and orientation of the tool attached to the tip of the robot arm are feedforwardly controlled by the tangential velocity v t k and rotational velocity v r k, respectively, referring x d k and o d k. v t k is given through an open-loop action so as not to interfere with the force feedback loop. The polishing force is regulated by v n k which is perpendicular to v t k. v n k is given to the normal direction referring the orientation vector o d k. It should be noted, however, that using only v t k is not enough to precisely carry out desired trajectory control along the CL data: actual trajectory tends to deviate from Fig. 9. Zigzag path generated from main-processor of CAM. ARTICLE IN PRESS Cartesian-Based Sander Control Law tegrated the desired one, so that the constant pick feed (e.g., 20mm) cannot be performed. This undesirable phenomenon leads to the lack of uniformity on the surface. To overcome this problem, a simple position feedback loop with small gains is added as shown in Fig. 10 so that the tool does not deviate from the desired pick feed. The position feedback control law generates another velocity v p k given by v p kS p K p E p kK i X k n1 E p n () , (21) where S p diagS x ;S y ;S z is a switch matrix to realize a weak coupling control in each direction. If S p diag1;1;1, then the coupling control is active in all directions; whereas if S p diag0;0;0, then the position feedback loop does not contribute to the force feedback loop in all directions. E p kx d kC0 xk is the position error vector. xk is the current position of the sanding tool attached to the tip of the arm and is obtained from the forward kinematics of the robot. K p diagK px ;K py ;K pz and K i diagK ix ;K iy ;K iz are the position feedback gain and its integral gain matrices, respectively. Each compo- nent of K p and K i must be set to small values so as not to obviously disturb the force control loop. Finally, recomposed velocities v n kv T n k 000C138 T , v t k T T T T T Position Feedback Control Law Servo Controller + + x d (k) x (k) x d (k) : desired position o d (k) : desired position Based on CL Data S p v p (k) Fig. 10. Block diagram of the surface following controller implemented in the robot sander. Force Feedback Control Law Robot + F d o d (k) F (k) F d : desired polishing force Position/Orientation Feedforward S p : switch matrix v t (k) v n (k) F. Nagata et al. / Robotics and Computer-In376 v t k v r kC138 and v p kv p k 000C138 are summed up, and those of which are given to the reference of the Cartesian-based servo controller of the industrial robot. It is known that the six constraints, which consist of 3- DOF positions and 3-DOF forces in a constraint frame, cannot be simultaneously satisfied 21. However, the delicate cooperation between the position feedback loop and force feedback loop is an