提高數(shù)控機(jī)床幾何精度使用生產(chǎn)過程分析技術(shù)外文文獻(xiàn)翻譯、中英文翻譯、外文翻譯,提高,數(shù)控機(jī)床,幾何,精度,使用,生產(chǎn)過程,分析,技術(shù),外文,文獻(xiàn),翻譯,中英文 附錄一： 提高數(shù)控機(jī)床幾何精度使用生產(chǎn)過程分析技術(shù) 文摘 現(xiàn)代數(shù)控設(shè)備的精度要求越來越高,加工制造工藝和裝配的結(jié)構(gòu)組件是一個(gè)越來越重要的因素建立幾何糾正機(jī)床。具體來說,平面度,垂直度、并行性和連接表面的平直度確定機(jī)床的基本精度。表現(xiàn)出更少的幾何誤差允許其他錯(cuò)誤,如熱增長,滾珠絲桿螺距誤差和控制更容易被孤立和糾正錯(cuò)誤。 幾何誤差具有較高的機(jī)床加工和裝配過程的一個(gè)因素。多個(gè)方向在夾具裝配和加工導(dǎo)致顯著的扭曲最終組裝產(chǎn)品。這是由于切削力,夾具變形,重力變形,螺栓力變形。通過詳細(xì)分析每個(gè)進(jìn)程使用虛擬仿真技術(shù),高保真模型相應(yīng)的錯(cuò)誤可以實(shí)現(xiàn)在每個(gè)生產(chǎn)步驟,不是身體上的可衡量的由于測量設(shè)備的約束。使用模擬數(shù)據(jù)作為抵消數(shù)據(jù)加工過程中以及在夾具及固定裝置設(shè)計(jì)確保了幾何準(zhǔn)確的最終產(chǎn)品。 關(guān)鍵詞:仿真;加工精度;機(jī)床制造;有限元法 1. 介紹 實(shí)際上，精密機(jī)床制造業(yè)是在飛速發(fā)展的。增量經(jīng)驗(yàn)基礎(chǔ)的改進(jìn)正在穩(wěn)步實(shí)現(xiàn)機(jī)械本身精度的進(jìn)步,機(jī)器的組件,這些組件構(gòu)成了下一代也提高。再加上附加值由技術(shù)熟練的工匠導(dǎo)致機(jī)床精度不斷增加。[1]然而,降低產(chǎn)品生命周期時(shí)間和機(jī)床行業(yè)競爭力的本質(zhì)要求改進(jìn)機(jī)床精度是不夠的。此外,成本效益的實(shí)際限制機(jī)械與高精度生產(chǎn)零部件將物理限制的精度水平,可用于制造過程。[2]過程產(chǎn)生更嚴(yán)格的公差比傳統(tǒng)加工和磨削往往是成本高昂,無法廣泛采用到流程鏈。因此找到一種方法來改進(jìn)過程是很重要的使用現(xiàn)有的設(shè)備。機(jī)器檢查是 NHX4000,400 毫米托盤臥式數(shù)控加工中心由 DMG Mori 精在戴維斯,CA。 1.1 在機(jī)床虛擬建模使用 在過去的的五年里,計(jì)算能力已經(jīng)足夠成熟來處理完整的機(jī)床系統(tǒng)的復(fù)雜模型。作為一個(gè)例子,DMG Mori 精數(shù)字技術(shù)實(shí)驗(yàn)室(迪泰)購買了 32 節(jié)點(diǎn) Linux 集群運(yùn)行仿真,桌面 PC 的 30 天的時(shí)間來解決。集群計(jì)算機(jī)的時(shí)間縮短到一天! 今天,桌面可以擊敗,性能幾乎任何級(jí)別的機(jī)床系統(tǒng)的計(jì)算機(jī)模擬現(xiàn)在是可能的。 重要研究已經(jīng)做了關(guān)于如何使用虛擬測試機(jī)床設(shè)計(jì)性能和造型是 Altintas CIRP 主題的一篇論文中總結(jié),等人一個(gè)非常有前途的方法,可以用來分析制造過程有限元建模和其他形式的虛擬仿真。在過去在 2005 年。[2]研究成功完成從組件級(jí)別的完全模擬機(jī)床虛擬樣機(jī)來證明傳統(tǒng)的設(shè)計(jì)周期可以現(xiàn)實(shí)地縮短消除物理原型迭代。從簡單的靜態(tài)分析完成復(fù)雜的動(dòng)態(tài)模型和熱模型剛度模型。雖然仍有改進(jìn),這種方法的機(jī)床虛擬仿真已迅速成為成熟。 已經(jīng)被充分研究過的另一個(gè)方面是使用有限元法對(duì)微觀的各個(gè)組件的性能復(fù)雜的內(nèi)部行為(滾珠絲桿接觸模型和阻尼運(yùn)動(dòng)組件的行為。健壯的組件模型可用于改善 產(chǎn)品質(zhì)量,也為開發(fā)更高的帶寬控制算法。[3]詳細(xì)接觸模型被用來協(xié)助經(jīng)驗(yàn)測試的組件發(fā)現(xiàn)阻尼值被回收用于整體機(jī)動(dòng)態(tài)模型。[4] 另一個(gè)相當(dāng)大的研究領(lǐng)域的仿真應(yīng)用到模擬切削過程本身。這些類型的物理現(xiàn)象往往很難添加儀器,因此模擬的交互是非?？扇〉?。是用來模擬切削過程的表面光潔度的決心,毛刺的形成,芯片形成溫度分散,刀具磨損等等。[5][6]中使用喋喋不休和切削穩(wěn)定性的預(yù)測也可以不去。[7] 很明顯,計(jì)算機(jī)模擬技術(shù)廣泛用于機(jī)床和加工的好處。然而,這項(xiàng)技術(shù)還沒有部署到研究機(jī)床本身的制造過程。這可能是由于精密機(jī)床的所有權(quán)性質(zhì)。無論如何,有足夠的機(jī)會(huì),應(yīng)用仿真技術(shù)以提高機(jī)床的精度。為了實(shí)現(xiàn)更大的精度,分析將顯示改善的領(lǐng)域。這包括集成的切削力、夾具設(shè)計(jì)、組裝順序,等等。夾具和夾具一起把機(jī)器精度高和重復(fù)精度也非常重要,檢查。這將是一個(gè)自然的結(jié)果上面的分析進(jìn)行的。 1.2 幾何測量誤差來源 進(jìn)行機(jī)床分析使用虛擬造型本身適用于只有某些錯(cuò)誤。具體來說,可以糾正的錯(cuò)誤本質(zhì)上是幾何和大量地重復(fù)。許多論文清晰地闡明幾何錯(cuò)誤。它們通常依賴。在旋轉(zhuǎn)的軸的情況下,線性幾何誤差可以認(rèn)為是比旋轉(zhuǎn)式軸誤差極小。然而,[8]的方法改善的準(zhǔn)確性機(jī)床生產(chǎn)過程機(jī)器適用于任何配置的工具。此外,直線運(yùn)動(dòng)誤差復(fù)合回轉(zhuǎn)軸線的不確定性誤差補(bǔ)償[9],建議盡可能降到最低。本研究將集中在錯(cuò)誤的生產(chǎn)過程,可以糾正一次確認(rèn)。 2. 生產(chǎn)過程鏈的統(tǒng)計(jì)分析 在制造精密數(shù)控設(shè)備,它是極其困難的,大大降低成本,同時(shí)保持產(chǎn)品質(zhì)量。因此,分析生產(chǎn)周期中的變量系統(tǒng)和識(shí)別改進(jìn)的重點(diǎn)領(lǐng)域有潛力提供最大限度的改善,在成本和精度/質(zhì)量,同時(shí)保持最小中斷生產(chǎn)。試圖分析和優(yōu)化每個(gè)測量和寬容將是理想的,但實(shí)際上是不可行的。也非常希望建立一個(gè)統(tǒng)計(jì)鏈接關(guān)鍵領(lǐng)域在生產(chǎn)過程的最終精度機(jī)床。 為此,XY 平面的統(tǒng)計(jì)分析。機(jī)床是一個(gè)復(fù)雜的機(jī)器與數(shù)以百計(jì)的測量和檢驗(yàn)點(diǎn),只有最相關(guān)的常見的切割操作需要分析。大多數(shù)削減在 XY 平面二維輪廓線測量,直接影響到 XY 運(yùn)動(dòng)鏈的精度被用來調(diào)查統(tǒng)計(jì)關(guān)系。為了得到一個(gè)合理的樣本量,30 臺(tái)取樣人口大約 150 臺(tái)機(jī)器生產(chǎn)。 為了進(jìn)行統(tǒng)計(jì)分析,數(shù)據(jù)的形式。就是做出假設(shè)依賴于正態(tài)分布的數(shù)據(jù),數(shù)據(jù)必須檢查正常。使用 Z 分?jǐn)?shù)正常的情節(jié)是一個(gè)可接受的方式建立一個(gè)正態(tài)分布。[10]的正常情節(jié)雙球棒循環(huán)測量有線性回歸與一個(gè)高度線性 R2 值為 0.96。其他數(shù)據(jù)集有類似的行為,所以是假設(shè) 30 機(jī)器的數(shù)據(jù)樣本正態(tài)分布和基本假設(shè)可以應(yīng)用正態(tài)分布。 比較每個(gè)參數(shù)的方法是獲取原始加工結(jié)果之間的相關(guān)系數(shù)和最終的精度測試。因此,發(fā)展關(guān)聯(lián)矩陣的測量。這允許一個(gè)快速查看的參數(shù)可能有強(qiáng)壯的,溫和,弱,或根本沒有關(guān)系。系數(shù)超過 0.4 是強(qiáng)大而超過 0.3 是溫和的。[10] 是決定之間有很強(qiáng)的相關(guān)性的切圓和直線度測試組裝機(jī)器單獨(dú)的鑄造精度。x 軸有強(qiáng)烈的相關(guān)性。y 軸的頂端安裝軸和錯(cuò)誤的軸通過這個(gè)運(yùn)動(dòng)鏈傳播工具提示。此外, 大型移動(dòng)質(zhì)量上的軸原因地方變形的初始精度軸直接增加了局部變形。此外,x 軸鑄造(床)上加工大東芝龍門磨(MPC),y 軸(列)是一個(gè)緊湊的臥式加工中心上加工(NHX10000)。NHX10000 展品更高程度的精度和可重復(fù)性比東芝 MPC。統(tǒng)計(jì)分析的結(jié)論是,提高幾何特性的 X,Y,Z 軸的鑄造加工重點(diǎn)是X 軸將導(dǎo)致最終直接提高機(jī)床精度。 3 .加工過程 加工過程包括各種變量。摘要進(jìn)行密切的兩個(gè)變形由于夾具設(shè)計(jì)和變形由于切削力本身。重力是一組默認(rèn)的加載,應(yīng)用在整個(gè)制造過程。 3.1 夾具的影響 加工中使用的設(shè)備有四個(gè)標(biāo)準(zhǔn),必須分析 1. 鑄件由于變形大的夾緊力 2. 足夠的支持在加工鑄造的最小變形 3. 中立的定位,以避免彈簧后切割和夾具釋放。 4. 足夠的支持和取向的引力誘導(dǎo)變形降到最低。 對(duì)于 NHX4000、夾具主要發(fā)現(xiàn)足夠的設(shè)計(jì)方面的支持和夾緊的一個(gè)例外。圖 3 所示的右下方夾從支持導(dǎo)致幾乎抵消 2 點(diǎn)位移顯示在圖 4。 由于機(jī)器的限制,鑄造組件可能需要加工的方向不同的定向組裝。這可能導(dǎo)致過度的重力變形的部分鑄件。的列所示,水平夾具定位結(jié)果在 y 軸的直線度誤差大于 4 點(diǎn)。 床上鑄有類似的結(jié)果,而是因?yàn)樗羌庸そM裝、定位 self-gravitational 效果取消,加工夾具是更健壯的床上。 3.2. 貢獻(xiàn)的力量 切削力可以很容易地預(yù)測和仿真。Altintas 提出了一個(gè)廣義切削力模型適用于各種刀具與給定的幾何和切削條件。[11][12],值得注意的是,切削力的影響很小引力效應(yīng)相比,決定研究中被認(rèn)為可以忽略不計(jì)。 4. 裝配過程 4.1. 夾具及固定裝置設(shè)計(jì) 部分機(jī)床組裝在不同單位盡可能以最佳效率。X 和 Z rails 是直接安裝在床上,但 y 軸 rails 安裝到列在一個(gè)獨(dú)立的車站。裝配工人的有效的地方和測量 rails 在安裝和調(diào)整,列必須放置在夾具上的水平方向與 rails 面臨向上。穩(wěn)定性和安全性,四點(diǎn)固定最初被設(shè)計(jì)為在圖 7 中。 分析顯示嚴(yán)重靈敏度調(diào)整夾具。只有增加 4 點(diǎn)一個(gè)夾具的高度支持導(dǎo)致 Y-rails 平行度誤差為 3.5 點(diǎn)。在這種情況下,夾具的腿沒有微米級(jí)別的調(diào)整能力作為他們的高度調(diào)整是由普通 SAE 機(jī)線程。因此,裝配調(diào)整并行的人為變形狀態(tài)。釋放后的變 形狀態(tài)列從夾具中移除并設(shè)置直立導(dǎo)致 y 軸失去并行性。由于并行性高依賴于夾具調(diào)整,變形也非可重復(fù)加工期間,不能得到補(bǔ)償。 找到的解決方案是使用三個(gè)點(diǎn)支持列在鐵路修復(fù)。雖然列仍然變形由于重力,rails 近對(duì)稱變形和沒有靈敏度小夾具的高度變化。這是在 4.2 節(jié)詳細(xì)討論。結(jié)果是一個(gè)可重復(fù)的重力變形,可以補(bǔ)償在加工步驟。 4.2. 取向的結(jié)構(gòu) 當(dāng)一個(gè)組件如列是聚集在一個(gè)取向有利于有效的裝配工作正如上一節(jié)所討論的,重力將發(fā)揮作用的測量步驟。這種引力效應(yīng)可以有效地抵消了理解存在變形,隨后裝配調(diào)整過程中占了。當(dāng)使用三個(gè)點(diǎn)支持,列會(huì)變形,但這將是可預(yù)測的,依賴于三個(gè)點(diǎn)的位置。因此,有必要總是使用相同的三個(gè)點(diǎn)位置每次測量列,以確保測量重復(fù)性。此外,因?yàn)樗强扇〉?Y Rails 準(zhǔn)確測量并行性,指出應(yīng)選擇導(dǎo)致平衡 Rails 的 z 三個(gè)方向變形。同時(shí),Y rails 變形在等量所以并行性是保存列時(shí)調(diào)整。下圖顯示了三個(gè)點(diǎn)位置選擇基于有限元分析重力變形。關(guān)鍵是抵消略向電機(jī)支架的一面。這抵消抵消更大的質(zhì)量。在質(zhì)量控制和裝配使用了相同的位置。 4.3. 裝配順序和群眾不移動(dòng) 組件的順序獲得機(jī)體創(chuàng)建大型機(jī)床結(jié)構(gòu)的局部變形由于大質(zhì)量的每個(gè)組件。當(dāng)緊公差的軸運(yùn)動(dòng)系統(tǒng)已經(jīng)在早期階段獲得,然后會(huì)產(chǎn)生大量添加二級(jí)精度設(shè)置,每個(gè)軸的保真度的準(zhǔn)確性可以完全丟失。這可能并不總是會(huì)在最后的精度測試整機(jī)信封通常不是測試和局部變形可能只影響局部的信封。然而,詳細(xì)檢查整個(gè)機(jī)器的信封將揭示缺陷在不同工作信封的位置。因此,建議檢查添加的效果通過有限元質(zhì)量在每個(gè)裝配步驟。 減少這種影響的一個(gè)方法是解決運(yùn)動(dòng)組件安裝后沉重的子單元的裝配過程。然而, 在很多情況下這是不可行的,因?yàn)檫M(jìn)入工作區(qū)域時(shí)抑制子單元連接,也因?yàn)殍T件本身仍然看到了變形。 一種更有效的解決方案是模擬裝配順序,并記錄產(chǎn)生的變形。因?yàn)檫@是高度可重復(fù)的,可以直接做鑄件加工補(bǔ)償?shù)窒冃?組裝后獲得一個(gè)中立的變形子單元。 4.4. 影響移動(dòng)組件 最后分析執(zhí)行檢查裝配機(jī)軸運(yùn)動(dòng)的影響下重力加載。軸,相對(duì)工具在中間沖程位置較高,由于不同的變形前后 X-rails 之間在床上。后方 X-rail 有積極弓雖然前面 Xrail 負(fù)弓沿著 Xstroke 隨著列。的微分軌道高度傳播到 2.3 點(diǎn)誤差在 Y 的工具提示結(jié)束行程的中間!調(diào)整方法是一種積極的皇冠后方鐵路。下圖所示的數(shù)據(jù)。 5. 最終的加工結(jié)果 5.1. 加工計(jì)劃 每個(gè)組件有一個(gè)加工計(jì)劃開發(fā)基于前面的分析結(jié)果。這個(gè)計(jì)劃是累積的。的列,加冕應(yīng)該相反的變形形狀在 Y 中風(fēng)。在質(zhì)檢過程中測量應(yīng)仰臥位時(shí)重力變形直立時(shí)加上加冕變形減去重力變形。一個(gè)表面加工補(bǔ)償目標(biāo)的一個(gè)例子是提供在圖 14。 5.2。與其他工廠相比 生產(chǎn)過程的分析是在戴維斯進(jìn)行的,日本。在 Iga DMG Mori 精也有工廠,日本生產(chǎn)NHX4000 機(jī)相同。理解如果戴維斯的方法真的不同,戴維斯和Iga 的箱線圖結(jié)果了。結(jié)果不僅顯示出近似從戴維斯Iga 的平均提高20%,戴維斯數(shù)據(jù)變化少,一些極端的異常值,表明分析過程不僅增加了最終產(chǎn)品的精度,但一致性。 重要的是要注意,所有最終機(jī)器測量改進(jìn)是基于國際 ISO 標(biāo)準(zhǔn)。ISO 230 是用于最后的質(zhì)量控制測量和 ISO 10791 用于最終的質(zhì)量控制測試。循環(huán)的最大公差 5 微米和 8 微米直線度測量。 6. 結(jié)論 一個(gè)創(chuàng)新的使用現(xiàn)有的虛擬仿真技術(shù)已被提出和實(shí)施。一系列削減概要文件為每個(gè)部分是計(jì)算累計(jì)添加所有先前解釋的影響。這些是有效的,一個(gè)特定的順序和方向裝配過程質(zhì)量控制步驟和計(jì)劃也交付。累積的結(jié)果完成機(jī)器是表明 20%的整體改進(jìn)最后 NHX4000 產(chǎn)品。 引用 [1] D. A. Dornfeld, 精密的道路:機(jī)床和他們創(chuàng)造的產(chǎn)品,First. Mori Seiki Co., Ltd., 2008. [2] Y.Altintas,C.Brecher,M.Weck,and s.Witt,“虛擬機(jī)床”,CIRP Ann.-Manuf.technol,vol.54，no.2,pp.115-138,2005. [3]M.F.Zaeh,T.Oertli,and J.Milberg,“有限元建模的滾珠絲桿進(jìn)給驅(qū)動(dòng)系統(tǒng),”CIRP Ann.-Manuf.technol,vol.53,no.1,pp.289-292,2004. [4] C.Brecher,M.Fey,and S.Ba,“阻尼模型線性軸機(jī)床組件,” CIRP Ann.-Manuf.technol,vol.62,pp.399-402,2013. 附錄二： Improving CNC Machine Tool Geometric Precision Using Manufacturing Process Analysis Techniques Abstract With the ever increasing demands for higher and higher accuracy on modern CNC equipment, the manufacturing processes for machining and assembling the structural components are an increasingly important factor in establishing a geometrically correct machine tool. Specifically, flatness, perpendicularity, parallelism, and straightness of interfacing surfaces determine whether the machine tool’s basic accuracy. Exhibiting less geometric error allows other errors such as thermal growth, ballscrew pitch error, and control error to be isolated and more easily corrected. The geometric errors are predominately a factor of the machine tool machining and assembly process. Multiple orientations during fixturing in both assembly and machining result in significant distortions to the final assembled product. These are a result of cutting forces, fixturing deformations, gravity deformations, and bolt force deformation. By analyzing each process in detail using virtual simulation techniques, a high-fidelity model of the corresponding error at each manufacturing step can be achieved that is not physically measurable due to constraints of measurement equipment. Using simulated data as offset data in the machining process as well as in the jig and fixture design ensures a geometrically accurate final product. Keywords: Simulation; machining accuracy; machine tool manufacturing; FEM 1. Introduction Precision manufacturing of machine tools is very evolutionary in nature. Incremental experience based improvements are steadily achieved and as the machinery itself advances in precision, the components that make up the next generation of machines also improve. This, together with value added by skilled craftsman results in ever increasing accuracy of machine tools.[1] However, decreasing product life cycle times and competitive nature of the machine tool industry dictate that incremental improvements to machine tool accuracy are not sufficient. Moreover, the practical limit of cost effective machinery to produce parts with high precision puts a physical limit on the level of precision that can be used in the manufacturing process.[2] Processes that produce tighter tolerances than conventional machining and grinding tend to be cost prohibitive and are not able to be widelyadopted into the process chain. It therefore becomes important to find a way to improve the process using equipment that is currently available. The machine checked is the NHX4000, a 400 mm pallet horizontal CNC machining center produced by DMG Mori Seiki in Davis, CA. 1.1. Virtual modeling uses in machine tools A very promising method that could be used to analyse the manufacturing process is Finite Element Modelling and other forms of virtual simulation. In the last five years, computing power has become mature enough to handle full complex models of machine tool systems in a very short amount of time. As an example, DMG Mori Seiki’s Digital Technology Laboratory (DTL) purchased a 32 node Linux cluster for running simulation’s that took a desktop PC 30 days to solve. That cluster computer shortened the time to one day! Today, a desktop is able to beat that performance so virtually any level of computer simulation is now possible for machine tool systems. Significant research has been done on how to use virtual modelling to test machine tool designs performance and is well summarized in a CIRP keynote paper by Altintas, et al. in 2005.[2] Research successfully accomplished has modelled machine tools from component level to full virtual prototype to prove that the traditional design cycle could be realistically shortened by eliminating physical prototype iterations. Analyses completed range from simple static rigidity models to complex dynamic models and thermal models. While there is still improvement to be made, this method of machine tool virtual simulation has rapidly become mature. Another area that has been well studied is the use of FEM for the micro performance of individual components that have complex internal behaviour such contact models for ballscrews and damping behaviour of motion components. Robust component models are useful for improved product quality and also for developing higher bandwidth control algorithms. [3] Detailed contact models have been used to assist empirical testing of components to find damping values which are recycled for use in overall machine dynamic models.[4] Another considerable research area simulation is applied toward is simulation of the cutting process itself. These types of physical phenomena are often very difficult to add instrumentation and thus simulating the interaction is highly desirable. It is used to model cutting processes for surface finish determination, burr formation, chip formation, temperature dispersion, tool wear, and so on. [5] [6] Use in the prediction of chatter and cutting stability can also not go unmentioned. [7] It is clear that computer modelling techniques are widely used for the benefit of machine tools and machining. However, this technology has not been deployed to study the manufacturing process of the machine tool itself. This is perhaps due to the proprietary nature of precision machine tools. Regardless, there is ample opportunity to apply simulation technology in order to improve the accuracy of machine tools. To achieve greater accuracy, the analysis will show areas of improvement to be made. This includes integration of cutting forces, fixture design, assembly order, and so on. The fixtures and jigs to put the machine together for high accuracy and repeatable accuracy are also very important and are examined. This will be a natural result of the analysis carried out above. 1.2. Geometric measurable error sources Carrying out a machine tool analysis using virtual modelling applies itself to only certain errors. Specifically, the errors that can be corrected for are geometric in nature and measurably repeatable. Many papers articulate geometric errors clearly. They are generally position dependent. In the case of rotating axes, the linear geometric errors may be assumed to be negligibly small compared to rotary axes error. [8] However, the methods of improving the accuracy of the machine tool production process are applicable to machines tools of any configuration. Furthermore, linear motion errors compound the uncertainty of rotary axis error compensation [9] and are advisable to minimize as much as possible. This research will focus on errors that are a result of the manufacturing process and can be corrected once identified. 2. Manufacturing process chain statistical analysis In manufacturing precision CNC equipment, it is extremely difficult to significantly reduce cost while maintaining product quality. Therefore, analysing the variables in the production cycle systematically and identifying key focus areas for improvement has potential to provide maximum improvement, both in cost and accuracy/quality, while maintaining minimal disruption to production. Attempting to analyse and optimize every measurement and tolerance would be ideal, but practically it is not feasible. It is also highly desirable to establish a statistical link to key areas in the manufacturing process to the final accuracy of the machine tool. To do so, a statistical analysis of the XY plane was carried out. A machine tool is a complex machine with hundreds of measurements and inspection points, only the most relevant for common cutting operations need be analysed. Most cutting is 2D contouring in the XY plane so the measurements that directly affect the XY accuracy in the kinematic chain were used to investigate a statistical relationship. In order to get a reasonable sample size, 30 machines were sampled out of a population of approximately 150 machines produced. In order to conduct a statistical analysis, the form of the data had to be established. That is, to make assumptions relying on the normal distribution of data, the data had to be checked for normalcy. A normal plot using the Z score is an acceptable way to establish a normal distribution.[10] The normal plot of the double ball bar circularity measurement has a linear regression line with an R 2 value of 0.96 which is highly linear. Other data sets had similar behaviour so it was assumed that the data sample of 30 machines had a normal distribution and basic assumptions regarding a normal distribution can be applied. The method used to compare each parameter was to obtain correlation coefficients between the initial machining results and the final accuracy tests. Thus, developing correlation matrices among the measurements was done. This allowed a quick view of what parameters may have strong, moderate, weak, or no relationship. Coefficients over 0.4 are strong while those over 0.3 are moderate. [10] It was determined that there is a very strong correlation between the circularity and straightness in the cutting tests of the assembled machine to the individual casting accuracy. The X-axis had the strongest correlations. The Y-axis sits on top of the X-axis and errors of the X-axis are propagated through this kinematic chain to the tool tip. Additionally, the large moving mass on top of the X-axis causes local deformations so the initial accuracy of the X-axis directly adds to this local deformation. Furthermore, the X-axis casting (bed) is machined on a large Toshiba Gantry mill (MPC) while the Y-axis (column) is machined on a compact horizontal machining center (NHX10000). The NHX10000 exhibits a higher degree of accuracy and repeatability than the Toshiba MPC. The conclusion of the statistical analysis was that improving the geometric qualities of the X, Y, and Z axes of the casting machining with an emphasis on the X-axis would result in directly improved final machine tool accuracy. 3. Machining Process The machining process involves a variety of variables. The two that are examined closely in this paper are the deformations due to the fixture design and also the deformation due to the cutting force itself. Gravity is a default load set that is applied across the entire manufacturing process. 3.1. Effect of fixturing The fixtures used in machining have four criteria that must be analysed 1. Deformation of casting due to large clamping force 2. Sufficient support of the casting for minimal deformation during machining 3. Neutral positioning to avoid spring back after cutting and fixture release. 4. Adequate support and orientation to minimize gravitationally induced deformations. In the case of the NHX4000, the fixtures were largely found to be of sufficient design in terms of support and clamping with one exception. The lower right clamp shown in Fig. 3 is offset from the support which results in an almost 2μm displacement indicated in Fig. 4. Due to machine constraints, casting components may need to be machined in orientations differing from the assembled orientation. This can result in excessive gravitational deformation for some sections of the casting. In the case of the column shown below, the horizontal fixture orientation results in a Y-axis straightness error of greater than 4μm. The bed casting had similar results, but because it is machined in the orientation of assembly, the self-gravitational effect is cancelled and the machining fixture is more robust for the bed. 3.2. Contribution of cutting forces Cutting forces can be fairly easily predicted and added to the simulation. Altintas proposed a generalized cutting force model suitable for a wide range of cutters with given geometry and cutting conditions. [11], [12] Notably, the cutting force effect was small in comparison to the gravitational effect and was decided to be assumed negligible in the study. 4. Assembly Process 4.1. Jig and fixture design Parts of the machine tool are assembled in separate units as much as possible for optimal efficiency. X and Z rails are installed directly onto the bed, but the Y-axis rails are installed to the column in an independent station. For assembly workers to efficiently place and measure the rails during installation and adjustment, the column must be placed in the horizontal orientation on a jig with the rails facing upward. For stability and safety, a four point fixture was originally designed as in Fig. 7. Analysis showed a severe sensitivity to jig adjustment. Only a 4 ?m increase in the height of one jig support resulted in a parallelism error of 3.5 ?m for the Y-rails. In this case, the jig legs do not have micron level adjustment capability as their height adjustment is determined by regular SAE machine threads. Therefore, assembly adjusts for parallelism in an artificially deformed state. The deformed state releases after the column is removed from the jig and set upright resulting in the Y-axis losing parallelism. Since parallelism is highly dependent on the fixture adjustment, the deformation is also non repeatable and cannot be compensated during machining. The solution found was to use a three point support for the column during rail fixing. Although the column still deforms due to gravity, both rails deform nearly symmetrically and there is no sensitivity to small height changes of the fixture. This is discussed in more detail in section 4.2. The result is a repeatable gravitational deformation that can be compensated in the machining step. 4.2. Orientation of structure When a component such as the column is assembled in an orientation conducive to efficient assembly work as discussed in the previous section, gravity will play a role in the measurements of that step. This gravitational effect can be effectively cancelled out by understanding what deformations are present and subsequently accounted for during the assembly adjustment process. When using three point support, the column will deform, but it will be predictable, dependent on the locations of the three points. Therefore, it is necessary to always use the same three point locations each time measuring the column to ensure measurement repeatability. In addition, since it is desirable to measure parallelism of the Y Rails accurately, points should be selected that cause a balanced Z-direction deformation of the rails. Also, both Y rails deform in equal amounts so parallelism is preserved when the column is reoriented. The diagram below shows the three point locations selected based on FE analysis g