請(qǐng)充值后下載本設(shè)計(jì)，，資源目錄下的文件，都可以點(diǎn)開(kāi)預(yù)覽到，，資料完整，充值下載就能得到。。?！咀ⅰ浚篸wg后綴為CAD圖，doc,docx為WORD文檔，有不明白之處，可咨詢(xún)QQ:1304139763
中 北 大 學(xué) 信 息 商 務(wù) 學(xué) 院 畢業(yè)設(shè)計(jì)任務(wù)書(shū) 學(xué) 院 系 機(jī)械工程與自動(dòng)化系 專(zhuān) 業(yè) 機(jī)械制造及其自動(dòng)化 學(xué) 生 姓 名 張曉飛 學(xué) 號(hào) 12020144X21 設(shè) 計(jì) 題 目 滾珠絲杠設(shè)計(jì)及相關(guān)技術(shù)研究 起 迄 日 期 2016 年 2 月 29 日 2016 年 6 月 5 日 指 導(dǎo) 教 師 龐學(xué)慧 系 主 任 暴建剛 發(fā)任務(wù)書(shū)日期 2016 年 2 月 29 日 畢 業(yè) 設(shè) 計(jì) 任 務(wù) 書(shū) 1 畢業(yè)設(shè)計(jì)的任務(wù)和要求 掌握機(jī)床傳動(dòng)絲杠的基本知識(shí) 研究數(shù)控機(jī)床滾珠絲杠的關(guān)鍵技術(shù) 掌握其選型 應(yīng)用及設(shè)計(jì)方法等 完成一種滾珠絲杠的設(shè)計(jì) 滿(mǎn)足精密數(shù)控機(jī)床 20m min 進(jìn)給速度 的需求 2 畢業(yè)設(shè)計(jì)的具體工作內(nèi)容 1 分析題目要求 查閱相關(guān)的國(guó)內(nèi)外文獻(xiàn) 設(shè)計(jì)資料 有關(guān)專(zhuān)利文獻(xiàn)等 在此基 礎(chǔ)上 了解開(kāi)題報(bào)告的撰寫(xiě)方法 基本要求 完成開(kāi)題報(bào)告 2 學(xué)習(xí)和掌握滾珠絲杠的有關(guān)知識(shí) 了解高速滾珠絲杠的關(guān)鍵技術(shù)及發(fā)展現(xiàn)狀 了解數(shù)控機(jī)床 加工中心對(duì)滾珠絲杠的要求 總結(jié)滾珠絲杠的設(shè)計(jì)要點(diǎn) 技術(shù) 關(guān)鍵及發(fā)展方向 力爭(zhēng)提出滾珠絲杠設(shè)計(jì)的發(fā)展方向 3 按題目要求 設(shè)計(jì)一種滿(mǎn)足數(shù)控機(jī)床進(jìn)給運(yùn)動(dòng)需要的滾珠絲杠 完成結(jié)構(gòu)圖 給出必要的計(jì)算說(shuō)明 4 編寫(xiě)設(shè)計(jì)說(shuō)明書(shū) 5 翻譯本專(zhuān)業(yè)外文科技文獻(xiàn)一份 畢 業(yè) 設(shè) 計(jì) 任 務(wù) 書(shū) 3 對(duì)畢業(yè)設(shè)計(jì)成果的要求 1 滾珠絲杠結(jié)構(gòu)圖 2 滾珠絲杠的研究及設(shè)計(jì)說(shuō)明書(shū)一份 3 本專(zhuān)業(yè)外文科技文獻(xiàn)譯文一份 4 畢業(yè)設(shè)計(jì)工作進(jìn)度計(jì)劃 起 迄 日 期 工 作 內(nèi) 容 2016 年 02 月 29 日 03 月 21 日 03 月 22 日 04 月 30 日 05 月 01 日 05 月 20 日 05 月 21 日 05 月 31 日 06 月 01 日 06 月 05 日 分析課題要求 查閱相關(guān)文獻(xiàn)資料 了解滾珠絲杠的國(guó)內(nèi) 外現(xiàn)狀及發(fā)展趨勢(shì) 提出自己的設(shè)計(jì)思路 完成開(kāi)題報(bào)告 全面掌握滾珠絲杠的基本知識(shí) 了解高速機(jī)床對(duì)進(jìn)給導(dǎo)軌 的要求 了解滾珠絲杠的設(shè)計(jì)特點(diǎn) 分析總結(jié)滾珠絲杠的 發(fā)展方向 完成滾珠絲杠結(jié)構(gòu)圖設(shè)計(jì) 完成研究總結(jié)及設(shè)計(jì)說(shuō)明書(shū) 撰寫(xiě)答辯講稿 準(zhǔn)備答辯 學(xué)生所在系審查意見(jiàn) 同意開(kāi)題 系主任 暴建崗 2016 年 3 月 3 日 一種新穎簡(jiǎn)單 成本低四自由度角索引校準(zhǔn)的精密轉(zhuǎn)臺(tái)技術(shù) W Jywe a C J Chenb W H Hsieha P D Linb H H Jwoa T Y Yanga 摘要 標(biāo)定一個(gè)角旋轉(zhuǎn)工作臺(tái) 無(wú)論是高精度的標(biāo)準(zhǔn)還是相關(guān)的光學(xué)激光干涉儀一般使 用成本都非常高 本文建立了一個(gè)新穎 簡(jiǎn)單 低成本的技術(shù)來(lái)校準(zhǔn) 4 度 的自由度 自由度 誤差 由使用一個(gè)可以旋轉(zhuǎn)一整圈 360 三角位置誤差和一個(gè)線性位置誤差 一個(gè)參考回轉(zhuǎn)工作臺(tái) 一個(gè) 1 維 1D 光柵和兩個(gè) 2 二維 2D 的位置感應(yīng)探測(cè)器 PSD 的 利用這種技術(shù) 沒(méi)有使用高度準(zhǔn)確參考轉(zhuǎn)盤(pán) 但是測(cè)試是具有良好的重復(fù) 性 經(jīng)過(guò)兩個(gè)大圈的測(cè)試 無(wú)論是目標(biāo)轉(zhuǎn)臺(tái)的四自由度誤差和參考轉(zhuǎn)盤(pán)可以測(cè)得 系統(tǒng) 校準(zhǔn) 穩(wěn)定性測(cè)試 系統(tǒng)測(cè)試驗(yàn)證和完整圓的測(cè)試的完成 該系統(tǒng)的角度穩(wěn)定性小于 2 弧秒 而位移穩(wěn)定性小于 1 2 毫米 2007 埃爾塞維爾有限公司保留所有權(quán)利 關(guān)鍵詞 旋轉(zhuǎn)表校準(zhǔn) 全循環(huán)試驗(yàn) 光柵 位置傳感探測(cè)器 4 自由度測(cè)量 誤差分離 1 簡(jiǎn)介 回轉(zhuǎn)工作臺(tái)是經(jīng)常用于有關(guān)工業(yè)生產(chǎn)的機(jī)床 三坐標(biāo)測(cè)量機(jī)和組裝線 因此 轉(zhuǎn) 盤(pán)校準(zhǔn)非常重要 該轉(zhuǎn)盤(pán)校準(zhǔn)要求角度測(cè)量?jī)x 與傳統(tǒng)儀器是旋轉(zhuǎn)編碼器 激光干涉儀 的自準(zhǔn)直儀測(cè)量精確程度 一個(gè)旋轉(zhuǎn)編碼器是常用的索引中測(cè)量工具 例如 一對(duì)多軸 轉(zhuǎn)臺(tái)機(jī)床 機(jī)器人的關(guān)節(jié) 機(jī)器主軸工具和滾珠絲杠索引 然而 旋轉(zhuǎn)編碼器只對(duì)誤差 的測(cè)量適當(dāng) 激光干涉儀經(jīng)常被用來(lái)衡量一個(gè)小角 但它只能測(cè)試過(guò)程中獲取一個(gè)索引 誤差 一個(gè)自準(zhǔn)直儀是經(jīng)常用于測(cè)量小角度 它可以應(yīng)用到兩個(gè)二維 平面 測(cè)角 俯 仰誤差和仰角誤差 但其測(cè)量范圍小 而且它要求有一個(gè)標(biāo)準(zhǔn)的多棱鏡 旋轉(zhuǎn)臺(tái)有 6 個(gè)自由度誤差 三線性位置誤差和 3 個(gè)角位置 誤差 但是傳統(tǒng)儀器只能測(cè)量任一維 1D 誤差或 2D 的誤差 該一個(gè)轉(zhuǎn)盤(pán)完整的校準(zhǔn)過(guò)程需要 360 自由度測(cè)量一大圈 但 此測(cè)量技術(shù)測(cè)量時(shí)大多數(shù)測(cè)量系統(tǒng)范圍小于 10 因此 激光測(cè)量范圍干涉儀和自準(zhǔn) 直儀的測(cè)量范圍時(shí)不夠的 而且他們非常昂貴 傳統(tǒng)的校準(zhǔn)技術(shù)在轉(zhuǎn)盤(pán)校準(zhǔn)時(shí)需要一個(gè) 完整的圓 360 一個(gè)參考轉(zhuǎn)盤(pán) 它必須具有較高的準(zhǔn)確度和高重復(fù)性 作者引用旋轉(zhuǎn)表 的誤差相對(duì)測(cè)量結(jié)果便可以被忽略 該儀器通常被記錄一次 當(dāng)目標(biāo)轉(zhuǎn)盤(pán)順時(shí)針旋轉(zhuǎn) 旋轉(zhuǎn)的參考轉(zhuǎn)盤(pán)逆時(shí)針旋轉(zhuǎn) 一般來(lái)說(shuō) 一個(gè)旋轉(zhuǎn) 360 表一整圈校準(zhǔn)記錄需要 36 此 即測(cè)量系統(tǒng)采樣周期 10 如果經(jīng)過(guò)一個(gè)更完整的測(cè)試實(shí)施 那么校準(zhǔn)過(guò)程將需要更長(zhǎng) 的時(shí)間 一般來(lái)說(shuō) 旋轉(zhuǎn)表包括的誤差 擺動(dòng)誤差和偏心率 但是傳統(tǒng)的旋轉(zhuǎn)表校準(zhǔn)技術(shù) 激光干涉儀或自動(dòng)準(zhǔn)直器 只校準(zhǔn)索引誤差和擺動(dòng)指數(shù)誤差 然而 高精確度旋轉(zhuǎn)表 必須校準(zhǔn)的更多細(xì)節(jié) 通過(guò)完整的旋轉(zhuǎn)表校準(zhǔn) 旋轉(zhuǎn)臺(tái)的誤差可以補(bǔ)償 在本文中 旋 轉(zhuǎn)表中的誤差六自由度定義 即三個(gè)線性位置誤差和三個(gè)角位置誤差 近年來(lái) 測(cè)角技術(shù)已是重點(diǎn)的干涉方法 1992 年 黃 等 建立了小角度測(cè)量系統(tǒng) 這是基于在一個(gè)玻璃內(nèi)部邊界反射效果和菲涅耳定律 在黃的制度 分辨率為 0 2 弧秒 測(cè)量范圍為 3 弧秒 1996 年 小麗等人 建立了一個(gè)二維小旋轉(zhuǎn)角度測(cè)量系統(tǒng) 使用 兩種不同并行干擾模式 畫(huà)中畫(huà) 這些正交對(duì)方 對(duì)小麗的體系標(biāo)準(zhǔn)偏差為 0 6 弧秒 在接下來(lái)的一年小麗等 改進(jìn)他們的系統(tǒng) 以便其分辨率為 0 2 弧秒 測(cè)量范圍為 30 弧分 1997 年 邱等人 建立了一種改進(jìn)的角測(cè)量技術(shù)與分辨率 0 333 弧秒 測(cè)量范圍 為 5 6 在其最佳性能 系統(tǒng)的分辨率 0 288 弧秒 1998 年 周 蔡 8 建立了一 個(gè)角度測(cè)量技術(shù) 它是根據(jù) 2005 年第 09 全內(nèi)反射效應(yīng)和外差干涉 系統(tǒng)的分辨率優(yōu)于 0 3 弧秒這取決于所選指數(shù)折射 1998 年 還 等 建立了測(cè)角基法在內(nèi)部的反射效 果 即使用了一個(gè)直角棱鏡 他們表明 角度測(cè)量與 500 弧分范圍 非線性誤差 0 1 而 0 1 弧秒分辨率可隨時(shí)實(shí)現(xiàn) 1999 年 郭等人開(kāi)發(fā)了一種光學(xué)小角度測(cè)量 方法的基礎(chǔ)上表面等離子體共振 SPR 和測(cè)量分辨率 0 2 弧秒 達(dá)到了實(shí)驗(yàn) 2003 年 葛 和麥克開(kāi)發(fā)了一種在此角度測(cè)量技術(shù)分析的基礎(chǔ)上的條紋相位測(cè)量輪廓 測(cè)量范圍 為 2160 弧秒 并從線性偏差優(yōu)于 0 02 弧秒 2004 年 邱等人 開(kāi)發(fā)了一種小角度 測(cè)量使用多個(gè)總外差干涉內(nèi)部分析 而角分辨率優(yōu)于 0 454 弧秒在測(cè)量范圍 1 12 2 12 得以在 20 以?xún)?nèi)的數(shù)值 大多數(shù)角度測(cè)量技術(shù)的研究重點(diǎn)在 1D 角度測(cè)量 干涉角度測(cè)量和 2D 干涉測(cè)量技術(shù) 但是 昂貴而復(fù)雜的干涉系統(tǒng) 不能被廣泛用于工業(yè) 因此 成本低 多自由度測(cè)量系 統(tǒng)在轉(zhuǎn)臺(tái)校準(zhǔn)時(shí)是非常重要的 位置傳感探測(cè)器 位置感應(yīng)探測(cè)器 可用于測(cè)量旋轉(zhuǎn)部 分誤差 回轉(zhuǎn)體零件的速度 旋轉(zhuǎn)方向扶輪的一部分角位置和誤差 Jywe 等 采用兩 種位置傳感器和一個(gè)反射光柵測(cè)試轉(zhuǎn)臺(tái)的性能 但其測(cè)量范圍非常小 11 沒(méi)有完整 的圓試驗(yàn)來(lái)提供整個(gè)圓的測(cè)量 然而 對(duì)于一般轉(zhuǎn)盤(pán)校準(zhǔn)的 360 整圈的測(cè)試是必要的 這兩個(gè)文件描述了一個(gè) 4 自由度測(cè)量系統(tǒng)的建設(shè)并建立一種新的技術(shù)轉(zhuǎn)盤(pán)一圈測(cè)試 四 自由度系統(tǒng) 本文提出包括一維反射光柵 一個(gè)激光二極管 四個(gè)位置傳感器及一個(gè)參 考回轉(zhuǎn)工作臺(tái) 干涉儀和自準(zhǔn)直儀是常用的轉(zhuǎn)臺(tái)測(cè)量系統(tǒng) 然而 在轉(zhuǎn)臺(tái)校準(zhǔn)過(guò)程中 激光干涉儀 和自準(zhǔn)直儀分別需要高精確度參考轉(zhuǎn)盤(pán)和一個(gè)多棱鏡 因此 使用激光干涉儀或自準(zhǔn)直 儀進(jìn)行校準(zhǔn)回轉(zhuǎn)工作臺(tái)是昂貴的 此外 在提出的方法 沒(méi)有高準(zhǔn)確的參考轉(zhuǎn)盤(pán) 但具有良好的重復(fù)性是必要的 即使索引誤差和幾何誤差參考轉(zhuǎn)盤(pán)大 他們將獲得所提 出的方法 2 四自由度測(cè)量系統(tǒng) 在這個(gè)文件中 四自由度測(cè)量系統(tǒng)包括一個(gè)參考回轉(zhuǎn)工作臺(tái) 一維光柵 一個(gè)激光二極 管 傳感器 反射光柵和兩個(gè)處理器 一個(gè) A D 卡和一臺(tái)個(gè)人電腦 PC 圖 1 給出 了電路圖 該參考轉(zhuǎn)盤(pán)被放置在目標(biāo)旋轉(zhuǎn) 然后一維光柵上由夾具回轉(zhuǎn)工作臺(tái)安裝表 激光二極管和位置傳感器被放在光柵的附近 從激光束激光二極管是一維光柵投影到一 維光柵 然后產(chǎn)生了許多衍射光束 在這個(gè)文件中 1 和 1 級(jí)衍射光束被使用 兩個(gè) 傳感器被用來(lái)檢測(cè)衍射光束 一般來(lái)說(shuō)定義在轉(zhuǎn)臺(tái)的六幾何誤差 即三個(gè)線性位置誤差 和三個(gè)角位置誤差 在此外 還有之間的光柵和偏心軸的轉(zhuǎn)盤(pán) 這是因?yàn)?Dx 和 Dy 定義 3 應(yīng)全面圈測(cè)試模型 大多數(shù)儀器的測(cè)量范圍為小于 10 所以一個(gè)完整的校準(zhǔn)轉(zhuǎn)盤(pán)需要一種特殊的方法 在正常轉(zhuǎn)臺(tái)校準(zhǔn) 自準(zhǔn)直儀使用一個(gè)多邊形鏡子和激光干涉儀并且使用一個(gè)參考回轉(zhuǎn)工 作臺(tái) 在這試驗(yàn)中 該技術(shù)還需要一個(gè)參考旋轉(zhuǎn)表 但參考轉(zhuǎn)盤(pán)要求測(cè)試參考旋轉(zhuǎn)臺(tái)的 誤差必須可重復(fù)的 1994 年 林建立了一個(gè)轉(zhuǎn)盤(pán)校準(zhǔn)技術(shù) 它可以測(cè)量索引誤差為 360 的整圈回轉(zhuǎn)工作臺(tái) 然而 該技術(shù)只能單次測(cè)量誤差 因此 一個(gè)改良的方法是 成立于本節(jié) 當(dāng)旋轉(zhuǎn)的誤差參考表進(jìn)行了審議 對(duì)旋轉(zhuǎn)的幾何誤差表是 其中 z 是目標(biāo)指數(shù)之間的差異旋轉(zhuǎn)表和參考表 并累計(jì)在不同的校準(zhǔn)程序 這 x y x y 和 z 不累積 因?yàn)橐徽y(cè)試需要兩個(gè)試驗(yàn)中 目標(biāo)轉(zhuǎn)盤(pán)和參 考轉(zhuǎn)盤(pán)重復(fù)性一定要做好 否則測(cè)量結(jié)果將不會(huì)重復(fù) 該校準(zhǔn)技術(shù)的基本要求是 目標(biāo)下校準(zhǔn)可旋轉(zhuǎn)臺(tái)旋轉(zhuǎn)作為參考不同方向旋轉(zhuǎn)相同的步 長(zhǎng) 即對(duì)順時(shí)針和逆時(shí)針的比較 每個(gè)部門(mén)根據(jù)測(cè)試表進(jìn)行了比較與每一個(gè)部門(mén)的參考 以建立第一組數(shù)據(jù) 例如 有一個(gè)轉(zhuǎn)盤(pán)進(jìn)行了測(cè)試 12 點(diǎn)左右 360 角位置 即 0 30 60 330 這是等距離的目標(biāo)轉(zhuǎn)盤(pán)和參考轉(zhuǎn)盤(pán)分割 同時(shí)在測(cè)試開(kāi)始后 的第一個(gè)目標(biāo)轉(zhuǎn)盤(pán)和參考轉(zhuǎn)盤(pán) 分別定為 0 第一組數(shù)據(jù)是由個(gè)人電腦所提取 然后 目標(biāo)旋轉(zhuǎn)工作臺(tái)順時(shí)針旋轉(zhuǎn) 30 和參考旋轉(zhuǎn)工作臺(tái)逆時(shí)針旋轉(zhuǎn) 30 第二組數(shù)據(jù)由個(gè)人 電腦所提取 從上面的實(shí)驗(yàn)過(guò)程中 可以得出以下關(guān)系 其中 z1n 是第一組角讀數(shù)和 N 是超過(guò) 360 增量 zt1 下標(biāo) t 象征目標(biāo)轉(zhuǎn)盤(pán) 下標(biāo)為 r 是指參考轉(zhuǎn)盤(pán)的誤差 在第二次測(cè)試的一圈中 再次將目標(biāo)轉(zhuǎn)盤(pán)和參考轉(zhuǎn)盤(pán)設(shè)置為 0 參考旋轉(zhuǎn)工作臺(tái) 例如 30 后參考旋轉(zhuǎn)回轉(zhuǎn)工作臺(tái) 樣品采取的第一套 然后 目標(biāo)旋轉(zhuǎn)工作臺(tái)順 時(shí)針旋轉(zhuǎn) 30 參考旋轉(zhuǎn)工作臺(tái)旋轉(zhuǎn) 30 反順時(shí)針再次采樣 從上面的實(shí)驗(yàn)過(guò)程中 第 二次測(cè)試的結(jié)果令人滿(mǎn)意 然后 整理轉(zhuǎn)動(dòng)的關(guān)系 可以得出 其中 z2n 是第二組角讀數(shù)和 N 是超過(guò) 360 的增量 測(cè)量?jī)山M數(shù)據(jù)可以被重新安 排如下 4 實(shí)驗(yàn)結(jié)果與討論 在這個(gè)文件中 對(duì) 4 自由度計(jì)量校準(zhǔn)系統(tǒng) 系統(tǒng)穩(wěn)定性 系統(tǒng)驗(yàn)證和全圓測(cè)試的完 成 系統(tǒng)的照片如圖 2 所示 組件圖 2 中沒(méi)有顯示附上通過(guò)臺(tái)式 PC 連接到位置感應(yīng)探測(cè) 器的信號(hào) 處理器 A D 卡 該元件的規(guī)格分別列在表 1 4DOF 試驗(yàn)系統(tǒng) 4 1 系統(tǒng)校準(zhǔn) 系統(tǒng)校準(zhǔn)是第一個(gè)實(shí)驗(yàn) 在這實(shí)驗(yàn)中 用自準(zhǔn)直儀波特角位置提供參考 其測(cè)量范 圍為 410 弧秒 分辨率為 0 02 弧秒 精度為 0 5 弧秒 圖 3 a 給出了校準(zhǔn)結(jié)果 圖 3 b 中給出了系統(tǒng)不確定性的標(biāo)準(zhǔn)差 在整個(gè)校準(zhǔn)過(guò)程中 顯然 良好的 z 線性和的 z不確定度約為 1 5 弧秒 角位置 z 的 4 自由度測(cè)量測(cè)量范圍約為 1 因?yàn)閹缀跛械臏y(cè)量位置感應(yīng)探測(cè)器的范圍應(yīng)用 4 2 系統(tǒng)的穩(wěn)定性試驗(yàn) 系統(tǒng)穩(wěn)定性試驗(yàn)是第二次實(shí)驗(yàn) 系統(tǒng)通過(guò)系統(tǒng)實(shí)驗(yàn)室條件下正常的平衡狀態(tài) 即無(wú) 特殊溫度或振動(dòng)隔離 允許穩(wěn)定性進(jìn)行了評(píng)價(jià) 然后連續(xù)記錄為 4000 秒的輸出信號(hào)圖 4 表明 原型系統(tǒng)的基本是穩(wěn)定合理的 即沒(méi)有特殊的隔離或過(guò)濾依然在 1 2 毫米 x y和 z 在 4000s內(nèi) 1 5 弧秒 4 3 系統(tǒng)驗(yàn)證 系統(tǒng)驗(yàn)證是第三個(gè)實(shí)驗(yàn) 自準(zhǔn)直儀也被用來(lái)驗(yàn)證 4 自由度測(cè)量系統(tǒng) 因?yàn)樗?以同時(shí)進(jìn)行對(duì) x和 y的測(cè)量 設(shè)置的自準(zhǔn)直儀在光柵背面 當(dāng)全部循環(huán)試驗(yàn)實(shí)施和誤 差分離方法沒(méi)有用時(shí) 自準(zhǔn)直儀記錄了目標(biāo)轉(zhuǎn)盤(pán)和參考轉(zhuǎn)盤(pán)誤差總和 4 自由度的自準(zhǔn) 直儀測(cè)量系統(tǒng)可記錄一次 當(dāng)目標(biāo)轉(zhuǎn)盤(pán)順時(shí)針旋轉(zhuǎn)一次 并再次測(cè)試參考轉(zhuǎn)盤(pán)逆時(shí)針旋 轉(zhuǎn)的程度 圖 5 顯示了該系統(tǒng)的核查結(jié)果 結(jié)果對(duì) 4 自由度自準(zhǔn)直儀的測(cè)量系統(tǒng)類(lèi)似 所以 4 自由度數(shù)學(xué)模型測(cè)量制度是正確的 4 4 全部循環(huán)測(cè)試 完整的循環(huán)測(cè)試是最后的實(shí)驗(yàn) 是在第 3 條所述 該 4 自由度測(cè)量系統(tǒng)的測(cè)量范圍 為 1 左右 要完成一整圈測(cè)試的時(shí)間 如果必須采取唯一位置感應(yīng)探測(cè)器 2 位置感 應(yīng)探測(cè)器 的使用 只有一組位置感應(yīng)探測(cè)器的要求記錄在第一和第二次測(cè)試 至少 72 0 分 因此 4 個(gè)位置感應(yīng)探測(cè)器來(lái)建立系統(tǒng) 位置感應(yīng)探測(cè)器 A 和 B 設(shè)置為位置感應(yīng) 探測(cè)器意義上的 1 級(jí)衍射光時(shí)的參考轉(zhuǎn)臺(tái)角位置是 0 然后 位置感應(yīng)探測(cè)器的 C 和 D 設(shè)置為位置感應(yīng)探測(cè)器意義上的 1 級(jí)衍射光時(shí)的參考轉(zhuǎn)臺(tái)角位置是在 5 在整 圈測(cè)試 位置感應(yīng)探測(cè)器 C 和位置感應(yīng)探測(cè)器 B 的一個(gè)用于第一次測(cè)試 而位置感應(yīng) 探測(cè)器 C 和 D 組用于第二次測(cè)試 因此 一個(gè)完整的循環(huán)測(cè)試只需要記錄在第一和第二 次測(cè)試 72 分 經(jīng)過(guò)兩年試驗(yàn)完成后 上述方法在第 3 節(jié)是用來(lái)隔離的目標(biāo)轉(zhuǎn)臺(tái)和參考轉(zhuǎn)臺(tái)的誤差 測(cè)試結(jié)果如圖所示 6 一 d 及 六 H 分別為目標(biāo)和參考轉(zhuǎn)盤(pán)旋轉(zhuǎn) 臺(tái)的誤差 在參考轉(zhuǎn)臺(tái)角位置誤差均高于目標(biāo)轉(zhuǎn)盤(pán) 但是 誤差是相似的 目標(biāo)轉(zhuǎn)盤(pán)的 y x y 和 z 約有 2 85 毫米 330 620 和 270 弧秒 分別為 y x y 和 z 轉(zhuǎn)盤(pán)轉(zhuǎn)了一下 分別為 2 90 毫米 210 500 和 250 弧秒 在 y 大是因?yàn)閮烧咧g的反射光柵表面和轉(zhuǎn)盤(pán)的中心軸偏心距較大 要調(diào)整目標(biāo) 之間的轉(zhuǎn)盤(pán) 轉(zhuǎn)盤(pán)參考偏心是容易的 但要調(diào)整光柵之間的偏心回轉(zhuǎn)工作臺(tái)是困難的 因?yàn)閷?duì)光柵和旋轉(zhuǎn)表是不同的幾何 5 結(jié)論 本文建立了一個(gè)新穎 簡(jiǎn)單 低成本的校準(zhǔn)技術(shù) 360 全圓旋轉(zhuǎn)表 三角位置誤差 和位置誤差的線性 的 4 自由度的誤差 利用這種技術(shù) 沒(méi)有高度準(zhǔn)確的參考轉(zhuǎn)盤(pán) 但 是具有良好的重復(fù)性是必要的 經(jīng)過(guò)充分循環(huán)試驗(yàn) 目標(biāo)和參考轉(zhuǎn)盤(pán)旋轉(zhuǎn)臺(tái)的四自由度 誤差可能確定 系統(tǒng)校準(zhǔn) 穩(wěn)定性試驗(yàn) 系統(tǒng)驗(yàn)證和測(cè)試已經(jīng)完成了一圈 從整個(gè)體系 的校準(zhǔn) 測(cè)量不確定度角系統(tǒng) 宰 小于 1 5 弧秒 該系統(tǒng)的角度穩(wěn)定性小于 2 弧秒 而位移穩(wěn)定性小于 1 2mm International Journal of Machine Tools fax 88656311500 E mail addresses jywe sunws nfu edu tw W Jywe table was rotated counterclockwise In general one rotary table calibration for a 3601 full circle requires 36 recording if the sampled period of measurement system is 101 Ifa 0890 6955 see front matter r 2007 Elsevier Ltd All rights reserved doi 10 1016 j ijmachtools 2007 02 004 pmc2 sunws nfu edu tw C J Chen allen nfu edu tw W H Hsieh pdlin mail ncku edu tw P D Lin schong nfu edu tw H H Jwo jeyang T Y Yang instruments are the rotary encoder the laser interferom eter the autocollimator and the precision level A rotary encoder 1 is commonly used in indexing measurement in a rotary machine e g a rotary table of the multi axis machine tool the joint of a robot the spindles of machine tools and the indexing of a ball screw However the rotary encoder is only suitable for the indexing error measure ment A laser interferometer 2 has often been used to measure a small angle but it can only obtain indexing error either one dimensional 1D error or 2D errors The complete calibration procedure of a rotary table requires 6 DOF measurement for a 3601 full circle but the measure ment range of most measurement systems is smaller than 101 Therefore the measurement range of the laser interferometer and autocollimator are not enough and in addition they are expensive The conventional calibration technique of the rotary table for a 3601 full circle requires one reference rotary table which must have high accuracy and high repeatability The error of the reference rotary C3 and the reference rotary table could be obtained The system calibration stability test system verification and full circle test were completed The angular stability of this system was less then 2arcsec while the displacement stability was less than 1 2mm r 2007 Elsevier Ltd All rights reserved Keywords Rotary table calibration Full circle test Grating Position sensing detector 4 Degree of freedom measurement Error separation 1 Introduction A rotary table is frequently used in industry in such things as machine tools CMM and assembly lines Therefore the calibration of the rotary table is very important The calibration of the rotary table requires an during an indexing test An autocollimator 3 is frequently used to measure small angles and it can be applied to two dimensional 2D angle measurement pitch error and yaw error but its measurement range is small and it require one standard polygon mirror A rotary table has 6 DOF errors 3 linear position errors and 3 angular position reference rotary table but with good repeatability is needed After two full circle tests the 4 DOF errors of both the target rotary table A novel simple and low cost 4 degree calibrating technique for W Jywe a C3 C J Chen b W H Hsieh a National Formosa University Department of Automation b National Cheng Kung University Department of Mechanical Received 30 October 2006 received in revised form Available online Abstract For calibrating an angular rotary table either a high precision standard employed at high cost This paper establishes a novel simple and low of a rotary table three angular position errors and one linear position one 1 dimensional 1D grating and two 2 dimensional 2D position sensing detectors ture 47 2007 1978 1987 of freedom angular indexing a precision rotary table P D Lin b H H Jwo a T Y Yang a g No 64 Wenhua Rd Huwei Taiwan ROC Engineering No 1 University Rd Tainan Taiwan ROC 1 February 2007 accepted 13 February 2007 February 2007 table or a laser interferometer and related optics are normally cost technique to calibrate the 4 degrees of freedom DOF errors error for a 3601full circle by employing one reference rotary table PSD With this technique no highly accurate ARTICLE IN PRESS more complete test is implemented the calibration process will takes a long time In general the rotary table includes the index error wobble error and eccentricity But conventional rotary table calibration techniques laser interferometer or auto collimator only calibrate the index error and the wobble error However the high precision rotary table must be calibrated in more details Through the complete rotary table calibration the errors of rotary table can be compensated In this paper the errors of rotary table were defined by 6 DOF i e three linear position errors d x d y d z and three angular position errors e x e y e z The index error was represented by e z the wobble error was represented by e x and e y the eccentricity was represented by d x and d y In recent years angular measuring techniques have focused on the interferometric methods In 1992 Huang et al 4 developed a small angle measurement system which was based on the internal reflection effect in a glass boundary and Fresnel s law In Huang s system the resolution was 0 2arcsec and the measuring range was 3arcsec In 1996 Xiaoli et al 5 established a 2D small rotation angle measurement system using two different parallel interference patterns PIP that were orthogonal to each other The standard deviation of Xiaoli s system was 0 6arcsec In the following year Xiaoli et al 6 improved their system so that its resolution was 0 2arcsec and measuring range was 730arcmin In 1997 Chiu et al 7 established a modified angle measurement technique with a resolution of 0 333arcsec and a measuring range of75 61 At its optimum performance the system s resolution was 0 288arcsec In 1998 Zhou and Cai 8 established an angle measurement technique which was based on the total internal reflection effect and heterodyne interferome try The system resolution was better than 0 3arcsec depending on the refractive index selected In 1998 Huang et al 9 established a method of angle measurement based on the internal reflection effects that used a single right angle prism They demonstrated that angle measurement with a range of 7500arcmin a nonlinearity error of 70 1 and a resolution of 0 1arcsec could be readily achieved In 1999 Guo et al 10 developed an optical method for small angle measurement based on surface plasma resonance SPR and a measurement resolution of 0 2arcsec was achieved experimentally In 2003 Ge and Makeda 11 developed an angle measurement tech nique based on fringe analysis for phase measuring profilometry The measurement range was 72160arcsec and the deviation from linearity was better than 70 02 arcsec In 2004 Chiu et al 12 developed an instru ment for measuring small angles using multiple total internal reflections in heterodyne interferometry and the angular resolution was better than 0 454arcsec over the measurement range C02 121pyp2 121 for 20 total internal reflections W Jywe et al International Journal of Machine Most angle measurement technique research focuses on 1D angle measurement and interferometric angle measurement and 2D measurement also focuses on interferometric techniques However interferometric systems are expensive and complex and cannot be used extensively in industry Therefore the low cost and multiple DOF measurement system is needed for rotary table calibration The position sensing detector PSD could be used to measure the rotary part error the speed of rotary part the rotation direction of rotary part the angular position and the indexing error 13 14 Jywe et al employed two PSDs and one reflective grating to test rotary table performance 15 but its measurement range was small o11 In 15 no full circle test was implemented and no analytic solution was provided However for the general rotary table calibra tion the 3601 full circle test is necessary This paper both describes the building of one 4 DOF measurement system and establishes a novel technique for rotary table full circle test The 4 DOF system presented in this paper comprises one 1D reflection grating one laser diode four PSDs and one reference rotary table The laser interferometer and the autocollimator were most used rotary table measurement system However in rotary table calibration process the laser interferometer and the autocollimator need a high accuracy reference rotary table and a polygon mirror respectively Therefore using the laser interferometer or autocollimator to calibrate rotary table is expensive Because the cost of 1D reflection grating PSD signal conditioning unit of PSD and laser diode and rotary table is about 1 5 of one laser interferometer system or 1 2 of one autocollimator system Moreover in the presented method no high accurate reference rotary table but with good repeatability is needed Even the indexing error and the geometric error of the reference rotary table is large they will be obtained by the presented method 2 The 4 DOF measurement system In this paper the 4 DOF measurement system includes one reference rotary table one 1D grating one laser diode two PSDs two PSD processors one A D card and one personal computer PC Fig 1 shows the schematic diagram The reference rotary table was placed on the target rotary table then the 1D grating was mounted on the rotary table by the fixture The laser diode and PSDs were placed near the 1D grating The laser beam from the laser diode was projected onto a 1D grating and then the 1D grating produced many diffraction light beams In this paper the 1 order and C01 order diffraction light beam are used and two PSDs were used to detect the diffraction light beam Generally six geometric errors are defined on a rotary table namely three linear position errors and three angular position errors pitch roll and yaw The three linear position errors are d x d y and d z and the three angular position errors are e x e y and e z respectively In addition there are eccentricity between the grating and the axis of the rotary table which are defined as D x and D y Tools d x d xt d xr C15 y C15 yt C15 yr d y d yt d yr C15 z C15 zt C0 C15 zr d z d zt d zr 13 where e z is the index difference between the target rotary table and the reference rotary table and it accumulatively varies during the calibration procedure The e x e y d x d y and d z are not accumulative Because one full circle test needs two tests the repeatability of the target rotary table and the reference rotary table must be good otherwise the measured results will not repeat The basic requirement of the calibrating technique is that the target rotary table under calibration can be rotated the same step size as the reference rotary table in different orientations say on for clockwise and the other counter clockwise Each sector of the table under test has been compared with every sector of the reference one in order to build the first set of data For example one rotary table was tested at 12 angular position points around 3601 i e at 01 301 601 y 3301 which were equally spaced segmented in the target rotary table and the reference rotary table At the start in 1000 C1C1C1 C010000C1C1C1 0 0100 C1C1C1 0 C010 00C1C1C1 0 0010 C1C1C1 00C0100C1C1C1 0 1000 C1C1C1 0 C010 00C1C1C1 0 0100 C1C1C1 00C0100C1C1C1 0 0010 C1C1C1 000C010C1C1C1 0 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 0 0 0 0 C1C1C11 C01 0 0 0 0 C1C1C1 0 C15 z1n C15 ztn C0 C15 zrn 14 where e z1n is the first set of angular readings and n is the number of increments over 3601 The subscript t of the symbol e zt1 means the error of the target rotary table and the subscript r means the error of the reference rotary table In the second test of full circle test the target rotary table and reference rotary table was set to 01 again and the reference rotary table was incremented by one nominal step ex 301 After the rotation of the reference rotary table the first set of sample was taken Then the target rotary table was rotated 301 clockwise and the reference rotary table was rotated 301 counter clock wise and the other sets of sample were taken From the above experiment process the results of second test were obtained Then the flowing relationship can be derived C15 z21 C15 zt1 C0 C15 zr2 C15 z22 C15 zt2 C0 C15 zr3 C15 z2n C15 ztn C0 C15 zr1 15 where e z2n is the second set of angular readings and n is the number of increments over 3601 The two sets of measured data can then be rearranged as follows C15 zt1 C15 zt2 C15 zt3 C15 zr1 C15 zr2 C15 zr3 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 C15 z11 C15 z12 C15 z13 C15 z21 C15 z22 C15 z23 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 16 C15 zrn C15 z2n and the original augmented matrix is shown as 1000 C1C1C1 C010000C1C1C1 C15 z11 0100 C1C1C1 0 C010 00C1C1C1 C15 z12 0010 C1C1C1 00C0100C1C1C1 C15 z13 1000 C1C1C1 0 C010 00C1C1C1 C15 z21 0100 C1C1C1 00C0100C1C1C1 C15 z22 0010 C1C1C1 000C010C1C1C1 C15 z23 0 0 0 0 C1C1C11 C01 0 0 0 0 C1C1C1 C15 z2n 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 17 An augmented matrix of the reduced system can then be derived as follows Since Eq 18 is linear dependent more equations are required An assumption is again made to presume that no closing error exists within the reference rotary table and consequently the following equation can be derived C15 zr1 C15 zr2 C15 zr3 C1C1C1 C15 zrnC01 C15 zrn 360 C14 20 ARTICLE IN PRESS Table 1 Components of the prototype 4 DOF measurement system PSD UDT SC 10D active area 100mm 2 PSD signal processor On Trak OT 301 PC Intel Pentium4 2 0G 256MB RAM 40G HD A D Card Advantech PCI 1716 16 bit sampling range 710V Max sampling frequency 250kHz Laser diode l 635nm 5mW 1D Grating Rolled diffraction grating 600grooves per mm Autocollimator NewPort LDS Vector measurement range 2000mrad W Jywe et al International Journal of Machine Tools Manufacture 47 2007 1978 19871982 1000C1C1C1 C010000C1C1C1 0 C15 z11 0100C1C1C1 0 C010 00C1C1C1 0 C15 z12 0010C1C1C1 00C0100C1C1C1 0 C15 z13 0000C1C1C1 1 C010 00C1C1C1 0 C15 z21 C0 C15 z11 0000C1C1C1 01C0100C1C1C1 0 C15 z22 C0 C15 z12 0000C1C1C1 001C010C1C1C1 0 C15 z23 C0 C15 z13 0000C1C1C1 10000C1C1C1 C01 P nC01 i 1 C15 z2i C0 C15 z1i 0000C1C1C1 C010000C1C1C1 1 C15 z2n C0 C15 z1n 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 18 From the last two rows in the reduced matrix it can be shown that C15 zr1 C0 C15 zrn X nC01 i 1 C15 z2i C0 C15 z1i C0 C15 z2n C0 C15 z1n 19 or X nC01 i 1 C15 z2i C0 C15 z1i 0 Fig 2 Photograph of the 4DOF measurement system with 4 PSD Fig 3 Calibration results b standard deviation Eq 20 is then incorporated into the augmented matrix in Eq 18 to give the following 1000 C1C1C1 C010 0 00C1C1C1 0 C15 z11 0100 C1C1C1 0 C010 00C1C1C1 0 C15 z12 0010 C1C1C1 00C0100C1C1C1 0 C15 z13 1000 C1C1C1 0 C010 00C1C1C1 0 C15 z21 0100 C1C1C1 00C0100C1C1C1 0 C15 z22 0010 C1C1C1 000C010C1C1C1 0 C15 z23 0000C1C1C11 C010 0 00C1C1C1 0 C15 z2n 0000C1C1C1011111C1C1C1 1 360 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 21 Finally using the Gaussian Elimination method the actual individual angle e zti and e zri at each target position can be calculated The calculation of e xti e xri e yti e yri d xti d xri d yti d yri d zti and d zri is different to e zti and e zri For instance C15 x11 C15 xt1 C15 xr1 C15 x12 C15 xt2 C15 xr2 C15 x1n C15 xtn C15 xrn 22 and C15 x21 C15 xt1 C0 C15 xr2 C15 x22 C15 xt2 C0 C15 xr3 C15 x2n C15 xtn C0 C15 xr1 23 The summation of e xri is C15 xr1 C15 xr2 C15 xr3 C1C1C1 C15 xrnC01 C15 xrn 0 C14 24 ARTICLE IN PRESS W Jywe et al International Journal of Machine Tools Manufacture 47 2007 1978 1987 1983 Fig 4 Stability test results a d 4 Experimental results and discussion In this paper the calibration of the 4 DOF measurement system system stability system verification and full circle test were accomplished The photograph of this system was shown in Fig 2 Components not shown in Fig 2 include a desktop PC connected to the PSD signal processor via an A D card The component specifications were listed in Table 1 4 1 System calibration System calibration was the first experiment In this experiment the NewPort autocollimator was used to provide the reference angular position Its measurement range was 7410arcsec resolution was 0 02arcsec and accuracy was 0 5arcsec Fig 3 a shows the calibration result and Fig 3 b gives the standard deviations for ARTICLE IN PRESS Tools Manufacture 47 2007 1978 1987 Therefore the matrix of e xti and e xri is 1000 C1C1C1 C010000C1C1C1 0 C15 x11 0100 C1C1C1 0 C010 00C1C1C1 0 C15 x12 0010 C1C1C1 00C0100C1C1C1 0 C15 x13 1000 C1C1C1 0 C010 00C1C1C1 0 C15 x21 0100 C1C1C1 00C0100C1C1C1 0 C15 x22 0010 C1C1C1 000C010C1C1C1 0 C15 x23 0000C1C1C11 C010000C1C1C1 0 C15 x2n 0000C1C1C1011111C1C1C1 10 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 25 Similarly 1000 C1C1C1 C010 0 00C1C1C1 0 C15 y11 0100 C1C1C1 0 C010 00C1C1C1 0 C15 y12 0010 C1C1C1 00C0100C1C1C1 0 C15 y13 1000 C1C1C1 0 C010 00C1C1C1 0 C15 y21 0100 C1C1C1 00C0100C1C1C1 0 C15 y22 0010 C1C1C1 000C010C1C1C1 0 C15 y23 0000C1C1C11 C010 0 00C1C1C1 0 C15 y2n 0000C1C1C1011111C1C1C1 10 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 26 1000 C1C1C1 C010000C1C1C1 0 d y11 0100 C1C1C1 0 C010 00C1C1C1 0 d y12 0010 C1C1C1 00C0100C1C1C1 0 d y13 1000 C1C1C1 0 C010 00C1C1C1 0 d y21 0100 C1C1C1 00C0100C1C1C1 0 d y22 0010 C1C1C1 000C010C1C1C1 0 d y23 0000C1C1C11 C010000C1C1C1 0 d y2n 0000C1C1C1011111C1C1C1 10 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 27 This technique can be used in the rotary table 6 DOF calibration but in this paper the measurement system could only measure 4 DOF errors so this paper lists only four equations Eqs 21 25 27 The recorded count was based on the measurement range of the system For example the measurement range of Lin s system laser interferometer 16 was about 101 W Jywe et al International Journal of Machine1984 Therefore one full circle test must record at least 36 points during the first and second tests respectively Fig 5 Verification result a and b ARTICLE IN PRESS W Jywe et al International Journal of Machine system uncertainty Throughout the calibration process it was clear that the linearity of e z was good and the uncertainty of e z was about 1 5arcsec The angular Fig 6 Full circle test Tools Manufacture 47 2007 1978 1987 1985 position e z measurement range of the 4 DOF measure ment system was about 11 because almost all measurement range of PSD was used results a h accurate reference rotary table but with good repeatability stability of this system was less then 2arcsec while the 1992 6047 6055 ARTICLE IN PRESS 4 2 System stability test System stability test was the second experiment System stability was evaluated by allowing the system to come to equilibrium under normal laboratory conditions i e no special temperature or vibrational isolation and then continuously recording the output signal for 4000s Fig 4 shows that the system stability of the basic prototype was reasonable i e with no special isolation or filtering the output of d y remained within 71 2mm and e x e y and e z remained within 71 5arcsec over 4000s 4 3 System verification System verification was the third experiment and the autocollimator was also used to verify the 4DOF measure ment system since it can measure the e x and e z simultaneously The autocollimator was set up at the back of the grating When the full circle test was implemented and error separation method was not used the autocolli mator recorded the error sum of the target rotary table and reference rotary table The autocollimator and the 4DOF measurement system recorded once when the target rotary table rotated one degree clockwise and once again when the reference rotary table rotated one degree counterclockwise Fig 5 shows the result of the system verification The result of 4DOF measurement system and autocollimator was similar so the mathematic model of 4DOF measurement system is correct 4 4 Full circle test The full circle test was the last experiment that was described in Section 3 The measurement range of the 4 D