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畢 業(yè) 設 計 開 題 報 告 文 獻 綜 述 1 1 課題研究背景 由于滾珠絲杠副獨特的優(yōu)良技術性能 其研究迅速得到了世界許多國家的高度 重視 滾珠絲杠傳動的應用也隨之擴展到其它領域中 隨著機床自動化的發(fā)展 特別 是 1965 年數控機床的出現 促進了滾珠絲杠副產品的品種和規(guī)格的發(fā)展 質量和產量 的提高 推動了設計技術和制造工藝的進步 迅速研制了加工和磨削滾珠螺母的專用 機床 隨著新工藝的發(fā)展 制造技術的進步 大幅度的提高了滾珠絲杠副的生產效率 和質量 同時縮短了生產的周期 降低了成本 反過來又促進了滾珠絲杠副品種和規(guī) 格的擴大 質量和產量的進一步提高 系列化等方面的重大發(fā)展 早在 19 世紀末就發(fā)明了滾珠絲杠副 但很長一段時間未能實際應用 因制造難度 太大 世界上第一個使用滾珠絲杠副的是美國通用汽車公司薩吉諾分廠 它將滾珠絲 杠副用于汽車的轉向機構上 由于設計制造等技術的進步 滾珠絲杠副的結構也有著一定的改進和變化 比如說日 本 THK 公司已經將帶有保持架的滾珠絲杠副產品化 其產品的綜合性能得到了很大的 提高 隨著機械產品向高速 高效 自動化方向發(fā)展 工業(yè)機器人 數控鍛壓機械 加工中心以及機電一體化自動機械等 其進給驅動速度不斷提高 大導程滾珠絲杠副 的出現 滿足了高速化的要求 日本 NSK 公司已開發(fā)出公稱直徑 導程為 15mm 40mm 16mm 50mm 20mm 60mm 25mm 80mm 超大導程滾珠絲杠副 快速進給 速度達 180m min 從前 擔心大導程滾珠絲杠副驅動對加工中心精度的影響 設計時 取導程 Ph 10mm 隨著科學技術的進步 從 1999 年日本國際機床展覽會上可看出 設 計與研究現在大部分高速加工中心都使用大導程滾珠絲杠副 4 1 2 課題研究的意義 1 2 1 滾珠絲杠的優(yōu)點 它是一種新的滾動摩擦傳動機構 與滑動絲杠螺母機構相比具有以下特點 1 傳動效率高 摩擦損失小 滾珠絲杠螺母傳動效率 92 96 比滑動絲杠螺母 的 20 40 提高 2 4 倍 而消耗的功率僅為滑動絲杠螺母的 1 4 1 3 2 動作靈敏無爬行現象 滾動摩擦的啟動阻力很小 幾乎與運動速度完全無關 運 動平穩(wěn) 動作靈敏 在低速下能均勻運動且不易出現爬行現象 特別適于位移速度較 低的高精度傳動 3 精度保持性好 滾動摩擦的磨損小 壽命長在長期運轉中能保持較好的精度 4 經適當預緊能實現無間隙傳動 采用雙螺母加預緊力控制彈性變形 經調整后能基 本上消除軸向間隙 提高軸向精度 在無間隙和過盈下能正常運轉 并具有較高的定 位精度和位移精度 機床上采用滾珠絲杠螺母傳動 是一種精密而又省力的運動轉換 裝置 性 1 2 2 研究滾珠絲杠的實用意義 機電一體化技術是機械工業(yè)發(fā)展的必然趨勢 有廣闊的技術前景 滾珠絲桿副是 為了適應機電一體化機械傳動系統(tǒng)的要求而發(fā)展起來的一種新型傳動機構 由滾珠絲 杠 滾珠螺母 組件 和滾珠組成 可以將旋轉運動變?yōu)橹本€運動 或者將直線運動 轉變成旋轉運動 它具有傳動效率高 啟動力矩小 傳動靈敏平穩(wěn) 工作壽命長等優(yōu) 點 但是由于制造和裝配的誤差 滾珠絲杠副總是存在間隙 同時 滾珠絲杠在軸向 載荷的作用下 滾珠和螺紋滾道接觸部位會產生彈性變形 影響滾珠絲杠的傳動精度 滾珠絲杠副不僅是各類數控裝備的核心功能部件 還是機械工業(yè)領域中資本密集型 和技術密集型的重要通用零部件 在線性傳動家族中滾珠絲杠副是應用面很廣 產業(yè) 化程度較高的產品 參考文獻 1 寧立偉 滾珠絲杠副 機床數控技術 高等教育出版社 2010 1 2 2012 滾珠絲杠副的發(fā)展報告 3 百度百科 滾珠絲杠副 4 肖正義 滾珠絲杠副的發(fā)展趨勢 制作技術與機床 2000 04 5 黃祖堯 21 世紀初海外滾動功能部件發(fā)展動態(tài) 世界制作技術與裝備市場 2003 2 6 程光仁 施祖康 滾珠螺旋傳動設計基礎 北京 機械工業(yè)出版社 1987 08 7 喻忠志 我國滾動功能部件產業(yè)現狀分析 制造技術與機床 2004 04 8 中國藝工滾動功能部件產品綜合樣本及資料 9 肖正義 焦?jié)?高速滾珠絲杠副的研發(fā)與測試技術 制造技術與機床 2004 04 10 滾珠絲杠譯文集 南京工藝裝備廠 1980 08 畢 業(yè) 設 計 開 題 報 告 本課題要研究或解決的問題和擬采用的研究手段 途徑 1 在圖書館借閱相關書籍 論文等 并進行整理 2 在學校數據庫查找相關資料 3 在網上查找相關資料 4 對找到的資料和數據進行分析和計算 5 整合查到的數據和資料開始寫畢業(yè)論文 6 論文撰寫按構思框架 編寫提綱 專題研討幾個步驟進行 在編寫過 程中征求老師和同學的意見使論文內容更加全面 畢 業(yè) 設 計 開 題 報 告 指導教師意見 對滾珠絲杠的初步認識比較明確 希望能將畢業(yè)設計做得更好 指導教師 2016 年 3 月 20 日 所在系審查意見 同意 系主任 2016 年 3 月 20 日 中 北 大 學 信 息 商 務 學 院 畢業(yè)設計任務書 學 院 系 機械工程與自動化系 專 業(yè) 機械制造及其自動化 學 生 姓 名 張曉飛 學 號 12020144X21 設 計 題 目 滾珠絲杠設計及相關技術研究 起 迄 日 期 2016 年 2 月 29 日 2016 年 6 月 5 日 指 導 教 師 龐學慧 系 主 任 暴建剛 發(fā)任務書日期 2016 年 2 月 29 日 畢 業(yè) 設 計 任 務 書 1 畢業(yè)設計的任務和要求 掌握機床傳動絲杠的基本知識 研究數控機床滾珠絲杠的關鍵技術 掌握其選型 應用及設計方法等 完成一種滾珠絲杠的設計 滿足精密數控機床 20m min 進給速度 的需求 2 畢業(yè)設計的具體工作內容 1 分析題目要求 查閱相關的國內外文獻 設計資料 有關專利文獻等 在此基 礎上 了解開題報告的撰寫方法 基本要求 完成開題報告 2 學習和掌握滾珠絲杠的有關知識 了解高速滾珠絲杠的關鍵技術及發(fā)展現狀 了解數控機床 加工中心對滾珠絲杠的要求 總結滾珠絲杠的設計要點 技術 關鍵及發(fā)展方向 力爭提出滾珠絲杠設計的發(fā)展方向 3 按題目要求 設計一種滿足數控機床進給運動需要的滾珠絲杠 完成結構圖 給出必要的計算說明 4 編寫設計說明書 5 翻譯本專業(yè)外文科技文獻一份 畢 業(yè) 設 計 任 務 書 3 對畢業(yè)設計成果的要求 1 滾珠絲杠結構圖 2 滾珠絲杠的研究及設計說明書一份 3 本專業(yè)外文科技文獻譯文一份 4 畢業(yè)設計工作進度計劃 起 迄 日 期 工 作 內 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 查閱相關文獻資料 了解滾珠絲杠的國內 外現狀及發(fā)展趨勢 提出自己的設計思路 完成開題報告 全面掌握滾珠絲杠的基本知識 了解高速機床對進給導軌 的要求 了解滾珠絲杠的設計特點 分析總結滾珠絲杠的 發(fā)展方向 完成滾珠絲杠結構圖設計 完成研究總結及設計說明書 撰寫答辯講稿 準備答辯 學生所在系審查意見 同意開題 系主任 暴建崗 2016 年 3 月 3 日 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