K20-支架零件機(jī)械加工工藝及夾具設(shè)計(jì)-車60孔夾具設(shè)計(jì)

資源目錄里展示的全都有，所見即所得。下載后全都有,請(qǐng)放心下載。原稿可自行編輯修改=【QQ：401339828 或11970985 有疑問可加】 學(xué)院機(jī)械加工工序卡片產(chǎn)品型號(hào)零件圖號(hào)產(chǎn)品名稱支架零件名稱支架共5頁第1頁車間工序號(hào)工序名稱材 料 牌 號(hào)機(jī)加工30銑HT200毛 坯 種 類毛坯外形尺寸每毛坯可制件數(shù)每 臺(tái) 件 數(shù)鑄件11設(shè)備名稱設(shè)備型號(hào)設(shè)備編號(hào)同時(shí)加工件數(shù)銑床X52K11夾具編號(hào)夾具名稱切削液1專用夾具普通乳化液工位器具編號(hào)工位器具名稱工序工時(shí) (分)準(zhǔn)終單件工步號(hào)工 步 內(nèi) 容工 藝 裝 備主軸轉(zhuǎn)速切削速度進(jìn)給量切削深度進(jìn)給次數(shù)工步工時(shí)/sr/minm/smm/rmm機(jī)動(dòng)輔助1銑底面YT15端銑刀, 125x0.02mm游標(biāo)卡尺，150mm鋼板尺755001.270.831 設(shè) 計(jì)（日 期） 校 對(duì)（日期） 審 核（日期） 標(biāo)準(zhǔn)化（日期） 會(huì) 簽（日期）標(biāo)記處數(shù)更改文件號(hào)簽 字 日 期標(biāo)記處數(shù)更改文件號(hào)簽 字 日 期學(xué)院機(jī)械加工工序卡片產(chǎn)品型號(hào)支架零件圖號(hào)產(chǎn)品名稱支架零件名稱支架共5頁第2頁車間工序號(hào)工序名稱材 料 牌 號(hào)機(jī)加工40銑HT200毛 坯 種 類毛坯外形尺寸每毛坯可制件數(shù)每 臺(tái) 件 數(shù)鑄件11設(shè)備名稱設(shè)備型號(hào)設(shè)備編號(hào)同時(shí)加工件數(shù)銑床X52K11夾具編號(hào)夾具名稱切削液1專用夾具普通乳化液工位器具編號(hào)工位器具名稱工序工時(shí) (分)準(zhǔn)終單件22工步號(hào)工 步 內(nèi) 容工 藝 裝 備主軸轉(zhuǎn)速切削速度進(jìn)給量切削深度進(jìn)給次數(shù)工步工時(shí)/sr/minm/smm/rmm機(jī)動(dòng)輔助1銑右端面，保證尺寸15mmYT15端銑刀, 125x0.02mm游標(biāo)卡尺，150mm鋼板尺755001.270.8311510 設(shè) 計(jì)（日 期） 校 對(duì)（日期） 審 核（日期） 標(biāo)準(zhǔn)化（日期） 會(huì) 簽（日期）標(biāo)記處數(shù)更改文件號(hào)簽 字 日 期標(biāo)記處數(shù)更改文件號(hào)簽 字 日 期學(xué)院機(jī)械加工工序卡片產(chǎn)品型號(hào)支架零件圖號(hào)產(chǎn)品名稱支架零件名稱支架共5頁第3頁車間工序號(hào)工序名稱材 料 牌 號(hào)機(jī)加工50銑HT200毛 坯 種 類毛坯外形尺寸每毛坯可制件數(shù)每 臺(tái) 件 數(shù)鑄件11設(shè)備名稱設(shè)備型號(hào)設(shè)備編號(hào)同時(shí)加工件數(shù)搖臂鉆床Z3511夾具編號(hào)夾具名稱切削液1專用夾具普通乳化液工位器具編號(hào)工位器具名稱工序工時(shí) (分)準(zhǔn)終單件22工步號(hào)工 步 內(nèi) 容工 藝 裝 備主軸轉(zhuǎn)速切削速度進(jìn)給量切削深度進(jìn)給次數(shù)工步工時(shí)/sr/minm/smm/rmm機(jī)動(dòng)輔助1銑寬度為30mm的槽YT15端銑刀, 125x0.02mm游標(biāo)卡尺，150mm鋼板尺7580012.70.5211510 設(shè) 計(jì)（日 期） 校 對(duì)（日期） 審 核（日期） 標(biāo)準(zhǔn)化（日期） 會(huì) 簽（日期）標(biāo)記處數(shù)更改文件號(hào)簽 字 日 期標(biāo)記處數(shù)更改文件號(hào)簽 字 日 期學(xué)院機(jī)械加工工序卡片產(chǎn)品型號(hào)支架零件圖號(hào)產(chǎn)品名稱支架零件名稱支架共5頁第4頁車間工序號(hào)工序名稱材 料 牌 號(hào)機(jī)加工60車HT200毛 坯 種 類毛坯外形尺寸每毛坯可制件數(shù)每 臺(tái) 件 數(shù)鑄件11設(shè)備名稱設(shè)備型號(hào)設(shè)備編號(hào)同時(shí)加工件數(shù)臥式車床CA614011夾具編號(hào)夾具名稱切削液1專用夾具普通乳化液工位器具編號(hào)工位器具名稱工序工時(shí) (分)準(zhǔn)終單件22工步號(hào)工 步 內(nèi) 容工 藝 裝 備主軸轉(zhuǎn)速切削速度進(jìn)給量切削深度進(jìn)給次數(shù)工步工時(shí)/sr/minm/smm/rmm機(jī)動(dòng)輔助1車60H7mm孔至圖紙尺寸125x0.02mm游標(biāo)卡尺，鏜刀56025.70.8211510 設(shè) 計(jì)（日 期） 校 對(duì)（日期） 審 核（日期） 標(biāo)準(zhǔn)化（日期） 會(huì) 簽（日期）標(biāo)記處數(shù)更改文件號(hào)簽 字 日 期標(biāo)記處數(shù)更改文件號(hào)簽 字 日 期學(xué)院機(jī)械加工工序卡片產(chǎn)品型號(hào)支架零件圖號(hào)產(chǎn)品名稱支架零件名稱支架共5頁第5頁車間工序號(hào)工序名稱材 料 牌 號(hào)機(jī)加工70鉆HT200毛 坯 種 類毛坯外形尺寸每毛坯可制件數(shù)每 臺(tái) 件 數(shù)鑄件11設(shè)備名稱設(shè)備型號(hào)設(shè)備編號(hào)同時(shí)加工件數(shù)鉆床Z52511夾具編號(hào)夾具名稱切削液1專用夾具普通乳化液工位器具編號(hào)工位器具名稱工序工時(shí) (分)準(zhǔn)終單件22工步號(hào)工 步 內(nèi) 容工 藝 裝 備主軸轉(zhuǎn)速切削速度進(jìn)給量切削深度進(jìn)給次數(shù)工步工時(shí)/sr/minm/smm/rmm機(jī)動(dòng)輔助1鉆孔3-M8底孔并進(jìn)行攻絲相應(yīng)規(guī)格的麻花鉆、絲錐, 鉆床夾具5001.270.8311510 設(shè) 計(jì)（日 期） 校 對(duì)（日期） 審 核（日期） 標(biāo)準(zhǔn)化（日期） 會(huì) 簽（日期）標(biāo)記處數(shù)更改文件號(hào)簽 字 日 期標(biāo)記處數(shù)更改文件號(hào)簽 字 日 期機(jī)械加工工藝過程卡片產(chǎn)品型號(hào)零件圖號(hào)產(chǎn)品名稱支架零件名稱支架共1頁第1頁材 料 牌 號(hào)HT200 毛 坯 種 類鑄造毛坯外形尺寸每毛坯件數(shù)1每 臺(tái) 件 數(shù)1備 注 工 序 號(hào) 工序 名稱 工 序 內(nèi) 容車間 工段設(shè) 備工 藝 裝 備 工時(shí)/min 準(zhǔn)終 單件10鑄造鑄造機(jī)20熱處理人工時(shí)效機(jī)30銑銑底面機(jī)立式銑床X52K125x0.02mm游標(biāo)卡尺，150mm鋼板尺7540銑銑右端面，保證尺寸15mm機(jī)立式銑床X52K125x0.02mm游標(biāo)卡尺，150mm鋼板尺7550銑銑寬度為30mm的槽機(jī)立式銑床X52K125x0.02mm游標(biāo)卡尺，150mm鋼板尺7560車車60H7mm孔至圖紙尺寸機(jī)臥式車床CA6140125x0.02mm游標(biāo)卡尺70鉆鉆孔3-M8底孔并進(jìn)行攻絲機(jī)鉆床Z525鉆床夾具80檢驗(yàn)按照?qǐng)D紙要求檢驗(yàn)各部尺寸及形位公差機(jī)90入庫清洗，加工表面涂防繡油，入庫檢 設(shè) 計(jì)（日 期） 校 對(duì)（日期） 審 核（日期） 標(biāo)準(zhǔn)化（日期） 會(huì) 簽（日期）標(biāo)記處數(shù)更改文件號(hào)簽 字 日 期標(biāo)記處數(shù)更改文件號(hào)簽 字 日 期學(xué)院設(shè)計(jì)說明書題目：支架零件機(jī)械加工工藝及夾具設(shè)計(jì) 姓 名：學(xué) 號(hào)：年 級(jí)：專 業(yè)：學(xué)生類別：指導(dǎo)教師：教學(xué)單位：2015年 5月1 日摘 要這篇文章是基于支架零件的機(jī)械加工工藝及夾具設(shè)計(jì),包含支架制定零件圖，毛坯的選擇，制定夾具，零部件的工藝路線，刀具選擇，切割的確定方法填充工藝文件的數(shù)量。選擇正確的加工方法，加工工藝的合理設(shè)計(jì)。此外，兩個(gè)流程加工件填充蓋設(shè)計(jì)了專用夾具。許多類型的夾具，夾具，其中最廣泛使用的通用夾具，尺寸和更加標(biāo)準(zhǔn)化，以及專業(yè)工廠進(jìn)行生產(chǎn)。在大規(guī)模生產(chǎn)應(yīng)用廣泛，適用于工件的加工流程服務(wù)專用夾具，你需要來設(shè)計(jì)和制造自己的工廠加工的工件。本文的主要內(nèi)容是完成加工車60孔夾具設(shè)計(jì)。關(guān)鍵詞：支架，工藝處理，夾具，工藝文件19AbstractThis article is a mechanical processing technology and fixture design based on bracket parts, including bracket making parts diagram, the choice of blank, making process, parts of the fixture, tool selection, the number of filling method determines cutting process documents. Choose the correct processing methods, reasonable design and processing technology. In addition, the two process filled cover designing special fixture.Many types of fixture, fixture, one of the most widely used universal fixture, size and more standardized, and professional production factory. Widely used in large-scale production and application, processing service special jig is suitable for the workpiece, you need to work to design and manufacture their own processing plant. The main content of this paper is to complete the processing of car of 60 hole fixture design.Keywords: support, process, fixture, process documents目 錄1 前言42 零件的分析52.1零件的作用52.2零件的工藝分析52.2.1孔的加工52.2.2面的加工53 工藝規(guī)劃設(shè)計(jì)63.1毛坯的制造形式63.2基面的選擇63.2.1粗基準(zhǔn)的選擇63.2.2精基準(zhǔn)的選擇63.3工藝路線的擬定63.3.1工藝路線方案73.3.2工藝方案的確定73.4毛坯尺寸及其加工余量的確定83.4.1兩側(cè)面毛坯尺寸及加工余量計(jì)算83.4.2毛坯尺寸及加工余量計(jì)算83.5確定各工序切削用量及基本工時(shí)94 車60孔夾具設(shè)計(jì)144.1車床夾具的設(shè)計(jì)要點(diǎn)144.2 車床夾具設(shè)計(jì)要求說明154.3 定位機(jī)構(gòu)164.4夾緊機(jī)構(gòu)164.5零件的車床夾具的加工誤差分析164.6 確定夾具體結(jié)構(gòu)尺寸和總體結(jié)構(gòu)174.7 零件的車床專用夾具簡單使用說明18總結(jié)19參考文獻(xiàn)201 前言1.簡介本次畢業(yè)設(shè)計(jì)內(nèi)容包括零件的分析，工藝路線的制定，工藝規(guī)劃設(shè)計(jì)，某道工序的夾具設(shè)計(jì)以及該道工序的工序卡，機(jī)械加工綜合卡片，夾具裝配圖以及夾具底座零件圖的繪制等等。就我個(gè)人而言，希望能通過這次畢業(yè)設(shè)計(jì)對(duì)未來即將從事的工作進(jìn)行一次適應(yīng)性的訓(xùn)練，從中鍛煉自己分析問題，解決問題的能力，并學(xué)會(huì)將所學(xué)到的理論知識(shí)應(yīng)用到具體的實(shí)際生產(chǎn)問題中來，為以后走向社會(huì)打下堅(jiān)實(shí)的基礎(chǔ)。由于能力有限，設(shè)計(jì)尚有許多不足之處，懇請(qǐng)老師批評(píng)指正。2.設(shè)計(jì)目的其目的如下：培養(yǎng)學(xué)生解決機(jī)械加工工藝問題的能力。通過畢業(yè)設(shè)計(jì)，熟練運(yùn)用機(jī)械技術(shù)基礎(chǔ)課程中的基本理論及在生產(chǎn)實(shí)習(xí)中學(xué)到的實(shí)踐知識(shí)，正確地解決一個(gè)零件在加工中定位、加緊以及工藝路線安排、工藝尺寸確定等問題，保證零件的加工質(zhì)量，初步具備設(shè)計(jì)一個(gè)中等復(fù)雜程度零件的能力。培養(yǎng)學(xué)生熟悉并運(yùn)用有關(guān)手冊(cè)、規(guī)范、圖表等技術(shù)資料的能力。進(jìn)一步培養(yǎng)學(xué)生識(shí)圖、制圖、運(yùn)用和編寫技術(shù)文件等基本技能。2 零件的分析2.1零件的作用 該零件為典型的桿類零件，而且為支架類。因此，其主要的要素包括兩側(cè)面，60mm孔和3個(gè)M8孔。通過孔連接即該支架的作用是實(shí)現(xiàn)運(yùn)動(dòng)的傳遞作用。2.2零件的工藝分析該支架的加工表面分三種，主要是孔的加工，兩側(cè)面的加工各組加工面之間有嚴(yán)格的尺寸位置度要求和一定的表面加工精度要求，特別是孔的加工，幾乎都要保證Ra3.2um的表面粗糙度，因而需精加工，現(xiàn)將主要加工面分述如下：2.2.1孔的加工該零件共有2個(gè)孔要加工：60mm孔、M8孔是零件的主要加工面，通過兩孔中心連線及對(duì)兩側(cè)對(duì)稱面，沒有位置尺寸度要求，M8孔只需要鉆床粗加工。2.2.2面的加工該零件共有2個(gè)側(cè)面要加工：兩個(gè)側(cè)面是配合孔后續(xù)工序的主要精基準(zhǔn)面，需要精加工。3 工藝規(guī)劃設(shè)計(jì)3.1毛坯的制造形式零件材料為HT200，根據(jù)選擇毛坯應(yīng)考慮的因素，該零件體積較小，形狀較復(fù)雜，外表面采用不去除材料方法獲得粗糙度要求，由于零件生產(chǎn)類型為成批，大批生產(chǎn)，而砂型鑄造生產(chǎn)成本低，設(shè)備簡單，故本零件毛坯采用普通鑄造。由于零件上兩孔都較大，且都有嚴(yán)格的表面精度要求，故都要留出足夠的加工余量。3.2基面的選擇基面選擇是工藝規(guī)劃設(shè)計(jì)中的重要工作之一，基準(zhǔn)選擇的正確與合理，可以使加工質(zhì)量得到保證，生產(chǎn)率得到提高，否則，不但使加工工藝過程中的問題百出，更有甚者，還會(huì)造成零件大批報(bào)廢，使生產(chǎn)無法正常進(jìn)行。3.2.1粗基準(zhǔn)的選擇粗基準(zhǔn)選擇應(yīng)為后續(xù)加工提供精基準(zhǔn)，由于兩側(cè)面較平整且加工精度較高，故以2個(gè)主要側(cè)面為基準(zhǔn)。3.2.2精基準(zhǔn)的選擇精基準(zhǔn)主要考慮如何保證加工精度和裝夾方便，該零件上重要表面是大頭孔38H8，由于其與底面有垂直度關(guān)系，所以底面自然成為精基準(zhǔn)面，考慮到第二基準(zhǔn)面選擇的方便性，該定位基準(zhǔn)組合在后續(xù)孔的加工中，以及孔上徑向孔的加工中都將作為精基準(zhǔn)面。3.3工藝路線的擬定擬定工藝路線的內(nèi)容除選擇定位基準(zhǔn)外，還要選擇各加工表面的加工方法，安排工序的先后順序，確定加工設(shè)備，工藝裝備等。工藝路線的擬定要考慮使工件的幾何形狀精度，尺寸精度及位置精度等技術(shù)要求得到合理保證，成批生產(chǎn)還應(yīng)考慮采用組合機(jī)床，專用夾具，工序集中，以提高效率，還應(yīng)考慮加工的經(jīng)濟(jì)性，以便使生產(chǎn)成本盡量下降。3.3.1工藝路線方案方案一10鑄造鑄造20熱處理人工時(shí)效30銑銑底面40銑銑右端面，保證尺寸15mm50銑銑寬度為30mm的槽60車車60H7mm孔至圖紙尺寸70鉆鉆孔3-M8底孔并進(jìn)行攻絲80檢驗(yàn)按照?qǐng)D紙要求檢驗(yàn)各部尺寸及形位公差90入庫清洗，加工表面涂防繡油，入庫方案二10鑄造鑄造20熱處理人工時(shí)效30車車60H7mm孔至圖紙尺寸40銑銑底面50銑銑右端面，保證尺寸15mm60銑銑寬度為30mm的槽70鉆鉆孔3-M8底孔并進(jìn)行攻絲80檢驗(yàn)按照?qǐng)D紙要求檢驗(yàn)各部尺寸及形位公差90入庫清洗，加工表面涂防繡油，入庫方案分析與比較：經(jīng)過分析發(fā)現(xiàn)，方案二先鉆孔后加工面，而方案一是先面后孔根據(jù)書本理論知識(shí)，應(yīng)該是先面后孔比較合理，因?yàn)殂@孔需要以加工了面的為精基準(zhǔn)。3.3.2工藝方案的確定10鑄造鑄造20熱處理人工時(shí)效30銑銑底面40銑銑右端面，保證尺寸15mm50銑銑寬度為30mm的槽60車車60H7mm孔至圖紙尺寸70鉆鉆孔3-M8底孔并進(jìn)行攻絲80檢驗(yàn)按照?qǐng)D紙要求檢驗(yàn)各部尺寸及形位公差90入庫清洗，加工表面涂防繡油，入庫3.4毛坯尺寸及其加工余量的確定支架零件材料為HT200,毛坯重量約為1.6kg，生產(chǎn)類型為中批或大批生產(chǎn)，采用普通鑄造生產(chǎn)。普通鑄造，材料為HT200鋼，分模線平直對(duì)稱，材質(zhì)系數(shù)M1,復(fù)雜系數(shù)=1.56/1.80.87,為S1級(jí)，厚度為25mm，普通級(jí)，查的上下偏差分別為+1.4和-0.63.4.1兩側(cè)面毛坯尺寸及加工余量計(jì)算根據(jù)工序要求，兩側(cè)面經(jīng)過四道工序，先粗銑端面B，再粗銑端面A，精銑端面B，最后精銑端面A，各步余量如下：粗銑：由機(jī)械加工工藝手冊(cè)第一卷表3.2-23，其余量值規(guī)定，零件厚度大于6mm到30mm，寬度小于100mm，其加工余量為1.0mm。精銑：由機(jī)械加工工藝手冊(cè)第一卷表3.2-25，其余量值規(guī)定，零件厚度大于6mm到30mm，寬度小于100mm，其加工余量為0.5mm。精銑后尺寸與零件尺寸相同，但由于設(shè)計(jì)零件圖紙并未給出具體的公差等級(jí)，現(xiàn)按機(jī)械加工工藝手冊(cè)表5.29，粗銑精銑所能達(dá)到的經(jīng)濟(jì)精度取IT8,按入體原則取值。3.4.2毛坯尺寸及加工余量計(jì)算根據(jù)工序要求，精銑后尺寸與零件尺寸相同，但由于設(shè)計(jì)零件圖紙并未給出具體的公差等級(jí)，現(xiàn)按機(jī)械加工工藝手冊(cè)表5.29，粗銑精銑所能達(dá)到的經(jīng)濟(jì)精度取IT8,按入體原則取值。3.5確定各工序切削用量及基本工時(shí)10.鑄造毛坯; 沒切削過程，無需計(jì)算20.人工時(shí)效 沒切削過程，無需計(jì)算工序30. 銑底面取背吃到量，選用X52型立式銑床 ，每齒進(jìn)給量工件材料 HT200 ，鑄造 ，高速鋼鑲齒銑刀、 齒數(shù) ，查表5.8確定銑削速度 采用X52k立式銑床 ，查表3.6，取轉(zhuǎn)速 ， 故實(shí)際銑削速度當(dāng)工作臺(tái)每分鐘進(jìn)給 為由工藝手冊(cè)得工序40. 銑右端面，保證尺寸15mm取背吃到量，選用X52K型立式銑床 ，每齒進(jìn)給量工件材料 HT200 ，鑄造 ，高速鋼鑲齒銑刀、 齒數(shù) ，查表5.8確定銑削速度 采用X52立式銑床 ，查表3.6，取轉(zhuǎn)速 ， 故實(shí)際銑削速度當(dāng)工作臺(tái)每分鐘進(jìn)給 為由工藝手冊(cè)得工序50：銑寬度為30mm的槽。機(jī)床：銑床刀具：錯(cuò)齒三面刃銑刀 粗銑槽切削深度：根據(jù)參考文獻(xiàn)3表查得：進(jìn)給量,根據(jù)參考文獻(xiàn)1表查得切削速度。機(jī)床主軸轉(zhuǎn)速：，按照參考文獻(xiàn)3表3.174，取實(shí)際切削速度：進(jìn)給量：工作臺(tái)每分進(jìn)給量： 被切削層長度：由毛坯尺寸可知， 刀具切入長度： =63mm刀具切出長度：取走刀次數(shù)為1機(jī)動(dòng)時(shí)間： 精銑槽根據(jù)參考文獻(xiàn)3表查得：進(jìn)給量,根據(jù)參考文獻(xiàn)1表查得切削速度，機(jī)床主軸轉(zhuǎn)速：，按照參考文獻(xiàn)3表3.174，取。實(shí)際切削速度：進(jìn)給量：工作臺(tái)每分進(jìn)給量： 被切削層長度：由毛坯尺寸可知， 刀具切入長度： =81mm刀具切出長度：取走刀次數(shù)為1機(jī)動(dòng)時(shí)間： 本工序機(jī)動(dòng)時(shí)間：工序60車60H7mm孔至圖紙尺寸本工序采用計(jì)算法。所選用刀具為硬質(zhì)合金（鎢鈷類），直徑為的圓形鏜刀。.確定切削深度 =.確定進(jìn)給量根據(jù)切削用量簡明使用手冊(cè)表1.5可知，當(dāng)粗鏜鑄件時(shí)，鏜刀直徑，鏜刀伸出長度為時(shí)： =0.150.40按CA6140機(jī)床的進(jìn)給量（表4.29），選擇， =0.25.確定切削速度 = （3-9）式中=，=0.2，=0.20，=，=0.15 （3-10） =39 = （3-11）按CA6140機(jī)床的轉(zhuǎn)速，選擇 =160=2.6.計(jì)算基本工時(shí)選鏜刀的主偏角=，則=，則： =119 工序70：鉆孔3-M8底孔并進(jìn)行攻絲鉆孔選用機(jī)床為Z525搖臂機(jī)床，刀具選用GB1436-85直柄短麻花鉆，機(jī)械加工工藝手冊(cè)第2卷。根據(jù)機(jī)械加工工藝手冊(cè)第2卷表10.4-2查得鉆頭直徑小于10的鉆孔進(jìn)給量為0.200.35。 則取確定切削速度，根據(jù)機(jī)械加工工藝手冊(cè)第2卷表10.4-9切削速度計(jì)算公式為 （3-20）查得參數(shù)為，刀具耐用度T=35則 =1.6所以 =72選取 所以實(shí)際切削速度為=2.64確定切削時(shí)間（一個(gè)孔） =（3）倒角機(jī)床：Z525鉆床刀具：倒角鉆頭量具：游標(biāo)卡尺型夾具：專用夾具工序80. 按照?qǐng)D紙要求檢驗(yàn)各部尺寸及形位公差 無切削加工工序90. 清洗，加工表面涂防繡油，入庫 無切削加工4 車60孔夾具設(shè)計(jì)4.1車床夾具的設(shè)計(jì)要點(diǎn)（1）定位裝置的設(shè)計(jì)特點(diǎn)和夾緊裝置的設(shè)計(jì)要求當(dāng)加工回轉(zhuǎn)表面時(shí)，要求工件加工面的軸線與機(jī)床主軸軸線重合，夾具上定位裝置的結(jié)構(gòu)和布置必須保證這一點(diǎn)。當(dāng)加工的表面與工序基準(zhǔn)之間有尺寸聯(lián)系或相互位置精度要求時(shí)，則應(yīng)以夾具的回轉(zhuǎn)軸線為基準(zhǔn)來確定定位元件的位置。工件的夾緊應(yīng)可靠。由于加工時(shí)工件和夾具一起隨主軸高速回轉(zhuǎn)，故在加工過程中工件除受切削力矩的作用外，整個(gè)夾具還要受到重力和離心力的作用，轉(zhuǎn)速越高離心力越大，這些力不僅降低夾緊力，同時(shí)會(huì)使主軸振動(dòng)。因此，夾緊機(jī)構(gòu)必須具有足夠的夾緊力，自鎖性能好，以防止工件在加工過程中移動(dòng)或發(fā)生事故。對(duì)于角鐵式夾具，夾緊力的施力方式要注意防止引起夾具變形。（2）夾具與機(jī)床主軸的連接車床夾具與機(jī)床主軸的連接精度對(duì)夾具的加工精度有一定的影響。因此，要求夾具的回轉(zhuǎn)軸線與臥式車床主軸軸線應(yīng)具有盡可能小的同軸度誤差。心軸類車床夾具以莫氏錐柄與機(jī)床主軸錐孔配合連接，用螺桿拉緊。有的心軸則以中心孔與車床前、后頂尖安裝使用。根據(jù)徑向尺寸的大小，其它專用夾具在機(jī)床主軸上的安裝連接一般有兩種方式：1)對(duì)于徑向尺寸D140mm，或D(23)d的小型夾具，一般用錐柄安裝在車床主軸的錐孔中，并用螺桿拉緊，如圖1-a所示。這種連接方式定心精度較高。2)對(duì)于徑向尺寸較大的夾具，一般用過渡盤與車床主軸軸頸連接。過渡盤與主軸配合處的形狀取決于主軸前端的結(jié)構(gòu)。圖1-b所示的過渡盤，其上有一個(gè)定位圓孔按H7/h6或H7/js6與主軸軸頸相配合，并用螺紋和主軸連接。為防止停車和倒車時(shí)因慣性作用使兩者松開，可用壓板將過渡盤壓在主軸上。專用夾具則以其定位止口按H7/h6或H7/js6裝配在過渡盤的凸緣上，用螺釘緊固。這種連接方式的定心精度受配合間隙的影響。為了提高定心精度，可按找正圓校正夾具與機(jī)床主軸的同軸度。對(duì)于車床主軸前端為圓錐體并有凸緣的結(jié)構(gòu)，如圖1-c所示，過渡盤在其長錐面上配合定心，用活套在主軸上的螺母鎖緊，由鍵傳遞扭矩。這種安裝方式的定心精度較高，但端面要求緊貼，制造上較困難。圖1-d所示是以主軸前端短錐面與過渡盤連接的方式。過渡盤推入主軸后，其端面與主軸端面只允許有0.050.1mm的間隙，用螺釘均勻擰緊后，即可保證端面與錐面全部接觸，以使定心準(zhǔn)確、剛度好。圖1 車床夾具與機(jī)床主軸的連接過渡盤常作為車床附件備用，設(shè)計(jì)夾具時(shí)應(yīng)按過渡盤凸緣確定專用夾具體的止口尺寸。過渡盤的材料通常為鑄鐵。各種車床主軸前端的結(jié)構(gòu)尺寸，可查閱有關(guān)手冊(cè)4.2 車床夾具設(shè)計(jì)要求說明車床夾具主要用于加工車60孔。因而車床夾具的主要特點(diǎn)是工件加工表面的中心線與機(jī)床主軸的回轉(zhuǎn)軸線同軸。（1） 安裝在車床主軸上的夾具。這類夾具很多，有通用的三爪卡盤、四爪卡盤，花盤，頂尖等，還有自行設(shè)計(jì)的心軸；專用夾具通常可分為心軸式、夾頭式、卡盤式、角鐵式和花盤式。這類夾具的特點(diǎn)是加工時(shí)隨機(jī)床主軸一起旋轉(zhuǎn)，刀具做進(jìn)給運(yùn)動(dòng)定心式車床夾具 在定心式車床夾具上，工件常以孔或外圓定位，夾具采用定心夾緊機(jī)構(gòu)。角鐵式車床夾具 在車床上加工殼體、支座、杠桿、接頭等零件的回轉(zhuǎn)端面時(shí)，由于零件形狀較復(fù)雜，難以裝夾在通用卡盤上，因而須設(shè)計(jì)專用夾具。這種夾具的夾具體呈角鐵狀，故稱其為角鐵式車床夾具。花盤式車床夾具 這類夾具的夾具體稱花盤，上面開有若干個(gè)T形槽，安裝定位元件、夾緊元件和分度元件等輔助元件，可加工形狀復(fù)雜工件的外圓和內(nèi)孔。這類夾具不對(duì)稱，要注意平衡。（2） 安裝在托板上的夾具。某些重型、畸形工件，常常將夾具安裝在托板上。刀具則安裝在車床主軸上做旋轉(zhuǎn)運(yùn)動(dòng)，夾具做進(jìn)給運(yùn)動(dòng)。由于后一類夾具應(yīng)用很少，屬于機(jī)床改裝范疇。而生產(chǎn)中需自行設(shè)計(jì)的較多是安裝在車床主軸上的專用夾具，所以零件在車床上加工用專用夾具。4.3 定位機(jī)構(gòu)本工件在加工孔時(shí)采用一面擋銷作為定位基準(zhǔn)，易于做到工藝過程中的基準(zhǔn)統(tǒng)一，保證工件的相對(duì)位置精度，且具有支撐面大，支撐剛性好等優(yōu)點(diǎn)；本工件采用底面和擋銷作為定位基準(zhǔn)，工件底面為第一定位基準(zhǔn)，限制了x、y方向轉(zhuǎn)動(dòng)，z方向移動(dòng)三個(gè)自由度；圓柱銷為第二定位基準(zhǔn)限制了x、y方向移動(dòng)兩個(gè)自由度；菱形銷為第三定位基準(zhǔn)，它和圓柱銷聯(lián)合限制了z方向轉(zhuǎn)動(dòng)自由度，所以此定位方案符合六點(diǎn)定位原理，采用對(duì)稱壓板將工件壓緊。4.4夾緊機(jī)構(gòu)選擇工件的夾緊方案，夾緊方案的選擇原則是夾得穩(wěn)，夾得勞，夾得快。選擇夾緊機(jī)構(gòu)時(shí)，要合理確定夾緊力的三要素：大小、方向、作用點(diǎn)。夾緊裝置的基本要求如下：二、 夾緊時(shí)不能破壞工件在夾具中占有的正確位置；三、 夾緊力要適當(dāng)，既要保證工件在加工過程中不移動(dòng)、不轉(zhuǎn)動(dòng)、不震動(dòng)，又不因夾緊力過大而使工件表面損傷、變形。四、 夾緊機(jī)構(gòu)的操作應(yīng)安全、方便、迅速、省力。五、 機(jī)構(gòu)應(yīng)盡量簡單，制造、維修要方便。分析零件加工要素的性質(zhì)，確定夾緊動(dòng)力源類型為手動(dòng)夾緊，夾緊裝置為壓板，壓緊力來源為螺旋力。夾具的具體結(jié)構(gòu)與參數(shù)見夾具裝配圖和零件圖。工件夾緊方式的確定從夾緊動(dòng)力源選擇：手動(dòng)夾緊確定主夾緊機(jī)構(gòu)： 螺栓壓板4.5零件的車床夾具的加工誤差分析工件在車床夾具上加工時(shí)，加工誤差的大小受工件在夾具上的定位誤差、夾具誤差、夾具在主軸上的安裝誤差和加工方法誤差的影響。如夾具圖所示，在夾具上加工時(shí)，尺寸的加工誤差的影響因素如下所述：2. 確定圓柱銷的尺寸及公差圓柱銷直徑的基本尺寸d1工件孔1的最小極限尺寸=10mm圓柱銷按g6制造（T=0.011mm）即=mm按h6級(jí)確定公差：=5. 計(jì)算定位誤差目的是分析定位方案的可行性 因?yàn)槎ㄎ环较蚺c加工尺寸方向垂直，且被加工表面無尺寸公差要求，為次要加工表面，只要保證粗糙度為Ra12.5，故只需進(jìn)行轉(zhuǎn)角誤差計(jì)算即可。=轉(zhuǎn)角誤差很小，符合定位要求，可以使用。定位方案設(shè)計(jì)如圖所示：4.6 確定夾具體結(jié)構(gòu)尺寸和總體結(jié)構(gòu)夾具體設(shè)計(jì)的基本要求（1）應(yīng)有適當(dāng)?shù)木群统叽绶€(wěn)定性夾具體上的重要表面，如安裝定位元件的表面、安裝對(duì)刀塊或?qū)蛟谋砻嬉约皧A具體的安裝基面，應(yīng)有適當(dāng)?shù)某叽缇群托螤罹龋鼈冎g應(yīng)有適當(dāng)?shù)奈恢镁?。為使夾具體的尺寸保持穩(wěn)定，鑄造夾具體要進(jìn)行時(shí)效處理，焊接和鍛造夾具體要進(jìn)行退火處理。（2）應(yīng)有足夠的強(qiáng)度和剛度 為了保證在加工過程中不因夾緊力、切削力等外力的作用而產(chǎn)生不允許的變形和振動(dòng)，夾具體應(yīng)有足夠的壁厚，剛性不足處可適當(dāng)增設(shè)加強(qiáng)筋。（3）應(yīng)有良好的結(jié)構(gòu)工藝性和使用性夾具體一般外形尺寸較大，結(jié)構(gòu)比較復(fù)雜，而且各表面間的相互位置精度要求高，因此應(yīng)特別注意其結(jié)構(gòu)工藝性，應(yīng)做到裝卸工件方便，夾具維修方便。在滿足剛度和強(qiáng)度的前提下，應(yīng)盡量能減輕重量，縮小體積，力求簡單。（4）應(yīng)便于排除切屑在機(jī)械加工過程中，切屑會(huì)不斷地積聚在夾具體周圍，如不及時(shí)排除，切削熱量的積聚會(huì)破壞夾具的定位精度，切屑的拋甩可能纏繞定位元件，也會(huì)破壞定位精度，甚至發(fā)生安全事故。因此，對(duì)于加工過程中切屑產(chǎn)生不多的情況，可適當(dāng)加大定位元件工作表面與夾具體之間的距離以增大容屑空間：對(duì)于加工過程中切削產(chǎn)生較多的情況，一般應(yīng)在夾具體上設(shè)置排屑槽。（5）在機(jī)床上的安裝應(yīng)穩(wěn)定可靠夾具在機(jī)床上的安裝都是通過夾具體上的安裝基面與機(jī)床上的相應(yīng)表面的接觸或配合實(shí)現(xiàn)的。當(dāng)夾具在機(jī)床工作臺(tái)上安裝時(shí)，夾具的重心應(yīng)盡量低，支承面積應(yīng)足夠大，安裝基面應(yīng)有較高的配合精度，保證安裝穩(wěn)定可靠。夾具底部一般應(yīng)中空，大型夾具還應(yīng)設(shè)置吊環(huán)或起重孔。確定夾具體的結(jié)構(gòu)尺寸，然后繪制夾具總圖。詳見繪制的夾具裝配圖。4.7 零件的車床專用夾具簡單使用說明（1）夾具的總體結(jié)構(gòu)應(yīng)力力求緊湊、輕便，懸臂尺寸要短，重心盡可能靠近主軸。（2）當(dāng)工件和夾具上個(gè)元件相對(duì)機(jī)床主軸的旋轉(zhuǎn)軸線不平衡時(shí)，將產(chǎn)生較大的離心力和振動(dòng)，影響工件的加工質(zhì)量、刀具的壽命、機(jī)床的精度和安全生產(chǎn)，特別是在轉(zhuǎn)速較高的情況下影響更大。因此，對(duì)于重量不對(duì)稱的夾具，要有平衡要求。平衡的方法有兩種：設(shè)置平衡塊或加工減重孔。在工廠實(shí)際生產(chǎn)中，常用適配的方法進(jìn)行夾具的平衡工作。（3）為了保證安全，夾具上各種元件一般不超過夾具的圓形輪廓之外。因此，還應(yīng)該注意防止切削和冷卻液的飛濺問題，必要時(shí)應(yīng)該加防護(hù)罩。總結(jié)本次畢業(yè)設(shè)計(jì)是在進(jìn)行畢業(yè)設(shè)計(jì)之前對(duì)所學(xué)各課程的一次深入的綜合性復(fù)習(xí)，是一次對(duì)我們所學(xué)的專業(yè)基礎(chǔ)知識(shí)的掌握情況的重要考察和檢驗(yàn)，更是培養(yǎng)我們理論聯(lián)系實(shí)際，分析并解決問題能力的重要內(nèi)容和階段。使我更好的掌握了CAD和PROE制圖軟件。這次畢業(yè)設(shè)計(jì)，其設(shè)計(jì)圖主要用CAD制圖軟件完成。自我感覺尚有很多不足和錯(cuò)誤，首先，在設(shè)計(jì)夾具裝配件時(shí)過于匆忙，裝配支架時(shí)放在了左手邊，不符合工人正常勞作習(xí)慣；其次是畢業(yè)設(shè)計(jì)前準(zhǔn)備工作沒做好，在圖書館很多資料和文獻(xiàn)都沒能借到（早已借空了），在借閱同學(xué)的相關(guān)資料時(shí)沒有時(shí)間認(rèn)真琢磨和分析相關(guān)信息和數(shù)據(jù)；最后就是畢業(yè)設(shè)計(jì)說明書的編寫過于匆忙，時(shí)間很緊，很多文字和標(biāo)準(zhǔn)，公式，數(shù)據(jù)，計(jì)算上的錯(cuò)誤沒有時(shí)間一一改正（確實(shí)，在打這篇文稿，發(fā)現(xiàn)了很多錯(cuò)誤和缺憾）。畢業(yè)設(shè)計(jì)，是一個(gè)系統(tǒng)性、知識(shí)點(diǎn)廣泛的學(xué)習(xí)過程。通過這樣一個(gè)系統(tǒng)性的學(xué)習(xí)和結(jié)合，使自己把學(xué)過的知識(shí)聯(lián)系起來，運(yùn)用到各個(gè)方面上去。同時(shí)，廣泛地運(yùn)用設(shè)計(jì)手冊(cè)及各種參考資料，學(xué)會(huì)了在實(shí)際中運(yùn)用工具書，和獨(dú)立完成每一步查找工作；整個(gè)零件的加工過程是和其他同學(xué)分工完成的，集中體現(xiàn)了團(tuán)隊(duì)精神，合作分工能很好的提高辦事效率！在這次設(shè)計(jì)中培養(yǎng)了我獨(dú)立分工合作的能力！為以后出身社會(huì)的工作打下基礎(chǔ)！參考文獻(xiàn)1、徐洪本 機(jī)床夾具設(shè)計(jì)手冊(cè)遼寧科技大學(xué)出版社2004.32、鄧文英等金屬工藝學(xué)高等教育出版社2008.43、付風(fēng)嵐等公差與檢測(cè)技術(shù)科學(xué)出版社2006.94、王先逵等機(jī)械加工工藝手冊(cè)機(jī)械工業(yè)出版社2007.95、陳宏鈞金屬切削速算手冊(cè)機(jī)械工業(yè)出版社2007.9Robotics and Computer-Integrated Manufacturing 21 (2005) 368378Locating completeness evaluation and revision in fixture planH. Song?, Y. RongCAM Lab, Department of Mechanical Engineering, Worcester Polytechnic Institute, 100 Institute Rd, Worcester, MA 01609, USAReceived 14 September 2004; received in revised form 9 November 2004; accepted 10 November 2004AbstractGeometry constraint is one of the most important considerations in fixture design. Analytical formulation of deterministiclocation has been well developed. However, how to analyze and revise a non-deterministic locating scheme during the process ofactual fixture design practice has not been thoroughly studied. In this paper, a methodology to characterize fixturing systemsgeometry constraint status with focus on under-constraint is proposed. An under-constraint status, if it exists, can be recognizedwith given locating scheme. All un-constrained motions of a workpiece in an under-constraint status can be automatically identified.This assists the designer to improve deficit locating scheme and provides guidelines for revision to eventually achieve deterministiclocating.r 2005 Elsevier Ltd. All rights reserved.Keywords: Fixture design; Geometry constraint; Deterministic locating; Under-constrained; Over-constrained1. IntroductionA fixture is a mechanism used in manufacturing operations to hold a workpiece firmly in position. Being a crucialstep in process planning for machining parts, fixture design needs to ensure the positional accuracy and dimensionalaccuracy of a workpiece. In general, 3-2-1 principle is the most widely used guiding principle for developing a locationscheme. V-block and pin-hole locating principles are also commonly used.A location scheme for a machining fixture must satisfy a number of requirements. The most basic requirement is thatit must provide deterministic location for the workpiece 1. This notion states that a locator scheme producesdeterministic location when the workpiece cannot move without losing contact with at least one locator. This has beenone of the most fundamental guidelines for fixture design and studied by many researchers. Concerning geometryconstraint status, a workpiece under any locating scheme falls into one of the following three categories:1. Well-constrained (deterministic): The workpiece is mated at a unique position when six locators are made to contactthe workpiece surface.2. Under-constrained: The six degrees of freedom of workpiece are not fully constrained.3. Over-constrained: The six degrees of freedom of workpiece are constrained by more than six locators.In 1985, Asada and By 1 proposed full rank Jacobian matrix of constraint equations as a criterion and formed thebasis of analytical investigations for deterministic locating that followed. Chou et al. 2 formulated the deterministiclocating problem using screw theory in 1989. It is concluded that the locating wrenches matrix needs to be full rank toachieve deterministic location. This method has been adopted by numerous studies as well. Wang et al. 3 consideredARTICLE IN PRESS front matter r 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.rcim.2004.11.012?Corresponding author. Tel.: +15088316092; fax: +15088316412.E-mail address: hsongwpi.edu (H. Song).locatorworkpiece contact area effects instead of applying point contact. They introduced a contact matrix andpointed out that two contact bodies should not have equal but opposite curvature at contacting point. Carlson 4suggested that a linear approximation may not be sufficient for some applications such as non-prismatic surfaces ornon-small relative errors. He proposed a second-order Taylor expansion which also takes locator error interaction intoaccount. Marin and Ferreira 5 applied Chous formulation on 3-2-1 location and formulated several easy-to-followplanning rules. Despite the numerous analytical studies on deterministic location, less attention was paid to analyzenon-deterministic location.In the Asada and Bys formulation, they assumed frictionless and point contact between fixturing elements andworkpiece. The desired location is q*, at which a workpiece is to be positioned and piecewisely differentiable surfacefunction is gi(as shown in Fig. 1).The surface function is defined as giq? 0: To be deterministic, there should be a unique solution for the followingequation set for all locators.giq 0;i 1;2;.;n,(1)where n is the number of locators and q x0;y0;z0;y0;f0;c0? represents the position and orientation of theworkpiece.Only considering the vicinity of desired location q?; where q q? Dq; Asada and By showed thatgiq giq? hiDq,(2)where hiis the Jacobian matrix of geometry functions, as shown by the matrix in Eq. (3). The deterministic locatingrequirement can be satisfied if the Jacobian matrix has full rank, which makes the Eq. (2) to have only one solutionq q?:rankqg1qx0qg1qy0qg1qz0qg1qy0qg1qf0qg1qc0:qgiqx0qgiqy0qgiqz0qgiqy0qgiqf0qgiqc0:qgnqx0qgnqy0qgnqz0qgnqy0qgnqf0qgnqc026666666664377777777758:9=; 6.(3)Upon given a 3-2-1 locating scheme, the rank of a Jacobian matrix for constraint equations tells the constraint statusas shown in Table 1. If the rank is less than six, the workpiece is under-constrained, i.e., there exists at least one freemotion of the workpiece that is not constrained by locators. If the matrix has full rank but the locating scheme hasmore than six locators, the workpiece is over-constrained, which indicates there exists at least one locator such that itcan be removed without affecting the geometry constrain status of the workpiece.For locating a model other than 3-2-1, datum frame can be established to extract equivalent locating points. Hu 6has developed a systematic approach for this purpose. Hence, this criterion can be applied to all locating schemes.ARTICLE IN PRESSX Y Z O X Y Z O (x0,y0,z0) gi UCS WCS Workpiece Fig. 1. Fixturing system model.H. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378369Kang et al. 7 followed these methods and implemented them to develop a geometry constraint analysis module intheir automated computer-aided fixture design verification system. Their CAFDV system can calculate the Jacobianmatrix and its rank to determine locating completeness. It can also analyze the workpiece displacement and sensitivityto locating error.Xiong et al. 8 presented an approach to check the rank of locating matrix WL(see Appendix). They also intro-duced left/right generalized inverse of the locating matrix to analyze the geometric errors of workpiece. It hasbeen shown that the position and orientation errors DX of the workpiece and the position errors Dr of locators arerelated as follows:Well-constrained :DX WLDr,(4)Over-constrained :DX WTLWL?1WTLDr,(5)Under-constrained :DX WTLWLWTL?1Dr I6?6? WTLWLWTL?1WLl,(6)where l is an arbitrary vector.They further introduced several indexes derived from those matrixes to evaluate locator configurations, followed byoptimization through constrained nonlinear programming. Their analytical study, however, does not concern therevision of non-deterministic locating. Currently, there is no systematic study on how to deal with a fixture design thatfailed to provide deterministic location.2. Locating completeness evaluationIf deterministic location is not achieved by designed fixturing system, it is as important for designers to knowwhat the constraint status is and how to improve the design. If the fixturing system is over-constrained, informa-tion about the unnecessary locators is desired. While under-constrained occurs, the knowledge about all the un-constrained motions of a workpiece may guide designers to select additional locators and/or revise the locatingscheme more efficiently. A general strategy to characterize geometry constraint status of a locating scheme is describedin Fig. 2.In this paper, the rank of locating matrix is exerted to evaluate geometry constraint status (see Appendixfor derivation of locating matrix). The deterministic locating requires six locators that provide full rank locatingmatrix WL:As shown in Fig. 3, for given locator number n; locating normal vector ai;bi;ci? and locating position xi;yi;zi? foreach locator, i 1;2;.;n; the n ? 6 locating matrix can be determined as follows:WLa1b1c1c1y1? b1z1a1z1? c1x1b1x1? a1y1:aibiciciyi? biziaizi? cixibixi? aiyi:anbncncnyn? bnznanzn? cnxnbnxn? anyn2666666437777775.(7)When rankWL 6 and n 6; the workpiece is well-constrained.When rankWL 6 and n46; the workpiece is over-constrained. This means there are n ? 6 unnecessary locatorsin the locating scheme. The workpiece will be well-constrained without the presence of those n ? 6 locators. Themathematical representation for this status is that there are n ? 6 row vectors in locating matrix that can be expressedas linear combinations of the other six row vectors. The locators corresponding to that six row vectors consist oneARTICLE IN PRESSTable 1RankNumber of locatorsStatuso 6Under-constrained 6 6Well-constrained 646Over-constrainedH. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378370locating scheme that provides deterministic location. The developed algorithm uses the following approach todetermine the unnecessary locators:1. Find all the combination of n ? 6 locators.2. For each combination, remove that n ? 6 locators from locating scheme.3. Recalculate the rank of locating matrix for the left six locators.4. If the rank remains unchanged, the removed n ? 6 locators are responsible for over-constrained status.This method may yield multi-solutions and require designer to determine which set of unnecessary locators shouldbe removed for the best locating performance.When rankWLo6; the workpiece is under-constrained.3. Algorithm development and implementationThe algorithm to be developed here will dedicate to provide information on un-constrained motions of theworkpiece in under-constrained status. Suppose there are n locators, the relationship between a workpieces position/ARTICLE IN PRESSFig. 2. Geometry constraint status characterization.X Z Y (a1,b1,c1) 2,b2,c2) (x1,y1,z1) (x2,y2,z2) (ai,bi,ci) (xi,yi,zi) (aFig. 3. A simplified locating scheme.H. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378371orientation errors and locator errors can be expressed as follows:DX DxDyDzaxayaz2666666666437777777775w11:w1i:w1nw21:w2i:w2nw31:w3i:w3nw41:w4i:w4nw51:w5i:w5nw61:w6i:w6n2666666666437777777775?Dr1:Dri:Drn2666666437777775,(8)where Dx;Dy;Dz;ax;ay;azare displacement along x, y, z axis and rotation about x, y, z axis, respectively. Driisgeometric error of the ith locator. wijis defined by right generalized inverse of the locating matrix Wr WTLWLWTL?15.To identify all the un-constrained motions of the workpiece, V dxi;dyi;dzi;daxi;dayi;dazi? is introduced such thatV DX 0.(9)Since rankDXo6; there must exist non-zero V that satisfies Eq. (9). Each non-zero solution of V represents an un-constrained motion. Each term of V represents a component of that motion. For example, 0;0;0;3;0;0? says that therotation about x-axis is not constrained. 0;1;1;0;0;0? means that the workpiece can move along the direction given byvector 0;1;1?: There could be infinite solutions. The solution space, however, can be constructed by 6 ? rankWLbasic solutions. Following analysis is dedicated to find out the basic solutions.From Eqs. (8) and (9)VX dxDx dyDy dzDz daxDax dayDay dazDaz dxXni1w1iDri dyXni1w2iDri dzXni1w3iDri daxXni1w4iDri dayXni1w5iDri dazXni1w6iDriXni1Vw1i;w2i;w3i;w4i;w5i;w6i?TDri 0.10Eq. (10) holds for 8Driif and only if Eq. (11) is true for 8i1pipn:Vw1i;w2i;w3i;w4i;w5i;w6i?T 0.(11)Eq. (11) illustrates the dependency relationships among row vectors of Wr: In special cases, say, all w1jequal to zero,V has an obvious solution 1, 0, 0, 0, 0, 0, indicating displacement along the x-axis is not constrained. This is easy tounderstand because Dx 0 in this case, implying that the corresponding position error of the workpiece is notdependent of any locator errors. Hence, the associated motion is not constrained by locators. Moreover, a combinedmotion is not constrained if one of the elements in DX can be expressed as linear combination of other elements. Forinstance, 9w1ja0;w2ja0; w1j ?w2jfor 8j: In this scenario, the workpiece cannot move along x- or y-axis. However, itcan move along the diagonal line between x- and y-axis defined by vector 1, 1, 0.To find solutions for general cases, the following strategy was developed:1. Eliminate dependent row(s) from locating matrix. Let r rank WL; n number of locator. If ron; create a vectorin n ? r dimension space U u1:uj:un?rhi1pjpn ? r; 1pujpn: Select ujin the way that rankWL r still holds after setting all the terms of all the ujth row(s) equal to zero. Set r ? 6 modified locating matrixWLMa1b1c1c1y1? b1z1a1z1? c1x1b1x1? a1y1:aibiciciyi? biziaizi? cixibixi? aiyi:anbncncnyn? bnznanzn? cnxnbnxn? anyn2666666437777775r?6,where i 1;2;:;niauj:ARTICLE IN PRESSH. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 3683783722. Compute the 6 ? n right generalized inverse of the modified locating matrixWr WTLMWLMWTLM?1w11:w1i:w1rw21:w2i:w2rw31:w3i:w3rw41:w4i:w4rw51:w5i:w5rw61:w6i:w6r26666666664377777777756?r3. Trim Wrdown to a r ? rfull rank matrix Wrm: r rankWLo6: Construct a 6 ? r dimension vector Q q1:qj:q6?rhi1pjp6 ? r; 1pqjpn: Select qjin the way that rankWr r still holds after setting all theterms of all the qjth row(s) equal to zero. Set r ? r modified inverse matrixWrmw11:w1i:w1r:wl1:wli:wlr:w61:w6i:w6r26666664377777756?6,where l 1;2;:;6 laqj:4. Normalize the free motion space. Suppose V V1;V2;V3;V4;V5;V6? is one of the basic solutions of Eq. (10) withall six terms undetermined. Select a term qkfrom vector Q1pkp6 ? r: SetVqk ?1;Vqj 0 j 1;2;:;6 ? r;jak;(5. Calculated undetermined terms of V: V is also a solution of Eq. (11). The r undetermined terms can be found asfollows.v1:vs:v62666666437777775wqk1:wqki:wqkr2666666437777775?w11:w1i:w1r:wl1:wli:wlr:w61:w6i:w6r2666666437777775?1,where s 1;2;:;6saqj;saqk;l 1;2;:;6 laqj:6. Repeat step 4 (select another term from Q) and step 5 until all 6 ? r basic solutions have been determined.Based on this algorithm, a C+ program was developed to identify the under-constrained status and un-constrained motions.Example 1. In a surface grinding operation, a workpiece is located on a fixture system as shown in Fig. 4. The normalvector and position of each locator are as follows:L1:0, 0, 10, 1, 3, 00,L2:0, 0, 10, 3, 3, 00,L3:0, 0, 10, 2, 1, 00,L4:0, 1, 00, 3, 0, 20,L5:0, 1, 00, 1, 0, 20.Consequently, the locating matrix is determined.WL0013?100013?300011?20010?203010?2012666666437777775.ARTICLE IN PRESSH. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378373This locating system provides under-constrained positioning since rankWL 5o6: The program then calculatesthe right generalized inverse of the locating matrix.Wr000000:50:5?1?0:51:50:75?1:251:5000:250:25?0:5000:5?0:50000000:5?0:526666666643777777775.The first row is recognized as a dependent row because removal of this row does not affect rank of the matrix. Theother five rows are independent rows. A linear combination of the independent rows is found according therequirement in step 5 of the procedure for under-constrained status. The solution for this special case is obvious that allthe coefficients are zero. Hence, the un-constrained motion of workpiece can be determined as V ?1; 0; 0; 0; 0; 0?:This indicates that the workpiece can move along x direction. Based on this result, an additional locator should beemployed to constraint displacement of workpiece along x-axis.Example 2. Fig. 5 shows a knuckle with 3-2-1 locating system. The normal vector and position of each locator in thisinitial design are as follows:L1:0, 1, 00, 896, ?877, ?5150,L2:0, 1, 00, 1060, ?875, ?3780,L3:0, 1, 00, 1010, ?959, ?6120,L4:0.9955, ?0.0349, 0.0880, 977, ?902, ?6240,L5:0.9955, ?0.0349, 0.0880, 977, ?866, ?6240,L6:0.088, 0.017, ?0.9960, 1034, ?864, ?3590.The locating matrix of this configuration isWL010515:000:8960010378:001:0600010612:001:01000:9955?0:03490:0880?101:2445?707:26640:86380:9955?0:03490:0880?98:0728?707:26640:82800:08800:0170?0:9960866:6257998:24660:093626666666643777777775,rankWL 5o6 reveals that the workpiece is under-constrained. It is found that one of the first five rows can beremoved without varying the rank of locating matrix. Suppose the first row, i.e., locator L1is removed from WL; theARTICLE IN PRESSXZYL3L4L5L2L1Fig. 4. Under-constrained locating scheme.H. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378374modified locating matrix turns intoWLM010378:001:0600010612:001:01000:9955?0:03490:0880?101:2445?707:26640:86380:9955?0:03490:0880?98:0728?707:26640:82800:08800:0170?0:996866:6257998:24660:09362666666437777775.The right generalized inverse of the modified locating matrix isWr1:8768?1:8607?20:666521:37160:49953:0551?2:0551?32:444832:44480?1:09561:086212:0648?12:4764?0:2916?0:00440:00440:0061?0:006100:0025?0:00250:0065?0:00690:0007?0:00040:00040:0284?0:0284026666666643777777775.The program checked the dependent row and found every row is dependent on other five rows. Without losinggenerality, the first row is regarded as dependent row. The 5 ? 5 modified inverse matrix isWrm3:0551?2:0551?32:444832:44480?1:09561:086212:0648?12:4764?0:2916?0:00440:00440:0061?0:006100:0025?0:00250:0065?0:00690:0007?0:00040:00040:0284?0:028402666666437777775.The undetermined solution is V ?1; v2; v3; v4; v5; v6?:To calculate the five undetermined terms of V according to step 5,1:8768?1:8607?20:666521:37160:499526666666643777777775T?3:0551?2:0551?32:444832:44480?1:09561:086212:0648?12:4764?0:2916?0:00440:00440:0061?0:006100:0025?0:00250:0065?0:00690:0007?0:00040:00040:0284?0:0284026666666643777777775?1 0; ?1:713; ?0:0432; ?0:0706; 0:04?.Substituting this result into the undetermined solution yields V ?1;0; ?1:713; ?0:0432; ?0:0706; 0:04?ARTICLE IN PRESSFig. 5. Knuckle 610 (modified from real design).H. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378375This vector represents a free motion defined by the combination of a displacement along ?1, 0, ?1.713 directioncombined and a rotation about ?0.0432, ?0.0706, 0.04. To revise this locating configuration, another locator shouldbe added to constrain this free motion of the workpiece, assuming locator L1was removed in step 1. The program canalso calculate the free motions of the workpiece if a locator other than L1was removed in step 1. This provides morerevision options for designer.4. SummaryDeterministic location is an important requirement for fixture locating scheme design. Analytical criterion fordeterministic status has been well established. To further study non-deterministic status, an algorithm for checking thegeometry constraint status has been developed. This algorithm can identify an under-constrained status and indicatethe un-constrained motions of workpiece. It can also recognize an over-constrained status and unnecessary locators.The output information can assist designer to analyze and improve an existing locating scheme.Appendix. Locating matrixConsider a general workpiece as shown in Fig. 6. Choose reference frame fWg fixed to the workpiece. Let fGg andfLig be the global frame and the ith locator frame fixed relative to it. We haveFiXw;Hw;rwi fiXli;Hli;rli,(12)where Xw2 3?1and Hw2 3?1(Xli2 3?1and Hli2 3?1) are the position and orientation of the workpiece(the ith locator) in the global frame fGg; rwi2 3?1(rli2 3?1) is the position of the ith contact point between theworkpiece and the ith locator in the workpiece frame fWg (the ith locator frame fLig).Assume that DXw2 3?1(DHw2 3?1) and Drwi2 3?1are the deviations of the position Xw2 3?1(orientationHw2 3?1) of the workpiece and the position of the ith contact point rwi2 3?1; respectively. Then we have the actualcontact on the wor