等臂杠桿的銑床夾具設(shè)計(jì)
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機(jī)械加工工序卡片產(chǎn)品型號(hào)零件圖號(hào)產(chǎn)品名稱杠桿零件名稱杠桿共6頁(yè)第1頁(yè)車間工序號(hào)工序名稱材 料 牌 號(hào)金工10銑削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198837711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)立式銑床X50321夾具編號(hào)夾具名稱切削液銑面夾具工位器具編號(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)r/minm/minmm/minmm機(jī)動(dòng)輔助1粗銑40上端面和寬度為30的平臺(tái)面高速鋼端銑刀,游標(biāo)卡尺16025.12144210.642粗銑30凸臺(tái)面高速鋼端銑刀,游標(biāo)卡尺16025.12144210.33 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)械加工工序卡片產(chǎn)品型號(hào)零件圖號(hào)產(chǎn)品名稱杠桿零件名稱杠桿共6頁(yè)第2頁(yè)車間工序號(hào)工序名稱材 料 牌 號(hào)金工20銑削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198837711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)立式銑床X50231夾具編號(hào)夾具名稱切削液銑面夾具工位器具編號(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)r/minm/minmm/minmm機(jī)動(dòng)輔助1粗銑40下端面高速鋼端銑刀,游標(biāo)卡尺16025.12144210.42粗銑30凸臺(tái)面高速鋼端銑刀,游標(biāo)卡尺16025.12144210.33 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)械加工工序卡片產(chǎn)品型號(hào)零件圖號(hào)產(chǎn)品名稱杠桿零件名稱杠桿共6頁(yè)第3頁(yè)車間工序號(hào)工序名稱材 料 牌 號(hào)金工30銑削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198 X 83 X 7711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)立式銑床X5023夾具編號(hào)夾具名稱切削液銑面夾具工位器具編號(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)r/minm/minmm/minmm機(jī)動(dòng)輔助1精銑40下端面高速鋼端銑刀,游標(biāo)卡尺16020100110.6 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)械加工工序卡片產(chǎn)品型號(hào)零件圖號(hào)產(chǎn)品名稱杠桿零件名稱杠桿共6頁(yè)第4頁(yè)車間工序號(hào)工序名稱材 料 牌 號(hào)金工40鉆孔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198 X 83 X 7711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)立式鉆床Z5163A1夾具編號(hào)夾具名稱切削液鉆 夾具工位器具編號(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)r/minm/minmm/rmm機(jī)動(dòng)輔助1鉆23的孔錐柄長(zhǎng)麻花鉆19514.080.4311510.782鉆9.8的孔錐柄加長(zhǎng)麻花鉆96029.540.174910.203鉆2X7.8的孔錐柄麻花鉆96023.520.173910.26 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)械加工工序卡片產(chǎn)品型號(hào)零件圖號(hào)產(chǎn)品名稱杠桿零件名稱杠桿共6頁(yè)第5頁(yè)車間工序號(hào)工序名稱材 料 牌 號(hào)金工50孔加工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198 X 83 X 7711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)立式鉆床Z5163A1夾具編號(hào)夾具名稱切削液鉆 夾具工位器具編號(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)r/minm/minmm/rmm機(jī)動(dòng)輔助1擴(kuò)23孔到24.8錐柄擴(kuò)孔鉆685.290.720911.332粗鉸9.8孔到9.96高速鋼機(jī)用鉸刀1956.11.300810.123粗鉸2X7.8孔到2X7.96高速鋼機(jī)用鉸刀1954.871.300810.16 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)械加工工序卡片產(chǎn)品型號(hào)零件圖號(hào)產(chǎn)品名稱杠桿零件名稱杠桿共6頁(yè)第6頁(yè)車間工序號(hào)工序名稱材 料 牌 號(hào)金工60鉸孔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198 X 83 X 7711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)立式鉆床Z5163A夾具編號(hào)夾具名稱切削液鉆 夾具工位器具編號(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)r/minm/minmm/rmm機(jī)動(dòng)輔助1鉸孔24.8到25高速鋼機(jī)用鉸刀685.341.220.110.782精鉸9.96到10高速鋼機(jī)用鉸刀1956.10.80.0210.32精鉸2X7.96到2X8高速鋼機(jī)用鉸刀1954.90.80.0210.26 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(guò)程卡片產(chǎn)品型號(hào)零件圖號(hào)產(chǎn)品名稱杠桿零件名稱杠桿共頁(yè)第頁(yè)材 料 牌 號(hào)HT200毛 坯 種 類鑄件毛坯外形尺寸1988377每毛坯件數(shù)1每 臺(tái) 件 數(shù)1備 注 工 序 號(hào) 工 名 序 稱 工 序 內(nèi) 容 車 間 工 段設(shè) 備工 藝 裝 備 工 時(shí) 夾具刀具量具 準(zhǔn)終 單件鑄造鑄時(shí)效熱涂底漆表10銑粗銑40上端面和寬度為30的平臺(tái)面和30凸臺(tái)面金工X5032專用銑夾具鑲齒套式面銑刀游標(biāo)卡尺20銑粗銑40下端面和30凸臺(tái)面金工X5032專用銑夾具鑲齒套式面銑刀游標(biāo)卡尺30銑精銑40下端面和30凸臺(tái)面金工X5032專用銑夾具鑲齒套式面銑刀游標(biāo)卡尺40鉆鉆23孔、9.8孔、2X7.8孔金工Z5163A專用鉆夾具麻花鉆游標(biāo)卡尺50擴(kuò)擴(kuò)23孔到24.7金工Z5163A專用鉆夾具錐柄擴(kuò)孔鉆游標(biāo)卡尺60鉸粗鉸9.8到9.96、7.8到7.96金工Z5163A專用鉆夾具高速鋼機(jī)用鉸刀游標(biāo)卡尺70鉸鉸9.96到25(H9)孔金工Z5163A專用鉆夾具高速鋼機(jī)用鉸刀游標(biāo)卡尺80鉸精鉸9.96到10(H7)、7.96到8(H7)金工Z5163A專用鉆夾具高速鋼機(jī)用鉸刀游標(biāo)卡尺90檢查、入庫(kù) 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 期畢業(yè)設(shè)計(jì)(論文)開題報(bào)告學(xué)生姓名系部機(jī)電工程系專業(yè)、班級(jí)指導(dǎo)教師姓名職稱從事專業(yè)機(jī)械設(shè)計(jì)是否外聘是否題目名稱等臂杠桿的銑床夾具設(shè)計(jì)一、 課題研究現(xiàn)狀,選題的目的、依據(jù)和意義研究現(xiàn)狀:在機(jī)械領(lǐng)域中,車床是應(yīng)用最為廣泛、使用最為頻繁的一種機(jī)床,它的加工精度就極其的重要,工件能否達(dá)到加工要求就取決于車床本身的精度,而杠桿是把旋轉(zhuǎn)運(yùn)動(dòng)及扭矩通過(guò)等臂杠桿端部的夾具傳遞給工件和刀具,因此要求有很高的強(qiáng)度及回轉(zhuǎn)精度。選題目的、依據(jù)和意義:本次設(shè)計(jì)選用此課題,主要是對(duì)等臂杠桿與夾具的設(shè)計(jì)過(guò)程,是對(duì)大學(xué)四年所學(xué)知識(shí)的檢測(cè)、總結(jié)與應(yīng)用。這次的設(shè)計(jì)過(guò)程是提高機(jī)械設(shè)計(jì)與創(chuàng)新能力的體現(xiàn),同時(shí)是對(duì)所學(xué)習(xí)過(guò)的理論知識(shí)與設(shè)計(jì)過(guò)程的結(jié)合。技術(shù)是產(chǎn)品形態(tài)發(fā)展的先導(dǎo),新材料,新工藝的出現(xiàn),必然給產(chǎn)品帶來(lái)新的結(jié)構(gòu),新的形態(tài)和新的造型風(fēng)格。材料,加工工藝,結(jié)構(gòu),產(chǎn)品形象有機(jī)地聯(lián)系在一起的,某個(gè)環(huán)節(jié)的變革,便會(huì)引起整個(gè)機(jī)體的變化。工業(yè)的迅速發(fā)展,對(duì)產(chǎn)品的品種和生產(chǎn)效率提出了越來(lái)越高的要求,使多品種,對(duì)中小批生產(chǎn)為機(jī)械生產(chǎn)的主流,為了適應(yīng)機(jī)械生產(chǎn)的這種發(fā)展趨勢(shì),必然對(duì)機(jī)床夾具提出更高的要求。二、 設(shè)計(jì)(論文)的基本內(nèi)容,擬解決的主要問(wèn)題基本內(nèi)容:等臂杠桿加工工藝過(guò)程,加工過(guò)程中的具體用量的計(jì)算,加工中鉆床.磨床夾具的設(shè)計(jì)。擬解決的主要問(wèn)題:加工過(guò)程中加工余量和切削用量的計(jì)算,夾具裝夾的計(jì)算,零件的選擇。三、 技術(shù)路線(研究方法)1.查閱相關(guān)文獻(xiàn)資料了解課題。2.對(duì)比分析現(xiàn)有幾個(gè)設(shè)計(jì)方案,選擇最適合本次設(shè)計(jì)的方案。3.計(jì)算各層臺(tái)體部分的質(zhì)量和轉(zhuǎn)動(dòng)慣量,選擇驅(qū)動(dòng)裝置和驅(qū)動(dòng)方式。4.根據(jù)選擇的設(shè)計(jì)方案,進(jìn)行總體設(shè)計(jì)。5.完成設(shè)計(jì)圖紙和說(shuō)明書,準(zhǔn)備答辯。四、 進(jìn)度安排14 周調(diào)研收集資料,并查閱相關(guān)文獻(xiàn),確定設(shè)計(jì)方案; 58 周初步進(jìn)行總體設(shè)計(jì),確定各部分組成,繪制草圖; 910周各零部件的校核,CAD出圖; 1112周整理打印設(shè)計(jì)說(shuō)明書,并讓老師對(duì)圖紙和說(shuō)明書審查; 13周對(duì)圖紙和說(shuō)明書,做最后修改,準(zhǔn)備答辯。五、 參考文獻(xiàn)1王季琨 沈中偉 劉錫珍.機(jī)械制造設(shè)計(jì)工藝學(xué)M.天津大學(xué)出版社,19842倪森壽.機(jī)械制造工藝與裝備M.化學(xué)工業(yè)出版社,2002 3魏抗民 王曉宏.機(jī)械制造工藝裝備M.重慶大學(xué)出版社,19984梁炳文 .機(jī)械加工工藝與竅門M .機(jī)械工業(yè)出版社,20015王啟平.機(jī)械機(jī)造工藝學(xué)M.哈工大工業(yè)大學(xué)出版社,20006王光斗 王春福.機(jī)床夾具設(shè)計(jì)手冊(cè)S.燕山大學(xué) 洛陽(yáng)工學(xué)院,19997符煒.切削加工手冊(cè)S 湖南科學(xué)技術(shù)出版社,20018吳宗澤.機(jī)械零件設(shè)計(jì)手冊(cè)S.機(jī)械工業(yè)出版社,2004六、備注指導(dǎo)教師意見(jiàn):簽字: 年 月 日 等臂杠桿的銑床夾具設(shè)計(jì) 序言機(jī)械制造工藝學(xué)畢業(yè)設(shè)計(jì)是在學(xué)完了大學(xué)的全部基礎(chǔ)課、技術(shù)基礎(chǔ)課以及大部分專業(yè)課,并進(jìn)行了生產(chǎn)實(shí)習(xí)的基礎(chǔ)上進(jìn)行的一個(gè)教學(xué)環(huán)節(jié)。這是我們?cè)诋厴I(yè)設(shè)計(jì)之前對(duì)所學(xué)各畢業(yè)的一次深入的綜合性的總復(fù)習(xí),也是一次理論聯(lián)系世紀(jì)的訓(xùn)練。這次設(shè)計(jì)使我們能綜合運(yùn)用機(jī)械制造工藝學(xué)中的基本理論,并結(jié)合生產(chǎn)實(shí)習(xí)中學(xué)到的實(shí)踐知識(shí),獨(dú)立地分析和解決工藝問(wèn)題,初步具備了設(shè)計(jì)一個(gè)中等復(fù)雜零件(杠桿)的工藝規(guī)程的能力和運(yùn)用夾具設(shè)計(jì)的基本原理和方法。在完成夾具結(jié)構(gòu)設(shè)計(jì)的同時(shí),也是熟悉和運(yùn)用有關(guān)手冊(cè)、圖表等技術(shù)資料及編寫技術(shù)文件等基本技能的一次實(shí)踐機(jī)會(huì)。 就我個(gè)人而言,我希望能通過(guò)這次畢業(yè)設(shè)計(jì)對(duì)未來(lái)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(wèn)題、解決問(wèn)題的能力。為自己未來(lái)的職業(yè)生涯打下一個(gè)良好的基礎(chǔ)。目錄第1章 畢業(yè)設(shè)計(jì)序言 1.1 零件的分析 11.1.1 零件的作用 11.1.2 零件的工藝分析 31.2 工藝規(guī)程的設(shè)計(jì) 31.2.1 確定毛坯的制造形式 31.2.2 基準(zhǔn)的選擇 31.2.3 工件表面加工方法的選擇 41.3 確定工藝路線 41.3.1 加工余量及毛坯尺寸的確定 61.3.2 選擇加工設(shè)備及刀、量、夾具 71.4 加工工序設(shè)計(jì) 191.5 夾具的設(shè)計(jì) 101.5.1 定位方案的確定 101.5.2 選擇定位元件 111.5.3 計(jì)算夾緊力 111.5.4 定位誤差計(jì)算 12第2章 綜合訓(xùn)練2.1 夾具體三維造型實(shí)現(xiàn)方法的概述 132.2 夾具三維造型過(guò)程簡(jiǎn)述 14小結(jié) 22參考文獻(xiàn) 23 等臂杠桿的銑床夾具設(shè)計(jì)第1章 畢業(yè)設(shè)計(jì)1.1零件的分析 設(shè)計(jì)的具體要求包括: 1. 零件圖 1張 2. 毛坯圖 1張 3. 機(jī)械加工工藝過(guò)程卡片 1套 4機(jī)械加工工序卡片 1套 5夾具總裝圖 1張 6夾具三維造型圖 1張 7. 夾具體零件圖 1張 7畢業(yè)設(shè)計(jì)說(shuō)明書 1份 1.1.1 零件的作用 題目所給定的零件是銑床杠桿。它的主要的作用是用來(lái)支承、固要求零件的配合符合要求。 圖1-1為銑床杠桿的零件圖,1-2為三維造型圖。 圖1-1 杠桿的零件圖 圖1-2 杠桿的三維圖1.1.2 零件的工藝分析 杠桿的25(H9)孔的軸線和兩個(gè)端面垂直度的要求,28(H7)孔的軸線與25H9孔的軸線有平行度要求.現(xiàn)分述如下: 本夾具用于在立式鉆床上,加工8(H7)孔。工件以25(H9) 孔及端面和水平面底、30的凸臺(tái)分別在定位銷10、活動(dòng)V形塊上實(shí)現(xiàn)完全定位。鉆8(H7)mm孔時(shí)工件為懸臂,為防止工件加工時(shí)變形,采用了螺旋輔助支承7,當(dāng)輔助支承7與工件接觸后,用螺母2鎖緊。要加工的主要工序包括:粗精銑寬度為40mm的上下平臺(tái)、粗精銑30凸臺(tái)的上下表面、鉆25(H9)的小孔 、鉆28(H7)的小孔 、鉆10(H7)孔。加工要求有:40mm的平臺(tái)的表面粗糙度各為Ra6.3um(上平臺(tái))、Ra3.2(下平臺(tái))、25(H9)和8(H7)孔表面粗糙度都為Ra1.6um。28(H7)孔有平行度分別為0.1um(A)、0.15um(A)。10(H7)孔的平行度為0.1um(A)、10(H7)孔為Ra3.6um。杠桿有過(guò)渡圓角為R5,則其他的過(guò)渡圓角則為R3。其中主要的加工表面是孔8(H7),要用8(H7)鋼球檢查。1.2 工藝規(guī)程的設(shè)計(jì)1.2.1 確定毛坯的制造形式 零件的材料HT200??紤]到零件在工作中處于潤(rùn)滑狀態(tài),因此采用潤(rùn)滑效果較好的鑄鐵。由于零件年產(chǎn)量為5000件,達(dá)到大批量生產(chǎn)的水平,而且零件的輪廓尺寸不大,鑄造表面質(zhì)量的要求高,故可采用鑄造質(zhì)量穩(wěn)定的,適合大批生產(chǎn)的金屬模鑄造。又由于零件的對(duì)稱特性,故采取兩件鑄造在一起的方法,便于鑄造和加工工藝過(guò)程,而且還可以提高生產(chǎn)率,保證加工質(zhì)量。1.2.2 基準(zhǔn)的選擇(1)粗基準(zhǔn)的選擇。對(duì)于本零件而言,按照粗基準(zhǔn)的選擇原則,選擇本零件的加工表面就是寬度為40mm的肩面表面作為加工的粗基準(zhǔn),可用壓板對(duì)肩臺(tái)進(jìn)行加緊,利用一組V形塊支承40mm的外輪廓作主要定位,以消除z、z、y、y四個(gè)自由度。再以一面定位消除x、x兩個(gè)自由度,達(dá)到完全定位,就可加工25(H9)的孔。(2)精基準(zhǔn)的選擇。精基準(zhǔn)的選擇主要應(yīng)該考慮基準(zhǔn)重合的問(wèn)題,當(dāng)設(shè)計(jì)基準(zhǔn)與工序基準(zhǔn)不重合時(shí),應(yīng)該進(jìn)行尺寸換算。本工序中為了便于裝夾,采用25(H7)的孔作為精基準(zhǔn)。1.2.3 工件表面加工方法的選擇 本零件的加工表面有:粗精銑寬度為40mm的上下平臺(tái)、鉆10(H7)孔、鉆28+0.015的小孔 、粗精銑30凸臺(tái)的平臺(tái)。材料為HT200,加工方法選擇如下:1、 40mm圓柱的上平臺(tái):公差等級(jí)為IT8IT10,表面粗糙度為Ra6.3,采用粗銑精銑的加工方法。2、 40mm圓柱的下平臺(tái):公差等級(jí)為IT8IT10,表面粗糙度為Ra3.2,采用采用粗銑精銑的加工方法。3、 30mm的凸臺(tái)上下表面:公差等級(jí)為IT13,表面粗糙度為Ra6.3,采用粗銑精銑的加工方法。4、 鉆25(H9)內(nèi)孔:公差等級(jí)為IT6IT8,表面粗糙度為Ra1.6,采用鉆孔擴(kuò)孔鉆鉆孔精鉸的加工方法,并倒145內(nèi)角。5、 鉆8(H7)內(nèi)孔:公差等級(jí)為IT6IT8,表面粗糙度為Ra1.6,采用鉆孔粗鉸精鉸的加工方法。6、 鉆10(H7)內(nèi)孔:公差等級(jí)為IT7IT8,表面粗糙度為Ra3.2,平行度為0.1m(A),采用鉆孔粗鉸精鉸的加工方法。1.3 確定工藝路線 由于該零件生產(chǎn)類型為大批量生產(chǎn),所以應(yīng)盡量使工序集中來(lái)提高生產(chǎn)率,除此之外,還應(yīng)降低生產(chǎn)成本。1、 工藝路線方案一:鑄造時(shí)效涂底漆 工序:粗精銑寬度為40mm的上下平臺(tái)和寬度為30mm的平臺(tái) 工序:鉆孔25(H9)使尺寸達(dá)到23mm 工序:擴(kuò)孔鉆鉆孔25(H9)使尺寸達(dá)到24.8mm 工序:鉸孔25(H9)使尺寸達(dá)到25(H9) 工序:鉆、粗、精鉸28(H7)小孔使尺寸達(dá)到8(H7) 工序 :鉆10(H7)的內(nèi)孔使尺寸達(dá)到9.8mm。 工序:粗鉸10(H7)內(nèi)孔使尺寸達(dá)到9.96mm。 工序:精鉸10(H7)內(nèi)孔使尺寸達(dá)到10(H7)mm。 工序:檢驗(yàn)入庫(kù)。2、工藝路線方案二:鑄造時(shí)效涂底漆 工序:粗精銑寬度為40mm的上下平臺(tái)和寬度為30mm的平臺(tái)。 工序:鉆孔25(H9)使尺寸達(dá)到23mm。 工序:鉆28(H7)的小孔使尺寸達(dá)到8(H7) 工序:擴(kuò)孔鉆鉆孔25(H9)使尺寸達(dá)到24.8mm 工序:鉸孔25(H9)使尺寸達(dá)到25(H9) 工序:鉆10(H7)的內(nèi)孔使尺寸達(dá)到9.8mm 工序 :粗鉸10(H7)內(nèi)孔使尺寸達(dá)到9.96mm 工序:精鉸10(H7)內(nèi)孔使尺寸達(dá)到10(H7)mm。 工序:粗鉸28(H7)小孔使尺寸達(dá)到7.96mm。 工序:精鉸28(H7)小孔使尺寸達(dá)到8(H7)。 工序:檢驗(yàn)入庫(kù)。3、工藝方案的比較和分析:上述兩種工藝方案的特點(diǎn)是:方案一是根據(jù)寬度為40mm的上下肩面作為粗基準(zhǔn),25(H9)孔作為精基準(zhǔn),所以就要加工25孔時(shí)期尺寸達(dá)到要求的尺寸,那樣就保證了28小孔的圓跳動(dòng)誤差精度等。而方案二則先粗加工孔25,而不進(jìn)一步加工就鉆8(H7),那樣就很難保證28的圓度跳動(dòng)誤差精度。所以決定選擇方案一作為加工工藝路線比較合理。具體工藝過(guò)程如下:1、工藝路線方案一:鑄造時(shí)效涂底漆 工序:粗精銑寬度為40mm的上下平臺(tái)和寬度為30mm的平臺(tái)(粗基準(zhǔn)的選擇如前所述) 工序:鉆孔25(H9)使尺寸達(dá)到23mm 工序:擴(kuò)孔鉆鉆孔25(H9)使尺寸達(dá)到24.8mm 工序:鉸孔25(H9)使尺寸達(dá)到25(H9) 工序:鉆、粗、精鉸28(H7)小孔使尺寸達(dá)到8(H7)(以25定位) 工序 :鉆10(H7)的內(nèi)孔使尺寸達(dá)到9.8mm 工序:粗鉸10(H7)內(nèi)孔使尺寸達(dá)到9.96mm 工序:精鉸10(H7)內(nèi)孔使尺寸達(dá)到10(H7)mm 工序:檢驗(yàn)入庫(kù)1.3.1 加工余量及毛坯尺寸的確定 根據(jù)工件的原始資料及加工工藝,分別確定各加工表面的加工余量及毛坯尺寸:查參考文獻(xiàn)(機(jī)械加工工藝簡(jiǎn)明手冊(cè))得: 各加工表面表面總余量加工表面基本尺寸加工余量等級(jí)加工余量數(shù)值(mm)說(shuō)明40mm的上下平臺(tái)寬度30mm的平臺(tái)4030GH43加工上下底面加工上表面30mm的凸臺(tái)上下面 30H3凸臺(tái)上下面10(H7)孔10 H3加工內(nèi)孔8(H7)孔 8 H3加工內(nèi)孔25(H9)孔25 G4加工內(nèi)孔又由參考文獻(xiàn)得出: 主要毛坯尺寸及公差主要尺寸零件尺寸總余量毛坯尺寸公差CT28(H7)之間的中心距離168168410(H7)孔尺寸 102.010 325(H9)孔尺寸253.02548(H7)孔尺寸82.08 3圖1-3 零件的毛坯圖1.3.2 選擇加工設(shè)備及刀、量、夾具由于生產(chǎn)類型為大批生產(chǎn),故加工設(shè)備宜以采用通用機(jī)床為主,輔以少量專用機(jī)床。其生產(chǎn)方式為以通用機(jī)床加專用夾具為主,輔以少量專用機(jī)床的流水生產(chǎn)線。工件在各級(jí)床上的裝卸及各機(jī)床間的傳送均由人工完成。粗精銑寬度為40mm的上下平臺(tái)和寬度為30mm的平臺(tái)??紤]到工件的定位夾緊方案及夾具結(jié)構(gòu)設(shè)計(jì)等問(wèn)題,采用立銑,選擇X5012立式銑床(參考文獻(xiàn):機(jī)械工藝設(shè)計(jì)手冊(cè),主編:李益民,機(jī)械工業(yè)出版社出版社),刀具選D=2mm的削平型立銑刀(參考文獻(xiàn):機(jī)械工藝設(shè)計(jì)手冊(cè),主編:李益民,機(jī)械工業(yè)出版社出版)、專用夾具、專用量具和游標(biāo)卡尺。粗精銑寬度為30mm的凸臺(tái)表面。采用X5021立式銑床,刀具選D=2mm的削平型銑刀,專用夾具、專用量檢具和游標(biāo)卡尺。鉆孔25(H9)使尺寸達(dá)到23mm。采用Z535型鉆床,刀具選莫氏錐柄麻花鉆(莫氏錐柄2號(hào)刀)D=23mm,專用鉆夾具,專用檢具。擴(kuò)孔鉆鉆孔25(H9)使尺寸達(dá)到24.8mm。采用立式Z535型鉆床,刀具選D=24.7mm的錐柄擴(kuò)孔鉆(莫氏錐度3號(hào)刀),專用鉆夾具和專用檢具。鉸孔25(H9)使尺寸達(dá)到25(H9)。采用立式Z535型鉆床,刀具選D=25mm的錐柄機(jī)用鉸刀,并倒145的倒角鉆用鉸夾具和專用檢量具。鉆28(H7)的小孔使尺寸達(dá)到7.8mm。采用立式Z518型鉆床,刀具選用D=7.8mm的直柄麻花鉆,專用鉆夾具和專用檢量具。粗鉸28(H7)小孔使尺寸達(dá)到7.96mm。采用立式Z518型鉆床,選擇刀具為D=8mm直柄機(jī)用鉸刀,使用專用夾具和專用量檢具。精鉸28(H7)小孔使尺寸達(dá)到8(H7)。采用立式Z518型鉆床,選擇刀具為D=8mm的直柄機(jī)用鉸刀,使用專用的夾具和專用的量檢具。鉆10(H7)的內(nèi)孔使尺寸達(dá)到9.8mm。采用立式Z518型鉆床,刀具選用D=9.8mm的直柄麻花鉆,專用的鉆夾具和量檢具。粗鉸10(H7)內(nèi)孔使尺寸達(dá)到9.96mm。采用立式Z518型鉆床,刀具選用D=10mm的直柄機(jī)用鉸刀,專用夾具和專用量檢具。精鉸10(H7)內(nèi)孔使尺寸達(dá)到10(H7)mm。采用立式Z518型鉆床,選擇刀具D=10mm的精鉸刀,使用專用夾具和量檢具。(參考資料和文獻(xiàn)均來(lái)自:機(jī)械工藝設(shè)計(jì)手冊(cè),主編:李益民,機(jī)械工業(yè)出版社出版)1.4 加工工序設(shè)計(jì)根據(jù)本次設(shè)計(jì)的要求,工序設(shè)計(jì)只設(shè)計(jì)老師所給出工序的計(jì)算。下面是對(duì)40上端面的加工設(shè)計(jì)。表 1余量和工序尺寸及公差 (mm)加工表面加工方法余量公差等級(jí)工序尺寸40上表面 粗銑0.21554.2740上表面 精銑0.055 541、 粗銑40平面使尺寸達(dá)到54.27mm。2、 精銑40平面使尺寸達(dá)到54.27mm。這兩道工序全都采用X5023機(jī)床來(lái)進(jìn)行加工的,故: (1)參考文獻(xiàn):機(jī)械設(shè)計(jì)工藝簡(jiǎn)明手冊(cè),并參考X5023機(jī)床主要技術(shù)參數(shù),取粗銑40上表面的進(jìn)給量f=0.3mm/r,求得40上表面的切削速度為V=0.435m/s=26.1m/min,由此算出轉(zhuǎn)速為:n=1000v/d=100026.1/3.148r/min1039r/min按機(jī)床實(shí)際轉(zhuǎn)速取n=1000r/min,則實(shí)際切削速度為V=3.141000/1000m/min22m/min.從參考文獻(xiàn)得知: =9.8142.7do(N) M=9.810.021(N.m)求出銑40平面的和M如下:=9.8142.781=1279NM=9.810.0211=5N.m根據(jù)所得出數(shù)據(jù),它們均少于機(jī)床的最大扭轉(zhuǎn)力矩和最大進(jìn)給力,故滿足機(jī)床剛度需求。(2)參考文獻(xiàn):機(jī)械設(shè)計(jì)工藝簡(jiǎn)明手冊(cè),并參考X5023機(jī)床主要技術(shù)參數(shù),取粗銑40平面的進(jìn)給量f=0.3mm/r,參考文獻(xiàn)得:切削速度為()V,故取Va=1/2V=1/222m/min=11m/min,由此算出轉(zhuǎn)速n=1000v/d=100011/3.148r/min=438r/min,取機(jī)床實(shí)際轉(zhuǎn)速n=450r/min。(3)參考文獻(xiàn):機(jī)械設(shè)計(jì)工藝簡(jiǎn)明手冊(cè),并參考Z5023機(jī)床主要技術(shù)參數(shù),取精銑40平面的進(jìn)給量f=0.3mm/r,參考文獻(xiàn)得:切削速度為V=0.3m/s=18m/min。由此算出轉(zhuǎn)速:n=1000v/d=100018/3.148r/min=717r/min按照機(jī)床的實(shí)際轉(zhuǎn)速n=720r/min。則實(shí)際切削速度為:V=dn/1000=3.148720/1000m/min=18.1m/min1.5 夾具的設(shè)計(jì)本次的夾具為工序:粗精銑寬度為40mm的上平臺(tái)和寬度為30mm的平臺(tái)而設(shè)計(jì)的。確定設(shè)計(jì)方案: 這道工序所加工的面在40凸臺(tái)平面上,表面粗糙度為6.3。1.5.1 根據(jù)工件結(jié)構(gòu)特點(diǎn),其定位方案有: 工件以40水平底面、40的圓柱分別在圓形凸臺(tái)、固定V形塊上實(shí)現(xiàn)完全定位,轉(zhuǎn)動(dòng)活動(dòng)扳手通過(guò)活動(dòng)V形塊對(duì)工件進(jìn)行夾緊。 圖1-4 活動(dòng)V形塊夾1.5.2 選擇定位元件(1)選擇圓形臺(tái)階面,以 40下端面為定位基準(zhǔn)。(2)選擇固定V形塊,以30凸臺(tái)下方、40圓柱外緣毛坯面定位 , 轉(zhuǎn)動(dòng)活動(dòng)扳手通過(guò)活動(dòng)V形塊對(duì)工件進(jìn)行夾緊。1.5.3 計(jì)算夾緊力參考文獻(xiàn)(機(jī)械加工工藝手冊(cè)),因夾具的的夾緊力與切削力方向相反,實(shí)際所需夾緊力與切削力F之間的關(guān)系為:=KF,式中的K為安全系數(shù)。由參考文獻(xiàn)得,當(dāng)夾緊力與切削力方向相反時(shí),取K=3。由前面的計(jì)算可知F=1279N。所以,為防止工件在切削扭矩M(N mm)的作用下打滑而轉(zhuǎn)動(dòng)所需的夾緊力=KF=12793N=3837N, 為防止工件在軸向力F的作用下打滑而軸向移動(dòng)所需的夾緊力=2174.3 N。1.5.4 定位誤差計(jì)算 (1)加工40平臺(tái)尺寸的定位誤差計(jì)算,由于基準(zhǔn)重合,故 :0.015+0.2=0.215mm,0.015-0.2=-0.185mm,上下偏差為:0.215-(-0.185)=0.4mm,符合尺寸要求。而基準(zhǔn)位移誤差為定位面 (40下端面)與固定V形塊的最大間隙,故:定位凸臺(tái)取直徑為40H9,盡量減少位移誤差。故:25-25=0,上偏差:0.052-0.052=0mm,下偏差:0-0=0mm。其基準(zhǔn)也符合設(shè)計(jì)要求。由此可知此定位方案能滿足尺寸 84 0.2mm的定位要求。(2)加工40面時(shí)軸線平行度 0.15mm 的定位誤差計(jì)算,由于基準(zhǔn)重合,故 :0.015+0.015=0.03mm而基準(zhǔn)位移誤差是定位面40下端面與定位面間的誤差。故 :0.052+0.052mm=0.104mm所以有:0.03+0.104mm=0.134mm 此方案能滿足定位要求。通過(guò)定位方案的確定,夾緊力與定位誤差的計(jì)算和選擇了可靠的定位元件以后,就設(shè)計(jì)出我們所需要的夾具。第2章 綜合訓(xùn)練2.1 夾具體三維造型實(shí)現(xiàn)方法的概述通過(guò)實(shí)體造型把夾具的三維圖簡(jiǎn)要的三維圖制作出來(lái),下面的設(shè)計(jì)是銑床桿的鉆孔夾具。這個(gè)夾具可以通過(guò)Pro/E,UG,AutoCAD,Mastercam等三維造型軟件實(shí)現(xiàn),我是用UG來(lái)實(shí)現(xiàn)造型的。下圖是用AutoCAD畫的夾具裝配圖。2.2 夾具三維造型過(guò)程簡(jiǎn)述 1下面是用UG軟件來(lái)實(shí)現(xiàn)三維造型步驟:步驟一:首先設(shè)計(jì)一個(gè)夾具體 ,形如下: 圖2-1 夾具體圖步驟二: 設(shè)計(jì)定位銷, 圖形如下:圖2-2 定位銷步驟三: 設(shè)計(jì)螺釘 ,圖形如下: 圖2-3 螺釘步驟四: 設(shè)計(jì)螺栓 圖形如下:圖2-4 螺栓步驟五: 設(shè)計(jì)六角螺母 圖形如下: 圖2-5 六角螺母步驟六: 設(shè)計(jì)兩個(gè)V形塊,圖形如下: 圖2-6a 固定V形塊 圖2-6b 活動(dòng) V形塊步驟七: 設(shè)計(jì)一個(gè)支撐板,圖形如下:圖2-7 支撐板步驟八: 設(shè)計(jì)一個(gè)蓋板,圖形如下:圖2-8 蓋板 步驟九: 設(shè)計(jì)一個(gè)V形塊,圖形如下: 圖2-9 活動(dòng) V形塊上面的三維造型都是為了夾具的整體裝配做準(zhǔn)備的下面我們就來(lái)實(shí)現(xiàn)夾具的三維圖.2 下面的是用UG軟件來(lái)實(shí)現(xiàn)裝配的過(guò)程:步驟如下:步驟一: 裝配固定V形塊 圖2-11 裝配固定V形塊步驟二: 裝配工件,圖形如下:圖2-12 裝配工件步驟三: 裝配支撐板,圖形如下:圖2-13 裝配支撐板步驟四: 裝配活動(dòng)V形塊,圖形如下:圖2-14 裝配活動(dòng)V形塊步驟五: 裝配蓋板,圖形如下:圖2-15 裝配蓋板步驟六: 裝配手柄,圖形如下:圖2-16 裝配手柄步驟七: 裝配定位鍵,圖形如下: 圖2-17 裝配定位鍵 下面是圖形的整體裝配圖:圖2-18 整體裝配圖小結(jié)五個(gè)星期的機(jī)械制造工藝學(xué)畢業(yè)設(shè)計(jì)馬上就要?jiǎng)澤暇涮?hào),經(jīng)過(guò)這五個(gè)星期的努力,我在老師的指導(dǎo)下,取得了自己滿意的效果,畢業(yè)設(shè)計(jì)作為機(jī)械制造工藝學(xué)、機(jī)床夾具設(shè)計(jì)畢業(yè)的重要環(huán)節(jié),使理論與實(shí)踐相結(jié)合,加深了理論知識(shí)的理解,強(qiáng)化了在運(yùn)用中的感性認(rèn)識(shí)。通過(guò)此次設(shè)計(jì),使我們基本掌握了零件的加工過(guò)程分析、工藝文件的編制、專用夾具設(shè)計(jì)的方法和步驟等。學(xué)會(huì)了查相關(guān)手冊(cè)、選擇使用工藝裝備以及更加熟練的運(yùn)用三維軟件造型等等??偟膩?lái)說(shuō),這次設(shè)計(jì),使我們?cè)诨纠碚摰木C合運(yùn)用及正確解決實(shí)際問(wèn)題等方面得到了一次較好的訓(xùn)練。提高了我們的思考、解決問(wèn)題創(chuàng)新設(shè)計(jì)的能力,為以后的設(shè)計(jì)工作打下了較好的基礎(chǔ)。同時(shí),廣泛地運(yùn)用設(shè)計(jì)手冊(cè),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;在整個(gè)零件的加工過(guò)程是和其他同學(xué)分工完成,所以在設(shè)計(jì)過(guò)程中需要和同學(xué)一起討論分析,在夾具設(shè)計(jì)過(guò)程中也想同學(xué)征求了意見(jiàn),是設(shè)計(jì)更加符合實(shí)際要求。參考文獻(xiàn)1、李益民,機(jī)械加工工藝簡(jiǎn)明手冊(cè)M,北京:機(jī)械工業(yè)出版社,19942、李洪,機(jī)械加工工藝手冊(cè)M,北京:北京出版社,19903、廖念釗等,互換性與技術(shù)測(cè)量(第四版)M,北京:中國(guó)計(jì)量出版社,19904、于駿一、鄒青,機(jī)械制造技術(shù)基礎(chǔ)M,北京:機(jī)械工業(yè)出版社,20045、劉華明,刀具設(shè)計(jì)手冊(cè)M,北京:機(jī)械工業(yè)出版社,19996、艾興、肖詩(shī)鋼,切削用量手冊(cè)M, 北京:機(jī)械工業(yè)出版社,1985 7、上海柴油機(jī)廠工藝設(shè)備研究所,金屬切削機(jī)床夾具設(shè)計(jì)手冊(cè)M, 北京:機(jī)械工業(yè)出版社,198426Robotics 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
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