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制造業(yè)原尺模型云
簡(jiǎn)介
本文作者研制了一種新的方法來(lái)整合逆向工程( Re )和快速成型( RP ) . unorganised云數(shù)據(jù)直接切片并仿照二維( 2d )交叉路段. 基于這樣一種二維CAD模型 數(shù)據(jù)點(diǎn)直接轉(zhuǎn)化為成型切片數(shù)據(jù)輸入到成型機(jī)的制造. 在這個(gè)過(guò)程中,無(wú)論是曲面模型或STL文件生成. 都是從三維數(shù)據(jù)點(diǎn)的幾個(gè)步驟做到這一點(diǎn)的:第一, 云數(shù)據(jù)是分割成若干層沿著用戶指定的方向前進(jìn). 點(diǎn),每一層都投射到平面. 其次,該平面的每一層都在清理和壓縮. 數(shù)據(jù)點(diǎn)平滑,然后用離散曲率的方法進(jìn)行分析. 第三,局部插值法用于添置點(diǎn)斷層處線的不足點(diǎn). 第四,兩平面之間的路段,每?jī)蓚€(gè)相鄰的平面是創(chuàng)造的直接連接特征點(diǎn)( fps )的直線. 最后,一個(gè)rp文件分層生成了SLA機(jī)器. 發(fā)達(dá)法已經(jīng)實(shí)施的C / C對(duì)unigraphics平臺(tái).
作者關(guān)鍵詞:海量數(shù)據(jù); 快速原型; 逆向工程; 分割
介紹
逆向工程(重) ,是指建立CAD模型,從現(xiàn)有的實(shí)物, 其中可利用作為設(shè)計(jì)工具制作拷貝一個(gè)對(duì)象, 提取設(shè)計(jì)概念,以現(xiàn)有的模式,或重整現(xiàn)有的部分[1] . 重組,建立了產(chǎn)品模型設(shè)計(jì)的設(shè)計(jì)方法, 通常是以木材或陶土模擬為第一采樣,然后對(duì)采樣數(shù)據(jù)進(jìn)行轉(zhuǎn)換,為進(jìn)一步制作stylist的模式可以利用光學(xué)非接觸測(cè)量技術(shù)迅速解決問(wèn)題,例如: 激光掃描器. 這通常產(chǎn)生大云數(shù)據(jù)集,通常是隨意散落的.
這種辦法改變了濃重的非結(jié)構(gòu)化數(shù)據(jù)集平面代表,可分為兩大類: 三角多面體網(wǎng)格法及分部和合適的方法[ 1 2 3 ] . 用以前的辦法,初步形成三角形構(gòu)造以捕獲未知的散亂的拓?fù)浣Y(jié)構(gòu). 將網(wǎng)格的質(zhì)量?jī)?yōu)化,以減少多余的頂點(diǎn),然后曲率連續(xù)曲面重構(gòu),在此基礎(chǔ)上運(yùn)用許多三角測(cè)量技術(shù)可以發(fā)現(xiàn),例如 三角算法[4 , 5] ,根據(jù)三角簽訂的距離函數(shù)[6]和三角基于α-形狀[7] . 得出三角云數(shù)據(jù)低效的過(guò)程[ 6 , 8 ] .
第二類, 云數(shù)據(jù)分成合適的小塊區(qū)域并使用一個(gè)適當(dāng)?shù)谋砻鎲窝b [9] .手動(dòng)分割三維實(shí)測(cè)數(shù)據(jù)是一個(gè)耗時(shí)且容易出錯(cuò)的過(guò)程, 一些研究者試圖執(zhí)行一個(gè)自動(dòng)分割算法[ 2月9日和10]. 但是,總的來(lái)說(shuō),目前分割的方法比較復(fù)雜或只能適用于簡(jiǎn)單的拓?fù)鋽?shù)據(jù)[10] . 因此,近年來(lái) 一些新穎的重新考慮直接制造云數(shù)據(jù)的方式并沒(méi)有涉及更有效率的表面重建和產(chǎn)品快速發(fā)展( rpd ) [8] . 不過(guò),這些方法只能適用于結(jié)構(gòu)點(diǎn)數(shù)據(jù).
本文作者提出了基于誤差分割的方法,隨意散落云數(shù)據(jù). 我們的目標(biāo)是重新整合和快速成型( RP ) ,以使廠商和設(shè)計(jì)者滿足 縮短產(chǎn)品開(kāi)發(fā)時(shí)間. 這要完成下列步驟. 首先,云數(shù)據(jù)分割成若干層沿著用戶指定的方向前進(jìn).,每一層都投射到平面. 其次是平面的每一層初始曲線的清理和壓縮. (即所謂的C曲線)，第三, 局部插值法(構(gòu)建R型曲線相應(yīng)點(diǎn)在不同層)用于添置點(diǎn) 切片線的不足點(diǎn). 最后,基于分層rp模型并直接傳送至快速成型機(jī)，基于這些技術(shù)的實(shí)驗(yàn),這是發(fā)達(dá)國(guó)家用來(lái)說(shuō)明效果的做法.
2 . 云數(shù)據(jù)的區(qū)域分割
在本質(zhì)上, C-曲線是由一系列的特征點(diǎn)的平面曲線構(gòu)成的. 它基于三個(gè)步驟. 首先,云數(shù)據(jù)進(jìn)行預(yù)處理,通過(guò)分割,預(yù)測(cè)和排序產(chǎn)生初始C-曲線. 其次, 最初的C曲線進(jìn)行壓縮,去除多余點(diǎn) ( fps ) ,對(duì)原來(lái)的形狀進(jìn)行改進(jìn)。資料記載的數(shù)據(jù)鏈路. 最后, C-曲線的構(gòu)造方法是把所有的fps用直線連接.在建設(shè)過(guò)程中這兩條曲線的形狀精度由幾個(gè)用戶指定的參數(shù)是控制的
2.1 數(shù)據(jù)預(yù)處理
第一步,是沿著用戶指定的分層方向和區(qū)間的直接切片云數(shù)據(jù)構(gòu)建C-曲線. 把整個(gè)數(shù)據(jù)集合,然后均勻切成片，其中有很多電腦投射的錯(cuò)誤觀點(diǎn). 假設(shè)用戶定義分層方向和一個(gè)數(shù)據(jù)集是X = ( p1 , p2 , ... , pn )分別. 該中心的數(shù)據(jù)集X計(jì)算
(1)
假設(shè)點(diǎn)o x是最接近PC機(jī)的, 字首平面與中心點(diǎn)O是單位正常的載體, 我們定義投影面數(shù)據(jù)集的十大預(yù)測(cè)誤差點(diǎn)丕x 然后計(jì)算
(2)
如果ei大于預(yù)先確定的形狀誤差,則數(shù)據(jù)集X均勻,再分成兩個(gè)亞群. 這個(gè)過(guò)程一直重復(fù),直到所有ei滿足需求.
經(jīng)過(guò)切片 各點(diǎn)投射到相應(yīng)的投影機(jī)和一個(gè)"清晰"的過(guò)程中
進(jìn)行投影點(diǎn)排序的目的分揀是成立一個(gè)拓?fù)浣Y(jié)構(gòu)的平面數(shù)據(jù)以及清除錯(cuò)誤數(shù)據(jù),如高峰和重復(fù)數(shù)據(jù)建構(gòu)初步C-曲線的投影面. 這是由于預(yù)測(cè)的數(shù)據(jù)點(diǎn)的層unorganised的錯(cuò)誤填寫(xiě) 但重要的是要選擇一個(gè)正確點(diǎn)開(kāi)始排序. 排序算法是基于估計(jì)的切線向量,共分為五個(gè)步驟如下:
估計(jì)面向切線向量每個(gè)X是點(diǎn)在平面上 我們將K點(diǎn)的X最接近丕k當(dāng)作樣本并表示這一數(shù)據(jù)集. K是一個(gè)用戶指定的參數(shù)，它用于控制估算準(zhǔn)確性的起源切線向量. 如圖. 1 ( a ) ,起源切線向量的計(jì)算方法如下
(3)
取出下一點(diǎn)的開(kāi)始點(diǎn)，丕X可以被選為第一起點(diǎn). 假定第一啟動(dòng)點(diǎn)和導(dǎo)向切線向量p0 ,分別為(圖1 ( b )款)殘值算法將先從P0開(kāi)始， 一旦發(fā)現(xiàn)一個(gè)終點(diǎn)，,算法可以追溯到P0和檢索的方向
(4)
當(dāng)ρ是由于形狀誤差形成的時(shí)候，將作為一個(gè)新的起點(diǎn)和檢索繼續(xù),其面向正切載體. 刪除雜散點(diǎn)--步驟( 2 ) ,下次點(diǎn)的起點(diǎn)是決定值, 我們定義循環(huán)利用這兩個(gè)點(diǎn)的直徑是相等距離的點(diǎn)并刪除所有其內(nèi)的圓.
( 1 ) - ( 3 )組成一個(gè)檢索周期. 當(dāng)一個(gè)周期已經(jīng)完成, 各檢索點(diǎn)的周期都是聯(lián)系在一起,形成一個(gè)C曲線. 如果所有點(diǎn)在平面上標(biāo)注,則算法終止. 否則一種新的回收周期,恢復(fù)檢索點(diǎn), 在平面上產(chǎn)生了新的C-曲線. C曲線數(shù)量在不同的投影可能有所不同.
圖. 1 . 數(shù)據(jù)排序.
2.2 數(shù)據(jù)壓縮數(shù)據(jù)
預(yù)處理初步C-曲線投影面. 不過(guò), 數(shù)據(jù)規(guī)模的曲線是非常大的,可能有大量復(fù)雜運(yùn)算,超過(guò)硬件設(shè)施了有限的內(nèi)存貯藏空間. 為了解決這個(gè)問(wèn)題, 使用特征點(diǎn)的數(shù)據(jù)壓縮算法,開(kāi)發(fā)壓縮重復(fù)每個(gè)平面參數(shù)多項(xiàng)式. 獲得解的參數(shù)化多項(xiàng)式曲線,應(yīng)該至少有四點(diǎn). 因此,每一個(gè)投影面, C-135型曲線都應(yīng)考慮到,只有當(dāng)相應(yīng)的點(diǎn)數(shù)超過(guò)4使才采用最小二乘法,得到未知系數(shù)的多項(xiàng)式.
由于基本形狀信息的平面曲線展示了它的fps或高曲率點(diǎn) 我們確定參數(shù)值及相應(yīng)的fps的逼近曲線如下:
目前壓縮算法是基于上述曲線的，其中包括下列步驟: (見(jiàn)圖. 2 ) :
找到所有的fps .
連接所有fps與直線生成多邊形. 計(jì)算距離點(diǎn)在C曲線的多邊形. 如果距離大于預(yù)先確定的形狀的誤差,這點(diǎn)是作為一種新的fp .
到步驟( 2 ) . 這個(gè)過(guò)程重復(fù),直到所有的點(diǎn)的曲線,滿足其相應(yīng)的距離,是在特定的形狀誤差.
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圖. 2 . 數(shù)據(jù)壓縮.
各點(diǎn)除fps外全部刪除. 最后C-曲線則由所有fps用直線連接
3 . 數(shù)據(jù)插值
在C曲線的建立 數(shù)據(jù)庫(kù)中的C曲線為構(gòu)建層(行) ,形成所謂的R曲線. 在本質(zhì)上建設(shè)R曲線的目的是建立一個(gè)拓?fù)浣Y(jié)構(gòu)點(diǎn)整齊, 從而協(xié)助i找到C曲線與不足點(diǎn). 所舉的例子顯示如圖. 3 ( a ) ,建設(shè)R曲線是基于預(yù)計(jì)切面,其中包括下列步驟:
估計(jì)切面每個(gè)點(diǎn)m -, m是一個(gè)用戶指定的參數(shù)，它用于控制精度估算的切面. 單位法線切平面可以計(jì)算單位向量3 × 3對(duì)稱 矩陣說(shuō)明如下:
(5)
如果λi1≥λi2≥λi3字首特征值的一個(gè)相關(guān)單位,分別有切線估計(jì).
確定面向點(diǎn) C-曲線與CI ( z ) , R曲線與RI ( p ) 點(diǎn)數(shù)據(jù)集X和切平面點(diǎn)丕t ( z0 ) . 假定算法展開(kāi)投影面t ( z0 ) ,如圖. 3 ( b )中,對(duì)象點(diǎn)丕整齊,是在C曲線上搜索所有要點(diǎn)p x
(6)
若ρ是由于形狀誤差形成的. 則上述不等式成立, p被稱為前排一點(diǎn)的檢索，否則必?zé)o取向爭(zhēng)論點(diǎn). 為了提高工作效率, 只是點(diǎn)的N區(qū)域投影面t 選定計(jì)算( N是指定的用戶) . 若N是選定沿著正常的正面的T , 面向點(diǎn)確定整齊的定義是下一行點(diǎn)的檢索. 若n是沿著相應(yīng)的消極點(diǎn),但已確定的一點(diǎn)是負(fù)點(diǎn)的有檢索點(diǎn). 這樣一來(lái),對(duì)每一個(gè)點(diǎn)的C -曲線,它的兩個(gè)對(duì)象點(diǎn)才能確定.
新建成R型曲線相交,然后形成一個(gè)新的起點(diǎn),因此增加了各自的C-曲線平面,如果它不存在的前相交(圖3 ( c )項(xiàng)) . 所取得的C-曲線faired使用一種基于離散曲率.
4 . 建設(shè)示范rp
雖然STL的文件已用于工業(yè)標(biāo)準(zhǔn)的快速成型機(jī), 基于分層切片文件如SLC的檔案格式也是可以接受的快速成型機(jī). 這里的RP模型是基于faired C-曲線采用固定分層策略的. 如圖. 4 ,假定切片是介于C曲線詞( zk )和CI 1 ( zk ' ) ,相應(yīng)點(diǎn), pj ,是由計(jì)算
(7)
當(dāng)時(shí)( zk )和PM』( zk ' )是兩個(gè)最近點(diǎn)的 ( zk )和CI 1 ( zk ' ) .
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圖. 4 . 數(shù)據(jù)點(diǎn)的切片層與C曲線.
當(dāng)所有的分切層的產(chǎn)生點(diǎn),每一層都關(guān)閉,產(chǎn)生一種反相模式,直接送到成型機(jī) 捏造.
5 . 應(yīng)用實(shí)例
計(jì)算上述已實(shí)施的C / C是針對(duì)惠普c200工作在unigraphics環(huán)境. 一個(gè)案例就是在這里提出來(lái)說(shuō)明效率的算法. 此案是一個(gè)模型,是由4個(gè)不同的數(shù)據(jù)塊. 原始數(shù)據(jù)云104,175點(diǎn)(見(jiàn)圖. 5 ) .
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圖5 . 原始數(shù)據(jù)的云層.
切片方向獲得如圖. 6 ( a ) . 基于這樣的方向發(fā)展,海量數(shù)據(jù)的處理,以營(yíng)造rp模式. 用一個(gè)用戶指定的形狀誤差形狀= 0.1毫米, 每一層厚度為0.2毫米. 經(jīng)過(guò)數(shù)據(jù)整理和壓縮,只有16,324點(diǎn)保存模型 (見(jiàn)圖. 6 ( b )項(xiàng)) . 它歷時(shí)約1小時(shí)的算法,運(yùn)行在惠普C200的工作環(huán)境. 最后三彎模型顯示圖7 ( A )和反相構(gòu)造模型圖. 七(二) . 這種模式是SLA成型機(jī)需要大約3小時(shí)才能完成的編造.
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圖6 . 模擬進(jìn)程.
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圖7 . 最后的模型.
6 . 結(jié)論
在這個(gè)文件中,一種新的方法被用來(lái)來(lái)處理隨意散云數(shù)據(jù)RP. 我們的方法是一種基于分層rp模型,它是直接摘自云數(shù)據(jù)并通過(guò)分層, 壓縮和交叉.無(wú)地表模型或STL文件生成. 該方法已被證明是有效的處理復(fù)雜曲面和提高運(yùn)算效率的方法. 然而,我們的做法目前只能處理海量數(shù)據(jù),無(wú)孔洞. 基于多回路所致切片云數(shù)據(jù)仍在發(fā)展中. 在另一方面,研究確定分層方向及其他參數(shù)也正在進(jìn)行之中.
序號(hào)（學(xué)號(hào)）：
長(zhǎng) 春 大 學(xué)
畢 業(yè) 設(shè) 計(jì)（論 文）譯文
制造業(yè)原尺模型云
姓 名
學(xué) 院
機(jī) 械 工 程 學(xué) 院
專 業(yè)
機(jī)械工程及自動(dòng)化
班 級(jí)
指導(dǎo)教師
教授
2007
年
6
月
20
日
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長(zhǎng) 春 大 學(xué) 畢業(yè)設(shè)計(jì)（論文）紙
開(kāi)題報(bào)告
一、設(shè)計(jì)題目
汽車同步帶精密測(cè)長(zhǎng)機(jī)設(shè)計(jì)
二、課題研究的目的和意義
同步帶是利用齒輪與帶齒輪之間的嚙合來(lái)傳遞運(yùn)動(dòng)和動(dòng)力的，它可實(shí)現(xiàn)無(wú)滑動(dòng)的同步傳動(dòng)及多軸傳動(dòng)。由于其具有傳動(dòng)準(zhǔn)確、適用于高速運(yùn)轉(zhuǎn)、維護(hù)方便、結(jié)構(gòu)緊湊、傳動(dòng)效率高、沖擊性小、速比大、載荷范圍小、噪音小等優(yōu)點(diǎn)，故可以滿足機(jī)械工業(yè)中高速化、自動(dòng)化、精密化和省力化的發(fā)展要求，因而被廣泛應(yīng)用于縫紉機(jī)、汽車、紡織機(jī)械、機(jī)床、辦公機(jī)械以及各種儀器儀表中，而且使用的領(lǐng)域還在日益擴(kuò)大。
同步帶的精度主要是指節(jié)線長(zhǎng)和節(jié)線精度。他的精度將直接影響到所傳遞運(yùn)動(dòng)的精度，從而影響整個(gè)機(jī)器設(shè)備的性能及精度，例如影響打印機(jī)字體的形狀、縫紉機(jī)跳針等。此外同步帶的精度將影響嚙合時(shí)的干涉，從而影響傳動(dòng)帶的使用壽命。
隨著機(jī)械傳動(dòng)發(fā)展，對(duì)同步帶的精度提出了極嚴(yán)格的要求，比如某個(gè)縫紉機(jī)公司引進(jìn)的GC20210高速平紉機(jī)上的250SL075G型同步帶，其節(jié)線長(zhǎng)L為632.19mm，因其工作轉(zhuǎn)速為4000r/min ，且上、下帶輪中心距不可調(diào)，為使帶的工作張力不致太小或太大，該帶的節(jié)線長(zhǎng)極偏差的要求為正負(fù)0.1mm，而同步帶生產(chǎn)中許多因素都會(huì)對(duì)精度造成影響，因此對(duì)要求較高的同步帶每跟都必須進(jìn)行長(zhǎng)度檢測(cè)。作為檢測(cè)批量生產(chǎn)的同步帶的儀器設(shè)備，同步帶測(cè)長(zhǎng)機(jī)的精度必須超過(guò)同步帶要求的精度而且必須方便、快速且穩(wěn)定可靠。
三、國(guó)內(nèi)外現(xiàn)狀和發(fā)展趨勢(shì)
同步帶在我國(guó)起步較晚，但發(fā)展較快，已形成生產(chǎn)規(guī)模，但面臨的問(wèn)題也很多。同步帶為節(jié)能產(chǎn)品，具有良好的經(jīng)濟(jì)效益和社會(huì)效益，為了大力發(fā)展我國(guó)同步帶行業(yè)，一方面要做好宣傳推廣工作，擴(kuò)大同步帶的應(yīng)用范圍;另一方面要進(jìn)一步提高同步帶的質(zhì)量，替代進(jìn)口產(chǎn)品
我國(guó)自改革開(kāi)放后，傳動(dòng)帶的標(biāo)準(zhǔn)陸續(xù)按國(guó)際標(biāo)準(zhǔn)和歐美標(biāo)準(zhǔn)制定，這些標(biāo)準(zhǔn)長(zhǎng)度是按基準(zhǔn)制和有效制表示的，擯棄了我過(guò)沿用幾十年內(nèi)周制，因此 需要專用的測(cè)量工具測(cè)量。我國(guó)在上世紀(jì)80年代中，上海飛機(jī)設(shè)計(jì)所為配合《汽車V帶尺寸》標(biāo)準(zhǔn)的制定開(kāi)始研制汽車V帶測(cè)長(zhǎng)機(jī)。隨著我國(guó)V帶新標(biāo)準(zhǔn)的實(shí)施，V帶測(cè)長(zhǎng)機(jī)成生產(chǎn)廠家必備的測(cè)量工具。青島橡膠工業(yè)研究所，營(yíng)口實(shí)驗(yàn)機(jī)廠，將都名著材料實(shí)驗(yàn)機(jī)廠均有生產(chǎn)，同步帶測(cè)長(zhǎng)機(jī)精度要求較高，一般采用比較法測(cè)量，無(wú)錫橡膠廠從SCHOLZ引進(jìn)一套同步帶測(cè)長(zhǎng)機(jī)，動(dòng)南大學(xué)為南京汽車制造廠研制過(guò)一臺(tái)，青島宜利大公司有生產(chǎn)。
同步帶為彈性嚙合件，需在一定張緊力的條件下實(shí)現(xiàn)傳動(dòng)，為保證同步帶與帶輪良好的嚙合，要求膠帶生產(chǎn)廠對(duì)帶長(zhǎng)進(jìn)行逐條測(cè)量，因此，汽車同步帶測(cè)長(zhǎng)機(jī)是生產(chǎn)必須的檢測(cè)設(shè)備。同步帶測(cè)長(zhǎng)機(jī)是就同步帶的跳動(dòng)誤差和長(zhǎng)度誤差來(lái)判斷同步帶質(zhì)量的測(cè)量設(shè)備，它根據(jù)測(cè)量結(jié)果來(lái)判斷同步帶是否符合相關(guān)的標(biāo)準(zhǔn)要求，以此來(lái)判定是“合格”還是“不合格”，在同步帶生產(chǎn)過(guò)程中，該機(jī)是確保各種傳動(dòng)帶產(chǎn)品質(zhì)量、提高產(chǎn)品合格率的必備設(shè)備之一。
目前國(guó)內(nèi)研制的同步帶測(cè)長(zhǎng)機(jī)測(cè)量精度最高達(dá)到，且沒(méi)有帶傳動(dòng)的橫向擺動(dòng)量的測(cè)量，2003年汽車同步帶GB12734-2003標(biāo)準(zhǔn)實(shí)施以來(lái)，國(guó)內(nèi)尚沒(méi)有測(cè)量精度為的測(cè)長(zhǎng)機(jī)。而日本、法國(guó)等國(guó)家的膠帶生產(chǎn)企業(yè)均有高精度、自動(dòng)化的同步帶測(cè)長(zhǎng)機(jī)、無(wú)錫貝爾特膠帶公司就從德國(guó)SCHOLE公司引進(jìn)了一套同步帶數(shù)控測(cè)長(zhǎng)機(jī)。而且采用光機(jī)電一體化技術(shù)研究帶的動(dòng)態(tài)測(cè)量是目前國(guó)內(nèi)外帶生產(chǎn)技術(shù)的發(fā)展方向。
總之，帶傳動(dòng)在現(xiàn)代機(jī)械傳動(dòng)中占據(jù)著重要的地位。帶傳動(dòng)品種開(kāi)發(fā)和理論研究、帶傳動(dòng)檢測(cè)裝置和試驗(yàn)設(shè)備、傳動(dòng)帶和帶輪制造設(shè)備和工藝控制技術(shù)等等方面，我國(guó)與工業(yè)發(fā)達(dá)國(guó)家都有相當(dāng)大的差距。我們應(yīng)針對(duì)帶傳動(dòng)行業(yè)發(fā)展現(xiàn)狀，切實(shí)解決一些基本和關(guān)鍵問(wèn)題，使帶傳動(dòng)技術(shù)真正為滿足各行業(yè)機(jī)械裝備對(duì)帶傳動(dòng)日益增長(zhǎng)的需求和提高質(zhì)量的要求服務(wù)。
四、方案擬定
（1） 測(cè)試臺(tái)
測(cè)試臺(tái)由上臺(tái)面、支撐架、直線導(dǎo)軌組成。支撐架用地腳螺栓牢固地固定在底板上；上臺(tái)面左右裝有稱輪，引導(dǎo)張緊裝置的張緊力；定同步帶輪架固定在直線導(dǎo)軌左端，動(dòng)同步帶輪固定在直線導(dǎo)軌的滑塊上；導(dǎo)軌末端裝有擋鐵。
（2） 中心距測(cè)量裝置
此裝置中光柵尺安裝在測(cè)試臺(tái)上，與直線導(dǎo)軌平行安裝，其動(dòng)頭用連接板與動(dòng)同步帶輪連接，與動(dòng)同步帶輪保持同步。動(dòng)同步帶輪可以在直線導(dǎo)軌上自由移動(dòng)，根據(jù)被測(cè)同步帶長(zhǎng)度確定位置。測(cè)量之前應(yīng)用標(biāo)定裝置標(biāo)定光柵尺，光柵尺讀數(shù)直接由工控機(jī)記錄。
（3）轉(zhuǎn)速測(cè)量裝置
光電轉(zhuǎn)速傳感器安裝在傳感器架上，在電機(jī)聯(lián)軸器上裝有帶孔鋁板，轉(zhuǎn)動(dòng)時(shí)光電傳感器即可記錄轉(zhuǎn)速數(shù)據(jù)，直接輸入工控機(jī)處理。
（4）橫向擺動(dòng)量測(cè)量裝置
激光測(cè)位儀是一種非接觸的測(cè)量?jī)x器。激光測(cè)位儀由測(cè)位儀架安裝在動(dòng)同步帶輪左側(cè)，通過(guò)測(cè)位儀架可以在豎直和水平方向進(jìn)行微調(diào)。測(cè)位儀架的長(zhǎng)度保證了測(cè)量位置在距動(dòng)同步帶輪中心125cm位置處。測(cè)量得到的數(shù)據(jù)直接輸入工控機(jī)進(jìn)行處理。
（5）張緊裝置
張緊裝置由重砣和鋼絲繩組成，用于使同步帶張緊。
（6）帶輪
該裝置配有與不同型號(hào)同步帶相配的成套標(biāo)準(zhǔn)帶輪，測(cè)量不同型號(hào)的同步帶時(shí)，可以方便而迅速地更換相應(yīng)的帶輪。
（7）控制系統(tǒng)
控制系統(tǒng)負(fù)責(zé)數(shù)據(jù)的采集、計(jì)算、處理、報(bào)表生成、結(jié)果判斷和動(dòng)作控制。它由PC工控機(jī)、顯示器、打印機(jī)和各外部信號(hào)處理器組成。
測(cè)長(zhǎng)機(jī)結(jié)構(gòu)圖
五、進(jìn)度安排
3月24日——4 月4日： 翻譯科技文獻(xiàn)，寫(xiě)開(kāi)題報(bào)告，確定方案。
4月7日—— 4 月11日：設(shè)計(jì)計(jì)算。
4月14日——6 月20日：測(cè)長(zhǎng)機(jī)整體設(shè)計(jì)并畫(huà)裝配圖
6月23日——6 月27日：整理說(shuō)明書(shū)。
6月30日——7月4日： 評(píng)審、答辯。
六、參考文獻(xiàn)
[1] 濮良貴、紀(jì)名剛主編.機(jī)械設(shè)計(jì).北京：高等教育出版社
[2] 邵芳，姚俊紅.我國(guó)汽車傳動(dòng)帶技術(shù)分析與展望.機(jī)械制造42卷第478期.2004.6
[3] Sachio H. Structure and mechanical properties of HNBR/ zinc dimethacrylate [A]polymer Blends "Toward 2000. Kasetsart University,Japan: 1997- 08- 18
[4] Michael E.W. Synchronous belt compounds: the new bench markin dynamic performance[A].ACS RDM[C].Orlando, Florida
[5] 吳貽珍.汽車用傳動(dòng)帶技術(shù)進(jìn)展[J].橡膠工業(yè)，1992, 39( 5)299～303
[6] 吳立言，王步流.同步帶傳動(dòng)的受力分析.西北工業(yè)大學(xué)科技資料,1991
[7] 秦書(shū)安.帶傳動(dòng)技術(shù)現(xiàn)狀與發(fā)展前景.機(jī)械傳動(dòng).2002,26(4):1～6
[8] 保城武，齒付きべルト，機(jī)械設(shè)計(jì)，27〔1〕,54(1983).
[9] 尼曼G,溫特爾H(著).機(jī)械零件(第二卷)[M].余夢(mèng)生(譯).北京:機(jī)械工業(yè)出版社,1989
[10]吳振彪主編.機(jī)電綜合設(shè)計(jì)指導(dǎo).北京：中國(guó)人民大學(xué)出版社
[11]機(jī)械工程手冊(cè)編委會(huì)編.機(jī)械工程手冊(cè)。第2版.北京：機(jī)械工業(yè)出版社，1995
[12]周開(kāi)勤主編.機(jī)械零件手冊(cè).第四版.北京：高等教育出版社，1994
[13]吳宗澤主編.機(jī)械結(jié)構(gòu)設(shè)計(jì).北京機(jī)械工業(yè)出版社，1988
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序號(hào)（學(xué)號(hào)）：
長(zhǎng) 春 大 學(xué)
畢 業(yè) 設(shè) 計(jì) 開(kāi) 題 報(bào) 告
汽車同步帶測(cè)長(zhǎng)機(jī)設(shè)計(jì)
姓 名
學(xué) 院
機(jī) 械 工 程 學(xué) 院
專 業(yè)
機(jī)械工程及自動(dòng)化
班 級(jí)
指導(dǎo)教師
教授
2007
年
6
月
20
日
Modelling cloud data for prototype manufacturing
Abstract
In this paper, the authors have developed a novel method to integrate reverse engineering (RE) and rapid prototyping (RP). Unorganised cloud data are directly sliced and modelled with two-dimensional (2D) cross-sections. Based on such a 2D CAD model, the data points are directly converted into RP slice data and fed to an RP machine for fabricating. In this process, neither a surface model nor a STL file is generated. This is accomplished from the 3D data points in several steps: first, the cloud data are sliced into a number of layers along a user-specified direction. The points in each layer are projected onto a plane. Secondly, the points on each plane are sorted and compressed. Data point smoothing is then carried out using a discrete curvature based method. Thirdly, a local interpolating method is used for adding additional points to the slice-lines having insufficient points. Fourthly, the cross-sections between every two neighbouring planes are created by directly connecting the feature points (FPs) with straight-line segments. Finally, an RP layered file is generated for an SLA machine. The developed methods have been implemented with C/C++ on the Unigraphics platform.
Author Keywords: Cloud data; Rapid prototyping; Reverse engineering; Segmentation
1. Introduction
Reverse engineering (RE) refers to creating a CAD model from an existing physical object, which can be utilised as a design tool for producing a copy of an object, extracting the design concept of an existing model, or re-engineering an existing part [1]. In RE, a product model designed by the stylist, usually in the form of wood or clay mock-up is first sampled and then the sampled data are transformed to a CAD representation for further fabrication. The shape of the stylist’s model can be rapidly captured by utilising optical non-contact measuring techniques, e.g. laser scanner. This normally produces a large cloud data set that is usually arbitrarily scattered.
Approaches to transform a dense unstructured data set to a CAD representation can be classified into two categories: triangular polyhedral mesh based method and segment-and-fit based method [1, 2 and 3]. In the former approach, an initial triangular mesh is constructed to capture the unknown topological structure of the scattered data. Then the mesh is optimised to reduce the redundant vertices and afterwards a curvature-continuous surface is reconstructed based on this structure. Many triangulation techniques can be found in the literature, e.g. Delaunay triangulation algorithm [4 and 5], triangulation based on signed distance function [6] and triangulation based on α-shapes [7]. Triangulation for cloud data is however a computationally inefficient process [6 and 8].
For the second, the cloud data is divided into a suitable patchwork of surface regions to which an appropriate single surface is fitted [9]. Since manually segmenting 3D measured data is a laborious and error-prone process, some researchers have attempted to implement an automatic segmentation algorithm [2, 9 and 10]. Nevertheless, in general, present segmentation algorithms are sensitive, computationally complex or can only be applied to simple topology data [10].
Hence, in recent years, some novel RE approaches take into account a direct manufacturing of cloud data without involving surface reconstruction for more efficient rapid product development (RPD) [8]. However, these algorithms can only be applied to structured point data.
In this paper, the authors propose an error-based segmentation approach to arbitrarily scattered cloud data. Our goal is to integrate RE and rapid prototyping (RP) to assist manufacturers and designers in meeting the demands of reduced product development time. This is accomplished in the following steps. First, the cloud data are sliced into a number of layers along a user-specified direction. The points in each layer are projected onto a plane. Secondly, the points on each plane are sorted and compressed. An initial curve for each layer (so-called C-curve) is then generated. Thirdly, a local interpolating method (constructing R-curves using the corresponding points in each layer) is used for adding additional points to the slice-lines having insufficient points. Finally, a layer-based RP model is constructed and directly fed to RP machine for prototype manufacturing. Based on these techniques, experiment results are presented to illustrate the efficacy of the developed approach.
2. Cloud data segmentation
In essence, a C-curve is made up of a series of feature-point based planar curves. It is constructed in three steps. First, cloud data is pre-processed through slicing, projecting and sorting to generate initial C-curve. Secondly, the initial C-curve is compressed by removing all the redundant points except feature points (FPs) that represent the original shape information recorded in the data link. Lastly, the C-curve is constructed by linking all the FPs using straight-line segments. In the constructing process of these two curves, the shape accuracy is controlled by several user-specified parameters.
2.1. Data pre-processing
The first step towards constructing C-curve is to directly slice cloud data along a user-specified slicing direction and interval. The whole data set is then uniformly sliced into many subsets by computing the projecting errors of the points. Suppose that user-defined slicing direction and a data subset is X={P1,P2,…,Pn}, respectively. The centre of the data set X is calculated by
(1)
Assume that point OX is the closest to Pc, denote a plane associated with the centre point O and unit normal vector by , we define to be the projecting plane of data set X. The projecting error of point PiX to is then calculated by
(2)
If ei is greater than the pre-defined shape error, data set X is uniformly re-subdivided into two subsets. This process repeats for all the subsets until all ei meet the demand.
After slicing, all the points in the subset are projected onto the corresponding projecting planes and a “cleaning” process is carried out to sort the projected points. The aim of sorting is to set up a topological structure for the planar data as well as remove spurious data such as peaks and duplicate data to construct initial C-curves in the projecting plane. Due to the projected data points in the layer are unorganised and error-filled, it is important to pick up a correct point as the start in the sorting algorithm. The sorting algorithm is based on an estimated oriented tangent vector, which consists of five steps as follows:
Estimate the oriented tangent vector of each point.Suppose PiX is a point in the plane, we call k points of X nearest to Pi to be the k-neighbourhood of Pi, and denote this data set with . k is an user-specified parameter used to control the estimating accuracy of the originated tangent vector. As shown in Fig. 1(a), the originated tangent vector of Pi is calculated as
(3)
where Pc is the centre of determined by Eq. (1).
Retrieve the next point of the start point.Any point PiX can be selected as the first start point. Assume that the first start point and its oriented tangent vector is P0, , respectively (Fig. 1(b)), the retrieving algorithm would start with P0 and . When an end point is detected, algorithm goes back to P0 and retrieving resumes in the direction of ?, and stops when the other end point is determined.For each point PiX and its oriented tangent vector , we determine the next point of Pi, Pi+1, by
(4)
where ρ is the given shape error. Pi+1 is then taken as a new start point and retrieving continues with this point and its oriented tangent vector.
Delete the spurious points.In step (2), when the next point of the start point is determined, we define a circle using these two points whose diameter is equal to the distance of the points and delete all the points within the circle.
Terminate the sorting algorithm.Steps (1)–(3) form a retrieving cycle. When a cycle is completed, all the retrieved points in the cycle are flagged and linked together to form a C-curve. If all points in the plane are flagged, the algorithm terminates. Otherwise, a new retrieving cycle resumes with an un-flagged point that produces a new C-curve in the plane. The number of C-curves in different projecting planes may be different.
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Fig. 1. Data sorting.
2.2. Data compressing
Data pre-processing constructs initial C-curves for each projecting plane. However, the data size of the curve is extremely large that could plummet the computational robust and exceed the limited memory storage of the hardware. To resolve this, a feature-point based compressing algorithm is developed to compress redundant points on each plane using parametric cubic polynomial. To obtain a solution for a parametric form of a cubic polynomial curve, there should be at least four points. Hence, for each projecting plane, the C-curve is taken into account only when the corresponding point number is more than 4. Employing a least-square method, the unknown coefficient of the cubic polynomial can be obtained.
Since the basic shape information of a planar curve is exhibited by its FPs: corners or high curvature points, we define the parameter values corresponding to the FPs of the approximating curve as follows:
The present compressing algorithm is based on the above-mentioned FPs, which consists of the following steps (see Fig. 2):
Find all the FPs.
Link all the FPs with straight-line segments to generate a polygon.
Calculate the distances from the points in the C-curve to the polygon. If the distance is greater than the pre-defined shape error, this point is added as a new FP.
Go to step (2). This process repeats until all the points in the curve satisfy that their corresponding distances are within the given shape error.
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Fig. 2. Data compressing.
All the points except FPs are deleted. The final C-curve is then constructed by connecting all FPs using straight-line segments.
3. Data interpolation
After the C-curves are established, the data in the C-curves serve to construct curves across the layers (rows) to form the so-called R-curves. In essence, the goal of construction of R-curve aims to establish a topological structure for points in rows, thus assisting in interpolating new points for C-curves with inadequate points. Take the example shown in Fig. 3(a), the construction of R-curve is based on an estimated tangent plane, which consists of the following steps:
Estimate the tangent plane of each point.Suppose point PiX, denote m-neighbourhood of Pi with , and m is a user-specified parameter used to control the estimating accuracy of the tangent plane. The unit normal vector of the tangent plane can be determined by calculating the unit eigenvectors of a 3×3 symmetric matrix A as described as follows:
(5)
If λi1≥λi2≥λi3 denote the eigenvalues of A associated with unit eigenvectors , respectively, the estimated tangent plane is determined by .
Identify the oriented points in rows.Denote C-curve with Ci(z), R-curve with Ri(p), point data set with X and the tangent plane of point PiT(z0) with . Assume that the algorithm commences with projecting plane T(z0), as shown in Fig. 3(b), the oriented point of Pi in rows is determined by searching all the points pX in C-curves using
(6)
where ρ is the given shape error. If the above inequality is tenable, p is termed as the next/front row point of Pi. Otherwise Pi has no oriented row points. In order to improve the efficiency, only points in n-neighbourhood of projecting plane T(zi) are selected for calculating (n is specified by user). If n is selected along the positive normal of T(zi), the oriented point identified in rows is defined as the positive/next row point of Pi. If n is done along correspondingly negative normal, the identified point is the negative/front point of Pi. In this way, for each point in the C-curve, its two oriented points in rows can be determined.
Generate R-curves.Based on the point relationship in rows determined in step (2), generation of R-curve is carried out plane by plane in two directions. In our algorithm, a projecting plane that contains the maximal number of points is chosen as the start position. As show in Fig. 3(b), suppose that the plane is T(z0), we take point P0 as an example. First, along the positive normal direction , the oriented point of P0, P1, is linked as the next row point with P0. Because there is no more rows in this direction, the algorithm returns to P0 and searches for the oriented points along the negative direction . P?1 is thus added into the link as a front row point of P0. Searching continues with P?1 and hereby P?2 is added. The data link P?2→P?1→P0→P1 is an R-curve. R-curves are constructed in this way by retrieving all the points in C-curves (Fig. 3(b)).
Interpolate new points.The constructed R-curves are then intersected with every plane. A new point is therefore added to the respective C-curve on a plane if it does not exist before the intersection (Fig. 3(c)).The achieved C-curves are then faired using an algorithm based on discrete curvatures.
4. Construction of RP model
Although STL file has been the de facto industrial standard for RP machine, layer-based slice file such as CLI or SLC file format is also acceptable by RP machine. Here, the RP model is constructed based on the faired C-curves using a constant slicing strategy. As shown in Fig. 4, assume that the slicing layer Li(zi) lies between C-curve Ci(zk) and Ci+1(zk′), the corresponding point in Li(zi), Pj(zi), is calculated by
(7)
where Pm(zk) and Pm′(zk′) are the two nearest points located in Ci(zk) and Ci+1(zk′), respectively.
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Fig. 4. Data points in slicing layers and C-curves.
When all the points for slicing layers are generated, points in each layer are closed to generate an RP model that is directly sent to an RP machine for fabrication.
5. Application example
The algorithm described above has been implemented with C/C++ on HP-C200 workstation in the Unigraphics environment. A case study is presented here to illustrate the efficacy of the algorithm. The case is of a mask, which is composed of four range data patches. The original data cloud contains 104,175 points (see Fig. 5).
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Fig. 5. The original data cloud.
The slicing direction was given interactively as shown in Fig. 6(a). Based on this direction, the cloud data is processed to construct an RP model. Using a user-specified shape error shape=0.1?mm, the thickness of each layer is chosen as 0.2?mm. After data sorting and compressing, only 16,324 points are kept for modelling (see Fig. 6(b)). It took about 1?h for the algorithm to run on the HP-C200 workstation. The final C-curved model is shown in Fig. 7(a) and the constructed RP model in Fig. 7(b). This model is fed to an SLA RP machine and needs approximate 3?h to complete the fabrication.
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Fig. 6. The modelling process.
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Fig. 7. The final models.
6. Conclusions
In this paper, a new approach to deal with arbitrarily scattered cloud data for RP is presented. In our approach, a layer-based RP model is directly extracted from the cloud data through slicing, projecting, compressing and intersecting. Neither a surface model nor the STL file is generated. The method has been proven effective in dealing with complex surfaces and computational efficient through experiments. However, our approach currently can only handle cloud data that has no holes and lobes. Research on the multi-loops caused by the slicing of cloud data is still under developing. On the other hand, research on setting the slicing direction and other parameters automatically is also underway.