切管機(jī)設(shè)計(jì)【車輛用金屬管材進(jìn)行加工的切管機(jī)】
切管機(jī)設(shè)計(jì)【車輛用金屬管材進(jìn)行加工的切管機(jī)】,車輛用金屬管材進(jìn)行加工的切管機(jī),切管機(jī)設(shè)計(jì)【車輛用金屬管材進(jìn)行加工的切管機(jī)】,切管機(jī),設(shè)計(jì),車輛,金屬,管材,進(jìn)行,加工
湖 南 農(nóng) 業(yè) 大 學(xué)全日制普通本科生畢業(yè)設(shè)計(jì) 切管機(jī)設(shè)計(jì)THE DESIGN OF PIPE CUTTER學(xué)生姓名：學(xué) 號(hào)：年級(jí)專業(yè)及班級(jí)：2009級(jí)機(jī)械設(shè)計(jì)制造及其自動(dòng)化（三）班指導(dǎo)老師及職稱： 講師 學(xué) 院：工學(xué)院 湖南長沙 提交日期：2013年05月 湖南農(nóng)業(yè)大學(xué)全日制普通本科生畢業(yè)設(shè)計(jì)誠 信 聲 明本人鄭重聲明：所呈交的本科畢業(yè)設(shè)計(jì)是本人在指導(dǎo)老師的指導(dǎo)下，進(jìn)行研究工作所取得的成果，成果不存在知識(shí)產(chǎn)權(quán)爭議。除文中已經(jīng)注明引用的內(nèi)容外，本論文不含任何其他個(gè)人或集體已經(jīng)發(fā)表或撰寫過的作品成果。對本文的研究做出重要貢獻(xiàn)的個(gè)人和集體在文中均作了明確的說明并表示了謝意。本人完全意識(shí)到本聲明的法律結(jié)果由本人承擔(dān)。 畢業(yè)設(shè)計(jì)作者簽名： 年 月 日目 錄摘要1關(guān)鍵詞11 前言22 工藝方案的擬定23 傳動(dòng)裝置的設(shè)計(jì)與計(jì)算33.1 原動(dòng)機(jī)的選擇33.1.1 切管機(jī)類型的選擇33.1.2 切管機(jī)轉(zhuǎn)速的選擇33.1.3 切管機(jī)功率的選擇33.1.4 切管機(jī)的傳動(dòng)比43.2 傳動(dòng)方案額擬定43.3 各軸的轉(zhuǎn)速、功率和轉(zhuǎn)矩的計(jì)算63.4 傳動(dòng)機(jī)構(gòu)的設(shè)計(jì)與計(jì)算83.4.1 帶傳動(dòng)設(shè)計(jì)83.4.2 齒輪模數(shù)的確定93.4.3 蝸輪蝸桿模數(shù)的確定103.4.4 齒數(shù)的確定103.5 結(jié)構(gòu)的總體設(shè)計(jì)114 結(jié)構(gòu)設(shè)計(jì)114.1 各軸的最小直徑的初算114.1.1 直徑初算124.1.2 軸的校核124.2 各主要傳動(dòng)件結(jié)構(gòu)尺寸的計(jì)算204.2.1 三角帶輪204.2.2 蝸輪、蝸桿214.2.3 齒輪224.3 裝配示意圖的繪制234.3.1 減速箱234.3.2 軸裝配的工藝設(shè)計(jì)234.4 滾筒系統(tǒng)與進(jìn)給系統(tǒng)274.4.1 滾筒系統(tǒng)的設(shè)計(jì)274.4.2 進(jìn)給系統(tǒng)的設(shè)計(jì)275 結(jié)論28參考文獻(xiàn)28致謝29切管機(jī)設(shè)計(jì)學(xué) 生：指導(dǎo)老師：(湖南農(nóng)業(yè)大學(xué)工學(xué)院，長沙 410128)摘 要：本次的設(shè)計(jì)是車輛用金屬管材進(jìn)行加工的切管機(jī)，完成的工作主要是切管機(jī)中滾子，機(jī)體和減速箱部分的設(shè)計(jì)。包括傳動(dòng)裝置的設(shè)計(jì)和計(jì)算，其中有電動(dòng)機(jī)的選擇，傳動(dòng)方案的擬訂，各軸的轉(zhuǎn)速，功率和轉(zhuǎn)矩的計(jì)算?？傮w結(jié)構(gòu)的設(shè)計(jì)，其中有各軸尺寸的設(shè)計(jì)，各主要傳動(dòng)件的結(jié)構(gòu)尺寸的設(shè)計(jì)。并且針對以上的設(shè)計(jì)計(jì)算進(jìn)行了詳細(xì)的校核。最后通過得到的數(shù)據(jù)，繪制了總體裝配圖，減速機(jī)和滾子部分的裝配圖。然后又針對各主要基本件，繪制了多張零件圖。關(guān)鍵詞：切管機(jī)；結(jié)構(gòu)設(shè)計(jì)；方案；設(shè)計(jì)計(jì)算；The Design of Pipe Cuttter Student:Lu Haitao Tutor:Xiong Ying(College of Engineering,Hunan Agricultural University, Changsha 410128, China)Abstract： What need to be finished is the design of body of the machine and the roll of it. It includes the design and calculate of the slowing speed box,. The choose of the electromotor, the design of the gearing, the rev, the measure design of the main deliver parts. Than do the emandation work. After all ,get the data and drawing the engineering picture. It includes one final assembling picture, two assembling pictures of each parts, some small pictures of the important accessary.Key words:pipe cutting machine, design of structure,plan,design and calculation1 前言鋼管主要用來輸送流體(一般叫做輸送管、英文叫“pipe”)和用作鍋爐等的熱交換器管(叫做管子，英文叫“tube”)。鋼管是一種多功能的經(jīng)濟(jì)斷面鋼材。它在國民經(jīng)濟(jì)各部門應(yīng)用愈來愈廣泛，需求量也越來越大。管材的需要量之所以急劇增長，是因?yàn)楣茏幽苡酶鞣N材料來制造。而且質(zhì)量和精度也高。鋼管作為輸送管廣泛地用于輸送油、氣、水等各種流體，如石油及天然氣的鉆探開采與輸送、鍋爐的油水與蒸汽管道、一般的水煤氣管道。化工部門一般用管道化方式生產(chǎn)與運(yùn)輸各種化工產(chǎn)品。所以鋼管被人們稱為工業(yè)的“血管”。隨著鋼管的需求量的日益增大，鋼管的生產(chǎn)也顯得尤其的重要，因此切管機(jī)的設(shè)計(jì)生產(chǎn)就成了當(dāng)前所急需解決的課題。此次設(shè)計(jì)的切管機(jī)，主要用于常用的通風(fēng)、通水管。因此，下料所要求的精度不高。本切管機(jī)主要切削大量的薄壁的金屬管。如果用手工切斷，勞動(dòng)強(qiáng)度大，生產(chǎn)效率低，產(chǎn)品質(zhì)量差。因此，需要一臺(tái)，通用性好，耐用以及抗磨損的切管機(jī)。切管機(jī)的運(yùn)用，主要是為了降低勞動(dòng)強(qiáng)度，節(jié)省人力，提高產(chǎn)品質(zhì)量。當(dāng)然，保證經(jīng)濟(jì)性也是這次設(shè)計(jì)的重要考慮項(xiàng)目之一。由于切管機(jī)在實(shí)際生產(chǎn)中早已廣泛應(yīng)用，在使用與制造方面，已有一定的經(jīng)驗(yàn)，本次設(shè)計(jì)中有關(guān)切管機(jī)的一些參數(shù)，都采用已有的規(guī)定。因水平有限，論文中不免有疏忽與錯(cuò)誤的地方，敬請批閱老師指正。2 工藝方案的擬定本次設(shè)計(jì)任務(wù)為設(shè)計(jì)一簡單高效的切管機(jī)，為此，對如下幾種設(shè)計(jì)方案1進(jìn)行比較：方案一：用鋸弓鋸斷金屬管：需要鋸弓往復(fù)的切削運(yùn)動(dòng)和滑枕擺動(dòng)的進(jìn)給與讓刀運(yùn)動(dòng)。機(jī)器的結(jié)構(gòu)比較復(fù)雜，鋸切運(yùn)動(dòng)也不是連續(xù)的。當(dāng)金屬直徑相差較大時(shí)，鋸片還要調(diào)換，生產(chǎn)效率低。方案二：用切斷刀切斷金屬管：如在車床上切斷，但是一般車床主軸不過幾十毫米，通不過直徑較大的金屬管，并且占有一臺(tái)普通機(jī)床，不太經(jīng)濟(jì)。或者用專用的切管機(jī)，其工作原理是工件夾緊不動(dòng)，裝在旋轉(zhuǎn)刀架上的兩把切斷刀，既有主切削的旋轉(zhuǎn)運(yùn)動(dòng)，又有進(jìn)給運(yùn)動(dòng)，工作效率高，但是機(jī)床結(jié)構(gòu)比較復(fù)雜。方案三：用砂輪切斷金屬管：需要砂輪旋轉(zhuǎn)的切削運(yùn)動(dòng)和搖臂向下的進(jìn)給運(yùn)動(dòng)。此機(jī)構(gòu)的結(jié)構(gòu)簡單，生產(chǎn)效率高，但是砂輪磨損較快費(fèi)用很高。方案四：用碾壓的方法切斷金屬管：其需要金屬管旋轉(zhuǎn)的切削運(yùn)動(dòng)和圓盤向下的進(jìn)給運(yùn)動(dòng)。這種方法是連續(xù)切削的，生產(chǎn)效率高，機(jī)器的結(jié)構(gòu)也不太復(fù)雜。但是會(huì)使管子的切口內(nèi)徑縮小，一般用于管子要求不高的場合。綜合考慮，在本次設(shè)計(jì)中選用方案四。方案四切管機(jī)的工作原理：動(dòng)力由原動(dòng)機(jī)通過傳動(dòng)裝置傳遞給滾子。由于滾子的旋轉(zhuǎn)運(yùn)動(dòng)，從而帶動(dòng)工件的旋轉(zhuǎn)，實(shí)現(xiàn)切削時(shí)的主運(yùn)動(dòng)。與此同時(shí)，操作手輪，通過螺旋傳動(dòng)，將圓盤刀片向下進(jìn)給移動(dòng)，并在不斷增加刀片對管子的壓力過程中，實(shí)現(xiàn)管子的切割工作。3 傳動(dòng)裝置的設(shè)計(jì)與計(jì)算3.1 原動(dòng)機(jī)的選擇一般機(jī)械裝置設(shè)計(jì)中，原動(dòng)機(jī)多選用電動(dòng)機(jī)。電動(dòng)機(jī)輸出連續(xù)轉(zhuǎn)動(dòng)，工作時(shí)經(jīng)傳動(dòng)裝置調(diào)整和轉(zhuǎn)矩，可滿足工作機(jī)的各種運(yùn)動(dòng)和動(dòng)力要求。要選擇電動(dòng)機(jī)，必須了解電動(dòng)機(jī)，出廠的每臺(tái)電動(dòng)機(jī)都有銘牌，上面標(biāo)有電動(dòng)機(jī)的主要技術(shù)參數(shù)。因此，要合理地選擇電動(dòng)機(jī)，就要比較電動(dòng)機(jī)的這些特性。在進(jìn)行簡單機(jī)械設(shè)計(jì)時(shí)，應(yīng)選擇好電動(dòng)機(jī)的類型，轉(zhuǎn)速和功率。3.1.1 電動(dòng)機(jī)類型的選擇工業(yè)上一般用三相交流電源，所以選用三相交流異步電動(dòng)機(jī)。三相交流異步電機(jī)具有結(jié)構(gòu)簡單，工作可靠，價(jià)格便宜，維護(hù)方便等優(yōu)點(diǎn)，所以應(yīng)用廣泛。在選擇電動(dòng)機(jī)的類型時(shí)，主要考慮的是：靜載荷或慣性載荷的大小，工作機(jī)械長期連續(xù)工作還是重復(fù)短時(shí)工作，工作環(huán)境是否多灰塵或水土飛濺等方面。在本次設(shè)計(jì)中由于其載荷變動(dòng)較小，有灰塵故選擇籠式三相交流異步電機(jī)。3.1.2 電動(dòng)機(jī)轉(zhuǎn)速的選擇 異步電機(jī)的轉(zhuǎn)速主要有3000r/min、1500r/min、1000r/min、750r/min幾種。當(dāng)工作機(jī)械的轉(zhuǎn)速較高時(shí)，選用同步轉(zhuǎn)速為3000r/min的電機(jī)比較合適。如果工作機(jī)械的轉(zhuǎn)速太低（即傳動(dòng)裝置的總傳動(dòng)比太大）將導(dǎo)致傳動(dòng)裝置的結(jié)構(gòu)復(fù)雜，價(jià)格較高。在本次設(shè)計(jì)中可選的轉(zhuǎn)速有1500r/min和750r/min。在一般機(jī)械中這兩種轉(zhuǎn)速的電機(jī)適應(yīng)性大，應(yīng)用比較普遍。3.1.3 電動(dòng)機(jī)功率的選擇選擇電動(dòng)機(jī)的容量就是合理確定電動(dòng)機(jī)的額定功率，電動(dòng)機(jī)功率的選擇與電動(dòng)機(jī)本身發(fā)熱、載荷大小、工作時(shí)間長短有關(guān)，但一般情況下電動(dòng)機(jī)容量主要由運(yùn)行發(fā)熱條件決定。故根據(jù)電動(dòng)機(jī)的額定功率大于所需功率10%來選擇電動(dòng)機(jī)。綜上所述，本次設(shè)計(jì)的切管機(jī)的電機(jī)額定功率為P=1.5Kw滿載轉(zhuǎn)速為N=1410r/min,每天工作10小時(shí)，載荷變動(dòng)小用于多塵場合。選用Y90L-42型電動(dòng)機(jī)，其額定功率電為1.5Kw，滿載轉(zhuǎn)速n電=1400r/min，同步轉(zhuǎn)速1500r/min(4極)，最大轉(zhuǎn)矩為2.3Nm，質(zhì)量為27kg。3.1.4 切管機(jī)傳動(dòng)比 考慮到工件的旋轉(zhuǎn)速度和刀片強(qiáng)度，初定滾筒轉(zhuǎn)速為70r/min。因此電動(dòng)機(jī)確定后，計(jì)算出切管機(jī)的傳動(dòng)比為：i總=20 在傳動(dòng)方案確定后,根據(jù)i總=i1i2的關(guān)系分配傳動(dòng)比. 3.2 傳動(dòng)方案的擬訂傳動(dòng)方案的擬定，通常是指傳動(dòng)機(jī)構(gòu)的選擇及其布置。這是彼此相聯(lián)系的兩個(gè)方面。其運(yùn)動(dòng)形式大致分為以下幾個(gè)方面。（1）傳遞回轉(zhuǎn)運(yùn)動(dòng)的有：帶傳動(dòng)，鏈傳動(dòng)，齒輪傳動(dòng)，蝸輪傳動(dòng)3等；表1 幾種主要傳動(dòng)機(jī)構(gòu)的特性比較Table 1 Main drive mechanism comparison主要特性帶傳動(dòng)齒輪傳動(dòng)蝸桿傳動(dòng)主要優(yōu)點(diǎn)中心距變化范圍較大,結(jié)構(gòu)簡單,傳動(dòng)平穩(wěn),能緩沖,起過載安全保護(hù)作用外廓尺寸小,傳動(dòng)比準(zhǔn)確,效率高,壽命長,適用的功率和速度范圍大外廓尺寸小,傳動(dòng)比大而準(zhǔn)確,工作平穩(wěn),可制成自鎖的傳動(dòng)單級(jí)傳動(dòng)比,i開口平型帶:24,最大值6,三角帶型: 24, 最大值7有張緊輪平型帶:35最大值8開式圓柱齒輪: 46,最大值15. 開式圓柱正齒輪: 34,最大值10. 閉式圓柱齒輪: 23,最大值6閉式: 1040,最大值100開式: 1560,最大值100外廓尺寸大中,小小成本低中高效率平型帶0.920.98三角帶0.90.96開式加工齒0.920.96閉式0.950.99開式0.50.7閉式0.70.94自鎖0.400.45（2）實(shí)現(xiàn)往復(fù)直線運(yùn)動(dòng)或擺動(dòng)的有：螺旋傳動(dòng)，齒輪齒條傳動(dòng)，凸輪機(jī)構(gòu)，曲柄滑塊機(jī)構(gòu)等；（3）實(shí)現(xiàn)間歇運(yùn)動(dòng)的有棘輪機(jī)構(gòu)和槽輪機(jī)構(gòu)等；（4）實(shí)現(xiàn)特定運(yùn)動(dòng)規(guī)律的有凸輪機(jī)構(gòu)和平面連桿機(jī)構(gòu)等。傳動(dòng)機(jī)構(gòu)的選擇就是根據(jù)機(jī)器工作機(jī)構(gòu)所要求的運(yùn)動(dòng)規(guī)律，載荷的性質(zhì)以及機(jī)器的工作循環(huán)進(jìn)行的。然后在全面分析和比較各種傳動(dòng)機(jī)構(gòu)特性的基礎(chǔ)上確定一種較好的傳動(dòng)方案。機(jī)器通常由原動(dòng)機(jī)、傳動(dòng)裝置和工作機(jī)等三部分組成。傳動(dòng)裝置位于原動(dòng)機(jī)和工作機(jī)之間，用來傳遞運(yùn)動(dòng)和動(dòng)力，并可以改變轉(zhuǎn)速、轉(zhuǎn)矩的大小或改變運(yùn)動(dòng)形式，以適應(yīng)工作機(jī)功能要求。傳動(dòng)裝置的設(shè)計(jì)對整臺(tái)車的性能、尺寸、重量和成本都有很大影響，因此需要合理的擬定傳動(dòng)方案。在本次畢業(yè)設(shè)計(jì)中，已知切管機(jī)的i總=20，若用蝸桿，一次降速原本可以達(dá)到，但是由于切割的管子最大直徑為80mm，故兩個(gè)滾筒的中心距不能小于80mm，因此帶動(dòng)兩個(gè)滾筒的齒輪外徑不能大于滾筒的直徑（70mm）。若取蝸桿z1=2，蝸輪z2=40，m=4，則蝸輪分度圓直徑d2=160mm,比同一軸上的齒輪大，按此布置，蝸輪將要和滾筒相撞，為此，應(yīng)該加大兩軸之間的中心距。這樣就要加上一個(gè)惰輪，才可以解決這個(gè)問題，如圖1。 在本次設(shè)計(jì)中，取蝸輪齒數(shù)為z2=50,模數(shù)m=4。由于帶傳動(dòng)具有緩沖和過載打滑的特性，故可將其作為電機(jī)之后的第一級(jí)傳動(dòng)，此外開式齒輪傳動(dòng)不宜放在高速級(jí)，因?yàn)樵谶@種條件下工作容易產(chǎn)生沖擊和噪音，故應(yīng)將齒輪傳動(dòng)放在低速級(jí)。一個(gè)好的傳動(dòng)方案，除了首先應(yīng)滿足機(jī)器的功能要求外，還應(yīng)當(dāng)工作可靠、結(jié)構(gòu)簡單、尺寸緊湊、成本低廉以及使用維護(hù)方便。經(jīng)比較各種傳動(dòng)方案，在本次設(shè)計(jì)中確定采用帶傳動(dòng)、蝸桿傳動(dòng)、齒輪傳動(dòng)等機(jī)構(gòu)組成的傳動(dòng)方案。并初步畫出其傳動(dòng)系統(tǒng)圖，如圖2?？紤]到傳動(dòng)裝置的結(jié)構(gòu)、尺寸、重量、工作條件和制造安裝等因素，必須對傳動(dòng)比進(jìn)行合理的分配.根據(jù)公式T=9550(Nm)3可知:當(dāng)傳動(dòng)的功率P(Kw)一定時(shí),轉(zhuǎn)速n(r/min)越高，轉(zhuǎn)矩T就越小。為此,在進(jìn)行傳動(dòng)比的分配時(shí)遵循”降速要先少后多”。V 圖1 蝸輪蝸桿加中間惰輪傳動(dòng)方案圖Fig.1 Worm gear plus intermediate idler gear diagram帶傳動(dòng)的傳動(dòng)比不能過大，否則會(huì)使大帶輪半徑超過減速器的中心高，造成尺寸不協(xié)調(diào)，并給機(jī)座設(shè)計(jì)和安裝帶來困難，又因?yàn)辇X輪在降速傳動(dòng)中,如果降速比較大,就會(huì)使被動(dòng)齒輪直徑過大,而增加徑向尺寸,或者因小齒輪的齒數(shù)太少而產(chǎn)生根切現(xiàn)象.而其在升速傳動(dòng)中,如果升速比過大,則容易引起強(qiáng)烈的震動(dòng)和噪音,造成傳動(dòng)不平穩(wěn),影響機(jī)器的工作性能.為此,各機(jī)構(gòu)的傳動(dòng)比分配情況如下:i1=1.2；i2=50；i3=1.5；i4= （1）i總= i1i2 i3i4=1.2501.5=20 （2）注:傳動(dòng)系統(tǒng)只大齒輪是個(gè)惰輪,它不改變傳動(dòng)比只起加大中心距,改變滾筒旋轉(zhuǎn)方向的作用.3.3 各軸轉(zhuǎn)速、功率和轉(zhuǎn)矩的計(jì)算已知電動(dòng)機(jī)的數(shù)據(jù)如下： 查表2可知各級(jí)傳動(dòng)效率如下： 圖2 帶傳動(dòng)、蝸輪蝸桿、中間惰輪、齒輪方案圖Fig.2 Belt drive, the worm gear, intermediate idler gear diagram（1）計(jì)算各軸轉(zhuǎn)速如下：（2）各軸功率計(jì)算如下：（3）各軸傳遞的轉(zhuǎn)矩計(jì)算如下：注：軸3為設(shè)計(jì)上特別增加的惰輪（過渡齒輪），所以，軸3不承受轉(zhuǎn)矩，只承受彎矩。表2 數(shù)據(jù)匯總Table 2 summarization of date軸號(hào)電動(dòng)機(jī)軸傳動(dòng)比1.2501.51/4.5效率0.960.720.940.99轉(zhuǎn)速r/min1410116.723.315.570功率kw1.51.441.030.960.89轉(zhuǎn)矩kg.cm104.5-120.44290.51238.53.4 傳動(dòng)機(jī)構(gòu)的設(shè)計(jì)與計(jì)算3.4.1 帶傳動(dòng)設(shè)計(jì)帶傳動(dòng)適用的場合：中心距變化范圍較大，結(jié)構(gòu)簡單，傳動(dòng)平穩(wěn)，能緩沖，可起過載安全保險(xiǎn)的作用。缺點(diǎn)是外廓尺寸大，軸上受力較大，傳動(dòng)比不能嚴(yán)格保證，壽命低（約30005000小時(shí)）（1）在本次設(shè)計(jì)中，取帶的工作情況系數(shù)K=1.12，則計(jì)算功率為： P計(jì)= KP電=1.11.5=1.65(Kw) （3）（2）由P計(jì)和n1=1400r/min，可查知，選用A型三角帶。（3）初步選定小帶輪直徑d1=100mm,大帶輪直徑d2=i1d1=1.2100=120mm,取其標(biāo)準(zhǔn)直徑d2=125mm驗(yàn)算帶速： （4）因?yàn)?m/sv30m/s，故帶速合適（4）初定中心距a0，按公式：0.7（d1+d2）a0 d1+2r r倒圓直徑，查閱手冊中非配合處的過度圓角半徑用凸肩定位時(shí)按此式計(jì)算，用套筒定位時(shí)另取帶輪的定位靠套筒，此處的d2是指套筒外徑d3安裝滾動(dòng)軸承處的直徑dd3 d2dd3 d1無套筒的；套筒的d3必須符合軸承的標(biāo)準(zhǔn)由于采用205型軸承，d3=25mmd4裝在兩滾動(dòng)軸承之間齒輪（蝸輪）處的直徑dd4 d3+2rr倒圓角半徑，查閱手冊確定如如軸d5一般軸肩和軸環(huán)的直徑dd5d4+2a a軸肩或軸環(huán)的高度，a=(0.070.1) d4如如軸，d4=55mm，a=3.855.5mm,取a=5mm,則d5=55+2*5=65mm因此處d4相當(dāng)于d3=25，a=0.1 d4則d5=25+2*2.5=30mmd6滾動(dòng)軸承定位軸肩直徑查閱手冊軸承部分的D1值L7安裝旋轉(zhuǎn)零件的軸頭長度LL7=（1.21.6）ddd-軸頭直徑一般要求L7要比旋轉(zhuǎn)零件的輪轂寬度要短一些L8軸環(huán)長度L81.4a或L8（0.10.15）d如軸L81.4*5=7mm4.2 主要傳動(dòng)件結(jié)構(gòu)尺寸的計(jì)算4.2.1 三角帶輪已知選用A型三角膠帶，小三角帶輪計(jì)算直徑為d小=100mm;查表可知：h頂=3.5mm、=6mm，H=12mm、e=15+ -0.3mm、f=10mm、0=34o、b0=13.1mm。輪寬B=(z-1)e+2f=(2-1)15+210=35mm；外徑d頂小=d小+2 h頂=100 +23.5=107mm；孔徑d等于電動(dòng)機(jī)輸出軸直徑，查電動(dòng)機(jī)JO2得d軸=22mm。其結(jié)構(gòu)形式由表可知為實(shí)心輪。大三角帶輪計(jì)算直徑d大=125mm；h頂、H、e、f、B等尺寸和小三角帶輪一樣。0=38o,b0=13.4mm。外徑d頂大=d+2h頂=125+23.5=132mm；孔徑d等于與其配合的軸的軸徑，查表三可知軸的d軸=20mm；結(jié)構(gòu)形式由表7-11可知為輻板式：輪緣直徑d緣=d頂大-2（H+）=132-2（12+6）=96mm；輪轂直徑d轂=（1.82）d軸=3640mm，取d轂=40mm；輪轂寬度L=(1.51.8) d軸=3036mm，取L=35mm；輻板厚度由表7-11查得為S=10mm；輻板孔圓周定位尺寸： （13），因此，孔直徑為4.2.2 蝸輪、蝸桿已知z1=1、z2=50，m=4，q=11，根據(jù)表10-2得到：蝸桿分度圓直徑d1=qm=114=44mm；蝸輪分度圓直徑d2=z2m=504=200mm；蝸桿齒頂圓直徑d頂1=m(q+2)=4(11+2)=52mm；蝸輪齒頂圓直徑d頂2=m(z2+2)=4(50+2)=208mm；蝸桿齒根圓直徑d根1=m(q-2.4)=4(11-2.4)=34.4mm；蝸輪齒根圓直徑d根2=m(z2-2.4)=4(50-2.4)=190.4mm；蝸桿分度圓圓柱上螺旋升角，當(dāng)z1=1、q=11時(shí)，查得；蝸桿切制螺紋部分的長度L（11+0.06z2）m=(11+0.0650)4=56mm；蝸輪外圓直徑d外=d頂2+2m=208+24=216mm；蝸輪寬度B0.75 d頂1=0.7552=39mm；、軸中心距：可知：輪緣厚度f=1.7m=1.74=6.8mm蝸輪的孔徑d取決于軸的結(jié)構(gòu)設(shè)計(jì)，因蝸輪軸的最小直徑為42mm，取孔徑d=55mm。輪轂外徑d轂=（1.61.8）d=（1.61.8）55=8899mm取d轂=90mm輪轂寬度L=（1.21.8）d=（1.21.8）55=6699mm取L=70mm輻板厚度c1.5m=1.54=6，一般采用c=10mm蝸輪包角2=90o100o,一般采用2=90o4.2.3 齒輪（1）已知軸上齒輪z 2=54，m=3，則：分度圓直徑d 2=m z 2=354=162mm齒頂圓直徑d 頂2=m(z 2+2)=3（54+2）=168mm齒根圓直徑d 根2=m(z 2-2.5)=3 (54-2.5)=154.5mm此次齒輪制造精度教低，且是懸臂布置，故齒寬系數(shù)宜選小值，現(xiàn)取m=10所以齒寬B=mm=30mm.由于d 頂2160mm，可采用輻板式結(jié)構(gòu)的鍛造齒輪。輪緣內(nèi)徑d緣= d 頂2-10m=168-30=138mm輪轂外徑d轂=1.6d軸2=1.645=72mm(d軸2齒輪的孔徑，由表三可知d軸2=45mm)輻板厚度c=0.3B=0.330=9mm輻板孔圓周定位尺寸：d0=0.5(d緣+d轂) =0.5(138+72)=105mm （14）輻板孔直徑：d孔=0.25(d緣- d轂)=0.25(138-72)=16.5mm，取d孔=17mm。（2）已知軸上齒輪z3=81，m=3，則：分度圓直徑d3=mz3=381=243mm齒頂圓直徑d頂3=m(z3+2)=3(81+2)=249mm齒根圓直徑d根3=m(z3-2.5)=3(81-2.5)=235.5mm齒寬B=30mm。由于d根3160mm，可采用輻板式結(jié)構(gòu)的鍛造齒輪。輪緣內(nèi)徑d緣= d頂3-10m=249-30=219mm輪轂外徑d轂=1.6d軸3=1.650=80mm(d軸3齒輪的孔徑，由表三可知d軸3=50mm)輻板厚度c=0.3B=0.330=9mm輻板孔圓周定位尺寸：d0=0.5(d緣+d轂) =0.5(219+80)=149.5mm （15）輻板孔直徑：d孔=0.25(d緣- d轂)=0.25(219-80)=34.75mm，取d孔=35mm。、軸的中心距： （16）（3）已知軸上的齒輪z4=18,m=3則：分度圓直徑d4=mz4=318=54mm齒頂圓直徑d頂4=m(z4+2)=3(18+2)=60mm齒根圓直徑d根4=m(z4-2.5)=3(18-2.5)=46.5mm齒寬B=30mm。由于d根3160mm，故必須采用實(shí)心式結(jié)構(gòu)鍛造齒輪。、軸的中心距： （17）4.3 裝配示意圖的繪制已知各主要傳動(dòng)件的基本參數(shù)和總體結(jié)構(gòu)圖如圖4，確定零件的位置和箱體的外廓。 4.3.1 減速箱根據(jù)表5中的數(shù)據(jù)和待定尺寸，并根據(jù)總體結(jié)構(gòu)圖。暫定箱殼外型尺寸為：長=d外+2+2=162+210+28=198mm，取為200mm寬度估計(jì)為165mm高=64+202.5+ d外/2=64+202.5+81+10+8=365.5mm，取為366mm。圖4 總體裝配圖Fig4 General Assembly圖5 減速箱輪廓圖Fig.5 Outline of the gear box表5 減速箱各零件間相互位置尺寸Table5 size positions relative to the 4-3-1-1 gear box part代號(hào)名 稱推薦尺寸說 明切管機(jī)減速箱取值B1齒輪寬度由結(jié)構(gòu)設(shè)計(jì)定B1=30B帶輪寬度由結(jié)構(gòu)設(shè)計(jì)定B=35b軸承寬度根據(jù)軸頸直徑，按中或輕窄系列決定查手冊待定，如蝸桿軸的軸承，暫選為6205，則b=15箱殼壁厚，a為蝸輪傳動(dòng)中心距取=8旋轉(zhuǎn)零件頂圓至箱殼內(nèi)壁的距離=1.2取=101蝸輪齒頂圓至軸承座邊緣的徑向距離1=1012取1=10L1蝸桿中心至軸承中心的距離L1=0.8a,a為蝸桿傳動(dòng)中心距已知a=122故L1=97.6L2軸的支承間跨距由設(shè)計(jì)定L3箱外旋轉(zhuǎn)零件的中面至支承點(diǎn)的距離待定，暫取L4滾動(dòng)軸承端面至箱殼內(nèi)壁的距離當(dāng)用箱殼內(nèi)的油潤滑軸承時(shí)，L45當(dāng)用脂潤滑軸承時(shí)，并有擋油環(huán)時(shí)，L4=1015取L4=5L5軸承端面至端蓋螺釘頭頂面的距離由端蓋結(jié)構(gòu)和固緊軸承的方法確定待定，暫選L5=20L6箱外旋轉(zhuǎn)零件端面至端蓋螺釘頭頂面的距離L6=1520取L6=204.3.2 軸的裝配工藝設(shè)計(jì)（1）初定軸承跨距、設(shè)計(jì)軸承組合的結(jié)構(gòu)形式。有經(jīng)驗(yàn)公式確定L1=0.8a，已知蝸桿傳動(dòng)中心距a=122mm,則L1=0.8122=97.6mm，從而得到軸承的跨距為150mm（蝸輪分度圓直徑）。由于蝸桿傳動(dòng)同時(shí)受到徑向力和軸向力，且此處的軸承跨距不大，故采用單列向心推力球軸承6000型。對于軸承尺寸的選擇，根據(jù)軸頸直徑選擇軸承的內(nèi)徑，再者考慮到負(fù)載荷能力和結(jié)構(gòu)上的特點(diǎn)，此處宜采用輕窄系列。對于軸承組合的結(jié)構(gòu)形式，此處的蝸桿軸較短，傳遞功率小和轉(zhuǎn)速中等，故采用正排列的向心推力球軸承，因軸的直徑為25mm，故選兩個(gè)6205型和兩端固定支座的結(jié)構(gòu)形式，并用墊片調(diào)整軸承間隙。（2）軸向零件的周向和軸向固定。軸端三角帶輪的周向固定是采用普通平鍵和過渡配合。根據(jù)軸的直徑d1(D)=20選用“鍵632GB1096-79”。三角帶輪的軸向固定是靠套筒和軸端檔圈。套筒的直徑尺寸參照（軸的各段直徑和長度）軸端檔圈的選用根據(jù)機(jī)械設(shè)計(jì)手冊選用，其中軸端直徑d=20mm選用“檔圈28GB892-76”，“螺栓M514GB30-76”，“銷2n610GB119-76”，“墊圈5GB93-76”。軸上其它零件的尺寸和固定方式按照下表的經(jīng)驗(yàn)公式確定。由于蝸桿蝸輪使用的是機(jī)油潤滑，而軸承使用的是油脂，因此，選用檔油歡這種密封結(jié)構(gòu)。為了軸向固定更加可靠，凡是與旋轉(zhuǎn)零件（如帶輪、齒輪、蝸輪、軸承等）配合的軸頭長度在設(shè)計(jì)時(shí)都比旋轉(zhuǎn)零件的輪轂寬度要短一些。（3）強(qiáng)度校核及結(jié)構(gòu)設(shè)計(jì)軸在載荷作用下，將產(chǎn)出彎曲或扭轉(zhuǎn)變形。若變形量超過允許的限度，將會(huì)影響軸上零件的正常工作，甚至?xí)适C(jī)器應(yīng)有的工作性能。例如，安裝齒輪的軸，若彎曲剛度（或扭轉(zhuǎn)剛度）不足而導(dǎo)致?lián)隙龋ɑ蚺まD(zhuǎn)角）過大時(shí)，將影響齒輪的正確嚙合，使齒輪沿齒寬和齒高方向接觸不良，造成載荷在齒面上嚴(yán)重分布不均。又如采用滑動(dòng)軸承的軸，若撓度過大而導(dǎo)致軸頸偏斜過大時(shí)，將使軸頸和滑動(dòng)軸承產(chǎn)生邊緣接觸，造成不均勻磨損和過渡發(fā)熱。因此，在設(shè)計(jì)有剛度要求的軸時(shí)，必須進(jìn)行剛度的校核計(jì)算。軸的結(jié)構(gòu)設(shè)計(jì)及強(qiáng)度校核：軸上裝有的主要零件為：軸承、鍵、軸環(huán)、帶輪等。由表三可知其最小直徑為45mm。已知：z 2齒輪分度圓直徑d 2162mm，z3齒輪分度圓直徑d3243mm，z4齒輪分度圓直徑d454mm，、軸中心距=202.5mm，、軸中心距=148.5mm，兩滾筒中心距108mm，軸轉(zhuǎn)矩420.2，軸轉(zhuǎn)矩122.3。驗(yàn)算過程：1）畫出受力分析圖31a，由于運(yùn)動(dòng)是從齒輪z 2經(jīng)惰輪z3傳給兩個(gè)z4齒輪，在惰輪z3的圓周上就同時(shí)作用著P1、P2、P3三個(gè)切向力；2）根據(jù)滾筒中心距108mm和=148.5mm，我們可以計(jì)算出角。因?yàn)樵谥苯侨切巍?中，所以；3）根據(jù)轉(zhuǎn)矩 （18） （19）4）利用力的平移和四邊形法則，求作用在軸上的合力。如圖31b，用作圖法可量得P48360N，P=P1+P4=5185.43+8360=13545.43N5）軸的最大彎矩發(fā)生在B支座、即惰輪z3的中面至滾動(dòng)軸承中面的距離，現(xiàn)取為l3=70mm的位置，其最大彎矩為： （20）6）當(dāng)軸的材料為45號(hào)鋼時(shí)，轉(zhuǎn)動(dòng)心軸的B0.26，則： （21）現(xiàn)在設(shè)計(jì)軸頸的直徑為55mm，所以合適。 7）結(jié)構(gòu)中所用潤滑為L-CPE/P蝸輪蝸桿油，滾珠軸承脂（SY1514-82），7407號(hào)齒輪潤滑脂（SY403684），所用密封方式有氈圈式密封，迷宮式密封槽密封。4.4 滾筒系統(tǒng)與進(jìn)給系統(tǒng)4.4.1 滾筒系統(tǒng)設(shè)計(jì)滾筒主要通過惰輪帶動(dòng)兩個(gè)連接在滾筒上的齒輪轉(zhuǎn)動(dòng)來旋轉(zhuǎn)，從而帶動(dòng)滾筒上的工件旋轉(zhuǎn)，滾筒的粗糙度設(shè)定為Ra25,采用T7碳素工具鋼，滾筒上設(shè)計(jì)有螺旋槽，主要是工作時(shí)可及時(shí)有效的排出加工廢料，保證工件與滾筒接觸良好。4.4.2 進(jìn)給系統(tǒng)設(shè)計(jì)本設(shè)計(jì)主要采用了螺旋傳動(dòng)的設(shè)計(jì)方法，通過轉(zhuǎn)動(dòng)手輪使刀片均勻進(jìn)給，其優(yōu)點(diǎn)是1摩擦阻力小，傳動(dòng)效率高，具有傳動(dòng)可逆性2運(yùn)轉(zhuǎn)穩(wěn)定，工作壽命長，不易發(fā)生故障。采用滑動(dòng)螺旋傳動(dòng)，螺紋為梯形螺紋，螺桿和螺母的材料為鋼對青銅，螺紋牙強(qiáng)度為鋼0.6Mpa,青銅30-40Mpa ?；瑒?dòng)螺旋副采用梯形螺紋，牙形角=30，螺紋副的大徑和小徑處有相等的徑向間隙。刀具是由高速工具鋼為材料的圓盤刀片。5 結(jié)論通過對相關(guān)資料的查閱和對切管機(jī)的設(shè)計(jì)計(jì)算，并且對切管機(jī)進(jìn)行了初步的設(shè)計(jì)。在設(shè)計(jì)過程中，主要的工作有如下幾點(diǎn)：第一，對傳動(dòng)方案的選擇和對機(jī)構(gòu)的設(shè)計(jì)計(jì)算,其中包括選擇合適的傳動(dòng)方案和對減速箱部分各個(gè)零件的設(shè)計(jì)計(jì)算以及校核。第二，設(shè)計(jì)計(jì)算結(jié)束后，在已有數(shù)據(jù)的基礎(chǔ)之上，畫出了總體裝配圖的輪廓，通過對各個(gè)參數(shù)的進(jìn)一步確定，最后終于得到了總體裝配圖。第三，對幾個(gè)主要的零部件進(jìn)行了繪制,其中包括滾子零件的工作圖，蝸桿的零件圖等。從這一設(shè)計(jì)題目的綜合運(yùn)用中，更是把所學(xué)的這些知識(shí)有了一個(gè)大的融會(huì)與應(yīng)用，從而所學(xué)的知識(shí)也不再是死的，有了一個(gè)比較全面的復(fù)習(xí)。在設(shè)計(jì)與計(jì)算的過程中，也遇到了許多的困難與問題。通過查找資料，將這些問題解決的這種獨(dú)立的解決問題和思考的方法，是在這次設(shè)計(jì)中我得到的一個(gè)最大的收獲。當(dāng)然，從中也大致了解了一些產(chǎn)品設(shè)計(jì)的基本方法，這也將是一次寶貴的實(shí)踐經(jīng)驗(yàn)。相信在以后的工作中，將會(huì)有很大幫助。參考文獻(xiàn)1 王昆等.機(jī)械設(shè)計(jì)、機(jī)械設(shè)計(jì)基礎(chǔ)課程設(shè)計(jì).北京:高等教育出版社,20052 吳宗澤.機(jī)械設(shè)計(jì)使用手冊.北京:化學(xué)工業(yè)出版社,20003 璞良貴，紀(jì)名剛主編.機(jī)械設(shè)計(jì).第七版.北京：高等教育出版社，20014 孫桓，陳作模主編.機(jī)械原理.第六版.北京：高等教育出版社，20025 艾云龍等.工程材料及成型技術(shù).南昌:南昌航空工業(yè)學(xué)院出版社,20046 劉鴻文.材料力學(xué).北京:高等教育出版社,20047 廖念釗等.互換性與技術(shù)測量.北京:中國計(jì)量出版社,20018 陳宏鈞.實(shí)用金屬切削手冊.北京:機(jī)械工業(yè)出版社,20059 于惠力等.機(jī)械零部件設(shè)計(jì)禁忌.北京:機(jī)械工業(yè)出版社,200610 成大先主編.機(jī)械設(shè)計(jì)手冊.北京：化學(xué)工業(yè)出版社，200411 阮忠唐.聯(lián)軸器、離合器設(shè)計(jì)與選用指南.北京:化學(xué)工業(yè)出版社,200512 周四新.Pro/ENGINEER Wildfire 綜合培訓(xùn)教程.北京:機(jī)械工業(yè)出版社,200413 劉慶國等.計(jì)算機(jī)繪圖.北京:高等教育出版社,200414 菜春源.新編機(jī)械設(shè)計(jì)手冊.沈陽:遼寧科學(xué)技術(shù)出版社,199315 Ye Zhonghe, Lan Zhaohui. Mechanisms and Machine Theory. Higher Education Press, 2001.7致 謝本論文是在熊瑛老師的悉心指導(dǎo)和熱情關(guān)懷下完成的，在此，再次感謝老師，同時(shí)，她不厭其煩的指導(dǎo)和幫助，以及其本人嚴(yán)謹(jǐn)而認(rèn)真的工作研究態(tài)度，也給我留下了深刻的印象。最后，再次向在我的這次畢業(yè)設(shè)計(jì)中幫助、指導(dǎo)我的各位老師與同學(xué)，表達(dá)最真誠的謝意。同時(shí)感謝這四年來老師們和輔導(dǎo)員等關(guān)心愛護(hù)我么你的人，這份畢業(yè)設(shè)計(jì)更是對你們過去四年來對我們關(guān)心的總結(jié)和回報(bào)。30Reel and sheet cutting at a paper millM. Helena Correia, Jose F. Oliveira, J. Soeiro FerreiraINESC Porto, Instituto de Engenharia de Sistemas e Computadores do Porto, 4200-465 Porto, PortugalFaculdade de Economia e Gestao, Universidade Catolica Portuguesa, 4169-005 Porto, PortugalFaculdade de Engenharia, Universidade do Porto, 4200-465 Porto, PortugalAbstractThis work describes a real-world industrial problem of production planning and cutting optimization of reels and sheets, occurring at a Portuguese paper mill. It will focus on a particular module of the global problem which is concerned with the determination of the width combinations of the items involved in the planning process: the main goal consists in satisfying an order set of reels and sheets that must be cut from master reels. The width combination process will determine the quantity/weight of the master reels to be produced and their cutting patterns, in order to minimize waste, while satisfying production orders.A two-phase approach has been devised, naturally dependent on the technological process involved.Details of the models and solution methods are presented. Moreover some illustrative computational results are included.2003 Elsevier Ltd. All rights reserved.Keywords: Combinatorial optimization; Cutting-stock; Heuristics1. IntroductionPlanning the paper production at a paper mill assumes several essentially distinct forms, each of which has its own particular characteristics, requiring different mathematical formulation and solution methods 13. However, trim loss minimization is usually a component of the objective function. Other components take account of factors such as setup processing time, number and characteristics of cutting patterns. Additionally, there are usually several constraints involved, concerning customers specifications, strategic decisions and technological characteristics of the production process.This paper describes a system developed by request of a Portuguese paper mill, Companhia dePapel do Prado (CPP), to support its production planning, focusing on the production and cutting of paper reels. This work is part of a broader system, named COOL (COOL stands for the Portuguese words meaning optimized combination of widths), which is intended to support the implementation of an optimizing policy for paper production and stock management.The problem tackled in this paper concerns the definition of cutting patterns and quantity of paper to produce in order to satisfy a set of ordered reels and sheets, grouped by type of paper and grade.It basically deals with the problem of planning the paper production and cutting of the master reels in order to satisfy a set of orders. The cutting plans to associate to the master reels must be defined considering minimization of waste while satisfying the ordered quantities. Varieties of technological and operational constraints are involved in the planning process, causing an interesting and dig cult trim problem.From this perspective, this problem can be included in the broad family of Cutting-Stock Problems 46. The problem formulation adopted disregards trim loss at the end of the reels (as it was considered irrelevant when compared with that occurring at the edges of the paper reels, which runs all along the paper length) and so, a 1D approach has been devised. The need of a two-phase methodology was determined by the technological characteristics of the cutting process. Other 1D two-phase cutting-stock problems can be found in published literature. Besides paper industry, similar approaches are also applied in other industries, such as the steel industry 7,8 and the plastic Flm industry 9.We propose an original solution method for the problem described above, which leads to considerable improvements in terms of paper savings when compared with those solutions obtained manually, as confirmed by the paper mill. The procedure developed is based on two distinct linear programming models, which are solved by a Simplex algorithm. Then, the solutions obtained are rounded in a post-optimization procedure, in order to satisfy integer constraints previously ignored. The quality of the solutions obtained are also validated by the resolution of an integer programming model of the problem, solved using the commercial optimization software CPLEX v.6.0.The paper is organized as follows. Section 2 introduces the production problem and its industrial background. Particular emphasis will be given to those features of the industrial environment, which were relevant for the solution approach developed. Sections 3 and 4 will describe the problem and the methodology developed to solve it, respectively. A small example is considered throughout Section 4 in order to illustrate the solution procedure. In Section 5 some results will be presented and discussed.2. Industrial environmentThis case study takes place at a Portuguese paper mill, which can be considered as a vertical industry, since it produces paper products from pulp. The products are supplied both in reels and sheets. This industry operates in two types of markets: one in which the paper products have standard dimensions and other where paper products have make-to-order dimensions. The production cycle is of 6 weeks and, for technological reasons, there is a pre-defend production sequence in which paper is produced in ascending or descending rates. Fig. 1 shows the production Jow of the paper products through out the production line. The paper is produced at the paper machine from pulp and is wound into a master reel of fixed width. Then, the master reel follows to the winder where it is cut into smaller reels. These reels either go straight to the customer or to the Intermediate Stock, or are cut into sheets at the cutters. These cut-to-sizes sheets either go to the customer or to the Standard Stock. Both at the winder and cutters there is a small shred of fixed width cut-o8 all along the paper length. This scrap has been quite determinant for the solution process adopted. Fig. 2 illustrates the relative perspectives of planning and production processes, emphasizing the products and sub-products involved. Planning and Production follow opposite directions. Plannings based on the customers specifications of ordered products. Ordered reels and sheets of the same type of paper and grade, and belonging to the same Production Order, are combined into auxiliary reels. These auxiliary reels may include either reels or sheets, but never both. So, two types of auxiliary reels will be distinguished: auxiliary reels of sheets and auxiliary reels of reels. Auxiliary reels are then combined into cutting patterns that are associated to master reels.The concept of auxiliary reel has been introduced for a better understanding of both the production procedure and the solution approach adopted. It is strictly related to the technological process involved, which requires the consideration of additional scrap width whenever the cutters are used. The definition of sub-patterns inside the main cutting patterns to be cut from the master reels has determined the two-phase solution approach considered. There is a set of constraints that must be considered in the generation of the auxiliary reels and cutting patterns and which will be described later in Section 3. These constraints determine pattern feasibility. The order system is schematized in Fig. 3. An order can be placed by the national market or by the international market (as this company also operates outside Portugal) and is processed by the Marketing Department. The Marketing Department can also generate an internal order, similar to the external orders, if it is considered appropriated. These orders can originate a Production Requisition, a Cutting Order or an Expedition Order. A Production Requisition is grouped with other existing Production Requisitions of the same type of paper and grade, resulting in a Production Order, which then follows to production. A Cutting Order occurs when a customer order of reels can be satisfied by existing reels (stocked at the Intermediate Stock) and an Expedition Order occurs when a customer order of sheets can be satisfied by existing sheets (stocked at the Standard Stock).3. Problem descriptionThe work presented in this paper is mainly concerned with the cutting patterns generation process, which will determine the quantity/weight of the master reels to produce and the associated cutting patterns, in order to minimize waste while satisfying a production order. The system developed will support the cutting planning of a Production Order, not interfering with decisions related to the orders to satisfy and the type of paper to produce in each production cycle. These are previous decisions made by the Marketing Department, eventually supported by a simulation using the system COOL.Some constraints must be considered during the definition of the cutting patterns to associate to a master reel. These constraints can be grouped in two sub-sets: Operational constraints (imposed by management and customers specifications): Only reels of identical weight per width unit (reels with the same length of paper) can be combined. Only reels of identical internal and external diameters can be combined. Customer specifications of internal and external diameters must be satisfied. Assignment of the auxiliary reels to the cutters must be considered, since cutters have different characteristics. Minimum width is imposed to cutting patterns, in order to optimize the use of the machinery available. Technological constraints (mainly due to machinery characteristics): Maximum and minimum widths of the master reel at the winder (input). Limited number of winder slitting knives. Maximum and minimum sheet lengths at the cutters. Maximum and minimum sheet widths at the cutters. Limited number of slitting knives at the cutters. Maximum diameter of input reels at the cutters. Edge trims loss both at the winder and cutters.There are European Standard Tolerances in use at the paper industry, which must be taken into account when fulfilling order (see Table 1). The client is obliged to accept deviations of the quantity ordered in these ranges. When over-production above maximum tolerances occurs, the Marketing Department can try to negotiate the acceptance of this extra quantity with the client. Due to losses inherent to production, negative tolerances are never considered during the planning phase.4. Solution procedureThe solution procedure adopted is clearly injected by the production Jow. It is divided into three main stages, which are represented in Fig. 4.The First stage consists in enumerating all the auxiliary reels and cutting patterns, based on a fixed width for the master reel and on the widths of the ordered items. The resultant set of cutting patterns is then submitted to a selection process through which undesirable auxiliary reels/cutting patterns are eliminated. All the remaining cutting patterns must be feasible in terms of the technological and operational constraints imposed to the production process. In the second stage, the cutting patterns generated and accepted during the First stage are used as columns in a linear programming model of the optimization problem. Two linear programming models were developed. These models are solved by a Simplex algorithm 10. In the following sections each one of these stages will be presented in detail. A small real industrial example is introduced to illustrate the solution procedure and will be followed through out its description. It concerns the production planning of paper in master reels of 2520 mm width. The paper grade is 250 g=m2 and its thickness is 345 _m. The Production Requisitions involved are described in Table 2.Rounding heuristicThe rounding procedure is applied to the solution of both LP models and is intended to fulfill those constraints of integer nature previously ignored, such as:(1) Fixed 7nished reels diameters imposed by the customer must be satisfied, meaning that the paper length of cutting patterns including such reels must always be multiple of the requested diameter. In order to minimize the impact of this heuristic procedure, the quantities ordered of reels of Fixed diameter are adjusted to the closest multiple of the length of one reel before building the LP model.Table 3(2) The minimum weight for combination of sheets constraint, equivalent to a minimum paper length, intends to avoid inefficient use of the cutters.(3) Alike the previous item, the minimum weight for cutting pattern constraint is intended to prevent inefficient use of the winder, while establishing a minimum quantity of paper to cut with each cutting pattern used.The rounding heuristic starts with the Final solution of the LP model (non-zero length patterns) and tries to adjust those pattern lengths in order to satisfy the referred constraints. The new solution is kept as close as possible to the LP one and must satisfy the ordered quantities. First, the rounding procedure tries to eliminate those patterns which do not respect the minimum weight conditions (constraints 2 and 3 above). Precaution must be taken not to eliminate the unique pattern containing some ordered item. Then, the remaining patterns must be rounded up in order to compensate the e8ect of the destroyed ones. This procedure consists basically in successively sorting the cutting patterns by the number of items not satisfied in each pattern, and augmenting the quantity to be cut with the First cutting pattern of the list until, at least, one unsatisfied item becomes satisfied. This procedure is repeated until all the items in all cutting patterns are satisfied.This rounding procedure can lead to over-production above standard tolerances, even when Model(1) is used.In the solution presented in Table 3, only the constraint concerning the minimum weight for combination of sheets is not being satisfied by the length of FP 16(x12) since it is smaller than the minimum weight for combination of sheets determined for that pattern (2730:00 mm). As the only order in that pattern is PR 1002 and it also exists in FP 21 (x14), pattern FP 16 can be eliminated and the length of FP 21 must be adjusted to include the quantity of PR 1002 that was being cut from FP 16. The Final solution is presented in Table 4. Fig.5.shows the output of COOL for the data in Table 2.Table 4Fig.5.Computational results for large-scale instances5. Computational resultsThe main purpose of the computational tests was to validate the solution procedure adopted and to establish a comparative analysis between the two linear programming models developed (Model(1) and Model(2). The data used in this First set of computational runs was provided by the Marketing Department of the company and corresponds to real problems solved at the paper mill. The number of ordered items involved range from 3 to 16 and the maximum and minimum width of the ordered items are 1392 and 238 mm, respectively, being the average width 690 mm, approximately. These are relative small instances but, by doing this, the company intends to allow the system user to easily evaluate the performance of COOL in the initial phase of usage. Data used in the computational tests is available at www.apdio/sicup. The algorithms were implemented using the C programming language. The computational results were obtained with a Pentium III at 450 MHz.In order to evaluate the quality of the solutions obtained with the linear models and rounding heuristic described above, an IP model was implemented. This IP model minimizes the amount of paper produced while strictly satisfying the ordered quantities. In order to consider those integer constraints mentioned above, several integer variables are included: Minimum weight for combination of sheets (Min Weight Sheets): The IP model was solved using the Mixed Integer Programming module of the optimization software CPLEX v.6.0.In Fig.6, the performance of each solution procedure developed (based on the two LP models, Model(1) and Model(2) is evaluated in terms of objective function value. In Fig.6(a), for each model, the ratio of the results obtained with the IP model and those obtained with the linear procedure followed by the rounding heuristic are depicted for each test instance: the value of 1.00 in the y-axis corresponds to the IP model solution. From this chart it can be observed that the results of the linear based procedure are, in most cases, coincident with those obtained with the IP model: Model(1) attains the same objective function values of IP in 70% of the test instances while only approximately 50% of the results obtained with Model(2) are coincident with the IP results. Though, with only one exception, the IP results are never exceeded in more than 22%. The chart in Fig.6(b) intends to prove the adequacy of the linear approach adopted and, so, the ratio of the results before and after the rounding procedure is computed. The value of 1.00 in the y-axis corresponds to the LP model solution before the rounding procedure. In most cases, the results of the LP routine are coincident with the Final result, which means that, in those cases, the constraints of integer nature considered in the rounding procedure do not change the linear programming result. Both charts show that the results obtained with Model(1), which minimizes the paper length produced and does not allow over production above tolerances, are never worse than those obtained with Model(2), which does not produce to the Intermediate Stock. Moreover, these results suggest the need to improve the rounding procedure in case of Model(2). Table 5Table 5 compares the results obtained with the two linear programming models in terms of the three exceeding components: quantity produced to the Intermediate Stock (QuantStock), overproduction above standard tolerances (QuantTolExc) and quantity of paper that cannot be re-used in any way (Waste). All the values are expressed in terms of a percentage of the total weight of paper produced and reject the objective function adopted in each model: Model(2) does not produce to the Intermediate Stock while Model(1) tries not to exceed standard tolerances. The amounts in which, sometimes, these tolerances are exceeded in Model(1) are a consequence of the rounding procedure. However, they are quite small when compared to those obtained with Model(2). Since waste is the only component which can not be re-used, Fig.7draws attention to the comparison between the values obtained with the two LP based procedures: Final solutions based on Model(1) are seldom significantly worse than those attained with Model(2), in terms of paper waste minimization. According to the comparative tests performed with this set of instances, Model(1) seems to perform better than Model(2) in all of them. Nevertheless, Model(2) was kept available in the Final version of COOL, as each model may generate solutions more adequate to, or even required by, different industrial situations: when production to the Intermediate Stock is allowed or even recommended, Model(1) can be used; situations in which Intermediate Stock levels are high enough to forbid stock enlargement, Model(2) solutions may be required. In terms of efficiency, the LP approach lead to a reduction of the processing time of approximately 75% of the time used by the IP approach. Although the average resolution time of the IP approach for the instances tested was of 18 s, situations may occur which would preclude the use of the IP approach in practice. A set of larger instances was generated and tested in order to evaluate the performance in terms of efficiency of the develo
收藏