家用紙杯成型機(jī)設(shè)計(jì)

1、杭州電子科技大學(xué)畢業(yè)設(shè)計(jì)（論文）外文文獻(xiàn)翻譯畢業(yè)設(shè)計(jì)（論文）題目家用紙杯成型機(jī)設(shè)計(jì)翻譯題目 對(duì)紙杯成型機(jī)桶形凸輪的優(yōu)化研究學(xué) 院信息工程學(xué)院專 業(yè)機(jī)械設(shè)計(jì)制造機(jī)器自動(dòng)化姓 名班 級(jí)學(xué) 號(hào)指導(dǎo)教師巢炎 對(duì)紙杯成型機(jī)桶形凸輪的優(yōu)化研究 摘要 旭賢基姆 韓國(guó)水原亞洲大學(xué)的博士生 Tae Won park 水原亞洲大學(xué)機(jī)械工程學(xué)院的一名教授。 紙杯成型機(jī)一分鐘最多可以生產(chǎn)140個(gè)紙杯。如果生產(chǎn)率提高，使凸輪的接觸力增加，會(huì)產(chǎn)生更多的振動(dòng)。因此，找一個(gè)減少凸輪振動(dòng)的方法是有必要的。槍管凸輪的輪廓線是通過使用多體動(dòng)力學(xué)模型去優(yōu)化。優(yōu)化的目標(biāo)是使?jié)L子與凸輪之間發(fā)生的接觸力最小。使用優(yōu)化的凸輪進(jìn)行了實(shí)驗(yàn)。對(duì)比

2、目前的利率進(jìn)行優(yōu)化率較高的生產(chǎn)減振。關(guān)鍵字：紙杯；凸輪；多體動(dòng)力學(xué)；優(yōu)化；接觸力1簡(jiǎn)介 紙杯的需求迅速增加由于他們?cè)诒Ｗo(hù)環(huán)境方面的便利性和有效性. 為了滿足需求，目前的生產(chǎn)力也應(yīng)該要增加。然而，簡(jiǎn)單地增加生產(chǎn)率的結(jié)果在機(jī)器的振動(dòng)床上，當(dāng)機(jī)器受到震動(dòng)床的影響，會(huì)產(chǎn)生有缺陷的紙杯。這是一個(gè)嚴(yán)重的問題。圖1顯示當(dāng)前的紙杯成型機(jī)。目前的機(jī)器每分鐘可生產(chǎn)140個(gè)紙杯。如果生產(chǎn)率增加，回使每個(gè)凸輪磨損得很快，使凸輪不得不更換。紙杯是在紙杯成型機(jī)轉(zhuǎn)塔中形成，七輥指數(shù)是連接到轉(zhuǎn)塔的。該凸輪使?jié)L子凸輪旋轉(zhuǎn)移動(dòng)，所以轉(zhuǎn)塔也是轉(zhuǎn)動(dòng)的。接觸力發(fā)生的凸輪與滾輪之間。紙杯成型機(jī)運(yùn)行一段時(shí)間后，由于有接觸力所以磨損發(fā)生在桶

3、凸輪和滾子的表面。然后，振動(dòng)和噪聲大大增加，需要更換凸輪和滾輪。 在這一領(lǐng)域的研究已廣泛。伊佩克調(diào)查磨損機(jī)制的變化與凸輪軸的磨損的表面形貌。該凸輪表面的變化沿接觸表面的磨損機(jī)理【1】 。提出了一種模擬彭內(nèi)斯特的變速凸輪致動(dòng)器。該致動(dòng)器是一個(gè)凸輪移動(dòng)銷根據(jù)規(guī)定的運(yùn)動(dòng)規(guī)律。在換擋仿真，接觸力和磨損行為進(jìn)行了比較2?？≌J(rèn)為，凸輪的磨損是由滾子和套筒之間的接觸力引起的。對(duì)圓柱凸輪的磨損點(diǎn)幾乎與多體動(dòng)力學(xué)模型的接觸力大點(diǎn)保持一致.3.。曉優(yōu)化使用一個(gè)新的多項(xiàng)式樣條曲線和B樣條凸輪驅(qū)動(dòng)發(fā)動(dòng)機(jī)的凸輪輪廓曲線。分析定義的優(yōu)化問題是一種獨(dú)特的凸輪機(jī)構(gòu)4。新提出了一種運(yùn)用相對(duì)速度設(shè)計(jì)圓柱凸輪的形狀的方法。局部坐標(biāo)

4、用相對(duì)速度的方法得出，桶凸輪的形狀是由CAD程序創(chuàng)建5?；烽_發(fā)了凸輪的形狀設(shè)計(jì)程序。用來參數(shù)輸入程序的凸輪輪廓數(shù)據(jù)點(diǎn)的計(jì)算。然后，數(shù)據(jù)被轉(zhuǎn)換成一個(gè)三維CAD模型6。暢作運(yùn)動(dòng)分析的一般框架對(duì)分度凸輪機(jī)構(gòu)的幾何設(shè)計(jì)。螺旋理論是用來描述凸輪結(jié)構(gòu)的機(jī)構(gòu)和運(yùn)動(dòng)方程的推導(dǎo) 7 。 圖1 紙杯成型機(jī)。 然而，不建議用一個(gè)解決方案去減少接觸力。這些研究沒有驗(yàn)證所設(shè)計(jì)的凸輪的性能。對(duì)紙杯成型加工，需要一個(gè)優(yōu)化的筒凸輪輪廓減少接觸力的方法。結(jié)果可用于驗(yàn)證所提出的方法的可靠性。 在這項(xiàng)研究中，每個(gè)凸輪型線優(yōu)化減少了滾子與凸輪之間的接觸力8，9 。一個(gè)多體動(dòng)力學(xué)模型，用亞當(dāng)斯的計(jì)算接觸力來創(chuàng)造。選擇設(shè)計(jì)參數(shù)，顯著影

5、響響應(yīng)變量的靈敏度分析，采用Plackett Burman設(shè)計(jì)表進(jìn)行。然后，根據(jù)中心復(fù)合實(shí)驗(yàn)設(shè)計(jì)表進(jìn)行。其次，利用響應(yīng)面分析，二階遞歸模型的功能，它提供對(duì)設(shè)計(jì)參數(shù)和響應(yīng)變量之間的關(guān)系估計(jì)信息。對(duì)模型的估計(jì)函數(shù)的可靠性進(jìn)行了驗(yàn)證通過方差分析（ANOVA）的方法。 最后，序列二次規(guī)劃（SQP）方法被用來找到設(shè)計(jì)變量，使模型的函數(shù)值滿足線性或非線性約束條件 10-13 。為了驗(yàn)證該優(yōu)化方法的可靠性，建立了紙杯成型機(jī)的多體仿真模型。該凸輪和電流和優(yōu)化系統(tǒng)的輥之間的接觸力比較。此外，采用一個(gè)桶形凸輪的CAM原型試驗(yàn)。對(duì)紙杯成型機(jī)電流和優(yōu)化系統(tǒng)在床的振動(dòng)進(jìn)行比較。2.動(dòng)態(tài)分析2.1動(dòng)態(tài)分析模型 紙杯成型機(jī)

6、的動(dòng)態(tài)模型的建立分析了圓柱凸輪和采用多體動(dòng)力學(xué)分析軟件亞當(dāng)斯，如圖2所示的輥之間的接觸力。在一個(gè)紙杯成型機(jī)的索引驅(qū)動(dòng)器是一個(gè)旋轉(zhuǎn)或停止連接各生產(chǎn)工藝。該指數(shù)是由凸輪驅(qū)動(dòng)操作。動(dòng)態(tài)模型是由24部分組成的。連接，驅(qū)動(dòng)彈簧和接觸模型中定義的。該模型有一個(gè)總22自由度。表1提供了對(duì)動(dòng)態(tài)模型的信息。 對(duì)圓柱凸輪三維模型，利用逆向工程技術(shù)建立.圖3顯示了逆向工程的程序。在這個(gè)過程中，真正的產(chǎn)品是用激光掃描儀，其中，在這項(xiàng)研究中，是一種非接觸式測(cè)量的激光探針。大約1000點(diǎn)，提出由線連接并轉(zhuǎn)化為在3D CAD程序進(jìn)行三維實(shí)體模型的表面2.2接觸力分析 俊認(rèn)為凸輪磨損由于凸輪與滾輪之間的接觸力 3 。圖5顯示

7、分析結(jié)果的接觸力在滾子與凸輪之間。在三部分，接觸力大大增加。圖6顯示了當(dāng)軋輥孔型的圓柱凸輪導(dǎo)槽。第一點(diǎn)說明進(jìn)入導(dǎo)向槽輥；第二指示輥通過轉(zhuǎn)動(dòng)部分；和最后指示逃生槽輥。三穿點(diǎn)重合的地方，接觸力大大增加。在這三個(gè)部分凸輪磨損非常嚴(yán)重。磨損不僅發(fā)生在槽的整個(gè)表面而且發(fā)生在凹槽的幾點(diǎn)。因此，接觸力可的凸輪磨損的一個(gè)非常重要的因素。 部分剛體24共同點(diǎn)外卷16平移7固定的1驅(qū)動(dòng)器1力彈簧14接觸點(diǎn)21 自由度22 表1.動(dòng)態(tài)模型的信息 圖2.紙杯成型機(jī)的多體動(dòng)力學(xué)模型 Fig. 3. 利用三維激光掃描儀的圓柱凸輪反求工程程序 圖4.凸輪和分度角比較 圖5.分析結(jié)果滾子和凸輪之間的接觸力 圖6.磨損的凸輪.

8、點(diǎn) 表2 優(yōu)化研究 變量結(jié)果凸輪曲線無量綱數(shù)X凸輪滾子幾何形狀滾子數(shù)X從從凸輪中心水平向距離X從從凸輪中心Z向距離X從凸輪中心Z向距離X半徑指數(shù)O滾子高O滾子半徑O軋輥凸度的角X 圖7.輥和指標(biāo)參數(shù)變量最?。?1）電流（0）最大（+1）滾子半徑12.731.7538.1滾子高度15.87538.144.45半徑指數(shù)180.0203.0206.5 表3 確定優(yōu)化設(shè)計(jì)的因素 3優(yōu)化 響應(yīng)面分析法作為優(yōu)化方法。該方法可用于在設(shè)計(jì)時(shí)參數(shù)的連續(xù)值。響應(yīng)函數(shù)是建立在假定的實(shí)驗(yàn)結(jié)果的基礎(chǔ)上，對(duì)設(shè)計(jì)參數(shù)，減少響應(yīng)函數(shù)的值是通過使用一個(gè)最小的算法。3.1設(shè)計(jì)的因素和水平 接觸力的磨損的重要因素，并對(duì)凸輪的形狀密

9、切相關(guān)。優(yōu)化的目標(biāo)函數(shù)是確定滾子與凸輪之間的接觸力。接觸力的峰值選擇最小化。表2顯示的凸輪和滾子值幾何位移的設(shè)計(jì)因素。 那是可以改變的設(shè)計(jì)選擇的因素考慮到當(dāng)前系統(tǒng)的結(jié)構(gòu)和其他部分的干擾。和改進(jìn)的正弦曲線提供最佳的性能考慮的力傳遞效率仍然使用。 如表2所示，滾筒的半徑和高度及半徑變化的指數(shù)。確定設(shè)計(jì)因素通過工程討論了這三個(gè)參數(shù)。表3給出了滾子的高度和半徑及被設(shè)置為設(shè)計(jì)因素指標(biāo)的半徑。圖7顯示了需要確定的圓柱凸輪的最佳形狀參數(shù)。3.2響應(yīng)面分析。 設(shè)計(jì)因素的正交數(shù)組創(chuàng)建。十五組實(shí)驗(yàn)，基于正交陣列三個(gè)設(shè)計(jì)因素。表4顯示實(shí)驗(yàn)的響應(yīng)，這是凸輪與滾輪之間的最大接觸力。實(shí)驗(yàn)結(jié)果的基礎(chǔ)上，響應(yīng)面分析法推導(dǎo)出的

10、響應(yīng)函數(shù)，并利用統(tǒng)計(jì)分析的方法和系統(tǒng)性能的設(shè)計(jì)因素之間的數(shù)學(xué)關(guān)系。當(dāng)有許多設(shè)計(jì)因素，二次回歸模型一般是作為響應(yīng)函數(shù) 和系統(tǒng)性能的設(shè)計(jì)因素之間的關(guān)系的非線性。在這項(xiàng)研究中，中心復(fù)合設(shè)計(jì)表包括中心點(diǎn)和軸點(diǎn)使用2水平因子實(shí)驗(yàn)來估計(jì)模型的功能。根據(jù)研究結(jié)果，二次回歸模型函數(shù)使用最小二乘法推導(dǎo)。 在這項(xiàng)研究中得到的回歸函數(shù)表示為： Y：桶凸輪與滾輪之間的接觸力R：滾子半徑H R：高輥ri：半徑指數(shù) 為了驗(yàn)證模型的函數(shù)，方差分析的實(shí)現(xiàn)。表5顯示了方差分析表的大小的變化是，自由度和V的平均平方 ，F(xiàn)0值從獲得的實(shí)驗(yàn)結(jié)果和F（0.01）是一個(gè)確定的值在參考根據(jù)水平和設(shè)計(jì)因素的數(shù)量。如表5所示，F(xiàn)0大于F（0.

11、01）。因此，該模型函數(shù)有顯著性水平百分之1的可靠性水平。因此，該模型可用于為目標(biāo)函數(shù)，因?yàn)楣烙?jì)的模型函數(shù)能非常好的表達(dá)設(shè)計(jì)因素和系統(tǒng)性之間的關(guān)系。 為了獲得的設(shè)計(jì)因素最小化目標(biāo)函數(shù)值，采用SQP方法。SQP是一種有效的優(yōu)化算法，得到一個(gè)函數(shù)的最低值給定出兩個(gè)以上的設(shè)計(jì)因素和非線性約束條件。表6顯示了設(shè)計(jì)因素最小化目標(biāo)函數(shù)值。 次數(shù) 滾子半徑滾子高度滾子半徑響應(yīng)1-1-1-1131332-1-11111353-11-1124024-111974951-1-161-11711-1811190002918610-1.2160049652111.21600120-1.2160220181301.21

12、601400-1.21615001.21652623 表4. 確定優(yōu)化設(shè)計(jì)的因素 Table 5. ANOVA table. 設(shè)計(jì)參數(shù)值（mm）滾子半徑23.8125滾子高度25.4半徑指數(shù) 表6優(yōu)化設(shè)計(jì)變量。電流電流電流滾子半徑（mm）31.7523.8125-26.05滾子高度（mm）38.125.4-33.33半徑指數(shù)（mm203204.7255+0.85凸輪高度（mm）1491490凸輪高度（mm）269222-17.47接觸力的峰值平均（N）29.1865.184-82.24接觸力的均方根值（N）5.5411.309-76.37 表7. 估計(jì)系統(tǒng)的優(yōu)化結(jié)果 圖8. 優(yōu)化后的凸輪和指數(shù)

13、位移圖 圖9. 當(dāng)前的和優(yōu)化的系統(tǒng)之間的接觸力的比較4. 優(yōu)化驗(yàn)證4.1 動(dòng)態(tài)模型 驗(yàn)證是否已進(jìn)行了優(yōu)化，利用動(dòng)態(tài)模型優(yōu)化的凸輪模型的建立。以及電流與優(yōu)化模型的接觸力比較。圖8顯示了當(dāng)前的和優(yōu)化的凸輪模型和指數(shù)單元的位移圖。優(yōu)化后的凸輪和分度裝置以及當(dāng)前凸輪的痕跡。七輥接觸力在圖9凸輪與滾輪之間的接觸力峰值相比顯著降低在優(yōu)化后。 設(shè)計(jì)值的變化，對(duì)凸輪的大小和接觸力影響如表7所示。該凸輪變得更輕比桶形凸輪體積減小約17.47%。圓柱凸輪和滾子之間接觸壓力的峰值下降約82.24%。此外，接觸力的均方根值降低約76.37%。因此，這次優(yōu)化用動(dòng)態(tài)模型的進(jìn)行了驗(yàn)證。4.2實(shí)驗(yàn) 一桶的CAM原型是基于優(yōu)化

14、結(jié)果制作。在紙杯成型機(jī)床的加速度測(cè)量實(shí)驗(yàn)驗(yàn)證了優(yōu)化結(jié)果。圖10顯示了1到6點(diǎn)的加速度的測(cè)量。實(shí)驗(yàn)進(jìn)行了五次是可靠的。獲得的測(cè)量值是平均值。紙杯成型機(jī)的當(dāng)前的和優(yōu)化的凸輪的加速度在圖10進(jìn)行了比較。優(yōu)化后的凸輪平均加速度降低約17%，因此，對(duì)著圓柱凸輪進(jìn)行了好的優(yōu)化。結(jié)論 進(jìn)行優(yōu)化以減少凸輪與滾輪之間的接觸力的紙杯成型機(jī)的設(shè)計(jì)。接觸力是通過使用凸輪動(dòng)態(tài)模型和指數(shù)單元分析，這是對(duì)紙杯成型機(jī)操作的一部分。通過工程的探討，為優(yōu)化確定了他們的價(jià)值觀的設(shè)計(jì)因素。 滾筒的半徑和高度及半徑進(jìn)行了優(yōu)化指標(biāo)。對(duì)圓柱凸輪的形狀也根據(jù)滾筒的半徑和高度及半徑的優(yōu)化指標(biāo)。為了驗(yàn)證在這項(xiàng)研究中使用優(yōu)化的組件的減振，對(duì)接觸力

15、進(jìn)行了分析。接觸力降低的動(dòng)態(tài)模型與優(yōu)化的組件。此外，通過實(shí)驗(yàn)測(cè)定了紙杯成型機(jī)床的加速度。加速度在優(yōu)化系統(tǒng)中下降?？傊?，通過優(yōu)化輥，指數(shù)和凸輪，讓紙杯成型機(jī)可以在一個(gè)高速，低磨損的環(huán)境中工作。 圖10.振動(dòng)的測(cè)點(diǎn) 圖11. 對(duì)機(jī)械振動(dòng)的比較 參考1R. Ipek and B. Selcuk,，凸輪軸的干磨損形貌，材料研究學(xué)報(bào)，168（2005）373-379.。2E. Pennestri, R. Stefanelli, P. P. Valentini and L. Vita,，凸輪曲線的動(dòng)態(tài)仿真驅(qū)動(dòng)變速，DETC04程序（2004）。 3 K.-J.Jun, T.-W. Park, K.-Y.

16、Cheong and Y.-G. Kim,，在紙杯中利用多體動(dòng)力學(xué)模型成型機(jī)因素造成的凸輪磨損研究，J. MST，24（3）（2010）361-367。 4 H. Xiao and J. W. Zu，一種新的凸輪驅(qū)動(dòng)凸輪型線優(yōu)化，機(jī)械科學(xué)與技術(shù)學(xué)報(bào)，23（2009）2592-2602。 5 J. H. Shin, S. W. Kim, D. W. Kang and H. E. Yoon，對(duì)凸輪的相對(duì)速度的設(shè)計(jì)研究，kspe學(xué)報(bào)，19（8）（2002）47-54。 6 W. H. Kim and T. W. Park.公園，一個(gè)凸輪設(shè)計(jì)方案一杯成型機(jī)的發(fā)展，ksme學(xué)報(bào)，35（4）（2011）4

17、33-438。 7 Z. Chang, C. Xu, T. Pan, L. Wang and X. Zhang，對(duì)分度凸輪機(jī)構(gòu)一般框架的幾何設(shè)計(jì)，機(jī)械原理，44（2009）2079-2084。 8 R. L. Norton，凸輪的設(shè)計(jì)和制造手冊(cè)，工業(yè)出版社有限公司，紐約。 9 F. Y. Chen，力學(xué)和凸輪機(jī)構(gòu)的設(shè)計(jì)，科學(xué)出版社，紐約。 10 S.-P. Jung, T.-W. Park, K.-J. Jun, J.-W. Yoon, S.-H. Lee and W.-S. Chung，一個(gè)優(yōu)化方法研究了響應(yīng)面分析，多體系統(tǒng)jmst，23（2009）950-953。 11 S.-P. Jun

18、g, T.-W. Park, K.-J. Jun, J.-W. Yoon and W.-S. Chung，使用實(shí)驗(yàn)設(shè)計(jì)，彈簧的優(yōu)化設(shè)計(jì)，ijpem，10（4）（2009）77-83.。 12 S. Park,，實(shí)驗(yàn)設(shè)計(jì)的理解，minyoungsa（2005）?！?3】G. N. Vanderplaats，應(yīng)用工程設(shè)計(jì)的數(shù)值優(yōu)化技術(shù)，McGraw-Hill（1984) 2009年在亞洲大學(xué)旭賢基姆收到他的機(jī)械工程理學(xué)學(xué)士。目前，他是一名韓國(guó)水原亞洲大學(xué)的博士生。他的興趣是研究該地區(qū)的多體系統(tǒng)，優(yōu)化和計(jì)算機(jī)輔助工程。 Tae Won park得到來自國(guó)立首爾大學(xué)的機(jī)械工程學(xué)士學(xué)位。他接著從愛荷華大

19、學(xué)獲得了碩士和博士學(xué)位。他目前是在韓國(guó)。水原亞洲大學(xué)機(jī)械工程學(xué)院的一名教授。 Study of optimization of the barrel cam in a paper-cup-forming machine Wook Hyeon Kim1 and Tae Won Park2,*Abstract A paper cup forming machine can produce a maximum of about 140 paper cups a minute. If the rate of production is increased to improve productivity

20、, the contact force in the barrel cam increases, producing more vibration. Therefore, a method for reduction of cam vibration is needed. The profile of the barrel cam is optimized by using a multibody dynamics model. The objective of the optimization is to minimize the contact force that occurs betw

21、een the rollers and the barrel cam. An experiment is carried out using the optimized barrel cam. The reduction of vibration at higher rates of production than the current rates validated the optimization.Keywords: Paper-cup; Barrel cam; Multi-body dynamics; Optimization; Contact force1. Introduction

22、 The demand for paper cups is increasing rapidly due to their convenience and effectiveness in protecting the environment. To satisfy the demand, current productivity also should be increased. However, simply increasing productivity would result in vibration at the bed on the machine, which is a ser

23、ious problem. When the machine is also affected by the vibration on the bed, defective paper cups are produced. Fig. 1 shows the current paper cup forming machine. The current machine can produce 140 paper cups per minute. If the productivity is increased, the barrel cam will wear out very quickly a

24、nd the barrel cam will have to be changed. The paper cup is formed on the turret in the paper cup forming machine,and an index with seven rollers is connected to the turret. The barrel cam makes the rollers move as the cam rotates, so the turret also rotates. Contact force occurs between the barrel

25、cam and the rollers. After the paper cup forming machine operates for a long time, wear occurs on the surfaces of the barrel cam and the roller because of the contact force. Then vibration and noise increase greatly, requiring replacement of the barrel cam and the rollers should be changed. Research

26、 in this field has been extensive. Ipek investigated the variation of the wear mechanism and worn surface profile of the cam shaft. The wear mechanism of the cam surface changes along the contact surface 1. Pennestri presented a simulation of the cam actuator of a robotized gearbox. The actuator is

27、a barrel cam which moves a pin according to a prescribed motion law. In the gear shifting simulation, the contact forces and wear action are compared 2. Jun suggested that barrel cam wear is caused by the contact force between roller and barrel cam. The wear spot of the barrel cam almost coincides w

28、ith the point of large contact force in the multi-body dynamics model 3. Xiao optimized the cam profile for a new cam drive engine using a general polynomial spline and B-spline. A unique cam mechanism is analyzed to define the optimization problem 4. Shin proposed a method for designing the shape o

29、f the barrel cam by using relative velocity. Local coordinates are derived using the relative velocity method, and the shape of the barrel cam is created by the CAD program 5. Kim developed a barrel cam shape design program. Parameters are input to the program and the point data of the cam profile a

30、re calculated. Then, the data are converted to a 3D solid CAD model 6. Chang presented a general frame work for kinematic analysis and geometry design of the indexing cam mechanism. Screw theory is applied to describe the structure of the cam mechanism, and kinematic equations are derived 7. Fig. 1.

31、 Paper cup forming machine. However, a solution to decrease the contact force has not been suggested. And those studies did not verify the performance of the designed barrel cam. For the paper cup forming machined, a method to optimize the barrel cam profile to decrease the contact force is needed.

32、The result can be used to verify for the reliability of the suggested method. In this study, the barrel cam profile is optimized to minimize the contact force between the rollers and the barrel cam 8, 9. A multi body dynamic model is created using ADAMS to calculate the contact force. To choose the

33、design parameters, which significantly affect the response variables, sensitivity analysis is performed by using the Plackett-Burman design table. Then, experiments are carried out according to the centralcomposite design table. Next, using response surface analysis, the second order recursive model

34、 function, which provides information on the relationship between the design parameters and the response variables, is estimated. The reliability of the estimated model function is verified according to the analysis variance (ANOVA) method. Finally, the sequential quadratic programming (SQP) method

35、is used to find the values of the design variables that minimize the model function and satisfy the linear or nonlinear constraint conditions 10-13. To verify the reliability of the optimization procedure, a multi-body simulation model of the paper-cup forming machine is created. The contact force b

36、etween the barrel cam and the rollers of the current and the optimized system is compared. In addition, an experiment using a prototype of the barrel cam is performed. The vibration on the bed of the paper- cup forming machine between the current and the optimized system is compared.2. Dynamic analy

37、sis2.1 Dynamic analysis model A dynamic model of the paper-cup forming machine is created to analyze the contact force between the barrel cam and the rollers by using a multi-body dynamic analysis program ADAMS as shown in Fig. 2. The index drive in a paper cup forming machine is a component that ro

38、tates or stops to connect each production process. The index drive is operated by the barrel cam. The dynamic model is composed of 24 parts. Joint, driver spring and contact are defined in the model. The model has a total DOF of 22. Table 1 provides the information on the dynamic model. A 3D model o

39、f the barrel cam is created by using reverse-engineering. Fig. 3 shows the reverse-engineering procedure. In this procedure, the real product is measured using a laser scanner, which, in this study, is a non-contact measurement laser probe. It measures about 1000 points, and points are connected by

40、a line and converted to a surface to make a 3D solid model in the 3D CAD program.2.2 Contact force analysis Jun suggested that the cam wears out due to the contact force between the cam and the rollers 3. Fig. 5 shows the analysis result of the contact force between a roller and the barrel cam. In t

41、hree sections, the contact force increases greatly. Fig. 6 shows the moment when a roller passes by the guide groove of the barrel cam. The first spot indicates the roller entering the guide groove; the second indicates the roller passing through the rotational section; and the last indicates roller

42、 escaping the guide groove. The three wear spots coincide with the parts where the contact force increases greatly. The barrel cam is worn out very much in these three parts. The wear often occurs not on the whole surface of the groove but at some points of the groove. Therefore, the contact force c

43、an be a very important factor of the barrel cam wear. Table 1. Information of dynamic model. Fig. 2. Multi-body dynamic model of the paper cup forming machine. Fig. 3. Procedure of reverse engineering of the barrel cam using 3D laser scanner. Fig.4.Comparison of cam and index angle. Fig. 5. Analysis

44、 result of contact force between roller and barrel cam. Fig. 6. Wear spots of the barrel cam. . Fig. 7. Parameter of roller and index. Table 2. Investigation for the optimization Table 3. Determined design factors for the optimization.3. Optimization The response surface analysis is used as the opti

45、mization method. This method can be used when the design parameters have continuous values. The response function is presumed based on the experimental results, and the values of the design parameters that minimize the response function are found by using a minimal algorithm.3.1 Design factors and l

46、evel The contact force is an important factor of the wear, and is closely related to the shape of the barrel cam. The objective function of the optimization is to determine the optimal shape of the barrel cam that minimizes the contact force between the rollers and the barrel cam. The peak value of

47、the contact force is chosen to be minimized. Table 2 shows the design factors of the displacement of the cam and geometric values of the roller. The design factors that can be changed are selected considering the structure of the current system and the interference of other parts. And the modified s

48、ine curve giving the best performance considering the force transfer efficiency is still used. As shown in Table 2, the radius and height of the roller and the radius of the index are changed. These three parameters are determined as design factors through engineering discussion. Table 3 presents th

49、e height and radius of the roller and the radius of the index which are set as design factor. Fig. 7 shows the parameters required to determine the optimal shape of the barrel cam.3.2 Response surface analysis An orthogonal array of the design factors is created. Fifteen experiments are carried out

50、based on the orthogonal array of three design factors. Table 4 shows the response of the experiments, which is the peak contact force between the barrel cam and the roller. Based on the experimental results, the response surface analysis method deduces the response function, a mathematical correlati

51、on between the design factors and system performances by using a statistical method. When there are many design factors, a quadratic regression model is，generally used as the response function because of the nonlinearity of the relation between the design factors and system performances. In this stu

52、dy, the central composite design table including the central point and the axial point is used in 2-level factor experiments to estimate the model function. Based on the result, a quadratic regressive model function is derived using the method of least squares. The regressive model function obtained in the study is expressed as Y : Cont