3D藥芯焊絲成型機設(shè)計【藥芯焊絲輥軋成型機的設(shè)計及齒輪減速箱運動仿真】【說明書+CAD+PROE】
3D藥芯焊絲成型機設(shè)計【藥芯焊絲輥軋成型機的設(shè)計及齒輪減速箱運動仿真】【說明書+CAD+PROE】,藥芯焊絲輥軋成型機的設(shè)計及齒輪減速箱運動仿真,說明書+CAD+PROE,3D藥芯焊絲成型機設(shè)計【藥芯焊絲輥軋成型機的設(shè)計及齒輪減速箱運動仿真】【說明書+CAD+PROE】,焊絲,成型,設(shè)計,齒輪,減速
湘潭大學(xué)本科畢業(yè)設(shè)計說明書 目錄
第一章 緒論
&1-1 任務(wù)分析與說明
一，主要任務(wù)
藥芯焊絲輥軋成型機的設(shè)計及齒輪減速箱運動仿真
二，主要內(nèi)容
1，藥芯焊絲軋輥成型機的原理
2，變速機構(gòu)與成型機構(gòu)的設(shè)計與仿真
3，加粉裝置的設(shè)計
三，主要技術(shù)指標(biāo)
1，鋼帶進(jìn)口速度：=12m/min(200mm/s),
2，出口速度： =15.29m/min(255mm/s)；
3，鋼帶規(guī)格：寬厚=160.3；
4，成型焊絲直徑：d=4mm；焊絲截面形狀:O形搭接;
5，變頻調(diào)速電動機型號：YVP90L-4, =1.5kw,=3.8A, =10NM,
6，工作壽命：10年，每年300個工作日，每天工作12個小時。
四，預(yù)計達(dá)到的目標(biāo)：
1，拉絲工藝簡單，生產(chǎn)速度高，表面質(zhì)量好；
2，有比較合理的價格和較低的使用成本；
3，操作、使用方便，舒適性好；
五，主要特色:
1，拉絲工藝比軋絲工藝更簡單，生產(chǎn)速度更高，成本更低。
2，易損件拉絲模是標(biāo)準(zhǔn)件，有專業(yè)工廠可批量生產(chǎn)，價格大大低于軋輥。
3，設(shè)備簡單，使用、造價低，各主動軸由一臺電動機拖動。
&1-2方案分析與說明
一，選題依據(jù)
我國藥芯焊絲的應(yīng)用和生產(chǎn)從上世紀(jì)90年代快速起步，近年來都以20%-30%速度快速發(fā)展，到2001年國內(nèi)市場消費總量已超過1.5-1.6萬噸，2002年可望達(dá)2萬噸左右，雖然其在焊材總量比例還僅占1.5%左右，但其增長潛力很大。業(yè)內(nèi)人士預(yù)測其在焊材中的比重3-5年內(nèi)年達(dá)到3-5萬噸，8-10年內(nèi)達(dá)到8-10萬噸，甚至更多。
藥芯焊絲屬于焊材中的高技術(shù)領(lǐng)域，它涉及成套生產(chǎn)裝備、相關(guān)制造工藝和
藥芯配方等三個方面。其中成套生產(chǎn)裝備則是重要的基礎(chǔ)硬件。由于它的特殊性和復(fù)雜性，國內(nèi)過去一直未能自行制造。因而研制開發(fā)出國產(chǎn)藥芯焊絲成套生產(chǎn)設(shè)備對于發(fā)展國產(chǎn)藥芯焊絲產(chǎn)業(yè)及其重要。
二， 方案比較
目前世界上制造焊絲的工藝有許多種，比較流行工藝方案：
藥芯焊絲
有縫型
冷軋帶鋼法
拔模法
連軋法
軋拔法
盤圓軋制法
軋拔法
無縫型
鋼管拔制法
在線焊合法
1，連軋法
連軋法是指藥芯焊絲從鋼帶到成品焊絲的全部加工過程都在一套連軋機組上完成，工藝過程如圖1。
圖1 連軋工藝示意圖
1）連軋法工藝特點：
（a）藥芯焊絲成型和減徑完全在同一臺機組上完成，因此工藝簡潔，設(shè)備緊湊，占地面積小。
（b）由于越細(xì)焊絲軋制困難，若不再拉拔工藝直接軋至1.2mm以下細(xì)焊絲比較困難，所以不宜用制造1.6mm以下細(xì)結(jié)果鋼用藥芯焊絲，比較適合制造粗徑迎面堆焊用藥芯焊絲。
（c）焊絲的直徑偏差、橢圓度、表面光潔度及焊絲挺度較差，因而送絲性能較差。
（d）由于軋輥尺寸有限，因此生產(chǎn)效率遠(yuǎn)不如軋—拔法制造工藝高。
（e）由于軋輥對材質(zhì)和加工精度要求很高，本身又是易損件，因此設(shè)備、備件費用較高。
（f）由于焊絲表面沒有拉絲潤滑劑殘留物，所以其熔敷金屬的擴(kuò)散氫含量較低。
2）連軋法結(jié)論。
由于上述原因，近年國內(nèi)外已經(jīng)較少適用連軋法工藝生產(chǎn)結(jié)構(gòu)鋼和不銹鋼用細(xì)徑焊絲，但在粗徑堆焊焊絲的生產(chǎn)中則適用較多。
2，軋—拔法
軋—拔法是將焊絲的成型、加粉、合口工序仍放在軋絲機上完成，即可采
用先軋，后拉的工藝。其工藝簡圖如下：
圖2 軋—拔法工藝簡圖
1) 軋—拔法工藝的優(yōu)點：
（a） 拉絲工藝比軋絲工藝簡單，生產(chǎn)速度更快，成本更低，表面質(zhì)量也更好。
（b） 由于拉絲機、拉絲模、潤滑劑的改進(jìn)，使得拉絲速度可以達(dá)12~14m/s，最快甚至可達(dá)25m/s。
（c） 易損部件是標(biāo)準(zhǔn)件，有專業(yè)工廠可以批量生產(chǎn)，價格大大低于軋輥，所以將焊絲的減徑工序大部分放在拉絲機上來完成是合理的。
2）被動式軋機
生產(chǎn)線中的軋輥完全是被動的，軋制過程完全依靠作為動力的拉絲機來牽引。軋輥本身無動力驅(qū)動，由于被動軋輥之間轉(zhuǎn)速可自協(xié)調(diào)不需要任何電氣控制系統(tǒng)，所以比較簡單。
3）集中傳動式軋機
軋絲機的各垂直軋輥為主動輥，各主動輥采用電機拖動。傳動系統(tǒng)可以采用一根長軸將動力依次分配到各機架，也可采用齒輪系統(tǒng)將動力分配到各機架。
三，方案選取
根據(jù)實際情況，本設(shè)計采用軋—拔法，采用集中式傳動設(shè)計。
以達(dá)到1，工藝簡單，生產(chǎn)速度更快，成本更低；2，傳動系統(tǒng)可以采用一根長軸將動力依次分配到各機架，并采用齒輪系統(tǒng)將動力分配到各機架。3，降低設(shè)備成本，管理方便。
第二章 傳動設(shè)計
&2-1 電機選擇
根據(jù)技術(shù)要求，選擇電機為YVP90L-4，技術(shù)參數(shù)如下：
=3.8A =1500r/min
&2-2 傳動方案分析
因為從電機輸出的功率有兩個方向，一個方向由電機經(jīng)過主軸傳遞到加粉裝置，還有一個方向傳遞到軋輥，并且兩個方向相互垂直。
所以需要錐齒輪來進(jìn)行垂直方向的功率傳遞，即經(jīng)過軸將功率傳遞到加粉裝置；另外一個方向由斜齒輪將功率傳遞到軋輥。
通過技術(shù)要求可以算出，在出口處，轉(zhuǎn)速n=600/9 r/min； 在電機處轉(zhuǎn)速
n=600 r/min。可以算出總的傳動比i=9。
因為需要將功率傳遞到成型機構(gòu)，所以變速箱里有2對齒輪只起傳遞作用，而不起變速作用。因此可以采用，錐齒輪處傳動比i=3，第一對斜齒輪傳動比i=3，其余斜齒輪的傳動均為1。
&2-3 錐齒輪設(shè)計
齒輪精度：機器為一般機器，速度不高，故選用8級精度（GB 10095-88）
材質(zhì)：小齒輪40（調(diào)質(zhì)），硬度280HBS；大齒輪45鋼（調(diào)質(zhì)），硬度240HBS。
參數(shù)： 小齒輪=18 大齒輪=54 α=20° 模數(shù)m=3mm i=3
2-3-1按齒面接觸強度設(shè)計
（1） 確定公式內(nèi)各數(shù)字
1）試選載荷系數(shù) =1.6
2）計算小齒輪傳遞的扭矩。
3）由《機械設(shè)計》表10-7選取齒寬系數(shù)=1，
4）由表查得材料的彈性影響系數(shù) =189
5）由表查得小齒輪接觸疲勞強度分別為，大齒輪的接觸疲勞強度為
6） 計算應(yīng)力循環(huán)次數(shù)
=4.32×
=
7) 取接觸疲勞壽命系數(shù)，
8) 計算接觸疲勞許用應(yīng)力
取失效率為1%，安全系數(shù)為1，由公式得
（2）計算
1）試算小齒輪分度圓直徑，代入中較小的值。
2）計算圓周速度v.
3) 計算齒寬b。
4) 計算齒寬與齒高之比
模數(shù)
齒高
5) 計算載荷系數(shù)
根據(jù)v=1.41m/s， 8級精度，由圖可以查得動載系數(shù)
錐齒輪
由表可查使用系數(shù)
動載系數(shù)
6) 按實際的載荷系數(shù)校正所算得的分度圓直徑，
7）計算模數(shù) m
2-3-2按齒根彎曲強度設(shè)計
（1）確定公式中的各個計算數(shù)值
1）由圖可查得小齒輪的彎曲疲勞強度極限，大齒輪的彎曲疲勞強度極限
2）由圖查得彎曲疲勞壽命系數(shù) ，
3）計算彎曲疲勞許用應(yīng)力
取彎曲疲勞安全系數(shù)S=1.4，由公式得
4）計算動載荷系數(shù)K
5）查取齒形系數(shù)與應(yīng)力校正系數(shù)。
錐齒輪的當(dāng)量齒數(shù)
由當(dāng)量齒數(shù)可查得：
6）計算大、小齒輪的并加以比較。
大齒輪的數(shù)值大，取大的數(shù)值。
（2）設(shè)計計算
由于齒面模數(shù)m的大小主要取決于彎曲強度所決定的承載能力，而齒面接觸疲勞強度所決定的承載能力，僅與齒輪直徑有關(guān)。因此可以取由彎曲強度所算的模數(shù)2.8并就近圓整為3為標(biāo)準(zhǔn)值。
因此，齒輪模數(shù) m=3
2-3-3幾何尺寸計算
（1） 計算分度圓直徑
（2） 計算平均分度圓直徑 mm
&2-4 斜齒輪設(shè)計
齒輪精度：機器為一般機器，速度不高，故選用8級精度（GB 10095-88）
材質(zhì)：小齒輪40（調(diào)質(zhì)），硬度280HBS；大齒輪45鋼（調(diào)質(zhì)），硬度240HBS。
由表查得小齒輪接觸疲勞強度分別為，大齒輪的接觸疲勞強度為
參數(shù)：小齒輪齒數(shù)，初選螺旋角°，由電機輸出的扭矩
2-4-1按齒面接觸強度設(shè)計
由公式可知：
（1）確定公式內(nèi)的各個數(shù)值
1）試選。
2）由圖所給定的區(qū)域，可以查到，
3) 由圖查 ，。則
4）許用接觸應(yīng)力
應(yīng)力循環(huán)次數(shù)： =1.44
接觸疲勞壽命系數(shù)：
材料的許用應(yīng)力： 取S=1
因為，所以
（2）計算
1） 試算小齒輪分度圓直徑，由計算公式得
2）計算圓周速度。
3)計算齒寬b及模數(shù)。
4）計算縱向重合度。
5）計算載荷系數(shù)K。
根據(jù)實際情況取, , ,
6)按實際的載荷系數(shù)校正所算得的分度圓直徑，由公式得
7）計算模數(shù)。
2-4-2按齒根彎曲強度設(shè)計。
（1） 確定計算參數(shù)
1） 計算載荷系數(shù)K。
2) 由=1.55知，螺旋角影響系數(shù).
3) 計算當(dāng)量齒數(shù)。
4）查取齒形系數(shù)。
查得
5）查取應(yīng)力校正系數(shù)。
查得
6）計算彎曲許用應(yīng)力
由圖可查得小齒輪的彎曲疲勞強度極限，大齒輪的彎曲疲勞強度極限
取彎曲疲勞壽命系數(shù)
取彎曲疲勞安全系數(shù) S=1.4，由公式得
7）計算大、小齒輪并加以比較。
大齒輪的數(shù)值大。
（2） 設(shè)計計算
根據(jù)齒輪的實際情況，模數(shù)主要由齒根彎曲強度決定。因此可取齒輪模數(shù)為2.
2-4-3幾何尺寸計算
（1）
第三章 變速箱機械設(shè)計與3D建模
本設(shè)計使用Pro-E軟件來進(jìn)行建立3D模型，并就行仿真。進(jìn)行仿真不僅可以就行動態(tài)分析，并且可以更加直觀的感受設(shè)計是否合理。同時又因為制造商面臨全球的激烈競爭，消費者的苛求，設(shè)計產(chǎn)品的日趨復(fù)雜，不得不大大縮短的產(chǎn)品開發(fā)周期，利潤壓力以及很多其它方面因素的挑戰(zhàn)。 這些挑戰(zhàn)給制造商在產(chǎn)品設(shè)計生命過程中造成巨大的壓力，它促使制造商尋求途徑加速產(chǎn)品設(shè)計，降低設(shè)計費用并同時提高產(chǎn)品質(zhì)量與創(chuàng)新。
傳統(tǒng)的設(shè)計流程嚴(yán)重的阻礙了企業(yè)對設(shè)計流程做出重大改進(jìn)。通常，設(shè)計人員設(shè)計好產(chǎn)品之后才把問題扔給分析專家來進(jìn)行分析。但是當(dāng)這些分析進(jìn)行完畢之后，對于產(chǎn)品性能提升與創(chuàng)新都已經(jīng)太晚了。 這樣的流程造成設(shè)計創(chuàng)新困難且費用昂貴。
因此前期的3D建模和仿真分析在現(xiàn)代設(shè)計顯得越來越重要，并且逐漸成為設(shè)計的主流。進(jìn)行仿真可以獲得非常好的結(jié)果：更早更好的決策，縮短產(chǎn)品推向市場的時間，降低設(shè)計，更快更有競爭力的創(chuàng)新。
在本設(shè)計中，將3D建模過程和仿真分析過程呈現(xiàn)出來，以便交流和分析。變速箱的主要模塊包括箱體，軸系零件，其他附件。
&3-1 箱體設(shè)計與建模
1，尺寸選擇。
1），取最大寬度。
要裝3個斜齒輪，每個齒輪的齒輪。
從《機械設(shè)計手冊》上查取，壁厚取12mm
齒輪與機壁的間隙 b=8~12mm,取 b=10mm
故，箱體總寬度為L=3a+2b+2×12+2×15=392mm
2），取最大高度。
要裝兩個斜齒輪，加上底座與間隙。
齒輪中心距： a=106mm
底座壁厚： 12mm
潤滑油的高度： l=50mm
因此，總高度H=289mm
3），取最大厚度。
壁厚： b=12mm
齒寬: B=30mm
試算總厚度： B=165mm
因此箱體外觀 L×B×H=392×165×289 mm
2，Pro—E建模。
1）拉伸底板
此時，底板為392×165×12 （mm）
2）拉伸箱壁
以拉伸平面為繪制平面，就行草繪，再拉伸。
3）拉伸孔特征。
在拉伸平面上進(jìn)行草繪，5個圓，半徑r=47mm。再拉伸至“選定的項”，選定需要拉伸至的平面即可，去除材料。即可生成如圖示的特征。
4）再次拉伸其他的圓。
5）箱體最后的3D模型。
&3-2 軸系設(shè)計與建模
在本設(shè)計中，軸系零件，包括軸，斜齒輪，鍵，套筒，軸承。
（一），軸建模。
1，尺寸確定。
因為有齒輪，軸承，套筒，鍵等零件，因此設(shè)計此齒輪階梯較多。
軸的基本直徑： =25mm =28mm
與聯(lián)軸器連接的直徑： =20mm
定位軸肩的高度：
軸環(huán)寬度：
因此，軸肩高度 =2.5mm =3mm 軸環(huán)寬度 d=5mm
軸的平面示意圖
2，軸的3D模型。
將以上繪制的草繪圖像，就行旋轉(zhuǎn)360°即可。
（二），鍵槽與鍵建模。
1，尺寸確定。
在《機械設(shè)計課程設(shè)計指導(dǎo)書》上查閱到：
軸
鍵
鍵槽
公稱直徑d
公稱尺寸
b×h
軸t
轂
22~30
8×7
4
3.3
因為本設(shè)計采用軸直徑為25，故取b×h=8×7, 長度L=18
2，鍵槽在軸上建模。
首先以TOP平面建立基準(zhǔn)平面
繪制草繪圖形。
拉伸，去除材料，對稱拉伸。
3，鍵的3D模型。
（三），齒輪的3維建模。
在斜齒輪有5個大齒輪，1個小齒輪。取大齒輪的模型作為代表進(jìn)行建模。
1，參數(shù)確定。
法面模數(shù) mm 齒數(shù)z=51 螺旋角°
齒寬 B=30mm 軸徑D=28mm 鍵槽t=3.3mm
2，斜齒輪建模。
1）輸入?yún)?shù)。
2）輸入關(guān)系。
3）繪制齒形。
4）特征復(fù)制、平移。
5）掃描混合。
6）陣列。
7）齒輪模型。
3，小齒輪建模。
小齒輪的建模與大齒輪建模過程類似，只有齒數(shù)不一樣，因此不再贅述。
（四），套筒建模
1，尺寸確定。
套筒直徑d=25mm， 長度為12mm。
2, 3D模型。
套筒建模簡單，只要一個拉伸特征即可。
（五） 軸承建模。
1，軸承選用。
本設(shè)計中采用了，斜齒輪傳動，斜齒輪具有很多優(yōu)點：
1） 嚙合性能好，傳動平穩(wěn)、噪音小。
2） 重合度小，降低了每對齒輪的載荷，提高了齒輪的承載能力
3） 不產(chǎn)生根切的齒數(shù)少。
但是也使得運轉(zhuǎn)時產(chǎn)生軸向推力。因此，本設(shè)計中，不能采用深溝球軸承。本設(shè)計采用角接觸軸承。
下表是角接觸球軸承的資料。
角
接
觸
球
軸
承
結(jié)構(gòu)代號
基本額定動載荷比
極限轉(zhuǎn)速比
軸向承載能力
性能和特點
70000C（=15°）
1.0~1.4
高
一般
可以承受徑向載荷及軸向載荷，也可以單獨承受軸向載荷。要成對使用。
70000AC（=25°）
1.0~1.3
較大
70000B（=40°）
1.0~1.2
更大
本設(shè)計中，軸的直徑為25mm，因此采用軸徑為25mm的軸承。國標(biāo)代號為7205AC。
2，軸承參數(shù)。
本設(shè)計采用的軸承代號為7205，角接觸球軸承。
小徑d=25mm 大徑D=52mm
軸承寬度B=15mm
3，軸承3D模型。
&3-3 裝配建模
3-3-1軸系裝配建模
在軸上需要裝配齒輪、鍵、套筒、軸承等零件，在之前所有的零件均已完成3D建模，現(xiàn)在只需要對其裝配即可。其裝配過程如下：
1，進(jìn)入“組件”環(huán)境。
2，加入“軸”。
3，與鍵進(jìn)行裝配。
4，與斜齒輪進(jìn)行裝配。
5，與套筒裝配。
6，與軸承裝配。
角接觸球軸承需要成對使用，因此在軸兩端都需要裝配軸承。
軸承代號為7205，滿足軸的工作需求。
此時，裝有斜齒輪的軸，已經(jīng)裝配完畢。但是還需要將此軸系裝配至箱體上。
3-3-2變速箱整體裝配
軸系裝配完成后，就將已經(jīng)裝配完成的軸系與箱體就行裝配，就可以完成整個變速箱的裝配過程。
注：為了顯示變速箱的內(nèi)部結(jié)構(gòu)，特意將箱蓋隱藏，即不顯示。
&3-4變速箱仿真
通過新建伺服電機，并且設(shè)定速度為36°/s 經(jīng)過10 s 時間，就可以看到一整圈的過程。
整個變速箱的仿真過程可以在電腦上展示，在此不在贅述。
第四章 加粉裝置機械設(shè)計與3D建模
加粉裝置是將藥粉輸送到軋成U型槽的鋼帶里的裝置。
其機械機構(gòu)主要由規(guī)則的塊狀機構(gòu)構(gòu)成，因而其零件建模與裝配均比較簡單。因此，下文將直接給出主要零件的建模結(jié)果和裝配結(jié)果。
&4-1 加粉裝置設(shè)計與建模
主要零件的建模結(jié)果
&4-2加粉裝置裝配過程
4-2-1機械底板的裝配模型
4-2-2帶輪部分建模結(jié)果
4-2-3整體裝配建模結(jié)果
&4-3加粉裝置仿真
加粉裝置采用帶傳動，由卷筒帶動皮帶。再由皮帶將藥粉加至U型鋼槽中。
仿真部分，由電腦演示，此處不再贅述。
第五章 零件校核
&5-1 軸校核
在第一級變速箱上，傳遞的功率最大。因此校核，第一級變速箱上的裝有錐齒輪的軸。
1，軸的尺寸。
軸的直徑d=25mm 裝有齒輪的部分直徑D=45mm
總長L=389mm
軸上的尺寸
2，錐齒輪參數(shù)。
模數(shù) m=2 mm 小齒輪齒數(shù) =18 大齒輪齒數(shù) =54
嚙合角=20° =18.43° =71.57°
傳動比 i=3
3，其他參數(shù)。
錐齒輪傳遞效率 =0.4~0.97 （8級，油潤滑） 取=0.95
球軸承傳遞效率 =0.99（一對） 轉(zhuǎn)速n=10=600
電機額定參數(shù) =1.5kw =3.8A =10
4，軸上的功率P，轉(zhuǎn)速n和轉(zhuǎn)矩T
P==1.5×0.95×0.99=1.42kw
n=n×1=600
T=9550000
5，求作用在齒輪上的力
由齒輪計算公式知，分度圓直徑
d=mz=3×18=54mm
=420.02×tan20°×cos18.43°=145.03N
=420.02×tan20°×sin18.43°=48.3813N
6，初步確定軸的最小直徑。
根據(jù)公式確定軸的最小直徑。選取軸的材料為45鋼，調(diào)質(zhì)處理。根據(jù)可查閱資料，取=112，于是得
所選的直徑d=25要大于最小直徑，初步符合設(shè)計要求。
7，求軸上的載荷。
在水平面內(nèi)，×72=×389
于是得 =77.74N
根據(jù)在水平方向，力平衡原理：
=—=420.02—77.74=342.27N
水平面內(nèi)最大彎矩：
=×72=24643.44
在垂直面內(nèi)，軸向力平衡得
=48.38=
軸端彎矩平衡，
=
垂直方向，力平衡，
=
彎矩，
=72×118.18=8507.54
= -28×317= -8876
==26070.21
==26193.1768
載荷
水平面H
垂直面V
支反力F
=77.74N =342.27N
=118.18N =26.84N
彎矩M
=24643.44
=8507.54
= -8876
總彎矩
=26070.21 =26193.1768
扭矩
T
8，按彎扭合成應(yīng)力校核軸的強度
進(jìn)行校核時，通常只校核軸上承受最大彎矩和扭矩的截面（即危險截面C）的強度。根據(jù)公式和上表的數(shù)據(jù)，以及軸的單向旋轉(zhuǎn)，扭轉(zhuǎn)切應(yīng)力為脈動應(yīng)力，取=0.6，軸的計算應(yīng)力
其中W為抗彎截面系數(shù)，截面為圓面，故
W=0.1
進(jìn)而，
前已選定軸的材料為45鋼，調(diào)質(zhì)處理，查得=60MPa。因此，，故安全。
9，精確校核軸的疲勞強度
（1）判斷危險截面
鍵槽，軸肩及過渡配合所引起的應(yīng)力集中均將削弱軸的 疲勞強度，但是軸的最小直徑是按扭轉(zhuǎn)強度較寬裕確定的，這些主要受扭矩的 截面均無需校核。
從應(yīng)力集中對軸的疲勞強度的影響來看，軸肩處的應(yīng)力集中最嚴(yán)重；從受載的情況來看，齒輪中心截面上的應(yīng)力最大；但是安裝齒輪處的軸徑較大，因此不需校核，因而該軸只要校核軸肩處的疲勞強度即可。
（2）截面左側(cè)
抗彎截面系數(shù) W=0.1d3=0.1×253=1562.5mm3
抗扭截面系數(shù) =0.2d3=0.2×253=3105mm3
彎矩 M=26193×（20-10）/20=13096.5
截面上的彎曲應(yīng)力
σb=M/W=13096.5/1562.5=8.38 MPa
截面的扭轉(zhuǎn)切應(yīng)力
τT=T/=/3105MP=7.3MPa
軸的材料為 45鋼，經(jīng)調(diào)質(zhì)處理，由表15-1，查得σB=640MPa，σ-1=275MPa, τ-1=155MPa
截面上由于軸肩而形成的理論應(yīng)力集中系數(shù)按表3-2查取，由r/d=1.6/25=0.064,D/d=30/25=1.2,查得ασ=1.89，ατ=1.5
又由附圖3-1得軸的材料的敏性系數(shù)qσ=0.82,qτ=0.85
則有效應(yīng)力集中系數(shù)為
kσ=1+qσ(ασ-1)=1+0.82*0.89=1.7298
kτ=1+ qτ(ατ-1)1+0.85*0.5=1.425
由附圖3-2得尺寸系數(shù)εσ=0.9,由附圖3-3得扭轉(zhuǎn)尺寸系數(shù)ετ=0.92
軸按磨削加工,由俯圖3-4得表面質(zhì)量系數(shù)為
βσ=βτ=0.92
軸未經(jīng)表面強化處理,即=1,則得綜合系數(shù)為
Kσ = kσ/εσ+1/βσ=1.7298/0.9+1/0.92-1=2
Kτ= kτ/ετ+1/βτ=1.425/0.92+1/0.92-1=1.64
又由《機械設(shè)計手冊.中冊.第二版》P772得碳鋼的特性系數(shù)
φσ=0.1~0.2，取φσ=0.1
φτ=0.05~0.1，取φτ=0.05
計算安全系數(shù)S值得
Sσ= ==14.3
Sτ===2.75
Sca===2.7≧S=1.5,
故按此方案設(shè)計的軸是安全的。
（3）右側(cè)截面
抗彎截面系數(shù) W=0.1d3=0.1×253=1562.5mm3
抗扭截面系數(shù) =0.2d3=0.2×253=3105mm3
彎矩 M=26193×（20-10）/20=13096.5
截面上的彎曲應(yīng)力
σb=M/W=13096.5/1562.5=8.38 MPa
截面的扭轉(zhuǎn)切應(yīng)力
τT=T/=/3105MP=7.3MPa
軸的材料為 45鋼，經(jīng)調(diào)質(zhì)處理，由表15-1，查得σB=640MPa，σ-1=275MPa, τ-1=155MPa
截面上由于軸肩而形成的理論應(yīng)力集中系數(shù)按表3-2查取，由r/d=1.6/25=0.064,D/d=30/25=1.2,查得ασ=1.89，ατ=1.5
又由附圖3-1得軸的材料的敏性系數(shù)qσ=0.82,qτ=0.85
則有效應(yīng)力集中系數(shù)為
kσ=1+qσ(ασ-1)=1+0.82*0.89=1.7298
kτ=1+ qτ(ατ-1)1+0.85*0.5=1.425
由附圖3-2得尺寸系數(shù)εσ=0.9,由附圖3-3得扭轉(zhuǎn)尺寸系數(shù)ετ=0.92
軸按磨削加工,由俯圖3-4得表面質(zhì)量系數(shù)為
βσ=βτ=0.92
軸未經(jīng)表面強化處理,即=1,則得綜合系數(shù)為
Kσ = kσ/εσ+1/βσ=1.7298/0.9+1/0.92-1=2
Kτ= kτ/ετ+1/βτ=1.425/0.92+1/0.92-1=1.64
又由《機械設(shè)計手冊.中冊.第二版》P772得碳鋼的特性系數(shù)
φσ=0.1~0.2，取φσ=0.1
φτ=0.05~0.1，取φτ=0.05
計算安全系數(shù)S值得
Sσ= ==14.3
Sτ===2.75
Sca===2.7≧S=1.5,
故按此方案設(shè)計的軸是安全的，故該軸在截面右側(cè)也是足夠的。
10，結(jié)論
根據(jù)上述計算，可證明本設(shè)計滿足軸工作時的安全要求。此軸因無大的瞬時過載及嚴(yán)重的 盈利循環(huán)不對稱，所以靜強度校核可以略去，此軸的設(shè)計計算完成。
11，附錄
提高軸的強度的常用措施
1）合理布置軸上零件以減小軸的載荷
為了減小軸所承受的彎矩，傳動件應(yīng)該盡量靠近軸承，并盡可能不采用懸臂的支撐形式，力求縮短支承跨距及懸臂長度等。
當(dāng)轉(zhuǎn)矩由一個傳動件輸入，而由幾個傳動件輸出時，為了減小軸上的扭矩，應(yīng)將輸入件放在中間，而不要置于一端。
2）改進(jìn)軸上零件的結(jié)構(gòu)以減小軸的載荷
3）改進(jìn)軸的結(jié)構(gòu)以減小應(yīng)力集中的影響
軸通常是在變應(yīng)力條件下工作的，軸的截面尺寸發(fā)生突變處要產(chǎn)生應(yīng)力集中，軸的疲勞破壞往往在此處發(fā)生。為了提高軸的疲勞強度，應(yīng)盡量較少應(yīng)力集中源和降低應(yīng)力集中的程度。為此，軸肩處應(yīng)采用較大的過度圓角半徑r來降低應(yīng)力。但對定位軸肩，還必須保證零件得到可靠定位。當(dāng)靠軸肩定位的零件的圓角半徑很小時，為了增大軸肩處的圓角半徑，可采用內(nèi)凹圓角或加裝隔離環(huán)。
4）改進(jìn)軸的表面質(zhì)量以提高軸的疲勞強度
軸的表面粗糙度和表面強化處理方法也會對軸的疲勞強度產(chǎn)生影響。軸的表面越粗糙，疲勞強度也越低。因此，應(yīng)合理減小軸的表面及圓角處的加工粗糙值。當(dāng)采用對應(yīng)力集中甚為敏感的高強度材料制作軸時，表面質(zhì)量尤為予以注意。
表面強化處理的方法有：表面高頻淬火等熱處理；表面滲碳、氰化、氮化等化學(xué)處理；碾壓、噴丸等強化處理。
&5-2 軸承校核
本設(shè)計采用的是角接觸球軸承，代號為7205AC。
滾動軸承是現(xiàn)代及其中廣泛應(yīng)用的部件之一，它是依靠主要元件間的滾動接觸來支撐轉(zhuǎn)動零件的。滾動軸承絕大多數(shù)已經(jīng)標(biāo)準(zhǔn)化，并由專業(yè)工廠大量制造及供應(yīng)各種常用規(guī)格的軸承。滾動軸承具有磨擦阻力小，功率消耗少，起動容易等優(yōu)點。
1，軸上的受力情況
1）軸上參數(shù)
軸上功率 P==1.5×0.91×0.91=1.242kw
軸的轉(zhuǎn)速 n=N/i=600/9=66.67
軸的力矩 T=9550000=9550000×1.242/66.67=17791.65
2）斜齒輪受力情況
斜齒輪參數(shù) =2mm ° z=51
分度圓直徑 d=106mm N
=
=
2，軸承受力情況
1）左側(cè)軸承受力情況
==96.19N
×77=127.39×36 得=59.5589N
2）右側(cè)軸承受力情況
==96.19N
=127.39—59.89=68.33N
可以看出，右側(cè)軸承的受力較大，因此校核右側(cè)軸承，如果右側(cè)軸承可以達(dá)到壽命要求，則左側(cè)必定會達(dá)到使用壽命要求。
3,軸承的當(dāng)量載荷
P=（X+Y）
X、Y分別為徑向動載荷系數(shù)和軸向動載荷系數(shù)
e=/=1.4
查取資料知，
X=0.41 Y=0.87
根據(jù)表：
載荷性質(zhì)
舉例
中等沖擊
1.2~1.8
動力機械、冶金機械、卷揚機、機床等
取 =1.2
于是得：
P=（0.41×68.33+0.87×96.19）×1.2=140.4
4，軸承的使用壽命
=
為指數(shù)。對于球軸承，=3；對于滾子軸承，=。
因為在本設(shè)計中，軸的運轉(zhuǎn)速度較低，溫度不高。因此溫度對軸承的影響，可以不考慮，即取=1。
在本設(shè)計中，預(yù)期工作壽命為10年，300個工作日，一天12個小時。
可以算得：=10×300×12=36000 h
計算得出基本額定載荷C
C==735.91N
查表得知，7205AC的基本額定負(fù)荷：
=15.8KN =9.88KN
因為計算出的基本額定載荷遠(yuǎn)遠(yuǎn)小于軸承所擁有的基本額定載荷，因此在本設(shè)計中，軸承的選用負(fù)荷設(shè)計要求。
參考文獻(xiàn)
[1] 濮良貴 紀(jì)名剛，機械設(shè)計。北京：高等教育出版社，2006.5
[2] 張云靜等，Pro/ENGINEER野火5.0從入門到精通。北京：電子工業(yè)出版社，2010.6
[3] 劉繼元 陳邦固 王秀文 吳愛國，年產(chǎn)1500t藥芯焊絲生產(chǎn)線的研制?！逗附印?，2000（2）
[4] 詹友剛，Pro/ENGINEER2001教程。北京：清華大學(xué)出版社，2003.4
[5] 孫桓 陳作模 葛文杰，機械原理。北京：高等教育出版社，2006.5
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Journal of Mechanical Science and Technology 22 (2008) 15371543 DOI 10.1007/s12206-008-0430-9 Journal of Mechanical Science and Technology Optimum design of roll forming process of slide rail using design of experiments Minjin Oh and Naksoo Kim * Department of Mechanical Engineering, Sogang University, Seoul, 121-742, Korea (Manuscript Received December 6, 2007; Revised April 4, 2008; Accepted April 26, 2008) - Abstract In the design of the roll forming process, design errors can be determined in advance by using an FE simulation tool such as SHAPE-RF. In the case of a product such as a slide rail having a complicated shape and requiring high- precision forming, a standard is necessary for quantitatively evaluating the quality of the formed shape. In the analysis of the roll forming process of a slide rail, the pass having the largest deformation is designated as the target pass and the positions and shapes of the rolls are set as design variables. A minimum number of simulations was performed by us- ing the table of orthogonal arrays. A cost function was obtained from the results by using the design of experiments such as the response surface method and it was minimized for satisfying the design constraints. By improving the de- sign of the target pass, the shape of the final product approaches that intended by the designer. Keywords: Design of experiments; Finite element method; Roll forming process; Shape difference factor - 1. Introduction Roll forming is a process that progressively bends a flat strip of sheet metal through pairs of forming rolls, and it can be used for inexpensively manufacturing long sheet metal products with a constant cross sec- tion. Since roll forming requires manpower only for loading the strip and unloading the product, the man- power required can be reduced. If the shape of the product is simple, it takes little time to change the die and to set up a process. Since the length of the prod- uct can be controlled easily, roll forming can also be used for the batch production of small quantities of a product. Since the roll forming process was designed based on the designers experience for developing a new product or improving the quality of existing products, the design defects were confirmed after the production of the prototype; therefore, the compatibil- ity of the corrected design could be verified after the production of the prototype. This process leads to an increase in the production cost, which reduces the competitiveness of manufacturers. In order to solve this problem, an FE simulation of the roll forming process is used prior to the production of a prototype in order to predict design defects and reduce the cost of design correction. Bhattacharayya et al. 1 performed a semi- empirical approach and by minimizing the total en- ergy produced an expression for predicting deforma- tion length of a channel section. Duggal et al. 2 compared the FE simulation results with Bhat- tacharayyas experimental results. And other numeri- cal 3-6 and experimental 7, 8 studies have been performed. Hong and Kim 9 developed a 3D FEM program for the roll forming process and predicted the scratch defect of the roll forming process with the rigid- plastic finite element method. The analysis using the rigid-plastic finite element method has also been ex- tended to predict the edge shape 10 and roll wear 11. Kim et al. 12 made the prediction of buckling * Corresponding author. Tel.: +82 2 705 8635, Fax.: +82 2 712 0799 E-mail address: nskimsogang.ac.kr KSME n d , the number of design variables; and i , the unknown coefficients. Eq. (2) is used to calculate the coefficients of RSM that minimize the square summation of the residuals using least square method. T1T () = XX XY (2) where X denotes the design matrix comprising experimental points and Y denotes the response vector. 2.2 Shape difference factor If products that are manufactured through the roll forming process do not meet the standards because of a design error, it is necessary to correct the design defects, as shown in Fig. 1. A slide rail having a complicated shape and requir- ing high precision in forming and straightness is manufactured by using the roll forming process 20. It is difficult to determine the compatibility of the design since the product has a complicated shape. A standard is necessary to quantitatively evaluate the quality of the formed shape; one such standard is called the shape difference factor (SDF). In order to quantitatively evaluate the precision of the shape of a Fig. 1. Flow chart for the correction of the roll forming proc- ess design. M. Oh and N. Kim / Journal of Mechanical Science and Technology 22 (2008) 15371543 1539 Fig. 2. Comparison of the raw plan and the simulation result. Fig. 3. Measurement of the difference between the raw plan and the simulation result. product manufactured by the roll forming process, the cross section of a simulation or experimental result is set on the center of the cross section of a raw plan with grids drawn on it, as shown in Fig. 2. As shown in Fig. 3, SDF is decided by the summation of the difference in the distance that is measured between the raw plan and the simulation or experimental result along the direction of thickness and it is defined as given by Eq. (3). 2 0 1 SDF ( / ) = = n i i dt (3) where d i denotes the difference in distance between the result and the raw plan at the i th elements and t 0 denotes the thickness of the initial strip. Since the shape of the cross section of the product is symmetric, the SDF is measured at the right cross section of the product. 3. Simulation and experimental results 3.1 Process condition A slide rail is comprised of an inner member, mid- dle member, outer member, and bearing balls. Since this research focuses on the slide rail, the middle member is analyzed because an inner rail and an outer rail are formed at the middle member. The middle member is manufactured with a 25-pass line. The distance between the passes is 350 mm; odd- numbered passes are set up as driving rolls, and even- numbered passes are set up as idle rolls, and the ve- locities of each pass roll are set up to produce a prod- uct with a constant velocity of 40m/min. The thickness and width of the initial strip is 2 mm and 60 mm, respectively; the strip is made of SCP10, whose material properties are listed in Table 1. The final shape of the cross section of the product manu- factured in the experiment is shown in Fig. 4. Table 1. Material properties of SCP10 Youngs modulus (GPa) 210 Poissons ratio 0.3 Yield Strength (MPa) 433 UTS (MPa) 460 Fig. 4. Cross section obtained from the experiment. 3.2 FE simulation software FE simulations are performed by the roll forming simulation program SHAPE-RF v4.0.0 based on the rigid-plastic finite element method. This program uses the normalized plane strain condition as the ini- tial boundary condition for initially determining the free surface. The velocity field is calculated by the FEA of the 3D kinematic steady state and the final shape is determined by an iterative method that cali- brates the boundary conditions and the free surface. Information such as the strain rate and pressure torque 1540 M. Oh and N. Kim / Journal of Mechanical Science and Technology 22 (2008) 15371543 Table 2. Process conditions of FE simulation. Flow stress (MPa) 0.024 502(0.002 )=+ f Initial thickness (mm) 2.0 Strip width (mm) 60.0 Friction coefficient 0.1 No. of PASS 25 Section 80 No. of elements Rolling direction 20 Fig. 5. Flower pattern of the slide rails middle member. Fig. 6. FE simulation result. is obtained based on the velocity field. The reliability of SHAPE-RF has been verified by several previous papers 9-13. The process conditions of the FE simulation are listed in Table 2. Swifts flow stress equation is used to express the stress-strain relation of a strip, and it is defined as given by Eq. (4). 0 () n f K =+ (4) where f denotes the flow stress; K, the strength coefficient; , the effective strain; 0 , the initial effective strain; and n, the strain hardening coefficient. The flow stress of the strip is obtained by using the “convert” function of SHAPE-RF and it is shown in Table 2. The flower pattern of the middle member is obtained by using the FE simulation program and it is shown in Fig. 5. The final shape of the cross section of the roll forming product is shown in Fig. 6. 3.3 Verification of FE simulation software The SDF obtained from the experimental and simu- Fig. 7. Longitudinal strain along the rolling direction. lation results is 0.87450 and 0.91677, respectively. The difference between the results and the raw plan mostly occurs at areas where the slide rail is bent. The relative error is 4.83%. The FE simulation cannot perfectly approximate the real process because obscure parameters exist at the site of the manufacturing process. For example, for any model of friction that expresses the contact between objects to be valid, it must explain the fric- tional behavior of two bodies under different loads, speed of relative sliding, temperature, surface condi- tions, environment, etc., as observed in practice. Con- sequently, many models have been proposed with varying degrees of success 21. Although many un- certain parameters exist, as mentioned above, the FE simulation is verified since the shape difference error between the FE simulation and experimental results that is evaluated at the final section increases to 4.83% as compared to the incipient shape. 4. Procedure for design correction and discussion 4.1 Designation of target pass For design variables to be applied to the design of experiments, they should be restricted because many process variables are found in the roll forming proc- ess. In the FE simulation of the roll forming process of the slide rail, the pass where the largest deforma- tion occurs is designated as the target pass for the design variables. The longitudinal strain along the rolling direction is shown in Fig. 7 and the largest deformation occurs at the 6.3 m spot along the rolling direction. Therefore, the 18 th pass is designated as the target pass. M. Oh and N. Kim / Journal of Mechanical Science and Technology 22 (2008) 15371543 1541 Table 3. Levels of the design variables (unit : mm). Design Variables Level 0 Level 1 Level 2 A 17.7 18.7 19.7 B 12.5603 13.5603 14.5603 C 5 5.4 5.8 4.2 Table of orthogonal arrays The strip is bent by the left and right rolls at the 18 th pass. Since the slide rail has a symmetric shape, the design variables are limited to the right roll. De- sign variable A is the x-coordinate of the flat part of the right roll and B is the y-coordinate of the same part. C is the curvature of the right roll. The design variables and levels are listed in Table 3 and a table of orthogonal arrays L 9 (3 4 ) is used. Table 4 shows the table of orthogonal arrays for the SDF obtained from the FE simulation results. 4.3Optimization of the cost function Based on the table of orthogonal arrays, the cost function obtained by RSM is given by Eq. (5) as: 12 3 13.90852-0.93098 +2.62837 -7.13367 +0.05303 -0.03022 1.08379 -0.08205 -0.37625 xx xxx + x xx xx = 22 12 2 31223 (5) where 1 x denotes the design variable A; 2 x , the design variable B; and 3 x , the design variable C. In order to examine the adequacy of the cost func- tion, Fig. 8 shows the comparison of the values be- tween the cost function in which the conditions of Table 4 are applied and the SDF obtained from the FE simulation results. In order to investigate how the numerical differences in the compared values exist, it is verified through Eq. (6) that the error is less than 1%. Therefore, the cost function can represent the SDF between the final shape of the product and the raw plan when the 18 th pass is corrected. ca c - Error(%) = 100 (6) where c denotes the SDF computed from each simu- lation and a denotes the value of the cost function when the same variables are inputted. Table 4. Table of orthogonal arrays for the SDF. No. A B C SDF of the simulation 1 0 0 0 1.38007 2 0 1 1 1.07844 3 0 2 2 0.88306 4 1 0 2 1.22510 5 1 1 0 1.35087 6 1 2 1 0.87713 7 2 0 1 1.18833 8 2 1 2 0.91890 9 2 2 0 1.32407 Fig. 8. Comparison of c and a In order to minimize the cost function, the BFGS method, which directly updates a Hessian matrix, is used. Initial design variables and the constraints are given as follows: 123 17.0, 12.0, 5.5xxx= = (7) 1 2 3 17.7 19.7 12.5603 14.5603 5.0 5.8 x x x (8) The result of minimization is given as follows: 12 3 19.7, 14.5603, 5.71xx x= = 0.60159= Based on this result, the 18 th pass is corrected and the FE simulation is performed. There is a difference of 30.87 % between the minimum value of the cost function and the SDF of the FE simulation result of 1542 M. Oh and N. Kim / Journal of Mechanical Science and Technology 22 (2008) 15371543 Fig. 9. Comparison of the SDF between the original design and the optimum design. Fig. 10. Comparison of the raw plan and the optimized simu- lation result. 0.87023. Although the result indicates a wide gap in the minimum of the cost function, the SDF of the optimized result decreases by 5.34 % as compared to the original result of 0.91677; the comparison of the results is shown in Fig. 9. The cross section of the optimized simulation result and the raw plan are compared, as shown in Fig. 10. A significant differ- ence is observed between c and a since the cost function obtained from the restricted design variables does not consider all conditions of the target pass such as the design of the top and bottom rolls. Further, roll forming has many design variables such as roll velocities, friction condition, and angle of roll. If more process variables are contained in the design variables, then the error between the FE simulation result and the cost function will be smaller than that in the above result. 5. Conclusions In order to improve the efficiency of the roll form- ing process, it is very important to immediately cor- rect a design that has some defects. There is a product called a slide rail that has a complex shape and whose design is difficult to modify. In this paper, the roll forming design was corrected by the design of ex- periments. The SDF was also introduced to determine the compatibility of the roll design. The conclusions drawn from this study are listed below. The correction of the design of the target pass, which is designated through the measurement of the longitudinal strain along the rolling direction of the entire process, affects the final shape of the roll form- ing product. The SDF, which represents the difference between the cross section of the product that is affected by the change of the design variables and the raw plan, is suggested as a standard. Further, the cost function that can evaluate the SDF is derived by using the design of experiments such as the RSM. The optimum de- sign is determined through the minimization of the cost function. The minimum value of the cost func- tion is applied to the design of the target pass and it decreases the SDF by 5.34 %. Consequently, the cross-sectional shape of the slide rail obtained by the simulation approaches the shape intended by the de- signer. Nomenclature- i x : Design variable i d : Difference between the simulation or experimental result and the raw plan 0 t : Thickness of initial strip : Cost function f : Flow stress : Effective strain 0 : Initial effective strain c : Computed shape difference factor a : Analytical shape difference factor References 1 D. Bhattacharayya, P. D. Smith, C. H. Yee and I. F. Collins, The prediction of Deformation length in cold roll forming, J. Mech. Working Technol., 9 (1984) 181-191. 2 N. Duggal, M. A. Ahmetoglu, G. L. Kinzel and T. Altan, Computer aided simulation of cold roll form- ing-a computer program for simple section profiles, J. Mater. Proc. Technol., 59 (1996) 41-48. 3 M. Brunet and S. Ronel, Finite element analysis of roll-forming of thin sheet metal, J. Mater. Proc. Technol., 45 (1994) 255-260. M. Oh and N. Kim / Journal of Mechanical Science and Technology 22 (2008) 15371543 1543 4 M. Brunet, B. Lay and P. Pol, Computer aided de- sign of roll-forming of channel sections, J. Mater. Proc. Technol., 60 (1996) 209-214. 5 C. Liu, Y. Zhou and W. Lu, Numerical simulation of roll-forming by B-spline finite strip method, J. Mater. Proc. Technol., 60 (1996) 215-218. 6 M. Farzin, M. S. Tehrani and E. Shameli, Determi- nation of buckling limit of strain in cold roll form- ing by the finite element analysis, J. Mater. Proc. Technol., 125-126 (2002) 626-632. 7 S. M. Panton, J. L. Duncan, S. D. Zhu, Longitudinal and shear strain development in cold roll forming, J. Mater. Proc. Technol., 60 (1996) 219-224. 8 M. Lindgren, Experimental investigations of the roll load and roll torque when high strength steel is roll formed, J. Mater. Proc. Technol., 191 (2007) 44-47. 9 S. Hong and N. Kim, Study on scratch defect of roll forming process, Trans. of the KSME (A). 25 (2001) 1213-1219. 10 S. Lee and N. Kim, Prediction and design of edge shape of initial strip for thick tube roll forming us- ing finite element method, Trans. of the KSME (A). 26 (2002) 644-652. 11 B. Kang and N. Kim, A study on roll wear in the roll forming process, Trans. of the KSME (A). 27 (2003) 644-652. 12 Y. Kim, J. Kim, Y. Jeoung and N. Kim, Buckling analysis of roll forming process using finite element method, Trans. of the KSME (A). 27 (2003) 1451- 1456. 13 M. A. Sheikh and R. R. Palavilayil, An assessment of finite element software for application to the roll- forming process, J. Mater. Proc. Technol. 180 (2006) 221-232. 14 A. Alsamhan, P. Hartely and I. Pillinger, The com- puter simulation of cold-roll-forming using FE methods and applied real time re-meshing tech- niques, J. Mater. Proc. Technol., 142 (2003) 102- 111. 15 A. K. Datta, G. Das, P. K. De, P. Ramachandrarao and M. Mukhopadhyaya, Finite element modeling of rolling process and optimization of process pa- rameter, Material Science and Engineering (A). 426 (2006) 11-20. 16 M. Lindgren, Cold roll forming of a U-channel made of high strength steel, J. Mater. Proc. Technol., 186 (2007) 77-81. 17 R. S. Senanayake, I. M. Cole and S. Thiruvarud- chelvan, The application of computational and ex- perimental techniques to metal deformation in cold roll forming, J. Mater. Proc. Technol., 45 (1994) 155-160. 18 E. Kim, I. Lee and B. Kim, Optimum design of washing machine flange using design of experiment, Trans. of the KSME (A). 31 (5) (2007) 601-608. 19 D. Lee, S. Baek, K. Lee, S Cho and W. Joo, Multi- objective optimization in discrete design space us- ing the design of experiment and the mathematical programming, Trans. of the KSME (A). 26 (10) (2002) 2150-2158. 20 S. Jeong, S. Lee, G. Kim, J. Kim and S. Shin, Rigid-plastic finite element method for develop- ment mold of dishwashers under rail roll forming, Trans. of the KSMPE Annual Meeting. (2006) 644- 652. 21 S. Kalpakjian and S. R. Schmid, Manufacturing processes for engineering materials, second ed. Ad- dison-Wesley Publishing Company, New York, USA, (1992).
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