CA6140主軸箱結(jié)構(gòu)設(shè)計【Z=12 φ=1.41 nmin=31.5r-min】【說明書+CAD】,Z=12 φ=1.41 nmin=31.5r-min,說明書+CAD,CA6140主軸箱結(jié)構(gòu)設(shè)計【Z=12,φ=1.41,nmin=31.5r-min】【說明書+CAD】,ca6140,主軸,結(jié)構(gòu)設(shè)計 金屬切削機床課程設(shè)計 CA6140型車床 一、設(shè)計目的 通過機床主運動機械變速傳動系統(tǒng)得結(jié)構(gòu)設(shè)計，在擬定傳動和變速的結(jié)構(gòu)方案過程中，得到設(shè)計構(gòu)思、方案分析、結(jié)構(gòu)工藝性、機械制圖、零件計算、編寫技術(shù)文件和查閱技術(shù)資料等方面的綜合訓(xùn)練，樹立正確的設(shè)計思想，掌握基本的設(shè)計方法，并具有初步的結(jié)構(gòu)分析、結(jié)構(gòu)設(shè)計和計算能力。 二、設(shè)計步驟 1.運動設(shè)計 1.1已知條件 [1]確定轉(zhuǎn)速范圍：主軸最小轉(zhuǎn)速。 [2]確定公比： [3]轉(zhuǎn)速級數(shù)： 1.2結(jié)構(gòu)分析式 ⑴ ⑵ [3] 從電動機到主軸主要為降速傳動，若使傳動副較多的傳動組放在較接近電動機處可使小尺寸零件多些，大尺寸零件少些，節(jié)省材料，也就是滿足傳動副前多后少的原則，因此取方案。在降速傳動中，防止齒輪直徑過大而使徑向尺寸常限制最小傳動比 ；在升速時為防止產(chǎn)生過大的噪音和震動常限制最大轉(zhuǎn)速比。在主傳動鏈任一傳動組的最大變速范圍。在設(shè)計時必須保證中間傳動軸的變速范圍最小， 根據(jù)中間傳動軸變速范圍小的原則選擇結(jié)構(gòu)網(wǎng)。從而確定結(jié)構(gòu)網(wǎng)如下： 檢查傳動組的變速范圍時，只檢查最后一個擴大組： 其中 ，， 所以 ，合適。 1.3 繪制轉(zhuǎn)速圖 ⑴選擇電動機 一般車床若無特殊要求，多采用Y系列封閉式三相異步電動機，根據(jù)原則條件選擇Y-132M-4型Y系列籠式三相異步電動機。 ⑵分配總降速傳動比 總降速傳動比 又電動機轉(zhuǎn)速 不符合轉(zhuǎn)速數(shù)列標準，因而增加一定比傳動副。 [3]確定傳動軸軸數(shù) 傳動軸軸數(shù) = 變速組數(shù) + 定比傳動副數(shù) + 1 = 3 + 1 + 1 = 5。 ⑷確定各級轉(zhuǎn)速并繪制轉(zhuǎn)速圖 由 　　z = 12確定各級轉(zhuǎn)速： 1400、1000、710、500、355、250、180、125、90、63、45、31.5r/min。 在五根軸中，除去電動機軸，其余四軸按傳動順序依次設(shè)為Ⅰ、Ⅱ、Ⅲ、Ⅳ。Ⅰ與Ⅱ、Ⅱ與Ⅲ、Ⅲ與Ⅳ軸之間的傳動組分別設(shè)為a、b、c?，F(xiàn)由Ⅳ（主軸）開始，確定Ⅰ、Ⅱ、Ⅲ軸的轉(zhuǎn)速： ① 先來確定Ⅲ軸的轉(zhuǎn)速 傳動組c 的變速范圍為 ，結(jié)合結(jié)構(gòu)式， Ⅲ軸的轉(zhuǎn)速只有一和可能： 125、180、250、355、500、710r/min。 ② 確定軸Ⅱ的轉(zhuǎn)速 傳動組b的級比指數(shù)為3，希望中間軸轉(zhuǎn)速較小，因而為了避免升速，又不致傳動比太小，可取 ， 軸Ⅱ的轉(zhuǎn)速確定為：355、500、710r/min。 ③確定軸Ⅰ的轉(zhuǎn)速 對于軸Ⅰ，其級比指數(shù)為1,可取 ，， 確定軸Ⅰ轉(zhuǎn)速為710r/min。 由此也可確定加在電動機與主軸之間的定傳動比 。下面畫出轉(zhuǎn)速圖（電動機轉(zhuǎn)速與主軸最高轉(zhuǎn)速相近）。 [5]確定各變速組傳動副齒數(shù) ①傳動組a: 查表8-1, ，， 時：……57、60、63、66、69、72、75、78…… 時：……58、60、63、65、67、68、70、72、73、77…… 時：……58、60、62、64、66、68、70、72、74、76…… 可取72,于是可得軸Ⅰ齒輪齒數(shù)分別為：24、30、36。 于是，， 可得軸Ⅱ上的三聯(lián)齒輪齒數(shù)分別為：48、42、36。 ②傳動組b: 查表8-1, ， 時：……69、72、73、76、77、80、81、84、87…… 時：……70、72、74、76、78、80、82、84、86…… 可取 84，于是可得軸Ⅱ上兩聯(lián)齒輪的齒數(shù)分別為：22、42。 于是 ，，得軸Ⅲ上兩齒輪的齒數(shù)分別為：62、42。 ③傳動組c: 查表8-1,, 時：……84、85、89、90、94、95…… 時： ……72、75、78、81、84、87、89、90…… 可取 90. 為降速傳動，取軸Ⅲ齒輪齒數(shù)為18； 為升速傳動，取軸Ⅳ齒輪齒數(shù)為30。 于是得, 得軸Ⅲ兩聯(lián)動齒輪的齒數(shù)分別為18，60； 得軸Ⅳ兩齒輪齒數(shù)分別為72，30。 1.4 繪制傳動系統(tǒng)圖 根據(jù)軸數(shù)，齒輪副，電動機等已知條件可有如下系統(tǒng)圖： 2.動力設(shè)計 2.1 確定各軸轉(zhuǎn)速 ⑴確定主軸計算轉(zhuǎn)速：主軸的計算轉(zhuǎn)速為 圖表 1 ⑵各傳動軸的計算轉(zhuǎn)速： 軸Ⅲ可從主軸90r/min按72/18的傳動副找上去，軸Ⅲ的計算轉(zhuǎn)速 125r/min；軸Ⅱ的計算轉(zhuǎn)速為355r/min；軸Ⅰ的計算轉(zhuǎn)速為710r/min。 [3]各齒輪的計算轉(zhuǎn)速 傳動組c中，18/72只需計算z = 18 的齒輪，計算轉(zhuǎn)速為355r/min；60/30只需計算z = 30的齒輪，計算轉(zhuǎn)速為250r/min；傳動組b計算z = 22的齒輪，計算轉(zhuǎn)速為355r/min；傳動組a應(yīng)計算z = 24的齒輪，計算轉(zhuǎn)速為710r/min。 [4]核算主軸轉(zhuǎn)速誤差 所以合適。 2.2 帶傳動設(shè)計 電動機轉(zhuǎn)速n=1440r/min,傳遞功率P=7.5KW,傳動比i=2.03，兩班制， 一天運轉(zhuǎn)16.1小時，工作年數(shù)10年。 ⑴確定計算功率 取1.1，則 ⑵選取V帶型 根據(jù)小帶輪的轉(zhuǎn)速和計算功率，選B型帶。 ⑶確定帶輪直徑和驗算帶速 查表小帶輪基準直徑 , 驗算帶速成 其中 -小帶輪轉(zhuǎn)速，r/min； -小帶輪直徑，mm； ，合適。 [4]確定帶傳動的中心距和帶的基準長度 設(shè)中心距為,則 0．55（）a2（） 于是 208.45a758,初取中心距為400mm。 帶長 查表取相近的基準長度，。 帶傳動實際中心距 [5]驗算小帶輪的包角 一般小帶輪的包角不應(yīng)小于。 。合適。 [6]確定帶的根數(shù) 其中： -時傳遞功率的增量； -按小輪包角，查得的包角系數(shù)； -長度系數(shù)； 為避免V型帶工作時各根帶受力嚴重不均勻，限制根數(shù)不大于10。 [7]計算帶的張緊力 其中： -帶的傳動功率,KW； v-帶速,m/s； q-每米帶的質(zhì)量，kg/m；取q=0.17kg/m。 v = 1440r/min = 9.42m/s。 [8]計算作用在軸上的壓軸力 2.3 各傳動組齒輪模數(shù)的確定和校核 ⑴模數(shù)的確定： a傳動組：分別計算各齒輪模數(shù) 先計算24齒齒輪的模數(shù)： 其中: -公比 ； = 2； -電動機功率； = 7.5KW； -齒寬系數(shù)； -齒輪傳動許允應(yīng)力; -計算齒輪計算轉(zhuǎn)速。 ， 取= 600MPa,安全系數(shù)S = 1。 由應(yīng)力循環(huán)次數(shù)選取 ，取S=1，。 取m = 4mm。 按齒數(shù)30的計算，，可取m = 4mm； 按齒數(shù)36的計算，, 可取m = 4mm。 于是傳動組a的齒輪模數(shù)取m = 4mm，b = 32mm。 軸Ⅰ上齒輪的直徑： 。 軸Ⅱ上三聯(lián)齒輪的直徑分別為： b傳動組： 確定軸Ⅱ上另兩聯(lián)齒輪的模數(shù)。 按22齒數(shù)的齒輪計算： 可得m = 4.8mm； 取m = 5mm。 按42齒數(shù)的齒輪計算： 可得m = 3.55mm； 于是軸Ⅱ兩聯(lián)齒輪的模數(shù)統(tǒng)一取為m = 5mm。 于是軸Ⅱ兩聯(lián)齒輪的直徑分別為： 軸Ⅲ上與軸Ⅱ兩聯(lián)齒輪嚙合的兩齒輪直徑分別為： c傳動組： 取m = 5mm。 軸Ⅲ上兩聯(lián)動齒輪的直徑分別為： 軸四上兩齒輪的直徑分別為： 3. 齒輪強度校核：計算公式 3.1校核a傳動組齒輪 校核齒數(shù)為24的即可，確定各項參數(shù) ⑴ P=8.25KW,n=710r/min, ⑵確定動載系數(shù)： 齒輪精度為7級，由《機械設(shè)計》查得使用系數(shù) ⑶ ⑷確定齒向載荷分配系數(shù):取齒寬系數(shù) 非對稱 ,查《機械設(shè)計》得 ⑸確定齒間載荷分配系數(shù): 由《機械設(shè)計》查得 ⑹確定動載系數(shù): ⑺查表 10-5 ⑻計算彎曲疲勞許用應(yīng)力 由圖查得小齒輪的彎曲疲勞強度極限。 圖10-18查得 ,S = 1.3 ， 故合適。 3.2 校核b傳動組齒輪 校核齒數(shù)為22的即可，確定各項參數(shù) ⑴ P=8.25KW,n=355r/min, ⑵確定動載系數(shù)： 齒輪精度為7級，由《機械設(shè)計》查得使用系數(shù) ⑶ ⑷確定齒向載荷分配系數(shù):取齒寬系數(shù) 非對稱 ,查《機械設(shè)計》得 ⑸確定齒間載荷分配系數(shù): 由《機械設(shè)計》查得 ⑹確定動載系數(shù): ⑺查表 10-5 ⑻計算彎曲疲勞許用應(yīng)力 由圖查得小齒輪的彎曲疲勞強度極限。 圖10-18查得 ,S = 1.3 ， 故合適。 3.3校核c傳動組齒輪 校核齒數(shù)為18的即可，確定各項參數(shù) ⑴ P=8.25KW,n=355r/min, ⑵確定動載系數(shù)： 齒輪精度為7級，由《機械設(shè)計》查得使用系數(shù) ⑶ ⑷確定齒向載荷分配系數(shù):取齒寬系數(shù) 非對稱 ,查《機械設(shè)計》得 ⑸確定齒間載荷分配系數(shù): 由《機械設(shè)計》查得 ⑹確定動載系數(shù): ⑺查表 10-5 ⑻計算彎曲疲勞許用應(yīng)力 由圖查得小齒輪的彎曲疲勞強度極限。 圖10-18查得 ,S = 1.3 ， 故合適。 4. 主軸撓度的校核 4.1 確定各軸最小直徑 [1]Ⅰ軸的直徑： [2]Ⅱ軸的直徑： [3]Ⅲ軸的直徑： [4]主軸的直徑： 4.2軸的校核 Ⅰ軸的校核：通過受力分析，在一軸的三對嚙合齒輪副中，中間的兩對齒輪對Ⅰ軸中點處的撓度影響最大，所以，選擇中間齒輪嚙合來進行校核 。 Ⅱ軸、Ⅲ軸的校核同上。 5. 主軸最佳跨距的確定 400mm車床，P=7.5KW. 5.1 選擇軸頸直徑,軸承型號和最佳跨距 前軸頸應(yīng)為75-100mm,初選=100mm,后軸頸 取,前軸承為NN3020K,后軸承為NN3016K,根據(jù)結(jié)構(gòu),定懸伸長度 5.2 求軸承剛度 考慮機械效率 主軸最大輸出轉(zhuǎn)距 床身上最大加工直徑約為最大回轉(zhuǎn)直徑的60%,取50%即200,故半徑為0.1. 切削力 背向力 故總的作用力 次力作用于頂在頂尖間的工件上主軸尾架各承受一半, 故主軸軸端受力為 先假設(shè) 前后支撐分別為 根據(jù) 。 6. 各傳動軸支承處軸承的選擇 主軸 前支承：NN3020K;中支承：N219E;后支承：NN3016K Ⅰ軸 前支承：30207;后支承：30207 Ⅱ軸 前支承：30207;中支承：NN3009;后支承：30207 Ⅲ軸 前支承：30208;后支承：30208 7. 主軸剛度的校核 7.1 主軸圖: 7.2 計算跨距 前支承為雙列圓柱滾子軸承，后支承為雙列圓柱滾子軸承 當量外徑 主軸剛度：由于 故根據(jù)式（10-8） 對于機床的剛度要求，取阻尼比 當v=50m/min,s=0.1mm/r時,, 取 計算 可以看出，該機床主軸是合格的. 三、總結(jié) 金屬切削機床的課程設(shè)計任務(wù)完成了，雖然設(shè)計的過程比較繁瑣，而且剛開始還有些不知所措，但是在同學(xué)們的共同努力下，再加上老師的悉心指導(dǎo)，我終于順利地完成了這次設(shè)計任務(wù)。本次設(shè)計鞏固和深化了課堂理論教學(xué)的內(nèi)容，鍛煉和培養(yǎng)了我綜合運用所學(xué)過的知識和理論的能力，是我獨立分析、解決問題的能力得到了強化. 四、參考文獻 ［1］工程學(xué)院機械制造教研室 主編.金屬切削機床指導(dǎo)書. ［2］濮良貴 紀名剛主編.機械設(shè)計(第七版).北京:高等教育出版社,2001年6月 [3］毛謙德 李振清主編.《袖珍機械設(shè)計師手冊》第二版.機械工業(yè)出版社,2002年5月 ［4］《減速器實用技術(shù)手冊》編輯委員會編.減速器實用技術(shù)手冊.北京:機械工業(yè)出版社,1992年 ［5］戴曙 主編.金屬切削機床.北京:機械工業(yè)出版社,2005年1月 [6]《機床設(shè)計手冊》編寫組 主編.機床設(shè)計手冊.北京:機械工業(yè)出版社,1980年8月 ［7］華東紡織工學(xué)院 哈爾濱工業(yè)大學(xué) 天津大學(xué)主編.機床設(shè)計圖冊.上海:上?？茖W(xué)技術(shù)出版社,1979年6月 （以上看不見的 鼠標右鍵—題注就可以了！） - 18 - 金屬切削機床課程設(shè)計說明書 目錄 一、設(shè)計目的 -1- 二、設(shè)計步驟 -1- 1.運動設(shè)計 -1- 1.1已知條件 -1- 1.2結(jié)構(gòu)分析式 -1- 1.3 繪制轉(zhuǎn)速圖 -2- 1.4 繪制傳動系統(tǒng)圖 -5- 2.動力設(shè)計 -5- 2.1 確定各軸轉(zhuǎn)速 -5- 2.2 帶傳動設(shè)計 -6- 2.3 各傳動組齒輪模數(shù)的確定和校核 -7- 3. 齒輪強度校核 -9- 3.1校核a傳動組齒輪 -9- 3.2 校核b傳動組齒輪 -10- 3.3校核c傳動組齒輪 -11- 4. 主軸撓度的校核 -13- 4.1 確定各軸最小直徑 -13- 4.2軸的校核 -13- 5. 主軸最佳跨距的確定 -14- 5.1 選擇軸頸直徑,軸承型號和最佳跨距 -14- 5.2 求軸承剛度 -14- 6. 各傳動軸支承處軸承的選擇 -15- 7. 主軸剛度的校核 -15- 7.1 主軸圖 -15- 7.2 計算跨距 -16- 三、總結(jié) -17- 四、參考文獻 -18- Bebek, Bearing load Bending stress beam is rate, parameter with the most important influence on design of the crankshaft. Results of bearing loads and web bending stresses are tabulated. must overall systems on parameters of the crankshaft system. Studies on crankshaft of internal combustion engines mainly fo- cus on vibration and stress analyses 19. Although stress analy- ses of crankshafts are available in literature, there are few studies on the effect of counterweight configuration on main bear- ing loads and crankshaft stresses. Sharpe et al. 10 studied balanc- ing of the crankshaft of a V-8 engine using a rigid crankshaft model tions are carried out at engine speed range of 10002000 rpm. Bending stresses at the centres of each web are also calculated. 2. Engine specifications The specifications of in-line six-cylinder diesel engine are given in Table 1. The 9.0 L engine crankshaft has eight counterweights at crank webs 1, 2, 5, 6, 7, 8, 11 and 12. 3D solid model of the crank- shaft is obtained using Pro/Engineer and is shown in Fig. 1. Sche- matic representation of the crankshaft is given in Fig. 2. Static * Corresponding author. Tel.: +90 212 359 7534; fax: +90 212 287 2456. Advances in Engineering Software 40 (2009) 95104 Contents lists available E-mail address: yasin.yilmazboun.edu.tr (Y. Yilmaz). being the main part responsible for power production. Crankshaft system mainly consists of piston, piston pin, con- necting rod, crankshaft, torsional vibration (TV) damper and fly- wheel. Counterweights are placed on the opposite side of each crank to balance rotating inertia forces. In general, counterweights are designed for balancing rates between 50% and 100%. For acceptable maximum and average main bearing loads, mass of counterweights and their positions are important. Maximum and average main bearing loads of an engine depend on cylinder pres- sure, counterweight mass, engine speed and other geometric study on effect of counterweight configuration on main bearing loads and crankshaft stresses is still needed. In this study, counterweight positions and masses of an in-line six-cylinder diesel engine crankshaft system are studied. Maxi- mum and average main bearing forces and crankshaft bending stresses are calculated for 12-counterweight configurations with a zero degree counterweight angle, and for eight-counterweight configurations with 30C176 counterweight angle for 0%, 50% and 100% counterweight balancing rates. Analyses are carried out using Multibody System Simulation Program, ADAMS/Engine. Simula- 1. Introduction New internal combustion engines power, good fuel economy, small engine harmless as possible to the environment. each component of the engine on its be investigated in detail. Crankshaft tion engines have important influence 0965-9978/$ - see front matter C211 2008 Elsevier Ltd. All doi:10.1016/j.advengsoft.2008.03.009 C211 2008 Elsevier Ltd. All rights reserved. have high engine size, and should be as Therefore, the effect of performance should of internal combus- engine performance and optimized counterweights to minimize main bearing loads. Stanley and Taraza 11 obtained maximum and average main bearing loads of four and six-cylinder symmetric in-line engines using a rigid crankshaft model and estimated ideal counterweight mass that resulted in acceptable maximum bearing load. Rigid crankshaft models that are used in counterweight analyses do not consider the effect of crankshaft flexibility on main bearing loads and can lead to considerable errors. Therefore, an extensive Crankshaft models Balancing rate Both configurations show the same trend. The load from gas pressure rather than inertia forces is the An investigation of the effect of counterweight load and crankshaft bending stress Yasin Yilmaz * , Gunay Anlas Department of Mechanical Engineering, Faculty of Engineering, Bogazici University, 34342 article info Article history: Received 11 February 2008 Received in revised form 17 March 2008 Accepted 24 March 2008 Available online 6 May 2008 Keywords: Counterweight configuration abstract In this study, effects of counterweight stress of an in-line six-cylinder ADAMS. In the analysis, rigid, rigid, beam and 3D solid models analyses. Twelve-counterweight terweight configurations with ing rates, are considered. It with increasing balancing Advances in Engineering journal homepage: rights reserved. configuration on main bearing Istanbul, Turkey mass and position on main bearing load and crankshaft bending diesel engine is investigated using Multibody System Simulation Program, and 3D solid crankshaft models are used. Main bearing load results of are compared and beam model is used in counterweight configuration configurations with a zero degree counterweight angle and eight-coun- 30C176 counterweight angle, each for 0%, 50% and 100% counterweight balanc- found that maximum main bearing load and web bending stress increase and average main bearing load decreases with increasing balancing rate. at ScienceDirect Software cate/advengsoft unbalance of each crank throw (with and w/o counterweights) is determined using Pro/Engineer and is given in Table 2. The balanc- ing system data for the crank train are given in Table 3. 3. Modeling of crankshaft system Using ADAMS/Engine, a crankshaft can be modeled in four dif- ferent ways: rigid crankshaft, torsionalflexible crankshaft, beam crankshaft and 3D solid crankshaft. Rigid crankshaft model is mainly used to obtain free forces and torques, and for balancing purposes. Torsionalflexible crankshaft model is used to investi- gate torsional vibrations where each throw is modeled as one rigid part, and springs are used between each throw to represent tor- sional stiffness. Beam crankshaft model is used to represent the torsional and bending stiffness of the crankshaft. Using beam mod- el bending stresses at the webs can be calculated 12. Table 1 Engine specifications Unit 9.0 L engine Bore diameter mm 115 Stroke mm 144 Axial cylinder distance mm 134 Peak firing pressure MPa 19 Rated power at speed kW/rpm 295/2200 Max. torque at speed Nm/rpm 1600/12001700 Main journal/pin diameter mm 95/81 Firing order 1-5-3-6-2-4 Flywheel mass kg 47.84 Flywheel moment of inertia kg mm 2 1.57E+9 Mass of TV damper ring kg 4.94 Mass of TV damper housing kg 6.86 Moment of inertia of the ring kg mm 2 1.27E+5 Moment of inertia of the housing kg mm 2 0.56E+5 Main Bearing #1 Main Bearing #2 Main Bearing #3 Main Bearing #4 Main Bearing #5 Main Bearing #6 Main Bearing #7 Counterweights Fig. 1. 3D solid model of the crankshaft. C3, C4, C5, C6 C1, C2, C7, C8 1, 6 3, 4 2, 5 C1 C2 C3 C4 C5 C6 1 2 Fig. 2. Eight-counterweight arrangement Table 2 Properties of the crank throws Throw 1 Throw 2 Mass (kg) 12.50 9.25 CG position from crank rotation axis (mm) 12.423 31.435 Static unbalance (kg mm) 155.265 290.767 96 Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 95104 C7 C8 3 4 5 6 of the 9.0 L engine crankshaft. Throw 3 Throw 4 Throw 5 Throw 6 12.50 12.50 9.28 12.55 11.967 11.966 31.027 11.702 149.734 149.734 287.871 146.856 Elastic 3D solid model of the crankshaft can be obtained using an additional finite element program. The procedure is lengthy and time consuming and usually one ends up with degrees of free- dom in order of millions. To simplify the finite element model, modal superposition technique is used. The elastic deformation of the structure is approximated by linear combination of suitable modes which can be shown as follows: u Uq 1 where q is the vector of modal coordinates andUis the shape func- tion matrix. Table 3 Crankshaft system data Crank radius (mm) 72 Connecting rod length (mm) 239 Mass of complete piston (kg) 3.42 Connecting rod reciprocating mass (kg) 0.92 Reciprocating mass (total per cylinder) (kg) 4.32 Connecting rod rotating mass (kg) 2.01 Y. Yilmaz, G. Anlas/Advances in Engineering An elastic body contains two types of nodes, interface nodes where forces and boundary conditions interact with the structure during multibody system simulation (MSS), and interior nodes. In MSS the position of the elastic body is computed by superposing its rigid body motion and elastic deformation. In ADAMS, this is performed using Component Mode Synthesis” technique based on CraigBampton method 13,14. The component modes contain static and dynamic behavior of the structure. These modes are con- straint modes which are static deformation shapes obtained by giving a unit displacement to each interface degree of freedom (DOF) while keeping all other interface DOFs fixed, and fixed boundary normal modes which are the solution of eigenvalue problem by fixing the entire interface DOFs. The modal transforma- tion between the physical DOF and the CraigBampton modes and their modal coordinates is described by 15 u u B u I C26C27 I0 U C U N C20C21 q C q N C26C27 2 where u B and u I are column vectors and represent boundary DOF and interior DOF, respectively. I, 0 are identity and zero matrices, respectively. U C is the matrix of physical displacements of the inte- rior DOF in the constraint modes. U N is the matrix of physical dis- Fig. 3. Model of the crankshaft system. placements of the interior DOF in the normal modes. q C is the column vector of modal coordinates of the constraint modes. q N is the column vector of modal coordinates of the fixed boundary nor- mal modes. To obtain decoupled set of modes, constrained modes and normal modes are orthogonalized. Elastic 3D solid crankshaft model of the 9.0 L engine is obtained in MSC.Nastran using modal superposition technique. First, 3D so- lid model of the crankshaft that is shown in Fig. 1 is exported to MSC.Nastran and finite element model of the crankshaft, which is characterized by approximately 300,000 ten-node tetrahedral ele- ments and 500,000 nodes is obtained. The modal model of the crankshaft is developed with 32 boundary DOFs associated with 16 interface nodes. Constrained modes obtained from static analy- sis correspond to these DOFs. Flexible crankshaft model is obtained through modal synthesis considering the first 40 fixed boundary normal modes. Therefore flexible crankshaft model is character- ized by a total of 72 DOFs. This model is exported to ADAMS/En- gine and crankshaft system model that is shown in Fig. 3 is obtained. 3D finite element model is run with ADAMS. 4. Forces acting on crankshaft system and balancing Forces in an internal combustion engine may be divided into inertia forces and pressure forces. Inertia forces are further divided into two main categories: rotating inertia forces and reciprocating inertia forces. The rotating inertia force for each cylinder can be written as shown below: F iR;j m R C1 r R C1 x 2 C1C0sinh j j cosh j k3 where m R is the rotating mass that consists of the mass of crank pin, crank webs and mass of rotating portion of the connecting rod; r R is the distance from the crankshaft centre of rotation to the centre of gravity of the rotating mass, x is angular velocity of the crankshaft, and h j is the angular position of each crank throw with respect to Top Dead Centre” (TDC). If there are two counterweights per crank throw, each counterweight force is given by 11 F CWi;j C0m CWi;j C1 r CWi;j C1 x 2 C1C0sinh j c i;j j cosh j c i;j k hi ; i 1;2 j 1;2;.;6 4 where c i,j is the offset angle of counterweight mass from 180C176 oppo- site of crank throw j”. There are two counterweights per throw. i” denotes the counterweight number. The counterweight size that is required to accomplish an assessed balancing rate is U CW K C1U Crank throw m cr-r C1 rC1cosc 2 5 where U CW is the static unbalance of each counterweight, U Crank_throw is the static unbalance of each crank throw, m cr-r is the mass of connecting rod rotating portion, r is the crank radius and K is the balancing rate of the internal couple due to rotating forces. From this formula follows the balancing rate for a given crankshaft and a given counterweight size: K 2 C1 U CW U Crank throw m cr-r C1 rC1cosc 6 For a standard in-line six-cylinder engine crankshaft with three pairs of crank throws disposed at angles of 120C176 that are arranged symmetrical to the crankshaft centre, rotating forces, and first and second order reciprocating forces are naturally balanced. This can be explained by the first and second order vector stars shown in Fig. 4. The six-cylinder crankshaft generates rotating and first Software 40 (2009) 95104 97 and second order reciprocating couples in each crankshaft half that balance each other but which result in internal bending moment. At high speeds, the two equally directed crank throws, 3 and 4 yield a high rotating load on centre main bearing. The rotating inertia force of each cylinder is usually offset at least partially by counterweights placed on the opposite side of each crank. In gen- eral, the counterweights are designed for balancing rates between 50% and 100% of the internal couple. Gas forces in cylinders are acting on piston head, cylinder head and on side walls of the cylinder. These forces are equal to F p;j C0 pD 2 4 C1P cyl;j hC0P cc;j hC138 k; j 1;2;.;6 7 1, 6 2, 5 3, 4 3, 4 1, 6 2, 5 Fig. 4. First and second order vector stars. 0 20 40 60 80 100 120 140 160 180 200 0 90 180 270 360 450 540 630 720 Crank Angle (degree) Pressure (bar) 1000rpm 1200rpm 1350rpm 1675rpm 2000rpm Fig. 5. Gas pressure values at different engine speeds for the 9.0 L engine. Bearing #1 0 25 50 75 100 125 150 0 120 240 360 480 600 720 Crank Angle deg Force kN Rigid Beam 3D solid Fig. 6. Forces acting on main bearing #1 for rigid, beam and 3D solid crankshaft models at 1000 rpm engine speed. Bearing #2 0 25 50 75 100 125 150 175 0 120 240 360 480 600 720 Crank Angle deg Force kN Rigid Beam 3D solid Fig. 7. Forces acting on main bearing #2 for rigid, beam and 3D solid crankshaft models at 1000 rpm engine speed. Bearing #3 0 25 50 75 100 125 150 0 120 240 360 480 600 720 Crank Angle deg Force kN Rigid Beam 3D solid Fig. 8. Forces acting on main bearing #3 for rigid, beam and 3D solid crankshaft models at 1000 rpm engine speed. Bearing #4 0 25 50 75 100 125 150 0 120 240 360 480 600 720 Crank Angle deg Force kN Rigid Beam 3D solid Fig. 9. Forces acting on main bearing #4 for rigid, beam and 3D solid crankshaft models at 1000 rpm engine speed. Bearing #5 125 150 Rigid Bam 3D solid 98 Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 95104 0 25 50 75 100 0 120 240 360 480 600 720 Crank Angle deg Force kN Fig. 10. Forces acting on main bearing #5 for rigid, beam and 3D solid crankshaft models at 1000 rpm engine speed. where D is cylinder diameter, P cyl is the gas pressure in the cylinder and P cc is the pressure in the crankcase. The gas forces are transmit- ted to the crankshaft through the piston and connecting rod. Cylin- der pressure curves for the 9.0 L engine studied under full load at different engine speeds are given in Fig. 5. Pressure curves are ob- tained using AVL/Boost engine cycle calculation program which simulates thermodynamic processes in the engine taking into ac- count one dimensional gas dynamics in the intake and exhaust sys- tems 16. 5. Main bearing loads: comparison of crankshaft models Main bearing loads are calculated using ADAMSs rigid, beam and 3D solid crankshaft models and compared. In the rigid model, no vibration effects are considered which can lead to considerable errors if vibration effects have a major role on the system (like in multithrow crankshafts). To consider vibration effects beam crank- shaft model is used and main bearing loads and bending stresses at webs are calculated. Rigid model assumes crankshaft to be stati- cally determinate and reaction force of any given bearing depends on the load exerted on the throws adjacent to that bearing. Beam model assumes the crankshaft to be statically indeterminate and the load exerted on a throw affects all bearings. Analyses are car- ried out at an engine speed range of 10002000 rpm. A more sophisticated 3D solid hybrid model that combines FE with ADAMS is used to check the results obtained by beam model. Maximum main bearing load occurs at bearing number two at Bearing #6 0 25 50 75 100 125 150 0 120 240 360 480 600 720 Crank Angle deg Force kN Rigid Beam 3D solid Fig. 11. Forces acting on main bearing #6 for rigid, beam and 3D solid crankshaft models at 1000 rpm engine speed. Bearing #7 0 25 50 75 100 125 150 0 120 240 360 480 600 720 Crank Angle deg Force kN Rigid Beam 3D solid Fig. 12. Forces acting on main bearing #7 for rigid, beam and 3D solid crankshaft models at 1000 rpm engine speed. Bearing #1 40 50 60 70 80 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) Maximum Bearing K=0% K=50% K=100% Force (kN) Fig. 13. (a) Maximum and (b) average bearing forces at Bearing #2 120 130 140 150 160 K=0% K=50% K=100% Maximum Bearing Force (kN) 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) Fig. 14. (a) Maximum and (b) average bearing forces at Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 95104 99 an engine speed of 1000 rpm, therefore results are plotted in Figs. 612 for 1000 rpm only. Rigid crankshaft model overestimates the maximum main bearing load at bearings 1 and 7 with respect to beam and flexible crankshaft models. However it underestimates the maximum main bearing load at other bearings. For example at bearing 2, beam model gives a maximum main bearing load that is 50% more than that of rigid models because the beam model as- sumes the crankshaft to be statically indeterminate and considers Bearing #1 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) 0 5 10 15 20 Average Bearing K=0% K=50% K=100% Force (kN) bearing #1 for 12-counterweight configurations. Bearing #2 20 25 30 35 40 K=0% K=50% K=100% 1000 1200 1400 1600 1800 2000 Average Bearing Force (kN) Crank Angular Velocity (rpm) bearing #2 for 12-counterweight configurations. bending vibrations. Maximum main bearing load difference of beam and 3D solid models is approximately 5%. Main bearing loads for beam and 3D solid crankshaft models are generally in good agreement. In bearings 3, 5 and 6, 3D solid model gives larger bear- ing loads at firing positions of the cylinders that are not adjacent to bearing. Because obtaining elastic 3D solid models for different counterweight configurations is difficult and time consuming, and beam model gives equally valid results, beam model is used Bearing #3 100 110 120 130 140 K=0% K=50% K=100% Bearing #3 20 25 30 35 40 K=0% K=50% K=100% Maximum Bearing Force (kN) 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) Average Bearing Force (kN) Fig. 15. (a) Maximum and (b) average bearing forces at bearing #3 for 12-counterweight configurations. Bearing #4 60 70 80 90 100 110 120 K=0% K=50% K=100% Bearing #4 10 15 20 25 30 35 40 K=0% K=50% K=100% Maximum Bearing Force (kN) 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) Average Bearing Force (kN) Fig. 16. (a) Maximum and (b) average bearing forces at bearing #4 for 12-counterweight configurations. Bearing #6 120 130 140 K=0% K=50% K=100% Bearing #6 35 40 45 50 K=0% K=50% K=100% Bearing #5 100 110 120 130 140 K=0% K=50% K=100% Bearing #5 20 25 30 35 40 K=0% K=50% K=100% Maximum Bearing Force (kN) 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) Average Bearing Force (kN) Fig. 17. (a) Maximum and (b) average bearing forces at bearing #5 for 12-counterweight configurations. 100 Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 95104 100 110 Maximum Bearing Force (kN) 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) Fig. 18. (a) Maximum and (b) average bearing forces at 20 25 30 1000 1200 1400 1600 1800 2000 Average Bearing Force (kN) Crank Angular Velocity (rpm) bearing #6 for 12-counterweight con