中型普通車床主軸箱設(shè)計(jì)【Dmax=350mm Nmin=212r-minN=5.5KW φ=1.26 Z=8】

中型普通車床主軸箱設(shè)計(jì)【Dmax=350mm Nmin=212r-minN=5.5KW φ=1.26 Z=8】,Dmax=350mm Nmin=212r-min N=5.5KW φ=1.26 Z=8,中型普通車床主軸箱設(shè)計(jì)【Dmax=350mm,Nmin=212r-min,N=5.5KW,φ=1.26,Z=8】,中型 寧XX大學(xué) 課程設(shè)計(jì)(論文) 中型普通車床主軸箱設(shè)計(jì)（題目14） 所在學(xué)院 專 業(yè) 班 級(jí) 姓 名 學(xué) 號(hào) 指導(dǎo)老師 年 月 日 5 摘 要 本設(shè)計(jì)著重研究機(jī)床主傳動(dòng)系統(tǒng)的設(shè)計(jì)步驟和設(shè)計(jì)方法，根據(jù)已確定的運(yùn)動(dòng)參數(shù)以變速箱展開圖的總中心距最小為目標(biāo)，擬定變速系統(tǒng)的變速方案，以獲得最優(yōu)方案以及較高的設(shè)計(jì)效率。在機(jī)床主傳動(dòng)系統(tǒng)中，為減少齒輪數(shù)目，簡(jiǎn)化結(jié)構(gòu)，縮短軸向尺寸，用齒輪齒數(shù)的設(shè)計(jì)方法是試算，湊算法，計(jì)算麻煩且不易找出合理的設(shè)計(jì)方案。本文通過對(duì)主傳動(dòng)系統(tǒng)中三聯(lián)滑移齒輪傳動(dòng)特點(diǎn)的分析與研究，繪制零件工作圖與主軸箱展開圖及剖視圖。 關(guān)鍵詞:傳動(dòng)系統(tǒng)設(shè)計(jì),傳動(dòng)副，結(jié)構(gòu)網(wǎng)，結(jié)構(gòu)式， 目 錄 摘 要 2 目 錄 4 第1章 緒論 6 1.1 課程設(shè)計(jì)的目的 6 1.2課程設(shè)計(jì)的內(nèi)容 6 1.2.1 理論分析與設(shè)計(jì)計(jì)算 6 1.2.2 圖樣技術(shù)設(shè)計(jì) 6 1.2.3編制技術(shù)文件 6 1.3 課程設(shè)計(jì)題目、主要技術(shù)參數(shù)和技術(shù)要求 6 第2章 車床參數(shù)的擬定 8 2.1車床主參數(shù)和基本參數(shù) 8 2.2擬定參數(shù)的步驟和方法 8 2.2.1 極限切削速度Vmax、Vmin 8 2.2.2 主軸的極限最低轉(zhuǎn)速 8 2.2.3 主電機(jī)功率——?jiǎng)恿?shù)的確定 9 2.2.4確定結(jié)構(gòu)式 9 2.2.5確定結(jié)構(gòu)網(wǎng) 9 2.2.6繪制轉(zhuǎn)速圖和傳動(dòng)系統(tǒng)圖 10 2.3 確定各變速組此論傳動(dòng)副齒數(shù) 10 2.4 核算主軸轉(zhuǎn)速誤差 11 第3章 傳動(dòng)件的計(jì)算 12 3.1 帶傳動(dòng)設(shè)計(jì) 12 3.2選擇帶型 13 3.3確定帶輪的基準(zhǔn)直徑并驗(yàn)證帶速 13 3.4確定中心距離、帶的基準(zhǔn)長(zhǎng)度并驗(yàn)算小輪包角 14 3.5確定帶的根數(shù)z 15 3.6確定帶輪的結(jié)構(gòu)和尺寸 15 3.7確定帶的張緊裝置 15 3.8計(jì)算壓軸力 16 3.2 計(jì)算轉(zhuǎn)速的計(jì)算 17 3.3 齒輪模數(shù)計(jì)算及驗(yàn)算 18 3.4 傳動(dòng)軸最小軸徑的初定 21 3.5 主軸合理跨距的計(jì)算 22 第4章 主要零部件的選擇 23 4.1 軸承的選擇 23 4.2 鍵的規(guī)格 23 4.3 主軸彎曲剛度校核 24 4.4.軸承校核 24 4.5 潤(rùn)滑與密封 24 第5章 摩擦離合器(多片式)的計(jì)算 25 第6章 主要零部件的選擇 27 6.1電動(dòng)機(jī)的選擇 27 6.2 軸承的選擇 27 6.3變速操縱機(jī)構(gòu)的選擇 27 6.4 軸的校核 27 6.5 軸承壽命校核 29 第7章 主軸箱結(jié)構(gòu)設(shè)計(jì)及說明 30 7.1 結(jié)構(gòu)設(shè)計(jì)的內(nèi)容、技術(shù)要求和方案 30 7.2 展開圖及其布置 31 結(jié)束語 32 參考文獻(xiàn) 33 第1章 緒論 1.1 課程設(shè)計(jì)的目的 課程設(shè)計(jì)是在學(xué)完本課程后，進(jìn)行一次學(xué)習(xí)設(shè)計(jì)的綜合性練習(xí)。通過課程設(shè)計(jì)，使學(xué)生能夠運(yùn)用所學(xué)過的基礎(chǔ)課、技術(shù)基礎(chǔ)課和專業(yè)課的有關(guān)理論知識(shí)，及生產(chǎn)實(shí)習(xí)等實(shí)踐技能，達(dá)到鞏固、加深和拓展所學(xué)知識(shí)的目的。通過課程設(shè)計(jì)，分析比較機(jī)械系統(tǒng)中的某些典型機(jī)構(gòu)，進(jìn)行選擇和改進(jìn)；結(jié)合結(jié)構(gòu)設(shè)計(jì)，進(jìn)行設(shè)計(jì)計(jì)算并編寫技術(shù)文件；完成系統(tǒng)主傳動(dòng)設(shè)計(jì)，達(dá)到學(xué)習(xí)設(shè)計(jì)步驟和方法的目的。通過設(shè)計(jì)，掌握查閱相關(guān)工程設(shè)計(jì)手冊(cè)、設(shè)計(jì)標(biāo)準(zhǔn)和資料的方法，達(dá)到積累設(shè)計(jì)知識(shí)和設(shè)計(jì)技巧，提高學(xué)生設(shè)計(jì)能力的目的。通過設(shè)計(jì)，使學(xué)生獲得機(jī)械系統(tǒng)基本設(shè)計(jì)技能的訓(xùn)練，提高分析和解決工程技術(shù)問題的能力，并為進(jìn)行機(jī)械系統(tǒng)設(shè)計(jì)創(chuàng)造一定的條件。 1.2課程設(shè)計(jì)的內(nèi)容 《機(jī)械系統(tǒng)設(shè)計(jì)》課程設(shè)計(jì)內(nèi)容由理論分析與設(shè)計(jì)計(jì)算、圖樣技術(shù)設(shè)計(jì)和技術(shù)文件編制三部分組成。 1.2.1 理論分析與設(shè)計(jì)計(jì)算 （1）機(jī)械系統(tǒng)的方案設(shè)計(jì)。設(shè)計(jì)方案的分析，最佳功能原理方案的確定。 （2）根據(jù)總體設(shè)計(jì)參數(shù)，進(jìn)行傳動(dòng)系統(tǒng)運(yùn)動(dòng)設(shè)計(jì)和計(jì)算。 （3）根據(jù)設(shè)計(jì)方案和零部件選擇情況，進(jìn)行有關(guān)動(dòng)力計(jì)算和校核。 1.2.2 圖樣技術(shù)設(shè)計(jì) （1）選擇系統(tǒng)中的主要機(jī)件。 （2）工程技術(shù)圖樣的設(shè)計(jì)與繪制。 1.2.3編制技術(shù)文件 （1）對(duì)于課程設(shè)計(jì)內(nèi)容進(jìn)行自我經(jīng)濟(jì)技術(shù)評(píng)價(jià)。 （2）編制設(shè)計(jì)計(jì)算說明書。 1.3 課程設(shè)計(jì)題目、主要技術(shù)參數(shù)和技術(shù)要求 題目：中型普通車床主軸箱設(shè)計(jì) 題目14 車床的主參數(shù)（規(guī)格尺寸）和基本參數(shù)如下： 工件最大回轉(zhuǎn)直徑 D(mm) 正轉(zhuǎn)最低轉(zhuǎn)速 nmin( ) 電機(jī)功率 N（kw） 公比 轉(zhuǎn)速級(jí)數(shù)Z 350 212 5.5 1.26 8 33 第2章 車床參數(shù)的擬定 2.1車床主參數(shù)和基本參數(shù) 車床的主參數(shù)（規(guī)格尺寸）和基本參數(shù)如下： 工件最大回轉(zhuǎn)直徑 D(mm) 正轉(zhuǎn)最低轉(zhuǎn)速 nmin( ) 電機(jī)功率 N（kw） 公比 轉(zhuǎn)速級(jí)數(shù)Z 350 212 5.5 1.26 8 2.2擬定參數(shù)的步驟和方法 2.2.1 極限切削速度Vmax、Vmin 根據(jù)典型的和可能的工藝選取極限切削速度要考慮： 允許的切速極限參考值如下： 表 1.1 加 工 條 件 Vmax(m/min) Vmin(m/min) 硬質(zhì)合金刀具粗加工鑄鐵工件 30～50 硬質(zhì)合金刀具半精或精加工碳鋼工件 150～300 螺紋加工和鉸孔 3～8 2.2.2 主軸的極限最低轉(zhuǎn)速 計(jì)算車床主軸極限轉(zhuǎn)速時(shí)的加工直徑，則主軸極限轉(zhuǎn)速應(yīng)為： 結(jié)合題目條件，取標(biāo)準(zhǔn)數(shù)列數(shù)值，即=212r/min 取 依據(jù)題目要求選級(jí)數(shù)Z=8， =1.26=1.064考慮到設(shè)計(jì)的結(jié)構(gòu)復(fù)雜程度要適中，故采用常規(guī)的擴(kuò)大傳動(dòng)。各級(jí)轉(zhuǎn)速數(shù)列可直接從標(biāo)準(zhǔn)的數(shù)列表中查出，按標(biāo)準(zhǔn)轉(zhuǎn)速數(shù)列為： 212，265，335，425，530，670，850，1060 2.2.3 主電機(jī)功率——?jiǎng)恿?shù)的確定 合理地確定電機(jī)功率N，使機(jī)床既能充分發(fā)揮其性能，滿足生產(chǎn)需要，又不致使電機(jī)經(jīng)常輕載而降低功率因素。 根據(jù)題設(shè)條件電機(jī)功率為5.5KW 可選取電機(jī)為：Y132S-4額定功率為5.5KW，滿載轉(zhuǎn)速為1440r/min. 2.2.4確定結(jié)構(gòu)式 已知Z=x3b a、b為正整數(shù)，即Z應(yīng)可以分解為2和3的因子，以便用2、3聯(lián)滑移齒輪實(shí)現(xiàn)變速。 取Z=8級(jí) 則Z=22 對(duì)于Z=8可分解為：Z=21×22×24。 綜合上述可得：主傳動(dòng)部件的運(yùn)動(dòng)參數(shù) =212 Z=8 =1.26 2.2.5確定結(jié)構(gòu)網(wǎng) 根據(jù)“前多后少” , “先降后升” , 前密后疏,結(jié)構(gòu)緊湊的原則,選取傳動(dòng)方案 Z=21×22×24,易知第二擴(kuò)大組的變速范圍r=φ(P3-1)x=1.264=3.95〈8 滿足要求，其結(jié)構(gòu)網(wǎng)如圖2-1。 圖2-1結(jié)構(gòu)網(wǎng) Z=21×22×24 2.2.6繪制轉(zhuǎn)速圖和傳動(dòng)系統(tǒng)圖 （1）選擇電動(dòng)機(jī)：采用Y系列封閉自扇冷式鼠籠型三相異步電動(dòng)機(jī)。 （2）繪制轉(zhuǎn)速圖： （3）畫主傳動(dòng)系統(tǒng)圖。根據(jù)系統(tǒng)轉(zhuǎn)速圖及已知的技術(shù)參數(shù)，畫主傳動(dòng)系統(tǒng)圖如圖2-3： 1-2軸最小中心距：A1_2min>1/2(Zmaxm+2m+D) 軸最小齒數(shù)和:Szmin>(Zmax+2+D/m) 2.3 確定各變速組此論傳動(dòng)副齒數(shù) (1)Sz100-120,中型機(jī)床Sz=70-100 (2)直齒圓柱齒輪Zmin18-20,m4 圖2-3 主傳動(dòng)系統(tǒng)圖 （7）齒輪齒數(shù)的確定。變速組內(nèi)取模數(shù)相等，據(jù)設(shè)計(jì)要求Zmin≥18~20,齒數(shù)和Sz≤100～120，由表4.1，根據(jù)各變速組公比，可得各傳動(dòng)比和齒輪齒數(shù)，各齒輪齒數(shù)如表2-2。 表2-2 齒輪齒數(shù) 傳動(dòng)比 基本組 第一擴(kuò)大組 第二擴(kuò)大組 1:1 1:1.58 1:1 1:1.26 1.26：1 1：2 代號(hào) Z Z Z Z Z Z Z Z’ Z5 Z5’ Z Z 齒數(shù) 47 47 36 58 42 42 37 47 49 39 29 59 2.4 核算主軸轉(zhuǎn)速誤差 實(shí)際傳動(dòng)比所造成的主軸轉(zhuǎn)速誤差，一般不應(yīng)超過±10(-1)％,即 〈10(-1)％=2.6％ 各級(jí)轉(zhuǎn)速誤差 n 1060 850 670 530 425 335 265 212 n` 1064.2 837.8 672.1 524.5 426.05 329.6 266.2 208.6 誤差 0.4％ 1.4％ 0.4％ 1.4％ 0.4％ 1.4％ 0.4％ 1.4％ 轉(zhuǎn)速誤差小于2.6％，因此不需要修改齒數(shù)。 第3章 傳動(dòng)件的計(jì)算 3.1 帶傳動(dòng)設(shè)計(jì) 輸出功率P=5.5kW,轉(zhuǎn)速n1=1440r/min,n2=850r/min 3.1.1計(jì)算設(shè)計(jì)功率Pd 表4 工作情況系數(shù) 工作機(jī) 原動(dòng)機(jī) ⅰ類 ⅱ類 一天工作時(shí)間/h 10~16 10~16 載荷 平穩(wěn) 液體攪拌機(jī)；離心式水泵；通風(fēng)機(jī)和鼓風(fēng)機(jī)（）；離心式壓縮機(jī)；輕型運(yùn)輸機(jī) 1.0 1.1 1.2 1.1 1.2 1.3 載荷 變動(dòng)小 帶式運(yùn)輸機(jī)（運(yùn)送砂石、谷物），通風(fēng)機(jī)（）；發(fā)電機(jī)；旋轉(zhuǎn)式水泵；金屬切削機(jī)床；剪床；壓力機(jī)；印刷機(jī)；振動(dòng)篩 1.1 1.2 1.3 1.2 1.3 1.4 載荷 變動(dòng)較大 螺旋式運(yùn)輸機(jī)；斗式上料機(jī)；往復(fù)式水泵和壓縮機(jī)；鍛錘；磨粉機(jī)；鋸木機(jī)和木工機(jī)械；紡織機(jī)械 1.2 1.3 1.4 1.4 1.5 1.6 載荷 變動(dòng)很大 破碎機(jī)（旋轉(zhuǎn)式、顎式等）；球磨機(jī)；棒磨機(jī)；起重機(jī)；挖掘機(jī)；橡膠輥壓機(jī) 1.3 1.4 1.5 1.5 1.6 1.8 根據(jù)V帶的載荷平穩(wěn)，兩班工作制（16小時(shí)），查《機(jī)械設(shè)計(jì)》P296表4， 取KA＝1.1。即 3.2選擇帶型 普通V帶的帶型根據(jù)傳動(dòng)的設(shè)計(jì)功率Pd和小帶輪的轉(zhuǎn)速n1按《機(jī)械設(shè)計(jì)》P297圖13－11選取。 根據(jù)算出的Pd＝6.05kW及小帶輪轉(zhuǎn)速n1＝1440r/min ，查圖得：dd=80～100可知應(yīng)選取A型V帶。 3.3確定帶輪的基準(zhǔn)直徑并驗(yàn)證帶速 由《機(jī)械設(shè)計(jì)》P298表13－7查得，小帶輪基準(zhǔn)直徑為80～100mm 則取dd1=100mm> ddmin.=75 mm（dd1根據(jù)P295表13-4查得） 表3 V帶帶輪最小基準(zhǔn)直徑 槽型 Y Z A B C D E 20 50 75 125 200 355 500 由《機(jī)械設(shè)計(jì)》P295表13-4查“V帶輪的基準(zhǔn)直徑”，得=170mm ① 誤差驗(yàn)算傳動(dòng)比： （為彈性滑動(dòng)率） 誤差 符合要求 ② 帶速 滿足5m/s300mm，所以宜選用E型輪輻式帶輪。 總之，小帶輪選H型孔板式結(jié)構(gòu)，大帶輪選擇E型輪輻式結(jié)構(gòu)。 帶輪的材料：選用灰鑄鐵，HT200。 3.7確定帶的張緊裝置 選用結(jié)構(gòu)簡(jiǎn)單，調(diào)整方便的定期調(diào)整中心距的張緊裝置。 3.8計(jì)算壓軸力 由《機(jī)械設(shè)計(jì)》P303表13－12查得，A型帶的初拉力F0＝130.59N，上面已得到=153.36o，z=6，則 對(duì)帶輪的主要要求是質(zhì)量小且分布均勻、工藝性好、與帶接觸的工作表面加工精度要高，以減少帶的磨損。轉(zhuǎn)速高時(shí)要進(jìn)行動(dòng)平衡，對(duì)于鑄造和焊接帶輪的內(nèi)應(yīng)力要小, 帶輪由輪緣、腹板（輪輻）和輪轂三部分組成。帶輪的外圈環(huán)形部分稱為輪緣，輪緣是帶輪的工作部分，用以安裝傳動(dòng)帶，制有梯形輪槽。由于普通V帶兩側(cè)面間的夾角是40°，為了適應(yīng)V帶在帶輪上彎曲時(shí)截面變形而使楔角減小，故規(guī)定普通V帶輪槽角 為32°、34°、36°、38°（按帶的型號(hào)及帶輪直徑確定），輪槽尺寸見表7-3。裝在軸上的筒形部分稱為輪轂，是帶輪與軸的聯(lián)接部分。中間部分稱為輪幅（腹板），用來聯(lián)接輪緣與輪轂成一整體。 表 普通V帶輪的輪槽尺寸（摘自GB/T13575.1-92） 項(xiàng)目 ? 符號(hào) 槽型 Y Z A B C D E 基準(zhǔn)寬度 b p 5.3 8.5 11.0 14.0 19.0 27.0 32.0 基準(zhǔn)線上槽深 h amin 1.6 2.0 2.75 3.5 4.8 8.1 9.6 基準(zhǔn)線下槽深 h fmin 4.7 7.0 8.7 10.8 14.3 19.9 23.4 槽間距 e 8 ± 0.3 12 ± 0.3 15 ± 0.3 19 ± 0.4 25.5 ± 0.5 37 ± 0.6 44.5 ± 0.7 第一槽對(duì)稱面至端面的距離 f min 6 7 9 11.5 16 23 28 最小輪緣厚 5 5.5 6 7.5 10 12 15 帶輪寬 B B =( z -1) e + 2 f ? z —輪槽數(shù) 外徑 d a 輪 槽 角 32° 對(duì)應(yīng)的基準(zhǔn)直徑 d d ≤ 60 - - - - - - 34° - ≤ 80 ≤ 118 ≤ 190 ≤ 315 - - 36° 60 - - - - ≤ 475 ≤ 600 38° - ＞ 80 ＞ 118 ＞ 190 ＞ 315 ＞ 475 ＞ 600 極限偏差 ± 1 ± 0.5 V帶輪按腹板（輪輻）結(jié)構(gòu)的不同分為以下幾種型式： （1） 實(shí)心帶輪：用于尺寸較小的帶輪(dd≤(2.5～3)d時(shí))，如圖7 -6a。  （2） 腹板帶輪：用于中小尺寸的帶輪(dd≤ 300mm 時(shí))，如圖7-6b。 （3） 孔板帶輪：用于尺寸較大的帶輪((dd－d)＞ 100 mm 時(shí))，如圖7 -6c 。 （4） 橢圓輪輻帶輪：用于尺寸大的帶輪(dd＞ 500mm 時(shí))，如圖7-6d。 （a） （b） （c） （d） 圖7-6 帶輪結(jié)構(gòu)類型 根據(jù)設(shè)計(jì)結(jié)果，可以得出結(jié)論：小帶輪選擇實(shí)心帶輪，如圖（a）,大帶輪選擇腹板帶輪如圖（b） 3.2 計(jì)算轉(zhuǎn)速的計(jì)算 （1）主軸的計(jì)算轉(zhuǎn)速nj，由公式n=n得，主軸的計(jì)算轉(zhuǎn)速nj=311.85r/min， 取335 r/min。 (2). 傳動(dòng)軸的計(jì)算轉(zhuǎn)速 軸2=670 r/min，軸1=850r/min。 （2）確定各傳動(dòng)軸的計(jì)算轉(zhuǎn)速。 表3-1 各軸計(jì)算轉(zhuǎn)速 軸 號(hào) Ⅰ 軸 Ⅱ 軸 Ⅲ 軸 計(jì)算轉(zhuǎn)速 r/min 850 850 670 （3） 確定齒輪副的計(jì)算轉(zhuǎn)速。3-2。 表3-2 齒輪副計(jì)算轉(zhuǎn)速 序號(hào) Z Z Z Z Z n 850 850 850 850 670 3.3 齒輪模數(shù)計(jì)算及驗(yàn)算 （1）模數(shù)計(jì)算。一般同一變速組內(nèi)的齒輪取同一模數(shù)，選取負(fù)荷最重的小齒輪，按簡(jiǎn)化的接觸疲勞強(qiáng)度公式進(jìn)行計(jì)算，即mj=16338可得各組的模數(shù)，如表3-3所示。 表3-3 模數(shù) 組號(hào) 基本組 第一擴(kuò)大組 模數(shù) mm 2.5 2.5 （2）基本組齒輪計(jì)算。 基本組齒輪幾何尺寸見下表 齒輪 Z1 Z1` Z2 Z2` 齒數(shù) 47 47 36 58 分度圓直徑 117.5 117.5 90 145 齒頂圓直徑 122.5 122.5 95 150 齒根圓直徑 111.25 111.25 83.75 138.75 齒寬 20 20 20 20 按基本組最小齒輪計(jì)算。小齒輪用40Cr，調(diào)質(zhì)處理，硬度241HB～286HB，平均取260HB，大齒輪用45鋼，調(diào)質(zhì)處理，硬度229HB～286HB，平均取240HB。計(jì)算如下： ① 齒面接觸疲勞強(qiáng)度計(jì)算： 接觸應(yīng)力驗(yàn)算公式為 彎曲應(yīng)力驗(yàn)算公式為： 式中 N----傳遞的額定功率（kW），這里取N為電動(dòng)機(jī)功率，N=5kW; -----計(jì)算轉(zhuǎn)速（r/min）. =335（r/min）; m-----初算的齒輪模數(shù)（mm）, m=2.5（mm）; B----齒寬（mm）;B=20（mm）; z----小齒輪齒數(shù)；z=36; u----小齒輪齒數(shù)與大齒輪齒數(shù)之比,u=1.6; -----壽命系數(shù)； = ----工作期限系數(shù)； T------齒輪工作期限，這里取T=15000h.; -----齒輪的最低轉(zhuǎn)速（r/min）, =500（r/min） ----基準(zhǔn)循環(huán)次數(shù)，接觸載荷取=，彎曲載荷取= m----疲勞曲線指數(shù)，接觸載荷取m=3；彎曲載荷取m=6; ----轉(zhuǎn)速變化系數(shù)，查【5】2上，取=0.60 ----功率利用系數(shù)，查【5】2上，取=0.78 -----材料強(qiáng)化系數(shù)，查【5】2上， =0.60 -----工作狀況系數(shù)，取=1.1 -----動(dòng)載荷系數(shù)，查【5】2上，取=1 ------齒向載荷分布系數(shù)，查【5】2上，=1 Y------齒形系數(shù)，查【5】2上，Y=0.386； ----許用接觸應(yīng)力（MPa）,查【4】，表4-7，取=650 Mpa； ---許用彎曲應(yīng)力（MPa），查【4】，表4-7，取=275 Mpa； 根據(jù)上述公式，可求得及查取值可求得： =635 Mpa =78 Mpa （3）擴(kuò)大組齒輪計(jì)算。 第一擴(kuò)大組 齒輪幾何尺寸見下表 齒輪 Z3 Z3` Z4 Z4` 齒數(shù) 42 42 37 47 分度圓直徑 105 105 92.5 117.5 齒頂圓直徑 110 110 97.5 122.5 齒根圓直徑 98.75 98.75 86.25 111.25 齒寬 20 20 20 20 第二擴(kuò)大組齒輪幾何尺寸見下表 齒輪 Z5 Z5` Z6 Z6` 齒數(shù) 49 39 29 59 分度圓直徑 147 117 87 117 齒頂圓直徑 153 123 93 183 齒根圓直徑 139.5 109.5 79.5 169.5 齒寬 24 24 24 24 按擴(kuò)大組最小齒輪計(jì)算。小齒輪用40Cr，調(diào)質(zhì)處理，硬度241HB～286HB，平均取260HB，大齒輪用45鋼，調(diào)質(zhì)處理，硬度229HB～286HB，平均取240HB。 同理根據(jù)基本組的計(jì)算， 查文獻(xiàn)【6】，可得 =0.62， =0.77，=0.60，=1.1， =1，=1，m=3.5，=355； 可求得： =619 Mpa =135Mpa 3.4 傳動(dòng)軸最小軸徑的初定 由【5】式6，傳動(dòng)軸直徑按扭轉(zhuǎn)剛度用下式計(jì)算： d=1.64（mm） 或 d=91（mm） 式中 d---傳動(dòng)軸直徑（mm） Tn---該軸傳遞的額定扭矩（N*mm） T=9550000； N----該軸傳遞的功率（KW） ----該軸的計(jì)算轉(zhuǎn)速 ---該軸每米長(zhǎng)度的允許扭轉(zhuǎn)角，==。 各軸最小軸徑如表3-3。 表3-3 最小軸徑 軸 號(hào) Ⅰ 軸 Ⅱ 軸 最小軸徑mm 35 40 3.5 主軸合理跨距的計(jì)算 由于電動(dòng)機(jī)功率P=5.5kw，根據(jù)【1】表3.20，前軸徑應(yīng)為60~90mm。初步選取d1=80mm。后軸徑的d2=（0.7~0.9）d1，取d2=60mm。根據(jù)設(shè)計(jì)方案，前軸承為NN3016K型，后軸承為圓錐滾子軸承。定懸伸量a=120mm，主軸孔徑為30mm。 軸承剛度，主軸最大輸出轉(zhuǎn)矩T=9550=9550×=424.44N.m 設(shè)該機(jī)床為車床的最大加工直徑為350mm。床身上最常用的最大加工直徑，即經(jīng)濟(jì)加工直徑約為最大回轉(zhuǎn)直徑的50%，這里取60%，即180mm，故半徑為0.09m； 切削力（沿y軸） Fc==4716N 背向力（沿x軸） Fp=0.5 Fc=2358N 總作用力 F==5272.65N 此力作用于工件上，主軸端受力為F=5272.65N。 先假設(shè)l/a=2，l=3a=240mm。前后支承反力RA和RB分別為 RA=F×=5272.65×=7908.97N RB=F×=5272.65×=2636.325N 根據(jù) 文獻(xiàn)【1】式3.7 得：Kr=3.39得前支承的剛度：KA= 1689.69 N/ ；KB= 785.57 N/；==2.15 主軸的當(dāng)量外徑de=(80+60)/2=70mm，故慣性矩為 I==113.8×10-8m4 η===0.14 查【1】圖3-38 得 =2.0，與原假設(shè)接近，所以最佳跨距=120×2.0=240mm 合理跨距為（0.75-1.5），取合理跨距l(xiāng)=360mm。 根據(jù)結(jié)構(gòu)的需要，主軸的實(shí)際跨距大于合理跨距，因此需要采取措施 增加主軸的剛度，增大軸徑：前軸徑D=100mm，后軸徑d=80mm。前軸承 采用雙列圓柱滾子軸承，后支承采用背對(duì)背安裝的角接觸球軸承。 第4章 主要零部件的選擇 4.1 軸承的選擇 I軸：與帶輪靠近段安裝雙列角接觸球軸承代號(hào)7007C 另一安裝深溝球軸承6012 II軸：對(duì)稱布置深溝球軸承6009 III軸：后端安裝雙列角接觸球軸承代號(hào)7015C 另一安裝端角接觸球軸承代號(hào)7010C 中間布置角接觸球軸承代號(hào)7012C 4.2 鍵的規(guī)格 I軸安裝帶輪處選擇普通平鍵規(guī)格： BXL=10X56 II軸選擇花鍵規(guī)格： N× d×D×B =8X36X40X7 III軸選擇鍵規(guī)格： BXL=14X90 4.3 主軸彎曲剛度校核 （1）主軸剛度符合要求的條件如下： a主軸的前端部撓度 b主軸在前軸承處的傾角 c在安裝齒輪處的傾角 (2)計(jì)算如下： 前支撐為雙列圓柱滾子軸承，后支撐為角接觸軸承架立放圓柱滾子軸承跨距L=450mm. 當(dāng)量外徑 de== 主軸剛度： 因?yàn)閐i/de=25/285=0.088<0.7,所以孔對(duì)剛度的影響可忽略； ks==2kN/mm 剛度要求：主軸的剛度可根據(jù)機(jī)床的穩(wěn)定性和精度要求來評(píng)定 4.4.軸承校核 4.5 潤(rùn)滑與密封 主軸轉(zhuǎn)速高，必須保證充分潤(rùn)滑，一般常用單獨(dú)的油管將油引到軸承處。 主軸是兩端外伸的軸，防止漏油更為重要而困難。防漏的措施有兩種： 1）密封圈——加密封裝置防止油外流。。 2）疏導(dǎo)——在適當(dāng)?shù)牡胤阶龀龌赜吐?，使油能順利地流回到油箱? 第5章 摩擦離合器(多片式)的計(jì)算 設(shè)計(jì)多片式摩擦離合器時(shí)，首先根據(jù)機(jī)床結(jié)構(gòu)確定離合器的尺寸，如為軸裝式時(shí)，外摩擦片的內(nèi)徑d應(yīng)比花鍵軸大2～6mm，內(nèi)摩擦片的外徑D的確定，直接影響離合器的徑向和軸向尺寸，甚至影響主軸箱內(nèi)部結(jié)構(gòu)布局，故應(yīng)合理選擇。 摩擦片對(duì)數(shù)可按下式計(jì)算 Z≥2MnK/fb[p] 式中 Mn——摩擦離合器所傳遞的扭矩（N·mm）； Mn＝955×η/＝955××11×0.98/800＝1.28×（N·mm）; Nd——電動(dòng)機(jī)的額定功率（kW）； ——安裝離合器的傳動(dòng)軸的計(jì)算轉(zhuǎn)速（r/min）； η——從電動(dòng)機(jī)到離合器軸的傳動(dòng)效率； K——安全系數(shù)，一般取1.3～1.5； f——摩擦片間的摩擦系數(shù)，由于磨擦片為淬火鋼，查《機(jī)床設(shè)計(jì)指導(dǎo)》表2-15，取f=0.08； ——摩擦片的平均直徑（mm）; =（D+d）/2＝67mm; b——內(nèi)外摩擦片的接觸寬度（mm）； b=（D-d）/2=23mm； ——摩擦片的許用壓強(qiáng)（N/）； ＝＝1.1×1.00×1.00×0.76＝0.836 ——基本許用壓強(qiáng)（MPa），查《機(jī)床設(shè)計(jì)指導(dǎo)》表2-15，取1.1； ——速度修正系數(shù) ＝n/6×=2.5（m/s） 根據(jù)平均圓周速度查《機(jī)床設(shè)計(jì)指導(dǎo)》表2-16，取1.00； ——接合次數(shù)修正系數(shù)，查《機(jī)床設(shè)計(jì)指導(dǎo)》表2-17，取1.00； ——摩擦結(jié)合面數(shù)修正系數(shù)，查《機(jī)床設(shè)計(jì)指導(dǎo)》表2-18，取0.76。 所以 Z≥2MnK/fb[p]＝2×1.28××1.4/（3.14×0.08××23×0.836＝11 臥式車床反向離合器所傳遞的扭矩可按空載功率損耗確定，一般取 ＝0.4＝0.4×11＝4.4 最后確定摩擦離合器的軸向壓緊力Q，可按下式計(jì)算： Q=b(N)＝1.1×3.14××23×1.00＝3.57× 式中各符號(hào)意義同前述。 摩擦片的厚度一般取1、1.5、1.75、2（mm），內(nèi)外層分離時(shí)的最大間隙為0.2～0.4（mm）,摩擦片的材料應(yīng)具有較高的耐磨性、摩擦系數(shù)大、耐高溫、抗膠合性好等特點(diǎn)，常用10或15鋼，表面滲碳0.3～0.5（mm）,淬火硬度達(dá)HRC52～62。 第6章 主要零部件的選擇 6.1電動(dòng)機(jī)的選擇 轉(zhuǎn)速n＝1440r/min，功率P＝5.5kW 選用Y系列三相異步電動(dòng)機(jī) 6.2 軸承的選擇 I軸：與帶輪靠近段安裝雙列角接觸球軸承代號(hào)7007C 另一安裝深溝球軸承6012 II軸：對(duì)稱布置深溝球軸承6009 III軸：后端安裝雙列角接觸球軸承代號(hào)7015C 另一安裝端角接觸球軸承代號(hào)7010C 中間布置角接觸球軸承代號(hào)7012C 6.3變速操縱機(jī)構(gòu)的選擇 選用左右擺動(dòng)的操縱桿使其通過桿的推力來控制II軸上的三聯(lián)滑移齒輪和二聯(lián)滑移齒輪。 6.4 軸的校核 （a） 主軸的前端部撓度 （b） 主軸在前軸承處的傾角 （c） 在安裝齒輪處的傾角 E取為， ， 由于小齒輪的傳動(dòng)力大，這里以小齒輪來進(jìn)行計(jì)算 將其分解為垂直分力和水平分力 由公式 可得 主軸載荷圖如下所示： 由上圖可知如下數(shù)據(jù)：a=364mm,b=161mm,l=525mm,c=87mm 計(jì)算（在垂直平面） ,, ，， ，， 計(jì)算（在水平面） ,, ，， ，， 合成： 6.5 軸承壽命校核 由П軸最小軸徑可取軸承為7008C角接觸球軸承,ε=3；P=XFr+YFaX=1，Y=0。 對(duì)Ⅱ軸受力分析 得：前支承的徑向力Fr=2642.32N。 由軸承壽命的計(jì)算公式：預(yù)期的使用壽命 [L10h]=15000h L10h=×=×=h≥[L10h]=15000h 軸承壽命滿足要求。 第7章 主軸箱結(jié)構(gòu)設(shè)計(jì)及說明 7.1 結(jié)構(gòu)設(shè)計(jì)的內(nèi)容、技術(shù)要求和方案 設(shè)計(jì)主軸變速箱的結(jié)構(gòu)包括傳動(dòng)件（傳動(dòng)軸、軸承、帶輪、齒輪、離合器和制動(dòng)器等）、主軸組件、操縱機(jī)構(gòu)、潤(rùn)滑密封系統(tǒng)和箱體及其聯(lián)結(jié)件的結(jié)構(gòu)設(shè)計(jì)與布置，用一張展開圖和若干張橫截面圖表示。課程設(shè)計(jì)由于時(shí)間的限制，一0般只畫展開圖。 主軸變速箱是機(jī)床的重要部件。設(shè)計(jì)時(shí)除考慮一般機(jī)械傳動(dòng)的有關(guān)要求外，著重考慮以下幾個(gè)方面的問題。 精度方面的要求，剛度和抗震性的要求，傳動(dòng)效率要求，主軸前軸承處溫度和溫升的控制，結(jié)構(gòu)工藝性，操作方便、安全、可靠原則，遵循標(biāo)準(zhǔn)化和通用化的原則。 主軸變速箱結(jié)構(gòu)設(shè)計(jì)時(shí)整個(gè)機(jī)床設(shè)計(jì)的重點(diǎn)，由于結(jié)構(gòu)復(fù)雜，設(shè)計(jì)中不可避免要經(jīng)過反復(fù)思考和多次修改。在正式畫圖前應(yīng)該先畫草圖。目的是： 1 布置傳動(dòng)件及選擇結(jié)構(gòu)方案。 2 檢驗(yàn)傳動(dòng)設(shè)計(jì)的結(jié)果中有無干涉、碰撞或其他不合理的情況，以便及時(shí)改正。 3 確定傳動(dòng)軸的支承跨距、齒輪在軸上的位置以及各軸的相對(duì)位置，以確 定各軸的受力點(diǎn)和受力方向，為軸和軸承的驗(yàn)算提供必要的數(shù)據(jù)。 7.2 展開圖及其布置 展開圖就是按照傳動(dòng)軸傳遞運(yùn)動(dòng)的先后順序，假想將各軸沿其軸線剖開并將這些剖切面平整展開在同一個(gè)平面上。 I軸上裝的摩擦離合器和變速齒輪。有兩種布置方案，一是將兩級(jí)變速齒輪和離合器做成一體。齒輪的直徑受到離合器內(nèi)徑的約束，齒根圓的直徑必須大于離合器的外徑，負(fù)責(zé)齒輪無法加工。這樣軸的間距加大。另一種布置方案是離合器的左右部分分別裝在同軸線的軸上，左邊部分接通，得到一級(jí)反向轉(zhuǎn)動(dòng)，右邊接通得到三級(jí)反向轉(zhuǎn)動(dòng)。這種齒輪尺寸小但軸向尺寸大。我們采用第一種方案，通過空心軸中的拉桿來操縱離合器的結(jié)構(gòu)。 總布置時(shí)需要考慮制動(dòng)器的位置。制動(dòng)器可以布置在背輪軸上也可以放在其他軸上。制動(dòng)器不要放在轉(zhuǎn)速太低軸上，以免制動(dòng)扭矩太大，是制動(dòng)尺寸增大。 齒輪在軸上布置很重要，關(guān)系到變速箱的軸向尺寸，減少軸向尺寸有利于提高剛度和減小體積。 結(jié)束語 1、本次課程設(shè)計(jì)是針對(duì)專業(yè)課程基礎(chǔ)知識(shí)的一次綜合性應(yīng)用設(shè)計(jì)，設(shè)計(jì)過程應(yīng)用了《機(jī)械制圖》、《機(jī)械原理》、《工程力學(xué)》等。 2、本次課程設(shè)計(jì)充分應(yīng)用了以前所學(xué)習(xí)的知識(shí)，并應(yīng)用這些知識(shí)來分析和解決實(shí)際問題。 3、本次課程設(shè)計(jì)進(jìn)一步掌握了一般設(shè)計(jì)的設(shè)計(jì)思路和設(shè)計(jì)切入點(diǎn)，同時(shí)對(duì)機(jī)械部件的傳動(dòng)設(shè)計(jì)和動(dòng)力計(jì)算也提高了應(yīng)用各種資料和實(shí)際動(dòng)手的能力。 4、本次課程設(shè)計(jì)進(jìn)一步規(guī)范了制圖要求，掌握了機(jī)械設(shè)計(jì)的基本技能。 5、本次課程設(shè)計(jì)由于學(xué)習(xí)知識(shí)面的狹窄和對(duì)一些概念的理解不夠深刻，以及缺乏實(shí)際設(shè)計(jì)經(jīng)驗(yàn)，使得設(shè)計(jì)黨中出現(xiàn)了許多不妥和錯(cuò)誤之處，誠(chéng)請(qǐng)老師給予指正和教導(dǎo)。 參考文獻(xiàn) 【1】、段鐵群 主編 《機(jī)械系統(tǒng)設(shè)計(jì)》 科學(xué)出版社 第一版 【2】、于惠力 主編 《機(jī)械設(shè)計(jì)》 科學(xué)出版社 第一版 【3】、戴 曙 主編 《金屬切削機(jī)床設(shè)計(jì)》 機(jī)械工業(yè)出版社 【4】、戴 曙 主編 《金屬切削機(jī)床》 機(jī)械工業(yè)出版社 第一版 【4】、趙九江 主編 《材料力學(xué)》 哈爾濱工業(yè)大學(xué)出版社 第一版 【6】、鄭文經(jīng) 主編 《機(jī)械原理》 高等教育出版社 第七版 【7】、于惠力 主編 《機(jī)械設(shè)計(jì)課程設(shè)計(jì)》 科學(xué)出版社 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