喜歡就充值下載吧。。資源目錄里展示的文件全都有，，請(qǐng)放心下載，，有疑問咨詢QQ:414951605或者1304139763 ======================== 喜歡就充值下載吧。。資源目錄里展示的文件全都有，，請(qǐng)放心下載，，有疑問咨詢QQ:414951605或者1304139763 ======================== 發(fā)動(dòng)機(jī)軸承設(shè)計(jì)的發(fā)展 F.A.馬丁 一些關(guān)于發(fā)動(dòng)機(jī)的重要軸承設(shè)計(jì)技術(shù)的最新發(fā)現(xiàn)被突出了。但增加的計(jì)算能力的可用性，使軸承的條件被認(rèn)為是更現(xiàn)實(shí)的假設(shè)。這些包括供油特性、油膜的歷史,非圓軸承、慣性，由于期刊的影響,提高了預(yù)測中心的運(yùn)動(dòng)主要軸承載荷、靈活的軸承座和特殊軸承。這些參考文獻(xiàn)進(jìn)步了，連同他們?nèi)绾斡绊戭A(yù)測插圖軸承性能。實(shí)驗(yàn)證據(jù)也正在得到，這有助于驗(yàn)證，并給予信任的分析預(yù)測。 關(guān)鍵詞：滑動(dòng)軸承，軸承設(shè)計(jì)，流體動(dòng)力潤滑，軸承的壓力，軸承座，油槽 從發(fā)動(dòng)機(jī)的機(jī)械配置石油電影流體力學(xué)看來，發(fā)動(dòng)機(jī)軸承性能取決于許多依賴因素。這個(gè)文件強(qiáng)調(diào)了更重要的考慮因素，并且與他們最近的進(jìn)展，發(fā)表和未發(fā)表的，遍布世界各地。在審查試圖引用不只是這些進(jìn)步，而是想說明他們?nèi)绾窝娱L性能預(yù)測，實(shí)驗(yàn)驗(yàn)證和特種軸承設(shè)計(jì)領(lǐng)域。從歷史上看，在動(dòng)態(tài)加載軸承設(shè)計(jì)的最初嘗試，是根據(jù)特定的最大允許負(fù)荷（如適用從預(yù)測的最大承載面積除以負(fù)載定義），這仍然是一個(gè)有價(jià)值的參數(shù)。隨著技術(shù)的圖形和數(shù)字。雖然仍高度簡化的解決水動(dòng)力軸承模型，精干的到來，最小油膜厚度可作出估計(jì)，并作為判斷一個(gè)比較新的發(fā)動(dòng)機(jī)上使用的問題的可能性。對(duì)那些早先的預(yù)測方法的綜合研究可以發(fā)現(xiàn)，在1967年由坎貝爾審查文件等我;作為案例，這曾經(jīng)是一個(gè)拉斯頓和Hornsby VEB的谷三600馬力，600轉(zhuǎn)/分柴油機(jī)大端軸承。近二十預(yù)測和各種來源的實(shí)驗(yàn)軌道雜志，其中以一，機(jī)械量討論。大腸桿菌的法律程序中所包含的文件，同樣的研究案例至今仍在使用的工人在這一領(lǐng)域今日（極性負(fù)荷圖，圖1（a）條;完整的數(shù)據(jù)，參考文獻(xiàn)1）。它已經(jīng)被用于在本次審查的預(yù)測能力，說明在隨后提出了一些。在早期的預(yù)測方法所用的主要假設(shè)，許多人肯定不太現(xiàn)實(shí)，但作為權(quán)宜之計(jì)用于獲取一個(gè)數(shù)學(xué)模型，可以在有限的計(jì)算能力，然后提供解決。這些假設(shè)包括圓形剛性軸承和一個(gè)'完美'的isoviscous牛頓石油供應(yīng)。在許多情況下，軸承表面被假定為在發(fā)達(dá)地區(qū)供油油膜壓力的特點(diǎn)和外部的關(guān)系不受干擾，主軸承載荷計(jì)算沒有采取任何曲軸和曲軸箱的剛度帳戶。在過去十年中增加計(jì)算能力，這就意味著那些早期的許多假設(shè)不再需要工作已進(jìn)行了2'3對(duì)軸承形狀彈性連桿軸承4，供油特性s'6，油膜歷史7，更現(xiàn)實(shí)的主軸承負(fù)荷分擔(dān)8'9。這一點(diǎn)，在保持雖然有點(diǎn)晚了，與1967年的預(yù)言，從坎貝爾，其中指出：'這是作者的相信，通過持續(xù)不斷的計(jì)算方法，并與強(qiáng)大的設(shè)計(jì)技術(shù)的迅速發(fā)展而日益認(rèn)識(shí)正成為可用，在未來十年將顯示進(jìn)度，甚至比這本文試圖描述'更大。在設(shè)計(jì)技術(shù)作為改進(jìn)的計(jì)算能力和更嚴(yán)格的方法結(jié)果的進(jìn)步，開辟了一體化工作，將直接有利于更廣泛領(lǐng)域的設(shè)計(jì)師。這包括： 考慮更現(xiàn)實(shí)的條件瞄準(zhǔn)>二少假設(shè) 數(shù)據(jù)表示理解，以便更好地結(jié)果 經(jīng)營狀況較好的預(yù)測（負(fù)載共享，熱平衡） 實(shí)驗(yàn)驗(yàn)證 在這些類別各自的發(fā)展進(jìn)程是非常重要的，每個(gè)部分補(bǔ)充了其他。 由于需要節(jié)約能源和燃油經(jīng)濟(jì)性的大問題，許多引擎現(xiàn)在正在設(shè)計(jì)具有較高的功率重量比。對(duì)軸承的影響，減少由此產(chǎn)生的軸承尺寸，高比負(fù)荷和使用低粘度油。所有這些變化帶來接近設(shè)計(jì)極限的軸承工作條件，從而把一個(gè)更大的重要性，不僅上材料和潤滑劑的選擇，但我也切合實(shí)際承載能力的預(yù)測。改進(jìn)的水動(dòng)力計(jì)算簡化和快速的方法許多數(shù)據(jù)編制方法顯示在此文件;有關(guān)VEB的大頭釘，搵工時(shí)使用的短軸承的移動(dòng)解決方案。在流動(dòng)的概念已成功應(yīng)用于在過去15年，是在其他地方詳細(xì)解釋。其強(qiáng)大的吸引力是它的方式分裂成兩個(gè)部分期刊擠壓和旋轉(zhuǎn)，這使富力軌道計(jì)算并在每個(gè)時(shí)間步?jīng)]有反復(fù)計(jì)算非常迅速的運(yùn)動(dòng)。為了完整的短軸承VEB的軸頸中心的軌道是在新的調(diào)查，包括在圖2a（參考我在補(bǔ)充者）自動(dòng)對(duì)焦的軌道，并在不同時(shí)期的變化新生力量最小油膜厚度各地。負(fù)載周期（由曲柄角度定義）如圖3。這本書的作者的工作的第二部分是電影制作間隙圓壓分布圖12給出的最大動(dòng)水壓力比在任何特定負(fù)載點(diǎn)間隙圓。在圖4插入的圖表顯示了與VEB的間隙循環(huán)軌道疊加膜壓力圖。請(qǐng)注意，這個(gè)軌道是不繪制相對(duì)空間 -傳統(tǒng)的方法- 但在清關(guān)的地圖，實(shí)際上是被一個(gè)角無動(dòng)于衷整個(gè)周期，這樣，應(yīng)用負(fù)載方向始終向下。這是一個(gè)重要和寶貴的技術(shù)，當(dāng)使用移動(dòng)方法。最小油膜壓力是從這些關(guān)系，并在整個(gè)負(fù)載周期變化的圖4所示的主要部分。里奇在英國通用電力公司開發(fā)出一種新的半雜志為中心的軌道預(yù)測分析方法;它采用短軸承容易得到優(yōu)化的解決方案，已經(jīng)改善了短軸承的標(biāo)準(zhǔn)方法，在高偏心率準(zhǔn)確性的VEB的大端軸承軌道如圖2（b）項(xiàng)。這看起來非常類似于一個(gè)普通軸承有限的軌道，顯然只發(fā)生在一個(gè)IBM 145分之370計(jì)算機(jī)（前幾年）16秒運(yùn)行。最低油0.0033毫米（0.00013英寸）薄膜厚度比較表1與其他來源（包括有限的全球環(huán)境變化影響使用'存儲(chǔ)的數(shù)據(jù)'的做法方案的結(jié)果見下一節(jié)）值。它被認(rèn)為是在較嚴(yán)格的方法分布帶軸承有限，但仍保持了快速解決方案的優(yōu)勢。油中的最小完整的運(yùn)作周期膜厚度是最重要的參數(shù)來判斷軸承的表現(xiàn)之一。它通常用來作為比較，代表了在有關(guān)預(yù)測與現(xiàn)有的類似經(jīng)驗(yàn)型發(fā)動(dòng)機(jī)軸承性能的主要因素。這是很難給出精確值最小油膜厚度的軸承損壞時(shí)可能出現(xiàn)的諸如高的軸承溫度，不對(duì)中，供油不足，安排和不利的環(huán)境條件等因素都會(huì)產(chǎn)生效果。布克會(huì)給予一定的薄膜厚度對(duì)危險(xiǎn)水平連桿軸承（適用于短軸承預(yù)測方法的使用）的指導(dǎo)。 有限軸承理論 用有限元法（有限元）解決有限軸承理論，通用汽車公司研究實(shí)驗(yàn)室2有能力考慮有不同的形狀和也讓在場的開槽。對(duì)于一個(gè)普通的圓軸承通用軸承從他們的有限元模型成功地曲線擬合的基本數(shù)據(jù)，并以此來建立一個(gè)快速的方法，通常計(jì)算時(shí)間從數(shù)小時(shí)縮短到數(shù)秒。這兩intermain種方法已應(yīng)用于馬丁發(fā)動(dòng)機(jī)軸承設(shè)計(jì)。拉斯頓VEB的大底，圖2（c）和（d）顯示了有限元程序和曲線擬合程序分別軸頸中心的軌道。這兩個(gè)軌道上看起來非常相似，雖然有一個(gè)對(duì)曲線擬合程序顯著節(jié)省計(jì)算時(shí)間。薄膜厚度比和我的兩個(gè)最大油膜壓力，部門首長進(jìn)行了比較，圖5（a）和（b）項(xiàng)。還要注意的是，從短軸承理論（圖4）薄膜壓力非常類似從有限的軸承有限元理論（圖5b）這一點(diǎn)?，F(xiàn)在有許多機(jī)構(gòu)或有限差分有限元的2 - D解決方案，使供油特性上動(dòng)水壓力的能力產(chǎn)生影響。在'標(biāo)準(zhǔn)'VEB的案例，結(jié)合它的圓周凹槽，是不是說明了這樣的效果適合，而不是一個(gè)1.8升汽油發(fā)動(dòng)機(jī)intermain軸承將被使用。開頭的圖如圖6所示，并進(jìn)一步行動(dòng)組可發(fā)現(xiàn)引用6和7。在圖7的軌道上圖顯示了薄膜的厚度減少作為一個(gè)石油洞的存在而在本體。但是應(yīng)當(dāng)指出，在周期的最小油膜厚度不一定受到損害。 一個(gè)設(shè)計(jì)方法已經(jīng)制定了在冰川金屬有限公司允許，在一個(gè)更完整的方式，在軸承的feed功能的影響。它認(rèn)為分為兩類這些法利效果。第一個(gè)問題涉及到發(fā)達(dá)國家的壓力過油養(yǎng)區(qū)（孔，槽等），軸承的傳遞地區(qū)產(chǎn)生不利影響。第二個(gè)涉及石油運(yùn)輸軸承內(nèi)的其他投資收益電影的研究，并考慮到了有害的影響程度時(shí)，油膜耗盡而由于沒有足夠的石油可供菲力的承載軸承的面積。這第二類是有時(shí)被稱為“油膜歷史”。 油膜歷史 關(guān)于歷史和油膜軸承油膜的動(dòng)態(tài)加載邊界的基礎(chǔ)性工作很多是率先在英國國家工程實(shí)驗(yàn)室，由已故機(jī)管局米爾恩，他的早逝留了一個(gè)空缺在這個(gè)非常專業(yè)的知識(shí)領(lǐng)域。米爾恩的做法視為是不斷變化的模式和移動(dòng)網(wǎng)相匹配的電影界。瓊斯在冰川開發(fā)的另一種方法考慮節(jié)間流通，使用每個(gè)節(jié)點(diǎn)控制周圍空間的邊界固定的有限差分網(wǎng)格。后一種方法是比較容易通過，并已用于在intermain軸承分析（一孔饋送）在1.8升發(fā)動(dòng)機(jī)。正如圖7圖所示的右手，與電影的歷史軌跡形狀一般的預(yù)測有很大的不同，當(dāng)油膜史上的影響被忽略。盡管在最小的負(fù)載周期膜厚度的影響不大時(shí)，又是考慮油膜史，人們可以感知的案件（對(duì)于低供油壓力實(shí)例）在該雜志的額外中心徑向偏移可能會(huì)產(chǎn)生危險(xiǎn)的小薄膜厚度。這強(qiáng)調(diào)了使用油膜史上節(jié)目中可能會(huì)遇到這些問題的重要性。同樣的原則也被應(yīng)用到VEB的大底承載力的研究和預(yù)測的情況下雜志和無油膜歷史的中心路徑顯示在圖2（e）和（f）分別。這個(gè)油膜史上降級(jí)為一個(gè)完全圓周槽軸承的影響不是一開始撰文預(yù)期。然而，效果相當(dāng)顯著的軌道上的右手邊看到，圖2（e）項(xiàng)和當(dāng)?shù)啬ず穸龋ㄒ姳?）。從0.0036毫米（0.00014英寸）降低到0.0023毫米（0.00009英寸），一個(gè)重要的數(shù)額。薄膜厚度在整個(gè)負(fù)載周期（比）不同的趨勢進(jìn)行了比較，圖8。頂部圖顯示（由線條的粗細(xì)）之間的有限軸承預(yù)測從不同來源（包括珀金斯發(fā)動(dòng)機(jī)有限公司17）相似。瓦圖中顯示從VEB的發(fā)動(dòng)機(jī)，我的實(shí)驗(yàn)結(jié)果，下圖顯示的預(yù)測考慮油膜歷史。標(biāo)記的點(diǎn)。甲，乙，丙幫助每個(gè)圖進(jìn)行比較的趨勢。在這兩個(gè)電影史上的預(yù)測和在B點(diǎn)的峰值比在一個(gè)較高的實(shí)驗(yàn)結(jié)果顯示，與傳統(tǒng)的方法（上圖），他們幾乎相同的高度。此外，隨著電影史上另一個(gè)高峰是在C顯然其中有與實(shí)驗(yàn)一致。而所有這一切都給出了'電影的歷史模型，有一種思想流派，這可能是偶然的廣泛協(xié)議，因?yàn)檩S承形狀各不相同，但在實(shí)踐中一直不斷在理論假設(shè)為剛性和循環(huán)支持。 慣性的影響 在蘇塞克斯大學(xué)的，有幾個(gè)動(dòng)態(tài)加載的發(fā)動(dòng)機(jī)軸承方案已經(jīng)開發(fā)了考慮對(duì)從軸心運(yùn)動(dòng)導(dǎo)致軸承間隙內(nèi)]裝載質(zhì)量加速度效應(yīng)。德德14的方案有所不同，較近期的油膜力，導(dǎo)出的方式。基本方案認(rèn)為，一個(gè)完整的2 - D溶液的雷諾方程和1.8升發(fā)動(dòng)機(jī)軸承從這個(gè)結(jié)果非常相似，冰川（圖7，上圖）預(yù)測的。德德還制作了一個(gè)更快的方法，假設(shè)在軸向壓力分布是拋物線。此相關(guān)的方程代入，讓雷諾方程式二階常微分方程，可通過直接矩陣求逆解決。系數(shù)矩陣是一個(gè)三對(duì)角之一，解決的辦法是加速只用對(duì)角線，而不是所有的矩陣元素打交道了。這種方法只需要幾分鐘來計(jì)算。它不是像快速移動(dòng)的方法，但大規(guī)模的慣性和槽影響，使一些優(yōu)勢。一個(gè)普通ungrooved軸承，一個(gè)完整的環(huán)形溝，或單洞（如狹窄的延長軸承寬度插槽充分考慮），可容納在這個(gè)快速1 - D溶液。對(duì)于一個(gè)完整的部分溝2 - D溶液必須使用。 表1比較實(shí)驗(yàn)和理論之間的最小油膜厚度為6 VEB的- X的谷三連桿軸承。為1.8升引擎使用德德的快速解決方案軸承軸頸中心的路徑顯示在圖7左手圖。無論是使用理論，有限或快速的方法，預(yù)測之間的滑動(dòng)軸承，并與供油特點(diǎn)之一差異非常相似。這本期刊的群眾運(yùn)動(dòng)關(guān)內(nèi)的空間效果似乎并不在1.8升發(fā)動(dòng)機(jī)軸承具有重要意義。作為一個(gè)練習(xí)，以顯示一個(gè)大期刊質(zhì)量的影響，選擇了極端值（不一定意圖]信息研究所）表示趨勢。較低的圖7下雪的極端情況下，軌道的形狀是完全改變了右手圖。與載荷的是相反的方向旋轉(zhuǎn)的軌道部分相關(guān)期刊似乎是受影響最嚴(yán)重，雖然最小油膜厚度維持不變。德德還審議了VEB的研究個(gè)案，并承擔(dān)了有效的質(zhì)量對(duì)應(yīng)于連桿的旋轉(zhuǎn)質(zhì)量的組成部分。由此產(chǎn)生的雜志從二維有限軸承解決方案和更迅速的一維解決方案中心的軌道都顯示在圖2（g）和2（高）分別。在圖2（h）的軌道大多數(shù)似乎是由大眾的慣性作用影響，雖然通常尖點(diǎn)，在反方向的軌道階段的開始，已完全消失，它聲稱，大眾慣性的影響軸承間隙內(nèi)的空間日志可能會(huì)顯著毗鄰主軸承飛輪。 Developments in engine bearing design F.A. Martin* Some of the important recent developments in engine bearing design tech- niques are highlighted. The availability of increased computing power has enabled more realistic assumptions about bearing conditions to be considered; these include oil feed features, oil film history, non-circular bearings, inertia effects due to journal centre movement, improved prediction of main bearing loads, flexible housings and special bearings. References to these advances are made, together with illustrations of how they affect predicted bearing performance. Experimental evidence is also being obtained, which helps to verify and give confidence in the analytical predictions Keywords: journal bearings, bearings + design, hydrodynamic lubrication, bearing stress, bearing housings, oil grooves Engine bearing performance is dependent upon many factors, from the mechanical configuration of the engine to the hydrodynamics of the oil film. This paper highlights the more important factors to be considered, and relates them to recent advances, both published and unpublished, throughout the world. The review attempts not just to reference these advances, but to illustrate how they extend the areas of performance prediction, experimental verifica- tion and the design of special bearings. Historically, the earliest attempts at the design of dynamic- ally loaded bearings were based on maximum allowable specific load (defined as maximum applied load divided by projected bearing area), and this is still a valuable parameter. With the advent of graphical and numerical techniques capable of solving a hydrodynamic bearing model, albeit still highly simplified, estimates of minimum oil film thick- ness could be made, and used as a comparator to judge the likelihood of problems on new engines. A comprehensive study of those early predictive methods can be found in the 1967 review paper by Campbell et al I ; as a study case this used the big end bearing of a Ruston and Hornsby VEB Mk III 600 hp, 600 r/min diesel engine. Nearly twenty predicted and experimental journal orbits from various sources were discussed in the volume of I. Mech. E. proceedings which contained that paper, and the same study case is still being used by workers in this field today (polar load diagram, Fig 1 (a); complete data, Ref 1). It has been used in this review to illustrate some of the subse- quent advances in prediction capabilities. Many of the major assumptions used in the early prediction methods were certainly not realistic, but were used as expedients to obtain a mathematical model which could be solved with the limited computing capabilities then available. These assumptions included circular rigid bearings and a perfect supply of isoviscous Newtonian oil. In many cases the bearing surface was assumed to be uninterrupted by oil feed features in the developed film pressure regions and, external to the bearing, the calculation of the main bearing loads took no account of the crankshaft and crank- case stiffnesses. Over the last decade increases in computing power have meant that many of those early assumptions are no longer *Department of Applications Engineering, The Glacier Metal Com- pany Limited, Alperton. Wembley, Middlesex HAO 1HD, UK necessary and work has been carried out on bearing shapes 23 elastic connecting rod bearing 4 , oil feed feat- ures s6 , oil film history 7 , and more realistic main bearing load sharing 89 . This is in keeping, although a little late, with the 1967 prophecy from Campbell , which stated that: It is the authors belief that, with the continuing rapid advance in computational methods and with the growing awareness of the powerful design techniques which are A AB a D - B k ,j b E C ,4 i i aT- C v Fig 1 Polar load diagrams for VEB connecting-rod bearing relative to: (a) connecting rod axis, (b) cylinder axis, (c) crankpin axis TRIBOLOGY international 0301 679X/83/030147 -18 $03.00 1983 Butterworth & Co (Publishers) Ltd 147 Mair - Engine bearing design I i ,/ / I ie aiming for fewer assumptions data presentation for better understem.ding of results better prediction of operating conditions (load sharing, heat balance) experimental verification. Progress in each of these categories is very importam and each section complements the others. With the need to conserve energy and with fuel economy a major issue, many engines are now being designed with higher power to weight ratios The resultant effects on bear- ings are reduction in bearing size, higher specific loads and the use of lower viscosity oils. All these changes bring the Simplified and quick method Many data oresentation techniques shown in this pape; relating to the VEB big end stud, case use EooKers short oearing Mobility solution. The Mobi!ity coT:co-or :qas been successfully applied over the last t 5 years, ano. .z explained in detail elsewhere u . its great attraction is the way L splits journal movement into two con:onents squeeze and whirl, which enab!e a FulI orbi! to be caicu lated ver)/ rapidly with no reiterative caicuiations a each time step. For completeness the short bearing VEB )er hal centre orbit is included in the new %urvev af orbits in Fig 2a (supplementing those in Ref I, and the variation fn minimum film thickness at different times tLroughot. the load cycle (defined by crank angle) is shown i: Fig 3. 148 983 Voi !8 N 3 A second part of Bookers work was to produce a clearance circle film pressure map 2 giving the ratio of the maximum hydrodynamic pressure to the specific load at any point in the clearance circle. The inset diagram in Fig 4 shows the clearance circle film pressure map with the VEB orbit superimposed. Note that this orbit is not plotted relative to space - the conventional method - but on a clearance map which is effectively being moved in an angular sense throughout the cycle, such that the direction of the applied load is always downwards. This is an important and valuable technique when using the Mobility method. The maximum oil film pressure is obtained from these relationships and Nomenclature Cr radial clearance, m D bearing diameter, m hmi n minimum film thickness, m e eccentricity vector F force vector JlOO f o2 (1 +ecosO) -1 dO 0 L bearing length, m M Mobility, dimensionless Pf oil feed pressure, N m-: Pmax maximum film pressure, N m-2 Pn specific load (W/LD), N m -2 QF oil flow considering film history, m 3 s - (rigorous solution) QH hydrodynamic flow, m 3s-1 (rapid solution) Qp feed pressure flow, m 3 s -1 (rapid solution) QR flow not considering film history, m 3 s - (rigorous solution) Qx flow from experiments, m 3 s-1 R shaft radius, m rl dynamic viscosity, Ns m-2 e eccentricity ratio, dimensionless k friction factor 0 angle of oil hole from centreline CF (see Fig 23) co and co are functions of journal and bearing angular velocity 0.5 0.4- 0,3- G .5 E 0.2- 0.1- F 1.875 ,5: : -)o ;,?., .-. ,2/0,1 0.001 , mL_ o 90 &o s;o 5 ,o Crank angle, degrees Fig 3 Short bearing film thickness ratio (VEB) do 720 Martin - Engine bearing design its variation throughout the load cycle is shown in the main part of Fig 4. At GEC in the UK Ritchie n developed a new semi- analytical method for predicting the journal centre orbit; it uses an easily obtained optimized short bearing solution which has improved accuracy at high eccentricities over the standard short bearing method; the orbit of the VEB big end bearing is shown in Fig 2(b). This looks very simi- lar to a general finite bearing orbit and apparently only took 16 seconds to run on an IBM 370/145 computer (several years ago). The minimum oil film thickness of 0.0033 mm (0.00013 inches) is compared in Table 1 with values from other sources (including the results of a GEC finite bearing program using the stored data approach - see next section). It is seen to be within the scatter band of the more rigorous finite bearing methods, but still main- tains the advantage of a rapid solution. The minimum oil film thickness during a complete cycle of operation is one of the most significant parameters on which to judge bearing performance. It is generally used as a comparator and represents a major factor in relating predicted performance with existing bearing experience on similar type engines. It is difficult to give precise values of minimum film thickness at which bearing damage might occur, as other factors such as high bearing temperature, misalignment, inadequate oil feed arrangements and adverse environmental conditions will all have an effect. Booker ll gives some guidance on danger levels for film thickness in connecting rod bearings (for use with short bearing predic- tion methods). Finite bearing theories Using a finite element method (fern) to solve the finite bearing theory, General Motors Research Laboratories 2 have the ability to consider different shapes of bearing and also to allow for the presence of grooving. For a plain cir- cular bearing GM have successfully curve-fitted basic data from their fem bearing model, and used this to develop a rapid method, typically reducing computational time from hours to seconds. Both methods have been applied to the Prolix 1.667 2 Pn 2.5 40 , 3 ;50 / l/i/: - 25 m = 2o _E 15 .E. E 1 I0 e 5 i i I 1 I I i 0 90 180 270 560 450 540 650 720 Crank angle, degrees Fig 4 Short bearing maximum film pressure (VEB) TR I BOLOGY international 149 MartL, . Engine bearing design Ruston VEB big end, and Figs 2(c) and (d) show the journal centre orbit for the finite element program and curve-fit program respectively. These two orbits look very similar, Nthough there was a remarkable saving in compu- tational time for the curve-fit program. Film thickness ratio and maximum film pressure from the two me,hods are com- pared in Figs 5(a) and (b). Also note that the film pressure from the short bearing theory (Fig 4) is very similar to that from the finite bearing fern theory (Fig 5b)o Many establistments now have finite element or finite difference 2-D solutions capable of allowing for the effect of oil feed features on hydrodynamic pressure generation , The %tandard VEB study case, with its circumferential groove, is not suitable for illustrating such effects, so instead the intermain bearing of a 1.8 itre gasoline engine will be used. The lead diagram is shown in Fig 6 and further dat can be found in References 6 and 7o The orbits in the torc diagram of Fig 7 show the film thickness reduced locaily as a result of the presence of an oil hole. tt should be noted however, that the smallest film thickness during the cycle may not necessarily be impaired A design method has been developed at the Glacier Metal Co whi.ch altows, in a more complete way, for the effects of feed features in the bearing o It considers these effects to fl into two categories. The first relates to the deh- :nentai effect of the developed pressure region passing over the oil feed region (hole, groove etc) of the bearing The second involves the study of oit transport within the bear- o .4 7! Curv fit program 0.5 Finite element orcgrarr . : ! o.i-, , 40- 90 t80 270 560 450 4, 6.30 720 g_ 50 m o E = 20. Curve fit program Fmffe element program . /m / / I / t/ t/ W ,j 1 r C 90 80 70 360 450 540 630 720 b Cro Ongledegrees Fig 5 General Motors rapid curve fit program compared ro rigorous fern program ( VEB: (a) dimensioMess film thick- ness, (b maximum film pressure ing oii film, and takes into accoum the deleterious effect when the oi1 fi!m extent is depleted due to insufficient eli being available to filI the ioad carrying area of the bear ind. This second category is sometimes referred to as cil fi Nstory. eli fIm history Much of the fundamental work on eli film history and or.; film. boundaries m dynamically loaded bearings was pione.:rc at the UZK National Engineering Laboratory by the iate A.Ao Milne s16 , whose untimely death left a vod in the knowledge of tNs very specialized fbldo Milne% apFroach considered an everchanging an_d me,and mesh )a:tem o mach .:he film boundaries. Arxther method developed at Glacier by Jones considered :,( J J f Experiments Qx o 3;0 Angular extent of oil feed, degrees Fig 10 Overestimate of flow QR using conventional Reynolds boundary conditions (intermain bearing, 1.8 litre engine) bearing and for a single oil hole. For a partially grooved main bearing an orbit relative to the bearing should be considered, whereas for a crank drilling and plain big end bearing one would consider an orbit relative to the crank pin. For a circumferentially grooved bearing any frame of reference would be suitable. The characteristics of feed pressure flow Qp, from equation 6 (Appendix 1) for the VEB bearing with a circumferential groove, are represented by the inset diagram in Fig 9(b). This shows the orbit superimposed on the lines representing values of constant flow. The predicted feed pressure flow is given in the main part of Fig 9(b). Actual flows from the 1.8 litre engine intermain bearing 6 with various oil feed arrangements (a single oil hole, a 180 groove and a full circumferential groove) all show that the predicted feed pressure flow (averaged over the operating cycle) gives a reasonable estimate of total flow. Similar conclusions were drawn by the author after he was privileged to have a preview of some National Engineering Laboratory reports on recent experimental work conducted by W L Cooke (See Experimental Support section). Total flow predicted from rigorous methods Improved predictive techniques and more rigorous programs are being developed and used. In many cases full 2-D solutions are being developed which take into account the groove shape, its size and position together with a dimensionless supply pressure parameter generally of the form: (Pffi7 co) (Cr/R ) 2 Such feed conditions are included in the two finite differ- ence solutions developed at Glacier, one using simple Reynolds boundary conditions and the other considering oil film history. These solutions give total flows defined as QR and QF respectively. The predicted total flow (QR) generally overestimates the flow, particularly for a single hole feed case. This is illustrated by the 1.8 litre engine results shown in Fig 10. The oil film history study of Jones 7 relating to the same 1.8 litre engine, with various bearing grooving arrangements, shows that the film history flow (QF) averaged over the load cycle gives excellent agreement with the measured flows from that engine. These rigorous solutions have also been applied to the VEB study case and the predicted total flows QR (conventional Reynolds boundary condition) and QF (with film history) are shown in Fig 1 1. It is of interest to see how QR gives an overestimate of flow, compared to QF, especially over the first 200 of crank angle position. Flows averaged through- 0.3- Conventional I O F Film history finite bearing / flow flow QR Ill (Pf =0) =0.193 v I A I i o , : 0 14t , i , / t I Average 0 180 360 540 720 Crank angle, degrees Fig Comparison of predicted flows (VEB) TR IBOLOGY international 153 Martin - E,qg/ne bearhE design out the operating cycle (including those using rapid solu- tions, ie Q! and Qp) are shown on the right hand side of this figure. The idea developed so far, that the average feed pressure flow Qp (rapid solution), wtt give a good guide to the Tim history flow QF (rigorous solution) is supported by the closeness of these points (Fig i !); both of these solutions, in terms of average flows are generally consistenz with experimental trends, as will be seen later. Heat balance and friction in engine bearings The prediction of friction in dynamically loaded bearings is important for two reasons. Firstly, when coupled with the oil flow, it forms the reiterative heat balance for dete mining the operating viscosity or viscosities in the bearing. Secondly the prediction of friction (and therefore power loss) is important in its own right when looking for minimum energy loss. A comprehensive text showing the development of frictior: and power loss equations for dynamicaty loaded bearings is given in the appendix of a paper by Booker, Goenka and van Leeuwen 9 . It is very general and considers a free body analysis of the lubricant film. The equation for friction power (the rate of work done on the film) involved three terms: Power loss = (Jr :qR3 L/C) A,oAoo- e x Fo d0 + F (3) The last term is often negligible; it dominates where there is I a. 5Oi , I, t- - z5 i! / i f J 15 I o IO - 5 Constant viscosity l . Viscosity calculated from 0.5 P,ex 0 Viscosity clculted from Pme ,I o-41 O.5. I o.,! 0 90 180 2_70 :560 450 540 6.30 720 Crenk angle 82 ,degrees Fig t2 Predicted performance considering pressure viscosity effects (VEB) (Pmax is the instantaneous maximum film pressure) little relative rotatmn, (eg squeeze fiim bearings). The first zerm generally predominates m ergine bearings and J( z 2r film fie. one that is active over the full circmfere,ce ; the bearing) this erm becomes. 2re (rgR3 LooP /C)/( i = uP) Tbds term is quoted extensively as part of the power loss equation, tt shotid be noted however, that for a fim exterlt (such as the short bearing Mobility method uses tiis verm is not simply halved, since for dynamical loaded bearings the load carrying (active) par of the film rare!;r extends from exactly hmax to the ,min positiotas. The heat balance is often used co predic a stogie efi?ctive: viscosity, found by considering the global effect of total heat generated by friction which is removed by 5e toal oil flow. A refinement on this, particularly for circumfbrentialiy grooved bearings, is to consider two v),scosities One toe- trois oii flow: which will be mostly from the coole thick film region, and the other controls load capacity and fric tion toss, which are meaniy inflenced by t29.e hotter thin lm region Other refinements involve the emperacure variaor throughou the bearing 202 and Jm pressure effects on yrs. cosity -2 . This latter effect can be very significant, as skow for the VEB study case in Fig 12; for tMs exerdse the bear-. ing temperature was assumed cor.szan. Another importan= aspect, with the introductio of ron-Newtonian muRigrade oils, is the effect of shear rae on viscosity (also influerced by temperature) =a . (it is interesting to note hat the VEB study case *s continnally being used independently by others 2 ), fain bearieg load sharing The loads on a big end bearing are reiativeiy simple ,:o calculate, being based on the inertia of the reciprocating and the rotating components and on the gas forces imposed on the piston. The main bearing loads must react agais the big end loads, and traditionatly a staticaRy determinate system has been considered in which the crankshaft is - Static determinate Uneoupled . . . . . Idetermmae coupled z . i I o = S i j -.f / Fig t3 Computed loads centre mum bearing, o,r cylinder engine (Booker/Stkkier, 2 982) t54 June 1983 Vol IG No 3 treated as if it were pin jointed at the axial mid-position of each main bearing. Effectively this means that any main bearing can be influenced by big end loads only in immedi- ately adjacent bays. In practice however both crankshaft and crankcase have finite stiffness, so that very complex interactions can be set up throughout the entire engine. Improved crankshaft mode/ling Many researchers have now attempted to take into account engine flexibility, and to couple this with the bearing analy- sis. In recent years work at Cornell University (USA) and Perkins Engines Ltd (UK) has been progressing in this field independently. At Cornell Unviersity, Stickler 24 carried out a feasibility study using simple beam type elements to represent the crankshaft in the structural analysis. Booker and Stickler 2s applied this procedure to a 4 cylinder inline automotive engine using a rigid crankcase and short bearing theory. The computed centre main bearing loads, using the static deter- minate (uncoupled) and indeterminate