畢業(yè)設(shè)計(jì)(論文)外文資料翻譯 外文出處：MitsubishiHeavyIndustries,Ltd.TechnicalReviewVol.39No.1(Feb.202)附 件： 1.外文資料翻譯譯文；2.外文原文。 (用外文寫)基于三維 Elasto 水力潤(rùn)滑理論的曲軸設(shè)計(jì)TakeroMakinoToshimitsuKoga長(zhǎng)崎研究和發(fā)展中心，技術(shù)總部 通用機(jī)械和特種機(jī)車總部 高效率的要求造成了大量柴油機(jī)引擎曲軸的設(shè)計(jì)困難。當(dāng)軸承油膜厚度不到幾微米 時(shí)，由于軸承負(fù)荷而產(chǎn)生的變形量也僅為幾毫米。本論文詳細(xì)敘述了三維 Elasto 水力潤(rùn) 滑理論理論在 4 沖程柴油機(jī)引擎的曲軸設(shè)計(jì)上的應(yīng)用。這些理論包括曲軸的變形和曲軸間 隙中油膜的產(chǎn)生原因。 緒論 近一個(gè)時(shí)期以來(lái)，內(nèi)燃機(jī)的出口量有所增加，但其比重卻在下降。這是因?yàn)?，軸承在 惡劣的的環(huán)境下使用，大式軸承和主要的軸承連桿的機(jī)架變形在軸承的特征上產(chǎn)生重大影 響。為解決這一問題，三菱重工業(yè)有限公司(以下簡(jiǎn)稱MHI)為這些動(dòng)態(tài)軸承負(fù)荷開發(fā)了一 種應(yīng)用elastohydrodynamic lubrication(EHL)原理的軸承特性預(yù)報(bào)方法，并且使用這種方法 來(lái)對(duì)MHI公司的大負(fù)載柴油機(jī)引擎進(jìn)行設(shè)計(jì)和評(píng)估。 EHL 技術(shù)分析軸承表面彈性形變導(dǎo)致的油膜壓 力，假設(shè)軸承剛體機(jī)構(gòu)，既考慮軸承局部表面變形的 影響，同時(shí)又準(zhǔn)確預(yù)測(cè)特征相對(duì)于傳統(tǒng)的分析 此外，在這些年里, 三菱重工引進(jìn) EHL 技術(shù)分 析研究由于油膜壓力而產(chǎn)生的軸承變形的油膜歷史 記錄，同時(shí)追蹤軸承清除根據(jù)時(shí)間歷史記錄的油填充 比例來(lái)改善評(píng)估的準(zhǔn)確性。 這份報(bào)告介紹了這一技術(shù)在大型連桿軸承上的 應(yīng)用實(shí)例和對(duì)三菱重工的四沖程柴油發(fā)動(dòng)機(jī)的主要 影響。理論 2.1 基本公式 圖 2 顯示了這份論文中采用坐標(biāo)系統(tǒng)。 影響油膜壓力的參數(shù)p 可用方程(1)來(lái)表示。)()(2(123 thhUphe p + - - r q r r a (1) 當(dāng)方程(1)和下面的力平衡組合成一個(gè)相對(duì)于時(shí)間 t 的聯(lián)立方程組，這樣一來(lái)就可以 得到軸中心局部和槽油膜厚度的信息。0)cos( = - W - W xWdp q (2) 圖 1 坐標(biāo)系統(tǒng)0)sin( = - W - W yWdp q (3) 由于開始的幾何間隙，軸的偏心率和彈性形變，所以公式(4) 這樣來(lái)表示油膜厚度h。 （4） 其中： ：粘度壓力系數(shù)xa：x軸的偏心率ya：y軸的偏心率rc：軸承半徑間隙xe：X方向的離心率ye：Y方向的離心率h：油膜厚度L：變形N：引擎速度 ：面積p：油膜壓力 ：油填充比例 ：軸承圓周坐標(biāo)t：時(shí)間U：滑動(dòng)速度xW：X方向負(fù)荷yW：Y方向負(fù)荷X：X軸方向坐標(biāo)Y：Y軸方向坐標(biāo)Z：Z軸方向坐標(biāo) 2.2 分析技術(shù) 2.2.1 考慮油膜歷史記錄曲線的EHL技術(shù)分析 我們開發(fā)了一個(gè)基于JONES提出的油膜歷史記錄曲線概念的EHL分析技術(shù)，來(lái)考慮 在軸承間隙中的油的運(yùn)動(dòng)。三菱重工的常規(guī)EHL技術(shù)分析，計(jì)算假設(shè)在整個(gè)軸承表面覆蓋 潤(rùn)滑油的情況下的壓力分布，替代由于計(jì)算周圍壓力獲得的負(fù)壓力區(qū)域，并且把油膜斷裂 邊界視為分界線。在以這個(gè)邊界為條件下，油膜斷裂區(qū)域的流動(dòng)連續(xù)性不能被滿足。另一 方面，EHL分析技術(shù)研究隨著油填充比率和時(shí)間的推移而變化的油膜歷史記錄曲線，則顯 示流動(dòng)連續(xù)性滿足。LpZaeZaech xyyxr + + + + + = q q sin)(cos)(至于受到波動(dòng)負(fù)荷的軸承,如發(fā)動(dòng)機(jī)軸承，在軸承上實(shí)際油膜壓力增長(zhǎng)受限制的區(qū)域， 在下文中EHL分析可以得出比常規(guī)EHL分析更高的壓力結(jié)果。這是主要用于檢驗(yàn)三菱重 工的大型船用柴油機(jī)引擎的實(shí)際尺寸的。EHL技術(shù)分析油膜壓力歷史記錄曲線是作為一個(gè)有 益的分析工具來(lái)用于設(shè)計(jì)和評(píng)價(jià)的。 2.2.2 計(jì)算方法 油膜壓力P和軸偏心率 xe 、ye 的結(jié)果可以從 聯(lián)立方程(1)到(4)中獲得。由于方程(1)和油膜 壓力的非線性關(guān)系，我們用“牛頓-拉斐爾”方 法 來(lái) 確 定 它 們 。 我 們 用 有 限 元 方 法 (FEM)(Galerkin方 法 ) 進(jìn) 行 數(shù) 字 計(jì) 算 ， four-point等參數(shù)原理被看做是原理內(nèi)容和線 性方程系統(tǒng)的數(shù)字化解決方法。為了測(cè)定油膜 斷裂邊界，我們改進(jìn)并使用了適用于油膜歷史 記錄曲線的有限元運(yùn)算方法的Kumar技術(shù)。圖2 顯示的是流量計(jì)算。 3個(gè)案研究 3.1 連桿頭軸承 例如 S3l 發(fā)動(dòng)機(jī)的大型連桿頭軸承，我們 比較剛體分析和 EHL 技術(shù)分析、 并且比較了 EHL 技術(shù)分析的油膜歷史記錄曲線和傳統(tǒng)的 EHL 技 術(shù)分析。 此外，我們測(cè)算了連桿頭軸承在軸承特性 上對(duì)曲柄銷外形的影響。 表格 1 所示為軸承規(guī)格，圖 3 顯示了影響 軸承和用于計(jì)算執(zhí)行 3DFEM 模型的負(fù)載向量。 表格 1 S3l 引擎大型連接頭軸承的尺寸參數(shù) 圖 2 流量計(jì)算 （a）軸承負(fù)載 （b）連桿頭 FEM 模型 圖 3 軸承工作狀況的計(jì)算當(dāng)考慮到彈性形變，則計(jì)算油膜壓力的減少 量和油膜厚度的增加量。如果考慮到油膜歷史曲 線，則軸承上油膜壓力的實(shí)際受力面積的發(fā)展受 限制，并且壓力最大值會(huì)變的更大。 3.1.1 技術(shù)分析對(duì)比 在圖 4(a)里顯示了油膜壓力隨著時(shí)間改變而 產(chǎn)生的最大變化量。幾乎在所有的時(shí)間點(diǎn)，取決 軸承直徑 軸承寬度 徑向間隙 桿長(zhǎng) 沖程 引擎速度 潤(rùn)滑油粘度 48mm 21mm 0.025mm 145mm 78.5mm 3600rpm 10cP180200160140120100806040200 180 360 540分析EHL考慮油膜歷史的 分析EHL的 常規(guī) 分析 剛體 曲柄角度(deg) (a)最大變化，油膜壓力的時(shí)間變化曲線 (b) 軸心軌跡 軸承的圓周坐標(biāo) (deg) 軸承的圓周坐標(biāo)(deg) (c)軸承中心部分的油膜壓力(曲軸角度10度) (d)軸承中心部分的油膜壓力(曲軸角度10度) 圖 4 大端軸承特性分析結(jié)果于剛體分析的油膜壓力高于由 EHL 分析獲得的數(shù)值。這顯然表明，比如說(shuō)，相對(duì)于瞬時(shí)時(shí) 間，曲軸角度大約在 10 度左右的地方負(fù)載相當(dāng)大。當(dāng)取決于剛體分析的油膜壓力是 180 （MPa）時(shí)，取決于 EHL 分析的壓力是 133（MPa）。圖 4 (c)和(d)顯示的是曲柄角度在 10 度時(shí)軸承中心部分的油膜厚度分布狀態(tài)和油膜壓力分布狀態(tài)。 由于考慮到彈性變形， 由 EHL 技術(shù)分析得到的油膜厚度相比于由剛體分析得到的幾乎差不多大，并且在壓力區(qū)域幾乎一 致。比起剛體分析，由 EHL 分析給出的壓力分布區(qū)域在圓周方向更寬，并且顯示出較低的 油膜壓力最大值。顯然，從圖 4(b)顯示的軸中心軌跡和 EHL 技術(shù)分析表明，軸中心是明顯 偏離曲軸間隙的。 在圖 4(a)中顯示了，在曲軸角度約 250 度時(shí)，由 EHL 技術(shù)分析決定的油膜壓力最大值 不同于由傳統(tǒng) EHL 技術(shù)分析所決定的數(shù)值。當(dāng)軸向油膜斷裂面的一邊運(yùn)動(dòng)時(shí)，曲柄角度調(diào) 整符合從上部金屬到下部金屬負(fù)載的轉(zhuǎn)變。 圖 4（e）顯示的是油膜壓力分布狀態(tài)和曲柄角度在 250 度時(shí)的油填充比例。從這個(gè)圖 表上明顯看出，考慮油膜歷史曲線的分析顯示出，軸承正壓力區(qū)域的發(fā)展由于油量的缺乏 而受限制，并且給出相比于傳統(tǒng) EHL 分析所得到的更高的油膜壓力。 考慮油膜歷史的 EHL 分析 常規(guī) EHL 分析 壓力 分布 油比 例 (e)壓力分布在考慮油膜歷史的 EHL 分析和不考慮油膜歷史分析的情況下的差異(在曲軸角度 250 度) 3.1.2 曲柄銷外形在軸承特性上的影響我們?cè)u(píng)估曲柄銷外形在大型連桿頭軸承特性上的影響。圖 5 中顯示的是我們研究的三 種曲柄銷外形，即(1)直線型，(2)桶形，(3)曲線形。圖 6 顯示的是油膜壓力最大值和油 膜厚度最小值的分析結(jié)果。這表明，在直線外形的曲柄銷(1)顯示出更大的油膜厚度，并 且適合于曲軸的操作條件。 3.2 主 要 影 響 這一方法不僅可以適用于分析大型連桿頭軸承，而且也適用于大部分軸承和小型連桿 頭軸承。下面是個(gè)一臺(tái) S6r 引擎的 4 號(hào)主軸承的分析實(shí)例。表格 2 顯示了軸承的規(guī)格，圖 7 顯示了包括軸承負(fù)載和主要軸承的發(fā)動(dòng)機(jī)框架結(jié)構(gòu)的 FEM 模型。 直線形 桶形 曲線形 圖5 曲柄銷外形的形式 曲線形 桶形 直線形 圖6 由于銷的幾何誤差引起的曲軸特性差異 （a）曲軸負(fù)載 （b）發(fā)動(dòng)機(jī)框架結(jié)構(gòu)的FEM模型 圖7 主要影響的計(jì)算情況表格 2 S6r 引擎四號(hào)主軸承的尺寸參數(shù) 軸承直徑 軸承寬度 徑向間隙 引擎速度 潤(rùn)滑油粘度 油槽 140mm 53mm 0.07mm 1800rpm 10cp 水平向和側(cè)面，45，100 毫米范圍 圖 8(a)所示的油膜壓力最大值的時(shí)間變化歷史記錄曲線，顯示了剛體分析評(píng)估的壓力 值高于 EHL 分析的結(jié)果。圖 8(b) 明顯顯示了曲柄角度在 245 度時(shí)的壓力分布狀態(tài)，考慮 了油膜歷史記錄曲線的 EHL 分析認(rèn)為，軸承上由于潤(rùn)滑油的不足而導(dǎo)致油膜壓力發(fā)展受限 制,并且得出比常規(guī) EHL 分析結(jié)果更高的油膜壓力數(shù)值。因此,有人認(rèn)為，主要軸承的分析 顯示了和大型連桿頭軸承分析相類似的趨勢(shì)。 考慮油膜歷史的 EHL 分析 常規(guī) EHL 分析 壓力 分布 油比 例 (b)壓力分布在考慮油膜歷史的 EHL 分析和不考慮油膜歷史記錄分析的情況下的差異(曲軸角度 270 度) 圖8 軸承主要特性分析的計(jì)算結(jié)果 4結(jié)論 考慮油膜歷史的 EHL 分析 常規(guī) EHL 分析 剛體分析 曲柄角度(deg) (a)最大變化，油膜壓力的時(shí)間變化曲線EHL分析和研究油膜歷史記錄曲線的EHL分析是做為一種能夠改善發(fā)動(dòng)機(jī)曲軸系統(tǒng)可靠 性的先進(jìn)技術(shù)來(lái)提出的。 為了給輕型高功率引擎的開發(fā)設(shè)計(jì)軸承，我們必須用上述評(píng)估技術(shù)來(lái)保證高度的可靠 性，并且提高三維CAD設(shè)計(jì)系統(tǒng)化技術(shù)連接的便利性。這項(xiàng)開發(fā)的部分是與Truck&BusResearch、開發(fā)中心和三菱汽車公司合作的。Mitsubishi Heavy Industries, Ltd.Technical Review Vol.39 No.1 (Feb. 2002)16Crank Bearing Design Based on 3-D Elasto-hydrodynamicLubrication TheoryTakero Makino*1Toshimitsu Koga*2The demand for high efficient diesel engines makes ample design of crank shaft bearings difficult. Deformationdue to bearing load is in millimeters, while bearing oil film thickness is less than several microns. This paper detailsthe application of 3-D elasto-hydrodynamic lubrication theory to crank shaft bearings for 4-stroke diesel engines. Thetheory includes bearing deformation and oil film history in a bearing gap.XYBearingShaftFig. 1 System of coordinates*1 Nagasaki Research & Development Center, Technical Headquarters*2 General Machinery & Special Vehicle Headquarters1. IntroductionRecently, the output of internal combustion engineshas been increased and their weight has been reduced.As the result of this, bearings are used under severeroperating conditions, and deformation of housings ofconnecting rod big-end bearings and main bearingshave significant influence upon the bearingcharacteristics. To solve this problem, MitsubishiHeavy Industries, Ltd. (hereinafter referred to asMHI) has developed a bearing characteristicprediction method(1)applying the elasto-hydrodynamic lubrication (EHL) theory for thesedynamically loaded bearings, and used the method todesign and evaluate MHIs large-bore diesel engines.The EHL analysis coupling oil film pressure withelastic deformation of bearing surface enables toconsider the influence of local bearing surfacedeformation and evaluate the quantitative bearingperformance with remarkably improved accuracy ofbearing characteristic prediction as compared to theconventional analysis assuming bearings to be rigidbodies.In addition, in these years, MHI has introducedthe EHL analysis considering oil film history thatcouples oil film pressure with bearing deformationwhile tracing the oil filling ratio in bearing clearanceaccording to the time history to improve theevaluation accuracy.This report introduces examples of application ofthis technique to connecting rod big-end bearings andmain bearings of MHIs 4-stroke diesel engines.2. Theory2.1 Basic equationsFig. 11 shows the system of coordinates used in thisreport.Reynolds equation that controls the oil filmpressure distribution p is expressed as eq. (1).(1)When the equation (1) and the following equationsof force equilibrium are combined into a simultaneoussystem of equations with respect to time t, informationon shaft center locus and oil film thickness can beobtained.(2)(3)The oil film thickness h is expressed by eq. (4) inconsideration of the initial geometrical clearance,misalignment of shaft, and elastic deformation.(4)where,: Viscosity pressure coefficientx: Misalignment around X axisy: Misalignment around Y axisc r: Bearing radial clearancee x: Eccentricity in X directione y: Eccentricity in Y directionh : Oil film thicknessL : ComplianceN : Engine speed: Areap: Oil film pressureMitsubishi Heavy Industries, Ltd.Technical Review Vol.39 No.1 (Feb. 2002)17: Oil filling ratio: Bearing circumferential coordinatet : TimeU : Sliding velocityW x: X direction loadW y: Y direction loadX: Horizontal coordinateY: Vertical coordinateZ: Axial coordinate2.2 Analyzing technique2.2.1 EHL analysis considering oil film historyWe developed an EHL analysis considering themovement of oil in the bearing clearance based on theconcept of oil film history proposed by Jones(2). MHIsconventional EHL analysis calculated the pressuredistribution on the assumption that the wholebearing surface is covered with lube oil, replacedthe negative pressure region obtained as the resultof the calculation with the ambient pressure andregarded the boundary of the region as the oil filmrupture boundary. Under this boundary condition,flow continuity on the oil film rupture boundarycannot be filled. On the other hand, the EHLanalysis considering oil film history follows the oilfilling ratio with time so that the flow continuity isfilled.For bearings that receive fluctuating load, such asengine bearings, the bearing area where positive oilfilm pressure can develop is restricted, and, therefore,the EHL analysis may show higher pressure than thatobtained by the conventional EHL analysis. This wasverified by actual measurement on the main bearingsof MHIs large-bore marine diesel engines. The EHLanalysis considering oil film history is used for designand evaluation as a useful analysis tool.2.2.2 Calculating methodThe oil film pressure p and shaft eccentricities exand ey can be obtained by the simultaneous equations(1) to (4). Since the equation (1) is nonlinear withrespect to the oil film pressure, we used Newton-Raphson method to determine them. We used thefinite element method (FEM) (Galerkin method) fornumerical calculation, four-point isoparametricelements as elements and Skyline method fornumerical solution of the linear equation system. Todetermine the oil film rupture boundary, we improvedand used the technique of Kumar, et al.(3)that appliesthe oil film history algorithm to the finite elementmethod. Fig. 22 shows the flow of the calculation.3. Case study3.1 Connecting rod big-end bearingUsing the connecting rod big-end bearing of an S3Lengine, we compared the rigid body analysis and theEHL analysis, and compared the EHL analysisconsidering oil film history and the conventional EHLanalysis.Moreover, we evaluated the influence of the shapeof the crank pin on the bearing characteristics of theconnecting rod big-end bearing.Table 11 shows the specifications for the bearing,and Fig. 3 shows the load vector that affects thebearing and the 3D FEM model used to calculate thecompliance.StartReading of input dataSetting of initial valuesSetting of oil film rupture boundaryAssumption of journal eccentricity and translation speedCalculation of oil film thickness distributionFind non-ruptured oil film regionCoefficient matrix of Newton Raphson method Calculation of correction values of pressuredistribution and eccentricityJudgment of convergence of load and eccentricityJudgment of convergence atcurrent crank angleJudgment of convergence of 1 cycleOutputEndCalculation of changein oil filling ratioRenewal of time stepTable 1 Dimensions of S3L engine connecting rod bigg-end bearing Bearing diameter 48 mm Bearing width 21 mm Radial clearance 0.025 mm Rod length 145 mm Stroke 78.5 mmEngine speed 3 600 rpm Lube oil viscosity 10 cP Fig. 2 Flow of calculationMitsubishi Heavy Industries, Ltd.Technical Review Vol.39 No.1 (Feb. 2002)18-5 000-25 00025 000-50 0005 00000XYZ360o300o120o240o60o0o(a) Bearing load (b) FEM model of big-end180o720540360180801001201401601802006040200(a) Change in max. oil film pressure with timeMax. oil film pressure (MPa)Crank angle (deg): EHL analysis considering oil film history: Conventional EHL analysis: Rigid body analysis-0.0500.050-0.0250.0250.000-0.05 -0.0 25 0.0250 0.05(b) Shaft center locus: EHL analysis considering oil film history: Conventional EHL analysis: Rigid body analysis3.1.1 Comparison of analyzing techniquesFig. 4(a) shows the change in the maximum oil filmpressure with time. At almost all timing points, theoil film pressure determined by the rigid body analysisis higher than that obtained by the EHL analysis. Thisis apparently indicated, for example, at the explosiontiming at a crank angle of about 10 where the loadis relatively large. The maximum oil film pressuredetermined by the EHL analysis is 133 (MPa), whilethat determined by the rigid body analysis is 180(MPa). Figs .4 (c) and (d) show the oil film thicknessdistribution and the oil film pressure distribution inthe bearing center part at a crank angle of 10. Inconsideration of the elastic deformation, the oil filmthickness obtained by the EHL analysis is larger ascompared to that obtained by the rigid body analysisand almost uniform in the pressure region. Comparedwith the rigid body analysis, the EHL analysis givespressure distribution wider in the circumferentialdirection and shows lower maximum oil film pressure.As is evident from the shaft center locus shown inFig. 3 Conditions of calculation for bearingChange in bearing load and 3D solid model for calcula-tion of deformation are shown.Results of analysis of characteristics ofbig-end bearingWhen the elastic deformation is taken into con-sideration, the calculated oil film pressure de-creases, and the calculated oil film thickness in-creases. When the oil film history is taken intoconsideration, the bearing area where positive oilfilm pressure can develop is restricted, and thepressure peak becomes higher.608010012014016020018040200 90 180 270 360(c) Oil film pressure in bearing center part (at crank angle of 10o )Oil film pressure (MPa)Circumferential coordinate of bearing (deg): Conventional EHL analysis: Rigid body analysis1020304050600 90 180 270 360(d) Oil film thickness in bearing center part (at crank angle of 10o )Circumferential coordinate of bearing (deg): Conventional EHL analysis: Rigid body analysis1010(e) Difference in pressure distribution between EHL analysis considering oil film history and EHL analysis without considering oil film history (at crank angle of 250o )EHL analysis considering oil film historyConventional EHL analysisPressure distribu-tionOil filling ratioFig. 4Mitsubishi Heavy Industries, Ltd.Technical Review Vol.39 No.1 (Feb. 2002)19Fig. 4(b), the EHL analysis indicates that the shaftcenter is remarkably eccentric over the bearingclearance.In Fig. 4(a), the maximum oil film pressure at acrank angle of about 250 determined by the EHLanalysis considering oil film history is different fromthat determined by the conventional EHL analysis.This crank angle timing corresponds to the point ofshift of load from the upper metal to the lower metal,where the shaft moves toward the side having an oilfilm rupture.Fig. 4(e) shows the oil film pressure distributionand oil filling ratio at a crank angle of 250. As isevident from this figure, the analysis considering oilfilm history shows that the bearing area wherepositive oil film pressure can develop is restrictedowing to the shortage of oil, and gives higher oil filmpressure as compared to that given by theconventional EHL analysis.3.1.2 Influence of crank pin shape on bearingcharacteristicsWe evaluated the influence of the crank pin shapeon the characteristics of connecting rod big-endbearings. We examined three crank pin shapesshown in Fig. 55, i.e. (1) straight, (2) barrel shape,and (3) hourglass shape. Fig. 66 shows the results ofanalysis of the maximum oil film pressure andminimum oil film thickness. It is revealed that thestraight crank pin (1) gives higher oil film thicknessand is suitable for the operating conditions of thebearings.3.2 Main bearingThis analyzing technique is applicable not only tobig-end bearings, but also to main bearings and small-end bearings. An example of analysis of the No.4 mainbearing of an S6R engine is shown below. Table 2shows the specifications for the bearing, and Fig. 7shows an FEM model of the engine frame includingthe bearing load and main bearing.The time history of maximum oil film pressurez=1z=-1z=1z=-1z=1z=-12120015010050064 46012345220Max. oil film pressure (MPa)Hourglass shapeStraightBarrel shapeTable 2 Dimensions of S6R engine No. 4 main bearing Bearing diameter 140 mm Bearing width 53 mm Radial clearance 0.07 mm Engine speed 1 800 rpm Lube oil viscosity 10 cP Oil groove Horizontal and lateral, 45, 100 mm wide -50 000 50 0000100 000-100 000-100 000100 000-50 00050 000XYZ300o120o240o180o60o0o(a) Bearing load (b) FEM model of engine frameshown in Fig. 8 (a) indicates that the rigid bodyanalysis estimates the pressure higher as comparedto the EHL analysis. As is evident from the pressuredistribution at a crank angle of 245 shown in Fig. 8(b), the EHL analysis considering oil film historyrestricts the bearing area where positive oil filmpressure can develop owing to the shortage of lubeoil and gives higher oil film pressure than thatobtained by the conventional EHL analysis.Accordingly, it is considered that the analysis of mainbearings shows a sim