校园电动车的设计

喜欢就充值下载吧。。资源目录里展示的文件全都有，，请放心下载，，有疑问咨询QQ:414951605或者1304139763 ======================== 喜欢就充值下载吧。。资源目录里展示的文件全都有，，请放心下载，，有疑问咨询QQ:414951605或者1304139763 ======================== 发动机轴承设计的发展 F.A.马丁 一些关于发动机的重要轴承设计技术的最新发现被突出了。但增加的计算能力的可用性，使轴承的条件被认为是更现实的假设。这些包括供油特性、油膜的历史,非圆轴承、惯性，由于期刊的影响,提高了预测中心的运动主要轴承载荷、灵活的轴承座和特殊轴承。这些参考文献进步了，连同他们如何影响预测插图轴承性能。实验证据也正在得到，这有助于验证，并给予信任的分析预测。 关键词：滑动轴承，轴承设计，流体动力润滑，轴承的压力，轴承座，油槽 从发动机的机械配置石油电影流体力学看来，发动机轴承性能取决于许多依赖因素。这个文件强调了更重要的考虑因素，并且与他们最近的进展，发表和未发表的，遍布世界各地。在审查试图引用不只是这些进步，而是想说明他们如何延长性能预测，实验验证和特种轴承设计领域。从历史上看，在动态加载轴承设计的最初尝试，是根据特定的最大允许负荷（如适用从预测的最大承载面积除以负载定义），这仍然是一个有价值的参数。随着技术的图形和数字。虽然仍高度简化的解决水动力轴承模型，精干的到来，最小油膜厚度可作出估计，并作为判断一个比较新的发动机上使用的问题的可能性。对那些早先的预测方法的综合研究可以发现，在1967年由坎贝尔审查文件等我;作为案例，这曾经是一个拉斯顿和Hornsby VEB的谷三600马力，600转/分柴油机大端轴承。近二十预测和各种来源的实验轨道杂志，其中以一，机械量讨论。大肠杆菌的法律程序中所包含的文件，同样的研究案例至今仍在使用的工人在这一领域今日（极性负荷图，图1（a）条;完整的数据，参考文献1）。它已经被用于在本次审查的预测能力，说明在随后提出了一些。在早期的预测方法所用的主要假设，许多人肯定不太现实，但作为权宜之计用于获取一个数学模型，可以在有限的计算能力，然后提供解决。这些假设包括圆形刚性轴承和一个'完美'的isoviscous牛顿石油供应。在许多情况下，轴承表面被假定为在发达地区供油油膜压力的特点和外部的关系不受干扰，主轴承载荷计算没有采取任何曲轴和曲轴箱的刚度帐户。在过去十年中增加计算能力，这就意味着那些早期的许多假设不再需要工作已进行了2'3对轴承形状弹性连杆轴承4，供油特性s'6，油膜历史7，更现实的主轴承负荷分担8'9。这一点，在保持虽然有点晚了，与1967年的预言，从坎贝尔，其中指出：'这是作者的相信，通过持续不断的计算方法，并与强大的设计技术的迅速发展而日益认识正成为可用，在未来十年将显示进度，甚至比这本文试图描述'更大。在设计技术作为改进的计算能力和更严格的方法结果的进步，开辟了一体化工作，将直接有利于更广泛领域的设计师。这包括： 考虑更现实的条件瞄准>二少假设 数据表示理解，以便更好地结果 经营状况较好的预测（负载共享，热平衡） 实验验证 在这些类别各自的发展进程是非常重要的，每个部分补充了其他。 由于需要节约能源和燃油经济性的大问题，许多引擎现在正在设计具有较高的功率重量比。对轴承的影响，减少由此产生的轴承尺寸，高比负荷和使用低粘度油。所有这些变化带来接近设计极限的轴承工作条件，从而把一个更大的重要性，不仅上材料和润滑剂的选择，但我也切合实际承载能力的预测。改进的水动力计算简化和快速的方法许多数据编制方法显示在此文件;有关VEB的大头钉，搵工时使用的短轴承的移动解决方案。在流动的概念已成功应用于在过去15年，是在其他地方详细解释。其强大的吸引力是它的方式分裂成两个部分期刊挤压和旋转，这使富力轨道计算并在每个时间步没有反复计算非常迅速的运动。为了完整的短轴承VEB的轴颈中心的轨道是在新的调查，包括在图2a（参考我在补充者）自动对焦的轨道，并在不同时期的变化新生力量最小油膜厚度各地。负载周期（由曲柄角度定义）如图3。这本书的作者的工作的第二部分是电影制作间隙圆压分布图12给出的最大动水压力比在任何特定负载点间隙圆。在图4插入的图表显示了与VEB的间隙循环轨道叠加膜压力图。请注意，这个轨道是不绘制相对空间 -传统的方法- 但在清关的地图，实际上是被一个角无动于衷整个周期，这样，应用负载方向始终向下。这是一个重要和宝贵的技术，当使用移动方法。最小油膜压力是从这些关系，并在整个负载周期变化的图4所示的主要部分。里奇在英国通用电力公司开发出一种新的半杂志为中心的轨道预测分析方法;它采用短轴承容易得到优化的解决方案，已经改善了短轴承的标准方法，在高偏心率准确性的VEB的大端轴承轨道如图2（b）项。这看起来非常类似于一个普通轴承有限的轨道，显然只发生在一个IBM 145分之370计算机（前几年）16秒运行。最低油0.0033毫米（0.00013英寸）薄膜厚度比较表1与其他来源（包括有限的全球环境变化影响使用'存储的数据'的做法方案的结果见下一节）值。它被认为是在较严格的方法分布带轴承有限，但仍保持了快速解决方案的优势。油中的最小完整的运作周期膜厚度是最重要的参数来判断轴承的表现之一。它通常用来作为比较，代表了在有关预测与现有的类似经验型发动机轴承性能的主要因素。这是很难给出精确值最小油膜厚度的轴承损坏时可能出现的诸如高的轴承温度，不对中，供油不足，安排和不利的环境条件等因素都会产生效果。布克会给予一定的薄膜厚度对危险水平连杆轴承（适用于短轴承预测方法的使用）的指导。 有限轴承理论 用有限元法（有限元）解决有限轴承理论，通用汽车公司研究实验室2有能力考虑有不同的形状和也让在场的开槽。对于一个普通的圆轴承通用轴承从他们的有限元模型成功地曲线拟合的基本数据，并以此来建立一个快速的方法，通常计算时间从数小时缩短到数秒。这两intermain种方法已应用于马丁发动机轴承设计。拉斯顿VEB的大底，图2（c）和（d）显示了有限元程序和曲线拟合程序分别轴颈中心的轨道。这两个轨道上看起来非常相似，虽然有一个对曲线拟合程序显着节省计算时间。薄膜厚度比和我的两个最大油膜压力，部门首长进行了比较，图5（a）和（b）项。还要注意的是，从短轴承理论（图4）薄膜压力非常类似从有限的轴承有限元理论（图5b）这一点。现在有许多机构或有限差分有限元的2 - D解决方案，使供油特性上动水压力的能力产生影响。在'标准'VEB的案例，结合它的圆周凹槽，是不是说明了这样的效果适合，而不是一个1.8升汽油发动机intermain轴承将被使用。开头的图如图6所示，并进一步行动组可发现引用6和7。在图7的轨道上图显示了薄膜的厚度减少作为一个石油洞的存在而在本体。但是应当指出，在周期的最小油膜厚度不一定受到损害。 一个设计方法已经制定了在冰川金属有限公司允许，在一个更完整的方式，在轴承的feed功能的影响。它认为分为两类这些法利效果。第一个问题涉及到发达国家的压力过油养区（孔，槽等），轴承的传递地区产生不利影响。第二个涉及石油运输轴承内的其他投资收益电影的研究，并考虑到了有害的影响程度时，油膜耗尽而由于没有足够的石油可供菲力的承载轴承的面积。这第二类是有时被称为“油膜历史”。 油膜历史 关于历史和油膜轴承油膜的动态加载边界的基础性工作很多是率先在英国国家工程实验室，由已故机管局米尔恩，他的早逝留了一个空缺在这个非常专业的知识领域。米尔恩的做法视为是不断变化的模式和移动网相匹配的电影界。琼斯在冰川开发的另一种方法考虑节间流通，使用每个节点控制周围空间的边界固定的有限差分网格。后一种方法是比较容易通过，并已用于在intermain轴承分析（一孔馈送）在1.8升发动机。正如图7图所示的右手，与电影的历史轨迹形状一般的预测有很大的不同，当油膜史上的影响被忽略。尽管在最小的负载周期膜厚度的影响不大时，又是考虑油膜史，人们可以感知的案件（对于低供油压力实例）在该杂志的额外中心径向偏移可能会产生危险的小薄膜厚度。这强调了使用油膜史上节目中可能会遇到这些问题的重要性。同样的原则也被应用到VEB的大底承载力的研究和预测的情况下杂志和无油膜历史的中心路径显示在图2（e）和（f）分别。这个油膜史上降级为一个完全圆周槽轴承的影响不是一开始撰文预期。然而，效果相当显着的轨道上的右手边看到，图2（e）项和当地膜厚度（见表1）。从0.0036毫米（0.00014英寸）降低到0.0023毫米（0.00009英寸），一个重要的数额。薄膜厚度在整个负载周期（比）不同的趋势进行了比较，图8。顶部图显示（由线条的粗细）之间的有限轴承预测从不同来源（包括珀金斯发动机有限公司17）相似。瓦图中显示从VEB的发动机，我的实验结果，下图显示的预测考虑油膜历史。标记的点。甲，乙，丙帮助每个图进行比较的趋势。在这两个电影史上的预测和在B点的峰值比在一个较高的实验结果显示，与传统的方法（上图），他们几乎相同的高度。此外，随着电影史上另一个高峰是在C显然其中有与实验一致。而所有这一切都给出了'电影的历史模型，有一种思想流派，这可能是偶然的广泛协议，因为轴承形状各不相同，但在实践中一直不断在理论假设为刚性和循环支持。 惯性的影响 在苏塞克斯大学的，有几个动态加载的发动机轴承方案已经开发了考虑对从轴心运动导致轴承间隙内]装载质量加速度效应。德德14的方案有所不同，较近期的油膜力，导出的方式。基本方案认为，一个完整的2 - D溶液的雷诺方程和1.8升发动机轴承从这个结果非常相似，冰川（图7，上图）预测的。德德还制作了一个更快的方法，假设在轴向压力分布是抛物线。此相关的方程代入，让雷诺方程式二阶常微分方程，可通过直接矩阵求逆解决。系数矩阵是一个三对角之一，解决的办法是加速只用对角线，而不是所有的矩阵元素打交道了。这种方法只需要几分钟来计算。它不是像快速移动的方法，但大规模的惯性和槽影响，使一些优势。一个普通ungrooved轴承，一个完整的环形沟，或单洞（如狭窄的延长轴承宽度插槽充分考虑），可容纳在这个快速1 - D溶液。对于一个完整的部分沟2 - D溶液必须使用。 表1比较实验和理论之间的最小油膜厚度为6 VEB的- X的谷三连杆轴承。为1.8升引擎使用德德的快速解决方案轴承轴颈中心的路径显示在图7左手图。无论是使用理论，有限或快速的方法，预测之间的滑动轴承，并与供油特点之一差异非常相似。这本期刊的群众运动关内的空间效果似乎并不在1.8升发动机轴承具有重要意义。作为一个练习，以显示一个大期刊质量的影响，选择了极端值（不一定意图]信息研究所）表示趋势。较低的图7下雪的极端情况下，轨道的形状是完全改变了右手图。与载荷的是相反的方向旋转的轨道部分相关期刊似乎是受影响最严重，虽然最小油膜厚度维持不变。德德还审议了VEB的研究个案，并承担了有效的质量对应于连杆的旋转质量的组成部分。由此产生的杂志从二维有限轴承解决方案和更迅速的一维解决方案中心的轨道都显示在图2（g）和2（高）分别。在图2（h）的轨道大多数似乎是由大众的惯性作用影响，虽然通常尖点，在反方向的轨道阶段的开始，已完全消失，它声称，大众惯性的影响轴承间隙内的空间日志可能会显着毗邻主轴承飞轮。 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