外文翻译--主轴平衡力和曲轴弯曲应力的研究【中英文文献译文】
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南 京 理 工 大 学 紫 金 学 院毕业设计(论文)外文资料翻译系： 机械工程系 专 业： 机械工程及自动化 姓 名： 张跃 学 号： 060104201 (用外文写)外文出处： Advances in Engineering Software 40（2009）95104 附 件：1.外文资料翻译译文2.外文原文。 指导教师评语：文献翻译基本符合科技论文语法习惯，语句较通顺，用词较简练。但还需注意专业词汇的合理翻译。整篇文章翻译良好。 签名： 年 月 日注：请将该封面与附件装订成册。附件1：外文资料翻译译文主轴平衡力和曲轴弯曲应力的研究关键词：平衡力 曲轴模型 平衡率 轴承负荷 弯曲应力摘要：在这项研究中，使用了多体系统仿真程序ADAMS。研究同轴6缸柴油发动机上平衡物的质量和位置对主轴负荷和弯曲应力的影响，在分析中，用刚性，梁和曲轴三维实体模型对主轴承负荷和三维实体模型进行了比较，在平衡力的分析中使用了横梁模型。平衡角为零的平衡物和平衡角为30的平衡物，它们的平衡率认为是0，50和100。而且研究结果发现，随着最大主轴承负荷和弯曲应力增加，平衡率的增加和平均主轴承平衡率随负载随之减少。两种结构都表现出同样的趋势。从轴承负载和网站弯曲应力的表列中可以看出来，与惯性力的负荷相比气体压力对曲轴设计的影响更为显著。2007科学版权有1 . 导言 新的内燃机引擎必须具有很高的电力，燃油经济性好，体积小的发动机，能减少对环境的污染。因此，引擎每个部分的整体性能和效果都需要仔细的调查改进。内燃机曲轴系统发动机作为主要负责为电力生产对发动机性能有着重要的影响。 曲轴系统主要由活塞销，活塞连接连杆，曲轴，扭转振动阻尼器和飞轮构成的。平衡物放置在每个曲柄的对面用来平衡旋转惯性力。一般而言，平衡物的设计其平衡率为50至100。为了可承受最大值和平均主轴承载力，平衡物的质量和他们的位置很重要。最大值和平均发动机主轴承载力取决于气缸的压力，平衡物的质量，发动机转速和其他曲轴几何参数。 对内燃机曲轴的研究主要集中振动和应力分析上。尽管曲轴压力分析可以查看文献资料，但是没有平衡物对主轴负载和曲轴压力的影响这方面的研究文献资料。夏普采用刚性模型研究了V - 8发动机曲轴的平衡，优化了平衡力来尽量减少主轴的承载负荷。斯坦利和塔拉扎采用刚性曲轴模型和理想通过研究获得的4到6缸对称行发动机的最高和平均主轴承的负荷，估算出理想的平衡物质量，和在可接受范围内的最大负载所造成得影响。在用刚性曲轴模型分析平衡力时，如果不考虑对曲轴主轴承的弹性效应会导致极大的错误。因此，广泛对平衡物在主轴负载和曲轴压力所产生的影响的研究仍然是很重要的。 在这项研究中，对轴向六缸柴油机曲轴系统上的平衡物的位置和质量进行了研究。在对平衡角为零的平衡物和平衡角为30的平衡物，其配重平衡率为0，50和100的的主轴的承载负荷和曲轴弯曲应力的最大值和平均值计算中，使用多体系统仿真程序， ADAMS/引擎，进行了分析。模拟平均转速在1000-2000范围内的发动机。2. 发动机规格表1给出直列6缸柴油发动机的规格。 9.0升发动机的曲轴有8个平衡物在曲柄上1，2，5，6，7，8，11和12。用Pro / E绘制三维曲轴实体模型如图1所示，图中给出了曲轴的示意图。表2中给出曲柄行程的性质。表3给出曲柄的系统数据。表1 发动机规格单位9.0升发动机孔径mm115冲程mm144气缸轴向距离Mm134峰值发射压力MPa19额定功率转速kw/rpm295/2200最大转矩转速Nm/rpm1600/1200-1700主要杂志/针直径mm95/81点火顺序-1-5-3-6-2-4飞轮质量kg47.84飞轮转动惯量Kg mm21.57E+9TV阻尼环的质量kg4.94TV damper housing质量kg6.86Moment of inertia of the ringkg mm21.27E+9Moment of inertia of the housingKg mm20.56E+9表2 曲柄行程性质123456质量（kg）12.509.2512.5012.509.2812.55重心位置的曲柄旋转轴(mm)12.42331.43511.96711.96631.02711.702静态不平衡(kg mm)155.265290.767149.734149.734287.871146.856表3 曲轴系统数据曲柄半径（mm）72连杆长度()239质量完全活塞( )3.42连杆往复质量( )0.92往复式质量（每个气缸总） ()4.32连杆转动质量（ ）2.013. 曲轴系统建模用ADAMS/发动机，曲轴，可以建立四个不同的模型方式：刚性曲轴，扭灵活的曲轴，横梁曲轴和曲轴三维实体。刚性曲轴模型主要用于获取自由的力和力矩，来达到平衡的目的。扭灵活的曲轴模型用于研究扭转振动。横梁曲轴模型是代表扭转和弯曲刚度曲轴，用梁模型可以计算出弯曲应力。弹性曲轴三维实体模型，可使用额外的有限元程序。该过程是漫长的而费时，通常自由度以百万计的。为了简化有限元模型，我们使用模态叠加技术。弹性变形结构是近似的线性组合可表现为模式如下： U=q (1)其中q是模态向量的坐标和是形状函数矩阵。弹性体包含两种类型的节点，在多体仿真系统（MMS）结构的边界和焦点的交换处的接口节点，和内部节点。在MSS中对弹性体的位置和弹性变形是由叠加法计算的。在ADAMS，是用以CraigBampton 方法为基础的模态综合技术。这种组件模式包含了静态和动态特性的结构。这些模式的约束模式是通过给每个DOF一个位移而发生静态变形，同时保持其他所有接口自由度固定，固定边界是解决方案的特征值，我们用固定整个界面的自由度来解决这个问题。模态在物理自由度和CraigBampton模式之间转换，这种模型是通过他们的模态坐标来描述：式中的UB和U1分别代表着边界自由度和内部自由度的列向量，分别表示恒等式和零矩阵，C表示在约束模式中物理位移的内部自由度的矩阵，n表示在正常模式中物理位移的内部自由度的矩阵，qc表示在约束模式中列向量的模态坐标，qn表示在固定边界的正常模式中列向量的模态坐标，我们为了能得到分离设置的模式，通常将约束模式和正常模式正交。 在MSC.Nastran利用模态叠加技术可以得到9.0升发动机的弹性曲轴三维实体模型。首先，图中所示是曲轴的三维实体模型，1是曲轴的有限元模型，特点是它有30万十节点四面体和5000000节点。曲轴的模态模式具有三十二个边界自由度和十六个接口节点。从静态分析中得到的模态模式与这些自由度相符合。获得柔性曲轴模型是通过模态综合考虑了40个固定边界正常模式。因此灵活曲轴模式的特点是它总共有72个自由度，这种模式出口到ADAMS/引擎和曲轴系统模型，如图。4. 曲轴系统和平衡力 在内燃机里的作用力可以分为惯性力和压力，而惯性力可以进一步划分为两大类：旋转惯性力和往复式惯性力。每个气缸的旋转惯性力可以用下面的公式表示： 式中的mR 表示旋转质量其中包括了曲柄的质量和旋转连杆的部分质量； rR从曲轴的旋转中心到旋转质量的重心的这段距离；W曲轴的角速度，h表示与TDC有关的曲柄行程的角位置。如果每个曲柄行程有两个平衡力，每个平衡力的作用力由下式给出；式中的yi,j表示偏移角；每个行程有两个平衡力。“i”表示了平衡力的数目。我们要完成对平衡率的评估才能得到配重的大小。如下： 式中的UCW表示每个配重的静态不平衡量；UCrank_throw表示每个曲柄行程的静态不平衡量；mcr-r表示连杆转动部分的质量;r表示曲柄半径；K表示一对内部旋转力的不平衡率。下面这个公式表示在已知曲轴和平衡力大小情况下的平衡率： 对于一个轴向的六缸发动机曲轴，它的三对曲柄行程分布在对称轴中心的一百二十度处，旋转力和一二阶往复力处于平衡状态。这可以用一二阶的向量坐标来解释，如图4所示。六缸曲轴产生的旋转力和往复力相互平衡，但是这也导致了内部弯矩的产生。高速运转，两个相同的定向曲柄行程导致中心轴上产生一个旋转载荷。气缸的旋转惯性力通常可以抵消部分曲轴对面的平衡力。一般来说，设计平衡物时平衡率在50%到100%之间。附件2：外文原文An investigation of the effect of counterweight configuration on main bearingload and crankshaft bending stressYasin Yilmaz*, Gunay AnlasDepartment of Mechanical Engineering, Faculty of Engineering, Bogazici University, 34342 Bebek, Istanbul, Turkeya r t i c l ei n f oArticle history:Received 11 February 2008Received in revised form 17 March 2008Accepted 24 March 2008Available online 6 May 2008Keywords:Counterweight configurationCrankshaft modelsBalancing rateBearing loadBending stressa b s t r a c tIn this study, effects of counterweight mass and position on main bearing load and crankshaft bendingstress of an in-line six-cylinder diesel engine is investigated using Multibody System Simulation Program,ADAMS. In the analysis, rigid, beam and 3D solid crankshaft models are used. Main bearing load results ofrigid, beam and 3D solid models are compared and beam model is used in counterweight configurationanalyses. Twelve-counterweight configurations with a zero degree counterweight angle and eight-coun-terweight configurations with 30? counterweight angle, each for 0%, 50% and 100% counterweight balanc-ing rates, are considered. It is found that maximum main bearing load and web bending stress increasewith increasing balancing rate, and average main bearing load decreases with increasing balancing rate.Both configurations show the same trend. The load from gas pressure rather than inertia forces is theparameter with the most important influence on design of the crankshaft. Results of bearing loads andweb bending stresses are tabulated.? 2008 Elsevier Ltd. All rights reserved.1. IntroductionNew internal combustion engines must have high enginepower, good fuel economy, small engine size, and should be asharmless as possible to the environment. Therefore, the effect ofeach component of the engine on its overall performance shouldbe investigated in detail. Crankshaft systems of internal combus-tion engines have important influence on engine performancebeing 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 eachcrank to balance rotating inertia forces. In general, counterweightsare designed for balancing rates between 50% and 100%. Foracceptable maximum and average main bearing loads, mass ofcounterweights and their positions are important. Maximum andaverage main bearing loads of an engine depend on cylinder pres-sure, counterweight mass, engine speed and other geometricparameters 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 fewstudies 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 modeland optimized counterweights to minimize main bearing loads.Stanley and Taraza 11 obtained maximum and average mainbearing loads of four and six-cylinder symmetric in-line enginesusing a rigid crankshaft model and estimated ideal counterweightmass that resulted in acceptable maximum bearing load. Rigidcrankshaft models that are used in counterweight analyses donot consider the effect of crankshaft flexibility on main bearingloads and can lead to considerable errors. Therefore, an extensivestudy on effect of counterweight configuration on main bearingloads and crankshaft stresses is still needed.In this study, counterweight positions and masses of an in-linesix-cylinder diesel engine crankshaft system are studied. Maxi-mum and average main bearing forces and crankshaft bendingstresses are calculated for 12-counterweight configurations witha zero degree counterweight angle, and for eight-counterweightconfigurations with 30? counterweight angle for 0%, 50% and100% counterweight balancing rates. Analyses are carried out usingMultibody System Simulation Program, ADAMS/Engine. Simula-tions are carried out at engine speed range of 10002000 rpm.Bending stresses at the centres of each web are also calculated.2. Engine specificationsThe specifications of in-line six-cylinder diesel engine are givenin Table 1. The 9.0 L engine crankshaft has eight counterweights atcrank 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. Static0965-9978/$ - see front matter ? 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.advengsoft.2008.03.009* Corresponding author. Tel.: +90 212 359 7534; fax: +90 212 287 2456.E-mail address: yasin.yilmaz.tr (Y. Yilmaz).Advances in Engineering Software 40 (2009) 95104Contents lists available at ScienceDirectAdvances in Engineering Softwarejournal homepage: /locate/advengsoftunbalance of each crank throw (with and w/o counterweights) isdetermined 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 systemUsing ADAMS/Engine, a crankshaft can be modeled in four dif-ferent ways: rigid crankshaft, torsionalflexible crankshaft, beamcrankshaft and 3D solid crankshaft. Rigid crankshaft model ismainly used to obtain free forces and torques, and for balancingpurposes. Torsionalflexible crankshaft model is used to investi-gate torsional vibrations where each throw is modeled as one rigidpart, and springs are used between each throw to represent tor-sional stiffness. Beam crankshaft model is used to represent thetorsional and bending stiffness of the crankshaft. Using beam mod-el bending stresses at the webs can be calculated 12.Table 1Engine specificationsUnit9.0 L engineBore diametermm115Strokemm144Axial cylinder distancemm134Peak firing pressureMPa19Rated power at speedkW/rpm295/2200Max. torque at speedNm/rpm1600/12001700Main journal/pin diametermm95/81Firing order1-5-3-6-2-4Flywheel masskg47.84Flywheel moment of inertiakg mm21.57E+9Mass of TV damper ringkg4.94Mass of TV damper housingkg6.86Moment of inertia of the ringkg mm21.27E+5Moment of inertia of the housingkg mm20.56E+5Main Bearing #1 Main Bearing #2 MainBearing #3 Main Bearing #4 MainBearing #5 MainBearing #6 Main Bearing #7 CounterweightsFig. 1. 3D solid model of the crankshaft.C3, C4, C5, C6 C1, C2, C7, C8 1, 6 3, 4 2, 5 C1C2C3C4 C5C6C7C8123456Fig. 2. Eight-counterweight arrangement of the 9.0 L engine crankshaft.Table 2Properties of the crank throwsThrow 1Throw 2Throw 3Throw 4Throw 5Throw 6Mass (kg)12.509.2512.5012.509.2812.55CG position from crank rotation axis (mm)12.42331.43511.96711.96631.02711.702Static unbalance (kg mm)155.265290.767149.734149.734287.871146.85696Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 95104Elastic 3D solid model of the crankshaft can be obtained usingan additional finite element program. The procedure is lengthyand 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 deformationof the structure is approximated by linear combination of suitablemodes which can be shown as follows:u Uq1where q is the vector of modal coordinates and U is the shape func-tion matrix.An elastic body contains two types of nodes, interface nodeswhere forces and boundary conditions interact with the structureduring multibody system simulation (MSS), and interior nodes. InMSS the position of the elastic body is computed by superposingits rigid body motion and elastic deformation. In ADAMS, this isperformed using Component Mode Synthesis” technique basedon CraigBampton method 13,14. The component modes containstatic and dynamic behavior of the structure. These modes are con-straint modes which are static deformation shapes obtained bygiving a unit displacement to each interface degree of freedom(DOF) while keeping all other interface DOFs fixed, and fixedboundary normal modes which are the solution of eigenvalueproblem by fixing the entire interface DOFs. The modal transforma-tion between the physical DOF and the CraigBampton modes andtheir modal coordinates is described by 15u uBuI?I0UCUN?qCqN?2where uBand uIare column vectors and represent boundary DOFand interior DOF, respectively. I, 0 are identity and zero matrices,respectively. UCis the matrix of physical displacements of the inte-rior DOF in the constraint modes. UNis the matrix of physical dis-placements of the interior DOF in the normal modes. qCis thecolumn vector of modal coordinates of the constraint modes. qNisthe column vector of modal coordinates of the fixed boundary nor-mal modes. To obtain decoupled set of modes, constrained modesand normal modes are orthogonalized.Elastic 3D solid crankshaft model of the 9.0 L engine is obtainedin MSC.Nastran using modal superposition technique. First, 3D so-lid model of the crankshaft that is shown in Fig. 1 is exported toMSC.Nastran and finite element model of the crankshaft, which ischaracterized by approximately 300,000 ten-node tetrahedral ele-ments and 500,000 nodes is obtained. The modal model of thecrankshaft is developed with 32 boundary DOFs associated with16 interface nodes. Constrained modes obtained from static analy-sis correspond to these DOFs. Flexible crankshaft model is obtainedthrough modal synthesis considering the first 40 fixed boundarynormal 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 isobtained. 3D finite element model is run with ADAMS.4. Forces acting on crankshaft system and balancingForces in an internal combustion engine may be divided intoinertia forces and pressure forces. Inertia forces are further dividedinto two main categories: rotating inertia forces and reciprocatinginertia forces. The rotating inertia force for each cylinder can bewritten as shown below:FiR;j mR? rR? x2? ?sinhjj coshjk3where mRis the rotating mass that consists of the mass of crank pin,crank webs and mass of rotating portion of the connecting rod; rRisthe distance from the crankshaft centre of rotation to the centre ofgravity of the rotating mass, x is angular velocity of the crankshaft,and hjis the angular position of each crank throw with respect toTop Dead Centre” (TDC). If there are two counterweights per crankthrow, each counterweight force is given by 11FCWi;j ?mCWi;j? rCWi;j? x2? ?sinhj ci;jj coshj ci;jkhi;i 1;2j 1;2;.;64where ci,jis the offset angle of counterweight mass from 180? oppo-site of crank throw j”. There are two counterweights per throw. i”denotes the counterweight number. The counterweight size that isrequired to accomplish an assessed balancing rate isUCWK ? UCrank throw mcr-r? r ? cosc25whereUCWisthestaticunbalanceofeachcounterweight,UCrank_throwis the static unbalance of each crank throw, mcr-risthe mass of connecting rod rotating portion, r is the crank radiusand K is the balancing rate of the internal couple due to rotatingforces. From this formula follows the balancing rate for a givencrankshaft and a given counterweight size:K 2 ? UCWUCrank throw mcr-r? r ? cosc6For a standard in-line six-cylinder engine crankshaft with threepairs of crank throws disposed at angles of 120? that are arrangedsymmetrical to the crankshaft centre, rotating forces, and first andsecond order reciprocating forces are naturally balanced. This canbe explained by the first and second order vector stars shown inFig. 4. The six-cylinder crankshaft generates rotating and firstand second order reciprocating couples in each crankshaft half thatbalance each other but which result in internal bending moment.At high speeds, the two equally directed crank throws, 3 and 4Table 3Crankshaft system dataCrank radius (mm)72Connecting rod length (mm)239Mass of complete piston (kg)3.42Connecting rod reciprocating mass (kg)0.92Reciprocating mass (total per cylinder) (kg)4.32Connecting rod rotating mass (kg)2.01Fig. 3. Model of the crankshaft system.Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 9510497yield a high rotating load on centre main bearing. The rotatinginertia force of each cylinder is usually offset at least partially bycounterweights placed on the opposite side of each crank. In gen-eral, the counterweights are designed for balancing rates between50% and 100% of the internal couple.Gas forces in cylinders are acting on piston head, cylinder headand on side walls of the cylinder. These forces are equal toFp;j ?pD24? Pcyl;jh ? Pcc;jh?k;j 1;2;.;671, 6 2, 5 3, 4 3, 4 1, 6 2, 5 Fig. 4. First and second order vector stars.020406080100120140160180200090180270360450540630720Crank Angle (degree) Pressure (bar)1000rpm1200rpm1350rpm1675rpm2000rpmFig. 5. Gas pressure values at different engine speeds for the 9.0 L engine.Bearing #102550751001251500120240360480600720Crank Angle degForce kNRigidBeam3D solidFig. 6. Forces acting on main bearing #1 for rigid, beam and 3D solid crankshaftmodels at 1000 rpm engine speed.Bearing #202550751001251501750120240360480600720Crank Angle degForce kNRigidBeam3D solidFig. 7. Forces acting on main bearing #2 for rigid, beam and 3D solid crankshaftmodels at 1000 rpm engine speed.Bearing #302550751001251500120240360480600720Crank Angle degForce kNRigidBeam3D solidFig. 8. Forces acting on main bearing #3 for rigid, beam and 3D solid crankshaftmodels at 1000 rpm engine speed.Bearing #402550751001251500120240360480600720Crank Angle deg Force kNRigidBeam3D solidFig. 9. Forces acting on main bearing #4 for rigid, beam and 3D solid crankshaftmodels at 1000 rpm engine speed.Bearing #502550751001251500120240360480600720Crank Angle degForce kNRigidBam3D solidFig. 10. Forces acting on main bearing #5 for rigid, beam and 3D solid crankshaftmodels at 1000 rpm engine speed.98Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 95104where D is cylinder diameter, Pcylis the gas pressure in the cylinderand Pccis 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 atdifferent engine speeds are given in Fig. 5. Pressure curves are ob-tained using AVL/Boost engine cycle calculation program whichsimulates 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 modelsMain bearing loads are calculated using ADAMSs rigid, beamand 3D solid crankshaft models and compared. In the rigid model,no vibration effects are considered which can lead to considerableerrors if vibration effects have a major role on the system (like inmultithrow crankshafts). To consider vibration effects beam crank-shaft model is used and main bearing loads and bending stresses atwebs are calculated. Rigid model assumes crankshaft to be stati-cally determinate and reaction force of any given bearing dependson the load exerted on the throws adjacent to that bearing. Beammodel assumes the crankshaft to be statically indeterminate andthe load exerted on a throw affects all bearings. Analyses are car-ried out at an engine speed range of 10002000 rpm. A moresophisticated 3D solid hybrid model that combines FE with ADAMSis used to check the results obtained by beam model.Maximum main bearing load occurs at bearing number two atan engine speed of 1000 rpm, therefore results are plotted in Figs.612 for 1000 rpm only. Rigid crankshaft model overestimates themaximum main bearing load at bearings 1 and 7 with respect tobeam and flexible crankshaft models. However it underestimatesthe maximum main bearing load at other bearings. For exampleat bearing 2, beam model gives a maximum main bearing load thatis 50% more than that of rigid models because the beam model as-sumes the crankshaft to be statically indeterminate and considersBearing #602550751001251500120240360480600720Crank Angle degForce kNRigidBeam3D solidFig. 11. Forces acting on main bearing #6 for rigid, beam and 3D solid crankshaftmodels at 1000 rpm engine speed.Bearing #702550751001251500120240360480600720Crank Angle degForce kNRigidBeam3D solidFig. 12. Forces acting on main bearing #7 for rigid, beam and 3D solid crankshaftmodels at 1000 rpm engine speed.Bearing #1Bearing #14050607080100012001400160018002000100012001400160018002000Crank Angular Velocity (rpm)Crank Angular Velocity (rpm)Maximum Bearing K=0%K=50%K=100%05101520Average Bearing K=0%K=50%K=100%Force (kN)Force (kN)Fig. 13. (a) Maximum and (b) average bearing forces at bearing #1 for 12-counterweight configurations.Bearing #2120130140150160K=0%K=50%K=100%Bearing #22025303540K=0%K=50%K=100%Maximum Bearing Force (kN)100012001400160018002000Crank Angular Velocity (rpm)100012001400160018002000Crank Angular Velocity (rpm)Average Bearing Force (kN)Fig. 14. (a) Maximum and (b) average bearing forces at bearing #2 for 12-counterweight configurations.Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 9510499bending vibrations. Maximum main bearing load difference ofbeam and 3D solid models is approximately 5%. Main bearing loadsfor beam and 3D solid crankshaft models are generally in goodagreement. In bearings 3, 5 and 6, 3D solid model gives larger bear-ing loads at firing positions of the cylinders that are not adjacent tobearing. Because obtaining elastic 3D solid models for differentcounterweight configurations is difficult and time consuming,and beam model gives equally valid results, beam model is usedBearing #3100110120130140K=0%K=50%K=100%Bearing #32025303540K=0%K=50%K=100%Maximum Bearing Force (kN)100012001400160018002000Crank Angular Velocity (rpm)100012001400160018002000Crank Angular Velocity (rpm)Average Bearing Force (kN)Fig. 15. (a) Maximum and (b) average bearing forces at bearing #3 for 12-counterweight configurations.Bearing #460708090100110120K=0%K=50%K=100%Bearing #410152025303540K=0%K=50%K=100%Maximum Bearing Force (kN)100012001400160018002000Crank Angular Velocity (rpm)100012001400160018002000Crank Angular Velocity (rpm)Average Bearing Force (kN)Fig. 16. (a) Maximum and (b) average bearing forces at bearing #4 for 12-counterweight configurations.Bearing #6100110120130140K=0%K=50%K=100%Bearing #620253035404550K=0%K=50%K=100%Maximum Bearing Force (kN)100012001400160018002000Crank Angular Velocity (rpm)100012001400160018002000Crank Angular Velocity (rpm)Average Bearing Force (kN)Fig. 18. (a) Maximum and (b) average bearing forces at bearing #6 for 12-counterweight configurations.Bearing #5100110120130140K=0%K=50%K=100%Bearing #52025303540K=0%K=50%K=100%Maximum Bearing Force (kN)100012001400160018002000Crank Angular Velocity (rpm)100012001400160018002000Crank Angular Velocity (rpm)Average Bearing Force (kN)Fig. 17. (a) Maximum and (b) average bearing forces at bearing #5 for 12-counterweight configurations.100Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 95104in the rest of the work to study the effect of counterweight config-uration on main bearing loads and crankshaft bending stresses.6. Effect of counterweight configuration on main bearing loadand crankshaft bending stressThe effect of counterweight arrangement on bearing forces andcrankshaft bending stresses is investigated using beam model forthe following cases:? No counterweights, K = 0%.? 12 counterweights with K = 50%, c = 0? and K = 100%, c = 0?.? eight counterweights with K = 50%, c = 30? and K = 100%, c = 30?.6.1. Twelve counterweights, c = 0?, K = 0%, K = 50% and K = 100%In this configuration, counterweights are placed on oppositesides of all webs. Counterweight static unbalance is calculatedusing Eq. (5) for K = 50% and K = 100% balancing rates. Maximumand average main bearing loads are calculated using the beamcrankshaft model considering inertial and gas pressure forces andare plotted in Figs. 1319 as function of crankshaft angular velocityand balancing rate.In Figs. 1319, maximum bearing load increases with increasingbalancing rate. This behavior can be explained as follows: For six-cylinder in-line engine crankshafts, the rotating inertia force andfirst harmonic component of the reciprocating inertia force arein-phase and add in the direction of the cylinder. The pressureforce is almost maximum at TDC position where the reciprocatinginertia force and the component of the rotating inertia force in cyl-inder direction are also at maximum levels. Because the pressureand inertia forces are opposite in-sign, they subtract from eachother which increases the maximum bearing load at high balancingrates. On the other hand, average bearing force increases withdecreasing balancing rate. Maximum main bearing load occurs atbearing number two at engine speed of 1000 rpm and averagemain bearing load of bearing 6 is larger than other bearings aver-age loads because bending vibrations of damper and flywheel oc-cur. At main bearings 3, 4 and 5, where the influence of damperand flywheel bending vibrations is minimal, only torsional vibra-tion occurs and their loads are less. Maximum bending stresses oc-cur at webs 1 and 12 and are given in Table 4 for 0%, 50% and 100%balancing rates.6.2. Eight counterweights, c = 30?, K = 50% and K = 100%Eight-counterweight configuration shows the same trend as the12-counterweight configuration for maximum and average bearingforces: maximum bearing force increases with increasing balanc-ing rate whereas average bearing force increases with decreasingbalancing rate. Maximum and average bearing forces for c = 30?,K = 50% and K = 100% counterweight configurations are calculatedBearing #75060708090K=0%K=50%K=100%Bearing #705101520K=0%K=50%K=100%Maximum Bearing Force (kN)100012001400160018002000Crank Angular Velocity (rpm)100012001400160018002000Crank Angular Velocity (rpm)Average Bearing Force (kN)Fig. 19. (a) Maximum and (b) average bearing forces at bearing #7 for 12-counterweight configurations.Bearing #14050607080K=0%K=50%K=100%Bearing #105101520K=0%K=50%K=100%Maximum Bearing Force (kN)100012001400160018002000Crank Angular Velocity (rpm)100012001400160018002000Crank Angular Velocity (rpm)Average Bearing Force (kN)Fig. 20. (a) Maximum and (b) average bearing forces at bearing #1 for eight-counterweight configurations.Table 4Maximum bending stresses for no counterweight configuration and 12-counter-weight configurations with K = 50% and 100%Maximum bending stress (MPa)1000 rpm1200 rpm1350 rpm1675 rpm2000 rpmK = 0%Web #1135.9133.4136.5135127.8Web #12145.7141.7144.2140.3131.8K = 50%Web #1138.4136.8140.9141.2135.9Web #12147.8144.8148.4146.6140.1K = 100%Web #1140.6140.0145.0147.3143.8Web #12149.9147.8152.3152.7148.4Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 95104101Bearing #2120130140150160K=0%K=50%K=100%Bearing #22025303540K=0%K=50%K=100%Maximum Bearing Force (kN)100012001400160018002000Crank Angular Velocity (rpm)100012001400160018002000Crank Angular Velocity (rpm)Average Bearing Force (kN)Fig. 21. (a) Maximum and (b) average bearing forces at bearing #2 for eight-counterweight configurations.Bearing #3100110120130140K=0%K=50%K=100%Bearing #32025303540K=0%K=50%K=100%Maximum Bearing Force (kN)100012001400160018002000Crank Angular Velocity (rpm)100012001400160018002000Crank Angular Velocity (rpm)Average Bearing Force (kN)Fig. 22. (a) Maximum and (b) average bearing forces at bearing #3 for eight-counterweight configurations.Bearing #460708090100110120K=0%K=50%K=100%Bearing #410152025303540K=0%K=50%K=100%Maximum Bearing Force (kN)100012001400160018002000Crank Angular Velocity (rpm)100012001400160018002000Crank Angular Velocity (rpm)Average Bearing Force (kN)Fig. 23. (a) Maximum and (b) average bearing forces at bearing #4 for eight-counterweight configurations.Bearing #5Bearing #5100110120130140K=0%K=50%K=100%2025303540K=0%K=50%K=100%Maximum Bearing Force (kN)100012001400160018002000Crank Angular Velocity (rpm)100012001400160018002000Crank Angular Velocity (rpm)Average Bearing Force (kN)Fig. 24. (a) Maximum and (b) average bearing forces at bearing #5 for eight-counterweight configurations.102Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 95104for beam crankshaft model considering inertial and gas pressureforces and given in Figs. 2026.Maximum bending stresses for two crankshaft configurationsare given in Table 5. When compared to 12 counterweights withc = 0? and K = 50% and K = 100% configurations, the maximumbending stresses for eight counterweights with c = 30?, K = 50%and K = 100% configurations are smaller.7. Summary and conclusionsIn this study, the effect of counterweight configuration on bear-ing load and bending stress is investigated for a 9.0 L in-line six-cylinder diesel engine crankshaft system in the presence of inertialand gas pressure forces. Five different counterweight configura-tions are studied in the analyses: no counterweights, 12-counter-weights with K = 50% and 100%, and eight-counterweights with30? counterweight angle, and K = 50% and 100%. Analyses are car-ried out at an engine speed range of 10002000 rpm.First, 3D solid model of the crankshaft is obtained using Pro/Engineer and MSC.Nastran. The crankshaft is also modeled using ri-gid and beam models of ADAMS/Engine. Main bearing loads are ob-tained for the models using ADAMS, and the results are comparedto each other. It is seen that main bearing loads for beam and elas-tic 3D solid crankshaft models are in good agreement. As a result,because obtaining elastic 3D solid models for different counter-weight configurations is difficult and time consuming, beam modelis used in this work to study the effect of counterweight configura-tion on main bearing loads and crankshaft bending stresses.Using beam model of ADAMS/Engine, main bearing reactionloads are obtained for no counterweight configuration, and 12-counterweight configurations with 50% and 100% balancing rates.It is observed that maximum bearing reaction force increases withincreasing balancing rate. Average bearing loads and maximumweb bending stresses are also calculated. Maximum web bendingstress is higher for 100% balancing rate than for 50% and 0% balanc-ing rates. On the other hand, as the balancing rate increases, theaverage bearing load decreases due to lower inertia force.Similarly, maximum and average bearing loads and bendingstresses are calculated for eight-counterweight configuration witha counterweight angle of 30?. In the case of maximum and averagebearing forces, eight-counterweight configurations shows thesame trend as that of 12-counterweight configurations: the maxi-mum bearing load decreases with decreasing balancing rate,whereas average bearing load increases with decreasing balancingrate. In the case of eight-counterweight configurations withK = 50% and 100%, the maximum bending stress is smaller whencompared to 12-counterweight configurations with K = 50% and100%, respectively.For this specific 9.0 L engine, which has a peak firing pressure of190 bar and rated speed of 2200 rpm, inertial forces are less impor-tant than gas pressure forces for the design of the crankshaft. Addi-tion of counterweights increases maximum bearing load butdecreases average bearing load as shown in Figs. 1326. Maximumbearing load determines maximum stress and its location on theBearing #6100110120130140K=0%K=50%K=100
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