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An investigation of the effect of counterweight confi guration on main bearing load and crankshaft bending stress Yasin Yilmaz*, Gunay Anlas Department of Mechanical Engineering, Faculty of Engineering, Bogazici University, 34342 Bebek, Istanbul, Turkey a r t i c l ei n f o Article history: Received 11 February 2008 Received in revised form 17 March 2008 Accepted 24 March 2008 Available online 6 May 2008 Keywords: Counterweight confi guration Crankshaft models Balancing rate Bearing load Bending stress a b s t r a c t In this study, effects of counterweight mass and position on main bearing load and crankshaft bending stress 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 of rigid, beam and 3D solid models are compared and beam model is used in counterweight confi guration analyses. Twelve-counterweight confi gurations with a zero degree counterweight angle and eight-coun- terweight confi gurations 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 increase with increasing balancing rate, and average main bearing load decreases with increasing balancing rate. Both confi gurations show the same trend. The load from gas pressure rather than inertia forces is the parameter with the most important infl uence on design of the crankshaft. Results of bearing loads and web bending stresses are tabulated. ? 2008 Elsevier Ltd. All rights reserved. 1. Introduction New internal combustion engines must have high engine power, good fuel economy, small engine size, and should be as harmless as possible to the environment. Therefore, the effect of each component of the engine on its overall performance should be investigated in detail. Crankshaft systems of internal combus- tion engines have important infl uence on engine performance being the main part responsible for power production. Crankshaft system mainly consists of piston, piston pin, con- necting rod, crankshaft, torsional vibration (TV) damper and fl y- wheel. Counterweights are placed on the opposite side of each crank to balance rotating inertia forces. In general, counterweights are designed for balancing rates between 50% and 100%. For acceptable maximum and average main bearing loads, mass of counterweights and their positions are important. Maximum and average main bearing loads of an engine depend on cylinder pres- sure, counterweight mass, engine speed and other geometric parameters of the crankshaft system. Studies on crankshaft of internal combustion engines mainly fo- cus on vibration and stress analyses 19. Although stress analy- ses of crankshafts are available in literature, there are few studies on the effect of counterweight confi guration on main bear- ing loads and crankshaft stresses. Sharpe et al. 10 studied balanc- ing of the crankshaft of a V-8 engine using a rigid crankshaft model and optimized counterweights to minimize main bearing loads. Stanley and Taraza 11 obtained maximum and average main bearing loads of four and six-cylinder symmetric in-line engines using a rigid crankshaft model and estimated ideal counterweight mass that resulted in acceptable maximum bearing load. Rigid crankshaft models that are used in counterweight analyses do not consider the effect of crankshaft fl exibility on main bearing loads and can lead to considerable errors. Therefore, an extensive study on effect of counterweight confi guration on main bearing loads and crankshaft stresses is still needed. In this study, counterweight positions and masses of an in-line six-cylinder diesel engine crankshaft system are studied. Maxi- mum and average main bearing forces and crankshaft bending stresses are calculated for 12-counterweight confi gurations with a zero degree counterweight angle, and for eight-counterweight confi gurations with 30? counterweight angle for 0%, 50% and 100% counterweight balancing rates. Analyses are carried out using Multibody 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 specifi cations The specifi cations of in-line six-cylinder diesel engine are given in Table 1. The 9.0 L engine crankshaft has eight counterweights at crank webs 1, 2, 5, 6, 7, 8, 11 and 12. 3D solid model of the crank- shaft is obtained using Pro/Engineer and is shown in Fig. 1. Sche- matic representation of the crankshaft is given in Fig. 2. Static 0965-9978/$ - 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: .tr (Y. Yilmaz). Advances in Engineering Software 40 (2009) 95104 Contents lists available at ScienceDirect Advances in Engineering Software journal homepage: unbalance of each crank throw (with and w/o counterweights) is determined using Pro/Engineer and is given in Table 2. The balanc- ing system data for the crank train are given in Table 3. 3. Modeling of crankshaft system Using ADAMS/Engine, a crankshaft can be modeled in four dif- ferent ways: rigid crankshaft, torsionalfl exible crankshaft, beam crankshaft and 3D solid crankshaft. Rigid crankshaft model is mainly used to obtain free forces and torques, and for balancing purposes. Torsionalfl exible crankshaft model is used to investi- gate torsional vibrations where each throw is modeled as one rigid part, and springs are used between each throw to represent tor- sional stiffness. Beam crankshaft model is used to represent the torsional and bending stiffness of the crankshaft. Using beam mod- el bending stresses at the webs can be calculated 12. Table 1 Engine specifi cations Unit9.0 L engine Bore diametermm115 Strokemm144 Axial cylinder distancemm134 Peak fi ring pressureMPa19 Rated power at speedkW/rpm295/2200 Max. torque at speedNm/rpm1600/12001700 Main journal/pin diametermm95/81 Firing order1-5-3-6-2-4 Flywheel masskg47.84 Flywheel moment of inertiakg mm21.57E+9 Mass of TV damper ringkg4.94 Mass of TV damper housingkg6.86 Moment of inertia of the ringkg mm21.27E+5 Moment of inertia of the housingkg mm20.56E+5 Main Bearing #1 Main Bearing #2 Main Bearing #3 Main Bearing #4 Main Bearing #5 Main Bearing #6 Main Bearing #7 Counterweights Fig. 1. 3D solid model of the crankshaft. C3, C4, C5, C6 C1, C2, C7, C8 1, 6 3, 4 2, 5 C1C2 C3C4 C5C6 C7C8 1 2 3 4 5 6 Fig. 2. Eight-counterweight arrangement of the 9.0 L engine crankshaft. Table 2 Properties of the crank throws Throw 1Throw 2Throw 3Throw 4Throw 5Throw 6 Mass (kg)12.509.2512.5012.509.2812.55 CG position from crank rotation axis (mm)12.42331.43511.96711.96631.02711.702 Static unbalance (kg mm)155.265290.767149.734149.734287.871146.856 96Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 95104 Elastic 3D solid model of the crankshaft can be obtained using an additional fi nite element program. The procedure is lengthy and time consuming and usually one ends up with degrees of free- dom in order of millions. To simplify the fi nite element model, modal superposition technique is used. The elastic deformation of the structure is approximated by linear combination of suitable modes which can be shown as follows: u Uq1 where q is the vector of modal coordinates and U is the shape func- tion matrix. An elastic body contains two types of nodes, interface nodes where forces and boundary conditions interact with the structure during multibody system simulation (MSS), and interior nodes. In MSS the position of the elastic body is computed by superposing its rigid body motion and elastic deformation. In ADAMS, this is performed using Component Mode Synthesis” technique based on CraigBampton method 13,14. The component modes contain static and dynamic behavior of the structure. These modes are con- straint modes which are static deformation shapes obtained by giving a unit displacement to each interface degree of freedom (DOF) while keeping all other interface DOFs fi xed, and fi xed boundary normal modes which are the solution of eigenvalue problem by fi xing the entire interface DOFs. The modal transforma- tion between the physical DOF and the CraigBampton modes and their modal coordinates is described by 15 u uB uI ? I0 UCUN ? qC qN ? 2 where uBand uIare column vectors and represent boundary DOF and 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 the column vector of modal coordinates of the constraint modes. qNis the column vector of modal coordinates of the fi xed boundary nor- mal modes. To obtain decoupled set of modes, constrained modes and normal modes are orthogonalized. Elastic 3D solid crankshaft model of the 9.0 L engine is obtained in MSC.Nastran using modal superposition technique. First, 3D so- lid model of the crankshaft that is shown in Fig. 1 is exported to MSC.Nastran and fi nite element model of the crankshaft, which is characterized by approximately 300,000 ten-node tetrahedral ele- ments and 500,000 nodes is obtained. The modal model of the crankshaft is developed with 32 boundary DOFs associated with 16 interface nodes. Constrained modes obtained from static analy- sis correspond to these DOFs. Flexible crankshaft model is obtained through modal synthesis considering the fi rst 40 fi xed boundary normal modes. Therefore fl exible crankshaft model is character- ized by a total of 72 DOFs. This model is exported to ADAMS/En- gine and crankshaft system model that is shown in Fig. 3 is obtained. 3D fi nite element model is run with ADAMS. 4. Forces acting on crankshaft system and balancing Forces in an internal combustion engine may be divided into inertia forces and pressure forces. Inertia forces are further divided into two main categories: rotating inertia forces and reciprocating inertia forces. The rotating inertia force for each cylinder can be written as shown below: FiR;j mR? rR? x2? ?sinhjj coshjk3 where mRis the rotating mass that consists of the mass of crank pin, crank webs and mass of rotating portion of the connecting rod; rRis the distance from the crankshaft centre of rotation to the centre of gravity of the rotating mass, x is angular velocity of the crankshaft, and hjis the angular position of each crank throw with respect to Top Dead Centre” (TDC). If there are two counterweights per crank throw, each counterweight force is given by 11 FCWi;j ?mCWi;j? rCWi;j? x2? ?sinhj ci;jj coshj ci;jk hi ; i 1;2 j 1;2;.;6 4 where 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 is required to accomplish an assessed balancing rate is UCW K ? UCrank throw mcr-r? r ? cosc 2 5 whereUCWisthestaticunbalanceofeachcounterweight, UCrank_throwis the static unbalance of each crank throw, mcr-ris the mass of connecting rod rotating portion, r is the crank radius and K is the balancing rate of the internal couple due to rotating forces. From this formula follows the balancing rate for a given crankshaft and a given counterweight size: K 2 ? UCW UCrank throw mcr-r? r ? cosc 6 For a standard in-line six-cylinder engine crankshaft with three pairs of crank throws disposed at angles of 120? that are arranged symmetrical to the crankshaft centre, rotating forces, and fi rst and second order reciprocating forces are naturally balanced. This can be explained by the fi rst and second order vector stars shown in Fig. 4. The six-cylinder crankshaft generates rotating and fi rst and second order reciprocating couples in each crankshaft half that balance each other but which result in internal bending moment. At high speeds, the two equally directed crank throws, 3 and 4 Table 3 Crankshaft system data Crank radius (mm)72 Connecting rod length (mm)239 Mass of complete piston (kg)3.42 Connecting rod reciprocating mass (kg)0.92 Reciprocating mass (total per cylinder) (kg)4.32 Connecting rod rotating mass (kg)2.01 Fig. 3. Model of the crankshaft system. Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 9510497 yield a high rotating load on centre main bearing. The rotating inertia force of each cylinder is usually offset at least partially by counterweights placed on the opposite side of each crank. In gen- eral, the counterweights are designed for balancing rates between 50% and 100% of the internal couple. Gas forces in cylinders are acting on piston head, cylinder head and on side walls of the cylinder. These forces are equal to Fp;j ? pD2 4 ? Pcyl;jh ? Pcc;jh?k;j 1;2;.;67 1, 6 2, 5 3, 4 3, 4 1, 6 2, 5 Fig. 4. First and second order vector stars. 0 20 40 60 80 100 120 140 160 180 200 090180270360450540630720 Crank Angle (degree) Pressure (bar) 1000rpm 1200rpm 1350rpm 1675rpm 2000rpm Fig. 5. Gas pressure values at different engine speeds for the 9.0 L engine. Bearing #1 0 25 50 75 100 125 150 0120240360480600720 Crank Angle deg Force kN RigidBeam3D solid Fig. 6. Forces acting on main bearing #1 for rigid, beam and 3D solid crankshaft models at 1000 rpm engine speed. Bearing #2 0 25 50 75 100 125 150 175 0120240360480600720 Crank Angle deg Force kN RigidBeam3D solid Fig. 7. Forces acting on main bearing #2 for rigid, beam and 3D solid crankshaft models at 1000 rpm engine speed. Bearing #3 0 25 50 75 100 125 150 0120240360480600720 Crank Angle deg Force kN RigidBeam3D solid Fig. 8. Forces acting on main bearing #3 for rigid, beam and 3D solid crankshaft models at 1000 rpm engine speed. Bearing #4 0 25 50 75 100 125 150 0120240360480600720 Crank Angle deg Force kN RigidBeam3D solid Fig. 9. Forces acting on main bearing #4 for rigid, beam and 3D solid crankshaft models at 1000 rpm engine speed. Bearing #5 0 25 50 75 100 125 150 0120240360480600720 Crank Angle deg Force kN RigidBam3D solid Fig. 10. Forces acting on main bearing #5 for rigid, beam and 3D solid crankshaft models at 1000 rpm engine speed. 98Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 95104 where D is cylinder diameter, Pcylis the gas pressure in the cylinder and 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 at different engine speeds are given in Fig. 5. Pressure curves are ob- tained using AVL/Boost engine cycle calculation program which simulates thermodynamic processes in the engine taking into ac- count one dimensional gas dynamics in the intake and exhaust sys- tems 16. 5. Main bearing loads: comparison of crankshaft models Main bearing loads are calculated using ADAMSs rigid, beam and 3D solid crankshaft models and compared. In the rigid model, no vibration effects are considered which can lead to considerable errors if vibration effects have a major role on the system (like in multithrow crankshafts). To consider vibration effects beam crank- shaft model is used and main bearing loads and bending stresses at webs are calculated. Rigid model assumes crankshaft to be stati- cally determinate and reaction force of any given bearing depends on the load exerted on the throws adjacent to that bearing. Beam model assumes the crankshaft to be statically indeterminate and the load exerted on a throw affects all bearings. Analyses are car- ried out at an engine speed range of 10002000 rpm. A more sophisticated 3D solid hybrid model that combines FE with ADAMS is used to check the results obtained by beam model. Maximum main bearing load occurs at bearing number two at an engine speed of 1000 rpm, therefore results are plotted in Figs. 612 for 1000 rpm only. Rigid crankshaft model overestimates the maximum main bearing load at bearings 1 and 7 with respect to beam and fl exible crankshaft models. However it underestimates the maximum main bearing load at other bearings. For example at bearing 2, beam model gives a maximum main bearing load that is 50% more than that of rigid models because the beam model as- sumes the crankshaft to be statically indeterminate and considers Bearing #6 0 25 50 75 100 125 150 0120240360480600720 Crank Angle deg Force kN RigidBeam3D solid Fig. 11. Forces acting on main bearing #6 for rigid, beam and 3D solid crankshaft models at 1000 rpm engine speed. Bearing #7 0 25 50 75 100 125 150 0120240360480600720 Crank Angle deg Force kN RigidBeam3D solid Fig. 12. Forces acting on main bearing #7 for rigid, beam and 3D solid crankshaft models at 1000 rpm engine speed. Bearing #1Bearing #1 40 50 60 70 80 100012001400160018002000100012001400160018002000 Crank Angular Velocity (rpm)Crank Angular Velocity (rpm) Maximum Bearing K=0%K=50%K=100% 0 5 10 15 20 Average 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 confi gurations. Bearing #2 120 130 140 150 160 K=0%K=50%K=100% Bearing #2 20 25 30 35 40 K=0%K=50%K=100% Maximum Bearing Force (kN) 100012001400160018002000 Crank Angular Velocity (rpm) 100012001400160018002000 Crank Angular Velocity (rpm) Average Bearing Force (kN) Fig. 14. (a) Maximum and (b) average bearing forces at bearing #2 for 12-counterweight confi gurations. Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 9510499 bending vibrations. Maximum main bearing load difference of beam and 3D solid models is approximately 5%. Main bearing loads for beam and 3D solid crankshaft model