中型普通車床主軸箱設計【Dmax=350mm Nmin=212r-minN=5.5KW φ=1.26 Z=8】

中型普通車床主軸箱設計【Dmax=350mm Nmin=212r-minN=5.5KW φ=1.26 Z=8】,Dmax=350mm Nmin=212r-min N=5.5KW φ=1.26 Z=8,中型普通車床主軸箱設計【Dmax=350mm,Nmin=212r-min,N=5.5KW,φ=1.26,Z=8】,中型 Bebek, Bearing load Bending stress beam is rate, parameter with the most important influence on design of the crankshaft. Results of bearing loads and web bending stresses are tabulated. must overall systems on 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 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 model tions are carried out at engine speed range of 10002000 rpm. Bending stresses at the centres of each web are also calculated. 2. Engine specifications The specifications 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 * Corresponding author. Tel.: +90 212 359 7534; fax: +90 212 287 2456. Advances in Engineering Software 40 (2009) 95104 Contents lists available E-mail address: yasin.yilmazboun.edu.tr (Y. Yilmaz). 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 fly- 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 study on effect of counterweight configuration 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 configurations with a zero degree counterweight angle, and for eight-counterweight configurations with 30C176 counterweight angle for 0%, 50% and 100% counterweight balancing rates. Analyses are carried out using Multibody System Simulation Program, ADAMS/Engine. Simula- 1. Introduction New internal combustion engines power, good fuel economy, small engine harmless as possible to the environment. each component of the engine on its be investigated in detail. Crankshaft tion engines have important influence 0965-9978/$ - see front matter C211 2008 Elsevier Ltd. All doi:10.1016/j.advengsoft.2008.03.009 C211 2008 Elsevier Ltd. All rights reserved. have high engine size, and should be as Therefore, the effect of performance should of internal combus- engine performance 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 flexibility on main bearing loads and can lead to considerable errors. Therefore, an extensive Crankshaft models Balancing rate Both configurations show the same trend. The load from gas pressure rather than inertia forces is the An investigation of the effect of counterweight load and crankshaft bending stress Yasin Yilmaz * , Gunay Anlas Department of Mechanical Engineering, Faculty of Engineering, Bogazici University, 34342 article info Article history: Received 11 February 2008 Received in revised form 17 March 2008 Accepted 24 March 2008 Available online 6 May 2008 Keywords: Counterweight configuration abstract In this study, effects of counterweight stress of an in-line six-cylinder ADAMS. In the analysis, rigid, rigid, beam and 3D solid models analyses. Twelve-counterweight terweight configurations with ing rates, are considered. It with increasing balancing Advances in Engineering journal homepage: rights reserved. configuration on main bearing Istanbul, Turkey mass and position on main bearing load and crankshaft bending diesel engine is investigated using Multibody System Simulation Program, and 3D solid crankshaft models are used. Main bearing load results of are compared and beam model is used in counterweight configuration configurations with a zero degree counterweight angle and eight-coun- 30C176 counterweight angle, each for 0%, 50% and 100% counterweight balanc- found that maximum main bearing load and web bending stress increase and average main bearing load decreases with increasing balancing rate. at ScienceDirect Software cate/advengsoft 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, torsionalflexible crankshaft, beam crankshaft and 3D solid crankshaft. Rigid crankshaft model is mainly used to obtain free forces and torques, and for balancing purposes. Torsionalflexible 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 specifications Unit 9.0 L engine Bore diameter mm 115 Stroke mm 144 Axial cylinder distance mm 134 Peak firing pressure MPa 19 Rated power at speed kW/rpm 295/2200 Max. torque at speed Nm/rpm 1600/12001700 Main journal/pin diameter mm 95/81 Firing order 1-5-3-6-2-4 Flywheel mass kg 47.84 Flywheel moment of inertia kg mm 2 1.57E+9 Mass of TV damper ring kg 4.94 Mass of TV damper housing kg 6.86 Moment of inertia of the ring kg mm 2 1.27E+5 Moment of inertia of the housing kg mm 2 0.56E+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 C1 C2 C3 C4 C5 C6 1 2 Fig. 2. Eight-counterweight arrangement Table 2 Properties of the crank throws Throw 1 Throw 2 Mass (kg) 12.50 9.25 CG position from crank rotation axis (mm) 12.423 31.435 Static unbalance (kg mm) 155.265 290.767 96 Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 95104 C7 C8 3 4 5 6 of the 9.0 L engine crankshaft. Throw 3 Throw 4 Throw 5 Throw 6 12.50 12.50 9.28 12.55 11.967 11.966 31.027 11.702 149.734 149.734 287.871 146.856 Elastic 3D solid model of the crankshaft can be obtained using an additional finite 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 finite 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 Uq 1 where q is the vector of modal coordinates andUis the shape func- tion matrix. 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 Y. Yilmaz, G. Anlas/Advances in Engineering 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 fixed, and fixed boundary normal modes which are the solution of eigenvalue problem by fixing 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 u B u I C26C27 I0 U C U N C20C21 q C q N C26C27 2 where u B and u I are column vectors and represent boundary DOF and interior DOF, respectively. I, 0 are identity and zero matrices, respectively. U C is the matrix of physical displacements of the inte- rior DOF in the constraint modes. U N is the matrix of physical dis- Fig. 3. Model of the crankshaft system. placements of the interior DOF in the normal modes. q C is the column vector of modal coordinates of the constraint modes. q N is the column vector of modal coordinates of the fixed 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 finite 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 first 40 fixed boundary normal 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 is obtained. 3D finite 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: F iR;j m R C1 r R C1 x 2 C1C0sinh j j cosh j k3 where m R is the rotating mass that consists of the mass of crank pin, crank webs and mass of rotating portion of the connecting rod; r R is 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 h j is 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 F CWi;j C0m CWi;j C1 r CWi;j C1 x 2 C1C0sinh j c i;j j cosh j c i;j k hi ; i 1;2 j 1;2;.;6 4 where c i,j is the offset angle of counterweight mass from 180C176 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 U CW K C1U Crank throw m cr-r C1 rC1cosc 2 5 where U CW is the static unbalance of each counterweight, U Crank_throw is the static unbalance of each crank throw, m cr-r is 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 C1 U CW U Crank throw m cr-r C1 rC1cosc 6 For a standard in-line six-cylinder engine crankshaft with three pairs of crank throws disposed at angles of 120C176 that are arranged symmetrical to the crankshaft centre, rotating forces, and first and second order reciprocating forces are naturally balanced. This can be explained by the first and second order vector stars shown in Fig. 4. The six-cylinder crankshaft generates rotating and first Software 40 (2009) 95104 97 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 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 F p;j C0 pD 2 4 C1P cyl;j hC0P cc;j hC138 k; j 1;2;.;6 7 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 0 90 180 270 360 450 540 630 720 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 0 120 240 360 480 600 720 Crank Angle deg Force kN Rigid Beam 3D 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 0 120 240 360 480 600 720 Crank Angle deg Force kN Rigid Beam 3D 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 0 120 240 360 480 600 720 Crank Angle deg Force kN Rigid Beam 3D 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 0 120 240 360 480 600 720 Crank Angle deg Force kN Rigid Beam 3D solid Fig. 9. Forces acting on main bearing #4 for rigid, beam and 3D solid crankshaft models at 1000 rpm engine speed. Bearing #5 125 150 Rigid Bam 3D solid 98 Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 95104 0 25 50 75 100 0 120 240 360 480 600 720 Crank Angle deg Force kN Fig. 10. Forces acting on main bearing #5 for rigid, beam and 3D solid crankshaft models at 1000 rpm engine speed. where D is cylinder diameter, P cyl is the gas pressure in the cylinder and P cc is 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 Bearing #6 0 25 50 75 100 125 150 0 120 240 360 480 600 720 Crank Angle deg Force kN Rigid Beam 3D 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 0 120 240 360 480 600 720 Crank Angle deg Force kN Rigid Beam 3D solid Fig. 12. Forces acting on main bearing #7 for rigid, beam and 3D solid crankshaft models at 1000 rpm engine speed. Bearing #1 40 50 60 70 80 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) Maximum Bearing K=0% K=50% K=100% Force (kN) Fig. 13. (a) Maximum and (b) average bearing forces at Bearing #2 120 130 140 150 160 K=0% K=50% K=100% Maximum Bearing Force (kN) 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) Fig. 14. (a) Maximum and (b) average bearing forces at Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 95104 99 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 flexible 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 #1 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) 0 5 10 15 20 Average Bearing K=0% K=50% K=100% Force (kN) bearing #1 for 12-counterweight configurations. Bearing #2 20 25 30 35 40 K=0% K=50% K=100% 1000 1200 1400 1600 1800 2000 Average Bearing Force (kN) Crank Angular Velocity (rpm) bearing #2 for 12-counterweight configurations. 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 models are generally in good agreement. In bearings 3, 5 and 6, 3D solid model gives larger bear- ing loads at firing positions of the cylinders that are not adjacent to bearing. Because obtaining elastic 3D solid models for different counterweight configurations is difficult and time consuming, and beam model gives equally valid results, beam model is used Bearing #3 100 110 120 130 140 K=0% K=50% K=100% Bearing #3 20 25 30 35 40 K=0% K=50% K=100% Maximum Bearing Force (kN) 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) Average Bearing Force (kN) Fig. 15. (a) Maximum and (b) average bearing forces at bearing #3 for 12-counterweight configurations. Bearing #4 60 70 80 90 100 110 120 K=0% K=50% K=100% Bearing #4 10 15 20 25 30 35 40 K=0% K=50% K=100% Maximum Bearing Force (kN) 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) Average Bearing Force (kN) Fig. 16. (a) Maximum and (b) average bearing forces at bearing #4 for 12-counterweight configurations. Bearing #6 120 130 140 K=0% K=50% K=100% Bearing #6 35 40 45 50 K=0% K=50% K=100% Bearing #5 100 110 120 130 140 K=0% K=50% K=100% Bearing #5 20 25 30 35 40 K=0% K=50% K=100% Maximum Bearing Force (kN) 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) Average Bearing Force (kN) Fig. 17. (a) Maximum and (b) average bearing forces at bearing #5 for 12-counterweight configurations. 100 Y. Yilmaz, G. Anlas/Advances in Engineering Software 40 (2009) 95104 100 110 Maximum Bearing Force (kN) 1000 1200 1400 1600 1800 2000 Crank Angular Velocity (rpm) Fig. 18. (a) Maximum and (b) average bearing forces at 20 25 30 1000 1200 1400 1600 1800 2000 Average Bearing Force (kN) Crank Angular Velocity (rpm) bearing #6 for 12-counterweight con