Design, Optimization and Finite Element Analysis of Crankshaft

Transcription

1 ISSN Design, Optimization and Finite Element Analysis of Crankshaft # Bhalerao Ganesh Nandkumar, # Prof. Zope Sanjay Bhaskar bhaleraoganesh35@gmail.om P. G. Student, Mehanial (Design Engineering), Prinipal Sahyadri Valley College of Engineering & Tehnology Rajuri, Junnar Pune, Maharashtra-4409, India. ABSTRACT In this paper disus the modal analysis of a 4-ylinder diesel engine rankshaft using finite element analysis. The design of rankshaft onsiders dynami loading and optimization satisfying the requirement of automobile speifiation. Three-dimension model of diesel engine rankshaft was reated using Pre-software. The finite element analysis (FEM) software Abaqus is used to analyze the vibration modal of the rankshaft. The analysis is done on different materials whih are based on their omposition. In the analysis of rankshaft maximum stress point and deformation are found. This projet is an appliation for optimizing and improving engine design. Keywords Optimization. Fatigue failure, Solid modeling, FEM Analysis, Dynami loading, ARTICLE INFO Artile History Reeived :8 th November 05 Reeived in revised form : 9 th November 05 Aepted : st November, 05 Published online : nd November 05 I. INTRODUCTION 05, IERJ All Rights Reserved Page

2 In Internal Combustion Engine Crankshaft play an important role to onvert the reiproating motion of the piston into rotational motion with the help of four link mehanism. The rankshaft is must be strong enough to take the downward fore of the power stroked without exessive bending so mostly the life and reliability of engine depend on the strength of rankshaft. A Crankshaft is a ompliate ontinuous struture; it onsist of two or more entrally loated oaxial ylindrial journals (shaft) and one or more offset ylindrial rankpin journals (rod). The rankshaft main journals rotate in a set of supporting bearings, ausing the offset rod journals to rotate in a irular path around the main journal enters. Need When engine is working, a power impulse hits a rankpin toward the front of the engine and at end of the power stroke torsional vibration appears. If it is not ontrol it harms the rankshaft; also ontinuously hitting of power impulse breaks the rankshaft. Life of the engine is ensurie to Strength alulation of rankshaft. In past to alulate the strength, stress of rankshaft Beam and spae frame model are used. The number of a node is limited in these models and It is onventional, time- onsuming, a non-auray method to find the strength alulation. With the development of advaned and number of simulation method, more and more design of the rankshaft is using in finite element method (FME) to alulate the stress of rankshaft. The appliation of numerial simulation is help design engineer for the design of rankshaft to effiiently improve the proess development and avoiding the ost and limitations. Causes of rankshaft failure In Internal Combustion engines, the transient load of maximum ylinder gas pressure is (whih is dynami in nature with respet to magnitude and diretion.) transmitted to rankshaft through the onneting rod, However Crankshaft onvert reiproating motion of the piston along with onneting rod to the rotating system of omponents. Due to torsion the dynami load and rotating system exerts ontinues repeated bending and shear stress on rankshaft, that are ommon stresses ating on rankshaft and it is mostly responsible for rankshaft fatigue failure. Hene, fatigue strength and life assessment is an important phenomenon in rankshaft development. Fatigue failure is a omplex physial proess whih is governed by a great number of parameters related to, loal geometry and material properties of the strutural region surrounding the rak growth path. It is ommonly reognized that it is impossible for a physial model to aount for all fatigue influening parameters, thus a many of approximate models have been oneived for pratial fatigue assessments. Fores imposed on a rankshaft In rankshaft rankpin is behaved like a beam with a distributed load along its overall length that varies with rank position. In rankshaft design of eah web right and left handed are like a antilever beam subjeted to bending and twisting. Bearing is subjets to twisting. Bending auses tensile and ompressive stresses. Twisting auses shear stress and due to shrinkage of web onto the journal ompressive stresses are set up in journal and tensile hoop stresses in the web. Material Seletion of rankshaft To manufature the rankshaft, urrently in industry material use are forged steel and aste iron. To selet the best material for manufaturing of rankshaft some riteria or parameter is onsidered suh as performane of this material with respet to stati, yli, and impat loading. A omprehensive omparison study of material is onsidered for manufaturing proess with respet to mehanial properties, manufaturing aspets, and finished ost of rankshaft. The main objetive of material seletion is to give or to manufature the omponent has desired geometry without any external or internal defet in manufaturing proess. Several operation are arried in manufaturing proess. Initially we selet materials for rankshaft for analysis are Strutural steel, SAE 4340, EN30B, Cast Iron, C-70 Alloy Steel. After FEA analysis we selet one of the best material onsidering parameters like Deformation (mm), Maximum value of Mass (Kg), Max Prinipal Stress (N/mm ), Maximum Prinipal Strain, Von Mises Stress (N/mm ) Maximum Value. II. OBJECTIVES In ontinuously running of an engine the problem ours at in ylinder engine rankshaft is formation of raks after ertain time period. Overall objetive of present projet work is as follow:. To find out the failure reason of rankshaft with the help of previous researh. Design of the rankshaft by assuming rankshaft is a beam with two or more supports.. In the design of rankshaft or heked at least for two rank position one when the bending movement is maximum and the other when the twisting moment is a maximum. 3. After mathematial alulation or with the help of design alulation we reate a Three-dimension model of diesel engine rankshaft by using modeling CATIA software. 4. The omputational (FEA) analysis is done on five seleted material onsidering some parameter whih are based on their omposition. 5. In the analysis of rankshaft maximum stress point and deformation areas are found. After FEA analysis we selet one material from seleted materials.. After seletion the material we manufature the rankshaft by forging proess. Condut experimental analysis on different engine speed. 7. Results from FEA are verified by strain gauge attahed to several loations on rankshaft in experimental analysis. The result shows in this work are using for optimizing and improving engine design III. LITERATURE REVIEW Rajesh M. Metkar et al. [] they present the work is based on omparative studies of two methods of fatigue life assessment of a single ylinder diesel engine rankshaft. 05, IERJ All Rights Reserved Page

3 One is frature mehanis approah by linear elasti frature mehanis (LEFM) and other is reently developed ritial distane approah (CDA). These methods shows rak growth, time required for failure and other parameters essential in life and reliability of rankshaft. These methods are based on the frature mehanis. Analysis is done in Ansys and ncode ommerial software, Analysis result are also been used for prediting the fatigue life but are based on the stress and strain method, hene are not been used for omparative fatigue life predition. Milan Saga, Peter Kopes et al. [] determined of fatigue lifetime of strutural materials during by multiaxial yli loading. The theoretial work fouses on fatigue and riteria for evaluation of the multi-axial fatigue lifetime. The experimental work deals with modeling of ombined bending - torsion loading and determining the number of yles to frature in region low-yle fatigue and also during of the loading with the sinusoidal wave form under in phase. Adeknle A. et al. [3] design a shaft under various load onditions using Computer Aided Design, and results obtained are proved that it saves wastage of materials, time onsumption in FEA of rankshaft, and a software program was developed using the formulas initially derived and a numerial proedure for omputing the defletion using the double integration methods. Solanki et al. [4] present the researh work on rankshaft design and optimization. Seletion of materials, manufaturing proess for rankshaft, failure analysis, design onsideration et. are studied. In design of rankshaft onsiders the dynami loading ondition and optimization of shaft satisfying the requirements of the automobile speifiation with minimize ost and size effetiveness. There onlusion is the rak grows faster on the free surfae while the entral part of the rak front beomes straighter. Fatigue is the main fator for failure of the rankshaft. Meng et al. [5] they worked on a 4 ylinder rankshaft. Model is reate in modeling software and analysis is done FEM software and for vibration modal and distortion and stress status of rank throw ANSYS software is used. Analysis result shows the relationship between frequeny and the vibration modal. This used for theoretial foundation of the optimization and improvement of engine design. Maximum deformation appears at the entre of the rankpin nek surfae. The maximum stress loation are appears at the fillet between the rankshaft journal and rank heeks, and near the entral point journal. The rankshaft deformation is mainly bending deformation under the lower frequeny. Maximum deformation areas are loating at the link between main bearing journal and rankpin and rank heeks. So, the area prone to appear the bending fatigue rak. Rinkle Garg, Sunil Baghla [] they work on a ast iron single ylinder engine rankshaft. A stati analysis is done on a ast iron rankshaft. 3D model of rankshaft is reated in ProE software. FEA is done and obtain result shows the variation of the stress magnitude at ritial loation. Obtained results are used in optimization of rankshaft. They onlude the strength of the rankshaft as the maximum limits of stresses, total deformation and strain is dereased. The weight of the rankshaft is also dereased by 3934g also derease the inertia fore. Weight redued hene the ost of rankshaft is redued and inrease the engine performane. Gongzhi et al. [7] he studied on a dynami strength analysis of rankshaft for marine diesel engine. The finite element models of rankshaft, bearing, piston and onneting rod is reate in ANSYS and simplified by sub struture tehnique. FEA analysis results are ompared with single rankshaft strength analysis; non linear multibody dynamis method is loser to the atual boundary onditions. They researh work show that under normal operating onditions, the maximum stress of rankshaft ours on journal fillet. Yingkui and Zhibo [8] they reate a three dimensional model of a diesel engine rankshaft by using Pro E software. The finite element analysis is done in ANSYS under extreme operation onditions and giving the boundary ondition stress distribution regions are found on the rankshaft surfae. The rank stress hange model and suggest the improvement method for the rankshaft struture design. There researh work shows that the high stress region mainly onentrates in the Knukles of the rank arm & the main journal, and the rank arm and the onneting rod journal, whih is the area most easily broken. Balamurugan et al. [9] done modeling and optimization analysis of rankshaft and estimate the ompressive study of the fatigue performane. They ompare two rankshafts, ast iron and forged steel, from a single ylinder four stroke engines. Finite element analysis is done an obtained result are shows the variation of stress magnitude at ritial point. The dynami analysis is done analytially and results are verified by simulation in ANSYS tool. In the optimization proess geometry hanges ompare with the urrent engine, fillet rolling and results in inreased fatigue strength and redued ost of the rankshaft, without hanging onneting rod and engine blok. Analysis results in testing the rankshaft under stati load ontaining stresses and deformation. Forged iron rankshaft is able to withstand the stati load, it is onluded that there is no objetion from strength point of view also, in the proess of replaing the ast iron rankshaft by forged steel rankshaft. Jian et al. [0] work on three dimensional model of 380 diesel engine rankshaft. They used ProE and ANSYS as FEA tools improvement of engine design. Model is an imported to ANSYS software, Material properties, onstraints boundary ondition and mehanial boundary ondition of the 380 diesel engine rankshaft determined. Finally the strain and the stress loation of rankshaft are alulated and result ombined with maximum stress point and deformation area. They found out the maximum deformation ours in the end of the seond ylinder balane weight. Bin et al. [] three dimensional models of 480 diesel engine rankshaft and rankpin is reated through the Pro E software. For finite element analysis ANSYS is used to analyze the vibration model and the distortion and the stress status of the rankpin. These results explain the relationship between the frequeny and the vibration model. Stress analysis of rankpin provides the maximum 05, IERJ All Rights Reserved Page 3

4 deformation and maximum stress point. The rankshaft deformation is mainly the bending deformation under lower frequeny. The maximum deformation is loated at the link between main bearing journal and rankpin and rank heeks. So the bending rak was prone to appear at this area. The maximum deformation appears the bottom of rank heek. The maximum stress appears at the transition radius of rank heek and onneting rod journal. IV. DESIGN CALCULATION In the design of the rankshafts, it is assumed that the rankshaft is a beam with two or more supports. Every rankshaft must be designed or heked at least for two rank positions,. When the bending moment is maximum.. When the twisting moment is a maximum. For initial design we onsider enter rankshaft for a single ylinder engine for following data: Table No. 0: given data onsider for design alulation When the rank has turned through 35 o from the top dead enter, the pressure on the piston is N/m m and the torque on the rank is maximum. The ratio of the onneting road length to the rank radius is 5. Assuming suitable data when is required. We design the rankshaft for two position of the rank Steps:- Design of the rankshaft when the Crank is at Dead Center (Maximum bending moment) We know that piston gas load () (40)5.8 PF Dp 44 Fp Dp (40) kN kn Assume that the distane (b) between the bearing and is equal to twie the piston diameter (D) 800 bb 400 We Know that due to the piston gas load, there will be two horizontal reations H and H at bearing and respetively, suh that pfb H 57. kn b 80 pfb H 57. kn b 80 And Assume that the length of the main bearing to be equal, i.e. /. We know that due to the weight of the flywheel ating downwards, there will be two vertial reations V and V 3 at bearings and 3 respetively, suh that W WW / 50 V 5 kn W WW / 50 V3 5 kn And ( T T ) Due to the resultant belt tension ating horizontally, there will be two horizontal reation H and ' H 3 respetively, suh that ' ( TTTT ) ( )/( TT ) H.5/3.5 kn ' ( TTTT ) ( )/( TT ) H3.5/3.5 kn And Bore D 400 mm Stroke L 00 mm Engine Speed N 00 rpm Mean Effetive Pressure P m 0.5 N/mm Maximum Combustion Pressure p.5 N/m m Weight of Flywheel used as pulley W 50 kn Total Belt Pull.5 kn Now the various parts of the rankshaft are designed suh as: (a) Design of rankpin Let, d Diameter of the rankpin in mm; l Length of the rankpin in mm; and b Allowable bending stress for the rankpin, It may assumed that as 75 MPa or N/mm We know that the )bending moment at the enter of the rankpin, MHb k We also know that M () d 3 b Thefore, for solving the above equation we get d say 05 m Length of the rankpin is Fp l say m dp b (b) Design of left hand rank web We know that thikness of thikness of the rank web, t0.5 d.35 m t 39. say 40 m And width of the rank web, w.5 d.7 m ' 05, IERJ All Rights Reserved Page 4

5 w 43.3 say 45 We know that maximum bending moment on the rank web, l t M Hb M398 kn mm 3 Setion modulus, Z wt 800 m Bending stress, Z M b 49./ We know that diret ompressive stress on the rank web, wt H 4.58/ Total stress on the rank web / b Sine the total stress on the rank web is less than the allowable bending stress of the 75 MPa, therefore the design of the left hand rank web is safe. () Design of right hand rank web From the balaning point of view, the dimensions of the right hand rank web are made equal to the dimensions of the left hand rank web is safe. (d) Design of shaft under flywheel d Diameter of the shaft in mm. Let, s Sine the length of the main bearings are equal, therefore b l lll 35 3 t m Assuming width of the flywheel as 300 mm, we have m Allowing spae for gearing and learane, let us take 800mm m We know that bending moment due to the weight of flywheel, WMV 00 3 And bending moment on the shaft, ' TMH.30 3 Resultant bending moment on the shaft, MMM S()()0.80 W T We also know that bending moment on the shaft ( M S ) sd 34.7 say 35 m StepsII:- Design of the rankshaft when the Crank is at an angle of maximum twisting moment. ' Fp Dp (40)5.8 kn 4 4 In order to find the thrust in the onneting rod ( F Q ), we should first find out the angle of inlination of the onneting rod with the line of stroke ( ). We know that, 0 sin sin35 sin 0.47 lr 5 sin(0.47).58 We know that thrust in onneting rod, FQ 5.8 FQ, 0.5 kn os os.58 Tangential fore ating on the rankshaft, FF 00 TQ sin().5sin(35.58) FkN 84 T And radial fore, FF 00 RQ os().5sin(35.58) FkN 94. R Due to tangential fore ( F T ), there will be two reations at the bearings and, suh that Fb Fb H H b b T T T T 4 kn Due to the radial fore ( F R ),there will be two reations at the bearings and, suh that Fb Fb H H b b R T R R 47.3 kn Now the various parts of the rankshaft are designed suh as: (a) Design of rankpin d Diameter of the rankpin in mm; Let, We know that the bending moment at the enter of the rankpin, MHb R k And the twisting moment on the rankpin, THr 4300 T k Equivalent twisting moment on the rankpin, TMT k e ()().74 We know that equivalent twisting moment,.740 () d Take 35MPa d 49mm 3 Sine this value of rankpin diameter is less than the already alulated value of d 05mm (d) Design of shaft under flywheel d Diameter of the shaft in mm. Let, s The resultant bending moment on the shaft will be same as alulated sm And the twisting moment on the shaft, TFr ST Equivalent twisting moment on the shaft, 05, IERJ All Rights Reserved Page 5

6 TMT k e ()()7.4 s s We know that equivalent twisting moment ( T e ), 7.40 () sd 35 m / 3 From above, we see that by taking the already alulated d 35 mm, the indued shear stress is more value of s than the allowable shear stress of 3 to 4 MPa. Hene, the value of d s is alulated by taking 35 m / in above equation, ()35 sd d 58 say 0 s () Design of shaft at the juntion of right hand rank web Let, ds Diameter of the shaft at the junture of the right hand rank arm. We know that the pressure fore at the bearing, RH ( )( H )3.3 kn T R Bending moment at the junture of the right hand rank arm, lt lt MRb S F Q SM 0 N m And twisting moment at the juntion of the junture of the right hand rank arm, TFr ST 5.0 Equivalent twisting moment at the junture of the right hand rank arm, TMT ()()9.850 e S s ( )4 Sd Take 4MPa sd 53.5 say 55 (d) Design of right hand rank web Let, br Bending stress in the radial diretion; and bt = Bending stress in the tangential diretion We know that bending moment due to the radial omponent of F Q, lt MHb RR.940 We also know that bending moment, MR br ZbR wt 4.9 m / br We know the bending moment due to the tangential omponent of ( F Q ) d MFr s TT 8.90 We also know that bending moment, M Z T bt 3.35/ N m bt Diret ompressive stress, FR.38/ d wt And total ompressive stress We know that twisting moment on the arm, l THb T And shear stress on the arm, 4.5 T.7 MPa wt We know that total or maximum ombined stress, C ( C ) max () 4 ( ) MPa Cmax Sine the maximum ombined stress is within the safe limits, therefore, the diretion w 45 mm is aepted. (e) Design of left hand rank web The dimension for the left hand rank web may be made same as for right hand rank web. (f) Design of rankshaft bearings Sine the bearing is the most heavily loaded, therefore, only this bearing should be heked for bearing pressure. We know that the total reation at bearing, PF WTT R R kn Total bearing pressure R ld S 3.7/ Sine this bearing pressure is less than the safe limit of 5 to 8 N / mm, therefore the design is safe. V. 3-D MODELING OF CRANKSHAFT A. Solid modeling. CATIA modeling software is use to reate 3D model of rankshaft with the help of slandered dimension. This Computer Aided Drawing inludes following proedure.. Skether. Part modeling (part design) 3. Advaned Part Design 4. Surfae Design 5. Assembly Design. Drafting 05, IERJ All Rights Reserved Page

7 Fig. 0: 3D modelling of Crankshft using CATIA B. Finite Element Analysis Due to the omplex struture of rankshaft and onsidering various loads ating on it; finding the strength of rankshaft and stress loation and deformation areas by using lassial alulation method has limitations. Finite Element Method is a numerial alulation method is used to analysis suh problems. In operating ondition of rankshaft the rankpin fillet and journal fillet are the weakest parts. Therefore these parts are mainly evaluated for safety operating. For finite element analysis (FEM) Abaqus/ANSYS is use to strutural analysis is done on seleting five material by giving the input and we selet one material onsidering parameters like Deformation (mm), Maximum value of Mass (Kg), Max Prinipal Stress (N/mm ), Maximum Prinipal Strain, Von Mises Stress (N/mm ) Maximum Value. C. Need of Finite Element Method There are number of needs of finite element method. But we are onsidering some basi needs. i) To redue the amount of prototype testing. ii) To simulate design that is not suitable for prototype testing. iii) Cost saving. iv)time saving. D. Basi Steps in F.E.M. Basially following steps are onsidered in finite element analysis. i) Mesh generation. ii) Seleting the displaement funtion. iii) Develop the element matries and equations. iv) Assemble element matries. v) To find the unknowns. vi) Interpretation of the results. E. Meshed model of rankshaft Fig. 0: Meshed model of Crankshft Above figure is the meshed model of rankshaft in analysis. The Mesh Generation is the first Step in Finite Element Method. In this steps the objet whih is modeled in modeling software are divided into number of small parts. In meshing number of nodes formed and number of elements are formed. After giving foresee and required parameter the effet of fores on eah portion of the objet is not same. The purpose of meshing is to perform the analysis on eah small division separately. F. loading and boundary ondition. Boundary onditions play an important role in finite element analysis. Crankshaft is onstrits with a ball bearing from one side and with a journal on other side. The ball bearing is press fit to the rankshaft and does not allow the rankshaft to have any motion other than rotation about its main axis. Sine 80 degrees of the surfae faing the load diretion onstrits the motion of the rankshaft. 3 Fig. 03:load and boundary ondition applied on rankshaft. Stati strutural analysis Strutural analysis is a proess to analysis a strutural system in order to predit the responses of the real struture under the exitation of loading and external environment during the operation of the struture. The purpose of a strutural analysis is to ensure the auray of the design from the view point of safety, life, reliability and working ondition of the struture. First we have prepared Assembly of rankshaft in CATIA and save this part as STP for Exporting into 05, IERJ All Rights Reserved Page 7

8 ANSYS workbenh Environment. Import.Stp model in ANSYS Workbenh simulation module. Apply material for rankshaft whih properties are shown in below shows more realisti anaylisis. Material Details Material: - C-70 Alloy Steel Yield Strength (MPa):- 07 MPa Ultimate tensile strength: MPa Poisson ratio: Shear Modules: - 79GPa Behavior: - Isotropi Table No. 0: Input parameter of material for ANSYS workbenh Analysis. OUTPUT Material Fig. 04: Deformation of C-70 Alloy Steel Deformation (mm) Max. Value Mass (Kg.) Max. Prinipal (N/mm ) Max. Value Fig. 05: Maximum Prinipal Strain of C-70 Alloy Steel Max. Strain (N/mm ) Max. Value Strutural Steel 4.75E SAE E EN E Cast Iron 5.59E C-70 Alloy Steel 4.08E Fig. 0: Maximum Prinipal Stress Deformation of C-70 Alloy Steel Sr. No. Material INPUT Young s Modules (N/mm ) Poisson ratio Density (kg/mm Strutural Steel.0E SAE E EN 30b.05E Cast Iron.78E C-70 Alloy Steel.07E Fig. 07: Mises stress of C-70 Alloy Steel Result:- Table No. 03: Output parameter of material in ANSYS workbenh Analysis. Comments:- ) Material No. 5 i.e. C-70 Alloy steel is meeting the maximum no of requirements. ) Though it is not onfirming the minimum available deformation, the differene between the minimum deformation available and the deformation when C70 alloy is used, is 0.05 Mirons whih is too less & an be ignored. 3) Though it is not onfirming the minimum mass of the body, the differene between the minimum mass available & the mass when C70 alloy is used, is 0.309Kg whih an be negleted to get the optimum design. 4) C70 alloy steel will give optimum results as ompared to the other materials given in the ase study. VI. TOPOLODY OPTIMIZATION The topology optimization method is use to solves the basi engineering problem of distributing a limited 05, IERJ All Rights Reserved Page 8

9 amount of material in a design spae. Optimal design whih are onerned with the optimization of strutural topology, shape and material. It also enompasses a omprehensive and unified desription of the state-of-theart of the so-alled material distribution method, based on the use of mathematial programming and finite elements. In the topology optimization alulation of an optimized material distribution in a speified area onsidering boundary ondition VII. EXPERIMENTAL WORK In a work the analysis is done for different engine speed and as a result riteria engine speed and ritial region on rankshaft are obtained. Stress variation over the engine yle and effet of tensional load in the analysis are to be found. Results from FEA are verified by using strain gauge attahed to several loations on the rankshaft. ACKNOWLEDGEMENT a The author gratefully aknowledges the support of guide ( Dr. Prof. (Mr.) Zope S. B. and Mr. Karanjule D. B.) a researh sholar, SVCET for his guidane and help. REFRENCES [] Rajesh M. Metkar, Vivek K. Sunnapwar, Subhash Deo Hiwase, Vidya SagarAnki, Mahendra Dumpa Evaluation of FEM based frature mehanis tehnique to estimate life of an automotive forged steel rankshaft of a single ylinder diesel engine, Proedia Engineering 5 ( 03 ) [] Milan Sága, Peter Kopas, Milan Uhríík, Modeling and Experimental Analysis of the Aluminium Alloy Fatigue Damage in the ase of Bending Torsion Loading Proedia Engineering 48 ( 0 ) [3] A.A. Adekunle, Development of CAD Software for Shaft under various Loading Conditions, Proedia Engineering 38 ( 0 ) [4] A. Solanki, K. Tamboli,M.J, M.J, M.J, M.J. Zinjuwadia, (0), Crankshaft Design and Optimization- A Review National Conferene on Reent Trends in Engineering & Tehnology. [5] J. Meng, Y. Liu, R. Liu, (0), Finite Element analysis of 4-Cylinder Diesel Crankshaft I.J. Image, Graphis and Signal Proessing, vol 5, pp. -9 [] Rinkle Garg, Sunil baghala finite Element and anylisis and optimization of rankshaft design International jornal of engineering and management researh, Vol Issue Deember 0. [7] Y. Gongzhi, Y. Hongliang, D. Shulin, (0), Crankshaft Dynami Strength Analysis for Marine Diesel Engine Third International Conferene on Measuring Tehnology and Mehatronis Automation, pp [8] G. Yingkui, Z. Zhibo (0), Strength Analysis of Diesel Engine Crankshaft Based on PRO/E and ANSYS Third International Conferene on measuring Tehnology and Mehatronis Automation, pp [9] C. M. Balamurung R. Krishnaraj, M. Sakthivel. K. Kanthavel, D. Marudanhalam. R. Palani, (0), Computer Aided Modeling and optimization of Crankshaft International Journal of Sinetifi & Engineering Reserh, Vol, issue8. [0] M. Jian, L. Yong-qi, L. Rui-xiang, Z. Bin, (00), Intension Analysis on 380 diesel rankshaft International onferene on Computaional and Information Sienes, pp 9-7. [] M. Jian, L. Yong-qi, L. Rui-xiang, Z. Bin, (00), 3- D Finite Elemen Analysis on 480 diesel rankshaft Institute of Eletrial and Eletroni Engineers. 05, IERJ All Rights Reserved Page 9