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Momin Muhammad Zia Muhammad Idris, Prof. Vinayak H. Khatawate / International Journalof Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.252-258252 | P a g eOptimization of Crankshaft using Strength AnalysisMomin Muhammad Zia Muhammad Idris*, Prof. Vinayak H.Khatawate***(SEM IV, M.E (CAD/CAM & Robotics), PIIT, New Panvel, India,)** (Assistant Professor, Department of Mechanical Engineering, PIIT, New Panvel, India,)ABSTRACTThe crankshaft is an importantcomponent of an engine. This paper presentsresults of strength analysis done on crankshaft ofa single cylinder two stroke petrol engine, tooptimize its design, using PRO/E and ANSYSsoftware. The three dimensional model ofcrankshaft was developed in PRO/E andimported to ANSYS for strength analysis. Thiswork includes, in analysis, torsion stress which isgenerally ignored. A calculation method is usedto validate the model. The paper also proposes adesign modification in the crankshaft to reduceits mass. The modal analysis of modified design isalso done to investigate possibility of resonance.Keywords – ANSYS, Crankshaft, Finite ElementMethod, PRO/E, Strength Analysis, Modal AnalysisI. INTRODUCTIONIn strength analysis, considering loadsacting on the component, equivalent stresses arecalculated and compared with allowable stresses tocheck if the dimensions of the component areadequate. Crankshaft is an important and mostcomplex component of an engine. Due tocomplexity of its structure and loads acting on it,classical calculation method has limitations to beused for strength analysis [1]. Finite ElementMethod is a numerical calculation method used toanalyze such problems. The crankpin fillet andjournal fillet are the weakest parts of the crankshaft[1] [2]. Therefore these parts are evaluated forsafety.Any physical system can vibrate. Thefrequencies at which vibration naturally occurs, andthe modal shapes which the vibrating systemassumes are properties of the system, and can bedetermined analytically using Modal Analysis.Analysis of vibration modes is a critical componentof a design, but is often overlooked. Inherentvibration modes in structural components ormechanical support systems can shorten equipmentlife, and cause premature or completelyunanticipated failure, often resulting in hazardoussituations. Detailed modal analysis determines thefundamental vibration mode shapes andcorresponding frequencies. This can be relativelysimple for basic components of a simple system, andextremely complicated when qualifying a complexmechanical device or a complicated structureexposed to periodic wind loading. These systemsrequire accurate determination of naturalfrequencies and mode shapes using techniques suchas Finite Element Analysis [7].II. FINITE ELEMENT MODELFig.1 shows the 3-Dimensional model inPRO/E environment. As the crankshaft is of a singlecylinder two stroke petrol engines used for twowheelers, it doesn’t have a flywheel attached to it, avibration damper and oil holes, making themodeling even simpler. The dimensions ofcrankshaft are listed in Table 1.Fig.1 The 3-Dimensional model in PRO/ETable1. DIMENSIONS OF CRANKSHAFTParameter Value (mm)Crankpin Outer Diameter 18Crankpin Inner Diameter 10Journal Diameter 25Crankpin Length 50Journal Length 10Web Thickness 13III. STRESS CALCULATION USINGFEMThe procedure of using FEM usuallyconsists of following steps. (a) modeling; (b)meshing; (c) determining and imposing loads andboundary conditions; (d) result analysisA. MeshingGreater the fineness of the mesh better the accuracyof the results [5]. The Fig. 2 shows the meshedmodel in ANSYS consisting of 242846 nodes and67723 elements.
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Momin Muhammad Zia Muhammad Idris, Prof. Vinayak H. Khatawate / International Journalof Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.252-258253 | P a g eFig.2 Meshing the model in ASYSB. Defining Material PropertiesThe ANSYS demands for material properties whichare defined using module ENGINERING DATA.The material used for crankshaft is 40Cr4Mo2.Thematerial properties are listed in Table 2.Table 2 . THE MATERIAL PROPERTIESDensity 7800 kg m^-3Young’s Modulus 2.05e+011PaPoisson’s Ratio 0.3Tensile Strength 7.7e+008 PaC. Loads and Boundary ConditionsBoundary conditions play an important role in FEM.Therefore they must be carefully defined toresemble actual working condition of the componentbeing analyzed. The crankshaft is subjected to threeloads namely Gas Force F, Bending Moment M andTorque T. The boundary conditions for these loadsare as follows [3].1. Gas Force FGas Force F is calculated using maximum cylinderpressure, 50 bar for petrol engines [4], and borediameter of engine cylinder. This load is assumed tobe acting at the centre of crankpin. Displacements inall three directions (x, y and z) are fully restrained atside face of both journals as shown in Fig.3. Fromthis loading case, maximum compressive stress inthe journal fillet is obtained.Fig.3 Gas Force applied at the centre of crankpin2. Bending Moment MFor strength analysis crankshaft is assumedto be a simply supported beam with a point loadacting at the centre of crankpin. The maximumBending Moment M is calculated accordingly. Onejournal of the crankshaft is kept free (six degree offreedom) and Bending Moment M is applied to thisjournal as shown in Fig.4. The degrees of freedom atthe other journal are fully restrained. From thisloading case maximum bending stresses in thecrankpin fillet and journal fillet are obtained.Fig.4 Bending Moment applied at one of thejournals3. Torque TMaximum Torque T is obtained frommanufacturer’s engine specifications. One journal ofthe crankshaft is kept free (six degree of freedom)and Torque T is applied to this journal. The degreesof freedom at the other journal are fully restrained asshown in Fig.5. From this loading case maximumtorsion stress in crankpin fillet and journal fillet areobtained.
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Momin Muhammad Zia Muhammad Idris, Prof. Vinayak H. Khatawate / International Journalof Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.252-258254 | P a g eFig.5 Torque applied at one of the journalsD. Calculation of Equivalent StressAs the boundary condition in each loadcase is different, it is impossible to combine them inANSYS to find equivalent stress. Therefore, stressvalues obtained from various load cases are used informulae given in [3] to obtain equivalent stress incrankpin fillet and journal fillet. As the load on thecrankshaft is fluctuating, the equivalent stress is tobe compared with fatigue strength of crankshaftmaterial. This is done by calculating fatigue strength𝜎𝐷𝑊 and acceptability factor Q as given in [3].Fatigue Strength:𝜎𝐷𝑊 = ±𝐾. (0.42. 𝜎𝐵 + 39.3)[0.264+ 1.073. 𝐷−0.2+785 − 𝜎𝐵4900+196𝜎𝐵1𝑅𝐻]Where𝜎𝐵[𝑁/𝑚𝑚2] minimum tensile strength ofcrankshaft materialK [-] factor for different types of crankshaftswithout surface treatment. Values greater than 1 areonly applicable to fatigue strength in fillet area.= 1.05 for continuous grain flow forged or drop-forged crankshafts= 1.0 for free form forged crankshafts (withoutcontinuous grain flow)RH [mm] fillet radius of crankpin or journal𝜎𝐷𝑊 = ±468.24 𝑁/𝑚𝑚2related to crankpinfillet𝜎𝐷𝑊 = ±413.3 𝑁/𝑚𝑚2related to journal filletAcceptability Factor:𝑄 =𝜎𝐷𝑊𝜎𝑣(1)Adequate dimensioning of the crankshaft is ensuredif the smallest of all acceptability factors satisfiesthe criteria [3]:Q ≥ 1.151. Equivalent Stress 𝝈𝒗 and Acceptability FactorQ in Crankpin FilletThe maximum bending stress and torsion stress incrankpin fillet were obtained from equivalent stressdiagrams for the load cases Bending Moment andTorque respectively. (Fig.6 and Fig.7)Fig.6 Maximum bending stress in crankpin filletFig.7 Maximum torsion stress in crankpin filletThe Equivalent Stress in crankpin fillet is calculatedas:𝜎𝑣 = ± 𝜎𝐵𝐻2 + 3 × 𝜏𝐻2 (2)= ± 287. 52 + 3 × 20.342𝜎𝑣 = ±289.65 𝑁/𝑚𝑚2The Acceptability Factor is calculated using (1)𝑄 =1.6162. Equivalent Stress 𝝈𝒗 and Acceptability FactorQ in Journal FilletThe maximum bending stress, torsion stress andmaximum compressive stress in journal fillet wereobtained from equivalent stress diagrams for theload case Bending Moment, Torque and Gas Forcerespectively. (Fig.8, Fig.9 and Fig.10)
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Momin Muhammad Zia Muhammad Idris, Prof. Vinayak H. Khatawate / International Journalof Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.252-258255 | P a g eFig.9 Maximum bending stress in journal filletThe Equivalent Stress in journal fillet is calculatedas:𝜎𝑣 = ± 𝜎𝐵𝐺2 + 3 × 𝜏𝐺2 (3)= ± 266.462 + 3 × 9.0422𝜎𝑣 = ±267.01 𝑁/𝑚𝑚2The Acceptability Factor is calculated using (1)𝑄 =1.547Fig.9 Maximum torsion stress in journal filletFig.10 Maximum compressive stress in journal filletIV. MODEL VALIDATIONAlternatively, a classical calculationmethod given in [3] was used to validate the model.The equivalent stress and acceptability factor werecalculated and compared with values obtained fromFinite Element Method described earlier.1. Equivalent Stress 𝜎𝑣 and Acceptability Factor Qin Crankpin FilletThe Equivalent Stress in crankpin fillet is calculatedas:𝜎𝑣 = ± 𝜎𝐵𝐻2 + 3 × 𝜏𝐻2 (4)= ± 3012 + 3 × 14.832𝜎𝑣 = ±468.24 𝑁/𝑚𝑚2The Acceptability Factor is calculated using (1)𝑄 =1.552. Equivalent Stress 𝜎𝑣 and Acceptability Factor Qin Journal FilletThe Equivalent Stress in journal fillet is calculatedas:𝜎𝑣 = ± 𝜎𝐵𝐺2 + 3 × 𝜏𝐺2 (5)= ± 270.742 + 3 × 5.0182𝜎𝑣 = ±270.88 𝑁/𝑚𝑚2The Acceptability Factor is calculated using (1)𝑄 =1.525V. RESULT ANALYSISThe stress concentration is high in crankpinfillet and journal fillet. The values of equivalentstress and acceptability factor obtained from FEMand classical calculation method were almost equalfor both crankpin fillet as well as journal fillet.Therefore it is concluded that it is safe to considerstress values obtained from FEM for strengthanalysis. The results obtained from both themethods are listed in Table 3.Table3. RESULT ANALYSISArea ParameterByFEMBy CalculationCrankpinFilletEquivalentStress 𝜎𝑣289.65N/mm2302.09N/mm2AcceptabilityFactor Q1.616 1.55JournalFilletEquivalentStress 𝜎𝑣267.01N/mm2270.88N/mm2AcceptabilityFactor Q1.547 1.525The large difference between the specifiedvalue of Acceptability Factor, Q ≥ 1.15, and itscalculated value proved that crankshaft is overdimensioned. Therefore a scope for theimprovement in the design was investigated. Theoriginal thickness of the web is 13 mm which is
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Momin Muhammad Zia Muhammad Idris, Prof. Vinayak H. Khatawate / International Journalof Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.252-258256 | P a g ereduced in step of 1 mm and acceptability factor wascalculated for each thickness value using FiniteElement Method.Table 4 lists the summary of these iterations whichwere done to arrive at final acceptable value of webthickness. It is clear from Table4 that web thicknesscan be reduced to 10 mm still keeping theacceptability factor above the specified limit(iteration No. 4). Although there is still a littlemargin between calculated value and specified valueof acceptability factor, it is better not to reduce webthickness further to be on the safer side. Furtherreduction in web thickness results in acceptabilityfactor values which are less than specified value(iteration No.5 and 6) indicating that web thicknesscan’t be reduced below 10 mm.Table4: DESIGN MODIFICATION STEPSVI. MODAL ANALYSISIn order to determine fundamental modeshapes and corresponding natural frequencies,Modal Analysis of the modified design of crankshaftwas done. All six modes of vibration andcorresponding natural frequencies were determined.Table 5 lists all six natural frequencies of vibration.Table5. NATURAL FREQUENCIES OFVIBRATIONMODEFREQUENCY[HZ]1 1432.72 2332.3 3215.4 3598.95 3918.96 4218.4First Mode of VibrationThe first mode of vibration is bendingvibration in X-direction at natural frequency of1432.7 Hz. The maximum deformation appears atthe bottom of crank WEB, as shown in Figure11.Second Mode of VibrationThe second mode of vibration is torsionalvibration of right web about Y-direction at naturalfrequency of 2332 Hz. The maximum deformationappears at the sides of crank WEB as shown inFigure12.Figure 11 First mode of vibrationFigure 12 Second mode of vibrationSr.NOWebThicknessmmAreaEquivalent StressσV(N/mm2)Acceptability Factor(Q ≥ 1.15)1 13Crankpin Fillet289.65 1.616JournalFillet267.01 1.5472 12Crankpin Fillet352.08 1.329JournalFillet322.1 1.2833 11Crankpin Fillet366.45 1.277JournalFillet333.84 1.2384 10Crankpin Fillet400.76 1.168JournalFillet355.056 1.1645 9Crankpin Fillet434.53 1.077JournalFillet361.98 1.1416 8Crankpin Fillet481.7 0.972JournalFillet363 1.138
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Momin Muhammad Zia Muhammad Idris, Prof. Vinayak H. Khatawate / International Journalof Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.252-258257 | P a g eThird Mode of VibrationThe third mode of vibration is torsionalvibration about Y-direction at natural frequency of3215 Hz. The maximum deformation appears at thesides of left crank WEB as shown in Figure 13.Figure 13 Third mode of vibrationFourth Mode of VibrationThe fourth mode of vibration is torsionvibration about Z-direction at natural frequency of3598.9 Hz. The maximum deformation appears atthe edges of crank WEB as shown in Figure 14.Figure 14 Fourth mode of vibrationFifth Mode of VibrationThe fifth mode of vibration is torsionvibration about X-direction at natural frequency of3918.9 Hz. The maximum deformation appears atthe edges of crank WEB as shown in Figure 15.Figure 15 Fifth mode of vibrationSixth Mode of VibrationThe sixth mode of vibration is bendingvibration in Z-direction at natural frequency of3598.9 Hz. The maximum deformation appears atthe edges of crank WEB as shown in Figure 16.Figure 16 Sixth mode of vibrationVII. CONCLUSION1. Strength Analysis is a powerful tool to checkadequacy of crankshaft dimensions and find scopefor design modification.2. It is found that weakest areas in crankshaft arecrankpin fillet and journal fillet. Hence these areas
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Momin Muhammad Zia Muhammad Idris, Prof. Vinayak H. Khatawate / International Journalof Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.252-258258 | P a g emust be evaluated for safety.3. This project includes torsion stresses in analysis.But it is found that the torsion stresses are negligibleas compared to bending stresses. Hence they can beignored while doing strength analysis of crankshaft.4. The crankshaft was found to be overdimensioned. Therefore web thickness was reducedfrom 13 mm to 10 mm. The reduction in massobtained by this design modification is:Mass Reduction = 1.9725 kg - 1.6375 kg = 0.335 kgPercentage Mass Reduction = 16.98 %5. The lowest value of natural frequency is 1432.7Hz while the highest value is 4218.4 Hz (Table 5).When the engine is running at its maximum speed of6000 rpm, the driving frequency is merely 100 Hz.As the lowest natural frequency is far higher thandriving frequency, possibility of resonance is rare.REFERENCES[1] Gu Yingkui, Zhou Zhibo, StrengthAnalysis of Diesel Engine CrankshaftBased on PRO/E and ANSYS, 2011 ThirdInternational Conference on MeasuringTechnology and Mechatronics Automation.[2] Yu Ding, Xiaobo Li, Crankshaft StrengthAnalysis of a Diesel Engine UsingFinite Element Method, Power and EnergyEngineering Conference (APPEEC), 2011Asia-Pacific, 978-1-4244-6255-1,2011.[3] IACS Publication, UR M53, Calculation ofCrankshafts for I.C Engines, Rev.1 2004,Rev. II 2011.[4] Ahmed Al-Durra, Lisa Fiorentini, MarcelloCanova and Stephen Yurkovich, A Model-Based Estimator of Engine CylinderPressure Imbalance for CombustionFeedback Control Applications, 2011American Control Conference on OFarrellStreet, San Francisco, CA, USA June 29 -July 01, 2011[5] MENG Jian, LIU Yong-qi, LIU Rui-xiangand ZHENG Bin, 3-D Finite ElementAnalysis on 480 Diesel Crankshaft,Information Engineering and ComputerScience (ICIECS), 2010 2nd InternationalConference.[6]. Meshing Users Guide – ANSYS(www1.ansys.com/customer/content/documentation/130/wb_msh.pdf)[7] HGC Engineering, Acoustical, NoiseControl and Vibration Isolation Services,(http://www.acoustical-consultants.com/noise-control-vibration-isolation-acoustical-engineering-services/)
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