Analysis & Optimization of Torsional Vibrations in a Four-Stroke Single Cylinder Diesel Engine Crankshaft

Transcription

1 International Journal of Engineering and ehnial Researh (IJER) ISSN: , Volume-3, Issue-4, April 205 Analysis & Optimization of orsional Vibrations in a Four-Stroke Single Cylinder Diesel Engine Crankshaft Amitpal Singh Punewale, Mr. ushar Khobragade, Mr. Amit Chaudhari, Prof. N. M. Khandre Abstrat Every material system ontaining individual mass and stifess distribution is suseptible to vibrate. hese vibrations an be aused either by single impulse load or a periodial load. Analysis of free vibration is essential to determine natural frequenies of material system, responsible for resonane phenomenon, ourred due to equalizing periodial load frequeny with natural frequenies and leads to high amplitude of vibration & high fatigue stress into material. orsional vibrations of engines has reeived onsiderable attention from researhers and engineers from many years, but influene of eah drive train omponent on engine's torsional vibration has reeived less attention. In this paper, the influene of individual rankshaft geometrial parameters on torsional vibrations are studied. Crankshaft torsional vibration is one of the most important fators affeting engine operation and in rankshaft design of IC engines. he rankshaft is subeted to omplex loading due to motion of onneting rod, the mass of piston assembly & onneting rod inreases resultant moment of inertia, that derease natural frequeny of first and seond mode within range of engine rotational speed, resulting in resonane with low order harmoni of tangential fore ating on rankpin, whih is very undesirable. orsional vibrations detoriate the NVH performane of engine and redues fatigue life of rankshaft. Hene, there is neessity to redue torsional vibrations. In this study, by employing finite element analysis (FEA) on rankshaft, different methods will be proposed to redue torsional vibrations and inrease fatigue life. Index erms Crankshaft, Fatigue, FEA, orsional Rigidity, orsional Vibration. I. INRODUCION Crankshaft is the main omponent of internal ombustion engine, onverting reiproating motion of piston into rotational motion. Crankshaft vibration is one of the most important fators affeting engine operation. he different vibrations affeting the rankshaft are lateral vibrations and torsional vibrations. he problem of torsional vibrations are very severe, as they are very diffiult to detet and the first symptom of problem is often a broken shaft, gear tooth, or oupling. he diffiulty of deteting inipient failures in the field makes Manusript reeived April 07, 205. Amitpal Singh Punewale, Seond Year (M.eh CAD/CAM), Department of Prodution Engineering, SGGSIE&, Nanded, India, Mr. ushar Khobragade, Deputy General Manager, Greaves Cotton Limited, Aurangabad, India. Mr. Amit Chaudhari, Manager (FEA), Greaves Cotton Limited, Aurangabad, India. Prof. N. M. Khandre, Assoiate Professor, Department of Prodution Engineering, SGGSIE&, Nanded, India.. thorough torsional vibration analysis as an essential omponent of the engine design proess. Aording to Montazersadgh. F. H. and Fatemi. A. [], the rankshaft torsional vibration ours as eah power stroke tends to slightly twist the shaft. When the power stroke subsides, the rankshaft untwists. One would think that something like rankshaft would not twist signifiantly, but any piee of metal always deflets a bit when fore is applied, and in ase of IC engines, where large amount of power is generated, these fores an beome huge indeed. orsional vibrations of engines arise due to appliation of periodi ombustion fores in the ylinder and assoiated inertial fores. Boysal. A. and Rahneat. H. [2] shown that rankshaft experienes large number of load yles resulting from gas ombustion (F g ) and inertia fores (F i ), during its servie life. hese fores ating on the rankshaft auses two types of flutuating loads on the rankshaft struture i.e. torsional load (F t ) and bending load (F r ) as shown in fig.. Fig.. Fores ating on Crankshaft Aording to Feese.. and Hill. C. [3] traditionally torsional vibrations have been studied only from the standpoint of reduing noise and improving omfort. However, one must also bear in mind that this kind of vibration, and resonane in partiular, an generate loads that far exeed the maximum engine torque. orsional vibration is a onern in the rankshafts of internal ombustion engines beause it ould break the rankshaft itself, shear-off flywheel or ause driven belts, gears and attahed omponents to fail, espeially when frequeny of vibration mathes the torsional resonant frequeny of the rankshaft. Charles. P., Sinhala. J. K., Gu. F., Lidstone. L., and Ball. A. D. [4] states that engines always have some ree of torsional vibration during operation due to their reiproating nature. he measurements of torsional vibrations is a diffiult task. he enoder signal has been used to onstrut IAS (Instantaneous Angular Speed) waveform, representing signature of torsional vibration. IAS signal and its Fast Fourier ransform (FF) analysis are effetive for monitoring engines with less than eight ylinders. Aording to Wilson. W. K. [5] A favorable solution of torsional vibration problem is provided by inherent mass, 87

2 Analysis & Optimization Of orsional Vibrations In Four-Stroke Single Cylinder Diesel Engine Crankshaft elasti, exiting & damping harateristis of the system, either as originally designed or after simple and inexpensive adustments of one or more harateristis. In some ases, the modifiations may found impratiable or ostly or involve sarifie of performane or other desirable design requirements. In suh ases, speial devies for reduing torsional vibration are used. his speial devies are usually termed as tuning or damping devies. he primary funtion of these tuning devies is to assist in produing a favorable adustment of natural frequeny. At the same time, they an be arranged to provide a signifiant ontribution to overall damping of the system. A heavy flywheel situated at the driving end of an engine rankshaft an also be lassified as a tuning member, and the natural frequeny of the system an be adusted by hanging the flywheel inertia. herefore, the different methods to redue torsional vibrations of rankshafts are: a) Use of speial Devies, known as orsional Vibration Damper (VD), to redue vibration amplitude in resonant points. b) By inreasing torsional rigidity of rankshaft, so that resonane points are shifted outside the IC engine operating range. Among the two methods, this study fous towards the aim of reduing torsional vibration of rankshaft, by improving the torsional rigidity or torsional stifess of the engine rankshaft. II. ORSIONAL ANALYSIS he torsional analysis is used for determining torsional response of system. Ronald L. Eshleman [6] states that the torsional analysis is the analysis of torsional dynami behavior of a rotating shaft system as a result of fored vibration. A omprehensive torsional analysis has been arried out for omplex omponents, in whih various modes of torsional vibrations are analyzed. he ompliated ombinations of various effets in steady state and transient operating ases are also onsidered in torsional analysis. A torsional system an be modeled as mass-elasti system (inertia & stifess) to predit stresses in eah omponent. he mass elasti properties of suh system an be hanged by adding flywheel (additional inertia), using as soft oupling (hange in stifess), or by visous damping (absorbing natural frequeny). As with other forms of vibration, torsional vibration in mahines ours in harateristi patterns alled Modes. he mode shape is dependent on torsional stifess, polar moment of inertia, and damping of various omponents in the system. he frequeny of vibration at whih the mode shape ours is alled Natural Frequeny. When a natural frequeny oinides with an exitation frequeny, a state of resonane ours. At resonane, the system damping alone ontrols the motions and stresses in the system. he rankshaft of a reiproating engine or the rotors of a turbine or motor, and all moving parts driven by them, omprise a torsional elasti system. Suh a system has several modes of free torsional osillation. Eah mode is haraterized by a natural frequeny and by a pattern of relative amplitudes of parts of the system when it is osillating at its natural frequeny. he harmoni omponents of the driving torque exite vibration of the system in its modes. If the frequeny of any harmoni omponent of the torque is equal to or lose to the frequeny of any mode of vibration, a ondition of resonane ours and the mahine is said to be running at a ritial speed. he operation of the system at suh ritial speeds an be very dangerous, resulting in frature of the shaft. he number of omplete osillations of the elasti system per unit revolution of the shaft is alled an Order of the operating speed. III. ORSIONAL SIFFNESS he first step in analytially determining torsional response is to alulate torsional natural frequenies of the system. As per Wilson. W. K. [7] For simpler geometry, suh as, ylindrial shafts, the mass-moment of inertia and torsional stifess an be alulated using simple formulae. For more ompliated geometries suh as rankshafts, the rankshaft an be simplified into several main omponents, suh as, stub shaft, ournals, webs, and rankpins. hereby, a mass-elasti model of the rankshaft is reated by lumping inertia at eah throw & alulating equivalent torsional stifess between throws. Fig. 2. Simple Crank-hrow Fig. 2 shows a basi rankshaft throw, onsisting of two webs, rankpin & ournal. Many equations are available for alulating the torsional stifess of rankshaft, suh as, Ker Wilson, Carter, et. requiring basi dimensions of the ournals, webs, and rankpins as well as shear modulus of the shaft material. a) CARER FORMULA: G L 0.8Lw 0.75L.5R D d D d Lw W b) WILSON FORMULA: G L 0.4D L ( ) D R D D D d D d Lw W Carter s formula is appliable to rankshafts with flexible webs with stiff ournals and rankpins as well as for rankshafts with no overlapping of ournals & rankpins, while Ker Wilson s formula is better for stiff webs with flexible ournals, rankpins and for rankshafts with overlapping of ournals & rankpin. A Finite Element Method (FEM) an also be used to determine torsional stifess for rankshaft setion. Milasinovi. A., Filipovi. I. & Hribernik. A. [8] explained FEA boundary onditions to determine torsional stifess of single throw rankshaft whih simulates engine ondition i.e. ournal mounted inside bearing. In their study, an attempt is made to determine torsional stifess of single throw rankshaft by establishing FEA 88

3 boundary onditions similar to rankshaft physial fatigue test, i.e. one end is fixed and torque is applied at other end. he angular displaement (θ) is alulated and torsional stifess (K t ) is alulated as, After alulating torsional stifess, the natural frequeny is alulated as, K t n I p I p = Mass moment of Inertia, kg-mm 2 ω n = Natural frequeny, rad/s, n f n 2 Ukhande. M., Mane. R. and Shegavi. G. [9] arried an extensive analytial study for evaluation of torsional stifess for various rankshafts by varying different geometri parameters and ompared analytial results with FEA results. hey found that torsional stifess is diretly proportional to rank pin diameter (D ), web width (W), web thikness (L w ) & inversely proportional to throw (R) and pin width (L ).he torsional rigidity evaluated by analytial method and FEA orrelates with % auray. hus, by hanging different geometri parameters in a rankshaft, its torsional rigidity an be hanged, whih hanges natural frequeny of rankshaft. International Journal of Engineering and ehnial Researh (IJER) ISSN: , Volume-3, Issue-4, April 205 Fig. 5. Boundary Conditions For Crank-hrow he torsional stifess is also evaluated using analytial formulas given by Carter & Wilson and ompared with FEA results V. FEA RESULS: he value of Angular Displaement (θ) is, herefore, the value of torsional stifess (K t ) is given as, 6 N mm VI. CARER FORMULA: Using arter formula, torsional stifess (K t ) is given, G 6 N mm L Lw L R D d D d Lw W Perentage error between FEA result & Carter formula, K t perentage _ error % IV. ANALYSIS AND RESULS For arrying out Finite Element Analysis (FEA), First, a CAD model of rankshaft geometry is prepared, by PRO-E WILDFIRE 5.0, as shown in fig. 3. he CAD model is developed for rankshaft of Greaves 435 Engine. During engine working, the fore in engine ylinder produes a torque to the rankshaft. he magnitude of this torque an be determined by proedure given by Kimura. J., Kai. R., & Shibata. S. [9] Fig. 3. CAD Model of Crankshaft Geometry In order to estimate the torsional stifess, Finite Element Method (FEM) is employed. he analysis is first performed on a simple rank-throw, shown in figure 4. Fig. 4. Crank-hrow of Crankshaft First, the torsional stifess of simple rank-throw is determined using FEA. he boundary onditions, shown in figure 5, i.e. one end is fixed and torque is applied at the other end. A unit torque, i.e. N-mm, is applied. VII. WILSON FORMULA: Using wilson formula, torsional stifess (K w ) is given, G L ( ) D L D R D D D d D d Lw W 6 N mm Perentage error between FEA result & Wilson formula, K t Kw perentage _ error 00.67% As there is an overlapping of rankpin & ournal in the rank-throw, the Wilson formula should be employed for aurate results. Also, the results of FEA mathes losely with Wilson's formula results. he torsional natural frequeny of rank-throw, shown in fig. 4, determined by analytial method is as follows: I kg m 2 p 6 N mm 5 N m rad he fundamental natural frequeny of torsional vibration is, K t rad n 6.39 Ip s hus, the natural frequeny of torsional vibration is given as, n he torsional natural frequeny of same rank-throw determined by FEA is shown in fig

4 Analysis & Optimization Of orsional Vibrations In Four-Stroke Single Cylinder Diesel Engine Crankshaft Fig. 6. orsional Natural Frequeny of Crank-hrow Depending upon the results at different mode shapes, the torsional mode is identified and the assoiated frequeny of is the torsional natural frequeny. By FEA method, the torsional natural frequeny (f n2 ) is found to be, Perentage error among analytial method & FEA method is, f n 2 perentage _ error % he use of analytial method for alulating torsional natural frequeny is limited to simple geometrial shape omponents, for omplex shape omponents, analytial method is not feasible. he analysis is done on omplete rankshaft by FEA, as analytial method annot be employed for omplex geometry. he boundary onditions employed in the analysis are same as earlier i.e. one side is fixed, and torque is applied on other side, as shown in fig. 7. proportional to throw (R) and pin width (L ). hus, by hanging any of the parameters, orresponding hange in torsional stifess an be ahieved. he different hanges made in the rankshaft geometry are as follows: ) Crankpin Diameter: In this ase, diameter of rankpin is inreased by 0%, in order to find resultant effet on torsional stifess. he boundary onditions were similar to the original model. Using FEA, torsional stifess of rankshaft prior inreasing rankpin diameter was, N mm After 0% inrease in D, modified torsional stifess (K t ) was found to be, N mm he perentage inrease in torsional rigidity (I) is, K t I % he natural frequeny of the modified rankshaft an be evaluated similar to original rankshaft, as shown in fig. 9. Fig. 7. Boundary Conditions for Crankshaft he alulated torsional stifess (K t ) will be equal to the applied torque () divided by the angle of twist or angular displaement (θ) at the free end. he value of angular displaement (θ) is found to be, he torsional stifess of rankshaft is, N mm he torsional natural frequeny of rankshaft determined by FEA is shown in fig. 8. Fig. 8. orsional Natural Frequeny of Crankshaft he torsional natural frequeny (f n ) is found to be, f n As said earlier, the study fous towards the aim of reduing torsional vibration, by improving torsional stifess of the engine rankshaft. his is done by hanging the different geometri parameters of the rankshaft. Referring to Ukhande. M., Mane. R. and Shegavi. G. [9], torsional stifess is diretly proportional to pin diameter (D ), web width (W), web thikness (L w ) & inversely Fig. 9. orsional Natural Frequeny of Crankshaft for first ase he torsional natural frequeny (f n ) is found to be, Perentage inrease in natural frequeny is, f n I % hus, Inrease in torsional stifess is about 0.5%, whereas inrease in natural frequeny is about 5%. However, inreasing rankpin diameter alls for hange in design of other omponents, suh as, onneting-rod, bearings, et. resulting in high ost. Hene, solution is not optimal. 2) Journal Diameter: In this ase, diameter of ournal is inreased by 0%, in order to find resultant effet on torsional stifess. he boundary onditions were similar to the original model. Using FEA, torsional stifess of rankshaft prior inreasing ournal diameter was, N mm After 0% inrease in ournal diameter (D ), modified torsional stifess (K t ) is, N mm he perentage inrease in torsional stifess (I) is, 90

5 K t I % he natural frequeny in this ase an be evaluated as, Fig. 0. orsional Natural Frequeny of Crankshaft for seond ase he torsional natural frequeny (f n ) is found to be, International Journal of Engineering and ehnial Researh (IJER) ISSN: , Volume-3, Issue-4, April 205 adversely affets torsional vibrations, but it alls for hange in design of onneting-rod. 4) Fae-inlination: he various geometrial parameters of rankshaft, like, rankpin diameter (D ), ournal diameter (D ), length of rankpin (L ), throw (R), web thikness (L w ), & web width (W), affets its torsional stifess. But hanging any one of the parameter affets design of one or several adoining omponents. hus, there is a need to optimize torsional vibrations in engine rankshaft without hanging other omponents. Hene, a new geometrial parameter, Fae-inlination (FI), is onsidered to optimize torsional vibrations, as shown in figure 2. Perentage inrease in natural frequeny is given by, f n I % Hene, by inreasing ournal diameter (D ) by 0%, an inrease of about 6% is ahieved in torsional stifess and about 4.5% in torsional natural frequeny. 3) hrow: In this ase, throw (R) distane is inreased by.5 mm. he hange is applied to rankshaft, and boundary onditions are similar to previous ase. he torsional stifess of the original rankshaft was, N mm After suggested hange, torsional stifess is found to be, N mm he perentage inrease in torsional stifess (I) is, K t I % he Negative (-) sign speifies derease in torsional stifess. he torsional natural frequeny an be evaluated as shown in fig.. Fig. 2. Fae-Inlination (FI) Area of Crankshaft Addition of material in FI area results in inreased torsional stifess, without affeting design of other omponents. he amount of material added in FI area is 44 gm, as shown in fig. 3. Fig. 3. Material Addition in Fae-Inlination (FI) Area he torsional stifess in this ase is evaluated using same boundary onditions. he torsional stifess of original rankshaft prior to addition of material in fae-inlination (FI) area was, N mm he torsional stifess in this ase is found to be, N mm he perentage inrease in torsional rigidity (I) is, K t I % he torsional natural frequeny an be evaluated as, Fig.. orsional Natural Frequeny of Crankshaft for third ase he torsional natural frequeny (f n ) is found to be, he perentage inrease in natural frequeny is, f n I 00 0.% he Negative (-) sign speifies derease in torsional natural frequeny. Hene, by inreasing throw (R) distane in rankshaft by.5 mm, torsional stifess is dereased by about 0.0%, whereas, torsional natural frequeny gets redued by 0.%. hus, inreasing throw (R) distane Fig. 4. orsional Natural Frequeny of Crankshaft for fourth ase he torsional natural frequeny (f n ) is found to be, he perentage inrease in natural frequeny is, f n I % 9

6 Analysis & Optimization Of orsional Vibrations In Four-Stroke Single Cylinder Diesel Engine Crankshaft hus, a material addition of 44 gm. in fae-inlination (FI) area results in inreased torsional stifess of about 5% and about 2.5% inrease in natural frequeny. Also, this hange does not affet design of any adoining omponents. Hene, this hange overomes drawbaks of previous ases and is most optimal, ompared to other ases. VIII. FAIGUE LIFE Another obetive of the study involves inreasing fatigue life of the original rankshaft. First, the fatigue life of existing rankshaft is evaluated by FEM, as shown in fig. 5. Fig. 5. Fatigue Life of original rankshaft he fatigue life of the original rankshaft model is found to be, N yles he fatigue life of the most optimal hange (fae-inlination) employed in rankshaft geometry for inreasing torsional stifess is also evaluated by FEM. he results of the fatigue life analysis are shown in fig. 6. Fig. 6. Fatigue Life of modified design he fatigue life of the suggested modifiation is, N yles hus, Addition of material in Fae-inlination area results in an inreased torsional stifess. Also, the fatigue life of rankshaft inreases by this hange. I. CONCLUSION In this way, the phenomenon of torsional vibrations and its influene on engine performane, partiularly on engine rankshaft is studied. he study an be onluded as follows: Firstly, a proedure to determine the torsional stifess of the given omponents is prepared. he torsional stifess of the rank throw (fig. 4) is determined by analytial & FEA method and their omparison is arried out. he results of analytial & FEA method are in good agreement. he same proedure is adopted to determine torsional stifess of existing omplete rankshaft (fig. 7) through FEA method, as the analytial method is not feasible, for evaluation of torsional stifess of rankshaft. Seondly, another proedure for evaluation of the torsional natural frequeny is prepared. he proedure is first applied to rank throw (fig. 4) and omparison is made between analytial & FEA results, the results also mathes losely. Similarly, the proedure is applied to rankshaft, for determining torsional natural frequeny. hen, the different parameters affeting torsional stifess are identified, and their effet on torsional stifess is studied to redue the torsional vibrations in engine rankshaft, followed by suggestion of most optimal modifiation. he hange in fatigue life produed by most optimal modifiation of torsional stifess, is ompared with original one. ACKNOWLEDGMEN he Author wish to aknowledge the support of Greaves Cotton Limited, during the study. REFERENCES [] Montazersadgh. F. H., Fatemi. A, Optimization of a Forged Steel Crankshaft Subet to Dynami Loading, SAE Paper No [2] Boysal. A., Rahneat. H., orsional Vibration Analysis of a Multi-Body Single ylinder Internal Combustion Engine Model, Department of Mehanial & Manufaturing Engineering, University of Bradford, Bradford, West Yorkshire, UK, 997, 2:48-493, August. [3] Feese.., Hill. C., Prevention of orsional Vibration Problems in Reiproating Mahinery, Proeedings of the hirty-eight urbo mahinery Symposium, [4] Charles. P., Sinhala. J. K., Gu. F., Lidstone. L., Ball. A. D., Deteting Crankshaft orsional Vibration of Diesel Engines for Combustion Related Diagnosis, Journal Of Sound & Vibration, (2009) [5] Wilson. W. K., Pratial Solution of the orsional Vibration Problems, Devies For Measuring Vibration Amplitude, Volume No.4, Chapman & Hall Publiation, 972. [6] Ronald L. Eshleman, Chapter 38. orsional Vibration in Reiproating & Rotating Mahines, Harris Shok & Vibration Handbook, Harris. C. M. & Piersol. A.G. Fifth Edition, MGraw Hill Publiation. [7] Wilson. W. K., Pratial Solution of the orsional Vibration Problems, Frequeny Calulations Volume No., Chapman & Hall Publiation, 946. [8] Milasinovi. A., Filipovi. I. & Hribernik. A., Contribution to the Definition of the orsional Stifess of Crankshaft of a Diesel Engine used in Heavy-Duty Vehiles, International Journal of Automobile Engineering, Vol. 223, page , [9] Ukhande. M, Mane. R and Shegavi. G, Optimization of Crankshaft orsional Rigidity for Fatigue Strength Improvement Using CAE, CDFD Engineering. Bharat Forge Ltd. Pune, India, SAE Paper No [0] Kimura. J., Kai. R., & Shibata. S., Six-ylinder Inline urbo-harged Diesel Engine Crankshaft orsional Vibration Charateristis, SAE Paper No Amitpal Singh Punewale is the student in the final semester of the Master of ehnology (Mehanial - CAD/CAM) in SGGSIE&, Nanded, India, having researh interests in CAD/CAE field. Mr. ushar Khobragade is the Deputy General Manager of Greaves Cotton Limited, Aurangabad, India, ompleted his Master of Engineering (Mehanial Engineering) from BIS Pilani, having more than 0 years of industrial experiene. Mr. Amit Chaudhari is the Manager (FEA), in Greaves Cotton Limited, Aurangabad, India, ompleted his Master of ehnology (Design Engineering) from II Chennai, having industrial experiene of 7 years. Prof. N. M. Khandre is the Assoiate Professor in Department of Prodution Engineering in SGGSIE&, Nanded, India, ompleted his Master of Engineering (Mehanial - CAD/CAM) from SGGSIE&, Nanded, having teahing experiene of about 20 years. 92