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Optimum design of automotive composite drive shaft
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1. INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME AND TECHNOLOGY (IJMET)ISSN 0976 – 6340 (Print)ISSN 0976 – 6359 (Online) IJMETVolume 3, Issue 3, September - December (2012), pp. 438-449© IAEME: www.iaeme.com/ijmet.aspJournal Impact Factor (2012): 3.8071 (Calculated by GISI) ©IAEMEwww.jifactor.com OPTIMUM DESIGN OF AUTOMOTIVE COMPOSITE DRIVE SHAFT WITH GENETIC ALGORITHM AS OPTIMIZATION TOOL Ghatage K.D1, Hargude N.V2 1 Department of Mechanical Engineering, RIT Sakhrale 415414, Sangli, Maharashtra, India; 2 Department of Mechanical Engineering,PVPIT Budhgon 416416, Sangli, Maharashtra, India E-mail- ghatagekishor89@gmail.com; nvhargude@gmail.com 1. ABSTRACT Substituting composite materials for conventional metallic structures has many advantages because of higher specific stiffness and strength of composite materials. Advanced composite materials seem ideally suited for long, power drive shaft applications. Their elastic properties can be tailored to increase the torque and the rotational speed at which they operate. This study has been carried out to investigate maximum torque; buckling torque transmission and critical speed of composite drive shaft. Main aim of this work is to investigate either replacing steel structure of drive shaft; for rear wheel drive passenger cars; by composite structures such as carbon/Epoxy and Glass/Epoxy materials will be convenient or not. For finding out the suitability of composite structures for automotive drive shaft application the parameters such as; ply thickness, number of plies and stacking sequence are optimized for carbon/Epoxy and Glass/Epoxy shafts using Genetic Algorithm as an optimization tool with the objective of weight minimization of the composite shaft which is subjected to constraints such as torque transmission, torsional buckling load and fundamental natural frequency. 2. INTRODUCTION A driveshaft is the connection between the transmission and the rear axle of the car. The advanced composite materials such as Boron, Graphite, Carbon, Kevlar and Glass with suitable resins are widely used because of their high specific strength (strength/density) and high specific modulus (modulus/density). Polymer matrix composites were proposed for light weight shafts in drivelines for automotive, industries. 438
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME Fig 1: The conventional two-piece steel drive shaft for a rear wheel driving vehicle.The entire driveline of the car is composed of several components, each with rotating mass. The rule ofthumb is that 17-22% of the power generated by the engine is lost in rotating mass of the drive train. Thepower is lost because it takes more energy to spin heavier parts. This energy loss can be reduced bydecreasing the amount of rotating mass. Light weight flywheels and transmission gears, aluminum andcarbon-fiber drive shafts, riffle-drilled axels, and aluminum hubs are all examples of replacement ormodified parts used to reduce the amount of rotating mass.The torque capability of the drive shaft for passenger cars should be larger than 3500 Nm and thefundamental bending natural frequency should be higher than 9200 rpm to avoid whirling vibration [2].Since the fundamental bending natural frequency of a one-piece drive shafts made of steel or aluminum isnormally lower than 5700 rpm when the length of the drive shaft is around 1.5 m [2], the steel drive shaftis usually manufactured in two pieces to increase the fundamental bending natural frequency because thebending natural frequency of a shaft is inversely proportional to the square of beam length andproportional to the square root of specific modulus. The two-piece steel drive shaft consists of threeuniversal joints, a center supporting bearing and a bracket, which increases the total weight of anautomotive vehicle and decreases fuel efficiency.In the previous study by the authors [12], Genetic algorithm (GA) is applied for the design optimizationof steel leaf springs. Although design optimization of steel springs and composite leaf springs has beenthe subject for quite few investigators; but few of the attempts were involving Genetic Algorithm as anoptimization tool.In the present work an attempt has been made to evaluate the suitability of composite material such as E-glass / epoxy and Carbon / epoxy for the purpose of automotive transmission applications. A one-piececomposite drive shaft for rear wheel drive automobile is designed optimally by using GA with theobjective of minimization of weight of the shaft which is subjected to the constraints such as torquetransmission, torsional buckling strength capabilities and natural bending frequency.3. PROBLEMS ASSOCIATED WITH THE CONVENTIONAL STEEL DRIVE SHAFTThe torque transmission capability of the drive shaft for passenger cars, small trucks, and vans should belarger than 3500 Nm (Tmax) and fundamental natural bending frequency of the drive shaft should be higherthan 6500 rpm (Nmax) to avoid whirling vibration. The drive shaft outer diameter do should not exceed100 mm due to space limitations. Here outer diameter of the shaft is taken as 90 mm. For the purpose ofexperimentation the composite drive shaft of 200 mm length and do= 32 mm amd di= 22 mm wasmanufactured. Conventional steel drive shafts ; having less specific modulus and strength; are usuallymanufactured in two pieces to increase the fundamental bending natural frequency because the bendingnatural frequency of a shaft is inversely proportional to the square of beam length and proportional to the 439
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEMEsquare root of specific modulus. Therefore the steel drive shaft is made in two sections connected by asupport structure, bearings and U-joints and hence over all weight of assembly will be more.While on the other hand the fundamental natural frequency of the carbon fiber composite drive shaft canbe twice as high as that of steel or aluminium because the carbon fiber composite material has more than 4times the specific stiffness of steel or aluminium, which makes it possible to manufacture the drive shaft ofpassenger cars in one piece. A one-piece composite shaft can be manufactured so as to satisfy the vibrationrequirements. Lower rotating weight transmits more of available power. This eliminates all the assembly,connecting the two piece steel shafts and thus minimizes the overall weight, vibrations and the total cost.Due to the weight reduction, fuel consumption will be reduced. Composite materials have high dampingcapacity and hence they produce less vibration and noise with the ability of good corrosion resistance.Composite structures have longer fatigue life than steel or aluminium shaft.4. DESIGN OF COMPOSITE DRIVE SHAFTWhile designing the composite drive shaft some assumptions are made such as the shaft rotates at aconstant speed about its longitudinal axis and has uniform circular cross section. All damping andnonlinear effects are excluded and since lamina is thin and no out-of-plane loads are applied, it isconsidered as under the plane stress. The stress-strain relationship for composite material is linear &elastic; hence, Hook’s law is applicable for composite materials.The drive shaft can be solid circular or hollow circular. Here hollow circular cross-section was chosenbecause the hollow circular shafts are stronger in per kg weight than solid circular and the stressdistribution in case of solid shaft is zero at the centre and maximum at the outer surface while in hollowshaft stress variation is smaller. In solid shafts the material close to the centre are not fully utilized. Table 1: Mechanical properties of E-glass / epoxy and HM carbon / epoxy Property Glass / epoxy Carbon / epoxy E11 (GPa) 50.0 190.0 E22 (GPa) 12.0 7.7 G12 (GPa) 5.6 4.2 ν12 0.3 0.3 T C σ 1= σ 1 800.0 870.0 (MPa) T C σ 2= σ 2 40.0 54.0 (MPa) τ12 (MPa) 72.0 30.0 3 ρ (kg/m ) 2000.0 1600.0 Vf 0.6 0.6Table shows the properties of the E-glass / epoxy and high modulus carbon / epoxy materials used forcomposite drive shafts. E11 , E22 , G12 , σT1 , σC1 , σT2 and σC2 represent lamina properties in longitudinal andtransverse directions (Fig. 2) respectively. ν12 , τ12 , ρ and Vf are the Poisons ratio, shear stress and fibervolume fractions. Since, composites are highly orthotropic and their fractures were not fully studied thefactor of safety is taken as 2 440
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME4.1. Torque transmission of the composite drive shaftSince the lamina is thin and no out-of-plane loads are applied, it is considered as the plane stress problemand 3-D problem can be reduced into 2-D problem. For unidirectional 2-D lamina, the stress-strainrelationship in terms of physical material direction for unidirectional is given by [11], σଵ Qଵଵ Qଵଶ 0 εଵ൝ σଶ ൡ = Qଵଶ Q ଶଶ 0 ൩ ൝ εଶ ൡ, τଵଶ 0 0 Q γଵଶwhere σ, τ, γ and ε represent stresses and strains in material directions. The matrix Q is referred as thereduced stiffness matrix for the layer and its terms are given by [11]: ாభభ ௩భమ ாమమܳଵଵ = ܳଵଶ = ; ଵି௩భమ ௩మభ ଵି௩భమ ௩మభ , ாܳଶଶ = ଵି௩ మమ௩ , ܳ = ܩଵଶ . ܳଶଵ = ܩଵଶ . భమ మభ4.2. STRESS-STRAIN RELATIONSHIP FOR ANGLE-PLY LAMINAThe relation between material co-ordinate system and X-Y-Z co-ordinate system is shown in figure 2below. Co-ordinate 1-2-3 are principle material directions co-ordinate X-Y-Z are transferred or laminateaxis Fig 2: Relation between material coordinate system and X-Y coordinate systemFor an angle-ply lamina, where fibbers are oriented at an angle with the positive X-axis (Longitudinalaxis of shaft), the effective elastic properties are given by [11], ଵ ଵ ଵ ଶ௩ ଵ1. ா = ா ܥସ +ቂீ − ா ቃ ܵ ଶ ܥଶ + ா ܵ ସ ೣ భభ భమ భభ మమ ଵ ଵ ଵ ଶ௩ ଵ2. ா = ா ܵ ସ +ቂீ − ா ቃ ܵ ଶ ܥଶ + ா ܥସ భభ భమ భభ మమ ଵ ଶ ଶ ଶ௩ ଵ ଵ3. ீ = 2 ቂா + ா + ா − ீ ቃ ܵ ଶ ܥଶ + ீ [ ܥଶ + ܵ ଶ ] భభ మమ భభ భమ భమThe Stress strain relationship for an angle-ply lamina is given by; 441
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME σ୶ തതതതത Qଵଵ തതതതത Qଵଶ തതതതത εଵ Qଵ൝ σ୷ ൡ = തതതതത Qଵଶ തതതതത Q ଶଶ തതതതത ൝ εଶ ൡ; Q ଶ τ୶୷ തതതതത Qଵ തതതതത Q ଶ തതതതത γଵଶ Q ܳ matrix denotes transformed reduced stiffness. Its terms are individually given by [11]:where σ and ε represent normal stresses and strains in X, Y and XY directions respectively and bar overതതതതതQଵଵ = Qଵଵ c ସ + Q ଶଶ sସ + 2(Qଵଶ + 2Q )sଶ c ଶ;തതതതത = (Qଵଵ + Q ଶଶ − 4Q )s ଶ c ଶ + Qଵଶ (c ସ + s ସ );Qଵଶതതതതത = (Qଵଵ − Qଵଶ − 2Q )c ଷ s − (Q ଶଶ − Qଵଶ − 2Q )csଷ ;Qଵതതതതത = Qଵଵ sସ + Q ଶଶ s ସ + 2(Qଵଵ + 2Q )s ଶ c ଶ ;Q ଶଶതതതതത = (Qଵଵ − Qଵଶ − 2Q )csଷ − (Q ଶଶ − Qଵଶ − 2Q )c ଷ s;Q ଶതതതതത = (Qଵଵ + Q ଶଶ − 2Qଵଶ − 2Q )sଶ c ଶ + Q (s ସ + c ସ ); with C = cosθ and S = sinθ.Q 4.3. TORSIONAL BUCKLING CAPACITY:Since long thin hollow shafts are vulnerable to torsional buckling, the possibility of the torsional bucklingof the composite shaft was checked by the expression for the torsional buckling load Tcr of a thin walled .ଶହ ݐ ଵ.ହorthotropic tube, which is expressed below [3]: ܶ = (2ߨ ݎଶ )272.0()ݐ൫ܧ௫ ܧ௬ ଷ ൯ ൬ ൰ ݎwhere Ex and Ey are the Young’s modulus of the composite shaft in axial and hoop direction, r and t arethe mean radius and thickness of the composite shaft.This equation has been generated from the equation of isotropic cylindrical shell and has been used forthe design of drive shafts. From the equation, the torsional buckling capability of composite shaft isstrongly dependent on the thickness of composite shaft and the average modulus in the hoop direction.4.4. Timoshenko beam theory (Nୡ୰୲ ):Timoshenko beam theory considers both transerverse shear deformation as well as rotary inertia. Naturalfrequency fnt based on the Timoshenko beam theory is given by: ଷగమ ாೣ మ݂௧ = ܭ௦ ට ଶఘ ; మ ଵ మ గమ మ ா =1+ 1 + ீ ೞ ൨, ೞೞ మ ଶమ ೣwhere fnt and p are the natural and first natural frequency. Ks is the shear coefficient of the naturalfrequency (< 1), fs is a shape factor (equals to 2) for hollow circular cross-sections [7].ܰ௧ = 60݂௧ .Critical speed:5. DESIGN OPTIMIZATION OF COMPOSITE DRIVE SHAFTFirst, fibers are selected to provide the best stiffness and strength beside cost consideration. It is the bestselection, indeed, to use carbon fibers in all layers but due to their high prices a hybrid of layers ofcarbon-epoxy and E-glass-epoxy could be utilized. Since the fiber orientation angle that offers themaximum bending stiffness which leads to the maximum bending natural frequency is to place the fiberslongitudinally at zero angles from the shaft axis, on the other hand, the angle of ±45º orientation realizes 442
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEMEthe maximum shear strength and 90º is the best for buckling strength [4]. The main design goal is toachieve the minimum weight while adjusting the variables to meet a sufficient margin of safety, which istranslated in a critical speed (natural frequency) higher than the operating speed, a critical torque higherthan the ultimate transmitted torque and a nominal stress (the maximum at fiber direction) less than theallowable stress after applying any of the failure criteria like the maximum stress criteria [4].Due to the physical geometry (larger radius) of the drive shafts used in the mentioned applicationsincluding automotive applications, the shear strength which specify the load carrying capacity, is of minordesign importance since the failure mode is dominated by buckling, therefore the main design factors arethe bending natural frequency and the torsional buckling strength, which are functions of the longitudinaland hoop bending stiffness, respectively [4]. The variable of the laminate thickness has a big effect on thebuckling strength and slight effect on bending natural frequency.5.1. Objective Function: The objective for the optimum design of the composite drive shaft is the minimization of weight,݉ = ߩ,ܮܣso the objective function of the problem is given as weight of the shaft: గ݉ = ߩ (݀ ଶ − ݀ ଶ ),ܮOr ସ5.2. Design Variables:The design variables of the problem are • Number of plies [n]; • Stacking Sequence [θk]; • Thickness of the ply [tk].The limiting values of the design variables are; 2] -90≤ ߠ ≤90 1] n ≥ 0 3] 0.1≤ ݐ ≤0.5where k = 1, 2,…, n and n = 1, 2, 3,…, 32.The number of plies required depends on the design constraints, allowable material properties, thicknessof plies and stacking sequence. Based on the investigations it was found that up to 32 numbers of plies aresufficient.5.3. Design Constraints:1. Torque transmission capacity of the shaft: ܶ ≥ ܶ௫2. Bucking torque capacity of the shaft: ܶ ≥ ܶ௫3. Lateral fundamental natural frequency: ܰ௧ ≥ ܰ௫The constraint equations may be written as: ்ܥଵ = ቀ1 − ் ቁ, If ܶ < ܶ௫ ೌೣ = 0 Otherwise; ்ܥଶ = ቀ1 − ்ೌೣ ቁ, If ܶ < ܶ௫ = 0 Otherwise; ேܥଷ = ቀ1 − ቁ, If ܰ௧ < ܰ௫ ேೌೣܥ=ܥଵ + ܥଶ + ܥଷ. = 0 Otherwise 443
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEMEA new algorithm has been developed using MATLAB R2007b for optimum design of automobilecomposite drive shaft for following design specification which should be sustained by both steel andcomposite drive shafts. Table 2: constraints of design optimization of composite drive shaft Material Steel (SM45C) Glass/Epoxy and Carbon Epoxy Length 200mm 200 mm Inner Diameter 22 24 mm Outer Diameter 32 34 mm (in terms of ߠ) Possible angle combination - -45/0/45/90 (Stacking sequence) Maximum number of plies 1 10 Maximum torque transmission 1350 Nm 1350 Nm capacity (ܶ௫ ) Maximum buckling torque 1350 Nm 1350 Nm transmission capacity (ܶ ௫ ) Critical Speed (ܰ௧ ) 4500 Nm 4500 rpm6. RESULTS AND DISCUSSIONFollowing table 3 & 4 shows the optimized results for Carbon/Epoxy and Glass/Epoxy composite driveshaft; Table 3: Optimization of carbon/epoxy drive shaft NO. OF STACKING MAXIMUM BUCKLING Critical Speed MASS (In ࣂ and from LAYERS SEQUENCE TORQUE TORQUE (Ncrt) (m) TRANSMISS- TRANSMISSI-ON (rpm) (KG) Inner layer to ION CAPACITY CAPACITY outer layer) (Tmsx) (Tcrt) (Nm) (Nm) 1 0 340.32 507.55 19187 0.101 2 0/0 528.65 1029.01 27285 0.131 3 0/0/0 730.23 1564.02 27936 0.271 4 90/0/0/0 947.78 2112.25 28534 0.418 5 45/90/0/0/0 1179.58 2317.90 29087 0.573 6 -45/45/90/0/0/0 1429.5472 2526.4331 29595 0.612 7 0/-45/45/90/0/0/0 1698.96 3093.27 30067 0.894 8 90/0/- 1985.24 3672.69 30495 1.082 45/45/90/0/0/0 444
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME Table 4: Optimization of glass-carbon/epoxy drive shaft NO. OF STACKING MAXIMUM BUCKLING Critical MASS (In ࣂ and from LAYERS SEQUENCE TORQUE TORQUE Speed (m) TRANSMISS- TRANSMISSI- (Ncrt) (KG) Inner layer to outer ION ON CAPACITY (rpm) layer) CAPACITY (Tcrt) (Tmsx) (Nm) (Nm) 1 0 309.52 463.8619 8747 0.105 2 0/90 480.49 1244.0453 8486 0.131 3 0/90/90 663.29 2044.4965 8887 0.271 4 0/90/90/90 860.13 2864.7149 9013 0.418 5 -45/0/90/90/90 1072.09 3085.8766 10376 0.573 6 45/-45/0/90/90/90 1299.57 3309.3942 8281 0.635 7 90/- 1543.5649 4145.5415 9325 0.829 45/45/0/90/90/90 8 0/90/- 1804.76 4705.2754 9410 1.082 45/45/0/90/90/90 Graph: Maximum torque transmission capacity of Carbon/Epoxy Shaft CARBON/EPOXY: MAXIMUM TORQUE TRANSMISSION CAPACITY (Nm) Transmission Capacity 2000 Maximum Toeque 1500 1 1000 2 (Nm) 500 3 0 0 2 4 6 8 10 4 5 Stacking Sequence in Degrees 445
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME Graph: Maximum torque transmission capacity of Glass-Carbon/Epoxy Shaft GLASS-CARBON/EPOXY:- MAXIMUM TORQUE TRANSMISSION CAPACITY (Nm) 2000 transmission Capacity 1500 1 Maximum Torque 1000 2 500 ()Nm 0 3 0 2 4 6 8 10 4 Stacking Sequence in Degrees 5 Graph: Buckling torque transmission capacity of Carbon/Epoxy Shaft CARBON/EPOXY: BUCKLING TORQUE TRANSMISSION CAPACITY (Nm) Capacity in (Nm) Transmission Buckling 4000 1 2000 2 0 3 1 2 3 4 5 6 7 8 4 Stacking Sequence in Degrees 5 Graph: Buckling torque transmission capacity of Glass-Carbon/Epoxy Shaft GLASS-CARBON/EPOXY:-BUCKLING TORQUE TRANSMISSION CAPACITY Buckling Torque capacty (Nm) Transmission 6000 1 4000 2000 2 0 3 0 2 4 6 8 10 4 Stacking Sequence in Degrees 5 446
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep Dec (2012) © IAEME Sep- Graph: Carbon/Epoxy: Number of layers Vs Critical speed CARBON/EPOXY: NOMBER OF LAYERS Vs CRITICAL 40000 SPEED (rpm) Critical Speed (rpm) 1 20000 2 3 0 4 0 2 4 Number Of layers 6 8 10 Graph: Glass-Carbon/Epoxy: Number of layers Vs Critical speed Carbon/Epoxy: GLASS-CARBON/EPOXY: NUMBER OF LAYERS Vs CRITICAL SPEEED (rpm) CARBON/EPOXY:- 15000 1 Critical Speed (rpm) 10000 2 5000 0 3 0 2 4 6 8 10 4 Number Of Layers 5 Graph: Critical speed analy in composite drive shafts analysis Shaft Length and Critical Speed 20000 Critical Speed (rpm) 15000 10000 Composite Drive Shaft 5000 Steel Drive Shaft 0 0 1000 2000 3000 4000 Shaft Length (mm)Graph shows that for the steel drive shaft having about 6000 revolutions per minute can be manufacturedof length about 1m to 1.5m while on the other hand for composite drive shaft it is possible to manufacturea shaft of length 1.5m to 2 m for same revolutions. f 447
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME6.1. Mass Comparison between Steel and Composite drive ShaftsFollowing table gives the comparison of masses of conventional steel drive shaft, Carbon/Epoxy andGlass-Carbon/Epoxy composite drive shaft. Material Weight Weight (Kg) Reduction (%) Steel 0.489 - Glass- 0.412 15.75 Carbon/Epoxy Carbon Epoxy 0.352 28.01 Graph: Mass Comparison of three shafts Mass comparison between Steel and Composite Drive Shaft 0.6 0.5 STEEL Mass in Kg 0.4 0.3 0.2 Glass- 0.1 Carbon/Epoxy 0 Carbon Epoxy7. CONCLUSIONFrom preliminary experiments and studies of physical properties like weight, material combination,torque transmitting capacities, etc. it is concluded that: • A one-piece composite drive shaft made of Carbon/Epoxy and Glass-Carbon/Epoxy is designed optimally with Genetic Algorithm as optimization tool with the objective of minimization of weight of drive shaft which is subjected to constraints such as Maximum torque transmission capacity, Buckling torque transmission capacity and critical speed. • About 28.01 % of weight saving is achieved with Carbon/Epoxy shaft with increase in critical speed enabling manufacturing of shaft of length 1.8m to 2 m; as compared to steel shaft; by experimentation. • About 15.75% weight saving is achieved with Glass-Carbon/Epoxy composite shaft with increase in critical speed enabling manufacturing of shaft of length 1.7 m to 2m; as compared to steel shaft; by experimentation. • The results reveal that the orientation of fibers has great influence on the dynamic characteristics of the composite material shafts in a positive direction. • Genetic Algorithm is suggested as an effective optimization tool. 448
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME8. REFERENCES1. Thimmegowda Rangaswamy, and Sabapathy Vijayarangan “Optimal Sizing and Stacking Sequence ofComposite Drive Shafts” journal of Material science, Vol.11, No.2, 2005.2. R.R Ajith, T. Rangaswamy, S. Vijayarangan and G. Chandramohan “Genetic Algorithm BasedOptimal Design Of Composite Shaft” International journal of Material Science and Engineering,December2004.3. Dai Gil Lee and Hak Sung Kim “Design and manufacture of an automotive hybridaluminum/composite drive shaft” journal of composite structure, Vol 63, 2004 pp.87-99.4. M. A. Badie, A. Mahdi, and A. R. Abutalib “Automotive composite drive shafts: Investigation of thedesign variable effects” International Journal of Engineering and Technology, Vol. 3, No.2, 2006, pp.227-237.5. Durk Hyun Cho, Dai Gil Li, Jin Ho Choi “Manufacture of one-piece automotive drive shafts withaluminum and composite materials” journals of Composite structure, Vol. 38, No. l-4, 1997 pp. 309-319.6. M.A.K. Chowdhuri , R.A. Hossain, Design Analysis of an Automotive Composite DriveShaft,International Journal of Engineering and Technology Vol.2(2), 2010, 45-48.7. Rajeev., S., Krishnamoorthy, C. S. Discrete Optimization of Structure Using Genetic Algorithms J.Structural Engg. ASCE 118 1992: pp. 1233 – 1250.8. Goldberg, D. E. Genetic Algorithms in Search, Optimization and Machine Learning, Reading MA,Addison-Wesley, 1989.9.Rastogi, N. (2004), Design of composite driveshafts for automotive applications, SAE, Technical PaperSeries, 2004-01-0485.10. Darlow, M. S. and Creonte, J. (1995), Optimal design of composite helicopter power transmissionshafts with axially varying fibre lay-up, Journal of the American Helicopter Society 40 (2): 50-56.11. Rao, S. S. Mechanical Vibrations. Addision-Wesely Publishing Company, NY: pp. 537 – 541.12. Vijayarangan, S., et. al. Design Optimization of Leaf Springs Using Genetic Algorithms Inst. Engrs.India Mech. Engng. Div. 79 1999: pp. 135 – 139.13. A.R. Abu Talib et al “Developing a hybrid, carbon/glass fiber-reinforced, epoxy composite automotive drive shaft” journal of Materials and Design 31 (2010) 514–521 449
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