IJMST Vol. 6 No. 2 July-December 2012; pp. 117-128

Serials Publications

1 M.Tech Student, QIS College of Engineering & Technology Ongole - 523272, Andhra Pradesh.2 Associate Professor, QIS College of Engineering & Technology Ongole - 523272, Andhra Pradesh.3 Assistant Professor Department of Mechanical Engineering,3 Sankethika Vidya Parishad Engineering College, PM Palem ,Visakhapatnam

Optimal Design and Analysis of Polymer CompositeAutomobile Propeller Shaft

V P Pavan Peddineni1, T. Seshaiah2, and T. Victor Babu3

Abstract: Almost all automobiles (at least those which correspond to design with rear wheel driveand front engine installation) have transmission shafts. The weight reduction of the drive shaft canhave a certain role in the general weight reduction of the vehicle and is a highly desirable goal.Substituting composite structures for conventional metallic structures has many advantages becauseof higher specific stiffness and strength of composite materials.

The advanced composite materials such as graphite, carbon, Kevlar and glass with suitable resinsare widely used because of their high specific strength and high specific modulus. Advanced compositematerials seem ideally suited for long power driver shaft applications. The automotive industry isexploiting composite material technology for structural components construction in order to obtainthe reduction of the weight without decrease in vehicle quality and reliability. This work deals withthe replacement of conventional two-piece steel drive shaft with a one-piece drive shaft for rearwheel drive automobile was designed optimally using E-Glass/Epoxy, High modulus (HM) Carbon/Epoxy, and High strength carbon/Epoxy composites.

In this paper a Genetic Algorithm (GA) is used to minimize the weight of shaft which is subjected tothe constraints such as torque transmission, torsional buckling capacities and fundamental naturalfrequency. The GA is used to perform static and buckling using ANSYS software.

Keywords: Optimal Design; Static Analysis; Bucking Analysis; Genetic Algorithm; Compositematerial; Automobile Propeller Shaft

1. INTRODUCTION

The two main functional requirements for power transmission rotating shafts such as driveshafts of machinery and automotive propeller shafts are the transmission of static and dynamictorsional loads and the high fundamental bending natural frequency to avoid whirling vibrationat a high rotational speed. Long shafts made of conventional material such as aluminum andsteel cannot satisfy easily these two functional requirements simultaneously because they havelower specific stiffness, which limits the magnitude of fundamental bending natural frequency.

Almost all automobiles (at least those which correspond to design with rear wheel driveand front engine installation) have transmission shafts. The weight reduction of the drive shaftcan have a certain role in the general weight reduction of the vehicle and is a highly desirablegoal, if it can be achieved without increase in cost and decrease in quality and reliability. It is

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possible to achieve design of composite drive shaft with less weight to increase the first naturalfrequency of the shaft and to decrease the bending stresses using various stacking sequences.By doing the same, maximize the torque transmission and torsional buckling capabilities arealso maximized.

Figure 1: Conventional Two-Piece Drive Shaft Arrangement for Rear WheelVehicle Driving System

1.1. Composite Materials

Composites consist of two or more materials or material phases that are combined to producea material that has superior properties to those of its individual constituents. The constituentsare combined at a macroscopic level and or not soluble in each other. The main differencebetween composites, where as in alloys, constituent materials are soluble in each other andform a new material which has different properties from their constituents.

The advanced composite materials such as graphite, carbon, Kevlar and Glass with suitableresins are widely used because of their high specific strength (strength/density) and highspecific modulus (modulus/density). Advanced composite materials seem ideally suitedfor long, power driver shaft (propeller shaft) applications. Their elastic properties can betailored to increase the torque they can carry as well as the rotational speed at which theyoperate. The drive shafts are used in automotive, aircraft and aerospace applications. Theautomotive industry is exploiting composite material technology for structural componentsconstruction in order to obtain the reduction of the weight without decrease in vehiclequality and reliability. It is known that energy conservation is one of the most importantobjectives in vehicle design and reduction of weight is one of the most effective measuresto obtain this result. Actually, there is almost a direct proportionality between the weightof a vehicle and its fuel consumption, particularly in city driving.

2. DESIGN OF STEEL DRIVE SHAFT

The fundamental natural bending frequency for passenger cars, small trucks, and vans of thepropeller shaft should be higher than 3500 rpm to avoid whirling vibration and the torque

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transmission capability of the drive shaft should be larger than 500 Nm. The drive shaft outerdiameter should not exceed 100 mm due to space limitations. Here outer diameter of the shaftis taken as 90 mm. The drive shaft of transmission system is to be designed optimally forfollowing specified design requirements as shown in Table 1.

Table 1Design Requirements and Specifications

Sl.No Name Notation Unit Value

1. Ultimate torque Tmax

Nm 1512. Max. speed of shaft N

maxrpm 2400

3. Length of shaft L mm 12504. Outer diameter d

0mm 100

5. Inner diameter di

mm 80

Steel (SM45C) used for automotive drive shaft applications. The material properties of thesteel (SM45C) are given in Table 2. The steel drive shaft should satisfy three design specificationssuch as torque transmission capability, buckling torque capability and bending natural frequency.

Table 2Mechanical Properties of Steel (SM45C)

Mechanical properties Symbol Units Steel

Youngs Modulus E GPa 207.0Shear modulus G GPa 80.0Poissons ratio 0.3Density kg/m3 7600Yield Strength Sy MPa 370

2.1. Torque Transmission Capacity of the Drive Shaft

Torque Transmission capacity of the Drive Shaft is

T =4 4

50

( )16

o id dStd

= 3525.43 N-m

2.2. Mechanical Properties of Composite Material

Mechanical properties Symbol Units E-Glass /Epoxy HS Carbon /Epoxy HM Carbon /Epoxy

Longitudinal elastic modulus E11

GPa 50.0 134.0 190.0Transverse elastic modulus E

22GPa 12.0 7.0 7.7

Shear modulus G12

GPa 5.6 5.8 4.2Density kg/m3 2000 1600 1600Ultimate longitudinal St

1= sc

1MPa 800.0 880.0 870.0

tensile & compressive strengthUltimate transverse tensile & St

2= sc

2MPa 40.0 60.0 54.0

compressive strengthUltimate in-plane shear S

12MPa 72.0 97.0 30.0

strengthPoissons ratio v

120.3 0.3 0.3

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3. STATIC ANALYSIS

Static analysis deals with the conditions of equilibrium of the bodies acted upon by forces. Astatic analysis can be either linear or non-linear. All types of non-linearities are allowed such aslarge deformations, plasticity, creep, stress stiffening, contact elements etc. this chapter focuseson static analysis. A static analysis calculates the effects of steady loading conditions on astructure, while ignoring inertia and damping effects, such as those carried by time varyingloads. A static analysis is used to determine the displacements, stresses, strains and forces instructures or components caused by loads that do not induce significant inertia and dampingeffects A static analysis can however include steady inertia loads such as gravity, spinning andtime varying loads.

In static analysis loading and response conditions are assumed, that is the loads and thestructure responses are assumed to vary slowly with respect to time. The kinds of loading thatcan be applied in static analysis includes,

1. Externally applied forces, moments and pressures

2. Steady state inertial forces such as gravity and spinning

3. Imposed non-zero displacements

A static analysis result of structural displacements, stresses and strains and forces instructures for components caused by loads will give a clear idea about whether the structure orcomponents will withstand for the applied maximum forces. If the stress values obtained in thisanalysis crosses the allowable values it will result in the failure of the structure in the staticcondition itself. To avoid such a failure, this analysis is necessary.

Boundary Conditions

The finite element model of HS Carbon/Epoxy shaft is shown in Figure 2 and 3 0ne end is fixedand torque is applied at other end.

Figure 2: Fixed Support on Universal Joint

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Figure 3: Moment Applied on Yoke

4. MODAL ANALYSIS

When an elastic system free from external forces is disturbed from its equilibrium position itvibrates under the influence of inherent forces and is said to be in the state of free vibration. Itwill vibrate at its natural frequency and its amplitude will gradually become smaller with timedue to energy being dissipated by motion. The main parameters of interest in free vibration arenatural frequency and the amplitude. The natural frequencies and the mode shapes are importantparameters in the design of a structure for dynamic loading conditions.

Modal analysis is used to determine the vibration characteristics such as natural frequenciesand mode shapes of a structure or a machine component while it is being designed. It can alsobe a starting point for another more detailed analysis such as a transient dynamic analysis, aharmonic response analysis or a spectrum analysis. Modal analysis is used to determine thenatural frequencies and mode shapes of a structure or a machine component.

The rotational speed is limited by lateral stability considerations. Most designs are subcritical, i.e. rotational speed must be lower than the first natural bending frequency of the shaft.The natural frequency depends on the diameter of the shaft, thickness of the hollow shaft,specific stiffness and the length. Boundary conditions for the modal analysis are shown in Fig. 3

5. BUCKLING ANALYSIS

Buckling analysis is a technique used to determine buckling loads (critical loads) at which astructure becomes unstable, and buckled mode shapes (The characteristic shape associatedwith a structures buckled response). For thin walled shafts, the failure mode under an appliedtorque is torsional buckling rather than material failure. For a realistic driveshaft system,improved lateral stability characteristics must be achieved together with improved torque carryingcapabilities. The dominant failure mode, torsional buckling, is strongly dependent on Fiberorientation angles and ply stacking sequence.

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6. STATIC ANALYSIS OF DRIVE SHAFT

6.1. Steel

The twist about the axis of the shaft the deflection and stresses are show in below.

Figure 4: Total Deformed Shape of Steel Drive Shaft

Figure 5: Equivalent Stress of Steel Drive Shaft

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6.2. E-Glass/Epoxy

The twist about the axis of the shaft the deflection and stresses are show in below.

Figure 6: Total Deformed Shape of E-Glass/Epoxy Drive Shaft

Figure 7: Equivalent Stress of E-Glass/Epoxy Drive Shaft

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6.3. HS Carbon /Epoxy

The twist about the axis of the shaft the deflection and stresses are show in below

Figure 8: Total Deformed Shape of HS Carbon /Epoxy Drive Shaft

Figure 9: Equivalent Stress of E-Glass/Epoxy Drive Shaft

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7. DEFLECTION

The deflection of E-Glass/Epoxy, HS Carbon/Epoxy and HM Carbon/Epoxy drive shafts areshown in Table. 3

Table 3Deflection of Drive Shafts

Material Deflection(cm)

Steel 0.011298E-Glass/Epoxy 0.13602

HS Carbon/Epoxy 0.11990HM Carbon/Epoxy 0.11402

8. EQUIVALENT STRESS

The Equivalent Stress of E-Glass/Epoxy, HS Carbon/Epoxy and HM Carbon/Epoxy drive shaftsare shown in Table 4.

Table 4Equivalent Stress of Drive Shafts

Material Equivalent Stress(minimum) Equivalent Stress(maximum)dyne/cm2 dyne/cm2

Steel 2.2301e5 1.1823e9E-Glass/Epoxy 3.128e5 1.0357e9

HS Carbon/Epoxy 3.2633e5 1.0350e9HM Carbon/Epoxy 3.314e5 1.0348e9

Figure 10: Deflection of Drive Shafts

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Figure 11: Equivalent Stress of Drive Shafts

9. GA RESULTS

A one-piece composite drive shaft for rear wheel drive automobile was designed optimally byusing genetic Algorithm for E-Glass/ Epoxy, High Strength Carbon/Epoxy and High ModulusCarbon/Epoxy composites with the objective of minimization of weight of the shaft which issubjected to the constraints such as torque transmission, torsional buckling capacities and naturalbending frequency.

Summarization of GA Results

The GA results are shown in Table 5.

Table 5GA Results

Parameters Steel E-glass/Epoxy HS Carbon /Epoxy HM Carbon /Epoxy

do(mm) 90 90 90 90

L(mm) 1250 1250 1250 1250Deflection(cm) 0.068 0.15 0.26 0.29Optimum no. of Layers 1 6 6 6Stresses(mpa) 329 236 257 264Weight (Kg) 8.064 4.443 1.1273 1.1274Weight saving (%) - 48.36 86.90 86.90

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10. CONCLUSION

The following conclusions are drawn from the present work.

1. The E-Glass/ Epoxy, High Strength Carbon/Epoxy and High Modulus Carbon/Epoxycomposite drive shafts have been designed to replace the steel drive shaft of anautomobile.

2. A one-piece composite drive shaft for rear wheel drive automobile has been designedoptimally by using Genetic Algorithm for E-Glass/ Epoxy, High Strength Carbon/Epoxy and High Modulus Carbon/Epoxy composites with the objective of minimizationof weight of the shaft which was subjected to the constraints such as torque transmission,torsional buckling capacities and natural bending frequency.

3. The weight savings of the E-Glass/Epoxy, High Strength Carbon/Epoxy and HighModulus Carbon/Epoxy shafts were equal to 48.36%, 86.90% and 86.90% of the weightof steel shaft respectively.

4. The deflection of Steel, E-Glass/Epoxy, High Strength Carbon/Epoxy and HighModulus Carbon/Epoxy shafts were equal to 0.011298, 0.13602, 0.11990 and 0.11402cm respectively.

5. The fundamental natural frequency of Steel, E-Glass/Epoxy, High Strength Carbon/Epoxy and High Modulus Carbon/Epoxy shafts were 9319.98, 6514.56, 7495.42 and9270.28 rpm respectively.

6. The torsional buckling capacity of Steel, E-Glass/ Epoxy, High Strength Carbon/Epoxyand High Modulus Carbon/Epoxy shafts were 43857.96, 29856.45, 3772.11 and 3765.75N-m respectively.

7. The torque transmission capacity of the composite drive shafts has been calculated byneglecting and considering the effect of centrifugal forces and it has been observedthat centrifugal forces will reduce the torque transmission capacity of the shaft.

8. Natural frequency using Bernoulli-Euler and Timoshenko beam theories was compared.The frequency calculated by using the Bernoulli Euler beam theory is high, because itneglects the effect of rotary inertia & transverse shear.

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