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D.Dinesh, F.Anand Raju / International Journal Of Engineering Research And Applications
(IJERA) ISSN: 2248-9622 Www.Ijera.Com
Vol. 2, Issue4, July-August 2012, Pp.1874-1880
Optimum Design And Analysis Of A Composite Drive Shaft For An
Automobile By Using Genetic Algorithm And Ansys
D.DINESH*, F.ANAND RAJU**
*Department of Mechanical Engineering, SIETK College, Puttur, Chittoor Dist, AndhraPradesh, INDIA.
** Department of Mechanical Engineering, SIETK College, Puttur, Chittoor Dist, Andhra Pradesh, INDIA.

Abstract:
Substituting composite structures for It is the reinforcement which is primarily responsible
conventional metallic structures has many for the mechanical properties of ACMs. Usually all
advantages because of higher specific stiffness and the reinforcements (fibers) are stronger in tension
strength of composite materials. This work deals than steel, but weak in shear ( i.e. brittle ) requiring
with the replacement of conventional two-piece the filler material (Matrix) relatively strong in shear
steel drive shafts with a single-piece e-glass/epoxy, which will protect reinforcement against abrasion or
high strength carbon/epoxy and high modulus environmental corrosion. Matrix also helps in
carbon/epoxy composite drive shaft for an distributing the load from reinforcement, absorbing
automotive application. The design parameters energy, reducing stress concentration and preventing
were optimized with the objective of minimizing cracks propagation. Thermosetting and thermo plastic
the weight of composite drive shaft. The design types of organic polymers are used as Matrix ( e.g.
optimization also showed significant potential epoxide, phenolic, polyamide resins etc.).
improvement in the performance of drive shaft. Some of the important fibers used as
Keywords:-Torque transmission, Torsional reinforcement in ACMs along with their characteristic
buckling capacities, Fundamentallateral Natural properties are discussed briefly.
frequency, Bernoulli Euler theory, Timoshenko Glass fiber properties.
beam theory, Static analysis, Modal analysis,
Buckling analysis, Ansys. Property
E-glass R-glass D-glass S-glass

1. INTRODUCTION Density (g/cm3) 2.60 2.55 2.16 2.49
Advancedcomposite materials can be
defined as combination of materials appropriately Tensile strength 3400 4400 2500 4580
arranged using reinforcing fibers, carefully chosen (Mpa)
matrixes, and some times auxiliary materials like
adhesive core and other inserts. These combinations Tensile modulus 73 86 55 86.93
after proper manipulation and processing result in (Gpa)
finished structure/item with synergistic properties i.e.
properties achieved after fabrication cannot be Elongation at break 4.5 5.2 4.5 5.4
obtained by individual components acting alone. The (%)
ACMs can be classified in different categories on the
basis of micro structures, multiphases, Filament diameter 3-14 3-14 3-14 –
reinforcements, manner of packing fibers layered
compositions, method of composition, matrix system Properties of Aramid fibers
processing methods etc. Basic components of ACMs
are (i) Reinforcement (fibers) (ii) Matrix (iii) Honey property Polyester Monex Kevlar29 Kevlar49 Teflon
comb core/adhesives ( for sand witched structures ).
The great variety of fibers materials in various forms, Density 9/cm3 1.38 1.38 1.44 1.45 2.15
shapes and sizes have been recently developed for use
in ACMs and in the construction industries. Steel, Tensile 900 670 2700 3500 -
glass, carbon, Strength(MPa)
Aramid (kevlar), boron, silicon carbide,
silicon nitrates, alumina fibers are some of the Tensile 18 60 135 133 –
commonly used high performance reinforcement Modulus(GPa)
fibers in ACMs. The reinforcements may be called by
different names according to sizes such as Whisker ( Elongation at 10-15 20-30 4 2.5 20-30
< 0.025 mm ), fiber ( 0.025 – 0.8 mm ), Wire ( 0.8 – break %
6.4 mm ), rod ( 6.4 – 50 mm ) and bar ( > 50 mm ).
Filament 10-12 – – – 20
In general the continuous filamentary type
diameter
reinforcement is important from structural application
point of view.

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2. Design of a Composite Drive Shaft 2.5 Selection of Resin System
2.1 Specification of the Problem The important considerations in selecting
The specifications of the composite drive resin are cost, temperature capability, elongation to
shaft of an automotive transmission are same as that failure and resistance to impact (a function of
of the steel drive shaft for optimal design. modulus of elongation). The resins selected for most
of the drive shafts are either epoxies or vinyl esters.
2.2 Assumptions Here, epoxy resin was selected due to its high
1. The shaft rotates at a constant speed about its strength, good wetting of fibers, lower curing
longitudinal axis. shrinkage, and better dimensional stability.
2. The shaft has a uniform, circular cross section.
3. The shaft is perfectly balanced, i.e., at every cross E- HS HM
S. Proper Unit
section, the mass center coincides with the Glass / Carbon Carbon
No. ty s
geometric center. Epoxy / Epoxy / Epoxy
4. All damping and nonlinear effects are excluded. 1 E11 GPa 50.00 134.0 190.0
5. The stress-strain relationship for composite 2. E22 GPa 12.0 7.0 7.7
material is linear & elastic; hence, Hooke’s law is 3. G12 GPa 5.6 5.8 4.2
applicable for composite materials. 4. 12 - 0.3 0.3 0.3
6. Acoustical fluid interactions are neglected, i.e., the 5. St1=Sc1 MPa 800.00 880.00 870.0
shaft is assumed to be acting in a vacuum. 6. St2=Sc2 MPa 40.0 60.0 54.0
7. Since lamina is thin and no out-of-plane loads are 7. S12 MPa 72.0 97.0 30.0
applied, it is considered as under the plane stress. 8.  Kg/ 2000.00 1600.0 1600.0
m3
2.3 Selection of Cross-Section
The drive shaft can be solid circular or
hollow circular. Here hollow circular cross-section 2.6 Selection of Materials
was chosen because: Properties of E-Glass/Epoxy, HS Carbon/Epoxy and
 The hollow circular shafts are stronger in per kg HM Carbon/Epoxy
weight than solid circular. Based on the advantages discussed earlier,
 The stress distribution in case of solid shaft is zero the E-Glass/Epoxy, High Strength Carbon/Epoxy and
at the center and maximum at the outer surface High Modulus Carbon/Epoxy materials are selected
while in hollow shaft stress variation is smaller. In for composite drive shaft. The Table shows the
solid shafts the material close to the center are not properties of the E-Glass/Epoxy, High Strength
fully utilized. Carbon/Epoxy and High Modulus Carbon/Epoxy
2.4 Selection of Reinforcement Fiber materials used for composite drive shafts.
Fibers are available with widely differing properties.
Review of the design and performance 3. Design optimization:
requirements usually dictate the fiber/fibers to be Optimization of an engineering design is an
used. improvement of a proposed design that results in the
 Carbon/Graphite fibers: Its advantages best properties for minimum cost. Most of the
include high specific strength and modulus, low methods used for design optimization assume that the
coefficient of thermal expansion, and high fatigue design variables are continuous. In structural
strength. Graphite, when used alone has low impact optimization, almost all design variables are discrete.
resistance. Its drawbacks include high cost, low A simple Genetic Algorithm (GA) is used to obtain
impact resistance, and high electrical conductivity. the optimal number of layers, thickness of ply and
 Glass fibers: Its advantages include its low cost, fiber orientation of each layer. All the design
high strength, high chemical resistance, and good variables are discrete in nature and easily handled by
insulating properties. The disadvantages are low GA. With reference to the middle plane, symmetrical
elastic modulus, poor adhesion to polymers, low fiber orientations are adopted.
fatigue strength, and high density, which increase
shaft size and weight. Also crack detection 3.2 Optimization Techniques.
becomes difficult. GA´s differs from traditional optimization
 Kevlar fibers: Its advantages are low density, high algorithm in many ways. A few are listed here .
tensile strength, low cost, and higher impact1. GA does not require a problem specific
resistance. The disadvantages are very low knowledge to carry out a search. GA uses only the
compressive strength, marginal shear strength, and values of the objective function. For instance,
high water absorption. Kevlar is not recommended calculus based search algorithms use derivative
for use in torque carrying application because of its information to carry out a search.
low strength in compression and shear Here, both GA uses a population of points at a time in
glass and carbon fibers are selected as contrast to the single point approach by the traditional
potential materials for the design of shaft.

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optimization methods. That means at the same time
 T 
GAs process a number of designs. 2. C2  1  cr 
In GA, the design variables are represented  Tmax 
as strings of binary variables that correspond to the
chromosomes in natural genetics. Thus the search If Tcr  Tmax
method is naturally applicable for solving discrete =0
and integer programming problems. For continuous Otherwise
variable, the string length can be varied to achieve
any desired resolution.
 N 
GAs uses randomized operators in place of 3. C3  1  crt 
the usual deterministic ones. In every generation, a
new set of strings is produced by using randomized
 N max 
parents selection and crossover from the old If N crt  N max
generation (old set of strings). =0
Otherwise
3.3 Objective Function C  C1  C2  C3
The objective for the optimum design of the
composite drive shaft is the minimization of weight, Using the method of Rajeev and
so the objective function of the problem is given as Krishnamoorthy, the constrained optimization can be
Weight of the shaft, m   AL
converted to unconstrained optimization by
modifying the objective function is
   m 1  k1C 
m
4
d 2
0  d i2  L
For all practical purposes, k1 is a penalty constant and
3.4 Design Variables is assumed to be 10.
The design variables of the problem are 3.6 Input GA Parameters
 Number of plies Input GA parameters of E-Glass / Epoxy, HS
 Thickness of the ply Carbon / Epoxy and HIM Carbon / Epoxy composite
 Stacking Sequence drive shafts are shown in the table
The limiting values of the design variables are given
as follows. Input GA Parameters
1. n0 Number of Parameters n/2+2 if n is even
2. 90   k  90 (n+1)/2+2 if n is odd
Total string length 139
3. 0.1  tk  0.5 Population size 50
Where k = 1, 2 …………….. n and n = 1, 2, 3, Maximum generations 150
…………. 32 Cross-over probability 1
The number of plies required depends on the Mutation probability 0.003
design constraints, allowable material properties,
String length for number of 5
thickness of plies and stacking, sequence. Based on
plies
the investigations it was found that up to 32 numbers
of plies are sufficient. String length of fiber 8
3.5 Design Constraints orientation
1. Torque transmission capacity of the shaft String length for thickness of 6
T  Tmax ply

2. Bucking torque capacity of the shaft
4. Design Analysis
Tcr  Tmax Finite Element Analysis (FEA) is a
3. Lateral fundamental natural frequency computer-based numerical technique for calculating
N  N crt the strength and behavior of engineering structures. It
can be used to calculate deflection, stress, vibration,
 The constraint equations may be written as
buckling behavior and many other phenomena. It also
 T  can be used to analyze either small or large scale
1. C1  1   If deflection under loading or applied displacement. It
 Tmax  uses a numerical technique called the finite element
T  Tmax method (FEM). In finite element method, the actual
continuum is represented by the finite elements.
=0 Otherwise These elements are considered to be joined at
specified joints called nodes or nodal points. As the
actual variation of the field variable (like

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displacement, temperature and pressure or velocity)
inside the continuum is not known, the variation of
 A1 A2 A3 A4 A5 A6 
the field variable inside a finite element is A A7 A8 A9 A10 A11 
approximated by a simple function.  2   A1 A2 A3 
A A8 A12 A13 A14 A15   
The approximating functions are also called
as interpolation models and are defined in terms of  A   A3 A9 A13 A16 A17
 or  A  A2 A4 A5 
A18  33
field variable at the nodes. When the equilibrium  4  A3 A5 A6 
equations for the whole continuum are known, the  A5 A10 A14 A17 A19 A20   
unknowns will be the nodal values of the field  
variable.  A6
 A11 A15 A18 A20 A21 

In this project finite element analysis was
carried out using the FEA software ANSYS. The Sub matrices [B] and [D] are input similarly.
primary unknowns in this structural analysis are Note that all sub matrices are symmetric. {MT} and
displacements and other quantities, such as strains, {BT} are for thermal effects. The layer number (LN)
stresses, and reaction forces, are then derived from can range from 1 to 250.
the nodal displacements. In this local right-handed system, the x'-axis
is rotated an angle THETA (LN) (in degrees) from
4.1 Modeling Linear Layered Shells the element x-axis toward the element y-axis. The
SHELL99 may be used for layered total number of layers must be specified (NL). The
applications of a structural shell model as shown in properties of all layers should be entered (LSYM =
Figure SHELL99 allows up to 250 layers. The 0). If the properties of the layers are symmetrical
element has six degrees of freedom at each node: about the mid-thickness of the element (LSYM = 1),
translations in the nodal x, y, and z directions and only half of properties of the layers, up to and
rotations about the nodal x, y, and z-axes. including the middle layer (if any), need to be
entered. While all layers may be printed, two layers
may be specifically selected to be output (LP1 and
LP2, with LP1 usually less than LP2).
The results of GA forms input to the FEA.
Here Finite Element Analysis is done on the HS
Carbon/Epoxy drive shaft.

4.3 Static Analysis
Static analysis deals with the conditions of
equilibrium of the bodies acted upon by forces. A
static analysis can be either linear or non-linear. All
Figure : SHELL99 Linear Layered Structural Shell types of non-linearities are allowed such as large
deformations, plasticity, creep, stress stiffening,
4.2 Input Data contact elements etc. this chapter focuses on static
The element is defined by eight nodes, analysis. A static analysis calculates the effects of
average or corner layer thicknesses, layer material steady loading conditions on a structure, while
direction angles, and orthotropic material properties. ignoring inertia and damping effects, such as those
A triangular-shaped element may be formed by carried by time varying loads. A static analysis is
defining the same node number for nodes K, L and O. used to determine the displacements, stresses, strains
The input may be either in matrix form or layer form, and forces in structures or components caused by
depending upon KEYOPT (2). Briefly, the force- loads that do not induce significant inertia and
strain and moment-curvature relationships defining damping effects. A static analysis can however
the matrices for a linear variation of strain through the include steady inertia loads such as gravity, spinning
thickness (KEYOPT (2) = 2) may be defined as: and time varying loads.
In static analysis loading and response
conditions are assumed, that is the loads and the
structure responses are assumed to vary slowly with
respect to time. The kinds of loading that can be
applied in static analysis includes,
Externally applied forces, moments and pressures
Steady state inertial forces such as gravity and
spinning
Imposed non-zero displacements
A static analysis result of structural
displacements, stresses and strains and forces in
structures for components caused by loads will give a

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clear idea about whether the structure or components
will withstand for the applied maximum forces. If the
stress values obtained in this analysis crosses the
allowable values it will result in the failure of the
structure in the static condition itself. To avoid such a
failure, this analysis is necessary.

4.4 Boundary Conditions
The finite element model of HS
Carbon/Epoxy shaft is shown in Figure .One end is
fixed and torque is applied at other end,

Figure: Boundary Conditions for the Modal
Analysis

For thin walled shafts, the failure mode
under an applied torque is torsional buckling rather
than material failure. For a realistic driveshaft system,
improved lateral stability characteristics must be
achieved together with improved torque carrying
capabilities. The dominant failure mode, torsional
buckling, is strongly dependent on fiber orientation
Figure : Finite element model of HS Carbon/Epoxy
angles and ply stacking sequence.
shaft

4.5 Modal Analysis 5. Results
When an elastic system free from external 5.1GA Results
forces is disturbed from its equilibrium position it A composite drive shaft for rear wheel drive
vibrates under the influence of inherent forces and is automobile was designed optimally by using genetic
said to be in the state of free vibration. It will vibrate Algorithm for E-Glass/ Epoxy, High Strength
at its natural frequency and its amplitude will Carbon/Epoxy and High Modulus Carbon/Epoxy
gradually become smaller with time due to energy composites with the objective of minimization of
being dissipated by motion. The main parameters of weight of the shaft which is subjected to the
interest in free vibration are natural frequency and the constraints such as torque transmission, torsional
amplitude. The natural frequencies and the mode buckling capacities and natural bending frequency.
shapes are important parameters in the design of a
structure for dynamic loading conditions. 5.2 Summarization of GA Results
Modal analysis is used to determine the The GA results are shown in Table
vibration characteristics such as natural frequencies Parameter Steel E-Glass / HS HM
and mode shapes of a structure or a machine Epoxy Carbon/Epoxy Carbon/Ep
component while it is being designed. It can also be a
oxy
starting point for another more detailed analysis such
as a transient dynamic analysis, a harmonic response do (mm) 90 90 90 90
analysis or a spectrum analysis. Modal analysis is L (mm) 1250 1250 1250 1250
used to determine the natural frequencies and mode tk (mm) 3.318 0.4 0.12 0.12
shapes of a structure or a machine component. Optimum 1 17 17 17
The rotational speed is limited by lateral no. of
stability considerations. Most designs are sub critical, layers
i.e. rotational speed must be lower than the first t (mm) 3.318 6.8 2.04 2.04
natural bending frequency of the shaft. The natural Optimum - [46/-64/-15/- [-56/-51/74/-82/ [-65/25/68/
frequency depends on the diameter of the shaft, stacking 13/ 67/70/13/- 44/-- 63/
thickness of the hollow shaft, specific stiffness and sequence 39/-84/- 75]S 36/- 40/-
the length. Boundary conditions for the modal 28/20/-27]s 39/74/- 39]S
analysis are shown in Figure.
Weight 8.604 4.443 1.1273 1.1274
4.6 Buckling Analysis (kg)
Buckling analysis is a technique used to
determine buckling loads (critical loads) at which a Weight - 48.36 86.90 86.90
structure becomes unstable, and buckled mode shapes saving (%)
(The characteristic shape associated with a structure's
buckled

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5.5 Buckling Analysis of HS Carbon/Epoxy Drive
Shaft

5.3 Static Analysis of HS Carbon/Epoxy Drive
Shaft
The twist about the axis of the shaft and 1st principal Figure : 1st Buckling Mode shape of HS
stress along the fiber direction are shown in Figures Carbon/Epoxy shaft

6. Conclusion
The following conclusions are drawn from the present
work.
The E – Glass / Epoxy, High Strength Carbon/ Epoxy
and High Modulus Carbon/Epoxy composite drive
shifts have been designed to replace the steel drive
shaft of an automobile.
A composite drive shaft for wheel drive
automobile has been designed optimally by using
Genetic Algorithm for E – Glass/ Epoxy, High
Strength Carbon/ Epoxy and High Modulus Carbon/
Epoxy composites with the objective of minimization
of weight of the shaft which was subjected to the
constraints such as torque transmission, torsional
bucking capacities and natural bending frequency.
Fig: 1st principal stresses along longitudinal The weight savings of the E – Glass/ Epoxy, High
direction for HS Carbon / Epoxy shaft Strength Carbon/ Epoxy and High Modulus Carbon/
Epoxy shafts were equal to 48.36%, 86.90%, and
5.4 Modal Analysis of HS Carbon/Epoxy Drive 86.90% of the weight of steel shaft respectively.
Shaft The optimum stacking sequence of E –
Glass/ Epoxy, High Strength Carbon/ Epoxy and
High Modulus Carbon / Epoxy shafts are shown in
Table.
Table: Optimum Stacking Sequence
Material Stacking Sequence
E – Glass / [46/-64/-15/-13/39/-
Epoxy 84/-28/20/-27]s
High Strength [-56/-51/74/-
Carbon/ Epoxy 8267/70/13/-44/-75]s
High Modulus [-65/25/68/-6363/-40/-
Carbon/Epoxy 39/74/-39]s
By using CLT, the variations of the stresses and
strains along thickness of the E – Glass/ Epoxy, High
Strength Carbon/Epoxy and High Modulus
Fig : 1st Vibration Mode shape of HS Carbon/Epoxy Carbon/Epoxy composite drive shafts were plotted
shaft CLT. It has been observed that all the stresses were
within the allowable limit.
The deflection of Steel, E – Glass/ Epoxy,
High Strength Carbon/Epoxy and High Modulus

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Carbon/Epoxy shafts were equal to 7. John W.Weeton et.al. 1986, “Engineers
0.012407, 0.025262, 0.019288 and 0.012919 mm guide to composite materials, American
respectively. Society for Metal, New York”.
The fundamental natural frequency of Steel, E – 8. Beardmore.P and Johnson C.F., 1986, “The
Glass/ Epoxy, High Strength Carbon/Epoxy and High Potential for Composites In Structural
Modulus Carbon/ Epoxy shafts were 9319.98, Automotive Applications,” Journal of
6514.56, 7495.42 and 9270.28 rpm respectively. Composites Science and Technology,
The torsional buckling capacity of Steel, E – Vol.26, pp 251-581.
Glass/Epoxy, High Strength Carbon/ Epoxy and High 9. Pollard.A, 1980, “Polymer Matrix
Modulus Carbon/Epoxy shafts were 43857.96, Composites in Driveline Applications”,
29856.45, 3772.11 and 3765.75 N-m respectively. Journal of Composite Structures, Vol.25, pp.
The torque transmission capacity of the composite 165-175.
drive shafts has been calculated by neglecting and 10. Faust.H. et.al., 1990, “A Compressive Rotor
considering the effect of centrifugal forces and it has Shaft for Chinook, Journal of Americian
been observed that centrifugal forces will be reduce Helicopter society,” Vol., 29, pp.54-58.
the torque transmission capacity of the shaft.
Natural frequency using Bernoulli – Euler and 8.Authors Biography:
Timoshenko beam theories was compared. The
frequency calculated by using the Bernoulli Euler D.DINESH was born in India, A.P. in
beam theory is high, because it neglects the effect of 1987. He received his B.Tech
rotary inertia & transverse shear (Mechanical) SKIT College,
SRIKALAHASTHI, Affliated from JNTU
References Ananthapur,in 2009, from June 2009 to
1. Jones, R.M., 1990, Mechanics of Composite December 2010 worked as a Production Engineer in
Materials, 2e McGraw – Hill Book KRISHNA SAA FABS PVT LTD, RENIGUNTA,
Company, New York. Chittoor DIST, Andhra Pradesh, Present he is doing
2. Aurtar K.Kaw, 1997, Mechanics of M.Tech (CAD/CAM)from SIETK College, Affliated
Composite Materials, CRC Press, New from JNTU Ananthapur, PUTTUR , Chittoor DIST,
York. Andhra Pradesh. His research areas are Modelling
3. Belingardi.G. Calderale.P.M. and Rosetto.M. &Analysing on Mechanical components.
1990, “Design of Composite Material Drive
shafts for Vehicular Applications”, Int.J.of
Vehicle Design, Vol.11, No.6pp.553-563. F.ANAND RAJU was born in India, A.P in 1976. He
4. Jin Kook Kim.Dai GiLee, and Durk Hyun received his diploma in GMR
Cho, 2001, “Investigation of Adhesively polytechnic college, Srisailam on Sep
Bonded Joints for Composite Propeller 1995 ,He completed his B.Tech
shafts” Journal of Composite Materials, (Mechanical) in 2000 from
Vol.35, No.11, pp. 999-1021. S.V.University, he did his M.Tech
5. Dai Gil Lee, et.al., 2004, “Design and (Production Engineering) from S.V.U College of
Manufacture of an Automotive Hybrid Engineering, Tirupathi in May 2002.
Aluminum /Composite Drive Shaft” Journal He is having 10 yearsteaching experience, At Present
of Composite Structures, Vol. 63, 99 87-89. he is working as a HOD of Mechanical Engineering
6. Agarwal B.D. and Broutman L.J., 1990, in SIETK College, PUTTUR, Chittoor DIST, Andhra
“Analysis and performance of fiber Pradesh,India
composites” John Wiley and Sons Inc.
.

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