Finite Element Modelling of Composite Rotor-Shaft-System Bachelor of Technology in Mechanical Engineering

Finite Element Modelling of Composite Rotor-Shaft-System
A thesis submitted in partial requirements for the degree of
Bachelor of Technology
in
Mechanical Engineering
By
Satyaranjan Sahoo (108ME036)
Ajay Shankar Suman (108ME045)
Manoj Kumar Beldar (108ME056)
Under the guidance
Of
Prof. T. Roy
National Institute of Technology
Rourkela
Orissa-769008
2012
National Institute Of Technology
Rourkela
CERTIFICATE
This is to certify that the thesis entitled, “Finite Element Modelling of Composite
Rotor-Shaft-System” submitted by Mr. Satyaranjan Sahoo (108ME036), Mr. Ajay
Shankar Suman (108ME045) and Mr. Manoj Kumar Beldar (108ME056) in partial
fulfilments for the requirement of the award of Bachelor of Technology Degree in
Mechanical Engineering at National Institute of Technology, Rourkela is an authentic work
carried out by them under our guidance. To the best of our knowledge, the matter embodied
in the thesis has not been submitted to any other University / Institute for the award of any
Degree or Diploma.
Prof. Tarapada Roy
Dept. of Mechanical Engineering
National Institute of Technology
Rourkela-769008
Date:
i
ACKNOWLEDGEMENT
I wish to express my sincere thanks and gratitude to Prof. Tarapada Roy for
suggesting me the topic and providing me the guidance, motivation and constructive criticism
throughout the course of the project.
I am grateful to Prof. (Dr.) K. P. Maity, Head of the Department, Mechanical
Engineering for providing me the necessary opportunities for the completion of my project.
Our project supervisors were instrumental in the process of bringing this project to its present
form. Without their key support, knowledge and experience, procurement of set-up, set-up of
project equipment and analysis work would not have been possible.
Date:
Satyaranjan Sahoo (108ME036)
Ajay Shankar Suman (108ME045)
Manoj Kumar Beldar (108ME056)
ii
Abstract:
The objective while manufacturing various machinery or automobile parts is usually to make
components of high strength and durability along with less weight or density. Generally
composite materials are preferred as compared to single material for high performance.
Composite consists of two or more material having same or different physical and chemical
properties. One of the materials serves as matrix holding together the other material
embedded in it which provides the reinforcement in the form of fibres. Glass epoxy materials
are generally used for its sustainability under heavy electrical and mechanical stresses under
high temperature operating conditions. In this project, various type of rotor-shaft system with
bearings is used having unbalance in rotor to study and compare better performance between
composite and single material under transient analysis. The material property was set to
orthotropic and isotropic for composite and single material respectively. E-Glass/Epoxy and
steel are used as composite and single material respectively for the analysis. The study uses
ANSYS-13 software for developing finite element model of the rotor-shaft system. The
element type for shaft, disk rotor and bearing were defined as beam188, mass21 and
combin14 respectively. The shafts were defined as solid and hollow by calculating the mass
moment of inertia and polar moment of inertia accordingly. Based on these models, analyses
were carried out to obtain a more stable rotor-shaft system. Graphs for bending stress vs. time
and displacement vs. time were studied for each case.
iii
Contents
Certificate
i
Acknowledgement
ii
Abstract
iii
List of figures
iv
List of tables
v
CHAPTER 1: Introduction
1.1 Common Categories of Composite Materials
2
1.2 Benefits of Composites
4
1.3 About Fibre Reinforced Polymer (FRP)
5
1.4 Applications of FRP Composites
5
1.5 Rotor-shaft system
6
1.6 Classification of bearings and its application
7
CHAPTER 2: Literature survey
2.1 Literature survey
9
2.2 Objective
10
CHAPTER 3: Material and methods
3.1 Composite Materials
12
3.2 Finite element Modeling
13
iv
CHAPTER 4: Results and discussion
4.1 Static analysis of a shaft
19
4.1.1 Application of torsion on solid and hollow shaft
19
4.1.2 Application of bending load on solid and hollow shaft
22
4.1.3 Application of combination of torsion and bending
25
load on solid and hollow shaft
4.2 Transient analysis of rotor-shaft system
29
CHAPTER 5: Conclusion and scope of future work
5.1 Conclusion
5.1.1 Based on the static analysis
35
5.1.2 Based on the transient analysis
35
5.2 Scope of future work
36
References
37
v
List of figures
Figure No.
Caption
Page No.
Fig 1.
Random fibre (short fibre) reinforced composites
3
Fig 2.
Continuous fibre (long fibre) reinforced composites
3
Fig 3.
Particles as the reinforcement (Particulate composites)
3
Fig 4.
Flat flakes as the reinforcement (Flake composites)
4
Fig 5.
Reinforcement is filler (Filler composites)
4
Fig 6.
Isometric view of a model of rotor-shaft system with bearings
13
Fig 7.
Mesh view of solid rotor-shaft system
13
Fig 8.
Mesh view of hollow rotor-shaft system
14
Fig 9.
Mesh view of solid shaft
16
Fig. 10
Mesh view of hollow shaft
16
Fig. 11
Smooth contours view for equivalent elastic strain
19
Fig. 12
Smooth contours view for maximum principal stress
20
Fig. 13
Smooth contours view for total deformation
20
Fig. 14
Smooth contours view for equivalent elastic strain
21
Fig. 15
Smooth contours view for maximum principal stress
21
Fig. 16
Smooth contours view for total deformation
22
Fig. 17
Smooth contours view for equivalent elastic strain
22
Fig. 18
Smooth contours view for maximum principal stress
23
Fig. 19
Smooth contours view for total deformation
23
Fig. 20
Smooth contours view for equivalent elastic strain
24
Fig. 21
Smooth contours view for maximum principal stress
24
Fig. 22
Smooth contours view for total deformation
25
Fig. 23
Smooth contours view for equivalent elastic strain
25
Fig. 24
Smooth contours view for maximum principal stress
26
vi
Fig. 25
Smooth contours view for total deformation
26
Fig. 26
Smooth contours view for total deformation
27
Fig. 27
Smooth contours view for total deformation
27
Fig. 28
Smooth contours view for total deformation
28
Fig. 29
Bending stress vs time diagram for solid rotor-shaft system
29
Fig. 30
Bending stress vs time diagram for hollow rotor-shaft system
30
Fig. 31
Displacement vs time diagram for solid rotor-shaft system
30
Fig. 32
Displacement vs time diagram for hollow rotor-shaft system
31
Fig. 33
Bending stress vs time diagram for solid rotor-shaft system
31
Fig. 34
Bending stress vs time diagram for hollow rotor-shaft system
32
Fig. 35
Displacement vs time diagram for solid rotor-shaft system
32
Fig. 34
Displacement vs time diagram for hollow rotor-shaft system
33
List of tables
Table No.
Caption
Page No.
Table 1.
Material properties used in analyses
12
Table 2.
Dimension of shaft and disk, and properties of bearing
15
vii
CHAPTER
INTRODUCTION
1
1
INTRODUCTION
Generally, a composite material is made up of two components acting together i.e.,
reinforcement (fibres, particles, flakes, and/or fillers) embedded in a matrix (polymers,
metals, or ceramics). The matrix holds the reinforcement to form the desired shape and size
while the reinforcement improves the mechanical properties of the matrix as per requirement.
A common example of a composite is disc brake pads, which consist of hard ceramic
particles embedded in soft metal matrix.
1.1 Common Categories of Composite Materials
Classification based on the form of reinforcement
a. Based on matrix material
i.
Metal matrix composites: It composed of metal matrix like aluminium, copper, cobalt,
iron and magnesium and dispersed ceramic like oxides and carbides or metallic phase like
lead, tungsten and molybdenum
ii. Ceramic matrix composites: They are composed of a ceramic matrix and embedded fibres
of other ceramic material
iii. Polymer matrix composites: they are composed of matrix from thermoset i.e. unsaturated
polyester and epoxy or thermoplastic i.e. polycarbonate, polyvinylchloride, nylon and
polysterene and embedded glass, carbon, steel or Kevlar fibres
2
b. Based on fibres as reinforcement:
Fig 1 . Random fibre (short fibre) reinforced composites [1]
Fig 2. Continuous fibre (long fibre) reinforced composites [1]
Fig 3. Particles as the reinforcement (Particulate composites) [1]
3
Fig 4. Flat flakes as the reinforcement (Flake composites) [1]
Fig 5. Reinforcement is filler (Filler composites) [1]
1.2 Benefits of Composites
a. Cost efficient for mass production, maintenance, fatigue life, durability and maturity of
technology.
b. Light weight with proper weight distribution
c. High strength and stiffness as it has high strength to weight ratio and high directional
strength and/or stiffness.
d. Highly useful in manufacture of large parts and special geometry
e. Better surface properties i.e. corrosion resistance, weather resistance and tailored surface
finish
4
f. Thermal properties is good i.e. low thermal conductivity and low coefficient of thermal
expansion
g. Useful electric properties were achieved i.e. high dielectric strength, non-magnetic and
radar transparency.
1.3 About Fibre Reinforced Polymer (FRP)
FRPs are typically organized in a laminate structure, such that each lamina or flat layer
contains an arrangement of unidirectional fibres fabrics embedded within a thin layer of
polymer matrix material. The fibres consist of carbon or glass which provides the strength
and stiffness. The matrix commonly made of polyester, Epoxy or Nylon which binds and
protects the fibres from damage and transfers the stresses between fibres.
1.4
Applications of FRP Composites
a) Uses in structural engineering: When a FRP specimen is tested in axial tension, the
applied stress is proportional to the ratio of strain. When the applied load is removed, it
returns to its original shape or size. In other words, FRP follows linear-elastically to axial
stress. FRP composite compression failure occurs when the fibres exhibit extreme lateral or
sides-way deflection, often in sudden and dramatic condition, called fibre buckling. Usually,
failure occurs within the matrix material parallel to the fibres. FRP's high strength properties
also include excellent durability and corrosion resistance. Furthermore, their high strength-toweight ratio is of significant benefit; a member composed of FRP can support larger live
loads since its dead weight does not contribute significantly to the loads that it must carry out.
Other advantages include its versatility, excellent fatigue life and fire resistant.
5
b) Uses in construction: Its applications for new construction repair and rehabilitation
applications and architectural applications are common. FRP is used in building structures
like bridges and columns. It demonstrated exceptional durability, and effective resistance to
effects of environmental exposure. Several companies across the world are beginning to
renovate damaged bridge piers to prevent collapse and steel-reinforced columns to improve
the structural integrity and to prevent buckling of the reinforcement. Architects have
discovered the applications of FRP in structures such as siding/cladding, roofing, flooring and
partitions. Intelligent Sensing for Innovative Structures (ISIS), of Canadian Universities, is a
program that consists of collaborative research and development efforts in various
engineering disciplines. Its primary aim is in the development of innovative uses of FRPs in
concrete
structures.
In Canada,
engineers
have integrated fibre
optic
sensors
into numerous FRP systems to ensure that adequate supervision of the systems is provided
1.5
Rotor-shaft system
ROTARY machines are commonly used in turbine, generators, and electrical motors. Primary
role of rotary shafts are in power transmission. Its applications are commonly seen in
automobiles, induced draft fans in blast furnace. These shafts consist of different parts such
as bearings, disks, gears and etc. on them. Common problem that occurs in this system is
unbalance, due to which vibration occurs while operating. So bearings are used to diminish
this vibration and prolong the tolerance of the system usage before it is balanced.
6
1.6
Classification of bearings and its application
a. Based on the direction of load
i. Radial bearings: It reduces support loads and rotational friction. As the bearing rotates the
balls also rotate simultaneously. It lowers rolling resistance and coefficient of friction as
compared to two flat surfaces was rotating. It’s used in of aircraft engines, wing flaps, fans,
trains and automobiles joints, etc.
ii. Thrust bearings: It is designed to manage axial loads and provide high shock load
resistance in a variety of operating conditions. It usually used in clutches, water pump, etc.
b. Based on nature of contact
i. Sliding contact bearings: It has excellent vibration and shock resistance. Damping
capability is excellent normal to direction of motion due to squeeze film damping. It enables
heat generated to conduct away. It is usually used in cam followers, insulators, liners, valve
seats, etc.
ii. Rolling contact bearings: They are used widely in instruments and machines in order to
support the shafts. It minimizes the friction and power loss associated with relative motion. It
is used in gear pump, hydraulic pump, helicopter rotors and transmission, material handling
equipment, etc.
iii. Journal bearings: There are no rolling elements in these bearings. Journal bearings operate
in the boundary region (metal-to-metal contact) only during the start-up and shutdown of the
equipment when the rotational speed of the shaft (journal) is insufficient to create an oil film.
It is used in automobile and aircraft engine, marine steam engine, steam turbines, etc.
7
CHAPTER
LITERATURE SURVEY
8
2
2.1 Literature survey
In the study of numerical modelling and analysis of composite beam structures subjected to
torsional loading by Kunlin Hsieh [2], his work deals with the effect of torsion of cylindrical
composite shaft. To solve the problem, eigen function expansion method is used. Torsion
response of laminated composite beam was studied in detail. Finite element model was
prepared using ANSYS PLANE77 (2D 8-node Thermal Solid) element. PLANE77 element
type has one degree of freedom, temperature at every node. The loading condition of the heat
transfer problem is specified as heat generation rate equals to twice the angle of twist per unit
length. After thermal analysis of the model, temperature at each node was obtained. Torsional
rigidity is concluded by summation of temperature at each node. For the composite model,
material properties were defined for graphite-polymer and glass-polymer. Finally, the results
were compared between the values of present analytic method and ansys.
In genetic algorithm based optimal control of smart composite shell structures under
mechanical loading and thermal gradient by Tarapada Roy and Debabrata Chakraborty, they
used material properties as shown in the table below.
In the study of a simple spinning laminated composite shaft model by Min-Yung Chang,
Jeng-Keag Chen, Chin-Yung Chang [3], a simple spinning composite shaft model was
developed. Its material was defined isotropically. The model contains bearing at both ends of
the shaft and a rigid disk at middle of the shaft. Using first order shear deformable beam
theory, strain energy of the shaft was obtained by considering three dimensional constitutive
relation of the material with the use of coordinate transformation. Kinetic energy of the shaft
was also obtained. Critical speed for the developed model was compared with the result
available in the literature.
9
In analysis of composite bars in torsion by Filiz ÇIVGIN [4], his objective was to develop a
finite element model of a composite bar and analyse for transmission application. The
material was defined as E-Glass/ Epoxy composites. The load condition was torque
transmission, torsional buckling strength capabilities. The element type was defined for the
model was Pipe Elast Straight i.e. Pipe16 with material property for anisotropic material. The
bar was constrained at one end i.e. at first node by setting all degree of freedom to zero. At
other end torsion was applied as -3e+06. The analysis was static and as result, displacements
were noted.
2.2 Objective:
In this study, a simply supported shaft is modelled using finite element modelling method.
The model is used for static analysis. The shaft is designed for both solid and hollow. One
material is defined for the shaft. Stress, strain and deformation were obtained. Secondly, the
shaft in rotor-shaft system is considered of composite material and single material and
transient analysis is carried out. Bending stress with respect to time and displacement wrt
time were calculated. From these results, the most stable system is concluded.
10
CHAPTER
MATERIALS AND METHODS
11
3
3.1 Composite material
The material properties were set to orthotropic medium for modelling of composite rotor
shaft system. For simply supported shaft, graphite material was used. Secondly, for rotor
shaft system, Glass-Epoxy material was used. The material properties used in the study are
shown below.
Table 1. Material properties used in analyses [2,5]
Material properties
GR/E laminae
Glass/Epoxy
Structural steel
172.5
55.77
200
6.9
17.92
--
3.45
8.96
--
G23 (GPa)
1.38
7.58
--
ὐ 12 = ὐ 23 = ὐ 13
0.25
0.25
0.30
ρ (Kg/m3)
1600
2550
7800
E1 (GPa)
E2=E3 (GPa)
G12=G13 (GPa)
12
3.2 Finite element Modelling
Fig 6. Isometric view of a model of rotor-shaft system with bearings
A rotor shaft system with bearings at both the ends of the shaft view was developed by
CATIA V9 is shown above in fig. 6. Mesh view of the system of solid and hollow shaft are
shown in the proceeding figure 7 and figure 8 respectively.
Fig 7. Mesh view of solid rotor-shaft system
13
Fig 8. Mesh view of hollow rotor-shaft system
The above finite element models were set to spin at 8000 rpm for 5 seconds. The element
type for shaft, disk rotor and bearing were defined as beam188, mass21 and combin14
respectively.
Beam 188: It has six or seven degrees of freedom at each node. These include translations in
the x, y, and z directions and rotations about the x, y, and z directions. A seventh degree of
freedom (warping magnitude) is optional. This element is well-suited for linear, large
rotation, and/or large strain nonlinear applications [6].
Mass 21: It is a point element having up to six degrees of freedom: translations in the nodal
x, y, and z directions and rotations about the nodal x, y, and z axes [6].
Combin 14: It has longitudinal or torsional capability in 1-D, 2-D or 3-D applications. The
longitudinal spring-damper option is a uniaxial tension-compression element with up to three
degrees of freedom at each node: translations in the nodal x, y, and z directions. No bending
14
or torsion is considered. The torsional spring-damper option is a purely rotational element
with three degrees of freedom at each node: rotations about the nodal x, y, and z axes. No
bending or axial loads are considered [6].
Dimensions of the shaft and disk are mentioned in table 3 as shown below.
Table 2. Dimension of shaft and disk, and properties of bearing [3]
Shaft
Disk
Bearing
Length(m)
0.72
--
--
Inner diameter(m)
0.028
--
--
Outer diameter(m)
0.048
--
--
Mass(Kg)
--
2.4364
--
Polar moment of
--
0.3778
--
--
0.1901
--
--
--
1.75
inertia(Kgm2)
Diameter moment of
inertia(Kgm2)
Kyy=Kzz(107 Nm-1)
15
Mesh view of simply supported shaft of graphite material is shown below for solid and
hollow shaft respectively in figure 9 and figure 10.
Fig 9. Mesh view of solid shaft
Fig. 10 Mesh view of hollow shaft
16
The above finite element models element type for shaft was defined as SOLID 272 and
SOLID 45 for solid and hollow shaft respectively.
SOLID 272: It is used to model axisymmetric solid structures. It is defined by four nodes on
the master plane, and nodes created automatically in the circumferential direction based on
the four master plane nodes. Each node has three degrees of freedom: translations in the
nodal x, y and z directions [6].
SOLID 45: It is used for the 3-D modelling of solid structures. The element is defined by
eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z
directions [6].
17
CHAPTER
RESULTS AND DISCUSSIONS
18
4
4.1 Static analysis of a shaft
A finite element model of simply supported solid and hollow shaft was designed. The
material properties were set for GR/E. Static analysis was carried out for bending load and
torsion, as loading conditions for each model. Also for the same models, both bending load
and torsion were applied together at one end.
4.1.1 Application of torsion on solid and hollow shaft:
1) Boundary conditions for torsion are: UX and UY is free
UZ = constant
2) Loading conditions for torsion are: Moment (at both ends in opposite direction) =
100Nm
Results for solid shaft:
a)
Fig. 11 Smooth contours view for equivalent elastic strain
The maximum limit of equivalent elastic strain is noted as 3.0714e-3 m/m
19
b)
Fig. 12 Smooth contours view for maximum principal stress
Maximum principal stress it is notes as 8.1326e6 Pa
c)
Fig. 13 Smooth contours view for total deformation
Maximum total deformation is 8.4431e-4 m
20
Results for hollow shaft:
a)
Fig. 14 Smooth contours view for equivalent elastic strain
The maximum limit of equivalent elastic strain is 3.3247e-3 m/m
b)
Fig. 15 Smooth contours view for maximum principal stress
21
The maximum principal stress is 8.711e6 Pa
c)
Fig. 16 Smooth contours view for total deformation
The maximum limit of total deformation is 9.5197e-4 m
4.1.2 Application of bending load on solid and hollow shaft:
Boundary conditions are: UX =UY =UZ = constant
Loading conditions = 10 N along negative Y axis direction(at mid-span)
Results for solid shaft:
a)
22
Fig. 17 Smooth contours view for equivalent elastic strain
The maximum limit of equivalent elastic strain is noted as 8.5629e-6 m/m.
b)
Fig. 18 Smooth contours view for maximum principal stress
The maximum principal stress limit is notes as 55235 Pa.
c)
Fig. 19 Smooth contours view for total deformation
23
The maximum limit for total deformation is noted as 5.8322e-6 m.
Results for hollow shaft:
a)
Fig. 20 Smooth contours view for equivalent elastic strain
The maximum limit of equivalent elastic strain is 1.3694e-5 m/m.
b)
24
Fig. 21 Smooth contours view for maximum principal stress
The maximum limit of maximum principal stress is 84764 Pa
c)
Fig. 22 Smooth contours view for total deformation
The maximum limit of total deformation is 6.9404e-6 m
4.1.3 Application of combination of torsion and bending load on solid and hollow shaft:
1) At one end boundary conditions are: UX =UY =UZ = constant
2) At other end loading conditions = 10N along -ve Y axis direction and moment = 100Nm
Results for solid shaft:
a)
25
Fig. 23 Smooth contours view for equivalent elastic strain
The maximum limit of equivalent elastic strain is noted as 3.0977e-3 m/m
b)
Fig. 24 Smooth contours view for maximum principal stress
The maximum limit of maximum principal stress is notes as 1.0957e7 Pa.
c)
26
Fig. 25 Smooth contours view for total deformation
The maximum limit of total deformation is 2.3833e-3 m
Results for hollow shaft:
a)
Fig. 26 Smooth contours view for total deformation
The maximum limit of equivalent elastic strain is 3.4109e-3 m/m.
b)
27
Fig. 27 Smooth contours view for total deformation
The maximum limit of maximum principal stress is 1.096e7 Pa.
c)
Fig. 28 Smooth contours view for total deformation
The maximum limit of total deformation is 2.6867e-3 m.
28
4.2 Transient analysis of rotor-shaft system
Transient analysis of a rotor-shaft system with bearing was studied. ANSYS 13.0
(Mechanical APDL) platform was used for the above analysis. The analysis was performed
on both composite and single material system of solid and hollow shaft. For composite
system, material properties of Glass/Epoxy material were used. Secondly, for single material
system, material properties of steel were used. The material properties of Glass/Epoxy and
steel are defined in table 2. Dimensions of shaft and disk, and properties of bearing are
defined in table 3.
Results for Epoxy/Glass composite:
Fig. 29 Bending stress vs time diagram for solid rotor-shaft system
29
Fig. 30 Bending stress vs time diagram for hollow rotor-shaft system
Fig. 31 Displacement vs time diagram for solid rotor-shaft system
30
Fig. 32 Displacement vs time diagram for hollow rotor-shaft system
Results for steel material:
Fig. 33 Bending stress vs time diagram for solid rotor-shaft system
31
Fig. 34 Bending stress vs time diagram for hollow rotor-shaft system
Fig. 35 Displacement vs time diagram for solid rotor-shaft system
32
Fig. 34 Displacement vs time diagram for hollow rotor-shaft system
33
CHAPTER
CONCLUSIONS
&
SCOPE OF FUTURE WORK
34
5
5.1 Conclusion
5.1.1 Based on the static analysis
i) For the application of torsion on solid shaft, the maximum limit of equivalent elastic strain,
maximum principal stress and total deformation are less as compared to the maximum limit
of equivalent elastic strain, maximum principal stress and total deformation of hollow shaft
respectively.
ii) For the application of bending load on solid shaft, the maximum limit of equivalent elastic
strain, maximum principal stress and total deformation are less as compared to the maximum
limit of equivalent elastic strain, maximum principal stress and total deformation of hollow
shaft respectively.
iii) For the application of both torsion and bending load at a time on solid shaft, the maximum
limit of equivalent elastic strain, maximum principal stress and total deformation are less as
compared to the maximum limit of equivalent elastic strain, maximum principal stress and
total deformation of hollow shaft respectively.
iv) From above readings, it shows that for an applied torsion, bending load or both, hollow
shaft is more susceptible than solid shaft. Solid shaft has a more stiffness and brittleness as
compared to hollow shaft.
5.1.2 Based on transient analysis
The Glass/Epoxy material system is having more strength and light weight as compared to
steel material system. Due to unbalance in rotor, the vibration in hollow rotor-shaft of
Glass/Epoxy material is low as compared to solid Glass/Epoxy rotor-shaft system. In other
words, hollow rotor-shaft system of Glass/Epoxy material is the most stable system.
35
5.2 Scope of future work
1. Fatigue life could be determined for the above rotor-shaft systems of each component.
2. Better performance could be optimized through using different types of bearings having
good stiffness coefficient and damping coefficient.
3. The study could be performed on various composite materials available of better strength,
cheaper and less weight as compared to Glass/Epoxy composite material.
4. Various analyses could be carried out to obtain more results and study various effects on
the rotor-shaft system. For an example, harmonic analysis could be performed to study about
critical speeds of the rotor-shaft system under various operating conditions.
36
REFERENCES:
[1] http://www.efunda.com/formulae/solid_mechanics/composites/comp_intro.cfm
[2] Kunlin Hsieh 2007, Numerical Modelling and Analysis of Composite Beam
Structures subjected to torsional loading pp. 28-30.
[3] Min-Yung Chang, Jeng-Keag Chen, Chih-Yung Chang 2003, A simple spinning
laminated composite shaft model, J. Solids and Structures 41 pp. 649-651.
[4] Filiz ÇIVGIN 2005, Analysis of composite bars in torsion pp. 87-109.
[5] Tarapada Roy and Debabrata Chakraborty 2009, Genetic algorithm based optimal
control of smart composite shell structures under mechanical loading and thermal
gradient J.Smart Mater. Struct. 18 pp.8-9.
[6] ANSYS, “Documentation and Theory Reference,” Version 9.0, ANSYS, Inc., 2004.
[7] P.Beardmore, and Johnson C.F, "The Potential for Composites in Structural
Automotive 1986, Journal of Composites Science and Technology, 26, pp. 251-281.
[8] A.S. Das, M.C. Nighil, J.K. Dutt , H. Irretier 2007, Vibration control and stability
analysis of rotor-shaft system with electromagnetic exciters, J. Mechanism and Machine
Theory 43, pp. 1295–1316.
[9] Y Chen, HB Zhao, ZP Shen, I Grieger, B.-H. Kro¨plin 1993, Vibrations of high
speed rotating shells with calculations for cylindrical shells, Journal of Sound and
Vibration, 160 pp. 137–160.
[10] Lien-Wen Chen Wen-Kung Peng 1998, The stability behavior of rotating composite
shafts under axial compressive loads, Composite Structures 41 pp. 254-258.
[11] SB Dong 1968, Free vibration of laminated orthotropic cylindrical shells, The
Journal of the Acoustical Society of America, 44 pp. 1628–1635.
37
[12] CW Bert 1993, The effect of bending-twisting coupling on the critical speed of a
driveshaft, Proceedings of the 6th Japan-U.S. Conference on Composite Materials pp.
29–36.
[13] Mohammad Reza Khoshravan, Iran Amin Paykani, Iran Aidin Akbarzadeh 2011,
Design and modal analysis of composite drive shaft for automotive application J. of
Engineering Science and Technology (IJEST) pp. 2544-2549.
38

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