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International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1004
DESIGN AND ANALYSIS OF HELICOPTER MAIN ROTOR HEAD
M. Akhila 1, S.Vivekananda 2
1MTECH Student of Mechanical Engineering Department, Machine Design,
Malla Reddy College of Engineering and Technology,
Hyderabad, Telangana, India, akhila.muruganparvathy@gmail.com
2 Assistant Professor, Dept. of Mechanical Engineering, Malla Reddy College of Engineering and Technology,
Hyderabad, Telangana, India, somavivek@mrcet.ac.in
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - The rotating component of a helicopter that
produces lift is called the rotor system. The hub, rotor
blades, and mast make up this rotor. A mast is a hollow,
cylindrical metal shaft that stretches upward and is
propelled. It is occasionally additionally supported by a
transmission. In this scenario, a rotor hub must support the
weight of the blades as well as aerodynamic forces. The
strength of the helicopter blades and rotor hub will be
determined. The rotor blades' attachment point to a top is a
mast (hub).The helicopter main rotor head consist of rotor
hub, mash, rotor blade and a swash plate. The Helicopter
Rotor Head Model and Assemble will be completed, along
with theoretical calculations, a Structural Analysis & Modal
Analysis on two different materials for the Helicopter Rotor
Head, and analysis in ANSYS. In order to calculate
displacements and stresses under static conditions,
structural analysis is used. A three component system's
vibration characteristics (natural frequencies & mode
shapes) are determined via modal analysis.
The main focus of this study was the modeling and analysis
of the helicopter rotor head. SOLIDWORKS, a cutting-edge
modeling programme, was used to model and assemble the
components . In ANSYS 2022 R2, an analysis is performed.
Key Words: Analysis, Optimization, Solid works
(Modelling), ANSYS (Static structural analysis, Fatigue
analysis, modal analysis).
1. INTRODUCTION
Although helicopters exist in a wide range of sizes
and designs, the most of them have similar main parts. A
chapter introduces the main portions and components of a
helicopter as well as the systems that go along with it.
Knowing how a helicopter's parts and systems function
helps a pilot see problems and potential emergency
situations more quickly. A revolving component of a
helicopter that produces lift is the rotor system. A mast,
hub, and rotor blades make up a rotor. A mast is an
upward-extending hollow cylindrical metal shaft that is
powered by and occasionally supported by a transmission.
A hub, which serves as a rotor blade's connection point, is
located at the top of a mast. There are several different
ways to attach rotor blades to a hub. The way a main rotor
blade is attached to and moves in relation to a main rotor
hub determines what type of main rotor system it is.
Semirigid, rigid, or completely articulated are the three
fundamental categories. An designed combination of ase
types is used in several contemporary rotor systems, such
as bearingless rotor systems.
2. LITERATURE REVIEW
Richard L. Rotelli, Jr. did a three-dimensional
stress analysis of a new main rotor hub design for an SH-2F
helicopter using a cycle symmetry feature of MSC/NASTAN.
The investigation used cyclic symmetry. A one-eighth
symmetry finite element model was made using the
FEMGEN interaction graphics mesh generator. A graphic
representation of the structural reaction of a rotor hub to
various loading situations, as predicted by MSC/NASTAN,
was provided using an interactive results viewing tool
developed by FEMGEN. A novel design for a primary rotor
hub benefited from the NASTRAN analysis results when
they were presented in this manner.
Modes form and harmonic analysis of various
helicopter blade architectures by Yon CHEVALIER, Abd-el-
Kader NOUR, and Mohamed Tahar GHERBI. This research
focuses on the helicopter blade's dynamic behaviour. A
goal is to mimic the behaviour of a blade made of various
materials under an aerodynamic force using the finite
elements approach. This study was carried out to compute
the stresses operating on a structure for various modes and
to analyse the aerodynamic loads imposed and evaluated
using a numerical simulation of frequencies and Eigen
modes. The determination of vibration responses resulting
from unbalance and other stimulation modes has been
made possible through the study of transient behaviour.
Moritz Grawunder, Roman Reß, Victor Stein,
Christian Breitsamter, and Nikolaus A. Adams, "Flow
Characteristics of a Five-Bladed Rotor Head," This paper
gives an examination of the flow properties, including
cyclic pitch, of a spinning five-bladed rotor head. Finding
opportunities for efficiency gains is a key goal. Through
numerical simulations based on incompressible unstable
Reynolds average Navier Stokes equations, findings are
produced. Mesh deformation is used to simulate cyclic
pitch motion. It is demonstrated that a pitch control system
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1005
significantly increases parasite drag. Thus, there is
potential for reducing drag by increasing the aerodynamic
fairing of ase components. Additionally, it is demonstrated
that the aerodynamic properties are significantly impacted
by the cyclic pitch motion of a blade cuff.
3. METHODOLOGY
For improved performance, the design and
material of the helicopter's main rotor head have been
adjusted. The main rotor head of the helicopter should be
optimised for durability, toughness, high dimension
stability, wear resistance, strength, and cost of materials
as well as economic considerations.
• Perform Helicopter Main Rotor Head design in
Solidworks based on design calculation and design model
dimension.
• Make design calculations for various types of Helicopter
Main Rotor Head.
• To create a solid works model of the helicopter's main
rotor head's structural integrity Analytical calculations
were utilised to calculate a part's dimensions, which were
then applied to modelling. A base of the main rotor head of
the helicopter was an extruded object. On a top, extruded
cut profiles were used. An ANSYS workbench model was
imported after being saved.
• To create and store static, modal, and fatigue analyses for
a helicopter main rotor head's structural study in ANSYS
• Following the completion of a finite element analysis,
data collection, and comparison of the designs for
helicopter main rotor heads, By experimenting with
several materials, choose the optimum material that will
work for the helicopter's main rotor head (steel or
alluminium)
• Perform static analysis where force, displacement, total
deformation, and equivalent stress are determined.
• Perform a fatigue analysis, which determines a fatigue
life and a fatigue safety factor.
• determine the natural frequency and perform modal
analysis at various frequencies.
• Perform a modal analysis, which identifies various
modes at various frequencies.
• Helicopter design Various materials are analysed for the
Main Rotor Head, and data is gathered to determine
whether the design is safe or not.
4. HELICOPTER MAIN ROTOR HEAD DIMENSIONS
For improved performance, the design and
material of the helicopter's main rotor head have been
adjusted. The main rotor head of the helicopter should be
optimised for durability, toughness, high dimension
stability, wear
Figure 1: side view 1
Figure 2: side view 2
Figure 3: dimension of Helicopter rotor head top view
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1006
Figure 4: isometric view
5. ANALYTICAL DESIGN OF HELICOPTER MAIN
ROTOR HEAD
5.1 Design Specifications conditions
Analyzing the benefits and drawbacks of various
rotor head designs was the first step in the rotor head
selection process. The following criteria for a design were
decided upon:
1. diameter of a rotor would be approximately one meter
2. rotor head should be fully articulated and Coaxial
3. blades must be easily interchangeable to test different
designs
4. number of blades should be variable
parameters were met by a final design, which was
built based on a Coaxial system. Changing a total number
of blades can be accomplished by removing a blade grip
assemblies and reattaching am to a different hub built for
a appropriate number of blades. Individual blades are
changed by disconnecting am from a blade grip and
attaching a new blade.
5.2 Design Specifications
We are going to design a helicopter main rotor
head using analytical method of calculation for that taking
some standard specification are given on following Table
5.2.1 Specification of Coaxial helicopters
Length: 16 m (52 ft 6 in)
Height: 4.93 m (16 ft 2 in)
Empty weight: 7,700 kg (16,976 lb)
Gross weight: 9,800 kg (21,605 lb)
Max takeoff weight: 10,800 kg (23,810 lb)
Powerplant: 2 × Klimov VK-2500
turboshaft engines, 1,800
kW (2,400 shp) each
Main rotor
diameter:
2 × 14.5 m (47 ft 7 in)
Main rotor area: 330.3 m2 (3,555 sq ft)
contra-rotating 3-bladed
main rotors
Table 1: Specification of Coaxial helicopters
Kind of load
Value Unit
Aerodynamic lift
force
1500 N
Centrifugal force of a
blade
6156 N
Aerodynamic drag
force of a blade
40 N
Torque 160 Nm
Rotational speed 180 rad/s
Table 2: Loads in Coaxial helicopters
5.3 Design Calculations
5.3.1 Blade sizing
A very first step of our design is to determine a
dimension of a rotor blade of a rotor mechanism. This
part is done by following various design approach of RC
helicopter blades.
A primary assumption of a dimension for a blade is, Disc
radius = Blade span = R = 0.5m , Blade Chord = C = 0.1m ,
N = Number of blades
From Blade elementary aory,
Solidity Factor, Solidity Factor,
𝜎 = (Blade Area)/(Disc Area )= ((N×C) )/(π×R )
Now, For 3 Blade, N = 3, Solidity Factor,
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1007
𝜎 = ((3×0.1))/((π×0.5) )= 0.191
Again, For 2 Blade, N = 2, Solidity Factor,
𝜎 = ((2×0.1))/((π×0.5) )= 0.127
Lift curve slope,
a =
Here, a0= First term in Fourier series = 2 π/ rad E =
Oswald Efficiency Factor = 0.9 AR = aspect ratio = R/C =
0.5/0.1 = 5 So, Lift Curve slope,
a = = 4.34/rad
Now, Flapping Frequency,
λ= [√( ) ]
λ [√( ) ]=0.5381
Here, θ = Pitch angle of a blade varies from 0-120
Angular velocity for a rotor blade,
=2 ×(π/60)× N =2 ×(π/60)× 3=0.3151
And blade tip velocity,
VT = 0.5 × = 0.5× 0.3141 =0.1570
coefficient of thrust
CT =4 λ 2 =4× 0.53812 =2.1524
Thrust,
T = 0.5 × 1.225× 0.15702 × 0.7853 × 2.1524 = 0.02551
Here,
Density of Air, ρ=1.225 kg/m3 Area = 0.7853981634 m2
Coefficient of power,
CP = 4λ3 =4× 0.53813 =0.6232
Power,
P = 0.5 × ρ × VT
3 × A × CP =0.5 × 1.225× 0.15703 × 0.7853 ×
0.6232=1.1600× 10 -3
Here,
Density of Air, ρ=1.225 kg/m3
Area = 0.7853981634 m2
In order to determine if a rotor head design will
withstand a forces it will be subjected to during normal
operations, a maximum forces and moments were
calculated. A forces were needed to calculate a stresses on
individual components while a moments were used to
calculate a coning angle. By calculating a coning angle it
was possible to evaluation of a various force components.
A two most significant forces and moments on a
components are those generated by a centrifugal force and
a lift force
A rotor head is designed to operate between 1000
to 1350 rpms with a maximum radius of 0.6 meters based
on this a forces and moments are calculated using
1500rpms. By using 1500rpm a margin of safety was built
directly into a calculations. When a moment generated by
centrifugal force and moment generated by lift are equal a
coning angle can be calculated.
6. RESULT AND DISCUSSION
6.1 3D Model in Solidworks
Figure 5: Part Design of Blade
Figure 6: Part Design of Helicopter main rotor Hub
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1008
Figure 7: Part Design of Helicopter swash plate
6.2 3D MODEL of Helicopter Main Rotor Head
Assembly
Figure 8 : 3D MODEL Assembly of Helicopter Main Rotor
Head
6.3 Helicopter Main Rotor Head Model in Ansys
Figure 9: Helicopter main rotor head in Ansys
Figure 10: mesh
Figure 11: cylindrical support
Figure 12: displacement
Figure 13: force 1
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1009
Figure 14: force 2
6.4 Helicopter Main Rotor Head of steel
6.4.1 Static analysis
Figure 15: total deformation- steel material
Figure 16: equivalent stress - steel material
Time
[s]
Minimum
[mm]
Maximum
[mm]
Average [mm]
1. 0. 1.7523 0.32282
Table 3: total deformation
Time
[s]
Minimum
[MPa]
Maximum
[MPa]
Average
[MPa]
1. 3.8096e-007 88.663 1.1991
Table 4: equivalent stress
6.4.2 Fatigue analysis
Figure 17: life- steel material
Figure 18: safety factor- steel material
Time [s] Minimum Maximum Average
1. 8.5025e+005 1.e+006 1.e+006
Table 5: life
Time [s] Minimum Maximum Average
1. 8.5025e+005 1.e+006 1.e+006
Table 6: safety factor
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1010
Figure 19: Fatigue Sensitivity
6.4.3 Modal analysis
Figure 20: Total deformation 1- steel material
Figure 21: Total deformation 2- steel material
Figure 22: Total deformation 3- steel material
Mode Frequency [Hz] Maximum [mm]
1. 4.878 74.95
2. 4.8791 74.26
3. 4.8793 74.26
Table 7 : Frequency
6.5 Helicopter Main Rotor Head of Aluminum
6.5.1 Static analysis
Figure 23: total deformation- Aluminium material
Figure 24: equivalent stress- Aluminium material
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1011
Time
[s]
Minimu
m [mm]
Maximum
[mm]
Average [mm]
1. 0. 4.9236 0.90716
Table 8: total defornation
Time
[s]
Minimum
[MPa]
Maximum
[MPa]
Average
[MPa]
1. 5.8888e-007 87.354 1.2
Table 9: equivalent stress
6.5.2 Fatigue analysis
Figure 25 : life- Aluminium material
Figure 26: safety factor- Aluminium material
Time
[s]
Minimum Maximum Average
1. 6.7006e+007 1.e+008 1.e+008
Table 10 : life
Time [s] Minimum Maximum Average
1. 0.94718 15. 14.763
Table 11 : safety factor
Figure 31: Fatigue Sensitivity
6.5.3 Modal analysis
Figure 27: total deformation 1- Aluminium material
Figure 28: total deformation 2- Aluminium material
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1012
Figure 29: total deformation 3- Aluminium material
Mode Frequency [Hz] Maximum[mm]
1. 4.8932 126.18
2. 4.8943 125.89
3. 4.8945 125.89
Table 12 : Frequency
Compressive
Ultimate
Strength MPa
Compressive
Yield Strength
MPa
Tensile
Yield
Strength
MPa
Tensile
Ultimate
Strength
MPa
0 250 250 460
Table 13: Structural steel parameter
Alternating Stress MPa Cycles Mean Stress MPa
3999 10 0
2827 20 0
1896 50 0
1413 100 0
1069 200 0
441 2000 0
262 10000 0
214 20000 0
138 1.e+005 0
114 2.e+005 0
86.2 1.e+006 0
Table 14: S-N Curve of Structural steel
Strength
Coefficient
z (MPa)
Strength
Expone
n-t
Ductility
Coefficie
n-t
Cyclic
Strength
Coefficie
nt (MPa}
Cyclic
Strain
Hardenin
g
Exponent
920 0.106 0.213 1000 0.2
Table 15: Strain-Life Parameters of Structural steel
Young's
Modulu
s MPa
Poisson'
s Ratio
Bulk
Modulus
MPa
Shear
Modulu
s MPa
Relative
Permeabilit
y
2.e+00
5
0.3 1.6667e+00
5
76923 10000
Table 16: Isotropic Elasticity of Structural steel
Compressive
Ultimate
Strength MPa
Compressive
Yield Strength
MPa
Tensile
Yield
Strength
MPa
Tensile
Ultimate
Strength
MPa
0 280 280 310
Table 17 : alluminium alloy properties
Alternating Stress
MPa
Cycles R-Ratio
275.8 1700 -1
241.3 5000 -1
206.8 34000 -1
172.4 1.4e+005 -1
137.9 8.e+005 -1
117.2 2.4e+006 -1
89.63 5.5e+007 -1
82.74 1.e+008 -1
170.6 50000 -0.5
139.6 3.5e+005 -0.5
108.6 3.7e+006 -0.5
87.91 1.4e+007 -0.5
77.57 5.e+007 -0.5
72.39 1.e+008 -0.5
144.8 50000 0
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1013
120.7 1.9e+005 0
103.4 1.3e+006 0
93.08 4.4e+006 0
86.18 1.2e+007 0
72.39 1.e+008 0
74.12 3.e+005 0.5
70.67 1.5e+006 0.5
66.36 1.2e+007 0.5
62.05 1.e+008 0.5
Table 18 : S-N Curve of alluminium alloy
Young's
Modulus
MPa
Poisson's
Ratio
Bulk
Modulus
MPa
Shear
Modulus
MPa
Relative
Permeability
71000 0.33 69608 26692 1
Table 19 : Aluminum alloy property
[1] Manually calculated permissible stress of modified
design= 11.43 N/mm2
Analytically calculated equivalent stress of modified
design for steel = 89.445 Mpa
Analytically calculated equivalent stress of modified
design for aluminum = 88.131 Mpa
Fatigue life of steel = 1×106
Fatigue life of aluminum = 1×108
Fatigue Safety factor of steel and aluminum = 15
[2] Equivalent von-Mises stresses of our helicopter's main
rotor head design are less than a yield strength. These
results have been compared with current results of a
similar model under the same loading conditions to
validate FEA results. The yield stress, which is 250 MPa for
steel and 280 MPa for aluminium, is far below the stress
value. Analysis revealed that the von-Mises stresses for the
two materials were nearly identical.
Tensile yield strength of steel = 250 MPa
Tensile yield strength of aluminum = 280 MPa
Endurance limit of steel = 230 MPa
Endurance limit of aluminum = 310 MPa
The structural behaviour of the main rotor head
of a helicopter was investigated for various materials. A
blade weight and aerodynamic forces are carried by the
main rotor head of the helicopter in this illustration. In
that situation, the strength of the helicopter's main rotor
head will be determined. Therefore, a static analysis,
fatigue analysis, and modal analysis are carried out on the
main rotor head of the helicopter for various materials,
such as steel and aluminium alloy.
Equivalent von-Mises stress is lower than yield
strength and fatigue limit, thus steel has a lower fatigue
life and endurance limit than aluminium. Since steel is
lighter than aluminium and can handle enormous loads or
weight, it is a more ideal material for the main rotor head
of a helicopter. We discovered a distortion in modal
analysis at various frequencies.
7. CONCLUSION
Extensive historical research makes it evident
that the issue has not yet been fully resolved, and
designers are still having many difficulties, particularly
with stress concentration and the impact of loading other
oar variables. The most well-liked strategy for analysing
fracture mechanics issues is the finite element approach.
Some helicopter main rotor heads made of steel are almost
as light as those made of aluminium. However, steel's key
benefit is that it is more rigid and has higher fatigue
strength than aluminium. We can therefore conclude that
aluminium is good for producing inexpensive helicopter
main rotor heads whereas steel is a better material in
terms of strength. SOLIDWORKS was used to successfully
complete a project's design. Using SOLIDWORKS, issues
that arose during the design of a machine were
successfully resolved.
The majority of the key components of SOLIDWORKS, a
flexible and all-inclusive programme for three-
dimensional solid modelling, were used in the project
design.
The primary features used to develop
components are protrusion and cut. Using SOLIDWORKS, a
component is drawn very precisely. Hence, When
compared to the existing design of the helicopter's main
rotor head at the same applied force, the modified design
for the variable valve actuation system carries less stress.
It demonstrates that a modified helicopter main rotor
head is more durable than an existing one over a lengthy
period of time, and according to a design assessment, the
new design is simpler than the existing one and exhibits
less deformation. Equivalent von-Misses stress is smaller
than yield strength and fatigue limit. A steel's endurance
limit is lower than an aluminium’s in terms of fatigue life.
Since steel is lighter than aluminium and can handle
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1014
enormous loads or weight, it is a more ideal material for
the main rotor head of a helicopter. We discovered a
distortion in modal analysis at various frequencies. Each
blade of a rotor responds to inputs from a control system
as it rotates, enabling helicopter control. A centre of lift
affects pitch, roll, and upward motion on a full rotor
system in response to inputs. The structural behaviour of
the main rotor head of a helicopter was investigated for
various materials. Here, a helicopter rotor hub must
support the weight of the blades and aerodynamic forces
as they rotate. In that situation, the strength of the
helicopter's main rotor head will be determined.
In this project, a 3D model of the helicopter's main
rotor head was created in SOLIDWORKS and imported
into the ANSYS software for static, fatigue, and modal
analyses to examine its strength and dynamic properties.
The model was then optimised using various materials,
such as steel and aluminium alloy.
The main rotor head of a helicopter has stresses and
deflections within the design parameters of the materials
employed, according to the structural analysis discussed
above. We can infer from the data that a steel material
model for the helicopter main rotor hub had better FOS
and weight reduction than an oar material model.
By altering the way a stress in a helicopter's main rotor
head varied under heavy load conditions, we were able to
make this observation. We have suggested the optimum
material for a helicopter's main rotor head under
conditions of heavy stress. The effects of loading and oar
variables, as well as stress concentration, are major issues
for designers. A steel helicopter's main rotor head is
almost as light as an aluminium one, and steel has higher
stiffness and fatigue strength than aluminium.
REFERENCES
[1]. Design and power transmission of an advanced light
helicopter, July-August 2013, Prof. Amarnath V. Hegne and
Prof. Preethi Hegne.
[2]. "Detailed analysis of rotor blades of helicopter" by
Hardeep Singh and Jag Sahil Saini, Gurukul Vidyapeeth
Institute of Engineering and Technology, September 2014.
[3]. Jag Sahil Saini is an engineer and technology professor
at Gurukul Vidyapeeth Institute. "Analysis of Helicopter
Rotor Blade" published in June 2015 Spring 2016: Mitchell
Brush, Scott Novak, Matthew Montana, and Michael
Roemer.
[4]. "The development and study of helicopter rotor
blades," by Mitchell Brush, Scott Novak, Matthew Montana,
and Michael Roemer, published in April 2016.
[5] Third Edition of Theory of Mechanism and Machines by
AmitabhaGhosh and Ashok Kumar Malik was published in
1998 by Affiliated press pvt limited in New Delhi.
[6] Joseph Edward Shigley, Theory of Machines and
Mechanisms, Tata McGraw Hill, 2003, New York
[7] Pravallika Reddy, "Static Structural Analysis of a
Helicopter Rotor Blade," Department of Aeronautical
Engineering, MLR Institute of Technology and
Management, Hyderabad, September–December 2015.
[8]. 1994's "Design of Machine Elements," by V. Bhandari
[9] Tata McGraw-Hill.

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DESIGN AND ANALYSIS OF HELICOPTER MAIN ROTOR HEAD

  • 1. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1004 DESIGN AND ANALYSIS OF HELICOPTER MAIN ROTOR HEAD M. Akhila 1, S.Vivekananda 2 1MTECH Student of Mechanical Engineering Department, Machine Design, Malla Reddy College of Engineering and Technology, Hyderabad, Telangana, India, akhila.muruganparvathy@gmail.com 2 Assistant Professor, Dept. of Mechanical Engineering, Malla Reddy College of Engineering and Technology, Hyderabad, Telangana, India, somavivek@mrcet.ac.in ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - The rotating component of a helicopter that produces lift is called the rotor system. The hub, rotor blades, and mast make up this rotor. A mast is a hollow, cylindrical metal shaft that stretches upward and is propelled. It is occasionally additionally supported by a transmission. In this scenario, a rotor hub must support the weight of the blades as well as aerodynamic forces. The strength of the helicopter blades and rotor hub will be determined. The rotor blades' attachment point to a top is a mast (hub).The helicopter main rotor head consist of rotor hub, mash, rotor blade and a swash plate. The Helicopter Rotor Head Model and Assemble will be completed, along with theoretical calculations, a Structural Analysis & Modal Analysis on two different materials for the Helicopter Rotor Head, and analysis in ANSYS. In order to calculate displacements and stresses under static conditions, structural analysis is used. A three component system's vibration characteristics (natural frequencies & mode shapes) are determined via modal analysis. The main focus of this study was the modeling and analysis of the helicopter rotor head. SOLIDWORKS, a cutting-edge modeling programme, was used to model and assemble the components . In ANSYS 2022 R2, an analysis is performed. Key Words: Analysis, Optimization, Solid works (Modelling), ANSYS (Static structural analysis, Fatigue analysis, modal analysis). 1. INTRODUCTION Although helicopters exist in a wide range of sizes and designs, the most of them have similar main parts. A chapter introduces the main portions and components of a helicopter as well as the systems that go along with it. Knowing how a helicopter's parts and systems function helps a pilot see problems and potential emergency situations more quickly. A revolving component of a helicopter that produces lift is the rotor system. A mast, hub, and rotor blades make up a rotor. A mast is an upward-extending hollow cylindrical metal shaft that is powered by and occasionally supported by a transmission. A hub, which serves as a rotor blade's connection point, is located at the top of a mast. There are several different ways to attach rotor blades to a hub. The way a main rotor blade is attached to and moves in relation to a main rotor hub determines what type of main rotor system it is. Semirigid, rigid, or completely articulated are the three fundamental categories. An designed combination of ase types is used in several contemporary rotor systems, such as bearingless rotor systems. 2. LITERATURE REVIEW Richard L. Rotelli, Jr. did a three-dimensional stress analysis of a new main rotor hub design for an SH-2F helicopter using a cycle symmetry feature of MSC/NASTAN. The investigation used cyclic symmetry. A one-eighth symmetry finite element model was made using the FEMGEN interaction graphics mesh generator. A graphic representation of the structural reaction of a rotor hub to various loading situations, as predicted by MSC/NASTAN, was provided using an interactive results viewing tool developed by FEMGEN. A novel design for a primary rotor hub benefited from the NASTRAN analysis results when they were presented in this manner. Modes form and harmonic analysis of various helicopter blade architectures by Yon CHEVALIER, Abd-el- Kader NOUR, and Mohamed Tahar GHERBI. This research focuses on the helicopter blade's dynamic behaviour. A goal is to mimic the behaviour of a blade made of various materials under an aerodynamic force using the finite elements approach. This study was carried out to compute the stresses operating on a structure for various modes and to analyse the aerodynamic loads imposed and evaluated using a numerical simulation of frequencies and Eigen modes. The determination of vibration responses resulting from unbalance and other stimulation modes has been made possible through the study of transient behaviour. Moritz Grawunder, Roman Reß, Victor Stein, Christian Breitsamter, and Nikolaus A. Adams, "Flow Characteristics of a Five-Bladed Rotor Head," This paper gives an examination of the flow properties, including cyclic pitch, of a spinning five-bladed rotor head. Finding opportunities for efficiency gains is a key goal. Through numerical simulations based on incompressible unstable Reynolds average Navier Stokes equations, findings are produced. Mesh deformation is used to simulate cyclic pitch motion. It is demonstrated that a pitch control system
  • 2. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1005 significantly increases parasite drag. Thus, there is potential for reducing drag by increasing the aerodynamic fairing of ase components. Additionally, it is demonstrated that the aerodynamic properties are significantly impacted by the cyclic pitch motion of a blade cuff. 3. METHODOLOGY For improved performance, the design and material of the helicopter's main rotor head have been adjusted. The main rotor head of the helicopter should be optimised for durability, toughness, high dimension stability, wear resistance, strength, and cost of materials as well as economic considerations. • Perform Helicopter Main Rotor Head design in Solidworks based on design calculation and design model dimension. • Make design calculations for various types of Helicopter Main Rotor Head. • To create a solid works model of the helicopter's main rotor head's structural integrity Analytical calculations were utilised to calculate a part's dimensions, which were then applied to modelling. A base of the main rotor head of the helicopter was an extruded object. On a top, extruded cut profiles were used. An ANSYS workbench model was imported after being saved. • To create and store static, modal, and fatigue analyses for a helicopter main rotor head's structural study in ANSYS • Following the completion of a finite element analysis, data collection, and comparison of the designs for helicopter main rotor heads, By experimenting with several materials, choose the optimum material that will work for the helicopter's main rotor head (steel or alluminium) • Perform static analysis where force, displacement, total deformation, and equivalent stress are determined. • Perform a fatigue analysis, which determines a fatigue life and a fatigue safety factor. • determine the natural frequency and perform modal analysis at various frequencies. • Perform a modal analysis, which identifies various modes at various frequencies. • Helicopter design Various materials are analysed for the Main Rotor Head, and data is gathered to determine whether the design is safe or not. 4. HELICOPTER MAIN ROTOR HEAD DIMENSIONS For improved performance, the design and material of the helicopter's main rotor head have been adjusted. The main rotor head of the helicopter should be optimised for durability, toughness, high dimension stability, wear Figure 1: side view 1 Figure 2: side view 2 Figure 3: dimension of Helicopter rotor head top view
  • 3. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1006 Figure 4: isometric view 5. ANALYTICAL DESIGN OF HELICOPTER MAIN ROTOR HEAD 5.1 Design Specifications conditions Analyzing the benefits and drawbacks of various rotor head designs was the first step in the rotor head selection process. The following criteria for a design were decided upon: 1. diameter of a rotor would be approximately one meter 2. rotor head should be fully articulated and Coaxial 3. blades must be easily interchangeable to test different designs 4. number of blades should be variable parameters were met by a final design, which was built based on a Coaxial system. Changing a total number of blades can be accomplished by removing a blade grip assemblies and reattaching am to a different hub built for a appropriate number of blades. Individual blades are changed by disconnecting am from a blade grip and attaching a new blade. 5.2 Design Specifications We are going to design a helicopter main rotor head using analytical method of calculation for that taking some standard specification are given on following Table 5.2.1 Specification of Coaxial helicopters Length: 16 m (52 ft 6 in) Height: 4.93 m (16 ft 2 in) Empty weight: 7,700 kg (16,976 lb) Gross weight: 9,800 kg (21,605 lb) Max takeoff weight: 10,800 kg (23,810 lb) Powerplant: 2 × Klimov VK-2500 turboshaft engines, 1,800 kW (2,400 shp) each Main rotor diameter: 2 × 14.5 m (47 ft 7 in) Main rotor area: 330.3 m2 (3,555 sq ft) contra-rotating 3-bladed main rotors Table 1: Specification of Coaxial helicopters Kind of load Value Unit Aerodynamic lift force 1500 N Centrifugal force of a blade 6156 N Aerodynamic drag force of a blade 40 N Torque 160 Nm Rotational speed 180 rad/s Table 2: Loads in Coaxial helicopters 5.3 Design Calculations 5.3.1 Blade sizing A very first step of our design is to determine a dimension of a rotor blade of a rotor mechanism. This part is done by following various design approach of RC helicopter blades. A primary assumption of a dimension for a blade is, Disc radius = Blade span = R = 0.5m , Blade Chord = C = 0.1m , N = Number of blades From Blade elementary aory, Solidity Factor, Solidity Factor, 𝜎 = (Blade Area)/(Disc Area )= ((N×C) )/(π×R ) Now, For 3 Blade, N = 3, Solidity Factor,
  • 4. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1007 𝜎 = ((3×0.1))/((π×0.5) )= 0.191 Again, For 2 Blade, N = 2, Solidity Factor, 𝜎 = ((2×0.1))/((π×0.5) )= 0.127 Lift curve slope, a = Here, a0= First term in Fourier series = 2 π/ rad E = Oswald Efficiency Factor = 0.9 AR = aspect ratio = R/C = 0.5/0.1 = 5 So, Lift Curve slope, a = = 4.34/rad Now, Flapping Frequency, λ= [√( ) ] λ [√( ) ]=0.5381 Here, θ = Pitch angle of a blade varies from 0-120 Angular velocity for a rotor blade, =2 ×(π/60)× N =2 ×(π/60)× 3=0.3151 And blade tip velocity, VT = 0.5 × = 0.5× 0.3141 =0.1570 coefficient of thrust CT =4 λ 2 =4× 0.53812 =2.1524 Thrust, T = 0.5 × 1.225× 0.15702 × 0.7853 × 2.1524 = 0.02551 Here, Density of Air, ρ=1.225 kg/m3 Area = 0.7853981634 m2 Coefficient of power, CP = 4λ3 =4× 0.53813 =0.6232 Power, P = 0.5 × ρ × VT 3 × A × CP =0.5 × 1.225× 0.15703 × 0.7853 × 0.6232=1.1600× 10 -3 Here, Density of Air, ρ=1.225 kg/m3 Area = 0.7853981634 m2 In order to determine if a rotor head design will withstand a forces it will be subjected to during normal operations, a maximum forces and moments were calculated. A forces were needed to calculate a stresses on individual components while a moments were used to calculate a coning angle. By calculating a coning angle it was possible to evaluation of a various force components. A two most significant forces and moments on a components are those generated by a centrifugal force and a lift force A rotor head is designed to operate between 1000 to 1350 rpms with a maximum radius of 0.6 meters based on this a forces and moments are calculated using 1500rpms. By using 1500rpm a margin of safety was built directly into a calculations. When a moment generated by centrifugal force and moment generated by lift are equal a coning angle can be calculated. 6. RESULT AND DISCUSSION 6.1 3D Model in Solidworks Figure 5: Part Design of Blade Figure 6: Part Design of Helicopter main rotor Hub
  • 5. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1008 Figure 7: Part Design of Helicopter swash plate 6.2 3D MODEL of Helicopter Main Rotor Head Assembly Figure 8 : 3D MODEL Assembly of Helicopter Main Rotor Head 6.3 Helicopter Main Rotor Head Model in Ansys Figure 9: Helicopter main rotor head in Ansys Figure 10: mesh Figure 11: cylindrical support Figure 12: displacement Figure 13: force 1
  • 6. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1009 Figure 14: force 2 6.4 Helicopter Main Rotor Head of steel 6.4.1 Static analysis Figure 15: total deformation- steel material Figure 16: equivalent stress - steel material Time [s] Minimum [mm] Maximum [mm] Average [mm] 1. 0. 1.7523 0.32282 Table 3: total deformation Time [s] Minimum [MPa] Maximum [MPa] Average [MPa] 1. 3.8096e-007 88.663 1.1991 Table 4: equivalent stress 6.4.2 Fatigue analysis Figure 17: life- steel material Figure 18: safety factor- steel material Time [s] Minimum Maximum Average 1. 8.5025e+005 1.e+006 1.e+006 Table 5: life Time [s] Minimum Maximum Average 1. 8.5025e+005 1.e+006 1.e+006 Table 6: safety factor
  • 7. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1010 Figure 19: Fatigue Sensitivity 6.4.3 Modal analysis Figure 20: Total deformation 1- steel material Figure 21: Total deformation 2- steel material Figure 22: Total deformation 3- steel material Mode Frequency [Hz] Maximum [mm] 1. 4.878 74.95 2. 4.8791 74.26 3. 4.8793 74.26 Table 7 : Frequency 6.5 Helicopter Main Rotor Head of Aluminum 6.5.1 Static analysis Figure 23: total deformation- Aluminium material Figure 24: equivalent stress- Aluminium material
  • 8. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1011 Time [s] Minimu m [mm] Maximum [mm] Average [mm] 1. 0. 4.9236 0.90716 Table 8: total defornation Time [s] Minimum [MPa] Maximum [MPa] Average [MPa] 1. 5.8888e-007 87.354 1.2 Table 9: equivalent stress 6.5.2 Fatigue analysis Figure 25 : life- Aluminium material Figure 26: safety factor- Aluminium material Time [s] Minimum Maximum Average 1. 6.7006e+007 1.e+008 1.e+008 Table 10 : life Time [s] Minimum Maximum Average 1. 0.94718 15. 14.763 Table 11 : safety factor Figure 31: Fatigue Sensitivity 6.5.3 Modal analysis Figure 27: total deformation 1- Aluminium material Figure 28: total deformation 2- Aluminium material
  • 9. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1012 Figure 29: total deformation 3- Aluminium material Mode Frequency [Hz] Maximum[mm] 1. 4.8932 126.18 2. 4.8943 125.89 3. 4.8945 125.89 Table 12 : Frequency Compressive Ultimate Strength MPa Compressive Yield Strength MPa Tensile Yield Strength MPa Tensile Ultimate Strength MPa 0 250 250 460 Table 13: Structural steel parameter Alternating Stress MPa Cycles Mean Stress MPa 3999 10 0 2827 20 0 1896 50 0 1413 100 0 1069 200 0 441 2000 0 262 10000 0 214 20000 0 138 1.e+005 0 114 2.e+005 0 86.2 1.e+006 0 Table 14: S-N Curve of Structural steel Strength Coefficient z (MPa) Strength Expone n-t Ductility Coefficie n-t Cyclic Strength Coefficie nt (MPa} Cyclic Strain Hardenin g Exponent 920 0.106 0.213 1000 0.2 Table 15: Strain-Life Parameters of Structural steel Young's Modulu s MPa Poisson' s Ratio Bulk Modulus MPa Shear Modulu s MPa Relative Permeabilit y 2.e+00 5 0.3 1.6667e+00 5 76923 10000 Table 16: Isotropic Elasticity of Structural steel Compressive Ultimate Strength MPa Compressive Yield Strength MPa Tensile Yield Strength MPa Tensile Ultimate Strength MPa 0 280 280 310 Table 17 : alluminium alloy properties Alternating Stress MPa Cycles R-Ratio 275.8 1700 -1 241.3 5000 -1 206.8 34000 -1 172.4 1.4e+005 -1 137.9 8.e+005 -1 117.2 2.4e+006 -1 89.63 5.5e+007 -1 82.74 1.e+008 -1 170.6 50000 -0.5 139.6 3.5e+005 -0.5 108.6 3.7e+006 -0.5 87.91 1.4e+007 -0.5 77.57 5.e+007 -0.5 72.39 1.e+008 -0.5 144.8 50000 0
  • 10. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1013 120.7 1.9e+005 0 103.4 1.3e+006 0 93.08 4.4e+006 0 86.18 1.2e+007 0 72.39 1.e+008 0 74.12 3.e+005 0.5 70.67 1.5e+006 0.5 66.36 1.2e+007 0.5 62.05 1.e+008 0.5 Table 18 : S-N Curve of alluminium alloy Young's Modulus MPa Poisson's Ratio Bulk Modulus MPa Shear Modulus MPa Relative Permeability 71000 0.33 69608 26692 1 Table 19 : Aluminum alloy property [1] Manually calculated permissible stress of modified design= 11.43 N/mm2 Analytically calculated equivalent stress of modified design for steel = 89.445 Mpa Analytically calculated equivalent stress of modified design for aluminum = 88.131 Mpa Fatigue life of steel = 1×106 Fatigue life of aluminum = 1×108 Fatigue Safety factor of steel and aluminum = 15 [2] Equivalent von-Mises stresses of our helicopter's main rotor head design are less than a yield strength. These results have been compared with current results of a similar model under the same loading conditions to validate FEA results. The yield stress, which is 250 MPa for steel and 280 MPa for aluminium, is far below the stress value. Analysis revealed that the von-Mises stresses for the two materials were nearly identical. Tensile yield strength of steel = 250 MPa Tensile yield strength of aluminum = 280 MPa Endurance limit of steel = 230 MPa Endurance limit of aluminum = 310 MPa The structural behaviour of the main rotor head of a helicopter was investigated for various materials. A blade weight and aerodynamic forces are carried by the main rotor head of the helicopter in this illustration. In that situation, the strength of the helicopter's main rotor head will be determined. Therefore, a static analysis, fatigue analysis, and modal analysis are carried out on the main rotor head of the helicopter for various materials, such as steel and aluminium alloy. Equivalent von-Mises stress is lower than yield strength and fatigue limit, thus steel has a lower fatigue life and endurance limit than aluminium. Since steel is lighter than aluminium and can handle enormous loads or weight, it is a more ideal material for the main rotor head of a helicopter. We discovered a distortion in modal analysis at various frequencies. 7. CONCLUSION Extensive historical research makes it evident that the issue has not yet been fully resolved, and designers are still having many difficulties, particularly with stress concentration and the impact of loading other oar variables. The most well-liked strategy for analysing fracture mechanics issues is the finite element approach. Some helicopter main rotor heads made of steel are almost as light as those made of aluminium. However, steel's key benefit is that it is more rigid and has higher fatigue strength than aluminium. We can therefore conclude that aluminium is good for producing inexpensive helicopter main rotor heads whereas steel is a better material in terms of strength. SOLIDWORKS was used to successfully complete a project's design. Using SOLIDWORKS, issues that arose during the design of a machine were successfully resolved. The majority of the key components of SOLIDWORKS, a flexible and all-inclusive programme for three- dimensional solid modelling, were used in the project design. The primary features used to develop components are protrusion and cut. Using SOLIDWORKS, a component is drawn very precisely. Hence, When compared to the existing design of the helicopter's main rotor head at the same applied force, the modified design for the variable valve actuation system carries less stress. It demonstrates that a modified helicopter main rotor head is more durable than an existing one over a lengthy period of time, and according to a design assessment, the new design is simpler than the existing one and exhibits less deformation. Equivalent von-Misses stress is smaller than yield strength and fatigue limit. A steel's endurance limit is lower than an aluminium’s in terms of fatigue life. Since steel is lighter than aluminium and can handle
  • 11. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1014 enormous loads or weight, it is a more ideal material for the main rotor head of a helicopter. We discovered a distortion in modal analysis at various frequencies. Each blade of a rotor responds to inputs from a control system as it rotates, enabling helicopter control. A centre of lift affects pitch, roll, and upward motion on a full rotor system in response to inputs. The structural behaviour of the main rotor head of a helicopter was investigated for various materials. Here, a helicopter rotor hub must support the weight of the blades and aerodynamic forces as they rotate. In that situation, the strength of the helicopter's main rotor head will be determined. In this project, a 3D model of the helicopter's main rotor head was created in SOLIDWORKS and imported into the ANSYS software for static, fatigue, and modal analyses to examine its strength and dynamic properties. The model was then optimised using various materials, such as steel and aluminium alloy. The main rotor head of a helicopter has stresses and deflections within the design parameters of the materials employed, according to the structural analysis discussed above. We can infer from the data that a steel material model for the helicopter main rotor hub had better FOS and weight reduction than an oar material model. By altering the way a stress in a helicopter's main rotor head varied under heavy load conditions, we were able to make this observation. We have suggested the optimum material for a helicopter's main rotor head under conditions of heavy stress. The effects of loading and oar variables, as well as stress concentration, are major issues for designers. A steel helicopter's main rotor head is almost as light as an aluminium one, and steel has higher stiffness and fatigue strength than aluminium. REFERENCES [1]. Design and power transmission of an advanced light helicopter, July-August 2013, Prof. Amarnath V. Hegne and Prof. Preethi Hegne. [2]. "Detailed analysis of rotor blades of helicopter" by Hardeep Singh and Jag Sahil Saini, Gurukul Vidyapeeth Institute of Engineering and Technology, September 2014. [3]. Jag Sahil Saini is an engineer and technology professor at Gurukul Vidyapeeth Institute. "Analysis of Helicopter Rotor Blade" published in June 2015 Spring 2016: Mitchell Brush, Scott Novak, Matthew Montana, and Michael Roemer. [4]. "The development and study of helicopter rotor blades," by Mitchell Brush, Scott Novak, Matthew Montana, and Michael Roemer, published in April 2016. [5] Third Edition of Theory of Mechanism and Machines by AmitabhaGhosh and Ashok Kumar Malik was published in 1998 by Affiliated press pvt limited in New Delhi. [6] Joseph Edward Shigley, Theory of Machines and Mechanisms, Tata McGraw Hill, 2003, New York [7] Pravallika Reddy, "Static Structural Analysis of a Helicopter Rotor Blade," Department of Aeronautical Engineering, MLR Institute of Technology and Management, Hyderabad, September–December 2015. [8]. 1994's "Design of Machine Elements," by V. Bhandari [9] Tata McGraw-Hill.