“i hereby, declare that i have read this thesis and in my...
TRANSCRIPT
“I hereby, declare that I have read this thesis and in my opinion this thesis is sufficient in
terms of scope and quality for the award of the degree of Bachelor Mechanical
Engineering (Design and Innovation)”
Signature : …………………………
Name of Supervisor : …………………………
Date : …………………………
STUDY OF AIRCRAFT PROPELLER –
STRUCTURAL STRENGTH
CHIN WAI PICK
This report is submitted in
partial fulfilment of the requirements for the award of the
Degree of Bachelor of Mechanical Engineering (Design and innovation)
Faculty of Mechanical Engineering
University Technical Malaysia Melaka
MAY 2010
ii
DECLARATION
“I hereby, declare this thesis is the result of my own research
except as cited in the reference”
Signature : …………………………
Author’s Name : …………………………
Date : …………………………
iii
PENGAKUAN
“Saya akui laporan ini adalah hasil kerja saya sendiri kecuali ringkasan dan petikan yang
tiap-tiap satunya saya telah jelaskan sumbernya”
Tandatangan : …………………………
Nama Penulis : …………………………
Tarikh : …………………………
v
AKNOWLEDGEMENT
I would like to express my profound gratitude my parents for their unwavering
support throughout my entire education and especially for their support over the past
three years in university. I am not embarrassed to admit that this project sometimes
proved to be almost too stressful to handle, but my parents and family were always there
to encourage and cheer me all the way.
I would also like to thank my most honored advisor, En Ahmad Rivai, for his
patient guidance to correct and coach me through the project. he has taught me so much
about propellers which otherwise not be able to gain by myself. beyond that, he has
taught the correct attitude of learning, both directly and indirectly from his own life’s
testimony.
I want to appreciate the partner which is doing the similar propeller project as I
did. He has been actively putting his hands together in carrying out effective discussions
and generating solutions for questions. His partnership has made learning and
researching much enriching and enjoyable.
The last but not least, I am grateful to everyone that has come alongside of mine
and showed me help in one way or another. Your generosity in lending your helping
hands has indeed contributed to the success of this project.
vi
ABSTRACT
A propeller is part of the propulsive system of an aircraft. It is powered by an
internal combustion engine which is used to turn propeller blades and transform rotary
power into forward thrust. The rotating propeller, being one of the high risk parts of
aircraft are constantly subjected to various dynamic loads. Therefore, it is often desired
to analyze and check the strength of propeller to ensure safe operation. This project is
purposed to analyze the propeller blade strength. It is carried out through two approaches,
namely the theoretical approach and finite element method. The beam theory presented
by D. W. Taylor has been employed and used in the theoretical analysis. Results obtained
through calculations were tabulated and corresponding graphs were plotted to show the
distribution of stress on the propeller blade. This approach suggested that stresses
decrease in proportion toward the blade edges and with increase in blade radius from the
center of hub. Meanwhile, the finite element method presented a more accurate result
than the theoretically approach but still having results with similar trends as the
theoretical approach. Both results are compared against each other and rational
discussions are made. The result is used to compare against the material ultimate stress
to obtain the safety factor for safe operation.
vii
ABSTRAK
kipas adalah sebahagian daripada sistem dorongan sebuah pesawat. Ia
dikuasakan oleh satu enjin pembakaran dalam yang digunakan untuk menjana putaran
kipas serta mengubah kuasa putaran itu kepada daya tolakan untuk pesawat. Kipas yang
berputar ini menjadi satu bahagian yang berisiko tinggi kerana sentiasa dibebankan oleh
pelbagai daya dinamik. Oleh itu, analisis terhadap kekuatan kipas dijalankan bagi
memastikan operasi yang selamat. Projek ini bertujuan untuk menjalankan analisis
kekuatan terhadp bilah kipas. Ia dilaksanakan melalui dua cara, iaitu cara teoritikal dan
kaedah unsur terhingga. Teori yang disampai oleh D W Taylor telah diambil dan
digunakan dalam teori analisis. Keputusan-keputusan diperolehi melalui pengiraan telah
dijadualkan dan graf-graf yang berkaitan telah dilukis untuk menunjukkan taburan
tekanan yang bertindak di bilah kipas. Cara ini mencadangkan bahawa semakin besar
jejarinya daripada pusat kipas itu, semakin menurun taburan tekanan itu. Sementara itu,
kaedah unsur terhingga itu telah menghasilkan keputusan lebih tepat berbanding dengan
cara teoritikal, namum masih mengandungi sifat-sifat dan tren keputusan yang serupa
dengan cara teoritikal. Kedua-dua keputusan yang didapatkan itu telah dibanding antara
satu sama lain dan perbincangan yang rasional telah dilakukan. Keputusan itu juga
digunakan untuk perbandingan terhadap stres utama bahan untuk mendapatkan faktor
keselamatan bagi memastikan operasi yang selamat.
viii
LIST OF CONTENTS
CHAPTER TOPIC PAGE
DECLARATION ii
PENGAKUAN iii
DEDICATION iv
AKNOWLEDGEMENT v
ABSTRACT vi
ABSTRAK vii
LIST OF CONTENTS viii
LIST OF TABLES xi
LIST OF FIGRUES xii
LIST OF SYMBOL xiv
LIST OF ABBREVIATIONS xv
CHAPTER 1 INTRODUCTION 1
1.1 Overview 1
1.2 Problem Statement 3
1.3 Motivation And Aim Of Project 4
1.4 Scope Of Project 4
1.5 Baseline Model 5
1.6 Organization Of Report 6
ix
CHAPTER TOPIC PAGE
CHAPTER 2 LITERATURE REVIEW 6
2.1 Development of Propeller 6
2.2 Propeller Geometry 9
2.2.1 Pitch 9
2.2.2 Propeller Outlines and Area 10
2.2.3 Blade Thickness Distribution 11
2.3 Review on Previous Research 12
2.3.1 Aerodynamic and Lift Distribution 12
2.3.2 Propeller Blade Strength Analysis 13
2.3.3 Common Problem In Propeller 15
Blade Strength
2.4 Concept of Stress, Bending Moments, and Torque 16
2.4.1 Stress 16
2.4.2 Allowable Stress and Safety Factors 16
2.4.3 Bending Moments 17
2.4.4 Torque 18
2.5 Propeller Theory 19
2.5.1 Momentum Theory 19
2.5.2 Blade Element Theory 20
2.6 Forces Acting On Propeller 21
2.6.1 Centrifugal Force 22
2.6.2 Thrust Bending Force 22
2.6.3 Torque Bending Force 23
2.6.4 Aerodynamic Twisting Force 23
2.6.5 Centrifugal Twisting Force 24
2.7 Finite Element Method (FEM) Theory 24
2.7.1 Basic Approach 26
2.7.2 General Procedures for FEM 28
x
CHAPTER TOPIC PAGE
CHAPTER 3 METHODOLOGY 32
3.1 Flow Chart 32
3.2 Structural Analysis 34
3.2.1 Cantilever Beam Method 34
3.2.2 Finite Element Method 39
CHAPTER 4 RESULTS AND DISCUSSION 44
4.1 Theoretical Approach 44
4.2 FEM Approach 53
4.3 Results Comparison 58
CHAPTER 5 CONCLUSION AND RECOMMENDATIONS 60
5.1 Conclusion 60
5.2 Recommendations And Further Reading 61
REFERENCES 63
APPENDIX A 65
APPENDIX B 67
APPENDIX C 69
xi
LIST OF TABLES
NO. TITLE PAGE
2.1 The Preprocessing Operations and Description 30
4.1 The Tabulated Centrifugal Force and Tensile 47
Stress across Radius of Propeller
4.2 The Tabulated Bending Force and Tensile Stress Across 47
Radius of Propeller
4.3 The Total Stress Distribution Acting On Propeller 51
xii
LIST OF FIGURES
NO. TITLE PAGE
1. 1 The Airfoil Cross Section Of Airplane Propeller 2
2.1 Wright Brothers’ Propeller Between 1911 And 1903 8
2.2 The Pitch Lines 10
2.3 Terminology of Airfoil Section 11
2.4 Variations of Blade Thickness Along Propeller Radius 11
And The Cross Sectional Airfoil Design
2.5 Kutta-Joukowski Lift Theorem 13
2.6 The General Concept of Momentum Theory 19
2.7 The Blade Element Theory 20
2.8 Propeller Centrifugal Force 22
2.9 Thrust Bending Force 23
2.10 Propeller Torque Bending Force 23
2.11 Propeller Twisting Moment 24
2.12 Propeller Centrifugal Twisting Moment 24
2.13 The Various Methods Available In Engineering Analysis 25
2.14 The Elements Are Connected To Each Other By Node 26
2.15 The Derivation of Global Equation from Elemental Equation 27
2.16 The Global Matrix Equation with Boundary Condition Applied 28
2.17 The Results of Deformation and Stress Plot 28
2.18 The Summary of General Procedures in FEM 29
2.19 Example of Stress Analysis Using FEM 31
3.1 Flow Chart for the Analysis Methodology 33
3.2 The Scanning Process with CMM Machine 40
xiii
NO. TITLE PAGE
3.3 The CAD Model Of Propeller 41
4.1 Graph of Centrifugal Force Distribution 48
4.2 Graph of Tensile Stress Distribution Due To 48
Centrifugal Force
4.3 Graph of Shear Force Distribution 49
4.4 Graph of Moment Distribution 49
4.5 Distribution of Stress Across The Radius 50
4.6 Distribution of Total Stress Acting On Propeller 51
4.7 Solid Imported From CAD 53
4.8 Lines And Points Constructed To Create Mesh Seed 54
4.9 3D-Mesh, With TET4 Elements Constructed On 54
Propeller Blade
4.10 3D-Mesh, With TET10 Elements Constructed On 55
Propeller Blade
4.11 Force Input Along The Propeller Surface 56
4.12 Zero Degree Freedom Applied At Surface Attaching To Hub 56
4.13 Stress Contour Plot From MSC Nastran Patran 57
5.1 Corresponding Propeller Fatigue Analysis With 61
Stress Simulation Input
xiv
LIST OF SYMBOLS
σ Normal stress
P Force acting on member
A Area prependicualr to force
M Moment about the neutral axis
y Perpendicular distance to the neutral axis
I Second moment of area
T Torque
Τmax Maximum shearing stress
c Distance from shaft axis where stress is maximum
{u} Displacement vector
[k]e Stiffness matrix
{U} Displacement vector, primary variable
{f}e Load vector, secondary variable
w Weight of propeller
g Acceleration due to gravity
ω Angular velocity
r Distance of particle from center of rotation
N Propeller RPM
A Cross section area
ρ Density of material
b Blade width
hu Upper chamber
hL Lower chamber
yt Distance from mutual axis to outermost surface
xv
LIST OF ABBREVIATIONS
RPM Round per minute
CAD Computer Aided design
FEM Finite element method
CMM Coordinate measuring machine
FS Factor of safety
1
CHAPTER 1
INTRODUCTION
1.1 Overview
Thrust is the force required by the aircraft to travel forward through the air.
Thrust is often greater than drag both to achieve the forward acceleration during take-off
and to increase speed during level flight. Most aircrafts in the early designs had utilized
the propeller to generate thrust. The propeller that pushes aircraft through the air is a
pusher propeller, while the propeller that pulls the aircraft through the air is a tractor
propeller. Both applied the same principle of Newton’s Third Law and provide thrust for
the aircraft as needed.
A propeller consists of two or more blades attached to a central hub that is
mounted on engine crankshaft. It is powered by an internal combustion engine which is
used to turn the propeller blades and transform rotary power to forward thrust. As the
propeller blade is rotated, a slipstream of fast moving air will be created and produces
pressure difference across the blade. The pressure difference causes large amounts of air
to be accelerated through the plane of the propeller to produce the thrust that propels
aircraft forward. Aircraft with more blades will lead to relatively higher noise level than
those with lesser blades. However, with the advanced material and design; much
reduced vibration and noise are generated even though high numbers of blades are used
in current designs.
2
A propeller with ideal efficiency is able to convert energy supplied from engine
fully into forward thrust. The geometry of blade plays an important role to optimize the
efficiency of propeller. Propeller blade is generally long and thin. It is often thought as a
rotated wing due to their shape of airfoil section which is similar to the wing. When the
blade is rotated, the tip moves faster than the hub. The blade is therefore made to be
twisted along the edge as it proceeds from hub toward the tip to ensure that each cross
section meets the air at about the same time. Besides, the blade thickness also varies
along the radius, which is higher thickness in the hub area than the tip to prevent failure
due to intense stress.
Figure1.1: The airfoil cross section of airplane propeller
(Source: Philip W.F. 2004, Mechanics of Flight, John Wiley&Sons, New Jersey, pg 131)
Propeller propulsion system was the primary system in all aircrafts for forty
years after the first flight of Wright brothers until the development of jet engines during
World War II. Today, propellers are still used on general aviation and private aircraft
due to the performance of propeller that is suited to the weight and height of the level
flight of the aircrafts.
Airfoil Section
Propeller
Hub / Spinner
3
1.2 Problem Statement
The rotating propeller, being one of the high risk parts of aircraft are constantly
subjected to various substantial loads. A great deal of attention is therefore paid to
provide for its reliability and avoid failure. This failure of propeller, if occurred, may
results in high material cost by means of replacement and higher consumption of fuel in
aircraft. Besides, the structural failure of propeller shall lead to undescrible damage in
the course of just one short flight, some cases reported that failure happened can be as
soon as five second after take-off. The incident of propeller failure is never uncommon
among all aircraft accidents. One of the major accidents recorded in propeller failure
history was Stratocruiser N1039U that crushed into the Brazilian dense jungle with no
survivors. In close examination, the cause of the propeller failure was due to the
application of force upon the propeller structure is beyond which it was designed.
Therefore, it is extremely important to analyze the propeller blade strength after the
design process to ensure that the propeller has met the desired performance and
sufficient strength for safe operation.
However, the problem with strength analysis of propeller is it often involves high
complexity. The stressed state of blades is mainly determined by the aerodynamic load
which, in turn, depends on propeller blades geometry and velocity of aircraft. The
integration of these parameters has caused the strength analysis to be complicated,
especially due to the non-uniformity cross section of propeller blade that causes periodic
variations in loads acting on blade. A list of stress formulation for propeller blade has
been developed through the effort of various researchers as a guide for the designers to
make their analysis on propeller designed. Even though the usage of Finite Element
Analysis is in rise, the formulation method is still widely used today. This had caused
the concerns by designers on how well the results from both methods comply with each
other in order to ensure accurate evaluation in strength of propeller.
4
1.3 Motivation and Aim
Determining propeller strength is complex and research in the aeronautical
application has for long been dedicated to this analysis. Lately, the application of
turboprop in aircraft propulsion has marked the expansion of propeller technology.
Turboprop engines are a type of aircraft powerplant that use a gas turbine to drive a
propeller. The most recent Airbus A400M is one of the examples that powered by
four turboprops TP400 engines. The propeller technology has been the motivation to
investigate the capabilities of propeller, particularly in strength analysis. The project is
carried out with the aim to examine and analyze the strength of the propeller blade. The
details of the aim can be stated as follow:
• To research on the propeller blades profile based on a selected model of
propeller-driven aircraft.
• To derive analytical blade strength of propeller through cantilever beam
calculations method.
• To verify and validate the results from calculations using simulation in FEM
1.4 Scope of Project
A specific case of blade failure of the UAV propeller is calculated to illustrate
the application of theoretical and FEM analysis method. The project shall involve a
specific field on the propeller blade analysis. The scopes are as stated below:
• Literature research to understand aircraft propeller in general
• Theoretical hand calculation for the propeller strength
• Simulation of propeller blade on structural strength using Finite Element
Analysis (MSC Nastran / Patran).
• Make comparisons and draw corresponding conclusions on the strength of
propeller blade analyzed.
5
1.5 Baseline Model
In order to study effectively both the stress formulation and FEM analysis, a
model of propeller driven aircraft was chosen as project baseline model. The chosen
representative propeller design is used in the locally manufactured ALUDRA UAV
(Unmanned Aerial Vehicle). This model was chosen due to its reasonable size and
specification which can be used as the input data for the project. However, to ease the
analysis, the structural material used for UAV has been changed from composite
material to iron. The analysis on composite material requires a great deal of
considerations on material since it is not the isotropic material and made up from layers
of composite material.
Being the first UAV deployed by Malaysia Military, the ALUDRA (Alianced
Unmanned Development Research Aircraft) was developed primarily for battlefield
surveillance and reconnaissance, and also regarded suitable for Maritime patrol, air
enforcement, border patrol and monitoring of forest fires or other hazardous situation. It
has a 2.44m (8ft) wing span, gross weight of 15kg (33Ib), and remotely piloted from a
tactical Grand Control Station. The detail specification of the UAV is as follow:
• Gross Weight: 15kg
• Structural Material: Composite (Glass Fibre, Carbon Fibre, Foam)
• Dimension: Length 14ft, Wing Span 8ft
• Endurance: 6 Hours
• Max. Cruise Speed: 120 Knots (220km/h)
• Powerplant: 50hp, Twin Cylinder Gas Engine, Propeller Driven
• Max. Altitude: 12,000 Ft
• Data Link Range: 150km
• Take Off Distance: 250m
6
1.5 Organization of Report
This report presents the strength analysis for both computational method and
Finite Element Method. Chapter 1 of this report is introduction, covering the overview,
problem statement, motivation and aim of project and scope of project. Chapter 2 is
dedicated to literature review, where the relevant theory of propeller is adopted and
presented. Previous findings are also illustrated. Meanwhile, methodology and approach
to the project is given in details in chapter 3. A list of formulation is developed and
presented through the methodology chapter. The following chapter shall present the
results and discussion obtained from both the theoretical and simulation analysis. Lastly,
a brief conclusion is included to summarize all the theories and findings presented.
7
CHAPTER 2
LITERATURE REVIEW
Theoretical methods used to predict the force exerted on propellers blade began
to be developed in the late nineteenth century. The most notable of the early findings
was that of Rankine, with his momentum theory, which was then closely followed by the
blade element theories of Froude. The chapter is dedicated to review and examine the
development of propeller and its strength formulations. Theories and findings besides
Rankine’s and Froude’s were also presented. Literature review carried out has been part
of the factors contributed to successful analysis of propeller in this project.
2.1 Development of Propeller
The creation of the propeller can be traced back to Leonardo da Vinci’s helical
screw helicopter which believed is the ancestor of the air propeller. The first idea of a
propulsive airscrew, however, belongs to J.P. Paucton, a French mathematician found
during the late 1700 to early 1800. After several experimentations, it was concluded that
more propulsive power could be obtained by straightening out the surface of the
airscrew blades. In 1875, Thomas Moy finally created a large model that had twin 12-
foot propellers with 6 blades each. These massive propellers produced 1,100-pounds of
thrust each during full power while rotating at 425rpm. However, this jumbo creation
did not last long when it suffered an extensive damage during a test flight.
8
In human history, the most influential aviation pioneers were the Wright brothers’
propeller. They had concluded that a propeller was simply a whirling wing. They learned
that large propeller diameters would produce high thrust for a given power input. On
their first aircraft, they utilized 8-foot propellers installed behind the aircraft to minimize
airflow disturbance and incorporated counter-rotating propellers to eliminate the
gyroscopic problems. They have also gained thrust efficiency by reducing the blades
rotational speed using a chain and sprocket transmission. The Wright brothers’ propeller
was 66% efficient which was much higher than any other propeller of the time.
Figure 2.1: Wright Brothers’ propeller between 1911 and 1903
(Source: Robert L.Ash et al. (2000), Evolution Of Wright Flyer Propeller Between 1903
and 1912, Aerospace Engineering Department, Old Dominion University, Norfolk)
By 1910, experiments with metal propellers and variable pitch blades were
developed. Results showed that the metal propeller could be made thinner than a
comparable wooden propeller, which allowed for faster cruising speeds due to less drag.
It allowed operations in all climates where the wooden propeller would easily fail in
extreme conditions. The only drawbacks to the early metal propeller were their weight.
After WWII, the rising of the Turboprop brought a few changes to the propeller. Many
large propeller transports switched to this new system for its reliability and pilot friendly
features. It is expected a saving of 25% in fuel costs through Turboprop.