“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 : …………………………

iv

Specially dedicated

to my family and beloved companion

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.