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Page 1: Project Report Windmill

UNIVERSITY

MAKERERE

FACULTY OF TECHNOLOGY

DEPARTMENT OF MECHANICAL ENGINEERING

BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING

DESIGN AND SIMULATION OF A WINDMILL TRANSMISSION

SYSTEM FOR PUMPING WATER AT LOW AND INTERMITTENT

WIND SPEEDS

A FINAL YEAR PROJECT REPORT SUBMITTED IN PARTIAL

FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF THE

DEGREE OF BACHELOR OF SCIENCE IN MECHANICAL

ENGINEERING OF MAKERERE UNIVERSITY

JONAH MUMBYA

05/U/564

May-2009

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DECLARATION

I Jonah Mumbya declare that this report is original and that it has never been produced in

part or full by anyone for any award in any university, college and institution of learning.

Signature…………………………………

Jonah Mumbya

Date……………………………………….

We, the undersigned supervisors declare that this report fulfills the examiners’ requirements

for the award of a bachelor’s degree in Mechanical Engineering of Makerere University.

Supervisor

DR. KARIKO BUHWEZI

Senior Lecturer

Department of Mechanical Engineering

Faculty of Technology

Signature …………………………….

Date………………………………….

Co-supervisor

MR. PAUL ISAAC MUSASIZI

Assistant Lecturer

Department of Mechanical Engineering

Faculty of Technology

Signature …………………………….

Date………………………………….

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DEDICATION This work is dedicated to my late mother, may her soul rest in eternal peace

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ACKNOWLEDGEMENT I have the pleasure and honor to thank the Almighty God for the gift of wonderful life he has

given me without which nothing would be done by me.

In addition, I would like to acknowledge the marvelous contribution made by the Italian Co-

operation towards this research by availing me with the simulation software that was a

prerequisite for the successful completion of this research.

Special thanks go to my supervisor Dr. Kariko B. Buhwezi for the advice and direction offered to

me during this research

I would also like to extend my many thanks to Mr. Paul Isaac Musasizi for the academic and

professional guidance offered to me during the entire research period from the word go.

Many thanks go to Mr. James Herzing the Product Support Engineer Autodesk Algor for all the

technical support he extended to me without which it would be difficult to realize the objectives

of this research.

Last but not least, I would like to especially thank my family members robina, agness, peter,

Charles and my dad for all the support psychological and financial that was rendered to enable

me finish this research, God bless you all.

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CONTENTS DECLARATION .................................................................................................................................... i

DEDICATION ....................................................................................................................................... ii

ACKNOWLEDGEMENT .................................................................................................................... iii

LIST OF TABLES............................................................................................................................... vii

LIST OF FIGURES ............................................................................................................................. vii

LIST OF ACRONYMS ......................................................................................................................... x

ABSTRACT .......................................................................................................................................... xi

CHAPTER ONE: INTRODUCTION .................................................................................................. 1

1.1 Background ............................................................................................................................ 1

1.2 Problem Statement ................................................................................................................. 2

1.3 Objectives ............................................................................................................................... 2

1.3.1 Main Objective ................................................................................................................. 2

1.3.2 Specific Objectives ............................................................................................................ 2

1.4 Justification ............................................................................................................................ 2

1.5 Scope ....................................................................................................................................... 3

1.6 Summary of Methodology ...................................................................................................... 3

1.7 Summary of Results ............................................................................................................... 3

1.8 Limitations ............................................................................................................................. 4

1.9 Ethical Considerations: .......................................................................................................... 4

1.10 Report Outline........................................................................................................................ 5

CHAPTER TWO: LITERATURE REVIEW ..................................................................................... 6

2.1 Introduction ........................................................................................................................... 6

2.2 Wind Resource ....................................................................................................................... 6

2.3 Wind Power ............................................................................................................................ 6

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2.4 Windmill ................................................................................................................................. 7

2.5 Windmill components ............................................................................................................ 7

2.6 Transmission System ............................................................................................................ 11

2.6.1 Belt Transmission Mechanism ......................................................................................... 11

2.6.2 Chain Drive Transmission Mechanism ............................................................................. 12

2.6.3 Gear Drive Transmission Mechanism .............................................................................. 13

2.6.4 Drive Shaft Mechanism ................................................................................................... 15

2.6.5 Crank Transmission Mechanism ...................................................................................... 16

2.7 Drag Devices ......................................................................................................................... 17

2.7.1 Torque ............................................................................................................................ 18

2.7.2 Power Coefficient ........................................................................................................... 19

2.7.3 Torque coefficient ............................................................................................................. 2

2.8 Hydraulic Power .................................................................................................................... 2

2.9 Transmission System Design and Modeling ........................................................................ 22

2.9.1 Physical Product Design .................................................................................................. 22

2.9.2 Computer Aided Drawing ................................................................................................ 22

2.10 Transmission System Testing............................................................................................... 22

2.10.1 Physical Testing .............................................................................................................. 22

2.10.2 Computer Simulation ...................................................................................................... 23

2.11 Conclusion ............................................................................................................................ 23

CHAPTER THREE: METHODOLOGY .......................................................................................... 25

3.1 Introduction ......................................................................................................................... 25

3.2 Preliminary Design............................................................................................................... 25

3.3 Detailed Design ..................................................................................................................... 29

3.3.1 Wind Power .................................................................................................................... 29

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3.3.2 Rotational Shaft Speed ................................................................................................... 31

3.3.3 Shaft Torque ................................................................................................................... 32

3.3.4 Hydraulic Power ............................................................................................................. 33

3.3.5 Water Flow Rate ............................................................................................................. 35

3.3.6 Design Stroke Volume ..................................................................................................... 36

3.3.7 Pump Size ....................................................................................................................... 37

3.3.8 Pump Rod Design............................................................................................................ 38

3.3.9 Crank Mechanism Design................................................................................................ 42

3.3.10 Crank Shaft Design ......................................................................................................... 45

3.3.11 Design of Connecting Rod ............................................................................................... 51

3.3.13 Design of Yoke Pin .......................................................................................................... 53

3.4 Bearing Selection .................................................................................................................. 54

3.5 Computer Aided Drawings .................................................................................................. 57

3.6 Simulation ............................................................................................................................ 58

3.4 Conclusion ............................................................................................................................ 59

CHAPTER FOUR: PRESENTATION AND DISCUSSION OF RESULTS .................................... 61

4.1 Introduction ......................................................................................................................... 61

4.2 Mechanical Events Simulation ............................................................................................. 61

4.3 Conclusion ............................................................................................................................ 66

CHAPTER FIVE: CONCLUSION AND RECOMMENDATIONS................................................. 67

5.1 Recommended Specifications ............................................................................................... 67

5.2 Further Related Research .................................................................................................... 67

REFERENCES .................................................................................................................................... 68

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LIST OF TABLES

Table 1: Different Pump Types and Their Head Ranges and Maximum Efficiencies ................................. 10

Table 2: Drag Coefficient of Different Blade Shapes .............................................................................. 18

Table 3: Power Coefficient as a Function of Tip Speed Ratio .................................................................. 19

Table 4: Transmission System Concepts ................................................................................................ 25

Table 5: Concept Selection Creteria ...................................................................................................... 27

Table 6: A table Showing Values of Euler Constant C ............................................................................. 40

Table 7: Table of Preferred Sizes ........................................................................................................... 41

Table 8: Table of Fatigue Stress Constants ............................................................................................ 47

Table 9: Bearing Size Selection Table .................................................................................................... 50

Table 10: Table of Reliability Factors ..................................................................................................... 54

Table 11: Comparison of Bearing Types ................................................................................................ 54

Table 12: The Selection Scoring Matrix Is Table ..................................................................................... 56

Table 13: Table of Results on Connecting Rod ....................................................................................... 62

Table 14: Table of Results on Yoke Pins ................................................................................................. 64

Table 15: Table of Results on Crank Shaft ............................................................................................. 66

LIST OF FIGURES Figure 1: Horizontal Axis Windmill .......................................................................................................... 7

Figure 2: ................................................................................................................................................ 10

Figure 3: Flat Belt .................................................................................................................................. 11

Figure 4: Pair of V-Belts ........................................................................................................................ 11

Figure 5: Chain Drive............................................................................................................................. 12

Figure 6: Spur Gear Interaction ............................................................................................................. 14

Figure 7: Spur-Rack Interaction ............................................................................................................. 14

Figure 8: Bevel Gear Interaction............................................................................................................ 14

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Figure 9: Shaft Drive Mechanism .......................................................................................................... 15

Figure 10: Single Crank Shaft ................................................................................................................ 16

Figure 11: An Example of a Cranking Transmission System .................................................................... 17

Figure 12: (a) Principle of a Persian Wind wheel (b) Siplified Model .................................................. 17

Figure 13: Isometric View Of The Transmission System ......................................................................... 28

Figure 14: Exploded View Of The Transmission System ......................................................................... 28

Figure 15: Monogram for Selecting Flow Rate of the Pump ................................................................... 35

Figure 16: Monogram for Selecting Pump Capacity ............................................................................... 36

Figure 17: Monogram for Determining Pump Size ................................................................................. 37

Figure 19: Euler Column........................................................................................................................ 39

Figure 18: Pump Rod Free Body Diagram .............................................................................................. 39

Figure 20: Crank Slide Mechanism ........................................................................................................ 42

Figure 21: Slide Crank Motion ............................................................................................................... 43

Figure 22: Figure for Selection of Crank Linkages .................................................................................. 44

Figure 23: Shaft Engineering Drawing ................................................................................................... 45

Figure 24: Shaft Free Body Diagram ...................................................................................................... 45

Figure 25: Shaft Moment Free Body Diagram ........................................................................................ 48

Figure 26: Shaft Bending Moment Diagram ........................................................................................... 49

Figure 27: Bearing Outline .................................................................................................................... 50

Figure 28: Engineering Drawing Of Connecting Rod .............................................................................. 51

Figure 29: Solid View Of Connecting Rod .............................................................................................. 51

Figure 30: Crank Pin Layout .................................................................................................................. 52

Figure 31: Crank Pin Bending Moment Diagram .................................................................................... 52

Figure 32: Solid View of Yoke ................................................................................................................ 53

Figure 33: Solid Model of Transmission System Assembly ..................................................................... 57

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Figure 34: Exploded View of Transmission System ................................................................................ 57

Figure 35: Model Mesh ......................................................................................................................... 59

Figure 36: MES Analysis of Connecting Rod Showing Von Mises Stress .................................................. 61

Figure 37: MES Analysis of Connecting Rod With Webs Showing Von Mises Stress................................ 62

Figure 38: MES Analysis of Yoke Showing Von Mises Stress................................................................... 63

Figure 39: MES Analysis of YOke With Bosses Showing Von Mises Stress .............................................. 63

Figure 40: MES Analysis of Upper Yoke Pin Showing Von Mises Stress .................................................. 64

Figure 41: MES Analysis of Lower Yoke Pin Showing Von Mises Stress .................................................. 65

Figure 42: MES Analysis of Crank Shaft Showing Von Mises Stress ........................................................ 65

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LIST OF ACRONYMS B Number of Blades

C Coefficient of Variation in Column

Loading

CAD Computer Aided Design

dC Drag Coefficient

pC Power Coefficient

D Drag Force (N), Diameter (mm)

E Kinetic Energy, Modulus of

Elasticity (N/m2)

FAO Food and Agriculture Organization

of the United Nations

FEA Finite Element Analysis

g Acceleration due to Gravity (m2/s)

H Head (m)

I Second Moment of Area (m4)

l Length (m)

m Mass (kg)

MES Mechanical Event Simulation

N Factor of Safety

aP Allowable Load (N)

crP Critical Load (N)

hP Hydraulic Power (Watts)

shaftP Shaft Power (Watts)

windP Wind Power (Watts)

q Flow Rate (m3/s) or (l/s)

R Rotor Radius (m)

T Torque (Nm)

V Linear Velocity (m/s)

Efficiency

Angle (degrees)

Tip-Speed Ratio

a Air Density (kg/m3)

w Water Density (kg/m3)

Rotor Diameter (m)

Rotational Speed (rads/sec)

2D Two Dimensions

3D Three Dimensions

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ABSTRACT Many areas in Uganda are faced with an acute shortage of water supply for agricultural use and

domestic needs. With dry spells increasingly getting prolonged manifested with drying water

streams and inadequate rain falls, it leaves many persons especially rural dwellers with few

options for survival since they primarily depend on rain water and small streams as their primary

supply source.

Wind pumps are seen to be good alternatives to the steady supply of water with economic

feasibility. It has however been noted that some windmills that have been fabricated locally and

installed have failed to meet the desired objectives as they malfunction or fail to work at

commissioning sighting problems with the designs.

In this respect, a project was launched in 2007 under the Department of Mechanical Engineering

Faculty of Technology Makerere University funded by the Italian co-operation to optimize the

design of a wind mill able to operate in low and medium wind speed regimes.

So far a windmill rotor has been optimized and this research sought to optimize the transmission

system by using computer aided tools like CAD and computer simulation using Algor and

develop appropriate design specifications for the system. This involved MES of the models

aimed at establishing failure patterns, resultant stresses, forces and displacements.

From the research, recommendations were made sighting that a simple crank mechanism would

do well with the specifications thereof came up with.

Further research is hence needed in the optimization of the tower and the pumping system that

would pave way for the construction of better design windmills with foresight into their

operation and this will reduce on the sole dependence on rain fall as a source of water which is

becoming increasingly unreliable.

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CHAPTER ONE: INTRODUCTION

1.1 Background

Windmills are machines designed to convert wind energy into mechanical energy using rotating

blades or sails. They were first built to automate the task of grinding grain and pumping water

for irrigation, domestic use and for livestock.

There are two types of windmill today which are the horizontal–axis wind machines and vertical-

axis windmills deriving the respective names from the orientation of the power transmission

shaft from the rotor. (www.westaustrianvista.com, 2008)

Windmills are not much in use in Uganda yet even when they could be a solution to the

unreliable supply of power to deliver both piped and natural water for domestic, irrigation and

livestock farming. In a few cases where they have been put up, they are either inefficient at work

or fail to work completely from the time of erection a typical example is of a windmill on a

Ranch in Mukono district that was installed to pump water for livestock and failed to work.

Failures of such windmills can be attributed to poor and rudimentary design practices that could

have been used paying little attention design parameters like materials used, dimensions, weight

and fabrication procedures. (Njuki, 2008)

It is against this background that a research program was instituted in January 2007 funded by

the Italian co-operation aimed at building research capacity and there after availing windmill

technology to the local manufacturers for development. If well developed, this technology can

help curb the acute problem of insufficient and unreliable supply of water by utilizing the

abundant wind energy resource that would see great improvements in agricultural practices like

commercializing farming, fish farming, livestock farming and many more.

Research therefore was commenced in 2007/08 by optimizing the design of a rotor (a component

of the windmill that transforms wind energy into rotary kinetic energy as wind strikes its blades)

that can work effectively in regions with low and irregular winds a typical scenario with Uganda.

This research is ongoing and now therefore seeks to design a transmission system that can work

with the optimized design of the rotor.

This involves the use of improved product design techniques like using structured engineering

design procedures and using computerized design tools like 3D computer modeling and

simulation tools like Algor to predict the performance of the models way before they are

fabricated and hence determining appropriate manufacturing procedures.

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1.2 Problem Statement

Since research study in the optimization of design of a windmill rotor was done, there is need for

continuation into the design research of a windmill to operate in low and intermittent wind

speeds.

This therefore calls for the design and simulation of a transmission system to work with the

designed rotor in order to optimize performance of the windmill, using design tools like 3D

modelers like solid Edge and Algor to simulate the performance prior to fabrication and

installation.

1.3 Objectives

1.3.1 Main Objective

The main objective is to develop design specifications for the transmission system to operate at

low and intermittent wind speeds.

1.3.2 Specific Objectives

The specific objectives are to;

1. Determine input parameters to the transmission system using the wind and rotor available

data.

2. Develop Computer Aided Drawings of the transmission system components and their

assembly.

3. Simulate the different components of the transmission system and their assemblies to obtain

stress reaction forces and displacement behaviors

4. Recommend appropriate design specifications of the transmission system based on

simulation results.

1.4 Justification

The following justifications are given for undertaking the above stated project;

This study can act as a benchmark for further studies in the design and development of windmills

on scholarly or commercial grounds.

Other windmills can be developed for other regions which even have different wind regimes

other than Mukono using the design parameters that shall be developed in this project. This can

be done by altering a few conditions like transmission system parameters to fit the conditions

prevailing in such areas like wind speeds, required heads and required rate of pumping.

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This research can provide cheaper means of development of windmills locally designed to meet

local working conditions, an alternative to importation that ranges between US$9,000 and

US$25,000.

This research shall provide documented design specifications and parameters that can be based

on for further commercial and scholarly research into the operation of windmill water pumps in

Uganda and other regions.

After successful completion of this research, academic expertise and knowledge shall be

obtained in the field of product design and simulation.

1.5 Scope

A prerequisite research to this was conduct in 2007/08 which put emphasis on the design of a

windmill rotor, in this research therefore, focus shall be directed to the design and simulation of a

transmission system to work with the designed rotor. It shall look at the various types of

transmission systems selection of an appropriate system, the different components and hence

their design. It shall therefore not involve the design and simulation of the rotor, the support

structure, and the pumping unit.

1.6 Summary of Methodology

The methods that were used during the research study where;

Preliminary design that tackled the design considerations, the customer requirements, concept

generation and selection criteria, the components to be designed and the layout of the assembly

of the system and the selection criteria for materials

The detailed designed gave a detailed mathematical analysis of the power, torque and rotational

speed at the different wind speeds that are used in the design, pump sizing, design water flow

rate, component detailed design, bearing selection criteria and simulation of the modeled parts

and the assembly.

1.7 Summary of Results

The results obtained at the end of this research are as summarized below;

Shaft: Shaft diameter 80mm and of length 1.5m with a crank offset located at 1.1m from the

rotor side.

Crank Pin: Diameter of crank pin of 50mm and length 100mm

Connecting Rod: It is of 400mm length with webs of thickness 25mm with a yoke pin bore of

14mm diameter.

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Yoke: This is of circular section of out diameter of 73.36mm and inner bore of diameter 40mm

and 40mm height, with bosses of protrusion 5mm at the upper pin bore.

Yoke Pins: Upper Pin Diameter of 14mm, Lower Pin diameter of 15mm

Pump Rod: This is of hollow circular section with outer diameter of 40mm and inner diameter

of 25mm and overall length of 15m.

Bearings: Spherical roller bearings are to be used.

1.8 Limitations

The major constraints to this research were as stated below;

Lower System’s Specifications Requirements: The biggest challenge was the inadequacy of

the computer that was used for this research had specifications below the minimum requirement

for some simulations like MES of assemblies. The minimum requirements for proper Algor

operation are, for a 32-bit processor;

Dual Intel® Xeon™ or AMD Opteron™ Processor, 3 GHz or higher, 2 GB RAM or higher (3

GB for MES and CFD applications), 30 GB of free disk space or higher, 256 MB or higher

OpenGL accelerated graphics card, DVD-R drive.

While the computer used was a single 3.4GHz though it met all the other requirements, making it

difficult to carry out bulky simulations especially for assemblies.

Late Software Licensing: This affected the research in that the time for practicing and fully

appreciating the use of the simulation package was reduced. This was majorly as a result of poor

coordination amongst the three parties that were involve, Algor, Italian co-operation and the end

user.

Slow Internet Connections: The fact that the software licensing was done late, licensing was to

be done online which took some time to do because most of the trials were futile due to slow

internet connections at the faculty of technology by then.

Abrupt Load-Shedding in the Faculty: With a slow speed machine, setting up and running a

single simulation would take several hours and power cuts would occur amidst some simulation

processes calling for undesirable restarts of the analyses.

1.9 Ethical Considerations:

During the entire research study, there was keen observation of patent rights, copy rights and all

other rights covering the publication of research findings by other researchers and publishers as

governed by Makerere University and other regulating bodies.

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1.10 Report Outline

This report starts with giving a deep background in chapter one that gives the state of windmill

technology; it then defines the problem and sets the desired objectives giving clear justification

of the research. It also gives a precise and concise spell on the summaries of the methodology,

results forth obtained and limitations with ethical considerations.

Chapter two reviews the literature that gives better understanding of the wind resource and the

power within the wind. It further gives account on the different components of the windmill

thereafter emphasizing the transmission system and its different mechanisms; it handles the CAD

method of modeling and computer simulation as a method of testing designs.

The methods that were used to realize the set objectives are presented in chapter three giving a

detailed spell of preliminary and detailed design, the CAD models and simulation procedures.

Chapter four presents the discussion of results obtained from the simulation of the CAD models

generated in chapter three.

Recommendations are presented in chapter five concluding with the areas for future research

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CHAPTER TWO: LITERATURE REVIEW

2.1 Introduction

This chapter shall give coverage of the works and researches that have been carried out prior to

this one in the exploitation of wind energy for the pumping of water using windmills as working

equipments. It will give a deep oversight into the information that shall be important in the

design and simulation of a windmill transmission system as a requirement for this study.

2.2 Wind Resource

Global winds are caused by pressure differences across the earth’s surface due to the uneven

heating of the earth by the solar radiation. For example the amount of solar radiation absorbed at

the earth’s surface is greater at the equator than at the poles. The variation in incoming energy

sets up convective cells in the lower layers of the atmosphere (the troposphere). Thus is simple

flow model, air rises at the equator and sinks at the poles. The circulation of the atmosphere that

results from uneven heating is greatly affected by the effects of the rotation of the earth (at

speeds of about 600km/h at the equator, decreasing to zero at the poles) In addition; seasonal

variations in the distribution of solar energy give rise to variations in the circulation. (R. Gasch,

2002)

2.3 Wind Power

This refers to the power that can be tapped from the wind which relates to the velocity of the

wind V, the area impacted A, and the density of the flowing air ρ as below;

3

2

1AVP awind ………………………………………… (i)

The expression above shows that the power in the wind P is proportional to the air density, the

intercepting area A and the third power of velocity V. Since the power held within the wind is

kinetic energy, we can equate power to the rate of kinetic energy;

2

2

1mVE ………………………………………….. (ii)

Then equating equations (i) and (ii), we obtain the mass of air through the area A over a period

of time as;

dt

dxAAV am

.

This is itself proportional to the velocity, the power is;

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22..

2

1

2

1AVVp awind mE …….....……......... (iii) (R. Gasch, 2002)

2.4 Windmill

A windmill is a machine that is powered by the energy of the wind. It is designed to convert the

energy of the wind into more useful forms using rotating blades or sails. The term also refers to the

structure it is commonly built on. There are two classifications of windmills that are; vertical and

horizontal axis windmills depending on the orientation of the transmission shaft connected to the

rotor.

Figure 1: Horizontal Axis Windmill

2.5 Windmill components

In order for the windmill to change the kinetic engergy in the wind to mechanical energy and to

transmit it to the where it is to be applied, the following components are necessary.

(a) Rotor

It is a circular wheel with a couple of curved blades mounted on it that help in the tapping of

wind energy (kinetic) and changing it into rotational (mechanical) energy. Therefore the rotor is

regarded as the most important part of the windmill because it determines the amount of work

the windmill can perform, the size of the windmill will always be described by the diameter id its

rotor. The rotor attaches to the windmill’s drive train to which it delivers its energy. (2004 Paul

Gipe Wind power)

The rotor speed is similar to the principal dimensions-one of the main design parameters of a

windmill. The power of a windmill

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nTTP 2 is equivalent to rotor torque T times rotor speed 2

n with

11

2v

R

v

nR , the rotor speed is linked to the tip speed and free stream velocity v1. The

tip speed ratio is an important parameter for the aerodynamic design of the rotor blades. Slow

speed windmills have a tip speed ratio of 1 and provide a high torque (R. Gasch, 2002)

Solidity: This is the percentage of the circumference of the rotor filled by the blades. It is infact

the swept area of the rotor, which is filled with metal. The general equation for calculatng

solidity is given by;

NBsolidity 8.31

Where

N- Is the number of the blades

B- Is the blade width (m)

- Is the diameter of the rotor (m)

The greater the solidity of the rotor, the slower it needs to turn to intercept the wind. The high

speed two or three bladed turbine is caused by the fact is has to rotate very fast to intercept the

wind otherwise a lot of the wind energy would be lost through the large gaps between the blades.

The typical solidity of a multi-bladed rotor of a wind pump is between 40%-60%.

Tip-speed ratio: This is the ratio of the speed of the rotor blade tips to the speed of the wind.

The general formula for calculating the tip-speed ratio is;

vratiospeedTip 052.0

Where;

- is the rotor diameter (m)

- is the rotational speed of the rotor (rpm)

v - is the wind speed (m/s)

If the rotor is rotating faster than the wind speed ratio, it will have a tip-speed ratio of greater

than one and if it rotates slower than the wind speed, its tip-speed ratio will be less than one.

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Rotors that rely on drag forces to turn them such as panamones can never rotate faster than the

wind speed and will always have their tip-speed ratio of less than one.

(b) Yawing

The yawing system is used to orient the rotor into the wind. Horizontal axis devices orient their

rotors into the wind passively by wind vanes or actively by using fantails or yaw devices. (R.

Gasch, 2002)

(c) Braking System

It would not be feasible to dimension all components of a windmill so that they can extract the

immense power potential of storms. The cost for this extra yield would be too high, taking into

consideration the few incidents of such extreme wind speeds, hence windmills are shut down

during high wind speeds and having only to ‘survive’ typical cut out speeds are between 20-

25m/s most windmills use brakes for the storm shutdown, they are triggered by a control

command of the supervisory system and operates mechanically on the drive train or

aerodynamically on the rotor, wind turbines with an active power control, the storm shutdown

can be considered an ‘extreme’ limitation of the power output, a condition which the windmill

reaches gradually with increasing wind speed. Often the windmill is not completely stopped but

left spinning that is, idling at a very low rotational speed. (R. Gasch, 2002)

(d) Tower

The tower is as important for static stability of the windmill as it is for the dynamic behavior of

the windmill, therefore when preparing documentation, the manufacturer is obliged to analyze

his/her construction in details. The head assembly of the windmill (rotor, transmission, and

safety system) is supported by a tower. This tower raises the assembly over any obstructions into

a fair, unobstructed wind. (R. Gasch, 2002)

In addition the tower serves as a rig when installing the pipes of deep well pumps. Windmill

towers are normally of lattice construction, factory welded as complete sections, or bolted

together at the installation site. Normally they have four legs, sometimes three. Tower heights

range from 6 m for small windmills to 18m for large windmills

(e) Pumping System

A pump is a mechanical device used to move fluids, such as gases, liquids slurries. A pump

displaces a volume by physical or mechanical action

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Table 1: Different Pump Types and Their Head Ranges and Maximum Efficiencies

Working

Principle Displacement Flow Lift by Elevation Lift

Design

Type

Piston

Pump

Diaphragm

Pump

Eccentric

Screw Pump

Centrifugal

Singe Stage

Centrifugal

Multi

Stage

Screw

Pump

Chain

Pump

Mammoth

Pump

H/m 10-300 2-4 10-300 1-10 10-300 1-3 2-5 5-30

optimum 85% 70% 75% 75% 75% 65% 50% 50%

Figure 2:

Pumping from bore holes and deep wells require different pump designs and types from those

pumping from the earth surface. Sub merged pumps are used for deep well and bore hole

pumping. These pumps are normally one of the two major categories of water pumps that are

centrifugal or positive displacement pumps.

Surface water pumping on the other hand uses surface mounted pumps with suction lift. These

pumps are of many different categories but the most power driven is the axial flow, centrifugal

or mixed flow suction pump.

Positive displacement pumps: They may have a reciprocating or rotary drive, both types are

used for windmills but they require different transmission design and arrangements.

Piston pumps normally operate at very low speeds of between 1-50 strokes per minute. They

should not be operated faster than this because there is a danger of causing serious damage to the

pump rod from compression forces. The stroke speeds are similar to the rotation al speeds of

large wind pump rotors, so that wind pump rotors of more than 5m diameter can be directly

coupled to piston pumps without any need for gearing to reduce or increase the speed, small

wind pumps rotate faster than larger ones and in general need gearing down meaning pumps will

rotate/operate efficiently over their complete range of speeds but only disadvantageous in that

they require a much more greater torque to start than they do to keep them running.

Rotary positive displacement pumps: These share advantages with piston pumps for wind

pumping. They have an added advantage that they are not subject to such large impulse forces

such as piston pumps and may therefore be made from cheaper lighter components. They have a

disadvantage of starting torque being larger that running torque, although for different reasons.

When a rotary positive displacement pump is not in use the rotor tends to stick to the stator and a

larger force is needed to overcome this sticking when the pump is starting from rest. As the

pump becomes older and the stator wears, the sticking force lessens but the pump efficiency

drops because water can flow back the stator.

(f) Transmission System

After extracting energy from the wind by a rotor, it is required to be transferred to where it is to

be used to do work; a transmission system is therefore responsible for the transmission of this

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mechanical energy from the prime mover (rotor) to where work is to be done and this can be

done by a mechanical connection which can either rotate (shafts, belts or gears) or reciprocate

(pump rods or levers), Where power has to be transmitted some distance, then electricity,

hydraulic pressure or compressed air can be used, since it is difficult to transmit mechanical

power any distance, especially if changes of direction or bends are needed.

2.6 Transmission System

There are several transmission mechanisms that can be exploited for the transmission of power

from the rotor to the pump and some of these include;

2.6.1 Belt Transmission Mechanism

A Belt is a looped strip of flexible material, used to mechanically link two or more rotating

shafts. They may be used as a source of motion, to efficiently transmit power, or to track

relative movement. Belts are looped over pulleys. In a two pulley system, the belt can either

drive the pulleys in the same direction, or the belt may be crossed, so that the direction of the

shafts is opposite. As a source of motion, a conveyor belt is one application where the belt is

adapted to continually carry a load between two points.

Figure 3: Flat Belt

Figure 4: Pair of V-Belts

(a) Power Transmission

Belts are the cheapest utility for power transmission between shafts that may not be parallel.

Power transmission is achieved by specially designed belts and pulleys. The demands on a belt

drive transmission system are large and this has led to many variations on the theme. They run

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smoothly and with little noise, and cushion motor and bearings against load changes, albeit with

less strength than gears or chains. However, improvements in belt engineering allow use of belts

in systems that only formerly allowed chains or gears.

(b) Pros and Cons

Belt drive, moreover, is simple, inexpensive, and does not require parallel shafts. Load

fluctuations are shock-absorbed (cushioned). They need no lubrication and minimal

maintenance. They have high efficiency (90-98%, usually 95%), high tolerance for

misalignment, and are inexpensive if the shafts are far apart. Clutch action is activated by

releasing belt tension. Different speeds can be obtained by step or tapered pulleys.

However, the angular-velocity ratio is not constant or equal to that of the pulley diameters, due to

slip and stretch. Heat accumulation is present, and speed is limited to approximately 2134m/min,

and a power of only 500 hp (370 kW). Temperatures range from -35 to 85 °C. Adjustment of

center distance or addition of an idler pulley is crucial to compensate for wear and stretch.

2.6.2 Chain Drive Transmission Mechanism

Chain drive is a way of transmitting mechanical power from one place to another. It is often used

to convey power to the wheels of a vehicle, particularly bicycles and motorcycles. It is also used

in a wide variety of machines besides vehicles.

Most often, the power is conveyed by a roller chain, known as the drive chain, passing over a

sprocket gear, with the teeth of the gear meshing with the holes in the links of the chain. The

gear is turned, and this pulls the chain putting mechanical force into the system. Another type of

drive chain is the Morse chain, invented by the Morse Chain Company of Ithaca, New York,

USA. This has inverted teeth

Figure 5: Chain Drive

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Sometimes the power is output by simply rotating the chain, which can be used to lift or drag

objects. In other situations, a second gear is placed and the power is recovered by attaching

shafts or hubs to this gear. Though drive chains are often simple oval loops, they can also go

around corners by placing more than two gears along the chain; gears that do not put power into

the system or transmit it out are generally known as idler-wheels. By varying the diameter of the

input and output gears with respect to each other, the gear ratio can be altered, so that, for

example, the pedals of a bicycle can spin all the way around more than once for every rotation of

the gear that drives the wheels.

Chains versus Belts: Drive chains are similar to drive belts in many ways, and which device is

used is subject to several design tradeoffs. Drive chains are most often made of metal, while belts

are often rubber, plastic, or other substances. This makes drive chains heavier, so more of the

work put into the system goes into moving a chain versus moving a belt. On the other hand, well-

made chains are often stronger than belts. Also, drive belts can often slip (unless they have teeth)

which means that the output side may not rotate at a precise speed, and some work gets lost to

the friction of the belt against its rollers.

Teeth on toothed drive belts generally wear faster than links on chains, but wear on rubber or

plastic belts and their teeth is often easier to observe; you can often tell a belt is wearing out and

about to break more easily than a chain. Chains often last longer.

Chains are often narrower than belts, and this can make it easier to shift them to larger or smaller

gears in order to vary the gear ratio. Multi-speed bicycles with derailleur make use of this. Also,

the more positive meshing of a chain can make it easier to build gears that can increase or shrink

in diameter, again altering the gear ratio.

Both can be used to move objects by attaching pockets, buckets, or frames to them; chains are

often used to move things vertically by holding them in frames, as in industrial toasters, while

belts are good at moving things horizontally in the form of conveyor belts. It is not unusual for

the systems to be used in combination; for example the rollers that drive conveyor belts are

themselves often driven by drive chains.

2.6.3 Gear Drive Transmission Mechanism

A gear is a component within a transmission device that transmits rotational force to another

gear or device. A gear is different from a pulley in that a gear is a round wheel that has linkages

("teeth" or "cogs") that mesh with other gear teeth, allowing force to be fully transferred without

slippage. Depending on their construction and arrangement, geared devices can transmit forces at

different speeds, torques, or in a different direction, from the power source.

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The most common situation is for a gear to mesh with another gear, but a gear can mesh with any

device having compatible teeth, such as linear moving racks.

Figure 6: Spur Gear Interaction

Figure 7: Spur-Rack Interaction

Figure 8: Bevel Gear Interaction

The gear's most important feature is that gears of unequal sizes (diameters) can be combined to

produce a mechanical advantage, so that the rotational speed and torque of the second gear are

different from those of the first. In the context of a particular machine, the term "gear" also refers

to one particular arrangement of gears among other arrangements (such as "first gear"). Such

arrangements are often given as a ratio, using the number of teeth or gear diameter as units. The

term "gear" is also used in non-geared devices that perform equivalent tasks:

The interlocking of the teeth in a pair of meshing gears means that their circumferences

necessarily move at the same rate of linear motion (for example, meters per second, or feet per

minute). Since rotational speed (for example measured in revolutions per second, revolutions per

minute, or radians per second) is proportional to a wheel's circumferential speed divided by its

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radius, we see that the larger the radius of a gear, the slower will be its rotational speed, when

meshed with a gear of given size and speed. The same conclusion can also be reached by a

different analytical process: counting teeth. Since the teeth of two meshing gears are locked in a

one to one correspondence, when all of the teeth of the smaller gear have passed the point where

the gears meet –that is to say, when the smaller gear has made one revolution -- not all of the

teeth of the larger gear will have passed that point -- the larger gear will have made less than one

revolution. The smaller gear makes more revolutions in a given period of time; it turns faster.

The speed ratio is simply the reciprocal ratio of the numbers of teeth on the two gears.

(Speed A * Number of teeth A) = (Speed B * Number of teeth B)

This ratio is known as the gear ratio.

2.6.4 Drive Shaft Mechanism

A drive shaft is a mechanical component for transmitting torque and rotation, usually used to

connect other components of a drive train that cannot be connected directly because of distance

or the need to allow for relative movement between them.

Drive shafts are carriers of torque: they are subject to torsion and shear stress, equivalent to the

difference between the input torque and the load. They must therefore be strong enough to bear

the stress, whilst avoiding too much additional weight as that would in turn increase their inertia.

Figure 9: Shaft Drive Mechanism

These are typically ideal for VAWT where there is direct connection between the windmill rotor

and the pump. This mechanism has the following advantages;

Drive system is less likely to become jammed or broken, a common problem with chain-driven

bicycles

More consistent performance. Drive shafts consistently deliver 94% efficiency, whereas a

chain-driven system can deliver anywhere from 75-97% efficiency based on condition.

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They are ideal for systems in which the pump and rotor are at a considerable distance hence

gears cannot apply.

However a drive shaft system weighs more than a chain system and at optimum upkeep, a chain

delivers greater efficiency

2.6.5 Crank Transmission Mechanism

A crank is an arm at right angles to a shaft (an axle or spindle), by which motion is imparted to

or received from the shaft; it is also used to change circular into reciprocating motion, or

reciprocating into circular motion. The arm may be a bent portion of the shaft, or a separate arm

keyed to it.

This mechanism is used well in pumping systems that use reciprocating pumps like piston and

diaphragm pumps.

Figure 10: Single Crank Shaft

The distance the axis of the crank throws from the axis of the crankshaft determines the piston

stroke measurement; a common way to increase the low-speed torque of an engine is to increase

the stroke.

Shaft

Connecting

rod

Crankshaft

Webs

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Figure 11: An Example of a Cranking Transmission System

2.7 Drag Devices

Drag devices utilize the force that acts on an area perpendicular to the wind direction. The force

is referred to as drag. Torque, rotational speed and power of the designed vertical-axis windmill

working by the drag principal can easily be determined based on the simplification that the

torque of the substitute system in (b) above is equivalent to that of the actual wheel in (a). The

substitute system ignores the coming and going and the effect of the preceding and the following

sail.

The air velocity at the plate is uvw , a composition of wind speed v and the blade tip speed

u=w/rpm of the interrupting area at a mean radius mR . The drag force is thus (R. Gasch, 2002)

Figure 12: (a) Principle of a Persian Wind wheel (b) Siplified Model

22 )(22

uvCAwCD a

D

a

D

.............................................. (iv)

This gives the mean driving power (actual power is slightly pulsating) of

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v

u

v

uCAvCuDp D

a

D

2

3 12

…………….……………… (v)

v

uCAvuDp p

a 3

2

……………………………….…………….. (vi)

The term in the curly brackets is equal to the power coefficient pC (aerodynamic efficiency). It

gives the portion of the total wind power that is converted into mechanical energy. This

coefficient has to be smaller than the maximum BetzpC = 0.59 determined by Betz. It depends on

tip speed ratio v

R

v

u m . At complete stand still, 0 , no power is extracted from the

wind. Neither it is at idling 1 Idle when the intercepting area moves at a blade speed

equal to the speed of the wind. In between, the power coefficient reaches its optimum of

16.0max pC at 33.0optimum hence only 16% of the wind energy can be converted to

mechanical energy. DC = drag coefficient is a proportional constant and describes the

aerodynamic quality of the body; the smaller DC is the smaller are the drag forces.

Table 2: Drag Coefficient of Different Blade Shapes

DC Body

1.11 Circular plate

1.10 Square plate

0.34 Semi-sphere (open back)

1.33 Semi-sphere (open front)

2.7.1 Torque

This is the turning force produced by the rotor. It depends on the solidity and tip-speed ratio of

the rotor. High solidity rotors with low tip-speed ratios (such as the wind pump rotors) produce

much more torque than low solidity high speed machines (such as wind turbines)

However, the high speed rotors have a slightly higher maximum performance coefficient but low

staring torque. On the other hand the high solidity machines produce high starting torque but

slightly lower maximum performance coefficient.

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The choice hence of the rotor depends on the load characteristics, a positive displacement pump

such as those used in bore holes demands a higher staring torque and hence a higher solidity

rotor is essential unless some method of unloading the rotor to make it start is included.

Positive displacement pumps that are invariably used with the wind pumps need fairly high

torque to start but will then continue to run with a lower torque. The rotor of a wind pump will

always rotate at a speed such that the torque produced exactly matches the torque required by the

pump. For this reason the torque characteristics of a windmill are important. In order to produce

a high staring torque, a high solidity rotor is needed and this is why high solidity multi-bladed

rotors are used in windmills.

For reciprocating positive displacement pumps approximately three times as much torque is

needed to start it to keep it running. This means that a wind pump will be able to operate even at

low speeds of the wind, it will just need a gust of high speed to actually start it. For example a

wind pump will need about 4.5m/s wind speed to start it but will continue to run at speeds even

lower than 2.5m/s.

2.7.2 Power Coefficient

Is the ratio of the mechanical power delivered by the windmill to the power that is in the wind

passing the rotor disc if the rotor were not present. This is represented as;

35.0 Av

Pc

a

p

Where,

P- Is the power delivered by the windmill.

a - Is the air density

A- Is the swept area of the rotor.

v-Is the wind speed

Table 3: Power Coefficient as a Function of Tip Speed Ratio

optimumPC

optimumPC

0.5 0.289 2.5 0.533

1.0 0.416 5.0 0.750

1.5 0.477 7.5 0.581

2.0 0.511 10.0 0.585

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2.7.3 Torque coefficient

This is the ratio of the torque delivered by the windmill to the reference wind torque. Since

power = rotational speed times Torque, ( TP ), a similar relation is found for the

corresponding coefficient

RAv

Tcq 25.0 Where,

A- Is the rotor swept area

T- Torque

R-Rotor radius

v- Wind speed

a - Air density

2.8 Hydraulic Power

Once the effective output, the actual amount of water the user needs, has been determined, one

must calculate the amount of power needed to pump this volume of water. The net amount of

hydraulic (pumping) energy required to lift a volume of water over a head H is given by;

gHqP wh

Where;

hP - is the required energy (Watts)

w - is the water density (1000kg/m3)

H- is the head (m)

g- Acceleration due to gravity (9.81m/s2)

q- Is the flow rate or the volume of water lifted per second in m3/s

This equation can be expressed as;

HqPh

3810.9 Watts

This can take two alternative forms as seen below;

HqPh 81.9 - if q is expressed in liters/second and,

HqPh 113.0 - if q is expressed in liters/day.

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2.9 Transmission System Design and Modeling

2.9.1 Physical Product Design

Physical product design and modeling has been and is still in use for the production of

windmills. This method involves making either full size or scaled down models of the windmill

and then subjecting them to varying wind conditions to check their performance. The procedure

followed is; data on the wind speeds is collected from the area where the installation is to be

made. This data is then used to determine the parameters needed for windmill design.

2.9.2 Computer Aided Drawing

Computer Aided Drawing (CAD) is the use of computer technology to aid in the design and

particularly the drafting (technical and engineering drawings) of a part or product, including

entire buildings. It is both a visual (or drawing) and symbol-based method of communication

whose conventions are particular to a specific technical field. Drafting can be done in two

dimensions (2D) and three dimensions (3D). Drafting is the integral communication of technical

or engineering drawings and is the industrial art sub-discipline that underlies all involved

technical endeavors. In representing complex, three-dimensional objects in two-dimensional

drawings, these objects have traditionally been represented by three projected views at right

angles.

This technique is replacing the traditional way of generating design drawings and brings so many

advantages to the engineering world of design like improved accuracy, lowered design time,

better visualization and cost cuts. Many programs are on the market now to do this for example

Solid Edge, Solid Works, Unigraphics and so on.

2.10 Transmission System Testing

2.10.1 Physical Testing

After all the parameters have been ascertained, a scaled or full size windmill model is then

manufactured and subjected to tests. In the earlier years and in some cases now the physical

models are subjected to tests at the site of the windmill installation or outdoors using the

naturally occurring wind. In the previous years, and to some extent today, wind tunnels are used

for these tests.

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2.10.2 Computer Simulation

Computer simulation is the discipline of designing a model of an actual or theoretical physical

system, executing the model on a digital computer to determine its real behavior when being

operated in the real world, it is hence used to predict the performance of the model before actual

physical modeling, Simulation embodies the principle of ``learning by doing’’ to learn about the

system we must first build a model of some sort and then operate the model. To understand

reality and all of its complexity, we must build artificial objects and dynamically act out roles

with them. Computer simulation is the electronic equivalent of this type of role playing and it

serves to drive synthetic environments and virtual worlds. Within the overall task of simulation,

there are three primary sub-fields: model design, model execution and model analysis

Computer simulation can be very vital in the following cases, when;

The model is very complex with many variables and interacting components

The underlying variables relationships are nonlinear

The model contains random variants

The model output is to be visual as in a 3D computer animation.

(Fishwick, Thu Oct 19 10:30:41 EDT 1995)

FEA consists of a computer model of a material or design that is stressed and analyzed for

specific results. It is used in new product design, and existing product refinement. A company is

able to verify a proposed design will be able to perform to the client's specifications prior to

manufacturing or construction. Modifying an existing product or structure is utilized to qualify

the product or structure for a new service condition. In case of structural failure, FEA may be

used to help determine the design modifications to meet the new condition and resources like

Algor, Unigraphics, SIMULIA, SolidWorks and Abaqus from Dassult systems and many more.

2.11 Conclusion

The literature review has presented the wind source and the energy that can be extracted from

wind, a renewable and abundant source of energy, the technology that can be used to tap into the

extraction of this energy with its history and the components of the technology. The methods of

development and testing of this technology have been explored and a gap between the traditional

rudimentary and modern methods can be seen. It is hence pertinent in this research to design a

windmill that can effectively work in this modern age which requires modern methods of design

and testing.

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The following chapter hence presents the methodology of the research that shall be explored by

the student during the design.

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CHAPTER THREE: METHODOLOGY

3.1 Introduction

After realizing a research problem, setting the necessary objectives of a research study and

justifying the problem, it is necessary to explain how the set objectives shall be realized. This

chapter hence gives an account of the design and simulation of the transmission system

This chapter is devoted to the presentation of the progress of events in the design and

simulation of the windmill rotor. The criterion for development of the simulation model is

the heart of this chapter.

3.2 Preliminary Design

(a) Design Considerations

These shall include the following;

Weight

Rotor outputs

Durability

Efficiency

Ease of fabrication/ manufacture

Cost of production

Safety

Cost

Maintenance

Corrosion

Serviceability

Noise

Reliability Size

(b) Customer Needs

The following are some of the customer needs that were established in this design research;

Transmission System that can operate with already designed rotor

System which is able to pump water for over 100 heads of cattle and sheep

A system that is affordable, durable and easily maintained

Operates at low and intermittent speeds of wind

(c) Target Specifications

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These are a reflection of the needs of customers structured in an engineering language with

design parameters and are as follows;

The system that can pump over 7500 liters of water per day

A system the can run at wind speeds as low as 2.5 m/s and that are intermittent

The system capable of operating with a rotor of diameter 8m with 24 blades pitched at 450.

(d) Concept Generation

After benchmarking with the existing windmills locally fabricated and those available on

international markets in addition to brainstorming, the following concepts were generated in

regards to the transmission system to use in this research.

Table 4: Transmission System Concepts

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(e) Concept Criteria

Table 5: Concept Selection Creteria

Parameters for

Selection Of Concept

Concepts

1 2 3 (REF)

4

5 6 7

Weight + - + 0 + + +

Torque requirement + 0 + 0 - - -

Cost of

manufacturing

+ + - 0 + + +

Cost of maintenance + 0 + 0 + + +

Space requirements + + + 0 + + +

Easy of assembly + + + 0 + + +

Noise levels + 0 - 0 - - -

Water output quantity - - - 0 - - -

Sum of +’s 7 3 5 0 5 5 5

Sum of 0’s 0 3 0 8 0 0 0

Sum of –‘s 1 2 3 0 3 3 3

Net score 6 1 2 0 2 2 2

Rank 1 6 2 7 2 2 2

Continue? YES NO NO NO NO NO NO

The selected concept is concept one, that is the simple crank mechanism since it has ranked

highest of all the concepts developed. Concept 4 was taken as a reference in the selection.

(f) Components for Design

The transmission system has got the following components that are to be designed;

Crank shaft

Connecting rod

Crank pin

Pumping rod

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Pump size

Bearings

Connecting pins

Yoke

(g) Transmission system layout

The system has the lay out shown below;

Figure 13: Isometric View Of The Transmission

System

Figure 14: Exploded View Of The Transmission

System

(h) Materials selection

Materials to be used are selected basing on the following factors;

Strength

Corrosion resistance

Machinability

Weldability

Cost

Availability

The material chosen from rule of thumb is steel AISI 1040 as a standard material but final

material to be used is to be selected after the simulations. This means that the materials that shall

display better results at simulation are to be selected since most of the AISI 104X steels have

almost the same machinability, availability, weldability and cost, the prime factors for

consideration shall be strength and corrosion resistance

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3.3 Detailed Design

3.3.1 Wind Power

(a) At 2.5m/s wind speed

This is given by the expression below;

3

2

1AvP awind

Where; windP is the power that is in the wind

a is the air density

V is the wind velocity

A is the swept area of the rotor

The blades are 2.5m in length hence do not sweep over the entire 8m rotor diameter when

rotating (this means that a diameter of 3m is not swept by the rotor blades) therefore, actual

swept area is given by;

222 2.43)38(4

mA

35.22.432.15.0 windP

Watts405

But not all this power is trapped by the rotor therefore the rotor power is much smaller that the

wind power and can be expressed as below (for drag machines);

v

u

v

uCAvCP D

aDshaft

2

3 12

Where shaftP is the power at the shaft

DC is the drag coefficient

And the parameters in the carry brackets equal to the power factor pC

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From table 1, DC =1.10 for square blades. And from table 2; the design power ratio at design

tip speed ratio of 1 (for wind mills), is 0.416., design wind speed v=2.5m/s2.

35.25.0416.010.1 APshaft

A-is the swept area of the rotor.

35.22.435.0416.010.1 shaftP

Watts4.154

(a) At 6m/s wind speed

This is given by the expression below;

3

2

1AvP awind

Where; windP is the wind power.

a is the air density

V is the wind velocity

A is the swept area of the rotor

The blades are 2.5m in length hence do not sweep over the entire 8m rotor diameter when

rotating (this means that a diameter of 3m is not swept by the rotor blades) therefore, actual

swept area is given by;

222 2.43)38(4

mA

362.432.15.0 windP

kW

Watts

6.5

7.5598

But not all this power is trapped by the rotor therefore the rotor power is much smaller that the

wind power and can be expressed as below (for drag machines);

v

u

v

uCAvCP D

aDshaft

2

3 12

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Where shaftP is the power at the shaft

DC is the drag coefficient

And the parameters in the carry brackets equal to the power factor pC

From table 1, DC =1.10 for square blades. And from table 2; the design power ratio at design

tip speed ratio of 1 (for wind mills), is 0.416., design wind speed v=2.5m/s2.

365.0416.010.1 APshaft

A-is the swept area of the rotor.

362.435.0416.010.1 shaftP

Watts2135

3.3.2 Rotational Shaft Speed

(a) At 6m/s wind speed;

Given that 1 , and the expression of the tip speed ratio is given by

V

R

Where;

Is the rotor rotational speed (rads/s)

V is the wind speed

R is the rotor radius

R

V

4

60.1

srads /5.1

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(b) at 2.5m/s wind speed

Given that 1 , and the expression of the tip speed ratio is given by

(c) V

R

Where;

Is the rotor rotational speed (rads/s)

V Is the wind speed

R Is the rotor radius

R

V

4

5.20.1

srads /625.0

3.3.3 Shaft Torque

(a) At 6m/s wind speed

This is obtained from the expression for the shaft power which is;

TPshaft

Where T is the shaft torque

shaftPT

3.14235.1

2135

Therefore the shaft toque

NmTshaft 3.1423

(b) At 2.5m/S Wind Speed

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This is obtained from the expression for the shaft power which is;

TPshaft

Where T is the shaft torque

shaftPT

247625.0

4.154

Therefore the shaft toque

NmTshaft 247

3.3.4 Hydraulic Power

This is the power that is required by the windmill to pump water through a given head H. This

can be found from an expression below;

HqPhyd 113.0

Where q is the volume flow rate in litters/day and H is the total head in meters.

The design required rate of water flow is 7500 liters/day and H=20m.

Or

HqPh 81.9 When q is the flow rate in liters per second.

Given that the rotational speed of the rotor and hence the shaft is 0.625rads/s since there is no

gearing.

But srevsrads /1/2

srevssrad /2

1/1

srevssrads /2

1625.0/625.0

srevs /0995.0

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But since each complete revolution made by the shaft represents a single stroke by the piston

pump; then this means that the pump will be running at a speed of 0.0995 strokes per second and

in a minute there would be 5.97 strokes made.

Using a pump of design capacity of 4 liters per stroke (Designed by Agricultural Engineering

Appropriate Technology Institue-Namalele)

From table 3; piston pumps have an efficiency of 85%. This means that for each stroke then, the

piston shall deliver;

strokeliters /4.385.04

This then can give the flow rate per second as;

ondstrokesstrokeliters sec/0995.0)/(4.3

ondliters sec/3383.0

ondlitersq sec/3383.0

From previous research (Victoria Njuki; Simulation of a Windmill Rotor Suitable for Pumping

Water at Low and Intermittent Wind Regimes

; 2008), it was established that in Uganda, on average the wind speed is at 2.5m/s for about 6.5

hours a day, therefore;

The daily water delivery would be;

ondsondsHrs sec000,23sec)60605.6(5.6

dayliters

deliverywaterDaily

/79162.7916

234003383.0

Note: This is more than the least design water delivery rate per day of 7500 liters per each day.

But this delivery rate can be enhanced by modifying the pump to a double acting one in which

the delivery is doubled for the same design parameters, the pump delivers;

ondliters sec/6766.03383.02

Therefore, on a daily basis in the 6.5 hours that the wind speed is at least 2.5m/s, the rate of

water delivery would be;

4.15832234006766.0

dayliters /15832

Page 47: Project Report Windmill

35

Therefore, the design flow rate ondlitersq sec/3383.0 to give at least 7500liters per need.

Hydraulic power required therefore is;

Watts

HqPhyd

4.64

3383.02081.9

81.9

If the piston used is double acting, then the hydraulic power shall eventually double to

64.4x2=128.8 Watts

Therefore the hydraulic power required is WattsP hyd 4.66

Since shaft power is greater than hydraulic power, and then it means that the windmill is able to

deliver the required water.

3.3.5 Water Flow Rate

This can be obtained from the monogram as seen below which is done by matching the known

parameters on the monogram like the average wind speed, rotor diameter and water lifting head.

Figure 15: Monogram for Selecting Flow Rate of the Pump

Page 48: Project Report Windmill

36

This is found to be about 0.34 liters/second which is approximately equal to that found by

calculation.

3.3.6 Design Stroke Volume

Using the monogram below and by matching parameters like rotor diameter, wind speed and the

total static head. This is found to be equal to 4liters per stroke from the monogram below.

Figure 16: Monogram for Selecting Pump Capacity

Page 49: Project Report Windmill

37

3.3.7 Pump Size

Using the monogram below, on the basis of the stroke volume thus obtained, one will depend on

the stroke settings available in the windmill’s transmission and on the pump diameters available.

Sometimes an important limiting factor for the pump diameter is the tube-well in which the

pump has to fit.

Figure 17: Monogram for Determining Pump Size

For purposes of reducing the jerking forces on the shaft as it sweeps through the crank diameter,

the stroke of 200mm is selected which is below the maximum stroke and from the chart the

corresponding diameter is obtained at a stroke volume of 4 liters

Page 50: Project Report Windmill

38

3.3.8 Pump Rod Design

(a) Forces Acting on the Pump Rod

This is the force required to lift the piston and is given by the total weight of the water column

above the piston. The cross section of the column is taken to be less than a half of that of the

pump piston that is 100mm.

For analysis, it is assumed that the pump rod is weightless; therefore the only force acting on the

rod is that due to the water column above the piston.

gHwAF

Where

A is the cross section area of the piston

w is the water density

g is the acceleration due to gravity

H is the total static head

Using the water column diameter of 100mm, the cross section area is;

Cross section area of the piston

2

22

0079.0

4

1.0142.3

4

m

d

Therefore, using a static head of 10m above the pump level to the storage tank,

N

iscolumnwatertheofWeight

99.774

10100081.90079.0

Hence the force acting on the pump rod is 774.99N

Page 51: Project Report Windmill

39

(b) Pump Rod Diameter

Treating this rod as a strut and using the Euler treatment of struts, since both ends are considered

to be rounded or pivoted as shown below;

Figure 19: Euler Column

Using Euler’s equation, the critical load Pcr is

given by;

2

2

l

EICPcr

where Pcr -is the critical load

E- is the modulus of elasticity

I-is the second moment of area

C-is the coefficient of variation in column

loading

774.99N

774.99N

Figure 18: Pump Rod Free Body Diagram

Page 52: Project Report Windmill

40

Table 6: A table Showing Values of Euler Constant C

Column end

condition

End condition constant C

Theoretical value Conservative

value

Recommended

value*

Fixed-free 0.25 0.25 0.25

Rounded-rounded 1 1 1

Fixed-rounded 2 1 1.2

Fixed-fixed 4 1 1.2

Source: mechanical Engineering design-Joseph Edward Shigley.

*To be used only with liberal factors of safety when the column load is accurately known.

Using the theoretical value of C=1 (for rounded-rounded situation)

2

2

l

EIPcr

E

lPI cr

2

2

The allowable loadN

PP cr

a , where N-is the design factor of safety

Using the factor of safety of N=1.2;

Then

NPcr 99.92999.7742.1

This gives the second moment of area as below;

47

92

2

2

2

101.1

10193142.3

1599.929

99.92999.7742.1

mI

E

lPI

NP

cr

cr

Page 53: Project Report Windmill

41

But

4

1

4

64

64

ID

DI

mmmD

D

7.381087.3

101.164

2

4

1

7

The slenderness ratio for this size is obtained as follows;

42.1550

47.38

15000

4

d

l

k

l

To be sure that this is Euler column; we use the limiting slenderness ratio expression as below;

8.95

10415

1019312

2

lim

21

6

92

21

2

lim

k

l

CE

k

l

y

Table 7: Table of Preferred Sizes

0.05 0.06 0.08 0.10 0.12 0.16 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.80 0.90

1.0 1.1 1.2 1.4 1.5 1.6 1.8 2.0 2.2 2.5 2.8 3.0 3.5 4.0 4.5

5.0 5.5 6.0 6.5 7.0 8.0 9.0 10 11 12 14 16 18 20 22

25 28 30 32 35 40 45 50 60 80 100 120 140 160 180

200 250 300

Source: Table A-17 Mechanical Engineering Design; Joseph Edward Shigley.

Page 54: Project Report Windmill

42

Since the limiting slenderness ratio is less than k

l and greater than

6

1, the column is indeed a

Euler column and hence using the table above, the rod diameter is 40mm.

A solid pump rod of 40mm diameter would be an over design for this operation hence an

equivalent piped rod can be used giving the same results of operation but lighter and hence lesser

materials used in its production.

Since the desired outside diameter is established and the second moment of are I is to remain

unchanged; an equivalent rod can be obtained from;

41

4

44

64

64

)(

IDd

dDI

Where, d is the internal diameter of the rod and D is the outside diameter of the rod.

Using D=40mm,

mmmd

d

8.231038.2

142.3

101.164)1040(

2

41

743

Using the table above (of proffered sizes), the internal diameter is set to be 25mm

3.3.9 Crank Mechanism Design

This is a mechanism responsible for transforming the rotary motion of the shaft at a given

rotational speed to reciprocating motion of the pump rod and hence the pump piston which uses

an up and down movement to pump a fluid.

The schematic layout of this mechanism takes the shape below;

Figure 20: Crank Slide Mechanism

Page 55: Project Report Windmill

43

(a) Design Equations

Using the above figure, the analysis of position, velocity and acceleration of the different

linkages can be carried out using the following formulae;

)....(..........0

)(.0

)....(..........0

0

32

321

321

0

1

321

321

iielell

ieqntointhisfeedingBut

ielelel

giveswhichlll

jj

jjj

This gives the following

;

,

)....(..........0

)(.

).........(0sincossincos

32

33221

.

333322221

belowasequationonaccelarati

theobtainweequationvelocitytheatingdifferentiand

ivejlejll

iswhich

obtainedisequationvelocitytheiieqnatingDifferenti

iiijlljlll

jj

).....(0

).....(0

3322

3322

2

3333

2

22221

..

2

3

2

333

2

2

2

2221

..

vielejlelejll

givesthis

vejlejlejlejll

jjjj

jjjj

But of interest in this design is establishing the lengths of the different linkages to give the

desired motion of the crank mechanism therefore, this can be done using the following analysis;

Figure 21: Slide Crank Motion

Page 56: Project Report Windmill

44

(b) Crank Parameters

For a symmetrical slider motion

Crank length 2

)( max42

Rl

But max4 )(R is the stroke length that is the distance between the top dead center and the bottom

dead center of the piston pump cylinder which is 200mm.

mml 1002

2002

To produce smooth acceleration of the crank mechanism, l3>>l2

Then, by rule of thumb;

mml

l

400

1004

4lL3

3

3

2

Using the graph below for an inline slider crank

Figure 22: Figure for Selection of Crank Linkages

With l1=0, implying that 02

1 l

l, then using the curve of 0

2

1 l

l as shown on the graph, it is

shown that smooth acceleration can be achieved between 52

1 l

l and 10

2

1 l

l. But in the interest

Page 57: Project Report Windmill

45

of limiting the space occupied by the system as a design consideration, a trade-off between the

absolute smoothness and space is made therefore taking the coupler ratio of 5.42

1 l

l for this

design is appropriate enough.

mm

l

ll

400

1004

4

3

23

3.3.10 Crank Shaft Design

This is designed to withstand the worst wind conditions, that is; at a maximum likely wind speed.

From the research, simulation of a windmill rotor suitable for pumping water at low and

intermittent wind regimes, Design and simulation of a windmill rotor to operate at low and

intermittent wind regimes: Njuki Victoria 2008, the likely maximum average wind speed was

found to be 6m/s, therefore at this speed;

(a) Engineering Drawing of the Shaft

Figure 23: Shaft Engineering Drawing

(b) Free Body Diagram

Figure 24: Shaft Free Body Diagram

Page 58: Project Report Windmill

46

In designing of the shaft, it is designed against fatigue loading, bending moment and axial

loading. The diameter of the shaft is obtained using the Soderberg formula as shown below;

31

21

22

32

ey

shaftS

M

S

TNd

Where;

shaftd is the diameter of the shaft

N is the design factor of safety

T is the applied torque

M is the maximum bending moment

Sy is the yield strength of the material

Se is the modified endurance strength of the shaft

But efedcbae SKKKKKKS 1

Where;

Ka=surface factor

Kb=size factor

Kc=reliability factor

Kd=temperature factor

Ke=modifying factor for stress concentration

Kf=miscellaneous effects factor

Where;

utb

a aSK And assuming the shaft is to be machined, using the table below;

Page 59: Project Report Windmill

47

Table 8: Table of Fatigue Stress Constants

Surface finish Factor a (MPa) Exponent b

Ground 1.58 -0.085

Machined or cold drawned 4.51 -0.265

Hot rolled 57.7 -0.718

As forged 272 -0.995

SOURCE: Joseph Edward Shigley-mechanical engineering design

This means, from the table above that a=4.51MPa, b=-0.265 and utbS =620MPa.

821.062051.4265.0

aK

mmdmmd

indind

Kb

5179.262.7

211.03.0

1133.0

1133.0

But for large sizes of shaft, Kb varies between 0.60-0.75 for bending and torsion

Taking Kb=0.75.

shearandtorsion

bending

MPaSloadingaxial

MPaSloadingaxial

Kut

ut

c

577.0

1

15201

1520923.0

577.0 cK

The temperature factor is obtained as below.

CTC

CTKd 00

0

5003505.0

3501

1 dK Since the operating temperature of the windmill hence the shaft is assumed to be less

than 3500C.

Ke is assumed to be equal to 1 with no stress risers and taking the miscellaneous factor is also

assumed to be 1.

Using a low carbon steel AISI 1045 as rolled;

Page 60: Project Report Windmill

48

MPa

Se

3.220

62011577.075.082.0

(c) Shear and Bending Moment of Shaft

Free body diagram of the shaft;

Figure 25: Shaft Moment Free Body Diagram

1.7

87.01.31.3

0

044.005.087.01

BA

BA

RR

RR

Fy

Then

kNmM

kNR

R

BMB

A

A

6.135.0

82.6

5.11.36.01.3044.03.087.05.0

0)(.

And kN

RB

5.6

6.131.7

Page 61: Project Report Windmill

49

Figure 26: Shaft Bending Moment Diagram

From the diagram of bending moment, the maximum bending moment is 3.41kNm and using the

torque T=1.4233kNm.

Then from

31

21

22

32

ey

shaftS

M

S

TNd

Note: for machine elements which are ductile under conditions of moderate uncertainty with

regard to material properties, nature of loading or adequacy of stress of the stress analysis, N=3.

Therefore the diameter of the shaft can be obtained as below;

31

21

2

6

2

6 103.220

3410

10415

3.1423332

shaftd

This gives diameter as

mmmd shaft 5.780785.0

The standard shaft diameter can be obtained from the table below; this is used because standard

bearings are to be used.

Page 62: Project Report Windmill

50

Figure 27: Bearing Outline

Table 9: Bearing Size Selection Table

Inner diameter d(mm) Outer diameter D(mm)

10 30

12 32

15 35

17 40

20 47

25 52

30 62

35 72

40 80

45 85

50 90

55 100

60 110

65 120

70 125

75 130

80 140

85 150

90 160

95 170

100 180

Source: Robert L. Mott-machine elements in mechanical design (third edition)

Therefore the shaft standard nominal diameter is 80mm

Page 63: Project Report Windmill

51

3.3.11 Design of Connecting Rod

Assuming that it is made of the same material as that used for the main shaft, and that the forces

acting on it are a result of the pump rod and water column weight.

(a) Layout

Figure 28: Engineering Drawing Of Connecting Rod

Figure 29: Solid View Of Connecting

Rod

Since there are no loads in the perpendicular direction to the paper, the thickness can be assumed

to be 15mm and at the pin connections, it can be taken as 35mm.

The reactions on the crank pin constitute the force that acts on the crank webs at a distance equal

to the radius of the crank which is a half of the pump stroke, that is mm1002

200

3.3.12 Design of Crank Pin

Assuming that the crank pin is simply supported, with simple loading from the water column and

pump rod weights.

Page 64: Project Report Windmill

52

(a) Lay Out

Figure 30: Crank Pin Layout

kNRR ED 435.02

187.0

Treating the pin as a shaft, of the same material as that of the main shaft.

(b) Shear and BM Diagrams

Figure 31: Crank Pin Bending Moment Diagram

Maximum bending moment is kN022.005.0435.0

And using N as 3 and Sy=415MPa

3

1322

122

MT

S

Nd

y

cp

3

1

21

22

6223.1423

10415

332

cpd

mmmdcp 1.470471.0

Page 65: Project Report Windmill

53

But since this is to be connected to a connecting rod and hence rotating in a bearing, the

appropriate size of the pin is obtained from the table above (of the nominal sizes of bearings)

mmdcp 50

3.3.13 Design of Yoke Pin

Note: Points on a shaft where no torque is applied and where the bending moments are zero or

very low often subjected to significant vertical shearing force which then govern the design

analysis.

Figure 32: Solid View of Yoke

A

V

3

4max Where; V is the vertical shearing force and A is the area of cross section.

When stress concentration factors are to be considered.

Using the distortion energy theory, the endurance strength in shear is nsn ss 11 577.0 but

max

1

snsN becomes

max

1577.0

nsN .

This gives

A

Vk

N

st

n

Design3

4577.0 1

therefore Vk

As

Vk

AsN

t

n

t

n )(433.0

)4(

)3(577.0 11

This gives the shear cross section area as;

nt

n

t

s

NVkD

s

VNkDA

1

1

2

)(94.2

31.2

4

For sharp fillets, 5.2tk and RSnn CCss 1 , where SC is the size factor and RC is the reliability

factor.

Page 66: Project Report Windmill

54

From table below;

Table 10: Table of Reliability Factors

Desired reliability Reliability factor

0.50 1.00

0.90 0.90

0.99 0.81

0.999 0.75

Source: Table 12-1, Reliability Factors RC , Mott.

Choosing a reliability of 0.99, the reliability factor RC =0.81 and SC =0.85, therefore;

MPasn 87.42681.085.06201

So, the pin diameter becomes

mmD

tablesizespreferredfromBut

mmD

D

14

,'

6.13

1087.426

31087.05.294.26

3

3.4 Bearing Selection

These were selected basing on the type of forces that act on them say;

Axial loads: which act towards the centre of the bearing along a radius. Such loads are typical

of those created by power transmission elements on shaft such as spur gears, belt drives and

chains.

Thrust loads: are those that act parallel to the axis of the shaft. Bearings supporting shafts with

vertical axes are subjected to thrust loads due to the weight of the shaft and the elements on the

shaft as well as from axial operating forces.

Table 11: Comparison of Bearing Types

Bearing type Radial load

capacity

Thrust load capacity Misalignment

capacity

Page 67: Project Report Windmill

55

Single deep-grove ball Good Fair Fair

Double-row deep-grove ball Excellent

good

Good Fair

Angular contact Good Excellent Poor

Cylindrical roller Excellent Poor Fair

Needle Excellent Poor Poor

Spherical roller Excellent Fair/good Excellent

Tapered roller Excellent Excellent poor

Source: Table 14-1 Mott-Mechanical Elements in Mechanical Design 3rd-Edition

Using a scoring matrix with a scale of 1-5 with 5-excellent, 4-good, 3-fair, and 1-poor.

Radial load capacity being the most vital attribute, a weight of 60% is attached to it and 25% to

thrust load capacity and 15% for misalignment capacity.

Page 68: Project Report Windmill

56

Table 12: The Selection Scoring Matrix Is Table

Selection

criteria

Wei

ght

Sin

gle

dee

p-

gro

ve

bal

l

Double

-row

dee

p-g

rove

bal

l

Angula

r

conta

ct

Cyli

ndri

cal

roll

er

Nee

dle

Spher

ical

roll

er

Tap

ered

roll

er

Rat

ing

Wei

ghte

d

score

R

atin

g

Wei

ghte

d

score

Rat

ing

Wei

ghte

d

score

R

atin

g

Wei

ghte

d

score

R

atin

g

Wei

ghte

d

score

R

atin

g

Wei

ghte

d

score

R

atin

g

Wei

ghte

d

score

Radial Load

Capacity 60% 4 2.4 5 3 4 2.4 5 3 5 3 5 3 5 3

Thrust Load

Capacity 25% 3

0.7

5 4 1 5

1.2

5 1

0.2

5 1

0.2

5 3

0.7

5 5

1.2

5

Misalignment

Capacity 15% 3

0.4

5 3

0.4

5 1

0.1

5 3

0.4

5 1

0.1

5 5

0.7

5 1

0.1

5

Total

score 3.6 4.45 3.8 3.7 3.4 4.5 4.4

Rank 6 2 4 5 7 1 3

Selec

t No No No No No Yes No

Therefore the spherical roller bearing is selected for use.

Machines for intermittent service where reliable operation is of great importance, the life of the

spherical bearings is 8-14kHrs.

Taking an average of 11kHr, the life in terms of total revolutions that have to be made before

change is given by, )min/60)()(( hrrpmhLd . Taking the worst average case of 6m/s wind

speed, the speed is about 85rpm hence life becomes

srevolution

Ld

000,100,56

)60)(85)(11000(

Page 69: Project Report Windmill

57

3.5 Computer Aided Drawings

These drawings were generated using a computer aided drawing’s package solid edge version 19

commercial. It has direct and simple interfacing with Algor the simulation package by easily

exporting the generated drawings into Algor or importing into it for analysis.

The following is an assembly CAD model of the of the transmission system and its exploded

view;

Figure 33: Solid Model of Transmission System Assembly

Figure 34: Exploded View of Transmission System

Page 70: Project Report Windmill

58

3.6 Simulation

The simulation was carried out to establish the forces that result from the loading of the

transmission system.

Assumption

The AISI 1045 steel is used for the construction of the transmission system with the properties

below;

Density 7.7-8.03×1000 kg/m3 Poisson's Ratio 0.27-0.30 Elastic Modulus 190-210GPa Tensile

Strength 585 Mpa Yield Strength 505Mpa

It is assumed that the operating temperature is 300C and hence simulation is carried out at this

operating temperature.

Procedures Followed in the Simulation

The solid edge models developed were imported into the Algor environment where the

simulation was carried out.

The model was assigned material properties of AISI 1045 steel in the materials’ options

The analysis type to be carried out was specified say mechanical events simulation with non

linear materials from the analysis menu.

The constraints were applied on the model fixing the bottom parts of the bearings

Loading at the different components with the obtained forces was done. This was done by

selecting the surfaces upon which the forces would be acting and assigned them with surface

forces with the desired directions of action

The input torques obtained from calculation was fed into the model

A model mesh was generated at a mesh size setting of 100%(4.39mm) fineness and 0.01

tolerance value

Page 71: Project Report Windmill

59

Figure 35: Model Mesh

The analysis parameters were set from the default ones, specifying the output parameters, the

time steps to use in the simulation and the conditions of the analysis

The analysis was then carried out to establish the forces and displacements that result from the

loading and constraining of the system.

3.4 Conclusion

This chapter has covered the methodology that was followed to meet the objectives of this

research. It has identified the input parameters to the transmission system for example the torque

that is generated at the rotor with the different wind speeds, the water flow rates for this design,

the power (hydraulic and shaft) that is required and generated by the system respectively.

Herein have been deep analyses of the linkage mechanisms and the forces that act on the

different components and the appropriate dimensions of the different parts as obtained from

standard equations.

In chapter four, the test results as carried on the CAD models herein generated are presented.

Page 72: Project Report Windmill

61

CHAPTER FOUR: PRESENTATION AND DISCUSSION OF RESULTS

4.1 Introduction

Following the setup procedures as described in the preceding chapter, the simulation were

carried out to determine whether the designed models confirm to the performance requirements

of the transmission system. This represents the forces acting on the components that are a result

of component interactions.

4.2 Mechanical Events Simulation

This was carried out with the worst case scenario with forces resultant at 6m/s wind speed. It

shows the forces that act on the individual parts and the failure patterns. This assumed non-

linear materials and analyzing each component as a unit.

Failure of the components start when the von Mises stress reaches a critical value known as the

yield strength, Sy. The von Mises stress is used to predict yielding of materials under any loading

condition from results of simple uniaxial tensile tests. The von Mises stress satisfies the property

that two stress states with equal distortion energy have equal von Mises stress.

(a) Connecting Rod

From the simulation, it is shown that the von Mises stress that the connecting rod is subjected to

as a result of its interaction with other system components is 15.9514N/mm2 (16Mpa) for a

connecting rod with no webs and 16.85N/mm2 for that with webs. These are far less than the

yield stress of 415Mpa or 415N/mm2.

Figure 36: MES Analysis of Connecting Rod Showing Von Mises Stress

Page 73: Project Report Windmill

62

Figure 37: MES Analysis of Connecting Rod With Webs Showing Von Mises Stress

Table 13: Table of Results on Connecting Rod

Case Von Mises (N/mm2) Displacement (mm) Reaction forces (N)

Without web 15.59 0.16 587.55

With web 16.85 0.13 354.1

The results above show that the connecting rod with webs of thickness 15mm and depth of

10mm does better than that without webs especially on displacement and reactions induced since

the Von misses stresses are almost the same therefore a webbed connecting rod is used.

(b) Yoke

This is used to connect the pump rod and the connecting rod. The simulation results are as

below;

Page 74: Project Report Windmill

63

Figure 38: MES Analysis of Yoke Showing Von Mises Stress

The simulation above shows that the resultant Von Mises stress is 7.27N/mm2 and the reaction

force as a result is 37.4N. When the upper part of the yoke is modified by adding protrusions of

bosses, the results change to 8.67N/mm2 Von Mises and 37.89N reaction force

Figure 39: MES Analysis of YOke With Bosses Showing Von Mises Stress

Page 75: Project Report Windmill

64

(c) Yoke Pins

These pins are vital for linking the connecting rod to the pump rod through the yoke and the

results obtained in the simulation show that they can withstand the calculated operating forces.

Figure 40: MES Analysis of Upper Yoke Pin Showing Von Mises Stress

Table 14: Table of Results on Yoke Pins

Yoke pin Von Mises (N/mm2) Displacement (mm) Reaction forces (N)

Top Pin (To

Connecting Rod)

90.43 0.01 36.19

Lower Pin (To Pump

Rod)

50.85 0.0047 5.15

Page 76: Project Report Windmill

65

Figure 41: MES Analysis of Lower Yoke Pin Showing Von Mises Stress

(d) Crank shaft

This is the prime part of the transmission system and test results should show that it operates far

below the limits of failure otherwise it can fail immediately after commissioning.

Figure 42: MES Analysis of Crank Shaft Showing Von Mises Stress

The results below were obtained from the simulation;

Page 77: Project Report Windmill

66

Table 15: Table of Results on Crank Shaft

Case Von Mises (N/mm2) Displacement (mm) Reaction forces (N)

Wind-speed of 6m/s 111.74 3.96 436.38

For shaft design of more than 1m length, the maximum deflection from its axis is 10mm hence

the displacement of 3.96mm is well in the allowable range and with the developed stresses being

lower than the failure stress, the design can operate safely.

4.3 Conclusion

Chapter four has presented the results of the simulation carried out on the components of the

transmission system and the assembly showing the resulting forces and displacements hence

giving an overview of how the system is likely to operate in the real world with all the operating

constraints subjected to it. It also has shown some areas that need some modifications from the

mathematical design parameters before manufacturing the system.

Chapter five presents the recommendations made basing on the results herein obtained from the

simulations and is presented below.

Page 78: Project Report Windmill

67

CHAPTER FIVE: CONCLUSION AND RECOMMENDATIONS

5.1 Recommended Specifications

The main objective of this research was to design and develop design specifications of the

transmission system that is to work with a rotor designed to run in a low and medium and

intermittent wind speeds.

This was intended to use improved methods in design that are better than the rudimentary means

that were more costly and gave difficult to predict performance of the systems.

From the research hence, the following specifications were developed and henceforth

recommended;

Shaft: The recommended shaft is of 80mm diameter and of length 1.5m with a crank offset

located at 1.1m from the rotor side.

Crank Pin: This is recommended to be of diameter 50mm and of length 100mm

Connecting Rod: It is of 400mm length with webs of thickness 25mm with a yoke pin bore of

14mm diameter.

Yoke: This gives a connection between the pump rod and the connecting rod and is of circular

section of out diameter of 73.36mm and inner bore of diameter 40mm and 40mm height, with

bosses of protrusion 5mm at the upper pin bore.

Upper Yoke Pin: Recommended diameter is 14mm

Lowe Yoke Pin: Diameter of 15mm

Pump Rod: This is a hollow circular structure with recommended outer diameter of 40mm and

inner diameter of 25mm with overall length of 15m.

Bearings: The bearings recommended for this system are the spherical roller bearings.

5.2 Further Related Research

For the complete set of wind mill technology, all the components of the windmill as were stated

herein this report (Chapter Two section 2.5) have to be designed and optimized. This hence

means that future research should be concentrated on the design and optimization of the pump

system and the tower unit after which the windmill shall be ready for construction.

Page 79: Project Report Windmill

68

REFERENCES

J.F. Manwell, J.G. McGowan and A.L. Rogers Wind Energy Explained Theory, Design and

Application (2006).

R. Gasch, J. Twele. Wind Power Plants (2002)

Robert L. Mott, Machine Elements in Mechanical Design, Third Edition

Beitz. W and K.-H. Kuttner, Handbook of Mechanical Engineering

P.L. Fraenkel FAO Irrigation and Drainage Paper 43: Water Lifting- Devices.

Shigley, Joseph Edward; Mechanical Engineering Design; McGraw-Hill, 1989

History of Windmills. www.westaustrianvista.com, 2008

Peter Fraenkel, A hand book for users and choosers, second edition, 1997; Intermediate

Technology Publications, 101/105 Southampton Row, London WC1B 4HH, UK.

Fishwick, Paul. The art and science of digital world construction

Illustrated History of Wind Power Development http://www.telosnet.com/wind/, 2008

http://www.fao.org/docrep/010/ah810e/AH810E00.HTM

Victoria Njuki (2007) Simulation and Design Modification of a Windmill Rotor Suitable for

Pumping Water at Low and Intermittent Wind Regimes.