Propulsion Unit of a 3DOF Helicopter

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Propulsion Unit of a 3DOF Helicopter

Gustav Ling

Jesper Persson

Division of Fluid and Mechatronic Systems

Bachelor Thesis

Department of Management and Engineering

LIU-IEI-TEK-G–15/00854—SE

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Propulsion Unit of a 3DOF Helicopter

Bachelor Thesis in Mechatronics

Department of Management and Engineering

Division of Fluid and Mechatronic Systems

Linköping University

by

Gustav Ling

Jesper Persson

LIU-IEI-TEK-G–15/00854—SE

Supervisors: Martin Hochwallner

IEI, Linköping University

Examiner: Magnus Sethson

IEI, Linköping University Linköping, 1 June, 2015

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Gustav Ling Jesper Persson

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Abstract

This bachelor thesis is a part of a bachelor project which includes building, pro-gramming and controlling a 3DOF tandem helicopter.

This particular report deals with the propulsion units, i.e. the motors and propellers of the helicopter. It covers the process of how to determine the most suitable propulsion units for the rig that eventually will enable it to run.

To achieve this, different data have been processed. Torque and thrust are two important parameters that have been studied. The data have been acquired by different tests, e.g. thrust measurements from a thrust rig. Also more complex analysis such as Blade Element Theory and Actuator Disk Theory have been carried out in order to determine the behaviour of the propulsion units. Study data sheets and databases was also a part of the work.

The result of this work was two equal propulsion units which were mounted in the helicopter. They proved to work satisfactory and provided wanted dynamics to the system.

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Acknowledgments

We want to give a special thank you to our supervisor, Martin Hochwallner, for all the support, suggestions and guidance throughout the entire project. We are grateful for all the components getting ordered with help from Hochwallner.

We also want to thank the personnel in the workshop for helping us manufac-ture the parts for the helicopter rig and managed to do this in time.

Also a thank you to our examiner Magnus Sethson for arranging the interesting field trip to CybAero.

Finally a big thank you to the rest of the project group for excellent group dynamics, cooperation and lots of fun.

Linköping, June, 2015 Gustav Ling

Jesper Persson

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Abbreviations

3DOF 3 Degrees Of Freedom

Rig Entire unit

Helicopter The unit which is mounted at the end of the arm where

the motors and propellers are placed Propulsion Unit Motor and propeller mounted together Tandem Helicopter Helicopter with two main rotors

rpm Revolutions per minute

AC Alternating current

DC Direct current

RC Remote control

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Introduction

1.1 Background

The institution of Fluid and Mechatronic Systems at Linköping University, Swe-den, has requested a prototype rig to investigate principles of automatic control and the dynamics of a tandem rotor helicopter system.

The rig, which is limited to 3DOF, offers a good simplification of a realistic full-scale system for evaluating performance of different automatic control principles.

The system could be used as a tool for laboratory classes in various control courses. The students could for example, as an exercise be given the task of calculating certain controller parameters with respect to some given specifications. This particular thesis is written as a part of this project and will focus specif-ically on the propulsion units, which is the combination of the motor and the propeller that powers the helicopter.

1.2 Objectives

The goal of the main project is to design and build a test rig to analyze and control a 3DOF tandem helicopter.

The goal of this part of the project is to find a satisfying combination of a motor and a propeller suitable for the entire system, and providing sufficient thrust and dynamics to the system.

A more personal goal is to increase theoretical knowledge about how a propul-sion unit works and its characteristics. And finally, to get a feeling about the principle of working as a part of a project and the engineering work process.

1.3 Delimitations

To make the project objectives achievable and not too comprehensive, due to time insufficiency, delimitation’s regarding equipment and materials for building the test rig was necessary.

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2 Introduction

Generally, the test rig is limited to 3DOF. The available hardware to build the test rig is limited to that provided by the institution of Fluid and Mechatronic Systems, Flumes.

Furthermore, the test rig should be built in a reasonable size, i.e, portable. And last, patents will not be observed.

The propulsion units are limited to indoor use only. Since there are many electrical components involved, the propulsion units should not be exposed to moist and low temperatures since it can affect the performance of the unit.

1.4 Method

As a part of the whole project, this thesis only focus on the propulsion units. The group, consisting of two people, have been working close together throughout the project. Likewise with the rest of the groups in order to adapt the respective parts to each other so that it would lead to a fully functioning rig.

In order to gain an understanding about the principles of a propulsion unit and achieve adequate knowledge there have been extensive research about the parts of a propulsion unit, both in the University library and on the Internet. The group’s supervisor has been supporting and guiding with knowledge and experience from the beginning to the end of the project.

Specifically this project, instead of only theory, is also based on tests and calculations. In order to obtain relevant data different tests have been carried out, providing useful data and insights of how the different parts correlated to each other.

Tests that have been carried out was for example to achieve a certain thrust for a given rpm. Furthermore, to some extent, theoretical analysis, i.e. the Blade Element Theory, gave an idea what performance to expect from the propulsion units. This were essential information for the project.

In the final phase of the project, all groups worked together with the assembling of the rig to get it up and running.

The project have been going on continuously during a spring semester. The overall time consumption has been the work with the testing of the motors and propellers, as well as on assembling the rig and writing the report.

Since this project involves a considerable amount of work, a brief time division was made in order to give a rough approximation of how the time should be spent. This is displayed in figure 1.1.

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1.5 Structure 3 15% 15% 20% 10% 40%

Initial Time Division

Research Calculations Tests Assembling Report Writing

Figure 1.1: Chart illustrating a rough time division between different parts of the project.

1.5 Structure

This thesis is, as mentioned before, written as a part of a larger project. A brief description of the project is described in this introduction chapter. Chapter 2 bring up information about the entire system where the propulsion units should be able to fit in. From the entire project’s point of view, chapter 2 provides necessary background information about the expectations of the propulsion units. Chapter 3, which is the core part of the project, thoroughly describes the work process. This chapter is followed by chapter 4 which explain tests that was carried out for analyzing the theoretical results from chapter 3. Furthermore, chapter 5 explains the mechanical integration of the propulsion units. Finally, chapter 6, describes the result of the project followed by analysis and discussions. Worth mentioning, some results and analysis have been written throughout the whole report making it easy to follow.

1.6 Safety

Throughout the project different tests have been carried out. Thus there were some safety issues that had to be taken into account, e.g due to high speeds up to 10 000 rpm, and fairly large power sources.

Therefore some preparations was made before starting. To avoid any injuries and unexpected events, preventative measures was carried out.

If any part was to unexpectedly fail while running the propulsion units, an important measure was to use a cover close to the propulsion units. Therefore a makeshift protective wall enclosing each propulsion unit was constructed in order to minimize unexpected events. The persons working near the propulsion units

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4 Introduction

was also obligated to use safety glasses.

An emergency switch had to be connected to the rig’s power supplies to quickly be able to stop operation in case of unexpected events.

The motors can become warm after extensive usage, use caution.

Since there is fairly high power sources, any contact with water or any other fluids could be dangerous. Therefore, no fluids were allowed around the rig.

The rig weighs around 30 kg. One have to be careful while carrying it to avoid any damage.

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Chapter 2

Theoretical Background

2.1 Mechanical Design

The mechanical design of the test rig was determined by the project group to look like figure 2.1. In short, this design was selected because of the limitations in degrees of freedom. By choosing this design the helicopter unit could have a continuous forward motion by turning around the main axis of the rig, meaning no limitation of angle b in figure 2.1.

Furthermore, it can be seen in figure 2.1 that the arm which extends to the helicopter is considerably balanced by a counterweight placed on the other side of the pivot point. This means that the propulsion units wont have to provide thrust in order to independently lift the helicopter by themselves, because there will be a moment from the counterweight which will help lifting the helicopter. The helicopter also has continuous power connection through wiring in the structure which means it is not dependent on a limited power source.

It should also be mentioned that the rig is to be controlled automatically through a controller which will rely on sensors measuring the angels marked a, b and c in figure 2.1.

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6 Theoretical Background

a

b

c

z

Counterweight Stand Arm Helicopter Propulsion unit

Figure 2.1: The principle design of the test rig displaying the three degrees of freedom denoted a, b and c. Note the helicopter and the counterweight positioned at each end of the arm. The arm pivots around the point were the stand connects to the arm.

2.2 Variable Mechanical Parameters

Considering the difficulties associated with calculating exactly what thrust and dynamics one could expect from the propulsion units in advance, the rig was designed in such a way that a few critical parameters could be changed after the complete rig was assembled. Those were:

• The mass of the counterweight • The lever of the counterweight • The lever of the helicopter

• The lenght of the helicopter pivot arm marked z in figure 2.1

It was initially said that the counterweight should compensate the weight of the arm and the helicopter should provide enough thrust to be able to lift itself. Worth mentioning is that the mechanical design of the rig, which was done by another part of the group, was going along at the same time as different propulsion units were analysed. This was carried out early in the project and it was relatively easy to scale all mechanical dimensions to fit the propulsion units which were considerably critical for the final dimensions. For example, heavier and more powerful propulsion units would require a stronger and larger structure compared to lighter ones. Because of that, communication with the mechanical design group

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2.3 System Control 7

during the first part of the project was essential. However the adjustability of the counterweight also meant that it easily could compensate for any mismatches with the mechanical design. E.g. if the propulsion unit would not be able to provide enough thrust making the helicopter lift, it was supposed to be easy adjusting the moment from the counterweight to make the thrust sufficient enough for take off.

2.3 System Control

Changing the thrust on the propulsion units were the only way to change the state of the helicopter meaning that the signals out from the control system were only going to the propulsion units. Thus it was necessary to understand in what way the propulsion units would perform to affect the angels shown in figure 2.1. The list below explains briefly how the propulsion units were supposed to perform due to make the helicopter move and change position.

• Both propulsion units provides equal thrust making the helicopter change its elevation, meaning, increasing or decreasing angle a in figure 2.1. • A difference in thrust between the propulsion units making the helicopter

pitch, meaning increasing or decreasing angle c in figure 2.1.

• When the helicopter pitches, meaning, angle c is not equal to 90 degrees, the helicopter will change the travel angle marked b in figure 2.1

2.4 System Specifications

At the beginning of the project a list of specifications for the rig was set up. Below is a brief summary of the list including the entries which affected the selection of propulsion units.

• Mechanical

– Minimum of 270 degrees of rotation about the travel axis.

– 45 degrees of angular displacement about the pitch axis, positive and

negative.

– 30 degrees of angular displacement about the elevation axis, positive

and negative.

– Mechanical three axis locking system to enable power up from a known

reference point.

– Maximum weight of 40 kg.

– The entire system should be able to fit and function in a space the size

of 3x3x2 meters. • Performance

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8 Theoretical Background

– Tangential acceleration and speed about the travel axis of at least 1

m/s2and 1 m/s respectively.

– Tangential acceleration and speed about the elevation axis of at least 1

m/s2_{and 1 m/s respectively.}

– Angular acceleration and speed about the pitch axis of at least 2π

rad/s2 _{and π/4 rad/s respectively.}

A direct conclusion from the list above was that the propulsion units could not be to large. As mentioned, the entire rig was somehow dimensioned with respect to the propulsion units. Larger propulsion units would lead to a larger and heavier rig. The specification list states a maximum weight of 40 kg and a maximum operation area of 3x3x2 meters.

2.5 Overall System Performance

Regarding the system’s performance it was preferable that the helicopter, or more correct its propulsion units, could generate as much thrust as possible. This meant that the moment from the counterweight could be smaller which in return would provide a faster system response around axis of elevation and travel. This due to the distance a in figure 2.2. A greater mass at a greater distance leads to an increased inertia around the axis of travel and elevation. As familiar, a greater inertia means that a greater force must be applied to change its current state. However, it should be mentioned that a slower system is considerably easier to control, but less exciting.

Fc

Ft

Fg O

a b

Figure 2.2: Displaying the forces which contributes to moments around the pivot point marked O.

2.5.1 Propeller Dynamics

Considering that the control system must be able to quickly alternate the thrust, it is preferable that the propeller dynamics is faster than the helicopter dynamics. This had to be kept in mind during the propulsion unit selection process since it would make the helicopter easier to control.

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Chapter 3

The Propulsion Unit

3.1 Prelude

Up to this point there has been specifications regarding the propulsion units per-formance from a complete system perspective. This is however very important information upon which the selection was based.

The propulsion unit itself consist of a propeller mounted upon a motor shaft. The motor spins the propeller at different speeds which provides various thrust. When the thrust alternates, the helicopter moves around its axis. As stated before, it is this thrust the control system will regulate in order to make the helicopter follow a reference signal.

3.2 The Motor

3.2.1 Different Electric Motors

To understand all the relevant variables for the selection of an appropriate motor, it is interesting to know some background facts about common electric motors.

Today’s market offers a wide selection of different electrical motors. A common one is the DC motor. The DC motors differ significantly when it comes to size, performance, appearance and functionality.

3.2.2 General Principle of a DC Motor

The DC motor is powered by direct current. Simplified, it works as a converter from DC to mechanical energy, i.e. torque. It is a common used motor due to its high torque, ability of speed control and good speed-torque characteristics [11, p.762]. Basic speed-torque behaviour of a DC motor is shown in figure 3.1.

The DC motor can be found in many areas of use, e.g. household appliances to more advanced products such as robotics, measure and analysis equipment, machines, etc.[5].

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10 The Propulsion Unit

DC motors are commonly constructed according to two different principles, brushed and brushless.

Speed in rpm

Torque in Nm

No load speed Stall Torque

Max Power, Pmax

ω

Figure 3.1: Correlation between Torque and Speed of a DC motor. What is often limiting a DC motor is the current which is related to the torque according to equation 3.1, where T is the torque and i is the current. Kt is the

torque constant which is a motor parameter. Every motor has a specification of what maximum current it can withstand. This has to do with the motor windings, which becomes overheated if exposed to a large current over a certain period of time.

T (t) = Kti(t) (3.1)

3.2.3 The Brushed DC Motor

The very basic operating principle of a brushed DC motor is based upon electricity and magnetism. According to Lorentz law, equation 3.2, a conductor of length l carrying current of magnitude i in a magnetic field B is exposed to a force F depending on the angle α between the conductor and the magnetic field. Basically described in figure 3.2.

F = Il × B (3.2)

Brushed DC motors are characterized by its commutators. The commutator is a type of mechanical switch which together with the coil windings creates a rotating armature. In a brushed DC motor the polarity in the stator is fixed while the polarity in the armature is changing with help from the commutator [9, p.15-16]. Brushes supply the armature through physical connection with the commutator, hence the name.

The torque from the motor is obtained by the force F which increases according to equation 3.2 and its lever which is the height of the armature measured from the center of the shaft. The greatest torque is obtained when the conductor is

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3.2 The Motor 11 N pole F S pole Magnetic Field B i Current Trough Conductor Current i Field B Force B α

Figure 3.2: Force on a conductor in a magnetic field [11, p.763].

perpendicular to the magnetic field. In a real brushed DC motor the armature consists of many coil windings which makes the torque relatively constant. The benefit of using a brushed motor is that it is cheap and does not necessarily need a controller of its own. On the other hand the motor needs more maintenance, e.g. the brushes wear out, it emits a loud noise and it has a limited efficiency due to the brushes [10].

3.2.4 The Brushless DC Motor

Unlike the brushed DC motor the basic principle of the brushless motor is rotating permanent magnets, i.e. the rotor or armature, on the contrary to the brushed DC motors [11, p.768]. The construction of the brushless DC motor is quite simple but to get the motor running it needs both a controller and a some hall sensors.

A brushless DC motor can have numerous coils, stationed in a circular pattern, depending on which motor it is. The hall sensors measure the location of the rotor so that the controller can decide which coil to energize and thereby get a steady torque of the rotor [3]. The principle design of a brushless DC motor is displayed in figure 3.3.

The brushless DC motor is more reliable, efficient, weighs less and emits a lower noise compared to the brushed motor [3].

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12 The Propulsion Unit W1 W2 W3 A V A BW2 I A 1 V2 V3 I U1-2 U2-3 U3-1 BW1 BN Hall 1 High Hall 2 High Hall 3 High M

Figure 3.3: Principle design of a brushless DC motor displaying the rotating per-manent magnet in the middle attempting to line up with the coil in front of it [6].

3.3 Provided Motor

The goal of this project is to provide the rig with the most suitable propulsion units. A main part of this goal is the motor, which is somewhat half the propulsion unit.

Early in the project it was noted that the University had a few motors to pro-vide, Maxon EC-Max 40, which could fit this project. This was a very interesting opportunity since they were "for free" and could be used and tested directly with-out having to wait for delivery. However, to decide whether they were suitable for the rig a few parameters had to be analysed and tested. A summary of important parameters of the Maxon EC-Max 40 is presented in table 3.1.

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3.3 Provided Motor 13

Table 3.1: Relevant data for the EC-max 40 [7].

Power 120 W

Voltage 48 V

No load speed 10100 rpm

No load current 310 mA

Nominal speed 9250 rpm

Nominal torque (max. continuous torque) 170 mNm

Nominal current (max. continuous current) 4.06 A

Stall torque 2090 mNm

Stall current 46.7 A

Max. efficiency 85 %

Torque constant 44.8 mNm/A

Speed constant 213 rpm/V

Speed / torque gradient 4.89 rpm/mNm

Number of phases 3 Weight 720 g Length 88 mm Diameter 40 mm Shaft Diameter 6 mm Shaft Length 20 mm

Figure 3.4: The provided Maxon EC-max 40 brushless DC motor connected with the encoder to the right. c Marcus Almén

3.3.1 Analysis of Provided Motor

The provided Maxon EC-Max 40 is a brushless DC motor equipped with an en-coder. Maxon control units for regulating the speed of each motor was also avail-able from the University.

The main characteristics that immediately could be analyzed was the motors weight of 720 grams. Considered as significantly heavy, this could affect the spec-ifications regarding the size of the complete rig. However, after consulting the mechanical group, who analyzed the effect on the structural dimensions, it was

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confirmed that the rig still would fulfill the mechanical specifications, although it would be bigger than initially expected. To directly conclude anything about the other parameters was almost impossible since there was at this point no informa-tion about the load.

The motor was to be able to spin a propeller at a speed which would provide a needed thrust. Because of the shape of the propeller it produces not only thrust when rotating in air but also drag. To deal with the drag at a certain rotation speed, the motor must be able to provide sufficient torque. To know anything about the torque a few details about the propeller had to be looked into.

3.4 The Propeller

There were many ways to begin the propeller selection process. For instance, the power rating from the motor could be used together with an estimation of desired thrust to calculate an approximation of the propeller diameter. But since it was familiar that the provided motor was rather large and heavy, it was decided to base calculations on the largest propeller that would fit in order to maximize the thrust. This was estimated to around 10" or 0,254 m in diameter. Propeller data is commonly given in inches, and therefore that unit will be used throughout this report.

3.4.1 Fixed or Collective Pitch?

During early research of RC-helicopters and drones on the Internet, there were a few important observations made. Basic RC-helicopters and most drones use propellers with a fixed pitch. The pitch is the length the propeller travels during one revolution around its through axis. For a better understanding, consider the length a certain screw travels when tightened one turn. The fixed pitch helicopters changes the thrust by changing the rotation speed of the propeller. As a result, the thrust increases with increasing speed.

On the other hand, real helicopters and also more advanced RC-helicopters use a propeller, or more correct, a rotor that alternate the pitch on all the blades at the same time using a collective [4, p.81]. When using this principle, the propeller rotates at constant speed and the pitch is instead changed on all blades at the same time generating an increase or decrease in thrust.

The benefit with the fixed pitch propeller is that it does not require the complex mechanics that is needed to alternate the pitch. However the disadvantage is that the propeller, due to its inertia, can not change its rotation speed momentarily. This means that it will be a delay before the wanted thrust is achieved. The delay is however very small when using small diameter lightweight propellers. Due to this, the decision was to use a constant pitch propeller, and it was preferable that it would be as light as possible to keep the inertia manageable.

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3.4 The Propeller 15

3.4.2 Estimation of Thrust

After deciding a maximum diameter of the propeller, an estimation of how much thrust one could expect from the propellers had to be carried out. Since there is a wide range of different propellers to choose from on the market it was not possible to buy and test them all.

There are several mathematical theories that provides this information. One of them, which is probably the simplest, is called Actuator Disk Theory [4, p.63]. This theory is based upon application of the flow momentum conservation principle. The propeller is here exchanged with an infinite thin actuator disk and the static pressure will be assumed to increase instantly over the disk. The disk is placed in a contracting stream tube through which the air stream of interest will flow according to figure 3.5. This theory is used for making a rough estimation of

V0 A3 p0 A1 p1 p2 V1 p0 V3 A0 0 1 2 3 const.

Figure 3.5: The principle stream tube used in the Actuator Disk Theory [4, p.65]. The propeller is replaced with an infinitely thin actuator disk with area A1marked

in the figure.

what maximum thrust could be expected from a propeller with a certain diameter. However, for the theory to be valid some limitations and simplifications needed to be done [2, p.69]:

• An incompressible, perfect fluid.

• Uniform fluid flow properties. One-dimensional flow.

• Continuous-flow velocity and pressure everywhere, except over the disk. • The flow in front of and behind the disk are lossless. Bernoulli’s equations

can be applied in these regions.

• The lines of the stream tube in figure 3.5 defines the limits of what air flows through the disk and which does not

Taking the above criteria in account, equation 3.3 can be used [4, p.67] to make a rough estimation of the thrust:

P0= F0w0= s F3 0 2ρA1 (3.3a)

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F0= P

2/3

0 (2ρA1)1/3 (3.3b)

Where P0, in this case, is the ideal static power required from the motor. F0 is

the ideal maximum thrust and w0 is the induced velocity. Furthermore, ρ is the

density of air which was chosen as 1.204 kg/m3 _{and A}

1is the area of the actuator

disk seen in figure 3.5.

Using a diameter of 10" in equation 3.3 resulted in an estimated thrust of around 11 N, using 120 W as static power. A considerable estimation is the usage of the given power rating, 120 W since this is rather an average power. The real power is the product of current through the motor and voltage. The voltage is limited to 48 V and the current depends on the load.

It is important to note that this theory does not take the shape of the propeller into consideration and assumes everything is ideal. It means that the calculated thrust is certainly higher than reality. At least, an approximation was obtained showing a thrust that would be sufficient to lift the motor and some part of the helicopter frame.

3.4.3 Different Propellers

The market offered a wide range of 10" propellers in many different shapes. One problem was the limited information about the specifications of the propellers. Research indicated what others recommended to RC-helicopters and what was available for fast delivery in Sweden. The preliminary decision was to choose the company APC Propellers [1]. They were able to provide more information about what air foils they used which was necessary for more exact calculations regarding thrust and torque.

3.4.4 UIUC Propeller Database

Another significant advantage with the APC Propellers is that many are available in the University of Illinois propeller database [13]. The database consists of measured data from a large amount of different RC-propellers. Static data for the APC Thin Electric 10" x 5" [14] provides measured data of, among other things, coefficient of thrust, CT, and coefficient of power, CP, for different rotation speeds.

The CT and CP are basically described as performance parameters which depends

on the shape of the propeller.

The APC Thin Electric 10" x 5" is a 10" diameter propeller with a 5" pitch. It was chosen because of its high similarity with the ones that were available in Sweden.

The correlation between CT and thrust is displayed in equation 3.4[4, p.72].

Correlation between CP and power is presented in equation 3.5[4, p.73].

F = CTρn2d4 (3.4)

PS = CPρn3d5 (3.5)

The parameter F is the thrust, PS is the power and n is the rotation speed

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diameter. With d set to 10", Matlab was used to interpolate between the given rpm values and extrapolate outside the given range to obtain data showing a correlation between rpm versus thrust and power. There was also a plot made with the rpm versus torque using the same Matlab script and equation 3.6. The resulting plots are shown in figures 3.6, 3.7 and 3.8. Since these plots are based upon measured data of CT and CP they are considered very reliable. The Matlab script used is

printed in appendix A. PS= Qω (3.6)

3.4.5 Performance Plots

Rotation Speed in RPM 2000 3000 4000 5000 6000 7000 8000 9000 10000 Thrust in Newton 0 5 10 15 Thrust vs RPM

Figure 3.6: Plot showing thrust with respect to rpm of the APC Thin Electric 10" x 5" propeller. Rotation Speed in RPM 2000 3000 4000 5000 6000 7000 8000 9000 10000 Power in Watt 0 20 40 60 80 100 120 140 160 180 Power vs RPM

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Rotation Speed in RPM

2000 3000 4000 5000 6000 7000 8000 9000 10000

Torque in Newton Meter

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Torque vs RPM

Figure 3.8: Plot of torque versus rpm for the APC Thin Electric 10" x 5" propeller.

3.4.6 Summary

These plots were of significant interest and presented many interesting findings. Firstly, it should be noted that none of the curves display linear characteristics but rather a second degree behaviour. This was interesting for the control system group which also had interest in the correlation between thrust and rpm.

This data, in comparison with the data of the given motor, outlined the limits within which the propulsion units could perform. This is displayed in figure 3.9.

A few important parameters could be set from figure 3.9. The torque curve crosses the border of the continuous operation area somewhere around 0.155 Nm and this occurs at a rotation speed of about 8300 rpm. During that speed, the propellers will provide approximately 10 N of thrust. This means, that if the provided motor was to be used with an APC Thin Electric 10" x 5" propeller, a maximum thrust close to 10 N could be expected. There might be some reactions due to the high proximity to the value of 11 N approximated with the actuator disk theory. This has to do with the power rating of the motor. The power rating of electrical motors is not, as stated before, the maximum power which the motor can provide but rather an average load power. As seen in figure 3.9, the power needed to spin the propeller at 8300 rpm is approximately 140 W. The provided Maxon motor is capable of providing around 150 W continuously at 8300 rpm. This may not be the case when the motor works at its highest efficiency, due to higher heat losses. The motor was however not supposed to provide maximum torque during all time of operation.

3.4.7 Blade Element Theory

Another way to estimate the performance of a certain propeller is to use the Blade Element Theory. This is a mathematical method that is more accurate than the Actuator Disk Theory but also more complex. The very basic principle of the

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3.4 The Propeller 19 Power in Watt 0 50 100 150 Rotation Speed in RPM 0 2000 4000 6000 8000 10000 12000 RPM vs Power Thrust in Newton 0 2 4 6 8 10 12 14 16 18 20 Rotation Speed in RPM 0 2000 4000 6000 8000 10000 12000 RPM vs Thrust

Torque in Newton Meter

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Rotation Speed in RPM 0 2000 4000 6000 8000 10000 12000 Torque vs RPM Performance Chart

Motor: Maxon EC-Max 120 W 48V Propeller: APC Thin Electric 10x5

Torque Thrust Power

Red Area: Continuous Operation Range

White Area: Short Term Operation Range

Figure 3.9: Plot showing propeller torque, thrust and power curves over the con-tinuous area of operation of the provided Maxon motor.

theory is a propeller blade with known air foil which is split up, or mathematically discretized, into a number of elements. The elements are then evaluated individu-ally looking at their aerodynamics. This evaluation is undertaken over the entirety of the blade and then put together to get a good estimation of the propeller per-formance [4, p.69]. While it was expected that the theory would produce similar results as those from the UIUC database calculations, it was interesting to explore the similarities.

The first step in the process was to obtain geometrical propeller data. This data was again retrieved from the UIUC database and the APC Thin Electric 10" x 5" propeller. The data of interest was the chord width and the pitch angle (β) displayed in figure 3.10. It should be noted that these calculations were based upon a hover situation meaning the forward velocity equals zero and pitch angle equals angle of attack (α).

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20 The Propulsion Unit Forward Velocity Rotational Vel ocity Chord Line Rel ative Wi nd Thrust Angl e of Atta ck Pitch Angle Chord Width

Figure 3.10: A principle side view of the propeller blade element. Note the pitch angle and chord width.

0.127 m. Each segment with an individual pitch angle and chord width according to the data from UIUC [12]. The first segment from 15 to 20 percent of the radius starting from the center and then with 5 percent increment. Below 15 percent is the propeller hub which does not contribute to the aerodynamics substantially. The radial stations and associated geometrical data was then stored in separate vectors shown in table 3.2. Refer to appendix A for all vector data and the Matlab code.

Table 3.2: Vectors for geometrical data at the 17 segments.

rR Proportion of Total Radius

cR Chord Widths

β Pitch Angles

A Average airflow area of each segment

The next step was to make an estimation of the speed of rotation at which the calculations would be valid, since there are different Reynolds Numbers at different speeds. Earlier calculations indicated that a speed around 8300 rpm would be the maximum for the provided motor. However, it was known that the Blade Element Theory overestimated the thrust and underestimated the torque. Due to this, the calculations was based on a speed of 9000 rpm to get some margin of the critical torque. Subsequently the air flow velocity for the respective data points of the propeller was calculated and stored in a separate vector shown in equation 3.7.

v = 2π9000

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Where r is the distance along the radius to the geometric data points, calculated in equation 3.8 and R is the radius in meters.

r = rRR (3.8)

The Reynolds Number (RN ) at each station was calculated with the propeller surface estimated as a flat plate according to equation 3.9

RN = vc

ν (3.9)

Where c is the chord width for respective geometric data points, calculated in equation 3.10, and ν is the kinematic viscosity.

c = cRR (3.10)

Next step was to estimate the coefficients of lift and drag, Cl and Cd. APC

Propellers states that the MRP propeller uses the Eppler E63 air foil inboards and Clark-Y air foil near the tip. Inboards is around 85 percent of the propeller with respect to centre. UIUC provides data of these air foils in their air foil database [8]. This data was then loaded into a software called XFLR5 [15] for analysis. The software was used to estimate Cl and Cd at a certain pitch angle (α), and

Reynolds number shown in figure 3.11 and 3.12. The Cl and Cd numbers were

then stored in separate vectors.

Figure 3.11: XFLR5 Plot with Clversus α. Different Reynolds Numbers illustrated

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Figure 3.12: XFLR5 Plot with Cd versus α. Different Reynolds Numbers showed

in different colors. Note that in this case α = β.

Another interesting aspect was the area over which the air flows at each segment creating lift and drag. This area was calculated as average radius multiplied with average chord width of each segment, and was also stored in a vector A.

The lift and drag components from each section was then calculated. This was done using equations 3.11 and 3.12 [4, p.69].

Fl= 1 2ρv 2_C lA (3.11) Fd= 1 2ρv 2_C dA (3.12)

The last task was to numerically integrate data from each section to get data for the entire blade. To obtain the torque, the drag components of each section was multiplied by the average radius of the section and then summed up. Finally, the total lift and torque was multiplied by two since it was a two blade propeller.

3.4.8 Blade Element Theory Evaluation

The final results indicated that a thrust of approximately 13 N and a torque of approximately 0.19 Nm could be expected. These values was very reasonable since the database calculation, which are very exact since they are based upon measured data, showed 10 N and 0.15 Nm at 8300 rpm. The Blade Element calculations were based upon a rotation speed of 9000 rpm. Therefore, it was logical that those values were a bit higher. This also due to the mentioned overestimate of thrust and underestimate of torque that occurs because of some simplifications.

To obtain a curve showing a correlation between thrust or torque and rpm is also possible with this theory. This was however not carried out since it was a time consuming process and the values of most interest were the maximum ones.

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3.5 Choice of Propeller 23

3.5 Choice of Propeller

3.5.1 About the Direction of Rotation

Another considered critical aspect when looking at certain propellers was the di-rection of the rotation. A propeller is designed to rotate in one didi-rection and does not perform well if rotated in the "wrong" direction. Since the helicopter was to have two propulsion units, each consisting of one motor and one propeller, it was preferable that the propellers turned in different directions. This since a torque from the helicopter is required to be able to hold the motors in place when spinning the propellers. If the motors and propellers are spinning in different di-rections these torques will eliminate each other. Although this will only occur if the propellers are turning at equal speed, which will be the case when hovering or changing elevation. As mentioned in section 2.3, the motors are to turn the propellers at different speeds when pitching the helicopter. This will in fact con-tribute to a net torque on the helicopter. This is however dealt with since the helicopter is locked by the arm in the direction of the torque. But even though the helicopter is locked in the torque direction it is not a preferable situation and therefore it was said that the propellers should turn in different directions. This fact eliminated a few of the propellers available in Sweden.

3.5.2 Final Chioce

As discussed before, the propeller which the database calculations shown in figure 3.9 were based on, was not available in Sweden. However a very similar propeller, the MRP 10" x 4.5", from the same company but with a slightly lower pitch was available for short delivery time and in different turning directions. One turning clockwise and the other turning counterclockwise. These were ordered along with some other propellers, some of them displayed in figure 3.13, of similar shapes and measurements. Since the final task was to test the propeller in a thrust rig, it was considered interesting to have a few different propellers to chose from and make comparisons.

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Figure 3.13: A few of the different propellers that were ordered for testing. The APC MRP 10" x 4.5" is the one to the right hand side.

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Chapter 4

Measuring the Thrust

4.1 Thrust Rig

To validate the calculations and get exact measurements a simple thrust rig was constructed. The thrust rig is displayed in figure 4.1. The rig is constructed like a

Figure 4.1: Principle design of the thrust rig

90 degree wooden arm. On the top, the propulsion unit was mounted with screws in order to get it as stable as possible while conducting tests, see figure 4.2 for the design of the mount. As figure 4.2 displays, the neck of the mount has a streamlined design. The reason for this is that the reactive force is considerably

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26 Measuring the Thrust

Figure 4.2: The thrust rig design displaying the mount and the streamlined neck

lower compared to a flat shaped rectangular neck. This will generate a larger thrust value while conducting the tests compared to what would be expected of the thrust generated by the helicopter rig.

4.1.1 Idea

The purpose for this type of test is to obtain a correlation between the speed and thrust for controlling the motor, and to obtain a graph that illustrates the behaviour of the propellers. To choose the most suitable propeller, tests with dif-ferent propellers were carried out. The obtained data would later be implemented in the control system for the helicopter rig.

4.2 Measuring Thrust in the Thrust Rig

As mentioned before, the propulsion unit was mounted on the top of the thrust rig and tightened with screws to get the rig as rigid as possible to reduce any thrust losses when testing. The speed was then increased via the controller with an increment of 200 rpm. During the tests, the wooden arm pushed the scale and the thrust was transferred directly onto the scale according to figure 4.3.

By using this method different values from the scale could be read. Using the values from the scale, the reaction force could be obtained due to the fact that the reaction force on the scale is proportional to the generated thrust from the

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4.2 Measuring Thrust in the Thrust Rig 27 DC motor Fthrust Fscale L1 L2 g FAx FAy A MA

Figure 4.3: FBD of the thrust rig. The masses of the motor and the rig are assumed to be negligible.

propulsion unit. This can be proved with help from a FBD. From the FBD in figure 4.3, equation 4.1 can be obtained.

X MA= 0 (4.1a) L1 Fthrust− L2 Fscale= 0 (4.1b) Fthrust= L1 L2 Fscale= Fscale (4.1c)

As can be seen in figure 4.3, the lengths L1and L2are equal meaning that Fthrust

and Fscale are equal. With the scale values can Fscale be calculated according to

Fscale = mscale g = Fthrust. Finally, the gravitational force zeroes the scale and

the forces acting on the pin support, denoted point A in 4.3, are not needed for solving equation 4.1.

4.2.1 Assumptions

The rig was made as rigid as possible to avoid any losses in thrust due to defor-mation. Small losses in thrust will always occur since it is difficult to make the thrust rig fully rigid. However the losses in this case was assumed to be very small and was thereby considered neglectable.

Similarly regarding the generated air flow. When testing the propulsion unit the air flow would not be ideal due to the fact that no equipment such as a wind tunnel model was used. This could induce some losses in the air flow, meaning less thrust.

4.2.2 Outcome of the Propeller Data

Measurements with different propellers was conducted and plotted in Matlab to illustrate the performance of the propellers. Matlab was also used for estimating the respective functions by interpolating the test results. The functions are stated in equation 4.2 for the 10" x 4.5" propeller respective equation 4.3 for the 11" x

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28 Measuring the Thrust

4.7" Slowfyer propeller . Since there is a wide number of different propellers on the market, only a few propellers were tested, see figure 3.13. Especially two propellers considered to be of more interest, the 11" x 4.7" and the 10" x 4.5". Performance of these propellers are displayed in figure 4.4 and 4.5.

y = 1.04 10−7 x2− 9.3 10−5 x (4.2) y = 2.6 10−7 x2− 0.00023 10−5 x (4.3) Speed in rpm 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Thrust in N 0 2 4 6 8 10

12 Thrust as a function of speed

Thust data Quadratic

Figure 4.4: Test results of the APC MRP 10" x 4.5" propeller. The y value denotes the maximal thrust, 10.16 N for a given speed, 8600 rpm, x

Speed in rpm 0 1000 2000 3000 4000 5000 6000 7000 Thrust in N 0 1 2 3 4 5 6 7 8 9

Thrust data Quadratic

Figure 4.5: Test results of the APC Slowflyer 11" x 4.7" propeller. The y value denotes the maximal thrust, 9.33 N for a given speed, 6400 rpm, x

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4.3 Summary 29

4.2.3 Dynamics of Different Propellers

An interesting observation during the tests was the dynamics of the different pro-pellers. This had been anticipated since the project’s start, but was hard to do calculations on since there was no data available. The motors had no problem when accelerating and decelerating all propellers up to 11" in diameter. However, one propeller, the APC MRP 13" x 4.5", showed a bit of delay when changing speed. Bearing this in mind, the choice was to exclude the APC MRP 13" x 4.5".

4.3 Summary

Between the two propellers, the APC MRP 10" x 4.5" propeller was finally chosen because it was able to provide slightly more thrust, 10.16 N, at a speed of 8600 rpm.

All propellers were tested up to the rotation speed at which they hit the motor limitation in torque according to table 3.1. Overriding this limit would result in a current above the limit of 4 A in the motor windings generating overheating which could destroy the motor.

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Chapter 5

Integration of the

Propulsion Units

5.1 Propeller Mount

To physically mount the propeller upon the motor shaft, an adapter was built. This had to be strong but yet have low inertia. It was lathed of steel and holes were drilled on the sides. Small locking screws were then used in the holes to lock the adapter on the shaft. Countersinks were made on the motor shaft, in which the head of the locking screws should fit. Finally the adapter was mounted upon the motor shaft and locked in position by the locking screws. These were then fixed with a thread locking glue to prevent them from falling out over time.

The upper shaft of the adapter was threaded so that a locking nut could be applied to lock the propeller on the adapter. The diameter of the shaft was selected to 6 mm since research showed that most of the propellers of interest used a 6 mm hole. The drawing of the propeller adapter is displayed in figure 5.1.

5.1.1 Integration

The installation of the propulsion units in the helicopter went very smooth due to a good communication with the mechanics group which had designed the helicopter to fit with the Maxon EC-Max motors. The integrated propulsion unit is showed in figure 5.2.

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32 Integration of the Propulsion Units Konstruerad av Artikel nr/Referens Ägare Utgåva Blad Titel/Benämning Skala Vyplacering jämnhet, RaGenerell

yt-Ritningsnummer Pos nr Antal

Granskad av Godkänd av - datum Generell tolerans SS-ISO2768-1 Titel/Benämning, beteckning, material, dimension o.d.

Godkänd av-datum Ändr nr c kunnacad.nu Ändringens art/Ändringsmeddelande Kandidatprojekt Helikopter M B B 10 15 14,5 3 6 20 6 H7 13 3 7,5 Propeller mount 2:1 GL Gustav Ling 0735257276 Alla mått i mm Material: delrin Antal: 2 st SCALE 2,000

Gängas hela vägen enl M6 standard

SECTION B-B

Gäller för båda 3mm hålen: Gängas invändigt enl M3 std Åtdragningsriktning: In mot centrum

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5.1 Propeller Mount 33

Figure 5.2: Entire propulsion unit consisting of the motor, the propeller and the adapter, mounted in the helicopter. One can also note the locking screw at the side of the adapter.

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Chapter 6

Result, Analysis &

Discussion

6.1 Result

The project has resulted in two working propulsion units which have been mounted in the final rig as figure 6.1 illustrates. Each propulsion unit consists of a Maxon EC-Max 40 brushless DC motor, one propeller adapter and one propeller. The chosen propellers were the APC’s Multi Rotor 10" x 4.5". The complete propulsion units proved to work in a satisfactory manner when mounted in the helicopter, making it move around providing sufficient dynamics to the system. As intended, the counterweight and the adjustability of the rig proved to work well and after some adjustments a fine balanced system was achieved.

6.1.1 Analysis

During the report, most results and analysis have been written down continuously. However, there are a few important things left to mention.

The motor was chosen mainly because it was available at the University. It proved to work well and it was considered easy to control the speed since it was supplied with both an encoder and a controller. If another motor had been chosen it would preferably be lighter and stronger in meaning to provide more thrust. Motors of this kind were available, but quite expensive and the shipping times could sometimes be long. By choosing the provided motors the project could have a larger budget to spend on other important details which improved the rig.

Selecting an "optimal" propeller proved to be a very difficult task. Different propellers are good for different applications and operation areas. Performing calculations on a certain propeller is a time consuming process.

The UIUC propeller database proved to be useful. It offered exact calculations on certain propellers. This data was valuable in order to make the first rough selection.

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36 Result, Analysis & Discussion

Figure 6.1: The complete final rig.

A large part of the main project was to develop a control system to the he-licopter. This required a functioning helicopter which meant that the propulsion units had to be completed quite early in the project. Due to this, analysis of different propellers had to be done in a limited time frame. If more time could have been used more propellers could have been analysed and a even better one could have been selected.

A consequence due to lack of communication with the mechanics group led to a helicopter construction which was not perfect in an aerodynamic fashion. During the construction of the thrust rig, the shape of the motor mount turned out to have a great impact regarding the obtained thrust. The initial helicopter had a relatively large area below the propellers which "consumed" a lot of the air flow. This led to a large loss of thrust as can be seen in figure 6.2, which illustrates the thrust provided by the propulsion units when mounted in the helicopter. From figure 6.2 a typical quadratic function can be obtained as equation 6.1 displays. By minimizing the background area of the helicopter, a larger thrust could be obtained, but still quite far from the thrust measured in the test rig. It should be noted that an aerodynamically perfectly shaped helicopter was not expected considering mechanical limitations and needs.

The propeller adapter was initially supposed to be made of Delrin plastic but after consulting the personnel in the workshop it was decided that steel would be more suitable mostly due to the threading. The steel adapter worked to satisfaction and did not affect the inertia substantially.

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6.1 Result 37 Speed in rpm 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Thrust in N 0 1 2 3 4 5

Thrust data Quadratic

Figure 6.2: Plot showing the thrust obtained from the helicopter. The y value denotes the maximal thrust, 5.63 N for a given speed, 9000 rpm, x .

6.1.2 Discussion

The results from the thesis are of interest for anyone who is interested in using the rig and develop a control system for it. The thesis can also provide adequate knowledge to anyone wishing to make a similar system, or in fact any kind of fixed pitch propulsion systems.

If the project was to proceed, an interesting aspect would be to test new pro-pellers with different shapes and number of blades. The system would probably behave differently which would indeed be interesting to explore further.

6.1.3 Ethics & Society

Building a mechatronic system, e.g. a helicopter rig, assumes responsibility. Both ethical and environmental.

Today’s society encounter all types of mechatronic systems. Fighter jets, mis-siles, etc. all are somehow based on a mechatronic system. From an ethical perspective it should be mentioned that these weaponry systems are developed for combat. Therefore policies about the responsibility when building this kind of systems should be provided for each concerned company.

From an environmental point of view there should be a plan for each company how to build the systems in the most environmental friendly way. There should also, to some extent, be proactive work before building a product to minimize the impact of the environment when the product is no longer working. For this part of the project, the motors of the rig could be important components to recycle due to the risk of hazardous material spreading in the environment.

During this project the gender equality haven’t been a topic since it’s not rel-evant for this particular project. It is obvious that the project has been carried through in a way that acknowledge both women’s and men’s abilities and devel-opments. Its been proven that both women and men are fully capable of working

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38 Result, Analysis & Discussion

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Bibliography

[1] APC. APC propellers. http://www.apcprop.com/default.asp, 2015. [2] R Archer. Introduction to aerospace propulsion. Prentice Hall, Upper Saddle

River, N.J, 1996.

[3] Learn Engineering. Brushless DC Motor, How it works? http://www.

learnengineering.org/2014/09/DC-motor-Working.html, 2012.

[4] David Greatrix. Powered flight the engineering of aerospace propulsion. Springer, London New York, 2012.

[5] Andreas Grönman. Compotech. URL:http://compotech.se/produkter/

motorer/dc-motorer/, 2014.

[6] Klas Lindsten Marcus Almén. Design and implementation of a software and electronics system for a 3DOF Helicopter. Technical report, 2015.

[7] Maxon. EC-max Ø40 mm, brushless, 120 W, Maxon motor. URL:

http://www.maxonmotor.com/medias/sys_master/root/8813561643038/ 14-207-EN.pdf, 2014.

[8] University of Illinois. Airfoil Database. http://m-selig.ae.illinois.edu/ ads/coord_database.html, 2015.

[9] Department of Industrial Electrical Engineering and IEA Automation. El-maskinsystem. Lund Institute of Technology, Lund, Sweden, 2000.

[10] Madaan Pushek. Brushless DC Motors – Part I: Construction and Oper-ating Principles. URL:http://www.edn.com/design/sensors/4406682/2/ Brushless-DC-Motors-Construction-and-Operating-Principles, 2013. [11] Clarence Silva. Mechatronics : an integrated approach. CRC Press, Boca

Raton, 2005.

[12] John Brandt University of Illinois. Geometrical Data APC Thin Electric

10x5. http://m-selig.ae.illinois.edu/props/data/apce_10x5_geom.

txt, 2015.

[13] John Brandt University of Illinois. Propeller Database. http://m-selig. ae.illinois.edu/props/propDB.html, 2015.

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40 Bibliography

[14] John Brandt University of Illinois. Static Data APC Thin

Elec-tric 10x5. http://m-selig.ae.illinois.edu/props/data/apce_10x5_

static_pg0819.txt, 2015.

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Appendix A

Matlab Code

A.1 Matlab Code for the Database Calculations

1 % C l e a r a l l

3 r h o = 1 . 2 2 5 ; %D e n s i t y o f A i r

5 p r o p e l l e r d i a m = 1 0 ; %D i a m e t e r o f p r o p e l l e r

7 A = dlmread(’ a p c e _ 1 0 x 5 _ s t a t i c _ p g 0 8 1 9 . t x t ’) ; %P r o p e l l e r d a t a from UIUC

9 D = p r o p e l l e r d i a m∗0 . 0 2 5 4 ; %P r o p e l l e r d i a m e t e r i n i n c h e s RPM_data = A ( : , 1 ) ; 11 CT_data = A ( : , 2 ) ; CP_data = A ( : , 3 ) ; 13 a n t a l =25; 15 RPM = z e r o s( 1 , a n t a l ) ; 17 f o r i =1: a n t a l i f i <= l e n g t h(RPM_data) 19 RPM( i ) = RPM_data( i ) ; e l s e 21 %E x t r a p o l a t i o n o f v a l u e s from o u t s i d e t h e g i v e n r a n g e

RPM( i ) = RPM_data(l e n g t h(RPM_data) ) + ( RPM_data(l e n g t h(

RPM_data) ) − RPM_data(l e n g t h(RPM_data) −1) ) ∗ ( i −l e n g t h(RPM_data)

) ; 23 end end 25 CT = z e r o s( 1 , a n t a l ) ; 27 f o r i =1: a n t a l i f i <= l e n g t h( CT_data ) 29 CT( i ) = CT_data ( i ) ; e l s e 31 %E x t r a p o l a t i o n o f v a l u e s from o u t s i d e t h e g i v e n r a n g e

CT( i ) = CT_data (l e n g t h( CT_data ) ) + ( CT_data (l e n g t h( CT_data ) )

− CT_data (l e n g t h( CT_data ) −1) ) ∗ ( i −l e n g t h( CT_data ) ) ;

33 end

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42 Matlab Code end 35 CP = z e r o s( 1 , a n t a l ) ; 37 f o r i =1: a n t a l i f i <= l e n g t h( CP_data ) 39 CP( i ) = CP_data ( i ) ; e l s e 41 %E x t r a p o l a t i o n o f v a l u e s from o u t s i d e t h e g i v e n r a n g e

CP( i ) = CP_data (l e n g t h( CP_data ) ) + ( CP_data (l e n g t h( CP_data ) )

− CP_data (l e n g t h( CP_data ) −1) ) ∗ ( i −l e n g t h( CP_data ) ) ;

43 end end 45 n = RPM. / 6 0 ; %P r o p e l l e r v e l o c i t y i n r e v o l u t i o n s p e r s e c o n d . 47 T h r u s t = r h o ∗ CT .∗ n . ^ 2 ∗ D^ 4 ; %T h r u s t [ N ] 49 Power = r h o ∗ CP .∗ n . ^ 3 ∗ D^ 5 ; %Power [W]

Torque = Power . / ( 2∗ p i ∗RPM/ 6 0 ) ; %Torque [Nm]

51 %P l o t t i n g 53 f i g u r e; p l o t( Torque ,RPM,’ g ’) ; 55 a x i s( [ 0 0 . 3 6 5 0 1 2 0 0 0 ] ) ; t i t l e(’ Torque v s RPM’) ;

57 x l a b e l(’ Torque i n Newton Meter ’)

y l a b e l(’ R o t a t i o n Speed i n RPM’) 59 f i g u r e; 61 p l o t( Power ,RPM,’ r ’) ; a x i s( [ 0 150 0 1 2 0 0 0 ] ) ; 63 t i t l e(’RPM v s Power ’) ; x l a b e l(’ Power i n Watt ’) 65 y l a b e l(’ R o t a t i o n Speed i n RPM’) 67 f i g u r e; p l o t( Thrust ,RPM,’ b ’) ; 69 a x i s( [ 0 20 0 1 2 0 0 0 ] ) ; t i t l e(’RPM v s T h r u s t ’) ; 71 x l a b e l(’ T h r u s t i n Newton ’) y l a b e l(’ R o t a t i o n Speed i n RPM’)

A.2 Matlab code for the Blade Element Theory

1 %APC Thin E l e c t r i c 10 x5 p r o p e l l e r d a t a 3 %G e o m e t r i c d a t a r_R = [ 0 . 1 5 0 0 . 2 0 0 0 . 2 5 0 0 . 3 0 0 0 . 3 5 0 0 . 4 0 0 0 . 4 5 0 0 . 5 0 0 0 . 5 5 0 0 . 6 0 0 0 . 6 5 0 0 . 7 0 0 0 . 7 5 0 0 . 8 0 0 0 . 8 5 0 0 . 9 0 0 0 . 9 5 0 1 . 0 0 0 ] ; %[ r /R ] 5 c_R = [ 0 . 1 3 0 0 . 1 4 9 0 . 1 7 3 0 . 1 8 9 0 . 1 9 7 0 . 2 0 1 0 . 2 0 0 0 . 1 9 4 0 . 1 8 6 0 . 1 7 4 0 . 1 6 0 0 . 1 4 5 0 . 1 2 8 0 . 1 1 2 0 . 0 9 6 0 . 0 8 1 0 . 0 6 1 0 . 0 4 1 ] ; %[ c /R ] b e t a = [ 3 2 . 7 6 3 7 . 1 9 3 3 . 5 4 2 9 . 2 5 2 5 . 6 4 2 2 . 5 4 2 0 . 2 7 1 8 . 4 6 1 7 . 0 5 1 5 . 9 7 1 4 . 8 7 1 4 . 0 9 1 3 . 3 9 1 2 . 8 4 1 2 . 2 5 1 1 . 3 7 1 0 . 1 9 8 . 9 9 ] ; %[ d e g r e e s ] 7 R = 5∗0 . 0 2 5 4 ; %A b s o l u t e r a d i u s [m] 9 r = r_R ∗ R ; %D i s t a n c e a l o n g r a d i u s t o g e o m e t r i c d a t a p o i n t s . [m]

Propulsion Unit of a 3DOF Helicopter

Propulsion Unit of a 3DOF Helicopter

Gustav Ling

Jesper Persson

Bachelor Thesis

Department of Management and Engineering

LIU-IEI-TEK-G–15/00854—SE

Propulsion Unit of a 3DOF Helicopter

Bachelor Thesis in Mechatronics

Department of Management and Engineering

Division of Fluid and Mechatronic Systems

Linköping University

by

Gustav Ling

Jesper Persson

Upphovsrätt

Copyright

Abstract

Acknowledgments

Abbreviations

Contents

List of Figures

List of Tables

Chapter 1

Introduction

1.1

Background

1.2

Objectives

1.3

Delimitations

1.4

Method

Initial Time Division

1.5

Structure

1.6

Safety

Chapter 2

Theoretical Background

2.1

Mechanical Design

a

b

c

z

2.2

Variable Mechanical Parameters

2.3

System Control

2.4

System Specifications

2.5

Overall System Performance

2.5.1

Propeller Dynamics

Chapter 3

The Propulsion Unit

3.1

Prelude

3.2

The Motor

3.2.1

Different Electric Motors

3.2.2

General Principle of a DC Motor

3.2.3

The Brushed DC Motor

3.2.4

The Brushless DC Motor

3.3

Provided Motor

3.3.1

Analysis of Provided Motor

3.4

The Propeller

3.4.1

Fixed or Collective Pitch?

3.4.2

Estimation of Thrust