Bachelor in aerospace engineeringAcademic year 2018-2019

Bachelor Thesis

“Nylon-based artificial muscle characterisation andapplication as an aircraft’s primary control surface

actuator”

Narciso Jesús Soto PicazoMentor: Luis Enrique Moreno Lorente

Leganés, Madrid. October 2019

This work is licensed under Creative Commons Attribution – Non Commercial –Non Derivatives

SUMMARY

The aim of this work is to characterise artificial muscle nylon fibres, a fairly new technol-ogy in the branch of linear actuation. This technology promises high ratios of generatedforce over actuator weight, which makes it very suitable for aerospace applications. More-over, these actuators are powered using heat, which can be easily obtained in an aircraftby bleeding air from the compressor, and can be cooled down using surrounding air. Tak-ing advantage of residual heat from the engine could also benefit the overall efficiency ofthe aircraft.In addition, in terms of reliability and redundancy, this technology presents some advan-tages compared to traditional actuators as an actuator composed of these fibres will havehundreds, if not thousands of them inside, making the failure of an individual fibre irrele-vant for the operation of the actuator.Therefore, the aim of this work is to design and build a suitable test bench that enablesthe testing such fibers, in order to get an insight in their behaviour and useful data thatwill allow further investigations and the theoretical design of an actuator for one of theprimary control surfaces of a small commercial passenger aircraft such as the Boeing 737or the Airbus 320.

Keywords: Control surfaces, actuator, artificial muscle, efficiency, aircraft, residualheat, reliability, weight reduction.

iii

DEDICATION

This project encompassed knowledge from many disciplines learned during my Bach-elor’s degree. In fact, it was a learning experience due to the high amounts of experimentalwork that needed to be done in order to bring it to life. Such a process would have beenimpossible without the help and support of the Bechtel Innovation Design Center at Pur-due University, and the people who work there: Jeff, JP, Frank, Brenna, etc. Not onlythey were of great help for this project, but they also are excellent coworkers, friends, andgreat people. I would like to thank specially to Dr. Matthew Swabey and Andrei Aldea,who not only did all of the above, but welcomed me in a new country and made me feellike home.Special thanks to my mentor, Luis Enrique Moreno Lorente, who trusted me with the de-velopment of this project and agreed to be my mentor even when I was studying abroad.Thanks to my fellow students and friends, Carlos, Chema, Gon and Porce. While earninga bachelor’s degree in Aerospace Engineering is hard, it was so much easier just by meet-ing people like you along the way.Last but not least, thanks to my family for supporting me in every possible aspect of mylife during these four years, backing up my decisions no matter how much of a long shotthey were, and being there for me when things did not go as planned.

v

CONTENTS

1. INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2. TEST BENCH DESIGN AND CONSTRUCTION . . . . . . . . . . . . . . . . . 2

2.1. State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.2. Muscle manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.3. Design and build of the test bench . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.1. Mechanical design and build . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.2. Electronic board design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.3. Heater element choice and calibration . . . . . . . . . . . . . . . . . . . . . 12

2.3.4. Thermodynamic analysis of the test bench. . . . . . . . . . . . . . . . . . . 15

2.3.5. Experimental procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.6. Elongation sensor design and calibration . . . . . . . . . . . . . . . . . . . 24

2.4. Heating cycle considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3. CHARACTERISATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.1. Testing procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.1.1. Temperature gradient inside the test tube . . . . . . . . . . . . . . . . . . . 35

3.1.2. Test bench setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.1.3. Data gathering and data structure . . . . . . . . . . . . . . . . . . . . . . . . 37

3.1.4. Data processing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.2. Interpretation of the results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.2.1. Defects in data due to poor heat cycle control . . . . . . . . . . . . . . . . . 41

3.2.2. Fibre response at room temperature . . . . . . . . . . . . . . . . . . . . . . 43

3.3. Behaviour modelling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4. AIRCRAFT ACTUATOR DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.1. Problem definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5. CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii

LIST OF FIGURES

2.1 Example of one of the artificial muscles under study in this work . . . . . 2

2.2 Electrical Schematic of the twisting mechanism . . . . . . . . . . . . . . 4

2.3 Rendered CAD design of the assembled 3D printed couplings . . . . . . 4

2.4 Fibre coiler using 3D printed parts . . . . . . . . . . . . . . . . . . . . . 5

2.5 Electrical circuit for the coiler . . . . . . . . . . . . . . . . . . . . . . . 5

2.6 Length change during coiling . . . . . . . . . . . . . . . . . . . . . . . . 6

2.7 Experimental relationship between spring index and load while coiling . . 7

2.8 CAD rendering of the first structure design . . . . . . . . . . . . . . . . . 9

2.9 CAD render (left) and final structure assembled (right) . . . . . . . . . . 10

2.10 Technical drawing of the pipe and temperature ports . . . . . . . . . . . . 10

2.11 Arduino Duemilanove/Uno (Left) vs Arduino Nano (Right) size comparison 11

2.12 PCB Milling Machine (Left) and manufactured PCB (Right) . . . . . . . 12

2.13 Schematics of the stock hot air gun . . . . . . . . . . . . . . . . . . . . . 13

2.14 Schematics of the modified hot air gun . . . . . . . . . . . . . . . . . . . 15

2.15 Heating element test run for calibration purposes . . . . . . . . . . . . . 18

2.16 Original sensor arrangement using a load cell to measure forces and alinear encoder to measure elongation . . . . . . . . . . . . . . . . . . . . 20

2.17 Thermistor in a voltage divider and passive low-pass filter configuration . 21

2.18 Resistance values of a 100 KOhm NTC thermistor . . . . . . . . . . . . . 22

2.19 Comparison of actual resistance values, the β equation and Steinhart-Hartmodels for a 100kΩ NTC thermistor . . . . . . . . . . . . . . . . . . . . 24

2.20 Gradient used for sensing the position of the fibre . . . . . . . . . . . . . 25

2.21 Features of the elongation sensor assembly . . . . . . . . . . . . . . . . . 26

2.22 Circuit for the operation of the TCRT5000 sensor . . . . . . . . . . . . . 26

2.23 Sensor assembly with slider (Left) and sensor IR beam (Not visible by thehuman eye) (Right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.24 Calibration curve for the elongation sensor . . . . . . . . . . . . . . . . . 27

2.25 Output from SSR with 3 identical PWM signals. T = 0.02s . . . . . . . . 30

ix

2.26 Output from SSR with 3 identical PWM signals. T = 0.2s . . . . . . . . . 31

2.27 Sample of a heating and cooling cycle . . . . . . . . . . . . . . . . . . . 32

3.1 Elongation sensor setup (Left) and full test bench ready for operation (Right) 36

3.2 Detail of the fibre mount mechanism . . . . . . . . . . . . . . . . . . . . 37

3.3 Elongation vs temperature curve for test case 11 using raw data . . . . . . 38

3.4 Filtering process for test cases 1 (Top) and 11 (Bottom) . . . . . . . . . . 39

3.5 Elongation vs temperature curve of processed data for test case 1 . . . . . 40

3.6 Elongation vs temperature curve against temperature history for test case 1 42

3.7 Elongation vs load curve and regression for each of the test specimens: 1(top left), 2 (top right), 3 (bottom left) and 4 (bottom right). . . . . . . . . 44

3.8 Elongation vs load curve vs temperature curve and regression model forspecimen 1 (top) and specimen 2 (bottom) . . . . . . . . . . . . . . . . . 47

3.9 Elongation vs load curve vs temperature curve and regression model forspecimen 3 (top) and specimen 4 (bottom) . . . . . . . . . . . . . . . . . 48

4.1 Actuator configuration inside of a wing + aileron setup . . . . . . . . . . 50

4.2 Top view of a B737-900 . . . . . . . . . . . . . . . . . . . . . . . . . . 52

x

LIST OF TABLES

3.1 Test specimens characteristics . . . . . . . . . . . . . . . . . . . . . . . 34

3.2 Test matrix with case numbers . . . . . . . . . . . . . . . . . . . . . . . 34

3.3 Sample output from test bench . . . . . . . . . . . . . . . . . . . . . . . 37

3.4 Average hysteresis values for each test case. . . . . . . . . . . . . . . . . 41

3.5 Regression coefficients for cold response . . . . . . . . . . . . . . . . . . 44

3.6 Regression coefficients for the heating process . . . . . . . . . . . . . . . 45

3.7 Regression coefficients for the cooling process . . . . . . . . . . . . . . . 46

3.8 Regression coefficients neglecting hysteresis . . . . . . . . . . . . . . . . 46

3.9 Initial and final lengths of the fibres after testing . . . . . . . . . . . . . . 49

xii

1. INTRODUCTION

Nowadays, the aerospace industry is making great efforts to increase efficiency andsafety of aircraft operations. This is particularly true in the commercial field of aviation,where fierce competition drives the development of new and innovative technologies. Inparticular, the area of control surface actuation seems to be increasingly active, since theiroptimal working amounts for a good portion of the reliability of the aircraft.Current actuation systems are often based in hydraulic pistons.While these are small andcan generate outstanding amounts of force, they are associated with hydraulic systemsthat are not only heavy, but are prone to leaking and other problems. The current ten-dency is to switch to electric motors with a mechanical system to transform their rotarymotion into a suitable motion for the actuation of the control surface, specially since fly-by-wire made its appearance. While these are much lighter than the hydraulic ones, theyhave a tendency to jam and they are not so easily fitted inside of the wing elements.Therefore, the aim of this work is to come up with a design of a control surface actuatorbased on artificial muscle nylon fibres that is lighter than current solutions and can be op-erated using residual heat from the aircraft’s engine or bleeding air from the compressor.The fact that this actuator is made using flexible nylon fibres also helps it fit into the wing,and could also be introduced in new flexible wing concepts in a much easier fashion thantraditional actuators.

1

2. TEST BENCH DESIGN AND CONSTRUCTION

In order to design an actuator, the properties of the material at hand need to be deter-mined. In the case of the Nylon artificial muscles that are being used for this work, theeffect of the different settings while manufacturing their final performance need to be de-termined. In addition, as they shrink when heated, the relationship between temperature,loading state and elongation should be established. In the following chapter, these issueswill be tackled, together with the manufacturing of the necessary testing equipment forthis purpose.

2.1. State of the art

The concept of artificial muscles has been around for a while already. In essence, actuatorsof this kind need to be light-weight, flexible and, usually, they provide tensile actuation.With these broad characteristics, there are many different kinds of actuators that fall underthis category, some of them using pneumatic, electric or thermal power to operate.The artificial muscles used during this project consist of twisted Nylon fibers that contractwhen heat is applied to them. An example of such fibre can be found in Figure 2.1 Inorder for the muscles to work, they need to be twisted until they start forming coils overthemselves. That is accomplished by loading the fibres with some static tensile load,then spinning the fibre until it coils over itself. There is not much information about thisparticular kind of artificial muscles, and there was only one study found regarding thismatter [1], which will be used as a reference for this project.

Fig. 2.1. Example of one of the artificial muscles under study in this work

The implementation of thermally-activated artificial muscles is difficult for the pur-poses these actuators are often intended for (Robotics), due to the hassle of having togenerate high and low temperatures in a small form factor. This is usually a very inef-ficient process and not suitable for compact robots, as the accessories needed to make itwork are often big and heavy. However, in an aircraft, the engines generate large amountsof residual heat, which in turn reduce the efficiency of the aircraft in operation. Moreover,at the altitudes these machines operate, the surrounding air reaches subzero temperatures.

2

In such an scenario, these thermally-activated artificial muscles could operate with virtu-ally no added machinery, taking advantage of residual heat from the engine and using thesurrounding air as a cooling agent.Moreover, in the study performed by Haines, it was found that these fibres were capableof attaining strokes in the range of 10 − 20% their initial length, lifting load hundreds oftimes heavier than the weight of the actuators themselves, making this fibres a promisingalternative to current hydraulic actuators.Current hydraulic actuators account for a good portion of the weight of an aircraft, accord-ing to [2], for a Boeing 737-200, the weight of the surface control actuators is of 2348lb, and the hydraulic and pneumatic systems account for another 873 lb all in all, thisis a heavy system which accounts for 5.93% of the empty weight of the aircraft. More-over, these are gradually been replaced by electrical actuators. This is due to the fact that,during the early stages of commercial aviation, hydraulic lines constituted a good wayof transmitting forces from the pilot to the control surfaces. However, since fly-by-wiretechnology appeared, the need to transmit such forces disappeared, and instead informa-tion is the only thing that needs to be transferred from the pilot to actuators in the controlsurfaces of the aircraft. Being this option available, hydraulic lines turned from a usefulengineering solution into an inefficient way to control the aircraft which was prone to er-rors and leaks, loosing control of the machine.This explains the tendency to switch to electric servomotors. However, these devices arestill fairly new in aviation and also have some tendency to jam. All in all, it can be seenthat the field of control surface actuation is still active and some improvements are stillbeing made, so that the development of this project might have a useful outcome.

2.2. Muscle manufacturing

In order to manufacture these muscles, a small mechanical and electronic system wascreated to spin the fibres a known amount of times. This setup utilizes a Nema 17 steppermotor together with an Arduino Uno as a controller for the system. The fibre was tied toa paper clip, and then this paper clip was attached to the stepper motor using 3D printedcouplings. On the other end, a water container was attached to the fibre and was filledwith different amounts of water to obtain the different tensile loads required. The electricalschematic, together with the CAD design of the couplings can be found in Figures 2.2 and2.3.

3

Fig. 2.2. Electrical Schematic of the twisting mechanism

Fig. 2.3. Rendered CAD design of the assembled 3D printed couplings

After designing this system making use of electronic tools, the structural parts were3D printed using black PLA plastic and the electronic circuit was created on a breadboard,as depicted in Figures 2.4 and 2.5.This system allows the user to start and stop the coilingprocess making use of the push-button in the circuit, while displaying the current amountof turns in a computer’s screen through the serial port. The code for the system can befound in the Appendix 5.

4

Fig. 2.4. Fibre coiler using 3D printed parts

Fig. 2.5. Electrical circuit for the coiler

Several tests were performed to determine how different factors during manufacturingaffected the properties of the final muscle, such as the amount of tension applied, thefibre diameter and the number of turns applied to it. An important parameter needs to bedefined in this stage, the so called spring index (C), which is a dimensionless parameterthat measures the ratio between the final coil diameter (D) and the original fiber diameter(d).

C =Dd

(2.1)

The experimental results for the manufacturing of a set of 61 sample muscles are sum-marized. This information is further compressed into the graph found in Figures 2.6 and2.7Figure 2.6 relates spring index with applied load while coiling and the ratio of the

5

original fibre length to the final muscle length. This information is not only useful forautomated manufacturing of the actuators, but will also allow for manufacturing of testspecimens with some specific required characteristics later in the project.

The mass of the nylon fibre used to manufacture an artificial muscle needs to be con-stant. If the original diameter of the original fibre is considered constant trough the man-ufacturing process, together with the density of the material, the volume of the fibre alsoneeds to be constant. Taking this into account the following relationship between springindex and the ratio between the original fibre and the muscle length can be achieved:

Dnπ2(d2

)2

= lπ(d2

)2

(2.2)

As coils are touching each other, the number of turns (n) equals the length of the coil(L) over the diameter of the fibre (d):

n =Ld

(2.3)

Plugging into the previous equation and simplifying gives the following relationship:

lL= π

Dd= πC (2.4)

This relationship can be checked by using the experimental results during musclemanufacturing, yielding the results depicted in Figure 2.6.

Fig. 2.6. Length change during coiling

6

As it can be seen, experimental results are quite scattered, and even though they followthe same trend as the analytical result, this result overestimates quite a bit the length ratio.Aside from the small dimensions involved in this process, which can result big relative er-rors as they are close to the tolerance of the measuring devices utilized (A digital caliper),this is most likely due to the fact that some of the assumptions made during the derivationof the analytical expression were not totally accurate. In fact, during the coiling process itwas observed that, before the fibre started generating coils over itself, it shortened a little.Taking into consideration that the volume of nylon must be conserved, this also meansthat the diameter of the fibre had to become larger. From equation 2.4, it follows that thischange (making d larger) will in fact reduce the resulting length ratio. For the purposesof this work, the current analytical expression is accurate enough, however for a morein-depth work, this phenomenon should be studied and characterized.After establishing a theoretical relationship between the length of the coil, all that is leftto do to define the properties of the final muscle as a function of the manufacturing param-eters is to find the experimental relationship between the spring index (C) and the tensileload while coiling (P). While there might exist an analytical relationship between thesetwo magnitudes, it will involve some extensive study of the mechanics that play a roleduring the coiling process, and that is beyond the scope of this project. The experimentalresults for the artificial muscles coiled can be seen in Figure 2.7, which also showcasequite a big amount of dispersion in the data, suggesting there might be more parametersat play and that these two magnitudes are not directly related to one another. Further studyis necessary.

Fig. 2.7. Experimental relationship between spring index and load while coiling

7

2.3. Design and build of the test bench

In order to reproduce the results from the article performed by Haines [1], the artificialmuscles need to undergo several heating cycles at different loads states in order to find anempirical relationship between elongation, temperature and load state. In order to performthose experiments, some machinery needs to be designed and built such that it allows to:

• Hold the artificial muscle in place

• Follow precise heating and cooling curves

• Record the temperature and time histories of the experiment

• Sense and record elongation

• Sense and record load state

• Provide sufficient heat flow to the artificial muscle in conditions similar to the finaldesign

Taking these requirements into consideration, the test equipment was designed andbuilt using primarily common hardware parts, Open-Source and custom circuits basedaround the Arduino platform and 3D printing as a complementary tool to build customsensors and structures. The accuracy obtained by such a cheap assembly will by no meanscompare to lab-grade equipment. Nevertheless, it should provide a first-order approxima-tion to the magnitude of the forces generated by these actuators to gain some insight intheir workings, at a fraction of the cost. This is especially true considering that the ma-chinery used for this kind of experiment is rare and its price its of the order of severalthousands (Or tens of thousands) of dollars.

Moreover, in order to maintain the test conditions as close as the working conditionsof the final actuator, the method chosen to heat up and then cool down the fibers is anelectric heat gun, similar to the hot and cool air that would be used in case these actuatorswere implemented in a real aircraft.

2.3.1. Mechanical design and build

In order to contain the stream of air that will heat up and cool the fibers, as well asisolate this air from the environment, the fibre used during testing will be encapsulatedinside a PVC pipe that will also serve as a support for the different temperature sensors.The whole mechanical construction revolves around this central piece. Regarding testingtemperature, PVC and Nylon have similar glass transition temperatures [3]. Taking thisinto consideration, the PVC pipe will have a much larger mass to dissipate the heat andone of its sides will be in contact with air at room temperature, which will make it safe to

8

use this polymer for the intended, since it can withstand the maximum temperatures theartificial muscle will be subjected to.A mechanical drawing of the pipe and the modifications made to it is shown in Figure2.10. In this Figure the point where the fibre will be suspended from can also be seen,together with the locations of the temperature sensors.

Moreover, a structure had to be designed to support the PVC pipe in the vertical posi-tion, since the loading method selected consists of weights hanging from the Nylon fibre.The first iteration of the design utilized threaded rods as legs that supported the wholestructure on the ground, as depicted in Figure 2.8.

Fig. 2.8. CAD rendering of the first structure design

After 3D printing the necessary couplings and manufacturing the structure, it turnedout not to be stable enough. So, for the second and final iteration of the design, theamount of supporting struts was doubled, the diameter of the threaded rods was increasedto 5 mm, and the struts were fixed to a wooden base to restrict their motion. This woodenbase will also serve as a mounting point for the electronics later on. The final CAD rendertogether with the structure after manufacturing can be found in Figure 2.9

9

Fig. 2.9. CAD render (left) and final structure assembled (right)

It should be noted that the PVC pipe that is the central piece of this design not onlyserves to contain the flow of air. In fact, it also provides a mounting point for the fibreunder testing and two ports that allow to install thermistors acting as temperature sensors.The location and size of those ports can be found in the technical drawing from Figure2.10.

Fig. 2.10. Technical drawing of the pipe and temperature ports

2.3.2. Electronic board design

Before proceeding to the design of any engineered system, regardless of its application, itis important to have the design requirements clear from the beginning. In the case of theelectronics for this project, the requirements were the following:

10

• Sensing the temperature of the flow of air

• Provide power regulation to the heater element to control the temperature

• Be able to follow a heating cycle predefined by the user.

• Provide some sort of control to the user over the test cycle

• Sense either the elongation or the force generated by the nylon fibre under testing

• Successfully log all the sensor data into an electronic file

With this criteria in mind, it was clear that for this application a micro-controller wasnecessary. In order to ease the design of the electronic circuit, instead of working with astand-alone micro-controller, the Arduino platform was utilized. For this particular appli-cation, the board selected was the Arduino Nano (Depicted in Figure 2.11, as it featuresan ATmega328P micro-controller, which has eight analog inputs which is more than themore common Arduino UNO. Moreover, this micro-controller has a very reduced size,which makes it perfect for implementation into a bigger, host board.

Fig. 2.11. Arduino Duemilanove/Uno (Left) vs Arduino Nano (Right) size comparison

Therefore, the goal of this design process is to come up with a board that will incorpo-rate the Arduino Nano as the brains of the system, together with all of the required sensorsto gather the data needed, and the power electronics to make the temperature regulation ofthe stream of air possible. Such a circuit was designed using an the online circuit designtool EasyEDA, and then manufactured in a PCB milling machine at Bechtel Innovationand Design Center (West Lafayette, IN). An image of the PCB Milling Machine can befound in Figure 2.12, together with the PCB after manufacturing.

11

Fig. 2.12. PCB Milling Machine (Left) and manufactured PCB (Right)

Such a manufacturing process involves removing sections of the copper layer on avirgin PCB board, in order to create the tracks and paths that conform the circuit. Itconstitutes a relatively easy method to develop near-professional PCBs with ease, butpresents one major flaw: The copper tracks are left exposed, as solder mask cannot beapplied with this manufacturing method. Due to this reason, the original task of the mainPCB was slightly modified. Instead of using phase angle control to regulate the powersent to the heating element, an external solid state relay will be used instead (As it will beseen in following sections). In addition, the power to the electric motor that blows air intothe system will be provided by an external power source, instead of regulating it througha double H bridge in the main board as intended at the beginning.These measures definitely constitute a compromise, since power regulation using a relayhas a slower response and introduces some oscillations as it will be seen in followingsections. Powering the blower motor using an external power supply also means that theability to control the power given to the motor will be lost, and therefore the ability tocontrol the mass flow of air and study the influence of the air speed in the heat transferprocess to the Nylon fibre. However, not only it would be unsafe to run high power ACand DC lines on a PCB with non-insulated tracks, but it can also introduce noise in ourmeasurements, since many of the sensors employed are analog. Therefore, due to thesesafety and noise reduction considerations, power to the blower and to the heating elementwill be provided externally.

2.3.3. Heater element choice and calibration

In order to heat up the fibers, it must be taken into account what the final applicationof these fibres is going to be. In this particular case, the goal is to implement them asactuators for control surfaces, operated by hot air coming from the engine and cool aircoming from the surroundings. Although it is not absolutely necessary, replicating asclosely as possible the working conditions seemed like a good way to go.

Other options under consideration were electrical heating, using either nicrom wireor some conductive coating, and heating using water. The first option was disregarded,

12

since if a nicrom wire was used, then the heat would not be spread evenly through thefibre, due to poor contact between the fibre and the wire. In addition, the nicrom wire,if wrapped around the nylon fibre too closely or too tightly (In order to improve contactand heat transfer between the two of them) could act as a structural element, providingresistance to the motion of the fibre, and therefore corrupting the results. The use of aconductive coating was disregarded too as it will slow down the manufacturing processof the fibers considerably, and coating a polymer with a metallic compound is not an easyprocess. Moreover, the electrical methods have an added difficulty: They only allow toheat up the fibre, but not cooling it down.

This problem could be avoided by using hot and cool water to heat and cool the fibers.By having two reservoirs and regulating the flow of water coming from both of them, anytemperature could be achieved. In addition, the heat transfer during forced convection ofwater over the fibre would be better than the one that could be achieved by using hot andcool air. However, manufacturing and operating such a system seemed cumbersome andmessy during operation. A much simpler solution was to modify a hot air gun with twopre-defined temperature settings so that any temperature within the gun’s capabilities canbe generated.

To start off, the schematics of such a tool were needed in order to know how to modifyit to fit the intended purposes. Such reverse-engineered schematics can be found in Figure2.13

Fig. 2.13. Schematics of the stock hot air gun

This hot air gun, in its stock configuration, has two different power settings of 1000W

13

and 1500W, and can output a maximum temperature on its high power setting of 500oC.Since this temperature is far beyond the maximum temperature required for the experi-ments, the part of the circuit associated with the low power setting will be used instead.Moreover, it also includes a blower motor that is directly fed from the AC Power lineswithout any transformer, utilizing solely a full bridge rectifier and taking advantage of thevoltage drop generated by the heating element earlier in the circuit. Since the existingcircuit will be modified, this motor will be fed by an external power supply to avoid anyproblems that can be derived from tinkering with the circuit that originally powered it.This motor has an approximate resistance of around 25.8 Ohms, as measured by feedingthe motor using a regulated power supply. This figure will be necessary in the followingcalculations to estimate the air flow present in the test tube during our experiments.

The modifications made to this heat gun consist of the following:

• Get rid of the power selection switch

• Replace such selection switch by a Solid State Relay that allows to generate a PWMsignal to control the RMS AC Voltage (An thus the power) sent to the heatingelement

• Isolate the motor from the AC Power lines and feed it independently using a 19.5DC power supply.

• Calibrate the system to get a suitable relationship between the air temperature andthe duty cycle of the control PWM signal.

Lets start by sketching the modified schematics of the system, which can be found inFigure 2.14

14

Fig. 2.14. Schematics of the modified hot air gun

After the electrical modification was accomplished, the hot air gun was fitted on topof the test tube in order to proceed with the calibration. But before going into the detailsof the experimental calibration, the theory behind the power regulation in the system thatwas just built will be studied. Starting from the point of view of fluid mechanics.

2.3.4. Thermodynamic analysis of the test bench

A thermodynamic analysis of the test volume can provide us with some useful insightson the heat transfer process from the surrounding air to the Nylon fibre. Some of thedata obtained from this analysis can be utilized to estimate the response time of the fibers,and can settle a basis to further predict the behaviour of such actuators with differenttemperatures and forced convection flow velocities.

Lets start by estimating the mass flow of air through the system, in order to have anidea of the air speeds that are involved in the process. The test bench utilizes a radialpump to push air through the heating element. The work exerted by an ideal pump in afluid is characterised by the Eq. 2.5:

W = Q[(Po + ρ0v2o/2 + ρoUo) − (Pi + ρiv2

i /2 + ρiUi)] (2.5)

The following simplifications can be made to this equation:

• The potential energy change is negligible (QUo − QUi ≈ 0)

15

• The sum of static and dynamic pressures at the inlet are equal to the static pressureat the outlet, which is the atmospheric pressure (Pi + ρv2

i /2 ≈ Po = Pa)

• The density of the air in the compressor remains almost constant and equal to thatof the surrounding atmosphere (ρi ≈ ρo = ρa)

Hence, equation 2.5 can be reduced to:

W =Qρav2

o

2(2.6)

Since Q = voAo, which is the volumetric flow rate of air through the outlet of thepump, then we can obtain an expression that can help us determine the mass flow of airthrough the system, based in the pump’s outlet velocity:

W =ρav3

oAo

2(2.7)

Now the power exerted by the pump on the system must be estimated. From previousmeasurements, we know that the resistance of the electric motor used for this purpose is25.8 Ω. The electrical power consumed by such a motor is described by:

P = VI =V2

R(2.8)

Where V stands for the Voltage applied to the motor, I is the current and R is theelectrical resistance of the motor. Since the motor is been fed 19.5V, the power fed tothe motor is 14.74 W. However, this is just the power consumed by the motor, which isnot the power transferred to the fluid itself. Since the motor is not ideal, some efficiencyhas to be applied to it, and the same goes for the pump itself. Being conservative, theefficiency for the electrical motor can be estimated to be of around 70%, while the one forthe compressor itself can be estimated to be of the order of 50%. Therefore, the overallefficiency η = ηm · ηp = 0.70 · 0.5 = 0.35

With this information we can estimate the air speed at the outlet of the pump and themass flow through the system using equation 2.7, since power transmitted to the fluid willbe: W f luid = Welectrical · η = 14.74 · 0.35 = 5.16W. This results in the following outletvelocity:

vo =3

√2WρaAo

(2.9)

Plugging the following known values for the variables involved in equation 2.9:

• W = 8.29W. Power transmitted to the fluid by the pump.

16

• ρa = 1.225 Kgm3 , according to the International Standard Atmosphere, since the tests

were made at sea level.

• Ao = 490mm2. Outlet area of the pump.

Resulting in vo = 25.8m/s, Q = 0.013m3/s and G = 15.5g/s.

This estimation of the mass flow rate circulating through the system is useful to obtainthe velocity of the flow of air over the fibre. While the ability to control the power to themotor was lost due to the limitations of the manufacturing process of the circuit, thisfigure can be a useful reference for further studies based upon this project.The velocityover the fibre can be calculated using equation 2.10.

v =G/ρAp

(2.10)

Where:

• v is the speed of the air over the fibre in m/s

• Ap is the area of the test section (Or the cross-section area of the pipe), which equalsto 1140mm2

• ρ is an average density for the stream of air, over the range of temperatures tested.

The resulting velocity is of 13.6[m/s].The amount of electrical power utilized by the heating element can be calculated withthe following expression: P = V2

rms/R. From all the electrical power utilized, only someportion of it will heat up the fluid, but there is no good way of estimating such an efficiencytheoretically, so a test was conducted in order to determine the temperature of the flowof air under steady state conditions for multiple power settings. This was done by doinga slow heating cycle, in order to allow the system to reach a quasi-steady temperature asthe power increases. A graph of such a test can be found in the following in Figure 2.15.

17

Fig. 2.15. Heating element test run for calibration purposes

It must be noted that, from the two temperature sensors present in the test bench, theone closer to the heating element was the one used for this calibration process. This isdue to the fact that as air moves inside of the test pipe, it will transfer heat to the wallsand loose temperature, so that the hottest air will be closer to the heating element. Usingthe hottest temperature sensor as a reference is a conservative measure. In addition, thedata represented in the X-Axis is the duty cycle of the solid state relay, connected to the230V AC power line. The electrical power consumed by the heating element can then becalculated using the expression: Pelectrical =

(Vrms·√

D)2

R , where D stands for "Duty Cycle",which is just the percentage period of the PWM control signal that the relay allows currentto pass, and Vrms is the RMS voltage of the mains power supply (230VAC in Europe).The linear relationship between the air temperature in Celsius and the duty cycle to theheating element is represented in equation 2.11.

T = 434 · D + 18.02 (2.11)

If the relationship between electrical power and duty cycle is introduced in equation2.11, a relationship between electrical power consumed and the temperature of the streamof air can be obtained, which is shown in equation 2.12.

T = 0.4 · Pelectrical + 18.02 (2.12)

Where Pelectrical is expressed in Watts.

18

2.3.5. Experimental procedure

General considerations

The final goal of this characterization process is to obtain the relationship between tem-perature, load and elongation, or in other terms: ϵ(L,T ). This is a two-variable functionthat can be represented in R3 as a surface. In order to find that surface, either the elon-gation or the load state of the fibre must be kept constant, while the fibre is subjected toa heating and cooling cycle and inspecting how the other variable responds. This way, ascan of such a surface will be made in such a way that, after doing enough of them, theycan be represented as cross-sections that allow to interpolate the whole surface.In order to decide which variable to keep constant and which variable subject to study, thekind of sensors that need to be used to study each of the variables must be considered:

• If the elongation is kept constant, the force exerted by the fibre must be measured.In order to do so, a suitable sensor is a load cell. In such a configuration, the looseend of the fibre would be attached and fixed to the load cell using an inextensiblecable, while the forces are recorded.

• If the load is kept constant, some mass must be attached to the loose end of thefibre, while another sensor is used to record how that mass moves. The choice ofsuch a sensor is not easy, since it must be moved by the fibre and therefore it musthave little to no friction, or at least it must be possible to quantify how it is affectingthe load state of the fibre.

In the first scenario, the remaining inextensible cable after fixing the loose end to theload cell could be attached to a linear encoder, therefore automating the recording of theelongation state of the fibre for every test. Moreover, the absence of moving parts in thisconfiguration is really attractive since it can reduce errors and noise in the measurements.This was the method used in the beginning, however, as it will be seen in followingsections, it was discarded due to some issues with the load cell. Afterwards, an elongationsensor was designed and manufactured to be able to conduct the experiments using thesecond method.

Sensing generated force

A load cell is a sensor whose purpose is to measure forces. Such a sensor is composedof two main parts: A strain gauge and an amplifier. A strain gauge consists of a resistorinside of a polymeric capsule which changes its resistance as it is elongated. Such a de-vice is fragile and must be glued to a tougher substrate in order to withstand higher loads.When in operation, the loads that substrate is subjected to (Generally, a piece of metal)change its shape, and since the strain gauge is glued to it changes its shape and resistance

19

accordingly.

Since these changes are very small, an amplifier circuit is absolutely necessary inorder to get suitable readings from the load cell. Such a circuit is generally sold with theload cell itself, and in the case of this project, this amplifier circuit is based around theHX711 Analog to Digital converter, sending the sensor values as an digital signal to theArduino board.

All in all, this is a very powerful sensor arrangement, but it was of no use duringthe development of this project. This was due to the fact that the sensor was placedunderneath the exit section of the PVC pipe. Even though the sensor has two differentstrain gauges connected in a Wheatstone bridge configuration, which is a special circuitto read analog sensors that avoids the temperature reading error, the adhesive that heldthe strain gauge to the metal beam failed due to the rising temperature. This failure wasdetected by inspection of the output of the strain gauge. Firstly, the output of the sensorwas much smaller than expected (Considering the calibration curve of the sensor and theforce applied), which was a symptom of the strain gauge not properly gripping to themetal beam’s surface and thus not elongating with it. On the other hand, abrupt changesin the force output were indicative of the strain gauge suddenly slipping over the metalsurface after a period of being properly gripping to the surface.This is a relatively common failure mode of load cells, since the adhesion of the straingauge to the surface of the load cell is so critical, and the strain gauge is able to sense tinydeformations. However, it was not detected until the system was built, calibrated and thefist tests were done. The original sensor arrangement can be found in Figure 2.16. Thisdebugging process was time consuming and a setback in the development of the project.

Fig. 2.16. Original sensor arrangement using a load cell to measure forces and a linear encoder tomeasure elongation

20

Thermistor operation

Small electronic devices that can change their internal electrical resistance according totheir temperature are called thermistors. This property can be utilized to measure temper-atures, and they constitute the temperature measurement device for this project. However,obtaining temperature readings from these devices is not an easy task, since the relation-ships involved in transforming the resistance of the device into a temperature reading arenon-linear and difficult to implement in a micro controller. Lets start with the theory ofoperation.

In the first place, these sensors constitute a variable resistor that changes its value withtemperature. Since a microcontroller cannot directly read a resistance value, we need toimplement these sensors in a voltage divider configuration. Moreover, it is typical fromthis analog circuits to pick up environmental noise, particularly in the 50Hz frequencyband since that is the frequency of AC power in Spain. A passive filter must then beimplemented together with the voltage divider in order to get rid of such noise. In fact,since the heating cycles that our system will be subjected to will be very slow, this filtercan be conFigured for frequencies well-below 50Hz, getting virtually rid of all noise inthat frequency range. The resulting schematic can be found in Figure 2.17

Fig. 2.17. Thermistor in a voltage divider and passive low-pass filter configuration

The values chosen for the passive components are strongly linked to the kind of ther-mistor that has been used. For this project, a 100 KOhm NTC thermistor was utilized.NTC stands for Negative Temperature Coefficient, indicating that the resistance of the de-vice decreases with rising temperature. The resistance values for different temperaturesare given by the manufacturer and have been displayed in Figure 2.18.

21

Fig. 2.18. Resistance values of a 100 KOhm NTC thermistor

Since the accuracy of the temperature sensor readings depend on how accurate theconversion from analog to digital in the Arduino is, the value of the resistor R1 (shown inthe schematic in Figure 2.17) must be chosen so that the output from the sensor circuithas the widest possible range. In this situation, the resolution achieved by the analog todigital converter is maximum. In order to achieve that, an optimization problem needs tobe solved where the objective is to maximize the difference between the maximum andminimum voltage output from the sensor circuit, in other words, Voutmax − Voutmin needs tobe maximized. Therefore:

ddR1

(Voutmax − Voutmin) = Vs ·

(Rtmin

(R1 + Rtmin)2 −Rtmax

(R1 + Rtmax)2

)= 0 (2.13)

Solving for R1 in equation 2.13, gives the result R1 =√

Rtmax · Rtmin . An estimationof the maximum and minimum values of Rt (The thermistor’s resistance) needs to beobtained. In order to do so, an estimation of the working temperature range of the systemis required, then by application of the manufacturer’s table of resistance values depicted inFigure 2.18 the range of resistance values can be obtained. Since the system is estimatedto work in the range [15C, 100C], Rtmin = 5572.62Ω and Rtmax = 161.7kΩ. This resultsin an ideal R1 value of 30kΩ.The other component that needs to be sized is the capacitor for the low pass filter. Thevalue of such a capacitor, in conjunction with the value of the series resistor will determinethe cut-off frequency of the filter according to equation 2.14

f =1

2πR1C(2.14)

Since the temperature changes system will be small (Less than 1C · s−1), the cut-offfrequency f can be chosen to be as low as 5 Hz. Since R1 is already fixed, the capacity

22

C is the only parameter that can still be adjusted, and after solving for it in equation 2.14gives a value close to 1µF, which is the closest commercially available capacitor value.After the values for the passive components of the circuit associated with the readings ofthe thermistors have been determined, a mathematical model of the relationship betweenthe temperature read by the thermistor and the voltage output of the system is needed.There already several models relating the resistance of the thermistor with temperature,such as the Steinhart-Hart model or the β equation. These models are defined by equations2.15 and 2.16 respectively.

1T= A + B ln Rt +C · (ln Rt)3 (2.15)

1T=

1T0+

1β· ln

Rt

Rt0(2.16)

Where T stands for Temperature in K, R stands for Resistance in Ohms, with Rt0 andT0 being the resistance of the thermistor at the nominal temperature (100 kOhm at 25Cfor a 100kΩ NTC thermistor). A, B,C, β are parameters of the models that need to be cal-culated beforehand for each specific thermistor using known resistance and temperaturevalues provided by the manufacturer. For a 100kΩ NTC thermistor such as the one uti-lized in this project, and applying the values provided in Figure 2.18, the values for suchparameters can be calculated giving the following results:

• A = 8.27 · 10−4[K−1]

• B = 2.09 · 10−4[K−1]

• C = 8.06 · 10−8[K−1]

• β = 4103.69[K]

One more modification must be made to the models in order to have a direct rela-tionship between temperature and the voltage read by the Arduino. The value of theresistance of the thermistor must be related to the output voltage of the circuit. Accordingto the equation for the output voltage in a voltage divider:

Rt =Vout · R1

Vs − Vout(2.17)

Where Vs stands for supply voltage to the voltage divider, in the case of this circuit,5V. Plugging eq. 2.17 into eqs. 2.15 and 2.16 results in the following models:

T =1

A + B ln Vout ·R1Vs−Vout

+C ·(ln Vout ·R1

Vs−Vout

)3 (2.18)

23

T =1

1T0+ 1β· ln

Vout ·R1Vs−Vout

Rt0

(2.19)

The β equation is computationally less intense that the Steinhart-Hart model, and thusmuch more suitable for implementation in a micro controller environment, where com-putational resources are limited. However, it must be first verified that both models arereasonably close to the actual values provided by the manufacturer. Such a comparisoncan be found in Figure 2.19

Fig. 2.19. Comparison of actual resistance values, the β equation and Steinhart-Hart models for a100kΩ NTC thermistor

As it can be seen, both models accurately represent the resistance vs temperature curveof the thermistor. Due to its computational advantage and its readily available libraries,which ease the implementation of the model while coding, the β equation was chosen forthis project instead of the Steinhart-Hart model.

2.3.6. Elongation sensor design and calibration

Sensing elongation is not an easy task. Existing solutions are often used during stress-strain material testing, where the loads involved are huge and provided by external ma-chinery, in such a way that the added resistance of the sensors does not play a very im-portant role. However, the forces generated by the kind of actuator under study for thisproject are really small, and so the resistance provided by the sensing element must bereduced or, at least, it must be possible to model it mathematically so that its effect over

24

the force generated by the actuator can be taken into account. As it was seen in section2.3.5, directly measuring force by clamping one end of the fibre was a failure, so that theonly option left is to measure elongation while the fibre is lifting a known load.In order to accomplish this task, an elongation sensor was developed so that the onlyinfluence this sensor would have in the load applied to the fibre under testing is some ad-ditional weight to whatever the load is attached to the fibre. In order to do so, the internalworkings of digital calipers will be used as an inspiration.The sensor is based around the analog sensor TCRT5000. This is a cheap and widelyavailable infrared sensor, composed of an IR emitting diode and an IR receiver diode.The receiver diode changes its voltage output according to the amount of IR radiationreflected from the IR emitting diode by a nearby surface. This sensor is been widely usedin line-following robots in order to distinguish black lines from black backgrounds, in asort of digital configuration. However, it can also be used to determine the reflectivityof a surface, which depends not only in the material itself but in other factors such as itscolor. By printing a black and white gradient in a strip of paper, such as the one shown inFigure 2.20, this sensor can be used to determine the relative position between the paperstrip and the sensor itself. In such a configuration, the strip of paper can be attached to thefibre so that both move together, and the sensor itself can be fixed, so that the elongationof the fibre can be measured.

Fig. 2.20. Gradient used for sensing the position of the fibre

In order to provide a mount for the paper strip and a guide for the motion of such astrip (So that the motion is restricted to a single axis), a structure was designed and 3Dprinted. This structure is composed of two main parts, a slider with the gradient depictedin Figure 2.20 glued to it which attaches to the inextensible wire connected to the fibre,moving along with it, and a support for the sensor that is mounted below the wooden baseof the structure. The sensor is contained in a compartment with opaque plastic walls thatextend all the way to the surface of the slider. This last fact is important since this sensoris sensitive to noise in the form of IR radiation, such as sunlight. If light other than theemitted by the IR emitting diode makes it to the receiver diode, then the measurementswould be compromised.These features can be seen in the technical drawing in Figure2.21.

25

Fig. 2.21. Features of the elongation sensor assembly

The required circuit for the operation of this sensor is much simpler than the oneutilized to read values from the thermistor, since the receiver diode already outputs ananalog voltage. The resulting circuit is the one recommended by the manufacturer in thedatasheet of the sensor [4], and is depicted in Figure 2.22.

Fig. 2.22. Circuit for the operation of the TCRT5000 sensor

After assembling the structure supporting the sensor and soldering the sensor with itsrequired circuit in a perforated board, the whole construction was assembled, tested andcalibrated. The resulting sensor assembly is depicted in Figure 2.23.

26

Fig. 2.23. Sensor assembly with slider (Left) and sensor IR beam (Not visible by the human eye)(Right)

Following the manufacturing of the sensor, a calibration process is required. Thisprocess consists of measuring the voltage output of the sensor at different positions ofthe slider, and applying a regression model to obtain a mathematical expression for theposition of the slider as a function of the voltage output of the sensor. The result of suchcalibration process is depicted in Figure 2.24.

Fig. 2.24. Calibration curve for the elongation sensor

As it can be seen, the relationship between the voltage output of the sensor and theposition of the slider is almost linear and can be approximated by the function described

27

in equation 2.20.

d(V) = −12.13 · V + 54.41 (2.20)

As a final note, the final weight of the slider resulted in 10 g, that must be added towhatever the load attached to the fibre is.

2.4. Heating cycle considerations

The experimental procedure to test the fibres under study in this project consists of sub-jecting them to cycles of heating and cooling. An important characteristic of these cyclesis that they must be done in a slow manner. This is mainly for two reasons:

On one hand, measuring the temperature of such fibers is not easy. Being so thinmakes it nearly impossible to use a temperature sensor in contact with them, since theyhave a thermal mass comparable to that of the temperature sensor. In this situation, thetemperature sensor would act as a heat sink and would modify the actual temperature ofthe muscle considerably, resulting in a poor temperature measurement. Moreover, usinglaser-aimed, infrared thermometers is not feasible either. The lack of big, planar surfacesin this kind of actuator and the fact that it will be elongating and contracting during testingmakes it almost impossible to correctly aim such a device.

Therefore, the only two options that are left are to use an infrared camera, which has amuch higher resolution that an infrared thermometer, avoiding the problem of aiming., ornot measuring the temperature at all. Since thermal imaging is expensive and not widelyavailable, instead of measuring the temperature of the fibre, the heating cycle will be donein a very slow, progressive fashion, assuming the temperature of the fibre to be equal tothat of the the surrounding air since the change in temperature is done so slowly.

This method has the disadvantage of being unable to study the transient response ofthe fibre with temperature, since the accuracy of the temperature measurement dependson how slow the cycle is. However, at this stage the transient response of the fibres isof no interest, firstly, the steady state properties need to be determined, together with thepossibility of hysteresis in the system.

Having established the need for the heating and cooling cycles to be slow, the range oftemperatures to be tested needs to be determined. In the study performed by Haines [1],these fibres were heated well-above 100C. However, this was done with professionalmachinery were the risk of melting the test chamber walls was non-existent. Since thetest chamber for the test bench utilized in this study is made out of a PVC pipe, a moreconservative temperature range of [0 − 100C]will be chosen. This value was chosen

28

since PVC melts at [100C] to [260C], depending on the specific additives present in it.The most conservative approach was used. In fact, after the tests were performed, somedeformation could be seen in the test tube due to the temperature being a bit too high.

The control variable that is available in the system to control the temperature is theduty cycle and period of the PWM (Pulse Width Modulation) signal sent by the Arduinoto the solid state relay that allows the heat gun to operate. While the duty cycle will bechanged during testing, as the temperature of the flow of air is directly proportional to itas seen in Equation 2.11, the period of such a signal is fixed during testing and must bechosen in advance.

Before choosing this period, the signal that needs to be switched on and off (220ACpower line) needs to be considered. Since in essence the solid state relay is just a switchthat either allows the current to flow or blocks it without any information of the currentstate of the signal, it can switch on and off at any point of the sinusoidal voltage of theAC signal. This means that two identical PWM signals can result in a very different Vrms

when applied to the same AC voltage, depending on the timing between the PWM andthe AC signal itself. This effect can be studied using the equation 2.21, which is just theexpression to calculate RMS voltage of a non-DC signal. The RMS (Root Mean Square)voltage is just the effective voltage of an equivalent DC signal.

Vrms =

√1T·

∫ T

0V(t)2dt (2.21)

Where:

• V(t) is the voltage dependency on time

• T is the period over which Vrms is being calculated.

In the case of Spain, the AC power lines have an RMS voltage of 230V, with a fre-quency of 50Hz (Equivalent to a period of 0.02s), and its function V(t) is denoted byequation 2.22.

V(t) = 230 ·√

2 cos (100πt) (2.22)

Using this information, the effect of the timing between the PWM and the AC signalcan be simulated. A graphical representation of such a simulation can be found in Figure2.25, where the output of the SSR (Solid State Relay) was simulated for 3 identical PWMsignals with the same period of 0.02s (The same as the AC signal) and duty cycle of 10%.The only difference between these signals is the fact that their firing times are random and

29

different to one another, as it is the case with the actual system, as the micro-controllerhas no information about the current state of the AC signal.

Fig. 2.25. Output from SSR with 3 identical PWM signals. T = 0.02s

The RMS voltages of the three different PWM signals can be calculated, yielding thefollowing results:

• Vrms(PWM1) = 36.15V

• Vrms(PWM2) = 96.99V

• Vrms(PWM3) = 61.46V

Which widely differ from one another. If instead of an AC signal, the regulated signalwas a 230V DC signal (Constant voltage with V(t) = Vrms, which is the definition of RMSVoltage), the resulting Vrms for a PWM signal with duty cycle of 10% will be V ·

√DC =

72.73V , which is also different from the results obtained previously. In order to minimizethis variability, the period of the PWM signal must be chosen so that at the smallestexpected power setting, the amount of time the relay is in the conductive state coincidesat least with one semi-period of the AC signal. Further increasing the period will reducethis effect even more, however for too long periods, larger fluctuations in the airflowtemperature can appear as the period of the PWM gets closer to the residency time of theair inside the heat gun. The final period chosen for the PWM signal is of 0.2s. Repeatingthe previous simulation for a PWM signal with this period and 10% duty cycle yields theresults shown in Figure 2.26

30

Fig. 2.26. Output from SSR with 3 identical PWM signals. T = 0.2s

The RMS voltages of the three different PWM signals can be calculated, yielding thefollowing results:

• Vrms(PWM1) = 72.7287V

• Vrms(PWM2) = 72.8074V

• Vrms(PWM3) = 72.8082V

Which is now much closer to the previously calculated value of 72.73 V. Note, how-ever, the accuracy of the power output using this method decays for smaller duty cycles,as the problem shown in Figure 2.25 arises all over again. Moreover, it is also vulnerableto small differences between the theoretical AC frequency and the actual one, since forfrequencies other than 50Hz, if a constant duty cycle PWM signal is left feeding the SSR,it will create a fluctuating power output.A more suitable way to control the power output of the system would have been usingphase angle control. This technique is similar to PWM, the period of the control signal isset to be equal to that of the AC, with the main difference being that in this case the ACsignal is fed to a micro-controller through an optocoupler. This way, the firing time of thecontrol signal can be coordinated with the AC signal, giving consistent results. However,as it was explained in previous sections, the manufacturing technique used to build thePCB for this project does not allow to isolate the copper tracks of the board. Since thismethod requires feeding the 230V AC signal to the micro-controller through such board,it was deemed unsafe due to the exposed tracks and this option was discarded.With this considerations taken into account, and using Equation 2.11, a controller for the

31

duty cycle, D, of the PWM control signal can be written with the heating rate set to 10Cs

and the cooling rate set to −20Cs . It must be taken into account that the maximum duty

cycle setting will be 20%, which corresponds to a temperature of ≈ 100C, and that theduty cycle must be entered in the micro-controller as an integer between 0 and 1023,and that time is measured in milliseconds from the start of each respective cycle. Suchcontrollers can be found in the form of eqs. 2.23 and 2.24.

D(t) = t · 0.00041667 (2.23)

D(t) = 200 − t · 0.00083333 (2.24)

A sample of the generated heating and cooling cycle can be found in Figure 2.27.Notice how, even if the cooling rate was set to be twice as high as the heating rate, inreality, the heating curve is almost symmetrical. This is due to the fact that energy isstored in the walls of the test tube as the temperature is rising, and when cooling down,this energy is released from the walls into the stream of air. This is also the reason that,in the final portion of the heat cycle, it takes so long for the air to reach its originaltemperature. After power sent to the heat gun is set to zero, it still takes a lot of time todissipate all of the energy stored in the system in the form of heat. In this regard, noticehow during the cooling period of the cycle, the temperature of the temperature sensorfurther away from the heat gun becomes larger than the closer one. This is due to the factthat the energy heating the airflow is now coming from the walls of the pipe, and not fromthe heat gun itself, so the further along the pipe the hotter the stream of air.

Fig. 2.27. Sample of a heating and cooling cycle

32

All in all, and taking into consideration the time it takes to dissipate all of the energystored into the system, the total amount of time it takes to perform one of the test casesdepicted in Table 3.2 can be as long as 25 minutes. For 12 test cases, this amounts for 5hours of total testing time. However, the actual time spent in testing, accounting for setupof the test bench and failed tests that needed to be repeated, easily doubled that amount.This is the reason behind the relatively high chosen heating and cooling rates as comparedto the original study performed by Haines [1]. Lowering the heating and cooling rates tothe ones used in that study would increase the testing time far beyond what is feasible forthis project.

33

3. CHARACTERISATION

After the test bench had been completed, it was time to use it to determine how theseNylon fibers perform when subjected to heat. In order to do so, some test specimensneeded to be manufactured. For this task, 0.5mm Nylon fishing line was chosen, since itis widely available and is one of the largest diameters that can be found in this categoryof products, thus generating larger forces and allowing for less error related to weightmeasurement. This is due to the fact that the weight used to perform these tests wascomposed of a water container that was filled as necessary in order to obtain any desiredweight, using a balance with a resolution of 1g. Four different fibres were manufactured,twisting them under different loads to obtain different characteristics in the final coils.The characteristics of such specimens can be found in Table 3.1

Specimennumber

Fibrelength [mm]

Stress whilecoiling [MPa]

Coillength [mm]

External coildiameter [mm]

SpringCoefficient [-]

1 691 10.0 91.76 1.7 2.42 733 18.3 114.5 1.55 2.13 704 26.5 119.3 1.45 1.94 709 34.8 131.5 1.32 1.64

Table 3.1. TEST SPECIMENS CHARACTERISTICS

Together with the test specimens, a test matrix was determined in order to properlydefine the test cases that would be evaluated. Such a matrix can be found in Table 3.2

Specimen number Load 1 [g] Load 2 [g] Load 3 [g]

1(Case 1)

99(Case 2)

150(Case 3)

199

2(Case 4)

98(Case 5)

149(Case 6)

199

3(Case 7)

146(Case 8)

194(Case 9)

245

4(Case 10)

100(Case 11)

152(Case 12)

200

Table 3.2. TEST MATRIX WITH CASE NUMBERS

After defining all of the test cases and the specimens that will be used, the testingstarted. From this point on, the different experiments performed will be referred to usingtheir case number from Table 3.2. However, it must be noted that the experiments de-scribed in Table 3.2 were not the only ones performed. In particular, testing for higher

34

loads was performed, but it was soon realized that those higher loads elongated the fibrebeyond what the elongation sensor could actually measure, so those tests were discarded.The tests with the 3 highest possible loads before saturating the elongation sensor werekept for this study.

3.1. Testing procedure

3.1.1. Temperature gradient inside the test tube

Before proceeding to the interpretation of the test results, one of the caveats with the testbench setup must be first solved. This consists in the fact that the stream of air, whilein the heating portion of the cycle, looses some heat through the walls of the test tubeas it travels through it, lowering its temperature. On the other hand, when in the coolingperiod of the cycle, the walls of the tube are the ones transmitting heat to the stream ofair, heating it up as it travels down the tube. This will generate a temperature gradient botin the flow of air and in the nylon fibre under testing. Since some temperature must beused as a reference, the average temperature of the fibre will be used.In order to obtain the average temperature of the fibre, data from both temperature sensors,as well as from the elongation sensor and the initial characteristics of the fibre will beused. By combining this data, the instantaneous average temperature of the fibre can beobtained no matter its elongation state. In order to do so, a temperature gradient insidethe test tube was estimated using temperature readings from both sensors and the distancebetween them as depicted in Figure 2.10. Then, the average temperature of the fibre canbe calculated using the distance from the first sensor to the fibre’s mounting point, as wellas the unloaded length of the fibre and its elongation, by means of equation 3.1

Tavg =Ti + T f

2=

2 · Ti + ∆T∆x · l

2=

2Th +∆T∆x · (2ds f + L)

2(3.1)

Where:

• Th is the temperature read by the sensor closest to the heat gun.

• Tc is the temperature read by the sensor furthest to the heat gun.

• ds f is the distance from the sensor closest to the heat gun to the mounting point ofthe fibre.

• dss is the distance between both temperature sensors.

• L is the instantaneous fibre length.

• ∆T∆x = (Th − Tc)/dss is the temperature gradient inside of the test tube in the stream-wise direction x.

35

• Ti = Th +∆T∆x · ds f is the temperature of the fibre at the fixed end in Celsius.

• T f = Ti +∆T∆x · L is the temperature of the fibre at the loose end.

3.1.2. Test bench setup

In order to keep experiments consistent, the following checklist was developed in orderto setup the test bench and perform the required tests:

1. Introduce fibre into test tube and fix it to its mounting point.

2. Attach inextensible cable to the loose end of the fibre.

3. Guide the inextensible cable through the base of the test bench and clamp it to theelongation sensor.

4. Record the elongation sensor’s output while the fibre is unloaded.

5. Introduce the necessary amount of water in the container to achieve desired weightand hang it from the inextensible cable.

6. Start the blower fan

7. Initiate the heating cycle and the data logging using the control sketch from theserial port of the computer connected to the Arduino.

8. Repeat steps 5-7 for each desired test using the same test specimen

Steps 1 through 3 are the required steps to setup the test bench. The test bench, readyfor operation, can be seen in Figure 3.1.

Fig. 3.1. Elongation sensor setup (Left) and full test bench ready for operation (Right)

36

In figure 3.2 a detail of the mounting point of the fibre can be seen. Originally, thisconsisted of a plastic part that slid into the test tube and to which the fibre was attachedusing a hook. However, the combined action of the high temperature and the tensiongenerated by the fibre warped this piece, so that an upgrade to a wooden part ended upbeing necessary.

Fig. 3.2. Detail of the fibre mount mechanism

3.1.3. Data gathering and data structure

The data logged by the sensors through the Arduino must be stored in some sort of digitalformat. The most straightforward way of retrieving data from the Arduino is through theserial port window. This allows the user to visualize the output data from the Arduino asa strings of text. The data for each of the test cases was then recorded into a text file thatwas later imported into Matlab. A sample of the output file from the test bench can beseen in Table 3.3.

Test #Time[ms]

Temp.sensor 1 [C]

Temp.sensor 2 [C]

Strain[mm]

Power setting(Duty cycle · 1024) [-]

1 3 31.66 30.67 5.36 01 8 31.44 30.31 5.30 01 12 31.44 30.55 5.30 01 17 31.21 30.07 5.36 01 41 31.21 30.31 5.30 01 66 31.55 30.67 5.36 0... ... ... ... ... ...

Table 3.3. SAMPLE OUTPUT FROM TEST BENCH

As it can be seen, the output obtained from the test bench is a rather big matrix con-taining all of the tests performed to a single fibre, under different loads. In order to workwith this data, it needs to be imported into Matlab with a suitable data structure. The data

37

structure chosen is just a cell array where each of the cells contains a matrix with the testresults for one of the cases displayed in Table 3.2. The structure followed by the cell arrayis the same as the one in such table, and the structure of the matrices in each of the cellsis the same as the output files from the test bench, shown in Table 3.3.

3.1.4. Data processing

After the data was imported into Matlab, it was realized that, despite the efforts madeduring the electronic and mechanical design of the circuit and sensors, the data was stillnoisy. This is somewhat expected, since it is impossible to eliminate all the noise from asystem. An example of a elongation vs temperature curve using raw data can be seen infigure 3.3.

Fig. 3.3. Elongation vs temperature curve for test case 11 using raw data

In order to make the data usable, it first need to be filtered. Firstly, the big randomnoise spikes need to be removed, and afterwards, the smaller and more consistent noisespikes that cause the output data to treble need to be smoothed out.In order to achieve the first task, a median filter needs to be applied. This filter works byreplacing each data point by the median of that point and several neighbors. In the case ofthis work, the number of neighbors was chosen to be 5 for filtering temperature and of 15for filtering elongation. The median, in a set of data, is just the data element that has anequal number of elements greater and smaller than that element itself. Unlike the average,it does not take into account the value of the data points, just whether they are greater orsmaller than the current value. That is the reason that it is so useful to remove big spikesin the data, since the influence of how big the spike is becomes irrelevant. Even though

38

the purpose of this filter was just to remove big spikes in the raw output data, it also goesa long way into smoothing the rest of the smaller spikes. Nevertheless, a second filter wasapplied, an averaging filter.Such filter operates in a similar fashion to the median filter, but instead of replacing eachdata point by the median of its neighbors, it uses their average instead. This serves tosmooth out general background noise from the signal. Notice that the order in whichthese filters were applied is not random. If the averaging filter had been applied first, theinfluence of the big noise spikes would have been translated into the neighboring point,and in that situation the median filter would have been less effective in removing them.In short, the median filter is useful to remove spurious data, while the averaging filterperforms the best in smoothing general white noise out. The result of the filtering processcan be seen in Figure 3.4.

Fig. 3.4. Filtering process for test cases 1 (Top) and 11 (Bottom)

After filtering the results, each of the experiments had their points classified accordingto which step of the heating cycle they corresponded to, either heating or cooling.

3.2. Interpretation of the results

In the following sub-sections, a few sample experiment results will be analyzed in orderto discover the main features and behaviour of the nylon fibers. Not all of the experimentswill be analyzed though, since the behaviour is very similar in each of the cases and anindividual analysis is of no use. Instead, test cases 1 and 11 will be studied, since they area good representation of how the Nylon fibre should perform.It must be remembered that, in order to obtain a relationship between elongation, temper-ature, and load state, several tests were performed at a constant load, giving isosurfaces

39

(Just planar ones in this case) with constant load of the strain vs temperature vs loadsurface (ϵ(T ; F)).

Fig. 3.5. Elongation vs temperature curve of processed data for test case 1

In Figure 3.5, one of those isosurfaces of constant load is displayed, corresponding totest case 1. From this curve, it can be clearly seen that there exists a non-linear relation-ship between the elongation of the fibre and its temperature. Moreover, a phenomenoncalled hysteresis takes place. Such phenomenon consists in the elongation of the fibre notonly depending on the current state of the rest of variables, but in their time histories.It follows then that two different elongation curves must exist, one for the heating portionof the test, and a different one for the cooling period of the test. The elongated loops thatcan be seen in the figure correspond to a combined action of this effect and oscillations inthe temperature of the surrounding air, and it will be studied more in depth in section 3.2.1.

The amount of hysteresis is typically quantified by the distance separating both elon-gation curves (Heating and cooling). Measuring such a distance at several points andaveraging gives the hysteresis values represented in Table 3.4, which are written in thesame order as the test matrix in Table 3.2.

40

Specimen number Average hysteresis [C]1 10.05 10.38 1.972 5.67 7.27 5.913 10.30 9.91 7.454 9.13 7.10 7.81

Table 3.4. AVERAGE HYSTERESIS VALUES FOR EACH TESTCASE.

Even though judging for the data obtained in this work hysteresis is definitely presentto some degree in this kind of actuator, these results differ from the ones obtained byHaines [1] in the article that served as a baseline for this project. In that study, this kindof actuator was found to behave with little to no hysteresis. The most likely cause for thisdiscrepancy is that the heating rates used in this project were much faster than the onesused by Haines. This could result in errors in the temperature measurement, and it will beanalyzed in the following section.

3.2.1. Defects in data due to poor heat cycle control

All of the defects found in the output data, such as the apparent hysteresis present in thesystem and the odd loops that appeared in the data can be explained due to too fast heatingand cooling rates and poor temperature control during the heat cycle. Regarding the loops,the reason they appeared becomes much clearer when comparing the temperature historyfor that specific test side by side with the elongation vs temperature curve, as it can beseen in Figure 3.6.

41

Fig. 3.6. Elongation vs temperature curve against temperature history for test case 1

As it can be seen, the loops are originated by a large fluctuation in temperature. Be-cause of the apparent hysteresis of the system, a reversal in the derivative of the tempera-ture (Switch to cooling while heating and vice-versa) does not result in the fibre followingthe same path it just traced in the elongation vs temperature curve. Instead, it has the ten-dency to move horizontally towards the curve with opposite temperature derivative, hencethe loops and the reason while the always appear in between both curves. The path followwhile heating is different than the one followed while cooling.

As explained in section 2.4, the bad thermal control is mainly because due to safetyconsiderations related to the manufacturing processes used for this project, which shouldbe revisited for further research.Regarding the apparent hysteresis in the system, it happens due to the heating and cooling

42

rates being to fast. In such a situation, the temperature of the stream of air changes toofast and the temperature of the fibre lags behind. Since the temperature of the fibre wasassumed to be the same as the one of the stream of air, this results in the actual temperatureof the fibre to be cooler than the air while heating and hotter than the air while cooling.Of course, this is just a theory that needs to be backed with tests performed with smallerheating rates. Nevertheless, the more in-depth study performed by Haines [1] suggeststhat these fibres present near zero hysteresis in their behaviour after testing with heatingand cooling rates as low as 2C · min−1. Such slow rates were not feasible for this projectin terms of time budgeting as explained in section 2.4.

3.2.2. Fibre response at room temperature

One important aspect of the behaviour of the nylon fibres is their stress-strain behaviourwhen no heat is applied to them. The reason behind the importance of this aspect is that,not only for the actuation of control surfaces, but many other applications, actuators mustbe used in tandem to perform opposite motions. In such configurations, one of the actu-ators will be activated by heat, contracting and generating some force, while elongatingthe opposite actuator, which remains at a neutral temperature. Therefore, in order to ob-tain models of the net force exerted by the actuators in any system, a good model of theirpassive behaviour must be obtained.While the focus of this work was not to obtain such a model, and so many experimentsare lacking for that matter, an attempt to model such behaviour will be made using theavailable data. Figure 3.7 depicts the response of the four testing specimens to varyingloads at room temperature, together with a regression of the data.

43

Fig. 3.7. Elongation vs load curve and regression for each of the test specimens: 1 (top left), 2(top right), 3 (bottom left) and 4 (bottom right).

Equation 3.2 constitutes the regression model utilized for this curves, where ϵ standsfor the elongation and L stands for the load in Newtons. The coefficients were adjustedusing Matlab’s curve fitting tool and are displayed in Table 3.5.

ϵ(L) = a · Lb (3.2)

Specimen number a b1 0.2121 1.7192 0.1463 1.4423 0.06229 24 0.04768 2.913

Table 3.5. REGRESSION COEFFICIENTS FOR COLD RESPONSE

3.3. Behaviour modelling

After all of the tests were performed, the data was processed and analyzed, looking forpossible answers to the irregularities in the data and gaining a general understanding ofhow these fibres perform, some empirical models of their behaviour were obtained. The

44

process has already been described several times through this document, using curvesrelating elongation and temperature at constant loads to construct the surface relatingtemperature, load an elongation. Since during the testing of the fibres it was found thattheir behaviour included hysteresis, and that this is most likely an artificial product of toofast heating and cooling rates, two regressions will be made for each test specimen, onefor heating and another for cooling. Afterwards, both surfaces will be averaged to obtaina single surface for both situations, neglecting the effect of hysteresis.This is due to the fact that, moving forward, not neglecting hysteresis can severely com-plicate the design of the actuator. However, this would be no excuse to neglect suchbehaviour if it was not for the fact that other deeper studies performed in better conditionshave found no hysteresis, which indicates that the behaviour observed in out experimentswas a byproduct of the heating and cooling rates as explained previously.After performing such a regression, it was found that a suitable model for the elongationas a function of the fibre’s temperature and load state was the one described by equation3.3, where ϵ represents elongation, T is the temperature in Celsius and L is the load inNewtons. Once again, the coefficients required for this model were obtained using Mat-lab’s curve fitting tool and are displayed in tables 3.6 and 3.5, for both the heating andcooling curves respectively.

ϵ(T, L) = a + b · L + c · T + d · L2 + e · LT + f · T 2 + g · L2T + h · LT 2 + i · T 3 (3.3)

Specimen 1 Specimen 2 Specimen 3 Specimen 4a -1,326 -0,006099 0,1044 0,393b 1,473 -0,1719 -0,4023 -0,346c 0,03552 0,01497 0,006006 -0,01071d -0,4439 0,137 0,2125 0,196e -0,01072 -0,005966 0,00683 0,001402f -0,0005027 -0,0001731 -0,000204 1,53E-04g 0,004598 0,002302 -0,003425 0,0004229h 1,47E-06 -1,65E-05 4,60E-05 -2,76E-05i 2,38E-06 9,11E-07 5,31E-07 -6,15E-07

R2 0,9931 0,9919 0.9881 0.9969

Table 3.6. REGRESSION COEFFICIENTS FOR THE HEATINGPROCESS

45

Specimen 1 Specimen 2 Specimen 3 Specimen 4a -0,7075 1,126 0,8944 0,411b 1,127 -1,136 -0,9749 -0,4554c 0,01102 -0,01222 -0,01164 -0,007893d -0,2628 0,3881 0,3281 0,2361e -0,008017 0,009606 0,01757 0,00147f -0,0001589 3,17E-05 -0,0001326 9,86E-05g 0,003385 -0,001092 -0,005301 0,0004752h -1,50E-05 -5,26E-05 1,96E-05 -3,32E-05i 9,64E-07 3,06E-07 6,23E-07 -2,43E-07

R2 0,9931 0,9919 0.9881 0.9969

Table 3.7. REGRESSION COEFFICIENTS FOR THE COOLINGPROCESS

Lastly, these coefficients can be combined to obtain the ones that describe the aver-age surface, neglecting hysteresis. Averaging the coefficients for the heating and coolingprocesses and rounding to 4 decimal places gives the results shown in Table3.8.

Specimen 1 Specimen 2 Specimen 3 Specimen 4a -1.0168 0.5600 0.4994 0.4020b 1.3000 -0.6539 -0.6886 -0.4007c 0.02330 0.0014 -0.0028 -0.0093d -0.3534 0.2626 0.2703 0.2161e -0.0094 0.0018 0.0122 0.0014f -0.0003 -0.0001 -0.0002 0.0001g 0.0040 0.0006 -0.0044 0.0004h 0 0 0 0i 0 0 0 0

Table 3.8. REGRESSION COEFFICIENTS NEGLECTINGHYSTERESIS

As it can be seen, the results from Table 2.20 suggest that the dependency of theelongation in the terms L ·T 2 and T 3 from equation 3.3. With the data from the regression,the experimental results for each of the fibres can be represented together with its model,which results in the plots available in Figure 3.8 and 3.9.

As it can be seen from previous plots, forces of the fibers were successful at liftingloads of nearly 2N. However, it was observed that the larger the spring coefficient, themore the fibres struggled to lift such a weight. This means that the strokes attained weresmaller, and the initial elongation of the fibre prior to heating was larger. However, thegeneral tendency is for fibres with larger spring coefficients (Coils larger in diameter) to

46

Fig. 3.8. Elongation vs load curve vs temperature curve and regression model for specimen 1(top) and specimen 2 (bottom)

47

Fig. 3.9. Elongation vs load curve vs temperature curve and regression model for specimen 3(top) and specimen 4 (bottom)

48

generate bigger strokes, deform more under load and generate smaller forces than theircounterparts with smaller spring coefficients, which were twisted during manufacturingunder a much higher load.As an example, specimen 1, which had a spring coefficient of 2.4, was able to attaina maximum stroke over the temperature range tested of 12.07% while lifting a load of1.939N, which generated a strain of 52.618% on the fibre while cold. On the other hand,specimen 4 only attained a stroke of 8.57% under an identical load, with an initial defor-mation of the fibre of 13.75% while cool.It must be noted that, even if the forces generated by these fibers seem small (Of theorder of 1 Newton), they must be compared to the weight of the fibre itself. The ratioof generated force over fibre weight is defined by expression 3.4, where r stands for thefibre’s radius, L f is the length of the fibre and ρ is the density of Nylon, which is 1150 Kg

m3 .Considering the maximum load attained as 2N, which might actually be larger, since noheavier loads were tested, the resulting ratio has a value of over 10000, meaning the fibreis lifting more than 10000 times its own weight. This results shows that, even though themaximum loads attained are small, the very small weight of the fibres, of less than 1 grameach, makes them really attractive for applications that need high force over weight ratios.

Fπ · r2 · L f · ρ

(3.4)

As a final note, one phenomenon that was observed during testing was the fact that,at times, the fibre under testing would end the test longer than it started. This could bea result of overloading the fibre or overheating it, or a combination of both. Neverthe-less, in the study performed by Haines [1], fibres were heated up to almost 200C, so itis unlikely that the amount of temperature is the problem, but rather loading the fibresslightly beyond their capabilities. Nevertheless, after letting the fibres cool down withoutany load attached, the seemed to return to their original lengths. Table 3.9 shows the ini-tial and final lengths of the coils. And it turns out that, in fact, the coils were becomingshorter after testing. This is a promising result, since it implies that after heating the fibresseveral times they are not unwinding themselves and turning into straight fibres insteadof coils again, retaining their springiness and being able to be used again for more cycles.However, further studies are needed to check whether or not this stays true for a highernumber of cycles.

Specimen numberCoil length (Initial)

[mm]Coil length (Final)

[mm]Spring coefficient

[-]1 91.76 85.3 2.42 114.5 109.5 2.13 119.3 112.8 1.94 131.5 120 1.64

Table 3.9. INITIAL AND FINAL LENGTHS OF THE FIBRES AFTERTESTING

49

4. AIRCRAFT ACTUATOR DESIGN

Along this section, the mathematical models and other information obtained over pastsections will be utilized to do a preliminary sizing of the an actuator based in the nylonartificial muscles studied during this project. In order to do this, the first step will beto define the problem, or in other words, define the worst case scenario in which theseactuators will be used and size them for that precise situation.

4.1. Problem definition

Consider the diagram depicted in Figure 4.1 of a cross section of a wing with a trailingedge device such as an aileron, which is the primary control surface the actuator will bedesigned for.

Fig. 4.1. Actuator configuration inside of a wing + aileron setup

The following elements have been depicted in diagram 4.1:

• Main wing, with chord c

• Aileron, of length 0.2 · c, placed at 0.8 times the chord of the main wing.

• Two artificial nylon muscle actuators of length L, in a configuration such that eachof them allows the deflection the aileron in one direction. For simplicity, the leverarm of this actuators will be consider as constant and equal to dimension r depictedin the figure, which is just half the thickness of the airfoil at the aileron’s hinge.

It must be noted that these actuators make sense in an aircraft using a turbofan/tur-boprop/turbojet engine, since they work by taking advantage of the hot air coming fromthese high mass-flow engines while it might make sense to use it in aircraft using piston-cylinder engines, these are typically smaller aircraft that are better of using just mechani-cal links to the pilot’s controls.That being said, the typical aircraft using such kinds of engines are commercial aviationaircraft. This is an important point since it will define the flight conditions and the aero-dynamic characteristics of the airfoil. Such aircraft operate at speeds close to Mach 1, andmake use of a very particular kind of airfoils called supercritical airfoils. Taking this into

50

consideration, the aerodynamic hinge moment coefficient for such kinds of airfoils mustbe found. According to a paper published by NASA [5] the hinge moment coefficient foran aircraft of those characteristics is almost linear and follows the expression found inequation 4.1:

Ch =−7 · δ850

−77

425(4.1)

Which was developed under the following conditions:

• High aspect ratio, supercritical wing with midspan control surface located at 0.8c

• Angle of attack of the main wing α = 0.8

• M = 0.8

• Altitude of 14021 meters

• Dynamic pressure q = 6.31kPa

These are flight conditions similar to those found by commercial aircraft during cruis-ing. By estimating the maximum amount of force the actuator will need to do in thissituation, the actuator can be scaled. In order to do so, the angle with the highest mag-nitude of the hinge moment coefficient in the interval tested by NASA, (-5 - 12) degrees,which is the typical range of deflection angles for such a control surface. The angle thatyields the highest aerodynamic moment is 12 degrees, yielding a hinge moment coef-ficient Ch = −0.28. The definition of the hinge moment coefficient utilized by NASAshould be recalled at this point:

Ch =H

q · S f · cav(4.2)

Where:

• Ch is the aerodynamic hinge moment coefficient

• H is the aerodynamic hinge moment

• S f is the control surface area

• cav is the average control surface chord

These values can be estimated by using a top view of Boeing 737 and its wingspan,then applying similarity between the actual measurements of the aircraft and the image tofind the values of S f and cav. The top view of the aircraft is shown in Figure 4.2, whichhas a wingspan of 34.31 m.

51

Fig. 4.2. Top view of a B737-900

After finding the relative dimensions of the ailerons with respect to the wingspan ofthe aircraft, the results were the following:

• cav is 1.31% of the wingspan, or 0.45m

• sav is the span of the control surface, which is 9.37% of the wingspan, or 3.21m.

• S f = 1.44m2

Using this data, the maximum torque needed can be calculated using equation 4.2, toyield a result of H = −1148.86N · m.

In order to find out the number of fibres needed, one of the test specimens from lastssections must be selected. The one selected will be number 4, since it provides the largestload bearing capabilities with the least amount of strain, which in this case is desirablesince the amount of space inside the wing is limited. In order to find how many of themare needed, the thickness of the airfoil at the hinge needs to be found. Assuming theratio between the chord of the wing and its thickness is similar between the airfoil studiedby NASA and the one used in the Boeing 737 (Which is reasonable, since they are bothsupercritical airfoils), the thickness is of 12% the local chord, which results in tav =cav0.2 · 0.12 = 0.27[m]. Since the torque generated by any force is just force multiplied bylever arm, the required net force by the actuator is:

F =Md=−1148.86

0.27= −4255.037N (4.3)

Since both actuators operate in tandem, one of them will actually work opposing to thedesired operation of the control surface. Ignoring this fact for a moment, and assuming

52

only one actuator is working towards achieving the required deflection angle, and that therequired force must be 25% of the total force the actuator is able to exert, total amountof fibres required is of around 8500 fibres. Assuming these fibres are similar to testspecimen one, then the weight of this actuator will be of around 5.44 Kg. And if twoof them were used in tandem, the total weight will be of only 10.88 Kg. While thesefigures are definitely not the final weight of the actuator, since the torques correspondingto the passive actuator pulling on the aileron and the torque generated by the weight ofthe control surface itself were not considered. Moreover, the weight of all of the conduitstaking hot air from the engine’s compressor must be added.Nevertheless, this data is difficult to obtain for an actual aircraft. In order to obtain thetorque generated by the opposing actuator, the strain of such actuator needs to be obtained,and in order to do that the length of the artificial muscle needs to be chosen. But thiscannot be done without information of the internal structure of the wing and the spaceavailable for the actuators, and that is proprietary information that is not available for thegeneral public.Moreover, as it was seen in previous sections, the data obtained from the muscles is notof the best quality, which means that any attempt at trying to design an actuator based onthis data will result in unsatisfactory results that are far from reality.These circumstances motivated the decision to leave the design of such actuator for furtheriterations of the project, when better data of the muscles and of the aircraft its use isintended for are available.

53

5. CONCLUSION

After the study performed during this project, some conclusions can be drawn fromeach of the steps involved in the process: Test bench design and build, testing and fibrebehaviour and actuator design.Regarding the design and build of the test bench, it was established since the very begin-ning that the experimental results obtained using such a cheap, homemade constructionwere not going to be comparable to the ones that could be obtained using high-end lab-grade equipment. however, such equipment was not available for the realization of thisproject, so designing and manufacturing the machinery became a necessary part of it.That being said, it was surprising to see that the main flaws of the system can be tracedback to their root and turn out to be simple mistakes that can easily be solved. In partic-ular, the biggest flaw of the design was the inaccuracy of the temperature control. Thisissue was the one that had the biggest impact in the final experimental results, togetherwith a too fast heat cycle. Some suggestions can be made in order to solve these issues:The main control board needs to be debugged to fix any mistakes present in the phase an-gle control section of the circuit, which was indeed designed, manufactured and presentin the board that has been used for the project. Phase angle control was discarded dueto safety and data noise reduction considerations, in order to solve those issues, the mainboard would need to be split into two boards, one controlling the data acquisition andanother one controlling the power management. By dividing these tasks in two differentboards, and setting them apart in the test bench, the noise level due to high power linesrunning nearby the data acquisition section of the circuit would be reduced. Moreover,by ordering these boards to a professional manufacturer who can comply with all thesafety requirements, Phase Angle control could be used and the temperature cycle couldbe much more tightly controlled.In addition to poor cycle control, one of the main issues was the supposedly artificialhysteresis introduced in the response of the artificial muscles due to too high heating andcooling rates. There is no way to know whether this is actually an artifact of the way theexperiments were conducted or not unless further testing at lower rates are performed.However, such tests would be of no use if the issue with the temperature control is notsolved first. This remains as a task for future iterations of the project as performing suchlong lasting experiments is outside the time budget for the present work.As a final note regarding the test bench manufacturing, the performance of the elongationsensor developed during this project was surprisingly good. The need to design this sen-sor raised due to the failure of commercially available load cells, and ended up becominga stronger alternative to the first option. While it introduced some noise into the outputdata, this could be easily removed by using filters, not corrupting the rest of the data.More testing is required to define the limits of what this sensor can do, as the deficienttemperature control of the system already messed with the experiments, so that origin of

54

the noisy data is uncertain.Regarding the test results, it must be said that the data obtained through the tests per-formed is not quite as good as it needs to be in order to develop an accurate mathematicalmodel of the behaviour of the fibres. Even though the quality of the data was probablynot good enough, the rest of the project was developed as an academic exercise which isstill applicable and of interest, and can serve as an example for similar projects utilizingbetter data. The relationship between the load state vs elongation vs temperature curvesand the spring coefficient and diameter of the fibres remains as a task for future projectsand developments. Doing so would require many more tests that could not be performedduring the given project, and even if they had been performed, the resulting data wouldprobably not be good enough to extract an adequate mathematical relationship linking allof the variables.Regarding the last step of this project, the design of an actuator based on this artificialmuscles could not be performed due to the lack of information about the wing of theaircraft and the poor quality of the data obtained. However, an estimation of the aerody-namic loads over an aileron were made, showing that the forces required to operate suchcontrol surfaces are definitely within reach of these nylon fibres. If specimens similar tothe ones studied in this work, a few thousand of them would be required, but taking intoaccount that each of them weights under 1 gram, the total weight of the actuator is of theorder of a few kilograms, demonstrating the feasibility of such technology as a competi-tive alternative to current actuators.Lastly, regarding the implementation of such a new technology into actual aircraft, it mustbe said that it is unlikely. This is due to the fact that any new development in the aerospaceindustry needs to go through extensive testing in order to asses the reliability and safetyof implementing such developments. Even though regulations are strict, and will pose anobstacle to the implementation of such technology, it is physically doable, since bleed airfrom the engine’s compressor is already used for a number of tasks in the aircraft, such asheating up the leading edge of the wing to melt and prevent ice. Ram air scoops also existthat allow outside air to flow into the aircraft. All in all, all of the supporting equipmentnecessary to use these fibres is already designed and has been previously tested, whichwill make the hypothetical implementation of this solution much more straightforward.

55

BIBLIOGRAPHY

[1] C. S. Haines et al., “New twist on artificial muscles.”, Proceedings of the NationalAcademy of Sciences of the United States of America, vol. 113 42, 2016.

[2] J. Roskam, Airplane design. DARcorporation, 2003.

[3] C. A. Harper, Handbook of plastics, elastomers, and composites. McGraw-Hill,2002.

[4] Tcrt5000 ir sensor datasheet, 2019. [Online]. Available: https://www.vishay.com/docs/83760/tcrt5000.pdf.

[5] B. Perry III, “Control-surface hinge-moment calculations for a high-aspect-ratiosupercritical wing”, NASA Technical Memorandum, vol. 78664, 1978.

[6] T. B. Company, 737 -600/-700/-800/-900 Operations manual. The Boeing Com-pany, 1997.

[7] G. R. Arce, Nonlinear signal processing. Wiley, 2005.

[8] J. S. Steinhart and S. R. Hart, “Calibration curves for thermistors”, Deep Sea Re-search and Oceanographic Abstracts, vol. 15, no. 4, pp. 497–503, 1968. doi: 10.1016/0011-7471(68)90057-0.

[9] A. L. Sánchez and J. Rodríguez-Rodríguez, Fluid Mechanics: an Introduction andsome Relevant Applications. Carlos III University of Madrid, 2011.

[10] Arduino language reference page, 2019. [Online]. Available: https : / / www .arduino.cc/reference/en/.

APPENDIX A: ELECTRICAL SCHEMATIC OF THE CONTROLBOARD

APPENDIX B: ARDUINO CODE FOR TEST BENCH OPERATION

1 //Libraries

2 #include "TimerOne.h"

3 #include <NTC_Thermistor.h>

4

5 //Hardware pin definitions

6 //Digital

7 int button = 3;

8 int buzzer = 13;

9

10 //Analog

11 int thermOne = A0;

12 int thermTwo = A1;

13 int slider = A7;

14

15

16 //Logic aux variable definitions

17 byte flag = 0;

18 byte backwards = 0;

19 byte marker = 0;

20 byte marker2 = 0;

21 int testNum = 1;

22

23 //Heating cycle timing definitions

24 long preTime = 750;

25 long offsetTime = 750;

26 unsigned long startTime = 0;

27 unsigned long heatTime = 480000;

28 unsigned long coolTime = 240000;

29

30 //Thermistor characteristics

31 #define thermNominalOne 106100

32 #define thermNominalTwo 113600

33 #define tempNominal 21.78

34 #define bCoeff 3799

35 #define seriesRes 30100

36

37 NTC_Thermistor* hotTherm = NULL;

38 NTC_Thermistor* coldTherm = NULL;

39

40 //Physical variables initialization

41 int powerOut = 9;

42 float strain = 0;

43 unsigned short dutyCycle = 0;

44 unsigned short rawTempOne = 0;

45 unsigned short rawTempTwo = 0;

46 float tempOne = 0;

47 float tempTwo = 0;

48

49

50

51 void setup()

52

53

54 Serial.begin(9600); // Initialize Serial Port for data transmision

55

56 Timer1.initialize(200000); // initialize timer1, and set a

1/2 second period

57 Timer1.pwm(powerOut, dutyCycle); // setup pwm on pin 3, 0% duty

cycle

58

59 //Declare thermisto objects

60 hotTherm = new NTC_Thermistor(

61 thermOne ,

62 seriesRes ,

63 thermNominalOne ,

64 tempNominal ,

65 bCoeff

66 );

67

68 coldTherm = new NTC_Thermistor(

69 thermTwo ,

70 seriesRes ,

71 thermNominalTwo ,

72 tempNominal ,

73 bCoeff

74 );

75

76 pinMode(button, INPUT); //Push button as an Input

77

78 Serial.print("TestNumber");

79 Serial.print("\t");

80 Serial.print("Time");

81 Serial.print("\t");

82 Serial.print("TempOne");

83 Serial.print("\t");

84 Serial.print("TempTwo");

85 Serial.print("\t");

86 Serial.print("Strain");

87 Serial.print("\t");

88 Serial.println("Power");

89

90

91

92 void loop()

93 while ((hotTherm->readCelsius() < 180) && (coldTherm ->readCelsius

() < 180) && (hotTherm ->readCelsius() > 0) && (coldTherm ->

readCelsius() > 0))

94 flag = 0;

95

96 if (millis() <= preTime)

97 //scale.read();

98 startTime = millis();

99 //Serial.println("Primando...");

100

101

102 else if ((millis() > preTime) && ((millis() - preTime) <=

offsetTime))

103 while (flag == 0)

104 if (digitalRead(button) == HIGH)

105 delay(750);

106 flag = 1;

107

108

109 if (marker == 0)

110 for (int k = 0; k < 20; k++)

111 //meanLoad = meanLoad + scale.read();

112 if (k == 19)

113 //meanLoad = meanLoad / (k+1);

114

115

116

117 while ((flag == 1) && (marker == 0))

118 if (digitalRead(button) == HIGH)

119 delay(750);

120 flag = 0;

121 marker = 1;

122

123

124 startTime = millis();

125 /*Serial.print("Start time: \t");

126 Serial.println(startTime);*/

127

128

129

130 else if ((millis() > (offsetTime + preTime)) && ((millis() -

startTime) <= heatTime))

131 dutyCycle = (millis() - startTime)*0.00041667;

132 Timer1.pwm(powerOut, dutyCycle);

133 readData();

134

135

136 else if (((millis() - startTime) > heatTime) && ((millis() -

startTime) <= (coolTime + heatTime)))

137 dutyCycle = 200 - ((millis() - startTime) - heatTime)

*0.00083333;

138 Timer1.pwm(powerOut, dutyCycle);

139 readData();

140

141

142 else if (((millis() - startTime) > (coolTime + heatTime)) && (((

hotTherm ->readCelsius() + coldTherm ->readCelsius())/2) > 34)

)

143 dutyCycle = 0;

144 Timer1.pwm(powerOut, dutyCycle);readData();

145 marker2 = 1;

146

147

148

149 else if (((millis() - startTime) > (coolTime + heatTime)) &&

(((hotTherm->readCelsius() + coldTherm ->readCelsius())/2) <

34) && marker2 == 1)

150 while (flag == 0)

151 tone(buzzer, 1000, 500);

152 delay(500);

153 dutyCycle = 0;

154 if (digitalRead(button) == HIGH)

155 delay(1000);

156 testNum = testNum + 1;

157 flag = 1;

158 marker2 = 0;

159 preTime = offsetTime + millis();

160

161

162

163

164

165

166

167

168

169

170

171

172 //Emergency stop in case thermistor is disconnected or reading

extreme values:

173

174 for (int i = 1; i < 2; i++)

175 Serial.println();

176 Serial.println();

177 Serial.println();

178 Serial.println("HALTED");

179 flag = 1;

180

181 while (flag == 1)

182 tone(buzzer, 800, 100);

183 delay(100);

184 if (digitalRead(button) == HIGH)

185 flag = 0;

186 delay (500);

187

188

189 while (1)

190

191

192

193

194

195 void readData()

196 rawTempOne = analogRead(thermOne);

197 rawTempTwo = analogRead(thermTwo);

198

199 tempOne = hotTherm->readCelsius();

200 tempTwo = coldTherm ->readCelsius();

201

202 strain = analogRead(slider)* -0.05924 + 54.41;

203

204 Serial.print(testNum);

205 Serial.print("\t");

206 Serial.print((millis() - startTime));

207 Serial.print("\t");

208 Serial.print(tempOne);

209 Serial.print("\t");

210 Serial.print(tempTwo);

211 Serial.print("\t");

212 Serial.print(strain);

213 Serial.print("\t");

214 Serial.println(dutyCycle);

215

216

217 /*

218 void readData()

219

220

221 strain = analogRead(slider)* -0.05924 + 54.41;

222

223

224 Serial.println(strain);

225

226 */

APPENDIX C: ARDUINO CODE FOR MUSCLE COILEROPERATION

1 const int stepPin = 10;

2 const int enablePin = 4;

3 int flag = 0;

4 long stepNum = 0;

5 int button = 7;

6

7 void setup()

8 // put your setup code here, to run once:

9 pinMode(stepPin, OUTPUT);

10 pinMode(enablePin , OUTPUT);

11 Serial.begin(9600);

12 pinMode(button, INPUT_PULLUP);

13

14

15 void loop()

16 // put your main code here, to run repeatedly:

17 while (flag == 0)

18

19 for(int j = 0; j<2; j++)

20 digitalWrite(enablePin , LOW);

21

22

23 digitalWrite(stepPin, HIGH);

24 delayMicroseconds(4);

25 stepNum = stepNum + 1;

26 digitalWrite(stepPin, LOW);

27 delayMicroseconds(20);

28

29 if (digitalRead(button) == LOW)

30 flag = 1;

31 delay(500);

32

33

34

35

36 while (flag == 1)

37

38 for(int i = 0; i < 2; i++)

39 digitalWrite(enablePin , HIGH);

40 Serial.println();

41 Serial.print("Number of turns");

42 Serial.print("\t");

43 Serial.println(stepNum / 3200);

44

45

46 if (digitalRead(button) == LOW)

47 flag = 0;

48 delay(500);

49

50

51