Experimental Investigation of Rolling Losses and Optimal Camber and Toe Angle

Home , Camber angle, Toe (automotive)

BETHUEL KARANJA ELIN SKOOG

Bachelor Thesis Stockholm, Sweden 2015

Experimental Investigation of Rolling Losses and Optimal Camber and Toe Angle

Bethuel Karanja Elin Skoog

Bachelor Thesis MMKB 2015:68 MKNB 079 KTH Industrial Engineering and Management Machine Design SE-100 44 STOCKHOLM

Bachelor Thesis MMKB 2015:68 MKNB 079

Experimental investigation of rolling losses and optimal camber angle

Bethuel Karanja Elin Skoog Approved Examiner Supervisor 2015-06-05 Ulf Sellgren Kjell Andersson Commissioner KTH Transport Labs/ Peter Georén

Abstract This Bachelor thesis project is an experimental investigation of the effect of camber and toe angles on rolling resistance. The experiments are done on Sleipner, a Prototype car made by KTH students, which takes part in the Shell Eco Marathon competition in Rotterdam. In order to succeed in the competition it is crucial to reduce energy losses in order to get an as energy efficient vehicle as possible. The experiment involves tests where Sleipner is manually dragged across a flat floor and its position and the dragging force are logged with a pulse encoder and a load cell respectively. This is done ten times for each chosen wheel alignment (specific camber and toe angle), in order to be able to find the optimal setting with respect to minimization of rolling losses. The tests are performed in the Integrated Transport Research Lab at KTH. The obtained data is then used to calculate the magnitude of the rolling friction. It is found that the more negative the camber angle, the larger the rolling resistance. The smallest camber angle investigated is -3º which gives a coefficient of rolling friction (Cr) of 0.0052. The second camber angle is -5º giving a Cr value of 0.016 and the largest camber angle is -7º giving a Cr value 0.019. It was also found that, with the minimum camber angle, toe out gives a larger coefficient of rolling resistance than toe in; 0.0081 compared to 0.0052. The report also delves into additional effects of camber and toe angles on the vehicle’s behaviour while driving and it is found that negative camber angle gives better stability in the car when cornering and that toe in gives better stability in straight line driving. With these results it is concluded that Sleipner should have a slight camber angle of -3º and toe in of 0.5º so as to have the best results in the Shell Eco Marathon.

Keywords: Camber, Toe, Rolling resistance, Shell Eco Marathon

Examensarbete MMKB 2015:68 MKNB 079

Experimentell undersökning av rullmotstånd och optimal camber och toe vinkel

Bethuel Karanja Elin Skoog Godkänt Examinator Handledare 2015-06-05 Ulf Sellgren Kjell Andersson Uppdragsgivare KTH Transport Labs/ Peter Georén Sammanfattning Detta kandidatexamensarbete i maskinkonstruktion är en experimentell undersökning av hur camber och toe- vinkeln påverkar rullmotstånd. Testerna är gjorda på Sleipner, ett fordon utvecklats av studenter på KTH, som tävlar i Prototyp-klassen i Shell Eco Marathon som hålls i Rotterdam i maj. För att få ett så energisnålt fordon som möjligt är det naturligtvis av största vikt att minska alla olika typer av förluster så mycket som möjligt. En stor del av dessa förluster är förluster som sker för att överkomma rullmotstånd, som i sin tur är beroende av många olika faktorer. Målet med undersökningen var att kunna ge en rekommendation på den optimala vinkelinställningen på Sleipner inför årets tävling.

Testerna som bedömdes ge det bästa resultatet var dragtest, då Sleipner drogs med handkraft över ett platt golv. Dragkraften registrerades med en kraftgivare fastsatt centrerat på ramen och en pulsgivare på bakaxel registrerade positionen. Den data som registrerades användes för att kunna räkna ut storleken på rullmotståndet. För varje vald inställd vinkel, både camber och toe, så drogs Sleipner tio gånger över golvet, fem gånger i varje riktning. Detta för att kunna räkna ut medelvärden och på så sätt minska osäkerheten i resultaten. Alla tester utfördes i Integrated Transport Lab på KTH. Resultaten visade att ju större negativ camber vinkel, desto större blev rullmotståndet. Den minsta camber vinkeln som undersöktes var -3º, vilket gav en rullmotståndskoefficient (Cr) på 0.0052. Nästa camber vinkel som prövades var -5º, vilket gav Cr till 0.016 och den sista vilken var -7º och det resulterade i Cr-värde på 0.019. När den bästa camber vinkeln funnits, så utfördes tester med toe out, vilket visade att toe out gav ett större värde på rullmotståndet än toe in, Cr på 0.0081 jämfört med 0.0052. Rapporten behandlar vidare andra effekter av camber och toe-vinklar, såsom inverkan på fordonet under körning. Det visar sig att negativ camber vinkel ger bättre stabilitet, speciellt vid kurvtagning, och toe in ger bättre stabilitet vid körning rakt fram. Med de resultat som erhölls resulterade i en rekommendation på att Sleipner skulle ha camber vinkel på -3º, och toe in på runt 0.5º för att kunna uppnå bästa resultat i tävlingen. Nyckelord: Camber, Toe, rullmotstånd, Shell Eco Marathon

PREFACE

Here we thank some people that have been important to us during this project.

We would like to acknowledge some people that have been especially important to us in order to succeed in this project. Firstly, we would like to thank our supervisor, Kjell Andersson, Professor in Mechanical Engineering, for his constant help, guidance, support and good feedback during the whole process. Secondly, we would like to extend our thanks to Mikael Hellgren, Research Engineer at KTH Transport Labs, for his invaluable help and advice with the preparations for the experiments, and his mechanical knowledge. We also extend our thanks to all the students that have been part of the KTH Team for the Shell Eco Marathon competition this year. They have been an inspiration to us and it has been a pleasure working together with them. Last but not least we thank all the sponsors that have made the KTH EcoCars project possible.

Bethuel Karanja Elin Skoog

Stockholm, June 2015

NOMENCLATURE

In this chapter are presented the symbols and abbreviations that are used throughout this report.

Notations

Symbol Description Unit

Cr Coefficient of rolling resistance - g Gravitational acceleration m/s2 m Mass kg

2 mj Equivalent mass of moment of inertia kg m

Cd Coefficient of air resistance - F Force N

FR Rolling resistance force N

Fd Air resistance force N α Camber Angle degrees (º) β Toe Angle degrees (º) s Distance m ṡ Speed m/s s̈ Acceleration m/s2 t Time s ρ Density of air kg/m3 A Frontal area m2

Abbreviations

SEM Shell Eco Marathon ITRL Integrated Transport Research Lab VI Virtual Instrument u.d. Unknown date

TABLE OF CONTENTS

PREFACE ...... 5

NOMENCLATURE ...... 7

TABLE OF CONTENTS ...... 9

1 INTRODUCTION ...... 11 1.1 Background ...... 11 1.2 Purpose ...... 11 1.3 Delimitations ...... 11 1.4 Method ...... 11

2 FRAME OF REFERENCE ...... 13 2.1 Shell Eco Marathon ...... 13 2.2 Rolling resistance ...... 14 2.2.1 Camber Angle ...... 15 2.2.2 Toe Angle ...... 15 2.2.3 Results from previous studies ...... 16 2.3 Equations ...... 17

3 THE PROCESS ...... 19 3.1 Preparation and Calibration of the instruments ...... 19 3.2 Changing and measuring of camber and toe angles ...... 20

4 RESULTS ...... 23

5 DISCUSSION AND CONCLUSIONS ...... 27 5.1 Discussion ...... 27 5.2 Conclusions ...... 28

6 RECOMMENDATIONS AND FUTURE WORK ...... 29 6.1 Recommendation ...... 29 6.2 Future work ...... 29

7 REFERENCES ...... 31

APPENDIX - SUPPLEMENTARY INFORMATION ...... 33 Appendix A: Data sheet for the tires ...... 33 Appendix B: Data sheet for the load cell ...... 34 Appendix C: Calibration of the load cell...... 35 Appendix D: Data sheet for the pulse encoder ...... 36 Appendix E: Listed results from the experiments ...... 38 Appendix F: Matlab code ...... 40

1 INTRODUCTION

In this chapter the background, purpose, limitations and the method that has been used to carry out to the project are presented.

In an average vehicle, about 20 percent of the energy from the fuel goes towards overcoming rolling resistance. On SEM vehicles this percentage can be as high as 70%. As such, it is very important to reduce rolling resistance as much as possible. (Michelin 2015)

1.1 Background Sleipner is a car that is raced by KTH students in the Shell Eco Marathon competition. Every year students work on it to make it as effective and fuel efficient as possible. Since its introduction 2011 several significant changes have been made to its original design. These include changing from a combustion engine to a hydrogen fuel cell and DC motor, replacing the original chassis and replacing the drive train. This year the focus lies in further reduction of rolling losses with the aim of making the car even more fuel efficient.

1.2 Purpose The aim of the project is to investigate the effect of both camber and toe angle on the rolling losses of Sleipner. Tests will be performed to investigate if there exists any relationship between the wheel alignment (camber angle and toe angle) and the rolling losses. The goal is that at the end of the experimental investigation, a recommendation be made on the optimal camber and toe angle for racing in the Shell Eco Marathon. Concisely put, this project aims to answer the following questions:  Is there a relationship between camber angle and rolling resistance?  Is there a relationship between toe angle and rolling resistance?  If so, what relationship is it?  Can a combination of camber and toe angle be chosen to give the minimum amount of rolling resistance?

1.3 Delimitations As the goal of the study is to determine the effect of different camber and toe angles, only the angles of the two front wheels of Sleipner have been investigated. The camber angles that are going to be investigated are -3º, -5º and -7º and toe angles are -0.5º and 0.5º. For an explanation of why these specific angles were chosen, see section 3.2. The report focuses on rolling resistance while driving straight forward as a big part of the track involves straight line driving. The project does not include any kind of re-designing, changes in the type of wheels or changes in the wheel suspension. Only optimization under the given conditions is considered.

1.4 Method A dragging experiment will be performed on a flat surface in order to determine the magnitude of the rolling friction. At low velocities, the wind resistance should be negligible compared to the rolling friction (including losses due to vibrations, mechanical losses in bearings etc.). For this experiment, a load cell will be mounted on a stand that will be attached to the car frame. The cell registers the force that Sleipner will be drawn with and it is important that the pulling force is parallel to the direction of the velocity. This is so that all of the force acting on the car is 11 registered by the cell. The car is dragged manually with a string tied to the load cell. A pulse encoder will be used to log the position of the car. The logging will be done at a rate of 100 Hz. Using equation (6) the rolling friction can then be calculated.

This experiment will be performed in the ITRL garage at Drottning Kristinas Väg 40. This location is chosen because it offers a relatively flat floor, it is indoors thereby protected from the wind and it offers quick access to the tools necessary in changing the wheel alignment.

The different camber angles to be tested are about -3°, -5°, and -7°. Ten tests will be done on each angle. This allows for the calculation of average values and aims to reduce the absolute error in the results. When all these tests have been done, the angle resulting in the least rolling resistance will be used as basis for new experiments with different toe angles. The car starts out with toe in and once the best camber has been determined toe out will also be tested.

2 FRAME OF REFERENCE

In this chapter are presented the theoretical relevant facts and information that form the basis for the task specified in the introduction. The information was mainly obtained in a literature study done before the testing started.

2.1 Shell Eco Marathon Shell Eco Marathon is a worldwide competition that challenges students to design, build and drive very energy-efficient vehicles. The goal of the competition is to go the furthest with the least amount of fuel. Every year three events are held; one in America, one in Asia and the last in Europe. This year’s European event is the 30th anniversary for the competitions and will take place in Rotterdam, the Netherlands, from the 21st to the 24th of May. It is estimated that the event will draw about 230 teams and 3000 students from all across Europe. The same track that has been used for the last 3 years will be used again. The circuit is a rather level urban track with five 90° turns. A lap on the track is 1.6 km and in order to qualify a vehicle must cover 10 laps, that is 16 kilometres, in less than 39 minutes, which gives an average speed of 25 km/h. The track has varying width ranging from roughly 6 to 10 metres. See Figure 1.

Figure 1. An aerial illustration of the track in Rotterdam. (Shell u.d.)

The competition is divided into two classes: Prototype and Urban Concept. In the Prototype class focus lies on maximum efficiency with passenger comfort all but disregarded. In the Urban Concept class more practical designs are encouraged. Competing vehicles are categorized by energy type. Internal combustion engines include petrol, diesel, natural gas and ethanol. There is also an electric mobility category that includes vehicles powered by hydrogen fuel cells and lithium based batteries.

On top of on-track awards, off-track awards are also given to recognise achievements such as safety, teamwork and design. The last few years KTH has been competing in the prototype class with Sleipner, which now is driven by a fuel cell and DC-motor.

2.2 Rolling resistance

Rolling resistance, also known as rolling friction, refers to the resistive force that acts on a body rolling on a surface, and is often calculated according to equation (1)

FRr C  m  g (1)

2 where Cr is a coefficient of rolling resistance, g the gravitational acceleration of 9.81 m/s and m the mass of the object. In this report we use the term ‘rolling losses’ to refer to the sum of rolling resistance and the energy losses due to friction in the bearings, vibrations and other moving connections. The rolling resistance is primarily linked to the deformation of the tire while rolling. Losses occur since the energy required to deform the part of the wheel in contact with the surface is more than that recovered when that part reverts to its original shape. The energy lost is dissipated as heat. This effect is known as hysteresis. In addition to this, rolling resistance is also dependent on other various factors such as the wheel alignment, the deformation of the surface, the normal force and the tire type. Due to this complexity, the rolling resistance, and its coefficient, is usually determined experimentally. (Kurtus 2015) (Michelin 2015)

Figure 2 below is taken from Tire Digest, a website published by Michelin, and shows the components and their contribution to the rolling resistance in the tires of a car.

Figure 2. Constituents of rolling resistance. (Michelin 2015)

The coefficient of rolling friction is proportional to the normal pressure and the width of the wheel and inversely proportional to its radius. It also increases with the surface of contact. (Peck 1859)

For the SEM competition, Michelin has especially developed an ultimate energy-efficient tire, which they claim is about five times more energy efficient than the best tires available for standard passenger cars. (Michelin 2015) All three of Sleipner’s tires are of this type. For more information on the tires, see appendix A.

2.2.1 Camber Angle

As stated above, the rolling friction is dependent on the wheel alignments. Camber angle refers to the angle, usually measured in degrees, between the vertical axis of the wheels and the vertical axis of the vehicle. If the top of the wheel leans inwards towards the axle, the wheel is said to have negative camber. Conversely, if the top leans outwards, away from the axle, the wheel is said to have positive camber. This is illustrated below in Figure 3. (Hagerman 2014)

Figure 3. Illustration of negative and positive camber angle. (Blue River Fleet Service Inc. u.d.)

Camber thrust refers to a force perpendicular to the direction of motion that is generated when a leaning and rotating tire, that would normally follow an elliptical path if no other force was applied, is forced to move in a straight line. Camber thrust is proportional to the camber angle. (Foale 2006) Negative camber angle is widely employed in vehicles as it gives good handling characteristics. Particularly, during heavy cornering, negative camber angle gives an increased contact patch between the tire and the ground thereby improving grip. Negative camber does however have its disadvantages. Firstly, during straight-line acceleration, wheels with negative camber have a smaller contact area with the ground than wheels with zero camber angle. Secondly, camber thrust, which when both wheels are on the ground cancels itself out, becomes a problem when either of the wheels loses grip causing the vehicle to steer towards that wheel. Positive camber is rarely used as it reduces the handling capability of the vehicle. (Viking Speed Shop 2015) Both positive and negative camber angles are disadvantageous in that they cause uneven tire wear; negative camber on the inside of the wheel and positive camber on the outside. (Yonehara 2013)

2.2.2 Toe Angle

Toe, also called slip angle, refers to the angle between the longitudinal axis of the wheels and that of the vehicle. If the front of the wheel points towards the centre of the vehicle, the wheels are said to have positive toe or toe in. If the front of the wheels point outwards then the wheels have negative toe or toe out. See Figure 4.

Figure 4. Illustration of toe in and toe out. (Shole 2013)

Toe in causes the wheels to continuously push against each other which offers better straight line driving stability but reduces turning ability. Toe out on the other hand decreases straight line stability but offers better cornering ability. This is because when turning around a bend, the inner wheel will be angled more than the outer and since its turning radius is smaller it pulls the vehicle in that direction. This can however be disadvantageous during straight line driving as the slightest deviation in direction will cause the car to pull towards that side. (Yonehara 2013)

2.2.3 Results from previous studies

According to a study conducted by John Yurko on behalf of the U.S. Environmental Protection Agency, minimum rolling losses are observed when one has a 0° toe angle (Yurko 1978). Following is a graph from the data obtained in his experiments.

Figure 5. Rolling resistance coefficient vs slip angle.

Andrea Quintarelli, a vehicle engineer, has conducted a study that concludes that the more negative camber a vehicle has, the larger the rolling resistances (Quintarelli 2011). His observation however was that the variation was so small that it could be considered negligible for all intents and purposes.

2.3 Equations

According to a report written in 2014 for another KTH car that takes part in SEM, Utveckling av Mätmetoder för färdmotstånd, an equation of force can be written as 1 F(mm)smgC  A C (s) v2  m g sin (2) j r2 d where F is the dragging force, m the mass of the vehicle, mj the equivalent mass of the moment of inertia, s the change in speed, g the gravitational force, Cr the coefficient of rolling resistance,  the density of air, A the frontal area, Cd coefficient of air resistance, s the speed, v the wind speed in the direction opposite to that of the car and  the angle of inclination of the surface. (Eqbal och Grönvik 2014) In the case of Sleipner and other lightweight vehicles, mj is small in comparison to the total mass of the vehicle, and as such the approximation m + mj ≈ m can be done. Due to difficulties in measuring the wind speed, it is further assumed that the test will take place in a windless environment, and hence v=0. The equation (2) can then be rewritten 1 F m(s g sin )  m g C A C s2 . (3) rd2

Equation (3) can be simplified further if the test track is flat and without any height differences, then the term g sin ≈ 0. This leads to 1 F m  s  m  g  C    A  C  s2 . (4) rd2

The acceleration s can be obtained as the derivative of the velocity or as the second derivative of the covered distance, which can be obtained from the pulse encoder connected to the rear axis.

One problem that is encountered during a free rolling outdoor experiment is the influence of the air resistance, which will affect the test results. Therefore, a dragging experiment at low velocity on a fairly flat surface will be done. When the velocity s is low, the influence of the air 1 resistance is negligible in comparison to the rolling resistance, thus  A  C  s2 m  g  C , 2 dr and equation (4) can be written

F m  a  m  g  Cr . (5)

From equation (1), the rolling resistance can be calculated as

FRr m  g  C  F  m  a (6)

where FR denotes the rolling resistance force.

From equation (6) it can be seen that F m a C  . (7) r mg

3 THE PROCESS

This chapter describes the actual process according to the method presented in chapter 1.4. 3.1 Preparation and Calibration of the instruments

Firstly, a control of both the inner and outer existing wheel bearings on both sides was done. It was noticed that the old bearings that had been used for several years were worn out and needed to be replaced with new ones. The tests were done with the old bearings, due to a delayed delivery time on the new bearings.

Sleipner was also weighed in order to find its mass to be used in the equations.

In order to measure the pulling force, a load cell with an operational range of 0-2 kg was used. See appendix B for more detailed information on the load cell. As the cell gives a very low voltage output it was connected to an instrumentation amplifier. The cell was then supplied with a voltage of 5 volts and it gave an analog signal varying from slightly above 0 V to slightly below 5 V depending on the force applied. To calibrate the load cell, different masses varying from 100 g to 2 kg were used. A linear regression model was then applied to the results to obtain an equation for the relationship between force and output voltage. The results from the calibration, see Table 2, and the accompanying equation can be found in appendix C.

To measure distance traveled an incremental pulse encoder was used, see appendix D for detailed information on the pulse encoder. The encoder was fastened at the rear of the vehicle, connected through an O-ring to a disk mounted on the rear axle. The diameter of the disk and the outer diameter of the O-ring resulted in a speed ratio of 4.3. This information along with the knowledge that the encoder gives 2500 pulses with every revolution of its axle and that the wheel diameter is 0.478 m can be used to calculate distance travelled according to equation (8)

N sd4.3 p   (8) np where s is the travelled distance, Np the number of pulses recorded, np the number of pulses per revolution (which is 2500 in this case), and d the diameter of the wheel. Once the distance travelled is calculated, the speed can be calculated as the first derivative of the distance. This is done according to equation (9) which is a central-difference formula of second order

ssii11 si  (9) ttii11 where t is the time at sampling number i.

The acceleration can thereafter be calculated from equation (10) as the second order time derivative of the distance as follows

si112 s i s i si  2 . (10) ((ttii11 ) / 2)

The signals from the load cell and the encoder are acquired through the use of a multifunctional DAQ. The DAQ acquires the signal data through a developed LabVIEW VI and logs it in

19 spreadsheet format. In this format the data can then be accessed by a Matlab script where the necessary calculations are done. This script can be found in appendix F.

The connections and setup of the measuring instruments are shown in Figure 6.

Figure 6. Circuit description for the measuring instruments.

The positioning of the instruments in the car is as follows in Figure 7.

Figure 7. The set-up of the instruments in the car. The green arrow shows the direction of the dragging force.

3.2 Changing and measuring of camber and toe angles

On Sleipner, the wheel sits on a steering knuckle that is connected to the car frame through two bolts; one above the wheel’s rotational axis and one below. See Figure 8. By inserting or removing washers on either of the bolts the camber angle can be changed. It was the thickness of these washers that dictated the camber angle attained. To achieve a camber angle smaller than -3º it would have been necessary to insert more than one washer and this would not have left any room for the nut to secure the bolt. Toe angle is changed by adjusting the length of the tie rods. This is done by changing how much the tie rod end is screwed onto the rod.

Figure 8. Two images showing the steering knuckle, bolts, washer and tie rod.

The camber angle was measured by standing a spirit level next to the wheel and manually holding it perpendicular to the ground. A ruler was then used to measure the distance, parallel to the ground, between the spirit level and the top of the tire. Finally the trigonometric relationship between this distance and the wheel diameter was used to calculate the angle. See Figure 9. To control the accuracy of this method, the width of the washer introduced, or removed, was measured and the expected change in angle was calculated. Both methods gave the same results.

Figure 9. Illustration showing how the camber angle was measured, wheel seen from behind.

Toe angle was calculated by measuring the distance between the back of both wheels and the distance between their fronts, Figure 10. The trigonometric relation between the difference of these distances, together with the wheel diameter, was used to calculate the toe angles.

Figure 10. Illustration showing the method used to measure toe angle, wheels seen from above.

4 RESULTS

In this chapter results from the experiments conducted are presented, analysed and compared to the existing knowledge and theory presented in the frame of reference chapter.

The weighing of Sleipner gave a mass of 37 kg, including the weight of the computer used to log the data, and this was the mass used in all of the calculations. Figure 11 below shows a graph of the data obtained from one of the tests. The graph includes curves for distance, force and acceleration.

Figure 11. Example graph from one of the tests.

Data recorded in the last five seconds of each try is disregarded as other external forces used to stop the car come into play. Data also obtained in the first one and a half seconds is also disregarded as focus lies on the region with relatively constant speed.

The experiments conducted showed that the more the camber angle the higher the coefficient of rolling resistance. They also show that toe out produces more rolling resistance than toe in. These results are presented in the following Table 1.

Table 1. Results obtained from the experiments.

Camber angle in Toe angle in degrees Average force [N] Average coefficient degrees of rolling resistance (Cr)

– 3 0.5 2.34 0.005187

– 5 0.5 5.28 0.01579

– 7 0.5 6.31 0.01945

– 3 – 0.5 3.28 0.008114

Figure 12 below is a chart that shows the minimum, average and maximum Cr values for each of the wheel alignments. As can be seen the variation for each wheel alignment is relatively small. For the values from each test see appendix E.

Coefficient of rolling friction 0,025

0,02

0,015 C r Minimun Value 0,01 Average 0,005 Maximum

0 -3º, 0.5º -5º, 0.5º -7º, 0.5º -3º, -0.5º Camber and toe angle respectively

Figure 12. Variation in Cr value for each of the wheel alignments.

It was observed that when force and acceleration were calculated they had noise and it was decided that a filter should be used. A second order Butterworth filter with a cut-off frequency of 10 Hz was chosen. It was observed that a delay occurs in the filtered data. This delay affects both the force and the acceleration signal in the same way so no additional adjustment needs to be made before or during the calculation for the coefficient of rolling resistance. Figure 13 below is an example from one of the tests, showing both a filtered and an unfiltered signal.

Figure 14 is a zoomed in segment of Figure 13 to better show the difference between the filtered and unfiltered signals. Figure 15 shows the corresponding plot of the acceleration.

Figure 13. Plot showing both the filtered and unfiltered force signals.

Figure 14. Zoomed in segment.

Figure 15. Showing both the filtered and unfiltered acceleration signals.

Despite the obvious difference in amplitude between the filtered and unfiltered acceleration signals, the Cr values calculated from the two signals are very similar. In the case shown above for example the filtered acceleration gives a Cr value of 0.005378 while the unfiltered one gives a Cr value of 0.005356. This is just a 0.4% difference.

5 DISCUSSION AND CONCLUSIONS

This chapter presents an analysis, discussion and summary of the results presented in the previous chapter. The aim is to answer the questions presented in chapter 1.

5.1 Discussion The camber angle is measured to the closest degree and the toe angle to the closest half degree. This was the accuracy allowed by the measuring methods used. This is not a problem as the focus of the report is on the overall pattern of the relationship between wheel alignment and rolling resistance and not on the absolute values of each test. It would have been interesting to conduct tests with 0º camber angle but as previously stated it was impossible to set up this angle. Achieving a toe angle of 0º was also tried but we were unsuccessful. This is because toe was very sensitive to the winding of the tie rod ends. The first peak seen on the force curve is to be expected, this is because a relatively large force is required to overcome static friction so as to accelerate the car from a stationary position. (Nave 2009) The rest of the peaks seen on the curve are caused in part due to the unevenness of the floor where the car was dragged. To compensate for this, the car was dragged 10 times for each wheel alignment, five times in one direction and five in the other. With the data collected it can be checked whether the assumption that air resistance is negligible is correct. The highest speed the car was drawn with was 0.68 m/s2. Given that there was no wind in the garage during the test, the air resistance can be calculated according to 1 F   A  C  s2 (11) dd2

3 2 where ρ is the density of air, using 1.225 kg/m , A the frontal area of the car, is 0.4 m and Cd the drag coefficient of the car, is 0.16 (Alagic 2011). The frontal area and drag coefficient of Sleipner are obtained from a report written by students who had worked with the car before. This gives an air resistance of 0.018 N. The lowest coefficient of rolling resistance obtained is 0.0052 and this gives a rolling resistance of 1.89 N. What this shows is that air resistance during the tests was less than 1% of the rolling resistance. We deem this to be indeed negligible. The results obtained show an increase in rolling resistance with an increase in the camber angle. We believe that this is caused by the change in contact area, and therefore deformation of the tire, caused by the change in camber angle. This pattern agrees with what was learned from the literary study. The difference in the coefficient of rolling resistance calculated for the different wheel alignments is quite large however. The largest coefficient is about four times as large as the smallest. This is in disagreement with the theory presented in chapter 2. One possible source of error is how tightly the lug nuts were wound on the wheels. It was discovered that tightly winding the nuts caused the wheels to spin with resistance. When conducting the experiment we aimed to avoid this but it is possible that it played a role. It is however unlikely as we repeated the tests several times and we kept getting the same results. Another possible source of error is that during the tests it was sometimes required that the person walking alongside the car steer it so as to avoid collision with other objects in the garage. This could have given rise to external forces but as the instances where this was necessary were evenly spread out among the tests it should not have an effect on the overall trend. Upon investigation of the data acquired it was realized that the force measured has a resolution of 0.0114 N whereas the acceleration has a resolution of 1.7·10-14 m/s2. Given the car’s mass of 37 kg, an increase in force by just 6.29·10-12 N would be needed to cause an increase in acceleration by 1.7·10-14 m/s2. What this means is that the equipment used will at times register

27 change in acceleration while still showing that the force is constant. This can be a source of error in the results. It is also likely that some slippage occurred between the wheel and the encoder causing the distance travelled to be measured incorrectly. Once again however, these phenomena affect all the data in the same way and as such it should not have an effect on the overall trend. The load cell gives a voltage output that is converted into force by the use of linear regression. This means that a line of best fit is used to approximate how much force the voltage output represents. Upon inspection it was found that the point that lies furthest from this line shows an error in force of 0.5N. This is quite large considering that it is 2.5% of the pulse encoder's scale. This point however is at the 20 N mark, a force never reached during the experiment. The point in the operational area that gives the largest error is 0 N mark with an error of 0.36 N. This is an equivalent of 1.8% of the operational scale. This is also still quite large. One possible way of solving this problem is by finding a better non-linear model for converting voltage to force. This report does not go into it but leaves it as a suggestion for future work. All in all, as the tests were performed several times and gave the same results each time, we are confident that our results hold up. An important factor that affects rolling losses in the car is the bearings used. While conducting the experiments it was realized that the ball bearings then in use were rather old and had deteriorated in quality. New bearings were ordered but their delivery time was not within the time frame of this project. Even though they will be replaced before the competition, it would have been interesting to test how replacing them will affect the rolling losses. It is to be expected that the old bearing have more friction than new ones. When changing the camber angle, the whole steering knuckle is adjusted so that the wheel retains the same contact area with the bearings. This means that the bearings remain properly loaded and are not misaligned which otherwise could have been a reason as to why more camber angle gives more rolling resistance. When it comes to the running of the car, rolling losses is not the only factor that is important. Stability in the vehicle must also be considered, and attained. The literary study has shown that a more negative camber angle offers more stability in the car, especially when cornering. With this this in mind a balance must be struck between low rolling resistance and stability in the car. We would recommend a camber angle of -3º as this gives quite low rolling resistance while still offering stability (Viking Speed Shop 2015). The literary study also showed that toe out offers better cornering response in contrast to toe in. Toe in does however offer better stability in straight line driving and as shown by our tests it gives less rolling resistance. According to Yurko’s report, a toe angle of 0º gives the least resistance but increasing to 0.5º should only cause a very slight increase (Yurko 1978). We believe that this compromise should be made in order to increase straight line driving stability. Considering that most of the track is straight and that the car has a turning radius well within the specified bounds, toe in is recommended.

5.2 Conclusions The investigation carried out has shown that there does indeed exist a relationship between camber angle and rolling resistance. The more negative the camber angle the larger the rolling resistance. It has also been observed that there exists a relationship between toe angle and rolling resistance. Toe in produces less rolling resistance than toe out. As such, to minimize rolling losses a combination of very little camber, if any at all, and toe in should be used on the car. However, for practicality it is recommended that a little camber should be used, even if this increases rolling resistance, it offers more stability on the vehicle.

6 RECOMMENDATIONS AND FUTURE WORK

In this chapter recommendations for more detailed, and possibly more accurate, solutions are presented, as well as ideas on possible future work.

6.1 Recommendation It would be recommended to anyone conducting an experiment similar to this one that they use more than just one form of measurement for acceleration. One could for example also employ an accelerometer in conjunction with the pulse encoder. Alternatively, a magnetic speed sensor could be used. Conducting the tests on flatter, more even floor and dragging the car over a longer stretch is also recommended. As noted in the discussion above, finding a better method of interpolation when converting voltage to force would improve the accuracy of the tests.

6.2 Future work There are still improvements that can be made on Sleipner. One of the sides of the fork that holds the rear axle is crooked. This leads to the gear wheel on the axle not aligning perfectly with the gear drive and thereby reduces the efficiency of the gear ratio. Moreover, the gear wheel is bent and it has bad tolerances. This combined with the fact that it is made of plastic and wears easily must lead to a significant decrease in efficiency. It is our recommendation that all this be fixed before next year’s competition. A better steering wheel design should be considered. The one currently employed makes it hard for the driver to steer and brake as there is very little room left for turning the steering wheel. A better design should also make it easier for the driver to enter and exit the car. This would especially be convenient in case of emergencies when the driver needs to be quickly removed from the car. If KTH wishes to compete with Sleipner in the hydrogen class again, a new fuel cell should be considered since the one that has been used these last two years is plagued with problems such as leakage. Lastly, as previously stated in this report, it was noticed that tightly winding the lug nuts on the wheel impeded the spinning of the wheel. In a proper construction this should not happen. For the wheels to spin without resistance the nuts had to be wound quite loosely and this is likely not safe, especially when the car is driving at higher speeds. We would strongly recommend that this problem be investigated and solved.

7 REFERENCES

Alagic, Almir et. al. "Fuel Cell Based Driveline fro Sleipner." Stockholm, 2011. Blue River Fleet Service Inc. Alignment Service. n.d. http://www.blueriverfleet.com/alignment.htm (accessed June 1, 2015). Eqbal, Qudus, and Gabriel-Andre Grönvik. "UTVECKLING AV MÄTMETODER FÖR FÄRDMOTSTÅND." Stockholm, 2014. Foale, Tony. Motorcycle Handling and Chassis Design. Alicante: Tony Foale Designs, 2006. Hagerman, John. "Smithees Race Car Technologies." 2014. http://www.ozebiz.com.au/racetech/theory/align.html (accessed March 26, 2015). Kurtus, Ron. "Rolling Friction." School for Champions. March 11, 2015. http://www.school-for- champions.com/science/friction_rolling.htm#.VRkWKPmUd8E (accessed March 30, 2015). Michelin. Ultimate Energy Tire. 2015. http://thetiredigest.michelin.com/michelin-ultimate- energy-tire (accessed April 1, 2015). Nave, Carl R. Hyperphysics. 2009. http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html (accessed May 11, 2015). Peck, William Guy. Elements of Mechanics: For the Use of Colleges, Academies, and High Schools. New York: A. S. Barnes & Burr, 1859. Quintarelli, Andrea. "DrRacing." November 13, 2011. https://drracing.wordpress.com/2011/11/13/camber-and-rolling-resistance/ (accessed May 6, 2015). Shell. Location and track. n.d. http://www.shell.com/global/environment- society/ecomarathon/events/europe/location-and-track.html (accessed June 1, 2015). Shole, Adrian S. Tips for Tyres. December 21, 2013. http://www.rfactor-racers.com/t1009-tips- for-tyres (accessed June 01, 2015). Viking Speed Shop. "Viking Speed Shop." February 20, 2015. http://www.vikingspeedshop.com/suspension-101-camber-caster-and-toe/ (accessed March 26, 2015). Yonehara, David. "Yospeed.com." February 19, 2013. http://yospeed.com/wheel-alignment- explained-camber-caster-toe/ (accessed March 26, 2015). Yurko, John. "United States Environmental Protection Agency." July 1978. http://nepis.epa.gov/Exe/ZyPDF.cgi/9100WY1W.PDF?Dockey=9100WY1W.PDF (accessed March 26, 2015).

APPENDIX - SUPPLEMENTARY INFORMATION

Appendix A: Data sheet for the tires

Appendix B: Data sheet for the load cell

Appendix C: Calibration of the load cell

Table 2. Values obtained from the calibration

Load mass [kg] Output Voltage [V] 0 0.095 0.1 0.195 0.2 0.420 0.3 0.645 0.4 0.873 0.5 1.100 1.0 2.245 1.2 2.695 1.4 3.145 1.5 3.375 2.0 4.283

A linear regression model resulting in the values for y a  b  V to be a 0.00653 and V  0.4554 . This gives the equation for converting the analogue voltage signal obtained from the load cell to force to be FV(  0.00653  0.4554  )  g where V denotes the voltage given from the load cell.

Appendix D: Data sheet for the pulse encoder

The model used in the experiments was RSI 503 61.

Appendix E: Listed results from the experiments All the test data can be obtained in excel-files from ITRL if requested.

Camber -3 degrees, toe in 0.5 degrees

Test number Average Force [N] Average coefficient (Cr) 1 2.83 0.005773 2 2.51 0.005888 3 2.69 0.005354 4 2.71 0.005135 5 2.43 0.005380 6 1.97 0.004671 7 1.94 0.004530 8 2.13 0.005192 9 2.18 0.004844 10 2.10 0.005106 Total average for all tests 2.34 0.005187

Camber -5 degrees, toe in 0.5 degrees

Test number Average Force [N] Average coefficient (Cr) 1 5.24 0.01548 2 5.15 0.01574 3 5.32 0.01603 4 5.17 0.01518 5 4.73 0.01470 6 5.23 0.01626 7 5.08 0.01546 8 5.59 0.01672 9 5.61 0.01617 10 5.65 0.01612 Total average for all tests 5.28 0.01579

Camber -7 degrees, toe in 0.5 degrees Test number Average Force [N] Average coefficient (Cr) 1 6.22 0.02026 2 5.69 0.01890 3 6.53 0.01948 4 6.82 0.01948 5 6.23 0.01965 6 6.25 0.01934 7 6.10 0.01889 8 6.27 0.01916 9 6.16 0.01944 10 6.81 0.01988 Total average for all tests 6.31 0.01945

Camber -7 degrees, toe out 0.5 degrees

Test number Average Force [N] Average coefficient (Cr) 1 3.35 0.009375 2 3.54 0.008258 3 3.17 0.007747 4 3.41 0.008717 5 3.28 0.007717 6 3.15 0.007325 7 3.07 0.007656 Total average for all tests 3.28 0.008114

Only seven tests were included in these calculations, since three of the tests were discarded due to technical problems.

Appendix F: Matlab code

%Bachelor's project Bethuel Karanja & Elin Skoog %Experimental Investigation of Rolling Losses and %Optimal Camber and Toe Angle clear all,close all, clc, format long; diameter=0.478; %wheel diameter ratio=86/20; ppr=2500; %pulses per revolution mass=37; % mass of Sleipner g=9.81; meanCr=[]; meanForce=[]; [b,a] = butter(2, 10/(100/2)); %second order butterworth filter for i=1:10 x=strcat('Sheet' ,num2str(i)); data=xlsread('newtest1',x); %datasheet voltage=data(:,1); counter=data(:,2); velocity=[]; acceleration=[]; accUnfiltered=[]; time = [0:0.01:(length(voltage)-1)/100]; forceUnfiltered=(-0.0065266+0.4554274*voltage)*g; force=filter(b,a,forceUnfiltered); %force filter meanforce=mean(force); meanForce=[meanForce meanforce]; distance= (0.478*pi/(ratio*ppr))*counter; for i=2:length(distance)-1 vel=(distance(i+1)-distance(i-1))/0.02; velocity=[velocity vel]; end for i=2:length(distance)-1 acc=(distance(i+1)-2*distance(i)+distance(i-1))/(0.01^2); accUnfiltered=[accUnfiltered acc]; end acceleration=filter(b,a,accUnfiltered); force=force(201:end-500); acceleration=acceleration(201:end-500);

Cr=(force(2:end-1)-mass*acceleration')/(mass*g); Coeff=mean(Cr); meanCr=[meanCr Coeff]; end meanForce=meanForce' Overall_meanForce=mean(meanForce) meanCr=meanCr' Overall_meanCR=mean(meanCr)