DEGREE PROJECT IN MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2019
Simulation of CamDrum for Shock Absorbers
ADAM OLSSON
ANDERS RASK
KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT
Simulation of CamDrum for Shock Absorbers
ADAM OLSSON ANDERS RASK
Master of Science Thesis KTH Industrial Engineering and Management Machine design SE-100 44 Stockholm Supervisor: Ulf Sellgren Industrial Supervisors: Carl Hesse & Andreas Bolin Examiner: Ulf Sellgren Approved: 2019-06-12
TRITA-ITM-EX 2019:249
Master of Science Thesis TRITA-ITM-EX 2019:249
Simulation of CamDrum for Shock Absorbers
Adam Olsson Anders Rask Approved Examiner Supervisor 2019-06-12 Ulf Sellgren Ulf Sellgren Commissioner Contact person Öhlins Racing AB Carl Hesse Abstract Simulation can play an important role when aiming to streamline extensive and time-consuming tests. It has the potential to save time, money and energy. One of the testing methods used to test shock absorbers (SA), is accelerated life testing using a rolling road, CamDrum. It is therefore of great interest to examine the possibilities to streamline this testing method. This master the- sis is conducted in co-operation with Öhlins Racing AB and the Machine Design department at KTH.
The thesis project aims to look into the following: How can the use of simulation software aid in streamlining the test sequence used for shock absorbers in CamDrum? What limitations is there when simulating the CamDrum method using the selected simulation soft- ware?
The goal was to develop an adequate model according to specified requirements, to facilitate early testing of new ideas and parameter changes. The delimitations includes, that the project only fo- cuses the test-rig for MTB shock absorbers, the parts of the test-rig are assumed to be rigid and the simulation of the shock absorber is out of scope, since the aim of this thesis is to simulate the test-rig.
To succeed with the project, a background research was conducted to gain knowledge about shock absorbers, test method and equipment, dynamics and useful software. The simulation model was verified against data obtained from tests. The tests were performed using the CamDrum with two different MTB shock absorbers and a stiff rod. The aim was to log and verify the change in position for the test-rig, shock absorbers and wheel. In addition the forces acting on the shock absorbers was investigated using strain gauges attached to the test-rig.
The mean deviation in % for configuration 70-30-30 [mm] bump: SA MTBM1899, A4: 11.6% - 23.2%. SA MTB1691, A4: 15.8% - 28.1%. Stiff rod, A3: 0.9% - 4.9%, A5: 2.0% - 5.1%. SA Force, 16.1% - 24.0%.
The deviation between the simulation and the test environment increases with the velocity. The use of stiff rod verifies the model against the CamDrum regarding the displacement. The resulting force from the use of strain gauges verifies the simulation models force regarding the shape. The Amesim model has the potential to be of great aid when designing tests.
Keywords : Amesim, Computer Aided Engineering, Rolling road
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Examensarbete TRITA-ITM-EX 2019:249
Simulering av CamDrum för stötdämpare
Adam Olsson Anders Rask Godkänt Examinator Handledare 2019-06-12 Ulf Sellgren Ulf Sellgren Uppdragsgivare Kontaktperson Öhlins Racing AB Carl Hesse
Sammanfattning Simulering kan vara en väg till att effektivisera tidskrävande och omfattande tester. Det finns poten- tial att spara såväl energi som tid och pengar. En av metoderna för att testa stötdämpare är rullande landsväg, CamDrum. Det är därför intressant att undersöka hur den processen kan effektiviseras. Examensarbetet utförs i samarbete mellan Öhlins Racing AB och institutionen för Maskinkonstruk- tion på KTH.
Det här examensarbetet avser att undersöka följande: Hur kan användandet av simuleringsprogram underlätta effektivisering av testmetoden som används för stötdämpare i CamDrum? Vilka avgränsningar finns vid användande av simulering för CamDrum-metoden med valt simule- ringsprogram?
Målet var att utveckla en modell som uppfyller givna krav och underlättar vid initieringsfasen för utveckling av tester för CamDrum. Projektets avgränsningar innebär att enbart riggen för MTB- stötdämpare undersöks, alla ingående komponenter i testriggen antas styva och dämparmodellen som utvecklats är förenklad då målet är att simulera riggen för dämparen.
För att lyckas med uppgiften har en förstudie genomförts för att samla nödvändig kunskap om stötdämpare, dynamik, testmetoden och lämplig mjukvara. Simuleringsmodellen verifieras mot data hämtat från utförda tester. Testerna utfördes i CamDrum med två olika MTB-stötdämpare och en rundstång med mål att logga och verifiera rörelser för riggen, stötdämpare och hjulet. Vidare har krafterna på stötdämparen undersökts med hjälp av trådtöjningsgivare monterade på testriggen.
Medelavvikelsen i % för guppkonfigurationen 70-30-30 [mm]: SA MTBM1899, A4: 11.6% - 23.2%. SA MTB1691, A4: 15.8% - 28.1%. Rundstång, A3: 0.9% - 4.9%, A5: 2.0% - 5.1%. SA Force, 16.1% - 24.0%.
Avvikelsen mellan simuleringen och testerna ökar med hastigheten. Användandet av rundstången verifierar modellen gentemot CamDrum med avseende på positions- förändring. Den resulterande kraften från användandet av trådtöjningsgivare verifierar simuleringsmodellen med avseende på form. Amesim-modellen har en möjlighet att underlätta vid framtagning av tester.
Nyckelord: Amesim, CAE, Rullande landsväg
v
Preface
We would like to thank the following persons for aiding and guiding us during this thesis, the final result would not have been the same without their expertise.
Carl Hesse for acting as the head supervisor on site and for making sure we got the help and material needed to perform this thesis. Ulf Sellgren at KTH for being our supervisor and guiding us with a firm and steady hand. Andreas Bolin for acting as the overall knowledge on site and our first contact when we needed assistance.
Niklas Klinteskog for aiding us with the use of strain gauges and providing MAT- LAB scripts for extracting the results from the logged data.
David Bolander, Jonas Jarlmark Näfver & Michel Chapuis for their valuable help with Amesim and damper dynamics. Johan Jarl, Erik Nordgren & Pär Åslund for helping us in designing tests and analysing results for the MTB dampers used in this thesis.
Lars Karlsson for his sharp mind, helping us making it to the end.
Fredrik Hedin and Mathias Raine for help with analysis of damper result with their broad experience within the subject.
Peter Stridh, Christoffer "Glassen" Andersson, Björn Meland och Tobias Karlsson for helping us disassemble dampers, running tests in the dynos, tips and trix and keeping the office environment cheerful.
And all other people that have been involved in this thesis.
Adam Olsson Anders Rask Stockholm, June, 2019
vii
Contents
Abstract iii
Sammanfattning v
Preface vii
Contents ix
Nomenclature xiii
1 Introduction 1 1.1 Background ...... 1 1.1.1 Purpose and Goals ...... 2 1.1.2 Requirements ...... 2 1.2 Delimitations ...... 3 1.3 Methodology ...... 3
2 Frame of reference 5 2.1 Shock absorbers ...... 5 2.1.1 Rebound/Compression ...... 5 2.1.2 Hysteresis - Internal components inertia ...... 6 2.1.3 General design features regarding shock absorbers ...... 7 2.2 Front fork ...... 8 2.3 Rear shock absorber ...... 10 2.4 Sprung and unsprung mass ...... 12 2.5 Tyre damper profile ...... 13 2.6 Linear transducer ...... 13 2.7 Strain gauges ...... 14 2.8 CamDrum ...... 15 2.9 Dyno ...... 17 2.10 Simulation software ...... 18 2.10.1 Simulink ...... 18 2.10.2 Simcenter Amesim ...... 19 2.10.3 MSC Adams ...... 21
ix 2.10.4 BikeSim ...... 22
3 Implementation 23 3.1 Possible solution strategies ...... 23 3.2 Test configuration ...... 24 3.3 Shock absorber #1 - MTBM1899 ...... 27 3.4 Shock absorber #2 - MTB1691 ...... 28 3.5 Stiff rod ...... 29 3.6 Tyre model ...... 30 3.7 Amesim model ...... 32 3.7.1 Detailed description of the assembly components ...... 36 3.8 Linear Transducers ...... 39 3.9 Strain gauge ...... 40 3.10 Verification ...... 44 3.10.1 Amesim versus Linear transducers ...... 44 3.10.2 Amesim versus Strain gauges ...... 45
4 Results 47 4.1 Displacement result ...... 47 4.1.1 MTBM1899 ...... 48 4.1.2 MTB1691 ...... 50 4.1.3 Stiff rod ...... 52 4.2 Force result ...... 54
5 Discussion and conclusions 57 5.1 Discussion ...... 57 5.1.1 Displacement ...... 58 5.1.2 Force ...... 59 5.1.3 General possible sources of error ...... 60 5.2 Conclusions ...... 61
6 Recommendations and future work 63 6.1 Recommendations ...... 63 6.2 Future work ...... 64
Bibliography 65
Appendices
A Risk Management 69
B Test configurations 71
C Pugh Matrix - Simulation Softwares 73
x D Stiff rod drawing 75
E Drawing of modified rod for strain gauge 77
F Drawing of test-rig 79
G Drawing of installation fixture to camdrum 81
H Bump drawing 83
I Strain gauge specification sheet 85
J Complementing displacement results MTBM1899 87
K Complementing displacement results MTB1691 93
L Complementing Force results 99
M MATLAB - Linear transducers 107
N MATLAB - Stiff rod 113
O MATLAB - Force script 117
P MATLAB - TSA for linear transducers 121
Q MATLAB - Force mean and percentage 123
R MATLAB - Theoretical maximum bending stress 125
S MATLAB - Tyre spring calculation 127
xi
Nomenclature
Symbols
Symbols Description c Damping constant [Ns/m] g Gravity costant [m/s2] k Spring constant [N/m] m Mass [kg] x1 Displacement of body 1 [m] x˙ 1 Velocity of body 1 [m/s] 2 x¨1 Acceleration of body 1 [m/s ] x2 Displacement of body 2 [m] x˙ 2 Velocity of body 2 [m/s] 2 x¨2 Acceleration of body 2 [m/s ] p Displacement of ground [m] p˙1 Velocity of body ground [m/s] 2 p¨1 Acceleration of ground [m/s ]
Abbreviations Abbreviation Description 1D-3D 1-3 Dimensions A3-A5 Analog03 - Analog05 CAD Computer Aided Design CAE Computer Aided Engineering DoF Degrees of Freedom EOM Equations of motion HMI Human-Machine Interface KTH Royal Institute of Technology MTB Mountain bike OEM Original Equipment Manufacturer SA Shock Absorber TSA Time-synchronous signal average UI User Interface
xiii
Chapter 1
Introduction
In this chapter the background, delimitation and methodology is introduced and stated.
1.1 Background
The following thesis work was conducted in co-operation with Öhlins Racing AB in Upplands Väsby north of Stockholm. Öhlins develops and manufactures advanced suspension technology for OEM (Original Equipment Manufacturer), racing and af- termarket, for both automotive and the motorcycle industry. It was founded in 1976 by Kenth Öhlin and today Öhlins is one of the leading companies within advanced suspension technology.
One of the tests performed when developing shock absorbers at Öhlins is CamDrum (Rolling road). It basically consists of a rotating drum with attached bumps, acting on a wheel connected to either a test-rig or a real motorcycle/MTB (Mountain bike) frame causing the shock absorber to oscillate. The test is extensive and is intended to act as an accelerated life test. The test can take up to a 100 hours and only one CamDrum exists on site. It is therefore interesting to look into how to avoid running unnecessary tests. One way of doing this could be to simulate the test, acting as a first iteration to see if a change in parameters has the intended effect. Therefore, this thesis looks into the possibility of mirroring the CamDrum test in a virtual environment.
1 CHAPTER 1. INTRODUCTION
1.1.1 Purpose and Goals The purpose of this thesis work is to investigate the possibility to simulate variation in length for a given damper at an early stage of testing depending on the input parameters, such as load, rebound, compression, tyre stiffness etc. The advantage would be that instead of running time-consuming actual tests at every change of input parameters, an initial test could be performed in a simulation environment to see the resulting motion. The simulation model has to be verified to mirror the CamDrum.
The goal of the thesis project is to develop an adequate model according to the spec- ified requirements to facilitate early testing of new ideas and parameter changes. This has the potential to save time, money and energy for the company and hope- fully contribute to the engineering society. Further the goal is to investigate which simulation software that is suitable to use for this type of simulation.
The thesis project aims to look into the following:
How can the use of simulation software aid in streamlining the test sequence used for shock absorbers in CamDrum?
What limitations is there when simulating the CamDrum method using the selected simulation software?
1.1.2 Requirements These requirements were based on the discussions between the project members, engineers and supervisors of what a reasonable result should be in order to find usage for the outcome of this thesis.
1. A mean of 10 percentage deviation from measured data using linear transduc- ers for the shock absorber displacement.
2. The shock absorbers parameters should be easily changed in the simulation.
3. User-friendly interface within the simulation software.
4. Be able to change the test-rig dimensions to be able to try different setups.
5. Be able to run the simulation on a regular office computer without the use of an external computational server.
6. A maximum force deviation for the force through the shock absorber of 10 percentage.
2 1.2. DELIMITATIONS
1.2 Delimitations
• Verification stages only includes, the force transmitted through the shock absorber, stroke, wheel axle vertical movement and angular movement of the upper beam (2) in CamDrum, see Figure 3.1.
• MTB shock absorber - This thesis will focus on a newly developed test-rig (swingarm) for mountain bike rear shock absorbers. Within the verification phase two different types of shock absorbers will be tested.
• MTB front fork - The MTB front fork was decided to be left out after con- sidering the time frame of this thesis.
• Testing method - The task is to design a simulation model of the CamDrum test equipment, also known as rolling road. This implies that it is the testing method that should be simulated.
• All parts of the test-rig is assumed to be rigid.
• Damper model will not be fully investigated as this project aims to simulate the CamDrum and not a specific damper.
• A simplified tyre model will be used and no thorough investigation of how the tyre model affects the results will be conducted.
1.3 Methodology
1. Background research In order to succeed with this project, a thorough background research is needed. This includes previous thesis within the subject[Nord, 2018], research on shock absorbers, simulation software, linear transducers, strain gauges, dis- cussions with engineers working with the CamDrum and learn to run tests in the CamDrum. In addition a risk analysis was performed to raise awareness of risks and the potential consequences, which can be seen in Appendix A.
2. Comparison and selection of simulation software A number of different simulation software will be investigated to find the one most suitable for the task at hand.
3. Introduction to new software Selected simulation software, WinARace, NX etc.
4. Build initial simulation model To fulfil the requirements and purpose of the task introduced earlier, an initial simulation model will be built in order to understand what data is needed from the test-rig. There is also a waiting queue to access the test equipment needed to run the tests. Furthermore, this will provide a better understanding of the
3 CHAPTER 1. INTRODUCTION
software and make the connection between the virtual and real environment clearer.
5. Run tests for damper type #1 Setup and conduct tests with linear transducers in CamDrum. Run tests in a dynamometer in order to get damper curves, for the damper used in the tests, to use as input data for the simulation model.
6. Verification/Tuning - First iteration When the initial CamDrum model has been designed in the simulation envi- ronment, the results will be compared with the results from the linear trans- ducers extracted from running the CamDrum. The model will be investigated and tuned to eliminate errors, to mirror the CamDrum. Depending on the accuracy of these tests, different action will be taken in order to understand and improve the results.
7. Run tests for damper type #2 To get more data, another damper type with a different total- and stroke length, will be used. For this test, strain gauges will be added together with the linear transducers, to be able to verify the force difference between real world and simulation. In accordance to damper type #1, damper curves will be extracted using the dynamometer and used for the simulation model.
8. Verification/Analysis In accordance with the previous mentioned verification phase above. Further iterations and tuning will be performed. Also, strain gauges will be used to investigate the forces on the shock absorber.
9. Documentation All data and results from the tests performed in the CamDrum, dynamometer and simulation model will be saved, documented and made available.
4 Chapter 2
Frame of reference
In this chapter, the frame of reference for this thesis project can be found. The aim has been to gather knowledge necessary to perform the tests and analysis required for this project. In addition, focus has been on subjects that is recognised by an engineer but still unexplored for most.
2.1 Shock absorbers
Shock absorbers are widely used in vehicles and other dynamic applications. It consists of a spring and damper configuration, where the spring handles the force applied and the damper handles at which speed the shock absorber compress and decompress. In Figure 2.1 a common configuration is shown with a regular steel spring revolving around the damper. The main purpose of a shock absorber is to cancel out irregularities in the surface that the application is acting upon. This is fulfilled by the shock absorber through its ability to absorb the energy, transforming it to heat. This to make the ride as smooth as possible for the different applications possible [Dixon, 2007].
Figure 2.1: Typical shock absorber [VitalMTB, 2019].
2.1.1 Rebound/Compression To get the intended and wanted behaviour of the damper, different damping forces depending on speed and direction is often advantageous. Thus, depending on what
5 CHAPTER 2. FRAME OF REFERENCE displacement direction, two different terms are used to more easily know which di- rection is addressed. Compression - when the length decreases. Rebound - when the length increases. In general a shock absorber has five settings when it comes to adjusting the compression and rebound behaviour. Three of them are, high speed compression damping, low speed compression damping and rebound damping. The settings are usually specified as number of clicks, the zero position is defined as when the adjustment screw is fully turned clockwise. Meaning that a setting of low speed compression of six clicks is defined as six clicks counterclockwise from max amount of clicks clockwise. The high speed compression damping adjustment mechanism exists as either a knob, turning screw or a lever. While low speed compression damp- ing and rebound damping adjustments is usually set using a knob or turning screw. In general, turning the adjuster for the compression damping and rebound damp- ing clockwise increases the compression damping and rebound damping respectively.
The stroke length is specified for each damper by a maximum length the damper is able to move freely. The spring rate directly affects the total stroke, the higher spring rate, the higher load required to achieve the same stroke. The spring rate is defined as Newton per millimetre [N/mm] and is considered as one of the main parameters that controls the behaviour of a shock absorber together with the preload [N/mm]. The preload is adjusted by turning the nut that holds the spring in place.
2.1.2 Hysteresis - Internal components inertia
The phenomena of hysteresis can be described as the dependency of the current states history. It is either naturally present in a system or built in on purpose. Hysteresis has the potential to be of both positive and negative character. To avoid a borderline behaviour of a system, hysteresis is wanted so that the system accepts lag instead of switching on and off as soon it passes a set value. [Duym et al., 1997].
"Alternatively, some hysteresis may be incorporated, so that if the damping required is scored by the logic on a scale of 0 to 1, and greater than 0.5 would favour high damping, then switching up to high damping may only be activated when the score is 0.6 or more for a given period, and switching down when the score is 0.4 or less for a given period. This obviously reduces the amount of switching that occurs when conditions are borderline, reducing wear on the actuator and valve adjustments, and also reducing switching noise"[Dixon, 2007]
In shock absorbers, hysteresis is associated with valve characteristics and the fric- tion present. Simplified, the higher frequency the higher hysteresis. This has the possibility to cause valve wear and it will greatly affect the damper characteristics. For low-cost shock absorbers this has been found to cause problems[Duym et al., 1997]. The presence of hysteresis in shock absorbers are also known as damper lag.
6 2.1. SHOCK ABSORBERS
2.1.3 General design features regarding shock absorbers To give the reader a simple overview of the different features and their effect when choosing a suiting shock absorber for a vehicle and its application, a table sum- marising this is presented in Figure 2.2.
Figure 2.2: Effects of design parameters on the vehicle’s vertical oscillations [Bosch, 1996].
7 CHAPTER 2. FRAME OF REFERENCE
2.2 Front fork
The front fork can be described as the shock absorber acting on the front wheel for most motorcycles and mountain bikes etc. One of its more important purposes is to at all times keeping the front wheel in contact with the road, unless the driver forces the vehicle to act differently. This makes the front fork one of the key components for a safe and smooth ride and it is taken to its extreme in race applications. Throughout history there have been many different solutions, not only the telescopic forks that is normally used for modern motorcycles. Different models have included leaf springs, trailing links and girder forks [Wikipedia contributors, 2019]. Today however, conventional and upside down telescopic front forks are mainly used, see Figure 2.3a and 2.3b.
(a) Conventional [Öhlins Racing AB, (b) Upside down [Öhlins Racing AB, 2019a]. 2019b].
Figure 2.3: Conventional and upside down telescopic front forks.
The tougher the application, the more common it is with upside down forks, this due its superior stability and stiffness. It also gives less unsprung mass, even though that advantage is considered minor. Early on, the racing teams turned their con- ventional fork upside down but today it is much more than that, which makes it more expensive. For a regular road bike, a conventional fork is usually good enough. For mountain bikes a conventional front fork is widely used even though the upside down fork exists today [TVS, 2019].
8 2.2. FRONT FORK
The inside of the telescopic front fork usually consists of a spring and damper which acts together with a medium, usually oil. However, front forks with an air configuration is becoming more common for certain applications [Becker and Lampman, 2003]. A simplified section view of both a damper and an air spring can be seen in Figure 2.4 and 2.5.
Figure 2.4: Section view of front fork, Type: oil [Pinkbike, 2019b].
Figure 2.5: Section view of front fork, Type: air [Pinkbike, 2019a].
9 CHAPTER 2. FRAME OF REFERENCE
2.3 Rear shock absorber
The rear shock absorber has the same main function and purpose as the front fork, but the design is different, a regular model is shown in Figure 2.6. Instead of acting on the front wheel it acts with the rear wheel via the swingarm. The two main rear shock absorbers today comes in either a monotube or twintube version.
Figure 2.6: TTX Shock Absorber [Öhlins Racing AB, 2019g].
The monotube shock absorber, see Figure 2.7a, is built with a single tube, divided with a piston, with an oil filled chamber. The main piston moves when the shock absorber oscillates, causing one side of the piston to function as a rebound chamber and the other as a compression chamber. The main piston movement causes the oil to act upon a floating piston, that acts as a partition from the main chamber and deals with the difference in volume due to the piston rod. The other side of the floating piston is a gas filled chamber acting as a reservoir. It usually contains nitrogen as a medium, which gives the reservoir a progressive resistance. Gas is used since it can be compressed and allows the oscillation to take place. When the damper is compressed the nitrogen compresses and when the rebound takes place the nitrogen once again decompresses.
10 2.3. REAR SHOCK ABSORBER
(a) Monotube [Dixon, 2007]. (b) Twintube [Dixon, 2007].
Figure 2.7: Section views of Monotube and Twintube.
The twintube shock absorber has dual cylinders, see Figure 2.7b, one gas filled cylinder inside the shell case and another inner cylinder that is oil filled causing the compression and rebound circuits to be completely separated as opposed to the monotube. For a short overview of advantages and disadvantages regarding monotube and twintube shock absorbers, see Table 2.1.
Table 2.1: Monotube versus Twintube[ISC, 2019] Comparison of Monotube and Twintube Advantages Disadvantages No restriction on installation Stiffer ride due to high pressured Monotube angle gas Expensive to manufacture Minor risk of cavitation compared to Twintube Damage to the shell case affects No mix of oil and gas the inner cylinder Effective throughout full Friction temperature range More comfortable ride Restrictions on installation angle Less expensive to manufacture Risk of cavitiation Twintube Inner cylinder not directly Aeration due to mix of oil and affected by damage to shell case gas Less friction Temperature sensitive
11 CHAPTER 2. FRAME OF REFERENCE
2.4 Sprung and unsprung mass
The sprung mass is the mass that is supported by springs and unsprung mass is the mass that is supported by the tyre. Simplified everything above the vehicles suspen- sion system is considered sprung mass. The wheels, brake calipers etc is considered unsprung mass. The spring itself is both considered sprung and unsprung weight but is of less importance due to its small weight in comparison to other components. In general, a high ratio of sprung to unsprung mass is considered preferable [Hrovat, 1988], even though some advantages with a slightly higher unsprung mass, have been found to be preferable when driving over potholes at higher speeds since the wheel then has a tendency to hop over the potholes for example [Purdy et al., 2004].
Even though the notation for a vehicles suspension system uses sprung and unsprung mass, the unsprung mass as described above is supported by the tyre. Which includes both a spring and damping constant. This will be described with a simple illustration of a two degrees of freedom (DoF), damped system and can be seen in Figure 2.8.
Figure 2.8: Two DoF damped system.
12 2.5. TYRE DAMPER PROFILE
The sprung mass acting on the shock absorber is m2 and the unsprung mass is m1. k2 is the spring constant for the spring in the shock absorber and k1 is the tyre spring constant. c2 is the damper constant for the shock absorber and c1 the tyre damper constant. p is the displacement of the ground. x1 and x2 is the position of the sprung and unsprung mass.
This system can be described with equations of motion (EOM) with help of Newtons second law, shown in Equation 2.1.
F = ma. (2.1)
The state for the lower mass m1 can then be described as in Equation 2.2 and the upper mass m2 as in Equation 2.3.
m1x¨1 = m1g + c2(x ˙ 2 − x˙ 1) − c1(x ˙ 1 − p˙) + k2(x2 − x1) − k1(x1 − xp). (2.2)
m2x¨2 = m2g − c2(x ˙ 2 − x˙ 1) − k2(x2 − x1). (2.3) By solving for the accelerations of Equations 2.2 and 2.3 the following expressions is achieved.
1 x¨1 = g + [c2(x ˙ 2 − x˙ 1) − c1(x ˙ 1 − p˙) + k2(x2 − x1) − k1(x1 − xp)]. (2.4) m1
1 x¨2 = g − [c2(x ˙ 2 − x˙ 1) − k2(x2 − x1)]. (2.5) m2 The simple 2DoF system shown in Figure 2.8 can then mathematically be described as the accelerations of the both masses by Equations 2.4 and 2.5.
2.5 Tyre damper profile
As described in section 2.4, a vehicles mass, for example, can be divided in sprung and unsprung mass. Even though the tyre has both a factor of damping and com- pression the wheel belongs to the unsprung mass. The tyre damper profile can be described both linear and non-linear. In general, the tyres damping effect is con- sidered small, for passenger cars for example it is therefore often neglected [Dixon, 2007].
2.6 Linear transducer
The linear transducer is a piston/cylinder configuration that emits an analogue voltage signal that varies with the pistons position within the cylinder [POSITEK
13 CHAPTER 2. FRAME OF REFERENCE
LIMITED, 2019]. It usually varies between 0-5 [V], this voltage signal is transformed to get the real displacement of the transducer. The possible translated signal that can be measured depends on the logger used. For example, for a simple application a regular multimeter could be enough to measure the raw voltage and then trans- formed by hand. While a more complex application with large measurement data requires a more sophisticated logger unit.
2.7 Strain gauges
A strain gauge is a device, that comes in different sizes and models, that is used to measure the strain and elongation of materials [Omega, 2019]. The sensors are mostly glued to the surface of the object where the sensors output varies with the materials elongation. The most common type of sensor consists of a flexible backing with a metallic foil in a parallel zigzag pattern. The electrical resistance in the sensor varies when the object surface becomes longer/shorter, shown in Figure 2.9, this signal is measured and calibrated to get the strain in the surface.
Figure 2.9: Illustration of the common type of strain gauge [Izantux, 2011].
Since the strain gauges consists of thin electric conductor, which is sensitive to thermal effects, most gauges are made from constantan-alloy. This is a material designed to have low variations in electrical resistance due to thermal variation [Reade, 2019].
14 2.8. CAMDRUM
2.8 CamDrum
The CamDrum, also described as Rolling road, that is used during this thesis project, can be described as a rotating cylinder with bumps attached. When rotat- ing, the bumps acts upon the tyre that transmits the force upon the shock absorber, a basic illustration can be seen in 2.10.
Figure 2.10: CAD model of CamDrum [Öhlins, 2019].
The cylinder in this figure has a diameter of 1.1 [m] and a dimension at the bottom of 2.8 [m] x 1.6 [m]. In the CamDrum there is a floor built around at the same height as the upper part of the drum, that is not shown in the CAD (Computer Aided Design) figure. The fixtures for mounting different shock absorbers are installed via the two high beams.
15 CHAPTER 2. FRAME OF REFERENCE
A typical configuration in the CamDrum for a rear MTB shock absorber is shown in Figure 2.11.
Figure 2.11: Typical CamDrum configuration.
The main purpose of using the CamDrum is destructive testing through an accel- erated life test, to see that the product can withstand a set number of cycles.
16 2.9. DYNO
2.9 Dyno
The damper-dynamometer, here denoted Dyno, is a machine to measure a shock absorbers damper characteristics for both compression and rebound. It consists of a linear actuator combined with a force sensor, as seen in Figure 2.12, that logs the damping force for different frequencies (oscillating velocities). These are used to get the characteristics of a shock absorber and can be used to get the change in characteristics after a full lifetime.
Figure 2.12: Two typical Dynos for damper measurements [Multimatic, 2019].
17 CHAPTER 2. FRAME OF REFERENCE
2.10 Simulation software
The following simulation software were investigated as potential solutions to the given problem. The software were compared with a Pugh matrix, see Appendix C. Together with the requirements for the final solution and the wishes from Öhlins Racing AB, Amesim was deemed the best solution for the task at hand.
2.10.1 Simulink The Simulink software from MathWorks, Inc. is a tool used for simulation and analysis of dynamic multi-body systems [MathWorks, Inc., 2019b] . It uses a block diagram environment, see Figure 2.13.
Figure 2.13: Block diagram example in Simulink, [MathWorks, Inc., 2019a].
Simulink provide features, other than simulation, such as: Automatic code genera- tion (C, C++, CUDA etc. for implementation in a hardware application), Graphical editor, System-level design etc. MATLAB [MathWorks, Inc., 2018] is fully inte- grated, which in short terms means that using scripts (for example when iterations are needed to mimic the real-life system) continuously in an ongoing simulations is easy. Raspberry Pi [RASPBERRY PI FOUNDATION, 2019] and Arduino [Ar- duino, 2019] are examples of third-party hardware support.
18 2.10. SIMULATION SOFTWARE
2.10.2 Simcenter Amesim One of many software distributed by Siemens, Simcenter Amesim handles the anal- ysis and modelling of multi-domain systems [Siemens, 2019] and is based on the open source and object-oriented language Modelica [Modelica Association, 2019]. It consists of numerous libraries that specialises in their own domain. The signal library for instance, is used to simulate steps or other kinds of input to a system. These input signals can then be transferred to different kinds of motions, displace- ments, pressures etc. depending on the input to the system. This thesis will focus on the mechanical (1D-, 2D- and 3D-libraries) and signal-libraries, hence the hy- draulic libraries etc. will be excluded. The mechanical libraries are powerful tools for calculating expected forces, displacements and behaviour of a system. The sys- tem can be inspected in every joint and the relevant data can be extracted. A simple example of how the 1D-mechanical and signal interface looks like is shown in Figure 2.14.
Figure 2.14: Shock Absorber example in Simcenter Amesim, [Siemens Industry Software NV, 2018c].
The main advantage of the 2D-mechanical library, apart from the 2D-calculations, is the feature called Planar Assembly. With this, the design can be visualised and verified so that all connections are set up like planned. In Figure 2.15 an example of the Planar Assembly interface is shown.
19 CHAPTER 2. FRAME OF REFERENCE
Figure 2.15: Double pendulum from Amesim demos [Siemens Industry Software NV, 2018b].
This double pendulum example consists of a grounded part, visualised as the purple quadrant, two beams in dark-blue with their centres of mass depicted as the yellow circles. The turquoise and red circles both represents spherical joints. After the simulation, this animation can be played and its motion can be viewed step by step for the duration of time the simulation affects.
Similar to the 2D-libraries feature Planar Assembly, a feature called 3D-assembly exists for the 3D-library offering the same main function. The only difference that are relevant to this thesis is the number of dimensions and hence the DoF for each component in a model. Since the EOM depends on the DoF, thus the 3D-library generates more calculation heavy simulations than the 2D-library. Hence, if not three dimensions is necessary, the 2D-library is favourable.
20 2.10. SIMULATION SOFTWARE
2.10.3 MSC Adams MSC Software provides the simulation environment Adams [MSC Software, 2019], which is a multibody dynamics simulation software utilising Fortran and C++ nu- merical solvers. This system provides a graphical environment, shown in Figure 2.16, where components are modelled directly on screen. The physical constraints are then added to the model and the given input- signal/motion is defined. The systems physical motion is expressed as curves and the graphic can be seen in mo- tion.
Figure 2.16: Example of the MSC Adams environment [MSC Software, 2012].
21 CHAPTER 2. FRAME OF REFERENCE
2.10.4 BikeSim BikeSim is a simulation software for two to three wheeled vehicles developed by Mechanical Simulation Corporation, which seven of the biggest motorcycle OEM manufacturers use extensively [Mechanical Simulation Co., 2019]. It can be used for development of active controllers, calculating system performance and of course, analysing motorcycle dynamics. BikeSim is compatible with, for instance, MAT- LAB, Simulink and LabVIEW which are other software widely used. To let first time users easily learn the environment BikeSim includes numerous example vehicles and roads. In Figure 2.17 some of the different features of BikeSim is shown.
Figure 2.17: Example of the BikeSim environment [Mechanical Simulation Co., 2013].
22 Chapter 3
Implementation
In this chapter the implementation, including the setup and use of software, will be described in detail.
The Amesim model with its components and libraries used can be found under 3.7. Two different shock absorbers were used in the CamDrum tests with linear transducers. In order to verify the model independently of the shock absorbers simulation accuracy, a stiff rod was used. Strain gauges were used to investigate the forces acting on the shock absorber and the purpose was to compare those with the simulation model. To inspect the deviations between simulation and CamDrum, a number of different measurements were needed to be able to calculate means and inspect motion/forces plotted together.
3.1 Possible solution strategies
Amesim offers different solution methods for the task at hand and provides three different libraries suitable, 1D-, 2D- and 3D-mechanical. For a shock absorber itself, the 1D library was sufficient since the resulting motion is in one dimension locally.
The test-rig on the other hand includes motion that could not as easily be converted to resulting forces in one dimension due to restrictions on the components available in the library. Both the 2D- and 3D-libraries provides the feature of Assembly, discussed is Section 2.10.2, which was deemed suitable and advantageous for verifi- cation and troubleshooting. To get the relevant verification points and result, two dimensions was found to be adequate.
A combination of the signal-, 1D- and 2D-libraries were chosen to be the optimal solution. Where the 1D-library manages the spring and dampers of both shock absorber and tyre. For the physical motion of the test-rig configuration, the 2D- library was used. "As simple as possible, but not to simple" [Sellgren, 2019].
23 CHAPTER 3. IMPLEMENTATION
Both linear and non-linear tyre models were investigated and experimented with. A non-linear tyre model was produced through measurements, see Section 3.6. The resulting mean, of the non-linear models varying spring constant, was used as the linear models spring constant. These were compared through the wheel axles po- sition in order to get the best estimation. Since it was found that the simulation time was almost the same and that the non-linear model provided a slightly better result, the non-linear model was chosen.
3.2 Test configuration
To be able to simulate the CamDrum environment, data must be recorded and extracted. To achieve this the following method was used.
Figure 3.1: Illustrative image of test setup.
The indexing shown in Figure 3.1 is described in Table 3.1 and used in this section.
24 3.2. TEST CONFIGURATION
Table 3.1: Explanatory table of test setup figure indexing
Description 1 Main X-beam 2 Horizontal X-beam 3 Vertical X-beam 4 Cantilever 5 Y-bearing 6 Shock absorber 7 Rear wheel 8 Weight stack 9 Y-bearing 10 Swingarm
• The initial setup of the CamDrum consists of a platform which contains the drum with its attached bumps and two vertical and parallel X-beams (1), fixed to the main frame rising up through the platform. With the aid of an overhead crane, another set of two parallel X-beams (2) was connected to (1) with the use of Y-bearings (9) (part number: SKF - SE 507-606), see Figure 3.2.
Figure 3.2: CamDrum setup.
25 CHAPTER 3. IMPLEMENTATION
• Another set of parallel X-beams (3), was then mounted orthogonally to (2), fixed with a set of cantilevers (4), two on each side of the X-beams (3), eight in total. On (3), a fastening beam for the upper mounting position of the shock absorber was attached.
• A swing arm fixture (10) for the MTB application was attached to (3) at the bottom via a another set of Y-bearings (5) (part number: P2B 203-TF). The shock absorber (6) was mounted between the fastening bracket on (3) and the fastening bracket on the swingarm, see Figure 3.3.
Figure 3.3: Shock Absorber setup.
• The wheel (7) was attached to the swingarm, with the rear axle.
• The stack of weights (8) on top of the rig had the purpose to reflect the weight of a standard driver and was concluded to be about 50 [kg] acting on the wheel for the two shock absorbers and about 21 [kg] for the stiff rod configuration.
• An overview drawing of the rig and its attachments can be seen in Appendix G. The finalised setup was then used for a number of different settings, see Ap- pendix B. Numerous bump setups were used for the tests with the MTBM1899 model, while the MTB1691 was tested with either a bump setup of 70-30-30 [mm] or 80-30-30 [mm]. All configurations of the shock absorbers were tested with three different velocities, v1, v2 and v3 (the specific velocities is not pre- sented due to secrecy). Two different click setups were used for the MTB1691 shock absorber and one for the MTBM1899. Each test had a duration of 50 cycles/rotations for each setting. A 200 [Hz] sample rate was used for the logger connected to the linear transducers and 10 [kHz] for the strain gauges.
26 3.3. SHOCK ABSORBER #1 - MTBM1899
• Bump configuration - The setup of 70-30-30 [mm] and 80-30-30 [mm] bumps was deemed suitable. This since the setup met the demand of keeping the damper temperature under the control limit and hence the energy level trans- mitted within the damper on a reasonable level. While still generating a suitable output. The drawing of a standard bump can be seen in Appendix H.
• CamDrum HMI (Human-Machine Interface) - The control unit of CamDrum is managed by an HMI by Siemens and controls the settings used for the tests.
3.3 Shock absorber #1 - MTBM1899
The TTX22M, MTBM1899, with a stroke length of 75 [mm] and a total length of 250 [mm] was used during the first tests with the linear transducers. The possible adjustments for this shock absorber is, 3 clicks high speed compression damping, 16 clicks low speed compression damping and 7 clicks rebound damping. In Figure 3.4 the shock absorber configuration is shown. The spring used during these tests had a spring stiffness of 72 [N/mm].
Figure 3.4: MTBM1899 [Öhlins Racing AB, 2019d].
27 CHAPTER 3. IMPLEMENTATION
3.4 Shock absorber #2 - MTB1691
The second shock absorber that was used in the test-rig with the linear transducers was the TTX22M, MTB1691, seen in Figure 3.5. The possible adjustments for this shock absorber is, 3 clicks high speed compression damping, 16 clicks low speed compression damping and 7 clicks rebound damping. The third click on the high speed adjuster is used for less technical climbs and increases the compression damp- ing to reduce the suspension movement [Öhlins Racing AB, 2019f]. This model has a stroke length of 63 [mm] and a total length of 216 [mm] [Öhlins Racing AB, 2019e]. The same spring rate as for Shock Absorber # 1 was used and both dampers were tested in the dyno to get their characteristics to be used in the simulation model.
Figure 3.5: MTB1691 [Öhlins Racing AB, 2019c].
28 3.5. STIFF ROD
3.5 Stiff rod
To be able to verify that the model in Amesim reflects the test-rig, regardless of the shock absorber, a solid aluminium rod was used to replace the shock absorber. The mounted rod is shown in Figure 3.6.
Figure 3.6: Stiff rod configuration.
This to exclude the possibility of errors in the comparison between the simulation model and test-rig that depends on the shock absorber model itself.
The rod was retrieved from Öhlins workshop. It was cut to an appropriate length using a band saw and both holes drilled using a manual cordless drilling machine with an HSS-grade drill of 8 [mm] and 10 [mm], see Appendix D for detailed dimensions.
29 CHAPTER 3. IMPLEMENTATION
3.6 Tyre model
As mentioned under 2.5, a tyres damping effect is considered small and often ne- glected. In this project it was found to have a small effect, it was therefore neglected. However, the spring rate could not be neglected. Since the linear transducer placed at the rear axle only logs the overall change in position and not individual parts, the effect on the displacement by the tyre had to be measured and calculated manually. For this reason, the tyre spring rate was measured using an electronic crane scale, with a division of 0.05 kg from VETEK AB, Serial number: GSC111183, with the following method. The setup was weighted by connecting a strap to the wheel in the lower end and the scale in the upper end, see Figure 3.7.
Figure 3.7: Tyre spring measuring setup.
The scale was then connected to the overhead crane. Stacks of weight was added to the rig. The weight on the wheel and its resulting compression can be seen in Table 3.2.
30 3.6. TYRE MODEL
Table 3.2: Tyre spring model Weight [kg] Force [N] Compression [mm] 32.3 317.2 6.6 41.2 404.6 7.4 50.4 494.4 8.8 59.7 585.8 9.8 68.6 673.7 10.8 77.7 763.0 11.6 86.9 853.4 12.4 96.1 943.7 13.2
For each stack of weight added, the crane was lowered onto the drum and the linear transducers position, attached between the wheel and the floor, was noted. The position represents the compression of the tyre in millimetres. Stacks of weight was experimented with until a sufficient amount of data was retrieved in order to build a model of the compression as Newton per millimetre, see Figure 3.8. The script used for analysis can be found in Appendix S.
Tyre model spring constant 1000
900
800
700
600 Force [N]
500
400
300 6 7 8 9 10 11 12 13 14 Compression [mm] Figure 3.8: Tyre spring model.
This data was imported into Amesim using Ametable inside the SIGFXA01-component, found in Table 3.3 to represent the tyre. The wheel and tyre used in the rig was, Rim: 27,5" Hope, tyre: Specialized Slaughter 650Bx2.3.
31 CHAPTER 3. IMPLEMENTATION
3.7 Amesim model
The model is built in Amesim with the 2D-library for all parts included, except for the shock absorber and the tyre model which was built with the 1D-library. This due to the simplicity in modelling damping- and spring forces using the 1D-library and the compatibility with already existing models from Öhlins own library. In Figure 3.9 the layout for the model is shown.
Figure 3.9: CamDrum model in Amesim.
The dark-green icons belong to the 2D-library and the light-green to the 1D-library. The red icons illustrate the signal-library functions, which is used for the velocity dependent damping force of the shock absorber and the displacement dependent spring force of the tyre. The different icons are shown in Figure 3.9 and can be seen in Table 3.3 for the 2D-icons and Table 3.4 for the 1D- and signal-icons. The model design is described in detail in Section 3.7.1.
32 3.7. AMESIM MODEL
Table 3.3: 2D-icons of Amesim model [Siemens Industry Software NV, 2018a] Amesim Name Function Short Description Library Icon
PLMASSEMBLY Assembly Generates the assembly 2D
Contour vs Contact between 2 PLMCONT00 2D contour contours
Multiple port mass PLMDBOD0 N port body 2D body
Displacement PLMDT11 Displacement sensor 2D transducer
PLMEMB01 End Restraint Reference fixed body 2D
PLMJ00 Jack Actuator 2D Revolute pair with x PLMPIV01 Pivot Juction 2D and y contact forces
Null to Conversion of signal to PLMSDISP0 2D displacement a planar motion
Piloted Driven prismatic pair PLMTRA11 translation 2D with contact forces junction
PLMZER00 Zero force source Zero force source 2D
33 CHAPTER 3. IMPLEMENTATION
Table 3.4: 1D/signal icons of Amesim model [Siemens Industry Software NV, 2018a] Amesim Name Function Short Description Library Icon
Linear damper with 2 ports Damper with 2 ports DAM0000 1D capable of linear (force outputs) motion
Null to force Conversion of signal FORC 1D units input into a force in N
Sets the gravity of the GRAV0 Sets the gravity 1D whole system Linear shaft node Linear transferring port 3 LCON13 1D mechanical node velocity and displacement
Velocity sensor with Linear velocity offset and gain MECVS1B 1D sensor (acceleration and displacement at ports)
Linear spring with 2 ports Ideal linear spring (no SPR000A 1D capable of linear states) motion Zero speed source Zero linear speed V001 (velocity, displacement, 1D source acceleration)
Constant signal CONS00 Constant signal Signal source
Differencing JUN3M Subtracting junction Signal junction
1D table Interpolate 1D or XY SIGFXA01 Signal interpolation u(x) table with respect to x
Signal SPLT0 Splitter junction Signal duplication
34 3.7. AMESIM MODEL
The earlier mentioned feature Planar Assembly generated from the model shown in Figure 3.9 is shown in Figure 3.10.
Figure 3.10: CamDrum assembly in Planar Assembly.
The lower orange shape represents the CamDrum, the upper orange circle represents the wheel attached to the fixture. The blue parts represent the beams and rim. The turquoise part represents the shock absorber configuration. The length and size of the different components were modelled to mirror the real test-rig with dimensions as shown in Appendix F and G. The dimensions and weights for every part is configured through local coordinate systems and parametric settings for each component. The Planar Assembly helps with the verification of the final assembly by illustrating the resulting model.
35 CHAPTER 3. IMPLEMENTATION
3.7.1 Detailed description of the assembly components
To explain the models different components and describe their purpose, the assembly is divided into subgroups, denoted A - H and can be seen in Figure 3.11. To get a better understanding, the test-rig components will be referred to, using the notations from Figure 3.1.
Figure 3.11: Model divided in sub groups.
• Subgroup A - Upper X-beams Group A consist of four different components that together form the grounded point of the test-rig. The End restraint combined with the Pivot Junction represents the centre position of the bearings (9), in relation to the centre of the CamDrum. The junction is connected to the upper X-beams (2) modelled by the N port body component, which has three connections where one is unused. This unused connection is only present to be able to visualise its length compared to the position of the connected X-beams (3) in the Planar
36 3.7. AMESIM MODEL
assembly. This components centre of mass is moved to the position of the weight stacks (8) and hence the loaded mass is added here.
• Subgroup B - Orthogonal X-beams The Pivot Junction that connects group A to B has its parameters for ro- tational stiffness and damping, set to high values to get a stiff connection representing the cantilevers (4) between the X-beams (2) and (3). Here, the N port body component represents the X-beams (3) and has four connections, where one is unused and has the same function as the unused one for group A. The two remaining is used for the connection to the bearings (5) and the upper fastening of the shock absorber (6).
• Subgroup C - Swingarm Between group B and C the Pivot Junction represents the bearings (5) and connects the whole swingarm (10) to the X-beams (3). The swingarm is modelled by the N port body component with three connections, one for the tyre axle and one for the lower fastening of the shock absorber.
• Subgroup D - Wheel The components of group D represents the tyre (7) and its spring function, and will be discussed top to bottom. The first N port body with two connections represent the tyres half diameter, this to be able to place the tyres compression at the accurate position. The Pivot Junction between group C and D is stiff like the one between group A and B. The Displacement transducer and its twin is used to extract the compression of the tyre and is used in its spring model. Where the Piloted translation junction manages the motion controlled by the spring model of group G and its connections is stiff regarding rotation. The second N port body with two connections has the same length as the first one and is used to position the tyres centre at the right place on the swingarm. The last N port body is a weight- and dimensionless body used for inspection of the tyres rotational movement and represents the centre of the wheel axle.
• Subgroup E - CamDrum This group manages the input motion from the CamDrum and the shape of the bodies in contact. This is done by the component Contour vs contour, where the two bodies in contact are modelled and the physical properties of the contact is specified. It models both the tyres outer diameter and the CamDrums outer shape, visualised as the orange shapes in Figure 3.10. The Null to displacement component manages the input motion of the system. Since the CamDrum only rotates, the velocities in the X- and Y-direction is both connected to a Zero force source, resulting in a stationary position. The rotational velocity port is connected to a Constant signal source which has the parametric setting of a constant value output and manages the rotational velocity of the CamDrum.
37 CHAPTER 3. IMPLEMENTATION
• Subgroup F - Shock absorber The Pivot Junction between group B and F acts as a stiff connection as earlier described. To be able to add the mass of a shock absorber and easily move the connection position, a N port body with two connections is used. The Jack component represents the shock absorber (6) itself and is controlled by group H in the same way as the tyre. The rotation of both connections for the Jack is non-stiff, as is the case for the connections in the test-rig.
• Subgroup G - Tyre characteristics The components in group G controls the tyres characteristics, with a variable spring rate depending on the tyres compression. The red signal lines is sub- tracted by the Differencing junction, as input to the 1D table interpolation u(x). This component contains a table with the tyres varying spring rate and the input generates the output based on the table. The Null to force units components then converts the signal into force in Newtons and represents the spring. Since the damping in this model was non-existent, the Linear damper with 2 ports capable of linear motion component only has the function of being able to add damping if needed.
• Subgroup H - Shock absorber characteristics The main function of group H is similar to the function of group G, the difference is the spring rate being linear and a varying damping rate. The Linear velocity sensor used, combined with the Differencing junction manages the direction dependent velocity used as input to the 1D table interpolation u(x). It contains the table of the varying damping for the shock absorber and is shown in Figure 3.12. With the velocity on the X-axis and the resulting force on the Y-axis. Since the spring rate is linear, a Linear spring with 2 ports capable of linear motion is used. This component takes a constant value as input.
Figure 3.12: Ametable example, MTB1691.
38 3.8. LINEAR TRANSDUCERS
3.8 Linear Transducers
In order to collect relevant data, the linear transducers were placed at three strategic positions, see Figure 3.13a, 3.13b and 3.13c, to make it relatively easy to search for the sources of error in sampled data. The linear transducers will be referred to as Analog03, Analog04 and Analog05.
(a) Analog03. (b) Analog04. (c) Analog05.
Figure 3.13: Linear transducers and locations used.
Analog03 (part number: S-LP075mm) was used to log the change in position of the upper beam (2), see Figure 3.1, later converted to degrees. Analog04 (part number: CLS1326-100mm) was placed parallel to the shock absorber with an offset in height and the results were post-processed with a scaling factor in order to match the actual stroke of the damper. Analog05 (part number: CLS1326-200mm), attached to the rear axle and the platform, was used to log the position of the rear axle. A number of different configurations of the test-rig setup were used, the different settings can be found in Appendix B, to get a broad database for the verification phase. Fur- ther, another goal with the span of settings was, to find a setup where the damper often tops out, as is the case for a mountain bikes shock absorber used professionally.
To record the voltage output signals given from the linear transducers, a logger (part number: Lg-uCAN1045), from 2D Debus & Diebold Meßsysteme GmbH was used. This device comes with a software called WinARace that transformed the signals to length units and had the feature of real time communication, that simplified the calibration of the linear transducers.
39 CHAPTER 3. IMPLEMENTATION
3.9 Strain gauge
To measure the forces acting on the shock absorber during the test-cycles, the test- rig was modified. Two beams, (10) in Figure 3.1, were switched out for another pair with strain gauges attached. These beams were manufactured at the KTH industrial production workshop, see Figure 3.14, using a manual lathe and milling machine.
Figure 3.14: Replacement beam during manufacturing.
The material, aluminium of unknown grade, was acquired from Öhlins workshop. The quadratic geometry of the part has the side of 20 [mm] and the circular part has the diameter of 10 [mm]. First, the length of each beam was manufactured to mirror the original beams using an end mill tool in the milling machine. It was then fixed in a lathe using a 4-jaw dependent chuck in one end and a tailstock with live centre in the other. A small centre drill was used to mark a centre hole for the tailstock. To manufacture the beams circular geometry, a turning insert with a 45◦ lead angle was used. A sandpaper with grit size P800 was used to achieve a satisfying surface roughness. The four threaded holes were drilled and threaded
40 3.9. STRAIN GAUGE using a drill press and a manual tap tool of size M5. The procedure was repeated for the second beam. For detailed dimensions, see Appendix E.
Four strain gauges, see Appendix I, were applied to each beams circular geometry with an even spacing. First the surface was roughed up using sandpaper with grit size P240 and then cleaned using, RMS1 cleaning agent for strain gauges containing acetone and isopropanol. This in order to get rid of the oxide layer that naturally covers the surface on aluminium. Strain gauge instantaneous adhesive, CC-33A, was applied to the backside of the strain gauge. The strain gauge was then pressed on to the surface with added pressure for about one minute. When all eight gauges had been applied, the harness was soldered onto the gauges. The harness contains two sections, first part using 0.25 [mm2] wires and second part 0.50 [mm2], with a total length of 3 [m]. To ensure the procedure was successful, the strain gauges were tested with a logger connected to ensure no short circuits etc existed. Finally the strain gauges and the soldered harness connectors were covered with a cold curing glue for robustness.
To be able to log the data, an in-house configured National instrument amplifier was used with a sample rate of 10 [kHz]. The strain gauges were then calibrated by measuring the surface bending stress, compared to the simple maximum bending stress calculation shown in Equation 3.1 [Sundström et al., 2013].
Mb σb = . (3.1) Wb
Mb is the applied moment at the measurement position and Wb for a circular cross section is shown in Equation 3.2 [Sundström et al., 2013]
πd3 Wb = , (3.2) 32 where d is the diameter at the measurement position. The measurement method is shown in Figure 3.15 where two different weights (731.5 [g], 1422.4 [g]) are applied at a fixed distance from the sensors. The rods are then rotated so that each side points upwards once, resulting in a total of eight measurements per beam. These were then evaluated independently against the theoretical maximum bending stress. The script used to calculate the bending stress manually can be seen in Appendix R.
41 CHAPTER 3. IMPLEMENTATION
Figure 3.15: Strain measurement method.
The data from the eight strain gauges were processed in MATLAB using an in- house existing MATLAB script (not published due to secrecy). The result from calibration phase can be seen in Figure 3.16 where the upper four graphs represent the strain gauges on one beam and the lower four the other.
42 3.9. STRAIN GAUGE
Figure 3.16: Stress calibration result.
All eight graphs share a common behaviour regarding the loaded mass. The first ledge represents the smaller weight attached, and the second ledge the larger weight. These yielded a stress level around 14 [MPa] and 25 [MPa] respectively for each rod. The calculation with Equation 3.1 for both loads, resulted in 11.5 [MPa] and 22.5 [MPa] in accordance with earlier stated results. By this the strain gauges were deemed to have been attached correctly and thus present a trustworthy estimation of the stress in each beam.
43 CHAPTER 3. IMPLEMENTATION
3.10 Verification
The two different verification stages are presented below. Note that for the result section only one cycle is extracted from the plotting methodology presented below, this to get a clearer inspection of the curves.
3.10.1 Amesim versus Linear transducers To verify and compare the test data with the simulation data from Amesim, both results were imported into MATLAB. The data from the logger was used to get a cyclic mean curve for the three measurement positions from each test, using the MATLAB function TSA (Time-synchronous signal average) [MathWorks, Inc., 2019c], the script is found in Appendix P. This to get an as realistic estimation of the real motion as possible. This yields the displacement mean for one cycle, while the Amesim models runs for three to five cycles (dependent of the drum velocity, simulation time kept constant). Therefore, the mean curves from the linear trans- ducers were extended by themselves to display two cycles.
These curves were then compared to each other with MATLABs plotting function. The difference for each point between the curves was calculated by comparing the vectors using the built-in function diff. To bridge the problem of the different length of the sample vectors, the function interp1 was used to sync the data. The mean of these values was chosen to represent the mean deviation between simulation and actual test for this thesis. Certain test results contained unrealistic extreme val- ues. These values were removed to get a second representation of the data and a more realistic mean value. Further, the percentage deviation was of interest and calculated, using a similar method as for the mean, by taking a total mean of the percentage deviation for all data points in one cycle. The values from the linear transducer represents the base. The reason behind these methods was to analyse the data, draw conclusions and use the result for future improvements. The script can be found in Appendix M.
For the stiff rod configuration, a similar method was used, the result from Analog03 and Analog05 was plotted and compared with the same displacement positions from Amesim and inspected visually. To get a percentage value of this deviation, a calculation was done for the difference in amplitude with the logged data as base. This amplitude was taken as the highest peak to the lowest valley for each curve and then compared. See Appendix N for the MATLAB script used.
44 3.10. VERIFICATION
3.10.2 Amesim versus Strain gauges To verify the result from Amesim for the forces acting on the shock absorber, strain gauges were used as described earlier. The data from those eight strain gauges were processed in MATLAB using the same in-house existing MATLAB script. This script extracted data from each strain gauge and presented their result as matri- ces and plots for strain and stress as earlier seen in Figure 3.16. The mean was calculated for the four strain gauges on the circular geometry for each beam, gen- erating the total stress in one beam. To get the resulting force acting on the shock absorber the two beams total stress was added together and the force was calculated.
Since the logging started in a position where the test-rig was loaded at zero velocity, an offset error for the unloaded state of the test-rig existed (to clarify, the in-house script presumed an unloaded state when setting the zero for the strain gauge, thus the offset). This was synchronised by taking the difference between the forces at the starting position of Amesim and the results from the strain gauges. Then the plot representing the strain gauges was adjusted using that value, to match the zero force position against Amesim. For the comparison, two cycles were extracted in the middle of the test with the strain gauges and plotted together with three to five cycles from Amesim (dependent of speed and the simulation time were kept constant), the script used can be seen in Appendix O. A mean peak deviation was calculated by taking the mean of the deviations from the two highest peak-loads from one cycle, using the Data Cursor function in MATLABs plot window. Only the high peaks were considered due to the relevance regarding this thesis depending on maximum loads mainly. The resulting plots with comparison and mean peak deviation will be presented under the result section.
The maximum percentage deviation of the force measurements compared to simu- lation value is an important parameter and were therefore calculated for the peak from one cycle that had the most deviation. The measured value from the strain gauges represents the base value. The MATLAB script used for the force evaluation can be seen in Appendix Q.
The earlier mentioned MATLAB function TSA was not used for the strain gauge measurements due to the relatively high variations on the time axis for 50 cycles of the result. For every test these variations were to big to get a relevant and usable end result using TSA.
45
Chapter 4
Results
Here, the results from the simulation model and CamDrum tests, with the use of linear transducers and strain gauges, will be presented. The different settings used and their result have a lot of similarities, therefore, only a selection of results will be presented.
It was found that the resulting behaviour shared differences, originating from the velocity and therefore only one setting with the three used velocities will be pre- sented as plots in this chapter. More plotted results can be seen in Appendices. A full list of test settings can be found in Appendix B.
4.1 Displacement result
In this section the comparison of resulting displacement for Amesim and CamDrum will be presented. The results in this section refers to the Analog04 transducer, in other words, the stroke of the damper, except for the stiff rod configuration.
47 CHAPTER 4. RESULTS
4.1.1 MTBM1899 The results from the relevant settings is presented in Table 4.1 and the behaviour regarding increasing velocity can be seen in Figures 4.1 - 4.3. For more plotted results, see Appendix J.
Table 4.1: Result MTBM1899 Mean Deviations Mean Test number Velocity deviation above 5mm percentage [mm] excluded [mm] 5 v1 1.5 - 12.8% 6 v2 1.3 - 23.2% 7 v3 2.7 2.1 19.0% 18 v1 1.5 - 11.6% 19 v2 1.7 - 12.2% 20 v3 2.0 1.7 14.3%
ANALOG4, 70-30-30, v1 35 AMEsim 30 2DTSA
25
20
15
Distance [mm] 10
5
0 0.8 1 1.2 1.4 1.6 1.8 2 Time [s] Figure 4.1: Comparison Analog04 test 18.
48 4.1. DISPLACEMENT RESULT
ANALOG4, 70-30-30, v2 40 AMEsim 35 2DTSA 30
25
20
15 Distance [mm] 10
5
0 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 Time [s] Figure 4.2: Comparison Analog04 test 19.
ANALOG4, 70-30-30, v3 40 AMEsim 35 2DTSA 30
25
20
15 Distance [mm] 10
5
0 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 Time [s] Figure 4.3: Comparison Analog04 test 20.
49 CHAPTER 4. RESULTS
4.1.2 MTB1691 The results from the relevant settings is presented in Table 4.2 and the behaviour regarding increasing velocity can be seen in Figures 4.4 - 4.6. For more plotted results, see Appendix K.
Table 4.2: Result MTB1691 Mean Deviations Mean Test number Velocity deviation above 5mm percentage [mm] excluded [mm] 37 v1 2.1 - 17.2% 38 v2 2.2 2.0 15.8% 39 v3 2.7 2.1 19.1% 43 v1 2.1 - 18.3% 44 v2 2.3 1.9 18.5% 45 v3 2.7 1.9 28.1%
ANALOG4, 70-30-30, v1 30 AMEsim 25 2DTSA
20
15
10
Distance [mm] 5
0
-5 1.4 1.6 1.8 2 2.2 2.4 2.6 Time [s] Figure 4.4: Comparison Analog04 test 37.
50 4.1. DISPLACEMENT RESULT
ANALOG4, 70-30-30, v2 35 AMEsim 30 2DTSA
25
20
15
Distance [mm] 10
5
0 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Time [s] Figure 4.5: Comparison Analog04 test 38.
ANALOG4, 70-30-30, v3 40 AMEsim 35 2DTSA 30
25
20
15 Distance [mm] 10
5
0 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 Time [s] Figure 4.6: Comparison Analog04 test 39.
51 CHAPTER 4. RESULTS
4.1.3 Stiff rod The results from the stiff rod test configurations is presented in Table 4.3 and in Figures 4.7 and 4.8. The velocities used for the stiff rod differs from the ones used with the shock absorbers.
Table 4.3: Result Stiff rod Test Velocity Percentage Analog03 Percentage Analog05 number [km/h] 34 4.44 4.9% 5.1% 35 3.0 4.7% 2.0% 36 1.56 0.9% 4.8%
ANALOG3, Stiff rod, 50-30-30, 4.44km/h ANALOG3, Stiff rod, 50-30-30, 3km/h 16 11 AMEsim AMEsim 15 2DTSA 2DTSA 10.5 14
13 10 ] ]
° 12 °
11 9.5
10 Angle [ Angle [ 9 9
8 8.5 7
6 8 0 1 2 3 4 5 6 7 8 0 2 4 6 8 10 12 time [s] time [s] (a) 4.44 [km/h]. (b) 3 [km/h].
ANALOG3, Stiff rod, 50-30-30, 1.56km/h 11 AMEsim 2DTSA 10.5
10 ] °
9.5 Angle [ 9
8.5
8 0 5 10 15 20 25 time [s] (c) 1.56 [km/h].
Figure 4.7: 50-30-30 [mm], Stiff rod, Test 34-36, Analog03.
52 4.1. DISPLACEMENT RESULT
ANALOG5, Stiff rod, 50-30-30, 4.44km/h ANALOG5, Stiff rod, 50-30-30, 3km/h 200 50 AMEsim AMEsim 2DTSA 2DTSA 40 150
30
100 20
10 50
Distance [mm] Distance [mm] 0
0 -10
-50 -20 0 1 2 3 4 5 6 7 8 0 2 4 6 8 10 12 time [s] time [s] (a) 4.44 [km/h]. (b) 3 [km/h].
ANALOG5, Stiff rod, 50-30-30, 1.56km/h 50 AMEsim 2DTSA 40
30
20
10 Distance [mm]
0
-10 0 5 10 15 20 25 time [s] (c) 1.56 [km/h].
Figure 4.8: 50-30-30 [mm], Stiff rod, Test 34-36, Analog05.
53 CHAPTER 4. RESULTS
4.2 Force result
The results from the strain gauges is presented in Table 4.4 and the plots can be seen in Figures 4.9 - 4.11. For more plotted results, see Appendix L.
Table 4.4: Force result Test number Velocity Mean deviation [N] Mean percentage 37 v1 401 16.1% 38 v2 492 18.1% 39 v3 536 17.8% 40 v1 402 16.3% 41 v2 529 19.0% 42 v3 599 18.7% 43 v1 464 17.9% 44 v2 597 20.7% 45 v3 742 24.0% 46 v1 500 19.6% 47 v2 596 20.4% 48 v3 706 22.9%
Strain Gauge, 70-30-30, v1 3000
2500
2000
1500
1000 Force [N]
500
0 AMEsim 1 cycle from strain gauges -500 0.8 1 1.2 1.4 1.6 1.8 2 Time [s] Figure 4.9: Comparison Analog04 force test 37.
54 4.2. FORCE RESULT
Strain Gauge, 70-30-30, v2 3500 AMEsim 1 cycle from strain gauges 3000
2500
2000
1500
1000 Force [N]
500
0
-500 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 Time [s] Figure 4.10: Comparison Analog04 force test 38.
Strain Gauge, 70-30-30, v3 4000 AMEsim 3500 1 cycle from strain gauges 3000
2500
2000
1500
1000 Force [N] 500
0
-500
-1000 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 Time [s] Figure 4.11: Comparison Analog04 force test 39.
55
Chapter 5
Discussion and conclusions
In this chapter the projects result including possible errors will be discussed, summed up and concluded. The discussion is based on an analysis of the results and aims to answer the purpose of this project.
5.1 Discussion
Neither CamDrum nor Amesim planar mechanics has been used earlier for testing and evaluation with this test-rig and the MTB shock absorbers used. Therefore, a large amount of freedom regarding methods for testing and evaluation were possible when designing the tests used in this project.
A main advantage of using a simulation model for initial testing could be that the engineer on site gets a possibility to try new ideas and more importantly get an almost instant response. The more precise the model is, the more it can be used. The response can be presented visually through graphs and physical motion in Pla- nar Assembly. The change in behaviour can then easily be compared to previous iteration. This visualised comparison is considered more important than the actual result stated in numbers. That is one of the main reasons the calculations of the results in numbers have been kept simple. The advantage of the model lies in its ability to present an overview to the engineer that he or she easily can discuss with colleagues and supervisors in order to develop a solid and suitable test.
The calculated results do not give a totally just picture when comparing between themselves for the different test sequences of displacement for shock absorbers and the stiff rod. The methods used differ, hence they become quite incomparable, it would have been preferable to use the same method for both applications. Although, as discussed below, the calculations themselves provide an unjust view of the real state. Combined with the fact that the plotted figures present a better evaluation, this was not investigated further. However, independently, they are still relevant in order to have an evaluation in numbers and was therefore included in the results.
57 CHAPTER 5. DISCUSSION AND CONCLUSIONS
An advantage of using the dyno at site to get the damper characteristics is that they presented a trustworthy result and the repeatability was deemed high. This meant that only a single run was needed to get the characteristics from the given damper to use it in the simulation model as input.
5.1.1 Displacement
The reason for the results magnifying spread with increasing velocity, has not been identified. Even though one possible reason could be the presence of hysteresis when the closing and opening of valves in the shock absorber occurs, which is not included in the Amesim model. When comparing the three velocities for the same configuration, the increasing spread is clearly visible and is easily seen after the landing of the wheel, after hitting the high bump. More about hysteresis under the discussion of possible sources of error. The problem with hysteresis will not be further investigated during this project, mainly due to the damper simulation being out of scope. However, a process of investigating this further has been delegated to an engineer with relevant competence and experience.
Regarding the deviation and its magnifying spread, a behaviour among the linear transducers was discovered. Two out of three measurement positions shared this magnifying behaviour. The wheel axle position was unaffected by the velocity. This was a big breakthrough for the project and resulted in the stiff rod tests, which in turn led to the verification and the concluded result of the project.
The CamDrum rotates, driven by an electric motor. The velocity is controlled by means of a velocity sensor, regardless, the rotation is not as ideal as it is in the Amesim model. This can be seen when looking at the phases in section 4.1. Because of this, the mean deviation calculations done for the shock absorbers displacements is not to be fully trusted. With a small difference in synchronisation of the time axis, the deviation in that point increases more than it should and hence gives a potential misleading result.
To verify that the simulation model itself was not at fault and that it was the damper simulation characteristics that were responsible for the deviation phenom- ena, a stiff rod application was used. The main goal was to verify the motion and amplitude for the Analog03 and Analog05 positions, without the interference of the shock absorber. This turned out to be successful for the three velocities used, note that the velocities used for this application differs from the ones used with the shock absorbers attached. This due to the force transmitted through the test-rig is much larger without the presence of a shock absorber that absorbs the energy. To avoid the risk of breaking the test-rig and test equipment the velocity had to be decreased. It would have been of great interest to compare the same velocities as used with the shock absorbers, but the risk for test-rig break down was considered too high. Using the stiff rod had one more positive effect, namely a more profound
58 5.1. DISCUSSION verification of the tyre model. Even though a certain deviation exists, where the largest portion of the total mean deviation caused by the Amesim model, for the tyres bouncing oscillation when hitting the ground. With a non-existent damping coefficient in the simulation, this is reasonable. The total displacement and ampli- tude was considered adequate for this application.
The non-linear tyre model was developed using a minimum weight of 32 [kg] up to the maximum weight of 96 [kg] acting on the tyre. A tyres spring rate is almost linear, except when the weight is low and the compression closes in to zero, according to experts on site. This yields an uncertainty mainly for low weights and could affect the simulation result.
5.1.2 Force
The sampled data from the strain gauges calibration phase were, as mentioned ear- lier, deemed to give a just result. Even though the calculated and measured values differed with about 2.5 [MPa]. The manual calculations performed origins from sim- plified equations, which gives an uncertainty. Together with the uncertainty from the mounting process of the strain gauges. The result corresponds fairly well and shares the same magnitude. The calibration was therefore deemed successful and thus accepted.
When looking at the figures comparing the Amesim model and logged data from the tests, in section 4.2, one can see that the shape and overall amplitude corresponds well. However, the logged data shows the same problem as for the displacement result in section 4.1, the higher velocity on the CamDrum, the more the results spread. This leads to the same suspicions as earlier regarding hysteresis and a too simplified damper model.
When performing and analysing tests with the strain gauges, a strange behaviour in the result was found. This implicates that the logger used sometimes stopped storing data for a short amount of time, hence the strange pattern of the curve in Figure L.8. This could also explain why the TSA function could not give any usable results for the analysis.
The setup of the shock absorber via the swingarm, bearings and X-beams will most definitely introduce some bending moments. This will make the readings from the strain gauges differ from each other and possibly the Amesim results, where the alignment is ideal. How much of the deviation that can be derived from this issue is still unclear.
The method for adjusting the zero position of the strain gauges could be faulty. Since the data was adjusted with a non-verified model, there is no guarantee that the offset value is correct. It was deemed to be close to the real offset through visual
59 CHAPTER 5. DISCUSSION AND CONCLUSIONS inspection when the two curves were compared after adjustment, hence no further investigation was made on the subject.
5.1.3 General possible sources of error During the project a number of deviations have been found when comparing the simulation model against the measured data from the CamDrum. One must take into account that our simulation model is not affected by tolerances of manufactured parts, human bias and tolerances of measurement instruments, to mention a few possible sources of error. Even if the simulation model is made to represent the test environment as close and accurate as possible, it still exists numerous uncertainties. Since the simulation model was created to mirror the test environment there is also the factor of how accurate the CamDrum test represents the reality. However, this is out of scope for this project. Therefore, complementing sources of error will only be discussed as a comparison between the simulation model and the CamDrum test. The real world application will be left out.
• There have been no measurements of the inertia of the CamDrum and all com- ponents involved in the test sequence. Therefore, this is also an uncertainty. However, this has been estimated to be non-critical, since experimentation in Amesim regarding the inertia have not shown any major impact on the results.
• The temperature of the shock absorbers has not been logged during the tests nor has it been controlled, thus the temperature during the performed tests have varied between approximately 30 to 60 [◦C]. The temperature at every test start have been between 30-45 [◦C]. Since the characteristics of an oil filled damper varies with its temperature, this could cause some errors, but has been deemed non-critical for this project.
• The usage of strain gauges to compare the acting forces on the shock absorber against those in Amesim has the possibility to introduce several errors. Since the strain gauges have to be manually attached to the beams used, the appli- cation process is critical. The material of the beams is aluminium of unknown grade. Also, they have to be calibrated using, in our case, a MATLAB script. Since no previous experience of using strain gauges existed, this could be a source of error. The beams used were manufactured using manual milling and turning techniques. The logger used was modified and programmed in-house. No investigation of the logger or script have been made during this project. Therefore, no guarantee of a correct data sample can be stated even though precautions were made by discussing the results with experienced personnel.
60 5.2. CONCLUSIONS
• The pressure gauge used to check the tyre pressure, often caused a significant drop in pressure. In order to avoid this and the risk of not finding the exact same level caused by the unwieldy tool, the tyre pressure was not measured between each change of setting. The tyre was instead trusted to hold pressure. However, the pressure was checked before starting the second phase where different weights were tested. The pressure had dropped 0.1 [bar], possibly when applying the pressure gauge instrument to the pressure valve. Weeks later when new tests were performed, the pressure had dropped significant, to 1.4 [bar], and was therefore refilled. This event leaves a possibility of leakage during actual tests, since the pressure was not checked directly after finishing the tests, that could affect the original tests but was deemed non-critical due to the conformity of the results. An early major leakage should have given more significant differences between the tests. However, for future tests the pressure should be logged more often to avoid this possible source of error.
• The design of the tyre model in Amesim was built in such a way that it constrains the displacement to take place in one direction. Even though all directional components of the force is registered, the simulated tyres compres- sion is only allowed to move orthogonal to the swingarm. This could generate a faulty result of the compression and its direction, hence affect the accuracy of the whole simulation.
• The delimitation of assuming all parts of the test-rig to be rigid could affect the result. This have been briefly experimented with but has not been fully verified. No large dependency between the beam-/joint stiffness and the sim- ulation results was discovered during these tests, hence a deeper investigation was left out. However, it remains as a possible error source and should be further investigated.
5.2 Conclusions
The mean displacement results varying from 1.3 [mm] (80-30-30 [mm], v2, Test 6) to 2.7mm (70-30-30 [mm], v3, Test 39) on a shock absorber. When all tests had been analysed, it was concluded the simulation model could confirm an adequate repre- sentation of the test-rig. Considering the many possible sources of error together with the demand from certain external vehicle manufacturers to use the testing method, the Amesim model cannot replace the use of the CamDrum. However, it can be of great aid when designing tests, to open up time slots in the CamDrum and save time, money and energy.
• With the results from the stiff rod tests the simulation was verified to mimic the CamDrum testing method regarding the displacement. With the calcu- lated mean percentage deviation ranging from 0.9% to 5.1%, the requirement of maximum mean 10% is fulfilled.
61 CHAPTER 5. DISCUSSION AND CONCLUSIONS
• For the tests performed with shock absorbers regarding displacement, the mean percentage deviation ranges from 11.6% to 23.2%, which does not fulfil the requirements. The deviation between simulation and the test environment becomes larger with higher velocity of the CamDrum, as can be seen in the figures under section 4.1, it was concluded with the use of the stiff rod that it is probably due to the damper model being too simple. This should be verified with a more accurate simulation of a shock absorber.
• The results from the force measurements with the strain gauges show a sim- ilar behaviour as the result for the displacements of the tests with the shock absorbers. The mean maximum deviation ranges from 16.1% to 24.0% which do not fulfil the requirement. The reason behind this is probably linked to the same problem as for the displacement but have not been investigated within this thesis.
• A main advantage of using a simulation model for initial testing could be that of an instant response when experimenting with parameters and the possibility to visualise the result, hence design the wanted movement and load more accurately through iteration.
• The influence of hysteresis could not be fully determined as the reason behind the deviation between simulation and actual tests, but remains as a main target for further investigation.
• The type of shock absorber used in Amesim can easily be changed via the connector between 1D- and 2D-library and is compatible with shock absorber simulations previously designed by Öhlins Racing AB.
• The use of global parameters allows for an easy procedure of changing the rigs dimensions in Amesim, minimal previous experience needed.
• The simulation model is developed on regular office computers without the use of any computational servers. The program should therefore be executable on any other regular office computer. However, this could not be confirmed due to the limitation of the software license used, they are bound to two specific computers.
• It was concluded that the sample rate of 200 [Hz] for the logger used with the linear transducers was not causing the spread in the results.
62 Chapter 6
Recommendations and future work
During the project a number of subjects have been found interesting but out of scope. This will be discussed and stated below as recommendations and future work to both the company and the interested academic peers.
6.1 Recommendations
• When the problem of increasing deviations with higher velocities is resolved, even higher velocities should be tested. To confirm and broaden the usage area of the simulation model.
• Implement the simulation model and design an actual CamDrum test to verify that the simulations user interface (UI) and the result is of use.
• More tests and simulations should be performed with other dimensions of tyres to broaden the verified area of usage of the model.
• When the simulation model is implemented and in use, expand the model to include other applications. Such as front forks etc.
• An evaluation of how the use of the simulation affects the choice of parameters, and how much time, money and energy it can save, should be carried out.
• An investigation of possible outsourcing could also be of good use. To see if the use of simulation software can be kept in-house, while the actual testing is handled at another site or by another company.
63 CHAPTER 6. RECOMMENDATIONS AND FUTURE WORK
6.2 Future work
Possible future work within the field of this project, could be:
• To get a more accurate result, a further developed simulation model of the shock absorber is proposed as a solution. Since the biggest deviations in the result, presented in this thesis, are deemed to depend on hysteresis and mechanical inertia inside an actual damper.
• The tyre has the potential of having a larger influence than is present in this project and should therefore be investigated. It should be further analysed if the non-linear model used is adequate or if it needs to be refined.
• It would be of great interest to run tests with the stiff rod at the same velocities used with the shock absorbers. This to further disconnect the impact of the shock absorber and then compare this against the Amesim model again.
• Further investigate and verify the deviation in force.
• Develop the UI of the program further to make it even more simple to use.
• Further tune the simulation model by using for example optimisation methods.
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[TVS, 2019] TVS (2019). Explained: Different types of front motor- cycle suspensions, their advantages and disadvantages. Accessed: 2019-05-07. Available from: https://www.tvsmotor.com/blog/ explained-different-types-of-front-motorcycle-suspensions/.
[VitalMTB, 2019] VitalMTB (2019). Rear shock absorber. Accessed: 2019-06-02. Available from: https://p.vitalmtb.com/photos/products/12627/photos/ 17007/s1600_Ohlins_TTX_Shock.jpg?1413757228.
67 BIBLIOGRAPHY
[Wikipedia contributors, 2019] Wikipedia contributors (2019). Motorcycle fork — Wikipedia, the free encyclopedia. Accessed: 2019-05-27. Avail- able from: https://en.wikipedia.org/w/index.php?title=Motorcycle_ fork&oldid=878567590.
[Öhlins, 2019] Öhlins (2019). CamDrum from NX. Instrumentvägen 8, 194 51 Upplands Väsby.
[Öhlins Racing AB, 2019a] Öhlins Racing AB (2019a). Front fork. Accessed: 2019-05-07. Available from: https://www.ohlins.com/app/uploads/2016/11/ Retro-43_blackgold_8-1280x770.jpg.
[Öhlins Racing AB, 2019b] Öhlins Racing AB (2019b). Front fork. Ac- cessed: 2019-05-07. Available from: https://www.ohlins.com/product/ rxf-48-s-mx-front-fork/#&gid=1&pid=4.
[Öhlins Racing AB, 2019c] Öhlins Racing AB (2019c). Ttx 22 m, mtbm1691. Ac- cessed: 2019-05-08. Available from: https://www.ohlins.eu/en/products/ mountainbike/85x25-216x63mm-mtb-1691--5554/.
[Öhlins Racing AB, 2019d] Öhlins Racing AB (2019d). Ttx 22 m, mtbm1899. Accessed: 2019-05-08. Available from: https://www.ohlins.eu/images/db/ highres/img-00000561.jpg.
[Öhlins Racing AB, 2019e] Öhlins Racing AB (2019e). Ttx 22m 216x63 am. Ac- cessed: 2019-05-27. Available from: https://www.ohlins.eu/en/products/ mountainbike/85x25-216x63mm-mtb-1691--5554/.
[Öhlins Racing AB, 2019f] Öhlins Racing AB (2019f). Ttx 22m 250x75 am. Ac- cessed: 2019-05-27. Available from: https://www.ohlins.eu/en/products/ mountainbike/250x75mm-mtbm-1899--6424/.
[Öhlins Racing AB, 2019g] Öhlins Racing AB (2019g). Twin tube shock absorber. Accessed: 2019-05-08. Available from: https://www.ohlins.com/app/uploads/ 2016/08/TTX-Flow-2018_3-1280x755.jpg.
68 Appendix A
Risk Management
The possible risks in the project were evaluated in a risk management matrix shown in Table A.1. [Petersen, 2013] Where 1 is low and 5 is the highest (probability (P) and consequence).
69 APPENDIX A. RISK MANAGEMENT
Table A.1: Risk management matrix Conseq- Means to Contingency Risk P uence prevent risk plan Following the Negotiate with Not Gantt-scheme, stakeholders 1 completing the 2 3 Continuous and project in time follow-ups supervisors Not Begin Negotiate with completing the development of stakeholders 2 2 3 simulation system according and models in time to schedule supervisors Not satisfying the Make 3 3 2 Pulse meetings stakeholder adjustments requirements Negotiate with Exceeding Communication stakeholders 4 3 2 project budget with stakeholders and supervisors Project not being to any Communication 5 2 2 Nothing use for the with stakeholders stakeholders Negotiate with Not fulfilling Carefully read stakeholders 6 NDA 1 5 and follow NDA and agreements agreement supervisors Documentation Continuous Re-Do Docu- 7 loss or 1 4 backups mentation corrupted files Communication Transparent Negotiate with misunder- communication stakeholders 8 standings 4 3 and continuous and against meetings supervisors stakeholders Meetings on a Project group weekly basis and communica- 9 3 3 discussions Compromises tion errors and regarding the disagreements project
70 Appendix B
Test configurations
Table B.1: Test configuration # Bump Velocity Pressure tyre Damper Comp Reb Force Mass [mm] [km/h] [Bar] [Inch] model [Click] [Click] logg [kg] 1 70-30-30 v1 2,5 27,5 1899 7-2 3 No 49,97 2 70-30-30 v2 2,5 27,5 1899 7-2 3 No 49,97 3 70-30-30 v3 2,5 27,5 1899 7-2 3 No 49,97 4 70-30-30 v2 2,5 27,5 1899 7-2 6 No 49,97 5 80-30-30 v1 2,5 27,5 1899 7-2 3 No 49,97 6 80-30-30 v2 2,5 27,5 1899 7-2 3 No 49,97 7 80-30-30 v3 2,5 27,5 1899 7-2 3 No 49,97 8 80-30-30 v2 2,5 27,5 1899 7-2 6 No 49,97 9 60-30-30 v1 2,5 27,5 1899 7-2 3 No 49,97 10 60-30-30 v2 2,5 27,5 1899 7-2 3 No 49,97 11 60-30-30 v3 2,5 27,5 1899 7-2 3 No 49,97 12 50-60-30 v1 2,5 27,5 1899 7-2 3 No 49,97 13 50-60-30 v2 2,5 27,5 1899 7-2 3 No 49,97 14 50-60-30 v3 2,5 27,5 1899 7-2 3 No 49,97 15 50-70-30 v1 2,5 27,5 1899 7-2 3 No 49,97 16 50-70-30 v2 2,5 27,5 1899 7-2 3 No 49,97 17 50-70-30 v3 2,5 27,5 1899 7-2 3 No 49,97 18 70-30-30 v1 2,5 27,5 1899 7-2 3 No 49,97 19 70-30-30 v2 2,5 27,5 1899 7-2 3 No 49,97 20 70-30-30 v3 2,5 27,5 1899 7-2 3 No 49,97 21 70-30-30 v1 2,5 29 1899 7-2 3 No 49,97 22 70-30-30 v2 2,5 29 1899 7-2 3 No 49,97 23 70-30-30 v3 2,5 29 1899 7-2 3 No 49,97 24 80-30-30 v1 2,5 29 1899 7-2 3 No 49,97 25 80-30-30 v2 2,5 29 1899 7-2 3 No 49,97
71 APPENDIX B. TEST CONFIGURATIONS
26 80-30-30 v3 2,5 29 1899 7-2 3 No 49,97 27 70-30-30 v1 2,4 27,5 1899 7-2 3 No 64,59 28 70-30-30 v2 2,4 27,5 1899 7-2 3 No 64,59 29 70-30-30 v2 2,4 27,5 1899 7-2 3 No 64,59 30 70-30-30 v3 2,4 27,5 1899 7-2 3 No 64,59 31 70-30-30 v1 2,4 27,5 1899 7-2 3 No 35,47 32 70-30-30 v2 2,4 27,5 1899 7-2 3 No 35,47 33 70-30-30 v3 2,4 27,5 1899 7-2 3 No 35,47 34 50-30-30 4,44 2,4 27,5 Rod - - No 20,75 35 50-30-30 3,00 2,4 27,5 Rod - - No 20,75 36 50-30-30 1,56 2,4 27,5 Rod - - No 20,75 37 70-30-30 v1 2,4 27,5 1691 7-3 3 Yes 49,97 38 70-30-30 v2 2,4 27,5 1691 7-3 3 Yes 49,97 39 70-30-30 v3 2,4 27,5 1691 7-3 3 Yes 49,97 40 70-30-30 v1 2,4 27,5 1691 7-3 5 Yes 49,97 41 70-30-30 v2 2,4 27,5 1691 7-3 5 Yes 49,97 42 70-30-30 v3 2,4 27,5 1691 7-3 5 Yes 49,97 43 80-30-30 v1 2,4 27,5 1691 7-3 3 Yes 49,97 44 80-30-30 v2 2,4 27,5 1691 7-3 3 Yes 49,97 45 80-30-30 v3 2,4 27,5 1691 7-3 3 Yes 49,97 46 80-30-30 v1 2,4 27,5 1691 7-3 5 Yes 49,97 47 80-30-30 v2 2,4 27,5 1691 7-3 5 Yes 49,97 48 80-30-30 v3 2,4 27,5 1691 7-3 5 Yes 49,97
72 Appendix C
Pugh Matrix - Simulation Softwares
Table C.1: Pugh matrix Baseline Weight Simulink Amesim MSC Adams BikeSim Criteria Usability 0 3 -1 +1 0 0 Graphical UI 0 3 -1 +1 +1 +1 Software complexity 0 1 +1 0 0 0 Possible applications 0 1 +1 0 0 +1 In-house competence 0 4 0 +1 -1 +1 Purpose of software 0 3 +1 +1 +1 -1 Software license in-house 0 3 -1 0 -1 +1 Sum 0 - -4 13 -1 8
73
Appendix D
Stiff rod drawing
Appendix E
Drawing of modified rod for strain gauge
77
Appendix F
Drawing of test-rig
Dimensions not published due to secrecy.
79
Appendix G
Drawing of installation fixture to camdrum
Dimesions not published due to secrecy.
81
Appendix H
Bump drawing
Drawing not published due to secrecy. An illustration of the shape is shown to get a better understanding.
Figure H.1: Bump illustration
83
Appendix I
Strain gauge specification sheet
85 Figure I.1: Strain gauge specification sheet. Appendix J
Complementing displacement results MTBM1899
The displacement between the shock absorbers fastening joints compared to the simulation for the configuration of 80-30-30 [mm], height in millimetre of attached bumps, is shown in Figures J.1 - J.3.
ANALOG4, 80-30-30, v1 35 AMEsim 30 2DTSA
25
20
15
10
5 Compression [mm]
0
-5 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure J.1: v1.
87 ANALOG4, 80-30-30, v2 40 AMEsim 35 2DTSA
30
25
20
15
10 Compression [mm]
5
0 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure J.2: v2.
ANALOG4, 80-30-30, v3 40 AMEsim 35 2DTSA
30
25
20
15
10 Compression [mm]
5
0 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure J.3: v3. An illustration of the deviations as a plot using the diff() and plot() function in MATLAB can be seen in Figure J.4
ANALOG4, 80-30-30, v3 40 AMEsim 2DTSA 35 Diff
30
25
20
15
Distance [mm] 10
5
0
-5
-10 0 50 100 150 200 250 300 350 samples [n]
Figure J.4: Analog04, Test 7 - Diff. The results for the 70-30-30 [mm] configuration will be presented below and the plotted displacement can be seen in Figures J.5 - J.7 and the evaluation of the stroke for the v3 velocity configuration in Figure J.8.
ANALOG4, 70-30-30, v1 35 AMEsim 2DTSA 30
25
20
15
10 Compression [mm] 5
0 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure J.5: v1. ANALOG4, 70-30-30, v2 40 AMEsim 35 2DTSA
30
25
20
15
10 Compression [mm]
5
0 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure J.6: v2.
ANALOG4, 70-30-30, v3 40 AMEsim 35 2DTSA
30
25
20
15
10 Compression [mm]
5
0 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure J.7: v3. ANALOG4, 70-30-30, v3 40 AMEsim 2DTSA 35 Diff
30
25
20
15
Distance [mm] 10
5
0
-5
-10 0 50 100 150 200 250 300 350 samples [n]
Figure J.8: Analog04, Test 20 - Diff. Appendix K
Complementing displacement results MTB1691
The illustration for the MTB1691 - shock absorber with the 70-30-30 [mm] con- figuration can be seen in Figures K.1 - K.3. The evaluation of the v3 velocity configuration is seen in Figure K.4.
ANALOG4, 70-30-30, v1 35 AMEsim 30 2DTSA
25
20
15
10
5 Compression [mm]
0
-5 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure K.1: v1.
93 ANALOG4, 70-30-30, v2 35 AMEsim 2DTSA 30
25
20
15
10 Compression [mm] 5
0 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure K.2: v2.
ANALOG4, 70-30-30, v3 40 AMEsim 35 2DTSA
30
25
20
15
10 Compression [mm]
5
0 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure K.3: v3. The deviation of the v3 velocity configuration is seen in Figure K.4.
ANALOG4, 70-30-30, v3 40 AMEsim 2DTSA 35 Diff
30
25
20
15
Distance [mm] 10
5
0
-5
-10 0 50 100 150 200 250 300 350 samples [n]
Figure K.4: Analog04, Test 39 - Diff. The illustration for the MTB1691 - shock absorber with the 80-30-30 [mm] config- uration can be seen in Figure K.5 - K.7.
ANALOG4, 80-30-30, v1 35 AMEsim 30 2DTSA
25
20
15
10
5 Compression [mm]
0
-5 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure K.5: v1. ANALOG4, 80-30-30, v2 40 AMEsim 35 2DTSA
30
25
20
15
10
5 Compression [mm]
0
-5 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure K.6: v2.
ANALOG4, 80-30-30, v3 40 AMEsim 35 2DTSA
30
25
20
15
10 Compression [mm]
5
0 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure K.7: v3. The deviation of the v3 velocity configuration is seen in Figure K.8.
ANALOG4, 80-30-30, v3 40 AMEsim 2DTSA 35 Diff
30
25
20
15
Distance [mm] 10
5
0
-5
-10 0 50 100 150 200 250 300 350 samples [n]
Figure K.8: Analog04, Test 45 - Diff. Appendix L
Complementing Force results
The result for the three first tests for the configuration: bump 70-30-30 [mm], low speed compression damping, 7 clicks, high speed compression damping,3 clicks and rebound damping, 3 clicks, is shown in Figures L.1 - L.3.
Strain Gauge, 70-30-30, v1 3000 AMEsim 2cycles from strain gauges 2500
2000
1500
1000 Force [N]
500
0
-500 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure L.1: v1.
99 Strain Gauge, 70-30-30, v2 3500 AMEsim 3000 2cycles from strain gauges
2500
2000
1500
1000 Force [N]
500
0
-500 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure L.2: v2.
Strain Gauge, 70-30-30, v3 4000 AMEsim 3500 2cycles from strain gauges 3000
2500
2000
1500
1000 Force [N] 500
0
-500
-1000 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure L.3: v3. For the configuration: bump 70-30-30 [mm], compression damping, 7 clicks, high speed compression damping, 3 clicks and rebound damping, 5 clicks. The result can be seen in Figures L.4 - L.6.
Strain Gauge, 70-30-30, v1 3000 AMEsim 2cycles from strain gauges 2500
2000
1500
1000 Force [N]
500
0
-500 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure L.4: v1. Strain Gauge, 70-30-30, v2 3500 AMEsim 3000 2cycles from strain gauges
2500
2000
1500
1000 Force [N]
500
0
-500 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure L.5: v2.
Strain Gauge, 70-30-30, v3 4000 AMEsim 3500 2cycles from strain gauges 3000
2500
2000
1500
1000 Force [N] 500
0
-500
-1000 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure L.6: v3. For the configuration: bump 80-30-30 [mm], compression damping, 7 clicks, high speed compression damping, 3 clicks and rebound damping, 3 clicks. The result can be seen in Figures L.7 - L.9.
Strain Gauge, 80-30-30, v1 3500 AMEsim 3000 2cycles from strain gauges
2500
2000
1500
1000 Force [N]
500
0
-500 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure L.7: v1. Strain Gauge, 80-30-30, v2 4000 AMEsim 3500 2cycles from strain gauges 3000
2500
2000
1500
1000 Force [N] 500
0
-500
-1000 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure L.8: v2.
Strain Gauge, 80-30-30, v3 5000 AMEsim 2cycles from strain gauges 4000
3000
2000 Force [N] 1000
0
-1000 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure L.9: v3. For the configuration: bump 80-30-30 [mm],compression damping, 7 clicks, high speed compression damping, 3 clicks and rebound damping, 5 clicks. The result can be seen in Figure L.10 - L.12.
Strain Gauge, 80-30-30, v1 3500 AMEsim 3000 2cycles from strain gauges
2500
2000
1500
1000 Force [N]
500
0
-500 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure L.10: v1. Strain Gauge, 80-30-30, v2 4000 AMEsim 3500 2cycles from strain gauges
3000
2500
2000
1500 Force [N] 1000
500
0
-500 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure L.11: v2.
Strain Gauge, 80-30-30, v3 5000 AMEsim 2cycles from strain gauges 4000
3000
2000 Force [N] 1000
0
-1000 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 time [s] Figure L.12: v3. Appendix M
MATLAB - Linear transducers
%% Anders Rask & Adam Olsson % Öhlins thesis % cmp_38.m % 2019-05-29 clear variables; close all; clc; sampling = 200; %Hz Test sampling set by actual logger used dist_bet_peak = 0.950; %Approx value between each peak (has to... %be smaller than each value between peaks) skjut = 0.375; B = open(’38.mat’); %Read & import data from saved and modified... %data logger k_val = [0.732751784298177 0]; %Polyfit between (difference of)... %logger and physical shockabsorber in CamDrum
ANALOG3 A3 = importdata(’Analog3.data’); %Read & import data from AMEsim plot
% findpeaks(B.a4_span,sampling,’MinPeakDistance’,dist_bet_peak) %Make... %sure to %validate timespan so that each peak is included
[pks3,locs3]=findpeaks(B.a3_span,sampling,’MinPeakDistance’,dist_bet_peak);... %[Peak_val,time_loc] tpulse3 = mean(diff(locs3)); %Mean differnce between peaks
107 conv3 = skjut + linspace(0,2*tpulse3,2*length(B.tsa3)); %Conversion... %of TSA to sync it with AMEsim-plot a0 = sind(5)*(221.1); tsatodeg = asind((a0+B.tsa3)/222.8); f0 = figure(); movegui(f0,’southeast’) plot(A3.data(4:end,1),-1*A3.data(4:end,2))%+min(A3.data(4:end,2))... %-min(B.tsa3)) AMEsim grid on hold on % f2 = figure(); % movegui(f2,’northwest’) plot(conv3,[tsatodeg’ tsatodeg’]) %LOGGER xlabel(’time [s]’,’FontSize’,18) ylabel(’Angle [\circ]’,’FontSize’,18) legend(’AMEsim’,’2DTSA’) title(’ANALOG3, 70-30-30, v2’,’FontSize’,18,’FontWeight’,’bold’)
ANALOG4 A4 = importdata(’Analog4.data’); %Read & import data %A4o = importdata(’Analog4_sim.data’); %Read & import data
% findpeaks(B.a4_span,sampling,’MinPeakDistance’,dist_bet_peak) %Make... %sure to %validate timespan so that each peak is included
[pks4,locs4]=findpeaks(B.a4_span,sampling,’MinPeakDistance’,dist_bet_peak);... %[Peak_val,time_loc] tpulse4 = mean(diff(locs4)); %Mean differnce between peaks conv4 = skjut+linspace(0,2*tpulse4,2*length(B.tsa4)); %Conversion of... %TSA to sync it with AMEsim-plot f1 = figure(); movegui(f1,’northeast’) plot(A4.data(4:end,1),-1*A4.data(4:end,2)+216)%Displaced 216 mm... %due to free length of damper (hole to hole) grid on hold on %plot(A4o.data(4:end,1),-1*A4o.data(4:end,2)+250) % f2 = figure(); % movegui(f2,’northwest’)
%plot(conv4,[B.tsa4’ B.tsa4’]) tsa4_converted = polyval(k_val,B.tsa4); plot(conv4,[tsa4_converted’ tsa4_converted’]) xlabel(’time [s]’,’FontSize’,18) ylabel(’Compression [mm]’,’FontSize’,18) legend(’AMEsim’,’2DTSA’) title(’ANALOG4, 70-30-30, v2’,’FontSize’,18,’FontWeight’,’bold’)
ANALOG5
A5 = importdata(’Analog5.data’); %Read & import data % figure() % findpeaks(B.a5_span,sampling,’MinPeakDistance’,dist_bet_peak) %Make... %sure to %validate timespan so that each peak is included
[pks5,locs5]=findpeaks(B.a5_span,sampling,’MinPeakDistance’,dist_bet_peak);... %[Peak_val,time_loc] tpulse5 = mean(diff(locs5)); %Mean differnce between peaks conv5 = skjut+linspace(0,2*tpulse5,2*length(B.tsa5)); %Conversion of... %TSA to sync it with AMEsim-plot f2 = figure(); movegui(f2,’northwest’) plot(A5.data(4:end,1),A5.data(4:end,2)-(530.5+27.5*25.4/2));% grid on hold on % f2 = figure(); % movegui(f2,’northwest’) plot(conv5,[B.tsa5’ B.tsa5’]) xlabel(’time [s]’,’FontSize’,18) ylabel(’Distance [mm]’,’FontSize’,18) legend(’AMEsim’,’2DTSA’) title(’ANALOG5, 70-30-30, v2’,’FontSize’,18,’FontWeight’,’bold’) Analysing difference of Analog4 and Amesim ay4 = interp1(A4.data(4:end,1),-1*A4.data(4:end,2)+216,conv4); figure() plot(ay4) hold on plot([tsa4_converted’ tsa4_converted’]) four = [ay4;[tsa4_converted’ tsa4_converted’]]; p4 = diff(four); plot(p4) xlabel(’samples [n]’,’FontSize’,18) ylabel(’Distance [mm]’,’FontSize’,18) legend({’AMEsim’,’2DTSA’,’Diff’},’FontSize’,18, ’FontWeight’,’bold’) title(’ANALOG4, 70-30-30, v2’,’FontSize’,18,’FontWeight’,’bold’)
NoNum = find(abs(isnan(p4))); p4(NoNum) = []; avg4 = mean(abs(p4));% SNITTAVVIKELSEN) disp([’T38: The absolute mean value of Analog 4 is: ’,num2str(avg4),... ’ mm’])
Cleansing of extreme values p4pop = p4; extremes = find(abs(p4pop)>5); p4pop(extremes) = []; avg4pop = mean(abs(p4pop)); disp([’T38_pop: The absolute mean value of Analog 4 with removed... diff above 5 mm due to possible hysteresis is: ’,num2str(avg4pop),’ mm’])
%REMEMBEr THAT THE DIFF I SIDLED AFFECTS The diFF IN HEIGHT GREATLY
Precentage Percent4 = (four(1,:)./four(2,:))-1; % plot(Percent4) NoNum = find(abs(isnan(Percent4))); Percent4(NoNum) = []; per4mean = mean(abs(Percent4)); if max(Percent4) Plot 1 cycle zoom t_round = 1; figure() plot(A4.data(4:end,1),-1*A4.data(4:end,2)+216)%Displaced 216 mm... %due to free length of damper (hole to hole) grid on hold on plot(conv4,[tsa4_converted’ tsa4_converted’]) xlim([t_round 2*t_round]) xlabel(’Time [s]’,’FontSize’,18) ylabel(’Distance [mm]’,’FontSize’,18) legend({’AMEsim’,’2DTSA’},’FontSize’,18, ’FontWeight’,’bold’) title(’ANALOG4, 70-30-30, v2’,’FontSize’,18,’FontWeight’,’bold’) Appendix N MATLAB - Stiff rod %% Anders Rask & Adam Olsson % Öhlins thesis % cmp_34.m % 2019-05-29 clear variables; close all; clc; sampling = 200; %Hz Test sampling set by actual logger used dist_bet_peak = 1.5; %Approx value between each peak (has to... %be smaller than each value between peaks) B = open(’34.mat’); %Read & import data from saved and... %modified data logger k_val = [0.000270709972145647 0.739843107340130 0.103708772810103];... %%Polyfit between (difference of) logger and physical shockabsorber... %in CamDrum ANALOG3 A3 = importdata(’Analog3.data’); %Read & import data from AMEsim plot findpeaks(B.a3_span,sampling,’MinPeakDistance’,dist_bet_peak) %Make... %sure to validate timespan so that each peak is included [pks3,locs3]=findpeaks(B.a3_span,sampling,’MinPeakDistance’,dist_bet_peak);... %[Peak_val,time_loc] tpulse3 = mean(diff(locs3)); %Mean differnce between peaks conv3 = 2.5 + linspace(0,2*tpulse3,length(B.tsa3)*2); ... 113 %X + linspace... (X is horisontal sync) The Conversion of... %TSA to sync it with AMEsim-plot a0 = sind(8.5)*(221.1); tsatodeg = asind((a0+B.tsa3)/221.1); f0 = figure(); movegui(f0,’southeast’) plot(A3.data(4:end,1),-1*A3.data(4:end,2))% AMEsim grid on hold on % f2 = figure(); % movegui(f2,’northwest’) plot(conv3,[tsatodeg’ tsatodeg’]) %LOGGER xlabel(’time [s]’,’FontSize’,18) ylabel(’Angle [\circ]’,’FontSize’,18) legend(’AMEsim’,’2DTSA’) title(’ANALOG3, Stiff rod, 50-30-30, 4.44km/h’,’FontSize’... ,18,’FontWeight’,’bold’) ANALOG5 A5 = importdata(’Analog5.data’); %Read & import data % figure() % findpeaks(B.a5_span,sampling,’MinPeakDistance’,dist_bet_peak) %Make... % sure to validate timespan so that each peak is included [pks5,locs5]=findpeaks(B.a5_span,sampling,’MinPeakDistance’,dist_bet_peak);... %[Peak_val,time_loc] tpulse5 = mean(diff(locs5)); %Mean differnce between peaks conv5 = 2.5+linspace(0,2*tpulse5,length(B.tsa5)*2); %Conversion of TSA... %to sync it with AMEsim-plot f2 = figure(); movegui(f2,’northwest’) plot(A5.data(4:end,1),A5.data(4:end,2)-(530.5+27.5*25.4/2));% grid on hold on % f2 = figure(); % movegui(f2,’northwest’) plot(conv5,[B.tsa5’ B.tsa5’]) xlabel(’time [s]’,’FontSize’,18) ylabel(’Distance [mm]’,’FontSize’,18) legend(’AMEsim’,’2DTSA’) title(’ANALOG5, Stiff rod, 50-30-30, 4.44km/h’,’FontSize’,18,... ’FontWeight’,’bold’) Analog3 comparison ay3 = interp1(A3.data(4:end,1),-1*A3.data(4:end,2),conv3); figure() plot(ay3) hold on plot([tsatodeg’ tsatodeg’]) Amp3Ame = max(ay3)-min(ay3) Amp3Tsa = max(tsatodeg)-min(tsatodeg) Analog 5 comparison ay5 = interp1(A5.data(4:end,1),A5.data(4:end,2)-(530.5+27.5*25.4/2),conv5); figure() plot(ay5) hold on plot([B.tsa5’ B.tsa5’]) Amp5Ame = max(ay5)-min(ay5) Amp5Tsa = max(B.tsa5)-min(B.tsa5) percentage Pro3 = 1e2*abs(Amp3Ame/Amp3Tsa-1) Pro5 = 1e2*abs(Amp5Ame/Amp5Tsa-1) Appendix O MATLAB - Force script %% Anders Rask & Adam Olsson % Öhlins thesis % avgstress.m % 2019-05-29 clear variables; close all; clc; Define constants sampling = 10000; %Hz Test sampling set by actual logger used dist_bet_peak = 1.2; %Approx value between each peak (has to be... %smaller than each value between peaks) ss = 160000; %SamplingSTART se = 155000; %SamplingEND test_num = 38; t_round = 1; % 4/3 s/varv 9 km, 1s/varv 12km, 0.8 s/varv 15km skjut = 0.3; %Förskjutning av kurva %Motstående: 0-2, 1-3, 4-6, 5-7 file =([’Stressfile’,num2str(test_num),’.mat’]); load(file) d = 0.01; A = pi*(d/2)^2; Amesim = importdata([’Strain_force_’,num2str(test_num),’.data’]); %Read... %& import data from AMEsim plot samp_cyc = round(10000*t_round) % samples per cycle % span = [352200:386300]; %span = (ss:length(Stress(:,1))-se); intervall =round( [1 1]*length(Stress(:,1))/2 + [-1 1]*1*samp_cyc); 117 span = [intervall(1):intervall(2)]; pair1 = (Stress(span,1)+Stress(span,3))/2; pair2 = (Stress(span,2)+Stress(span,4))/2; pair3 = (Stress(span,5)+Stress(span,7))/2; pair4 = (Stress(span,6)+Stress(span,8))/2; tot_beam1 = (pair1+pair2)/2; tot_beam2 = (pair3+pair4)/2; tot_F = (-(tot_beam1+tot_beam2)*A)+1258.76; % Förskjuten med... %hjälp av amesims värde för fixtur i vila Plots num_cyc = diff(intervall)/samp_cyc; conv = skjut + linspace(0,t_round*num_cyc,length(tot_F)); figure() plot(Amesim.data(4:end,1),1*Amesim.data(4:end,2)) hold on grid on % figure() plot(conv,tot_F) xlabel(’time [s]’,’FontSize’,18) ylabel(’Force [N]’,’FontSize’,18) legend(’AMEsim’,’2cycles from strain gauges’) title(’Strain Gauge, 80-30-30, 15km/h’,’FontSize’,18,’FontWeight’,’bold’) max(Amesim.data(4:end,2)) max(tot_F) Plot 1 cycle zoom %t_round = 0.8; % 4/3 s/varv 9 km, 1s/varv 12km, 0.8 s/varv 15km figure() plot(Amesim.data(4:end,1),1*Amesim.data(4:end,2)) hold on grid on % figure() plot(conv,tot_F) xlim([t_round/2 1.5*t_round]) xlabel(’Time [s]’,’FontSize’,18) ylabel(’Force [N]’,’FontSize’,18) legend(’AMEsim’,’1 cycle from strain gauges’) title(’Strain Gauge, 70-30-30, 12km/h’,’FontSize’,18,’FontWeight’,’bold’) Appendix P MATLAB - TSA for linear transducers %% Anders Rask & Adam Olsson % Öhlins thesis % avg_logger_data_v3.m % 2019-05-29 clear variables; close all; clc; Define constants sampling = 200; %Hz Test sampling set by actual logger used dist_bet_peak = 0.650; %Approx value between each peak (has to be... %smaller than each value between peaks) ss = 800; %SamplingSTART se = 1200; %SamplingEND test_num = 33; Read and reconstruct [~,~,data] = xlsread([num2str(test_num),’.csv’]); %Read & import data data(1:2,:)=[]; % Clear first two rows (txt) t = cell2mat(data(:,1)); %time vector a3 = cell2mat(data(:,3)); a4 = cell2mat(data(:,4)); % Position values for analog 4 (logger) a5 = cell2mat(data(:,5)); t_span = t((ss:end-se)); % Cleared unwanted start/stop values... %from time_vector 121 a3_span = a3((ss:end-se)); a4_span = a4((ss:end-se)); % Cleared unwanted start/stop values... %from pos_vector a5_span = a5((ss:end-se)); Plot f1 = figure(); %Validation plot for given span/start/stop movegui(f1,’northeast’) plot(t_span, a4_span) grid on % figure() %Validation plot for peaks f2 = figure(); %Validation plot for given span/start/stop movegui(f2,’southeast’) findpeaks(a4_span,sampling,’MinPeakDistance’,dist_bet_peak) %Make... %sure to validate timespan so that each peak is included [pks,locs]=findpeaks(a4_span,sampling,’MinPeakDistance’,dist_bet_peak);... %[Peak_val,time_loc] tpulse = mean(diff(locs)); %Mean differnce between peaks % figure() % f3 = figure(); %Validation plot for given span/start/stop % movegui(f3,’northwest’) % tsa(a3_span, sampling,tpulse);% Average for given data % figure() f4 = figure(); %Validation plot for given span/start/stop movegui(f4,’northwest’) tsa(a4_span, sampling,tpulse);% Average for given data % figure() % tsa(a5_span, sampling,tpulse);% Average for given data tsa3 = tsa(a3_span, sampling,tpulse); % Plot avg for above tsa4 = tsa(a4_span, sampling,tpulse); % Plot avg for above tsa5 = tsa(a5_span, sampling,tpulse); % Plot avg for above % dlmwrite([num2str(test_num),’.mat’],ta) save([num2str(test_num),’.mat’],’t_span’,’a3_span’,’a4_span’,... ’a5_span’,’tsa3’,’tsa4’,’tsa5’) Appendix Q MATLAB - Force mean and percentage %% Anders Rask & Adam Olsson % Öhlins thesis % MeanNpercent.m % 2019-05-29 clear all; close all; clc; Values from strain comparison plots %Highest peak in amesim, The after %[strain, amesim, strain, amesim] T37to48 = [2483 2967 2488 2806;... 2736 3478 2697 2939;... 2997 3879 3038 3228;... 2412 2929 2585 2871;... 2729 3478 2855 3155;... 2936 3839 2924 3119;... 2554 3166 2681 2997;... 2847 3698 2997 3340;... 3127 4155 2995 3450;... 2460 3125 2745 3079;... 2836 3693 3136 3471;... 3120 4077 3001 3456]; Mean in N First_peak = abs(T37to48(:,1)-T37to48(:,2)); Second_peak = abs(T37to48(:,3)-T37to48(:,4)); force_mean = (First_peak+Second_peak)/2 123 Pencentage First_peak_per = abs(T37to48(:,2)./T37to48(:,1)-1); Second_peak_per = abs(T37to48(:,4)./T37to48(:,3)-1); Perncetage_mean = (First_peak_per+Second_peak_per)/2 Appendix R MATLAB - Theoretical maximum bending stress %% Anders Rask & Adam Olsson % Öhlins thesis % Manual_strain_calc.m % 2019-05-29 clear vairables; close all; clc; Vars r = 5*1e-3; g = 9.81; % [m/s^2] F = [731.5 1422.4]*1e-3 * g; %[N] d = 10e-3; % [m] L1 = 156e-3; % [m] 160mm one sensor, black marked L2 = 159e-3; % [m] unmarkt Calc W_b = pi*d^3/32; M_b1 = F*L1; % [N/m] M_b2 = F*L2; % [N/m] sigma_b1 = M_b1/W_b*1e-6; sigma_b2 = M_b2/W_b*1e-6; A = pi*r^2; F = 200 sigma_v1 = F/A 125 disp(’Marked beam’) disp([’Weight: ’ num2str(F(1)*1e3/g),’g, ’ char(963) ’ = ’... num2str(sigma_b1(1)) ’[MPa]’]) disp([’Weight: ’ num2str(F(2)*1e3/g),’g, ’ char(963) ’ = ’... num2str(sigma_b1(2)) ’[MPa]’]) disp(’Unmarked beam’) disp([’Weight: ’ num2str(F(1)*1e3/g),’g, ’ char(963) ’ = ’... num2str(sigma_b2(1)) ’[MPa]’]) disp([’Weight: ’ num2str(F(2)*1e3/g),’g, ’ char(963) ’ = ’... num2str(sigma_b2(2)) ’[MPa]’]) Appendix S MATLAB - Tyre spring calculation %% Anders Rask & Adam Olsson % Öhlins thesis % tire_spring.m % 2019-05-29 clear variables; close all; clc; w = [32.3 41.2 50.35 59.65 68.6 77.7 86.9 96.1]; % Weight acting on rear wheel g = 9.82; % Gravity constant d = [6.6 7.42 8.75 9.8 10.8 11.6 12.4 13.17]; %wheel compression N = w*g; % Force plot(d,N) xlabel(’Compression [mm]’,’FontSize’,18) ylabel(’Force [N]’,’FontSize’,18) %legend({’N/mm’},’FontSize’,18) title(’Tire model spring constant’,’FontSize’,18,’FontWeight’,’bold’) 127 TRITA ITM-EX 2019:249 www.kth.se