DEGREE PROJECT IN MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2019
Vibration damping of alpine skis with implemented Flow Motion Technology
JOHN PALMBORG
HAMPUS SÖDERMAN
KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT
Master of Science Thesis TRITA-ITM-EX 2019:243
VIBRATION DAMPING OF ALPINE SKIS WITH IMPLEMENTED FLOW MOTION TECHNOLOGY
John Palmborg Hampus Söderman Approved Examiner Supervisor 2019-06-09 Ulf Sellgren Stefan Björklund Commissioner Contact person Flow Motion Technology AB Fredrik Andersson Abstract Flow Motion Technology AB has previously developed a technology to improve hockey skates and inlines. The technology called Flow Motion Technology (FMT) is utilizing the smooth and effective rolling motion of a human footstep, and has proven to be very successful after implementation in both hockey skates and inlines. Flow Motion Technology AB has interest in investigating whether the technology can be implemented in other sports applications, which this thesis project concerns. The project examines the implementation of FMT in the alpine skiing segment. The purpose is to provide Flow Motion Technology AB with a foundation for evaluating the potential of investing further in the development of FMT applied in alpine skiing. FMT is implemented in a feature positioned between ski and binding of most alpine race skis, commonly called a race plate. The work is divided into two parts; The first part covers the development and manufacturing of a prototype along with detailed description of the procedures and methods used. The second part is about the tests of the prototype’s vibration-damping properties carried out in laboratory environment along with analysis of the results. Initial field tests are also carried out followed by fundamental analysis. An existing plate intended for competition use is tested in parallel with the prototype and is used as a reference when analyzing the results. The results show that the ski equipped with the FMT plate dampened vibrations on an average of 27 % faster than the reference plate. Measurements was compiled for three damping intervals specified for the tests performed in laboratory. A statistically significant difference in all three cases was obtained. The measured maximum amplitude of the acceleration in the vibrations was also significantly lower for the ski implemented with the FMT plate compared to the reference plate. The eigen frequencies of the ski measured in laboratory were not significantly affected if the ski was fitted with the FMT plate or the reference plate. The eigen frequencies measured in field generally corresponded to the measured in laboratory, with the difference that they were offset on an average of 7 Hz higher in field.
Keywords: alpine skiing, damping, race plate, vibrations
Examensarbete TRITA-ITM-EX 2019:243
DÄMPNING AV VIBRATIONER I ALPINSKIDOR MED IMPLEMENTERAD FLOW MOTION TECHNOLOGY
John Palmborg Hampus Söderman Godkänt Examinator Handledare 2019-06-09 Ulf Sellgren Stefan Björklund Uppdragsgivare Kontaktperson Flow Motion Technology AB Fredrik Andersson Sammanfattning Flow Motion Technology AB har tidigare utvecklat en teknologi för att förbättra hockeyskridskor och inlines. Teknologin kallad Flow Motion Technology (FMT) utnyttjar den naturliga och effektiva rullande rörelse i en människas fotsteg, och har efter implementation i hockeyskridskor och inlines visat sig vara framgångsrik. Flow Motion Technology AB vill undersöka om denna teknologi kan implementeras i andra idrottssammanhang för att utvärdera möjligheter att bredda företagets affärsområde. Detta examensarbete är en del av denna undersökning, och i denna rapport beskrivs implementationen av FMT i segmentet alpinskidåkning. Syftet med projektet är att förse Flow Motion Technology AB med underlag för att utvärdera lönsamheten i att investera mer i utvecklingen av FMT riktad mot alpinskidåkning. FMT implementeras i projektet i en raceplatta, en komponent monterad mellan skida och bindning. Arbetet är uppdelat i två delar; utveckling och tillverkning av en funktionsprototyp med detaljerad beskrivning av tillvägagångssätt och metoder, samt tester av prototypens vibrationsdämpande prestanda i labbmiljö med tillhörande analys av resultat. Initiala tester utförs även i fält med enklare analys av resultat. En befintlig bindningsplatta avsedd för tävling testas parallellt med den utvecklade plattan och används som referens vid analys av resultaten. Resultaten visar att plattan implementerad med FMT dämpade en skidas vibrationer i genomsnitt 27 % snabbare än vad referensplattan gjorde vid de tre dämpningsintervall som specificerats för testen i labbmiljö. En statistiskt signifikant skillnad i alla tre fall. Den uppmätta maxamplituden för accelerationen i vibrationerna var även statistiskt signifikant lägre för skidan implementerad med FMT jämfört med referensplattan. Egenfrekvenserna uppmätta i labb påverkades inte nämnvärt om skidan var monterad med FMT-plattan eller referensplattan. De egenfrekvenser som uppmättes i fält motsvarade generellt de som uppmättes i labb med skillnaden att de var förskjutna till att i genomsnitt vara 7 Hz högre.
Nyckelord: alpin skidåkning, dämpning, raceplatta, vibrationer
FOREWORD
We would like to thank our supervisors, Stefan Björklund at KTH and Fredrik Andersson at Flow Motion Technology AB, for their guidance and help throughout the project. We would like thank the whole Flow Motion Technology team for the warm welcome and for letting us take on this exciting project. We would also like to give our greatest thanks to ESSIQ AB for all support and for letting us write our thesis at your office, especially to our mentor Jacob Leygraf, Lars Berglind and Magnus Engelmark for always assisting.
In addition, we would like to give special thanks to our sponsors for making our prototype possible to manufacture and tests possible to perform. We really can not thank you enough:
Mikael Östensson and Fredrik Lindblom at Marström Composite AB for inviting us to your factory and supplying us with material, tools and expertise in the field of carbon fiber manufacturing.
Jonas Lundström at Jönköpings Modelltillverkning AB for providing the core material of our prototype.
Magnus Asplund at Dewesoft AB for supplying us with top performance DAQ system and guidance.
Håkan Andersson at RISE, for supplying us with accelerometers and expertise within the field of vibration measurement.
Gustavsson Composite for providing carbon fiber and equipment for our prototype devel- opment.
Håkan Johansson at Composult AB for guidance in the field of composite theory and man- ufacturing and skiing dynamics.
NOMENCLATURE
FMT Flow Motion Technology
FFT Fast Fourier transform
DAQ Data acquisition
UD Uni directional
COM Center of mass
CAD Computer-aided design
FEA Finite element analysis
FEM Finite element method
CONTENTS
1 INTRODUCTION 1
1.1 Background and problem description ...... 1
1.1.1 Research question ...... 1
1.2 Purpose ...... 2
1.3 Method description ...... 2
1.4 Delimitations ...... 2
1.5 Risk assessment ...... 3
1.6 Project planning ...... 3
2 FRAME-OF-REFERENCE 5
2.1 Alpine ski dynamics and vibrations ...... 5
2.2 Test methods for ski vibrations and damping ...... 7
2.3 Alpine ski damping equipment - background and state of the art ...... 8
2.4 Flow Motion Technology ...... 11
2.5 Previous work ...... 12
2.5.1 Previous prototype ...... 13
2.5.2 Tests ...... 13
2.6 FIS regulations ...... 14
2.7 Fast Fourier Transform ...... 15
3 IMPLEMENTATION 17
3.1 Ski physics and calculations ...... 17
3.1.1 Ski bending when performing a carve turn ...... 17
3.1.2 Torsion of plate ...... 19
3.2 Prototype ...... 21
3.2.1 Requirement specification ...... 21
3.2.2 Materials ...... 21
3.2.3 Sandwich structure ...... 23 3.2.4 Composite layup & Rule of Mixtures ...... 24
3.2.5 Making a core ...... 28
3.2.6 Making a mould ...... 29
3.2.7 Layup of layers ...... 29
3.2.8 Vacuum forming and Autoclave ...... 31
3.2.9 Post manufacturing, finishing and mounting ...... 32
3.3 Test procedure ...... 35
3.3.1 Equipment and measurement system setup ...... 35
3.3.2 Lab test ...... 39
3.3.3 Field ...... 41
4 RESULTS AND ANALYSIS 43
4.1 Final design of prototype ...... 43
4.2 Stiffness of prototype ...... 43
4.3 Strength of prototype ...... 45
4.4 Lab test analysis ...... 46
4.5 Field test analysis ...... 49
4.6 Comparison of laboratory and field data ...... 51
5 CONCLUSION AND DISCUSSION 53
5.1 Conclusions ...... 53
5.2 Discussion ...... 54
6 RECOMMENDATIONS AND FUTURE WORK 57
7 APPENDICES 61
7.1 Risk Assessment ...... 61
7.2 Prototype Requirement Specification ...... 62
7.3 SikaBlock M700 - Technical specification ...... 63
7.4 DAQ: Dewe 43 A - Specification ...... 65 7.5 Brüel & Kjær DeltaTron Accelerometer Type 4397 - Specification ...... 66
7.6 Data sheet KISO 358 BUTYL Superior - Specification ...... 67
7.7 DEWESoft Set up - FFT Analyser ...... 68
7.8 DEWESoft Set up - Recorder ...... 69
7.9 Lab test data ...... 70
7.10 Field test data ...... 71
7.11 Gantt Chart ...... 73
7.12 MATLAB Scripts ...... 76
7.12.1 Solid Mechanics - design of prototype ...... 76
7.12.2 Test data - Function fitting ...... 79
7.13 Power supply - battery ...... 80
7.14 FMT Prototype - Drawings ...... 81
7.15 Composite properties ...... 86 List of Figures
1 An illustration of how an alpine slalom track is generalized [1]...... 5
2 Forces acting on skier: centrifugal force FC , gravitational force Fg, resultant force FR [2]...... 6
3 Dimensions and positioning of specific details in an ISO 6267 test rig [5]. . . 7
4 A diagram by Gary C. Foss and Bard Glenne which illustrates the power spectral density [g2/Hz], as function of frequency [Hz]. Field test on hard snow (Yellow) and soft snow (Green) [6]...... 8
5 Dynastar skis with the Contact System, a red plastic shock absorber on the tip of the ski...... 8
6 2019 model Völkl Racetiger SL skis with UVO mass damper in the tip [14]. 9
7 2019 model Atomic Redster G9 ski with Srevotec carbon fiber rod along the top of the ski connected to damper under the binding [15]...... 9
8 Salomon Pilot System binding with plate [17]...... 10
9 2019 model Head WCR plate with hydraulic oil dampening [18]...... 10
10 2019 model Marker WC Piston plate with hydraulic oil dampening [19]. . . 10
11 Illustration of the separated frame of a FMT implemented roller skate [20]. 11
12 Illustration of the Flow Motion Technology AB Roller Frame and an ice hockey skate. The marked point is where the contact is acting [20]...... 11
13 Illustration of the separated frame of a FMT implemented roller skate [21]. 12
14 FMT plate design concept developed by Linn Rilegård...... 13
15 The functional ski system referred to in FIS-regulations [24]...... 15
16 The width of the interface cannot exceed the width of the ski, w ≥ 0 [24]. . 15
17 A signal decomposed into its three sine wave elements [22]...... 16
18 The frequencies of the sine waves shown on the x-axis, and their amplitude on the y-axis [22]...... 16
19 Isometric view of positioned points A, B and C, on a ski laying with the base flat on the ground...... 17
20 Front view illustrating the re-positioned B2...... 18
21 Top view illustrating the bent ski, re-positioned points A2, B2 and C2. . . . 18
22 side view of alpine ski and a mounted FMT plate...... 19 23 A simplified model of a ski plus plate section view, while performing a carving turn with inclination angle α...... 20
24 Isometric view of torsional torque Tt occurring in the FMT plate...... 20
25 Different materials and their properties...... 22
26 Sandwich structure...... 23
27 Different ratios (core/composite)...... 24
28 The bending stiffness as function of composite face thickness...... 24
29 Different carbon fiber fabric weaves [33]...... 25
30 Directions on the sandwich structure...... 26
31 Examples of the efficiency factor for different fiber directions [34]...... 27
32 Directions in the sandwich structure...... 27
33 The milling process and the finished cores...... 28
34 The mould, consisting of 14 MDF boards glued together...... 29
35 The layup of layers...... 29
36 Close up of the end showing the difference in lenght of the layers on the radius side...... 30
37 Layup of bottom layers...... 30
38 Layup core and top layers...... 30
39 The vacuum bagging components. The breather is a breathable felt mem- brane allowing the air transfer to the coupling...... 31
40 The autoclave...... 31
41 Illustration of the plates to be cut out...... 32
42 The cut out plates in pairs...... 32
43 Holes being drilled...... 32
44 Heli coil installation procedure...... 33
45 Heli coil installation procedure, continuation...... 33
46 The bushings...... 34
47 The stoppers and bushings...... 34
48 The damping material attached to the FMT plate...... 34 49 DAQ unit, DEWE 43 A. [35]...... 35
50 Brüel & Kjær DeltaTron Accelerometer Type 4397...... 35
51 The plate with Marker Xcell Race 16 bindning mounted on a Blizzard GS Worldcup Magnesium ski...... 36
52 The Marker WC Piston plate with Marker Xcell Race 16 binding mounted on a Blizzard GS Worldcup Magnesium ski...... 36
53 Three accelerometers rigged on ski for initial laboratory tests...... 37
54 Vibration plot of a impact with chisel. The yellow plot shows the accelerom- eter close to the center of the ski (1), the blue shows the one between the center and the tip (2) and the red shows the one close to the tip (3). . . . . 37
55 The four first frequency modes shown as peaks at around 13, 50, 125 and 240 Hz. The yellow plot shows the accelerometer at position 1, the blue shows the one at position 2 and the red shows the one at position 3...... 38
56 The four first frequency modes shown as peaks. The yellow plot shows the accelerometer at position 1, the blue shows the one at position 2 and the red shows the one at position 3...... 38
57 The boot used in the lab tests, with a steel frame molded in epoxy resin. . . 39
58 The test rig set up with boot mounted to the prototype and ski...... 39
59 The accelerometer and cable mounted with tape...... 40
60 Front section view of the accelerometer mounted on the ski...... 40
61 Recorder diagram of a lab test on the FMT setup. Vibration utilized with the mechanical release of cutting the nylon line...... 41
62 The field test setup...... 41
63 The measurement system rigged for field test...... 42
64 The FMT plate final design...... 43
65 Position and direction of load forces used in ANSYS...... 44
66 Fixed support used in ANSYS...... 44
67 Resulting deflection of the FMT plate using FEA. d1 is the resulting distance of deflection, using a homogeneous plate design. d2 is the calculated deflection for a FMT plate with a core material...... 45
68 Von Mises stress simulation of FMT plate...... 45
69 The analysis method were to log the time from the max amplitude to the point where a specific percentage of that amplitude was reached...... 46 70 FFT diagram of a lab test on the FMT setup showing the four first frequency modes. Vibration excited by a hit with a chisel...... 48
71 FFT analysis of a carve turn run on soft snow...... 49
72 FFT analysis of a carve turn run on hard snow...... 49
73 FFT analysis of a straight run on hard snow...... 50
A.1 SikaBlock M700 - Technical specification...... 63
A.2 SikaBlock M700 - Technical specification...... 64
A.3 Dewe 43 A - Analog input specification...... 65
A.4 Brüel & Kjær DeltaTron Accelerometer Type 4397 - Specification...... 66
A.5 Data sheet KISO 358 BUTYL Superior - Specification...... 67
A.6 DEWESoft Set up - FFT Analyser...... 68
A.7 DEWESoft Set up - Recorder...... 69
A.8 Battery specification...... 80
A.9 FMT plate assembly drawing...... 81
A.10 FMT plate drawing...... 82
A.11 Stopper Drawing...... 83
A.12 Bushing front Drawing...... 84
A.13 Bushing back Drawing...... 85
A.14 Carbon fiber properties...... 86
A.15 Epoxy resin properties...... 87 List of Tables
1 Resultant g-forces gR by different inclination angle α of alpine skier . . . . . 6
2 Overview of the tests performed by Linn Rilegård [20] ...... 14
3 FIS regulations affecting this project [24]...... 14
4 Bending radius RB of ski as function of ski dimensions and inclination angle α. 19
5 Composite properties, as input values used in ANSYS...... 43
6 Mechanical release lab data...... 47
7 Lab test: results for t-test of acceleration for reference plate and FMT plate at maximum amplitude...... 47
8 Lab test: results for t-test of time for reference plate and FMT plate at different damping limits...... 47
9 Lab test: The first four frequency modes of the FMT plate and the refer- ence plate, presented with average frequency, standard deviation and devia- tion/average frequency...... 48
10 Analysis of the frequency modes measured in field tests...... 50
11 Comparison of laboratory and field test data...... 51
A.1 Risk assessment...... 61
A.2 Requirement specification of prototype properties...... 62
A.3 Lab test data - eigen frequencies...... 70
A.4 Lab test data - release test...... 70
A.5 Lab test data - differences...... 70
A.6 Field test data...... 71
A.7 Comparison between laboratory and field test data...... 71 1 INTRODUCTION
1.1 Background and problem description
Flow Motion Technology AB has developed a technology for ice-skates and inlines. The technology called Flow Motion Technology (FMT), is based on a two-part chassis where a rounded upper part rolls against a flat base which enables the natural movement of a human footstep. The purpose is to optimize performance by utilize this natural movement. In addition to the main focus on these products, a number of research projects are in progress investigating the possibilities of implementing FMT in equipment for other sports, such as alpine skiing, cross country skiing and fitness inlines, with intention to broaden the trademark. This degree project concerns if FMT could be of advantage in alpine skiing. Flow Motion Technology AB has a hypothesis of benefits by implementing FMT to a feature positioned between ski and binding of most alpine race skis. This feature has many names, commonly race plate or riser plate but will be referred to as plate in this thesis. The three hypothetical benefits stated by Flow Motion Technology AB is presented.
• Less vibrations - The movement between the ski and the plate dampens vibration, provides added comfort, better control and grip in the snow leading to consistent race runs.
• Improved flexibility - Aids the ski to bend in a harmonious arc, making carving turns cleaner and enabling smaller radius turns.
• Safety - The flex of the ski does not affect the ski-binding preload. This enables the binding an additional safety performance feature.
1.1.1 Research question
Of the three hypothetical benefits stated by Flow Motion Technology AB the vibration as- pect was investigated in this thesis. The other two were left to examine in future work. The question of interest to Flow Motion Technology AB is how a plate implemented with FMT performs compared to a state of the art reference plate, regarding its vibration damping properties. To be able to answer this, both a prototype and a test method is required. The work is built around a main research question, as follows:
Is there any difference of vibration damping properties between a ski mounted with a plate implemented with Flow Motion Technology and a ski mounted with a state of the art reference plate?
To be able to answer the main research question following two sub questions are stated:
How can a prototype of a plate with implemented Flow Motion Technology be designed and manufactured with the intention to perform vibration tests in both laboratory and field?
How can the test methods be designed to evaluate vibrations and what equipment is required?
1 1.2 Purpose
Flow Motion Technology AB needs test data and basis to evaluate whether Flow Motion Technology will benefit the vibration damping properties of an alpine ski, and for that reason worth investing in further research and development.
1.3 Method description
The project was divided into four phases. First phase is background research where state of the art and previous studies were analyzed as well as research within the areas of test methodology and prototype development.
In the second phase a prototype is developed and manufactured. The development of proto- type is based on the background research and the further designed requirement specification. Also the test method is designed by the knowledge of earlier studies and findings.
In the third phase, tests of the prototype are carried out. Two laboratory tests, one to sample ski eigen frequencies and another to sample vibration dampening data of a ski with either mounted FMT plate, or a reference plate. The eigen frequencies from laboratory test will strengthen reliability of data by comparing with ski vibration behavior in field. Field test is therefore performed with identical equipment setup as in laboratory, both with a mounted FMT plate and a reference plate.
The last phase intend analysis of test data, comparing the effect of mounting either one of the two different plates on a ski. Frequencies of vibration and amplitudes of acceleration values are compared between both plates, in laboratory respectively field test.
1.4 Delimitations
• The prototype will be developed as a function prototype, and not necessarily with all aesthetic features required for a commercial release.
• Only a certain range of ski boots size will be applicable with the prototype.
• The prototype development will be limited to reinforce and increase stiffness to make sure that the prototype will endure the tests of this study, although without complete optimization.
• No detailed development will be considered of the prototype features below: Mounting of prototype on ski, FMT radius size, front and back bushings, stoppers, damping material properties, torsion resistance enhancement,
• Tests will be performed to evaluate vibration and damping properties only
2 • Only initial field tests will be performed with intention to gather fundamental knowl- edge of the procedure
• No optimization of test methods will be made
1.5 Risk assessment
A risk assessment is made to foresee and prevent failure in the project. See Appendix 7.1.
1.6 Project planning
The project plan is included in appendix 7.11 as a Gantt chart.
3
2 FRAME-OF-REFERENCE
Before designing tests and preparing a functional prototype, a thorough background research was organized and made. The background research is focused around the topics listed below:
• Alpine ski dynamics and vibrations
• Test methods for ski vibrations and damping
• State of the art alpine ski damping equipment
• Flow Motion Technology
• Previous prototype
• FIS-regulations
• Fast Fourier Transform
2.1 Alpine ski dynamics and vibrations
As an alpine race skier rides down a slalom track, so called carve turns are performed. These turns follow a rounded path which ideally matches the radius curvature of the alpine ski. The resulting track of motion is shaped almost like a cosine curve, shown in Figure 1.
Figure 1: An illustration of how an alpine slalom track is generalized [1].
This means that the skier is shifting direction of motion, which requires acceleration. This acceleration force FC is theoretically acting in the center of mass (COM) of the skier, directing towards the center of turn curvature. The COM is not placed in the level of ground, hence the skier needs an inclination angle α from the normal vector of the slope, in the direction from the ground contact and COM. The gravitational force FG is constant and pointing vertically down, orthogonal to FC . These orthogonal forces combined with the inclination angle results in a force FR, which compress the skier by the legs and down through the ski. By the simplified free body diagram presented in Figure 2, the forces which the ski is exposed to FR can be calculated, as in Equation 1.
5 Figure 2: Forces acting on skier: centrifugal force FC , gravitational force Fg, resultant force FR [2].
Fg FR = (1) cos(α)
To generalize the equation and evaluate the impact of inclination independent of mass of skier, Equation 2 describes the g-force (multiples of the skier´s weight), gR = FR/Fg acting on skier, and Table 1 shows different g-forces as function of inclination angle.
FR 1 gR = = (2) Fg cos(α)
Inclination angle α [deg] 0 20 30 45 60 70 g-forces gR [g] 1 1.1 1.2 1.4 2 2.9
Table 1: Resultant g-forces gR by different inclination angle α of alpine skier
A recreational alpine skier commonly make a turn with an inclination angle of approximately 20-30 degrees, while professional alpine race skiers occasionally reach up to 60-70 degrees of inclination, corresponding to 1,1-1,2 and 2-2,9 g-forces respectively [3].
In the study Reducing On-Snow Vibrations of Skis and Snowboards by Gary C. Foss and Bard Glenne, it is concluded that what causes vibrations in skis are irregularities in the snow surface as they contact the ski and travel along the the base. These irregularities differ in shape and as result excite different frequencies of vibration. Other factors affecting the frequencies are speed and ski material properties. According to Foss and Glenne, the significant range of vibration appears to be in the range of 20-200 Hz when skiing on hard snow at high speed [4].
6 2.2 Test methods for ski vibrations and damping
Tests of vibrations in alpine skis have been performed in several previous studies. Usually two main types of physical tests are performed; laboratory and field tests.
Tom Wills has done an extensive test of different alpine skis, examining vibrations in lab- oratory environment [5]. He built a test rig that enabled a test procedure according to ISO 6267:1980 (International Organization for Standardization, Alpine skis - Measurement of bending vibrations). Figure 3 illustrates a test rig with dimensions and positioning of measurement tools and clamping.
Figure 3: Dimensions and positioning of specific details in an ISO 6267 test rig [5].
Tom Wills performed release tests with a starting deflection of 25 mm at the release point shown in Figure 3 above. The vibrations initiated were measured with a Laser Doppler Vibrometer (LDV) located 300mm from the clamping position of ski. To evaluate the damping properties of ski vibrations a so called half life analysis of the vibration amplitude was performed, which corresponds to the ISO standard for vibration measurements. The half life analysis investigates the time it takes for the amplitude of the acceleration to be reduced to 50% of the max amplitude. This procedure, using a distinct release of a deflected alpine ski initiate only the first mode of frequency in an ideal case. Tom Wills concluded the method to be less advantageous if the objective is to evaluate different frequencies occurring in a ski simultaneously [5].
Field tests have been performed and evaluated by Gary C. Foss and Bard Glenne in their study Reducing On-Snow Vibrations of Skis and Snowboards. They used accelerometers mounted on skis while riding down a slope, both on hard groomed snow and soft snow. The soft snow damped and reduced the higher frequencies of torsion modes at the range of 90- 120Hz, which occurred especially when turning. Figure 4 is taken from their study, which shows the difference between hard and soft snow. Three major conclusions were drawn, cited below [6]:
• "The dominant bending vibration of the ski forebody on snow is around 20Hz."
• "Vibrations are greatly amplified by hard snow conditions."
• "On hard snow, torsion and mixed vibration in the range 70-120Hz becomes critical to performance."
7 Figure 4: A diagram by Gary C. Foss and Bard Glenne which illustrates the power spectral density [g2/Hz], as function of frequency [Hz]. Field test on hard snow (Yellow) and soft snow (Green) [6].
Other studies seem to have similar results regarding the dominant bending frequency. Piziali and Mote [7] performed field tests using strain gauges mounted on skis, and concluded the range of 16-24Hz [4]. Foss and Glenne concluded that laboratory tests require ski binding, boot and the inertia of a user to reach similar test data as if tested on snow. A person who also did a major test and analysis of damped ski binding system was Gregory C. Causey, whom performed both on-hill and laboratory testing. When analysing data he used a fast Fourier transform program. This method was used to more easily compare frequencies and sorting out unwanted data. To ensure that no unwanted data was sampled before the desired test sequence the first 20 data points were removed. [8]
The idea of performing and comparing laboratory testing and field testing is something Causey also did in his study Testing of vibration damping binding systems used on alpine ski equipment. However, he questions the possibility to do so, especially pointing on the difficulty of replicating the surface of the snow and the dynamic behaviour of a skier making turns. Regarding this he refer to a conclusion from a test published by Skiing Magazine, saying "The Salomon binding had the lowest damping effect of the entire group in the lab, but it was the only ski in which the on-hill testers said they could feel a damping effect", pointing on the difficulty of making a legitimate comparison [9].
2.3 Alpine ski damping equipment - background and state of the art
The history of the development of vibration damping in alpine skis has its beginning in the 1980’s, when ski manufacturers such as K2, Dynastar, Salomon and Fischer began to experiment with different systems to handle vibrations [9]. The developement was much forced by the progression of alpine racing, where the ability to reach higher speeds led to more severe vibrations. The Contact System from Dynastar was one of the first launched vibration dampers, built up by a shock absorbing plastic ball mounted at the tip of the ski, working as a mass damper [10], see Figure 5.
Figure 5: Dynastar skis with the Contact System, a red plastic shock absorber on the tip of the ski.
8 Other solutions were for example integrated elastomer sections in the wood core by Blizzard, a plate mounted under the binding with rubber inserts like the Deflex by Salomon [9]. Today a combination of these solutions working as a system of damping units placed in the ski, on the ski, in the bindings and in the boots are common. The way damping is used also depends on which the intended user is. The damping system looks different depending on whether the ski is intended to be used by a recreational skier or in the world cup. Damping systems intended for skis used by recreational skiers are mainly developed to make the ride comfortable and easy in moderate speeds. This is usually achieved by adding rubber in boot soles and making skis and bindings softer. Systems for racing skis are on the other hand made to reduce vibrations in high speed at hard piste, with more performance and less comfort in mind [4]. This often requires more complex systems, with hard non-damped boots and skis and bindings with thoroughly engineered damping systems. Two examples of this, which both are used by some world cup racers in the 2018/2019 World Cup [11], are the Völkl UVO system and the Atomic Servotec. Völkl UVO is a mass damper mounted on the tip of the ski, much alike the system Dynastar presented in the 1980’s. The system works in such way as when the ski vibrates the mass damper delay the unwanted motion of the ski and prevents it from vibrating [12]. Atomic Servotec is built up by a carbon fiber rod running on top of the ski with a fixed joint below the tip. The rod can move free along the ski in under the binding, where it is connected to an elastomer damping compound. With the damping under the binding combined with a light weight rod to the tip, the system can dampen vibrations acting in the tip of the ski without adding significant weight in the tip, keeping down the swing weight [13].
Figure 6: 2019 model Völkl Racetiger SL skis with UVO mass damper in the tip [14].
Figure 7: 2019 model Atomic Redster G9 ski with Srevotec carbon fiber rod along the top of the ski connected to damper under the binding [15].
These two systems are mainly engineered to eliminate the large vibrations acting in the first frequency mode, which is the mode that easily could be seen when watching a ski race run in slow motion, around 20 Hz. The other frequency modes are higher frequencies hard to see even in slow motion footage, but can be felt and are affecting the performance as much [4]. These frequencies are not dampened in same extent by the UVO or the Servotec. These are
9 instead in large extent dampened by systems integrated in the bindings, or when looking at race equipment, often both in the binding and the plate. The plate has many advantages, for example to keep the boots away from digging into the snow when turning, to allow effective force transfer into the snow, and to damp vibrations [16]. Different solutions to eliminate these have also been thoroughly developed in bindings and plates since the 1980’s. Early concepts such as the Salomon Deflex evolved to Salomon Pilot System, see Figure 8, and furthermore into the plates of today. The dampening systems in plates differ depending on manufacturer, but usually takes advantage of elastomers or oil dampers. Two modern versions using hydraulic oil piston dampening is the Head WCR plate and the Marker WC Piston plate, see Figure 9, and Figure 10.
Figure 8: Salomon Pilot System binding with plate [17].
Figure 9: 2019 model Head WCR plate with hydraulic oil dampening [18].
Figure 10: 2019 model Marker WC Piston plate with hydraulic oil dampening [19].
10 2.4 Flow Motion Technology
As stated in Section 1 Flow Motion Technology AB is using their own Flow Motion Technol- ogy in their products. The main idea and beneficial aspect of this technology is to convert a line ground contact into a single point contact, which will affect the motion of the user when implemented in a pair of ice- or roller skates. This feature is achieved by separating the frame of a roller skate by the wheelbase which creates the line contact with the ground and the upper part. The upper part is rounded which creates a point contact when rock- ing against the flat wheelbase [20]. A graphic illustration from Flow Motion Technology is shown in Figure 11.
Figure 11: Illustration of the separated frame of a FMT implemented roller skate [20].
The reason for this conversion of contact shape is to be able to mimic ice hockey skates and their rounded blade shape, hence a point ground contact. The change of contact helps hockey players practise their balance, ice-skating technique and stimulate specific muscle groups as if they were skating on ice [20]. Figure 12 illustrates the similarities in the rounded contact shape between an ordinary ice hockey skate and the FMT roller skate.
Figure 12: Illustration of the Flow Motion Technology AB Roller Frame and an ice hockey skate. The marked point is where the contact is acting [20].
11 FMT is not only idealized to mimic on-ice hockey skating, but also to facilitate the natural movement of a walking human foot. The ground contact starts from the heel and rolls further out towards the toes. A thorough study like The advantages of a rolling foot in human walking by Peter G. Adamczyk et al. [21] shows results of how the metabolic rate and the movement of center of mass changes significantly with implemented rolling foot motion. Figure 13 is a capture from that article where it shows the general test setup of evaluating different radii of curvature under a human foot. A decrease in first heel impact achieved with an increasing radius of curvature, as well as a decreasing center of mass work rate compared to normal walking. The study did only test a maximum radius of value 0.4 [m].
Figure 13: Illustration of the separated frame of a FMT implemented roller skate [21].
2.5 Previous work
This thesis is a continuation of a previous thesis work by Linn Rilegård[20], where a design of a FMT plate was presented and tests were carried out both in field and in lab with an early prototype. However, the test results were not sufficient to conclude whether the FMT plate had advantages or not. Two factors were affecting the reliability of the results the most; the prototype were not stiff enough, making itself bend over the ski, preventing the ski from bending freely. The second factor was that the measuring equipment were not precise enough. The measuring system consisted of a Micro:Bit circuit board with a accelerometer with capacity of measuring +/- 8 g. The software Bitty Data Logger was used as DAQ-system on a mobile phone. The accelerometer and the DAQ-system connected via Bluetooth. The Micro:Bit logged data every 20 millisecond and sent the data to the phone where it was stored [20]. With a sampling rate of 20 ms, in other words 50 samples per second, the maximum frequency possible to measure was 25 Hz according to the Nyquist criteria, which says that maximal signal frequency adequately presented in digitized wave is half of the sampling rate [22].
Initial tests with more advanced measuring equipment were made in lab but needed to be further analyzed to draw any conclusions.
12 2.5.1 Previous prototype
A handful of different prototypes have previously been developed by Flow Motion Technol- ogy AB. Latest is the design concept Rilegård developed and presented in her thesis, shown in Figure 14.
Figure 14: FMT plate design concept developed by Linn Rilegård.
This concept is constructed out of carbon fiber and features a U-shape for optimized strength and bend resistance.
Another prototype of interest was the one that was used in the field and laboratory tests made in Rilegård’s thesis. This prototype was a sandwich construction made out of 1 mm carbon fiber composite on a pine plywood core. This prototype was essentially made for the tests carried out, but turned out to be too weak and did not perform as planned. The prototype did deflect until it had contact with the top sheet of the ski. As mentioned before this prevents the ski from bending freely, a criterion for the FMT theory to work. The carbon fiber did apparently not provide sufficient strength, and future recommendations were therefore to make the laminates thicker and with optimized fiber lay up. The carbon fiber laminate consisted of a total of 1 mm of plain 90/0-weave. More about carbon fiber composite design in Section 3.2.4. The pine plywood core did also tend to soak up water of molten snow which reduced its stiffness properties over time [20].
2.5.2 Tests
Previous tests on earlier prototypes have been carried out both in field and in laboratory environment. Latest are the five test series made by Rilegård, where a number of different approaches were made during the tests, both qualitative and quantitative. An overview of the test performed are shown in Table 2.
13 Table 2: Overview of the tests performed by Linn Rilegård [20]
The results from the tests were giving brief hints of the performance of the FMT plate, but since equipment such as the data acquisition system did not provide sufficient performance no more detailed conclusions could me drawn. The recommendation was therefore to redo the tests with more advanced measuring equipment to be able to draw reliable conclusions.
2.6 FIS regulations
Design of alpine ski racing equimpent is regulated by the FIS, Fédération Internationale de Ski. FIS is the world’s highest governing body for international winter sports and it is responsible for the Olympic disciplines of Alpine skiing and many more winter sports. The FIS is also responsible for setting the international competition rules. Typical regulations for alpine ski racing equipment are restrictions on ski construction, the aerodynamic properties of back protectors, competition suit design [23]. When developing new equipment this must be taken into consideration. In the case of this project some regulations are directly restricting the design possibilities. The first regulation, Bearing surface height hBS, affect what FIS refer to as the whole functional ski system, which is the assembled unit of the single components: (A) ski, (B) interfaces, (C) release bindings and (D) retention device, shown in Figure 15 [24]. The "Interface" is the component this project is developing, i.e. the plate. The regulations affecting this project are the presented in table 3, with illustrations presented in Figure 15 and Figure 16 after the table.
Table 3: FIS regulations affecting this project [24].
Feature Definition Value (mm) Tolerance (mm) Figure Distance between the bottom of Bearing surface the running surface of the ski and 50 ± 0, 1 15 height max the ski boot sole. At each point of the interface, its Interface width width must not exceed the width 63max ± 0, 1 16 of the running surface.
14 Figure 15: The functional ski system referred to in FIS-regulations [24].
Figure 16: The width of the interface cannot exceed the width of the ski, w ≥ 0 [24].
The interface width limitation is restricted by the regulations of the width of the ski. According to the FIS specifiactions for the 2018/2019 season the minimum waist width is 63 mm for SL skis and maximum 65 mm for the other disciplines SG, GS and DH [25].
2.7 Fast Fourier Transform
To be able to analyze vibration data, particular analysis methods can be used. Fast Fourier Transform (FFT) origins from the mathematician Fourier’s discoveries, which with he proved that any continuous function could be produced as an infinite sum of sine and cosine waves. When talking about vibrations FFT could be used to decompose vibration data into specific frequency modes. In this way the frequencies affecting the vibrations most can be identified. Figure 17 shows what could be a typical signal of vibrations. The signal can by using FFT be decomposed into three specific sine waves with the frequencies of 0,5 Hz, 1 Hz and 2 Hz [22].
15 Figure 17: A signal decomposed into its three sine wave elements [22]. [22]
Another convenient way of showing the waves is by placing them in a graph with the frequency on the x-axis and the amplitude on the y-axis, shown figure 18.
Figure 18: The frequencies of the sine waves shown on the x-axis, and their amplitude on the y-axis [22].
16 3 IMPLEMENTATION
In this chapter the working progress of design an manufacture of a prototype is presented followed by a description of the test procedure and the equipment used.
3.1 Ski physics and calculations
In this section the ski physics affecting the prototype design is presented.
3.1.1 Ski bending when performing a carve turn
As mentioned in Section 2.1 the alpine ski has a side cut radius which enables the carving turn when riding. Three key points (A, B, C) are positioned, shown in Figure 19. These points combined makes a triangle when the ski is laying with the base flat on the ground. Distance between A and C is named AC.
Figure 19: Isometric view of positioned points A, B and C, on a ski laying with the base flat on the ground.
When carving is utilized and the ski is tilted to the specific inclination angle α, point B is being forced down to the ground by FR mentioned in Section 2.1. Point B has a new relative position to the other points A and C, and is renamed as B2. Figure 20 illustrates the inclined ski and re-positioned point B2 seen from a front view.
17 Figure 20: Front view illustrating the re-positioned B2.
As the point B2 is re-positioned, a new distance projected in the front view between A,C and B2 can be calculated (AB2), see Equation 3. The previous relative projected distance between A,C and B is named AB.
AB AB = (3) 2 cos(α)
The re-positioned point B2 results in a bent ski, as it is still being inclined. A top view of the bent ski is illustrated in Figure 21. The three points A2, B2 and C2 combined will form a new triangle. Point A2 and C2 have relocated by the fact that the ski has a constant length.
Figure 21: Top view illustrating the bent ski, re-positioned points A2, B2 and C2.
By knowing the values and positions of the initial points and angles, the new bending radius RB of the ski can be known. One way is to use a Computer Aided Design(CAD) software to draw the line of bent ski trough the calculated points, restricting the length of the line to be constant. The software used in this study is Solid Edge ST10 [26]. Table 4 shows the resulting bending radius RB as function of the input values of a Blizzard GS Magnesium, R21.0, L189, model year 2007 ski and inclination angle.
18 Table 4: Bending radius RB of ski as function of ski dimensions and inclination angle α.
AC [m] AB [m] Inclination angle, α [deg] Bending ski radius, RB [m] 1,72 0,0175 60 21,1 1,72 0,0175 70 14,4
The radius RB of bent ski is essential in this project, due to that it limits the possible design of a plate and the rolling motion able to achieve by a FMT implemented plate. Figure 22 in next section illustrates the FMT plate mounted on a ski, and the resulting space mentioned. If the bent ski radius RB is less than the radius of the FMT plate, no space between the ends of the plate and the ski will occur. This disables all the three hypothetical benefits of implementing FMT to alpine skiing, mentioned in Section 1.1.
3.1.2 Torsion of plate
The plate is required to have a high bending stiffness, to maintain its shape and allow the theory of FMT to work. Even though the bending stiffness is of high importance, torsional stiffness can not be neglected. The space between ski and plate appearing due to the curvature shape is illustrated in Figure 22.
Figure 22: side view of alpine ski and a mounted FMT plate.
This space leads to no support for the plate at the ends and a torsional torque Tt is utilized when putting the ski on an edge when carving, Equation 4. Width of ski WS and resultant force from skier FR are illustrated in Figure 23 and 24.
FR Tt = · WS (4) 2
19 Figure 23: A simplified model of a ski plus plate section view, while performing a carving turn with inclination angle α.
Figure 24: Isometric view of torsional torque Tt occurring in the FMT plate.
A relative comparison of bending and torsional torque is essential to evaluate. This affect the requirement specification of the plate prototype. Bending torque Tb can be calculated with Equation 5, where DB is the distance from boot center (center of plate) to end of boot/ski binding load position, illustrated in previous Figure 22. Known is the size of boot to be used, 336 mm in sole length, which correspond to a distance DB of 168 mm. Maximized inclination angle of α = 70 [deg] and a known user weight of 90 kg, correspond to a gravitational force 2 FG of approximately 900 N (assuming acceleration of gravity g = 10 [m/s ], the resultant force is calculated by Equation 6, with input values from Table 1.
FR Tb = · DB (5) 2
20 FR = FG · gRmax = 900 · 2, 9 = 2610 [N] (6)
With a known WS = 64/2 = 31 [mm] of the ski model mentioned before, Blizzard GS Magnesium and assuming the same load force of FR, the bending and torsional torque can be relatively compared as WS/DB = 31/168 ≈ 18, 5 %, hence the torsional torque is approximated to be 18,5 % of the size of bending torque. The ratio will affect the choices of carbon fiber stacking sequence.
3.2 Prototype
In this chapter the design and manufacturing process of the prototype of a new FMT plate is presented, considering materials, manufacturing methods and delimitations. A new prototype is essential to be able to perform tests and further evaluate the performance of FMT plate with higher accuracy and reliability than previous tests. However, some designs from previous concepts, such as the design of the end stoppers with bushings, will be used and only be redesigned briefly, without any optimization. These originate from previous prototypes and the function of them will not be further investigated in this project. For the prototype developed in this project milled aluminum stoppers will be made and fitted with 3D-printed bushings. The function of these are to limit the movement of the plate on the ski and hold the plate in place. Design modifications were not made to the damping material used, which was a material used in previous tests and had shown sufficient performance for tests in this state of the project. The design and choice of damping material would require more research and has therefore been delimited from this study. Enough material was supplied so that two pairs of prototypes were possible to manufacture, the second pair as a back up.
3.2.1 Requirement specification
A requirement specification is formulated by the background research and also wanted criteria from the stakeholders Flow Motion Technology AB. The specification serves as a guide for developing the prototype. Some numbers are based on the properties of the person who will perform the field tests. The requirement specification is presented in appendix 7.2.
3.2.2 Materials
As the previous prototypes were made of both aluminum and carbon fiber composite with pine plywood as core material, an evaluation and comparison of these materials are essential for further improvement of the new prototype. The stiffness of the plate is as specified in the requirement specification of high importance and will be achieved mostly by the external material of the sandwich structure, due to its geometrical benefits explained in Section 3.2.3. In Figure 25 different materials are compared based on their Young’s Modulus, density, and stiffness/density ratio [27].
21 Figure 25: Different materials and their properties.
As seen in Figure 25 carbon fiber composite has the highest E-modulus relative to its weight compared to the other materials, hence it is suitable for making a stiff FMT plate relative to its weight.
A core material is needed to support the external material in a sandwich design. Since one of the previous prototype had pinewood as core material, which got soaked and tended to be too soft, alternative solutions are evaluated.
There are plenty of different types and properties of core materials used in similar products of sandwich structures. Mentioned as a delimitation was that the new prototype will be an improvement of the previous ones and not a general optimization. Therefore a core material that performs better than pinewood in terms of strength and water resistance is desirable, while still being easy to form by either milling or other accessible manufacturing methods, stand the temperatures of curing the matrix of fiber composite and also work well together with the cured matrix. Having a dense core material enables simple ways of mounting ski bindings onto the plate, even though the total mass will increase. Examples of solutions are a ski mounting screw that fastens directly into the core, or using inserts, which have a threaded inside.
Honeycomb solutions are effective in terms of lightweight structures but not as formable. Due to the low priority of reducing the weight, honeycomb is a less applicable choice. The prototype center at KTH has a specific polyurethane material available, type BM 5185 from Lindberg & Lund, which is easy to machine and has a low coefficient of thermal expansion. However, it is not made for combinations with epoxy or other resin types for laminating [28]. Another polyurethane material is the Sikablock® M700 which is a polyurethane block of higher density than the BM5185 and with good solvent resistance. It is specially made for vacuum moulding and to be well compatible with curing thermoplastics, such as resins for composites. Data sheet of Sikablock® M700 is presented in appendix 7.3.
22 3.2.3 Sandwich structure
The prototype was designed as a sandwich structure, with a core covered with a carbon fiber composite laminate. The advantages of a sandwich structure are generally its ability to make stiff and light weight constructions. A sandwich structure consists of a pair of thin strong facings, a thick lightweight core to separate the facings and carry loads from one facing to the other, and an attachment which is capable of transmitting shear and axial loads to and from the core [29]. The way a sandwich structure works is the same as that of an I-beam, where most of the material is placed in the flanges situated farthest from the center of bending. The material in between is only left to connect the flanges and make them work together and resist shear. In a sandwich structure the faces take the place of the flanges and the core take the place of the connecting material. The in-plane and bending loading are carried by the faces while the core resists transverse shear loads and keeps the faces in place [30]. An illustration of a sandwich structure is shown in Figure 26.
Figure 26: Sandwich structure.
However, in this project the choice of a sandwich structure is based on the advantages of having a core at all. The core provides the desired shape of the design, which will be kept when laminating with carbon fiber and ease the manufacturing process. Another advantage of using a core was that it would be possible to mount ski binding screws straight into the plate without the need of mounting inserts since the core material has similar properties as the wood used in skis in general [31]. If the plate would be made as a solid carbon fiber composite plate, inserts would have been desirable for mounting bindings. Another advantage of not making the prototype in solid carbon fiber is that carbon fiber is expensive and time consuming from a manufacturing point of view. By replacing solid carbon fiber with a core the amount of carbon fiber is reduced, consequently reducing the cost A.2. The core/laminate thickness ratio will affect the stiffness properties of the prototype, since the carbon fiber composite are the material with the highest tensile strength. Technical data shown in appendix 7.3 and 7.15. To determine the ratio, several aspects are needed to take into consideration. Such as meeting the required stiffness properties, the manufacturing of the prototype should be as simple as possible, it should be a plausible future design, binding screws should be possible to fasten in the core and the price should be kept down. With this in mind a reasonable assumption of the ratio is made, resulting in 8:8 ratio of the height in the center of the prototype, which means a 8 mm thick core laminated with 4 mm thick composite faces on each side.
Using this ratio as reference, calculations can be made to verify whether the aspects stated above are fulfilled, and if so worth developing further. The effect of implementing a core to the plate will affect the highly prioritized requirement bending stiffness. It will also affect the weight and price, since carbon fiber composite has higher density and is more expensive than the core material.
23 To calculate the effect on bending stiffness a flat sandwich structured plate with 8:8 ratio is taken as reference. Bending is then calculated for different core/composite ratios. From 0 % composite, only core material, to 100% composite, a solid composite plate, with steps of 2 mm (1 mm per face). The core/composite ratios 14:2 (27a), 8:8 (27b) and 2:14 (27c) is illustrated in Figure 27.
(a) 14:2 (b) 8:8 (c) 2:14
Figure 27: Different ratios (core/composite).
The bending stiffness as function of composite face thickness is illustrated in Figure 28. The 8:8 ratio provides 87,5% bending stiffness compared to solid carbon fiber composite, which is considered reasonably high.
Figure 28: The bending stiffness as function of composite face thickness.
3.2.4 Composite layup & Rule of Mixtures
The carbon fiber composite laminate consist of multiple layers of carbon fiber fabric drained in a so called matrix, commonly epoxy resin, data sheet in appendix 7.15. The carbon fiber fabric itself can have many different designs, providing different advantages. The design differences have two main reasons, fiber orientation and aesthetics, with fiber orientation being the most crucial subject in this project. The fabric consists of long thin carbon strands bundled together. Each fiber is about 5-10 micrometers in diameter and is composed mostly of carbon atoms. The fibers have several advantages such as lightweight, height tensile strength, corrosion resistance, low coefficient of thermal expansion, low thermal conductivity and many more [32]. Especially interesting for this project is the high tensile strength of the fibers. The tensile strength can be utilized to get very specific strength properties of
24 the design if placing the fibers in the correct direction. For example, one common fabric pattern is the so called plain weave, shown in Figure 29a. This is a bi axial weave, and consist of 50 % fibers aligned in one direction and 50 % aligned 90 degrees to that direction, woven together. Another common pattern are the bi axial twill weave, which also consist of two perpendicular fiber directions, but weaved together in a slightly different way. Shown in Figure 29b are a twill pattern with 45/45 degree alignment, which essentially is a rotated 90/0 pattern. Another pattern is the unidirectional, UD, which as the name tells fibers oriented in only one direction woven together with binding threads, shown in Figure 29c. This provides very high tensile strength in this direction since all fibers are aligned in the same way. On the other hand very low tensile strength is provided in the 90 degree direction. The plain weave and twill weave is providing 50 % strength in both fiber directions.
(a) Plain weave. (b) Twill weave. (c) Unidirectional weave.
Figure 29: Different carbon fiber fabric weaves [33].
Depending on appliance, different patterns are preferable. One of the main criterion for the prototype is that it needs to have high bending stiffness in the direction along the ski. Therefore UD-fabric will be used in large extent, combined with a 45/45 twill weave for torsional stiffness. There are a couple of other factors that also affecting the selection of proportions of UD and 45/45 twill weave. For maximal strength the stacking should be symmetrical, both in one laminate itself but also between the two laminates. There should be 45/45 twill weave in the outer layers to get a aesthetic carbon fiber look. An other factor was the composite material available, which was prepreg (pre-impregnated with epoxy resin) UD 600g/m3 and prepreg 45/45 twill weave 730g/m3, supplied by Marström Composite AB. Both weaves end up with a thickness of approximately 1 ‰ of the weight [g]/m3 after the manufacturing process. One UD layer will in other words be around 0,6 mm on a finished product. The last factor is the assumption of a 8:8 ratio of core/composite, which with a plate of total height 16 mm means 8 mm composite, divided into two faces of 4 mm thickness each. The factors are summarized below:
• Higher percentage UD than 45/45 twill
• Symmetrical stacking
• 45/45 twill in the outer layers
• 600 g UD weave, 730 g twill weave, both prepreg
• Face thickness 4 mm
25 With these factors in respect only one stacking design is possible. This stacking consist of 6 layers of weave per face; 45/45 twill weave on top and bottom and 4 layers of UD in between. Resulting in 62,2 % UD versus 38,8 % 45/45 twill in theory. The outcome of the face thickness in some extent depend on manufacturing method, but the theoretical face thickness is calculated to be 3,86 mm, which is considered reasonably close to 4 mm. The stacking design is illustrated in Figure 30.
Figure 30: Directions on the sandwich structure.
With the stacking determined the properties of the sandwich structure can be predicted. The properties depend on the components of the composite material. The final technical specifications of the materials such as carbon fiber and epoxy resin in the prepreg used will depend on the handling of the material in for example the manufacturing process and curing process. Therefore general properties for prepreg of the quality used in this project is used, and sources are presented in appendix 7.15. The Rule of Mixtures [34] is a method for prediction of stiffness, or Young’s modulus, in composite materials, consisting of materials with different properties. The formula can, except from stiffness, predict properties such as density and Poisson’s ratio can be calculated for a laminate consisting of different weaves and fiber directions. The Rule of Mixtures assumes that the composite consist of unidirectional fibers. The rule of mixtures formula is presented in Equation 7.
Ec = Ef Vf + EmVm (7)
Where Ef is the Young’s modulus for the fibers, Vf the fiber volume fraction, and vice versa for the matrix. The fiber volume fraction is calculated from the known fiber weight fraction combined with the known matrix weight fraction. The prepreg carbon fiber fabric used in this project consist of 35% matrix by weight, therefore 65% fiber by weight. The fiber volume fraction can be calculated by using Equation 8:
Wf ρf Vf = W (8) f + Wm ρf ρm
Where Wf is the weight fraction of the fibers, ρf the density of the fibers, Wm the weight fraction of the matrix and ρm the density of the matrix.
26 Since the Rule of Mixtures assumes unidirectional fibers and the prototype also will consist of the 45/45 twill, additional calculations is needed. To solve this a efficiency factor is used. This can be used to predict the effect of fibre orientation on stiffness, in this case the angle 45 degrees for the twill. The efficiency factor is described by the formula in Equation 9:
X 4 ηθ = ancos θ (9)
Where an is the proportion of total fibre content, θ the angle of the fibers and ηθ the composite efficiency factor. The rule of mixtures with efficiency factor is presented in Equation 10.
Ec = ηθEf Vf + EmVm (10)
The efficiency factor for some common fiber orientations is shown in Figure 31.
Figure 31: Examples of the efficiency factor for different fiber directions [34].
With these formulae prediction of the Young’s modulus for the composite can be made. The Young’s modulus may differ depending on direction of the sandwich structure, why the modulus in both x- and y-direction is calculated. The directions are illustrated in Figure 32.
Figure 32: Directions in the sandwich structure.
First the efficiency factor for the stacking with 62,2 % UD and 37,8 % twill in x- and y-direction is calculated by using Equation 9:
27 x X 4 4 4 ηθ = ancos θ = 0, 622 · cos (0) + 0, 378 · cos (45) (11)
y X 4 4 4 ηθ = ancos θ = 0, 622 · cos (90) + 0, 378 · cos (45) (12)
The fiber volume fraction is calculated from Equation 8 with:
Wf ρf Vf = W (13) f + Wm ρf ρm
Vm = 1 − Vf (14)
The resulting Young’s modulus of the sandwich structure is predicted for the x- and y- direction:
x x Ec = ηθ Ef Vf + EmVm = 118, 7 ≈ 118 GP a (15)
y y Ec = ηθ Ef Vf + EmVm = 14, 2 ≈ 14 GP a (16)
The Young’s modulus is used to analyze the bending stiffness of the plate using FEM in ANSYS. Worth to point out is again that this is a theoretical prediction. The actual modulus may differentiate depending on accuracy in for example the manufacturing process.
3.2.5 Making a core
SikaBlock® M700 was chosen as core material, and was supplied by Jonas Lundström at Jönköpings Modelltillverkning AB. The block was processed in a Roland MDX 540 CNC mill. The MDX 540 has a workspace of 400x400 mm, why the requested 490 mm long core was made in two pieces of 245 mm and then spliced with epoxy. The process and finished cores are presented in Figure 33.
(a) SikaBlock® in CNC mill. (b) Finished cores.
Figure 33: The milling process and the finished cores.
28 3.2.6 Making a mould
A mould was made to get the desired shape of the plates. The bottom mould was made of fourteen 25 mm MDF boards milled in a CNC-mill and afterwards joined together with glue, shown in Figure 34. The mould was then sandpapered for a smooth surface and wrapped in a Teflon coated release film which prevents the plates from sticking to the mould. A top mould was also made out of two flat MDF boards wrapped in release film.
Figure 34: The mould, consisting of 14 MDF boards glued together.
3.2.7 Layup of layers
With the stacking determinded in Section 3.2.4 the layup of the plates could start. First the length of each prepreg layer were calculated to make the desired shape possible. The layers on the radius side all needed to be specific lengths depending on their thickness and placement in the stacking. A illustration of the final layup design is shown in figures 35 and 36.
Figure 35: The layup of layers.
29 Figure 36: Close up of the end showing the difference in lenght of the layers on the radius side.
The core was wrapped in a epoxy film to enhance the binding of the first layer (Figure 38a) and the following layers and core were then put in order on the mould, the process is presented in figures 37 and 38.
(a) UD being put on the mould. (b) The stacking sequence visible.
Figure 37: Layup of bottom layers.
(a) The core covered with epoxy film. (b) The last twill layer being placed.
Figure 38: Layup core and top layers.
30 3.2.8 Vacuum forming and Autoclave
With the layup finished the mould and plates were ready for vacuum bagging and treatment in autoclave. The vacuum bagging is made to achieve the desired shape of the plates and force it to remain that shape during the autoclave process. A schematic view of the vacuum bagging is shown in Figure 39.
Figure 39: The vacuum bagging components. The breather is a breathable felt membrane allowing the air transfer to the coupling.
The autoclave is an pressure chamber with temperature alternation in which the vacuum bagged mould is cured, shown in Figure 40. The mould was cured at 125 degrees celsius at 6 bar for 2 hours.
Figure 40: The autoclave.
31 3.2.9 Post manufacturing, finishing and mounting
After curing in the autoclave the plates were released from the mould and cut into the correct dimensions, illustrated in Figure 41 and 42.
Figure 41: Illustration of the plates to be cut out.
Figure 42: The cut out plates in pairs.
After being cut the necessary holes of the plates were drilled, shown in Figure 43.
Figure 43: Holes being drilled.
32 After being drilled the egdes were chamfered with a diamond drill and sandpapered. To prevent fibers from split out and to protect the surface the plates were clear coated with Spraymax 2K Clear Coat. To be able to mount and dismount the bindings several times if needed, the plates were fitted with heli coil steel inserts. The inserts were placed according to a Marker template for the binding to be used for two sizes of boots. The sizes were chosen according to the test persons and the boot to be used in field and lab tests, which was 27,5 MP and 29,5 MP. MP (Mondopoint) is a boot measuring system used by many boot manufacturers and the same as the foot length in centimeters. The heli coil installation is shown in Figure 44 and 45.
(a) Measuring on template. (b) Drilling.
Figure 44: Heli coil installation procedure.
(a) Tap, threads and heli coil. (b) Threaded holes. (c) Installed heli coils.
Figure 45: Heli coil installation procedure, continuation.
The end stoppers were milled from aluminium and the bushings 3D-printed and glued onto the plates. The rear stopper limit the plate movement in z- and y-axis while the rear stopper limit z-, y- and x-axis, shown with the bushing design in Figure 46. This due to a theory originating from previous work, referencing to the same idea of having the toe part of the ski binding fixed while the heel part can travel in x-axis.
The stoppers and the stopper fitted in a bushing is shown in Figure 47a and 47.
33 (a) Front bushing. (b) Rear bushing.
Figure 46: The bushings.
(a) The stoppers. (b) Stopper in bushing.
Figure 47: The stoppers and bushings.
A viscoelastic damping material was attached to the bottom of the plate. The material used was butyl sealing tape. The tape was placed on the plate under the toe and heel binding, see Figure 48. The volume and position of the tape are not generalized or measured but placed on similar location as in previous tests by Flow Motion Technology AB. Technical specification for a butyl tape similar to the one used is presented in appendix 7.6.
Figure 48: The damping material attached to the FMT plate.
34 3.3 Test procedure
As stated in the introduction Section 1, vibrations are the main test subject in this study. The test method and equipment was designed and gathered with the background research as reference and source of comparable data. Both laboratory and field tests were performed during this study.
3.3.1 Equipment and measurement system setup
Dewesoft DEWE 43 A was used as a data acquisition system (DAQ), supplied by Magnus Asplund at Dewesoft AB. For technical specification see appendix 7.4. The DAQ is shown in Figure 49.
Figure 49: DAQ unit, DEWE 43 A. [35].
The accelerometers used were Brüel & Kjær DeltaTron Type 4397 piezoelectric Accelerom- eters, supplied by Håkan Andersson at RISE, Reasearch Institutes of Sweden. It has a measuring range of ± 750g, see full calibration chart and technical data in appendix 7.5. The fact that they are piezoelectric means that they start to recon vibration frequencies from 3-5 Hz and not from absolute zero. The reason why they will be applicable in this study is that the range of vibration frequencies in alpine skis starts at approximately 10 Hz, according to Gary C Foss et al. [4]. An accelerometer is shown in Figure 50.
Figure 50: Brüel & Kjær DeltaTron Accelerometer Type 4397.
35 The DAQ system was powered by a 12 V motor cycle battery, technical specification found in appendix 7.13. The software used was DEWESoft® X3 SP6, which was used for data acquisition, recording and analysis. A sampling rate of 1 ms was used, which corresponds to 1000 data points logged every second. According to the Nyquist criteria, this means that the maximum frequency to measure accurately is 500 Hz. The significant range of vibrations when skiing appears to be in the 20-200 Hz range as discovered by G. Foss et al. [4], why 1 ms was considered as an adequate sampling rate. The analysis was mainly made in the sub module FFT Analyzer. Other set up parameters used for the FFT Analyzer is presented in appendix 7.7. The set up parameters for the recorder is shown in appendix 7.8.
The plate was fitted with a Marker Xcell 16 Race binding and mounted on the ski to be used in both field and lab tests, a 2007 Blizzard GS Worldcup Magnesium ski. The plate were mounted on the recommended mounting position, with Quiver killer inserts. This to be able to mount and dismount the bindings without damaging the skis. The inserts will increase the endurance of the stopper screw-ski interface, which may be subjected to large loads. The binding, plate and ski are shown in Figure 51.
Figure 51: The plate with Marker Xcell Race 16 bindning mounted on a Blizzard GS Worldcup Magnesium ski.
The set up with the reference plate is shown in Figure 52.
Figure 52: The Marker WC Piston plate with Marker Xcell Race 16 binding mounted on a Blizzard GS Worldcup Magnesium ski.
36 To set up and prepare the measurement system and equipment a pretest sequence was made. A ski was rigged fixed at the center and free from the center to the tip, similar to the fixture used by Tom Wills, described in Section 2.2.
Three accelerometers of same type were rigged on the ski and connected to the DAQ system. One was placed close to the center of the ski, one between the center and the tip, and one close to the tip of the ski. This to be able to see how vibrations affect the ski on different positions but also to ensure that the final placement of sensor is not at a node of vibration, consequently giving no signal. The placement of the accelerometers is shown in Figure 53 and named as positions 1, 2, and 3.
Figure 53: Three accelerometers rigged on ski for initial laboratory tests.
The pretest procedure was to hit the tip of the ski with a chisel and measure the induced vibrations. Tests were also made by bending the ski by pulling down the tip approximately 25 mm and releasing. Vibrations induced by chisel impact are plotted in Figure 54.
Figure 54: Vibration plot of a impact with chisel. The yellow plot shows the accelerometer close to the center of the ski (1), the blue shows the one between the center and the tip (2) and the red shows the one close to the tip (3).
The vibrations were then analyzed in DEWESoft® X3 using the FFT module. In this way it could be seen how the different frequency modes affected the ski at the different positions, shown in the same plot in Figure 55 and separated in Figure 56.
37 Figure 55: The four first frequency modes shown as peaks at around 13, 50, 125 and 240 Hz. The yellow plot shows the accelerometer at position 1, the blue shows the one at position 2 and the red shows the one at position 3.
Figure 56: The four first frequency modes shown as peaks. The yellow plot shows the accelerometer at position 1, the blue shows the one at position 2 and the red shows the one at position 3.
In Figure 56 it can be seen that the closer the center of the ski the lesser the first frequency mode seem to affect the ski. Another observation is the absence of the second frequency mode close to the tip. The accelerometer mounted between the center of the ski and the tip seem to register all frequency modes adequately and seemed to be suitable for the following tests. The position was slightly adjusted to specifically 300 mm from the front ski mounting screw in the toe binding, the same position used by Tom Wills 2.2.
38 3.3.2 Lab test
The lab tests were set up by mounting the ski boot upside down in a heavy duty bench vise on a fixed workbench. To achieve a rigid mounting a cut off boot with a steel frame molded in epoxy resin was used, made in a previous project. The boot is shown in Figure 57.
Figure 57: The boot used in the lab tests, with a steel frame molded in epoxy resin.
To stiffen the test rig and reduce undesired vibrations due to the eigen frequency of the vise and workbench, the boot was mounted by the steel beam closest to the sole of the boot. A schematic illustration of the test rig is presented in Figure 58.
Figure 58: The test rig set up with boot mounted to the prototype and ski.
The procedure for the mechanical release test was to attach a line to a specified point 200 mm from the tip and pull it through a hook fixed in the workbench to make the ski bend.
39 To be able to neglect the mass of the line a thin nylon line was chosen. The thin line also allowed a fast cut with minimal impact on the release. The bend was limited by a wooden block, allowing the ski to bend 25 mm at the point 200 mm from the tip of the ski. The nylon line was then cut of, making the ski eject and start to oscillate. A trigger feature in DEWESoft® X3 SP6 was used with 10 ms pre-recording to ensure no undesirable data was recorded while having consistent starting point of time, similar to the method used by Gregory C Causey[8] The vibrations were then measured by the accelerometer mounted with tape 300 mm from the front ski mounting screw in the toe binding. The DAQ system was connected to the accelerometer by a thin cable installed with tape on the boot, binding and ski to prevent it from vibrate and affect the measurement. The mounting of the accelerometer and cable is shown in figures 59 and 60.
Figure 59: The accelerometer and cable mounted with tape.
Figure 60: Front section view of the accelerometer mounted on the ski.
The procedure was then repeated for a set of 10 times. The first set was performed with a ski with the reference plate mounted, and the second set with a ski with the prototype mounted. A vibration plot from test with the FMT setup is shown in Figure 61.
40 Figure 61: Recorder diagram of a lab test on the FMT setup. Vibration utilized with the mechanical release of cutting the nylon line.
3.3.3 Field
The field test was held at Gustavsbergsbacken ski slope in Östersund April 8 2019. The conditions were sunny with a temperature of around -5 degrees celsius in the beginning and close to 0 degrees at the end of the test. The snow were groomed, icy and hard in the beginning and soft in the end due to that the slope was facing south east and heated up by the sun. The equipment was similar to the one used in the lab tests, except the workbench, vise and wooden block. The cut off boot was replaced by a pair of fully functioning boots of similar performance. A schematic illustration of the FMT field setup is presented in Figure 62. The second setup with the reference plate looks the same except from the different plate.
Figure 62: The field test setup.
The measurement system was also the same as the one used in lab tests. To be able to carry the system and to measure during ski runs the system was fitted in a backpack. To protect the DAQ system and battery from damage and to prevent disconnection, the gear was installed in a box inside the backpack and fixed with tape, shown in Figure 63a.
41 The accelerometers were installed on the skis on the same location as in the lab tests and connected to the DAQ system with cables as before, and the laptop with recording software carried in the backpack, shown in Figure 63b.
(a) The DAQ and battery were fit- ted in a box for protection. (b) The DAQ system and laptop fitted in backpack with connected accelerome- ters on the skis.
Figure 63: The measurement system rigged for field test.
The test procedure was to make 10 runs of down a slope of approximately 100 m and varying inclination between approximately 15 and 25 degrees and log the vibrations data of both skis during the run. The runs were made in three different types; 2 times straight without turns on hard groomed snow, 4 times carve turns on hard groomed snow and 4 times carve turns on soft not groomed snow. The path of the carve turn test runs was not specified and consisted of a mix of clean carve turns and skidding turns. The skis were swapped between every run to log data of the FMT setup and reference setup from both left and right foot.
42 4 RESULTS AND ANALYSIS
4.1 Final design of prototype
The final design of the FMT plate is presented in Figure 64. Part and assembly drawings, including a BOM (bill of material) are presented in appendix 7.14.
Figure 64: The FMT plate final design.
4.2 Stiffness of prototype
The stiffness properties of the FMT plate were analyzed in the FEA software ANSYS Workbench R19.2 to evaluate whether it meets the required performance. Following values of material properties shown in Table 5 were applied to the FMT plate in ANSYS.
Table 5: Composite properties, as input values used in ANSYS.
Due to difficulties applying and simulating an assembly model of the external composite part and core material part in ANSYS, a homogeneous FMT plate was simulated as reference. Figure 65-66 illustrates the positions and choice of line contact shape applied for both load and support.
43 A total load of FR = 2600 [N] was applied, divided by two and placed at a distance of DB = 168 [mm] from center of plate, presented in requirement specification appendix 7.2.
Figure 65: Position and direction of load forces used in ANSYS.
Figure 66: Fixed support used in ANSYS.
An assumption was made that the bending stiffness and total deflection difference between a homogeneous plate and one with a core correlate to earlier presented diagram of Figure 28. This means that a deflection of the homogeneous plate simulated using FEM, will be 1 further multiplied by a factor of 0,875 to correspond to a plate with core as in the final design of prototype. This assumption means the core material strength is neglected, and hence this could be seen as a safety factor due to stronger properties of the total plate in reality. Results of the deflection both simulated d1 and calculated d2 are shown in Figure 67.
44 Figure 67: Resulting deflection of the FMT plate using FEA. d1 is the resulting distance of deflection, using a homogeneous plate design. d2 is the calculated deflection for a FMT plate with a core material.
The two radii of curvatures illustrated in the figure above RB1 and RB2 represent the radius of the plate shape simulated and further calculated respectively. Both these radii of curvature are less than the required limit of RB = 14 [m] presented in the requirement specification appendix 7.2.
4.3 Strength of prototype
ANSYS was used to simulate stresses as well, which is presented in Figure 68. The maximum (von Mises) stress occur in the holes at the center of the plate and has a value of 156 MPa.
Figure 68: Von Mises stress simulation of FMT plate.
The strain of the plate is the causing failure mode, hence the tensile strength is calculated by the material with least strain capability, Equation 17.
45 σ = (17) E
The resulted maximum strain per material is 0,021 for the carbon fiber, 0,026 for the epoxy matrix and 0,026 for the core material (SikaBlock® M700). This means the carbon fiber will cause the initial failure and the tensile strength is calculated by σ = 0, 021 · Ec, where Ec is the calculated composite Ec = 118 GP a presented in Section 3.2.4, Equation 10. This results in a composite tensile strength of σ = 0, 021 · 118 · 109 ≈ 2500 MPa which is above the 156 MPa measured as maximum von Mises stress.
4.4 Lab test analysis
The data recorded in the tests was analyzed in softwares Dewosoft® X3, MATLAB R2017b and Google Sheets.
For the lab tests a similar analyze method as Wills used was applied, where the time to a specific damping of acceleration amplitude was measured. More specifically the time count starts after the release of the ski when the max amplitude of the oscillation is reached. The count then stops when the first full period of vibration is below a specified percentage of amplitude of the first max peak where the count started. The percentage limits applied in this analysis were 50 %, 80% and 95 %. A schematic illustration of this principle is shown in Figure 69.
Figure 69: The analysis method were to log the time from the max amplitude to the point where a specific percentage of that amplitude was reached.
The reason for the added thresholds of dampening limits is that the 50 % occur very soon after the initiation, due to the characteristics of an exponential function shape (red line in Figure 69 above). To add further dampening data of 80 % and 95 % will facilitate analysis of the whole dampening process in the ski setup. The peaks of the sampled data were acquired by using an inbuilt program in MATLAB called findpeaks.
46 These values is then fitted by a function to get a consistent curve which represent the dampening of the ski oscillations. The function called power2 (f(x) = a · xbc) was used for all the data and was considered to fit the peak values best. The MATLAB script is presented in appendix 7.12. The results are shown in Table 6, while all the lab data is compiled in appendix 7.9. The maximum amplitude in acceleration is also presented in Table 6, where a clear difference between the FMT plate and the reference plate is noticed. The FMT plate had a lower value of maximum amplitude, which is the first peak after mechanical release of the test ski.
Table 6: Mechanical release lab data.
A t-test was performed in the Google Sheets application XLMiner Analysis ToolPak to investigate whether the difference between the results of the two plates in the lab test is significant with 95 % confidence level. The null hypothesis was that there is no difference between the reference plate and the FMT plate. The alternative hypothesis was therefore that there is a difference between the two. The t-test was performed on the mechanical release test and separately on the max amplitude data as well as the three analyzed levels of 50 %, 80 % and 95% damped amplitude. A F-test was performed and resulted in assuming unequal variances between the two data sets for the 50 % and 80 % damped amplitude. The f-test resulted in assuming equal variances between the 95 % damped amplitude and the max amplitude. The results from the two-tailed t-test of the max amplitude is presented in Table 7, and the t-test of the damped amplitudes in Table 8.
Table 7: Lab test: results for t-test of acceleration for reference plate and FMT plate at maximum amplitude.
Amplitude p-value Significance check Max amplitude [m/s2] 1, 0 · 10−12 < 0,05
Table 8: Lab test: results for t-test of time for reference plate and FMT plate at different damping limits.
Amplitude p-value Significance check 50 % damped [ms] 3, 6 · 10−3 < 0,05 80 % damped [ms] 2, 7 · 10−5 < 0,05 95 % damped [ms] 1, 8 · 10−11 < 0,05
47 The results tells that there is a significant difference between the two plates for the maximum acceleration amplitude and time to damp the vibrations at all limits, 50 %, 80 % and 95 %.
To investigate whether the lab test results could be adaptable to predict the damping properties of the plates when skiing on piste, a comparison between the eigen frequencies measured in lab was made. The FFT Analyzer was used to sample the frequency mode plots from the 10 lab tests and determine their frequencies. A typical FFT plot with frequency modes is presented in Figure 70.
Figure 70: FFT diagram of a lab test on the FMT setup showing the four first frequency modes. Vibration excited by a hit with a chisel.
The data from the 10 measurements was compared to the frequency modes measured in the field test, which were measured the same way using the FFT Analyzer. If the modes measured in both tests correspond the results could be compared and support conclusions. If the modes would not correspond, the performance in lab may not be relevant to the actual in field performance. The eigen frequencies measured in lab are presented in Table 9 and the eigen frequencies measured in field are presented in Table 10.
Table 9: Lab test: The first four frequency modes of the FMT plate and the reference plate, presented with average frequency, standard deviation and deviation/average frequency.
48 4.5 Field test analysis
FFT plots from different snow conditions during field test is shown in Figure 71, 72 and 73.
Figure 71: FFT analysis of a carve turn run on soft snow.
The FFT plot in Figure 71 above shows in general higher amplitude values in the low frequency regime of 18-120 Hz. The frequency mode with highest amplitude was around 120 Hz. The values and shape of plot curve between the FMT plate (green) and the reference plate (red) are much similar.
Figure 72: FFT analysis of a carve turn run on hard snow.
49 The FFT plot in Figure 72 of one of the test runs on hard snow shows clear peaks at the frequency modes, more distinct than the tests on soft snow. The most significant frequency was also here around 120 Hz.
Figure 73: FFT analysis of a straight run on hard snow.
The plot of a straight run on hard snow, shown in Figure 73 shows a clear difference between the amplitudes of the FMT plate and the reference plate. But the data may be misleading, since the run was finished with only one braking turn, which means one ski was subjected for the main impact of vibrations. By not removing the last acquired data this plot really illustrates the importance of performing a well executed test, later explained in the section of discussion 5.2.
An analysis of the frequency modes was made, however with some data missing due to the difficulty of pointing out peaks, which was done manually. This resulting in an average frequency mode of not always 10 samples, but at least 6. The results from this analysis is shown in Table 10, while all field data is shown in appendix 7.10.
Table 10: Analysis of the frequency modes measured in field tests.
50 4.6 Comparison of laboratory and field data
The frequency modes measured in field were compared to the modes measured in lab, presented in Table 11. The comparison shows that the frequency modes had a positive average offset approximately 7 Hz. The offset does not seem to depend on the frequency absolute value but rather seem to be a offset with a more or less constant number. Due to this, a t-test would not be made, since the significance of the difference of the frequency modes will differ a lot. This even though the distribution of the modes looks similar in both lab and field tests except from the slight offset.
Table 11: Comparison of laboratory and field test data.
51
5 CONCLUSION AND DISCUSSION
In this chapter conclusions are drawn to answer the research questions, and the results are discussed.
5.1 Conclusions
"How can a plate with implemented Flow Motion Technology be designed and manufactured with the intention to perform vibration tests in both laboratory and in field?"
Conclusion: A prototype of a FMT plate has been designed and manufactured to fulfill the specified requirements, described in section 3.1-3.2 and verified in section 4.1-4.3. It was applicable to the test procedures, both in laboratory and field. A thoroughly described manufacturing method has been presented, as well as the design choices to improve me- chanical properties. The final design was based on a pre-impregnated carbon fiber/epoxy composite, in a sandwich structure with a polyurethane core.
"How can the test methods be designed to evaluate vibrations and what equipment is required?"
Conclusion: Two different laboratory tests were conducted, both with 10 iterations and identical setup. The setup consisted of a boot, binding, plate and ski fixed to a vice. A DAQ system connected to piezoelectric accelerometers was used to measure vibrations of the ski when either exposed to an impulse or ejected from being bent. The tests were conducted using two different plates; the FMT plate developed in the project and a reference plate. In the mechanical release test, where the ski was bent by pulling a nylon line, the time was measured to conclude when 50 %, 80 % and 95 % of the initial acceleration amplitude were reached.
"Is there any difference of vibration damping properties between a ski mounted with a plate implemented with Flow Motion Technology and a ski mounted with a state of the art reference plate?"
Conclusion: For all three thresholds the FMT plate led to a significantly faster time of dampening in the ski, confirmed by a t-test. The time to dampen vibrations was in average approximately 27 % shorter in the ski mounted with the FMT plate compared to the ski mounted with the reference plate. The highest peak of acceleration amplitude was also measured, which resulted in an average of 123 m/s2 with FMT plate, and 157 m/s2 with reference plate. A significant difference was confirmed with a t-test.
The other laboratory test was conducted with an impulse to identify eigen frequencies, utilizing a FFT function. The average frequency modes of the ski mounted with the FMT plate were 12 Hz, 44 Hz, 112 Hz and 226 Hz, while for the ski with the reference plate 12 Hz, 43 Hz, 108 Hz and 232 Hz. These were compared to the field test frequency data, which was obtained using the same setup of measurement equipment as in the laboratory tests. Ten iterations of skiing down a slope with varying snow surface conditions were made. This test procedure included both straight runs and curved paths which were not generalized. Similar frequency modes were found but with an average offset of approximately 7 Hz higher for all modes compared to laboratory frequencies. Hence it can be concluded that the laboratory ski behavior can be comparable to field behavior if taking the offset into account.
53 5.2 Discussion
The results and conclusions of ski behavior in this study may not reflect the reality, as the tests and material properties always have errors. The methods used may also not be the optimal solution to answer the research question, but will lay ground for further research. The fact that the FMT plate reduces vibrations in the ski faster than the reference plate may not correspond to faster runs in the slope. This study also leaves out the knowledge of vibration directions, where a torsion mode could occur in the 120Hz regime as in the study of Gary C. Foss et al. [4].
The stiffness and strength criteria of the prototype was confirmed by simulations in a FEM software. This included assumptions about linear appearance and lack of experience. To ensure that a sustainable design is used, more comprehensive calculations and simulations is necessary.
The used viscoelastic dampening component of butyl tape compound was not evaluated in this study, which could affect the ski performance if changed. Further calculations and evaluations of dampening solutions may result in more optimized properties.
The limits of amplitude damping 80 % and 95 % were chosen without derivation but to store more data to analyze. Questionable is whether these limits are needed to be considered when the ski is used in field, since the vibrations probably would not have time to be dampened to such limit before a new impact from the snow trigger the ski again. Due to this the first limit of 50 % and the first maximum peak is very interesting, hence the results showing that the FMT plate damped the ski significantly faster than the reference plate is of high importance. Another way to compare the exponential decay of the oscillations is by calculating the relative damping ratio of each test. This dimensionless value may describe the decay even better than using several thresholds. Although this study evaluate the method used by Tom Wills.
The setup for laboratory and field tests did affect the measurements in some extent, due to the mass of the accelerometers, cables and tape attached to the skis. A higher mass would in this case lower the frequencies, however probably barely noticeable in the test performed in this project due to the very low weight of the equipment in relation to the ski itself. The installation of the equipment could also be discussed, since the tape and cables in some extent may affect the bending properties of the ski if attached without thought and subjected to major tension. A Laser Doppler Vibrometer would therefore be of advantage in laboratory tests as evaluated by Tom Wills [5].
It would be interesting to perform a more extensive track test series, collaborating with professional race skiers skiing on race prepared tracks. Such test would only focus on with which equipment are the fastest times and less disqualification runs performed rather than measuring damping properties. This test would not require as much measurement equipment and the results would be very evident, and eventually more interesting to race skiers who probably are more interested in fast race runs rather than the theory of different damping properties.
The field test may be observed as a pre study for further field tests, since more test runs, more generalized test method and analysis method would be needed to be able to draw reasonable conclusions. The field test was however very educative and the information obtained will be useful for further testing. The snow conditions seemed to play an important
54 role on the behaviour of the ski as well. This was clear when the field test was compared to the lab tests. The measurements from field tests were more complicated to analyze than the lab tests due to diffuse FFT plots and difficulty to determine the frequency modes with accuracy. The first and second mode tended to merge together and the peaks were not always consistent. Especially difficult to analyze were the plots of measurements on soft snow conditions, which had more smeared plots probably caused by dampening properties in the snow. The plots from hard snow tests were more consistent and had more distinctive frequency mode peaks. The reason for the soft and hard snow conditions tested is that the sun heated up the southeast facing slope quicker than expected. A more controlled and consistent environment would make it easier to compare lab data to field data. On the other hand, to test in both soft and hard conditions allowed us to analyze the difference in behaviour of both, which was educative for future testing. The plot in Figure 73 in Section 4.5 shows clearly the importance of measuring correct sequences of a test. The plot is the FFT analysis of a straight run on hard snow, where the FMT plate show quite significant difference to the reference plate. This is not necessary the case, since the stopping skid in the end is part of the recording, and the FMT plate was attached to the ski making the majority of the stopping action. This was noticed in this case, but could probably be missed if not being observant when analyzing, or even better be avoided by designing the test run carefully and record correct data in the beginning.
The field tests were also affected by the measurement system in some sense. The initial plan was to carry the DAQ system and computer in a backpack on the back of the skier. This were changed due to the short cables that were supplied with the accelerometers, that only enabled the backpack to be carried in hip height. The solution was to ski in a lower position and carry the back pack in front instead of on the back. The short cables combined with this stance limited the range of motion, the skiing speed and probably the skiing technique in some sense. For proper carve turns at higher speed longer cables would be needed to enable a more natural stance and the use of poles for balance.
Another field which would be interesting to perform more research within are subjective tests. If not only alpine ski racing would be of interest this field would rather focus on recreational skiing. Such study would focus on comfort and ease of skiing on soft prepared piste rather than optimizing damping performance for high speed on icy race tracks. Such test would correlate to the conclusion cited by Gregory C. Causey made by Skiing Magazine, where the ski with lowest measured damping effect of a group of skis in lab, but the only ski which were felt having a damping effect in piste. The tests would require more test persons, and especially independent test persons without relation what so ever to Flow Motion Technology AB to be able to draw trustworthy conclusions. The problem with such tests is to conclude how to measure and evaluate data without any physical measurement equipment.
55
6 RECOMMENDATIONS AND FUTURE WORK
To be able to collect trustworthy data the field tests is recommended to be redone with more test runs, more suitable measurement equipment and in more controlled conditions. The test procedure is recommended to also be more specified, for example a generalized test track for carving turns and a longer, flatter and inclination specified track for the straight test runs. As result of the difference shown between soft snow and hard snow the recommendation is to perform test on as hard snow as possible if alpine racing performance is the subject. It is also recommended to narrow the thesis project down to only the test and analysis part rather than also develop the prototype which was time consuming. The prototype developed in this thesis would fulfill many of the requirements for the tests as well as the measurement equipment used, if provided with longer cables for the accelerometers. The measurement equipment with software was both reliable and convenient to use. Due to the difficulty to correlate laboratory tests and field tests, subjective tests is also proposed.
More research should be made in the field of damping solution, to substitute the present butyl tape compound. The concept of having the damping under the plate interferes with the FMT theory in some sense. A proposal would be to place the damping outside the system, perhaps in the shape of a viscous damper mounted in the front or back of the plate. The problem would then instead be snow packed under the plate and interfering instead, which would require for example some sort of sealing solution to prevent snow from entering the space below the plate. Snow, and especially in molten form as water, have a tendency of finding its way past even the most effective seals though, especially seals with faces in motion, and if then frozen to ice again the system would jam. Another solution with this in mind is a damping material filling out the space between the plate completely, but with the ability to be compressed to not limit the FMT motion and still provide the damping properties required. Such material would perhaps be some sort of viscoelastic foam.
57
References
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59 [22] Dewesoft FFT guide. url: https://dewesoft.pro/online/course/fft-spectral- analysis. [23] FIS introduction. Last accessed 26 April 2019. url: https://www.fis-ski.com/en/ inside-fis/about-fis/history/history-of-fis. [24] FIS. “The International Ski Competition Rules (ICR)”. In: (2018), Book IV. [25] Specifications for Alpine Competition Equipment 2018/2019. Last accessed 29 April 2019. url: https://assets.fis- ski.com/image/upload/v1544601370/fis- prod/Specifications_for_Alpine_Competiton_Equipment_1.pdf. [26] Siemens. Solid edge ST10. Version 110.00.00107. url: https://support.industrysoftware. automation.siemens.com/gtac.shtml. [27] Material data. Accessed 25 May 2019. url: http://www-materials.eng.cam.ac. uk/mpsite/interactive_charts/stiffness-density/NS6Chart.html. [28] Lindberg % Lund, BM 5185. Accessed 25 May 2019. url: http://info.lindberg- lund.no/produktblad/Tekniske_datablad/VAN-BM5185-TD.pdf. [29] A. Marshall. SANDWICH CONSTRUCTION, pp. 557–558. url: https://link. springer.com/chapter/10.1007%5C%2F978-1-4615-7139-1_21. [30] Missouri Univerity of Sience and Technology. Sandwich construction, Sandwich Struc- tures, Chapter 7. url: https://link.springer.com/chapter/10.1007%5C%2F978- 1-4615-7139-1_21. [31] Mechanics of sport - Ski Construction. Accessed 25 May 2019. url: http://www. mechanicsofsport.com/skiing/equipment/skis/ski_construction.html. [32] The benefits of carbon fiber. Accessed 25 May 2019. url: https://zoltek.com/ carbon-fiber/the-benefits-of-carbon-fiber/. [33] Carbix carbon fiber weave images. Accessed 25 May 2019. url: http://www.carbix. se/category.html/kolfibervav. [34] Stacking efficiency factors. Accessed 25 May 2019. url: https://sedyono.files. wordpress.com/2016/01/property-prediction.pdf. [35] Dewesoft DEWE 43 A. Accessed 25 May 2019. url: https : / / dewesoft . com / products/daq-systems/dewe-43.
60 7 APPENDICES
7.1 Risk Assessment safety factors, aluating and contact- low profile, sign NDA ate many different pos- ate different options and ate different possibilities w schedule and fre- w schedule and revise if quently check forecasts needed.updated Keep stakeholders Action Follo Start ev ing suppliersschedule accordingEvalu to sibilities andPerform book thorough background instudy time. Evalu order or bookbrate in and time. install properly Evalu Cali- and suppliers.holders updated Keep stake- Design with allocate time,analysis use tools before computer manufac- turing Keep a Follo alue 9 9 3 27 27 27 27 27 Risk v 9 9 9 9 3 9 3 9 Impact 3 1 3 3 3 3 1 3 Probability etitors time, mal- time, mal- time or bad e too expen- e does not of snow and bad of time to accom- condition for alpine ski- ing quality presenting samenology, tech- basedknowledge on or not our plish prototypefacturing manu- and testing Scenario Lack Long lead Long lead Long lead Prototyp sive Prototyp meet the requirements External comp Lack functioning or not suit- able test equipment functioning or not suit- able test equipment t e faulty Risk Cost Time equipment Material Competition Environmen Manufacturing Test Prototyp
Table A.1: Risk assessment.
61 7.2 Prototype Requirement Specification
Requirement Specification Priority Comment Bending Maximum calculated load High Test person weighs 90 kg, strength of 2610 N, applied through with a ski turn inclination ski boot and mounted ski of 70 degrees and all the bindings weight on one ski, equation 6. Bending stiff- Deflection at plate ends High To maintain FMT when ness (max load) results in ski achieves full bend. an increased radius of curvature which should not exceed radius RB of fully bent ski Blizzard GS Magnesium, R21.0, L189 [blizzard ski], Figure 21. Torsion stiff- Maximize torsion stiffness Low Prevent torsional deflec- ness with respect to bending tion when carving. stiffness as priority Maximum 16 mm Low Boot, binding and ski de- height up to pendent (FIS). ski binding Maximum 63 mm High Width will enable usage width of plate on every ski, ap- proved by FIS. Minimum 600 mm High To fit the ski bindings length Marker Race Xcell 16 and enable use of similar to pre- vious end locking system. Prototype ma- Carbon fiber composite Low A request from the stake- terial holder. Ski binding Hole pattern for “2018 High Secure mounting of ski hole pattern Marker Race Xcell 16” binding. Enable disassem- bindings ble and reassemble. Damping Possible to change and ad- Low Enable further test possi- just damping properties bilities. Environment Withstands snow for more High Field test environment. than 8 h straight One day of test in snow. Temperature -25◦C to +40◦C High Storage and test en- range durance. Budget Total of 5000 kr for one Low If possible make several pair of plate prototype pairs within same budget. Prototype de- Implement FMT to such High Preferably aim for a small sign grade it has a rolling con- radius of curvature to ex- tact to ground aggerate FMT and facili- tate comparison.
Table A.2: Requirement specification of prototype properties.
62 7.3 SikaBlock M700 - Technical specification
Product Data Sheet Version 02 / 2016 SikaBlock® M700 Model board
Areas of Application Product Benefi ts
Manufacture of data control models and cubings Very high dimensional stability Manufacture of master models High compressive strength and edge stability Manufacture of moulds for low pressure reaction Good solvent resistance injection moulding High heat distortion temperature Vacuum forming moulds for lower number of Easy machinability pieces Low dust formation when milled Very dense, fi ne surface Easy to seal and good to varnish Description
Basis Polyurethane, light brown Adhesive Biresin® Kleber braun Neu, two component PUR system, brown Filler Biresin® Spachtel braun Neu, two component polyester system, brown
Physical Data (approx.-values) SikaBlock® M700 Density ISO 845 g/cm³ 0.7 Shore hardness ISO 868 - D 66
Composites Flexural strength ISO 178 MPa 26 E-Modulus ISO 178 MPa 1,000 & Compressive strength ISO 604 MPa 25* Impact resistance ISO 179 Ue kJ/m² 7 Heat distortion temperature ISO 75 B °C 90
-1 -6 Linear thermal expansion coeffi cient αT DIN 53 752 K 55 x 10 * at 10% compressive strain
Processing Data Adhesive / Filler Biresin® Kleber braun Neu Biresin® Spachtel braun Neu Mixing ratio A : B in parts by weight 100 : 65 100 : 2 Potlife min 20 5 Setting time h 8 - 10 > 20 min Tooling
Packaging Board materials SikaBlock® M700 1500 mm x 500 mm x 30 mm, 30 pieces / pallet 1500 mm x 500 mm x 50 mm, 36 pieces / pallet 1500 mm x 500 mm x 75 mm, 24 pieces / pallet 1500 mm x 500 mm x 100 mm, 18 pieces / pallet 1500 mm x 500 mm x 150 mm, 12 pieces / pallet Adhesive Biresin® Kleber braun Neu, resin (A) 1.5 kg net Biresin® G53, hardener (B) 4 kg; 0.975 kg net Filler Biresin® Spachtel braun Neu, resin (A) 2 x 8.34 kg net cartridges (A) 6 x 1.76 kg net tins (A) in a box BPO-Paste, hardener (B) 2 x 0.16 kg net sticks (B) (for cartridges - A) 6 x 0.04 kg net tubes (B) in a box (for tins - A) M700 1 / 2 ® SikaBlock
Figure A.1: SikaBlock M700 - Technical specification.
63 iueA2 ialc 70-Tcnclspecification. Technical - M700 SikaBlock A.2: Figure
® be suppliedonrequest. refer tothemostrecentissueoflocalProductDataSheetforproductconcerned,copieswhichwill must beobserved. All ordersareacceptedsubjecttoourcurrenttermsofsaleanddelivery. Usersmustalways purpose. Sikareservestherighttochangepropertiesofitsproducts. The proprietaryrightsofthirdparties other adviceoffered. The useroftheproductmusttestproduct’s suitabilityfortheintendedapplicationand whatsoever, canbeinferredeitherfromthisinformation,oranywrittenrecommendations, of merchantabilityorfi practice, thedif properly stored,handledandappliedundernormalconditionsinaccordancewithSika‘srecommendations.In products, aregiveningoodfaithbasedonSika‘scurrentknowledgeandexperienceoftheproductswhen The information,and,inparticular, therecommendationsrelatingtoapplicationandend-useofSika Legal Notice vary duetocircumstan ces beyondourcontrol. All technicaldatastatedinthisProductDataSheetarebasedonlaboratorytests. Actual measureddatamay Bases Value waste. ofasproduct disposed be should cleaned be cannot that Packaging recycling. for given be can packagings emptied Completely Recommendations: Packaging co the with accordance in unit wastedisposal aspecial ofin disposed be Must Recommendations: Product Disposal considerations data. related safety r shall users products, ofchemical disposal and storage handling, safe the on advice and For information Information Safety and Health Processing SikaBlock M700 2 / 2 Storage efer to the most recent Safety Data Sheet (SDS) containing physical, ecological, toxicological and other other and toxicological ecological, physical, (SDS) Sheet containing Data Safety recent most tothe efer moderate as could be. ascould moderate of transport and storage During Data Sheet). Product has un-limited shelf life when stored stored when life shelf un-limited has Product e. use g.Biresin For bondings oil. or grease ofdustand free and dry clean, mustbe areas Bonding hand. by or tools performance high with on so and milling by sawing, accomplished easily is block ofthe Machining tomachining. to18 -25°C prior acclimatised mustbe material The For correction or fi or For correction lea separate our or manufacturer tool cutting from advice seek please milling about information For more Sheet). Technical Data see braun information Neu (for more rresponding regulations. fl et. ferences inmaterials,substratesandactualsiteconditionsaresuchthatnowarrantyrespect nishing of surface use Biresin use ofsurface nishing tness foraparticularpurpose,noranyliabilityarisingoutoflegalrelationship Germany Internet: www.sika.com Internet: Germany [email protected] Email: Urach D -72574 Bad Str. 139 Fax: (0) 401 7125 +49 940 Stuttgarter Tel: (0) 492 7125 +49 940 Urach Bad Subsidiary GmbH Sika Deutschland Further informationavailableat: fi nished tools and models temperature variations should be kept be as should variations temperature models and tools nished 64 fl at in dry conditions. conditions. dry at in ® Spachtel braun Neu (for more information see Product Product see information (for more Neu braun Spachtel ® Kleber 7.4 DAQ: Dewe 43 A - Specification
Figure A.3: Dewe 43 A - Analog input specification.
65 7.5 Brüel & Kjær DeltaTron Accelerometer Type 4397 - Specification
Figure A.4: Brüel & Kjær DeltaTron Accelerometer Type 4397 - Specification.
66 7.6 Data sheet KISO 358 BUTYL Superior - Specification
TECHNICAL DATA SHEET
Date: 18/1/2016 KISO 358 BUTYL Superior Version 9 Page 1 of 2
Product
KISO 358 BUTYL Superior is a general purpose rubber based preformed extruded butyl tape.
Key Features
− Good adhesion to a wide range of substrates − Provides a water and air tight seal − Excellent UV resistance − Noise cancelling
− Solvent free − Highly conformable − Quick, clean and easy to apply with little waste − Remains flexible throughout service life
Areas of application
− Sealing of joints in mobile homes, motorhomes and caravan construction − Metal gutter joints − Side and end lap joints in metal roofing and cladding systems − Sealing of duct flanges in HVAC systems − Air, water and dust sealing of compression joints and seams − Acoustic solution in the automotive industry − Joint seal and gap filling for inland boat and leisure industries
Technical Features Unit Nominal Value Test Method Compression 50% kN/m2 110 KISO 5
Peel Adhesion N/cm >13 KISO 13 Strain Peak Force, Fmax kN/m2 35 KISO 5
Density g/cm3 1,60 DS/ISO 2781A, KISO 2 Needle Penetration (23OC) dmm 70 ASTM D 5 (adjusted), KISO 1 Service Temperature Range oC -30 - +80
KISO - KISO Test Method
Standard Dimensions and Packaging
KISO 358 BUTYL Superior is supplied as a preformed tape on a siliconised release paper or foil. The product is offered in various dimensions. The number of meter per roll and rolls per carton is determined by product dimensions and customer requirement.
Available colours: Black, white, grey and blue (other colours on request).
Figure A.5: Data sheet KISO 358 BUTYL Superior - Specification.
67 7.7 DEWESoft Set up - FFT Analyser
Figure A.6: DEWESoft Set up - FFT Analyser.
68 7.8 DEWESoft Set up - Recorder
Figure A.7: DEWESoft Set up - Recorder.
69 7.9 Lab test data
Table A.3: Lab test data - eigen frequencies.
Table A.4: Lab test data - release test.
Table A.5: Lab test data - differences.
70 7.10 Field test data
Table A.6: Field test data.
Table A.7: Comparison between laboratory and field test data.
71 72 7.11 Gantt Chart John Hampus Vacation Prepare presentation Finish and details Write report Report preparation Report and presentation Analyze data Compile data Execution Preparation Gather equipment Test and analysis Quality control Manufacture Order material Machines booked Design Prototype Planning seminar Background research Project planning Planning and background research Master Thesis GANTT Task January T W T M F T W T M F T W T M F T W T M F T W T M F T W T M F T W T M F T W T M Week 4 Week 5 February Week 6 Week 7 Week 8 Week 9 Mars Week 10 Week 11
73 Mars April May
Week 11 Week 12 Week 13 Week 14 Week 15 Week 16 Week 17 Week 18 Week 19 Week 20 Week 21 FMTWTFMTWTFMTWTFMTWTFMTWTFMTWTFMTWTFMTWTFMTWTFMT 74 May June
Week 21 Week 22 Week 23 (20) Week 24 WTFMTWTFMTWTFMTWTF 75 7.12 MATLAB Scripts
7.12.1 Solid Mechanics - design of prototype clear all , close all , clc %% Tyngden p dalskidan lskling weight_skier=90; %[Kg] inclination =70; %[deg] Angle of skier while turning ( relative vertical ) ratio_dalskidan=1; %Percentage of weight on dalskidan
G_force=1/cosd(inclination); g=10;
Force_ski=weight_skier∗g∗G_force∗ratio_dalskidan %% Material Parameters % Carbon fiber t_fiber=0.2∗10^−3; %[m] E_fiber=235∗10^9; %[Pa] density_fiber=1.78∗10^3; %[kg/m^3]
% Matrix − Epoxy E_matrix=3,5∗10^9; %[Pa] density_matrix=1.28∗10^3; %[kg/m^3]
% Composite ratio_weight=0.65; %weight percentage fiber, depends on manufacturing method ratio_volume=(ratio_weight/density_fiber)/((ratio_weight/density_fiber)+((1−ratio_weight)/density_matrix)) stacking=[45;45] %Stacking sequence eff_factor=sum((1/length(stacking)).∗(cosd(stacking).^4)); Ec=E_fiber∗eff_factor∗ratio_volume + E_matrix∗(1−ratio_volume) t_layer=t_fiber/ratio_volume %[m] with epoxy, depends on manufacturing
%% Geometry h_fixed=4∗10^−3; layers=2∗h_fixed/t_layer % Total number of layers fibre composite width=63∗10^−3; %[m] height=16∗10^−3; %[m] h_fiber=[0:1∗10^−3:height/2]; %[m] Thickness of fiber composite in height w_fiber=0∗10^−3; %[m] Thickness of fiber composite in width
%% Bend W_bend=(width∗height.^3 − (width−2∗w_fiber)∗(height−2∗h_fiber).^3)/6∗height;
figure (1) plot(h_fiber∗10.^3,100∗W_bend/W_bend(end)) title ('Bending stiffness as function of composite thickness')
76 ylabel ('Percent of maximum stiffness [%]') xlabel ('Composite thickness[mm]')
% Varying thickness in width h_fiber=3∗10^−3; w_fiber=[0:1∗10^−3:height/2];
W_bend=(width∗height.^3 − (width−2∗w_fiber).∗(height−2∗h_fiber).^3)/6∗height;
figure (2) plot(w_fiber∗10.^3,100∗W_bend/W_bend(end)) title ('Bending stiffness as function of composite thickness, in width') ylabel ('Percent[%]') xlabel ('Composite thickness[mm]')
%% Adding "Wings" width_wing=10∗10^−3; % Total width of wings height_wing=[0:1:10].∗10^−3;
% Areas A1=width∗height; A2=width_wing.∗height_wing;
% Distance to each "blocks" Center of Gravity Y1=height/2; Y2=height+height_wing./2; Y0=(A1∗Y1+A2.∗Y2)./(A1+A2);
% Distance to main Center of Gravity a1=abs(Y0−Y1); a2=abs(Y0−Y2);
% Moment of inertia I1=(width∗height^3)/12; I2=(width_wing.∗height_wing.^3)./12;
I=I1 + A1∗a1.^2 + I2 + A2.∗a2.^2; z=max(Y0,height+height_wing−Y0); z=3; W_wing=I./z;
figure (3) plot(height_wing∗10^3,W_wing∗100/max(W_wing))
%% h_fixed=3∗10^−3; layers=2∗h_fixed/t_layer % Total number of layers fibre composite width=[60,61,62,63,64,65]∗10^−3; %[m]
77 height=16∗10^−3; %[m] h_fiber=4∗10^−3;%[0:1∗10^−3:height/2]; %[m] Thickness of fiber composite in height w_fiber=0∗10^−3; %[m] Thickness of fiber composite in width
W_bend=(width.∗height^3 − (width−2∗w_fiber).∗(height−2∗h_fiber)^3)./6∗height;
figure (4) plot(width∗10^3,100∗W_bend/W_bend(end))
78 7.12.2 Test data - Function fitting close all , clc data_acc=Data1_Marker_Lab.∗(−1); data_time=Data1_time_Marker_Lab;
[peak,time]=findpeaks(data_acc,data_time,'MinPeakDistance',0.04,'MinPeakHeight',0); plot(data_time,data_acc,time,peak,'o')
[ f , coeff1 , coeff2]=fit (time,peak,'power2'); hold on plot(f ,time,peak) xlabel ('Time [s ]') ylabel ('[ m/2^2]') title ('Acceleration as function of time − Lab test')
Y=f(0:0.001:data_time(end)); amplitude=max(abs(data_acc)) tresh_50=amplitude/2; below50=find(Y 79 7.13 Power supply - battery Figure A.8: Battery specification. 80 7.14 FMT Prototype - Drawings 1 1 1 1 2 12 Quantity Ersatt av Ersatt 2019-05-19 DATE APPROVED Anmärkning Ersätter Datum Ritningsnr Material fiber/Epoxy Carbon SikaBlock® M700 Polylactide(PLA) Polylactide(PLA) Aluminum Stainless steel REVISION HISTORY 1 : 2,5 Ämne/Dimension Skala DESCRIPTION Assembly Material FMT Ski Plate - Ski Plate FMT - File Name FMT Ski Plate composite FMT Ski Plate core front Bushing back Bushing Stopper Helicoil M5 REV Material 1 3 5 4 2 6 Item 3 Godkänd av Godkänd MF2013X 1 5 Hampus Detaljnr Antal Benämning Skapad av Skapad 6 5 2 4 Figure A.9: FMT plate assembly drawing. 81 REVISION HISTORY REV DESCRIPTION DATE APPROVED R R 3756 3752 600 iueA.10: Figure 489,8 4 8 4 16 FMT 414,5 105,5 82 Helicoil M5 (12x) 6 O lt drawing. plate 25,8 4x 16 O 16 R 8 40 20 36 43 11,5 11,5 17,8 80 33 18,5 285 Detaljnr Antal Benämning Material Ämne/Dimension Anmärkning Skapad av Godkänd av Material Skala Ersätter Ersatt av Hampus Carbon fiber composite 1 : 2 Datum 2019-05-19 MF2013X FMT Ski Plate Ritningsnr REVISION HISTORY REV DESCRIPTION DATE APPROVED 4 18 iueA1:SoprDrawing. Stopper A.11: Figure O 10 83 O 5 Detaljnr Antal Benämning Material Ämne/Dimension Anmärkning Skapad av Godkänd av Material Skala Ersätter Ersatt av Hampus Aluminum 3 : 1 Datum O 24 2019-05-19 MF2013X Stopper Ritningsnr REVISION HISTORY REV DESCRIPTION DATE APPROVED 2 4,3° 7,9 iueA1:BsigfotDrawing. front Bushing A.12: Figure O 10,5 84 O 15,5 Detaljnr Antal Benämning Material Ämne/Dimension Anmärkning Skapad av Godkänd av Material Skala Ersätter Ersatt av Hampus Polylactide (PLA) 3 : 1 O 24 Datum 2019-05-19 Bushing front MF2013X Ritningsnr REVISION HISTORY REV DESCRIPTION DATE APPROVED 2 iueA1:Bsigbc Drawing. back Bushing A.13: Figure 6 4,3° 2x R 2 12 85 R R 5,25 16 24 10,5 Isometric view 18 Detaljnr Antal Benämning Material Ämne/Dimension Anmärkning Skapad av Godkänd av Material Skala Ersätter Ersatt av Hampus Polylactide (PLA) 3 : 1 Datum 2019-05-19 MF2013X Bushing back Ritningsnr 7.15 Composite properties TECHNICAL ¨ DATA SHEET No. CFA-005 T700S DATA SHEET Highest strength, standard modulus fiber available with excellent processing characteristics for filament winding and prepreg. This never twisted fiber is used in high tensile applications like pressure vessels, recreational, and industrial. FIBER PROPERTIES English Metric Test Method Tensile Strength 711 ksi 4,900 MPa TY-030B-01 Tensile Modulus 33.4 Msi 230 GPa TY-030B-01 Strain 2.1 % 2.1 % TY-030B-01 Density 0.065 lbs/in3 1.80 g/cm3 TY-030B-02 Filament Diameter 2.8E-04 in. 7 µm Yield 6K 3,724 ft/lbs 400 g/1000m TY-030B-03 12K 1,862 ft/lbs 800 g/1000m TY-030B-03 24K 903 ft/lbs 1,650 g/1000m TY-030B-03 Sizing Type 50C 1.0 % TY-030B-05 & Amount 60E 0.3 % TY-030B-05 F0E 0.7 % TY-030B-05 Twist Never twisted FUNCTIONAL PROPERTIES CTE -0.38 α⋅10-6/˚C Specific Heat 0.18 Cal/g⋅˚C Thermal Conductivity 0.0224 Cal/cm⋅s⋅˚C Electric Resistivity 1.6 x 10-3 Ω⋅cm Chemical Composition: Carbon 93 % Na + K <50 ppm COMPOSITE PROPERTIES* Tensile Strength 370 ksi 2,550 MPa ASTM D-3039 Tensile Modulus 20.0 Msi 135 GPa ASTM D-3039 Tensile Strain 1.7 % 1.7 % ASTM D-3039 Compressive Strength 215 ksi 1,470 MPa ASTM D-695 Flexural Strength 245 ksi 1,670 MPa ASTM D-790 Flexural Modulus 17.5 Msi 120 GPa ASTM D-790 ILSS 13 ksi 9 kgf/mm2 ASTM D-2344 90˚ Tensile Strength 10.0 ksi 69 MPa ASTM D-3039 * Toray 250˚F Epoxy Resin. Normalized to 60% fiber volume. TORAY CARBON FIBERS AMERICA, INC. (1).pdf Figure A.14: Carbon fiber properties. 86 RESIN SYSTEM DATA SHEET NAME: 2510 PREPREG SYSTEM MANUFACTURER Toray Composite Materials America, Inc. TYPE: 250‐270°F (121‐132°C) Cure Toughened Epoxy PRODUCT DESCRIPTION: The 2510 prepreg system is specifically formulated for out‐of‐autoclave (OOA) processing of aerospace primary structures. This prepreg system has excellent all‐around structural properties with a high wet and dry Tg while offering low‐energy curing (250‐270°F, 121‐132°C). Curing methods include autoclave or oven cure. Product can be cured with or without using a dwell. PRODUCT BENEFITS/FEATURES: TYPICAL APPLICATIONS: • High Heat Tolerance • Aircraft Structures • Easy layup with minimal cuts or ridge lines • Aerospace Material Specification 3914 NEAT RESIN PHYSICAL PROPERTIES: Resin Density: 1.267 g/cc Resin Gel Time @ 250°F (121°C) 8 ‐ 13 min. Dynamic Viscosity ~60 P @ 250°F (121°C) Tg DMA, Dry 294°F (146°C) Tg DMA, Wet 267°F (131°C) FABRIC LAMINATE PROPERTIES: MATERIAL: F6273C‐07M, T700S‐12K Fiber, 190 FAW (GSM), 42 RC% Weight. Oven Cure Tension and compression values are normalized to the indicated Vf herein. source: https://www.toraycma.com/file_viewer.php?id=4856 prepared by: Elevated Materials (www.elevatedmaterials.com) Figure A.15: Epoxy resin properties. 87 TRITA ITM-EX 2019:243 www.kth.se