Soutenance mémoire
Load Case
The load case of the study is based on a J/Z hydrofoil for an AClass catamaran, designed by Clemens Dransfeld, FHNW and called EH1. The concept uses the maximized geometrical envelope allowed on the class rules, inspired by the most successful commercial AClass designs, such as DNA (Figure 2.1), Scheurer G7 and Exploder A13. The load evaluation was done by F. Schadt (Schadt, 2016) during his masters work at FHNW as part of the EHYCOMP project. The load-case presented is based on an AClass catamaran with two submerged hydrofoils, as most commercial AClass catamarans do, to develop the needed vertical lift and achieve a Foiling state. The concept proposed in this thesis has the intention of using only one submerged hydrofoil to generate the needed vertical lift, as seen on Figure 2.2, a configuration adopted by many CClass and America’s Cup catamarans. This would be possible by a large deformation on the hydrofoils lower section up to the tip, converting a hydrofoil from a J/Z to an L/V geometry. Despite the fact that the concepts diverge from the fundamental application of two foils being submerged and sharing the vertical load to allow a Foiling state, joint decisions regarding the basic parameters were taken, allowing a maximum use of the calculated values for both studies.
The overall geometrical boundaries, the hydrofoils geometrical sub-sectioning, and the boat-speeds, just to name a few, were defined based on average or commonly used values. To begin with the hydrofoils load calculations, the minimum boat-weight allowed for racing along with AClass rules (75 kg) was used. The skipper weight, height and center of mass were considered to be the average of the population, being respectively 85 kg, 1.80 m and 1.10 m. The free body diagram of the boat and crew, with a general representation of the case-study loads can be seen on Figure 2.3. The EH1 hydrofoil on Figure 2.4, used for the load case study, was designed with a 1.3m span, a root and tip chords of 135mm, and 100mm respectively and a 10% overall profile thickness. It is composed by two airfoil profile geometries, being HQ1510 profile from the hydrofoil root to the elbow, transitioning towards an HQ3510 profile up to the tip. The choice of these profiles is a compromise between the lift/drag coefficients (Cl/Cd) of the sections and their purpose. In the case of a four supports foiling catamaran, the main foil section, where the low Cl/Cd HQ1510 is used, should not create a great hydrodynamic lift because the opposite side foil would generate the same force in the opposite direction, needing for a stronger structure. On the tip side, the cambered HQ3510 high Cl/Cd profile was chosen as both hydrofoils would collaborate mostly in the same z component direction.
To obtain the hydrodynamic forces acting on the EH1 hydrofoil when submitted to different configurations, a Vortex-Lattice method model was developed using Tornado, a MatLab based scrip able to simulate 3D airfoils and wings. MatLab scripts were adapted and used to evaluate the different sailing scenarios, based on common situations for wind and boat speeds, as well as hydrofoils foil-rake and leeway angles to simulate the hydrofoils behavior as realistically as possible. With the results of the Bending Moments and Shear-Loads acting on the hydrofoil for the defined boat speeds and hydrofoil conditions along the wing-span (Figure 2.5), it was necessary to define the section where the Non-Linear Passive Compliance was going to happen and under what conditions of the boat and hydrofoil. To exploit the EH1 hydrofoil geometry, the section at 0.85m from the hydrofoils root was chosen to study the compliance. The choice for the section is based on a continuation of the hydrofoils natural curvature of the elbow and the practicality of the application. At that section, when a boat achieves the objective morphing speed of 12kt, considered as the beginning of the transition phase between Archimedean and Foiling modes, an approximate bending moment of 115Nm is obtained. Then, at a speed of 24kt, considered as the foiling mode and maximum speed for the case study, the bending moment obtained is approximately 375Nm. A simplified diagram of the two geometrical states can be observed on Figure 2.6.
SMA
The SMA used for this project was the Super-Elastic UDIMET® NiTiNOL SMA wire _ 0.5mm from Special Metals. This wire has an Austenite Final temperature (Af ) of 4 °C, as specified in the Certificate of Test presented on Appendix I, meaning that above this temperature, the material behaves as super-elastic. For the application, the room temperature was defined at °C, making this alloy a good choice for the hydrofoil, supposed to be submerged in water. The wire was tested on a Zwick Z50kN tensile testing machine at the operation temperature, with an uncertainty of } 2 °C, measured during the testing phases. The cycle of loading was defined by the Standard Test ASTM F2516. A summary of the test procedure is presented on Image adapted from Admet.com Before the choice of the UDIMET wire was made, many other NiTiNOL wires with different compositions and diameters were tested. While being submitted to high strains, either when tested or during the actual application, the thin wire needs to be fully fixed, as any other member for any functional structure. To achieve this, the wire clamping technique seen on Figure 2.14a is usually unsuccessful because the induced stresses at the attachment point weakens the wire locally, creating failure before the maximum strength is achieved.
The use of Capstan Grips (see Fig. 2.14b) solves the previously described issue by using the friction along the circular grips to have a uniform loading and reduced stress concentration on the thin diameter wires. With the objective of finding a solution to secure the wire for the material characterization and training, as well as for the PCP application, a solution inspired from the previously described test methods was developed using the Pin Loaded Strap method (see Figure 2.15). This simple, efficient and strong solution is used in high strength tensile applications, like sailboat shrouds attachments, as seen on Figure 2.16, where the high stresses can be efficiently distributed over the hull structure. With this system, the wires could be characterized and installed for testing as well as for the PCP. The calculations for the high loading of the prototype were done following the equations from Fiber-Plastic Composite Structures (Schürmann, 2007). The equations and detailed descriptions, adapted from the literature can be seen on Figure 2.17. By using this technique, the SMA wire characterisation was completed and the final Stress- Strain results, as well as the complete material properties were determined. These are shown on Figure 2.18 and Table 2.1 respectively.
Tool Methodology To estimate the internal structure needed for a functional hydrofoil, this tool has the capability of defining the beam wall thickness, while the input parameters for this estimation come from the previous calculations on the Non-Linear Beam EI Tool. This means that for every calculated EI section GBE, a discrete CFRP I-Beam layup definition is determined to match the required local bending rigidity (EI). To do so, the process iterates over a user defined layup ply-stack and orientations where the lamina material properties are defined by the user, such as E1,E2,G12, v12 and the material tension and compression limits S− L , S+ L , S− T and S+ T . The optimization is based on the lamina thickness, where it is defined at least as 5 times thinner than the real material for the initial iteration. The process starts with a comparison of the target _EI from the Non-Linear Beam _EI Tool and the composite equivalent _EIxx from (Kollar & Springer, 2003) calculations. If the composite beam stiffness value is below the target value from the previous calculations, the lamina thickness is increased of 1% and the composite I-Beam is recalculated until the target value is achieved, providing the output of the flanges and web thickness ( ft ,wt) as seen on Figure 2.36. When all the GBE sections are calculated, the tool evaluates the Tsai-Hill criteria on the tension and compression side of the beam with the associated bending moment calculated by the Non57 Linear Beam EI Tool, outputting the maximum failure index as reference. In the case that the failure index is above 1, to which laminate failure is assumed, the local maximum strain would need to be reduced in the Non-Linear Beam EI Tool to stiffen the section, and the iteration restarts. The flowchart diagram of the tool can be seen on Figure 2.37..
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Table des matières
INTRODUCTION
CHAPTER 1 LITERATURE REVIEW
1.1 The physics of sailing
1.1.1 Displacement boats
1.1.2 Hydrofoils
1.2 Materials
1.2.1 Carbon Fiber Reinforced Polymers (CFRP)
1.2.2 Shape Memory Alloys
1.3 Morphing Structures
1.3.1 Embedded SMA concepts
1.3.2 Passive morphing concepts
CHAPTER 2 METHODS AND METHODOLOGY
2.1 Load Case
2.2 Hydrofoil Structure Design
2.3 Prototype Design and Materials
2.3.1 Design Methodology
2.3.2 Conceptual Design
2.3.3 Materials & Characterization
2.3.3.1 SMA
2.3.3.2 CFRP
2.4 Analytical Design Tools
2.4.1 Non-Linear Beam EI Tool
2.4.1.1 Methodology
2.4.1.2 Beam Model Definition
2.4.1.3 Model validation
2.4.1.4 Tool implementation and scripting
2.4.2 Beam CLT Tool
2.4.2.1 CLT Concepts Review
2.4.2.2 Tool Methodology
2.4.3 SMA Beam Tool
2.4.3.1 Motivation
2.4.3.2 Design boundaries and considerations
2.4.3.3 Methodology
2.4.3.4 Tool implementation and scripting
CHAPTER 3 PROTOTYPE DESIGN, MANUFACTURING & TESTING
3.1 Hydrofoil Prototype Design & Manufacturing
3.1.1 Compliant Section Design
3.1.2 Finite Element Model of Compliant Section
3.1.2.1 Motivation
3.1.2.2 Materials definition
3.1.2.3 Model Design
3.1.2.4 Boundary Conditions
3.1.2.5 Elements Definition, Meshing and Convergence
3.1.2.6 Results and Data Extraction
3.1.3 Mold design & Manufacturing
3.1.4 Compliant Beam Manufacturing
3.1.4.1 CFRP Beam Manufacturing
3.1.4.2 SMA Wires Installation
3.2 Testing
3.2.1 Setup
3.2.2 Testing Procedure
3.2.3 Data Analysis
3.2.3.1 Experimental Data
3.3 Results & Observations
3.3.1 Conclusions
CHAPTER 4 HYDROFOIL PRELIMINARY DESIGN PROCESS (PD)
4.1 Hydrofoil Definition and Load Case
4.2 Calculation Process
CONCLUSION AND RECOMMENDATIONS
APPENDIX I MATERIALS DATA SHEETS
APPENDIX II MOLD DRAWINGS FOR CAM
APPENDIX III WATER PHASES
APPENDIX IV NON-LINEAR BEAM EI TOOL CALCULATION MATRIX
BIBLIOGRAPHY AND REFERENCES
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