A durable mooring system for a winch-based
wave energy converter
Mingming Wang
Master of Science Thesis MMK 2017:90 MKN 205 KTH Industrial Engineering and Management
Examensarbete MMK 2017:90 MKN 205 Dellösning för en vinsch-baserad vågenergiomvandlare Mingming Wang Godkänt 2017-06-09 Examinator Ulf Sellgren Handledare Anders Hagnestål Uppdragsgivare KTH Kontaktperson Ulf Sellgren
Sammanfattning
Projektet har behandlat utvecklingen av en ny teknik för en förnybar energikälla, vågenergin, som anses vara en av de mest lovande förnybara resurserna med potential att bidra till en energiproduktion som motsvarar cirka 10 procent av världens energiförbrukning . Ett punktabsorberande koncept som använder en kraftuttagsenhet (PTO) omvandlar havsytans vågsrörelser till elektricitet. På grund av hårda arbetsförhållanden ger underhållsarbete stora problem och ett förtöjningssystem behöver utvecklas. Syftet med detta projekt är att utforma ett hållbart förtöjningssystem för minst 20 års drift, även i en hård havsmiljö.
En geometrisk modell av förtöjningssystemet har skapats baserad på dimensionering av dess komponenter. Flera koncept genererades och utvärderades med en Pugh-matris. En simulering av de olika spänningar som påverkar systemets prestanda gjordes för att validera designen.
Dessutom har detaljkonstruktion av de olika delarna av systemet gjorts, så att de kan tillverkas i ett framtida arbete.
Master of Science Thesis MMK 2017:90 MKN 205 Durable system for a winch-based wave energy
converter Mingming Wang Approved 2017-06-09 Examiner Ulf Sellgren Supervisor Anders Hagnestål Commissioner KTH Contact person Ulf Sellgren
Abstract
This project has dealt with the developing a new technology for a renewable energy source, the wave energy, which is considered as one of the renewable resources with a potential to contribute to an energy production corresponding to about 10% of the world’s energy consumption nowadays. A point absorber concept that is using a Power Take-off (PTO) unit converts the sea surface wave motion into electricity thanks to a buoy at the sea surface which is moved by the waves. Due to harsh working conditions, the maintenance would cause too many issues, and a mooring system needs to be developed. The aim in this paper is to design a durable mooring system for at least 20 years of operation even working in a harsh sea environment. A geometry model of the mooring system has been built since the dimensioning of its components was performed. Several concepts were generated and evaluated with a Pugh matrix. An analysis of the different stresses affecting the performance of the system was made to validate the design. In addition, the detail design of the different parts of the system has made to allow their manufacture in future work.
FOREWORD
This master thesis was carried out at the Department of Electric Power and Energy Systems at KTH Royal Institute of Technology, starting in January 2017. The author of the project is grateful to have had the opportunity of working with my supervisors, Anders Hagnestål and Ulf Sellgren. Thanks for their endless support, guidance and help. It has been really interesting to contribute in the developing of a renewable energy technology, which is a really important area in current research worldwide. Moreover, it has also been a really satisfying experience to study and work at KTH, with a lot of kind and lovely people around me during these months.
NOMENCLATURE
Notations
Symbol
Description
𝜎𝑡 Tensile stress (Pa)
𝐹 Peak force (N)
𝐴0 Sectional area of a bar (m2)
𝜎𝑡𝑚𝑎𝑥 Ultimate tensile stress (Pa)
𝐾𝑡 Stress concentration factor
𝐹𝑚𝑒𝑎𝑛 Mean force (N)
𝑑1 Inner diameter of the bearing (mm)
b1 Width of the bearing (mm)
𝐾 Specific wear rate
P Contact pressure (Pa)
V Sliding speed (m/s)
T Sliding time (hour)
n Bearing rotational speed (rpm)
𝐷𝑑 Diameter of the drum (m)
𝑉𝑑 Speed of drum (m/s)
𝑑𝑝 Diameter of the pin shaft (mm)
τ Shear stress (Pa)
Abbreviations
CAD Computer Aided Design
WEC Wave Energy Converter
TABLE OF CONTENTS
SAMMANFATTNING
1
ABSTRACT
3
FOREWORD
5
NOMENCLATURE
7
TABLE OF CONTENTS
9
1 INTRODUCTION
11
1.1 Background 11 1.2 Purpose 13 1.3 Delimitations 13 1.4 Method 132 FRAME OF REFERENCE
15
3 THE DESIGN PROCESS
17
3.1 Requirement specifications 17 3.2 Conceptualization 17 3.3 Initial concepts 17 3.3.1 Concept 1 17 3.3.2 Concept 2 18 3.3.3 Concept 3 19 3.3.4 Concept 4 19 3.3.5 Concept 5 20 3.3.6 Concept 6 20 3.3.7 Concept 7 21
3.4 Evaluation and selection of concepts 21
3.5 Component development 24
3.5.1 Link 24
3.5.2 Pin shaft 25
3.5.4 Linker 28
3.6 Validation 29
3.6.1 Simulation of Link 29
3.6.1 Simulation of Pin shaft 31
3.6.1 Simulation of Linker 34
3.7 Material Fatigue 35
4 RESULTS
37
5 DISCUSSION AND CONCLUSIONS
43
5.1 Discussion 43
5.2 Conclusions 43
6 RECOMMENDATIONS AND FUTURE WORK
45
6.1 Recommendations 45
6.2 Future work 45
7 REFERENCES
47
APPENDIX A: SUPPLEMENTARY INFORMATION
49
APPENDIX B: DATASHEET OF BEARING
51
APPENDIX C: WATER V SEAL
53
1 INTRODUCTION
This chapter describes the background, the purpose, the limitations and the methods used in the presented project.
1.1 Background
A Wave Energy Converter (WEC) is a technology that transfers the power of ocean waves to electricity. It belongs to a branch of the technology that aims to developing the renewable energies, and it is becoming a more and more important area on research, since with the global attention now is being drawn to the climate change and the rising levels of CO2 in the
atmosphere. The waves in the sea are a huge and largely untapped energy resource, whose potential to contribute to energy production is considerable.
There are several reviews of wave energy converter concepts (see references [2], [3]). Most of the existing wave energy devices are still being investigated, at the R&D stage. It is hard to build a wave power unit: it has to be considered that it has to withstand the harsh conditions at the sea and at the same time, it has to produce electric power at a competitive cost. So it can be said to be relatively immature when compared to other renewable energy technologies. However, using waves as a source of renewable energy has a number of significant advantages over other methods of energy generation. Compared to other renewable energy sources, ocean waves give a higher energy density [1]. Winds generate the waves and solar energy generate the in turn. A solar energy intensity of 2-3 kW/m2 in horizontal surfaces is converted to an average power flow intensity of 2-3 kW/m2 on a vertical plane, perpendicular to the direction of the propagation of the waves, just below the water surface [4]. Another advantage is also the low impact to environment the while using the waves’ energy. What is more, there are low energy losses during the large distance motion of the waves. Compared to wind and solar power devices, wave power can generate energy up to 90 percent of the time [5].
Figure 1: Fred Olsen’s Lifesaver concept, an example of a winch-based point absorber. A lifesaver, pictured in Figure (2) , is one of the developed WECs by Fred Olsen. It consists of a floater, the power Take-off (PTO) units, the primary mooring line and the secondary mooring system. The primary mooring line is fixed to the seabed at one side and rolls around a drum at the other side.
Figure 2: Conceptual sketch of lifesaver with the main PTO components; winch, gearbox and generator. Courtesy Fred Olsen.
1.2 Purpose
The aim of the project was to design a mooring system for WECs (Wave Energy Converter) for at least 20 years of operation in the sea environment. The primary focus was to design a durable mooring line for a selected wave energy converter concept. Considering the impact from the weather, the winch will oscillate badly with rough weather, such as storms. The mooring line is rolling on a specific drum. However, the calculations of the mooring line on the drum were not performed due to the lack of information of the drum’s dimension. A chain transmission was considered to replace the mooring line, because it does not suffer from the bending effect. Meanwhile, it was also possible to find out what the design requirements for a winch-based PTO are. Furthermore, a concept was generated and evaluated so that the predicted life time is was ensured to be over 80 million cycles. The key issue was the effect from wear and fatigue, which needed deeper analysis and simulations when the mooring system was operating. The selection of bearing and the arrangement of joint also needed to be considered.
1.3 Delimitations
The working conditions and environment for a mooring system is the sea. Therefore, the manufacture and running tests were not performed. However, the theoretical calculations and analysis are presented in the research and were validated with the results from software simulations. Due to lack of time, the test was passed on to future work and the accuracy of the predicted lifetime could not be proved. The whole system of the WEC has been divided into several groups, being the schedule on each group different, so it was decided to manufacture the prototype after future works. The electronic system of the WEC was not considered in this thesis work, whereas the developing of a durable mooring line was based on a point absorber wave energy converter. Since some technical data of the winch are not published, the used nominal data was as much close to the reality as possible.
1.4 Method
2 FRAME OF REFERENCE
The reference frame is a summary of the existing knowledge and former performed research on the subject. This chapter presents the theoretical reference frame that is necessary for the performed research, design or product development.
Designing a durable mooring line for winch-base requires the designer to have and generate enough knowledge about the structure of the design process. Product design, business and production are three important factors that determine the success or failure of a product. A product’s function is a description of what the object does, which belongs to the product design factor. Product’s form, materials and manufacturing processes are the product’s function. The form which means the product’s shape, color, texture… and other factors that affect its structure. The materials and manufacturing processes used to produce the product are as important as the form. Thus the designer needs to be concerned on the function, form, materials, and manufacturing processes firstly [7].
It is difficult to decide how to select the best concept when different solutions to a particular problem have been generated in the design process. It is certain that it is easier to select the wrong concept than the best concept. The design is said to be conceptually vulnerable if the wrong concept was selected. Conceptual vulnerability was and is a major problem in any design situation [8]. Stuart Pugh’s concept selection is a procedural tool for controlled convergence to the best possible solution to a design problem. The group number participants concept selection process should have good insight and awareness of the possible solutions and find that it simulates the generation of new concepts.
3 THE DESIGN PROCESS
In this chapter the working process is described. A structured process is often called a methodology and its purpose is to help the researcher/developer/designer to reach the goals for the project.
3.1 Requirement specifications
The aim is to design a mooring system, different from just a rope, which has two fixed degrees of freedom and a life of about 80 million bending cycles. There are some criteria that have to be considered, based on the requests from the WECs.
The following aspects are to be considered:
The mooring line must have two degrees of freedom at axial and vertical direction. The cost of the product should be as low as possible.
Detail design on the selected concept.
The mooring system should be able to operate 20 years. The load capability should be at least 200 kN.
The working environment for the system is going to be the sea.
3.2 Conceptualization
Some concepts have been generated and presented in this report as simple sketches. All the concepts were discussed and generated with different people from the mechanical engineering department. The conceptualization should aim at generating ideas without calculations or mathematical evaluations, and will be used as a guide to decide on a final concept. The chosen concept will be developed further.
3.3 Initial concepts
3.3.1 Concept 1
Figure 2: Universal joint.
A big problem with this concept, among some others, is that the peak force on the joint is around 200kN, so it is easy to for the joint to break before reaching its operational life of 20 years. Another problem could also be that it will not easy to assemble causing high costs on the maintenance.
3.3.2 Concept 2
A knuckle bearing is a spherical sliding bearing and consists of an inner and an outer ring which have as a contact surface a spherical sliding surface. Depending on its different types and structures, it could bear larger load and others load.
It can produce self-lubricating during the work due to the spherical outer surface of the inner ring with a composite material. Generally it is used for lower speeds of swing motion, but it can also be used for allowing tilt movement in a certain angle range.
Figure 3: Knuckle bearing.
3.3.3 Concept 3
The idea consisted of two welded crossed cylinders and adding the ribs on the side in order to make it stiffer. A pin shaft would go through and would place in the cylinder and support with a bearing. A link connects the joint with the pin shaft.
Figure 4: two cylinder joint.
A probable problem is that the geometry structure is hard to place on the drum, and doubtfully it could operate 20 years at high load capability, even though the ribs would increase its stiffness.
3.3.4 Concept 4
A wrist joint basically consists of a linker, a link and a pin shaft. The linker connects two links, and the pin shaft connects the link and linker. It has a bearing in the cylinder that supports the pin shaft so that the link can rotate. Therefore this joint has freedom of movement in the axial and vertical directions. It is also possible to come up with a seal solution for the joint.
Figure 5 : wrist joint.
3.3.5 Concept 5
A chain is a series of connected links which are tipically made of metal. It is simple and easy to find at the market. Compared to other solutions, it is lighter and cheaper.
Figure 6: Chain.
The problem in this concept is the large wear that will appear in the contact area between each link. It is hard to met the target operation life of 20 years and bending cycle of 80 million times.
3.3.6 Concept 6
The idea is to use a chain drive instead of the mooring, so a chain is placed on a gear shaft, which allowing it to tilt on a certain angle.
The problem in this concept is that it may request a high performance from the drum shaft. Due to the fact that the drum shaft should have high load capability and be movable at the same time, it is too difficult to design the drum shaft. However, it could be a selection in the future work.
3.3.7 Concept 7
A ball joint is a spherical bearing that connects the control arms to the steering knuckles. It consists of a bearing stud and a socket.
Figure 8: Ball joint.
The problem in this concept is that it will have lots of wear when a load close to 200 kN is applied during a period of time. The seal solution is also expected to be a challenge.
3.4 Evaluation and selection of concepts
In order to determine the best concept to start the detail design, a decision method should be implemented. In this case, a Pugh’s matrix was created to weigh the advantages and disadvantages of all concepts numerically. The Pugh method, also known as Decision Matrix Method, is a method to quantitatively assess the pros and cons of a design, and it is regularly used in engineering.
It consists of a dimensional matrix, where the current design is used as reference (values of zero), and the rest of the concepts are set in columns next to the reference. Each row in the matrix is a requirement (quantitative or qualitative), and each requirement is given a weight (numerically). Afterwards, a negative, a positive or a neutral value is assigned to each concept’s parameter, then they are summarized and a total sum is calculated. The design with the highest sum should be the most appropriate. This shall help in the decision-making process to start the design process of a new concept.
Table 1: Pugh’s evaluation matrix
Criteria
Weight
Synthetic
Rope Universal Joint Knuckle bearing
Two cylinder joint Wrist joint Chains Linear Chain driven with adjustable shaft Ball joint (1-5) High load capability(200kN) 4 R + + + + + + - Durability 5 E + + - + - - - Ease of Assembly 2 F - - - - 2 fixed DOF 5 E S S S S S S S Cost 5 R + + + + + + + Low weight 3 E - - - - Sea water resistance 3 N - - - - Ease of maintenance 3 C - - - - S - - Bending 5 E + + + + - + + Construction simplicity 1 - - - - Sum Neutrals(0) 0 1 1 1 1 2 1 1 Sum Positive(+) 0 4 4 3 4 2 3 2 Sum Negative(-) 0 5 5 6 5 6 6 7 Total Scoring 0 -1 -1 -3 -1 -4 -3 -5
Sum weighted Positive(+) 0 19 19 14 19 9 14 10
Sum weighted Negative(-) 0 12 12 17 12 19 17 21
Total weighted Score 0 7 7 -3 7 -10 -3 -11
Further Development 0 1 1 1
The criteria for assessing the concepts are: high load capability (200 kN), durability, ease of assembly, 2 fixed degrees of freedom, cost, low weight, sea water resistance, bending and construction simplicity. Between them, high load capability, durability, 2 fixed degrees of freedom, cost and bending are more important if compared to other criteria.
refers to the how much money will be spent on manufacturing the system. As this project is research project with limited funding, it is better and necessary to design a low cost solution. Bending refers to the stress when the mooring line is placed on the drums. All the other concepts have a bearing solution except the chains, so they all perform better if compare with rope.
From the previous results, a universal joint, a knuckle bearing or a wrist joint should be considered to further development. But the solution is supposed to one, so the next step is a further assessment of the concepts. Based on the design aspect, it is good to design a low weight system. Considering there is not harsh weather on the sea every day, a new idea is to combine the chain solution with a rope. Most bending cycles distribute on the normal waves, so it is good to using chain instead of rope. This way a big quantity of mass can be saved.
Under this text is the further assessment matrix. As it is used for a deeper development of the concept, universal joint was selected as the reference.
Table 2: Further evaluation Pugh’s matrix
Criteria Weight Universal joint and rope Sealed Universal Joint and rope Knuckle bearing and rope Two cylinder and rope Wrist joint and rope Chains and rope Linear Chin driven with adjustable shaft Ball joint and rope (1-5) High load capability(200kN) 4 R S - - + S + - Durability 5 E S - - + - - - Ease of Assembly 2 F - S - S + - - 2 fixed DOF 5 E S S S S S S + Cost 5 R - + - S + S - Low weight 3 E - - - - + - - Sea water resistance 3 N + - S + - - S Ease of maintenance 3 C - S S S S - - Bending 5 E S S S S S S S Construction simplicity 1 - + - S + - + Sum Neutrals(0) 0 4 4 4 6 4 3 2 Sum Positive(+) 0 1 2 0 3 4 1 2 Sum Negative(-) 0 5 4 6 1 2 6 6 Total Scoring 0 -4 -2 -6 2 2 -5 -4
Sum weighted Positive(+) 0 3 6 0 11 11 4 6
Sum weighted Negative(-) 0 14 15 20 3 8 17 22
Total weighted Score 0 -11 -9 -20 8 3 -13 -16
From the evaluation results it can be seen that the wrist joint got a higher score than the others. Therefore, the selected concept was the Wrist joint.
3.5 Component development
From the beginning, based on the fact that steel has a long-term durability and good performance, it was decided to use structural steel as the material for the components, with a yield stress of 250 MPa and a tensile stress of 500 MPa. The main components of the wrist joint are a link, a linker and a pin shaft.
3.5.1 Link
The geometry of the link is a cylinder that has two holes on both ends. In the hole there is a key slot that fixes it with the pin shaft. A simplified model of the link can be found in the following figure.
Figure 9: Sketch of the link.
In order to prevent the link from breaking while in the operation, it is needed to determine its minimum diameter. The required minimum diameter of the link can be calculated using this equation (1).
𝜎𝑡 = 𝐹
𝐴0 (1)
Where 𝜎𝑡 is the tensile stress of the material, 𝐹 is the peak force and 𝐴0 is the sectional area of the bar.
It is convenient to round the shaft corner to prevent the shaft failure. Theoretical stress concentration factors (Kt) of a shoulder fillet can be calculated for the equation for tension load.
Figure 10: Stress concentrations for bar with fillet.
𝐾𝑡 =𝜎𝑡𝑚𝑎𝑥
𝜎𝑡 (2)
Where 𝜎𝑡𝑚𝑎𝑥 is the ultimate tensile stress of material and 𝜎𝑡 is the tensile stress of sectional area
of bar.
The dimension of link is shown in the appendixes of this project, and the calculated rounding for the bar is 3 millimeter, which is connected to the link. The size of the keyway was designed using the standard keyway dimension, which can be found in the appended document. Moreover 2D PMI drawings are included in the appendixes also for the purpose of tolerance checks after manufacturing.
3.5.2 Pin shaft
The pin shaft connects the link and the linker. A simplified model is shown in Figure (11). There are two bearings placed on each side and they provide support for the pin shaft. In the middle of the shaft, the key locks the pin shaft to the link so that they rotate together. The size of the key follows the standard size table, which is shown in the appendix document.
For a uniform load distribution on the shaft with a peak force of 200 kN, the demanded diameter 𝑑𝑝 of the pin shaft can be calculated from the shear stress.
𝜏 = 𝐹
2𝐴𝑝 (3)
Where F is the load force, 𝐴𝑝 is the cross-sectional area.
𝐴𝑝 = (
𝑑𝑝 2)
2
𝜋 (4)
Where 𝑑𝑝 is the diameter of the shaft.
The size of the pin shaft is also determined from the standard dimension of the bearing. The value of the stress was simulated and proved with Ansys, which will be later presented in the Validation chapter.
3.5.3 Bearing
The joint includes two bearings to support the pin shaft. Its requirements are low speed and high radial force. The required life time for the mooring system is 20 years. It is important then to select a bearing that can also operate for 20 years. After searching and contacting with different suppliers, the WB802-T bearing was select to used in the mooring system.
WB802-T bearings are produced by D&E Bearing [19], which was established in 1966 and provides one of the market’s broadest and best-stocked range of slide bearings, roller bearings, plain bearing and associated bearing products. The properties of the WB802-material, together with the procedure of wrapping and calibration, make this type of bearing especially suitable for constructions, where high loads and relatively slow movements are occurring. The data sheet of WB802-T bearing can also be found in the appendixes of this thesis.
Figure 12:WB802-T plain bearing.
The selected WB802-T bearing has an inner diameter of 50 millimeter, an outer diameter of 55 millimeter and a width of 30 millimeter. It is vital to predict the life time of the bearing so that the mooring system can be ensured to work normally over its expected lifetime. The method to predict the bearing life is to estimate how much percentage of the thickness can be worn while the bearing still withstands the load. By calculating the wear caused on the bearing, it is possible to determine the life time of the bearing.
Where K is the specific wear rate, P is the contact pressure, V is the sliding velocity and T is the sliding time in hours.
With the specific wear rate depending on the lubrication conditions, the wear rate for different lubrication conditions is shown in the following table.
Table 3: The wear rate on different lubrication
Lubrication conditions Mm/(N/mm2/s.Hr) Mm/(kgt/cm2.m/min.Hr)
Dry 3×10-3 to 6×10-4 1 to 5×10-6
Periodic lubrication 3×10-4 to 6×10-5 1 to 5×10-7
Oil lubrication 3×10-5 to 6×10-6 1 to 5×10-8
The contact pressure can be calculated through the following equation 𝑃 = 𝐹𝑚𝑒𝑎𝑛
2 × 𝑑1× 𝑏1 (6)
Where 𝐹𝑚𝑒𝑎𝑛 is the mean load in N, d1 is the inner diameter of the bearing in mm and b1 is the
width of the bearing in mm.
As the WEC system has not been fully developed yet, it is not possible to collect the force on each numbers of the cycle. But the expected force distribution against the number of cycles is shown in the plot.
Figure 13: Expected force distribution against a number of cycles.
According to the assumptions made in the system definition, the maximum force is 200 kN and a minimum force is 20kN, thus the mean force is about 110 kN. But the winch design has to take into account the harsh weather in the sea, and ultimately the harsh weather is estimated occurs on the 20% of the total number of cycles. The mean force in this case is 150 kN.
The equation to calculate the sliding speed is
𝑉 =𝑛 × 𝑑1× 𝜋
60 × 1000 (7)
Where n is the bearing rotational speed in rpm and 𝑑1 is the inner diameter of the bearing.
In order to determine the sliding speed, the bearing rotation speed has to be calculated. It is estimated that the mean speed of the drum is 3 meter per second and the maximum speed is 5 meter per second. There are 5 links place on the drum on a round, so the angular displacement of a bearing is 72 degrees.
The idea is to calculate the total time when bearing is rotating and then calculate the bearing speed by dividing the displacement by the time.
The time during which the bearing is rotating on the drum is 𝑡𝑏 = 𝐷𝑑× 𝜋
𝑉𝑑 × 72°
360° (8)
Where 𝐷𝑑 is the diameter of the drum and 𝑉𝑑 is the speed of the drum.
The bearing rotates 36º in during this time, so the bearing speed is 𝑉𝑏 = (𝐷𝑏× 𝜋)
𝑡𝑏 × 36°
360° (9)
The number of cycles is about 80 million times, being the time in a cycle 𝑡𝑏 and assuming 20% present of the cycles act on the rope. Therefore, the required life time of the bearing is
𝑇 = 2 × 𝐵 × 𝑡𝑏× 80%
At the end, the designed mooring system will have a sealing solution, so the lubrication condition is oil lubrication. The wear rate is 6×10-6 Mm, the bearing contact pressure is 50 Pa and the sliding speed is 0.0937 meter per second.
3.5.4 Linker
The linker plays an important role in mooring system, and its dimensions are determined by the geometry of the link and the standard dimensions of the bearing. The linker provides two degrees of freedom for the mooring system, with two pin shafts that rotate in two directions. The bearing are located by the linker’s shoulder and lid, and with the geometrical structure is possible to seal the bearing in the linker. The simple geometry structure is shown in the Figure (15).
Figure 15: Sketch of the linker.
3.6 Validation
A CAD model was built in Solid Edge, whereas the performance of the components was simulated and demonstrated in Ansys. Few physical characteristics were validated.
3.6.1 Simulation of Link
In this section, it is a simulated the process of motion when the force pulls the link. The static structural conditions are shown in Figure (16), being the applied force the peak force of 200 kN, and a fixed support applied at the other side.
Figure (18) shows the element and node count for the model. This was the finest mesh that could be obtained with the license available at KTH (Royal Institute of Technology). Given the relative simplicity of the geometry, it is assumed to be enough node resolution to run a reliable simulation.
Figure 17: Meshed link geometry.
Figure 18: ANSYS element node count for link model.
Figure 19: Link Normal stress simulation.
Figure 20: Link deformation simulation.
3.6.1 Simulation of Pin shaft
Figure 21: Pin shaft static structural.
Figure (23) shows the element and node count for the model. As it happened before in the simulation of the linker, this was the finest achievable mesh with the available license of the software, and was considered to have enough resolution due to the relative simplicity of the parts.
Figure 22: Meshed pin shaft geometry.
Figure 23: ANSYS element node count for pin shaft model
from breaking. What is more, from Figure (26), it can be found that the maximum deformation happened on the connect area to the link and its value is 0.012 millimeter.
Figure 24: Pin shaft Normal stress analysis.
Figure 25: Pin shaft shear stress analysis.
3.6.1 Simulation of Linker
The motion of linker holding the pin shaft was simulated in Ansys and the boundary conditions set is shown in Figure (27). The applied force is 100 kN at Y direction and it applied at the surface that supports the bearings. The other holes are modelled as cylindrical supports.
Figure 27: Linker static structural.
Once again, the mesh and nodal counts shown in the following pictures is the finest and most precise that could be achieved with the available software license at KTH. The simplicity of the parts is enough to predict that the size of the mesh is adequate and the obtained results are reliable.
Figure 29: ANSYS element node count for linker model
The normal stress is shown in Figure (30) after running the simulation. It gives the highest values of normal stress of 201 MPa acting on the holes edge. For structural steel, the estimated tensile stress is 500 MPa steel and the yield stress is 250 MPa, so when stress value is bigger than 250 MPa unrecoverable deformation will occur. The total simulated deformation is shown in Figure (31), and the biggest deformation is 0.1 millimeter, present on the under edge of the hole. Due to its small value it is can be said that it will affect the link performance a lot.
Figure 30: Linker normal stress analysis
Figure 31: Linker deformation analysis
3.7 Material Fatigue
than the strength of the material itself, such as ultimate tensile stress limit or the yield stress limit.
The Wöhler curve, shown in Figure (32), is a graphical representation of the magnitude of a cyclic stress (S) against the logarithmic scale of cycles of cycles to failure (N). The material performance under high–cycle fatigue situations is shown in this curve.
Figure 32: Wöhler curve
The relation between the material’s stress and the number of load cycles is that the stress will decrease with the number of load cycles increasing until five millions of load cycles. If the material is also affected by other factors such as corrosion, temperature, residual stresses or the presence of notches, the fatigue limit will be even smaller.
4 RESULTS
In the results chapter the results that are obtained with the methods described in the method chapter are compiled, and analyzed and compared with the existing knowledge and theory presented in the frame of reference chapter.
Initially, from the Pugh’s evaluation matrix, the mooring system design was selected. The final concept was a wrist joint. The required dimension has been calculated and the geometry model was made in Solid Edge. Based on the calculation, results show that the minimum required sectional area of the bar on the link is 0.0004 m2 and the minimum required diameter pin shaft is 0.032 meter. According to the standard dimension of the bearing and taking into account lifetime considerations, the diameter of the pin shaft should be 50 millimeters. The detailed designed design detail of the three parts is depicted in the following figures in this chapter. In order to prevent the failure of the bar on the link, the rounding on the connecting edge should be 3 millimeters. The designed mooring system mainly consists of a link, a pin shaft and a linker. The component part list is presented later in the report. The standard components present in this design are bearings, seals and screws.
The designed mooring system has a seal solution to prevent the sea water from leaking inside the system, being the idea to use V-shaped seals. Therefore, it will be possible to use oil lubrication for the bearings. The estimated the limit of bearing to wear is 60% of thickness. So the expected life time of the bearing is 8990 hours. In 20 years, the total calculated working hours are 5960 hours, so the selected bearing will be enough to operate during the whole life of the designed mooring system. According to the simulation results, it could be proven that the designed mooring system could work in high load condition.
The main dimensions of the link, linker and pin shaft are shown in Figure (33), Figure (34) and Figure (35) respectively, with more detailed drawings presented in the appendixes.
Figure 34: Dimension of linker.
After a material fatigue analysis, stainless Steel 34CrNiMoS6 (SS2541) with yield strength 900 MPa and tensile strength 1100 MPa was selected as a suitable material for the system. Its values of yield stress and tensile stress are twice bigger than structural steel.
The method used to fix the link and linker is with a key and a key slot. Figure (36) is the section view that shows the form the key.
Figure 36: key and key slot arrangement.
The arrangement of the bearing is shown in Figure (37), with the bearing located by an extra bearing housing and a retaining ring. The bearing‘s housing is fixed with a lid and a linker’s shoulder. The diameter of the jack shaft is bigger than the outer diameter of the bearing, which is a reason for the given extra bearing housing. Considering about the seal from the sea water, there are V seals placed between the bearing and the shaft stepped shoulder and an O-ring seal between the lid and the linker. Section B-B has a detailed diagram of the arrangement.
Figure 37: Bearing and seal arrangement.
4 4 1 2 6 4 3 1 8 4 7 16 2 2 5 4
Figure 38: Assembly diagram of the mooring system. Table 4: Component part list
Item Number
Title Material Quantity Mass (Item)
1 Link Steel 2 12,584 kg
2 Pin Shaft Steel 2 2,049 kg
5 DISCUSSION AND CONCLUSIONS
A discussion of the results and the conclusions that the author have drawn during the Master of Science thesis are presented in this chapter. The conclusions are based from the analysis with the intention to answer the formulation of questions that is presented in Chapter 3 and Chapter 4.
5.1 Discussion
This project’s purpose was to design a mooring system for the developing WEC. A seal solution was made, but the life time of V-seal is hard to ensure. The requested life time for the mooring system was 20 years and the designed mooring system could operate over 20 years when the lubrication conditions for the bearing were oil lubricant. So it still needed to investigate the life time of the V seal. Due to the fact that the V-seal can rotate with shaft, it will lack a bit of oil lubricant. Nowadays, the developing of the technology allows a zero environment impact if a special oil lubricant is used. However, it is little complex to assemble, since screws are used to fix the lid.
5.2 Conclusions
6 RECOMMENDATIONS AND FUTURE WORK
In this chapter, recommendations on more detailed solutions and/or future work in this field are presented.
6.1 Recommendations
In this paper, the requested design for the mooring system is a chain transmission, hence it is not needed to compare it with the other type of transmission. But that kind of comparison could be done from other author. Due to the using the metal instead of rode, it must be cause a lot weight and need high performance from other system to cooperate. The other concepts, rejected in this paper, could also be interesting to consider for future developments of the system.
6.2 Future work
It is recommended that further work complements this research with the following activities: Manufacture of the design mooring system.
7 REFERENCES
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Sjöström, P., Søresen, H. C., and Thorpe, T. Wave energy in Europe: current status and perspectives. Renew. Sust. Energy Rev., 2002, 6(5), 405–431.
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APPENDIX A: SupplemEntary INFORMATION
Standard keyway and key sizes
APPENDIX B: DATASHEET OF BEARING
Technical data
Material: Homogeneous bronze Cu 91.3%, Sn 8.5%,P 0.2% Yield Point: (Rp0.2) ca 300N/mm2 Tensile strength: (Rm) ca 450 N/mm2 Hardness: ca 125-150 HB Friction: 0.08-0.25μ Max speed: 2.5 m/s Temperature range: -100/ +200 ˚C
Tolerances: Bearing pressed into housing H7 get tolerance H9. Recommended tolerance for the shaft IT 7 or IT 8with position of tolerance e or f.
Lubrication: Additional lubrication ought to be done through for the shafts or radial through the housings.
Benefits
High load capacity
Intended to working in difficult and dirty conditions specially. Good lubrication properties due to lubrication holes.
Has high level thermal conductivity.
Wide range of stock holds standard dimensions. Optimal lubrication intervals.
Complete solution with Intergard seal.
Special:
Bearing with one seal.
In-or outside lubrication grooves. WB800 with seals.
APPENDIX C: WATER V SEAL
Figure 39: Water V seal.
Specification
Standard or Nonstandard : Standard
Material: Rubber
Brand Name: AUTOX
Temperature: -35˚C--110˚C
Spring and punched part : Stainless Steel
Pressure: ≤ 40 MPa
Feature: Good sealing/ resistant friction
Style: Mechanical seal
Model Number: VA
Speed: ≤ 30 m/s
Medium: Water/ air
Size: Kinds of
Application: Rotary rod and the surface of bearing
APPENDIX D: Detail drawing of mooring system
The Linker drawing was scale 1:2, scale value 0.5 and made by Solid Edge.
