Modern engineering practices have fully embraced the use and trust of Computer Aided Engineering (CAE) tools. Such tools includes Finite Element Analysis (FEA) and Computational Fluid Dynamics (CFD). These tools are very important as they help in producing better designs faster and at a low cost. These tools are continuously being improved in their accuracy in estimating the real environment where the products are to be used. This thus enable designing of parts, assemblies and parts that can withstand the toughest conditions that they may be put in (Parag Nikam, Rahul Tanpure, 2016).
However, with continual use of engineering practices, it becomes apparent that the products designed for the worst scenario are not necessarily the best design for real environments. There is a lot of over engineering thus making the products heavy and hence expensive to manufacture. This ripples all the way to overall cost, selling price, and the competition edge with other products and ultimately the profit gained by the organisation. Thus, in order to achieve the optimum design and increase profitability, optimisation is necessary (Systèmes, 2010).
The masthead ring is the top most fixture of a masthead rig; It is on this ring that the backstay and the forestay are attached. The ring is therefore exposed to different kinds of forces and moments that it has to sustain. (Dedekan, 2001) The largest contributor to it failure is torsion due to the turning of the wind in different directions (Mohammad AlHamaydeh, Samer Barakat, Omar Nasif, 2017). Masthead rig design is one of the two designs of the rig that could be utilized. The other design is the fractional. The difference is that, for the fractional rig, the backstay is attached to the highest point of mast alone while the foreplay and the runners are attached on the lower section. This therefore means that the top ring does not have to bear large torsion as the tangential forces are distribute along the mast. On the masthead however, both of them are attached to the top and thus a stronger ring is need. In terms of functionality, there are much difference between the two. The fractional rig is better on wind per unit sail area. It therefore gives the consumer value for their money. However, its complexity makes it not use not favourable. The masthead is therefore the alternative especially for small boats of an average of 40 m heights. These boats are faster and easy to operated thus can be used for family or small scale cruising. Masthead rigs are also generally better on oceanic cruising (Dedekan, 2001).
The rig fixtures are not standard as they vary with the application and the size of the boat (Dedekan, 2001). The force of exacted on the ring will therefore vary with the area of the shroud. To determine the right dimension of the ring required, the forces exacted on the ring must be determined. The thickness is the most important dimension that will be varied during optimisation of such fixtures. Further, on analysis using FEA, it is possible to point points of load concentration. The design can thus be reconfigured to remove redundant weights. The thickness will be optimised and set as constant for ease of manufacturing.
There have been numerous attempt to study the structural behaviour of marine equipment. However, these studies focuses on the entire boat as a whole or on the engine. There seem to be a neglect on the structural behaviour of the mast which is the most important part in structural study. Specifically, the mast head ting is of big importance as the stays are attached here. This study gives a good opportunity for optimisation. This research is inspired by this need and hence the opportunity.
1.3 Aims and Objective
The Aim of the project is to analyse and optimise the design of a Sailing Yacht Mast, rigging attachment, identify design improvement, and optimisation opportunity.
The optimisation process focused on reducing the weight of the ring by removing redundant mass. The optimisation process was performed on a Solidworks 2017 CAD software.
- Produce Engineering Drawings for the component.
- Inspect the used component for Any possible structure failures.
- Establishing expected Load whilst in operation
- Produce CAD Module as well as appropriate software to analyse the component in terms of stress, displacement, and factor of safety.
In this section, a review of existing literature related to this project will be done. The focus will be on the ship structure. The design of the standing rigs will be discussed. The other point of focus will be on optimisation. The procedure is discussed here. Some few engineering components that has been optimised are reviewed as case studies. The conclusion of this section will be on a review of some gaps that do exist that this project will focus on bridging.
Rigging is combination of a system of ropes, chains and cables that are used to support the mast of a sailing ship’s or boat’s mast (Dedekan, 2001). The rigging includes standing rigging and running rigging. Standing rigging includes shrouds and stays which are mainly used for adjusting the position of the vessels sails and spars to which they are attached. On the other hand, the running rigging is used to for raising, lowering, shaping and controlling the sailing. The parts compromising the running rigging includes halyards, braces, sheets and vangs (Ph. Rigo, J D Caprace, 2016).
2.3 Standing Rigging
The standing rigging, also referred to as longitudinal rigging, supports the bowsprit on a sailing vessel and reinforces the spars from the wind load that is being transferred from the sails. The different components of standing riggings includes the backstays, forestay, runners, cutters stays, inner forestay, check stay and triatic stay.
: Ensures that the top mast does not move forward. It is adjusted using some tension device.
: It carries stay for genoa and jib. It prevents the mast from moving aft. Its tension is primarily affected by the backstay. However, cap shrouds, runners and sheeting of the mainsail also affects its tension. The forestay together with the backstay have the highest value of tension.
: It is attached within 6% of the fore-triangle height below the forestay fitting. It is tensioned by the backstay and it is the sail-carrying inners stay for stay sail.
: This stay is not sail-carrying. It is used for staying the mid-section of the mast fore-and-aft in conjunction with the checkstays
: Also known as runners. Mostly found in fractional rigs and are used to tension the forestay. On a masthead rig, they interact with stay.
: In principle, the chekcstay function as runners. They are however attached lower down the mast. They are for stabilizing the mid-section ton mast to prevent the uncontrolled mast head pumping.
2.4 Masthead rig vs Fractional Rig
The main difference between a masthead rig and a fractional rig is the position of the forestay on the vertical mast.
Figure 1 Masthead rig vs Fractional rig (Dedekan, 2001)
The diagram above represent the difference from the two types of longitudinal (standing) riggings. From the diagram, it can be clearly seen that form the masthead rig, the top ring is attached with both the forestay and he backstay. This is different for the fractional stay where the forestay is attached on a lower section of the mast.
The improvement on technology has closed the gap and application of the two types of riggings. This means that they can be interchangeably used comfortably. However, the fractional gives the best output in terms of speed and ease of control. The masthead is very simple to handle and its use greatly increased in the 1960s. Apart from the simplicity, a given sail area can be carried lower and thus with less heeling moment and thus many people favour it. This has changed recently as in that the modern handling has better blocks and cordage, slab meaning that even a family can be able to handle a boat as high as 40ft. The masthead rig also tends to be better for oceanic passage than the fractional rigs. The masthead rig is larger and contains more headsails, and a smaller mainsail compared to the fractional rig (F Castro, F Ciciliot, 2008).
A fractional rig on a sailing vessel consists of a foresail, the forestay that fixed the mast at the front of the Bow is attached to the mast at a lower point and the fore sail is fitted to this stay. The mast is further forward on the boat so it has a large main sail. The fractional rig is typically used on dinghy sailing boats and racing boats. Fractional rigs were established on race boats for the purpose of allowing greater power over the surface of the main sail whilst simultaneously reducing drag during tacking (Ph. Rigo, J D Caprace, 2016).
The masthead ring is the top most part of the mast. It is on this ring that that the stay, the forestay and the backstays are attached.
Figure 2 The Masthead rig ring
The ring could easily break and therefore careful considerations required for the size. The ring is not stand as the size varies with the size of the ship. The force on the ring is determined by the tension on the stays. The generally, these tension vary during the sails. For racing sailboats, the tension limits for the stays are set as standard and sailors are expected to work within the set range. Most sailors, set tensions as low as they can for fear of breaking (D.N. Dimou, V.J. Papazoglou, 1995).
2.5 Marine Threats
Marine structures such as ships are subjected to different types of threats in the marine industry; marine corrosion can be established as the main factor of metal deterioration when equipment and structures are in contact with sea water. Described as a natural process, corrosion can produce the elements of metal to be reduced to an original more stable condition. Due to atmospheric corrosion or contact with seawater (Mohammad AlHamaydeh, Samer Barakat, Omar Nasif, 2017).
Marine corrosion is a big problem faced in the Marine industry because of its high cost in maintenance; safety hazards, and the proper material to choose will not only be able to avoid a corrosion problem but also reduce the cost. Furthermore, if raw or processed materials or manufactured components are not available in the desired shapes, dimensions, and quantities or substitutes, additional processing will be required, which can contribute significantly to product cost. Proper selection of material also can reduce product failure or increase product life time. Working environment is also an important issue to be considered during material selection (Ph. Rigo, J D Caprace, 2016).
Some of the masthead components and parts that are not exposed to the moisture directly are made of mild steel. Mild steel is a carbon steel typically with not more than 0.25% of Carbon and its cheaper steel compare to the rest of steel types in the family. Uncoated mild steel can easily form corrosion. Therefore, all surfaces for the frame are painted. The components that are made of mild steel include body frame, motor stand, rotating shaft, cam, follower, connecting rod, and crank pins in the machine (J Case, A H Chilver, 1986).
2.6 Forces applied on the masthead:
The principle of the force polygon and the balance of the forces applied, ensure that the ring is in balance to avoid warping in one side. It uses the principle of law of levers which shows that if the distance from the fulcrum to the point in which the force is applied is larger than the distance from the fulcrum to where the output force is applied the force is amplified hence a higher mechanical advantage. By comparison if the load distance was greater than the effort distance then the input force will be greater than the output force hence no mechanical advantage (Surya Patnaik, Dale Hopkins, 2002).
The tensile strength of the material used to make the stainless steel masthead fitting should lie within the limits of the stress. The concepts of the forces acting on the thin cylinder of ring is very critical to the design of the ring. The tension from the cables generate radial and circumferential stress. The longitudinal stresses in such cases are close to zero. The material for making the ring should however be subjected to tensile testing to determine the ultimate stress in which the tension of the cables should not go beyond (Dowling, 2012).
During the design, tensile stress testing is carried out as described. A Tensile test is carried out to structural components to determine the strength properties of the metals. The metal is subject to tension until it fails. Different metals have different strengths depending on the ductility and brittleness of the metal. The tensile test helps material science engineers in carrying out the following: proper selection of the metals for various applications, quality control and predicting the behavior of the metal when subjected to various stresses.
The stress strain curve of the stainless steel follows the normal curve under the tensile test. The stress is obtained from the load per unit cross sectional area of the specimen. The strain is the ration of the change of the length of the specimen. The strain increases as the elongation of the specimen increases. The stainless steel alloy shows some characteristics of ductility until it enters the plastic region.
2.7 Rigging Load on a Sailing Vessel
In designing the most optimal naval structure, naval engineers use two main methods. They can do this first by estimating and analyzing the loads on the structure then calculating the stresses for each part as close as possible. The other option is to extrapolate from the results of past practices. The variation in dimensions is catered for and then every part is specified from the catalogues to ensure that the breaking points are well below the specified points (Sponberg, 2005).
Getting the right loads is very important for the best results from the analysis. There are 5 loads that need to be considered in a sailing rig. First, Pretension (dock tuning) is a one load case. Secondly the sail load which is a function of wind velocity. The third is the inertia load during rapid acceleration or deceleration when nose diving. Fourthly the weight of the boat itself and finally the extreme cases where there is vibration.
When the shroud is under blown by the wind, there exist a lift and a drag force that are computed using the dynamic pressure formula.
Figure 3: Forces on a sailboat
Lm=Clm0.5ρairAWS2Am STYLEREF 1 \s 2. SEQ Equation \* ARABIC \s 1 1
The drag force is given by:
Dm=CDm0.5ρairAWS2Am STYLEREF 1 \s 2. SEQ Equation \* ARABIC \s 1 2
In analysing the loads on the boat, the wind and the sea creates complex and unsteady loads since they are in continuous motions. Some simplifications are therefore necessary to ease the analysis. This simplification is then compensated by a factor of safety.
In this analysis, the boat is assumed to weigh 650 kg and balancing ballast of 250 kg and carrying three people. The mass of a single person taken as 80kg.
When considering the force on the ring, the force is used. As seen earlier, there are many uncertainties. Then ring is attached two backstays and a single forestay. The force acting on the ring is that of the tensions of each stay. The worst conditions are assumed where the forestay carries the entire balancing weight and the two backstay carries maximum weight equal to that of the boat.
2.8 Structural properties of the masthead ring
The design of the masthead uses the values of the ultimate tensile strength, the resilience strength and crushing strength of the stainless steel. The dimensions and the shape of the masthead ring are such that the ring offers the highest resistance to bending and crushing because of the tension of the wires. The number of the holes in the ring depends on the required number of the wires used. The tension of the wires result to twisting moment to the wires if the tensioning is not balanced. The material for making the mast head ring must therefore be subjected to the torsion test.
The modes of the failure of the components are examined to come up with the correct material and dimensions in the process of designing the mast head ring. The strength of the metal is depicted by the ductility and the toughness of the metal used. Mostly, stainless steel is used for the structural purposes because it has high strength compared to the other metals. The metal is also resistant to corrosion hence the best fit for the marine applications (B Sun, S Imai. K Kondoh, 2013).
The design of the mast head ring for the vessel depends on the properties of the metal which the torsion test was done. The characteristics of the metal which are investigated include the shear strength, the Poisson ratio and the modulus of rigidity.
Solid materials can withstand far higher tractable powers. Feeble materials shape necking immediately, even at low anxiety esteems, which implies they likewise tend to tear all the more rapidly. The last critical property is the separation amongst weak and extreme materials. Weak materials can't withstand high malleable powers and break essentially quicker. Intense materials likewise have the favorable position that when over-burden they frame checked deformation before they fracture. This implies material exhaustion is obvious some time before tearing, with the goal that move can be made accordingly.
The stress is calculated from the formulae
stress= Force appliedArea STYLEREF 1 \s 2. SEQ Equation \* ARABIC \s 1 3
The stress for the various points on the graph are calculated as follows: (J Case, A H Chilver, 1986)
Arear= πD24 STYLEREF 1 \s 2. SEQ Equation \* ARABIC \s 1 4
The strain is calculated from the formula (J Case, A H Chilver, 1986)
strain=Change in areaoriginal area STYLEREF 1 \s 2. SEQ Equation \* ARABIC \s 1 5
Design optimisation is an advance level concept in engineering. This is because it involves very rigorous and tedious mathematical operations. For advanced level designs, optimisation is required for over multi-valued parameters. Some of systems that require that requires high level optimisation includes composite lay-ups, heat exchangers and structural configurations. The aim of design optimisation is to come up with the most efficient design that is cost effective. In most cases, the final objective function that need to be optimised is has a single variable. However, there could be numerous or infinite parameters that contribute to different sets of designs. This therefore makes parametric design a must for any system that will need to be optimised. In other words, the existing Finite Elements Analysis (FEA) codes are parametric based (Parag Nikam, Rahul Tanpure, 2016).
2.10 Building blocks of Optimisation
There are 3 major components of an optimisation process.
- Constraints and
Thus, an opt Imation process involves maximising or minimising the objectives by varying the variables while maintain the critical responses within the set boundaries of the constraints (Systèmes, 2010).
This is the purpose for which optimisation is being carried out. For instance, if an organisation notices that the profit hence competitive advantage can be increased by reducing the weight or production cost of a product, this becomes the objective of optimisation. This is termed as single objective optimisation as there is only one purpose of the entire process. This is not always the case as in one project, the design engineer might be faced with more than one objective. For effectiveness, it is advisable to reduce all objectives into a single one or deal with each objectives at a time. Structural engineers most of the time, deal with weight reduction as the major objective. On the other side, the main objective of fluid flow application are minimizing of pressure drop or maximization of velocity (Javidinejad, 2012).
The constraint are the ones that brings reality into optimisation. This are the allowable extremes of a given condition that are affected by the variables. The programs, once given the constraints, come up with the most appropriate dimensional variables. There could be very many constraints including Factor of safety, deflection among others. Most of the constraints are related to some great extents. However, careful consideration should be given in choosing the constraints in order to the get that defines the allowable behaviour of the part within the system (Javidinejad, 2012).
2.10.3 Design Variables
These are the design parameters which the engineer can possibly change with the hope of getting the best of several possible designs configurations. These variable could include certain dimension, material property. Spring stiffness or any other design aspect detectable. The variables can either be continuous or discrete. Continuous variables has values within a specified minimum and maximum. A good example is dimension variables like length and thickness. Discrete valuables are specified within a definite set of possible valuable (Systèmes, 2010). A suitable example is a yes/no switch. Selection of variables should be very carefully done as it has a direct bearing on the effective of the process. Too many or too few variables can hamper the simulation process by the analysing program. In order to select the best variables, a sensitivity study is carried out. Sensitivity study is the process of systematically evaluating the changes in response to input variations. Large variation in response to the input change indicates high sensitivity while low variation in response to an input indicates low sensitivity. The study indicates the feature that need to be evaluated deeper (Mohammad AlHamaydeh, Samer Barakat, Omar Nasif, 2017).
2.11 Optimisation with SolidWorks
A DoE-based optimisation method was used in SolidWorks simulation. The program is provided with the minimum and the maximum values of a dimensional variables. The optimisation can either be standard or High Quality as chosen. For the standard approach, the objective response curve between the limiting values is assumed to be linear thus simply calculated as so. For High Quality optimisation, the possibility of a second order response between the limiting values is taken into consideration. This means that the mid value and the extreme values are all calculated.
For extremely high optimisation, most engineers prefer Ansys - Engineering Simulation software to any other program since it has the most detailed code that is purely dedicated to optimisation. Solidworks primarily is a design program with the FEA optimisation code as an Add-Ons. However, it is sufficient for small structural based design optimisation. It also allows for the changes to be made on the program within the program without having to transfer to another program once the updates are done.
In his section, the procedure that was used to carry out this project is discussed. The objective of this project is to come up with an optimised design of an existing masthead ring. The structural properties of this ring are therefore very important in this design. The torsion properties of the existing will be a very important point. The first task is therefore performing a tensile test on the ring. The properties will be used as some the constraint for the optimisation process. Since the exact dimension are required for accuracy, a 3-D scanner is used to scan the actual masthead ring. The data is input in SolidWorks software as .obj file. This format cannot be used for optimisation process. It is therefore converted into a respective fine and part file. Optimisation runs are done on the part and the optimised design developed. The respective response of the final part are simulated and recorded and are attached with this reports as appendix.
3.2 Tensile Test
Tensile test carried out to determine the tensile properties and the strength properties of materials by analysing test results.
The metal is subjected to tension until it fails. Different metals have different strengths depending on the ductility and brittleness of the metal. The tensile test helps material science engineers in carrying out the following: proper selection of the metals for various applications, quality control and predicting the behavior of the metal when subjected to various stresses.
In this test a Hounsfield test frame was used to apply a tensile load to a variety of test specimens (Hounsfield, 2017). According to the British Standards Data sheet for stainless steels 316 Alloy; Tensile test shows that the component material is suitable for the Loads applied, and operation environment.
Figure 4 Houndsfield test frame
The type of the fracture which is observed in the three specimen is the spiral fracture. The fracture is caused by application of more force on the axial bone of the specimen. The torsion happens when the structure of the material separates each other as a result of the torsion.
The torque in the mast head ring is expressed by the torsion formula (Surya Patnaik, Dale Hopkins, 2002).
TJ=GθL=γr STYLEREF 1 \s 3. SEQ Equation \* ARABIC \s 1 1
Where: T is the torque
J is the polar moment of inertia acting on the ring cross sectional area about the axis of the shaft rotation.
G is the Modulus of rigidity due to twisting moment
θ Is the displacement in radians?
L is the span of the ring
Is the shear stress on the ring?
R is the ring radius.
The torsion applied to the ring can be varying according to the power requirements of the marine vessel. The ring should therefore be able to withstand the angular acceleration requirements. The design should also consider the bending stresses which are present.
The mathematical formula which is used in the design is as shown below:
σ=myI STYLEREF 1 \s 3. SEQ Equation \* ARABIC \s 1 2
σIs the bending stress
m is the bending moments
I is the second moment of inertia of the mast head ring.
For marine mast head ring design, the combination of the torsion formula and bending formula breeds a formula which caters the two cases. The formula used is as shown below
Te=(Km ×m)2+(Kt ×T)2 STYLEREF 1 \s 3. SEQ Equation \* ARABIC \s 1 3
me=12((Km ×m+ Te STYLEREF 1 \s 3. SEQ Equation \* ARABIC \s 1 4
Where: K is the constants for the torque and moments.
For the design to be carried out, the torques to be subjected is used and the material is selected. The length required for the fitting is also utilized in the design (J Case, A H Chilver, 1986).
3.3 Dye Penetrant Test
To analyse the Stainless steel masthead fitting part, A Dye Penetrant Inspection is required in order to detect any cracks on the part, welding areas and holes to prevent failures; the dye penetrant process carried in four steps:
The first step is to pre-clean the test part surface from any paint or rust using a cleaner spray as shown in (figure -2 Cleaning the part surface) while paying close attention to the masthead as it has already been used as a worked piece for three months. Secondly apply a penetrant spray which contains a red color low viscosity oil which will penetrate into any cracks highlighting any defects and allow to soak for about 15 minutes (figure -3). Thirdly rinse the test part surface cautiously with water to remove the penetrant completely from the surface whilst ensuring it remains in the cracks and leave to dry. Lastly, apply Developer onto the surface of the part and leave to dry for 15 minutes (figure -4), the developer is a finely milled white powder suspended in a liquid, after drying it drives the penetrant out from the cracks on the surface.
3.4 3-D scanning
A 3-D scanner is a device that is analogous to a camera. They are used for collecting surface information of an object. In most cases, multiple scans are done, even hundreds in order to obtain the information for all sides (EBRAHIM, 2013). These scan are then merged to create a complete 3-D model, a process called 3-D scanning pipeline (Bernardin, 2002). Three Dimensional scanning technology was developed greatly in the mid-20th
century with major breakthroughs in the 1960. 3-D scanners. The advantage of 3-D scanning includes; accurate, fast, truly 3 Dimensional, capable of capturing colour surface and they are realistically priced.
There are several technologies developed for digitally acquiring the 3-D shapes of an object. An established method of classifying these technologies place them into contact and non-contact 3-D scanners. The non-contact scanners are further divided into active scanners and passive scanners.
Contact technique 3-D scanners are calibrated to operate on a fixed platform which often placed on the end of a manually manipulated mechanical arm. The arm can either be operated robotically or manually. The coordinated of different point s of the object are recorded on a software and are used for generating a mesh. These scanner are mostly used in manufacturing and can be very precise. However, their scanning rate is very slow and cannot be used delicate objects (EBRAHIM, 2013).
For non-contact technique, as the name suggests, collect the surface data of an object without making any physical contact with the object. Instead, they use non-contact, passive or active methods to scan an object. This achieves a highly accurate cloud of points that can be used for different engineering manipulation such as virtual assembly, engineering analysis, reverse engineering, feature and surface inspection or rapid prototyping (C Frohlich, M Mettenleiter, 2000).
Non-contact active technique scanners emits some kind of radiation or light to the object being scanned. The detected reflection are used for probing the object or the environment. The possible types of emission that could be used includes light, x-rays and ultrasound. 3-D laser scanners can use 3 different techniques for locating the position of a feature on the object. These includes Time of flight, phase shift and laser triangulation.
Time-of-flight 3-D laser scanner determine the time of flight for a refection to be detected back. The laser rangefinder identifies the distance from as single point. Thus, to collect the entire object, the rangefinder’s direction is changed.
The phase Shift is similar to time-of-flight in that the scanner is detect the distance from reflection. However, the reflected laser light further refines the distance analogous to the Vernier scale on a callipers (EBRAHIM, 2013).
Triangulation method shines a laser on a spot on the object. A camera is then used to capture the location on the spot on the object. Depending on where the dot is on the camera’s screen, using the know angle of strike and orientation, the position can be precisely determined (EMS-USA, 2017).
3.4.1 ROMER Absolute Arm 3-D Scanner
Roomer absolute Arm 3-D scanner was used for scanning the fixture. It is a non-contact active scanner that used radiation to measure locate the distance. It has a pointed laser point that strikes the ray on the object. It is fitted with a scanner which detects the reflection. The base of the scanner is fixed and fitted on a point for absolute coordinates. A flexible arms carries the scanner around the object making it very versatile. The scanners is connected with a software that enables the object being scanned to be converted into a 3-D model for further processes (Hexagon_Metrology, 2017). The ring is placed on the table and the scanner turned on and the coordinates set.
3.5 Simulation and Optimisation with Solidworks
The file scanned was saved as an .obj file and opened in Solidworks. The file is converted into a Solidworks file with parametric features. Simulation and optimisation can only be done on a parametric file.
Figure 5: The rigging Ring Drawing
The diagram above shows the isometric view of the rigging ring. The figure is however upside down as the scanning was done in that orientation to ensure that all details are well captured. Two procedures were done. The first one was simulation and the second one optimisation.
The aim of this procedure was to evaluate the behaviour of the part under specified loading conditions. The failure mode and the points of weakness are determined. The factor of Safety (FOS) can also be determined.
First, a simulation Add-On was activated and a new study selected, and the study was renamed as Masthead Study- 1 as shown in appendix.
The study need to be prepared and the boundary conditions set. On the left of the Solidworks window, are the conditions that need to be set and are shown on the figure 30.
They also indicate systematically how the procedure of simulation. The parameter are not grievously important at this stage. They are used during the optimisation stage.
The second part is the material. The material is very important as the properties specified are used in calculation and simulation and also optimisation. The material selected was Annealed stainless steel, which is the material for the feature.
Figure 9 Setting of material - Annealed Stainless Steel
The properties are well laid out. The density is
7860 kg/m3, the E is
2.07×1011 N/m2while the tensile strength is
There are no connecter within the part to be added. The other points to be specified are the fixed geometry. These includes the points of connection between the mast head and the ring. There are provisions for bolts on the solid parts. These are specified as fixed geometry.
Figure 10 Setting of fixed geometry
The three bolting holes are set as the fixed geometry.
The next and most important part involves setting up the loads. Here the loads are applied as tension from the forestay and the backstay. As indicated earlier, the tension of the stays is not constant. It varies during the sails. The aim of these simulation will to simulate for a standard loading of a boat carrying 3 people with standard rope tensions. For theoretical calculation, the back stay tension was set to 650 kgf (being divided by two stays hence 325 kgf for each stay) A balancing load of 250kgf is applied on the forestay to balance and ensure that the mast hence the boat is stable. This load acts as point load. However, the rope is tied on the holes on the ring ribs.
When simulating, the only logical and practical way to apply this load is as bearing load since the rope pulling the rope is close to if a bearing was there. For the direction of action, a plane perpendicular to the outer slanting face of the each rib is assumed. Perpendicularly acting load will be easily carried and the ring can take more load. From the design of the ring ribs, the direction of action differs between the backstays and the forestay. This means that the ring will not only experience a torque but also a turning moment. The software will thus compensate for it in calculations.
As a requirement before application of bearing load, a coordinate system was created in each of the three openings where the ropes are tired.
Figure 11 Load application on the flangs
This is done for all the flangs
Figure 12 The boundary conditions and loading conditions shown.
The simulation is now ready to run. However, meshing must be done first. For starters, a default course mesh is used.
Figure 13 Mesh diagram
The simulation is then run. The results are saved and are discussed in the chapter that follows. A word document result is attached to this report together with other index information.
The aim of this study to change the parametric features of the masthead ring such that the entire mass is reduced but still ensuring that that it is fully functional and up to the task. The parameters that will be toggled in this section are thicknesses of the three ribs and the thickness of the ring itself. From the analysis, it was apparent that there is a large discrepancy of Factor of Safety across the different sections of the ring. The displacement was also noted to be on the ribs on which the loads are applied. These two gives us our design constraints. For accuracy purpose, the overall diameter was also constrained.
A shortcut to creating a new design study is by right clicking the toggle bar on the bottom and selectin “Create New Design Study” as shown in the figure below.
Figure 14 Creating a new design study
The window shown below appears.
Figure 15 Optimisation window
As can be seen, the window has three requirements that need to be added. The variables, the constraints and the goals. Optimisation will simply be setting these 3 sets of factors and running. They are added by each sequentially by clicking the respective prompts.
First the parameters are added as shown below
Figure 16 Parameters setting
The variable limits were set as shown in the figure below.
Figure 17 Setting of parameters range
The constraints were also set
Figure 18 Setting the constraints
The goals of the simulation are indicted and set as shown below
Figure 19 Specifying the goals
The main goal is reduce the weight of the ring while maintaining the inner diameter. After running the results are given with the optimal solution chosen.
3.6 Re-designing the Optimised Ring
The goal of this project is to produce an optimised design of a masthead ring. Once the results for optimisation have been obtained the different dimensions the ring are updated; and simulation as previously carried out is repeated. The results are shown well discussed in the chapter that follows.
4 RESULTS AND DISCUSION
The inspection has shown that, there are some indications made visible through the use of a developer of false defects in certain areas of the part such as the welding area, however, these can be regarded as false defects as they are just a consequence of the part being in use for three months prior to inspection. There are some scratches on the surface of the part which may be due to poor welding in that area or due to the fact that the part has been in use before, but they are not defects in the part or the welding. As a result of these factors, these defects can be either overlooked or optimised.
Figure 20 Stress diagram
The stress result diagram is shown above. The points of minimum and maximum stresses are shown in the diagram. The minimum stress is
6.723×104 N/m2which is closer to the lowers bolting point. This could be explained by the fact that there are two other bolting point above which are closer to the loading and those take up most of the weights.
The maximum stress point is on the rib where the backstay is attached and the value of the stress is
1.242×108 N/m2.This is expected as the stay has the highest tension. However, this is still below the yield stress of stainless steel which is
2.92×108 N/m2(Shigley, Budynas, & Mischke, 2004).
Most of the parts of the ring are still coded blue. This indicate that the part is overdesigned and there could be redundant material. This gives a good opportunity for optimisation (Parag Nikam, Rahul Tanpure, 2016).
Displacement study is a key component of analysis of loaded parts. It is important to regulate the displacement especially when parts connected (D.N. Dimou, V.J. Papazoglou, 1995).
Figure 21 Displacement diagram
The figure above shows the displacement of different parts of the part. As expected, the magnitude and direction of displacement follows the magnitude and direction of force applied (Shigley, Budynas, & Mischke, 2004). The elongation for attaching the bolt has the least displacement as the place is least stressed. The displacement is
1×10-30 mm. This is almost like no displacement at all. The forestay rib has the highest displacement of
7.35×10-3mm. This displacement is within the allowable range of
This shows that there is opportunity for optimisation. This parameter will need to be observed to ensure that there won’t be large displacements.
4.2.3 Factor of Safety
In engineering, FOS is a primary consideration in designing. It gives a numerical value for how safe a structure is. In this design, FOS is observed as a constraints for regulating the design. The simulation gives the value before optimisation.
Figure 22 Factor of Safety Diagram
The mean factor of safety is 2.4 with the minimum being 2.35. This is a moderate factors of safety that can be maintained and worked out. However, on checking the maximum factor of safety, the value is
4.43×1011. This value is significantly large, indicating that there is some redundant material that need to be removed. This thus builds the case for optimisation (D.N. Dimou, V.J. Papazoglou, 1995).
On setting up for optimisation, there were 170 possible combinations and 107 of them were run successfully.
Figure 23 Results of Optimisation
In optimising, the knowledge of understanding how to deal with different parameters and constraint is important in achieving the required goals. For the case of this study, the parameters were all dimensions. There are 3 ribs whose thickness can be altered. Two ribs are similar as they are for the two backstays and have equal loading characteristics. For this reason, only one of them is used in the optimisation simulation. This is important as it reduces the number of scenarios that need to be calculated. For the thickness of ring, from the design of the ring, it was not possible to have a parameter called “Thickness” referencing the thickness of the masthead ring. The thickness is a driven dimension hence cannot be used as a parameter.
Figure 24 Initial sketch for the ring revolve
Thus the thickness of ring is determined by the inner diameter and the outer diameter such that;
Thickness=Outer diameter-Inner Diameter2 STYLEREF 1 \s 4. SEQ Equation \* ARABIC \s 1 1
Thickness=59.60-53.52=3.05 mm STYLEREF 1 \s 4. SEQ Equation \* ARABIC \s 1 2
In calculation therefore, changing any of the two dimensions can directly alter the thickness of the ring. The inner diameter should remain constant as the ring is to be fit in a mast head. This therefore should be put as a constraint such that it remain constant. The outer diameter is thus variable in order to alter the thickness. This was selected accordingly. The minimum outer diameter was set to be above 54 mm so as to be practical since the inner diameter is constant 53.5 mm.
The step sizes are set such that the calculation are more accurate but do not take much time. Small step size for the variables mean that there are many scenarios possible hence more time and memory required. While large step sizes mean that the accuracy of the calculation is compromised. The steps were set to 1 mm for all the three parameters giving a total of 170
The constraint is the internal diameter which must not change. For a loaded part, simulation parameters such as Factor of Safety FOS gives the best results. As seen from simulation results, the FOS was very big and largely varying on different sections of the masthead ring. The point with the maximum FOS was above 24 while the minimum was 2.4. 2.4 is a practical value as most of ship features have FOS ranging from 1.5- 4 (Sponberg, 2005).
4.4 Optimised Design
Once the optimal results are obtained, the values are incorporated in a new optimal model. The thickness is decreased by decreasing the external diameter from 59.6 mm as shown in Fig 20 above to 58 mm which is the optimal dimension as shown below.
Figure 25 Sketch for the optimised design
As it can easily be seen, the thickness is effectively reduced from 3.05 mm to 2.25 mm. The thicknesses of all the ribs were reduced to 5 mm are per the optimal results.
Figure 26 3 Drawing after optimisation
From the figure above, a slight change in thickness can easily be noted.
The optimised ring is loaded with similar loading and the results compared.
Figure 27 Factor of Safety for the Optimised Ring
From the diagram above, the factor of safety of the optimised has been reduced to 1.8 from 2.4. This is still acceptable and practical.
Figure 28 Stress diagram for the optimised ring
The diagram show the stress distribution. As it is apparent, most of the sections are blue and uniform. Two things can be deduced; first, that the stress is still low as most of the areas are blue. Secondly, the stress is uniform unlike in the previous design where there was more stress the ribs. The maximum stress is
Figure 29 Displacement Diagram of the optimised Ring
The maximum displacement is
9.678×103 mm. This is acceptable.
The optimisation comparison is simplified in the table below.
|Forestay Rib Thickness
|Backstay Rib Thickness
Table A Comparison before and after optimisation
From the table above, the changes achieved can clearly be seen. The main goal of this was to reduce the mass of the ring. The mass has been reduced by 105.86 g from 503.09 g to 397.23g. This a 21.04% decreasing. This will translate directly to the cost as the cost will also be reduced by 21.04%. The significance could be enormous especially when there are many pieces to be produced. This reduction in mass was achieved by reducing various thickness. The constraint was the Factor of Safety. The initial factor was 2.4. This was bound to reduce by decreasing the thickness. However, this had to be maintained above 1.5 which is the minimum recommendation for marine structures (D.N. Dimou, V.J. Papazoglou, 1995).
The recent years have seen more and more engineers embrace CAE and CAM. These tool are efficient in doing this these task thus saving time and consequently resources. These new modes of engineering offers a great opportunity for optimisation of engineering designs. For most structural features, this optimisation is with the aim of reducing mass and hence the overall cost. This gives a competitive edge in pricing.
In this project, a mast head ring was optimised. The follow involved scanning and analysing an existing ring. The ring is then scanned using a 3-D scanner to determine the dimensions. These parametric Solidworks part is used for simulation and optimisation. The first task involves simulating and determining the behaviour of the ring under the different loads. It was seen that the ring is stable with a minimum factor of safety of 2.4
. This is the minimum though there are some sections of the ring where the factor of safer is very large. This thus indicates the fitting is overdesign and justifies optimisation.
Thus with the goal of reducing the mass of the ring, parameters and constraints are set. The parameters are the main ring thickness and the ribs thicknesses. The constraints are the minimum internal thickness and FOS which was not to go below 1.5.
The optimal dimension were determined and various thicknesses reduced by as high as 30%. The implication is that the mass was effectively reduce by 21%
. This is significant value and it is expected to reflect even in costing.
This project was highly successful as all the set aims were achieved within the set time. The information and data contained here is helpful for industrial application. The research can be pushed further as the KAIZEN principle dictates, there is always a room to make better. There is still room to optimise marine products and fitting further.
B Sun, S Imai. K Kondoh. (2013). Fabrication of high-strength Ti materials by in-process solid solution strengthening of oxygen via P/M methods. Materials Science and Engineering
Bernardin, F. (2002). The 3-D Model Acquisition Pipeline. Computation Graphics Forum
C Frohlich, M Mettenleiter. (2000). Imaging Laser Radar for 3D Modelling of Real World Environment. International Conference on OPTO.
D.N. Dimou, V.J. Papazoglou. (1995). Sctructural design of sailing boats: A case study.
Athens: National Technical University of Athens.
Dedekan, I. (2001). Sail and Ring Tuning Illustrated.
West Sussex: Fernhurst Books.
Dowling, N. E. (2012). Mechanical Behaviour of Materials: Engineering Methods for Deformation, Fracture, and Fatigue.
EBRAHIM, M. A.-B. (2013). 3D Laser Scanners’ Techniques Overview. International Journal of Science and Research (IJSR)
EMS-USA. (2017). Types of 3D Scanners and 3D Scanning Technologies.
Retrieved from EMS_USA: www.ems-usa.com
F Castro, F Ciciliot. (2008). A Quantitative Look at Mediterranean Lateen- and Square-Riffed Ships. The International Journal of Nautical Archaeology
Hexagon_Metrology. (2017, December 17). Product Brochure-Romer Absolute Arm.
Retrieved from www.hexagon.com
Hounsfield. (2017, Dec 21). W-Series Operating Instruction.
Retrieved from Hounsfield Test Equipment: www.hounsfield.com
J Case, A H Chilver. (1986). Strength of Materials and Structures: An Introduction to the Mechanics of Solids and Structures.
Baltimore, Maryland: Edward Arnold.
Javidinejad, A. (2012). Theory of Parametric Design Optimisation Approach via Finite Element Analysis. Advanced Theory of Applied Mechanics
Mohammad AlHamaydeh, Samer Barakat, Omar Nasif. (2017). Optimisation of Support Structures for Offshore Wind Turbines Using Genetic Algorithm with Domain-Trimming. Mathematical Problems in Engineering
Parag Nikam, Rahul Tanpure. (2016). Design Optimisation Of Chain Sprocket Using Finite Element Analysis. International Journal of Engineering Research and Application
Ph. Rigo, J D Caprace. (2016). Optimisation of Ship Structures.
ANAST , Belgium: University of Liege.
Shigley, J. E., Budynas, R. G., & Mischke, C. R. (2004). Mechanical engineering design.
Sponberg, E. W. (2005, June). Engineering the Sailboat - Safety in Numbers. Sail Magazine
Surya Patnaik, Dale Hopkins. (2002). Strengths of Materials.
Systèmes, D. (2010, Dec 16). Solidworks Software Optimisation.
Retrieved from Solidworks Inc: www.solidworks.com
The British Standards Institution 2018 Stainless steel 316 Alloy, Accessed on 03/01/2018