Design Analysis

2. Task definition
A sailing vessel is normally steered by means of a rudder, controlled by either a steering wheel or (as in the case of this assignment) a tiller. Fig. 1 shows the assumed steering components for the sailing vessel to be considered. Note in particular the coordinate system to be used in this assignment; Y is the vertical (upwards positive) direction, X is the longitudinal (aft positive) direction and Z is the transverse (port positive) direction. The coordinate system origin (0,0,0) is on the shaft axis, on the interface between the shaft flange face and the top face of the rudder.
You will be looking at the design of the rudder shaft. You will develop a spreadsheet (based on a template provided) to determine the stresses in the shaft and to optimise the shaft for a specific product requirement. You will also carry out a Finite Element Analysis (FEA) of the shaft.

Figure 1 – Sailing vessel steering components
The rudder is designed to generate a sideforce to steer the boat (and also to complement the lift developed by the keel while the boat is sailing in a straight line, to prevent the boat slipping sideways under the action of a sidewind). Keen sailors will know that when a boat becomes overpowered in a strong gust of wind, the sideforce required to stop the boat making an unwanted turn to windward can be considerable, and the helmsman must pull hard on the tiller to generate that sideforce and keep the boat sailing in a straight line. A pulling force is required on the tiller because the sideforce tends to act on the rudder blade at a point aft (i.e. further back) of the rudder shaft axis. The sideforce can be assumed to act at a single point on the rudder blade. Fig. 2 below shows the defining dimensions of the steering assembly, including the assumed position at which the rudder sideforce acts.

Figure 2 – Definition of Dimensions
In Fig. 2, the crosshair on the tiller represents the force that the helmsman is applying to the tiller, and may be assumed to be acting in the positive Z direction (i.e. out of the page, towards the reader). The crosshair on the rudder represents the force that the water is imparting to the rudder, and may also be assumed to be acting in the positive Z direction (i.e. out of the page, towards the reader).
You have been given a set of input parameters that are unique to you – each student will work on a slightly different set of figures, so you will each get different results. To find out which parameters to use, open the parameters spreadsheet, and find the column with your name at the top. Marks will be lost for using the wrong inputs.
The input parameters that are provided are:
Property Symbol Units
Rudder Sideforce (in +ve Z direction) FR N
Distance of sideforce action below flange YS m
Distance of sideforce action behind Shaft Axis XS m
Tiller length XT m
Height of lower bearing above Flange YL m
Height of Upper Bearing above Flange YU m
Height of Tiller above flange YT m
Total length of shaft Ytot m
Shaft Outer Diameter OD m
Shaft Wall Thickness (= OD/2 if shaft is solid) W m
Mateial Yield Stress σyield N/m^2
Material Density ρ kg/m^3
Material Price P £/kg
Material Carbon Footprint CO kgCO2/kg
Optimisation task (Minimum weight/cost/CO2) none
You must open and save your own copy of the calculations template spreadsheet, enter your input parameters and then fill in all of the yellow boxes to calculate loads, stresses, Factor of Safety, etc.

Make sure you follow all of the following guidelines:
• You should rename your saved copy of the template with your own surname and first name, so the file name format should be, for example, “DSGN215_CWA_2014_Bloggs_Joe.xlsx”.
• You must ensure that your spreadsheet is fully parametric – so use Excel formulae such that if any inputs change, calculations automatically update. You will lose marks if they do not. (Note – in Row 86, it is OK to type a value rather than calculate it).
• Work your way through the spreadsheet step by step, and make sure you follow all the instructions carefully.
• Don’t change the structure of the spreadsheet (i.e. don’t add rows/columns or put additional calculations in cells outside the specified yellow boxes). If you change the structure, my automatic calculation checks won’t work and you will lose marks.
• Fill in yellow boxes in the Formula column, writing formulae using the nomenclature I have given, not Excel cell references. This helps you to check your work, and allows me to give you credit for using the right formula, even if you made a calculation error.
• Fill in the yellow boxes in the Comments/Working column to show HOW you worked out your answer – again so I can give credit for the method even if the answer is wrong. A simple explanation (e.g. “used Pythagoras to calculate length of the hypotenuse”) or a line or two of working would be ample.
• Change the colour of the cells in the Value column as you have done in the class exercises – so any typed in input value cell is green and any calculated value cell (i.e. containing a formula) is red.
• About half of the marks for this assignment are for your calculations, and half are for your answers to the 7 questions (including the optimisation task). So make sure you answer all 7 questions carefully.
• If you have followed the instructions on the spreadsheet correctly, you should end up with two worksheets (plus a worksheet for FEA inputs) in your final spreadsheet:
o Basic Calculations containing all your calculations based on the inputs assigned to you, with all seven questions answered.
o Optimised containing calculations revised for your optimised material property and diameter inputs (without answers in the 7 question cells). Make sure you have optimised for the parameter that you have been allocated – either minimum weight, minimum material cost or minimum material carbon footprint.
3. Assumptions
You calculations must assume the following:
• Neglect self-weight of the shaft (and weight of attached components) in your load calculations.
• Assume that the tiller is aligned with the centreline of the boat and that the sideforce you have been allocated represents the maximum hydrodynamic force that the rudder will experience. Also, you don’t need to consider drag force on the rudder, just sideforce.
• Assume that your shaft is some type of stainless steel, with a Young’s Modulus of 207 GPa.
• Ignore fatigue in your calculations. (In reality, this would be an important design consideration – we will learn more about this later in DSGN215 lectures).
• Assume that the only shear stress is that due to the torque that the shaft is carrying – neglect shear due to direct forces & reactions.
• Assume that the tiller is firmly bonded to the shaft, and there are no stress concentrations on the shaft associated with the connection to the tiller. In reality, there would probably be a key and keyway transmitting torque between tiller and shaft, so there would be a stress concentration associated with this.
• Assume that the rudder is firmly bonded to the shaft flange face, and that all loads are transferred purely through this bond. This means that you don’t need to account for the way that the flange bolts would load the flange in reality.
• Assume that the greatest stresses in the shaft occurs at the lower bearing, so you don’t need to calculate stresses at the flange, tiller or upper bearing. In reality, you would probably calculate stresses throughout the shaft to show this is a valid assumption.
• Assume that the radial stress (i.e. the stress pushing into the surface of the shaft) because of interference pressure of bearings press fitted onto the shaft is negligible.
Assume that the shaft has constant inner and outer diameters along its entire length. In reality it would probably have some steps for bearings to be pressed up against.