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– ‘Cambridge Engineering Selector’ database program
Below is a brief description of the theory regarding this lab: –
Oars are light, stiff beams. They must also have reasonable fracture toughness (KIC) and acceptable price per unit mass (Cm).
The performance index for a light, stiff beam is:
M1 = E1/2/?
Where E is the Young’s modulus and ? is the density.
To select the best materials, perform two selection stages:
(i) In stage 1, select materials with M1 > 7 (GPa) /(Mg/m)
(ii) In stage 2, select materials with KIC > 1 MPa.m and Cm < 100 GBP/kg.
CES Selector Materials for Oars: The solution
The performance index for a light, stiff beam (M1) is plotted in stage 1. ‘Density’ is plotted on the x-axis and ‘Young’s Modulus’ on the y-axis. A selection line of gradient 2, through the point (1.0, 49) is plotted.
The constraints on adequate fracture toughness and price are plotted in stage 2. ‘Fracture Toughness’ is plotted on the x axis and ‘Density’ on the y axis. A selection box whose upper left corner is at (1.0, 100) is defined.
In stage 1, the line representing the performance index is moved ‘up’ until only a small subset of records remains in the selection.
Magnified views of the two selection charts are shown in figures M5.3.1 and M5.3.2 (results intersection and hide failed records on), and the materials passing both stages are shown in figure M5.3.3. Oars for competitive rowing are made from Spruce, or (better) Carbon Fibre Reinforced Polymer (CFRP). ‘
Low Tech’ oars have been made for centuries out of bamboo. Boron Carbide might be acceptable, but it would be too brittle, despite its moderate fracture toughness.
The selection methodology behind CES Selector is described in section 1 of the online book CES In Depth ‘Background on Selection Systems’. The application of this selection methodology to a specific area (e.g. the selection of the optimum material for an engineering component) is dealt with in the section of CES In Depth for the relevant data module.
Before any selection can be performed, the user must specify which of the data tables will be the Selection Table (e.g. Materials, Process etc). This is done in the Project Settings dialog box (or on the Welcome screen when CES is first opened). Only one table can be used for selection in a given project. The filter and form for each data table must also be specified. The recommended filter and form combination for each type of selection is listed below.
Selecting records with Selector involves performing a series of independent selection ‘stages’. On each stage, the user selects a subset of records. Every record in the current filter for the Selection Table is considered during each stage, and the program automatically keeps track of all the results.
One way to perform a selection is to use a Selection Chart. The two axes of a selection chart specify record attributes. The user selects the area of the chart that fulfils the selection criteria. One selection chart is used for each selection stage.
A second way to perform a selection is to use a ‘Limit’ stage, in which numerical limits for one or more attributes are entered in a table. Limit stages can be combined with graphical stages (using selection charts).
A single functional requirement (e.g. the strength/density ratio of a material) can be represented by one stage in Selector. In many design situations it is necessary to identify records that satisfy several functional requirements simultaneously, for example high strength/density, high stiffness and low cost/kg for a material. In these cases Selector can perform several selection stages and the program will store the results of each stage automatically. The selection stages can be modified at any time if necessary. At the end of the selection (or at any other time), the user can find out which records passed all, or some of the selection stages.
It is important to realise that in this strategy, all records contained in the selection table with applicable data entries are considered in every selection stage (and are plotted on the charts). Therefore each stage is independent of the others. This means that records are never discarded from the selection process, even though they may fail a particular selection stage. So it is possible to find out how every entity performed on each of the stages. The ones that pass all stages will probably be the best choices.
Selector can also generate plots of ‘user-defined’ attributes, which are mathematical combinations of the attributes in the database. Examples are the specific strength el / (el is the ‘elastic limit’ and is the density), and the performance index for a light stiff beam E / (E is the Young’s Modulus). This facility greatly expands the versatility of the selection process and enables two complex performance requirements to be compared on one selection chart.
CALCULATION OF THE GRADIENT FOR BOTH GRAPHS
The gradient of the lines in both graphs were calculated using the performance index for the bending of rods, the formula used was: –
E/P = Young’s Modulus / Density
In order to get the above equation into the correct term for a gradient or a curve (y=m x + c) both sides of the equation had to be logged:
LOG E – LOG ? = LOG C
Transpose for LOG E
LOG E = LOG ? + LOG C
The equation for a straight line is y = mx + c
From the above it is fair to mention that: –
Y = LOG E
X = LOG ?
M = 1
The performance used in this lab was E 1/2 / P = C
If you take log on both sides of the equation above:
1/2 LOG E – LOG ? = LOG C
Transpose for 1/2 LOG E:
LOG C + LOG ? = 1/2 LOG E
Multiply both sides by 2 to get LOG E
LOG E = 2 LOG ? + 2 LOG C
From the above it can be assumed that:
Y = LOG E
M = 2
X = LOG ?
C = 2 LOG C
M (The gradient) = 2
The gradient in the first graph of Density Vs. Young’s
Modulus is 2.
If another performance index is used:
K IC / p = c
The log of both sides of the equation gives: –
2/3 LOG K ic = LOG ? + LOG C
Multiply both sides 3/2 gives:
LOG K ic = 3/2 log ? + 3/2 log c
Y = LOG K ic
M = 3/2
X = LOG ?
C = 3/2 LOG C
M = 3/2 = 1.5
The gradient of the line in the second graph of Fracture Toughness Vs. Density is 1.5
The Cambridge engineering selector was the program that was used in order to get the desired materials. The main two properties that the chosen material requires are strength and toughness. In order to get the right material two graphs had to be plotted. The first graph was Young’s Modulus vs. Density and the second graph was Fracture toughness vs. Density.
The first thing that had to be done was to select the right units, which are SI units. This was done by going onto ‘Tools’, selecting ‘options’ and then the correct units and currency which was GB Pounds.
Select New Project from the File menu
Choose the New Graphical Stage command from the Project menu.
The Graph Stage Wizard will appear, ready to define the x and y axis of your chart.
The procedure for selecting attributes for plotting on the selection chart axes is the same for both axes (and whichever selection table). The steps are as follows:
The X-Axis page is presented first.
To specify a single attribute, click once on the down arrow to display the drop down list box.
Select one attribute, “Density”.
(The Advanced function could be used to create a combination of attributes for one axis.)
The title can be changed by the user by typing in the Title field if desired.
Let the settings for the axis Scale remain as the default, Logarithmic and Autoscale.
You can change the scales to linear and back again, by clicking one of the ‘radio buttons’ marked ‘Logarithmic’ and ‘Linear’.
To switch to the Y-Axis page click once on the other tab.
Select the attribute “Young’s Modulus” from the drop down list box and let the scale be Logarithmic and Autoscale.
Click once on OK to exit the dialog.
The graph will then be created. Follow the same steps to create the other graph except this time, the y-axis is going to be Fracture toughness. Once both graphs are created, the gradient, which was worked out earlier, has to be put in. In the graph showing Young’s Modulus vs. Density the gradient is 2 and for the graph showing Fracture toughness vs. Density it is 1.5.
To put in a gradient line, simply click on the icon on the toolbar which has a picture of a gradient on it.
Then a box will appear asking you to enter a value for the gradient.
Once the value of the gradient is entered, the gradient will appear on the graph.
The line can be moved up and down the graph depending on what kinds of materials are needed. In order to narrow down the number of materials to a few, the line has to be moved carefully upwards until only a few materials are shown in the box.
This has to be done for both graphs until only 4 or 5 materials appear in the box showing both stages.
Engineering Materials Lab – All Stages
Epoxy/HS Carbon Fibre, UD Composite, 0ï¿½ Lamina MXP_CFTSEPHCUD001
Low Density Wood (Longitudinal) (0.22-0.45) MNW_L_LD
Medium Density Wood (Longitudinal) (0.45-0.85) MNW_L_MD
PEEK/IM Carbon Fibre, UD Composite, 0ï¿½ Lamina MXP_CFTPPEICUD001
After looking and analysing the results taken from the two graphs, the materials chosen were Epoxy SMC (carbon fibre), low density wood, and medium density wood. ). But in the economical end of manufacturing rowing boat oars, both the wood materials would be selected, as they are reasonably cheap to buy, whereas carbon fibre is more expensive.
Costs of materials are not the only concern, as the usage of each material is just as important. Questions could be asked; such as, how often is the boat going to be used? Is it going to be used on a regular basis? All of these questions should be taken into consideration before a decision is made.
If an average person who is not a professional rower was going to consume a rowing boat ore, he/she would be better off opting for the one made from low density wood as the wooden ore is a great deal cheaper. On the other hand if the same question was asked to a professional rower, then the rower would pick the ore made of carbon fibre since the price does not come at the top of the list of concern and winning the race is the major objective.
Basically, there is a good point and a bad point on each material. This largely depends on the object of buying the ore. If it is to win a race then money is not an option and the consumer would be better off buying the one made from carbon fibre but if the object is to just go rowing for a weekend then the best option would be to go for the oar made from wood simply because there is no likely consistent further use for the ore.