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Revision as of 08:34, 21 August 2015
Chromate Biosensor
Modeling and Physics Experiments
Bone Incision Experiments
Objective
The aim is to represent the relationship between the applied force, sliding distance and wear volume when a stainless steel knife collides with bone. By calculating the force required to make the incision, this could potentially indicate the size or strength of a possible suspect, while the sliding distance would correspond to the length of the blade. This relationship is determined by the Archard Equation for wear1:
where, W is the volume of wear, S is the sliding distance, P is the applied force and k the wear coefficient. This is intended to complement the chromium detector which would be used in a stabbing or decapitation case.
Results
From experimental methods a value of 6.23x10-9 was found for the wear coefficient. Using this the Archard Equation was modelled on matlab to produce a parabolic surface plot relating the volume of incision to the length of the bland and the force of stabbing. As expected the volume will increase, as the force and sliding distance increase. The following graph was obtained.
Method
To use the Archard Equation, first a value for the wear coefficient, k, between bone and stainless steal needed to be determined experimentally. The linear relationship between the volume of wear and force exerted can be investigated and the gradient of the produced graph found. The gradient will be equal to kS, where k is the wear coefficient and S is the known sliding distance. Therefore k can be calculated.
To do this, a piece of equipment called an Instron 4204 was used, this is a computer controlled electro-mechanical testing system capable of performing a variety of tests based on tension and compression2. This was used alongside the Bluehill program. For our needs, this equipment is used to measure the force needed to continue compression at a set rate, and therefore the force needed to cut through the bone. This was done for speeds of 5mm/min, 10mm/min and 20mm/min on 2 pig ribs and 4 pig shoulder bones, using the set up shown below. A knife is clamped to the Instron machine and a bone placed on a stand below. The program is started and the knife is lowered at a set speed using the following set up:
The program is started and stopped manually, allowing the extension to also be determined manually. For this purpose a start and end point is marked on the knife, meaning the extension is a control factor throughout the experiment and kept at 32mm. The Bluehill program then produces a graph of the force against extension, so the maximum force exerted to cut through bone can be found and recorded. This is done for 25 different incisions and the force exerted for each is recorded
The next stage is to determine the volume of each incision. As the incisions are so small they could not be measured by hand. A Kodax dxs 4000 Pro System was used to X-ray the bones. This was used along side two programs; Carestream and Image J. Carestream allowed a high resolution image of the incision to be produced, by choosing the optimum focal length and field of view. The image is then edited and the clearest contrast chosen. Then the image is imported into Image J and the scale set. Now the width and depth of the incision can be measured using the Line tool then Analyse and Measure. The results are then saved in a table. Finally the length if the incision is measured by had using a Vernier Calliper.
Now the volume is calculated by assuming the shape of the incision as a prism. The simple formula;
where W is the volume, h is the depth, b the width and l the length, is used. In Excel, the volume can be plotted against the force for each incision. A linear trendline is added and the gradient is found, in this case a value of 2e-11, and is equal to the wear coefficient times the blade length. The wear coefficient is therefore found to be 6.23x10-9 .
Now the wear coefficient has been found the Archard Equation can be modelled in matlab.
Disscussion
From the experimental process a value of 6.23x10-9 was obtained. However the graph itself had a very low R2 value. This value is the percentage of variance in the date which can be explained by the model. This low value means the graph could be considered inaccurate. As the values of volume measures are all relatively accurate, with all uncertainties in the range of 3x10-12 to 7x10-11. This would suggest that the anomalies are due to the method used to make incisions. Although the actual measurement of force was accurate, the force applied may not have been. The knife was clamped onto the jaws of the Instron 4204, but still swivelled slightly when force was applied. A manual attempt was made to ensure the blade stayed straight. However, as this coefficient had never been previously calculated it is unknown how much of an effect this had on the overall result.
References
[1] Thompson, J.M. and Thompson, M.K. A Proposal for the Calculation of Wear, Proc. of the 2006 International ANSYS Conference and Exhibition
[2] Instron Load Frame Standard Operating Procedure .
