Conor McCune
Topology Optimization Constrained by Stiffness
Overview
Provided an initial geometry, I optimized the topology in order to reduce the weight of the part with a constraint on stiffness. I also analyzed the stress and displacement of the part to ensure the part would not fail. The initial geometry and stress state is shown in Figure 1. The displacement is also shown but is amplified by a factor of nearly 10,000 in order to be perceptible. This optimization is valuable for any part in which resonance is a concern. The specific constraint I used was a non-dimensional ratio of the strain energy of the optimized geometry compared to initial strain energy of the part. The following optimizations are done with this ratio equal to 2.
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Figure 1. Initial Geometry, Stress and Displacement
Optimizations
I ran this optimization for two different physical scenarios. The first is where the optimization is only applied to the internal structure of the part thus keeping the overall dimensions and outer shape of the part the same. I called this internal optimization
(Figure 2). In the second problem the optimization was applied to the entire part. In this problem we do not care about the final shape of the part, as long as it does not exceed the size and shape of the initial geometry. (Figure 3)
Results
Figure 2. Internal Optimization
The results follow what we would expect. As the internal geometry changes, the stiffness decreases and as such the maximum stress and displacement increases. Comparing the internal optimization to the full optimization we would expect the the full optimization to have a smaller mass but larger stress and displacement. While the displacement is larger the stress is actually smaller for the full optimization. This is likely due to the stress concentration of the sharp outer edges.
Figure 3. Full Optimization
Here's a link to the full paper:
Location Finding of Surgical Tools for Arthroscopy
Overview
The overall idea is to use computer vision to locate the position and orientation of markers that are rigidly connected to the surgical tools in order to determine the lengths of defects in the body. The overall setup is shown in the image on the right. The camera sends high resolution video to the computer. Then on an image by image basis the computer determines the position and orientation of the marker relative to the camera. Because there is a known and fixed geometry between the markers and the tool tip, once we know the marker position and orientation we know the tooltip position and orientation (again relative to the camera). By comparing two different positions the surgeon can accurately measure size of defects within the body.
Defect Measuring
Accuracy Testing
The goal of the accuracy testing was to determine how accurately we could measure a defect in the body. The video on the right shows the test setup. We moved the tooltip in 20 mm increments across a caliper and recorded the data output by our system. The pink dot overlayed on the video is where our software believe the tooltip is. On the right side of the video is a 3D plot of both the marker and tooltip position.
Accuracy Results
The data shown below is the displacement of the tooltip vs. time for the video shown above. The solid black lines represent the distance the tooltip was actually moved. The dashed lines represent our acceptable 3mm tolerance and the red line is the data collected by our system.
Precision Testing
The set up for our precision testing is shown in the video on the right. We fixed the tooltip inside a clamped wooden block and rotated the marker. The video also shows the x,y, and z positions of the tooltip being collected. Because the tooltip location is fixed, these positions should be constant.
Precision Results
The image on the right shows the 3D plot of both the marker and tooltip position. As you can see the tooltip position remains fixed while the marker position rotates in the manner shown in the video above.
Hardware
The hardware required for this project is a camera mount that connects to the surgical table, a camera that can send high resolution video without compressing it, and a shield that that allows a clear line of sight to from the camera to the markers. The camera mount and camera were purchased, however we designed the shield. Our proposed design is shown on the right.
Rock Climbing Safety Equipment
Background
Cams are a type of rock climbing safety equipment that rely on spring loaded lobes that are placed into cracks. When a climber falls, they apply a downward force to the stem of the cam which is translated to a rotational force on the lobes. Because the lobes have an increasing radius the rotational force from the climber falling, jams the lobes into the crack and allows the device to hold significant weight. While there are many different cams on the market with varying strengths, this project was created out of my desire to have a device that could do it all! All specifics are omitted for patenting purposes.
Failure Analysis of the Deepwater Horizon Oil Rig
Overview
I analyzed the design of the production casing used in the Macondo well. The full analysis is available at the link on the right.
Results
Crack Length at Fracture = 27.6 mm
Wall thickness is 25.4 mm therefore the casing is designed to leak before break
90,500 cycles of loading in order to propagate an initial crack of 7.9 mm to the thickness of the casing
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This analysis supports the design of the casing, as it was made to leak before break, and would require significant cyclic loading for a crack to propagate through the entire casing. The fact the casing leaked therefore becomes a question not of how it was designed, but rather of how it was stored in order for the strength to deteriorate to the point of failure, and more specifically why the casing was not tested before use. Read the full paper to see how these numbers were found.
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