User:Brian P. Josey/Notebook/2010/03/17
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Neodymium Yoke in FEMMI created a really simple model of a neodymium yoke in FEMM as a comparison to our yoke with the soft iron core. Instead of modeling out the whole pieces, including "the monster" 90^{o} bends, I simplified the model. Essentially, I imagined that I had a long column magnet, with a sharp tip on one end, and a flat surface on the other that I bent around to form the shape of a yoke. I then put this into the FEMM, and changed the dimensions around so that the same crosssectional area and volume would be equal to the real life counterpart. Because of this, the model is a little lopsided looking, but it should be an accurate representation of the real thing. This above is an image of the field lines, black lines, and magnitude of the magnetic field, represented by the colors with reds being higher intensity. For comparison, here is the iron yoke: From the pictures, it is clear that there are more field lines for the neodymium core, but they also go outside of the inner area, and would effect everything else around it. But the area that I am mostly concerned about is the gap between the cone tip, and the flat surface. In both of them, the gap between the two is 1/2", which serves as a reasonable gap, giving us plenty of room for measurements that are both close too the proteins, and a general trend. On Monday, I ran the simulation for the iron yoke, and used MATLAB to calculate the derivative along the line connecting the cone tip to the flat surface. For reference, here are the images again, field on the left, derivative on the right: I did the same process for the neodymium yoke. This gave me the following field, left, and derivative, right. It is easy to see from the picture that the field is significantly stronger in some parts of the neodymium yoke than in the iron, especially towards the flat end of the gap. Unfortunately, from these two images, it isn't clear if there is any real difference between their derivatives. This is a graph of the difference of the magnetic field magnitude between the neodymium and iron yokes. It is set up mathematically so that the blue line, which represents the difference, is positive wherever the neodymium is stronger. I added the red line at y=0 as reference. Not surprisingly, the field is much stronger for the neodymium in the middle and towards the flat end than for iron. But what is surprising is that the field is actually stronger for iron in the vicinity of the tip. I tried updating the precession in the simulation for this point to a much higher level, however this did not remove the oddity. I am still debating why this occurred. It could be on account of how either problem was set up in FEMM, or the strong magnets in the neodymium model on the other side of the yoke could be fighting with it. Another likely reason, and this is the one that I favor, is the jump in the magnetic field at the interface between the magnet and the air. We have already seen this before on Monday with the second set of data. It could be showing its head again and throwing off the calculations. Whatever the case may be, the difference in the derivative is more important: Once again, this is set up so that a positive difference between the two derivatives represents neodymium having a higher derivative, and in turn a higher force. From this graph, it is clear that there would be a much larger force near the tip of the cone, minus the few points immediately near the tip that I'm still wondering about. The force would also be stronger near the flat portion of the yoke, far away from the tip. While the two ends of the gap have stronger forces and fields, in the intermediate portion, there is no clear difference in the derivative, and it appears that choosing iron or neodymium for these intervening points would be irrelevant. However, for the ends of the gap near the cone and flat surfaces, it is clear that neodymium is a better choice. Final thoughtI think upgrading to a permanent neodymium is the way to go. From the field strength graph, it is clear that there is there will be a stronger field. More importantly, from the derivative graph, there would be much stronger forces on a magnetic dipole near the tip with the neodymium magnets than with the iron yoke. However I do have some reservations about this. The horseshoe magnets are much larger than the cones and cylinder magnets that I was planning on using. From the manufacturer's website, the dimensions of the side surfaces are and 1 inch by 1 inch for a surface area of 1 in^{2}. Both the cone and cylinders that I was planning on using have a diameter of 1/2 in, giving an area of 0.196 in^{2}, a fifth of the size. Because of the geometry, I couldn't figure out a good way to represent the overflowing area that still represents what I imagine the yoke would look like. I noticed that there is an overflow of field lines when you have uneven surfaces, see thumbnail, and I would like to create a more exact model before I am perfectly satisfied with it. So right now, I think that it is a good idea to get the neodymium, but I want to make the simulation that accounts for the unusual geometry from the 90^{o} turns first. Over the brake I will come up with the points needed for the FEMM, and finalize my design of the yoke using the cylinders and bends that I found, if even after accounting for the unusual shapes the neodymium is a better choice, then we should get it and run with it. I created a really rough version of the yoke that I have in mind, and it doesn't appear to make any real difference in the magnetic field. Running a plot of the magnetic field along the same line as the others reveals that the only difference is that there is a stronger field near the flat portion than in the others. After seeing this, I am even more confident with getting the neodymium yoke set up.
