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Commit e7bc3d98 authored by David Preiss's avatar David Preiss
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Update images/BiotSavart.png, images/FEAflux.png, images/shear_v_ID.png,...

Update images/BiotSavart.png, images/FEAflux.png, images/shear_v_ID.png, images/annotated.png, images/B_dipole.png, images/shear_v_magHeight.png, README.md, images/shear_v_displacement.png
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# Motor Questions
![alt_text](images/image1.png "image_tooltip")
This project attempt to answer some non-intuitive motor design questions through simulation, fundamental equations, and hopefully some homemade discrete 2D EM (static) FEA.
![alt_text](images/FEAflux.png "image_tooltip")
## 1) What are the tradeoffs of using a larger magnet which provides more H, but increases the reluctance due to magnetic material's low permeability?**
......@@ -9,7 +10,7 @@
* Then model a coil with a yoke opposing it and increase the distance of the yoke to show diminishing returns there.
* Then with these two plots it should be possible to find an optimal distance, assuming nothing saturates. Some blogs have suggested that an infinitely long magnet is ideal. There must be flux contributed from both the rotor and stator to produce torque, but what is the right balance between these two? The plot below shows increasing magnet thickness (x-axis) and diminishing returns in shear force.
![alt_text](images/image2.png "image_tooltip")
![alt_text](images/shear_v_magHeight.png "shearVmagHeight")
This plot jumps right to the conclusion and shows shear force with increasing magnet thickness along the x-axis. Starting at about 2 mm, we begin to see very diminishing returns in terms of shear force vs. increasing magnet thickness. To be determined is the tradeoff between the PM's contribution and the relative increase from
......@@ -28,17 +29,17 @@ This plot jumps right to the conclusion and shows shear force with increasing ma
To start a simulation was run with constant amp-turns and increasing ID. Keep in mind that this was run with the optimal displacement as found in the sweep below for a 1mm ID at 2mm displacement. So it's possible that the magnet's location is convoluting this data a bit (more on that later). Interestingly there's a clear inflection point at 3.5mm corresponding to nearly double the shear force created in the .5mm case.
![alt_text](images/image3.png "image_tooltip")
![alt_text](images/shearVdisplacement1.png "shear_v_ID")
These results provide a strong basis for the possibility that tightly wound inner windings are contributing negatively, and so future sweeps here will need to be run manually to vary ID and have a % reduction in amp-turns corresponding with the coil area lost by increasing the coil's ID.
With that said, 3.5mm corresponds with the ID lying almost exactly on the center of the 3mm diameter of the magnet (see image below), so perhaps the takeaway is just that optimal shear will be produced at the point where the ID begins? To test this, lets re-run that offset code to make sure that the "Shear Displacement" parameter is still correctly set to 2mm with a now much larger ID.
![alt_text](images/image4.png "image_tooltip")
![alt_text](images/annotated.png "image_tooltip")
Again a sweep for optimal torque producing rotor displacement was run, analogous to load angle (max when 90 deg but unclear for this single pole linear displacement case). See CAD above for exact dimensions. Interestingly with this new ID, the optimal torque producing location has shifted up to 3.5mm. This suggests that iteration after tweaking certain parameters will be necessary to really converge on an optimal solution.
![alt_text](images/image5.png "image_tooltip")
![alt_text](images/shear_v_displacement.png "shear_v_displacement")
# EM Simulations
......@@ -46,17 +47,17 @@ Towards making a simple 2D simulation tool to answer some of these questions, it
<p id="gdcalert6" ><span style="color: red; font-weight: bold">>>>>> gd2md-html alert: inline image link here (to images/image6.png). Store image on your image server and adjust path/filename/extension if necessary. </span><br>(<a href="#">Back to top</a>)(<a href="#gdcalert7">Next alert</a>)<br><span style="color: red; font-weight: bold">>>>>> </span></p>
![alt_text](images/image6.png "image_tooltip")
![alt_text](images/BiotSavart.png "BiotSavart")
and (point source) [magnetic dipoles](https://en.wikipedia.org/wiki/Magnetic_moment) with:
![alt_text](images/image7.png "image_tooltip")
![alt_text](images/B_dipole.png "B_dipole")
Although for the latter it is not clear if a monolithic magnet can indeed be modeled as an array of infinitesimal magnetic dipoles, or if more complex math is required to represent what happens at the corners of a rectangular magnet for example.
Note that it's necessary to model everything with permeability of free space, and if different material permeability are included it will be necessary to converge on a solution with annealing as discussed below.
### Including materials with changing permeability
### A note on including materials with changing permeability
The math tells us that B = H x u, which makes it tempting to think that only the magnitude of our B field will change in comparison to H. However the presence of materials of different permeabilities (air vs. steel) will essentially create many small "permanent" magnets which will fundamentally alter
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