From da5a6909286c594e852b85818fe6773138914402 Mon Sep 17 00:00:00 2001
From: David Preiss <davepreiss@gmail.com>
Date: Wed, 30 Mar 2022 20:46:44 +0000
Subject: [PATCH] Update README.md, images/image1.png, images/image3.png,
 images/image4.png, images/image2.png, images/image5.png, images/image6.png

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diff --git a/README.md b/README.md
index 8eb565e..bbe7b72 100644
--- a/README.md
+++ b/README.md
@@ -1,92 +1,63 @@
-# MAS.862 Final Project
+# Motor Questions
 
+![alt_text](images/image1.png "image_tooltip")
 
 
-## Getting started
+## 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?**
 
-To make it easy for you to get started with GitLab, here's a list of recommended next steps.
+* Model an "infinitely long" 5mm diameter cylinder magnet and show diminishing returns for flux at the front of the magnet.
+* 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.
 
-Already a pro? Just edit this README.md and make it your own. Want to make it easy? [Use the template at the bottom](#editing-this-readme)!
+![alt_text](images/image2.png "image_tooltip")
 
-## Add your files
+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 
 
-- [ ] [Create](https://docs.gitlab.com/ee/user/project/repository/web_editor.html#create-a-file) or [upload](https://docs.gitlab.com/ee/user/project/repository/web_editor.html#upload-a-file) files
-- [ ] [Add files using the command line](https://docs.gitlab.com/ee/gitlab-basics/add-file.html#add-a-file-using-the-command-line) or push an existing Git repository with the following command:
+## 2) Is there a penalty to having a large insulator (which creates a high reluctance gap) between your motor steel and winding? Is it optimal to ensure that your winding is wrapped tightly against the inductor?**
 
-```
-cd existing_repo
-git remote add origin https://gitlab.cba.mit.edu/davepreiss/mas.862-final-project.git
-git branch -M main
-git push -uf origin main
-```
+* H field produced is defined as the product of amps flowing through a winding and number of turns in that winding. 
+* Having a larger diameter coil increases the resistance of the winding, so perhaps the tradeoff is that we are creating a lot of flux that doesn't get used or gets canceled because there are more windings in the way.
+* If you have a small steel core at the center of a large diameter of windings are you being punished?
 
-## Integrate with your tools
 
-- [ ] [Set up project integrations](https://gitlab.cba.mit.edu/davepreiss/mas.862-final-project/-/settings/integrations)
+# Winding Geometry Questions
 
-## Collaborate with your team
+## 3) What is the effect of filling an air core winding to the core with windings? Diminishing returns? Higher peak flux at center but lower exterior? Would an optimal coil have the smallest possible wall thickness?**
 
-- [ ] [Invite team members and collaborators](https://docs.gitlab.com/ee/user/project/members/)
-- [ ] [Create a new merge request](https://docs.gitlab.com/ee/user/project/merge_requests/creating_merge_requests.html)
-- [ ] [Automatically close issues from merge requests](https://docs.gitlab.com/ee/user/project/issues/managing_issues.html#closing-issues-automatically)
-- [ ] [Enable merge request approvals](https://docs.gitlab.com/ee/user/project/merge_requests/approvals/)
-- [ ] [Automatically merge when pipeline succeeds](https://docs.gitlab.com/ee/user/project/merge_requests/merge_when_pipeline_succeeds.html)
+* This would be a good one for FEA generally, but there's difficulty in that the ID increasing must effectively mean fewer coils, so it's necessary to compensate for both.
 
-## Test and Deploy
+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. 
 
-Use the built-in continuous integration in GitLab.
+![alt_text](images/image3.png "image_tooltip")
 
-- [ ] [Get started with GitLab CI/CD](https://docs.gitlab.com/ee/ci/quick_start/index.html)
-- [ ] [Analyze your code for known vulnerabilities with Static Application Security Testing(SAST)](https://docs.gitlab.com/ee/user/application_security/sast/)
-- [ ] [Deploy to Kubernetes, Amazon EC2, or Amazon ECS using Auto Deploy](https://docs.gitlab.com/ee/topics/autodevops/requirements.html)
-- [ ] [Use pull-based deployments for improved Kubernetes management](https://docs.gitlab.com/ee/user/clusters/agent/)
-- [ ] [Set up protected environments](https://docs.gitlab.com/ee/ci/environments/protected_environments.html)
+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.
 
-# Editing this README
+![alt_text](images/image4.png "image_tooltip")
 
-When you're ready to make this README your own, just edit this file and use the handy template below (or feel free to structure it however you want - this is just a starting point!).  Thank you to [makeareadme.com](https://www.makeareadme.com/) for this template.
+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. 
 
-## Suggestions for a good README
-Every project is different, so consider which of these sections apply to yours. The sections used in the template are suggestions for most open source projects. Also keep in mind that while a README can be too long and detailed, too long is better than too short. If you think your README is too long, consider utilizing another form of documentation rather than cutting out information.
+![alt_text](images/image5.png "image_tooltip")
 
-## Name
-Choose a self-explaining name for your project.
+# EM Simulations
 
-## Description
-Let people know what your project can do specifically. Provide context and add a link to any reference visitors might be unfamiliar with. A list of Features or a Background subsection can also be added here. If there are alternatives to your project, this is a good place to list differentiating factors.
+Towards making a simple 2D simulation tool to answer some of these questions, it seems as though the best place to begin would be to simply model conductors with [Biot-Savart](https://en.wikipedia.org/wiki/Biot%E2%80%93Savart_law):
 
-## Badges
-On some READMEs, you may see small images that convey metadata, such as whether or not all the tests are passing for the project. You can use Shields to add some to your README. Many services also have instructions for adding a badge.
+<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>
 
-## Visuals
-Depending on what you are making, it can be a good idea to include screenshots or even a video (you'll frequently see GIFs rather than actual videos). Tools like ttygif can help, but check out Asciinema for a more sophisticated method.
+![alt_text](images/image6.png "image_tooltip")
 
-## Installation
-Within a particular ecosystem, there may be a common way of installing things, such as using Yarn, NuGet, or Homebrew. However, consider the possibility that whoever is reading your README is a novice and would like more guidance. Listing specific steps helps remove ambiguity and gets people to using your project as quickly as possible. If it only runs in a specific context like a particular programming language version or operating system or has dependencies that have to be installed manually, also add a Requirements subsection.
+and (point source) [magnetic dipoles](https://en.wikipedia.org/wiki/Magnetic_moment) with:
 
-## Usage
-Use examples liberally, and show the expected output if you can. It's helpful to have inline the smallest example of usage that you can demonstrate, while providing links to more sophisticated examples if they are too long to reasonably include in the README.
+![alt_text](images/image7.png "image_tooltip")
 
-## Support
-Tell people where they can go to for help. It can be any combination of an issue tracker, a chat room, an email address, etc.
+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.
 
-## Roadmap
-If you have ideas for releases in the future, it is a good idea to list them in the README.
+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.
 
-## Contributing
-State if you are open to contributions and what your requirements are for accepting them.
+### Including materials with changing permeability
 
-For people who want to make changes to your project, it's helpful to have some documentation on how to get started. Perhaps there is a script that they should run or some environment variables that they need to set. Make these steps explicit. These instructions could also be useful to your future self.
+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 
 
-You can also document commands to lint the code or run tests. These steps help to ensure high code quality and reduce the likelihood that the changes inadvertently break something. Having instructions for running tests is especially helpful if it requires external setup, such as starting a Selenium server for testing in a browser.
-
-## Authors and acknowledgment
-Show your appreciation to those who have contributed to the project.
-
-## License
-For open source projects, say how it is licensed.
-
-## Project status
-If you have run out of energy or time for your project, put a note at the top of the README saying that development has slowed down or stopped completely. Someone may choose to fork your project or volunteer to step in as a maintainer or owner, allowing your project to keep going. You can also make an explicit request for maintainers.
+In other words a permanent magnet in infinite free space will have a symmetric B and H field, however if a steel yoke is placed around the right side of the magnet, the B (and H?) field around the left side of the magnet will be significantly reduced.
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-- 
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