mirror of
https://github.com/atomic14/kicad-coil-plugins.git
synced 2024-10-18 09:06:57 +00:00
526 lines
17 KiB
Text
526 lines
17 KiB
Text
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"from mpl_toolkits.mplot3d import Axes3D\n",
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"from biot_savart_v4_3 import parse_coil, plot_coil, slice_coil, plot_coil2\n",
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"from tqdm.notebook import trange, tqdm\n",
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"from helpers import get_arc_point, draw_arc, rotate, scale, rotate_point, translate"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Track width and spacing\n",
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"TRACK_WIDTH = 0.127\n",
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"TRACK_SPACING = 0.127\n",
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"\n",
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"# via defaults\n",
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"VIA_DIAM = 0.8\n",
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"VIA_DRILL = 0.4\n",
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"\n",
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"# this is for a 1.27mm pitch pin\n",
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"PIN_DIAM = 1.0\n",
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"PIN_DRILL = 0.65\n",
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"\n",
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"# this is for the PCB connector - see https://www.farnell.com/datasheets/2003059.pdf\n",
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"PAD_WIDTH = 3\n",
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"PAD_HEIGHT = 2\n",
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"PAD_PITCH = 2.5\n",
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"\n",
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"STATOR_HOLE_RADIUS = 5.5\n",
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"HOLE_SPACING = 0.25\n",
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"\n",
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"# PCB Edge size\n",
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"STATOR_RADIUS = 30\n",
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"\n",
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"# where to puth the mounting pins\n",
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"SCREW_HOLE_DRILL_DIAM = 2.3 # 2.3mm drill for a 2mm screw\n",
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"SCREW_HOLE_RADIUS = STATOR_RADIUS\n",
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"\n",
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"# Coil params\n",
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"TURNS = 16\n",
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"COIL_CENTER_RADIUS = 19.95\n",
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"COIL_VIA_RADIUS = 20.95\n",
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"\n",
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"\n",
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"def get_points(spacing, inner_radius, outer_radius, start_angle, end_angle):\n",
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" # first calculate the angle step size from the spacing and the inner_radius\n",
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" spacing_angle = np.rad2deg(np.arctan2(spacing, inner_radius))\n",
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" print(spacing_angle)\n",
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" # now calculate the points be iterating from start_angle to end_angle with the spacing_angle\n",
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" points = []\n",
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" for angle in np.arange(start_angle, end_angle, spacing_angle * 2):\n",
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" p1 = get_arc_point(angle, inner_radius)\n",
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" points.append([p1[0], p1[1], 0, 0.5])\n",
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" p2 = get_arc_point(angle + spacing_angle, outer_radius)\n",
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" points.append([p2[0], p2[1], 0, 0.5])\n",
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" points.append([p2[0], p2[1], -0.8, 0.5])\n",
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" points.append([p1[0], p1[1], -0.8, 0.5])\n",
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" return points\n",
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"\n",
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"\n",
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"coil1 = get_points(\n",
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" TRACK_SPACING + TRACK_WIDTH,\n",
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" (COIL_CENTER_RADIUS - 10),\n",
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" COIL_CENTER_RADIUS + 10,\n",
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" -15,\n",
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" 15,\n",
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")\n",
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"# move all the points in by COIL_CENTER_RADIUS\n",
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"for p in coil1:\n",
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" p[0] -= COIL_CENTER_RADIUS\n",
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"# rotate the points by 90 degrees\n",
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"for p in coil1:\n",
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" p[0], p[1] = rotate_point(p[0], p[1], 90)\n",
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"coil1 = np.array(coil1).T\n",
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"plot_coil2(coil1)\n",
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"coil1 = slice_coil(coil1, 0.1)\n",
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"coil1 = coil1.T\n",
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"print(coil1.shape)\n",
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"print(len(coil1))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Simple Simulation of a dipole magnet"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# magnetic field at a point x,y,z of a dipole magnet with moment m in the z direction\n",
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"def B(x, y, z, m=0.185):\n",
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" mu0 = 4 * np.pi * 1e-7\n",
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" r = np.sqrt(x**2 + y**2 + z**2)\n",
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" return (\n",
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" np.array(\n",
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" [3 * x * z / r**5, 3 * y * z / r**5, (3 * z**2 / r**5 - 1 / r**3)]\n",
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" )\n",
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" * m\n",
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" * mu0\n",
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" )\n",
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"\n",
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"\n",
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"def plot_field_slice(x, y, bx, by, mag, name=\"magnetic_field.png\"):\n",
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" # plot the magnetic field\n",
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" fig = plt.figure()\n",
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" ax = fig.add_subplot(111)\n",
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" ax.streamplot(\n",
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" x,\n",
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" y,\n",
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" bx,\n",
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" by,\n",
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" linewidth=1,\n",
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" cmap=plt.cm.inferno,\n",
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" density=2,\n",
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" arrowstyle=\"->\",\n",
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" arrowsize=1.5,\n",
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" )\n",
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"\n",
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" ax.set_xlabel(\"$x$\")\n",
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" ax.set_ylabel(\"$y$\")\n",
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" ax.set_xlim(-0.1, 0.1)\n",
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" ax.set_ylim(-0.1, 0.1)\n",
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" ax.set_aspect(\"equal\")\n",
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"\n",
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" # plot the magniture of the field as an image\n",
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" im = ax.imshow(\n",
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" mag, extent=[-0.1, 0.1, -0.1, 0.1], origin=\"lower\", cmap=plt.cm.inferno\n",
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" )\n",
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"\n",
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" fig.show()\n",
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" # save the figure\n",
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" fig.savefig(name)\n",
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"\n",
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"\n",
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"# # calculate the magnetic field at y = 0, over z = -1, 1 and x = -1, 1\n",
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"x = np.linspace(-0.1, 0.1, 100)\n",
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"z = np.linspace(-0.1, 0.1, 100)\n",
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"X, Z = np.meshgrid(x, z)\n",
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"Bx, By, Bz = B(X, 0, Z)\n",
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"\n",
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"plot_field_slice(\n",
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" X,\n",
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" Z,\n",
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" Bx,\n",
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" Bz,\n",
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" np.log(np.sqrt(Bx**2 + By**2 + Bz**2)),\n",
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" \"magnetic_field_side.png\",\n",
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")\n",
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"\n",
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"# # calculate the magnetic field at z = 1, over y = -1, 1 and x = -1, 1\n",
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"x = np.linspace(-0.1, 0.1, 100)\n",
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"y = np.linspace(-0.1, 0.1, 100)\n",
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"X, Y = np.meshgrid(x, y)\n",
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"Bx, By, Bz = B(X, Y, 0.01)\n",
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"\n",
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"plot_field_slice(\n",
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" X, Y, Bx, By, np.sqrt(Bx**2 + By**2 + Bz**2), \"magnetic_field_bottom.png\"\n",
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")\n",
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"\n",
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"# calculate the magnetic field in a 3d volume\n",
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"x = np.linspace(-0.1, 0.1, 100)\n",
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"y = np.linspace(-0.1, 0.1, 100)\n",
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"z = np.linspace(-0.1, 0.1, 100)\n",
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"X, Y, Z = np.meshgrid(x, y, z)\n",
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"Bx, By, Bz = B(X, Y, Z)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# calculate the force on a wire of length l carrying current I at a point x,y,z with a direction vector d\n",
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"def F(p, d, I, l):\n",
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" return I * l * np.cross(d, B(p[0], p[1], p[2]))\n",
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"\n",
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"\n",
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"def calculate_forces_on_wire_points(points):\n",
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" Fx = []\n",
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" Fy = []\n",
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" Fz = []\n",
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" # calculate the force on each point\n",
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" for i in range(len(points)):\n",
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" # calculate the direction vector\n",
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" dx = points[i][0] - points[(i + 1) % len(points)][0]\n",
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" dy = points[i][1] - points[(i + 1) % len(points)][1]\n",
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" dz = points[i][2] - points[(i + 1) % len(points)][2]\n",
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" d = np.array([dx, dy, dz])\n",
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" # get the length of d\n",
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" l = np.sqrt(dx**2 + dy**2 + dz**2)\n",
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" if l > 0:\n",
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" # normalise d\n",
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" d = d / l\n",
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" # calculate the force\n",
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" fx, fy, fz = F(points[i], d, points[i][3], l)\n",
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" Fx.append(fx)\n",
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" Fy.append(fy)\n",
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" Fz.append(fz)\n",
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" else:\n",
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" Fx.append(0)\n",
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" Fy.append(0)\n",
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" Fz.append(0)\n",
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" return Fx, Fy, Fz\n",
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"\n",
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"\n",
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"# locate the loop of wire directly below the magnet\n",
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"x = 0.01\n",
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"y = 0\n",
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"z = -0.002\n",
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"r1 = 0.001\n",
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"r2 = 0.01\n",
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"\n",
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"\n",
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"points = coil1.copy()\n",
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"# scale the points from mm to m\n",
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"# shift the coil to the correct position\n",
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"for i in range(len(points)):\n",
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" points[i][0] = points[i][0] / 1000 + x\n",
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" points[i][1] = points[i][1] / 1000 + y\n",
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" points[i][2] = points[i][2] / 1000 + z\n",
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"\n",
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"\n",
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"# plot the points in 2D x,y\n",
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"fig = plt.figure()\n",
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"ax = fig.add_subplot(111)\n",
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"ax.plot([p[0] for p in points], [p[1] for p in points])\n",
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"ax.set_xlabel(\"$x$\")\n",
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"ax.set_ylabel(\"$y$\")\n",
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"ax.set_xlim(-0.01 + x, 0.01 + x)\n",
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"ax.set_ylim(-0.01 + y, 0.01 + y)\n",
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"ax.set_aspect(\"equal\")\n",
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"fig.show()\n",
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"\n",
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"Fx, Fy, Fz = calculate_forces_on_wire_points(points)\n",
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"\n",
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"\n",
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"# plot the wire along with arrows showing the force\n",
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"fig = plt.figure()\n",
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"ax = fig.add_subplot(111, projection=\"3d\")\n",
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"ax.plot([p[0] for p in points], [p[1] for p in points], [p[2] for p in points])\n",
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"\n",
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"print(sum(Fx) / 9.8)\n",
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"\n",
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"# subsample the points and force vectors to make the plot clearer\n",
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"points = points[::50]\n",
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"Fx = Fx[::50]\n",
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"Fy = Fy[::50]\n",
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"Fz = Fz[::50]\n",
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"\n",
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"ax.quiver(\n",
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" [p[0] for p in points],\n",
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" [p[1] for p in points],\n",
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" [p[2] for p in points],\n",
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" np.sqrt(Fx),\n",
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" 0,\n",
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" 0,\n",
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" length=0.01,\n",
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" normalize=True,\n",
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")\n",
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"ax.set_xlabel(\"$x$\")\n",
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"ax.set_ylabel(\"$y$\")\n",
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"ax.set_zlabel(\"$z$\")\n",
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"ax.set_xlim(x - 0.02, x + 0.02)\n",
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"ax.set_ylim(y - 0.02, y + 0.02)\n",
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"ax.set_zlim(z - 0.02, z + 0.02)\n",
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"ax.set_aspect(\"equal\")\n",
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"\n",
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"# change the figure size\n",
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"fig.set_size_inches(10, 10)\n",
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"\n",
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"fig.show()\n",
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"# coil2 = -0.01311082557350831\n",
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"# coil1 = 0.0088435517657609"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"def sweep_coil(coil, X):\n",
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" Y = np.zeros(len(X))\n",
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" Z = -0.01 * np.ones(len(X))\n",
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"\n",
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" # loop through the locations and calculate the forces, sum up the force in the X direction for each location\n",
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" Fx = []\n",
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" Fy = []\n",
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" Fz = []\n",
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" for p in trange(len(X)):\n",
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" points = coil.copy()\n",
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" # scale the points from mm to m\n",
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" # shift the coil to the correct position\n",
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" for i in range(len(points)):\n",
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" points[i][0] = points[i][0] / 1000 + X[p]\n",
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" points[i][1] = points[i][1] / 1000 + Y[p]\n",
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" points[i][2] = points[i][2] / 1000 + Z[p]\n",
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" Fx_, Fy_, Fz_ = calculate_forces_on_wire_points(points)\n",
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" Fx.append(sum(Fx_))\n",
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" Fy.append(sum(Fy_))\n",
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" Fz.append(sum(Fz_))\n",
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" return Fx, Fy, Fz\n",
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"\n",
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"\n",
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"# sweep the coild from -3cm to 3cm in 0.01m steps\n",
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"X = np.linspace(-0.03, 0.03, 100)\n",
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"Fx_1_straight, Fy_1_straight, Fz_1_straight = sweep_coil(coil1, X)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# plot the force as a function of x\n",
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"plt.plot(X, -np.array(Fx_1_straight) / 9.8, label=\"coil1\", color=\"red\")\n",
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"# plot a dotted line along y = 0\n",
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"plt.plot([X[0], X[-1]], [0, 0], \"--\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# plot the force as a function of x\n",
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"plt.plot(X, -np.array(Fz_1_straight) / 9.8, label=\"coil1\", color=\"red\")\n",
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"# plot a dotted line along y = 0\n",
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"plt.plot([X[0], X[-1]], [0, 0], \"--\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# instead of sweeping horizontally, we'll sweep the coils around a circle\n",
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"def sweep_coil_cirlc(coil, coil_center_radius, theta):\n",
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" X = coil_center_radius * np.cos(np.deg2rad(theta))\n",
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" Y = coil_center_radius * np.sin(np.deg2rad(theta))\n",
|
||
|
" Z = -0.01 * np.ones(100)\n",
|
||
|
"\n",
|
||
|
" # loop through the locations and calculate the forces, sum up the force in the X direction for each location\n",
|
||
|
" Torque = []\n",
|
||
|
" Fx = []\n",
|
||
|
" Fy = []\n",
|
||
|
" Fz = []\n",
|
||
|
" for p in trange(len(theta)):\n",
|
||
|
" angle = np.deg2rad(theta[p]) - np.pi / 2\n",
|
||
|
" x = X[p]\n",
|
||
|
" y = Y[p]\n",
|
||
|
" z = Z[p]\n",
|
||
|
"\n",
|
||
|
" points = coil.copy()\n",
|
||
|
" for i in range(len(points)):\n",
|
||
|
" px = points[i][0] / 1000\n",
|
||
|
" py = points[i][1] / 1000\n",
|
||
|
" pz = points[i][2] / 1000\n",
|
||
|
" # rotate the points so the coil is correctly oriented\n",
|
||
|
" points[i][0] = px * np.cos(angle) - py * np.sin(angle) + x\n",
|
||
|
" points[i][1] = (\n",
|
||
|
" px * np.sin(angle) + py * np.cos(angle) + y - coil_center_radius\n",
|
||
|
" )\n",
|
||
|
" points[i][2] = pz + z\n",
|
||
|
" # feel the force\n",
|
||
|
" Fx_, Fy_, Fz_ = calculate_forces_on_wire_points(points)\n",
|
||
|
" Fx.append(sum(Fx_))\n",
|
||
|
" Fy.append(sum(Fy_))\n",
|
||
|
" Fz.append(sum(Fz_))\n",
|
||
|
" # calculate the torque - which should be 90 degress to the angle\n",
|
||
|
" torque_angle = np.deg2rad(theta[p] - 90)\n",
|
||
|
" Torque.append(sum(Fx_) * np.cos(torque_angle) + sum(Fy_) * np.sin(torque_angle))\n",
|
||
|
"\n",
|
||
|
" return Fx, Fy, Fz, Torque\n",
|
||
|
"\n",
|
||
|
"\n",
|
||
|
"# sweep the coils from -45 to 45 degrees in 1 degree steps\n",
|
||
|
"theta = np.linspace(0, 180, 100)\n",
|
||
|
"Fx_1_curve, Fy_1_curve, Fz_1_curve, Torque_1 = sweep_coil_cirlc(\n",
|
||
|
" coil1, 19.5 / 1000, theta\n",
|
||
|
")"
|
||
|
]
|
||
|
},
|
||
|
{
|
||
|
"cell_type": "code",
|
||
|
"execution_count": null,
|
||
|
"metadata": {},
|
||
|
"outputs": [],
|
||
|
"source": [
|
||
|
"plt.plot(theta, -np.array(Torque_1) / 9.8, label=\"coil1\", color=\"red\")\n",
|
||
|
"# plot a dotted line along y = 0\n",
|
||
|
"plt.plot([theta[0], theta[-1]], [0, 0], \"--\")"
|
||
|
]
|
||
|
},
|
||
|
{
|
||
|
"cell_type": "code",
|
||
|
"execution_count": null,
|
||
|
"metadata": {},
|
||
|
"outputs": [],
|
||
|
"source": [
|
||
|
"# plot arrows for the Fx and Fy components\n",
|
||
|
"X = 19.5 * np.cos(np.deg2rad(theta)) / 1000\n",
|
||
|
"Y = 19.5 * np.sin(np.deg2rad(theta)) / 1000\n",
|
||
|
"plt.quiver(X[::5], Y[::5], Fx_1_curve[::5], Fy_1_curve[::5], color=\"red\")\n",
|
||
|
"# make the axis equal so the arrows are not stretched\n",
|
||
|
"plt.axis(\"equal\")"
|
||
|
]
|
||
|
},
|
||
|
{
|
||
|
"cell_type": "code",
|
||
|
"execution_count": null,
|
||
|
"metadata": {},
|
||
|
"outputs": [],
|
||
|
"source": [
|
||
|
"plt.plot(theta, -np.array(Fz_1_curve) / 9.8, label=\"coil1\", color=\"red\")\n",
|
||
|
"plt.plot(theta, np.array(Fz_2_curve) / 9.8, label=\"coil2\", color=\"blue\")\n",
|
||
|
"# plot a dotted line along y = 0\n",
|
||
|
"plt.plot([theta[0], theta[-1]], [0, 0], \"--\")"
|
||
|
]
|
||
|
},
|
||
|
{
|
||
|
"cell_type": "code",
|
||
|
"execution_count": null,
|
||
|
"metadata": {},
|
||
|
"outputs": [],
|
||
|
"source": [
|
||
|
"# instead of sweeping horizontally, we'll sweep the coils around a circle\n",
|
||
|
"def sweep_coil_cirlc(coil, coil_center_radius):\n",
|
||
|
" # sweep the coils from -45 to 45 degrees in 1 degree steps\n",
|
||
|
" theta = np.linspace(0, 180, 20)\n",
|
||
|
" X = coil_center_radius * np.cos(np.deg2rad(theta))\n",
|
||
|
" Y = coil_center_radius * np.sin(np.deg2rad(theta))\n",
|
||
|
" Z = 1 * np.ones(100)\n",
|
||
|
"\n",
|
||
|
" # loop through the locations and calculate the forces, sum up the force in the X direction for each location\n",
|
||
|
" Fx = []\n",
|
||
|
" Fy = []\n",
|
||
|
" Fz = []\n",
|
||
|
" for p in trange(len(theta)):\n",
|
||
|
" angle = np.deg2rad(theta[p]) - np.pi / 2\n",
|
||
|
" x = X[p]\n",
|
||
|
" y = Y[p]\n",
|
||
|
" z = Z[p]\n",
|
||
|
"\n",
|
||
|
" points = coil.copy()\n",
|
||
|
" for i in range(len(points)):\n",
|
||
|
" px = points[i][0] / 1000\n",
|
||
|
" py = points[i][1] / 1000\n",
|
||
|
" pz = points[i][2] / 1000\n",
|
||
|
" # rotate the points so the coil is correctly oriented\n",
|
||
|
" points[i][0] = px * np.cos(angle) - py * np.sin(angle) + x\n",
|
||
|
" points[i][1] = (\n",
|
||
|
" px * np.sin(angle) + py * np.cos(angle) + y - coil_center_radius\n",
|
||
|
" )\n",
|
||
|
" points[i][2] = pz + z\n",
|
||
|
" plt.plot([p[0] for p in points], [p[1] for p in points], linewidth=0.5)\n",
|
||
|
" # add the torque arrow to the plot\n",
|
||
|
" torque_angle = np.deg2rad(theta[p] - 90)\n",
|
||
|
" torque_x1 = x\n",
|
||
|
" torque_y1 = y\n",
|
||
|
" torque_x2 = x + 0.01 * np.cos(torque_angle)\n",
|
||
|
" torque_y2 = y + 0.01 * np.sin(torque_angle)\n",
|
||
|
" plt.arrow(\n",
|
||
|
" torque_x1,\n",
|
||
|
" torque_y1,\n",
|
||
|
" torque_x2 - torque_x1,\n",
|
||
|
" torque_y2 - torque_y1,\n",
|
||
|
" head_width=0.001,\n",
|
||
|
" head_length=0.002,\n",
|
||
|
" fc=\"k\",\n",
|
||
|
" ec=\"k\",\n",
|
||
|
" )\n",
|
||
|
"\n",
|
||
|
"\n",
|
||
|
"sweep_coil_cirlc(coil2, 19.5 / 1000)"
|
||
|
]
|
||
|
}
|
||
|
],
|
||
|
"metadata": {
|
||
|
"kernelspec": {
|
||
|
"display_name": "Python 3.10.7 ('venv': venv)",
|
||
|
"language": "python",
|
||
|
"name": "python3"
|
||
|
},
|
||
|
"language_info": {
|
||
|
"codemirror_mode": {
|
||
|
"name": "ipython",
|
||
|
"version": 3
|
||
|
},
|
||
|
"file_extension": ".py",
|
||
|
"mimetype": "text/x-python",
|
||
|
"name": "python",
|
||
|
"nbconvert_exporter": "python",
|
||
|
"pygments_lexer": "ipython3",
|
||
|
"version": "3.10.7"
|
||
|
},
|
||
|
"vscode": {
|
||
|
"interpreter": {
|
||
|
"hash": "1ce20143987840b9786ebb5907032c9c3a8efacbb887dbb0ebc4934f2ad26cb3"
|
||
|
}
|
||
|
}
|
||
|
},
|
||
|
"nbformat": 4,
|
||
|
"nbformat_minor": 2
|
||
|
}
|