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Trying out some new visualisations

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Chris Greening 2022-11-19 08:24:27 +00:00
parent dcc9f8f7ec
commit 3db8c78be0
16 changed files with 2889 additions and 300 deletions
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@ -160,4 +160,6 @@ cython_debug/
#.idea/
*.json
*.png
*.png
*.csv
*.vol

10
README.md
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@ -25,6 +25,10 @@ ln -s ${PWD}/coil_plugin.py ~/Documents/KiCad/6.0/scripting/plugins/coil_plugin.
The project is still very experimental - so there are no guarantees that these will work or do anything useful...
* 6 circular coils - https://www.pcbway.com/project/shareproject/Proof_of_concept_6_coil_spiral_PCB_stator_23ae7370.html
* 6 wedge coils - https://www.pcbway.com/project/shareproject/Proof_of_concept_6_coil_wedge_PCB_stator_c231a379.html
* 12 wedge coils - https://www.pcbway.com/project/shareproject/Proof_of_concept_12_coil_wedge_PCB_stator_c54d9374.html
- 6 circular coils - https://www.pcbway.com/project/shareproject/Proof_of_concept_6_coil_spiral_PCB_stator_23ae7370.html
- 6 wedge coils - https://www.pcbway.com/project/shareproject/Proof_of_concept_6_coil_wedge_PCB_stator_c231a379.html
- 12 wedge coils - https://www.pcbway.com/project/shareproject/Proof_of_concept_12_coil_wedge_PCB_stator_c54d9374.html
## Building python to take advantage of the M1 Mac Multiprocessors
https://www.reddit.com/r/Python/comments/qog8x3/if_you_are_using_apples_m1_macs_compiling_numpy/

212
coil_generator-12.ipynb
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@ -106,7 +106,10 @@
"SCREW_HOLE_RADIUS = STATOR_RADIUS\n",
"\n",
"# Coil params\n",
"# for custom shape\n",
"TURNS = 16\n",
"# for spiral\n",
"# TURNS = 17\n",
"COIL_CENTER_RADIUS = 19.95\n",
"COIL_VIA_RADIUS = 20.95"
]
@ -120,7 +123,12 @@
"# where to put the input pads\n",
"INPUT_PAD_RADIUS = STATOR_RADIUS - (PAD_WIDTH / 2 + VIA_DIAM + TRACK_SPACING)\n",
"\n",
"USE_SPIRAL = False\n",
"USE_SPIRAL = True\n",
"\n",
"if USE_SPIRAL:\n",
" TURNS = 18\n",
" COIL_VIA_RADIUS = 20.5\n",
" COIL_CENTER_RADIUS = 20.5\n",
"\n",
"LAYERS = 4"
]
@ -238,18 +246,63 @@
"metadata": {},
"outputs": [],
"source": [
"template_f = []\n",
"for i in range(len(template)):\n",
" template_f.append(template[len(template) - i - len(template) // 2])\n",
"template_f = flip_x(template_f)\n",
"points_f = chaikin(\n",
" optimize_points(flip_x(get_points(template_f, TURNS, TRACK_SPACING + TRACK_WIDTH))),\n",
" 2,\n",
")\n",
"points_b = chaikin(\n",
" optimize_points(get_points(template, TURNS, TRACK_SPACING + TRACK_WIDTH)), 2\n",
")\n",
"def get_spiral(turns, start_radius, thickness, layer=Layer.FRONT):\n",
" points = []\n",
" # create a starting point in the center\n",
" for angle in np.arange(0, turns * 360, 1):\n",
" radius = start_radius + thickness * angle / 360\n",
" if layer == Layer.BACK:\n",
" x = radius * np.cos(np.deg2rad(angle + 180))\n",
" y = radius * np.sin(np.deg2rad(angle + 180))\n",
" points.append((x, -y))\n",
" else:\n",
" x = radius * np.cos(np.deg2rad(angle))\n",
" y = radius * np.sin(np.deg2rad(angle))\n",
" points.append((x, y))\n",
" return points"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"if not USE_SPIRAL:\n",
" print(\"Not using spiral\")\n",
" template_f = []\n",
" for i in range(len(template)):\n",
" template_f.append(template[len(template) - i - len(template) // 2])\n",
" template_f = flip_x(template_f)\n",
" points_f = chaikin(\n",
" optimize_points(\n",
" flip_x(get_points(template_f, TURNS, TRACK_SPACING + TRACK_WIDTH))\n",
" ),\n",
" 2,\n",
" )\n",
" points_b = chaikin(\n",
" optimize_points(get_points(template, TURNS, TRACK_SPACING + TRACK_WIDTH)), 2\n",
" )\n",
"else:\n",
" print(\"Using spiral\")\n",
" points_f = get_spiral(\n",
" TURNS, VIA_DIAM / 2 + TRACK_SPACING, TRACK_SPACING + TRACK_WIDTH, Layer.FRONT\n",
" )\n",
" points_b = get_spiral(\n",
" TURNS, VIA_DIAM / 2 + TRACK_SPACING, TRACK_SPACING + TRACK_WIDTH, Layer.BACK\n",
" )\n",
"\n",
" points_f = [(0, 0)] + points_f\n",
" points_b = [(0, 0)] + points_b\n",
" print(\"Track points\", len(points_f), len(points_b))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"points_f = [(COIL_VIA_RADIUS - COIL_CENTER_RADIUS, 0)] + points_f\n",
"points_b = [(COIL_VIA_RADIUS - COIL_CENTER_RADIUS, 0)] + points_b\n",
"\n",
@ -262,6 +315,47 @@
"print(\"Track points\", len(points_f), len(points_b))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# write the coil out in a format that can be simulated\n",
"# rotate the points by 90 degrees so that the x axis is horizontal\n",
"pf = rotate(points_f, 90)\n",
"pb = rotate(points_b, 90)\n",
"fname = \"simulations/coils/coil_12_custom\"\n",
"if USE_SPIRAL:\n",
" fname = \"simulations/coils/coil_12_spiral\"\n",
"\n",
"# write the coil out in a format that can be simulated\n",
"p_f = rotate(points_f, 90)\n",
"p_b = rotate(points_b, 90)\n",
"\n",
"with open(fname + \".csv\", \"w\") as f:\n",
" for point in p_f[::-1]:\n",
" f.write(f\"{point[0]},{point[1]},0,0.5\\n\")\n",
"\n",
"# two layer board\n",
"with open(fname + \"-2-layer.csv\", \"wt\") as f:\n",
" for point in p_f[::-1]:\n",
" f.write(f\"{point[0]},{point[1]},0,0.5\\n\")\n",
" for point in p_b:\n",
" f.write(f\"{point[0]},{point[1]},0-0.062,0.5\\n\")\n",
"\n",
"# all four layer board\n",
"with open(fname + \"-4-layer.csv\", \"wt\") as f:\n",
" for point in p_f[::-1]:\n",
" f.write(f\"{point[0]},{point[1]},0,0.5\\n\")\n",
" for point in p_b:\n",
" f.write(f\"{point[0]},{point[1]},0-0.011,0.5\\n\")\n",
" for point in p_f[::-1]:\n",
" f.write(f\"{point[0]},{point[1]},0-(0.011+0.04),0.5\\n\")\n",
" for point in p_b:\n",
" f.write(f\"{point[0]},{point[1]},0-(0.011+0.011+0.04),0.5\\n\")"
]
},
{
"cell_type": "code",
"execution_count": null,
@ -270,39 +364,33 @@
"source": [
"# write the coil out in a format that can be simulated\n",
"# shift the coils aronnd to make connections a bit easier\n",
"COIL_ROTATION = -360 / 12\n",
"pf = rotate(points_f, 90)\n",
"pb = rotate(points_b, 90)\n",
"fname = \"simulations/coils/coil_12_custom\"\n",
"if USE_SPIRAL:\n",
" fname = \"simulations/coils/coil_12_spiral\"\n",
"\n",
"for i in range(12):\n",
" angle = i * 360 / 12 + COIL_ROTATION\n",
" p_f = scale(translate(rotate(points_f, angle), COIL_CENTER_RADIUS, angle), 0.1)\n",
" p_b = scale(translate(rotate(points_b, angle), COIL_CENTER_RADIUS, angle), 0.1)\n",
"with open(fname + \".csv\", \"w\") as f:\n",
" for point in pf:\n",
" f.write(f\"{point[0]/10},{point[1]/10},0,0.5\\n\")\n",
"\n",
" # we'll have positive current through the A coils, and negative current through the B coils\n",
" current = 0\n",
" if i % 3 == 0:\n",
" current = 0.5\n",
" elif i % 3 == 1:\n",
" current = -0.5\n",
"# two layer board\n",
"with open(fname + \"-2-layer.csv\", \"wt\") as f:\n",
" for point in pf[::-1]:\n",
" f.write(f\"{point[0]/10},{point[1]/10},0,0.5\\n\")\n",
" for point in pb:\n",
" f.write(f\"{point[0]/10},{point[1]/10},0-0.062,0.5\\n\")\n",
"\n",
" # two layer board\n",
" with open(f\"simulations/coil-2-{i}.txt\", \"wt\") as f:\n",
" for point in p_f[::-1]:\n",
" f.write(f\"{point[0]},{point[1]},0, {current}\\n\")\n",
" for point in p_b:\n",
" f.write(f\"{point[0]},{point[1]},0-0.62,{current}\\n\")\n",
"\n",
" # four layer board\n",
" with open(f\"simulations/coil-4-top-{i}.txt\", \"wt\") as f:\n",
" for point in p_f[::-1]:\n",
" f.write(f\"{point[0]},{point[1]},0,{current}\\n\")\n",
" for point in p_b:\n",
" f.write(f\"{point[0]},{point[1]},0-0.11,{current}\\n\")\n",
"\n",
" with open(f\"simulations/coil-4-bottom-{i}.txt\", \"wt\") as f:\n",
" for point in p_f[::-1]:\n",
" f.write(f\"{point[0]},{point[1]},0-(0.11+0.4),{current}\\n\")\n",
" for point in p_b:\n",
" f.write(f\"{point[0]},{point[1]},0-(0.11+0.11+0.4),{current}\\n\")"
"# all four layer board\n",
"with open(fname + \"-4-layer.csv\", \"wt\") as f:\n",
" for point in pf[::-1]:\n",
" f.write(f\"{point[0]/10},{point[1]/10},0,0.5\\n\")\n",
" for point in pb:\n",
" f.write(f\"{point[0]/10},{point[1]/10},0-0.011,0.5\\n\")\n",
" for point in pf[::-1]:\n",
" f.write(f\"{point[0]/10},{point[1]/10},0-(0.011+0.04),0.5\\n\")\n",
" for point in pb:\n",
" f.write(f\"{point[0]/10},{point[1]/10},0-(0.011+0.011+0.04),0.5\\n\")"
]
},
{
@ -538,35 +626,35 @@
"\n",
"outer_cuts = (\n",
" draw_arc(-45 + nibble_angle_size / 2, 45 - nibble_angle_size / 2, STATOR_RADIUS, 5)\n",
" # + translate(\n",
" # rotate(draw_arc(1, 179, SCREW_HOLE_DRILL_DIAM / 2, 5)[::-1], 135),\n",
" # STATOR_RADIUS,\n",
" # 45,\n",
" # )\n",
" + translate(\n",
" rotate(draw_arc(5, 175, SCREW_HOLE_DRILL_DIAM / 2, 5)[::-1], 135),\n",
" STATOR_RADIUS,\n",
" 45,\n",
" )\n",
" + draw_arc(\n",
" 45 + nibble_angle_size / 2, 135 - nibble_angle_size / 2, STATOR_RADIUS, 5\n",
" )\n",
" # + translate(\n",
" # rotate(draw_arc(1, 179, SCREW_HOLE_DRILL_DIAM / 2, 5), 225)[::-1],\n",
" # STATOR_RADIUS,\n",
" # 135,\n",
" # )\n",
" + translate(\n",
" rotate(draw_arc(5, 175, SCREW_HOLE_DRILL_DIAM / 2, 5), 225)[::-1],\n",
" STATOR_RADIUS,\n",
" 135,\n",
" )\n",
" + draw_arc(\n",
" 135 + nibble_angle_size / 2, 225 - nibble_angle_size / 2, STATOR_RADIUS, 5\n",
" )\n",
" # + translate(\n",
" # rotate(draw_arc(1, 179, SCREW_HOLE_DRILL_DIAM / 2, 5), 315)[::-1],\n",
" # STATOR_RADIUS,\n",
" # 225,\n",
" # )\n",
" + translate(\n",
" rotate(draw_arc(5, 175, SCREW_HOLE_DRILL_DIAM / 2, 5), 315)[::-1],\n",
" STATOR_RADIUS,\n",
" 225,\n",
" )\n",
" + draw_arc(\n",
" 225 + nibble_angle_size / 2, 315 - nibble_angle_size / 2, STATOR_RADIUS, 5\n",
" )\n",
" # + translate(\n",
" # rotate(draw_arc(1, 179, SCREW_HOLE_DRILL_DIAM / 2, 5), 45)[::-1],\n",
" # STATOR_RADIUS,\n",
" # 315,\n",
" # )\n",
" + translate(\n",
" rotate(draw_arc(5, 175, SCREW_HOLE_DRILL_DIAM / 2, 5), 45)[::-1],\n",
" STATOR_RADIUS,\n",
" 315,\n",
" )\n",
")\n",
"\n",
"edge_cuts = [\n",

132
coil_generator-6.ipynb
View file

@ -65,6 +65,7 @@
"# PCB Edge size\n",
"STATOR_RADIUS = 25\n",
"STATOR_HOLE_RADIUS = 5.5\n",
"HOLE_SPACE = 2\n",
"\n",
"# where to puth the mounting pins\n",
"SCREW_HOLE_DRILL_DIAM = 2.3 # 2.3mm drill for a 2mm screw\n",
@ -72,16 +73,41 @@
"\n",
"HOLE_SPACING = 0.25\n",
"\n",
"# where to put the input pads\n",
"INPUT_PAD_RADIUS = STATOR_RADIUS - (PAD_WIDTH / 2 + VIA_DIAM + TRACK_SPACING)\n",
"\n",
"# Coil params\n",
"TURNS = 26\n",
"COIL_CENTER_RADIUS = 15\n",
"COIL_VIA_RADIUS = 16\n",
"COIL_VIA_RADIUS = 15.3"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Large 30 mm version\n",
"\n",
"# where to place the pins\n",
"# CONNECTION_PINS_RADIUS = 16.5\n",
"# PCB Edge size\n",
"# STATOR_RADIUS = 30\n",
"\n",
"# # where to puth the mounting pins\n",
"# SCREW_HOLE_DRILL_DIAM = 2.3 # 2.3mm drill for a 2mm screw\n",
"# SCREW_HOLE_RADIUS = STATOR_RADIUS\n",
"\n",
"# # Coil params\n",
"# TURNS = 31\n",
"# COIL_CENTER_RADIUS = 19\n",
"# COIL_VIA_RADIUS = 19.3"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# where to put the input pads\n",
"INPUT_PAD_RADIUS = STATOR_RADIUS - (PAD_WIDTH / 2 + VIA_DIAM + TRACK_SPACING)\n",
"\n",
"USE_SPIRAL = False\n",
"\n",
@ -218,8 +244,8 @@
" optimize_points(get_points(template, TURNS, TRACK_SPACING + TRACK_WIDTH)), 2\n",
" )\n",
"\n",
" points_f = [(0, 0)] + points_f\n",
" points_b = [(0, 0)] + points_b\n",
" points_f = [(COIL_VIA_RADIUS - COIL_CENTER_RADIUS, 0)] + points_f\n",
" points_b = [(COIL_VIA_RADIUS - COIL_CENTER_RADIUS, 0)] + points_b\n",
"\n",
" df = pd.DataFrame(points_f, columns=[\"x\", \"y\"])\n",
" ax = df.plot.line(x=\"x\", y=\"y\", color=\"blue\")\n",
@ -237,27 +263,7 @@
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# write the coil out in a format that can be simulated\n",
"\n",
"# two layer board\n",
"with open(\"simulations/coil-2.txt\", \"wt\") as f:\n",
" for point in points_f[::-1]:\n",
" f.write(f\"{point[0]},{point[1]},0,0.5\\n\")\n",
" for point in points_b:\n",
" f.write(f\"{point[0]},{point[1]},0-0.62,0.5\\n\")\n",
"\n",
"# four layer board\n",
"with open(\"simulations/coil-4.txt\", \"wt\") as f:\n",
" for point in points_f[::-1]:\n",
" f.write(f\"{point[0]},{point[1]},0,0.5\\n\")\n",
" for point in points_b:\n",
" f.write(f\"{point[0]},{point[1]},0-0.11,0.5\\n\")\n",
" for point in points_f[::-1]:\n",
" f.write(f\"{point[0]},{point[1]},0-(0.11+0.4),0.5\\n\")\n",
" for point in points_b:\n",
" f.write(f\"{point[0]},{point[1]},0-(0.11+0.11+0.4),0.5\\n\")"
]
"source": []
},
{
"cell_type": "markdown",
@ -309,6 +315,50 @@
" print(\"Using template\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Write out coils for simulation"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# write the coil out in a format that can be simulated\n",
"# rotate the points by 90 degrees so that the x axis is horizontal\n",
"pf = rotate(points_f, 90)\n",
"pb = rotate(points_b, 90)\n",
"fname = \"simulations/coils/coil_6_custom\"\n",
"if USE_SPIRAL:\n",
" fname = \"simulations/coils/coil_6_spiral\"\n",
"\n",
"with open(fname + \".csv\", \"w\") as f:\n",
" for point in pf:\n",
" f.write(f\"{point[0]/10},{point[1]/10},0,0.5\\n\")\n",
"\n",
"# two layer board\n",
"with open(fname + \"-2-layer.csv\", \"wt\") as f:\n",
" for point in pf[::-1]:\n",
" f.write(f\"{point[0]/10},{point[1]/10},0,0.5\\n\")\n",
" for point in pb:\n",
" f.write(f\"{point[0]/10},{point[1]/10},0-0.062,0.5\\n\")\n",
"\n",
"# all four layer board\n",
"with open(fname + \"-4-layer.csv\", \"wt\") as f:\n",
" for point in pf[::-1]:\n",
" f.write(f\"{point[0]/10},{point[1]/10},0,0.5\\n\")\n",
" for point in pb:\n",
" f.write(f\"{point[0]/10},{point[1]/10},0-0.011,0.5\\n\")\n",
" for point in pf[::-1]:\n",
" f.write(f\"{point[0]/10},{point[1]/10},0-(0.011+0.04),0.5\\n\")\n",
" for point in pb:\n",
" f.write(f\"{point[0]/10},{point[1]/10},0-(0.011+0.011+0.04),0.5\\n\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
@ -403,12 +453,12 @@
"tracks_b.append(coil_C_opp_b)\n",
"\n",
"# connect the front and back coils together\n",
"vias.append(create_via(get_arc_point(angle_A, COIL_CENTER_RADIUS)))\n",
"vias.append(create_via(get_arc_point(angle_B, COIL_CENTER_RADIUS)))\n",
"vias.append(create_via(get_arc_point(angle_C, COIL_CENTER_RADIUS)))\n",
"vias.append(create_via(get_arc_point(angle_A_opp, COIL_CENTER_RADIUS)))\n",
"vias.append(create_via(get_arc_point(angle_B_opp, COIL_CENTER_RADIUS)))\n",
"vias.append(create_via(get_arc_point(angle_C_opp, COIL_CENTER_RADIUS)))\n",
"vias.append(create_via(get_arc_point(angle_A, COIL_VIA_RADIUS)))\n",
"vias.append(create_via(get_arc_point(angle_B, COIL_VIA_RADIUS)))\n",
"vias.append(create_via(get_arc_point(angle_C, COIL_VIA_RADIUS)))\n",
"vias.append(create_via(get_arc_point(angle_A_opp, COIL_VIA_RADIUS)))\n",
"vias.append(create_via(get_arc_point(angle_B_opp, COIL_VIA_RADIUS)))\n",
"vias.append(create_via(get_arc_point(angle_C_opp, COIL_VIA_RADIUS)))\n",
"\n",
"# connect the front copper opposite coils together\n",
"common_connection_radius = SCREW_HOLE_RADIUS - (\n",
@ -426,7 +476,7 @@
"# vias.append(create_via(get_arc_point(angle_C_opp, common_connection_radius)))\n",
"\n",
"# wires for connecting to opposite coils\n",
"connection_radius1 = STATOR_HOLE_RADIUS + (2 * TRACK_SPACING)\n",
"connection_radius1 = STATOR_HOLE_RADIUS + (2 * TRACK_SPACING + HOLE_SPACING)\n",
"connection_radius2 = connection_radius1 + (2 * TRACK_SPACING + VIA_DIAM / 2)\n",
"\n",
"# draw a 45 degree line from each coil at connection radius 1\n",
@ -556,7 +606,7 @@
"outer_cuts = (\n",
" draw_arc(-45 + nibble_angle_size / 2, 45 - nibble_angle_size / 2, STATOR_RADIUS, 5)\n",
" + translate(\n",
" rotate(draw_arc(1, 179, SCREW_HOLE_DRILL_DIAM / 2, 5)[::-1], 135),\n",
" rotate(draw_arc(5, 175, SCREW_HOLE_DRILL_DIAM / 2, 5)[::-1], 135),\n",
" STATOR_RADIUS,\n",
" 45,\n",
" )\n",
@ -564,7 +614,7 @@
" 45 + nibble_angle_size / 2, 135 - nibble_angle_size / 2, STATOR_RADIUS, 5\n",
" )\n",
" + translate(\n",
" rotate(draw_arc(1, 179, SCREW_HOLE_DRILL_DIAM / 2, 5), 225)[::-1],\n",
" rotate(draw_arc(5, 175, SCREW_HOLE_DRILL_DIAM / 2, 5), 225)[::-1],\n",
" STATOR_RADIUS,\n",
" 135,\n",
" )\n",
@ -572,7 +622,7 @@
" 135 + nibble_angle_size / 2, 225 - nibble_angle_size / 2, STATOR_RADIUS, 5\n",
" )\n",
" + translate(\n",
" rotate(draw_arc(1, 179, SCREW_HOLE_DRILL_DIAM / 2, 5), 315)[::-1],\n",
" rotate(draw_arc(5, 175, SCREW_HOLE_DRILL_DIAM / 2, 5), 315)[::-1],\n",
" STATOR_RADIUS,\n",
" 225,\n",
" )\n",
@ -580,7 +630,7 @@
" 225 + nibble_angle_size / 2, 315 - nibble_angle_size / 2, STATOR_RADIUS, 5\n",
" )\n",
" + translate(\n",
" rotate(draw_arc(1, 179, SCREW_HOLE_DRILL_DIAM / 2, 5), 45)[::-1],\n",
" rotate(draw_arc(5, 175, SCREW_HOLE_DRILL_DIAM / 2, 5), 45)[::-1],\n",
" STATOR_RADIUS,\n",
" 315,\n",
" )\n",
@ -593,7 +643,7 @@
"\n",
"# dump out the json version\n",
"json_result = dump_json(\n",
" filename=\"coils_6.json\",\n",
" filename=f\"coils_6_{STATOR_RADIUS}.json\",\n",
" track_width=TRACK_WIDTH,\n",
" pin_diam=PIN_DIAM,\n",
" pin_drill=PIN_DRILL,\n",

579
coil_generator-radial.ipynb Normal file
View file

@ -0,0 +1,579 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"\n",
"import matplotlib.pyplot as plt\n",
"from skspatial.objects import LineSegment, Line, Vector\n",
"\n",
"# some helper functions\n",
"from helpers import (\n",
" get_arc_point,\n",
" draw_arc,\n",
" rotate,\n",
" translate,\n",
" flip_y,\n",
" flip_x,\n",
" optimize_points,\n",
" chaikin,\n",
" rotate_point,\n",
" scale,\n",
")\n",
"from pcb_json import (\n",
" dump_json,\n",
" plot_json,\n",
" create_via,\n",
" create_pad,\n",
" create_pin,\n",
" create_track,\n",
" create_silk,\n",
" create_silk,\n",
" create_mounting_hole,\n",
")\n",
"\n",
"from enum import Enum\n",
"\n",
"Layer = Enum(\"Layer\", \"FRONT BACK\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Track width and spacing\n",
"TRACK_WIDTH = 0.127\n",
"TRACK_SPACING = 0.127\n",
"\n",
"# via defaults\n",
"VIA_DIAM = 0.8\n",
"VIA_DRILL = 0.4\n",
"\n",
"# this is for a 1.27mm pitch pin\n",
"PIN_DIAM = 1.0\n",
"PIN_DRILL = 0.65\n",
"\n",
"# this is for the PCB connector - see https://www.farnell.com/datasheets/2003059.pdf\n",
"PAD_WIDTH = 3\n",
"PAD_HEIGHT = 2\n",
"PAD_PITCH = 2.5\n",
"\n",
"STATOR_HOLE_RADIUS = 5.5\n",
"HOLE_SPACING = 0.25"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Standard 25 mm version\n",
"\n",
"# PCB Edge size\n",
"STATOR_RADIUS = 25\n",
"STATOR_HOLE_RADIUS = 5.5\n",
"\n",
"# where to puth the mounting pins\n",
"SCREW_HOLE_DRILL_DIAM = 2.3 # 2.3mm drill for a 2mm screw\n",
"SCREW_HOLE_RADIUS = STATOR_RADIUS\n",
"\n",
"# Coil params\n",
"TURNS = 12\n",
"COIL_CENTER_RADIUS = 16\n",
"COIL_VIA_RADIUS = 17"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Large 30 mm version\n",
"\n",
"# PCB Edge size\n",
"STATOR_RADIUS = 30\n",
"\n",
"# where to puth the mounting pins\n",
"SCREW_HOLE_DRILL_DIAM = 2.3 # 2.3mm drill for a 2mm screw\n",
"SCREW_HOLE_RADIUS = STATOR_RADIUS\n",
"\n",
"# Coil params\n",
"TURNS = 16\n",
"COIL_CENTER_RADIUS = 19.95\n",
"COIL_VIA_RADIUS = 20.95"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# where to put the input pads\n",
"INPUT_PAD_RADIUS = STATOR_RADIUS - (PAD_WIDTH / 2 + VIA_DIAM + TRACK_SPACING)\n",
"\n",
"USE_SPIRAL = False\n",
"\n",
"LAYERS = 4"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Radial coil generator"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def get_points(spacing, inner_radius, outer_radius, start_angle, end_angle):\n",
" # first calculate the angle step size from the spacing and the inner_radius\n",
" spacing_angle = np.rad2deg(np.arctan2(spacing, inner_radius))\n",
" print(spacing_angle)\n",
" # now calculate the points be iterating from start_angle to end_angle with the spacing_angle\n",
" points = []\n",
" for angle in np.arange(start_angle, end_angle, spacing_angle * 2):\n",
" points.append(get_arc_point(angle, inner_radius))\n",
" points.append(get_arc_point(angle, outer_radius))\n",
" points.append(\n",
" (\n",
" get_arc_point(angle, outer_radius)[0],\n",
" get_arc_point(angle, outer_radius)[1] + spacing,\n",
" )\n",
" )\n",
" points.append(get_arc_point(angle + spacing_angle, inner_radius))\n",
" return points"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"points_f = get_points(\n",
" TRACK_SPACING + TRACK_WIDTH,\n",
" (COIL_CENTER_RADIUS - 10),\n",
" COIL_CENTER_RADIUS + 10,\n",
" -15,\n",
" 15,\n",
")\n",
"\n",
"df = pd.DataFrame(points_f, columns=[\"x\", \"y\"])\n",
"ax = df.plot.line(x=\"x\", y=\"y\", color=\"blue\")\n",
"ax.axis(\"equal\")\n",
"\n",
"# calculat the total length of the track to compute the resistance\n",
"total_length_front = 0\n",
"for i in range(len(points_f) - 1):\n",
" total_length_front += np.linalg.norm(\n",
" np.array(points_f[i + 1]) - np.array(points_f[i])\n",
" )\n",
"print(\"Total length front\", total_length_front)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"spacing = TRACK_SPACING + TRACK_WIDTH\n",
"inner_radius = COIL_CENTER_RADIUS - 10\n",
"outer_radius = COIL_CENTER_RADIUS + 10\n",
"start_angle = -15\n",
"end_angle = 15\n",
"# first calculate the angle step size from the spacing and the inner_radius\n",
"spacing_angle = np.rad2deg(np.arctan2(spacing, inner_radius))\n",
"# now calculate the points be iterating from start_angle to end_angle with the spacing_angle\n",
"i = 0\n",
"count = (end_angle - start_angle) // spacing_angle\n",
"print(spacing_angle, count)\n",
"# for angle in np.arange(start_angle, end_angle, spacing_angle):\n",
"for angle in [start_angle, end_angle]:\n",
" i = i + 1\n",
" current = 1\n",
" if i == 2:\n",
" current = -1\n",
" with open(f\"simulations/radial_{i}.csv\", \"w\") as f:\n",
" points = [\n",
" get_arc_point(angle, inner_radius),\n",
" get_arc_point(angle, outer_radius),\n",
" ]\n",
" points = translate(rotate(points, 90), -22.5, 90)\n",
" for point in points:\n",
" f.write(f\"{point[0]}/10,{point[1]}/10,0,{current}\\n\")\n",
"\n",
"\n",
"# # write the coil out in a format that can be simulated\n",
"p_f = translate(rotate(points_f, 90), -22.5, 90)\n",
"p_b = translate(rotate(points_f, 90), -22.5, 90)\n",
"\n",
"# df = pd.DataFrame(p_f, columns=[\"x\", \"y\"])\n",
"# ax = df.plot.line(x=\"x\", y=\"y\", color=\"blue\")\n",
"# ax.axis(\"equal\")\n",
"\n",
"with open(\"simulations/coils/coil_rad.csv\", \"w\") as f:\n",
" for point in p_f:\n",
" f.write(f\"{point[0]},{point[1]},0,0.5\\n\")\n",
"\n",
"# two layer board\n",
"with open(\"simulations/coils/coil-rad-2-layer.csv\", \"wt\") as f:\n",
" for point in p_f:\n",
" f.write(f\"{point[0]},{point[1]},0,0.5\\n\")\n",
" for point in p_b:\n",
" f.write(f\"{point[0]},{point[1]},{0-0.062},0.5\\n\")\n",
"\n",
"# all four layer board\n",
"with open(\"simulations/coils/coil-rad-4-layer.csv\", \"wt\") as f:\n",
" for point in p_f:\n",
" f.write(f\"{point[0]},{point[1]},0,0.5\\n\")\n",
" for point in p_b:\n",
" f.write(f\"{point[0]},{point[1]},{0-0.011},0.5\\n\")\n",
" for point in p_f:\n",
" f.write(f\"{point[0]},{point[1]},{0-(0.011+0.04)},0.5\\n\")\n",
" for point in p_b:\n",
" f.write(f\"{point[0]},{point[1]},{0-(0.011+0.011+0.04)},0.5\\n\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Generate PCB Layout"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# calculat the total length of the track to compute the resistance\n",
"total_length_front = 0\n",
"for i in range(len(points_f) - 1):\n",
" total_length_front += np.linalg.norm(\n",
" np.array(points_f[i + 1]) - np.array(points_f[i])\n",
" )\n",
"print(\"Total length front\", total_length_front)\n",
"\n",
"total_length_back = 0\n",
"for i in range(len(points_b) - 1):\n",
" total_length_back += np.linalg.norm(\n",
" np.array(points_b[i + 1]) - np.array(points_b[i])\n",
" )\n",
"print(\"Total length back\", total_length_back)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"vias = []\n",
"tracks_f = []\n",
"tracks_b = []\n",
"pads = []\n",
"pins = []\n",
"mounting_holes = []\n",
"silk = []\n",
"\n",
"\n",
"# shift the coils aronnd to make connections a bit easier\n",
"COIL_ROTATION = -360 / 12\n",
"\n",
"coil_angles = []\n",
"for i in range(12):\n",
" angle = i * 360 / 12 + COIL_ROTATION\n",
" coil_angles.append(angle)\n",
"\n",
"# the main coils\n",
"coil_labels = [\"A\", \"B\", \"C\"]\n",
"coils_f = []\n",
"coils_b = []\n",
"for i in range(12):\n",
" angle = coil_angles[i]\n",
" if (i // 3) % 2 == 0:\n",
" coil_A_f = translate(rotate(points_f, angle), COIL_CENTER_RADIUS, angle)\n",
" coil_A_b = translate(rotate(points_b, angle), COIL_CENTER_RADIUS, angle)\n",
" else:\n",
" # slightly nudge the coils so that they don't overlap when flipped\n",
" coil_A_f = translate(rotate(flip_y(points_f), angle), COIL_CENTER_RADIUS, angle)\n",
" coil_A_b = translate(rotate(flip_y(points_b), angle), COIL_CENTER_RADIUS, angle)\n",
" # keep track of the coils\n",
" coils_f.append(coil_A_f)\n",
" coils_b.append(coil_A_b)\n",
"\n",
" tracks_f.append(coil_A_f)\n",
" tracks_b.append(coil_A_b)\n",
" vias.append(create_via(get_arc_point(angle, COIL_VIA_RADIUS)))\n",
" silk.append(\n",
" create_silk(get_arc_point(angle, COIL_CENTER_RADIUS), coil_labels[i % 3])\n",
" )\n",
"\n",
"# raidus for connecting the bottoms of the coils together\n",
"connection_radius1 = STATOR_HOLE_RADIUS + 3 * TRACK_SPACING\n",
"\n",
"# create tracks to link the A coils around the center\n",
"connection_via_radius_A = connection_radius1 + 3 * TRACK_SPACING + VIA_DIAM / 2\n",
"coil_A1_A2_inner = (\n",
" [get_arc_point(coil_angles[0], connection_via_radius_A)]\n",
" + draw_arc(COIL_ROTATION, coil_angles[3], connection_radius1)\n",
" + [get_arc_point(coil_angles[3], connection_via_radius_A)]\n",
")\n",
"tracks_f.append(coil_A1_A2_inner)\n",
"coil_A3_A4_inner = (\n",
" [get_arc_point(coil_angles[6], connection_via_radius_A)]\n",
" + draw_arc(coil_angles[6], coil_angles[9], connection_radius1)\n",
" + [get_arc_point(coil_angles[9], connection_via_radius_A)]\n",
")\n",
"tracks_f.append(coil_A3_A4_inner)\n",
"# connect up the bottoms of the A coils\n",
"coils_b[0].append(coil_A1_A2_inner[0])\n",
"coils_b[3].append(coil_A1_A2_inner[-1])\n",
"coils_b[6].append(coil_A3_A4_inner[0])\n",
"coils_b[9].append(coil_A3_A4_inner[-1])\n",
"# add the vias to stitch them together\n",
"vias.append(create_via(coil_A1_A2_inner[0]))\n",
"vias.append(create_via(coil_A1_A2_inner[-1]))\n",
"vias.append(create_via(coil_A3_A4_inner[0]))\n",
"vias.append(create_via(coil_A3_A4_inner[-1]))\n",
"\n",
"# create tracks to link the B coils around the center - this can all be done on the bottom layer\n",
"coil_B1_B2_inner = draw_arc(coil_angles[1], coil_angles[4], connection_radius1)\n",
"tracks_b.append(coil_B1_B2_inner)\n",
"coil_B3_B4_inner = draw_arc(coil_angles[7], coil_angles[10], connection_radius1)\n",
"tracks_b.append(coil_B3_B4_inner)\n",
"# connect up the bottoms of the A coils\n",
"coils_b[1].append(coil_B1_B2_inner[0])\n",
"coils_b[4].append(coil_B1_B2_inner[-1])\n",
"coils_b[7].append(coil_B3_B4_inner[0])\n",
"coils_b[10].append(coil_B3_B4_inner[-1])\n",
"\n",
"# create tracks to link the C coils around the center\n",
"connection_via_radius_C = connection_via_radius_A + 3 * TRACK_SPACING + VIA_DIAM / 2\n",
"coil_C1_C2_inner = draw_arc(coil_angles[2], coil_angles[5], connection_via_radius_C)\n",
"tracks_f.append(coil_C1_C2_inner)\n",
"coil_C3_C4_inner = draw_arc(coil_angles[8], coil_angles[11], connection_via_radius_C)\n",
"tracks_f.append(coil_C3_C4_inner)\n",
"# connect up the bottoms of the B coils\n",
"coils_b[2].append(coil_C1_C2_inner[0])\n",
"coils_b[5].append(coil_C1_C2_inner[-1])\n",
"coils_b[8].append(coil_C3_C4_inner[0])\n",
"coils_b[11].append(coil_C3_C4_inner[-1])\n",
"# add the vias to stitch them together\n",
"vias.append(create_via(coil_C1_C2_inner[0]))\n",
"vias.append(create_via(coil_C1_C2_inner[-1]))\n",
"vias.append(create_via(coil_C3_C4_inner[0]))\n",
"vias.append(create_via(coil_C3_C4_inner[-1]))\n",
"\n",
"# connect the last three coils together\n",
"common_connection_radius = SCREW_HOLE_RADIUS - (SCREW_HOLE_DRILL_DIAM / 2 + 0.5)\n",
"tracks_f.append(draw_arc(coil_angles[9], coil_angles[11], common_connection_radius))\n",
"coils_f[9].append(get_arc_point(coil_angles[9], common_connection_radius))\n",
"coils_f[10].append(get_arc_point(coil_angles[10], common_connection_radius))\n",
"coils_f[11].append(get_arc_point(coil_angles[11], common_connection_radius))\n",
"\n",
"# connect the outer A coils together\n",
"outer_connection_radius_A = SCREW_HOLE_RADIUS - (SCREW_HOLE_DRILL_DIAM / 2 + 0.5)\n",
"tracks_f.append(draw_arc(coil_angles[3], coil_angles[6], outer_connection_radius_A))\n",
"coils_f[3].append(get_arc_point(coil_angles[3], outer_connection_radius_A))\n",
"coils_f[6].append(get_arc_point(coil_angles[6], outer_connection_radius_A))\n",
"\n",
"# connect the outer B coils together\n",
"outer_connection_radius_B = outer_connection_radius_A - TRACK_SPACING - VIA_DIAM / 2\n",
"tracks_b.append(\n",
" [get_arc_point(coil_angles[4], outer_connection_radius_B)]\n",
" + draw_arc(coil_angles[4], coil_angles[7], outer_connection_radius_A)\n",
" + [get_arc_point(coil_angles[7], outer_connection_radius_B)]\n",
")\n",
"coils_f[4].append(get_arc_point(coil_angles[4], outer_connection_radius_B))\n",
"coils_f[7].append(get_arc_point(coil_angles[7], outer_connection_radius_B))\n",
"vias.append(\n",
" create_via(get_arc_point(4 * 360 / 12 + COIL_ROTATION, outer_connection_radius_B))\n",
")\n",
"vias.append(\n",
" create_via(get_arc_point(7 * 360 / 12 + COIL_ROTATION, outer_connection_radius_B))\n",
")\n",
"\n",
"# connect the outer C coilds together\n",
"outer_connection_radius_C = outer_connection_radius_B - TRACK_SPACING - VIA_DIAM / 2\n",
"tracks_b.append(\n",
" draw_arc(\n",
" 5 * 360 / 12 + COIL_ROTATION,\n",
" 8 * 360 / 12 + COIL_ROTATION,\n",
" outer_connection_radius_C,\n",
" )\n",
")\n",
"coils_f[5].append(\n",
" get_arc_point(5 * 360 / 12 + COIL_ROTATION, outer_connection_radius_C)\n",
")\n",
"coils_f[8].append(\n",
" get_arc_point(8 * 360 / 12 + COIL_ROTATION, outer_connection_radius_C)\n",
")\n",
"vias.append(\n",
" create_via(get_arc_point(5 * 360 / 12 + COIL_ROTATION, outer_connection_radius_C))\n",
")\n",
"vias.append(\n",
" create_via(get_arc_point(8 * 360 / 12 + COIL_ROTATION, outer_connection_radius_C))\n",
")\n",
"\n",
"# create the pads for connecting the inputs to the coils\n",
"silk.append(\n",
" create_silk((INPUT_PAD_RADIUS - PAD_HEIGHT - 2.5, PAD_PITCH), \"C\", \"b\", 2.5, -900)\n",
")\n",
"silk.append(create_silk((INPUT_PAD_RADIUS - PAD_HEIGHT - 2.5, 0), \"B\", \"b\", 2.5, -900))\n",
"silk.append(\n",
" create_silk((INPUT_PAD_RADIUS - PAD_HEIGHT - 2.5, -PAD_PITCH), \"A\", \"b\", 2.5, -900)\n",
")\n",
"\n",
"pads.append(create_pad((INPUT_PAD_RADIUS, -PAD_PITCH), PAD_WIDTH, PAD_HEIGHT, \"b\"))\n",
"pads.append(create_pad((INPUT_PAD_RADIUS, 0), PAD_WIDTH, PAD_HEIGHT, \"b\"))\n",
"pads.append(create_pad((INPUT_PAD_RADIUS, PAD_PITCH), PAD_WIDTH, PAD_HEIGHT, \"b\"))\n",
"\n",
"# connect coil A to the top pad\n",
"pad_connection_point_x = INPUT_PAD_RADIUS\n",
"pad_angle = np.rad2deg(np.arcsin(PAD_PITCH / pad_connection_point_x))\n",
"coils_f[0].append(get_arc_point(coil_angles[0], pad_connection_point_x))\n",
"vias.append(create_via(get_arc_point(coil_angles[0], pad_connection_point_x)))\n",
"# connect coil B to the middle pad\n",
"coils_f[1].append((pad_connection_point_x + PAD_WIDTH / 2 + VIA_DIAM / 2, 0))\n",
"vias.append(create_via(((pad_connection_point_x + PAD_WIDTH / 2 + VIA_DIAM / 2, 0))))\n",
"# connect coil C to the bottom pad\n",
"coils_f[2].append(get_arc_point(coil_angles[2], pad_connection_point_x))\n",
"vias.append(create_via(get_arc_point(coil_angles[2], pad_connection_point_x)))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# if we are doing four layers then duplicate the front and back layers on (front and inner1), (inner2 and back)\n",
"tracks_in1 = []\n",
"tracks_in2 = []\n",
"if LAYERS == 4:\n",
" tracks_in1 = tracks_b.copy()\n",
" tracks_in2 = tracks_f.copy()\n",
"\n",
"# these final bits of wiring up to the input pads don't need to be duplicated\n",
"tracks_b.append(\n",
" [(pad_connection_point_x + PAD_WIDTH / 2, 0), (pad_connection_point_x, 0)]\n",
")\n",
"tracks_b.append(draw_arc(coil_angles[0], -pad_angle, pad_connection_point_x, 1))\n",
"tracks_b.append(draw_arc(coil_angles[2], pad_angle, pad_connection_point_x, 1))\n",
"\n",
"nibble_angle_size = 360 * SCREW_HOLE_DRILL_DIAM / (2 * np.pi * STATOR_RADIUS)\n",
"\n",
"outer_cuts = (\n",
" draw_arc(-45 + nibble_angle_size / 2, 45 - nibble_angle_size / 2, STATOR_RADIUS, 5)\n",
" + translate(\n",
" rotate(draw_arc(5, 175, SCREW_HOLE_DRILL_DIAM / 2, 5)[::-1], 135),\n",
" STATOR_RADIUS,\n",
" 45,\n",
" )\n",
" + draw_arc(\n",
" 45 + nibble_angle_size / 2, 135 - nibble_angle_size / 2, STATOR_RADIUS, 5\n",
" )\n",
" + translate(\n",
" rotate(draw_arc(5, 175, SCREW_HOLE_DRILL_DIAM / 2, 5), 225)[::-1],\n",
" STATOR_RADIUS,\n",
" 135,\n",
" )\n",
" + draw_arc(\n",
" 135 + nibble_angle_size / 2, 225 - nibble_angle_size / 2, STATOR_RADIUS, 5\n",
" )\n",
" + translate(\n",
" rotate(draw_arc(5, 175, SCREW_HOLE_DRILL_DIAM / 2, 5), 315)[::-1],\n",
" STATOR_RADIUS,\n",
" 225,\n",
" )\n",
" + draw_arc(\n",
" 225 + nibble_angle_size / 2, 315 - nibble_angle_size / 2, STATOR_RADIUS, 5\n",
" )\n",
" + translate(\n",
" rotate(draw_arc(5, 175, SCREW_HOLE_DRILL_DIAM / 2, 5), 45)[::-1],\n",
" STATOR_RADIUS,\n",
" 315,\n",
" )\n",
")\n",
"\n",
"edge_cuts = [\n",
" outer_cuts,\n",
" draw_arc(0, 360, STATOR_HOLE_RADIUS, 1),\n",
"]\n",
"\n",
"# dump out the json version\n",
"json_result = dump_json(\n",
" filename=f\"coils_12_{STATOR_RADIUS}mm.json\",\n",
" track_width=TRACK_WIDTH,\n",
" pin_diam=PIN_DIAM,\n",
" pin_drill=PIN_DRILL,\n",
" via_diam=VIA_DIAM,\n",
" via_drill=VIA_DRILL,\n",
" vias=vias,\n",
" pins=pins,\n",
" pads=pads,\n",
" silk=silk,\n",
" tracks_f=tracks_f,\n",
" tracks_in1=tracks_in1,\n",
" tracks_in2=tracks_in2,\n",
" tracks_b=tracks_b,\n",
" mounting_holes=mounting_holes,\n",
" edge_cuts=edge_cuts,\n",
")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# plot the json\n",
"plot_json(json_result)"
]
}
],
"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
}

29
coil_plugin.py
View file

@ -188,5 +188,34 @@ class CoilPlugin(pcbnew.ActionPlugin):
ec.SetPolyPoints(v)
board.Add(ec)
# put it on the solder mask as well - who knows why...
for edge_cut in coil_data["edgeCuts"]:
ec = pcbnew.PCB_SHAPE(board)
ec.SetShape(pcbnew.SHAPE_T_POLY)
ec.SetFilled(False)
ec.SetLayer(pcbnew.F_Mask)
ec.SetWidth(int(0.1 * pcbnew.IU_PER_MM))
v = pcbnew.wxPoint_Vector()
for point in edge_cut:
x = point["x"] + CENTER_X
y = point["y"] + CENTER_Y
v.append(pcbnew.wxPointMM(x, y))
ec.SetPolyPoints(v)
board.Add(ec)
for edge_cut in coil_data["edgeCuts"]:
ec = pcbnew.PCB_SHAPE(board)
ec.SetShape(pcbnew.SHAPE_T_POLY)
ec.SetFilled(False)
ec.SetLayer(pcbnew.B_Mask)
ec.SetWidth(int(0.1 * pcbnew.IU_PER_MM))
v = pcbnew.wxPoint_Vector()
for point in edge_cut:
x = point["x"] + CENTER_X
y = point["y"] + CENTER_Y
v.append(pcbnew.wxPointMM(x, y))
ec.SetPolyPoints(v)
board.Add(ec)
CoilPlugin().register() # Instantiate and register to Pcbnew])

8
requirements.txt
View file

@ -3,4 +3,10 @@ jupyter
numpy
pandas
scikit-spatial
pre-commit
pre-commit
tqdm
plotly
magpylib
pyvista
mayavi
PySide

BIN
simulations/.DS_Store vendored Normal file
View file

Binary file not shown.

545
simulations/biot_savart_v4_3.py
View file

@ -1,4 +1,4 @@
'''
"""
Biot-Savart Magnetic Field Calculator v4.3
Mingde Yin
Ryan Zazo
@ -6,7 +6,7 @@ Ryan Zazo
All lengths are in cm, B-field is in G
from - https://github.com/vuthalab/biot-savart
'''
"""
import numpy as np
import matplotlib.pyplot as plt
@ -14,17 +14,18 @@ from mpl_toolkits.mplot3d import Axes3D
import matplotlib.cm as cm
import matplotlib.ticker as ticker
'''
"""
Feature Wishlist:
improve plot_coil with different colors for different values of current
accelerate integrator to use meshgrids directly instead of a layer of for loop
get parse_coil to use vectorized function instead of for loop
'''
"""
def parse_coil(filename):
'''
"""
Parses 4 column CSV into x,y,z,I slices for coil.
Each (x,y,z,I) entry defines a vertex on the coil.
@ -35,157 +36,219 @@ def parse_coil(filename):
- There are 2 amps of current running between points 1 and 2
- There are 3 amps of current running between points 2 and 3
- The last bit of current is functionally useless.
'''
with open(filename, "r") as f: return np.array([[eval(i) for i in line.split(",")] for line in f.read().splitlines()]).T
"""
with open(filename, "r") as f:
return np.array(
[[eval(i) for i in line.split(",")] for line in f.read().splitlines()]
).T
def slice_coil(coil, steplength):
'''
"""
Slices a coil into pieces of size steplength.
If the coil is already sliced into pieces smaller than that, this does nothing.
'''
"""
def interpolate_points(p1, p2, parts):
'''
"""
Produces a series of linearly spaced points between two given points in R3+I
Linearly interpolates X,Y,Z; but keeps I the SAME
i.e. (0, 2, 1, 3), (3, 4, 2, 5), parts = 2:
(0, 2, 1, 3), (1.5, 3, 1.5, 3), (3, 4, 2, 5)
'''
return np.column_stack((np.linspace(p1[0], p2[0], parts+1), np.linspace(p1[1], p2[1], parts+1),
np.linspace(p1[2], p2[2], parts+1), p1[3] * np.ones((parts+1))))
"""
return np.column_stack(
(
np.linspace(p1[0], p2[0], parts + 1),
np.linspace(p1[1], p2[1], parts + 1),
np.linspace(p1[2], p2[2], parts + 1),
p1[3] * np.ones((parts + 1)),
)
)
newcoil = np.zeros((1, 4)) # fill column with dummy data, we will remove this later.
newcoil = np.zeros(
(1, 4)
) # fill column with dummy data, we will remove this later.
segment_starts = coil[:,:-1]
segment_ends = coil[:,1:]
segment_starts = coil[:, :-1]
segment_ends = coil[:, 1:]
# determine start and end of each segment
segments = segment_ends-segment_starts
segments = segment_ends - segment_starts
segment_lengths = np.apply_along_axis(np.linalg.norm, 0, segments)
# create segments; determine start and end of each segment, as well as segment lengths
# chop up into smaller bits (elements)
stepnumbers = (segment_lengths/steplength).astype(int)
stepnumbers = (segment_lengths / steplength).astype(int)
# determine how many steps we must chop each segment into
for i in range(segments.shape[1]):
newrows = interpolate_points(segment_starts[:,i], segment_ends[:,i], stepnumbers[i])
newrows = interpolate_points(
segment_starts[:, i], segment_ends[:, i], stepnumbers[i]
)
# set of new interpolated points to feed in
newcoil = np.vstack((newcoil, newrows))
if newcoil.shape[0] %2 != 0: newcoil = np.vstack((newcoil, newcoil[-1,:]))
if newcoil.shape[0] % 2 != 0:
newcoil = np.vstack((newcoil, newcoil[-1, :]))
## Force the coil to have an even number of segments, for Richardson Extrapolation to work
return newcoil[1:,:].T # return non-dummy columns
return newcoil[1:, :].T # return non-dummy columns
def calculate_field(coil, x, y, z):
'''
"""
Calculates magnetic field vector as a result of some position and current x, y, z, I
[In the same coordinate system as the coil]
Coil: Input Coil Positions, already sub-divided into small pieces using slice_coil
x, y, z: position in cm
Output B-field is a 3-D vector in units of G
'''
FACTOR = 0.1 # = mu_0 / 4pi when lengths are in cm, and B-field is in G
"""
FACTOR = 0.1 # = mu_0 / 4pi when lengths are in cm, and B-field is in G
def bs_integrate(start, end):
'''
"""
Produces tiny segment of magnetic field vector (dB) using the midpoint approximation over some interval
TODO for future optimization: Get this to work with meshgrids directly
'''
dl = (end-start).T
mid = (start+end)/2
position = np.array((x-mid[0], y-mid[1], z-mid[2])).T
"""
dl = (end - start).T
mid = (start + end) / 2
position = np.array((x - mid[0], y - mid[1], z - mid[2])).T
# relative position vector
mag = np.sqrt((x-mid[0])**2 + (y-mid[1])**2 + (z-mid[2])**2)
mag = np.sqrt((x - mid[0]) ** 2 + (y - mid[1]) ** 2 + (z - mid[2]) ** 2)
# magnitude of the relative position vector
return start[3] * np.cross(dl[:3], position) / np.array((mag ** 3, mag ** 3, mag ** 3)).T
return (
start[3]
* np.cross(dl[:3], position)
/ np.array((mag**3, mag**3, mag**3)).T
)
# Apply the Biot-Savart Law to get the differential magnetic field
# current flowing in this segment is represented by start[3]
B = 0
# midpoint integration with 1 layer of Richardson Extrapolation
starts, mids, ends = coil[:,:-1:2], coil[:,1::2], coil[:,2::2]
starts, mids, ends = coil[:, :-1:2], coil[:, 1::2], coil[:, 2::2]
for start, mid, end in np.nditer([starts, mids, ends], flags=['external_loop'], order='F'):
for start, mid, end in np.nditer(
[starts, mids, ends], flags=["external_loop"], order="F"
):
# use numpy fast indexing
fullpart = bs_integrate(start, end) # stage 1 richardson
halfpart = bs_integrate(start, mid) + bs_integrate(mid, end) # stage 2 richardson
fullpart = bs_integrate(start, end) # stage 1 richardson
halfpart = bs_integrate(start, mid) + bs_integrate(
mid, end
) # stage 2 richardson
B += (
4 / 3 * halfpart - 1 / 3 * fullpart
) # richardson extrapolated midpoint rule
return (
B * FACTOR
) # return SUM of all components as 3 (x,y,z) meshgrids for (Bx, By, Bz) component when evaluated using produce_target_volume
B += 4/3 * halfpart - 1/3 * fullpart # richardson extrapolated midpoint rule
return B * FACTOR # return SUM of all components as 3 (x,y,z) meshgrids for (Bx, By, Bz) component when evaluated using produce_target_volume
def produce_target_volume(coil, box_size, start_point, vol_resolution):
'''
Generates a set of field vector values for each tuple (x, y, z) in the box.
​
Coil: Input Coil Positions in format specified above, already sub-divided into small pieces
box_size: (x, y, z) dimensions of the box in cm
start_point: (x, y, z) = (0, 0, 0) = bottom left corner position of the box
vol_resolution: Spatial resolution (in cm)
'''
x = np.linspace(start_point[0], box_size[0] + start_point[0],int(box_size[0]/vol_resolution)+1)
y = np.linspace(start_point[1], box_size[1] + start_point[1],int(box_size[1]/vol_resolution)+1)
z = np.linspace(start_point[2], box_size[2] + start_point[2],int(box_size[2]/vol_resolution)+1)
"""
Generates a set of field vector values for each tuple (x, y, z) in the box.
​
Coil: Input Coil Positions in format specified above, already sub-divided into small pieces
box_size: (x, y, z) dimensions of the box in cm
start_point: (x, y, z) = (0, 0, 0) = bottom left corner position of the box
vol_resolution: Spatial resolution (in cm)
"""
x = np.linspace(
start_point[0],
box_size[0] + start_point[0],
int(box_size[0] / vol_resolution) + 1,
)
y = np.linspace(
start_point[1],
box_size[1] + start_point[1],
int(box_size[1] / vol_resolution) + 1,
)
z = np.linspace(
start_point[2],
box_size[2] + start_point[2],
int(box_size[2] / vol_resolution) + 1,
)
# Generate points at regular spacing, incl. end points
Z, Y, X = np.meshgrid(z, y, x, indexing='ij')
Z, Y, X = np.meshgrid(z, y, x, indexing="ij")
# NOTE: Requires axes to be flipped in order for meshgrid to have the correct dimensional order
return calculate_field(coil, X,Y,Z)
return calculate_field(coil, X, Y, Z)
def get_field_vector(targetVolume, position, start_point, volume_resolution):
'''
"""
Returns the B vector [Bx, By, Bz] components in a generated Target Volume at a given position tuple (x, y, z) in a coordinate system
start_point: (x, y, z) = (0, 0, 0) = bottom left corner position of the box
volume_resolution: Division of volumetric meshgrid (generate a point every volume_resolution cm)
'''
relativePosition = ((np.array(position) - np.array(start_point)) / volume_resolution).astype(int)
"""
relativePosition = (
(np.array(position) - np.array(start_point)) / volume_resolution
).astype(int)
# adjust to the meshgrid's system
if (relativePosition < 0).any(): return ("ERROR: Out of bounds! (negative indices)")
if (relativePosition < 0).any():
return "ERROR: Out of bounds! (negative indices)"
try: return targetVolume[relativePosition[0], relativePosition[1], relativePosition[2], :]
except: return ("ERROR: Out of bounds!")
try:
return targetVolume[
relativePosition[0], relativePosition[1], relativePosition[2], :
]
except:
return "ERROR: Out of bounds!"
# basic error checking to see if you actually got a correct input/output
'''
"""
- If you are indexing a targetvolume meshgrid on your own, remember to account for the offset (starting point), and spatial resolution
- You will need an index like <relativePosition = ((np.array(position) - np.array(start_point)) / volume_resolution).astype(int)>
'''
"""
def write_target_volume(input_filename,output_filename, box_size, start_point,
coil_resolution=1, volume_resolution=1):
'''
def write_target_volume(
input_filename,
output_filename,
box_size,
start_point,
coil_resolution=1,
volume_resolution=1,
):
"""
Takes a coil specified in input_filename, generates a target volume, and saves the generated target volume to output_filename.
box_size: (x, y, z) dimensions of the box in cm
start_point: (x, y, z) = (0, 0, 0) = bottom left corner position of the box AKA the offset
coil_resolution: How long each coil subsegment should be
volume_resolution: Division of volumetric meshgrid (generate a point every volume_resolution cm)
'''
coil = parse_coil(input_filename)
"""
coil = parse_coil(input_filename)
chopped = slice_coil(coil, coil_resolution)
targetVolume = produce_target_volume(chopped, box_size, start_point, volume_resolution)
targetVolume = produce_target_volume(
chopped, box_size, start_point, volume_resolution
)
with open(output_filename, "wb") as f: np.save(f, targetVolume)
with open(output_filename, "wb") as f:
np.save(f, targetVolume)
# stored in standard numpy pickle form
def read_target_volume(filename):
'''
"""
Takes the name of a saved target volume and loads the B vector meshgrid.
Returns None if not found.
'''
"""
targetVolume = None
try:
@ -195,12 +258,22 @@ def read_target_volume(filename):
except:
pass
## plotting routines
def plot_fields(Bfields,box_size,start_point,vol_resolution,which_plane='z',level=0,num_contours=50):
'''
Plots the set of Bfields in the given region, at the specified resolutions.
def plot_fields(
Bfields,
box_size,
start_point,
vol_resolution,
which_plane="z",
level=0,
num_contours=50,
):
"""
Plots the set of Bfields in the given region, at the specified resolutions.
Bfields: A 4D array of the Bfield.
box_size: (x, y, z) dimensions of the box in cm
start_point: (x, y, z) = (0, 0, 0) = bottom left corner position of the box AKA the offset
@ -208,269 +281,367 @@ def plot_fields(Bfields,box_size,start_point,vol_resolution,which_plane='z',leve
which_plane: Plane to plot on, can be "x", "y" or "z"
level : The "height" of the plane. For instance the Z = 5 plane would have a level of 5
num_contours: THe amount of contours on the contour plot.
'''
"""
# filled contour plot of Bx, By, and Bz on a chosen slice plane
X = np.linspace(start_point[0], box_size[0] + start_point[0],int(box_size[0]/vol_resolution)+1)
Y = np.linspace(start_point[1], box_size[1] + start_point[1],int(box_size[1]/vol_resolution)+1)
Z = np.linspace(start_point[2], box_size[2] + start_point[2],int(box_size[2]/vol_resolution)+1)
X = np.linspace(
start_point[0],
box_size[0] + start_point[0],
int(box_size[0] / vol_resolution) + 1,
)
Y = np.linspace(
start_point[1],
box_size[1] + start_point[1],
int(box_size[1] / vol_resolution) + 1,
)
Z = np.linspace(
start_point[2],
box_size[2] + start_point[2],
int(box_size[2] / vol_resolution) + 1,
)
print(Z)
if which_plane=='x':
if which_plane == "x":
converted_level = np.where(X >= level)
B_sliced = [Bfields[converted_level[0][0],:,:,i].T for i in range(3)]
x_label,y_label = "y","z"
x_array,y_array = Y,Z
elif which_plane=='y':
B_sliced = [Bfields[converted_level[0][0], :, :, i].T for i in range(3)]
x_label, y_label = "y", "z"
x_array, y_array = Y, Z
elif which_plane == "y":
converted_level = np.where(Y >= level)
B_sliced = [Bfields[:,converted_level[0][0],:,i].T for i in range(3)]
x_label,y_label = "x","z"
x_array,y_array = X,Z
B_sliced = [Bfields[:, converted_level[0][0], :, i].T for i in range(3)]
x_label, y_label = "x", "z"
x_array, y_array = X, Z
else:
converted_level = np.where(Z >= level)
print(converted_level[0][0])
B_sliced = [Bfields[:,:,converted_level[0][0],i].T for i in range(3)]
x_label,y_label = "x","y"
x_array,y_array = X,Y
Bmin,Bmax = np.amin(B_sliced),np.amax(B_sliced)
component_labels = ['x','y','z']
fig,axes = plt.subplots(nrows=4,ncols=1,figsize=(10,40))
B_sliced = [Bfields[:, :, converted_level[0][0], i].T for i in range(3)]
x_label, y_label = "x", "y"
x_array, y_array = X, Y
Bmin, Bmax = np.amin(B_sliced), np.amax(B_sliced)
component_labels = ["x", "y", "z"]
fig, axes = plt.subplots(nrows=4, ncols=1, figsize=(10, 40))
axes[0].set_ylabel(y_label + " (cm)")
for i in range(3):
contours = axes[i].contourf(x_array,y_array,B_sliced[i],
vmin=Bmin,vmax=Bmax,
cmap=cm.magma,levels=num_contours)
contours = axes[i].contourf(
x_array,
y_array,
B_sliced[i],
vmin=Bmin,
vmax=Bmax,
cmap=cm.magma,
levels=num_contours,
)
axes[i].set_xlabel(x_label + " (cm)")
axes[i].set_title("$\mathcal{B}$"+"$_{}$".format(component_labels[i]))
axes[i].set_title("$\mathcal{B}$" + "$_{}$".format(component_labels[i]))
axes[3].set_aspect(100)
fig.colorbar(contours,cax=axes[3],extend='both')
fig.colorbar(contours, cax=axes[3], extend="both")
plt.tight_layout()
plt.show()
return plt
def plot_coil(*input_filenames):
'''
"""
Plots one or more coils in space.
input_filenames: Name of the files containing the coils.
input_filenames: Name of the files containing the coils.
Should be formatted appropriately.
'''
"""
fig = plt.figure()
tick_spacing = 2
ax = fig.add_subplot(111, projection='3d')
ax = fig.add_subplot(111, projection="3d")
ax.set_xlabel("$x$ (cm)")
ax.set_ylabel("$y$ (cm)")
ax.set_zlabel("$z$ (cm)")
for input_filename in input_filenames:
coil_points = np.array(parse_coil(input_filename))
ax.plot3D(coil_points[0,:],coil_points[1,:],coil_points[2,:],lw=2)
for axis in [ax.xaxis,ax.yaxis,ax.zaxis]:
ax.plot3D(
coil_points[0, :], coil_points[1, :], coil_points[2, :], lw=2, color="red"
)
for axis in [ax.xaxis, ax.yaxis, ax.zaxis]:
axis.set_major_locator(ticker.MultipleLocator(tick_spacing))
plt.tight_layout()
# set the size of the plot
fig.set_size_inches(10, 10)
plt.show()
def create_B_x_rectangle(name,p0=[-21.59,-38.1,-21.59,1],L = 76.20,W= 43.18):
'''
# save the plot
fig.savefig("coil.png", dpi=300)
def plot_coil2(coil_points):
"""
Plots one or more coils in space.
input_filenames: Name of the files containing the coils.
Should be formatted appropriately.
"""
fig = plt.figure()
tick_spacing = 2
ax = fig.add_subplot(111, projection="3d")
ax.set_xlabel("$x$ (cm)")
ax.set_ylabel("$y$ (cm)")
ax.set_zlabel("$z$ (cm)")
coil_points = np.array(coil_points)
ax.plot3D(
coil_points[0, :], coil_points[1, :], coil_points[2, :], lw=2, color="red"
)
for axis in [ax.xaxis, ax.yaxis, ax.zaxis]:
axis.set_major_locator(ticker.MultipleLocator(tick_spacing))
plt.tight_layout()
# set the size of the plot
fig.set_size_inches(5, 5)
plt.show()
def create_B_x_rectangle(name, p0=[-21.59, -38.1, -21.59, 1], L=76.20, W=43.18):
"""
Creates a rectangle of the Y-Z plane that produces a B_x field.
name: filename to output to. Should be a .txt file.
p0: [x0,y0,z0,Current] Starting point of the rectangle.
L: Length (on Z)
W: Width (on y)
'''
f = open(name,"w")
p1 = [p0[0],p0[1]+W,p0[2],p0[3]]
p2 = [p0[0],p0[1]+W,p0[2]+L ,p0[3]]
p3 = [p0[0],p0[1],p0[2]+L,p0[3]]
"""
f = open(name, "w")
p1 = [p0[0], p0[1] + W, p0[2], p0[3]]
p2 = [p0[0], p0[1] + W, p0[2] + L, p0[3]]
p3 = [p0[0], p0[1], p0[2] + L, p0[3]]
line = str(p0)
line = line[1:len(line)-1] + "\n"
line = line[1 : len(line) - 1] + "\n"
f.write(line)
line = str(p1)
line = line[1:len(line)-1] + "\n"
line = line[1 : len(line) - 1] + "\n"
f.write(line)
line = str(p2)
line = line[1:len(line)-1] + "\n"
line = line[1 : len(line) - 1] + "\n"
f.write(line)
line = str(p3)
line = line[1:len(line)-1] + "\n"
line = line[1 : len(line) - 1] + "\n"
f.write(line)
line = str(p0)
line = line[1:len(line)-1] + "\n"
line = line[1 : len(line) - 1] + "\n"
f.write(line)
f.close()
def create_B_y_rectangle(name,p0=[-21.59,-38.1,-21.59,1], L = 76.20, D= 43.18):
def create_B_y_rectangle(name, p0=[-21.59, -38.1, -21.59, 1], L=76.20, D=43.18):
'''
"""
Creates a rectangle of the X-Z plane that produces a B_y field.
name: filename to output to. Should be a .txt file.
p0: [x0,y0,z0,Current] Starting point of the rectangle.
L: Length (on Z)
D: Depth (on X)
'''
f = open(name,"w")
"""
f = open(name, "w")
p1 = [p0[0], p0[1] , p0[2]+L, p0[3]]
p2 = [p0[0] + D , p0[1] , p0[2]+L, p0[3]]
p3 = [p0[0] + D , p0[1], p0[2], p0[3]]
p1 = [p0[0], p0[1], p0[2] + L, p0[3]]
p2 = [p0[0] + D, p0[1], p0[2] + L, p0[3]]
p3 = [p0[0] + D, p0[1], p0[2], p0[3]]
line = str(p0)
line = line[1:len(line)-1] + "\n"
line = line[1 : len(line) - 1] + "\n"
f.write(line)
line = str(p1)
line = line[1:len(line)-1] + "\n"
line = line[1 : len(line) - 1] + "\n"
f.write(line)
line = str(p2)
line = line[1:len(line)-1] + "\n"
line = line[1 : len(line) - 1] + "\n"
f.write(line)
line = str(p3)
line = line[1:len(line)-1] + "\n"
line = line[1 : len(line) - 1] + "\n"
f.write(line)
line = str(p0)
line = line[1:len(line)-1] + "\n"
line = line[1 : len(line) - 1] + "\n"
f.write(line)
f.close()
def create_B_z_rectangle(name,p0=[-26.67,-26.67,-26.67,1], H= 53.340, DD = 53.340):
'''
def create_B_z_rectangle(name, p0=[-26.67, -26.67, -26.67, 1], H=53.340, DD=53.340):
"""
Creates a rectangle of the X-Y plane that produces a B_z field.
name: filename to output to. Should be a .txt file.
p0: [x0,y0,z0,Current] Starting point of the rectangle.
H: Height (on Y)
DD: Depth (on X)
'''
f = open(name,"w")
"""
f = open(name, "w")
p1 = [p0[0] + DD, p0[1], p0[2], p0[3]]
p2 = [p0[0] + DD, p0[1]+H, p0[2], p0[3]]
p3 = [p0[0], p0[1]+H, p0[2], p0[3]]
p2 = [p0[0] + DD, p0[1] + H, p0[2], p0[3]]
p3 = [p0[0], p0[1] + H, p0[2], p0[3]]
line = str(p0)
line = line[1:len(line)-1] + "\n"
line = line[1 : len(line) - 1] + "\n"
f.write(line)
line = str(p1)
line = line[1:len(line)-1] + "\n"
line = line[1 : len(line) - 1] + "\n"
f.write(line)
line = str(p2)
line = line[1:len(line)-1] + "\n"
line = line[1 : len(line) - 1] + "\n"
f.write(line)
line = str(p3)
line = line[1:len(line)-1] + "\n"
line = line[1 : len(line) - 1] + "\n"
f.write(line)
line = str(p0)
line = line[1:len(line)-1] + "\n"
line = line[1 : len(line) - 1] + "\n"
f.write(line)
f.close()
def helmholtz_coils(fname1, fname2, numSegments, radius, spacing, current):
'''
"""
Creates a pair of Helmholtz Coils that are parallel to the X-Y plane.
fname1: Name of the file where the first coil will be saved.
fname2: Name of the file where the second coil will be saved.
numSegments: Number of segments per coil
radius: Radius of the coils
spacing: Spacing between the coils. The first coil will be located at -spacing/2 and the 2nd coil will be located at spacing/2 on the Z plane
current: The current that goest through each coil.
'''
f = open(fname1,"w")
"""
f = open(fname1, "w")
line = ""
for i in range(0,numSegments,1):
line = str(np.cos(2*np.pi*(i)/(numSegments-1))*radius) + "," + str(np.sin(2*np.pi*(i)/(numSegments-1))*radius) + "," + str(-spacing/2.0) + "," + str(current) + "\n"
for i in range(0, numSegments, 1):
line = (
str(np.cos(2 * np.pi * (i) / (numSegments - 1)) * radius)
+ ","
+ str(np.sin(2 * np.pi * (i) / (numSegments - 1)) * radius)
+ ","
+ str(-spacing / 2.0)
+ ","
+ str(current)
+ "\n"
)
f.write(line)
f.close()
f = open(fname2,"w")
f = open(fname2, "w")
line = ""
for i in range(0,numSegments,1):
line = str(np.cos(2*np.pi*(i)/(numSegments-1))*radius) + "," + str(np.sin(2*np.pi*(i)/(numSegments-1))*radius) + "," + str(spacing/2.0) + "," + str(current) + "\n"
for i in range(0, numSegments, 1):
line = (
str(np.cos(2 * np.pi * (i) / (numSegments - 1)) * radius)
+ ","
+ str(np.sin(2 * np.pi * (i) / (numSegments - 1)) * radius)
+ ","
+ str(spacing / 2.0)
+ ","
+ str(current)
+ "\n"
)
f.write(line)
f.close()
def create_Bx_circle(fname, numSegments, radius, spacing, current, center):
'''
"""
Creates a coil on the Y-Z plane that produces a B_x field.
fname: Name of the file where the first coil will be saved.
numSegments: Number of segments per coil
radius: Radius of the coil
spacing: Spacing between the coil and the Y-Z plane
current: The current that goest through the coil.
center: (y,z) The center of the coil on the Y-Z plane
'''
f = open(fname,"w")
"""
f = open(fname, "w")
line = ""
for i in range(0,numSegments,1):
line = str(spacing) + "," + str(np.cos(2*np.pi*(i)/(numSegments-1))*radius + center[0]) + "," + str(np.sin(2*np.pi*(i)/(numSegments-1))*radius + center[1]) + "," + str(current) + "\n"
for i in range(0, numSegments, 1):
line = (
str(spacing)
+ ","
+ str(np.cos(2 * np.pi * (i) / (numSegments - 1)) * radius + center[0])
+ ","
+ str(np.sin(2 * np.pi * (i) / (numSegments - 1)) * radius + center[1])
+ ","
+ str(current)
+ "\n"
)
f.write(line)
f.close()
def create_By_circle(fname, numSegments, radius, spacing, current, center):
'''
"""
Creates a coil on the X-Z plane that produces a B_y field.
fname: Name of the file where the first coil will be saved.
numSegments: Number of segments per coil
radius: Radius of the coil
spacing: Spacing between the coil and the X-Z plane
current: The current that goest through the coil.
center: (x,z) The center of the coil on the X-Z plane
'''
f = open(fname,"w")
"""
f = open(fname, "w")
line = ""
for i in range(0,numSegments,1):
line = str(np.cos(2*np.pi*(i)/(numSegments-1))*radius + center[0]) + "," + str(spacing) + "," + str(np.sin(2*np.pi*(i)/(numSegments-1))*radius + center[1]) + "," + str(current) + "\n"
for i in range(0, numSegments, 1):
line = (
str(np.cos(2 * np.pi * (i) / (numSegments - 1)) * radius + center[0])
+ ","
+ str(spacing)
+ ","
+ str(np.sin(2 * np.pi * (i) / (numSegments - 1)) * radius + center[1])
+ ","
+ str(current)
+ "\n"
)
f.write(line)
f.close()
def create_Bz_circle(fname, numSegments, radius, spacing, current, center):
'''
"""
Creates a coil on the X-Y plane that produces a B_z field.
fname: Name of the file where the first coil will be saved.
numSegments: Number of segments per coil
radius: Radius of the coil
spacing: Spacing between the coil and the X-Y plane
current: The current that goest through the coil.
center: (x,y) The center of the coil on the X-Y plane
'''
f = open(fname,"w")
"""
f = open(fname, "w")
line = ""
for i in range(0,numSegments,1):
line = str(np.cos(2*np.pi*(i)/(numSegments-1))*radius + center[0]) + "," + str(np.sin(2*np.pi*(i)/(numSegments-1))*radius + center[1]) + "," + str(spacing) + "," + str(current) + "\n"
for i in range(0, numSegments, 1):
line = (
str(np.cos(2 * np.pi * (i) / (numSegments - 1)) * radius + center[0])
+ ","
+ str(np.sin(2 * np.pi * (i) / (numSegments - 1)) * radius + center[1])
+ ","
+ str(spacing)
+ ","
+ str(current)
+ "\n"
)
f.write(line)
f.close()

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simulations/compare_coil_fields.ipynb Normal file
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{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import biot_savart_v4_3 as bs\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# set the size larger\n",
"plt.rcParams[\"figure.figsize\"] = (10, 10)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# COIL_NAME = \"coil_6_spiral\"\n",
"# COIL_NAME = \"coil_6_custom\"\n",
"# COIL_NAME = \"coil_12_spiral\"\n",
"COIL_NAME = \"coil_12_custom\"\n",
"COIL = \"coils/\" + COIL_NAME + \".csv\""
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"bs.plot_coil(COIL)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"bs.write_target_volume(\n",
" COIL,\n",
" COIL_NAME + \"volume.vol\",\n",
" (4, 4, 4),\n",
" (-2, -2, -2),\n",
" 0.1,\n",
" 0.1,\n",
")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# read in the results\n",
"total_volume = bs.read_target_volume(COIL_NAME + \"volume.vol\")\n",
"\n",
"total_volume = total_volume\n",
"\n",
"# reads the volume we created\n",
"bs.plot_fields(total_volume, (4, 4, 4), (-2, -2, -2), 0.1, which_plane=\"z\", level=0.1)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import plotly.graph_objects as go\n",
"\n",
"X, Y, Z = np.mgrid[-2:2:41j, -2:2:41j, -2:2:41j]\n",
"# values = np.sqrt(total_volume[:,:,:,0]*total_volume[:,:,:,0] +\n",
"# total_volume[:,:,:,1]*total_volume[:,:,:,1] +\n",
"# total_volume[:,:,:,2]*total_volume[:,:,:,2])\n",
"values = total_volume[:, :, :, 2]\n",
"fig = go.Figure(\n",
" data=go.Volume(\n",
" x=X.flatten(),\n",
" y=Y.flatten(),\n",
" z=Z.flatten(),\n",
" value=np.abs(values.flatten()),\n",
" isomin=0.1,\n",
" isomax=0.5,\n",
" opacity=0.1, # needs to be small to see through all surfaces\n",
" surface_count=17, # needs to be a large number for good volume rendering\n",
" )\n",
")\n",
"\n",
"coil = bs.parse_coil(\"coils/\" + COIL_NAME + \".csv\")\n",
"coil = coil[0:3, :]\n",
"# add the coil as a line plot\n",
"fig.add_trace(\n",
" go.Scatter3d(\n",
" x=coil[0, :],\n",
" y=coil[1, :],\n",
" z=coil[2, :],\n",
" mode=\"lines\",\n",
" line=dict(color=\"red\", width=5),\n",
" )\n",
")\n",
"# make the plotly graph bigger\n",
"fig.update_layout(\n",
" autosize=False,\n",
" width=1400,\n",
" height=1000,\n",
")\n",
"fig.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"slice = [total_volume[:, 21, :, i].T for i in range(3)]\n",
"x_contour = slice[0]\n",
"y_contour = slice[1]\n",
"z_contour = slice[2]\n",
"\n",
"print(x_contour.shape)\n",
"print(y_contour.shape)\n",
"print(z_contour.shape)\n",
"\n",
"x = np.arange(0, x_contour.shape[0], 1)\n",
"y = np.arange(0, z_contour.shape[1], 1)\n",
"xG, yG = np.meshgrid(x, y)\n",
"\n",
"# calclulate the magnitude of the field\n",
"mag = np.sqrt(x_contour**2 + y_contour**2 + z_contour**2)\n",
"\n",
"# color = 2 * np.log(np.hypot(x_contour, z_contour))\n",
"color = np.log(mag)\n",
"stream_plot = plt.streamplot(\n",
" x,\n",
" y,\n",
" x_contour,\n",
" z_contour,\n",
" color=color,\n",
" linewidth=1,\n",
" cmap=plt.cm.Reds,\n",
" density=2,\n",
" arrowstyle=\"->\",\n",
" arrowsize=1.5,\n",
")\n",
"# set the axis to be equal\n",
"plt.axis(\"equal\")\n",
"\n",
"# set the plt size to 5x5\n",
"plt.rcParams[\"figure.figsize\"] = (10, 10)\n",
"\n",
"# save the figure\n",
"plt.savefig(COIL_NAME + \"_field_lines.png\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.cm as cm\n",
"\n",
"# get the total left and right field in the X direction\n",
"slice = [total_volume[:, :, 21, i].T for i in range(3)]\n",
"x_contour = slice[0]\n",
"y_contour = slice[1]\n",
"z_contour = slice[2]\n",
"\n",
"# vmin = np.min([np.min(x_contour), np.min(z_contour), np.min(y_contour)])\n",
"# vmax = np.max([np.max(x_contour), np.max(z_contour), np.max(y_contour)])\n",
"\n",
"vmin = np.min(x_contour)\n",
"vmax = np.max(x_contour)\n",
"\n",
"# -7.970943527635176 7.775784181783158\n",
"vmin = -7.970943527635176\n",
"vmax = 7.775784181783158\n",
"\n",
"print(vmin, vmax)\n",
"\n",
"left_x = np.sum(x_contour[x_contour < 0])\n",
"right_x = np.sum(x_contour[x_contour > 0])\n",
"\n",
"print(\"Left X: \", left_x)\n",
"print(\"Right X: \", right_x)\n",
"\n",
"plt.rcParams[\"figure.figsize\"] = (5, 5)\n",
"\n",
"# make the plot larger\n",
"plt.rcParams[\"figure.figsize\"] = (10, 10)\n",
"\n",
"# plt.imshow(x_contour, cmap='hot', interpolation='nearest')\n",
"plt.contourf(\n",
" x_contour,\n",
" vmin=vmin,\n",
" vmax=vmax,\n",
" cmap=cm.magma,\n",
" levels=50,\n",
")\n",
"\n",
"plt.savefig(COIL_NAME + \"_field_x.png\")\n",
"\n",
"print(vmin, vmax)\n",
"\n",
"# 6 coil custom\n",
"# Left X: -565.6790142743889\n",
"# Right X: 544.1011578804321\n",
"\n",
"# 6 coil spiral\n",
"# Left X: -512.1107132193335\n",
"# Right X: 534.1946450523811\n",
"\n",
"# 12 coil spiral\n",
"# Left X: -218.54696343677543\n",
"# Right X: 233.84835661493196\n",
"\n",
"# 12 coil custom\n",
"# Left X: -361.95894587646944\n",
"# Right X: 347.13174239269904"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# plot the magitude of the slice\n",
"plt.imshow(np.log(mag), cmap=\"hot\", interpolation=\"nearest\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"slice = [total_volume[:, :, 25, i].T for i in range(3)]\n",
"x_contour = slice[0]\n",
"y_contour = slice[1]\n",
"z_contour = slice[2]\n",
"\n",
"mag = np.sqrt(x_contour**2 + y_contour**2 + z_contour**2)\n",
"\n",
"print(np.max(mag), np.min(mag))\n",
"\n",
"# plot a histogram of the magnitude\n",
"# plt.hist(mag.flatten(), bins=10)\n",
"\n",
"plt.hist(z_contour.flatten(), bins=10)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# show the z contour as a 3d surface plot\n",
"fig = plt.figure()\n",
"\n",
"# change the figure size to 16.9\n",
"ax = fig.add_subplot(111, projection=\"3d\")\n",
"\n",
"xG_ = xG[10:30, 10:30]\n",
"yG_ = yG[10:30, 10:30]\n",
"z_contour_ = z_contour[10:30, 10:30]\n",
"\n",
"print(xG.shape, yG.shape, z_contour.shape)\n",
"\n",
"# change the axis limits to 10 to 30\n",
"ax.set_xlim(10, 30)\n",
"ax.set_ylim(10, 30)\n",
"surf = ax.plot_surface(\n",
" xG_, yG_, z_contour_, cmap=cm.plasma, linewidth=0, antialiased=False, alpha=0.5\n",
")\n",
"# add the coil to the plot as a set of lines - the X and Y coordinates of the coil are in the first two elements of the coil array\n",
"coil = bs.parse_coil(\"coils/\" + COIL_NAME + \".csv\")\n",
"coil = coil[0:2, :]\n",
"# need to scale the coil by 10 and shift it by 20, 20\n",
"coil = coil * 10 + 20\n",
"# draw the coil in yellow\n",
"ax.plot(coil[0, :], coil[1, :], 0, color=\"black\")\n",
"\n",
"# hide the axes\n",
"ax.set_axis_off()\n",
"\n",
"# save to png\n",
"plt.savefig(COIL_NAME + \"_field_surface_z.png\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# write out the coil as SVG\n",
"coil = bs.parse_coil(\"coils/\" + COIL_NAME + \".csv\")\n",
"coil = coil[0:2, :]\n",
"with open(COIL_NAME + \"_coil.svg\", \"w\") as f:\n",
" # write the header\n",
" f.write('<svg viewBox=\"0 0 400 400\" xmlns=\"http://www.w3.org/2000/svg\">')\n",
" # the X and Y points of the coil the X and Y coordinates of the coil are in the first two elements of the coil array\n",
" # write out the coil as a set of lines\n",
" print(len(coil[0]) - 1)\n",
" # write out the coil as a polyline\n",
" f.write('<polyline points=\"')\n",
" for i in range(0, len(coil[0]), 10):\n",
" f.write(str(coil[0, i] * 100 + 200) + \",\" + str(coil[1, i] * 100 + 200) + \" \")\n",
" f.write('\" style=\"fill:none;stroke:black;stroke-width:1\" />')\n",
" # write the footer\n",
" f.write(\"</svg>\")"
]
}
],
"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
}

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simulations/helpers.py Normal file
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import numpy as np
# get the point on an arc at the given angle
def get_arc_point(angle, radius):
return (
radius * np.cos(np.deg2rad(angle)),
radius * np.sin(np.deg2rad(angle)),
)
# draw an arc
def draw_arc(start_angle, end_angle, radius, step=5):
# make sure start_angle is less then end_angle
if start_angle > end_angle:
start_angle, end_angle = end_angle, start_angle
points = []
for angle in np.arange(start_angle, end_angle, step):
x = radius * np.cos(np.deg2rad(angle))
y = radius * np.sin(np.deg2rad(angle))
points.append((x, y))
if angle != end_angle:
x = radius * np.cos(np.deg2rad(end_angle))
y = radius * np.sin(np.deg2rad(end_angle))
points.append((x, y))
return points
# roate the points by the required angle
def rotate(points, angle):
return [
[
x * np.cos(np.deg2rad(angle)) - y * np.sin(np.deg2rad(angle)),
x * np.sin(np.deg2rad(angle)) + y * np.cos(np.deg2rad(angle)),
]
for x, y in points
]
def scale(points, scale):
return [[x * scale, y * scale] for x, y in points]
# rotate a point
def rotate_point(x, y, angle, ox=0, oy=0):
x -= ox
y -= oy
qx = x * np.cos(np.deg2rad(angle)) - y * np.sin(np.deg2rad(angle))
qy = x * np.sin(np.deg2rad(angle)) + y * np.cos(np.deg2rad(angle))
qx += ox
qy += oy
return qx, qy
# move the points out to the distance at the requited angle
def translate(points, distance, angle):
return [
[
x + distance * np.cos(np.deg2rad(angle)),
y + distance * np.sin(np.deg2rad(angle)),
]
for x, y in points
]
# flip the y coordinate
def flip_y(points):
return [[x, -y] for x, y in points]
def flip_x(points):
return [[-x, y] for x, y in points]
def optimize_points(points):
# follow the line and remove points that are in the same direction as the previous poin
# keep doing this until the direction changes significantly
# this is a very simple optimization that removes a lot of points
# it's not perfect but it's a good start
optimized_points = []
for i in range(len(points)):
if i == 0:
optimized_points.append(points[i])
else:
vector1 = np.array(points[i]) - np.array(points[i - 1])
vector2 = np.array(points[(i + 1) % len(points)]) - np.array(points[i])
length1 = np.linalg.norm(vector1)
length2 = np.linalg.norm(vector2)
if length1 > 0 and length2 > 0:
dot = np.dot(vector1, vector2) / (length1 * length2)
# clamp dot between -1 and 1
dot = max(-1, min(1, dot))
angle = np.arccos(dot)
if angle > np.deg2rad(5):
optimized_points.append(points[i])
print("Optimised from {} to {} points".format(len(points), len(optimized_points)))
return optimized_points
def chaikin(points, iterations):
if iterations == 0:
return points
l = len(points)
smoothed = []
for i in range(l - 1):
x1, y1 = points[i]
x2, y2 = points[i + 1]
smoothed.append([0.95 * x1 + 0.05 * x2, 0.95 * y1 + 0.05 * y2])
smoothed.append([0.05 * x1 + 0.95 * x2, 0.05 * y1 + 0.95 * y2])
smoothed.append(points[l - 1])
return chaikin(smoothed, iterations - 1)

607
simulations/magnet_field.ipynb Normal file
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@ -0,0 +1,607 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
"from biot_savart_v4_3 import parse_coil, plot_coil, slice_coil\n",
"from tqdm.notebook import trange, tqdm"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# load up the simple spiral coil\n",
"coil1 = parse_coil(\"coils/coil_12_spiral.csv\")\n",
"plot_coil(\"coils/coil_12_spiral.csv\")\n",
"coil1 = slice_coil(coil1, 1)\n",
"coil1 = coil1.T\n",
"print(coil1.shape)\n",
"\n",
"coil2 = parse_coil(\"coils/coil_12_custom.csv\")\n",
"plot_coil(\"coils/coil_12_custom.csv\")\n",
"coil2 = slice_coil(coil2, 1)\n",
"coil2 = coil2.T\n",
"print(coil2.shape)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Simple Simulation of a dipole magnet"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# magnetic field at a point x,y,z of a dipole magnet with moment m in the z direction\n",
"def B_(x, y, z, m=0.185):\n",
" mu0 = 4 * np.pi * 1e-7\n",
" r = np.sqrt(x**2 + y**2 + z**2)\n",
" return (\n",
" np.array(\n",
" [3 * x * z / r**5, 3 * y * z / r**5, (3 * z**2 / r**5 - 1 / r**3)]\n",
" )\n",
" * m\n",
" * mu0\n",
" )\n",
"\n",
"\n",
"def B(x, y, z, m=0.185, l=0.003, d=0.01):\n",
" d = d * 0.75\n",
" # simulate multiple points in the cylinder and add them together to create a disk of field\n",
" bx = 0\n",
" by = 0\n",
" bz = 0\n",
" for degrees in range(0, 360, 30):\n",
" angle = np.deg2rad(degrees)\n",
" x_, y_, z_ = B_(\n",
" x + d / 2 * np.cos(angle),\n",
" y + d / 2 * np.sin(angle),\n",
" z - l / 2,\n",
" m / (360 / 60),\n",
" )\n",
" bx += x_\n",
" by += y_\n",
" bz += z_\n",
" x_, y_, z_ = B_(\n",
" x + d / 2 * np.cos(angle),\n",
" y + d / 2 * np.sin(angle),\n",
" z + l / 2,\n",
" m / (360 / 60),\n",
" )\n",
" bx += x_\n",
" by += y_\n",
" bz += z_\n",
" return np.array([bx, by, bz])\n",
"\n",
"\n",
"def plot_field_slice(x, y, bx, by, mag, name=\"magnetic_field.png\"):\n",
" # plot the magnetic field\n",
" fig = plt.figure()\n",
" ax = fig.add_subplot(111)\n",
" ax.streamplot(\n",
" x,\n",
" y,\n",
" bx,\n",
" by,\n",
" linewidth=1,\n",
" cmap=plt.cm.inferno,\n",
" density=2,\n",
" arrowstyle=\"->\",\n",
" arrowsize=1.5,\n",
" )\n",
"\n",
" ax.set_xlabel(\"$x$\")\n",
" ax.set_ylabel(\"$y$\")\n",
" ax.set_xlim(-0.1, 0.1)\n",
" ax.set_ylim(-0.1, 0.1)\n",
" ax.set_aspect(\"equal\")\n",
"\n",
" # plot the magniture of the field as an image\n",
" im = ax.imshow(\n",
" mag, extent=[-0.1, 0.1, -0.1, 0.1], origin=\"lower\", cmap=plt.cm.inferno\n",
" )\n",
"\n",
" # draw the magnet\n",
" ax.add_patch(plt.Rectangle((-0.005, -0.0015), 0.01, 0.003, fc=\"w\", ec=\"k\", lw=1))\n",
"\n",
" fig.show()\n",
" # save the figure\n",
" fig.savefig(name)\n",
"\n",
"\n",
"# # calculate the magnetic field at y = 0, over z = -1, 1 and x = -1, 1\n",
"x = np.linspace(-0.1, 0.1, 100)\n",
"z = np.linspace(-0.1, 0.1, 100)\n",
"X, Z = np.meshgrid(x, z)\n",
"Bx, By, Bz = B(X, 0, Z)\n",
"\n",
"print(Bx.shape, By.shape, Bz.shape)\n",
"\n",
"plot_field_slice(\n",
" X,\n",
" Z,\n",
" Bx,\n",
" Bz,\n",
" np.log(np.sqrt(Bx**2 + By**2 + Bz**2)),\n",
" \"magnetic_field_side.png\",\n",
")\n",
"\n",
"# # calculate the magnetic field at z = 1, over y = -1, 1 and x = -1, 1\n",
"x = np.linspace(-0.1, 0.1, 100)\n",
"y = np.linspace(-0.1, 0.1, 100)\n",
"X, Y = np.meshgrid(x, y)\n",
"Bx, By, Bz = B(X, Y, 0.01)\n",
"\n",
"plot_field_slice(\n",
" X,\n",
" Y,\n",
" Bx,\n",
" By,\n",
" np.log(np.sqrt(Bx**2 + By**2 + Bz**2)),\n",
" \"magnetic_field_bottom.png\",\n",
")\n",
"\n",
"# calculate the magnetic field in a 3d volume\n",
"x = np.linspace(-0.1, 0.1, 100)\n",
"y = np.linspace(-0.1, 0.1, 100)\n",
"z = np.linspace(-0.1, 0.1, 100)\n",
"X, Y, Z = np.meshgrid(x, y, z)\n",
"Bx, By, Bz = B(X, Y, Z)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# do a 3d quivwer plot of the magnetic field\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111, projection=\"3d\")\n",
"# down sample the results\n",
"ax.quiver(\n",
" X[::10, ::10, ::10],\n",
" Y[::10, ::10, ::10],\n",
" Z[::10, ::10, ::10],\n",
" Bx[::10, ::10, ::10],\n",
" By[::10, ::10, ::10],\n",
" Bz[::10, ::10, ::10],\n",
" length=0.01,\n",
" normalize=True,\n",
")\n",
"ax.set_xlabel(\"$x$\")\n",
"ax.set_ylabel(\"$y$\")\n",
"ax.set_zlabel(\"$z$\")\n",
"ax.set_xlim(-0.1, 0.1)\n",
"ax.set_ylim(-0.1, 0.1)\n",
"ax.set_zlim(-0.1, 0.1)\n",
"ax.set_aspect(\"equal\")\n",
"# make the plot larger\n",
"fig.set_size_inches(10, 10)\n",
"fig.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# use mayavi to plot the magnetic field\n",
"from mayavi import mlab\n",
"\n",
"mlab.figure(bgcolor=(1, 1, 1), size=(800, 800))\n",
"mlab.quiver3d(\n",
" X,\n",
" Y,\n",
" Z,\n",
" Bx,\n",
" By,\n",
" Bz,\n",
" mode=\"2ddash\",\n",
" scale_factor=1,\n",
" scale_mode=\"none\",\n",
" color=(0, 0, 0),\n",
")\n",
"mlab.axes(\n",
" xlabel=\"$x$\", ylabel=\"$y$\", zlabel=\"$z$\", ranges=[-0.1, 0.1, -0.1, 0.1, -0.1, 0.1]\n",
")\n",
"mlab.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# use myavi to plot a contour plot of the magnetic field\n",
"from mayavi import mlab\n",
"\n",
"mlab.figure(bgcolor=(1, 1, 1), size=(800, 800))\n",
"mlab.contour3d(\n",
" X, Y, Z, np.sqrt(Bx**2 + By**2 + Bz**2), contours=20, transparent=True\n",
")\n",
"mlab.axes(\n",
" xlabel=\"$x$\", ylabel=\"$y$\", zlabel=\"$z$\", ranges=[-0.1, 0.1, -0.1, 0.1, -0.1, 0.1]\n",
")\n",
"mlab.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# calculate the force on a wire of length l carrying current I at a point x,y,z with a direction vector d\n",
"def F(p, d, I, l):\n",
" return I * l * np.cross(d, B(p[0], p[1], p[2]))\n",
"\n",
"\n",
"def calculate_forces_on_wire_points(points):\n",
" Fx = []\n",
" Fy = []\n",
" Fz = []\n",
" # calculate the force on each point\n",
" for i in range(len(points)):\n",
" # calculate the direction vector\n",
" dx = points[i][0] - points[(i + 1) % len(points)][0]\n",
" dy = points[i][1] - points[(i + 1) % len(points)][1]\n",
" dz = points[i][2] - points[(i + 1) % len(points)][2]\n",
" d = np.array([dx, dy, dz])\n",
" # get the length of d\n",
" l = np.sqrt(dx**2 + dy**2 + dz**2)\n",
" if l > 0:\n",
" # normalise d\n",
" d = d / l\n",
" # calculate the force\n",
" fx, fy, fz = F(points[i], d, points[i][3], l)\n",
" Fx.append(fx)\n",
" Fy.append(fy)\n",
" Fz.append(fz)\n",
" else:\n",
" Fx.append(0)\n",
" Fy.append(0)\n",
" Fz.append(0)\n",
" return Fx, Fy, Fz\n",
"\n",
"\n",
"# locate the loop of wire directly below the magnet\n",
"x = 0.01\n",
"y = 0\n",
"z = -0.002\n",
"r1 = 0.001\n",
"r2 = 0.01\n",
"\n",
"\n",
"points = coil2.copy()\n",
"# scale the points from mm to m\n",
"# shift the coil to the correct position\n",
"for i in range(len(points)):\n",
" points[i][0] = points[i][0] / 1000 + x\n",
" points[i][1] = points[i][1] / 1000 + y\n",
" points[i][2] = points[i][2] / 1000 + z\n",
"\n",
"\n",
"# plot the points in 2D x,y\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111)\n",
"ax.plot([p[0] for p in points], [p[1] for p in points])\n",
"ax.set_xlabel(\"$x$\")\n",
"ax.set_ylabel(\"$y$\")\n",
"ax.set_xlim(-0.01 + x, 0.01 + x)\n",
"ax.set_ylim(-0.01 + y, 0.01 + y)\n",
"ax.set_aspect(\"equal\")\n",
"fig.show()\n",
"\n",
"Fx, Fy, Fz = calculate_forces_on_wire_points(points)\n",
"\n",
"\n",
"# plot the wire along with arrows showing the force\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111, projection=\"3d\")\n",
"ax.plot([p[0] for p in points], [p[1] for p in points], [p[2] for p in points])\n",
"\n",
"print(sum(Fx) / 9.8)\n",
"\n",
"# subsample the points and force vectors to make the plot clearer\n",
"points = points[::500]\n",
"Fx = Fx[::500]\n",
"Fy = Fy[::500]\n",
"Fz = Fz[::500]\n",
"\n",
"ax.quiver(\n",
" [p[0] for p in points],\n",
" [p[1] for p in points],\n",
" [p[2] for p in points],\n",
" np.sqrt(Fx),\n",
" 0,\n",
" 0,\n",
" length=0.01,\n",
" normalize=True,\n",
")\n",
"ax.set_xlabel(\"$x$\")\n",
"ax.set_ylabel(\"$y$\")\n",
"ax.set_zlabel(\"$z$\")\n",
"ax.set_xlim(x - 0.02, x + 0.02)\n",
"ax.set_ylim(y - 0.02, y + 0.02)\n",
"ax.set_zlim(z - 0.02, z + 0.02)\n",
"ax.set_aspect(\"equal\")\n",
"\n",
"# change the figure size\n",
"fig.set_size_inches(10, 10)\n",
"\n",
"fig.show()\n",
"# coil2 = 0.0375037573536258\n",
"# coil1 = 0.010254238165764389"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def sweep_coil(coil, X):\n",
" Y = np.zeros(len(X))\n",
" Z = -0.01 * np.ones(len(X))\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(X)):\n",
" points = coil.copy()\n",
" # scale the points from mm to m\n",
" # shift the coil to the correct position\n",
" for i in range(len(points)):\n",
" points[i][0] = points[i][0] / 1000 + X[p]\n",
" points[i][1] = points[i][1] / 1000 + Y[p]\n",
" points[i][2] = points[i][2] / 1000 + Z[p]\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",
" return Fx, Fy, Fz\n",
"\n",
"\n",
"# sweep the coild from -3cm to 3cm in 0.01m steps\n",
"X = np.linspace(-0.03, 0.03, 100)\n",
"Fx_1_straight, Fy_1_straight, Fz_1_straight = sweep_coil(coil1, X)\n",
"Fx_2_straight, Fy_2_straight, Fz_2_straight = sweep_coil(coil2, X)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# plot the force as a function of x\n",
"plt.plot(X, -np.array(Fx_1_straight) / 9.8, label=\"coil1\", color=\"red\")\n",
"plt.plot(X, np.array(Fx_2_straight) / 9.8, label=\"coil2\", color=\"blue\")\n",
"# plot a dotted line along y = 0\n",
"plt.plot([X[0], X[-1]], [0, 0], \"--\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# plot the force as a function of x\n",
"plt.plot(X, -np.array(Fz_1_straight) / 9.8, label=\"coil1\", color=\"red\")\n",
"plt.plot(X, np.array(Fz_2_straight) / 9.8, label=\"coil2\", color=\"blue\")\n",
"# plot a dotted line along y = 0\n",
"plt.plot([X[0], X[-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, theta):\n",
" X = coil_center_radius * np.cos(np.deg2rad(theta))\n",
" 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, 20.5 / 1000, theta\n",
")\n",
"Fx_2_curve, Fy_2_curve, Fz_2_curve, Torque_2 = sweep_coil_cirlc(\n",
" coil2, 19.5 / 1000, theta\n",
")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plt.plot(\n",
" theta, -np.array(Fx_1_curve) + np.array(Fx_1_curve), label=\"coil1\", color=\"red\"\n",
")\n",
"plt.plot(theta, np.array(Torque_2) - np.array(Fx_2_curve), 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": [
"plt.plot(theta, -np.array(Torque_1) / 9.8, label=\"coil1\", color=\"red\")\n",
"plt.plot(theta, np.array(Torque_2) / 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": [
"# 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",
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},
"vscode": {
"interpreter": {
"hash": "1ce20143987840b9786ebb5907032c9c3a8efacbb887dbb0ebc4934f2ad26cb3"
}
}
},
"nbformat": 4,
"nbformat_minor": 2
}

525
simulations/magnet_field_single_coil.ipynb Normal file
View file

@ -0,0 +1,525 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
"from biot_savart_v4_3 import parse_coil, plot_coil, slice_coil, plot_coil2\n",
"from tqdm.notebook import trange, tqdm\n",
"from helpers import get_arc_point, draw_arc, rotate, scale, rotate_point, translate"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Track width and spacing\n",
"TRACK_WIDTH = 0.127\n",
"TRACK_SPACING = 0.127\n",
"\n",
"# via defaults\n",
"VIA_DIAM = 0.8\n",
"VIA_DRILL = 0.4\n",
"\n",
"# this is for a 1.27mm pitch pin\n",
"PIN_DIAM = 1.0\n",
"PIN_DRILL = 0.65\n",
"\n",
"# this is for the PCB connector - see https://www.farnell.com/datasheets/2003059.pdf\n",
"PAD_WIDTH = 3\n",
"PAD_HEIGHT = 2\n",
"PAD_PITCH = 2.5\n",
"\n",
"STATOR_HOLE_RADIUS = 5.5\n",
"HOLE_SPACING = 0.25\n",
"\n",
"# PCB Edge size\n",
"STATOR_RADIUS = 30\n",
"\n",
"# where to puth the mounting pins\n",
"SCREW_HOLE_DRILL_DIAM = 2.3 # 2.3mm drill for a 2mm screw\n",
"SCREW_HOLE_RADIUS = STATOR_RADIUS\n",
"\n",
"# Coil params\n",
"TURNS = 16\n",
"COIL_CENTER_RADIUS = 19.95\n",
"COIL_VIA_RADIUS = 20.95\n",
"\n",
"\n",
"def get_points(spacing, inner_radius, outer_radius, start_angle, end_angle):\n",
" # first calculate the angle step size from the spacing and the inner_radius\n",
" spacing_angle = np.rad2deg(np.arctan2(spacing, inner_radius))\n",
" print(spacing_angle)\n",
" # now calculate the points be iterating from start_angle to end_angle with the spacing_angle\n",
" points = []\n",
" for angle in np.arange(start_angle, end_angle, spacing_angle * 2):\n",
" p1 = get_arc_point(angle, inner_radius)\n",
" points.append([p1[0], p1[1], 0, 0.5])\n",
" p2 = get_arc_point(angle + spacing_angle, outer_radius)\n",
" points.append([p2[0], p2[1], 0, 0.5])\n",
" points.append([p2[0], p2[1], -0.8, 0.5])\n",
" points.append([p1[0], p1[1], -0.8, 0.5])\n",
" return points\n",
"\n",
"\n",
"coil1 = get_points(\n",
" TRACK_SPACING + TRACK_WIDTH,\n",
" (COIL_CENTER_RADIUS - 10),\n",
" COIL_CENTER_RADIUS + 10,\n",
" -15,\n",
" 15,\n",
")\n",
"# move all the points in by COIL_CENTER_RADIUS\n",
"for p in coil1:\n",
" p[0] -= COIL_CENTER_RADIUS\n",
"# rotate the points by 90 degrees\n",
"for p in coil1:\n",
" p[0], p[1] = rotate_point(p[0], p[1], 90)\n",
"coil1 = np.array(coil1).T\n",
"plot_coil2(coil1)\n",
"coil1 = slice_coil(coil1, 0.1)\n",
"coil1 = coil1.T\n",
"print(coil1.shape)\n",
"print(len(coil1))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Simple Simulation of a dipole magnet"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# magnetic field at a point x,y,z of a dipole magnet with moment m in the z direction\n",
"def B(x, y, z, m=0.185):\n",
" mu0 = 4 * np.pi * 1e-7\n",
" r = np.sqrt(x**2 + y**2 + z**2)\n",
" return (\n",
" np.array(\n",
" [3 * x * z / r**5, 3 * y * z / r**5, (3 * z**2 / r**5 - 1 / r**3)]\n",
" )\n",
" * m\n",
" * mu0\n",
" )\n",
"\n",
"\n",
"def plot_field_slice(x, y, bx, by, mag, name=\"magnetic_field.png\"):\n",
" # plot the magnetic field\n",
" fig = plt.figure()\n",
" ax = fig.add_subplot(111)\n",
" ax.streamplot(\n",
" x,\n",
" y,\n",
" bx,\n",
" by,\n",
" linewidth=1,\n",
" cmap=plt.cm.inferno,\n",
" density=2,\n",
" arrowstyle=\"->\",\n",
" arrowsize=1.5,\n",
" )\n",
"\n",
" ax.set_xlabel(\"$x$\")\n",
" ax.set_ylabel(\"$y$\")\n",
" ax.set_xlim(-0.1, 0.1)\n",
" ax.set_ylim(-0.1, 0.1)\n",
" ax.set_aspect(\"equal\")\n",
"\n",
" # plot the magniture of the field as an image\n",
" im = ax.imshow(\n",
" mag, extent=[-0.1, 0.1, -0.1, 0.1], origin=\"lower\", cmap=plt.cm.inferno\n",
" )\n",
"\n",
" fig.show()\n",
" # save the figure\n",
" fig.savefig(name)\n",
"\n",
"\n",
"# # calculate the magnetic field at y = 0, over z = -1, 1 and x = -1, 1\n",
"x = np.linspace(-0.1, 0.1, 100)\n",
"z = np.linspace(-0.1, 0.1, 100)\n",
"X, Z = np.meshgrid(x, z)\n",
"Bx, By, Bz = B(X, 0, Z)\n",
"\n",
"plot_field_slice(\n",
" X,\n",
" Z,\n",
" Bx,\n",
" Bz,\n",
" np.log(np.sqrt(Bx**2 + By**2 + Bz**2)),\n",
" \"magnetic_field_side.png\",\n",
")\n",
"\n",
"# # calculate the magnetic field at z = 1, over y = -1, 1 and x = -1, 1\n",
"x = np.linspace(-0.1, 0.1, 100)\n",
"y = np.linspace(-0.1, 0.1, 100)\n",
"X, Y = np.meshgrid(x, y)\n",
"Bx, By, Bz = B(X, Y, 0.01)\n",
"\n",
"plot_field_slice(\n",
" X, Y, Bx, By, np.sqrt(Bx**2 + By**2 + Bz**2), \"magnetic_field_bottom.png\"\n",
")\n",
"\n",
"# calculate the magnetic field in a 3d volume\n",
"x = np.linspace(-0.1, 0.1, 100)\n",
"y = np.linspace(-0.1, 0.1, 100)\n",
"z = np.linspace(-0.1, 0.1, 100)\n",
"X, Y, Z = np.meshgrid(x, y, z)\n",
"Bx, By, Bz = B(X, Y, Z)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# calculate the force on a wire of length l carrying current I at a point x,y,z with a direction vector d\n",
"def F(p, d, I, l):\n",
" return I * l * np.cross(d, B(p[0], p[1], p[2]))\n",
"\n",
"\n",
"def calculate_forces_on_wire_points(points):\n",
" Fx = []\n",
" Fy = []\n",
" Fz = []\n",
" # calculate the force on each point\n",
" for i in range(len(points)):\n",
" # calculate the direction vector\n",
" dx = points[i][0] - points[(i + 1) % len(points)][0]\n",
" dy = points[i][1] - points[(i + 1) % len(points)][1]\n",
" dz = points[i][2] - points[(i + 1) % len(points)][2]\n",
" d = np.array([dx, dy, dz])\n",
" # get the length of d\n",
" l = np.sqrt(dx**2 + dy**2 + dz**2)\n",
" if l > 0:\n",
" # normalise d\n",
" d = d / l\n",
" # calculate the force\n",
" fx, fy, fz = F(points[i], d, points[i][3], l)\n",
" Fx.append(fx)\n",
" Fy.append(fy)\n",
" Fz.append(fz)\n",
" else:\n",
" Fx.append(0)\n",
" Fy.append(0)\n",
" Fz.append(0)\n",
" return Fx, Fy, Fz\n",
"\n",
"\n",
"# locate the loop of wire directly below the magnet\n",
"x = 0.01\n",
"y = 0\n",
"z = -0.002\n",
"r1 = 0.001\n",
"r2 = 0.01\n",
"\n",
"\n",
"points = coil1.copy()\n",
"# scale the points from mm to m\n",
"# shift the coil to the correct position\n",
"for i in range(len(points)):\n",
" points[i][0] = points[i][0] / 1000 + x\n",
" points[i][1] = points[i][1] / 1000 + y\n",
" points[i][2] = points[i][2] / 1000 + z\n",
"\n",
"\n",
"# plot the points in 2D x,y\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111)\n",
"ax.plot([p[0] for p in points], [p[1] for p in points])\n",
"ax.set_xlabel(\"$x$\")\n",
"ax.set_ylabel(\"$y$\")\n",
"ax.set_xlim(-0.01 + x, 0.01 + x)\n",
"ax.set_ylim(-0.01 + y, 0.01 + y)\n",
"ax.set_aspect(\"equal\")\n",
"fig.show()\n",
"\n",
"Fx, Fy, Fz = calculate_forces_on_wire_points(points)\n",
"\n",
"\n",
"# plot the wire along with arrows showing the force\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111, projection=\"3d\")\n",
"ax.plot([p[0] for p in points], [p[1] for p in points], [p[2] for p in points])\n",
"\n",
"print(sum(Fx) / 9.8)\n",
"\n",
"# subsample the points and force vectors to make the plot clearer\n",
"points = points[::50]\n",
"Fx = Fx[::50]\n",
"Fy = Fy[::50]\n",
"Fz = Fz[::50]\n",
"\n",
"ax.quiver(\n",
" [p[0] for p in points],\n",
" [p[1] for p in points],\n",
" [p[2] for p in points],\n",
" np.sqrt(Fx),\n",
" 0,\n",
" 0,\n",
" length=0.01,\n",
" normalize=True,\n",
")\n",
"ax.set_xlabel(\"$x$\")\n",
"ax.set_ylabel(\"$y$\")\n",
"ax.set_zlabel(\"$z$\")\n",
"ax.set_xlim(x - 0.02, x + 0.02)\n",
"ax.set_ylim(y - 0.02, y + 0.02)\n",
"ax.set_zlim(z - 0.02, z + 0.02)\n",
"ax.set_aspect(\"equal\")\n",
"\n",
"# change the figure size\n",
"fig.set_size_inches(10, 10)\n",
"\n",
"fig.show()\n",
"# coil2 = -0.01311082557350831\n",
"# coil1 = 0.0088435517657609"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def sweep_coil(coil, X):\n",
" Y = np.zeros(len(X))\n",
" Z = -0.01 * np.ones(len(X))\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(X)):\n",
" points = coil.copy()\n",
" # scale the points from mm to m\n",
" # shift the coil to the correct position\n",
" for i in range(len(points)):\n",
" points[i][0] = points[i][0] / 1000 + X[p]\n",
" points[i][1] = points[i][1] / 1000 + Y[p]\n",
" points[i][2] = points[i][2] / 1000 + Z[p]\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",
" return Fx, Fy, Fz\n",
"\n",
"\n",
"# sweep the coild from -3cm to 3cm in 0.01m steps\n",
"X = np.linspace(-0.03, 0.03, 100)\n",
"Fx_1_straight, Fy_1_straight, Fz_1_straight = sweep_coil(coil1, X)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# plot the force as a function of x\n",
"plt.plot(X, -np.array(Fx_1_straight) / 9.8, label=\"coil1\", color=\"red\")\n",
"# plot a dotted line along y = 0\n",
"plt.plot([X[0], X[-1]], [0, 0], \"--\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# plot the force as a function of x\n",
"plt.plot(X, -np.array(Fz_1_straight) / 9.8, label=\"coil1\", color=\"red\")\n",
"# plot a dotted line along y = 0\n",
"plt.plot([X[0], X[-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, theta):\n",
" X = coil_center_radius * np.cos(np.deg2rad(theta))\n",
" 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"
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"vscode": {
"interpreter": {
"hash": "1ce20143987840b9786ebb5907032c9c3a8efacbb887dbb0ebc4934f2ad26cb3"
}
}
},
"nbformat": 4,
"nbformat_minor": 2
}

67
simulations/simulate_coil.ipynb
View file

@ -7,7 +7,8 @@
"outputs": [],
"source": [
"import numpy as np\n",
"import biot_savart_v4_3 as bs"
"import biot_savart_v4_3 as bs\n",
"import matplotlib.pyplot as plt"
]
},
{
@ -16,7 +17,7 @@
"metadata": {},
"outputs": [],
"source": [
"bs.plot_coil(\"coil-4-top-1.txt\")"
"bs.plot_coil(\"coil-4-top-1.csv\")"
]
},
{
@ -25,7 +26,7 @@
"metadata": {},
"outputs": [],
"source": [
"bs.plot_coil(\"coil-4-bottom-1.txt\")"
"bs.plot_coil(\"coil-4-bottom-1.csv\")"
]
},
{
@ -36,7 +37,7 @@
"source": [
"for i in range(0, 12):\n",
" bs.write_target_volume(\n",
" f\"coil-4-top-{i}.txt\",\n",
" f\"coil-4-top-{i}.csv\",\n",
" f\"targetvol-top-{i}.vol\",\n",
" (6, 6, 1),\n",
" (-3, -3, -0.5),\n",
@ -44,7 +45,7 @@
" 0.1,\n",
" )\n",
" bs.write_target_volume(\n",
" f\"coil-4-bottom-{i}.txt\",\n",
" f\"coil-4-bottom-{i}.csv\",\n",
" f\"targetvol-bottom-{i}.vol\",\n",
" (6, 6, 1),\n",
" (-3, -3, -0.5),\n",
@ -74,6 +75,62 @@
"# reads the volume we created\n",
"bs.plot_fields(volume, (60, 60, 10), (0, 0, 0), 1, which_plane=\"z\", level=6)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib as plt\n",
"\n",
"# get a slice of the volume at z=6\n",
"slice = [volume[50, :, :, i].T for i in range(3)]\n",
"x_contour = slice[0]\n",
"y_contour = slice[1]\n",
"z_contour = slice[2]\n",
"\n",
"print(x_contour.shape)\n",
"print(y_contour.shape)\n",
"print(z_contour.shape)\n",
"\n",
"x = np.arange(0, 61, 1)\n",
"y = np.arange(0, 11, 1)\n",
"xG, yG = np.meshgrid(x, y)\n",
"# do a quiver plot of the x and the z components - we won't worry about y\n",
"plt.pyplot.quiver(xG, yG, y_contour, z_contour)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"fig = plt.pyplot.figure()\n",
"ax = fig.add_subplot(111)\n",
"\n",
"# Plot the streamlines with an appropriate colormap and arrow style\n",
"# color = 2 * np.log(np.hypot(x_contour, z_contour))\n",
"ax.streamplot(\n",
" x,\n",
" y,\n",
" y_contour,\n",
" z_contour,\n",
" linewidth=1,\n",
" cmap=plt.cm.inferno,\n",
" density=2,\n",
" arrowstyle=\"->\",\n",
" arrowsize=1.5,\n",
")\n",
"\n",
"ax.set_xlabel(\"$x$\")\n",
"ax.set_ylabel(\"$y$\")\n",
"# ax.set_xlim(-2,2)\n",
"# ax.set_ylim(-2,2)\n",
"ax.set_aspect(\"equal\")\n",
"fig.show()"
]
}
],
"metadata": {