How to create a helicoil spring mesh

[adtzlr]

import felupe as fem
import numpy as np

line = fem.mesh.Line(b=5, n=501)

radius = 10
height = 5

x = radius * np.cos(2 * np.pi * line.x)
y = radius * np.sin(2 * np.pi * line.x)
z = height * line.x

line.update(points=np.array([x, y, z]).T)
ax = line.imshow(line_width=5)

[adtzlr]

This is an extension with sections. It's super slow because of multiple fill_between() calls. We need some way to vectorize it.

import felupe as fem
import numpy as np

diameter = 100
radius = 10
height = 25

line = fem.mesh.Line(b=3.5, n=101)

x = diameter / 2 * np.cos(2 * np.pi * line.x)
y = diameter / 2 * np.sin(2 * np.pi * line.x)
z = height * line.x

helix = line.copy(points=np.array([x, y, z]).T)
ax = helix.imshow(line_width=5)

sect = fem.Circle(radius=radius, n=4).expand(n=1)
sect = sect.translate(move=diameter / 2, axis=0)
sect = sect.rotate(90, axis=0)

alpha = np.rad2deg(np.arctan(height / (diameter * np.pi)))
sect = sect.rotate(alpha, axis=0)

sects = [sect.rotate(np.rad2deg(2 * np.pi * phi), axis=2) for phi in line.x]
sects = [s.translate(zi, axis=2) for s, zi in zip(sects, z)]

meshes = [start.fill_between(end, n=2) for start, end in zip(sects[:-1], sects[1:])]
mesh = fem.MeshContainer(meshes, merge=True).stack()
mesh.plot().show()

[adtzlr]

This one is much faster, as it first calls fill_between(n=n_sections) only once and then the points-array is modified.

import felupe as fem
import numpy as np

diameter = 100
radius = 10
height = 25

line = fem.mesh.Line(b=3.5, n=101)

x = diameter / 2 * np.cos(2 * np.pi * line.x)
y = diameter / 2 * np.sin(2 * np.pi * line.x)
z = height * line.x

helix = line.copy(points=np.array([x, y, z]).T)
ax = helix.imshow(line_width=5)

sect = fem.Circle(radius=radius, n=4).expand(n=1)
sect = sect.translate(move=diameter / 2, axis=0)
sect = sect.rotate(90, axis=0)

alpha = np.rad2deg(np.arctan(height / (diameter * np.pi)))
sect = sect.rotate(alpha, axis=0)

sects = [sect.rotate(np.rad2deg(2 * np.pi * phi), axis=2) for phi in line.x]
sects = [s.translate(zi, axis=2) for s, zi in zip(sects, z)]

mesh = sects[0].fill_between(sects[-1], n=len(sects))
mesh.update(points=np.vstack([m.points for m in sects]))
mesh.plot().show()