Add a gear example

Author: FranzBangar

examples/complex/gear/gear.py

@@ -0,0 +1,191 @@
+#!/usr/bin/env python
+import os
+import time
+
+import numpy as np
+import scipy.optimize
+from involute_gear import InvoluteGear
+from tooth import ToothSketch
+
+import classy_blocks as cb
+from classy_blocks.util import functions as f
+
+time_start = time.time()
+
+mesh = cb.Mesh()
+
+# parameters
+RADIUS_EXPANSION = 1.1
+
+# create an interpolated curve that represents a gear tooth
+fillet = 0.1  # Must be more than zero!
+gear = InvoluteGear(fillet=fillet, arc_step_size=0.1, max_steps=1000, teeth=15)
+tng_points = gear.generate_tooth_and_gap()
+
+z_coords = np.zeros(len(tng_points[0]))
+tng_points = np.stack((tng_points[0], tng_points[1], z_coords)).T
+tng_points = np.flip(tng_points, axis=0)
+
+# add start and end points exactly on the 2pi/teeth
+start_point = f.to_polar(tng_points[0], axis="z")
+start_point[1] = np.pi / gear.teeth
+start_point = f.to_cartesian(start_point)
+
+end_point = f.to_polar(tng_points[-1], axis="z")
+end_point[1] = -np.pi / gear.teeth
+end_point = f.to_cartesian(end_point)
+
+tng_points = np.concatenate(([start_point], tng_points, [end_point]))
+
+tooth_curve = cb.LinearInterpolatedCurve(tng_points)
+gear_params = np.linspace(0, 1, num=8)
+
+
+# fix points 1 and 3:
+# 1 is on radius gear.root_radius + fillet/2
+def frad(t, radius):
+    return f.norm(tooth_curve.get_point(t)) - radius
+
+
+gear_params[1] = scipy.optimize.brentq(lambda t: frad(t, gear.root_radius + fillet / 2), 0, 0.25)
+
+# 3 is on radius gear.outer_radius - fillet/2
+gear_params[3] = scipy.optimize.brentq(lambda t: frad(t, gear.outer_radius - fillet / 2), 0.25, 0.5)
+
+gear_params[6] = 1 - gear_params[1]
+gear_params[4] = 1 - gear_params[3]
+
+gear_params[2] = (gear_params[1] + gear_params[3]) / 2
+gear_params[5] = (gear_params[4] + gear_params[6]) / 2
+
+gear_points = np.array([tooth_curve.get_point(t) for t in gear_params])
+
+outer_radius = f.norm(gear_points[3] * RADIUS_EXPANSION)
+p11_polar = f.to_polar(gear_points[-1], axis="z")
+p14_polar = f.to_polar(gear_points[0], axis="z")
+angles = np.linspace(p11_polar[1], p14_polar[1], num=4)
+tangential_points = np.array([f.to_cartesian([outer_radius, angle, 0]) for angle in angles])
+
+radial_points_1 = np.linspace(gear_points[-1], tangential_points[0], axis=0, num=5)[1:-1]
+radial_points_2 = np.linspace(tangential_points[-1], gear_points[0], axis=0, num=5)[1:-1]
+
+outer_points = np.concatenate((gear_points, radial_points_1, tangential_points, radial_points_2))
+inner_points = np.zeros((6, 3))
+
+positions = np.concatenate((outer_points, inner_points))
+
+# At this point, a smoother would reliably
+# produce almost the best blocking if this was a convex sketch.
+# Alas, this is a severely concave case so smoothing will produce
+# degenerate quads which even optimizers won't be able to fix.
+# It's best to manually position points, then optimize the sketch.
+
+
+def mirror(target, source):
+    # once a position is obtained, the mirrored counterpart is also determined
+    positions[target] = [positions[source][0], -positions[source][1], 0]
+
+
+# fix points 18 and 23 because optimization doesn't 'see' curved edges
+# and produces high non-orthogonality
+dir_0 = f.unit_vector(gear_points[0] - gear_points[1])
+dir_2 = f.unit_vector(gear_points[2] - gear_points[1])
+dir_18 = f.unit_vector(dir_0 + dir_2)
+
+positions[18] = gear_points[1] + dir_18 * f.norm(gear_points[0] - gear_points[1]) / 2
+mirror(23, 18)
+
+positions[17] = positions[0] + f.unit_vector(positions[17] - positions[0]) * f.norm(positions[18] - positions[1])
+mirror(8, 17)
+
+
+# other points are somewhere between...
+def midpoint(target, left, right):
+    positions[target] = (positions[left] + positions[right]) / 2
+
+
+midpoint(19, 2, 16)
+midpoint(20, 3, 13)
+
+# and their mirrored counterparts
+mirror(22, 19)
+mirror(21, 20)
+
+
+sketch = ToothSketch(positions, tooth_curve)
+
+# Optimize the sketch:
+optimizer = cb.SketchOptimizer(sketch)
+
+# point 2 is on gear curve
+optimizer.add_clamp(cb.CurveClamp(positions[2], tooth_curve))
+
+# point 13 is movable radially
+optimizer.add_clamp(cb.RadialClamp(positions[13], [0, 0, 0], [0, 0, 1]))
+
+# 15-17 move along a line
+for i in (15, 16, 17):
+    optimizer.add_clamp(cb.LineClamp(positions[i], gear_points[0], tangential_points[-1]))
+
+# freely movable points (on sketch plane)
+# TODO: easier clamp definition for sketch optimization
+for i in (19, 20):
+    optimizer.add_clamp(cb.PlaneClamp(sketch.positions[i], sketch.positions[i], sketch.normal))
+
+# Links!
+symmetry_pairs = [
+    (2, 5),
+    (19, 22),
+    (20, 21),
+    (17, 8),
+    (16, 9),
+    (15, 10),
+]
+
+for pair in symmetry_pairs:
+    optimizer.add_link(cb.SymmetryLink(positions[pair[0]], positions[pair[1]], f.vector(0, 1, 0), f.vector(0, 0, 0)))
+
+optimizer.optimize()
+
+stack = cb.TransformedStack(
+    sketch,
+    [cb.Translation([0, 0, 4]), cb.Rotation(sketch.normal, 10 * np.pi / 180, [0, 0, 0])],
+    2,
+    [cb.Translation([0, 0, 2]), cb.Rotation(sketch.normal, 5 * np.pi / 180, [0, 0, 0])],
+)
+
+# TODO: this be mighty clumsy; unclumsify
+bulk_size = 0.1
+wall_size = 0.01
+
+stack.shapes[0].chop(0, start_size=bulk_size)
+stack.shapes[0].chop(1, start_size=wall_size, end_size=bulk_size / 2)
+stack.shapes[0].operations[10].chop(1, start_size=bulk_size)
+stack.chop(count=8)
+
+# patches
+for shape in stack.shapes:
+    for i in range(7):
+        shape.operations[i].set_patch("front", "gear")
+
+    for i in (9, 10, 11):
+        shape.operations[i].set_patch("front", "outer")
+
+for operation in stack.shapes[0].operations:
+    operation.set_patch("bottom", "bottom")
+
+for operation in stack.shapes[-1].operations:
+    operation.set_patch("top", "top")
+
+mesh.add(stack)
+
+for i, angle in enumerate(np.linspace(0, 2 * np.pi, num=gear.teeth, endpoint=False)[1:]):
+    print(f"Adding tooth {i+2}")
+    mesh.add(stack.copy().rotate(angle, [0, 0, 1], [0, 0, 0]))
+
+print("Writing mesh...")
+mesh.write(os.path.join("..", "..", "case", "system", "blockMeshDict"), debug_path="debug.vtk")
+
+time_end = time.time()
+
+print(f"Elapsed time: {time_end - time_start}s")