kopia lustrzana https://github.com/vilemduha/blendercam
295 wiersze
14 KiB
Python
295 wiersze
14 KiB
Python
"""BlenderCAM 'involute_gear.py' Ported by Alain Pelletier Jan 2022
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from:
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Public Domain Parametric Involute Spur Gear (and involute helical gear and involute rack)
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version 1.1
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by Leemon Baird, 2011, Leemon@Leemon.com
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http:www.thingiverse.com/thing:5505
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This file is public domain. Use it for any purpose, including commercial
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applications. Attribution would be nice, but is not required. There is
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no warranty of any kind, including its correctness, usefulness, or safety.
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This is parameterized involute spur (or helical) gear. It is much simpler and less powerful than
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others on Thingiverse. But it is public domain. I implemented it from scratch from the
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descriptions and equations on Wikipedia and the web, using Mathematica for calculations and testing,
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and I now release it into the public domain.
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http:en.wikipedia.org/wiki/Involute_gear
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http:en.wikipedia.org/wiki/Gear
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http:en.wikipedia.org/wiki/List_of_gear_nomenclature
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http:gtrebaol.free.fr/doc/catia/spur_gear.html
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http:www.cs.cmu.edu/~rapidproto/mechanisms/chpt7.html
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The module gear() gives an involute spur gear, with reasonable defaults for all the parameters.
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Normally, you should just choose the first 4 parameters, and let the rest be default values.
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The module gear() gives a gear in the XY plane, centered on the origin, with one tooth centered on
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the positive Y axis. The various functions below it take the same parameters, and return various
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measurements for the gear. The most important is pitch_radius, which tells how far apart to space
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gears that are meshing, and adendum_radius, which gives the size of the region filled by the gear.
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A gear has a "pitch circle", which is an invisible circle that cuts through the middle of each
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tooth (though not the exact center). In order for two gears to mesh, their pitch circles should
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just touch. So the distance between their centers should be pitch_radius() for one, plus pitch_radius()
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for the other, which gives the radii of their pitch circles.
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In order for two gears to mesh, they must have the same mm_per_tooth and pressure_angle parameters.
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mm_per_tooth gives the number of millimeters of arc around the pitch circle covered by one tooth and one
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space between teeth. The pitch angle controls how flat or bulged the sides of the teeth are. Common
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values include 14.5 degrees and 20 degrees, and occasionally 25. Though I've seen 28 recommended for
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plastic gears. Larger numbers bulge out more, giving stronger teeth, so 28 degrees is the default here.
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The ratio of number_of_teeth for two meshing gears gives how many times one will make a full
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revolution when the the other makes one full revolution. If the two numbers are coprime (i.e.
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are not both divisible by the same number greater than 1), then every tooth on one gear
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will meet every tooth on the other, for more even wear. So coprime numbers of teeth are good.
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The module rack() gives a rack, which is a bar with teeth. A rack can mesh with any
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gear that has the same mm_per_tooth and pressure_angle.
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Some terminology:
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The outline of a gear is a smooth circle (the "pitch circle") which has mountains and valleys
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added so it is toothed. So there is an inner circle (the "root circle") that touches the
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base of all the teeth, an outer circle that touches the tips of all the teeth,
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and the invisible pitch circle in between them. There is also a "base circle", which can be smaller than
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all three of the others, which controls the shape of the teeth. The side of each tooth lies on the path
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that the end of a string would follow if it were wrapped tightly around the base circle, then slowly unwound.
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That shape is an "involute", which gives this type of gear its name.
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An involute spur gear, with reasonable defaults for all the parameters.
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Normally, you should just choose the first 4 parameters, and let the rest be default values.
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Meshing gears must match in mm_per_tooth, pressure_angle, and twist,
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and be separated by the sum of their pitch radii, which can be found with pitch_radius().
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"""
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from math import (
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acos,
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cos,
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degrees,
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pi,
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sin,
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sqrt
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)
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from shapely.geometry import Polygon
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import bpy
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from . import (
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simple,
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utils,
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)
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# convert gear_polar to cartesian coordinates
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def gear_polar(r, theta):
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return r * sin(theta), r * cos(theta)
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# unwind a string this many degrees to go from radius r1 to radius r2
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def gear_iang(r1, r2):
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return sqrt((r2 / r1) * (r2 / r1) - 1) - acos(r1 / r2)
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# radius a fraction f up the curved side of the tooth
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def gear_q7(f, r, b, r2, t, s):
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return gear_q6(b, s, t, (1-f) * max(b, r) + f * r2)
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# point at radius d on the involute curve
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def gear_q6(b, s, t, d):
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return gear_polar(d, s * (gear_iang(b, d) + t))
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# mm_per_tooth = this is the "circular pitch", the circumference of the pitch circle divided by the number of teeth
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# number_of_teeth = total number of teeth around the entire perimeter
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# hole_diameter = diameter of the hole in the center, in mm
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# pressure_angle = Controls how straight or bulged the tooth sides are. In radians.
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# clearance = gap between top of a tooth on one gear and bottom of valley on a meshing gear( in millimeters)
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# backlash = gap between two meshing teeth, in the direction along the circumference of the pitch circle
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def gear(mm_per_tooth=0.003, number_of_teeth=5, hole_diameter=0.003175,
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pressure_angle=0.3488, clearance=0.0, backlash=0.0, rim_size=0.0005, hub_diameter=0.006, spokes=4):
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"""Generate a 3D gear model based on specified parameters.
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This function creates a 3D representation of a gear using the provided
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parameters such as the circular pitch, number of teeth, hole diameter,
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pressure angle, clearance, backlash, rim size, hub diameter, and the
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number of spokes. The gear is constructed by calculating various radii
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and angles based on the input parameters and then using geometric
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operations to form the final shape. The resulting gear is named
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according to its specifications.
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Args:
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mm_per_tooth (float): The circular pitch of the gear in millimeters (default is 0.003).
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number_of_teeth (int): The total number of teeth on the gear (default is 5).
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hole_diameter (float): The diameter of the central hole in millimeters (default is 0.003175).
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pressure_angle (float): The angle that controls the shape of the tooth sides in radians (default
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is 0.3488).
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clearance (float): The gap between the top of a tooth and the bottom of a valley on a
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meshing gear in millimeters (default is 0.0).
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backlash (float): The gap between two meshing teeth along the circumference of the pitch
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circle in millimeters (default is 0.0).
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rim_size (float): The size of the rim around the gear in millimeters (default is 0.0005).
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hub_diameter (float): The diameter of the hub in millimeters (default is 0.006).
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spokes (int): The number of spokes on the gear (default is 4).
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Returns:
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None: This function does not return a value but modifies the Blender scene to
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include the generated gear model.
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"""
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simple.deselect()
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p = mm_per_tooth * number_of_teeth / pi / 2 # radius of pitch circle
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c = p + mm_per_tooth / pi - clearance # radius of outer circle
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b = p * cos(pressure_angle) # radius of base circle
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r = p-(c-p)-clearance # radius of root circle
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t = mm_per_tooth / 2 - backlash / 2 # tooth thickness at pitch circle
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# angle to where involute meets base circle on each side of tooth
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k = - gear_iang(b, p) - t / 2 / p
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shapely_gear = Polygon([
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(0, 0),
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gear_polar(r, k if r < b else -pi / number_of_teeth),
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gear_q7(0, r, b, c, k, 1),
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gear_q7(0.1, r, b, c, k, 1),
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gear_q7(0.2, r, b, c, k, 1),
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gear_q7(0.3, r, b, c, k, 1),
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gear_q7(0.4, r, b, c, k, 1),
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gear_q7(0.5, r, b, c, k, 1),
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gear_q7(0.6, r, b, c, k, 1),
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gear_q7(0.7, r, b, c, k, 1),
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gear_q7(0.8, r, b, c, k, 1),
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gear_q7(0.9, r, b, c, k, 1),
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gear_q7(1.0, r, b, c, k, 1),
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gear_q7(1.0, r, b, c, k, -1),
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gear_q7(0.9, r, b, c, k, -1),
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gear_q7(0.8, r, b, c, k, -1),
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gear_q7(0.7, r, b, c, k, -1),
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gear_q7(0.6, r, b, c, k, -1),
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gear_q7(0.5, r, b, c, k, -1),
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gear_q7(0.4, r, b, c, k, -1),
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gear_q7(0.3, r, b, c, k, -1),
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gear_q7(0.2, r, b, c, k, -1),
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gear_q7(0.1, r, b, c, k, -1),
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gear_q7(0.0, r, b, c, k, -1),
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gear_polar(r, -k if r < b else pi / number_of_teeth)
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])
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utils.shapelyToCurve('tooth', shapely_gear, 0.0)
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i = number_of_teeth
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while i > 1:
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simple.duplicate()
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simple.rotate(2 * pi / number_of_teeth)
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i -= 1
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simple.join_multiple('tooth')
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simple.active_name('_teeth')
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bpy.ops.curve.simple(align='WORLD', location=(0, 0, 0), rotation=(0, 0, 0), Simple_Type='Circle',
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Simple_radius=r, shape='3D', use_cyclic_u=True, edit_mode=False)
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simple.active_name('_hub')
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simple.union('_')
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simple.active_name('_gear')
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simple.remove_doubles()
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if spokes > 0:
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bpy.ops.curve.simple(align='WORLD', location=(0, 0, 0), rotation=(0, 0, 0), Simple_Type='Circle',
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Simple_radius=r-rim_size, shape='3D', use_cyclic_u=True, edit_mode=False)
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simple.active_name('_hole')
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simple.difference('_', '_gear')
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bpy.ops.curve.simple(align='WORLD', location=(0, 0, 0), rotation=(0, 0, 0), Simple_Type='Circle',
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Simple_radius=hub_diameter/2, shape='3D', use_cyclic_u=True, edit_mode=False)
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simple.active_name('_hub')
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bpy.ops.curve.simple(align='WORLD', location=(0, 0, 0), rotation=(0, 0, 0), Simple_Type='Circle',
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Simple_radius=hole_diameter/2, shape='3D', use_cyclic_u=True, edit_mode=False)
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simple.active_name('_hub_hole')
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simple.difference('_hub', '_hub')
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simple.join_multiple('_')
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simple.add_rectangle(r-rim_size-((hub_diameter-hole_diameter)/4 +
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hole_diameter/2), hub_diameter/2, center_x=False)
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simple.move(x=(hub_diameter-hole_diameter)/4 + hole_diameter/2)
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simple.active_name('_spoke')
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angle = 2 * pi / spokes
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while spokes > 0:
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simple.duplicate()
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simple.rotate(angle)
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spokes -= 1
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simple.union('_spoke')
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simple.remove_doubles()
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simple.union('_')
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else:
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bpy.ops.curve.simple(align='WORLD', location=(0, 0, 0), rotation=(0, 0, 0), Simple_Type='Circle',
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Simple_radius=hole_diameter, shape='3D', use_cyclic_u=True, edit_mode=False)
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simple.active_name('_hole')
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simple.difference('_', '_gear')
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name = 'gear-' + str(round(mm_per_tooth*1000, 1))
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name += 'mm-pitch-' + str(number_of_teeth)
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name += 'teeth-PA-' + str(round(degrees(pressure_angle), 1))
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simple.active_name(name)
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def rack(mm_per_tooth=0.01, number_of_teeth=11, height=0.012, pressure_angle=0.3488, backlash=0.0,
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hole_diameter=0.003175, tooth_per_hole=4):
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"""Generate a rack gear profile based on specified parameters.
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This function creates a rack gear by calculating the geometry based on
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the provided parameters such as millimeters per tooth, number of teeth,
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height, pressure angle, backlash, hole diameter, and teeth per hole. It
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constructs the gear shape using the Shapely library and duplicates the
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tooth to create the full rack. If a hole diameter is specified, it also
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creates holes along the rack. The resulting gear is named based on the
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input parameters.
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Args:
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mm_per_tooth (float): The distance in millimeters for each tooth. Default is 0.01.
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number_of_teeth (int): The total number of teeth on the rack. Default is 11.
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height (float): The height of the rack. Default is 0.012.
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pressure_angle (float): The pressure angle in radians. Default is 0.3488.
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backlash (float): The backlash distance in millimeters. Default is 0.0.
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hole_diameter (float): The diameter of the holes in millimeters. Default is 0.003175.
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tooth_per_hole (int): The number of teeth per hole. Default is 4.
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"""
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simple.deselect()
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mm_per_tooth *= 1000
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a = mm_per_tooth / pi # addendum
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# tooth side is tilted so top/bottom corners move this amount
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t = (a * sin(pressure_angle))
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a /= 1000
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mm_per_tooth /= 1000
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t /= 1000
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shapely_gear = Polygon([
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(-mm_per_tooth * 2/4*1.001, a-height),
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(-mm_per_tooth * 2/4*1.001 - backlash, -a),
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(-mm_per_tooth * 1/4 + backlash - t, -a),
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(-mm_per_tooth * 1/4 + backlash + t, a),
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(mm_per_tooth * 1/4 - backlash - t, a),
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(mm_per_tooth * 1/4 - backlash + t, -a),
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(mm_per_tooth * 2/4*1.001 + backlash, -a),
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(mm_per_tooth * 2/4*1.001, a-height)
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])
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utils.shapelyToCurve('_tooth', shapely_gear, 0.0)
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i = number_of_teeth
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while i > 1:
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simple.duplicate(x=mm_per_tooth)
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i -= 1
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simple.union('_tooth')
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simple.move(y=height/2)
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if hole_diameter > 0:
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bpy.ops.curve.simple(align='WORLD', location=(mm_per_tooth/2, 0, 0), rotation=(0, 0, 0), Simple_Type='Circle',
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Simple_radius=hole_diameter/2, shape='3D', use_cyclic_u=True, edit_mode=False)
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simple.active_name('_hole')
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distance = (number_of_teeth-1) * mm_per_tooth
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while distance > tooth_per_hole * mm_per_tooth:
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simple.duplicate(x=tooth_per_hole * mm_per_tooth)
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distance -= tooth_per_hole * mm_per_tooth
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simple.difference('_', '_tooth')
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name = 'rack-' + str(round(mm_per_tooth * 1000, 1))
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name += '-PA-' + str(round(degrees(pressure_angle), 1))
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simple.active_name(name)
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