423 lines
21 KiB
Python
423 lines
21 KiB
Python
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# Copyright (c) 2020-2024, Nerius Anthony Landys. All rights reserved.
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# neri-engineering 'at' protonmail.com
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# https://svn.code.sf.net/p/nl10/code/cq-code/common/metric_threads.py
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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 no
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# warranty of any kind, including its correctness, usefulness, or safety.
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#
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# Simple code example to create meshing M3x0.5 threads:
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###############################################################################
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#
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# male = external_metric_thread(3.0, 0.5, 4.0, z_start= -0.85,
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# top_lead_in=True)
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#
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# # Please note that the female thread is meant for a hole which has
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# # radius equal to metric_thread_major_radius(3.0, 0.5, internal=True),
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# # which is in fact very slightly larger than a 3.0 diameter hole.
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#
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# female = internal_metric_thread(3.0, 0.5, 1.5,
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# bottom_chamfer=True, base_tube_od= 4.5)
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#
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###############################################################################
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# Left hand threads can be created by employing one of the "mirror" operations.
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# Thanks for taking the time to understand and use this code!
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import math
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import cadquery as cq
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###############################################################################
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# The functions which have names preceded by '__' are not meant to be called
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# externally; the remaining functions are written with the intention that they
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# will be called by external code. The first section of code consists of
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# lightweight helper functions; the meat and potatoes of this library is last.
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###############################################################################
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# Return value is in degrees, and currently it's fixed at 30. Essentially this
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# results in a typical 60 degree equilateral triangle cutting bit for threads.
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def metric_thread_angle():
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return 30
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# Helper func. to make code more intuitive and succinct. Degrees --> radians.
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def __deg2rad(degrees):
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return degrees * math.pi / 180
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# In the absence of flat thread valley and flattened thread tip, returns the
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# amount by which the thread "triangle" protrudes outwards (radially) from base
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# cylinder in the case of external thread, or the amount by which the thread
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# "triangle" protrudes inwards from base tube in the case of internal thread.
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def metric_thread_perfect_height(pitch):
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return pitch / (2 * math.tan(__deg2rad(metric_thread_angle())))
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# Up the radii of internal (female) thread in order to provide a little bit of
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# wiggle room around male thread. Right now input parameter 'diameter' is
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# ignored. This function is only used for internal/female threads. Currently
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# there is no practical way to adjust the male/female thread clearance besides
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# to manually edit this function. This design route was chosen for the sake of
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# code simplicity.
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def __metric_thread_internal_radius_increase(diameter, pitch):
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return 0.1 * metric_thread_perfect_height(pitch)
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# Returns the major radius of thread, which is always the greater of the two.
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def metric_thread_major_radius(diameter, pitch, internal=False):
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return (__metric_thread_internal_radius_increase(diameter, pitch) if
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internal else 0.0) + (diameter / 2)
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# What portion of the total pitch is taken up by the angled thread section (and
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# not the squared off valley and tip). The remaining portion (1 minus ratio)
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# will be divided equally between the flattened valley and flattened tip.
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def __metric_thread_effective_ratio():
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return 0.7
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# Returns the minor radius of thread, which is always the lesser of the two.
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def metric_thread_minor_radius(diameter, pitch, internal=False):
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return (metric_thread_major_radius(diameter, pitch, internal)
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- (__metric_thread_effective_ratio() *
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metric_thread_perfect_height(pitch)))
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# What the major radius would be if the cuts were perfectly triangular, without
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# flat spots in the valleys and without flattened tips.
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def metric_thread_perfect_major_radius(diameter, pitch, internal=False):
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return (metric_thread_major_radius(diameter, pitch, internal)
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+ ((1.0 - __metric_thread_effective_ratio()) *
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metric_thread_perfect_height(pitch) / 2))
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# What the minor radius would be if the cuts were perfectly triangular, without
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# flat spots in the valleys and without flattened tips.
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def metric_thread_perfect_minor_radius(diameter, pitch, internal=False):
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return (metric_thread_perfect_major_radius(diameter, pitch, internal)
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- metric_thread_perfect_height(pitch))
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# Returns the lead-in and/or chamfer distance along the z axis of rotation.
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# The lead-in/chamfer only depends on the pitch and is made with the same angle
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# as the thread, that being 30 degrees offset from radial.
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def metric_thread_lead_in(pitch, internal=False):
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return (math.tan(__deg2rad(metric_thread_angle()))
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* (metric_thread_major_radius(256.0, pitch, internal)
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- metric_thread_minor_radius(256.0, pitch, internal)))
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# Returns the width of the flat spot in thread valley of a standard thread.
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# This is also equal to the width of the flat spot on thread tip, on a standard
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# thread.
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def metric_thread_relief(pitch):
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return (1.0 - __metric_thread_effective_ratio()) * pitch / 2
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###############################################################################
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# A few words on modules external_metric_thread() and internal_metric_thread().
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# The parameter 'z_start' is added as a convenience in order to make the male
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# and female threads align perfectly. When male and female threads are created
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# having the same diameter, pitch, and n_starts (usually 1), then so long as
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# they are not translated or rotated (or so long as they are subjected to the
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# same exact translation and rotation), they will intermesh perfectly,
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# regardless of the value of 'z_start' used on each. This is in order that
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# assemblies be able to depict perfectly aligning threads.
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# Generates threads with base cylinder unless 'base_cylinder' is overridden.
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# Please note that 'use_epsilon' is activated by default, which causes a slight
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# budge in the minor radius, inwards, so that overlaps would be created with
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# inner cylinders. (Does not affect thread profile outside of cylinder.)
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###############################################################################
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def external_metric_thread(diameter, # Required parameter, e.g. 3.0 for M3x0.5
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pitch, # Required parameter, e.g. 0.5 for M3x0.5
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length, # Required parameter, e.g. 2.0
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z_start=0.0,
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n_starts=1,
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bottom_lead_in=False, # Lead-in is at same angle as
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top_lead_in =False, # thread, namely 30 degrees.
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bottom_relief=False, # Add relief groove to start or
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top_relief =False, # end of threads (shorten).
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force_outer_radius=-1.0, # Set close to diameter/2.
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use_epsilon=True, # For inner cylinder overlap.
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base_cylinder=True, # Whether to include base cyl.
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cyl_extend_bottom=-1.0,
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cyl_extend_top=-1.0,
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envelope=False): # Draw only envelope, don't cut.
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cyl_extend_bottom = max(0.0, cyl_extend_bottom)
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cyl_extend_top = max(0.0, cyl_extend_top)
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z_off = (1.0 - __metric_thread_effective_ratio()) * pitch / 4
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t_start = z_start
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t_length = length
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if bottom_relief:
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t_start = t_start + (2 * z_off)
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t_length = t_length - (2 * z_off)
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if top_relief:
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t_length = t_length - (2 * z_off)
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outer_r = (force_outer_radius if (force_outer_radius > 0.0) else
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metric_thread_major_radius(diameter,pitch))
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inner_r = metric_thread_minor_radius(diameter,pitch)
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epsilon = 0
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inner_r_adj = inner_r
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inner_z_budge = 0
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if use_epsilon:
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epsilon = (z_off/3) / math.tan(__deg2rad(metric_thread_angle()))
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inner_r_adj = inner_r - epsilon
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inner_z_budge = math.tan(__deg2rad(metric_thread_angle())) * epsilon
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if envelope:
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threads = cq.Workplane("XZ")
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threads = threads.moveTo(inner_r_adj, -pitch)
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threads = threads.lineTo(outer_r, -pitch)
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threads = threads.lineTo(outer_r, t_length + pitch)
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threads = threads.lineTo(inner_r_adj, t_length + pitch)
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threads = threads.close()
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threads = threads.revolve()
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else: # Not envelope, cut the threads.
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wire = cq.Wire.makeHelix(pitch=pitch*n_starts,
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height=t_length+pitch,
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radius=inner_r)
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wire = wire.translate((0,0,-pitch/2))
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wire = wire.rotate(startVector=(0,0,0), endVector=(0,0,1),
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angleDegrees=360*(-pitch/2)/(pitch*n_starts))
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d_mid = ((metric_thread_major_radius(diameter,pitch) - outer_r)
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* math.tan(__deg2rad(metric_thread_angle())))
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thread = cq.Workplane("XZ")
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thread = thread.moveTo(inner_r_adj, -pitch/2 + z_off - inner_z_budge)
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thread = thread.lineTo(outer_r, -(z_off + d_mid))
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thread = thread.lineTo(outer_r, z_off + d_mid)
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thread = thread.lineTo(inner_r_adj, pitch/2 - z_off + inner_z_budge)
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thread = thread.close()
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thread = thread.sweep(wire, isFrenet=True)
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threads = thread
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for addl_start in range(1, n_starts):
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# TODO: Incremental/cumulative rotation may not be as accurate as
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# keeping 'thread' intact and rotating it by correct amount
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# on each iteration. However, changing the code in that
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# regard may disrupt the delicate nature of workarounds
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# with repsect to quirks in the underlying B-rep library.
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thread = thread.rotate(axisStartPoint=(0,0,0),
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axisEndPoint=(0,0,1),
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angleDegrees=360/n_starts)
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threads = threads.union(thread)
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square_shave = cq.Workplane("XY")
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square_shave = square_shave.box(length=outer_r*3, width=outer_r*3,
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height=pitch*2, centered=True)
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square_shave = square_shave.translate((0,0,-pitch)) # Because centered.
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# Always cut the top and bottom square. Otherwise things don't play nice.
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threads = threads.cut(square_shave)
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if bottom_lead_in:
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delta_r = outer_r - inner_r
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rise = math.tan(__deg2rad(metric_thread_angle())) * delta_r
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lead_in = cq.Workplane("XZ")
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lead_in = lead_in.moveTo(inner_r - delta_r, -rise)
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lead_in = lead_in.lineTo(outer_r + delta_r, 2 * rise)
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lead_in = lead_in.lineTo(outer_r + delta_r, -pitch - rise)
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lead_in = lead_in.lineTo(inner_r - delta_r, -pitch - rise)
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lead_in = lead_in.close()
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lead_in = lead_in.revolve()
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threads = threads.cut(lead_in)
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# This was originally a workaround to the anomalous B-rep computation where
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# the top of base cylinder is flush with top of threads, without the use of
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# lead-in. It turns out that preferring the use of the 'render_cyl_early'
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# strategy alleviates other problems as well.
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render_cyl_early = (base_cylinder and ((not top_relief) and
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(not (cyl_extend_top > 0.0)) and
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(not envelope)))
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render_cyl_late = (base_cylinder and (not render_cyl_early))
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if render_cyl_early:
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cyl = cq.Workplane("XY")
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cyl = cyl.circle(radius=inner_r)
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cyl = cyl.extrude(until=length+pitch+cyl_extend_bottom)
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# Make rotation of cylinder consistent with non-workaround case.
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cyl = cyl.rotate(axisStartPoint=(0,0,0), axisEndPoint=(0,0,1),
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angleDegrees=-(360*t_start/(pitch*n_starts)))
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cyl = cyl.translate((0,0,-t_start+(z_start-cyl_extend_bottom)))
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threads = threads.union(cyl)
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# Next, make cuts at the top.
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square_shave = square_shave.translate((0,0,pitch*2+t_length))
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threads = threads.cut(square_shave)
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if top_lead_in:
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delta_r = outer_r - inner_r
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rise = math.tan(__deg2rad(metric_thread_angle())) * delta_r
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lead_in = cq.Workplane("XZ")
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lead_in = lead_in.moveTo(inner_r - delta_r, t_length + rise)
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lead_in = lead_in.lineTo(outer_r + delta_r, t_length - (2 * rise))
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lead_in = lead_in.lineTo(outer_r + delta_r, t_length + pitch + rise)
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lead_in = lead_in.lineTo(inner_r - delta_r, t_length + pitch + rise)
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lead_in = lead_in.close()
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lead_in = lead_in.revolve()
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threads = threads.cut(lead_in)
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# Place the threads into position.
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threads = threads.translate((0,0,t_start))
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if (not envelope):
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threads = threads.rotate(axisStartPoint=(0,0,0), axisEndPoint=(0,0,1),
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angleDegrees=360*t_start/(pitch*n_starts))
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if render_cyl_late:
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cyl = cq.Workplane("XY")
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cyl = cyl.circle(radius=inner_r)
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cyl = cyl.extrude(until=length+cyl_extend_bottom+cyl_extend_top)
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cyl = cyl.translate((0,0,z_start-cyl_extend_bottom))
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threads = threads.union(cyl)
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return threads
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###############################################################################
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# Generates female threads without a base tube, unless 'base_tube_od' is set to
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# something which is sufficiently greater than 'diameter' parameter. Please
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# note that 'use_epsilon' is activated by default, which causes a slight budge
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# in the major radius, outwards, so that overlaps would be created with outer
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# tubes. (Does not affect thread profile inside of tube or beyond extents.)
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###############################################################################
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def internal_metric_thread(diameter, # Required parameter, e.g. 3.0 for M3x0.5
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pitch, # Required parameter, e.g. 0.5 for M3x0.5
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length, # Required parameter, e.g. 2.0.
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z_start=0.0,
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n_starts=1,
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bottom_chamfer=False, # Chamfer is at same angle as
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top_chamfer =False, # thread, namely 30 degrees.
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bottom_relief=False, # Add relief groove to start or
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top_relief =False, # end of threads (shorten).
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use_epsilon=True, # For outer cylinder overlap.
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# The base tube outer diameter must be sufficiently
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# large for tube to be rendered. Otherwise ignored.
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base_tube_od=-1.0,
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tube_extend_bottom=-1.0,
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tube_extend_top=-1.0,
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envelope=False): # Draw only envelope, don't cut.
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tube_extend_bottom = max(0.0, tube_extend_bottom)
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tube_extend_top = max(0.0, tube_extend_top)
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z_off = (1.0 - __metric_thread_effective_ratio()) * pitch / 4
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t_start = z_start
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t_length = length
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if bottom_relief:
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t_start = t_start + (2 * z_off)
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t_length = t_length - (2 * z_off)
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if top_relief:
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t_length = t_length - (2 * z_off)
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outer_r = metric_thread_major_radius(diameter,pitch,
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internal=True)
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inner_r = metric_thread_minor_radius(diameter,pitch,
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internal=True)
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epsilon = 0
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outer_r_adj = outer_r
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outer_z_budge = 0
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if use_epsilon:
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# High values of 'epsilon' sometimes cause entire starts to disappear.
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epsilon = (z_off/5) / math.tan(__deg2rad(metric_thread_angle()))
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outer_r_adj = outer_r + epsilon
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outer_z_budge = math.tan(__deg2rad(metric_thread_angle())) * epsilon
|
||
|
|
|
||
|
|
if envelope:
|
||
|
|
threads = cq.Workplane("XZ")
|
||
|
|
threads = threads.moveTo(outer_r_adj, -pitch)
|
||
|
|
threads = threads.lineTo(inner_r, -pitch)
|
||
|
|
threads = threads.lineTo(inner_r, t_length + pitch)
|
||
|
|
threads = threads.lineTo(outer_r_adj, t_length + pitch)
|
||
|
|
threads = threads.close()
|
||
|
|
threads = threads.revolve()
|
||
|
|
|
||
|
|
else: # Not envelope, cut the threads.
|
||
|
|
wire = cq.Wire.makeHelix(pitch=pitch*n_starts,
|
||
|
|
height=t_length+pitch,
|
||
|
|
radius=inner_r)
|
||
|
|
wire = wire.translate((0,0,-pitch/2))
|
||
|
|
wire = wire.rotate(startVector=(0,0,0), endVector=(0,0,1),
|
||
|
|
angleDegrees=360*(-pitch/2)/(pitch*n_starts))
|
||
|
|
thread = cq.Workplane("XZ")
|
||
|
|
thread = thread.moveTo(outer_r_adj, -pitch/2 + z_off - outer_z_budge)
|
||
|
|
thread = thread.lineTo(inner_r, -z_off)
|
||
|
|
thread = thread.lineTo(inner_r, z_off)
|
||
|
|
thread = thread.lineTo(outer_r_adj, pitch/2 - z_off + outer_z_budge)
|
||
|
|
thread = thread.close()
|
||
|
|
thread = thread.sweep(wire, isFrenet=True)
|
||
|
|
threads = thread
|
||
|
|
for addl_start in range(1, n_starts):
|
||
|
|
# TODO: Incremental/cumulative rotation may not be as accurate as
|
||
|
|
# keeping 'thread' intact and rotating it by correct amount
|
||
|
|
# on each iteration. However, changing the code in that
|
||
|
|
# regard may disrupt the delicate nature of workarounds
|
||
|
|
# with repsect to quirks in the underlying B-rep library.
|
||
|
|
thread = thread.rotate(axisStartPoint=(0,0,0),
|
||
|
|
axisEndPoint=(0,0,1),
|
||
|
|
angleDegrees=360/n_starts)
|
||
|
|
threads = threads.union(thread)
|
||
|
|
# Rotate so that the external threads would align.
|
||
|
|
threads = threads.rotate(axisStartPoint=(0,0,0), axisEndPoint=(0,0,1),
|
||
|
|
angleDegrees=180/n_starts)
|
||
|
|
|
||
|
|
square_len = max(outer_r*3, base_tube_od*1.125)
|
||
|
|
square_shave = cq.Workplane("XY")
|
||
|
|
square_shave = square_shave.box(length=square_len, width=square_len,
|
||
|
|
height=pitch*2, centered=True)
|
||
|
|
square_shave = square_shave.translate((0,0,-pitch)) # Because centered.
|
||
|
|
# Always cut the top and bottom square. Otherwise things don't play nice.
|
||
|
|
threads = threads.cut(square_shave)
|
||
|
|
|
||
|
|
if bottom_chamfer:
|
||
|
|
delta_r = outer_r - inner_r
|
||
|
|
rise = math.tan(__deg2rad(metric_thread_angle())) * delta_r
|
||
|
|
chamfer = cq.Workplane("XZ")
|
||
|
|
chamfer = chamfer.moveTo(inner_r - delta_r, 2 * rise)
|
||
|
|
chamfer = chamfer.lineTo(outer_r + delta_r, -rise)
|
||
|
|
chamfer = chamfer.lineTo(outer_r + delta_r, -pitch - rise)
|
||
|
|
chamfer = chamfer.lineTo(inner_r - delta_r, -pitch - rise)
|
||
|
|
chamfer = chamfer.close()
|
||
|
|
chamfer = chamfer.revolve()
|
||
|
|
threads = threads.cut(chamfer)
|
||
|
|
|
||
|
|
# This was originally a workaround to the anomalous B-rep computation where
|
||
|
|
# the top of base tube is flush with top of threads w/o the use of chamfer.
|
||
|
|
# This is now being made consistent with the 'render_cyl_early' strategy in
|
||
|
|
# external_metric_thread() whereby we prefer the "render early" plan of
|
||
|
|
# action even in cases where a top chamfer or lead-in is used.
|
||
|
|
render_tube_early = ((base_tube_od > (outer_r * 2)) and
|
||
|
|
(not top_relief) and
|
||
|
|
(not (tube_extend_top > 0.0)) and
|
||
|
|
(not envelope))
|
||
|
|
render_tube_late = ((base_tube_od > (outer_r * 2)) and
|
||
|
|
(not render_tube_early))
|
||
|
|
if render_tube_early:
|
||
|
|
tube = cq.Workplane("XY")
|
||
|
|
tube = tube.circle(radius=base_tube_od/2)
|
||
|
|
tube = tube.circle(radius=outer_r)
|
||
|
|
tube = tube.extrude(until=length+pitch+tube_extend_bottom)
|
||
|
|
# Make rotation of cylinder consistent with non-workaround case.
|
||
|
|
tube = tube.rotate(axisStartPoint=(0,0,0), axisEndPoint=(0,0,1),
|
||
|
|
angleDegrees=-(360*t_start/(pitch*n_starts)))
|
||
|
|
tube = tube.translate((0,0,-t_start+(z_start-tube_extend_bottom)))
|
||
|
|
threads = threads.union(tube)
|
||
|
|
|
||
|
|
# Next, make cuts at the top.
|
||
|
|
square_shave = square_shave.translate((0,0,pitch*2+t_length))
|
||
|
|
threads = threads.cut(square_shave)
|
||
|
|
|
||
|
|
if top_chamfer:
|
||
|
|
delta_r = outer_r - inner_r
|
||
|
|
rise = math.tan(__deg2rad(metric_thread_angle())) * delta_r
|
||
|
|
chamfer = cq.Workplane("XZ")
|
||
|
|
chamfer = chamfer.moveTo(inner_r - delta_r, t_length - (2 * rise))
|
||
|
|
chamfer = chamfer.lineTo(outer_r + delta_r, t_length + rise)
|
||
|
|
chamfer = chamfer.lineTo(outer_r + delta_r, t_length + pitch + rise)
|
||
|
|
chamfer = chamfer.lineTo(inner_r - delta_r, t_length + pitch + rise)
|
||
|
|
chamfer = chamfer.close()
|
||
|
|
chamfer = chamfer.revolve()
|
||
|
|
threads = threads.cut(chamfer)
|
||
|
|
|
||
|
|
# Place the threads into position.
|
||
|
|
threads = threads.translate((0,0,t_start))
|
||
|
|
if (not envelope):
|
||
|
|
threads = threads.rotate(axisStartPoint=(0,0,0), axisEndPoint=(0,0,1),
|
||
|
|
angleDegrees=360*t_start/(pitch*n_starts))
|
||
|
|
|
||
|
|
if render_tube_late:
|
||
|
|
tube = cq.Workplane("XY")
|
||
|
|
tube = tube.circle(radius=base_tube_od/2)
|
||
|
|
tube = tube.circle(radius=outer_r)
|
||
|
|
tube = tube.extrude(until=length+tube_extend_bottom+tube_extend_top)
|
||
|
|
tube = tube.translate((0,0,z_start-tube_extend_bottom))
|
||
|
|
threads = threads.union(tube)
|
||
|
|
|
||
|
|
return threads
|