From 7fdbf9d3267810cd4a92fd02bf899ae739bd2a2f Mon Sep 17 00:00:00 2001 From: Michael Krelin Date: Fri, 15 Jul 2016 12:42:08 +0000 Subject: Threads library as seen at http://dkprojects.net/openscad-threads/ --- diff --git a/threads.scad b/threads.scad new file mode 100644 index 0000000..8dd0b7b --- a/dev/null +++ b/threads.scad @@ -0,0 +1,332 @@ +/* + * ISO-standard metric threads, following this specification: + * http://en.wikipedia.org/wiki/ISO_metric_screw_thread + * + * Dan Kirshner - dan_kirshner@yahoo.com + * + * You are welcome to make free use of this software. Retention of my + * authorship credit would be appreciated. + * + * Version 1.9. 2016-07-03 Option: tapered. + * Version 1.8. 2016-01-08 Option: (non-standard) angle. + * Version 1.7. 2015-11-28 Larger x-increment - for small-diameters. + * Version 1.6. 2015-09-01 Options: square threads, rectangular threads. + * Version 1.5. 2015-06-12 Options: thread_size, groove. + * Version 1.4. 2014-10-17 Use "faces" instead of "triangles" for polyhedron + * Version 1.3. 2013-12-01 Correct loop over turns -- don't have early cut-off + * Version 1.2. 2012-09-09 Use discrete polyhedra rather than linear_extrude () + * Version 1.1. 2012-09-07 Corrected to right-hand threads! + */ + +// Examples. +// +// Standard M8 x 1. +// metric_thread (diameter=8, pitch=1, length=4); + +// Square thread. +// metric_thread (diameter=8, pitch=1, length=4, square=true); + +// Non-standard: long pitch, same thread size. +//metric_thread (diameter=8, pitch=4, length=4, thread_size=1, groove=true); + +// Non-standard: 20 mm diameter, long pitch, square "trough" width 3 mm, +// depth 1 mm. +//metric_thread (diameter=20, pitch=8, length=16, square=true, thread_size=6, +// groove=true, rectangle=0.333); + +// English: 1/4 x 20. +//english_thread (diameter=1/4, threads_per_inch=20, length=1); + +// Tapered. Example -- pipe size 3/4" -- per: +// http://www.engineeringtoolbox.com/npt-national-pipe-taper-threads-d_750.html +// english_thread (diameter=1.05, threads_per_inch=14, length=3/4, taper=1/16); + +// Thread for mounting on Rohloff hub. +//difference () { +// cylinder (r=20, h=10, $fn=100); +// +// metric_thread (diameter=34, pitch=1, length=10, internal=true, n_starts=6); +//} + + +// ---------------------------------------------------------------------------- +function segments (diameter) = min (50, ceil (diameter*6)); + + +// ---------------------------------------------------------------------------- +// internal - true = clearances for internal thread (e.g., a nut). +// false = clearances for external thread (e.g., a bolt). +// (Internal threads should be "cut out" from a solid using +// difference ()). +// n_starts - Number of thread starts (e.g., DNA, a "double helix," has +// n_starts=2). See wikipedia Screw_thread. +// thread_size - (non-standard) size of a single thread "V" - independent of +// pitch. Default: same as pitch. +// groove - (non-standard) subtract inverted "V" from cylinder (rather than +// add protruding "V" to cylinder). +// square - Square threads (per +// https://en.wikipedia.org/wiki/Square_thread_form). +// rectangle - (non-standard) "Rectangular" thread - ratio depth/width +// Default: 1 (square). +// angle - (non-standard) angle (deg) of thread side from perpendicular to +// axis (default = standard = 30 degrees). +// taper - diameter change per length (National Pipe Thread/ANSI B1.20.1 +// is 1" diameter per 16" length). +module metric_thread (diameter=8, pitch=1, length=1, internal=false, n_starts=1, + thread_size=-1, groove=false, square=false, rectangle=0, + angle=30, taper=0) +{ + // thread_size: size of thread "V" different than travel per turn (pitch). + // Default: same as pitch. + local_thread_size = thread_size == -1 ? pitch : thread_size; + local_rectangle = rectangle ? rectangle : 1; + + n_segments = segments (diameter); + h = (square || rectangle) ? local_thread_size*local_rectangle/2 : local_thread_size * cos (angle); + + h_fac1 = (square || rectangle) ? 0.90 : 0.625; + + // External thread includes additional relief. + h_fac2 = (square || rectangle) ? 0.95 : 5.3/8; + + if (! groove) { + metric_thread_turns (diameter, pitch, length, internal, n_starts, + local_thread_size, groove, square, rectangle, angle, + taper); + } + + difference () { + + // Solid center, including Dmin truncation. + tapered_diameter = diameter - length*taper; + if (groove) { + cylinder (r1=diameter/2, r2=tapered_diameter/2, + h=length, $fn=n_segments); + } else if (internal) { + cylinder (r1=diameter/2 - h*h_fac1, r2=tapered_diameter/2 - h*h_fac1, + h=length, $fn=n_segments); + } else { + + // External thread. + cylinder (r1=diameter/2 - h*h_fac2, r2=tapered_diameter/2 - h*h_fac2, + h=length, $fn=n_segments); + } + + if (groove) { + metric_thread_turns (diameter, pitch, length, internal, n_starts, + local_thread_size, groove, square, rectangle, + angle, taper); + } + } +} + + +// ---------------------------------------------------------------------------- +// Input units in inches. +// Note: units of measure in drawing are mm! +module english_thread (diameter=0.25, threads_per_inch=20, length=1, + internal=false, n_starts=1, thread_size=-1, groove=false, + square=false, rectangle=0, angle=30, taper=0) +{ + // Convert to mm. + mm_diameter = diameter*25.4; + mm_pitch = (1.0/threads_per_inch)*25.4; + mm_length = length*25.4; + + echo (str ("mm_diameter: ", mm_diameter)); + echo (str ("mm_pitch: ", mm_pitch)); + echo (str ("mm_length: ", mm_length)); + metric_thread (mm_diameter, mm_pitch, mm_length, internal, n_starts, + thread_size, groove, square, rectangle, angle, taper); +} + +// ---------------------------------------------------------------------------- +module metric_thread_turns (diameter, pitch, length, internal, n_starts, + thread_size, groove, square, rectangle, angle, + taper) +{ + // Number of turns needed. + n_turns = floor (length/pitch); + + intersection () { + + // Start one below z = 0. Gives an extra turn at each end. + for (i=[-1*n_starts : n_turns+1]) { + translate ([0, 0, i*pitch]) { + metric_thread_turn (diameter, pitch, internal, n_starts, + thread_size, groove, square, rectangle, angle, + taper, i*pitch); + } + } + + // Cut to length. + translate ([0, 0, length/2]) { + cube ([diameter*3, diameter*3, length], center=true); + } + } +} + + +// ---------------------------------------------------------------------------- +module metric_thread_turn (diameter, pitch, internal, n_starts, thread_size, + groove, square, rectangle, angle, taper, z) +{ + n_segments = segments (diameter); + fraction_circle = 1.0/n_segments; + for (i=[0 : n_segments-1]) { + rotate ([0, 0, i*360*fraction_circle]) { + translate ([0, 0, i*n_starts*pitch*fraction_circle]) { + current_diameter = diameter - taper*(z + i*n_starts*pitch*fraction_circle); + thread_polyhedron (current_diameter/2, pitch, internal, n_starts, + thread_size, groove, square, rectangle, angle); + } + } + } +} + + +// ---------------------------------------------------------------------------- +// z (see diagram) as function of current radius. +// (Only good for first half-pitch.) +function z_fct (current_radius, radius, pitch, angle) + = 0.5* (current_radius - (radius - 0.875*pitch*cos (angle))) + /cos (angle); + +// ---------------------------------------------------------------------------- +module thread_polyhedron (radius, pitch, internal, n_starts, thread_size, + groove, square, rectangle, angle) +{ + n_segments = segments (radius*2); + fraction_circle = 1.0/n_segments; + + local_rectangle = rectangle ? rectangle : 1; + + h = (square || rectangle) ? thread_size*local_rectangle/2 : thread_size * cos (angle); + outer_r = radius + (internal ? h/20 : 0); // Adds internal relief. + //echo (str ("outer_r: ", outer_r)); + + // A little extra on square thread -- make sure overlaps cylinder. + h_fac1 = (square || rectangle) ? 1.1 : 0.875; + inner_r = radius - h*h_fac1; // Does NOT do Dmin_truncation - do later with + // cylinder. + + translate_y = groove ? outer_r + inner_r : 0; + reflect_x = groove ? 1 : 0; + + // Make these just slightly bigger (keep in proportion) so polyhedra will + // overlap. + x_incr_outer = (! groove ? outer_r : inner_r) * fraction_circle * 2 * PI * 1.02; + x_incr_inner = (! groove ? inner_r : outer_r) * fraction_circle * 2 * PI * 1.02; + z_incr = n_starts * pitch * fraction_circle * 1.005; + + /* + (angles x0 and x3 inner are actually 60 deg) + + /\ (x2_inner, z2_inner) [2] + / \ + (x3_inner, z3_inner) / \ + [3] \ \ + |\ \ (x2_outer, z2_outer) [6] + | \ / + | \ /| + z |[7]\/ / (x1_outer, z1_outer) [5] + | | | / + | x | |/ + | / | / (x0_outer, z0_outer) [4] + | / | / (behind: (x1_inner, z1_inner) [1] + |/ | / + y________| |/ + (r) / (x0_inner, z0_inner) [0] + + */ + + x1_outer = outer_r * fraction_circle * 2 * PI; + + z0_outer = z_fct (outer_r, radius, thread_size, angle); + //echo (str ("z0_outer: ", z0_outer)); + + //polygon ([[inner_r, 0], [outer_r, z0_outer], + // [outer_r, 0.5*pitch], [inner_r, 0.5*pitch]]); + z1_outer = z0_outer + z_incr; + + // Give internal square threads some clearance in the z direction, too. + bottom = internal ? 0.235 : 0.25; + top = internal ? 0.765 : 0.75; + + translate ([0, translate_y, 0]) { + mirror ([reflect_x, 0, 0]) { + + if (square || rectangle) { + + // Rule for face ordering: look at polyhedron from outside: points must + // be in clockwise order. + polyhedron ( + points = [ + [-x_incr_inner/2, -inner_r, bottom*thread_size], // [0] + [x_incr_inner/2, -inner_r, bottom*thread_size + z_incr], // [1] + [x_incr_inner/2, -inner_r, top*thread_size + z_incr], // [2] + [-x_incr_inner/2, -inner_r, top*thread_size], // [3] + + [-x_incr_outer/2, -outer_r, bottom*thread_size], // [4] + [x_incr_outer/2, -outer_r, bottom*thread_size + z_incr], // [5] + [x_incr_outer/2, -outer_r, top*thread_size + z_incr], // [6] + [-x_incr_outer/2, -outer_r, top*thread_size] // [7] + ], + + faces = [ + [0, 3, 7, 4], // This-side trapezoid + + [1, 5, 6, 2], // Back-side trapezoid + + [0, 1, 2, 3], // Inner rectangle + + [4, 7, 6, 5], // Outer rectangle + + // These are not planar, so do with separate triangles. + [7, 2, 6], // Upper rectangle, bottom + [7, 3, 2], // Upper rectangle, top + + [0, 5, 1], // Lower rectangle, bottom + [0, 4, 5] // Lower rectangle, top + ] + ); + } else { + + // Rule for face ordering: look at polyhedron from outside: points must + // be in clockwise order. + polyhedron ( + points = [ + [-x_incr_inner/2, -inner_r, 0], // [0] + [x_incr_inner/2, -inner_r, z_incr], // [1] + [x_incr_inner/2, -inner_r, thread_size + z_incr], // [2] + [-x_incr_inner/2, -inner_r, thread_size], // [3] + + [-x_incr_outer/2, -outer_r, z0_outer], // [4] + [x_incr_outer/2, -outer_r, z0_outer + z_incr], // [5] + [x_incr_outer/2, -outer_r, thread_size - z0_outer + z_incr], // [6] + [-x_incr_outer/2, -outer_r, thread_size - z0_outer] // [7] + ], + + faces = [ + [0, 3, 7, 4], // This-side trapezoid + + [1, 5, 6, 2], // Back-side trapezoid + + [0, 1, 2, 3], // Inner rectangle + + [4, 7, 6, 5], // Outer rectangle + + // These are not planar, so do with separate triangles. + [7, 2, 6], // Upper rectangle, bottom + [7, 3, 2], // Upper rectangle, top + + [0, 5, 1], // Lower rectangle, bottom + [0, 4, 5] // Lower rectangle, top + ] + ); + } + } + } +} + + -- cgit v0.9.0.2