My self-made 3D-printable designs, mainly in OpenSCAD
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  1. /*
  2. * ISO-standard metric threads, following this specification:
  3. * http://en.wikipedia.org/wiki/ISO_metric_screw_thread
  4. *
  5. * Copyright 2020 Dan Kirshner - dan_kirshner@yahoo.com
  6. * This program is free software: you can redistribute it and/or modify
  7. * it under the terms of the GNU General Public License as published by
  8. * the Free Software Foundation, either version 3 of the License, or
  9. * (at your option) any later version.
  10. *
  11. * This program is distributed in the hope that it will be useful,
  12. * but WITHOUT ANY WARRANTY; without even the implied warranty of
  13. * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
  14. * GNU General Public License for more details.
  15. *
  16. * See <http://www.gnu.org/licenses/>.
  17. *
  18. * Version 2.4. 2019-07-14 Add test option - do not render threads.
  19. * Version 2.3. 2017-08-31 Default for leadin: 0 (best for internal threads).
  20. * Version 2.2. 2017-01-01 Correction for angle; leadfac option. (Thanks to
  21. * Andrew Allen <a2intl@gmail.com>.)
  22. * Version 2.1. 2016-12-04 Chamfer bottom end (low-z); leadin option.
  23. * Version 2.0. 2016-11-05 Backwards compatibility (earlier OpenSCAD) fixes.
  24. * Version 1.9. 2016-07-03 Option: tapered.
  25. * Version 1.8. 2016-01-08 Option: (non-standard) angle.
  26. * Version 1.7. 2015-11-28 Larger x-increment - for small-diameters.
  27. * Version 1.6. 2015-09-01 Options: square threads, rectangular threads.
  28. * Version 1.5. 2015-06-12 Options: thread_size, groove.
  29. * Version 1.4. 2014-10-17 Use "faces" instead of "triangles" for polyhedron
  30. * Version 1.3. 2013-12-01 Correct loop over turns -- don't have early cut-off
  31. * Version 1.2. 2012-09-09 Use discrete polyhedra rather than linear_extrude ()
  32. * Version 1.1. 2012-09-07 Corrected to right-hand threads!
  33. */
  34. // Examples.
  35. //
  36. // Standard M8 x 1.
  37. // metric_thread (diameter=8, pitch=1, length=4);
  38. // Square thread.
  39. // metric_thread (diameter=8, pitch=1, length=4, square=true);
  40. // Non-standard: long pitch, same thread size.
  41. //metric_thread (diameter=8, pitch=4, length=4, thread_size=1, groove=true);
  42. // Non-standard: 20 mm diameter, long pitch, square "trough" width 3 mm,
  43. // depth 1 mm.
  44. //metric_thread (diameter=20, pitch=8, length=16, square=true, thread_size=6,
  45. // groove=true, rectangle=0.333);
  46. // English: 1/4 x 20.
  47. //english_thread (diameter=1/4, threads_per_inch=20, length=1);
  48. // Tapered. Example -- pipe size 3/4" -- per:
  49. // http://www.engineeringtoolbox.com/npt-national-pipe-taper-threads-d_750.html
  50. // english_thread (diameter=1.05, threads_per_inch=14, length=3/4, taper=1/16);
  51. // Thread for mounting on Rohloff hub.
  52. //difference () {
  53. // cylinder (r=20, h=10, $fn=100);
  54. //
  55. // metric_thread (diameter=34, pitch=1, length=10, internal=true, n_starts=6);
  56. //}
  57. // ----------------------------------------------------------------------------
  58. function segments (diameter) = min (50, max (ceil (diameter*6), 25));
  59. // ----------------------------------------------------------------------------
  60. // diameter - outside diameter of threads in mm. Default: 8.
  61. // pitch - thread axial "travel" per turn in mm. Default: 1.
  62. // length - overall axial length of thread in mm. Default: 1.
  63. // internal - true = clearances for internal thread (e.g., a nut).
  64. // false = clearances for external thread (e.g., a bolt).
  65. // (Internal threads should be "cut out" from a solid using
  66. // difference ()). Default: false.
  67. // n_starts - Number of thread starts (e.g., DNA, a "double helix," has
  68. // n_starts=2). See wikipedia Screw_thread. Default: 1.
  69. // thread_size - (non-standard) axial width of a single thread "V" - independent
  70. // of pitch. Default: same as pitch.
  71. // groove - (non-standard) true = subtract inverted "V" from cylinder
  72. // (rather thanadd protruding "V" to cylinder). Default: false.
  73. // square - true = square threads (per
  74. // https://en.wikipedia.org/wiki/Square_thread_form). Default:
  75. // false.
  76. // rectangle - (non-standard) "Rectangular" thread - ratio depth/(axial) width
  77. // Default: 0 (standard "v" thread).
  78. // angle - (non-standard) angle (deg) of thread side from perpendicular to
  79. // axis (default = standard = 30 degrees).
  80. // taper - diameter change per length (National Pipe Thread/ANSI B1.20.1
  81. // is 1" diameter per 16" length). Taper decreases from 'diameter'
  82. // as z increases. Default: 0 (no taper).
  83. // leadin - 0 (default): no chamfer; 1: chamfer (45 degree) at max-z end;
  84. // 2: chamfer at both ends, 3: chamfer at z=0 end.
  85. // leadfac - scale of leadin chamfer (default: 1.0 = 1/2 thread).
  86. // test - true = do not render threads (just draw "blank" cylinder).
  87. // Default: false (draw threads).
  88. module metric_thread (diameter=8, pitch=1, length=1, internal=false, n_starts=1,
  89. thread_size=-1, groove=false, square=false, rectangle=0,
  90. angle=30, taper=0, leadin=0, leadfac=1.0, test=false)
  91. {
  92. // thread_size: size of thread "V" different than travel per turn (pitch).
  93. // Default: same as pitch.
  94. local_thread_size = thread_size == -1 ? pitch : thread_size;
  95. local_rectangle = rectangle ? rectangle : 1;
  96. n_segments = segments (diameter);
  97. h = (test && ! internal) ? 0 : (square || rectangle) ? local_thread_size*local_rectangle/2 : local_thread_size / (2 * tan(angle));
  98. h_fac1 = (square || rectangle) ? 0.90 : 0.625;
  99. // External thread includes additional relief.
  100. h_fac2 = (square || rectangle) ? 0.95 : 5.3/8;
  101. tapered_diameter = diameter - length*taper;
  102. difference () {
  103. union () {
  104. if (! groove) {
  105. if (! test) {
  106. metric_thread_turns (diameter, pitch, length, internal, n_starts,
  107. local_thread_size, groove, square, rectangle, angle,
  108. taper);
  109. }
  110. }
  111. difference () {
  112. // Solid center, including Dmin truncation.
  113. if (groove) {
  114. cylinder (r1=diameter/2, r2=tapered_diameter/2,
  115. h=length, $fn=n_segments);
  116. } else if (internal) {
  117. cylinder (r1=diameter/2 - h*h_fac1, r2=tapered_diameter/2 - h*h_fac1,
  118. h=length, $fn=n_segments);
  119. } else {
  120. // External thread.
  121. cylinder (r1=diameter/2 - h*h_fac2, r2=tapered_diameter/2 - h*h_fac2,
  122. h=length, $fn=n_segments);
  123. }
  124. if (groove) {
  125. if (! test) {
  126. metric_thread_turns (diameter, pitch, length, internal, n_starts,
  127. local_thread_size, groove, square, rectangle,
  128. angle, taper);
  129. }
  130. }
  131. }
  132. }
  133. // chamfer z=0 end if leadin is 2 or 3
  134. if (leadin == 2 || leadin == 3) {
  135. difference () {
  136. cylinder (r=diameter/2 + 1, h=h*h_fac1*leadfac, $fn=n_segments);
  137. cylinder (r2=diameter/2, r1=diameter/2 - h*h_fac1*leadfac, h=h*h_fac1*leadfac,
  138. $fn=n_segments);
  139. }
  140. }
  141. // chamfer z-max end if leadin is 1 or 2.
  142. if (leadin == 1 || leadin == 2) {
  143. translate ([0, 0, length + 0.05 - h*h_fac1*leadfac]) {
  144. difference () {
  145. cylinder (r=diameter/2 + 1, h=h*h_fac1*leadfac, $fn=n_segments);
  146. cylinder (r1=tapered_diameter/2, r2=tapered_diameter/2 - h*h_fac1*leadfac, h=h*h_fac1*leadfac,
  147. $fn=n_segments);
  148. }
  149. }
  150. }
  151. }
  152. }
  153. // ----------------------------------------------------------------------------
  154. // Input units in inches.
  155. // Note: units of measure in drawing are mm!
  156. module english_thread (diameter=0.25, threads_per_inch=20, length=1,
  157. internal=false, n_starts=1, thread_size=-1, groove=false,
  158. square=false, rectangle=0, angle=30, taper=0, leadin=0,
  159. leadfac=1.0, test=false)
  160. {
  161. // Convert to mm.
  162. mm_diameter = diameter*25.4;
  163. mm_pitch = (1.0/threads_per_inch)*25.4;
  164. mm_length = length*25.4;
  165. echo (str ("mm_diameter: ", mm_diameter));
  166. echo (str ("mm_pitch: ", mm_pitch));
  167. echo (str ("mm_length: ", mm_length));
  168. metric_thread (mm_diameter, mm_pitch, mm_length, internal, n_starts,
  169. thread_size, groove, square, rectangle, angle, taper, leadin,
  170. leadfac, test);
  171. }
  172. // ----------------------------------------------------------------------------
  173. module metric_thread_turns (diameter, pitch, length, internal, n_starts,
  174. thread_size, groove, square, rectangle, angle,
  175. taper)
  176. {
  177. // Number of turns needed.
  178. n_turns = floor (length/pitch);
  179. intersection () {
  180. // Start one below z = 0. Gives an extra turn at each end.
  181. for (i=[-1*n_starts : n_turns+1]) {
  182. translate ([0, 0, i*pitch]) {
  183. metric_thread_turn (diameter, pitch, internal, n_starts,
  184. thread_size, groove, square, rectangle, angle,
  185. taper, i*pitch);
  186. }
  187. }
  188. // Cut to length.
  189. translate ([0, 0, length/2]) {
  190. cube ([diameter*3, diameter*3, length], center=true);
  191. }
  192. }
  193. }
  194. // ----------------------------------------------------------------------------
  195. module metric_thread_turn (diameter, pitch, internal, n_starts, thread_size,
  196. groove, square, rectangle, angle, taper, z)
  197. {
  198. n_segments = segments (diameter);
  199. fraction_circle = 1.0/n_segments;
  200. for (i=[0 : n_segments-1]) {
  201. rotate ([0, 0, i*360*fraction_circle]) {
  202. translate ([0, 0, i*n_starts*pitch*fraction_circle]) {
  203. //current_diameter = diameter - taper*(z + i*n_starts*pitch*fraction_circle);
  204. thread_polyhedron ((diameter - taper*(z + i*n_starts*pitch*fraction_circle))/2,
  205. pitch, internal, n_starts, thread_size, groove,
  206. square, rectangle, angle);
  207. }
  208. }
  209. }
  210. }
  211. // ----------------------------------------------------------------------------
  212. module thread_polyhedron (radius, pitch, internal, n_starts, thread_size,
  213. groove, square, rectangle, angle)
  214. {
  215. n_segments = segments (radius*2);
  216. fraction_circle = 1.0/n_segments;
  217. local_rectangle = rectangle ? rectangle : 1;
  218. h = (square || rectangle) ? thread_size*local_rectangle/2 : thread_size / (2 * tan(angle));
  219. outer_r = radius + (internal ? h/20 : 0); // Adds internal relief.
  220. //echo (str ("outer_r: ", outer_r));
  221. // A little extra on square thread -- make sure overlaps cylinder.
  222. h_fac1 = (square || rectangle) ? 1.1 : 0.875;
  223. inner_r = radius - h*h_fac1; // Does NOT do Dmin_truncation - do later with
  224. // cylinder.
  225. translate_y = groove ? outer_r + inner_r : 0;
  226. reflect_x = groove ? 1 : 0;
  227. // Make these just slightly bigger (keep in proportion) so polyhedra will
  228. // overlap.
  229. x_incr_outer = (! groove ? outer_r : inner_r) * fraction_circle * 2 * PI * 1.02;
  230. x_incr_inner = (! groove ? inner_r : outer_r) * fraction_circle * 2 * PI * 1.02;
  231. z_incr = n_starts * pitch * fraction_circle * 1.005;
  232. /*
  233. (angles x0 and x3 inner are actually 60 deg)
  234. /\ (x2_inner, z2_inner) [2]
  235. / \
  236. (x3_inner, z3_inner) / \
  237. [3] \ \
  238. |\ \ (x2_outer, z2_outer) [6]
  239. | \ /
  240. | \ /|
  241. z |[7]\/ / (x1_outer, z1_outer) [5]
  242. | | | /
  243. | x | |/
  244. | / | / (x0_outer, z0_outer) [4]
  245. | / | / (behind: (x1_inner, z1_inner) [1]
  246. |/ | /
  247. y________| |/
  248. (r) / (x0_inner, z0_inner) [0]
  249. */
  250. x1_outer = outer_r * fraction_circle * 2 * PI;
  251. z0_outer = (outer_r - inner_r) * tan(angle);
  252. //echo (str ("z0_outer: ", z0_outer));
  253. //polygon ([[inner_r, 0], [outer_r, z0_outer],
  254. // [outer_r, 0.5*pitch], [inner_r, 0.5*pitch]]);
  255. z1_outer = z0_outer + z_incr;
  256. // Give internal square threads some clearance in the z direction, too.
  257. bottom = internal ? 0.235 : 0.25;
  258. top = internal ? 0.765 : 0.75;
  259. translate ([0, translate_y, 0]) {
  260. mirror ([reflect_x, 0, 0]) {
  261. if (square || rectangle) {
  262. // Rule for face ordering: look at polyhedron from outside: points must
  263. // be in clockwise order.
  264. polyhedron (
  265. points = [
  266. [-x_incr_inner/2, -inner_r, bottom*thread_size], // [0]
  267. [x_incr_inner/2, -inner_r, bottom*thread_size + z_incr], // [1]
  268. [x_incr_inner/2, -inner_r, top*thread_size + z_incr], // [2]
  269. [-x_incr_inner/2, -inner_r, top*thread_size], // [3]
  270. [-x_incr_outer/2, -outer_r, bottom*thread_size], // [4]
  271. [x_incr_outer/2, -outer_r, bottom*thread_size + z_incr], // [5]
  272. [x_incr_outer/2, -outer_r, top*thread_size + z_incr], // [6]
  273. [-x_incr_outer/2, -outer_r, top*thread_size] // [7]
  274. ],
  275. faces = [
  276. [0, 3, 7, 4], // This-side trapezoid
  277. [1, 5, 6, 2], // Back-side trapezoid
  278. [0, 1, 2, 3], // Inner rectangle
  279. [4, 7, 6, 5], // Outer rectangle
  280. // These are not planar, so do with separate triangles.
  281. [7, 2, 6], // Upper rectangle, bottom
  282. [7, 3, 2], // Upper rectangle, top
  283. [0, 5, 1], // Lower rectangle, bottom
  284. [0, 4, 5] // Lower rectangle, top
  285. ]
  286. );
  287. } else {
  288. // Rule for face ordering: look at polyhedron from outside: points must
  289. // be in clockwise order.
  290. polyhedron (
  291. points = [
  292. [-x_incr_inner/2, -inner_r, 0], // [0]
  293. [x_incr_inner/2, -inner_r, z_incr], // [1]
  294. [x_incr_inner/2, -inner_r, thread_size + z_incr], // [2]
  295. [-x_incr_inner/2, -inner_r, thread_size], // [3]
  296. [-x_incr_outer/2, -outer_r, z0_outer], // [4]
  297. [x_incr_outer/2, -outer_r, z0_outer + z_incr], // [5]
  298. [x_incr_outer/2, -outer_r, thread_size - z0_outer + z_incr], // [6]
  299. [-x_incr_outer/2, -outer_r, thread_size - z0_outer] // [7]
  300. ],
  301. faces = [
  302. [0, 3, 7, 4], // This-side trapezoid
  303. [1, 5, 6, 2], // Back-side trapezoid
  304. [0, 1, 2, 3], // Inner rectangle
  305. [4, 7, 6, 5], // Outer rectangle
  306. // These are not planar, so do with separate triangles.
  307. [7, 2, 6], // Upper rectangle, bottom
  308. [7, 3, 2], // Upper rectangle, top
  309. [0, 5, 1], // Lower rectangle, bottom
  310. [0, 4, 5] // Lower rectangle, top
  311. ]
  312. );
  313. }
  314. }
  315. }
  316. }