My self-made 3D-printable designs, mainly in OpenSCAD
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threads.scad 15KB

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