mirror of
https://github.com/DJSundog/NopSCADlib.git
synced 2024-11-30 02:30:03 -05:00
Added a utility for making involute spur gears
This commit is contained in:
Chris Palmer
parent
e4d93366fa
commit
71ac571346
1
lib.scad
1
lib.scad
@ -84,6 +84,7 @@ use <utils/rounded_cylinder.scad>
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use <utils/dogbones.scad>
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use <utils/tube.scad>
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use <utils/quadrant.scad>
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use <utils/gears.scad>
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use <utils/hanging_hole.scad>
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use <utils/fillet.scad>
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use <utils/rounded_polygon.scad>
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64
readme.md
64
readme.md
@ -22,19 +22,19 @@ See [usage](docs/usage.md) for requirements, installation instructions and a usa
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<tr><td> <a href = "#Ball_bearings">Ball_bearings</a> </td><td> <a href = "#KP_pillow_blocks">KP_pillow_blocks</a> </td><td> <a href = "#Ring_terminals">Ring_terminals</a> </td><td> <a href = "#Butt_box">Butt_box</a> </td><td> <a href = "#Bezier">Bezier</a> </td><td> <a href = "#Clip">Clip</a> </td></tr>
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<tr><td> <a href = "#Batteries">Batteries</a> </td><td> <a href = "#LDRs">LDRs</a> </td><td> <a href = "#Rockers">Rockers</a> </td><td> <a href = "#Cable_grommets">Cable_grommets</a> </td><td> <a href = "#Dogbones">Dogbones</a> </td><td> <a href = "#Global">Global</a> </td></tr>
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<tr><td> <a href = "#Belts">Belts</a> </td><td> <a href = "#LED_meters">LED_meters</a> </td><td> <a href = "#Rod">Rod</a> </td><td> <a href = "#Carriers">Carriers</a> </td><td> <a href = "#Fillet">Fillet</a> </td><td> <a href = "#Polyholes">Polyholes</a> </td></tr>
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<tr><td> <a href = "#Blowers">Blowers</a> </td><td> <a href = "#LEDs">LEDs</a> </td><td> <a href = "#SCS_bearing_blocks">SCS_bearing_blocks</a> </td><td> <a href = "#Corner_block">Corner_block</a> </td><td> <a href = "#Hanging_hole">Hanging_hole</a> </td><td> <a href = "#Rounded_rectangle">Rounded_rectangle</a> </td></tr>
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<tr><td> <a href = "#Bulldogs">Bulldogs</a> </td><td> <a href = "#Leadnuts">Leadnuts</a> </td><td> <a href = "#SK_brackets">SK_brackets</a> </td><td> <a href = "#Door_hinge">Door_hinge</a> </td><td> <a href = "#Layout">Layout</a> </td><td> <a href = "#Sphere">Sphere</a> </td></tr>
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<tr><td> <a href = "#Buttons">Buttons</a> </td><td> <a href = "#Light_strips">Light_strips</a> </td><td> <a href = "#SMDs">SMDs</a> </td><td> <a href = "#Door_latch">Door_latch</a> </td><td> <a href = "#Maths">Maths</a> </td><td> <a href = "#Teardrops">Teardrops</a> </td></tr>
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<tr><td> <a href = "#Cable_strips">Cable_strips</a> </td><td> <a href = "#Linear_bearings">Linear_bearings</a> </td><td> <a href = "#SSRs">SSRs</a> </td><td> <a href = "#Fan_guard">Fan_guard</a> </td><td> <a href = "#Offset">Offset</a> </td><td></td></tr>
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<tr><td> <a href = "#Cameras">Cameras</a> </td><td> <a href = "#Mains_sockets">Mains_sockets</a> </td><td> <a href = "#Screws">Screws</a> </td><td> <a href = "#Fixing_block">Fixing_block</a> </td><td> <a href = "#Quadrant">Quadrant</a> </td><td></td></tr>
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<tr><td> <a href = "#Circlips">Circlips</a> </td><td> <a href = "#Microswitches">Microswitches</a> </td><td> <a href = "#Sealing_strip">Sealing_strip</a> </td><td> <a href = "#Flat_hinge">Flat_hinge</a> </td><td> <a href = "#Round">Round</a> </td><td></td></tr>
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<tr><td> <a href = "#Components">Components</a> </td><td> <a href = "#Microview">Microview</a> </td><td> <a href = "#Sheets">Sheets</a> </td><td> <a href = "#Foot">Foot</a> </td><td> <a href = "#Rounded_cylinder">Rounded_cylinder</a> </td><td></td></tr>
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<tr><td> <a href = "#DIP">DIP</a> </td><td> <a href = "#Modules">Modules</a> </td><td> <a href = "#Spades">Spades</a> </td><td> <a href = "#Handle">Handle</a> </td><td> <a href = "#Rounded_polygon">Rounded_polygon</a> </td><td></td></tr>
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<tr><td> <a href = "#D_connectors">D_connectors</a> </td><td> <a href = "#Nuts">Nuts</a> </td><td> <a href = "#Spools">Spools</a> </td><td> <a href = "#PCB_mount">PCB_mount</a> </td><td> <a href = "#Sector">Sector</a> </td><td></td></tr>
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<tr><td> <a href = "#Displays">Displays</a> </td><td> <a href = "#O_ring">O_ring</a> </td><td> <a href = "#Springs">Springs</a> </td><td> <a href = "#PSU_shroud">PSU_shroud</a> </td><td> <a href = "#Sweep">Sweep</a> </td><td></td></tr>
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<tr><td> <a href = "#Extrusion_brackets">Extrusion_brackets</a> </td><td> <a href = "#Opengrab">Opengrab</a> </td><td> <a href = "#Stepper_motors">Stepper_motors</a> </td><td> <a href = "#Printed_box">Printed_box</a> </td><td> <a href = "#Thread">Thread</a> </td><td></td></tr>
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<tr><td> <a href = "#Extrusions">Extrusions</a> </td><td> <a href = "#PCB">PCB</a> </td><td> <a href = "#Swiss_clips">Swiss_clips</a> </td><td> <a href = "#Ribbon_clamp">Ribbon_clamp</a> </td><td> <a href = "#Tube">Tube</a> </td><td></td></tr>
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<tr><td> <a href = "#Fans">Fans</a> </td><td> <a href = "#PCBs">PCBs</a> </td><td> <a href = "#Toggles">Toggles</a> </td><td> <a href = "#SSR_shroud">SSR_shroud</a> </td><td></td><td></td></tr>
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<tr><td> <a href = "#Blowers">Blowers</a> </td><td> <a href = "#LEDs">LEDs</a> </td><td> <a href = "#SCS_bearing_blocks">SCS_bearing_blocks</a> </td><td> <a href = "#Corner_block">Corner_block</a> </td><td> <a href = "#Gears">Gears</a> </td><td> <a href = "#Rounded_rectangle">Rounded_rectangle</a> </td></tr>
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<tr><td> <a href = "#Bulldogs">Bulldogs</a> </td><td> <a href = "#Leadnuts">Leadnuts</a> </td><td> <a href = "#SK_brackets">SK_brackets</a> </td><td> <a href = "#Door_hinge">Door_hinge</a> </td><td> <a href = "#Hanging_hole">Hanging_hole</a> </td><td> <a href = "#Sphere">Sphere</a> </td></tr>
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<tr><td> <a href = "#Buttons">Buttons</a> </td><td> <a href = "#Light_strips">Light_strips</a> </td><td> <a href = "#SMDs">SMDs</a> </td><td> <a href = "#Door_latch">Door_latch</a> </td><td> <a href = "#Layout">Layout</a> </td><td> <a href = "#Teardrops">Teardrops</a> </td></tr>
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<tr><td> <a href = "#Cable_strips">Cable_strips</a> </td><td> <a href = "#Linear_bearings">Linear_bearings</a> </td><td> <a href = "#SSRs">SSRs</a> </td><td> <a href = "#Fan_guard">Fan_guard</a> </td><td> <a href = "#Maths">Maths</a> </td><td></td></tr>
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<tr><td> <a href = "#Cameras">Cameras</a> </td><td> <a href = "#Mains_sockets">Mains_sockets</a> </td><td> <a href = "#Screws">Screws</a> </td><td> <a href = "#Fixing_block">Fixing_block</a> </td><td> <a href = "#Offset">Offset</a> </td><td></td></tr>
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<tr><td> <a href = "#Circlips">Circlips</a> </td><td> <a href = "#Microswitches">Microswitches</a> </td><td> <a href = "#Sealing_strip">Sealing_strip</a> </td><td> <a href = "#Flat_hinge">Flat_hinge</a> </td><td> <a href = "#Quadrant">Quadrant</a> </td><td></td></tr>
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<tr><td> <a href = "#Components">Components</a> </td><td> <a href = "#Microview">Microview</a> </td><td> <a href = "#Sheets">Sheets</a> </td><td> <a href = "#Foot">Foot</a> </td><td> <a href = "#Round">Round</a> </td><td></td></tr>
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<tr><td> <a href = "#DIP">DIP</a> </td><td> <a href = "#Modules">Modules</a> </td><td> <a href = "#Spades">Spades</a> </td><td> <a href = "#Handle">Handle</a> </td><td> <a href = "#Rounded_cylinder">Rounded_cylinder</a> </td><td></td></tr>
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<tr><td> <a href = "#D_connectors">D_connectors</a> </td><td> <a href = "#Nuts">Nuts</a> </td><td> <a href = "#Spools">Spools</a> </td><td> <a href = "#PCB_mount">PCB_mount</a> </td><td> <a href = "#Rounded_polygon">Rounded_polygon</a> </td><td></td></tr>
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<tr><td> <a href = "#Displays">Displays</a> </td><td> <a href = "#O_ring">O_ring</a> </td><td> <a href = "#Springs">Springs</a> </td><td> <a href = "#PSU_shroud">PSU_shroud</a> </td><td> <a href = "#Sector">Sector</a> </td><td></td></tr>
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<tr><td> <a href = "#Extrusion_brackets">Extrusion_brackets</a> </td><td> <a href = "#Opengrab">Opengrab</a> </td><td> <a href = "#Stepper_motors">Stepper_motors</a> </td><td> <a href = "#Printed_box">Printed_box</a> </td><td> <a href = "#Sweep">Sweep</a> </td><td></td></tr>
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<tr><td> <a href = "#Extrusions">Extrusions</a> </td><td> <a href = "#PCB">PCB</a> </td><td> <a href = "#Swiss_clips">Swiss_clips</a> </td><td> <a href = "#Ribbon_clamp">Ribbon_clamp</a> </td><td> <a href = "#Thread">Thread</a> </td><td></td></tr>
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<tr><td> <a href = "#Fans">Fans</a> </td><td> <a href = "#PCBs">PCBs</a> </td><td> <a href = "#Toggles">Toggles</a> </td><td> <a href = "#SSR_shroud">SSR_shroud</a> </td><td> <a href = "#Tube">Tube</a> </td><td></td></tr>
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<tr><td> <a href = "#Fuseholder">Fuseholder</a> </td><td> <a href = "#PSUs">PSUs</a> </td><td> <a href = "#Transformers">Transformers</a> </td><td> <a href = "#Screw_knob">Screw_knob</a> </td><td></td><td></td></tr>
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<tr><td> <a href = "#Geared_steppers">Geared_steppers</a> </td><td> <a href = "#Panel_meters">Panel_meters</a> </td><td> <a href = "#Tubings">Tubings</a> </td><td> <a href = "#Socket_box">Socket_box</a> </td><td></td><td></td></tr>
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<tr><td> <a href = "#Green_terminals">Green_terminals</a> </td><td> <a href = "#Pillars">Pillars</a> </td><td> <a href = "#Variacs">Variacs</a> </td><td> <a href = "#Strap_handle">Strap_handle</a> </td><td></td><td></td></tr>
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@ -5221,6 +5221,44 @@ Rounded fillet for adding to corners.
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<a href="#top">Top</a>
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---
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<a name="Gears"></a>
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## Gears
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Utilities for making involute gears.
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Formulas from <https://khkgears.net/new/gear_knowledge/gear_technical_reference/involute_gear_profile.html>
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and <https://www.tec-science.com/mechanical-power-transmission/involute-gear/calculation-of-involute-gears/>
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```involute_gear_profile()``` returns a polygon that can have the bore and spokes, etc, subtracted from it before linear extruding it to 3D.
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Helical gears can be made using ```twist``` and bevel gears using ```scale``` parameters of ```linear_extrude()```.
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Gears with less than 19 teeth (when pressure angle is 20) are profile shifted to avoid undercutting the tooth root. 7 teeth is considered
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the practical minimum.
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The clearance between tip and root defaults to module / 6, but can be overridden by setting the ```clearance``` parameter.
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[utils/gears.scad](utils/gears.scad) Implementation.
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[tests/gears.scad](tests/gears.scad) Code for this example.
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### Functions
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| Function | Description |
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|:--- |:--- |
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| ```centre_distance(m, z1, z2, pa)``` | Calculate distance between centres taking profile shift into account |
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| ```involute(r, u)``` | Involute of circle radius r at angle u in radians |
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| ```profile_shift(z, pa)``` | Calculate profile shift for small gears |
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### Modules
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| Module | Description |
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|:--- |:--- |
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| ```involute_gear_profile(m, z, pa = 20, clearance = undef, steps = 20)``` | Calculate profile given module, number of teeth and pressure angle |
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<a href="#top">Top</a>
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---
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58
tests/gears.scad
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58
tests/gears.scad
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@ -0,0 +1,58 @@
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//
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// NopSCADlib Copyright Chris Palmer 2020
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// nop.head@gmail.com
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// hydraraptor.blogspot.com
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//
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// This file is part of NopSCADlib.
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//
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// NopSCADlib is free software: you can redistribute it and/or modify it under the terms of the
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// GNU General Public License as published by the Free Software Foundation, either version 3 of
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// the License, or (at your option) any later version.
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//
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// NopSCADlib is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
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// without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
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// See the GNU General Public License for more details.
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//
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// You should have received a copy of the GNU General Public License along with NopSCADlib.
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// If not, see <https://www.gnu.org/licenses/>.
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//
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include <../utils/core/core.scad>
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use <../utils/gears.scad>
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// left gear teeth
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z1 = 39; // [7 : 1 : 99]
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// Right gear teeth
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z2 = 7; // [7 : 1 : 99]
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// Modulus
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m = 2.0; // [0.1 : 0.1 : 5.0]
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// Pressure angle
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pa = 20; // [14.5, 20, 22.5, 25]
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$show_numbers = false;
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module gears() {
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color(pp1_colour)
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rotate($t * 360)
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linear_extrude(eps, center = true, convexity = z1)
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difference() {
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involute_gear_profile(m, z1, pa);
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circle(r = m * z1 / 10);
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}
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color(pp2_colour)
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translate([centre_distance(m, z1, z2, pa), 0])
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rotate(180 + 180 / z2 + -$t * 360 * z1 / z2)
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linear_extrude(eps, center = true, convexity = z2)
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difference() {
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involute_gear_profile(m, z2, pa);
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circle(r = m * z2 / 10);
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}
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}
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rotate(is_undef($bom) ? 0 : [70, 0, 315])
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gears();
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BIN
tests/png/gears.png
Normal file
BIN
tests/png/gears.png
Normal file
Binary file not shown.
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After Width: | Height: | Size: 58 KiB |
96
utils/gears.scad
Normal file
96
utils/gears.scad
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@ -0,0 +1,96 @@
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//
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// NopSCADlib Copyright Chris Palmer 2020
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// nop.head@gmail.com
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// hydraraptor.blogspot.com
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//
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// This file is part of NopSCADlib.
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//
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// NopSCADlib is free software: you can redistribute it and/or modify it under the terms of the
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// GNU General Public License as published by the Free Software Foundation, either version 3 of
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// the License, or (at your option) any later version.
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//
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// NopSCADlib is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
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// without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
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// See the GNU General Public License for more details.
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//
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// You should have received a copy of the GNU General Public License along with NopSCADlib.
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// If not, see <https://www.gnu.org/licenses/>.
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//
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//
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//! Utilities for making involute gears.
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//!
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//! Formulas from <https://khkgears.net/new/gear_knowledge/gear_technical_reference/involute_gear_profile.html>
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//! and <https://www.tec-science.com/mechanical-power-transmission/involute-gear/calculation-of-involute-gears/>
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//!
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//! ```involute_gear_profile()``` returns a polygon that can have the bore and spokes, etc, subtracted from it before linear extruding it to 3D.
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//! Helical gears can be made using ```twist``` and bevel gears using ```scale``` parameters of ```linear_extrude()```.
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//!
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//! Gears with less than 19 teeth (when pressure angle is 20) are profile shifted to avoid undercutting the tooth root. 7 teeth is considered
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//! the practical minimum.
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//!
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//! The clearance between tip and root defaults to module / 6, but can be overridden by setting the ```clearance``` parameter.
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//
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include <core/core.scad>
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use <maths.scad>
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function involute(r, u) = let(a = degrees(u), c = cos(a), s = sin(a)) r * [c + u * s, s - u * c]; //! Involute of circle radius r at angle u in radians
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function profile_shift(z, pa) = max(1 - z * sqr(sin(pa)) / 2, 0); //! Calculate profile shift for small gears
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function centre_distance(m, z1, z2, pa) = //! Calculate distance between centres taking profile shift into account
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let(x1 = profile_shift(z1, pa), x2 = profile_shift(z2, pa)) m * (z1/2 + z2/2 + x1 + x2);
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module involute_gear_profile(m, z, pa = 20, clearance = undef, steps = 20) { //! Calculate profile given module, number of teeth and pressure angle
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assert(z >= 7, "Gears must have at least 7 teeth.");
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d = m * z; // Reference pitch circle diameter
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x = profile_shift(z, pa); // Profile shift
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c = is_undef(clearance) ? m / 6 : clearance; // Clearance from tip to root
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base_d = d * cos(pa); // Base diameter
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root_r = d / 2 + m * (x - 1) - c; // Root radius (dedendum circle radius)
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tip_d = d + 2 * m * (1 + x); // Tip diameter (addendum circle diameter)
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tpa = acos(base_d / tip_d); // Tip pressure angle
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inva = tan(pa) - radians(pa); // Involute alpha
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invaa = tan(tpa) - radians(tpa); // Involute alphaa
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ta = PI / (2 * z) + 2 * x * tan(pa) / z + inva - invaa; // Tooth tip thickness angle, radians
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crest_w = ta * tip_d; // Crest width
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umax = sqrt(sqr(tip_d / base_d) - 1); // Max value of the involute parameter
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base_r = base_d / 2;
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p1 = involute(base_r, 0);
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p2 = involute(base_r, umax);
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dist = norm(p2 - p1); // distance between beginning and end of the involute curve
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base_angle = 2 * acos((sqr(base_r) + sqr(tip_d / 2) - sqr(dist)) / base_r / tip_d) + degrees(2 * ta);
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root_angle = 360 / z - base_angle;
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root_circle_r = base_r * sin(root_angle / 2);
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if(!is_undef($show_numbers) && $show_numbers) {
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echo(d=d);
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echo(base_d=base_d);
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echo(tip_d=tip_d);
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echo(tpa = tpa);
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echo(inva=inva);
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echo(invaa=invaa);
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echo(x=x);
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echo(ta=ta);
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echo(crest_w=crest_w);
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echo(umax = umax);
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echo(base_angle=base_angle);
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echo(root_angle=root_angle);
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}
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involute = [for(i = [0 : steps], u = umax * i / steps) involute(base_r, u)]; // involute for the bottom side of the tooth
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truncated = [for(p = involute) if((rot2_z(-base_angle / 2) * p).y <= 0) p]; // removed any above the centreline to prevent overlap
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reflection = reverse([for(p = truncated) rot2_z(base_angle) * [p.x, -p.y] ]); // reflect and rotate to make the top edge
|
||||
|
||||
root = reverse([for(a = [90 : 180 / steps : 270]) rot2_z(base_angle + root_angle / 2) * ([base_r, 0] + root_circle_r * [cos(a), sin(a)]) ]);
|
||||
tooth = concat(truncated, reflection, root);
|
||||
gear = concat([for(i = [0 : z - 1], p = tooth) rot2_z(i * 360 / z) * p]);
|
||||
rotate(-base_angle / 2)
|
||||
union() {
|
||||
polygon(gear);
|
||||
|
||||
circle(root_r);
|
||||
}
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user