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Added a utility for making involute spur gears

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This commit is contained in:
Chris Palmer 2020-07-06 23:22:11 +01:00
parent e4d93366fa
commit 71ac571346
5 changed files with 206 additions and 13 deletions
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1
lib.scad
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@ -84,6 +84,7 @@ use <utils/rounded_cylinder.scad>
use <utils/dogbones.scad> use <utils/dogbones.scad>
use <utils/tube.scad> use <utils/tube.scad>
use <utils/quadrant.scad> use <utils/quadrant.scad>
use <utils/gears.scad>
use <utils/hanging_hole.scad> use <utils/hanging_hole.scad>
use <utils/fillet.scad> use <utils/fillet.scad>
use <utils/rounded_polygon.scad> use <utils/rounded_polygon.scad>

64
readme.md
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@ -22,19 +22,19 @@ See [usage](docs/usage.md) for requirements, installation instructions and a usa
<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> <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>
<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> <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>
<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> <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>
<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> <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>
<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> <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>
<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> <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>
<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> <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>
<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> <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>
<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> <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>
<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> <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>
<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> <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>
<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> <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>
<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> <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>
<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> <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>
<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> <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>
<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> <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>
<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> <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>
<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> <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>
<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> <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>
@ -5221,6 +5221,44 @@ Rounded fillet for adding to corners.
![fillet](tests/png/fillet.png) ![fillet](tests/png/fillet.png)
<a href="#top">Top</a>
---
<a name="Gears"></a>
## Gears
Utilities for making involute gears.
Formulas from <https://khkgears.net/new/gear_knowledge/gear_technical_reference/involute_gear_profile.html>
and <https://www.tec-science.com/mechanical-power-transmission/involute-gear/calculation-of-involute-gears/>
```involute_gear_profile()``` returns a polygon that can have the bore and spokes, etc, subtracted from it before linear extruding it to 3D.
Helical gears can be made using ```twist``` and bevel gears using ```scale``` parameters of ```linear_extrude()```.
Gears with less than 19 teeth (when pressure angle is 20) are profile shifted to avoid undercutting the tooth root. 7 teeth is considered
the practical minimum.
The clearance between tip and root defaults to module / 6, but can be overridden by setting the ```clearance``` parameter.
[utils/gears.scad](utils/gears.scad) Implementation.
[tests/gears.scad](tests/gears.scad) Code for this example.
### Functions
| Function | Description |
|:--- |:--- |
| ```centre_distance(m, z1, z2, pa)``` | Calculate distance between centres taking profile shift into account |
| ```involute(r, u)``` | Involute of circle radius r at angle u in radians |
| ```profile_shift(z, pa)``` | Calculate profile shift for small gears |
### Modules
| Module | Description |
|:--- |:--- |
| ```involute_gear_profile(m, z, pa = 20, clearance = undef, steps = 20)``` | Calculate profile given module, number of teeth and pressure angle |
![gears](tests/png/gears.png)
<a href="#top">Top</a> <a href="#top">Top</a>
--- ---

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@ -0,0 +1,58 @@
//
// NopSCADlib Copyright Chris Palmer 2020
// nop.head@gmail.com
// hydraraptor.blogspot.com
//
// This file is part of NopSCADlib.
//
// NopSCADlib is free software: you can redistribute it and/or modify it under the terms of the
// GNU General Public License as published by the Free Software Foundation, either version 3 of
// the License, or (at your option) any later version.
//
// NopSCADlib is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
// without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
// See the GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License along with NopSCADlib.
// If not, see <https://www.gnu.org/licenses/>.
//
include <../utils/core/core.scad>
use <../utils/gears.scad>
// left gear teeth
z1 = 39; // [7 : 1 : 99]
// Right gear teeth
z2 = 7; // [7 : 1 : 99]
// Modulus
m = 2.0; // [0.1 : 0.1 : 5.0]
// Pressure angle
pa = 20; // [14.5, 20, 22.5, 25]
$show_numbers = false;
module gears() {
color(pp1_colour)
rotate($t * 360)
linear_extrude(eps, center = true, convexity = z1)
difference() {
involute_gear_profile(m, z1, pa);
circle(r = m * z1 / 10);
}
color(pp2_colour)
translate([centre_distance(m, z1, z2, pa), 0])
rotate(180 + 180 / z2 + -$t * 360 * z1 / z2)
linear_extrude(eps, center = true, convexity = z2)
difference() {
involute_gear_profile(m, z2, pa);
circle(r = m * z2 / 10);
}
}
rotate(is_undef($bom) ? 0 : [70, 0, 315])
gears();

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@ -0,0 +1,96 @@
//
// NopSCADlib Copyright Chris Palmer 2020
// nop.head@gmail.com
// hydraraptor.blogspot.com
//
// This file is part of NopSCADlib.
//
// NopSCADlib is free software: you can redistribute it and/or modify it under the terms of the
// GNU General Public License as published by the Free Software Foundation, either version 3 of
// the License, or (at your option) any later version.
//
// NopSCADlib is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
// without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
// See the GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License along with NopSCADlib.
// If not, see <https://www.gnu.org/licenses/>.
//
//
//! Utilities for making involute gears.
//!
//! Formulas from <https://khkgears.net/new/gear_knowledge/gear_technical_reference/involute_gear_profile.html>
//! and <https://www.tec-science.com/mechanical-power-transmission/involute-gear/calculation-of-involute-gears/>
//!
//! ```involute_gear_profile()``` returns a polygon that can have the bore and spokes, etc, subtracted from it before linear extruding it to 3D.
//! Helical gears can be made using ```twist``` and bevel gears using ```scale``` parameters of ```linear_extrude()```.
//!
//! Gears with less than 19 teeth (when pressure angle is 20) are profile shifted to avoid undercutting the tooth root. 7 teeth is considered
//! the practical minimum.
//!
//! The clearance between tip and root defaults to module / 6, but can be overridden by setting the ```clearance``` parameter.
//
include <core/core.scad>
use <maths.scad>
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
function profile_shift(z, pa) = max(1 - z * sqr(sin(pa)) / 2, 0); //! Calculate profile shift for small gears
function centre_distance(m, z1, z2, pa) = //! Calculate distance between centres taking profile shift into account
let(x1 = profile_shift(z1, pa), x2 = profile_shift(z2, pa)) m * (z1/2 + z2/2 + x1 + x2);
module involute_gear_profile(m, z, pa = 20, clearance = undef, steps = 20) { //! Calculate profile given module, number of teeth and pressure angle
assert(z >= 7, "Gears must have at least 7 teeth.");
d = m * z; // Reference pitch circle diameter
x = profile_shift(z, pa); // Profile shift
c = is_undef(clearance) ? m / 6 : clearance; // Clearance from tip to root
base_d = d * cos(pa); // Base diameter
root_r = d / 2 + m * (x - 1) - c; // Root radius (dedendum circle radius)
tip_d = d + 2 * m * (1 + x); // Tip diameter (addendum circle diameter)
tpa = acos(base_d / tip_d); // Tip pressure angle
inva = tan(pa) - radians(pa); // Involute alpha
invaa = tan(tpa) - radians(tpa); // Involute alphaa
ta = PI / (2 * z) + 2 * x * tan(pa) / z + inva - invaa; // Tooth tip thickness angle, radians
crest_w = ta * tip_d; // Crest width
umax = sqrt(sqr(tip_d / base_d) - 1); // Max value of the involute parameter
base_r = base_d / 2;
p1 = involute(base_r, 0);
p2 = involute(base_r, umax);
dist = norm(p2 - p1); // distance between beginning and end of the involute curve
base_angle = 2 * acos((sqr(base_r) + sqr(tip_d / 2) - sqr(dist)) / base_r / tip_d) + degrees(2 * ta);
root_angle = 360 / z - base_angle;
root_circle_r = base_r * sin(root_angle / 2);
if(!is_undef($show_numbers) && $show_numbers) {
echo(d=d);
echo(base_d=base_d);
echo(tip_d=tip_d);
echo(tpa = tpa);
echo(inva=inva);
echo(invaa=invaa);
echo(x=x);
echo(ta=ta);
echo(crest_w=crest_w);
echo(umax = umax);
echo(base_angle=base_angle);
echo(root_angle=root_angle);
}
involute = [for(i = [0 : steps], u = umax * i / steps) involute(base_r, u)]; // involute for the bottom side of the tooth
truncated = [for(p = involute) if((rot2_z(-base_angle / 2) * p).y <= 0) p]; // removed any above the centreline to prevent overlap
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);
}
}