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Added involute_worm_profile() and involute_rack_tooth_profile() functions.

This commit is contained in:
Chris Palmer 2020-07-14 09:47:45 +01:00
parent bc919529d3
commit 1ca485b66b
2 changed files with 38 additions and 29 deletions
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7
readme.md
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@ -5229,6 +5229,7 @@ Rounded fillet for adding to corners.
Utilities for making involute gears.
Formulas from <https://khkgears.net/new/gear_knowledge/gear_technical_reference/involute_gear_profile.html>
<https://khkgears.net/new/gear_knowledge/gear_technical_reference/calculation_gear_dimensions.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.
@ -5241,6 +5242,8 @@ The clearance between tip and root defaults to module / 6, but can be overridden
The origin of the rack is the left end of the pitch line and its width is below the pitch line. I.e. it does not include the addendum.
```involute_worm_profile()``` returns a tooth profile that can be passed to ```thread()``` to make worms.
[utils/gears.scad](utils/gears.scad) Implementation.
@ -5249,8 +5252,10 @@ The origin of the rack is the left end of the pitch line and its width is below
### Functions
| Function | Description |
|:--- |:--- |
| ```centre_distance(m, z1, z2, pa)``` | Calculate distance between centres taking profile shift into account |
| ```centre_distance(m, z1, z2, pa = 20)``` | Calculate distance between centres taking profile shift into account |
| ```involute(r, u)``` | Involute of circle radius r at angle u in radians |
| ```involute_rack_tooth_profile(m, pa = 20, clearance = undef)``` | Calculate rack tooth profile given module and pressure angle |
| ```involute_worm_profile(m, pa = 20, clearance = undef)``` | Calculate worm profile suitable for passing to thread() |
| ```profile_shift(z, pa)``` | Calculate profile shift for small gears |
### Modules

60
utils/gears.scad
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@ -21,6 +21,7 @@
//! Utilities for making involute gears.
//!
//! Formulas from <https://khkgears.net/new/gear_knowledge/gear_technical_reference/involute_gear_profile.html>
//! <https://khkgears.net/new/gear_knowledge/gear_technical_reference/calculation_gear_dimensions.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.
@ -32,6 +33,8 @@
//! The clearance between tip and root defaults to module / 6, but can be overridden by setting the ```clearance``` parameter.
//!
//! The origin of the rack is the left end of the pitch line and its width is below the pitch line. I.e. it does not include the addendum.
//!
//! ```involute_worm_profile()``` returns a tooth profile that can be passed to ```thread()``` to make worms.
//
include <core/core.scad>
use <maths.scad>
@ -40,7 +43,7 @@ function involute(r, u) = let(a = degrees(u), c = cos(a), s = sin(a)) r * [c + u
function profile_shift(z, pa) = z ? max(1 - z * sqr(sin(pa)) / 2, 0) : 0; //! Calculate profile shift for small gears
function centre_distance(m, z1, z2, pa) = //! Calculate distance between centres taking profile shift into account
function centre_distance(m, z1, z2, pa = 20) = //! 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 gear profile given module, number of teeth and pressure angle
@ -62,7 +65,7 @@ module involute_gear_profile(m, z, pa = 20, clearance = undef, steps = 20) { //!
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
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;
@ -97,35 +100,36 @@ module involute_gear_profile(m, z, pa = 20, clearance = undef, steps = 20) { //!
}
}
function involute_rack_tooth_profile(m, pa = 20, clearance = undef) = //! Calculate rack tooth profile given module and pressure angle
let(p = PI * m, // Pitch
ha = m, // Addendum
c = is_undef(clearance) ? m / 4 : clearance, // Tip root clearance
hf = m + c, // Dedendum
hw = 2 * m, // Working depth
h = ha + hf, // Tooth depth
crest_w = p / 2 - 2 * ha * tan(pa), // Crest width
base_w = crest_w + 2 * hw * tan(pa), // Base width
root_w = p - base_w, // Root width
clearance_w = root_w - 2 * c * tan(pa), // Width of clearance without fillet
kx = tan(pa / 2 + 45), // Fillet ratio of radius and xoffset
pf = min(0.38 * m, kx * clearance_w / 2), // Dedendum fillet radius
x = pf / kx, // Fillet centre x offset from corner
sides = ceil(r2sides(pf) * (90 - pa) / 360), // Fillet facets taking $fa, $fs and $fn into account
fillet = [ for(i = [0 : sides - 1], a = i * (90 - pa) / sides + 270) [clearance_w / 2 - x, -hf + pf] + pf * [cos(a), sin(a)] ],
reflection = reverse([for(pt = fillet) [p - pt.x, pt.y] ]) // reflect for trailing edge
) concat(fillet, [ [root_w / 2, -hw / 2], [p / 2 - crest_w / 2, ha], [p / 2 + crest_w / 2, ha], [p - root_w / 2, -hw / 2] ], reflection);
module involute_rack_profile(m, z, w, pa = 20, clearance = undef) { //! Calculate rack profile given module, number of teeth and pressure angle
p = PI * m; // Pitch
ha = m; // Addendum
hf = 1.25 * m; // Dedendum
hw = 2 * m; // Working depth
h = ha + hf; // Tooth depth
c = is_undef(clearance) ? m / 4 : clearance; // Tip root clearance
crest_w = p / 2 - 2 * ha * tan(pa); // Crest width
base_w = crest_w + 2 * hw * tan(pa); // Base width
root_w = p - base_w; // Root width
clearance_w = root_w - 2 * c * tan(pa); // Width of clearance without fillet
kx = tan(pa / 2 + 45); // Fillet ratio of radius and xoffset
pf = min(0.38 * m, kx * clearance_w / 2); // Dedendum fillet radius
x = pf / kx; // Fillet centre x offset from corner
tooth = [ [root_w / 2, -hw / 2], [p / 2 - crest_w / 2, ha], [p / 2 + crest_w / 2, ha], [p - root_w / 2, -hw / 2] ];
tooth = involute_rack_tooth_profile(m, pa, clearance);
teeth = [for(i = [0 : z - 1], pt = tooth) [pt.x + i * p, pt.y] ];
difference() {
polygon(concat([[0, -w], [0, -hf]], teeth, [[z * p, -hf ], [z * p, -w]])); // Add the corners
for(i = [0 : z]) // Add fillets
hull() {
for(side = [-1, 1])
translate([i * p + side * (clearance_w / 2 - x), -hf + pf])
circle(pf);
translate([i * p, -hw /2 + eps / 2]) // Need to extend to fillet up to meet the root at high pressure angles
square([root_w, eps], center = true);
}
}
polygon(concat([[0, -w], [0, -hf]], teeth, [[z * p, -hf ], [z * p, -w]])); // Add the corners
}
function involute_worm_profile(m, pa = 20, clearance = undef) = //! Calculate worm profile suitable for passing to thread()
let(tooth = involute_rack_tooth_profile(m),
pitch = PI * m,
y_min = min([for(p = tooth) p.y])
) [for(p = tooth) [p.x - pitch / 2, p.y - y_min, 0]]; // Offset to be positive in y, centred in x and add 0 z ordintate