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Added involute_worm_profile() and involute_rack_tooth_profile() functions.

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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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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