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Add rack to mesh with involute spur gears.

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This commit is contained in:
Chris Palmer
2020-07-07 22:36:34 +01:00
parent 71ac571346
commit 7ce055373a
4 changed files with 51 additions and 5 deletions
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39
utils/gears.scad
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@@ -30,18 +30,20 @@
//! the practical minimum.
//!
//! 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.
//
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 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
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
module involute_gear_profile(m, z, pa = 20, clearance = undef, steps = 20) { //! Calculate gear 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
@@ -94,3 +96,36 @@ module involute_gear_profile(m, z, pa = 20, clearance = undef, steps = 20) { //!
circle(root_r);
}
}
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] ];
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);
}
}
}