mirror of
https://github.com/bherbruck/solidcraft.git
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Ladder 06: pipe threads, the buttress's steep flank, the tip options and the square refusal
G 1/2 external and Rp 1/2 internal (ISO 228-1 / ISO 7-1, 55 deg) by Pappus turn by turn; R 1/2 and 1/2-14 NPT external and Rc 1/2 internal tapers (1 in 16 from the standard's diameter at the free end, crests cut by the major or minor cone) by the screw sweep's Jacobian, integrated exactly (ladder_lib.sweep_removed); an S20x4 run down to a shoulder with its steep flank toward the end and toward the start, which moves where the groove stops; tip: start, and a Tr20x4 chamfered at its own 30 deg and 2.5 mm; refusals for a Tr chamfer without a depth and for the square form. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
This commit is contained in:
jyviko
@@ -0,0 +1,11 @@
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{
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||||
"sources": [],
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"what": "a modelled G 1/2 parallel pipe thread (ISO 228-1, 55 deg) on a d20.955 shaft, six turns",
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"source": "analytic",
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"method": "groove volume per turn 2 pi int r w(r) dr over the material it cuts (Pappus on the axial section; a screw motion), w(r) = P - flat - depth (tan a + tan b); six whole turns between free ends, so V = stock - 6 x that. Tolerance 0.01%: SMLib's exact screw sweep. the space between the teeth is a groove of straight flanks, its tooth (H - h) tan(half angle) wide at the crest and its groove as wide at the root (the truncations split equally); the standard's crest and root rounds are flats here. ISO 228-1 G 1/2: d = 20.955, 14 threads per inch, H = 0.960491 P, h = 0.640327 P, so the crest flat (H - h) tan27.5 = 0.16667 P and the minor d1 = d - 2h = 18.631",
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"body_count": 1,
|
||||
"volume_mm3": 3355.923237102,
|
||||
"tolerance": {
|
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"rel": 0.0001
|
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}
|
||||
}
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||||
@@ -0,0 +1,30 @@
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{
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||||
"commands": [
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||||
{
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||||
"command": "solid.cylinder",
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||||
"params": {
|
||||
"base": [
|
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0,
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0,
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0
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],
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"radius": 10.4775,
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"height": 10.885714285714286,
|
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"body_name": "Part"
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||||
}
|
||||
},
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||||
{
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||||
"command": "solid.thread",
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||||
"params": {
|
||||
"face": [
|
||||
10.4775,
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||||
0,
|
||||
5.442857142857143
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||||
],
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||||
"modeled": true,
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||||
"form": "bspp",
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"designation": "G 1/2"
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}
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||||
}
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]
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}
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@@ -0,0 +1,11 @@
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{
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"sources": [],
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"what": "a modelled Rp 1/2 parallel internal pipe thread (ISO 7-1) in a d18.631 (its minor) bore through a 40x40 block six turns thick",
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"source": "analytic",
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"method": "groove volume per turn 2 pi int r w(r) dr over the material it cuts (Pappus on the axial section; a screw motion), w(r) = P - flat - depth (tan a + tan b); six whole turns through the block, both ends free, so V = stock - 6 x that. Tolerance 0.01%: SMLib's exact screw sweep. the space between the teeth is a groove of straight flanks, its tooth (H - h) tan(half angle) wide at the crest and its groove as wide at the root (the truncations split equally); the standard's crest and root rounds are flats here. ISO 7-1 Rp 1/2, the parallel internal thread an R screws into: the ISO 228-1 profile (H = 0.960491 P, h = 0.640327 P) at the gauge diameters, d = 20.955, D1 = d - 2h = 18.631, the bore; the groove from the bore wall out to r 10.4775, w(r) = P - 0.16667 P - (r - 9.3155) 2 tan27.5",
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"body_count": 1,
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"volume_mm3": 14061.219568064,
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"tolerance": {
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"rel": 0.0001
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}
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}
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@@ -0,0 +1,53 @@
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{
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"commands": [
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{
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"command": "solid.box",
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"params": {
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"corner": [
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-20,
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-20,
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0
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],
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"length": 40,
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"width": 40,
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"height": 10.885714285714286,
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"body_name": "Part"
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}
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},
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{
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"command": "solid.cylinder",
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"params": {
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"base": [
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0,
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0,
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-1
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],
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"radius": 9.31576387142857,
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"height": 12.885714285714286,
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"body_name": "Bore"
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}
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},
|
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{
|
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"command": "solid.combine",
|
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"params": {
|
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"target": "Part",
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||||
"tools": [
|
||||
"Bore"
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||||
],
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||||
"operation": "cut"
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}
|
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},
|
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{
|
||||
"command": "solid.thread",
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"params": {
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"face": [
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9.31576387142857,
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0,
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5.442857142857143
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],
|
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"modeled": true,
|
||||
"designation": "Rp 1/2"
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||||
}
|
||||
}
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||||
]
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}
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@@ -0,0 +1,23 @@
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{
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"sources": [],
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"what": "a modelled R 1/2 taper pipe thread (ISO 7-1, 55 deg, 1 in 16) on a 21.3 mm pipe (ISO 65), its standard 13.2 mm from the pipe's end",
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"source": "analytic",
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"method": "ISO 7-1 / ASME B1.20.1 taper 1 in 16 on the diameter. The thread starts at its free end with the standard's diameter there and its diameters grow into the material (the external major d0 + y/16 at y mm in; the internal minor d1 - y/16). The crests are the cone's: the material outside the external major cone (inside the internal minor cone) along the thread is cut as the die (tap) cuts it. The groove is the sweep of the profile's section, rising P a turn and moving P/32 a turn off the axis, so a point (rho, zeta) of the section at turn t lies at r = rho + c t, z = z0 + zeta + P t, the volume element is 2 pi r dA dt, and the groove removes 2 pi int_0^T (int int r dA over the section within the material) dt, exact while turns don't overlap (Gauss on 400 panels a turn: the integrand is piecewise polynomial in t). the space between the teeth is a groove of straight flanks, its tooth (H - h) tan(half angle) wide at the crest and its groove as wide at the root (the truncations split equally); the standard's crest and root rounds are flats here. ISO 7-1 R 1/2 (Table 1): gauge diameter d = 20.955 a basic gauge length 8.2 from the small end, so d0 = 20.955 - 8.2/16 = 20.4425 at the pipe's end; 14 threads per inch, H = 0.960237 P, h = 0.640327 P; useful thread 13.2. The pipe is ISO 65's 21.3 OD, outside the major cone over the whole thread (21.2675 at its end). It starts at the free top end z = 25 and runs the standard length L = 13.2000 down to z = 11.8000, where it stops square inside the face (the groove's section centred there, the cut below it bounded by the pipe's surface only). V = pi R^2 25 - the ring outside the cone (pi int (R^2 - r_cone^2) where the cone is inside the pipe) - the groove (481.264581). Bbox: the pipe's",
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||||
"body_count": 1,
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"volume_mm3": 8233.026663883,
|
||||
"bbox": {
|
||||
"min": [
|
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-10.65,
|
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-10.65,
|
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0
|
||||
],
|
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"max": [
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10.65,
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10.65,
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25
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]
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},
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"tolerance": {
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"rel": 0.0001
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}
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}
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@@ -0,0 +1,34 @@
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{
|
||||
"commands": [
|
||||
{
|
||||
"command": "solid.cylinder",
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"params": {
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"base": [
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0,
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0,
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0
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],
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"radius": 10.65,
|
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"height": 25,
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"body_name": "Part"
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}
|
||||
},
|
||||
{
|
||||
"command": "solid.thread",
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||||
"params": {
|
||||
"face": [
|
||||
10.65,
|
||||
0,
|
||||
12.5
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||||
],
|
||||
"modeled": true,
|
||||
"designation": "R 1/2",
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||||
"from": [
|
||||
0,
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0,
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25
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]
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}
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}
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]
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}
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||||
@@ -0,0 +1,23 @@
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||||
{
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||||
"sources": [],
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||||
"what": "a modelled 1/2-14 NPT taper pipe thread (ASME B1.20.1, 60 deg, 1 in 16) on its 0.840 in pipe, its effective thread L2 from the end",
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"source": "analytic",
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||||
"method": "ISO 7-1 / ASME B1.20.1 taper 1 in 16 on the diameter. The thread starts at its free end with the standard's diameter there and its diameters grow into the material (the external major d0 + y/16 at y mm in; the internal minor d1 - y/16). The crests are the cone's: the material outside the external major cone (inside the internal minor cone) along the thread is cut as the die (tap) cuts it. The groove is the sweep of the profile's section, rising P a turn and moving P/32 a turn off the axis, so a point (rho, zeta) of the section at turn t lies at r = rho + c t, z = z0 + zeta + P t, the volume element is 2 pi r dA dt, and the groove removes 2 pi int_0^T (int int r dA over the section within the material) dt, exact while turns don't overlap (Gauss on 400 panels a turn: the integrand is piecewise polynomial in t). ASME B1.20.1 (H28 Table VII.2) 1/2-14 NPT: pipe OD D = 0.840 in, E0 = 0.75843 in the pitch diameter at the small end, h = 0.8 P truncated equally at crest and root (0.033 P each, a 0.038 P flat), so the major at the end is E0 + h = 20.7156 mm, growing 1/16; L2 = 0.5337 in = 13.556. The major cone passes the pipe's OD (10.668) 9.93 mm in, so from there to L2 the crests are the pipe's surface, as the standard's imperfect threads are. It starts at the free top end z = 25 and runs the standard length L = 13.5560 down to z = 11.4440, where it stops square inside the face (the groove's section centred there, the cut below it bounded by the pipe's surface only). V = pi R^2 25 - the ring outside the cone (pi int (R^2 - r_cone^2) where the cone is inside the pipe) - the groove (609.702166). Bbox: the pipe's",
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"body_count": 1,
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||||
"volume_mm3": 8226.404941856,
|
||||
"bbox": {
|
||||
"min": [
|
||||
-10.668,
|
||||
-10.668,
|
||||
0
|
||||
],
|
||||
"max": [
|
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10.668,
|
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10.668,
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25
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]
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},
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"tolerance": {
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"rel": 0.0001
|
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}
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||||
}
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||||
@@ -0,0 +1,34 @@
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{
|
||||
"commands": [
|
||||
{
|
||||
"command": "solid.cylinder",
|
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"params": {
|
||||
"base": [
|
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0,
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0,
|
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0
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],
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"radius": 10.668,
|
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"height": 25,
|
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"body_name": "Part"
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "solid.thread",
|
||||
"params": {
|
||||
"face": [
|
||||
10.668,
|
||||
0,
|
||||
12.5
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||||
],
|
||||
"modeled": true,
|
||||
"designation": "1/2-14 NPT",
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||||
"from": [
|
||||
0,
|
||||
0,
|
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25
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]
|
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}
|
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}
|
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]
|
||||
}
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@@ -0,0 +1,23 @@
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||||
{
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||||
"sources": [],
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||||
"what": "a modelled Rc 1/2 internal taper pipe thread (ISO 7-1) in a d17.6 hole (the tap maker's) through a 13.2 mm plate, from its top face",
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"source": "analytic",
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||||
"method": "ISO 7-1 / ASME B1.20.1 taper 1 in 16 on the diameter. The thread starts at its free end with the standard's diameter there and its diameters grow into the material (the external major d0 + y/16 at y mm in; the internal minor d1 - y/16). The crests are the cone's: the material outside the external major cone (inside the internal minor cone) along the thread is cut as the die (tap) cuts it. The groove is the sweep of the profile's section, rising P a turn and moving P/32 a turn off the axis, so a point (rho, zeta) of the section at turn t lies at r = rho + c t, z = z0 + zeta + P t, the volume element is 2 pi r dA dt, and the groove removes 2 pi int_0^T (int int r dA over the section within the material) dt, exact while turns don't overlap (Gauss on 400 panels a turn: the integrand is piecewise polynomial in t). the space between the teeth is a groove of straight flanks, its tooth (H - h) tan(half angle) wide at the crest and its groove as wide at the root (the truncations split equally); the standard's crest and root rounds are flats here. ISO 7-1 Rc 1/2: the gauge diameter d = 20.955 at the face (z = 13.2), so the minor there is d1 = d - 2h = 18.631, shrinking 1/16 per mm down; the plate is the useful thread 13.2 thick, so the minor cone stays outside the 17.6 hole (17.806 at the bottom). Both faces are free ends, the groove running a pitch past each. V = 40^2 13.2 - pi 8.8^2 13.2 - the ring inside the minor cone (pi int (r_m^2 - 8.8^2), 230.460888) - the groove (460.876764)",
|
||||
"body_count": 1,
|
||||
"volume_mm3": 17217.301204408,
|
||||
"bbox": {
|
||||
"min": [
|
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-20,
|
||||
-20,
|
||||
0
|
||||
],
|
||||
"max": [
|
||||
20,
|
||||
20,
|
||||
13.2
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||||
]
|
||||
},
|
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"tolerance": {
|
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"rel": 0.0001
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,58 @@
|
||||
{
|
||||
"commands": [
|
||||
{
|
||||
"command": "solid.box",
|
||||
"params": {
|
||||
"corner": [
|
||||
-20,
|
||||
-20,
|
||||
0
|
||||
],
|
||||
"length": 40,
|
||||
"width": 40,
|
||||
"height": 13.2,
|
||||
"body_name": "Part"
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "solid.cylinder",
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"params": {
|
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"base": [
|
||||
0,
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0,
|
||||
-1
|
||||
],
|
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"radius": 8.8,
|
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"height": 15.2,
|
||||
"body_name": "Bore"
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "solid.combine",
|
||||
"params": {
|
||||
"target": "Part",
|
||||
"tools": [
|
||||
"Bore"
|
||||
],
|
||||
"operation": "cut"
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "solid.thread",
|
||||
"params": {
|
||||
"face": [
|
||||
8.8,
|
||||
0,
|
||||
6.6
|
||||
],
|
||||
"modeled": true,
|
||||
"designation": "Rc 1/2",
|
||||
"from": [
|
||||
0,
|
||||
0,
|
||||
13.2
|
||||
]
|
||||
}
|
||||
}
|
||||
]
|
||||
}
|
||||
+23
@@ -0,0 +1,23 @@
|
||||
{
|
||||
"sources": [],
|
||||
"what": "a modelled S20x4 buttress thread on a d20 shaft down to a d30 shoulder, the steep flank toward the thread's end (up, the default): the 3 deg wall faces the shoulder",
|
||||
"source": "analytic",
|
||||
"method": "DIN 513-1 S20x4: 3 deg load flank, 30 deg clearance flank, flats (P - 0.75 P (tan3 + tan30))/2 = 0.26384 P, external minor d3 = d - 2 x 0.86777 P = 13.058. steep_flank end puts the 3 deg wall on the groove's side toward the shoulder (z = 10); the groove stops with its section clear of the shoulder, its centre 0.571741 above it (the section's extent that way at r = 10.2, 0.05 P past the crest, the tool's outer edge), and runs out a pitch past the free top end. V = pi 15^2 10 + pi 10^2 30 - the groove 2 pi int_0^T (int int r dA of the section within the shaft) dt (2507.160140; a straight screw sweep, Pappus turn by turn, with the free end's partial turn integrated). 025 and 026 differ by where the groove stops",
|
||||
"body_count": 1,
|
||||
"volume_mm3": 13986.201291602,
|
||||
"bbox": {
|
||||
"min": [
|
||||
-15,
|
||||
-15,
|
||||
0
|
||||
],
|
||||
"max": [
|
||||
15,
|
||||
15,
|
||||
40
|
||||
]
|
||||
},
|
||||
"tolerance": {
|
||||
"rel": 0.0001
|
||||
}
|
||||
}
|
||||
+46
@@ -0,0 +1,46 @@
|
||||
{
|
||||
"commands": [
|
||||
{
|
||||
"command": "solid.cylinder",
|
||||
"params": {
|
||||
"base": [
|
||||
0,
|
||||
0,
|
||||
0
|
||||
],
|
||||
"radius": 15,
|
||||
"height": 10,
|
||||
"body_name": "Part"
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "solid.cylinder",
|
||||
"params": {
|
||||
"base": [
|
||||
0,
|
||||
0,
|
||||
10
|
||||
],
|
||||
"radius": 10,
|
||||
"height": 30,
|
||||
"operation": "join",
|
||||
"targets": [
|
||||
"Part"
|
||||
]
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "solid.thread",
|
||||
"params": {
|
||||
"face": [
|
||||
10,
|
||||
0,
|
||||
25
|
||||
],
|
||||
"modeled": true,
|
||||
"designation": "S20x4",
|
||||
"steep_flank": "end"
|
||||
}
|
||||
}
|
||||
]
|
||||
}
|
||||
+23
@@ -0,0 +1,23 @@
|
||||
{
|
||||
"sources": [],
|
||||
"what": "a modelled S20x4 buttress thread on a d20 shaft down to a d30 shoulder, the steep flank toward the thread's start (down): the 30 deg wall faces the shoulder",
|
||||
"source": "analytic",
|
||||
"method": "DIN 513-1 S20x4: 3 deg load flank, 30 deg clearance flank, flats (P - 0.75 P (tan3 + tan30))/2 = 0.26384 P, external minor d3 = d - 2 x 0.86777 P = 13.058. steep_flank start puts the 30 deg wall on the groove's side toward the shoulder (z = 10); the groove stops with its section clear of the shoulder, its centre 2.498847 above it (the section's extent that way at r = 10.2, 0.05 P past the crest, the tool's outer edge), and runs out a pitch past the free top end. V = pi 15^2 10 + pi 10^2 30 - the groove 2 pi int_0^T (int int r dA of the section within the shaft) dt (2439.158513; a straight screw sweep, Pappus turn by turn, with the free end's partial turn integrated). 025 and 026 differ by where the groove stops",
|
||||
"body_count": 1,
|
||||
"volume_mm3": 14054.202918026,
|
||||
"bbox": {
|
||||
"min": [
|
||||
-15,
|
||||
-15,
|
||||
0
|
||||
],
|
||||
"max": [
|
||||
15,
|
||||
15,
|
||||
40
|
||||
]
|
||||
},
|
||||
"tolerance": {
|
||||
"rel": 0.0001
|
||||
}
|
||||
}
|
||||
+46
@@ -0,0 +1,46 @@
|
||||
{
|
||||
"commands": [
|
||||
{
|
||||
"command": "solid.cylinder",
|
||||
"params": {
|
||||
"base": [
|
||||
0,
|
||||
0,
|
||||
0
|
||||
],
|
||||
"radius": 15,
|
||||
"height": 10,
|
||||
"body_name": "Part"
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "solid.cylinder",
|
||||
"params": {
|
||||
"base": [
|
||||
0,
|
||||
0,
|
||||
10
|
||||
],
|
||||
"radius": 10,
|
||||
"height": 30,
|
||||
"operation": "join",
|
||||
"targets": [
|
||||
"Part"
|
||||
]
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "solid.thread",
|
||||
"params": {
|
||||
"face": [
|
||||
10,
|
||||
0,
|
||||
25
|
||||
],
|
||||
"modeled": true,
|
||||
"designation": "S20x4",
|
||||
"steep_flank": "start"
|
||||
}
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -0,0 +1,11 @@
|
||||
{
|
||||
"sources": [],
|
||||
"what": "001's modelled M10 thread with ISO 4753's chamfered end at the end it starts from only (`tip: start`, from the top)",
|
||||
"source": "analytic",
|
||||
"method": "ISO 68-1 basic profile (60 deg, root flat P/4 at d - 5H/4 ... minor d1 = d - 1.0825 P, crest flat P/8): a helical groove of fixed section is a screw motion, so averaged over the turn every meridian half-plane holds the same section and V = 2 pi int int r m(r) dr dz over the stock's section, m the material fraction per pitch; the groove runs out past free ends. Tolerance 0.01%: SMLib's exact screw sweep; as 017 at the top end only: the 45 deg cone down to d3 = d - 2 (17/24) H = 8.160 (ISO 724) at z = 30, cut after the groove, lowers the stock's radius to r_f + (30 - z); the bottom end stays as cut, the groove running out past it",
|
||||
"body_count": 1,
|
||||
"volume_mm3": 1949.80017257,
|
||||
"tolerance": {
|
||||
"rel": 0.0001
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,35 @@
|
||||
{
|
||||
"commands": [
|
||||
{
|
||||
"command": "solid.cylinder",
|
||||
"params": {
|
||||
"base": [
|
||||
0,
|
||||
0,
|
||||
0
|
||||
],
|
||||
"radius": 5,
|
||||
"height": 30,
|
||||
"body_name": "Part"
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "solid.thread",
|
||||
"params": {
|
||||
"face": [
|
||||
5,
|
||||
0,
|
||||
15
|
||||
],
|
||||
"modeled": true,
|
||||
"designation": "M10",
|
||||
"tip": "start",
|
||||
"from": [
|
||||
0,
|
||||
0,
|
||||
30
|
||||
]
|
||||
}
|
||||
}
|
||||
]
|
||||
}
|
||||
+11
@@ -0,0 +1,11 @@
|
||||
{
|
||||
"sources": [],
|
||||
"what": "011's modelled Tr20x4 thread with chamfered ends at its own angle and depth: 30 deg to the axis, 2.5 mm in from the major diameter",
|
||||
"source": "analytic",
|
||||
"method": "ISO 2904 Tr20x4 (011): crest flat 0.366 P, minor d3 = 15.5. Averaged over the turn every meridian half-plane holds the same sections (a screw motion), so V = 2 pi int int r m(r) dr dz over the stock's section, m = 1 - w(r)/P the tooth's share of a pitch (1 below the root r 7.75). Both ends are free: the chamfer, axisymmetric and cut after the groove, lowers the stock's radius to 7.5 + y tan30 at y mm from each end (the cone at 30 deg to the axis through d_f = d - 2 x 2.5 = 15, below the root, so a whole ring is left on the end), reaching the major 4.330 mm in",
|
||||
"body_count": 1,
|
||||
"volume_mm3": 5769.125597583,
|
||||
"tolerance": {
|
||||
"rel": 0.0001
|
||||
}
|
||||
}
|
||||
+32
@@ -0,0 +1,32 @@
|
||||
{
|
||||
"commands": [
|
||||
{
|
||||
"command": "solid.cylinder",
|
||||
"params": {
|
||||
"base": [
|
||||
0,
|
||||
0,
|
||||
0
|
||||
],
|
||||
"radius": 10,
|
||||
"height": 24,
|
||||
"body_name": "Part"
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "solid.thread",
|
||||
"params": {
|
||||
"face": [
|
||||
10,
|
||||
0,
|
||||
12
|
||||
],
|
||||
"modeled": true,
|
||||
"designation": "Tr20x4",
|
||||
"tip": "both",
|
||||
"chamfer_angle": "30 deg",
|
||||
"chamfer_depth": "2.5 mm"
|
||||
}
|
||||
}
|
||||
]
|
||||
}
|
||||
+8
@@ -0,0 +1,8 @@
|
||||
{
|
||||
"sources": [],
|
||||
"what": "011's Tr20x4 thread with a chamfered tip and no depth: refused, ISO 4753 is for metric threads",
|
||||
"source": "invariants",
|
||||
"method": "ISO 4753's chamfered end (d_f at most the external minor diameter, ISO 724's d3) is defined for ISO metric threads only: a trapezoidal thread has no standard chamfer depth, so without `chamfer_depth` there is no right answer and the thread must be refused, naming the depth to give",
|
||||
"outcome": "refused",
|
||||
"refusal": "ISO 4753's chamfered end is for ISO metric threads"
|
||||
}
|
||||
+30
@@ -0,0 +1,30 @@
|
||||
{
|
||||
"commands": [
|
||||
{
|
||||
"command": "solid.cylinder",
|
||||
"params": {
|
||||
"base": [
|
||||
0,
|
||||
0,
|
||||
0
|
||||
],
|
||||
"radius": 10,
|
||||
"height": 24,
|
||||
"body_name": "Part"
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "solid.thread",
|
||||
"params": {
|
||||
"face": [
|
||||
10,
|
||||
0,
|
||||
12
|
||||
],
|
||||
"modeled": true,
|
||||
"designation": "Tr20x4",
|
||||
"tip": "both"
|
||||
}
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -0,0 +1,8 @@
|
||||
{
|
||||
"sources": [],
|
||||
"what": "a square thread on a d10 x 30 cylinder: refused, no current standard defines one",
|
||||
"source": "invariants",
|
||||
"method": "ISO, ASME and DIN define no square thread (Machinery's Handbook gives only historical proportions), so no dimension of it can be taken from a standard: the right answer is a refusal pointing to trapezoidal (ISO 2904) or acme (ASME B1.5)",
|
||||
"outcome": "refused",
|
||||
"refusal": "no current standard defines a square thread"
|
||||
}
|
||||
@@ -0,0 +1,29 @@
|
||||
{
|
||||
"commands": [
|
||||
{
|
||||
"command": "solid.cylinder",
|
||||
"params": {
|
||||
"base": [
|
||||
0,
|
||||
0,
|
||||
0
|
||||
],
|
||||
"radius": 5,
|
||||
"height": 30,
|
||||
"body_name": "Part"
|
||||
}
|
||||
},
|
||||
{
|
||||
"command": "solid.thread",
|
||||
"params": {
|
||||
"face": [
|
||||
5,
|
||||
0,
|
||||
15
|
||||
],
|
||||
"modeled": true,
|
||||
"form": "square"
|
||||
}
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -120,7 +120,18 @@
|
||||
"ladder/06-threads/002-external-m10x1-fine",
|
||||
"ladder/06-threads/017-external-m10-chamfered-tip",
|
||||
"ladder/06-threads/008-multi-start-thread",
|
||||
"ladder/06-threads/018-external-m10-both-hands"
|
||||
"ladder/06-threads/018-external-m10-both-hands",
|
||||
"ladder/06-threads/020-external-g-1-2",
|
||||
"ladder/06-threads/021-internal-rp-1-2",
|
||||
"ladder/06-threads/022-external-r-1-2-taper",
|
||||
"ladder/06-threads/023-external-1-2-npt",
|
||||
"ladder/06-threads/024-internal-rc-1-2-taper",
|
||||
"ladder/06-threads/025-external-s20x4-steep-flank-end-to-shoulder",
|
||||
"ladder/06-threads/026-external-s20x4-steep-flank-start-to-shoulder",
|
||||
"ladder/06-threads/027-external-m10-chamfered-start",
|
||||
"ladder/06-threads/028-external-tr20x4-chamfer-30-deg-2.5-deep",
|
||||
"ladder/06-threads/029-external-tr20x4-chamfer-needs-depth",
|
||||
"ladder/06-threads/030-square-thread-refused"
|
||||
],
|
||||
"tier": "06-threads",
|
||||
"what": "modelled threads"
|
||||
|
||||
@@ -791,6 +791,133 @@ case(T6, "017-external-m10-chamfered-tip", "001's modelled M10 thread with ISO 4
|
||||
"; the chamfer is axisymmetric and cut after the groove, so it only lowers the stock's outer radius: r <= d_f/2 + distance from the end (45 deg), d_f the external minor diameter d3 = d - 1.226869 P = 8.160 "
|
||||
"(ISO 724; ISO 4753 chamfered end: the end's diameter at most the minor diameter), below the modelled root d1")
|
||||
|
||||
# Pipe threads (crates/doc/src/thread_forms.rs, pipe_thread_sizes.rs): ISO 228-1 / ISO 7-1, 55 deg,
|
||||
# the triangle H truncated to the depth h, equally at crest and root, flats where the standard has
|
||||
# rounds; ASME B1.20.1 NPT, 60 deg, H = 0.866025 P truncated to h = 0.8 P.
|
||||
P14 = INCH / 14
|
||||
H_PAR, H_TAP, H55 = 0.960491 * P14, 0.960237 * P14, 0.640327 * P14
|
||||
t275 = math.tan(math.radians(27.5))
|
||||
G12 = 20.955
|
||||
PIPE = ("the space between the teeth is a groove of straight flanks, its tooth (H - h) tan(half angle) wide at the crest and its groove as wide at the root (the truncations "
|
||||
"split equally); the standard's crest and root rounds are flats here. ")
|
||||
shaft_form("020-external-g-1-2", "a modelled G 1/2 parallel pipe thread (ISO 228-1, 55 deg) on a d20.955 shaft, six turns", "bspp", "G 1/2", G12, P14,
|
||||
(H_PAR - H55) * t275, 27.5, 27.5, G12 / 2 - H55,
|
||||
PIPE + "ISO 228-1 G 1/2: d = 20.955, 14 threads per inch, H = 0.960491 P, h = 0.640327 P, so the crest flat (H - h) tan27.5 = 0.16667 P and the minor d1 = d - 2h = 18.631")
|
||||
r1rp = G12 / 2 - H55
|
||||
vrp = 6 * form_turn(P14, (H_PAR - H55) * t275, r1rp, 27.5, 27.5, r1rp, G12 / 2, internal=True)
|
||||
case(T6, "021-internal-rp-1-2", "a modelled Rp 1/2 parallel internal pipe thread (ISO 7-1) in a d18.631 (its minor) bore through a 40x40 block six turns thick",
|
||||
[box([-20, -20, 0], 40, 40, 6 * P14, body_name="Part"), cyl([0, 0, -1], r1rp, 6 * P14 + 2, body_name="Bore"), C("solid.combine", target="Part", tools=["Bore"], operation="cut"),
|
||||
thr([r1rp, 0, 3 * P14], designation="Rp 1/2")],
|
||||
{"body_count": 1, "volume_mm3": 1600 * 6 * P14 - PI * r1rp ** 2 * 6 * P14 - vrp, "tolerance": TOL_F},
|
||||
FMETH.replace("between free ends", "through the block, both ends free") + PIPE + "ISO 7-1 Rp 1/2, the parallel internal thread an R screws into: the ISO 228-1 profile "
|
||||
"(H = 0.960491 P, h = 0.640327 P) at the gauge diameters, d = 20.955, D1 = d - 2h = 18.631, the bore; the groove from the bore wall out to r 10.4775, "
|
||||
"w(r) = P - 0.16667 P - (r - 9.3155) 2 tan27.5")
|
||||
|
||||
# Taper pipe threads: a screw sweep whose section moves off the axis 1/32 of its rise (1 in 16 on
|
||||
# the diameter), the crests cut by the major cone (external) or minor cone (internal) as a die or tap
|
||||
# cuts them. What a moving section removes is exact by the sweep's Jacobian (sweep_removed).
|
||||
TAPER = ("ISO 7-1 / ASME B1.20.1 taper 1 in 16 on the diameter. The thread starts at its free end with the standard's diameter there and its diameters grow into the material "
|
||||
"(the external major d0 + y/16 at y mm in; the internal minor d1 - y/16). The crests are the cone's: the material outside the external major cone (inside the internal "
|
||||
"minor cone) along the thread is cut as the die (tap) cuts it. The groove is the sweep of the profile's section, rising P a turn and moving P/32 a turn off the axis, so "
|
||||
"a point (rho, zeta) of the section at turn t lies at r = rho + c t, z = z0 + zeta + P t, the volume element is 2 pi r dA dt, and the groove removes "
|
||||
"2 pi int_0^T (int int r dA over the section within the material) dt, exact while turns don't overlap (Gauss on 400 panels a turn: the integrand is piecewise polynomial in t). ")
|
||||
def taper_ext(name, what, desig, d0, L, P, flat, half, h, Rcyl, Ls, extra):
|
||||
a = Ls - L
|
||||
cone = lambda z: d0 / 2 + (Ls - z) / 32
|
||||
crest_a = cone(a)
|
||||
sec = groove_section(P, flat, crest_a, half, half, crest_a - h, max(crest_a, Rcyl) + 0.1)
|
||||
A = [(0, -1, a), (0, 1, -Ls), (1, 1 / 32, -(d0 / 2 + Ls / 32)), (1, 0, -Rcyl)]
|
||||
B = [(0, 1, -a), (0, -1, 0), (1, 0, -Rcyl)]
|
||||
turns = (L + P) / P
|
||||
groove_v = sweep_removed(sec, a, P, turns, -P / 32, [A, B])
|
||||
env = PI * quad_split(lambda z: max(0.0, Rcyl ** 2 - cone(z) ** 2), a, Ls, 200, 8)
|
||||
v = PI * Rcyl ** 2 * Ls - env - groove_v
|
||||
case(T6, name, what, [cyl([0, 0, 0], Rcyl, Ls, body_name="Part"), thr([Rcyl, 0, Ls / 2], designation=desig, **{"from": [0, 0, Ls]})],
|
||||
{"body_count": 1, "volume_mm3": v, "bbox": {"min": [-Rcyl, -Rcyl, 0], "max": [Rcyl, Rcyl, Ls]}, "tolerance": TOL_F},
|
||||
TAPER + extra + " It starts at the free top end z = %g and runs the standard length L = %.4f down to z = %.4f, where it stops square inside the face (the groove's section centred "
|
||||
"there, the cut below it bounded by the pipe's surface only). V = pi R^2 %g - the ring outside the cone (pi int (R^2 - r_cone^2) where the cone is inside the pipe) "
|
||||
"- the groove (%.6f). Bbox: the pipe's" % (Ls, L, a, Ls, groove_v))
|
||||
taper_ext("022-external-r-1-2-taper", "a modelled R 1/2 taper pipe thread (ISO 7-1, 55 deg, 1 in 16) on a 21.3 mm pipe (ISO 65), its standard 13.2 mm from the pipe's end",
|
||||
"R 1/2", G12 - 8.2 / 16, 13.2, P14, (H_TAP - H55) * t275, 27.5, H55, 21.3 / 2, 25,
|
||||
PIPE + "ISO 7-1 R 1/2 (Table 1): gauge diameter d = 20.955 a basic gauge length 8.2 from the small end, so d0 = 20.955 - 8.2/16 = 20.4425 at the pipe's end; "
|
||||
"14 threads per inch, H = 0.960237 P, h = 0.640327 P; useful thread 13.2. The pipe is ISO 65's 21.3 OD, outside the major cone over the whole thread (21.2675 at its end).")
|
||||
E0, L1, L2 = 0.75843, 0.320, 0.5337
|
||||
taper_ext("023-external-1-2-npt", "a modelled 1/2-14 NPT taper pipe thread (ASME B1.20.1, 60 deg, 1 in 16) on its 0.840 in pipe, its effective thread L2 from the end",
|
||||
"1/2-14 NPT", (E0 + 0.8 / 14) * INCH, L2 * INCH, P14, (0.866025 - 0.8) * P14 * math.tan(math.radians(30)), 30.0, 0.8 * P14, 0.840 * INCH / 2, 25,
|
||||
"ASME B1.20.1 (H28 Table VII.2) 1/2-14 NPT: pipe OD D = 0.840 in, E0 = 0.75843 in the pitch diameter at the small end, h = 0.8 P truncated equally at crest and root "
|
||||
"(0.033 P each, a 0.038 P flat), so the major at the end is E0 + h = 20.7156 mm, growing 1/16; L2 = 0.5337 in = 13.556. The major cone passes the pipe's OD "
|
||||
"(10.668) 9.93 mm in, so from there to L2 the crests are the pipe's surface, as the standard's imperfect threads are.")
|
||||
# Rc internal: the minor cone shrinks into the hole from the face (the gauge plane, ISO 7-1: the
|
||||
# internal thread's reference diameter is at its face).
|
||||
Lrc, rb = 13.2, 8.8
|
||||
m0 = (G12 - 2 * H55) / 2
|
||||
rm = lambda z: m0 - (Lrc - z) / 32
|
||||
sec_rc = groove_section(P14, (H_TAP - H55) * t275, rm(-P14), 27.5, 27.5, rm(-P14) + H55, rb - 0.2, internal=True)
|
||||
g_rc = sweep_removed(sec_rc, -P14, P14, (Lrc + 2 * P14) / P14, P14 / 32, [[(0, -1, 0), (0, 1, -Lrc), (-1, 1 / 32, m0 - Lrc / 32), (1, 0, -19)]])
|
||||
env_rc = PI * quad_split(lambda z: rm(z) ** 2 - rb ** 2, 0, Lrc, 200, 8)
|
||||
case(T6, "024-internal-rc-1-2-taper", "a modelled Rc 1/2 internal taper pipe thread (ISO 7-1) in a d17.6 hole (the tap maker's) through a 13.2 mm plate, from its top face",
|
||||
[box([-20, -20, 0], 40, 40, Lrc, body_name="Part"), cyl([0, 0, -1], rb, Lrc + 2, body_name="Bore"), C("solid.combine", target="Part", tools=["Bore"], operation="cut"),
|
||||
thr([rb, 0, Lrc / 2], designation="Rc 1/2", **{"from": [0, 0, Lrc]})],
|
||||
{"body_count": 1, "volume_mm3": 1600 * Lrc - PI * rb ** 2 * Lrc - env_rc - g_rc, "bbox": {"min": [-20, -20, 0], "max": [20, 20, Lrc]}, "tolerance": TOL_F},
|
||||
TAPER + PIPE + "ISO 7-1 Rc 1/2: the gauge diameter d = 20.955 at the face (z = 13.2), so the minor there is d1 = d - 2h = 18.631, shrinking 1/16 per mm down; "
|
||||
"the plate is the useful thread 13.2 thick, so the minor cone stays outside the 17.6 hole (17.806 at the bottom). Both faces are free ends, the groove running a pitch "
|
||||
"past each. V = 40^2 13.2 - pi 8.8^2 13.2 - the ring inside the minor cone (pi int (r_m^2 - 8.8^2), %.6f) - the groove (%.6f)" % (env_rc, g_rc))
|
||||
|
||||
# A buttress thread's steep flank (DIN 513-1, 3 deg): which way it faces decides how near the shoulder
|
||||
# the groove may come, since it stops with its whole section clear of it (004's rule): the section's
|
||||
# extent toward the shoulder at the tool's outer edge (0.05 P past the crest) is the 3 deg flank's or
|
||||
# the 30 deg one's.
|
||||
PS, dS = 4.0, 20.0
|
||||
tS3, tS30 = math.tan(math.radians(3)), math.tan(math.radians(30))
|
||||
flatS = (PS - 0.75 * PS * (tS3 + tS30)) / 2
|
||||
r3S = dS / 2 - 0.86777 * PS
|
||||
for name, steep, lo, hi, what in [("025-external-s20x4-steep-flank-end-to-shoulder", "end", 3, 30, "the steep flank toward the thread's end (up, the default): the 3 deg wall faces the shoulder"),
|
||||
("026-external-s20x4-steep-flank-start-to-shoulder", "start", 30, 3, "the steep flank toward the thread's start (down): the 30 deg wall faces the shoulder")]:
|
||||
sec = groove_section(PS, flatS, dS / 2, lo, hi, r3S, dS / 2 + 0.05 * PS)
|
||||
w_lo = -min(z for _, z in sec)
|
||||
s0 = 10 + w_lo
|
||||
g = sweep_removed(sec, s0, PS, (40 + PS - s0) / PS, 0.0, [[(0, -1, 10), (0, 1, -40), (1, 0, -10)], [(0, 1, -10), (0, -1, 0), (1, 0, -15)]])
|
||||
case(T6, name, "a modelled S20x4 buttress thread on a d20 shaft down to a d30 shoulder, " + what,
|
||||
[cyl([0, 0, 0], 15, 10, body_name="Part"), cyl([0, 0, 10], 10, 30, operation="join", targets=["Part"]), thr([10, 0, 25], designation="S20x4", steep_flank=steep)],
|
||||
{"body_count": 1, "volume_mm3": PI * 225 * 10 + PI * 100 * 30 - g, "bbox": {"min": [-15, -15, 0], "max": [15, 15, 40]}, "tolerance": TOL_F},
|
||||
"DIN 513-1 S20x4: 3 deg load flank, 30 deg clearance flank, flats (P - 0.75 P (tan3 + tan30))/2 = 0.26384 P, external minor d3 = d - 2 x 0.86777 P = 13.058. "
|
||||
"steep_flank %s puts the %d deg wall on the groove's side toward the shoulder (z = 10); the groove stops with its section clear of the shoulder, its centre "
|
||||
"%.6f above it (the section's extent that way at r = 10.2, 0.05 P past the crest, the tool's outer edge), and runs out a pitch past the free top end. "
|
||||
"V = pi 15^2 10 + pi 10^2 30 - the groove 2 pi int_0^T (int int r dA of the section within the shaft) dt (%.6f; a straight screw sweep, Pappus turn by turn, "
|
||||
"with the free end's partial turn integrated). 025 and 026 differ by where the groove stops" % (steep, lo, w_lo, g), base=None)
|
||||
|
||||
# The tip options (ISO 4753 chamfered end): none is 001, both is 017.
|
||||
case(T6, "027-external-m10-chamfered-start", "001's modelled M10 thread with ISO 4753's chamfered end at the end it starts from only (`tip: start`, from the top)",
|
||||
cylT + [thr([5, 0, 15], designation="M10", tip="start", **{"from": [0, 0, 30]})],
|
||||
{"body_count": 1, "volume_mm3": ext_volume(10, 1.5, [(0, 25 + rf10, lambda z: 5), (25 + rf10, 30, lambda z: rf10 + 30 - z)]), "tolerance": {"rel": 1e-4}},
|
||||
TMETH.replace("Tolerance 0.5%: solid.thread cuts faceted by design (chords within P/200 on the body, P/100 on the tool)", "Tolerance 0.01%: SMLib's exact screw sweep") +
|
||||
"; as 017 at the top end only: the 45 deg cone down to d3 = d - 2 (17/24) H = 8.160 (ISO 724) at z = 30, cut after the groove, lowers the stock's radius to r_f + (30 - z); "
|
||||
"the bottom end stays as cut, the groove running out past it")
|
||||
cT = 2.5 / math.tan(math.radians(30))
|
||||
def tr_volume(sections, P=4.0, crest=10.0, r3=7.75):
|
||||
flat = P / 2 * (1 - t15)
|
||||
m = lambda r: 1.0 if r <= r3 else 1 - (P - flat - (crest - r) * 2 * t15) / P
|
||||
def ring(R):
|
||||
return quad(lambda r: r, 0, min(R, r3)) + (quad(lambda r: r * m(r), r3, R, 64) if R > r3 else 0.0)
|
||||
return 2 * PI * sum(quad(lambda z: ring(f(z)), z0, z1, 64) for z0, z1, f in sections)
|
||||
trS = [cyl([0, 0, 0], 10, 24, body_name="Part")]
|
||||
case(T6, "028-external-tr20x4-chamfer-30-deg-2.5-deep", "011's modelled Tr20x4 thread with chamfered ends at its own angle and depth: 30 deg to the axis, 2.5 mm in from the major diameter",
|
||||
trS + [thr([10, 0, 12], designation="Tr20x4", tip="both", chamfer_angle="30 deg", chamfer_depth="2.5 mm")],
|
||||
{"body_count": 1, "volume_mm3": tr_volume([(0, cT, lambda z: 7.5 + z * math.tan(math.radians(30))), (cT, 24 - cT, lambda z: 10.0),
|
||||
(24 - cT, 24, lambda z: 7.5 + (24 - z) * math.tan(math.radians(30)))]), "tolerance": TOL_F},
|
||||
"ISO 2904 Tr20x4 (011): crest flat 0.366 P, minor d3 = 15.5. Averaged over the turn every meridian half-plane holds the same sections (a screw motion), so "
|
||||
"V = 2 pi int int r m(r) dr dz over the stock's section, m = 1 - w(r)/P the tooth's share of a pitch (1 below the root r 7.75). Both ends are free: the chamfer, "
|
||||
"axisymmetric and cut after the groove, lowers the stock's radius to 7.5 + y tan30 at y mm from each end (the cone at 30 deg to the axis through d_f = d - 2 x 2.5 = 15, "
|
||||
"below the root, so a whole ring is left on the end), reaching the major 4.330 mm in")
|
||||
case(T6, "029-external-tr20x4-chamfer-needs-depth", "011's Tr20x4 thread with a chamfered tip and no depth: refused, ISO 4753 is for metric threads",
|
||||
trS + [thr([10, 0, 12], designation="Tr20x4", tip="both")], {"outcome": "refused", "refusal": "ISO 4753's chamfered end is for ISO metric threads"},
|
||||
"ISO 4753's chamfered end (d_f at most the external minor diameter, ISO 724's d3) is defined for ISO metric threads only: a trapezoidal thread has no standard chamfer depth, "
|
||||
"so without `chamfer_depth` there is no right answer and the thread must be refused, naming the depth to give", source="invariants")
|
||||
case(T6, "030-square-thread-refused", "a square thread on a d10 x 30 cylinder: refused, no current standard defines one",
|
||||
cylT + [thr([5, 0, 15], form="square")], {"outcome": "refused", "refusal": "no current standard defines a square thread"},
|
||||
"ISO, ASME and DIN define no square thread (Machinery's Handbook gives only historical proportions), so no dimension of it can be taken from a standard: the right answer "
|
||||
"is a refusal pointing to trapezoidal (ISO 2904) or acme (ASME B1.5)", source="invariants")
|
||||
|
||||
# ---------------------------------------------------------------- 07 fillets
|
||||
F = lambda edges, r, **p: C("solid.fillet", edges=edges, radius=r, **p)
|
||||
case(T7, "001-single-edge-r5", "an r5 round on the stock's top front edge", [F([[30, 0, 20]], 5)],
|
||||
|
||||
@@ -182,3 +182,62 @@ def cyclic_spline(P):
|
||||
(P[j][k] - P[i][k]) / h[i] + (-(3 * a * a - 1) * M[k][i] + (3 * c * c - 1) * M[k][j]) * h[i] / 6) for k in range(2))
|
||||
return h[i], f
|
||||
return [span(i) for i in range(n)]
|
||||
|
||||
def clip_half(poly, a, b, c):
|
||||
"""The part of a convex polygon [(x, y)] where a x + b y + c <= 0 (Sutherland-Hodgman)."""
|
||||
out = []
|
||||
n = len(poly)
|
||||
for i in range(n):
|
||||
p, q = poly[i], poly[(i + 1) % n]
|
||||
fp, fq = a * p[0] + b * p[1] + c, a * q[0] + b * q[1] + c
|
||||
if fp <= 0:
|
||||
out.append(p)
|
||||
if (fp < 0 < fq) or (fq < 0 < fp):
|
||||
s = fp / (fp - fq)
|
||||
out.append((p[0] + s * (q[0] - p[0]), p[1] + s * (q[1] - p[1])))
|
||||
return out
|
||||
|
||||
def moment_r(poly):
|
||||
"""int int r dA over a polygon in the (r, z) half-plane: what a ring of that section holds, over 2 pi."""
|
||||
m = 0.0
|
||||
for i in range(len(poly)):
|
||||
(x0, y0), (x1, y1) = poly[i], poly[(i + 1) % len(poly)]
|
||||
m += (x0 + x1) * (x0 * y1 - x1 * y0)
|
||||
return abs(m) / 6
|
||||
|
||||
def sweep_removed(section, z0, lead, turns, rate, regions, panels_per_turn=400):
|
||||
"""What a screw sweep removes from an axisymmetric solid: `section` [(r, dz)] (convex, about the
|
||||
axial position z0), carried `turns` turns rising `lead` a turn and moving `rate` mm a turn off
|
||||
the axis (a taper); the solid is the union of disjoint convex `regions`, each a list of
|
||||
half-planes (a, b, c): a r + b z + c <= 0. A point (rho, zeta) of the section at turn t is at
|
||||
r = rho + rate t, z = z0 + zeta + lead t, so the volume element is 2 pi r dA dt (the map's
|
||||
Jacobian), and V = 2 pi int_0^turns (int int_{section_t within the solid} r dA) dt, exact while
|
||||
successive turns don't overlap (the groove is narrower than the lead). Gauss-Legendre on
|
||||
panels: the integrand is piecewise polynomial in t."""
|
||||
def at(t):
|
||||
placed = [(r + rate * t, z0 + dz + lead * t) for r, dz in section]
|
||||
total = 0.0
|
||||
for hp in regions:
|
||||
p = placed
|
||||
for a, b, c in hp:
|
||||
p = clip_half(p, a, b, c)
|
||||
if len(p) < 3:
|
||||
break
|
||||
if len(p) >= 3:
|
||||
total += moment_r(p)
|
||||
return total
|
||||
pieces = max(1, int(math.ceil(turns * panels_per_turn)))
|
||||
return 2 * PI * quad_split(at, 0.0, turns, pieces, 6)
|
||||
|
||||
def groove_section(P, flat, crest, flank_lo, flank_hi, r_root, r_far, internal=False):
|
||||
"""A thread groove's axial section [(r, dz)] between r_root (its root) and r_far (past the crest,
|
||||
out of the material), its root flat centred on dz = 0: the tooth is `flat` wide at the crest
|
||||
radius and both walls are straight flanks (flank_lo toward -z, flank_hi toward +z, degrees
|
||||
from the radial)."""
|
||||
tl, th = math.tan(math.radians(flank_lo)), math.tan(math.radians(flank_hi))
|
||||
w_root = P - flat - abs(crest - r_root) * (tl + th)
|
||||
def ext(r):
|
||||
d = abs(r - r_root)
|
||||
return w_root / 2 + d * tl, w_root / 2 + d * th
|
||||
(l0, h0), (l1, h1) = ext(r_root), ext(r_far)
|
||||
return [(r_root, -l0), (r_far, -l1), (r_far, h1), (r_root, h0)]
|
||||
|
||||
Reference in New Issue
Block a user