solvecraft/docs/threads.md

Threads

solid.thread puts a thread on a cylindrical face: cosmetic (an annotation, model.threads lists it) or modelled (the groove between the teeth cut into the body along a helix, SMLib's exact screw sweep). This page gives the forms, the values each uses and where they come from, and how a thread's extent is decided. The code is crates/doc/src/thread_forms.rs (forms, sizes, designations) and crates/doc/src/eval_thread.rs (the thread on its face, the cut).

Forms

Every groove is a polygon in an axial half-plane: straight flanks, flat crest and root. Crest and root radii (the ISO metric root radius, the buttress root radius R, DIN 405 knuckle and Whitworth rounds) are not modelled. External threads are cut from the shaft's surface (a little past it, so no skin is left) down to the external thread's minor diameter; internal threads from the hole wall out to the internal thread's root. Pitch-diameter allowances and tolerance classes are not modelled: a modelled thread is the maximum-material design profile below.

Form	form	Designation	Flanks	Depth	Crest flat	External minor	Internal minor, root
ISO metric	metric	M10, M10x1, M16xPh3P1.5	30° / 30°	5H/8, H = P √3/2	P/8 at d, P/4 at D1	d − 5H/4	D1 = d − 5H/4, D = d
Trapezoidal	trapezoidal	Tr20x4, Tr40x14(P7)	15° / 15°	H1 = P/2	P/2 (1 − tan 15°) = 0.366 P	d3 = d − 2 (H1 + ac)	D1 = d − P, D4 = d + 2 ac
Acme (general purpose)	acme	1/2-10 ACME	14.5° / 14.5°	h = P/2	P/2 (1 − tan 14.5°) = 0.3707 P	d − P − 0.020″ (0.010″ finer than 10 tpi)	D − P, D + 0.020″ (0.010″)
Metric buttress	buttress	S20x4, S40x14(P7)	3° (load) / 30°	H1 = 0.75 P	(P − 0.75 P (tan 3° + tan 30°))/2 = 0.26384 P	d3 = d − 2 × 0.86777 P	D1 = d − 1.5 P, D = d
Buttress inch	buttress_asme	2.5-8 BUTT	7° (load) / 45°	h = 0.6 P	(P − 0.6 P (tan 7° + 1))/2 = 0.16316 P	d − 1.2 P (basic)	d − 1.2 P, d (basic)

| Parallel pipe | bspp | G 1/2 | 27.5° / 27.5° | h = 0.640327 P of H = 0.960491 P | (H − h) tan 27.5° = 0.1667 P, both | d − 2h | d − 2h, d | | Parallel internal (ISO 7-1) | rp | Rp 1/2 | 27.5° / 27.5° | h = 0.640327 P of H = 0.960491 P | (H − h) tan 27.5° = 0.1667 P, both | (internal only) | d − 2h, d | | Taper pipe (ISO 7-1) | bspt | R 1/2, Rc 1/2 | 27.5° / 27.5° | h = 0.640327 P of H = 0.960237 P | (H − h) tan 27.5°, both | d − 2h at the gauge plane | d − 2h, d at the gauge plane | | NPT | npt | 1/2-14 NPT | 30° / 30° | h = 0.8 P of H = 0.866025 P | (H − h) tan 30° = 0.038 P, both | E − h at the plane of E | E − h, E + h |

The pipe threads' crest and root rounds (ISO 228-1/7-1 r = 0.137329 P, 0.137278 P taper) are modelled as flats at the basic height, as the other forms' radii; NPT takes the minimum truncation 0.033 P at both. The flanks' bisector is square to the axis in all three.

Taper pipe threads (bspt, npt): the diameters change 1 in 16 along the axis. The thread starts at a free end, the pipe's end or the hole's mouth (from), with the diameter its standard puts there: an external thread its major diameter at the gauge (reference) plane its gauge length in from the small end (ISO 7-1: the basic gauge length, R 1/2 20.955 mm at 8.2 mm; NPT: E1 + h at the hand-tight length L1, E1 = E0 + L1/16), an internal one the reference diameter at its face (ISO 7-1's gauge plane; NPT's E1 at the large end). The groove is SMLib's screw sweep with its section moved 1/32 of the axial travel off the axis per unit length (the radial law that also makes runouts), its walls within the sweep's tolerance of the true surfaces; its section reaches just past the crest, and the material beyond the major cone (external) or inside the minor cone (internal) is cut with it, as the die or tap cuts the crests. Past the major cone the crests vanish into the pipe's surface (ISO 7-1's incomplete thread). An external taper thread runs its standard length unless length or up_to says otherwise (ISO 7-1's useful thread for the basic gauge length, NPT's effective thread L2); an internal one the face. A pipe thread has one start and turns one way. A taper thread's chamfered tip (tip, with its chamfer_depth) is measured from the major diameter the taper has at that end. ISO 228-1's G sizes are ISO 7-1's gauge-plane diameters (1/16 to 6); ISO 228-1's extra sizes (5/8, 7/8, …) are not tabulated yet. ISO 7-1's parallel internal thread Rp (rp, Rp 1/2), the one an R screws into, has the parallel form (H = 0.960491 P) at the gauge diameters; it is internal only.

Trapezoidal clearance ac (ISO 2904): 0.15 mm for P = 1.5, 0.25 mm for P 2 to 5, 0.5 mm for P 6 to 12, 1 mm for P 14 to 44.

The square thread is refused: no current ISO, ASME or DIN standard defines one. Machinery's Handbook gives only historical proportions (depth and width P/2; the "modified square" 10°); the trapezoidal and Acme forms replaced it.

Sizes. Without a designation the thread takes the standard size that fits the face: a shaft its major diameter, a hole its drill (metric: the tap maker's drill, docs/thread-catalogue.md; the other forms: the internal minor diameter). Metric uses the ISO 261/262 coarse pitches (M1.6 to M56); trapezoidal and metric buttress the ISO 2902 middle pitch of each diameter (Tr8x1.5 to Tr130x14; buttress from S10x2), the series DIN 513-2 shares; Acme ASME B1.5's preferred sizes (1/4-16 to 5-2). Buttress inch has no size table here: its pitch is always given.

Hand. hand: right | left | both. A left-handed groove is the right-handed one's mirror image (the screw motion about the reversed axis, rising along it); both cuts a right- and a left-handed groove crossing on the face (a reversing screw).

Buttress direction. steep_flank: end | start says which way the steep (load) flank of the screw's teeth faces along the thread's axis; a nut cut with the same setting mates with it (its own steep flanks face the other way).

Extent

extent: full | length | up_to, length, up_to (a point's place along the axis, or where a plane crosses it), from (a point near the end the thread starts at).

A face end is free when no material lies past it in the groove's way: over the span from one pitch to one and a half past the end, within the radii the groove cuts (the external minor diameter to the major, a nut's minor diameter to its root, and the face itself). A cap, a chamfer the groove runs out through, a counterbore wider than the thread are free; a shoulder, a head whose corners reach past the root, a blind hole's bottom are not.

• At a free end the groove runs out a pitch past the end, into the air.
• At a shoulder that starts at the end of an external thread's face and stays beyond the plane of that end, a thread running the whole face goes on through the plane and is trimmed there: the root reaches the shoulder at every angle of the last turn, so a nut bottoms out on it, and nothing past the plane is cut. A fillet or chamfer at the base stays whole: the groove ends where the cylinder does. With no runout, each slice along the axis loses the same, so the groove takes exactly length / P turns.
• At any other closed end (a shoulder rising back along the face, a blind hole's bottom, a taper's far end, a length stopping within half a pitch of the end) it stops with its section clear of the end: its centre as far inside as the section reaches that way, so it stays out of the shoulder at that end.
• Inside the face it stops square. For a symmetric section a square stop inside material removes exactly length / P turns (what the last section leaves uncut ahead of the stop, it cuts behind it in mirror image).

A thread of some length starts at the end nearest from; without it, at the face's only free end; without one, at the end the face point lies within a third of the face of. A pick in the middle of a face whose ends are alike is refused, naming from. A length as long as the face runs the whole face.

Runout and tip

Runout (ease_out: a length, standard = 2.5 P or short = 1.25 P, ISO 3508's normal and short thread runouts x): the thread's inner end, away from where it starts, fades out over that length, shorter than a turn too: its section moves out of the material as it turns (an external thread's away from the axis, past the surface; a nut's towards it, into the hole), linearly, by SMLib's radial screw sweep, and no end face is left. Without it the groove stops square there, ending in its own profile, a flat face in the axial plane. The runout lies past the full-form length: beyond a square stop, and before a shoulder up to its clearance (the full form then ends a runout short of it); at a free end it lies inside the face, the groove reaching nothing at the end. The start never fades: it runs off its free end, cut by the end face, plain or chamfered (tip); ease_in is refused. Where the section moves, the sweep's walls are within its tolerance (1e-4 P) of the true surfaces; full-depth turns are exact radially.

Tip (ISO 4753's chamfered end; tip: start the end the thread starts from, which must be free, tip: both each free end it reaches): at those ends of a modelled external thread, after the groove, the material outside a cone chamfer_angle to the axis (45°) reaching d_f = d − 2 chamfer_depth at the end is cut, the last teeth tapering into it. ISO 4753 bounds d_f by the minor diameter; the default is that bound, the external minor diameter d3 = d − 1.226869 P of ISO 724 (8.160 for M10), which lies below the modelled basic root d1. The cone therefore crosses the root and leaves the end a whole disk of d3 inside a whole conical ring; a cone ending on the root itself would pinch to nothing wherever the groove reaches the end. ISO 4753 is for ISO metric threads, so the other forms give chamfer_depth. An internal thread takes the hole's countersink instead.

Sources

• ISO 68-1 (basic profile), ISO 261/262 (sizes), ISO 965-1 (multi-start designation Ph).
• ISO 2901 to 2904 (trapezoidal: basic and design profiles, series, basic dimensions); the design diameters checked against the Bornemann Gewindetechnik tables of DIN 103 (Tr10x2: d3 7.5, D4 10.5, D1 8; Tr40x7: 32, 41, 33; Tr100x20: 78, 102, 80): https://www.bornemann-gewindetechnik.de/de/produkte/trapezgewinde/daten/.
• DIN 513-1/-2 (metric buttress): the formulas (ac = 0.11777 P, h3 = 0.86777 P, flat w = 0.26384 P, D1 = d − 2 H1) and the diameter-pitch table as IS 4696 (Part 3): 2004 publishes them in line with DIN 513 (https://law.resource.org/pub/in/bis/S01/is.4696.3.2004.pdf), and the Bornemann tables (S10x2: d3 6.529, D1 7; S40x7: 27.851, 29.5): https://www.bornemann-gewindetechnik.de/de/produkte/saegengewinde/daten/.
• ASME B1.5 (Acme): flat 0.3707 P, h = P/2, the 0.020″/0.010″ minor and major allowances and the preferred sizes, as reproduced at https://torqbolt.com/unified-acme-threads-dimensions-specifications.
• ASME B1.9 (buttress inch): 7°/45°, basic height of engagement 0.6 P; the flat follows from the fundamental triangle H = P / (tan 7° + tan 45°) = 0.89064 P truncated equally at crest and root.
• ISO 3508 (thread runouts) and ISO 4753 (ends of parts with external threads) for the runout and the chamfered tip. ISO 4753:2011, figure 1 b) (chamfered end CH; the public preview at https://cdn.standards.iteh.ai/samples/55928/38ddde12863b4c2db35dc929fd502a4d/ISO-4753-2011.pdf): the end's diameter "Maximum diameter at the minor thread diameter", the angle ≤ 50°, the incomplete thread u ≤ 2 P.
• ISO 7-1:1978 (taper and parallel 55° profiles: H = 0.960237 P / 0.960491 P, h = 0.640327 P, r = 0.137278 P / 0.137329 P, figures 1 and 2; Table 1, columns 1 to 8 and 15: threads per 25.4 mm, major diameter at the gauge plane, basic gauge length, useful thread), from the public preview https://cdn.standards.iteh.ai/samples/2856/96e1948d3d734f28b2563bcab2920245/ISO-7-1-1978.pdf; the same diameters as G sizes in https://en.wikipedia.org/wiki/British_Standard_Pipe and the Yamawa YEU23 tables pipe_thread_catalog.rs cites.
• ASME B1.20.1 (NPT) as NBS Handbook H28 (1957) Part II, section VII publishes it: 60°, H = 0.866025 p, h = 0.800 p, truncation at least 0.033 p, taper 1 in 16, E0 = D − (0.05 D + 1.1) p, E1 = E0 + 0.0625 L1, L2 = (0.80 D + 6.8) p, and Table VII.2 (D, n, E0, L1, L2 for 1/16 to 12): https://nvlpubs.nist.gov/nistpubs/Legacy/hb/nbshandbook28supp1957pt2.pdf.
• ISO 724 (external minor diameter d3 = d1 − H/6 = d − 1.226869 P, M10x1.5: 8.16), as given at https://www.valvias.com/miscellanea-metric-thread-din-13.php.