§1Making the mate
Cutting a thread means removing the groove and leaving the ridge — internally with a tap, externally with a die, or either way with a single point traversing under the lathe’s leadscrew.
Each tool embodies the thread differently. A tap is a hardened master screw with flutes ground through it: the flutes create cutting edges from the thread form itself and give the chips somewhere to live, so the tool cuts its own mirror image into a drilled hole — the hole the calculating page sized at d − p for its deliberate 77%. A die is the inverse, a master nut with the same treatment, cutting the external thread onto a bar. And single-point threading abandons the embodied form altogether: one tool ground to the thread’s profile angle, driven along the work at exactly one pitch per revolution by the lathe’s gearing, generates any pitch and any diameter the machine can swing — the method behind every thread too big, too odd or too precise for the taps in the drawer, and the method by which the taps themselves were first made. The uniting problem is depth: a full thread is far too much metal to remove in one bite, and §2’s chamfer, §3’s point styles and §6’s pass schedule are three answers to the one question of how to share the cut.
Contents§2The hand-tap set
The classic set of three — taper, plug, bottoming — are the same tap with different chamfers, and the chamfer is a cut-sharing device: the more lead threads, the more teeth divide the work.
The hero shows the only difference. The taper tap’s point is relieved over 8–10 threads, so the full depth of cut is spread across many partial teeth: it starts squarely almost by itself, cuts with the least torque, and is the set’s opener — but its long lead cannot thread near the bottom of a blind hole. The plug tap (3–5 threads of chamfer) is the general worker, and the bottoming tap (1–1½) exists purely to finish a blind hole after another tap has done the establishing: started from scratch it would ask its two lead teeth to take the whole cut, which is how taps break. Hand technique is torque management for a tool that is hard, brittle and buried. Start square — a tap entering at an angle cuts a drunken oversize thread and snaps at the surface; use a proper tap wrench, both hands balanced, never an adjustable spanner’s one-sided twist; and in tougher materials break the chip: half a turn back for every turn or so forward snaps the curl before it packs the flutes, because a flute jammed with its own chips is the other way taps break. Cutting fluid throughout — tapping is the highest-torque, worst-access cut in the shop, and it gets every advantage available.
Contents§3Machine taps
Power tapping cannot stop to break chips, so machine taps redesign the problem: point the chips somewhere harmless, or make no chips at all.
The spiral-point (gun) tap grinds an angled shear at its lead so the chips are driven forward, ahead of the tap and out through a through-hole — the flutes stay empty, torque stays low, and it is the default for every through-hole on a machine. The spiral-flute tap answers the blind hole: its helical flutes act as a conveyor, pulling chips backward and out of the hole against gravity, at the cost of a weaker, more delicate tool. The third answer abolishes the chip: the forming (roll) tap has no flutes and no edges at all — polished lobes displace the metal into thread form, the tapping cousin of the thread-rolling page ahead, leaving a burnished, work-hardened, grain-flowed thread that out-pulls a cut one in ductile materials. Its one non-obvious demand: the pilot hole must be larger than a cutting tap’s, because the displaced metal must have room to rise and form the crests — the drilled size comes from the tap maker’s table, not from d − p, and the tell-tale of the process is the tiny seam along each crest where the risen flows meet. On the machine side, modern rigid (synchronised) tapping locks spindle rotation to feed at exactly one pitch per revolution, retiring the old floating tension-compression holders — the same one-pitch-per-rev law §5 runs through a leadscrew.
Contents§4Dies and chasers
The external cut mirrors the internal: the button die is a fluted master nut, its split is an adjustment, and production replaces it with chasers in a self-opening head.
A circular (button) die carries its chamfered lead on one face — the marked face, which goes toward the work — and cuts a bar to size in one pass, held square in a die stock exactly as §2 demanded of the tap: an external thread started crooked is a drunken thread forever. The split through one side is not a flaw but the fit adjustment: screws in the die stock bear on the gap, springing the die a few hundredths open or closed, so the first workpiece is cut, tried against its nut or gauge, and the die tuned — the tolerance pages’ limits, adjusted with a screwdriver. Two practical rules do most of the field’s work: chamfer the bar end so the die’s lead can find a purchase rather than a corner, and on long threads back off periodically as with the tap, for the same chip reasons. Production abandons the one-piece die for chasers — sets of partial-thread cutters carried in a die head that closes onto the bar, cuts at full feed, then snaps open at length so the spindle never reverses: the self-opening die head of the capstan and turret world, cutting a thread in the seconds its cycle allows. One tool family, three scales: stock-and-die at the bench, die head on the turret, and §5’s single point wherever neither reaches.
Contents§5Single-point on the lathe
One tool, ground to the profile, fed one pitch per revolution by the leadscrew — the master method, and the one where the machinist personally manages everything the tap’s designer pre-decided.
The lathe pages set the mechanics: change gears or the quick-change box tie spindle to leadscrew at the chosen pitch, the half-nut clamps the carriage to it, and the thread dial says when to re-engage so every pass lands in the same groove. This page adds the cutting judgement. The tool is ground and set to the thread’s included angle — checked against a centre (fishtail) gauge so the vee stands square to the axis — and depth is fed not straight in but with the compound slide set over to 29–30°, so the tool advances down one flank: the leading flank takes the real cut while the trailing flank merely shaves, halving the engaged edge, the load and the chatter of plunging the full vee at once. The extra degree in the traditional 29° setting is deliberate — it keeps a whisker of cut on the trailing flank so it cleans up rather than rubs. Withdraw at the end of each pass, return, re-feed, re-engage on the dial’s mark; and when the numbers of §6 say depth is reached, take spring passes — repeats at zero added feed — until the tool stops cutting, because a slender toolpost deflects under load and the thread is not at size until the deflection has been cut out of it.
Contents§6The pass schedule, worked
How deep, and in how many bites? For the standing M10×1.5 the answer is 0.920 mm of thread — and the square-root rule shares it so every pass removes the same area of metal.
| Pass | Cumulative depth | This cut |
|---|---|---|
| 1 | 0.325 mm | 0.325 mm |
| 2 | 0.460 mm | 0.135 mm |
| 3 | 0.563 mm | 0.103 mm |
| 4 | 0.651 mm | 0.087 mm |
| 5 | 0.727 mm | 0.077 mm |
| 6 | 0.797 mm | 0.069 mm |
| 7 | 0.861 mm | 0.064 mm |
| 8 | 0.920 mm | 0.059 mm |
| The logic: a vee cut’s width grows with its depth, so equal depth increments would load the tool ever harder — the √ rule shrinks the increments instead, from a first bite of 0.325 mm to a last shave of 0.059 mm, holding the chip area (and the cutting force) level across all eight passes. Fed down the 30° compound of §5, the slide travels D/cos 30° = 1.062 mm total. Then the spring passes, then the wires of the measuring page — and the section’s arithmetic has gone full circle, from defining the thread to cutting and proving one. | ||
§7Quick reference
The working core of the page on one card rack.
Tap set
taper 8–10 · plug 3–5
bottoming 1–1½ lead threads
Machine taps
spiral point → chips forward
spiral flute back · form = none
Dies
split = adjustment
chasers snap open at length
Single point
compound at 29–30°
thread dial · spring passes
Schedule
depth = 0.920 mm, √ rule
0.325 first, 0.059 last