November 3, 2026 · Indumor
In this chapter
What key fits a 40 mm shaft? A 12 × 8, cut 5 mm deep into the shaft and 3.3 mm into the hub. The answer comes from a German table of 1968, revised in 2021, DIN 6885. It is here in full, with Woodruff keys, the ANSI inch keys, gear cutter numbers, T-slots and the sums for helical milling.
Enter the table with the shaft diameter: each range has its section b × h, the keyseat depth t1 in the shaft and t2 in the hub. The two add up to slightly more than the key height; the difference, 0.2 to 0.5 mm, is the back clearance that makes the key carry on its flanks. On the drawing the shaft is dimensioned d − t1 and the hub d + t2, which is what a caliper measures: 35 and 43.3 for the 40 mm shaft.
d: shaft diameter (mm); t1, t2: table depths (mm); h: key height (mm). The dimensions d − t1 and d + t2 carry the t1 and t2 tolerance (minus on the shaft, plus on the hub).
| Shaft d over – to incl., mm | b × h mm | t1 shaft mm | t2 hub mm | Tol. t1, t2 mm | r keyseat min – max, mm | Length l from – to, mm |
|---|---|---|---|---|---|---|
| 6–8 | 2 × 2 | 1.2 | 1.0 | +0.1 | 0.08–0.16 | 6–20 |
| 8–10 | 3 × 3 | 1.8 | 1.4 | +0.1 | 0.08–0.16 | 6–36 |
| 10–12 | 4 × 4 | 2.5 | 1.8 | +0.1 | 0.08–0.16 | 8–45 |
| 12–17 | 5 × 5 | 3.0 | 2.3 | +0.1 | 0.16–0.25 | 10–56 |
| 17–22 | 6 × 6 | 3.5 | 2.8 | +0.1 | 0.16–0.25 | 14–70 |
| 22–30 | 8 × 7 | 4.0 | 3.3 | +0.2 | 0.16–0.25 | 18–90 |
| 30–38 | 10 × 8 | 5.0 | 3.3 | +0.2 | 0.25–0.40 | 22–110 |
| 38–44 | 12 × 8 | 5.0 | 3.3 | +0.2 | 0.25–0.40 | 28–140 |
| 44–50 | 14 × 9 | 5.5 | 3.8 | +0.2 | 0.25–0.40 | 36–160 |
| 50–58 | 16 × 10 | 6.0 | 4.3 | +0.2 | 0.25–0.40 | 45–180 |
| 58–65 | 18 × 11 | 7.0 | 4.4 | +0.2 | 0.25–0.40 | 50–200 |
| 65–75 | 20 × 12 | 7.5 | 4.9 | +0.2 | 0.40–0.60 | 56–220 |
| 75–85 | 22 × 14 | 9.0 | 5.4 | +0.2 | 0.40–0.60 | 63–250 |
| 85–95 | 25 × 14 | 9.0 | 5.4 | +0.2 | 0.40–0.60 | 70–280 |
| 95–110 | 28 × 16 | 10.0 | 6.4 | +0.2 | 0.40–0.60 | 80–320 |
| 110–130 | 32 × 18 | 11.0 | 7.4 | +0.2 | 0.40–0.60 | 90–360 |
| 130–150 | 36 × 20 | 12.0 | 8.4 | +0.3 | 0.70–1.00 | 100–400 |
| 150–170 | 40 × 22 | 13.0 | 9.4 | +0.3 | 0.70–1.00 | 110–400 |
| 170–200 | 45 × 25 | 15.0 | 10.4 | +0.3 | 0.70–1.00 | 125–400 |
| 200–230 | 50 × 28 | 17.0 | 11.4 | +0.3 | 0.70–1.00 | 140–400 |
| 230–260 | 56 × 32 | 20.0 | 12.4 | +0.3 | 1.20–1.60 | 160–400 |
| 260–290 | 63 × 32 | 20.0 | 12.4 | +0.3 | 1.20–1.60 | 180–400 |
| 290–330 | 70 × 36 | 22.0 | 14.4 | +0.3 | 1.20–1.60 | 200–400 |
| 330–380 | 80 × 40 | 25.0 | 15.4 | +0.3 | 2.00–2.50 | 220–400 |
| 380–440 | 90 × 45 | 28.0 | 17.4 | +0.3 | 2.00–2.50 | 250–400 |
| 440–500 | 100 × 50 | 31.0 | 19.5 | +0.3 | 2.00–2.50 | 280–400 |
Standard lengths (mm): 6, 8, 10, 12, 14, 16, 18, 20, 22, 25, 28, 32, 36, 40, 45, 50, 56, 63, 70, 80, 90, 100, 110, 125, 140, 160, 180, 200, 220, 250, 280, 320, 360, 400. Key: width h9, height h9 up to 6 × 6 and h11 from 8 × 7 up; length −0.2 up to 28 mm, −0.3 from 32 to 80 and −0.5 from 90 to 400 (the keyseat, the same on the plus side). The radius r is the fillet at the bottom of the keyseat; the key carries a larger chamfer (0.16–0.25 on the small sizes up to 2.5–3 on the large ones), so it seats without riding on that fillet.
Width b is the dimension that matters, and there are three fits. Normal, N9 in the shaft and JS9 in the hub, is the everyday one: the key is tapped in and the hub slides on. Tight, P9 in both, is for reversing loads. In the sliding fit the key is screwed to the shaft and the hub travels along it in D10.
| Fit | Shaft keyseat | Hub keyway | Key | When it is used |
|---|---|---|---|---|
| Tight (interference) | P9 | P9 | h9 | Reversing loads, hubs that stay put |
| Normal | N9 | JS9 | h9 | The usual fit: the key is tapped into the shaft, the hub slides on at assembly |
| Sliding (feather key) | H9 | D10 | h9 | Key screwed to the shaft (forms C to H), hub travels along it |
Keys are ordered by form, section and length: key A 12 × 8 × 50 DIN 6885. Form A has rounded ends and sits in a closed keyseat cut with an end mill; form B has square ends and goes in an open keyseat cut with a side-milling cutter. Thin keys to DIN 6885-3 (ISO 2491) are for thin-walled hubs.
One detail that ruins keyseats: measured with a depth gauge resting on the edge of the slot, the depth reads less than t1, because the edge sits lower than the crest of the shaft. On a 40 mm shaft with a 12 mm slot the difference is 0.92 mm, more than the whole tolerance.
f: how far the keyseat edge sits below the crest of the shaft (mm); d: shaft diameter (mm); b: keyseat width (mm). True depth = reading at the edge + f.
Type the shaft diameter and read the key section, the depths and the drawing dimensions.
A Woodruff key is a segment of a disc: it seats deep in the shaft and tilts to follow the hub. The seat is cut in one plunge with a Woodruff keyseat cutter (DIN 850) of the same diameter d1 and width b as the key. American Woodruff keys carry an ANSI B17.2 number that spells out the size: the last two digits are the diameter in eighths of an inch, the digits before them the width in thirty-seconds. A number 808 is 1/4 in wide by 1 in in diameter.
| b × h mm | d1 disc mm | t1 shaft mm | t2 hub mm | Shaft: torque / locating only mm |
|---|---|---|---|---|
| 2 × 3.7 | 10 | 2.9 | 1.0 | 6–8 / 10–12 |
| 2.5 × 3.7 | 10 | 2.9 | 1.0 | 8–10 / 12–17 |
| 3 × 5 | 13 | 3.8 | 1.4 | 8–10 / 12–17 |
| 3 × 6.5 | 16 | 5.3 | 1.4 | – / 12–17 |
| 4 × 6.5 | 16 | 5.0 | 1.7 | 10–12 / 17–22 |
| 4 × 7.5 | 19 | 6.0 | 1.7 | – / 17–22 |
| 5 × 6.5 | 16 | 4.5 | 2.2 | 12–17 / 22–30 |
| 5 × 7.5 | 19 | 5.5 | 2.2 | 12–17 / 22–30 |
| 5 × 9 | 22 | 7.0 | 2.2 | – / 22–30 |
| 6 × 9 | 22 | 6.6 | 2.6 | 17–22 / 30–38 |
| 6 × 10 | 25 | 7.6 | 2.6 | 17–22 / 30–38 |
| 8 × 11 | 28 | 8.2 | 3.0 | 22–30 / over 38 |
| 10 × 13 | 32 | 9.8 | 3.4 | 30–38 / over 38 |
The Woodruff keyseat cutter (DIN 850) has the diameter d1 and the width b of the key: the seat is cut in one plunge. Seat width N9 (normal) or P9 (tight); t1 toleranced +0.1 up to 5 × 7.5 and +0.2 from 5 × 9 up. Depths are series A, the one the standard prefers. In the shaft column the first range applies when the key carries all the torque and the second when it only locates and a taper or another element carries the torque. The 2.5 × 3.7 is for automotive use only and the 6 × 10 is best avoided.
On an American machine the shaft is in inches and so is the key. ANSI B17.1 picks the key by shaft diameter just as DIN does, but splits the depth evenly: half the key height in the shaft and half in the hub. Keystock is held to +0.001 in / −0.000 for tight fits; ordinary cold-finished bar runs a couple of thousandths under and gives a clearance fit.
| Shaft over – to incl., in | Shaft mm | Square key in | Square mm | Rectangular w × h in |
|---|---|---|---|---|
| 7/16–9/16 | 11.1–14.3 | 1/8 | 3.18 | 1/8 × 3/32 |
| 9/16–7/8 | 14.3–22.2 | 3/16 | 4.76 | 3/16 × 1/8 |
| 7/8–1 1/4 | 22.2–31.8 | 1/4 | 6.35 | 1/4 × 3/16 |
| 1 1/4–1 3/8 | 31.8–34.9 | 5/16 | 7.94 | 5/16 × 1/4 |
| 1 3/8–1 3/4 | 34.9–44.5 | 3/8 | 9.53 | 3/8 × 1/4 |
| 1 3/4–2 1/4 | 44.5–57.2 | 1/2 | 12.70 | 1/2 × 3/8 |
| 2 1/4–2 3/4 | 57.2–69.9 | 5/8 | 15.88 | 5/8 × 7/16 |
| 2 3/4–3 1/4 | 69.9–82.6 | 3/4 | 19.05 | 3/4 × 1/2 |
| 3 1/4–3 3/4 | 82.6–95.3 | 7/8 | 22.23 | 7/8 × 5/8 |
| 3 3/4–4 1/2 | 95.3–114.3 | 1 | 25.40 | 1 × 3/4 |
Keyseat depth: half the key height in the shaft and half in the hub. Shafts of 5/16 to 7/16 in take a 3/32 key; 4 1/2 to 6 1/2 in take 1 1/4 and 1 1/2 keys.
The involute changes with the tooth count: the space between two teeth of a 12-tooth pinion is not the shape of the space on a 100-tooth gear. Since nobody keeps a cutter for every gear, the set of 8 covers 12 teeth to a rack in ranges, and each cutter is formed to the profile of the lowest tooth count in its range.
Here is the trap. Brown & Sharpe cutters, the American standard, run from No. 1 (135 teeth to rack) to No. 8 (12 and 13 teeth). European cutters to DIN 3972 are numbered the other way round, and more than one gear has come off the machine with thin teeth because of it. Read the tooth range stamped on the cutter, not the number. The stamp also gives the module or diametral pitch, the pressure angle (20° on current sets, 14½° on many old American ones).
| Teeth in the gear z | DIN 3972 No. | Brown & Sharpe No. |
|---|---|---|
| 12–13 | 1 | 8 |
| 14–16 | 2 | 7 |
| 17–20 | 3 | 6 |
| 21–25 | 4 | 5 |
| 26–34 | 5 | 4 |
| 35–54 | 6 | 3 |
| 55–134 | 7 | 2 |
| 135–rack | 8 | 1 |
| Teeth z | DIN No. | B&S No. | Teeth z | DIN No. | B&S No. | Teeth z | DIN No. | B&S No. |
|---|---|---|---|---|---|---|---|---|
| 12 | 1 | 8 | 19–20 | 3½ | 5½ | 35–41 | 6 | 3 |
| 13 | 1½ | 7½ | 21–22 | 4 | 5 | 42–54 | 6½ | 2½ |
| 14 | 2 | 7 | 23–25 | 4½ | 4½ | 55–79 | 7 | 2 |
| 15–16 | 2½ | 6½ | 26–29 | 5 | 4 | 80–134 | 7½ | 1½ |
| 17–18 | 3 | 6 | 30–34 | 5½ | 3½ | 135–rack | 8 | 1 |
To cut the gear: the blank between the dividing head and its tailstock, the cutter centered on the blank's axis (touch each side of the blank and split the difference), and a whole depth of 2.25 times the module. Indexing is chapter 12; pitch diameter, outside diameter and tooth dimensions are in chapter 15, and cutter speed in chapter 9.
A T-slot is cut in two passes: a plain slot of width a to the full depth h with an end mill or a side cutter, then the T-slot cutter (DIN 851), whose diameter is the undercut width b and whose thickness is the undercut height c, goes in through the open slot. Each slot width takes a T-bolt to DIN 787 and a T-nut to DIN 508.
| a slot width mm | b undercut width min, mm | c undercut height min, mm | h total depth min – max, mm | T-bolt DIN 787 | a slot width mm | b undercut width min, mm | c undercut height min, mm | h total depth min – max, mm | T-bolt DIN 787 |
|---|---|---|---|---|---|---|---|---|---|
| 6 | 11.0 | 5 | 11–13 | M6 | 22 | 37.0 | 16 | 38–45 | M20 |
| 8 | 14.5 | 7 | 15–18 | M8 | 28 | 46.0 | 20 | 48–56 | M24 |
| 10 | 16.0 | 7 | 17–21 | M10 | 36 | 56.0 | 25 | 61–71 | M30 |
| 12 | 19.0 | 8 | 20–25 | M12 | 42 | 68.0 | 32 | 74–85 | M36 |
| 14 | 23.0 | 9 | 23–28 | M12 | 48 | 80.0 | 36 | 84–95 | M42 |
| 18 | 30.0 | 12 | 30–36 | M16 | 54 | 90.0 | 40 | 94–106 | M48 |
The width a is H8 on reference slots and H12 on fixing slots. T-nut to DIN 508 (and the ISO 299 bolt): M5, M6, M8 and M10 in the 6, 8, 10 and 12 slots; from 14 up, the same thread as the DIN 787 bolt.
In a helix the table feeds and the work turns at the same time; what links the two is the lead L. The rotation comes from the dividing head, geared to the table lead screw. With a 40:1 head the work turns once for 40 turns of the screw, so the lead of the machine is 40 times the screw pitch: 240 mm with a 6 mm screw, 10 in with a 1/4 in screw. The train ratio is the lead of the helix divided by the lead of the machine. The table is swiveled to the helix angle β so that the side cutter lies in the plane of the groove; with an end mill in a vertical head the table stays square.
β: helix angle at the diameter D (mm or in) of the work; L: lead of the helix; p: pitch of the table lead screw (same unit as L); 40: dividing head ratio (60, 90 or 120 on some heads); z′: virtual number of teeth for choosing the gear cutter.
The change gears are the Brown & Sharpe set of twelve: 24, 24, 28, 32, 40, 44, 48, 56, 64, 72, 86 and 100 teeth. The ratio seldom comes out exact; you take the closest train and accept that β shifts a few tenths of a degree. What does show is the hand: one idler too many and the helix comes out left-hand.
For a helical gear cut with a disc cutter, use the normal module and pick the cutter by the virtual number of teeth, the spur gear with the same flank curvature: z′ = z / cos³β. A 24-tooth gear at 25° is cut with the cutter for 32 teeth.
Diameter and lead give the table angle; screw pitch and head ratio give the train from the twelve Brown & Sharpe change gears (24, 24, 28, 32, 40, 44, 48, 56, 64, 72, 86 and 100).
Worked example · a roll with helical grooves and a 24-tooth gear
Helical grooves on a 50 mm roll with a lead of 300 mm, on a universal mill with a 6 mm lead screw and a 40:1 head.
And if the roll has a key on its 40 mm journal: 12 × 8, dimensions 35 and 43.3, key A 12 × 8 × 50.
Four things ruin this work more than anything else: a keyseat off center, a depth measured at the edge, a cutter number read without the range, and a train tried for the first time with the work already mounted. All four are fixed before the spindle starts.
Under ANSI B17.1, shafts over 7/8 to 1 1/4 in take a 1/4 in square key (or 1/4 × 3/16 rectangular), seated 1/8 in deep in the shaft. The metric table gives 8 × 7 for a 25 mm shaft.
The cutter for 26 to 34 teeth: No. 4 in the Brown & Sharpe numbering, No. 5 in the DIN numbering. The two run opposite ways, so check the tooth range stamped on the cutter.
tan β = π × D / L, with D the work diameter and L the lead. A 50 mm roll with a 300 mm lead gives β = 27.6°, and the table of the universal mill is swiveled to that angle.
Sources: DIN 6885-1 (1968 and 2021 editions: parallel keys and keyseats), DIN 6885-3 and ISO 2491 (thin keys), ISO 773 (rectangular and square parallel keys), DIN 6888 (Woodruff keys) and DIN 850 (Woodruff keyseat cutters), ASME B17.1-1967 (S2023) and ANSI B17.2 (Woodruff keys), DIN 3972 (reference profiles of gear cutting tools), DIN 650 and ISO 299 (T-slots), DIN 787 and DIN 508 (T-bolts and T-nuts), Machinery's Handbook (helical milling and the Brown & Sharpe change gear set).
Simple, differential and angular indexing, with the table from 2 to 100 divisions.
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